From: Lyberta Date: Wed, 29 Mar 2017 09:59:25 +0000 (+0300) Subject: Fixed build of Debian-based systems by not using precompiled binaries. X-Git-Url: https://git.rm.cloudns.org/?a=commitdiff_plain;h=7d7b1345deabc8d02a91a4c1efa6cfad10d53d8b;p=xonotic%2Fxonotic.git Fixed build of Debian-based systems by not using precompiled binaries. --- diff --git a/misc/builddeps/linux32/d0_blind_id/bin/blind_id b/misc/builddeps/linux32/d0_blind_id/bin/blind_id deleted file mode 100755 index 35bb6834..00000000 Binary files a/misc/builddeps/linux32/d0_blind_id/bin/blind_id and /dev/null differ diff --git a/misc/builddeps/linux32/d0_blind_id/include/d0_blind_id/d0.h b/misc/builddeps/linux32/d0_blind_id/include/d0_blind_id/d0.h deleted file mode 100644 index 4c8708e3..00000000 --- a/misc/builddeps/linux32/d0_blind_id/include/d0_blind_id/d0.h +++ /dev/null @@ -1,66 +0,0 @@ -/* - * FILE: d0.h - * AUTHOR: Rudolf Polzer - divVerent@xonotic.org - * - * Copyright (c) 2010, Rudolf Polzer - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * 3. Neither the name of the copyright holder nor the names of contributors - * may be used to endorse or promote products derived from this software - * without specific prior written permission. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTOR(S) ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTOR(S) BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - * - * $Format:commit %H$ - * $Id: 6c55afeb50f24bd316079ae46582e65f8020b19b $ - */ - -#ifndef __D0_H__ -#define __D0_H__ - -#include // size_t - -#define D0_EXPORT __attribute__((__visibility__("default"))) -#define D0_USED __attribute__((used)) -#define D0_WARN_UNUSED_RESULT __attribute__((warn_unused_result)) -#define D0_BOOL int - -typedef void *(d0_malloc_t)(size_t len); -typedef void (d0_free_t)(void *p); -typedef void *(d0_createmutex_t)(void); -typedef void (d0_destroymutex_t)(void *); -typedef int (d0_lockmutex_t)(void *); // zero on success -typedef int (d0_unlockmutex_t)(void *); // zero on success - -extern d0_malloc_t *d0_malloc; -extern d0_free_t *d0_free; -extern d0_createmutex_t *d0_createmutex; -extern d0_destroymutex_t *d0_destroymutex; -extern d0_lockmutex_t *d0_lockmutex; -extern d0_unlockmutex_t *d0_unlockmutex; - -void d0_setmallocfuncs(d0_malloc_t *m, d0_free_t *f); -void d0_setmutexfuncs(d0_createmutex_t *c, d0_destroymutex_t *d, d0_lockmutex_t *l, d0_unlockmutex_t *u); -void d0_initfuncs(void); // initializes them, this needs to be only called internally once - -extern const char *d0_bsd_license_notice; - -#endif diff --git a/misc/builddeps/linux32/d0_blind_id/include/d0_blind_id/d0_blind_id.h b/misc/builddeps/linux32/d0_blind_id/include/d0_blind_id/d0_blind_id.h deleted file mode 100644 index f546b679..00000000 --- a/misc/builddeps/linux32/d0_blind_id/include/d0_blind_id/d0_blind_id.h +++ /dev/null @@ -1,91 +0,0 @@ -/* - * FILE: d0_blind_id.h - * AUTHOR: Rudolf Polzer - divVerent@xonotic.org - * - * Copyright (c) 2010, Rudolf Polzer - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * 3. Neither the name of the copyright holder nor the names of contributors - * may be used to endorse or promote products derived from this software - * without specific prior written permission. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTOR(S) ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTOR(S) BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - * - * $Format:commit %H$ - * $Id: bf838f43093aceadcd2d20071684f1e7148a4332 $ - */ - -#ifndef __D0_BLIND_ID_H__ -#define __D0_BLIND_ID_H__ - -#include "d0.h" - -typedef struct d0_blind_id_s d0_blind_id_t; -typedef D0_BOOL (*d0_fastreject_function) (const d0_blind_id_t *ctx, void *pass); - -D0_EXPORT D0_WARN_UNUSED_RESULT d0_blind_id_t *d0_blind_id_new(void); -D0_EXPORT void d0_blind_id_free(d0_blind_id_t *a); -D0_EXPORT void d0_blind_id_clear(d0_blind_id_t *ctx); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_copy(d0_blind_id_t *ctx, const d0_blind_id_t *src); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_generate_private_key(d0_blind_id_t *ctx, int k); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_generate_private_key_fastreject(d0_blind_id_t *ctx, int k, d0_fastreject_function reject, void *pass); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_read_private_key(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_read_public_key(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_write_private_key(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_write_public_key(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_fingerprint64_public_key(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_generate_private_id_modulus(d0_blind_id_t *ctx); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_read_private_id_modulus(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_write_private_id_modulus(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_generate_private_id_start(d0_blind_id_t *ctx); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_generate_private_id_request(d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_answer_private_id_request(const d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_finish_private_id_request(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_read_private_id_request_camouflage(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_write_private_id_request_camouflage(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_read_private_id(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_read_public_id(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_write_private_id(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_write_public_id(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_authenticate_with_private_id_start(d0_blind_id_t *ctx, D0_BOOL is_first, D0_BOOL send_modulus, const char *message, size_t msglen, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_authenticate_with_private_id_challenge(d0_blind_id_t *ctx, D0_BOOL is_first, D0_BOOL recv_modulus, const char *inbuf, size_t inbuflen, char *outbuf, size_t *outbuflen, D0_BOOL *status); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_authenticate_with_private_id_response(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_authenticate_with_private_id_verify(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen, char *msg, size_t *msglen, D0_BOOL *status); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_authenticate_with_private_id_generate_missing_signature(d0_blind_id_t *ctx); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_sign_with_private_id_sign(d0_blind_id_t *ctx, D0_BOOL is_first, D0_BOOL send_modulus, const char *message, size_t msglen, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_sign_with_private_id_sign_detached(d0_blind_id_t *ctx, D0_BOOL is_first, D0_BOOL send_modulus, const char *message, size_t msglen, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_sign_with_private_id_verify(d0_blind_id_t *ctx, D0_BOOL is_first, D0_BOOL recv_modulus, const char *inbuf, size_t inbuflen, char *msg, size_t *msglen, D0_BOOL *status); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_sign_with_private_id_verify_detached(d0_blind_id_t *ctx, D0_BOOL is_first, D0_BOOL recv_modulus, const char *inbuf, size_t inbuflen, const char *msg, size_t msglen, D0_BOOL *status); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_fingerprint64_public_id(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_verify_public_id(const d0_blind_id_t *ctx, D0_BOOL *status); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_verify_private_id(const d0_blind_id_t *ctx); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_sessionkey_public_id(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); // can only be done after successful key exchange, this performs a modpow; key length is limited by SHA_DIGESTSIZE for now; also ONLY valid after successful d0_blind_id_authenticate_with_private_id_verify/d0_blind_id_fingerprint64_public_id - -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_INITIALIZE(void); -D0_EXPORT void d0_blind_id_SHUTDOWN(void); - -D0_EXPORT void d0_blind_id_util_sha256(char *out, const char *in, size_t n); - -// for exporting -D0_EXPORT void d0_blind_id_setmallocfuncs(d0_malloc_t *m, d0_free_t *f); -D0_EXPORT void d0_blind_id_setmutexfuncs(d0_createmutex_t *c, d0_destroymutex_t *d, d0_lockmutex_t *l, d0_unlockmutex_t *u); - -#endif diff --git a/misc/builddeps/linux32/d0_blind_id/include/d0_blind_id/d0_rijndael.h b/misc/builddeps/linux32/d0_blind_id/include/d0_blind_id/d0_rijndael.h deleted file mode 100644 index e1c8f71b..00000000 --- a/misc/builddeps/linux32/d0_blind_id/include/d0_blind_id/d0_rijndael.h +++ /dev/null @@ -1,21 +0,0 @@ -// from http://www.efgh.com/software/rijndael.htm (public domain) - -#ifndef H__RIJNDAEL -#define H__RIJNDAEL - -#include "d0.h" - -D0_EXPORT int d0_rijndael_setup_encrypt(unsigned long *rk, const unsigned char *key, - int keybits); -D0_EXPORT int d0_rijndael_setup_decrypt(unsigned long *rk, const unsigned char *key, - int keybits); -D0_EXPORT void d0_rijndael_encrypt(const unsigned long *rk, int nrounds, - const unsigned char plaintext[16], unsigned char ciphertext[16]); -D0_EXPORT void d0_rijndael_decrypt(const unsigned long *rk, int nrounds, - const unsigned char ciphertext[16], unsigned char plaintext[16]); - -#define D0_RIJNDAEL_KEYLENGTH(keybits) ((keybits)/8) -#define D0_RIJNDAEL_RKLENGTH(keybits) ((keybits)/8+28) -#define D0_RIJNDAEL_NROUNDS(keybits) ((keybits)/32+6) - -#endif diff --git a/misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.a b/misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.a deleted file mode 100644 index 89452058..00000000 Binary files a/misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.a and /dev/null differ diff --git a/misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.la b/misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.la deleted file mode 100755 index b631320f..00000000 --- a/misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.la +++ /dev/null @@ -1,41 +0,0 @@ -# libd0_blind_id.la - a libtool library file -# Generated by ltmain.sh (GNU libtool) 2.2.6b Debian-2.2.6b-2ubuntu1 -# -# Please DO NOT delete this file! -# It is necessary for linking the library. - -# The name that we can dlopen(3). -dlname='' - -# Names of this library. -library_names='' - -# The name of the static archive. -old_library='libd0_blind_id.a' - -# Linker flags that can not go in dependency_libs. -inherited_linker_flags='' - -# Libraries that this one depends upon. -dependency_libs=' -L/tmp/d0_blind_id.deps/lib/ /tmp/gg/lib/libgmp.la' - -# Names of additional weak libraries provided by this library -weak_library_names='' - -# Version information for libd0_blind_id. -current=0 -age=0 -revision=0 - -# Is this an already installed library? -installed=yes - -# Should we warn about portability when linking against -modules? -shouldnotlink=no - -# Files to dlopen/dlpreopen -dlopen='' -dlpreopen='' - -# Directory that this library needs to be installed in: -libdir='/usr/local/lib' diff --git a/misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.so b/misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.so deleted file mode 120000 index 6adf4aa9..00000000 --- a/misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.so +++ /dev/null @@ -1 +0,0 @@ -libd0_blind_id.so.0.0.0 \ No newline at end of file diff --git a/misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.so.0 b/misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.so.0 deleted file mode 120000 index 6adf4aa9..00000000 --- a/misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.so.0 +++ /dev/null @@ -1 +0,0 @@ -libd0_blind_id.so.0.0.0 \ No newline at end of file diff --git a/misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.so.0.0.0 b/misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.so.0.0.0 deleted file mode 100755 index d17b4e57..00000000 Binary files a/misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.so.0.0.0 and /dev/null differ diff --git a/misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.a b/misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.a deleted file mode 100644 index 58897695..00000000 Binary files a/misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.a and /dev/null differ diff --git a/misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.la b/misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.la deleted file mode 100755 index 49c9909f..00000000 --- a/misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.la +++ /dev/null @@ -1,41 +0,0 @@ -# libd0_rijndael.la - a libtool library file -# Generated by ltmain.sh (GNU libtool) 2.2.6b Debian-2.2.6b-2ubuntu1 -# -# Please DO NOT delete this file! -# It is necessary for linking the library. - -# The name that we can dlopen(3). -dlname='' - -# Names of this library. -library_names='' - -# The name of the static archive. -old_library='libd0_rijndael.a' - -# Linker flags that can not go in dependency_libs. -inherited_linker_flags='' - -# Libraries that this one depends upon. -dependency_libs=' -L/tmp/d0_blind_id.deps/lib/ /tmp/gg/lib/libgmp.la' - -# Names of additional weak libraries provided by this library -weak_library_names='' - -# Version information for libd0_rijndael. -current=0 -age=0 -revision=0 - -# Is this an already installed library? -installed=yes - -# Should we warn about portability when linking against -modules? -shouldnotlink=no - -# Files to dlopen/dlpreopen -dlopen='' -dlpreopen='' - -# Directory that this library needs to be installed in: -libdir='/usr/local/lib' diff --git a/misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.so b/misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.so deleted file mode 120000 index 01dce017..00000000 --- a/misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.so +++ /dev/null @@ -1 +0,0 @@ -libd0_rijndael.so.0.0.0 \ No newline at end of file diff --git a/misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.so.0 b/misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.so.0 deleted file mode 120000 index 01dce017..00000000 --- a/misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.so.0 +++ /dev/null @@ -1 +0,0 @@ -libd0_rijndael.so.0.0.0 \ No newline at end of file diff --git a/misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.so.0.0.0 b/misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.so.0.0.0 deleted file mode 100755 index b98c986b..00000000 Binary files a/misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.so.0.0.0 and /dev/null differ diff --git a/misc/builddeps/linux32/d0_blind_id/lib/pkgconfig/d0_blind_id.pc b/misc/builddeps/linux32/d0_blind_id/lib/pkgconfig/d0_blind_id.pc deleted file mode 100644 index 8c9bb32b..00000000 --- a/misc/builddeps/linux32/d0_blind_id/lib/pkgconfig/d0_blind_id.pc +++ /dev/null @@ -1,11 +0,0 @@ -prefix=/usr/local -exec_prefix=${prefix} -libdir=${exec_prefix}/lib -includedir=${prefix}/include - -Name: Blind-ID -Description: Library for user identification using RSA blind signatures -Requires: -Version: 0.5 -Libs: -L${libdir} -ld0_blind_id -Cflags: -I${includedir}/d0_blind_id diff --git a/misc/builddeps/linux32/d0_blind_id/lib/pkgconfig/d0_rijndael.pc b/misc/builddeps/linux32/d0_blind_id/lib/pkgconfig/d0_rijndael.pc deleted file mode 100644 index 1040d658..00000000 --- a/misc/builddeps/linux32/d0_blind_id/lib/pkgconfig/d0_rijndael.pc +++ /dev/null @@ -1,11 +0,0 @@ -prefix=/usr/local -exec_prefix=${prefix} -libdir=${exec_prefix}/lib -includedir=${prefix}/include - -Name: Rijndael -Description: Library for Rijndael encryption -Requires: -Version: 0.5 -Libs: -L${libdir} -ld0_rijndael -Cflags: -I${includedir}/d0_blind_id diff --git a/misc/builddeps/linux32/gmp/include/gmp.h b/misc/builddeps/linux32/gmp/include/gmp.h deleted file mode 100644 index 7b531f57..00000000 --- a/misc/builddeps/linux32/gmp/include/gmp.h +++ /dev/null @@ -1,2280 +0,0 @@ -/* Definitions for GNU multiple precision functions. -*- mode: c -*- - -Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1999, 2000, 2001, 2002, 2003, -2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc. - -This file is part of the GNU MP Library. - -The GNU MP Library is free software; you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation; either version 3 of the License, or (at your -option) any later version. - -The GNU MP Library is distributed in the hope that it will be useful, but -WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY -or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public -License for more details. - -You should have received a copy of the GNU Lesser General Public License -along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ - -#ifndef __GMP_H__ - -#if defined (__cplusplus) -#include /* for std::istream, std::ostream, std::string */ -#include -#endif - - -/* Instantiated by configure. */ -#if ! defined (__GMP_WITHIN_CONFIGURE) -#define __GMP_HAVE_HOST_CPU_FAMILY_power 0 -#define __GMP_HAVE_HOST_CPU_FAMILY_powerpc 0 -#define GMP_LIMB_BITS 32 -#define GMP_NAIL_BITS 0 -#endif -#define GMP_NUMB_BITS (GMP_LIMB_BITS - GMP_NAIL_BITS) -#define GMP_NUMB_MASK ((~ __GMP_CAST (mp_limb_t, 0)) >> GMP_NAIL_BITS) -#define GMP_NUMB_MAX GMP_NUMB_MASK -#define GMP_NAIL_MASK (~ GMP_NUMB_MASK) - - -/* The following (everything under ifndef __GNU_MP__) must be identical in - gmp.h and mp.h to allow both to be included in an application or during - the library build. */ -#ifndef __GNU_MP__ -#define __GNU_MP__ 5 - -#define __need_size_t /* tell gcc stddef.h we only want size_t */ -#if defined (__cplusplus) -#include /* for size_t */ -#else -#include /* for size_t */ -#endif -#undef __need_size_t - -/* Instantiated by configure. */ -#if ! defined (__GMP_WITHIN_CONFIGURE) -/* #undef _LONG_LONG_LIMB */ -#define __GMP_LIBGMP_DLL 0 -#endif - - -/* __STDC__ - some ANSI compilers define this only to 0, hence the use of - "defined" and not "__STDC__-0". In particular Sun workshop C 5.0 - sets __STDC__ to 0, but requires "##" for token pasting. - - _AIX - gnu ansidecl.h asserts that all known AIX compilers are ANSI but - don't always define __STDC__. - - __DECC - current versions of DEC C (5.9 for instance) for alpha are ANSI, - but don't define __STDC__ in their default mode. Don't know if old - versions might have been K&R, but let's not worry about that unless - someone is still using one. - - _mips - gnu ansidecl.h says the RISC/OS MIPS compiler is ANSI in SVR4 - mode, but doesn't define __STDC__. - - _MSC_VER - Microsoft C is ANSI, but __STDC__ is undefined unless the /Za - option is given (in which case it's 1). - - _WIN32 - tested for by gnu ansidecl.h, no doubt on the assumption that - all w32 compilers are ansi. - - Note: This same set of tests is used by gen-psqr.c and - demos/expr/expr-impl.h, so if anything needs adding, then be sure to - update those too. */ - -#if defined (__STDC__) \ - || defined (__cplusplus) \ - || defined (_AIX) \ - || defined (__DECC) \ - || (defined (__mips) && defined (_SYSTYPE_SVR4)) \ - || defined (_MSC_VER) \ - || defined (_WIN32) -#define __GMP_HAVE_CONST 1 -#define __GMP_HAVE_PROTOTYPES 1 -#define __GMP_HAVE_TOKEN_PASTE 1 -#else -#define __GMP_HAVE_CONST 0 -#define __GMP_HAVE_PROTOTYPES 0 -#define __GMP_HAVE_TOKEN_PASTE 0 -#endif - - -#if __GMP_HAVE_CONST -#define __gmp_const const -#define __gmp_signed signed -#else -#define __gmp_const -#define __gmp_signed -#endif - - -/* __GMP_DECLSPEC supports Windows DLL versions of libgmp, and is empty in - all other circumstances. - - When compiling objects for libgmp, __GMP_DECLSPEC is an export directive, - or when compiling for an application it's an import directive. The two - cases are differentiated by __GMP_WITHIN_GMP defined by the GMP Makefiles - (and not defined from an application). - - __GMP_DECLSPEC_XX is similarly used for libgmpxx. __GMP_WITHIN_GMPXX - indicates when building libgmpxx, and in that case libgmpxx functions are - exports, but libgmp functions which might get called are imports. - - libmp.la uses __GMP_DECLSPEC, just as if it were libgmp.la. libgmp and - libmp don't call each other, so there's no conflict or confusion. - - Libtool DLL_EXPORT define is not used. - - There's no attempt to support GMP built both static and DLL. Doing so - would mean applications would have to tell us which of the two is going - to be used when linking, and that seems very tedious and error prone if - using GMP by hand, and equally tedious from a package since autoconf and - automake don't give much help. - - __GMP_DECLSPEC is required on all documented global functions and - variables, the various internals in gmp-impl.h etc can be left unadorned. - But internals used by the test programs or speed measuring programs - should have __GMP_DECLSPEC, and certainly constants or variables must - have it or the wrong address will be resolved. - - In gcc __declspec can go at either the start or end of a prototype. - - In Microsoft C __declspec must go at the start, or after the type like - void __declspec(...) *foo()". There's no __dllexport or anything to - guard against someone foolish #defining dllexport. _export used to be - available, but no longer. - - In Borland C _export still exists, but needs to go after the type, like - "void _export foo();". Would have to change the __GMP_DECLSPEC syntax to - make use of that. Probably more trouble than it's worth. */ - -#if defined (__GNUC__) -#define __GMP_DECLSPEC_EXPORT __declspec(__dllexport__) -#define __GMP_DECLSPEC_IMPORT __declspec(__dllimport__) -#endif -#if defined (_MSC_VER) || defined (__BORLANDC__) -#define __GMP_DECLSPEC_EXPORT __declspec(dllexport) -#define __GMP_DECLSPEC_IMPORT __declspec(dllimport) -#endif -#ifdef __WATCOMC__ -#define __GMP_DECLSPEC_EXPORT __export -#define __GMP_DECLSPEC_IMPORT __import -#endif -#ifdef __IBMC__ -#define __GMP_DECLSPEC_EXPORT _Export -#define __GMP_DECLSPEC_IMPORT _Import -#endif - -#if __GMP_LIBGMP_DLL -#if __GMP_WITHIN_GMP -/* compiling to go into a DLL libgmp */ -#define __GMP_DECLSPEC __GMP_DECLSPEC_EXPORT -#else -/* compiling to go into an application which will link to a DLL libgmp */ -#define __GMP_DECLSPEC __GMP_DECLSPEC_IMPORT -#endif -#else -/* all other cases */ -#define __GMP_DECLSPEC -#endif - - -#ifdef __GMP_SHORT_LIMB -typedef unsigned int mp_limb_t; -typedef int mp_limb_signed_t; -#else -#ifdef _LONG_LONG_LIMB -typedef unsigned long long int mp_limb_t; -typedef long long int mp_limb_signed_t; -#else -typedef unsigned long int mp_limb_t; -typedef long int mp_limb_signed_t; -#endif -#endif -typedef unsigned long int mp_bitcnt_t; - -/* For reference, note that the name __mpz_struct gets into C++ mangled - function names, which means although the "__" suggests an internal, we - must leave this name for binary compatibility. */ -typedef struct -{ - int _mp_alloc; /* Number of *limbs* allocated and pointed - to by the _mp_d field. */ - int _mp_size; /* abs(_mp_size) is the number of limbs the - last field points to. If _mp_size is - negative this is a negative number. */ - mp_limb_t *_mp_d; /* Pointer to the limbs. */ -} __mpz_struct; - -#endif /* __GNU_MP__ */ - - -typedef __mpz_struct MP_INT; /* gmp 1 source compatibility */ -typedef __mpz_struct mpz_t[1]; - -typedef mp_limb_t * mp_ptr; -typedef __gmp_const mp_limb_t * mp_srcptr; -#if defined (_CRAY) && ! defined (_CRAYMPP) -/* plain `int' is much faster (48 bits) */ -#define __GMP_MP_SIZE_T_INT 1 -typedef int mp_size_t; -typedef int mp_exp_t; -#else -#define __GMP_MP_SIZE_T_INT 0 -typedef long int mp_size_t; -typedef long int mp_exp_t; -#endif - -typedef struct -{ - __mpz_struct _mp_num; - __mpz_struct _mp_den; -} __mpq_struct; - -typedef __mpq_struct MP_RAT; /* gmp 1 source compatibility */ -typedef __mpq_struct mpq_t[1]; - -typedef struct -{ - int _mp_prec; /* Max precision, in number of `mp_limb_t's. - Set by mpf_init and modified by - mpf_set_prec. The area pointed to by the - _mp_d field contains `prec' + 1 limbs. */ - int _mp_size; /* abs(_mp_size) is the number of limbs the - last field points to. If _mp_size is - negative this is a negative number. */ - mp_exp_t _mp_exp; /* Exponent, in the base of `mp_limb_t'. */ - mp_limb_t *_mp_d; /* Pointer to the limbs. */ -} __mpf_struct; - -/* typedef __mpf_struct MP_FLOAT; */ -typedef __mpf_struct mpf_t[1]; - -/* Available random number generation algorithms. */ -typedef enum -{ - GMP_RAND_ALG_DEFAULT = 0, - GMP_RAND_ALG_LC = GMP_RAND_ALG_DEFAULT /* Linear congruential. */ -} gmp_randalg_t; - -/* Random state struct. */ -typedef struct -{ - mpz_t _mp_seed; /* _mp_d member points to state of the generator. */ - gmp_randalg_t _mp_alg; /* Currently unused. */ - union { - void *_mp_lc; /* Pointer to function pointers structure. */ - } _mp_algdata; -} __gmp_randstate_struct; -typedef __gmp_randstate_struct gmp_randstate_t[1]; - -/* Types for function declarations in gmp files. */ -/* ??? Should not pollute user name space with these ??? */ -typedef __gmp_const __mpz_struct *mpz_srcptr; -typedef __mpz_struct *mpz_ptr; -typedef __gmp_const __mpf_struct *mpf_srcptr; -typedef __mpf_struct *mpf_ptr; -typedef __gmp_const __mpq_struct *mpq_srcptr; -typedef __mpq_struct *mpq_ptr; - - -/* This is not wanted in mp.h, so put it outside the __GNU_MP__ common - section. */ -#if __GMP_LIBGMP_DLL -#if __GMP_WITHIN_GMPXX -/* compiling to go into a DLL libgmpxx */ -#define __GMP_DECLSPEC_XX __GMP_DECLSPEC_EXPORT -#else -/* compiling to go into a application which will link to a DLL libgmpxx */ -#define __GMP_DECLSPEC_XX __GMP_DECLSPEC_IMPORT -#endif -#else -/* all other cases */ -#define __GMP_DECLSPEC_XX -#endif - - -#if __GMP_HAVE_PROTOTYPES -#define __GMP_PROTO(x) x -#else -#define __GMP_PROTO(x) () -#endif - -#ifndef __MPN -#if __GMP_HAVE_TOKEN_PASTE -#define __MPN(x) __gmpn_##x -#else -#define __MPN(x) __gmpn_/**/x -#endif -#endif - -/* For reference, "defined(EOF)" cannot be used here. In g++ 2.95.4, - defines EOF but not FILE. */ -#if defined (FILE) \ - || defined (H_STDIO) \ - || defined (_H_STDIO) /* AIX */ \ - || defined (_STDIO_H) /* glibc, Sun, SCO */ \ - || defined (_STDIO_H_) /* BSD, OSF */ \ - || defined (__STDIO_H) /* Borland */ \ - || defined (__STDIO_H__) /* IRIX */ \ - || defined (_STDIO_INCLUDED) /* HPUX */ \ - || defined (__dj_include_stdio_h_) /* DJGPP */ \ - || defined (_FILE_DEFINED) /* Microsoft */ \ - || defined (__STDIO__) /* Apple MPW MrC */ \ - || defined (_MSL_STDIO_H) /* Metrowerks */ \ - || defined (_STDIO_H_INCLUDED) /* QNX4 */ \ - || defined (_ISO_STDIO_ISO_H) /* Sun C++ */ -#define _GMP_H_HAVE_FILE 1 -#endif - -/* In ISO C, if a prototype involving "struct obstack *" is given without - that structure defined, then the struct is scoped down to just the - prototype, causing a conflict if it's subsequently defined for real. So - only give prototypes if we've got obstack.h. */ -#if defined (_OBSTACK_H) /* glibc */ -#define _GMP_H_HAVE_OBSTACK 1 -#endif - -/* The prototypes for gmp_vprintf etc are provided only if va_list is - available, via an application having included or . - Usually va_list is a typedef so can't be tested directly, but C99 - specifies that va_start is a macro (and it was normally a macro on past - systems too), so look for that. - - will define some sort of va_list for vprintf and vfprintf, but - let's not bother trying to use that since it's not standard and since - application uses for gmp_vprintf etc will almost certainly require the - whole or anyway. */ - -#ifdef va_start -#define _GMP_H_HAVE_VA_LIST 1 -#endif - -/* Test for gcc >= maj.min, as per __GNUC_PREREQ in glibc */ -#if defined (__GNUC__) && defined (__GNUC_MINOR__) -#define __GMP_GNUC_PREREQ(maj, min) \ - ((__GNUC__ << 16) + __GNUC_MINOR__ >= ((maj) << 16) + (min)) -#else -#define __GMP_GNUC_PREREQ(maj, min) 0 -#endif - -/* "pure" is in gcc 2.96 and up, see "(gcc)Function Attributes". Basically - it means a function does nothing but examine its arguments and memory - (global or via arguments) to generate a return value, but changes nothing - and has no side-effects. __GMP_NO_ATTRIBUTE_CONST_PURE lets - tune/common.c etc turn this off when trying to write timing loops. */ -#if __GMP_GNUC_PREREQ (2,96) && ! defined (__GMP_NO_ATTRIBUTE_CONST_PURE) -#define __GMP_ATTRIBUTE_PURE __attribute__ ((__pure__)) -#else -#define __GMP_ATTRIBUTE_PURE -#endif - - -/* __GMP_CAST allows us to use static_cast in C++, so our macros are clean - to "g++ -Wold-style-cast". - - Casts in "extern inline" code within an extern "C" block don't induce - these warnings, so __GMP_CAST only needs to be used on documented - macros. */ - -#ifdef __cplusplus -#define __GMP_CAST(type, expr) (static_cast (expr)) -#else -#define __GMP_CAST(type, expr) ((type) (expr)) -#endif - - -/* An empty "throw ()" means the function doesn't throw any C++ exceptions, - this can save some stack frame info in applications. - - Currently it's given only on functions which never divide-by-zero etc, - don't allocate memory, and are expected to never need to allocate memory. - This leaves open the possibility of a C++ throw from a future GMP - exceptions scheme. - - mpz_set_ui etc are omitted to leave open the lazy allocation scheme - described in doc/tasks.html. mpz_get_d etc are omitted to leave open - exceptions for float overflows. - - Note that __GMP_NOTHROW must be given on any inlines the same as on their - prototypes (for g++ at least, where they're used together). Note also - that g++ 3.0 demands that __GMP_NOTHROW is before other attributes like - __GMP_ATTRIBUTE_PURE. */ - -#if defined (__cplusplus) -#define __GMP_NOTHROW throw () -#else -#define __GMP_NOTHROW -#endif - - -/* PORTME: What other compilers have a useful "extern inline"? "static - inline" would be an acceptable substitute if the compiler (or linker) - discards unused statics. */ - - /* gcc has __inline__ in all modes, including strict ansi. Give a prototype - for an inline too, so as to correctly specify "dllimport" on windows, in - case the function is called rather than inlined. - GCC 4.3 and above with -std=c99 or -std=gnu99 implements ISO C99 - inline semantics, unless -fgnu89-inline is used. */ -#ifdef __GNUC__ -#if (defined __GNUC_STDC_INLINE__) || (__GNUC__ == 4 && __GNUC_MINOR__ == 2) -#define __GMP_EXTERN_INLINE extern __inline__ __attribute__ ((__gnu_inline__)) -#else -#define __GMP_EXTERN_INLINE extern __inline__ -#endif -#define __GMP_INLINE_PROTOTYPES 1 -#endif - -/* DEC C (eg. version 5.9) supports "static __inline foo()", even in -std1 - strict ANSI mode. Inlining is done even when not optimizing (ie. -O0 - mode, which is the default), but an unnecessary local copy of foo is - emitted unless -O is used. "extern __inline" is accepted, but the - "extern" appears to be ignored, ie. it becomes a plain global function - but which is inlined within its file. Don't know if all old versions of - DEC C supported __inline, but as a start let's do the right thing for - current versions. */ -#ifdef __DECC -#define __GMP_EXTERN_INLINE static __inline -#endif - -/* SCO OpenUNIX 8 cc supports "static inline foo()" but not in -Xc strict - ANSI mode (__STDC__ is 1 in that mode). Inlining only actually takes - place under -O. Without -O "foo" seems to be emitted whether it's used - or not, which is wasteful. "extern inline foo()" isn't useful, the - "extern" is apparently ignored, so foo is inlined if possible but also - emitted as a global, which causes multiple definition errors when - building a shared libgmp. */ -#ifdef __SCO_VERSION__ -#if __SCO_VERSION__ > 400000000 && __STDC__ != 1 \ - && ! defined (__GMP_EXTERN_INLINE) -#define __GMP_EXTERN_INLINE static inline -#endif -#endif - -/* Microsoft's C compiler accepts __inline */ -#ifdef _MSC_VER -#define __GMP_EXTERN_INLINE __inline -#endif - -/* Recent enough Sun C compilers want "inline" */ -#if defined (__SUNPRO_C) && __SUNPRO_C >= 0x560 \ - && ! defined (__GMP_EXTERN_INLINE) -#define __GMP_EXTERN_INLINE inline -#endif - -/* Somewhat older Sun C compilers want "static inline" */ -#if defined (__SUNPRO_C) && __SUNPRO_C >= 0x540 \ - && ! defined (__GMP_EXTERN_INLINE) -#define __GMP_EXTERN_INLINE static inline -#endif - - -/* C++ always has "inline" and since it's a normal feature the linker should - discard duplicate non-inlined copies, or if it doesn't then that's a - problem for everyone, not just GMP. */ -#if defined (__cplusplus) && ! defined (__GMP_EXTERN_INLINE) -#define __GMP_EXTERN_INLINE inline -#endif - -/* Don't do any inlining within a configure run, since if the compiler ends - up emitting copies of the code into the object file it can end up - demanding the various support routines (like mpn_popcount) for linking, - making the "alloca" test and perhaps others fail. And on hppa ia64 a - pre-release gcc 3.2 was seen not respecting the "extern" in "extern - __inline__", triggering this problem too. */ -#if defined (__GMP_WITHIN_CONFIGURE) && ! __GMP_WITHIN_CONFIGURE_INLINE -#undef __GMP_EXTERN_INLINE -#endif - -/* By default, don't give a prototype when there's going to be an inline - version. Note in particular that Cray C++ objects to the combination of - prototype and inline. */ -#ifdef __GMP_EXTERN_INLINE -#ifndef __GMP_INLINE_PROTOTYPES -#define __GMP_INLINE_PROTOTYPES 0 -#endif -#else -#define __GMP_INLINE_PROTOTYPES 1 -#endif - - -#define __GMP_ABS(x) ((x) >= 0 ? (x) : -(x)) -#define __GMP_MAX(h,i) ((h) > (i) ? (h) : (i)) - -/* __GMP_USHRT_MAX is not "~ (unsigned short) 0" because short is promoted - to int by "~". */ -#define __GMP_UINT_MAX (~ (unsigned) 0) -#define __GMP_ULONG_MAX (~ (unsigned long) 0) -#define __GMP_USHRT_MAX ((unsigned short) ~0) - - -/* __builtin_expect is in gcc 3.0, and not in 2.95. */ -#if __GMP_GNUC_PREREQ (3,0) -#define __GMP_LIKELY(cond) __builtin_expect ((cond) != 0, 1) -#define __GMP_UNLIKELY(cond) __builtin_expect ((cond) != 0, 0) -#else -#define __GMP_LIKELY(cond) (cond) -#define __GMP_UNLIKELY(cond) (cond) -#endif - -#ifdef _CRAY -#define __GMP_CRAY_Pragma(str) _Pragma (str) -#else -#define __GMP_CRAY_Pragma(str) -#endif - - -/* Allow direct user access to numerator and denominator of a mpq_t object. */ -#define mpq_numref(Q) (&((Q)->_mp_num)) -#define mpq_denref(Q) (&((Q)->_mp_den)) - - -#if defined (__cplusplus) -extern "C" { -using std::FILE; -#endif - -#define mp_set_memory_functions __gmp_set_memory_functions -__GMP_DECLSPEC void mp_set_memory_functions __GMP_PROTO ((void *(*) (size_t), - void *(*) (void *, size_t, size_t), - void (*) (void *, size_t))) __GMP_NOTHROW; - -#define mp_get_memory_functions __gmp_get_memory_functions -__GMP_DECLSPEC void mp_get_memory_functions __GMP_PROTO ((void *(**) (size_t), - void *(**) (void *, size_t, size_t), - void (**) (void *, size_t))) __GMP_NOTHROW; - -#define mp_bits_per_limb __gmp_bits_per_limb -__GMP_DECLSPEC extern __gmp_const int mp_bits_per_limb; - -#define gmp_errno __gmp_errno -__GMP_DECLSPEC extern int gmp_errno; - -#define gmp_version __gmp_version -__GMP_DECLSPEC extern __gmp_const char * __gmp_const gmp_version; - - -/**************** Random number routines. ****************/ - -/* obsolete */ -#define gmp_randinit __gmp_randinit -__GMP_DECLSPEC void gmp_randinit __GMP_PROTO ((gmp_randstate_t, gmp_randalg_t, ...)); - -#define gmp_randinit_default __gmp_randinit_default -__GMP_DECLSPEC void gmp_randinit_default __GMP_PROTO ((gmp_randstate_t)); - -#define gmp_randinit_lc_2exp __gmp_randinit_lc_2exp -__GMP_DECLSPEC void gmp_randinit_lc_2exp __GMP_PROTO ((gmp_randstate_t, - mpz_srcptr, unsigned long int, - mp_bitcnt_t)); - -#define gmp_randinit_lc_2exp_size __gmp_randinit_lc_2exp_size -__GMP_DECLSPEC int gmp_randinit_lc_2exp_size __GMP_PROTO ((gmp_randstate_t, mp_bitcnt_t)); - -#define gmp_randinit_mt __gmp_randinit_mt -__GMP_DECLSPEC void gmp_randinit_mt __GMP_PROTO ((gmp_randstate_t)); - -#define gmp_randinit_set __gmp_randinit_set -__GMP_DECLSPEC void gmp_randinit_set __GMP_PROTO ((gmp_randstate_t, __gmp_const __gmp_randstate_struct *)); - -#define gmp_randseed __gmp_randseed -__GMP_DECLSPEC void gmp_randseed __GMP_PROTO ((gmp_randstate_t, mpz_srcptr)); - -#define gmp_randseed_ui __gmp_randseed_ui -__GMP_DECLSPEC void gmp_randseed_ui __GMP_PROTO ((gmp_randstate_t, unsigned long int)); - -#define gmp_randclear __gmp_randclear -__GMP_DECLSPEC void gmp_randclear __GMP_PROTO ((gmp_randstate_t)); - -#define gmp_urandomb_ui __gmp_urandomb_ui -__GMP_DECLSPEC unsigned long gmp_urandomb_ui __GMP_PROTO ((gmp_randstate_t, unsigned long)); - -#define gmp_urandomm_ui __gmp_urandomm_ui -__GMP_DECLSPEC unsigned long gmp_urandomm_ui __GMP_PROTO ((gmp_randstate_t, unsigned long)); - - -/**************** Formatted output routines. ****************/ - -#define gmp_asprintf __gmp_asprintf -__GMP_DECLSPEC int gmp_asprintf __GMP_PROTO ((char **, __gmp_const char *, ...)); - -#define gmp_fprintf __gmp_fprintf -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC int gmp_fprintf __GMP_PROTO ((FILE *, __gmp_const char *, ...)); -#endif - -#define gmp_obstack_printf __gmp_obstack_printf -#if defined (_GMP_H_HAVE_OBSTACK) -__GMP_DECLSPEC int gmp_obstack_printf __GMP_PROTO ((struct obstack *, __gmp_const char *, ...)); -#endif - -#define gmp_obstack_vprintf __gmp_obstack_vprintf -#if defined (_GMP_H_HAVE_OBSTACK) && defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_obstack_vprintf __GMP_PROTO ((struct obstack *, __gmp_const char *, va_list)); -#endif - -#define gmp_printf __gmp_printf -__GMP_DECLSPEC int gmp_printf __GMP_PROTO ((__gmp_const char *, ...)); - -#define gmp_snprintf __gmp_snprintf -__GMP_DECLSPEC int gmp_snprintf __GMP_PROTO ((char *, size_t, __gmp_const char *, ...)); - -#define gmp_sprintf __gmp_sprintf -__GMP_DECLSPEC int gmp_sprintf __GMP_PROTO ((char *, __gmp_const char *, ...)); - -#define gmp_vasprintf __gmp_vasprintf -#if defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vasprintf __GMP_PROTO ((char **, __gmp_const char *, va_list)); -#endif - -#define gmp_vfprintf __gmp_vfprintf -#if defined (_GMP_H_HAVE_FILE) && defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vfprintf __GMP_PROTO ((FILE *, __gmp_const char *, va_list)); -#endif - -#define gmp_vprintf __gmp_vprintf -#if defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vprintf __GMP_PROTO ((__gmp_const char *, va_list)); -#endif - -#define gmp_vsnprintf __gmp_vsnprintf -#if defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vsnprintf __GMP_PROTO ((char *, size_t, __gmp_const char *, va_list)); -#endif - -#define gmp_vsprintf __gmp_vsprintf -#if defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vsprintf __GMP_PROTO ((char *, __gmp_const char *, va_list)); -#endif - - -/**************** Formatted input routines. ****************/ - -#define gmp_fscanf __gmp_fscanf -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC int gmp_fscanf __GMP_PROTO ((FILE *, __gmp_const char *, ...)); -#endif - -#define gmp_scanf __gmp_scanf -__GMP_DECLSPEC int gmp_scanf __GMP_PROTO ((__gmp_const char *, ...)); - -#define gmp_sscanf __gmp_sscanf -__GMP_DECLSPEC int gmp_sscanf __GMP_PROTO ((__gmp_const char *, __gmp_const char *, ...)); - -#define gmp_vfscanf __gmp_vfscanf -#if defined (_GMP_H_HAVE_FILE) && defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vfscanf __GMP_PROTO ((FILE *, __gmp_const char *, va_list)); -#endif - -#define gmp_vscanf __gmp_vscanf -#if defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vscanf __GMP_PROTO ((__gmp_const char *, va_list)); -#endif - -#define gmp_vsscanf __gmp_vsscanf -#if defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vsscanf __GMP_PROTO ((__gmp_const char *, __gmp_const char *, va_list)); -#endif - - -/**************** Integer (i.e. Z) routines. ****************/ - -#define _mpz_realloc __gmpz_realloc -#define mpz_realloc __gmpz_realloc -__GMP_DECLSPEC void *_mpz_realloc __GMP_PROTO ((mpz_ptr, mp_size_t)); - -#define mpz_abs __gmpz_abs -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_abs) -__GMP_DECLSPEC void mpz_abs __GMP_PROTO ((mpz_ptr, mpz_srcptr)); -#endif - -#define mpz_add __gmpz_add -__GMP_DECLSPEC void mpz_add __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_add_ui __gmpz_add_ui -__GMP_DECLSPEC void mpz_add_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_addmul __gmpz_addmul -__GMP_DECLSPEC void mpz_addmul __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_addmul_ui __gmpz_addmul_ui -__GMP_DECLSPEC void mpz_addmul_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_and __gmpz_and -__GMP_DECLSPEC void mpz_and __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_array_init __gmpz_array_init -__GMP_DECLSPEC void mpz_array_init __GMP_PROTO ((mpz_ptr, mp_size_t, mp_size_t)); - -#define mpz_bin_ui __gmpz_bin_ui -__GMP_DECLSPEC void mpz_bin_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_bin_uiui __gmpz_bin_uiui -__GMP_DECLSPEC void mpz_bin_uiui __GMP_PROTO ((mpz_ptr, unsigned long int, unsigned long int)); - -#define mpz_cdiv_q __gmpz_cdiv_q -__GMP_DECLSPEC void mpz_cdiv_q __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_cdiv_q_2exp __gmpz_cdiv_q_2exp -__GMP_DECLSPEC void mpz_cdiv_q_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long)); - -#define mpz_cdiv_q_ui __gmpz_cdiv_q_ui -__GMP_DECLSPEC unsigned long int mpz_cdiv_q_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_cdiv_qr __gmpz_cdiv_qr -__GMP_DECLSPEC void mpz_cdiv_qr __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_cdiv_qr_ui __gmpz_cdiv_qr_ui -__GMP_DECLSPEC unsigned long int mpz_cdiv_qr_ui __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_cdiv_r __gmpz_cdiv_r -__GMP_DECLSPEC void mpz_cdiv_r __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_cdiv_r_2exp __gmpz_cdiv_r_2exp -__GMP_DECLSPEC void mpz_cdiv_r_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, mp_bitcnt_t)); - -#define mpz_cdiv_r_ui __gmpz_cdiv_r_ui -__GMP_DECLSPEC unsigned long int mpz_cdiv_r_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_cdiv_ui __gmpz_cdiv_ui -__GMP_DECLSPEC unsigned long int mpz_cdiv_ui __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_ATTRIBUTE_PURE; - -#define mpz_clear __gmpz_clear -__GMP_DECLSPEC void mpz_clear __GMP_PROTO ((mpz_ptr)); - -#define mpz_clears __gmpz_clears -__GMP_DECLSPEC void mpz_clears __GMP_PROTO ((mpz_ptr, ...)); - -#define mpz_clrbit __gmpz_clrbit -__GMP_DECLSPEC void mpz_clrbit __GMP_PROTO ((mpz_ptr, mp_bitcnt_t)); - -#define mpz_cmp __gmpz_cmp -__GMP_DECLSPEC int mpz_cmp __GMP_PROTO ((mpz_srcptr, mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_cmp_d __gmpz_cmp_d -__GMP_DECLSPEC int mpz_cmp_d __GMP_PROTO ((mpz_srcptr, double)) __GMP_ATTRIBUTE_PURE; - -#define _mpz_cmp_si __gmpz_cmp_si -__GMP_DECLSPEC int _mpz_cmp_si __GMP_PROTO ((mpz_srcptr, signed long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define _mpz_cmp_ui __gmpz_cmp_ui -__GMP_DECLSPEC int _mpz_cmp_ui __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_cmpabs __gmpz_cmpabs -__GMP_DECLSPEC int mpz_cmpabs __GMP_PROTO ((mpz_srcptr, mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_cmpabs_d __gmpz_cmpabs_d -__GMP_DECLSPEC int mpz_cmpabs_d __GMP_PROTO ((mpz_srcptr, double)) __GMP_ATTRIBUTE_PURE; - -#define mpz_cmpabs_ui __gmpz_cmpabs_ui -__GMP_DECLSPEC int mpz_cmpabs_ui __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_com __gmpz_com -__GMP_DECLSPEC void mpz_com __GMP_PROTO ((mpz_ptr, mpz_srcptr)); - -#define mpz_combit __gmpz_combit -__GMP_DECLSPEC void mpz_combit __GMP_PROTO ((mpz_ptr, mp_bitcnt_t)); - -#define mpz_congruent_p __gmpz_congruent_p -__GMP_DECLSPEC int mpz_congruent_p __GMP_PROTO ((mpz_srcptr, mpz_srcptr, mpz_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpz_congruent_2exp_p __gmpz_congruent_2exp_p -__GMP_DECLSPEC int mpz_congruent_2exp_p __GMP_PROTO ((mpz_srcptr, mpz_srcptr, mp_bitcnt_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_congruent_ui_p __gmpz_congruent_ui_p -__GMP_DECLSPEC int mpz_congruent_ui_p __GMP_PROTO ((mpz_srcptr, unsigned long, unsigned long)) __GMP_ATTRIBUTE_PURE; - -#define mpz_divexact __gmpz_divexact -__GMP_DECLSPEC void mpz_divexact __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_divexact_ui __gmpz_divexact_ui -__GMP_DECLSPEC void mpz_divexact_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long)); - -#define mpz_divisible_p __gmpz_divisible_p -__GMP_DECLSPEC int mpz_divisible_p __GMP_PROTO ((mpz_srcptr, mpz_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpz_divisible_ui_p __gmpz_divisible_ui_p -__GMP_DECLSPEC int mpz_divisible_ui_p __GMP_PROTO ((mpz_srcptr, unsigned long)) __GMP_ATTRIBUTE_PURE; - -#define mpz_divisible_2exp_p __gmpz_divisible_2exp_p -__GMP_DECLSPEC int mpz_divisible_2exp_p __GMP_PROTO ((mpz_srcptr, mp_bitcnt_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_dump __gmpz_dump -__GMP_DECLSPEC void mpz_dump __GMP_PROTO ((mpz_srcptr)); - -#define mpz_export __gmpz_export -__GMP_DECLSPEC void *mpz_export __GMP_PROTO ((void *, size_t *, int, size_t, int, size_t, mpz_srcptr)); - -#define mpz_fac_ui __gmpz_fac_ui -__GMP_DECLSPEC void mpz_fac_ui __GMP_PROTO ((mpz_ptr, unsigned long int)); - -#define mpz_fdiv_q __gmpz_fdiv_q -__GMP_DECLSPEC void mpz_fdiv_q __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_fdiv_q_2exp __gmpz_fdiv_q_2exp -__GMP_DECLSPEC void mpz_fdiv_q_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, mp_bitcnt_t)); - -#define mpz_fdiv_q_ui __gmpz_fdiv_q_ui -__GMP_DECLSPEC unsigned long int mpz_fdiv_q_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_fdiv_qr __gmpz_fdiv_qr -__GMP_DECLSPEC void mpz_fdiv_qr __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_fdiv_qr_ui __gmpz_fdiv_qr_ui -__GMP_DECLSPEC unsigned long int mpz_fdiv_qr_ui __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_fdiv_r __gmpz_fdiv_r -__GMP_DECLSPEC void mpz_fdiv_r __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_fdiv_r_2exp __gmpz_fdiv_r_2exp -__GMP_DECLSPEC void mpz_fdiv_r_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, mp_bitcnt_t)); - -#define mpz_fdiv_r_ui __gmpz_fdiv_r_ui -__GMP_DECLSPEC unsigned long int mpz_fdiv_r_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_fdiv_ui __gmpz_fdiv_ui -__GMP_DECLSPEC unsigned long int mpz_fdiv_ui __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_ATTRIBUTE_PURE; - -#define mpz_fib_ui __gmpz_fib_ui -__GMP_DECLSPEC void mpz_fib_ui __GMP_PROTO ((mpz_ptr, unsigned long int)); - -#define mpz_fib2_ui __gmpz_fib2_ui -__GMP_DECLSPEC void mpz_fib2_ui __GMP_PROTO ((mpz_ptr, mpz_ptr, unsigned long int)); - -#define mpz_fits_sint_p __gmpz_fits_sint_p -__GMP_DECLSPEC int mpz_fits_sint_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_fits_slong_p __gmpz_fits_slong_p -__GMP_DECLSPEC int mpz_fits_slong_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_fits_sshort_p __gmpz_fits_sshort_p -__GMP_DECLSPEC int mpz_fits_sshort_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_fits_uint_p __gmpz_fits_uint_p -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_fits_uint_p) -__GMP_DECLSPEC int mpz_fits_uint_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_fits_ulong_p __gmpz_fits_ulong_p -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_fits_ulong_p) -__GMP_DECLSPEC int mpz_fits_ulong_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_fits_ushort_p __gmpz_fits_ushort_p -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_fits_ushort_p) -__GMP_DECLSPEC int mpz_fits_ushort_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_gcd __gmpz_gcd -__GMP_DECLSPEC void mpz_gcd __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_gcd_ui __gmpz_gcd_ui -__GMP_DECLSPEC unsigned long int mpz_gcd_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_gcdext __gmpz_gcdext -__GMP_DECLSPEC void mpz_gcdext __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_get_d __gmpz_get_d -__GMP_DECLSPEC double mpz_get_d __GMP_PROTO ((mpz_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpz_get_d_2exp __gmpz_get_d_2exp -__GMP_DECLSPEC double mpz_get_d_2exp __GMP_PROTO ((signed long int *, mpz_srcptr)); - -#define mpz_get_si __gmpz_get_si -__GMP_DECLSPEC /* signed */ long int mpz_get_si __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_get_str __gmpz_get_str -__GMP_DECLSPEC char *mpz_get_str __GMP_PROTO ((char *, int, mpz_srcptr)); - -#define mpz_get_ui __gmpz_get_ui -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_get_ui) -__GMP_DECLSPEC unsigned long int mpz_get_ui __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_getlimbn __gmpz_getlimbn -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_getlimbn) -__GMP_DECLSPEC mp_limb_t mpz_getlimbn __GMP_PROTO ((mpz_srcptr, mp_size_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_hamdist __gmpz_hamdist -__GMP_DECLSPEC mp_bitcnt_t mpz_hamdist __GMP_PROTO ((mpz_srcptr, mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_import __gmpz_import -__GMP_DECLSPEC void mpz_import __GMP_PROTO ((mpz_ptr, size_t, int, size_t, int, size_t, __gmp_const void *)); - -#define mpz_init __gmpz_init -__GMP_DECLSPEC void mpz_init __GMP_PROTO ((mpz_ptr)); - -#define mpz_init2 __gmpz_init2 -__GMP_DECLSPEC void mpz_init2 __GMP_PROTO ((mpz_ptr, mp_bitcnt_t)); - -#define mpz_inits __gmpz_inits -__GMP_DECLSPEC void mpz_inits __GMP_PROTO ((mpz_ptr, ...)); - -#define mpz_init_set __gmpz_init_set -__GMP_DECLSPEC void mpz_init_set __GMP_PROTO ((mpz_ptr, mpz_srcptr)); - -#define mpz_init_set_d __gmpz_init_set_d -__GMP_DECLSPEC void mpz_init_set_d __GMP_PROTO ((mpz_ptr, double)); - -#define mpz_init_set_si __gmpz_init_set_si -__GMP_DECLSPEC void mpz_init_set_si __GMP_PROTO ((mpz_ptr, signed long int)); - -#define mpz_init_set_str __gmpz_init_set_str -__GMP_DECLSPEC int mpz_init_set_str __GMP_PROTO ((mpz_ptr, __gmp_const char *, int)); - -#define mpz_init_set_ui __gmpz_init_set_ui -__GMP_DECLSPEC void mpz_init_set_ui __GMP_PROTO ((mpz_ptr, unsigned long int)); - -#define mpz_inp_raw __gmpz_inp_raw -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpz_inp_raw __GMP_PROTO ((mpz_ptr, FILE *)); -#endif - -#define mpz_inp_str __gmpz_inp_str -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpz_inp_str __GMP_PROTO ((mpz_ptr, FILE *, int)); -#endif - -#define mpz_invert __gmpz_invert -__GMP_DECLSPEC int mpz_invert __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_ior __gmpz_ior -__GMP_DECLSPEC void mpz_ior __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_jacobi __gmpz_jacobi -__GMP_DECLSPEC int mpz_jacobi __GMP_PROTO ((mpz_srcptr, mpz_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpz_kronecker mpz_jacobi /* alias */ - -#define mpz_kronecker_si __gmpz_kronecker_si -__GMP_DECLSPEC int mpz_kronecker_si __GMP_PROTO ((mpz_srcptr, long)) __GMP_ATTRIBUTE_PURE; - -#define mpz_kronecker_ui __gmpz_kronecker_ui -__GMP_DECLSPEC int mpz_kronecker_ui __GMP_PROTO ((mpz_srcptr, unsigned long)) __GMP_ATTRIBUTE_PURE; - -#define mpz_si_kronecker __gmpz_si_kronecker -__GMP_DECLSPEC int mpz_si_kronecker __GMP_PROTO ((long, mpz_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpz_ui_kronecker __gmpz_ui_kronecker -__GMP_DECLSPEC int mpz_ui_kronecker __GMP_PROTO ((unsigned long, mpz_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpz_lcm __gmpz_lcm -__GMP_DECLSPEC void mpz_lcm __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_lcm_ui __gmpz_lcm_ui -__GMP_DECLSPEC void mpz_lcm_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long)); - -#define mpz_legendre mpz_jacobi /* alias */ - -#define mpz_lucnum_ui __gmpz_lucnum_ui -__GMP_DECLSPEC void mpz_lucnum_ui __GMP_PROTO ((mpz_ptr, unsigned long int)); - -#define mpz_lucnum2_ui __gmpz_lucnum2_ui -__GMP_DECLSPEC void mpz_lucnum2_ui __GMP_PROTO ((mpz_ptr, mpz_ptr, unsigned long int)); - -#define mpz_millerrabin __gmpz_millerrabin -__GMP_DECLSPEC int mpz_millerrabin __GMP_PROTO ((mpz_srcptr, int)) __GMP_ATTRIBUTE_PURE; - -#define mpz_mod __gmpz_mod -__GMP_DECLSPEC void mpz_mod __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_mod_ui mpz_fdiv_r_ui /* same as fdiv_r because divisor unsigned */ - -#define mpz_mul __gmpz_mul -__GMP_DECLSPEC void mpz_mul __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_mul_2exp __gmpz_mul_2exp -__GMP_DECLSPEC void mpz_mul_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, mp_bitcnt_t)); - -#define mpz_mul_si __gmpz_mul_si -__GMP_DECLSPEC void mpz_mul_si __GMP_PROTO ((mpz_ptr, mpz_srcptr, long int)); - -#define mpz_mul_ui __gmpz_mul_ui -__GMP_DECLSPEC void mpz_mul_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_neg __gmpz_neg -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_neg) -__GMP_DECLSPEC void mpz_neg __GMP_PROTO ((mpz_ptr, mpz_srcptr)); -#endif - -#define mpz_nextprime __gmpz_nextprime -__GMP_DECLSPEC void mpz_nextprime __GMP_PROTO ((mpz_ptr, mpz_srcptr)); - -#define mpz_out_raw __gmpz_out_raw -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpz_out_raw __GMP_PROTO ((FILE *, mpz_srcptr)); -#endif - -#define mpz_out_str __gmpz_out_str -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpz_out_str __GMP_PROTO ((FILE *, int, mpz_srcptr)); -#endif - -#define mpz_perfect_power_p __gmpz_perfect_power_p -__GMP_DECLSPEC int mpz_perfect_power_p __GMP_PROTO ((mpz_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpz_perfect_square_p __gmpz_perfect_square_p -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_perfect_square_p) -__GMP_DECLSPEC int mpz_perfect_square_p __GMP_PROTO ((mpz_srcptr)) __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_popcount __gmpz_popcount -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_popcount) -__GMP_DECLSPEC mp_bitcnt_t mpz_popcount __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_pow_ui __gmpz_pow_ui -__GMP_DECLSPEC void mpz_pow_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_powm __gmpz_powm -__GMP_DECLSPEC void mpz_powm __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_powm_sec __gmpz_powm_sec -__GMP_DECLSPEC void mpz_powm_sec __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_powm_ui __gmpz_powm_ui -__GMP_DECLSPEC void mpz_powm_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int, mpz_srcptr)); - -#define mpz_probab_prime_p __gmpz_probab_prime_p -__GMP_DECLSPEC int mpz_probab_prime_p __GMP_PROTO ((mpz_srcptr, int)) __GMP_ATTRIBUTE_PURE; - -#define mpz_random __gmpz_random -__GMP_DECLSPEC void mpz_random __GMP_PROTO ((mpz_ptr, mp_size_t)); - -#define mpz_random2 __gmpz_random2 -__GMP_DECLSPEC void mpz_random2 __GMP_PROTO ((mpz_ptr, mp_size_t)); - -#define mpz_realloc2 __gmpz_realloc2 -__GMP_DECLSPEC void mpz_realloc2 __GMP_PROTO ((mpz_ptr, mp_bitcnt_t)); - -#define mpz_remove __gmpz_remove -__GMP_DECLSPEC unsigned long int mpz_remove __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_root __gmpz_root -__GMP_DECLSPEC int mpz_root __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_rootrem __gmpz_rootrem -__GMP_DECLSPEC void mpz_rootrem __GMP_PROTO ((mpz_ptr,mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_rrandomb __gmpz_rrandomb -__GMP_DECLSPEC void mpz_rrandomb __GMP_PROTO ((mpz_ptr, gmp_randstate_t, mp_bitcnt_t)); - -#define mpz_scan0 __gmpz_scan0 -__GMP_DECLSPEC mp_bitcnt_t mpz_scan0 __GMP_PROTO ((mpz_srcptr, mp_bitcnt_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_scan1 __gmpz_scan1 -__GMP_DECLSPEC mp_bitcnt_t mpz_scan1 __GMP_PROTO ((mpz_srcptr, mp_bitcnt_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_set __gmpz_set -__GMP_DECLSPEC void mpz_set __GMP_PROTO ((mpz_ptr, mpz_srcptr)); - -#define mpz_set_d __gmpz_set_d -__GMP_DECLSPEC void mpz_set_d __GMP_PROTO ((mpz_ptr, double)); - -#define mpz_set_f __gmpz_set_f -__GMP_DECLSPEC void mpz_set_f __GMP_PROTO ((mpz_ptr, mpf_srcptr)); - -#define mpz_set_q __gmpz_set_q -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_set_q) -__GMP_DECLSPEC void mpz_set_q __GMP_PROTO ((mpz_ptr, mpq_srcptr)); -#endif - -#define mpz_set_si __gmpz_set_si -__GMP_DECLSPEC void mpz_set_si __GMP_PROTO ((mpz_ptr, signed long int)); - -#define mpz_set_str __gmpz_set_str -__GMP_DECLSPEC int mpz_set_str __GMP_PROTO ((mpz_ptr, __gmp_const char *, int)); - -#define mpz_set_ui __gmpz_set_ui -__GMP_DECLSPEC void mpz_set_ui __GMP_PROTO ((mpz_ptr, unsigned long int)); - -#define mpz_setbit __gmpz_setbit -__GMP_DECLSPEC void mpz_setbit __GMP_PROTO ((mpz_ptr, mp_bitcnt_t)); - -#define mpz_size __gmpz_size -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_size) -__GMP_DECLSPEC size_t mpz_size __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_sizeinbase __gmpz_sizeinbase -__GMP_DECLSPEC size_t mpz_sizeinbase __GMP_PROTO ((mpz_srcptr, int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_sqrt __gmpz_sqrt -__GMP_DECLSPEC void mpz_sqrt __GMP_PROTO ((mpz_ptr, mpz_srcptr)); - -#define mpz_sqrtrem __gmpz_sqrtrem -__GMP_DECLSPEC void mpz_sqrtrem __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr)); - -#define mpz_sub __gmpz_sub -__GMP_DECLSPEC void mpz_sub __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_sub_ui __gmpz_sub_ui -__GMP_DECLSPEC void mpz_sub_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_ui_sub __gmpz_ui_sub -__GMP_DECLSPEC void mpz_ui_sub __GMP_PROTO ((mpz_ptr, unsigned long int, mpz_srcptr)); - -#define mpz_submul __gmpz_submul -__GMP_DECLSPEC void mpz_submul __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_submul_ui __gmpz_submul_ui -__GMP_DECLSPEC void mpz_submul_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_swap __gmpz_swap -__GMP_DECLSPEC void mpz_swap __GMP_PROTO ((mpz_ptr, mpz_ptr)) __GMP_NOTHROW; - -#define mpz_tdiv_ui __gmpz_tdiv_ui -__GMP_DECLSPEC unsigned long int mpz_tdiv_ui __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_ATTRIBUTE_PURE; - -#define mpz_tdiv_q __gmpz_tdiv_q -__GMP_DECLSPEC void mpz_tdiv_q __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_tdiv_q_2exp __gmpz_tdiv_q_2exp -__GMP_DECLSPEC void mpz_tdiv_q_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, mp_bitcnt_t)); - -#define mpz_tdiv_q_ui __gmpz_tdiv_q_ui -__GMP_DECLSPEC unsigned long int mpz_tdiv_q_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_tdiv_qr __gmpz_tdiv_qr -__GMP_DECLSPEC void mpz_tdiv_qr __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_tdiv_qr_ui __gmpz_tdiv_qr_ui -__GMP_DECLSPEC unsigned long int mpz_tdiv_qr_ui __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_tdiv_r __gmpz_tdiv_r -__GMP_DECLSPEC void mpz_tdiv_r __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_tdiv_r_2exp __gmpz_tdiv_r_2exp -__GMP_DECLSPEC void mpz_tdiv_r_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, mp_bitcnt_t)); - -#define mpz_tdiv_r_ui __gmpz_tdiv_r_ui -__GMP_DECLSPEC unsigned long int mpz_tdiv_r_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_tstbit __gmpz_tstbit -__GMP_DECLSPEC int mpz_tstbit __GMP_PROTO ((mpz_srcptr, mp_bitcnt_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_ui_pow_ui __gmpz_ui_pow_ui -__GMP_DECLSPEC void mpz_ui_pow_ui __GMP_PROTO ((mpz_ptr, unsigned long int, unsigned long int)); - -#define mpz_urandomb __gmpz_urandomb -__GMP_DECLSPEC void mpz_urandomb __GMP_PROTO ((mpz_ptr, gmp_randstate_t, mp_bitcnt_t)); - -#define mpz_urandomm __gmpz_urandomm -__GMP_DECLSPEC void mpz_urandomm __GMP_PROTO ((mpz_ptr, gmp_randstate_t, mpz_srcptr)); - -#define mpz_xor __gmpz_xor -#define mpz_eor __gmpz_xor -__GMP_DECLSPEC void mpz_xor __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - - -/**************** Rational (i.e. Q) routines. ****************/ - -#define mpq_abs __gmpq_abs -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpq_abs) -__GMP_DECLSPEC void mpq_abs __GMP_PROTO ((mpq_ptr, mpq_srcptr)); -#endif - -#define mpq_add __gmpq_add -__GMP_DECLSPEC void mpq_add __GMP_PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr)); - -#define mpq_canonicalize __gmpq_canonicalize -__GMP_DECLSPEC void mpq_canonicalize __GMP_PROTO ((mpq_ptr)); - -#define mpq_clear __gmpq_clear -__GMP_DECLSPEC void mpq_clear __GMP_PROTO ((mpq_ptr)); - -#define mpq_clears __gmpq_clears -__GMP_DECLSPEC void mpq_clears __GMP_PROTO ((mpq_ptr, ...)); - -#define mpq_cmp __gmpq_cmp -__GMP_DECLSPEC int mpq_cmp __GMP_PROTO ((mpq_srcptr, mpq_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define _mpq_cmp_si __gmpq_cmp_si -__GMP_DECLSPEC int _mpq_cmp_si __GMP_PROTO ((mpq_srcptr, long, unsigned long)) __GMP_ATTRIBUTE_PURE; - -#define _mpq_cmp_ui __gmpq_cmp_ui -__GMP_DECLSPEC int _mpq_cmp_ui __GMP_PROTO ((mpq_srcptr, unsigned long int, unsigned long int)) __GMP_ATTRIBUTE_PURE; - -#define mpq_div __gmpq_div -__GMP_DECLSPEC void mpq_div __GMP_PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr)); - -#define mpq_div_2exp __gmpq_div_2exp -__GMP_DECLSPEC void mpq_div_2exp __GMP_PROTO ((mpq_ptr, mpq_srcptr, mp_bitcnt_t)); - -#define mpq_equal __gmpq_equal -__GMP_DECLSPEC int mpq_equal __GMP_PROTO ((mpq_srcptr, mpq_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpq_get_num __gmpq_get_num -__GMP_DECLSPEC void mpq_get_num __GMP_PROTO ((mpz_ptr, mpq_srcptr)); - -#define mpq_get_den __gmpq_get_den -__GMP_DECLSPEC void mpq_get_den __GMP_PROTO ((mpz_ptr, mpq_srcptr)); - -#define mpq_get_d __gmpq_get_d -__GMP_DECLSPEC double mpq_get_d __GMP_PROTO ((mpq_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpq_get_str __gmpq_get_str -__GMP_DECLSPEC char *mpq_get_str __GMP_PROTO ((char *, int, mpq_srcptr)); - -#define mpq_init __gmpq_init -__GMP_DECLSPEC void mpq_init __GMP_PROTO ((mpq_ptr)); - -#define mpq_inits __gmpq_inits -__GMP_DECLSPEC void mpq_inits __GMP_PROTO ((mpq_ptr, ...)); - -#define mpq_inp_str __gmpq_inp_str -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpq_inp_str __GMP_PROTO ((mpq_ptr, FILE *, int)); -#endif - -#define mpq_inv __gmpq_inv -__GMP_DECLSPEC void mpq_inv __GMP_PROTO ((mpq_ptr, mpq_srcptr)); - -#define mpq_mul __gmpq_mul -__GMP_DECLSPEC void mpq_mul __GMP_PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr)); - -#define mpq_mul_2exp __gmpq_mul_2exp -__GMP_DECLSPEC void mpq_mul_2exp __GMP_PROTO ((mpq_ptr, mpq_srcptr, mp_bitcnt_t)); - -#define mpq_neg __gmpq_neg -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpq_neg) -__GMP_DECLSPEC void mpq_neg __GMP_PROTO ((mpq_ptr, mpq_srcptr)); -#endif - -#define mpq_out_str __gmpq_out_str -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpq_out_str __GMP_PROTO ((FILE *, int, mpq_srcptr)); -#endif - -#define mpq_set __gmpq_set -__GMP_DECLSPEC void mpq_set __GMP_PROTO ((mpq_ptr, mpq_srcptr)); - -#define mpq_set_d __gmpq_set_d -__GMP_DECLSPEC void mpq_set_d __GMP_PROTO ((mpq_ptr, double)); - -#define mpq_set_den __gmpq_set_den -__GMP_DECLSPEC void mpq_set_den __GMP_PROTO ((mpq_ptr, mpz_srcptr)); - -#define mpq_set_f __gmpq_set_f -__GMP_DECLSPEC void mpq_set_f __GMP_PROTO ((mpq_ptr, mpf_srcptr)); - -#define mpq_set_num __gmpq_set_num -__GMP_DECLSPEC void mpq_set_num __GMP_PROTO ((mpq_ptr, mpz_srcptr)); - -#define mpq_set_si __gmpq_set_si -__GMP_DECLSPEC void mpq_set_si __GMP_PROTO ((mpq_ptr, signed long int, unsigned long int)); - -#define mpq_set_str __gmpq_set_str -__GMP_DECLSPEC int mpq_set_str __GMP_PROTO ((mpq_ptr, __gmp_const char *, int)); - -#define mpq_set_ui __gmpq_set_ui -__GMP_DECLSPEC void mpq_set_ui __GMP_PROTO ((mpq_ptr, unsigned long int, unsigned long int)); - -#define mpq_set_z __gmpq_set_z -__GMP_DECLSPEC void mpq_set_z __GMP_PROTO ((mpq_ptr, mpz_srcptr)); - -#define mpq_sub __gmpq_sub -__GMP_DECLSPEC void mpq_sub __GMP_PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr)); - -#define mpq_swap __gmpq_swap -__GMP_DECLSPEC void mpq_swap __GMP_PROTO ((mpq_ptr, mpq_ptr)) __GMP_NOTHROW; - - -/**************** Float (i.e. F) routines. ****************/ - -#define mpf_abs __gmpf_abs -__GMP_DECLSPEC void mpf_abs __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_add __gmpf_add -__GMP_DECLSPEC void mpf_add __GMP_PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr)); - -#define mpf_add_ui __gmpf_add_ui -__GMP_DECLSPEC void mpf_add_ui __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int)); -#define mpf_ceil __gmpf_ceil -__GMP_DECLSPEC void mpf_ceil __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_clear __gmpf_clear -__GMP_DECLSPEC void mpf_clear __GMP_PROTO ((mpf_ptr)); - -#define mpf_clears __gmpf_clears -__GMP_DECLSPEC void mpf_clears __GMP_PROTO ((mpf_ptr, ...)); - -#define mpf_cmp __gmpf_cmp -__GMP_DECLSPEC int mpf_cmp __GMP_PROTO ((mpf_srcptr, mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_cmp_d __gmpf_cmp_d -__GMP_DECLSPEC int mpf_cmp_d __GMP_PROTO ((mpf_srcptr, double)) __GMP_ATTRIBUTE_PURE; - -#define mpf_cmp_si __gmpf_cmp_si -__GMP_DECLSPEC int mpf_cmp_si __GMP_PROTO ((mpf_srcptr, signed long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_cmp_ui __gmpf_cmp_ui -__GMP_DECLSPEC int mpf_cmp_ui __GMP_PROTO ((mpf_srcptr, unsigned long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_div __gmpf_div -__GMP_DECLSPEC void mpf_div __GMP_PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr)); - -#define mpf_div_2exp __gmpf_div_2exp -__GMP_DECLSPEC void mpf_div_2exp __GMP_PROTO ((mpf_ptr, mpf_srcptr, mp_bitcnt_t)); - -#define mpf_div_ui __gmpf_div_ui -__GMP_DECLSPEC void mpf_div_ui __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int)); - -#define mpf_dump __gmpf_dump -__GMP_DECLSPEC void mpf_dump __GMP_PROTO ((mpf_srcptr)); - -#define mpf_eq __gmpf_eq -__GMP_DECLSPEC int mpf_eq __GMP_PROTO ((mpf_srcptr, mpf_srcptr, unsigned long int)) __GMP_ATTRIBUTE_PURE; - -#define mpf_fits_sint_p __gmpf_fits_sint_p -__GMP_DECLSPEC int mpf_fits_sint_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_fits_slong_p __gmpf_fits_slong_p -__GMP_DECLSPEC int mpf_fits_slong_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_fits_sshort_p __gmpf_fits_sshort_p -__GMP_DECLSPEC int mpf_fits_sshort_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_fits_uint_p __gmpf_fits_uint_p -__GMP_DECLSPEC int mpf_fits_uint_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_fits_ulong_p __gmpf_fits_ulong_p -__GMP_DECLSPEC int mpf_fits_ulong_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_fits_ushort_p __gmpf_fits_ushort_p -__GMP_DECLSPEC int mpf_fits_ushort_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_floor __gmpf_floor -__GMP_DECLSPEC void mpf_floor __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_get_d __gmpf_get_d -__GMP_DECLSPEC double mpf_get_d __GMP_PROTO ((mpf_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpf_get_d_2exp __gmpf_get_d_2exp -__GMP_DECLSPEC double mpf_get_d_2exp __GMP_PROTO ((signed long int *, mpf_srcptr)); - -#define mpf_get_default_prec __gmpf_get_default_prec -__GMP_DECLSPEC mp_bitcnt_t mpf_get_default_prec __GMP_PROTO ((void)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_get_prec __gmpf_get_prec -__GMP_DECLSPEC mp_bitcnt_t mpf_get_prec __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_get_si __gmpf_get_si -__GMP_DECLSPEC long mpf_get_si __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_get_str __gmpf_get_str -__GMP_DECLSPEC char *mpf_get_str __GMP_PROTO ((char *, mp_exp_t *, int, size_t, mpf_srcptr)); - -#define mpf_get_ui __gmpf_get_ui -__GMP_DECLSPEC unsigned long mpf_get_ui __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_init __gmpf_init -__GMP_DECLSPEC void mpf_init __GMP_PROTO ((mpf_ptr)); - -#define mpf_init2 __gmpf_init2 -__GMP_DECLSPEC void mpf_init2 __GMP_PROTO ((mpf_ptr, mp_bitcnt_t)); - -#define mpf_inits __gmpf_inits -__GMP_DECLSPEC void mpf_inits __GMP_PROTO ((mpf_ptr, ...)); - -#define mpf_init_set __gmpf_init_set -__GMP_DECLSPEC void mpf_init_set __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_init_set_d __gmpf_init_set_d -__GMP_DECLSPEC void mpf_init_set_d __GMP_PROTO ((mpf_ptr, double)); - -#define mpf_init_set_si __gmpf_init_set_si -__GMP_DECLSPEC void mpf_init_set_si __GMP_PROTO ((mpf_ptr, signed long int)); - -#define mpf_init_set_str __gmpf_init_set_str -__GMP_DECLSPEC int mpf_init_set_str __GMP_PROTO ((mpf_ptr, __gmp_const char *, int)); - -#define mpf_init_set_ui __gmpf_init_set_ui -__GMP_DECLSPEC void mpf_init_set_ui __GMP_PROTO ((mpf_ptr, unsigned long int)); - -#define mpf_inp_str __gmpf_inp_str -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpf_inp_str __GMP_PROTO ((mpf_ptr, FILE *, int)); -#endif - -#define mpf_integer_p __gmpf_integer_p -__GMP_DECLSPEC int mpf_integer_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_mul __gmpf_mul -__GMP_DECLSPEC void mpf_mul __GMP_PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr)); - -#define mpf_mul_2exp __gmpf_mul_2exp -__GMP_DECLSPEC void mpf_mul_2exp __GMP_PROTO ((mpf_ptr, mpf_srcptr, mp_bitcnt_t)); - -#define mpf_mul_ui __gmpf_mul_ui -__GMP_DECLSPEC void mpf_mul_ui __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int)); - -#define mpf_neg __gmpf_neg -__GMP_DECLSPEC void mpf_neg __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_out_str __gmpf_out_str -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpf_out_str __GMP_PROTO ((FILE *, int, size_t, mpf_srcptr)); -#endif - -#define mpf_pow_ui __gmpf_pow_ui -__GMP_DECLSPEC void mpf_pow_ui __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int)); - -#define mpf_random2 __gmpf_random2 -__GMP_DECLSPEC void mpf_random2 __GMP_PROTO ((mpf_ptr, mp_size_t, mp_exp_t)); - -#define mpf_reldiff __gmpf_reldiff -__GMP_DECLSPEC void mpf_reldiff __GMP_PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr)); - -#define mpf_set __gmpf_set -__GMP_DECLSPEC void mpf_set __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_set_d __gmpf_set_d -__GMP_DECLSPEC void mpf_set_d __GMP_PROTO ((mpf_ptr, double)); - -#define mpf_set_default_prec __gmpf_set_default_prec -__GMP_DECLSPEC void mpf_set_default_prec __GMP_PROTO ((mp_bitcnt_t)) __GMP_NOTHROW; - -#define mpf_set_prec __gmpf_set_prec -__GMP_DECLSPEC void mpf_set_prec __GMP_PROTO ((mpf_ptr, mp_bitcnt_t)); - -#define mpf_set_prec_raw __gmpf_set_prec_raw -__GMP_DECLSPEC void mpf_set_prec_raw __GMP_PROTO ((mpf_ptr, mp_bitcnt_t)) __GMP_NOTHROW; - -#define mpf_set_q __gmpf_set_q -__GMP_DECLSPEC void mpf_set_q __GMP_PROTO ((mpf_ptr, mpq_srcptr)); - -#define mpf_set_si __gmpf_set_si -__GMP_DECLSPEC void mpf_set_si __GMP_PROTO ((mpf_ptr, signed long int)); - -#define mpf_set_str __gmpf_set_str -__GMP_DECLSPEC int mpf_set_str __GMP_PROTO ((mpf_ptr, __gmp_const char *, int)); - -#define mpf_set_ui __gmpf_set_ui -__GMP_DECLSPEC void mpf_set_ui __GMP_PROTO ((mpf_ptr, unsigned long int)); - -#define mpf_set_z __gmpf_set_z -__GMP_DECLSPEC void mpf_set_z __GMP_PROTO ((mpf_ptr, mpz_srcptr)); - -#define mpf_size __gmpf_size -__GMP_DECLSPEC size_t mpf_size __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_sqrt __gmpf_sqrt -__GMP_DECLSPEC void mpf_sqrt __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_sqrt_ui __gmpf_sqrt_ui -__GMP_DECLSPEC void mpf_sqrt_ui __GMP_PROTO ((mpf_ptr, unsigned long int)); - -#define mpf_sub __gmpf_sub -__GMP_DECLSPEC void mpf_sub __GMP_PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr)); - -#define mpf_sub_ui __gmpf_sub_ui -__GMP_DECLSPEC void mpf_sub_ui __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int)); - -#define mpf_swap __gmpf_swap -__GMP_DECLSPEC void mpf_swap __GMP_PROTO ((mpf_ptr, mpf_ptr)) __GMP_NOTHROW; - -#define mpf_trunc __gmpf_trunc -__GMP_DECLSPEC void mpf_trunc __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_ui_div __gmpf_ui_div -__GMP_DECLSPEC void mpf_ui_div __GMP_PROTO ((mpf_ptr, unsigned long int, mpf_srcptr)); - -#define mpf_ui_sub __gmpf_ui_sub -__GMP_DECLSPEC void mpf_ui_sub __GMP_PROTO ((mpf_ptr, unsigned long int, mpf_srcptr)); - -#define mpf_urandomb __gmpf_urandomb -__GMP_DECLSPEC void mpf_urandomb __GMP_PROTO ((mpf_t, gmp_randstate_t, mp_bitcnt_t)); - - -/************ Low level positive-integer (i.e. N) routines. ************/ - -/* This is ugly, but we need to make user calls reach the prefixed function. */ - -#define mpn_add __MPN(add) -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_add) -__GMP_DECLSPEC mp_limb_t mpn_add __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr,mp_size_t)); -#endif - -#define mpn_add_1 __MPN(add_1) -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_add_1) -__GMP_DECLSPEC mp_limb_t mpn_add_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t)) __GMP_NOTHROW; -#endif - -#define mpn_add_n __MPN(add_n) -__GMP_DECLSPEC mp_limb_t mpn_add_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); - -#define mpn_addmul_1 __MPN(addmul_1) -__GMP_DECLSPEC mp_limb_t mpn_addmul_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t)); - -#define mpn_cmp __MPN(cmp) -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_cmp) -__GMP_DECLSPEC int mpn_cmp __GMP_PROTO ((mp_srcptr, mp_srcptr, mp_size_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpn_divexact_by3(dst,src,size) \ - mpn_divexact_by3c (dst, src, size, __GMP_CAST (mp_limb_t, 0)) - -#define mpn_divexact_by3c __MPN(divexact_by3c) -__GMP_DECLSPEC mp_limb_t mpn_divexact_by3c __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t)); - -#define mpn_divmod_1(qp,np,nsize,dlimb) \ - mpn_divrem_1 (qp, __GMP_CAST (mp_size_t, 0), np, nsize, dlimb) - -#define mpn_divrem __MPN(divrem) -__GMP_DECLSPEC mp_limb_t mpn_divrem __GMP_PROTO ((mp_ptr, mp_size_t, mp_ptr, mp_size_t, mp_srcptr, mp_size_t)); - -#define mpn_divrem_1 __MPN(divrem_1) -__GMP_DECLSPEC mp_limb_t mpn_divrem_1 __GMP_PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t)); - -#define mpn_divrem_2 __MPN(divrem_2) -__GMP_DECLSPEC mp_limb_t mpn_divrem_2 __GMP_PROTO ((mp_ptr, mp_size_t, mp_ptr, mp_size_t, mp_srcptr)); - -#define mpn_gcd __MPN(gcd) -__GMP_DECLSPEC mp_size_t mpn_gcd __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_ptr, mp_size_t)); - -#define mpn_gcd_1 __MPN(gcd_1) -__GMP_DECLSPEC mp_limb_t mpn_gcd_1 __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE; - -#define mpn_gcdext_1 __MPN(gcdext_1) -__GMP_DECLSPEC mp_limb_t mpn_gcdext_1 __GMP_PROTO ((mp_limb_signed_t *, mp_limb_signed_t *, mp_limb_t, mp_limb_t)); - -#define mpn_gcdext __MPN(gcdext) -__GMP_DECLSPEC mp_size_t mpn_gcdext __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t *, mp_ptr, mp_size_t, mp_ptr, mp_size_t)); - -#define mpn_get_str __MPN(get_str) -__GMP_DECLSPEC size_t mpn_get_str __GMP_PROTO ((unsigned char *, int, mp_ptr, mp_size_t)); - -#define mpn_hamdist __MPN(hamdist) -__GMP_DECLSPEC mp_bitcnt_t mpn_hamdist __GMP_PROTO ((mp_srcptr, mp_srcptr, mp_size_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpn_lshift __MPN(lshift) -__GMP_DECLSPEC mp_limb_t mpn_lshift __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, unsigned int)); - -#define mpn_mod_1 __MPN(mod_1) -__GMP_DECLSPEC mp_limb_t mpn_mod_1 __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE; - -#define mpn_mul __MPN(mul) -__GMP_DECLSPEC mp_limb_t mpn_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t)); - -#define mpn_mul_1 __MPN(mul_1) -__GMP_DECLSPEC mp_limb_t mpn_mul_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t)); - -#define mpn_mul_n __MPN(mul_n) -__GMP_DECLSPEC void mpn_mul_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); - -#define mpn_sqr __MPN(sqr) -__GMP_DECLSPEC void mpn_sqr __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t)); - -#define mpn_neg __MPN(neg) -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_neg) -__GMP_DECLSPEC mp_limb_t mpn_neg __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t)); -#endif - -#define mpn_com __MPN(com) -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_com) -__GMP_DECLSPEC void mpn_com __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t)); -#endif - -#define mpn_perfect_square_p __MPN(perfect_square_p) -__GMP_DECLSPEC int mpn_perfect_square_p __GMP_PROTO ((mp_srcptr, mp_size_t)) __GMP_ATTRIBUTE_PURE; - -#define mpn_perfect_power_p __MPN(perfect_power_p) -__GMP_DECLSPEC int mpn_perfect_power_p __GMP_PROTO ((mp_srcptr, mp_size_t)) __GMP_ATTRIBUTE_PURE; - -#define mpn_popcount __MPN(popcount) -__GMP_DECLSPEC mp_bitcnt_t mpn_popcount __GMP_PROTO ((mp_srcptr, mp_size_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpn_pow_1 __MPN(pow_1) -__GMP_DECLSPEC mp_size_t mpn_pow_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_ptr)); - -/* undocumented now, but retained here for upward compatibility */ -#define mpn_preinv_mod_1 __MPN(preinv_mod_1) -__GMP_DECLSPEC mp_limb_t mpn_preinv_mod_1 __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE; - -#define mpn_random __MPN(random) -__GMP_DECLSPEC void mpn_random __GMP_PROTO ((mp_ptr, mp_size_t)); - -#define mpn_random2 __MPN(random2) -__GMP_DECLSPEC void mpn_random2 __GMP_PROTO ((mp_ptr, mp_size_t)); - -#define mpn_rshift __MPN(rshift) -__GMP_DECLSPEC mp_limb_t mpn_rshift __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, unsigned int)); - -#define mpn_scan0 __MPN(scan0) -__GMP_DECLSPEC mp_bitcnt_t mpn_scan0 __GMP_PROTO ((mp_srcptr, mp_bitcnt_t)) __GMP_ATTRIBUTE_PURE; - -#define mpn_scan1 __MPN(scan1) -__GMP_DECLSPEC mp_bitcnt_t mpn_scan1 __GMP_PROTO ((mp_srcptr, mp_bitcnt_t)) __GMP_ATTRIBUTE_PURE; - -#define mpn_set_str __MPN(set_str) -__GMP_DECLSPEC mp_size_t mpn_set_str __GMP_PROTO ((mp_ptr, __gmp_const unsigned char *, size_t, int)); - -#define mpn_sqrtrem __MPN(sqrtrem) -__GMP_DECLSPEC mp_size_t mpn_sqrtrem __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t)); - -#define mpn_sub __MPN(sub) -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_sub) -__GMP_DECLSPEC mp_limb_t mpn_sub __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr,mp_size_t)); -#endif - -#define mpn_sub_1 __MPN(sub_1) -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_sub_1) -__GMP_DECLSPEC mp_limb_t mpn_sub_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t)) __GMP_NOTHROW; -#endif - -#define mpn_sub_n __MPN(sub_n) -__GMP_DECLSPEC mp_limb_t mpn_sub_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); - -#define mpn_submul_1 __MPN(submul_1) -__GMP_DECLSPEC mp_limb_t mpn_submul_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t)); - -#define mpn_tdiv_qr __MPN(tdiv_qr) -__GMP_DECLSPEC void mpn_tdiv_qr __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t)); - -#define mpn_and_n __MPN(and_n) -__GMP_DECLSPEC void mpn_and_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); -#define mpn_andn_n __MPN(andn_n) -__GMP_DECLSPEC void mpn_andn_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); -#define mpn_nand_n __MPN(nand_n) -__GMP_DECLSPEC void mpn_nand_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); -#define mpn_ior_n __MPN(ior_n) -__GMP_DECLSPEC void mpn_ior_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); -#define mpn_iorn_n __MPN(iorn_n) -__GMP_DECLSPEC void mpn_iorn_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); -#define mpn_nior_n __MPN(nior_n) -__GMP_DECLSPEC void mpn_nior_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); -#define mpn_xor_n __MPN(xor_n) -__GMP_DECLSPEC void mpn_xor_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); -#define mpn_xnor_n __MPN(xnor_n) -__GMP_DECLSPEC void mpn_xnor_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); - -#define mpn_copyi __MPN(copyi) -__GMP_DECLSPEC void mpn_copyi __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t)); -#define mpn_copyd __MPN(copyd) -__GMP_DECLSPEC void mpn_copyd __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t)); -#define mpn_zero __MPN(zero) -__GMP_DECLSPEC void mpn_zero __GMP_PROTO ((mp_ptr, mp_size_t)); - -/**************** mpz inlines ****************/ - -/* The following are provided as inlines where possible, but always exist as - library functions too, for binary compatibility. - - Within gmp itself this inlining generally isn't relied on, since it - doesn't get done for all compilers, whereas if something is worth - inlining then it's worth arranging always. - - There are two styles of inlining here. When the same bit of code is - wanted for the inline as for the library version, then __GMP_FORCE_foo - arranges for that code to be emitted and the __GMP_EXTERN_INLINE - directive suppressed, eg. mpz_fits_uint_p. When a different bit of code - is wanted for the inline than for the library version, then - __GMP_FORCE_foo arranges the inline to be suppressed, eg. mpz_abs. */ - -#if defined (__GMP_EXTERN_INLINE) && ! defined (__GMP_FORCE_mpz_abs) -__GMP_EXTERN_INLINE void -mpz_abs (mpz_ptr __gmp_w, mpz_srcptr __gmp_u) -{ - if (__gmp_w != __gmp_u) - mpz_set (__gmp_w, __gmp_u); - __gmp_w->_mp_size = __GMP_ABS (__gmp_w->_mp_size); -} -#endif - -#if GMP_NAIL_BITS == 0 -#define __GMPZ_FITS_UTYPE_P(z,maxval) \ - mp_size_t __gmp_n = z->_mp_size; \ - mp_ptr __gmp_p = z->_mp_d; \ - return (__gmp_n == 0 || (__gmp_n == 1 && __gmp_p[0] <= maxval)); -#else -#define __GMPZ_FITS_UTYPE_P(z,maxval) \ - mp_size_t __gmp_n = z->_mp_size; \ - mp_ptr __gmp_p = z->_mp_d; \ - return (__gmp_n == 0 || (__gmp_n == 1 && __gmp_p[0] <= maxval) \ - || (__gmp_n == 2 && __gmp_p[1] <= ((mp_limb_t) maxval >> GMP_NUMB_BITS))); -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_fits_uint_p) -#if ! defined (__GMP_FORCE_mpz_fits_uint_p) -__GMP_EXTERN_INLINE -#endif -int -mpz_fits_uint_p (mpz_srcptr __gmp_z) __GMP_NOTHROW -{ - __GMPZ_FITS_UTYPE_P (__gmp_z, __GMP_UINT_MAX); -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_fits_ulong_p) -#if ! defined (__GMP_FORCE_mpz_fits_ulong_p) -__GMP_EXTERN_INLINE -#endif -int -mpz_fits_ulong_p (mpz_srcptr __gmp_z) __GMP_NOTHROW -{ - __GMPZ_FITS_UTYPE_P (__gmp_z, __GMP_ULONG_MAX); -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_fits_ushort_p) -#if ! defined (__GMP_FORCE_mpz_fits_ushort_p) -__GMP_EXTERN_INLINE -#endif -int -mpz_fits_ushort_p (mpz_srcptr __gmp_z) __GMP_NOTHROW -{ - __GMPZ_FITS_UTYPE_P (__gmp_z, __GMP_USHRT_MAX); -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_get_ui) -#if ! defined (__GMP_FORCE_mpz_get_ui) -__GMP_EXTERN_INLINE -#endif -unsigned long -mpz_get_ui (mpz_srcptr __gmp_z) __GMP_NOTHROW -{ - mp_ptr __gmp_p = __gmp_z->_mp_d; - mp_size_t __gmp_n = __gmp_z->_mp_size; - mp_limb_t __gmp_l = __gmp_p[0]; - /* This is a "#if" rather than a plain "if" so as to avoid gcc warnings - about "<< GMP_NUMB_BITS" exceeding the type size, and to avoid Borland - C++ 6.0 warnings about condition always true for something like - "__GMP_ULONG_MAX < GMP_NUMB_MASK". */ -#if GMP_NAIL_BITS == 0 || defined (_LONG_LONG_LIMB) - /* limb==long and no nails, or limb==longlong, one limb is enough */ - return (__gmp_n != 0 ? __gmp_l : 0); -#else - /* limb==long and nails, need two limbs when available */ - __gmp_n = __GMP_ABS (__gmp_n); - if (__gmp_n <= 1) - return (__gmp_n != 0 ? __gmp_l : 0); - else - return __gmp_l + (__gmp_p[1] << GMP_NUMB_BITS); -#endif -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_getlimbn) -#if ! defined (__GMP_FORCE_mpz_getlimbn) -__GMP_EXTERN_INLINE -#endif -mp_limb_t -mpz_getlimbn (mpz_srcptr __gmp_z, mp_size_t __gmp_n) __GMP_NOTHROW -{ - mp_limb_t __gmp_result = 0; - if (__GMP_LIKELY (__gmp_n >= 0 && __gmp_n < __GMP_ABS (__gmp_z->_mp_size))) - __gmp_result = __gmp_z->_mp_d[__gmp_n]; - return __gmp_result; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) && ! defined (__GMP_FORCE_mpz_neg) -__GMP_EXTERN_INLINE void -mpz_neg (mpz_ptr __gmp_w, mpz_srcptr __gmp_u) -{ - if (__gmp_w != __gmp_u) - mpz_set (__gmp_w, __gmp_u); - __gmp_w->_mp_size = - __gmp_w->_mp_size; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_perfect_square_p) -#if ! defined (__GMP_FORCE_mpz_perfect_square_p) -__GMP_EXTERN_INLINE -#endif -int -mpz_perfect_square_p (mpz_srcptr __gmp_a) -{ - mp_size_t __gmp_asize; - int __gmp_result; - - __gmp_asize = __gmp_a->_mp_size; - __gmp_result = (__gmp_asize >= 0); /* zero is a square, negatives are not */ - if (__GMP_LIKELY (__gmp_asize > 0)) - __gmp_result = mpn_perfect_square_p (__gmp_a->_mp_d, __gmp_asize); - return __gmp_result; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_popcount) -#if ! defined (__GMP_FORCE_mpz_popcount) -__GMP_EXTERN_INLINE -#endif -mp_bitcnt_t -mpz_popcount (mpz_srcptr __gmp_u) __GMP_NOTHROW -{ - mp_size_t __gmp_usize; - mp_bitcnt_t __gmp_result; - - __gmp_usize = __gmp_u->_mp_size; - __gmp_result = (__gmp_usize < 0 ? __GMP_ULONG_MAX : 0); - if (__GMP_LIKELY (__gmp_usize > 0)) - __gmp_result = mpn_popcount (__gmp_u->_mp_d, __gmp_usize); - return __gmp_result; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_set_q) -#if ! defined (__GMP_FORCE_mpz_set_q) -__GMP_EXTERN_INLINE -#endif -void -mpz_set_q (mpz_ptr __gmp_w, mpq_srcptr __gmp_u) -{ - mpz_tdiv_q (__gmp_w, mpq_numref (__gmp_u), mpq_denref (__gmp_u)); -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_size) -#if ! defined (__GMP_FORCE_mpz_size) -__GMP_EXTERN_INLINE -#endif -size_t -mpz_size (mpz_srcptr __gmp_z) __GMP_NOTHROW -{ - return __GMP_ABS (__gmp_z->_mp_size); -} -#endif - - -/**************** mpq inlines ****************/ - -#if defined (__GMP_EXTERN_INLINE) && ! defined (__GMP_FORCE_mpq_abs) -__GMP_EXTERN_INLINE void -mpq_abs (mpq_ptr __gmp_w, mpq_srcptr __gmp_u) -{ - if (__gmp_w != __gmp_u) - mpq_set (__gmp_w, __gmp_u); - __gmp_w->_mp_num._mp_size = __GMP_ABS (__gmp_w->_mp_num._mp_size); -} -#endif - -#if defined (__GMP_EXTERN_INLINE) && ! defined (__GMP_FORCE_mpq_neg) -__GMP_EXTERN_INLINE void -mpq_neg (mpq_ptr __gmp_w, mpq_srcptr __gmp_u) -{ - if (__gmp_w != __gmp_u) - mpq_set (__gmp_w, __gmp_u); - __gmp_w->_mp_num._mp_size = - __gmp_w->_mp_num._mp_size; -} -#endif - - -/**************** mpn inlines ****************/ - -/* The comments with __GMPN_ADD_1 below apply here too. - - The test for FUNCTION returning 0 should predict well. If it's assumed - {yp,ysize} will usually have a random number of bits then the high limb - won't be full and a carry out will occur a good deal less than 50% of the - time. - - ysize==0 isn't a documented feature, but is used internally in a few - places. - - Producing cout last stops it using up a register during the main part of - the calculation, though gcc (as of 3.0) on an "if (mpn_add (...))" - doesn't seem able to move the true and false legs of the conditional up - to the two places cout is generated. */ - -#define __GMPN_AORS(cout, wp, xp, xsize, yp, ysize, FUNCTION, TEST) \ - do { \ - mp_size_t __gmp_i; \ - mp_limb_t __gmp_x; \ - \ - /* ASSERT ((ysize) >= 0); */ \ - /* ASSERT ((xsize) >= (ysize)); */ \ - /* ASSERT (MPN_SAME_OR_SEPARATE2_P (wp, xsize, xp, xsize)); */ \ - /* ASSERT (MPN_SAME_OR_SEPARATE2_P (wp, xsize, yp, ysize)); */ \ - \ - __gmp_i = (ysize); \ - if (__gmp_i != 0) \ - { \ - if (FUNCTION (wp, xp, yp, __gmp_i)) \ - { \ - do \ - { \ - if (__gmp_i >= (xsize)) \ - { \ - (cout) = 1; \ - goto __gmp_done; \ - } \ - __gmp_x = (xp)[__gmp_i]; \ - } \ - while (TEST); \ - } \ - } \ - if ((wp) != (xp)) \ - __GMPN_COPY_REST (wp, xp, xsize, __gmp_i); \ - (cout) = 0; \ - __gmp_done: \ - ; \ - } while (0) - -#define __GMPN_ADD(cout, wp, xp, xsize, yp, ysize) \ - __GMPN_AORS (cout, wp, xp, xsize, yp, ysize, mpn_add_n, \ - (((wp)[__gmp_i++] = (__gmp_x + 1) & GMP_NUMB_MASK) == 0)) -#define __GMPN_SUB(cout, wp, xp, xsize, yp, ysize) \ - __GMPN_AORS (cout, wp, xp, xsize, yp, ysize, mpn_sub_n, \ - (((wp)[__gmp_i++] = (__gmp_x - 1) & GMP_NUMB_MASK), __gmp_x == 0)) - - -/* The use of __gmp_i indexing is designed to ensure a compile time src==dst - remains nice and clear to the compiler, so that __GMPN_COPY_REST can - disappear, and the load/add/store gets a chance to become a - read-modify-write on CISC CPUs. - - Alternatives: - - Using a pair of pointers instead of indexing would be possible, but gcc - isn't able to recognise compile-time src==dst in that case, even when the - pointers are incremented more or less together. Other compilers would - very likely have similar difficulty. - - gcc could use "if (__builtin_constant_p(src==dst) && src==dst)" or - similar to detect a compile-time src==dst. This works nicely on gcc - 2.95.x, it's not good on gcc 3.0 where __builtin_constant_p(p==p) seems - to be always false, for a pointer p. But the current code form seems - good enough for src==dst anyway. - - gcc on x86 as usual doesn't give particularly good flags handling for the - carry/borrow detection. It's tempting to want some multi instruction asm - blocks to help it, and this was tried, but in truth there's only a few - instructions to save and any gain is all too easily lost by register - juggling setting up for the asm. */ - -#if GMP_NAIL_BITS == 0 -#define __GMPN_AORS_1(cout, dst, src, n, v, OP, CB) \ - do { \ - mp_size_t __gmp_i; \ - mp_limb_t __gmp_x, __gmp_r; \ - \ - /* ASSERT ((n) >= 1); */ \ - /* ASSERT (MPN_SAME_OR_SEPARATE_P (dst, src, n)); */ \ - \ - __gmp_x = (src)[0]; \ - __gmp_r = __gmp_x OP (v); \ - (dst)[0] = __gmp_r; \ - if (CB (__gmp_r, __gmp_x, (v))) \ - { \ - (cout) = 1; \ - for (__gmp_i = 1; __gmp_i < (n);) \ - { \ - __gmp_x = (src)[__gmp_i]; \ - __gmp_r = __gmp_x OP 1; \ - (dst)[__gmp_i] = __gmp_r; \ - ++__gmp_i; \ - if (!CB (__gmp_r, __gmp_x, 1)) \ - { \ - if ((src) != (dst)) \ - __GMPN_COPY_REST (dst, src, n, __gmp_i); \ - (cout) = 0; \ - break; \ - } \ - } \ - } \ - else \ - { \ - if ((src) != (dst)) \ - __GMPN_COPY_REST (dst, src, n, 1); \ - (cout) = 0; \ - } \ - } while (0) -#endif - -#if GMP_NAIL_BITS >= 1 -#define __GMPN_AORS_1(cout, dst, src, n, v, OP, CB) \ - do { \ - mp_size_t __gmp_i; \ - mp_limb_t __gmp_x, __gmp_r; \ - \ - /* ASSERT ((n) >= 1); */ \ - /* ASSERT (MPN_SAME_OR_SEPARATE_P (dst, src, n)); */ \ - \ - __gmp_x = (src)[0]; \ - __gmp_r = __gmp_x OP (v); \ - (dst)[0] = __gmp_r & GMP_NUMB_MASK; \ - if (__gmp_r >> GMP_NUMB_BITS != 0) \ - { \ - (cout) = 1; \ - for (__gmp_i = 1; __gmp_i < (n);) \ - { \ - __gmp_x = (src)[__gmp_i]; \ - __gmp_r = __gmp_x OP 1; \ - (dst)[__gmp_i] = __gmp_r & GMP_NUMB_MASK; \ - ++__gmp_i; \ - if (__gmp_r >> GMP_NUMB_BITS == 0) \ - { \ - if ((src) != (dst)) \ - __GMPN_COPY_REST (dst, src, n, __gmp_i); \ - (cout) = 0; \ - break; \ - } \ - } \ - } \ - else \ - { \ - if ((src) != (dst)) \ - __GMPN_COPY_REST (dst, src, n, 1); \ - (cout) = 0; \ - } \ - } while (0) -#endif - -#define __GMPN_ADDCB(r,x,y) ((r) < (y)) -#define __GMPN_SUBCB(r,x,y) ((x) < (y)) - -#define __GMPN_ADD_1(cout, dst, src, n, v) \ - __GMPN_AORS_1(cout, dst, src, n, v, +, __GMPN_ADDCB) -#define __GMPN_SUB_1(cout, dst, src, n, v) \ - __GMPN_AORS_1(cout, dst, src, n, v, -, __GMPN_SUBCB) - - -/* Compare {xp,size} and {yp,size}, setting "result" to positive, zero or - negative. size==0 is allowed. On random data usually only one limb will - need to be examined to get a result, so it's worth having it inline. */ -#define __GMPN_CMP(result, xp, yp, size) \ - do { \ - mp_size_t __gmp_i; \ - mp_limb_t __gmp_x, __gmp_y; \ - \ - /* ASSERT ((size) >= 0); */ \ - \ - (result) = 0; \ - __gmp_i = (size); \ - while (--__gmp_i >= 0) \ - { \ - __gmp_x = (xp)[__gmp_i]; \ - __gmp_y = (yp)[__gmp_i]; \ - if (__gmp_x != __gmp_y) \ - { \ - /* Cannot use __gmp_x - __gmp_y, may overflow an "int" */ \ - (result) = (__gmp_x > __gmp_y ? 1 : -1); \ - break; \ - } \ - } \ - } while (0) - - -#if defined (__GMPN_COPY) && ! defined (__GMPN_COPY_REST) -#define __GMPN_COPY_REST(dst, src, size, start) \ - do { \ - /* ASSERT ((start) >= 0); */ \ - /* ASSERT ((start) <= (size)); */ \ - __GMPN_COPY ((dst)+(start), (src)+(start), (size)-(start)); \ - } while (0) -#endif - -/* Copy {src,size} to {dst,size}, starting at "start". This is designed to - keep the indexing dst[j] and src[j] nice and simple for __GMPN_ADD_1, - __GMPN_ADD, etc. */ -#if ! defined (__GMPN_COPY_REST) -#define __GMPN_COPY_REST(dst, src, size, start) \ - do { \ - mp_size_t __gmp_j; \ - /* ASSERT ((size) >= 0); */ \ - /* ASSERT ((start) >= 0); */ \ - /* ASSERT ((start) <= (size)); */ \ - /* ASSERT (MPN_SAME_OR_SEPARATE_P (dst, src, size)); */ \ - __GMP_CRAY_Pragma ("_CRI ivdep"); \ - for (__gmp_j = (start); __gmp_j < (size); __gmp_j++) \ - (dst)[__gmp_j] = (src)[__gmp_j]; \ - } while (0) -#endif - -/* Enhancement: Use some of the smarter code from gmp-impl.h. Maybe use - mpn_copyi if there's a native version, and if we don't mind demanding - binary compatibility for it (on targets which use it). */ - -#if ! defined (__GMPN_COPY) -#define __GMPN_COPY(dst, src, size) __GMPN_COPY_REST (dst, src, size, 0) -#endif - - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_add) -#if ! defined (__GMP_FORCE_mpn_add) -__GMP_EXTERN_INLINE -#endif -mp_limb_t -mpn_add (mp_ptr __gmp_wp, mp_srcptr __gmp_xp, mp_size_t __gmp_xsize, mp_srcptr __gmp_yp, mp_size_t __gmp_ysize) -{ - mp_limb_t __gmp_c; - __GMPN_ADD (__gmp_c, __gmp_wp, __gmp_xp, __gmp_xsize, __gmp_yp, __gmp_ysize); - return __gmp_c; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_add_1) -#if ! defined (__GMP_FORCE_mpn_add_1) -__GMP_EXTERN_INLINE -#endif -mp_limb_t -mpn_add_1 (mp_ptr __gmp_dst, mp_srcptr __gmp_src, mp_size_t __gmp_size, mp_limb_t __gmp_n) __GMP_NOTHROW -{ - mp_limb_t __gmp_c; - __GMPN_ADD_1 (__gmp_c, __gmp_dst, __gmp_src, __gmp_size, __gmp_n); - return __gmp_c; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_cmp) -#if ! defined (__GMP_FORCE_mpn_cmp) -__GMP_EXTERN_INLINE -#endif -int -mpn_cmp (mp_srcptr __gmp_xp, mp_srcptr __gmp_yp, mp_size_t __gmp_size) __GMP_NOTHROW -{ - int __gmp_result; - __GMPN_CMP (__gmp_result, __gmp_xp, __gmp_yp, __gmp_size); - return __gmp_result; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_sub) -#if ! defined (__GMP_FORCE_mpn_sub) -__GMP_EXTERN_INLINE -#endif -mp_limb_t -mpn_sub (mp_ptr __gmp_wp, mp_srcptr __gmp_xp, mp_size_t __gmp_xsize, mp_srcptr __gmp_yp, mp_size_t __gmp_ysize) -{ - mp_limb_t __gmp_c; - __GMPN_SUB (__gmp_c, __gmp_wp, __gmp_xp, __gmp_xsize, __gmp_yp, __gmp_ysize); - return __gmp_c; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_sub_1) -#if ! defined (__GMP_FORCE_mpn_sub_1) -__GMP_EXTERN_INLINE -#endif -mp_limb_t -mpn_sub_1 (mp_ptr __gmp_dst, mp_srcptr __gmp_src, mp_size_t __gmp_size, mp_limb_t __gmp_n) __GMP_NOTHROW -{ - mp_limb_t __gmp_c; - __GMPN_SUB_1 (__gmp_c, __gmp_dst, __gmp_src, __gmp_size, __gmp_n); - return __gmp_c; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_neg) -#if ! defined (__GMP_FORCE_mpn_neg) -__GMP_EXTERN_INLINE -#endif -mp_limb_t -mpn_neg (mp_ptr __gmp_rp, mp_srcptr __gmp_up, mp_size_t __gmp_n) -{ - mp_limb_t __gmp_ul, __gmp_cy; - __gmp_cy = 0; - do { - __gmp_ul = *__gmp_up++; - *__gmp_rp++ = -__gmp_ul - __gmp_cy; - __gmp_cy |= __gmp_ul != 0; - } while (--__gmp_n != 0); - return __gmp_cy; -} -#endif - -#if defined (__cplusplus) -} -#endif - - -/* Allow faster testing for negative, zero, and positive. */ -#define mpz_sgn(Z) ((Z)->_mp_size < 0 ? -1 : (Z)->_mp_size > 0) -#define mpf_sgn(F) ((F)->_mp_size < 0 ? -1 : (F)->_mp_size > 0) -#define mpq_sgn(Q) ((Q)->_mp_num._mp_size < 0 ? -1 : (Q)->_mp_num._mp_size > 0) - -/* When using GCC, optimize certain common comparisons. */ -#if defined (__GNUC__) && __GNUC__ >= 2 -#define mpz_cmp_ui(Z,UI) \ - (__builtin_constant_p (UI) && (UI) == 0 \ - ? mpz_sgn (Z) : _mpz_cmp_ui (Z,UI)) -#define mpz_cmp_si(Z,SI) \ - (__builtin_constant_p (SI) && (SI) == 0 ? mpz_sgn (Z) \ - : __builtin_constant_p (SI) && (SI) > 0 \ - ? _mpz_cmp_ui (Z, __GMP_CAST (unsigned long int, SI)) \ - : _mpz_cmp_si (Z,SI)) -#define mpq_cmp_ui(Q,NUI,DUI) \ - (__builtin_constant_p (NUI) && (NUI) == 0 \ - ? mpq_sgn (Q) : _mpq_cmp_ui (Q,NUI,DUI)) -#define mpq_cmp_si(q,n,d) \ - (__builtin_constant_p ((n) >= 0) && (n) >= 0 \ - ? mpq_cmp_ui (q, __GMP_CAST (unsigned long, n), d) \ - : _mpq_cmp_si (q, n, d)) -#else -#define mpz_cmp_ui(Z,UI) _mpz_cmp_ui (Z,UI) -#define mpz_cmp_si(Z,UI) _mpz_cmp_si (Z,UI) -#define mpq_cmp_ui(Q,NUI,DUI) _mpq_cmp_ui (Q,NUI,DUI) -#define mpq_cmp_si(q,n,d) _mpq_cmp_si(q,n,d) -#endif - - -/* Using "&" rather than "&&" means these can come out branch-free. Every - mpz_t has at least one limb allocated, so fetching the low limb is always - allowed. */ -#define mpz_odd_p(z) (((z)->_mp_size != 0) & __GMP_CAST (int, (z)->_mp_d[0])) -#define mpz_even_p(z) (! mpz_odd_p (z)) - - -/**************** C++ routines ****************/ - -#ifdef __cplusplus -__GMP_DECLSPEC_XX std::ostream& operator<< (std::ostream &, mpz_srcptr); -__GMP_DECLSPEC_XX std::ostream& operator<< (std::ostream &, mpq_srcptr); -__GMP_DECLSPEC_XX std::ostream& operator<< (std::ostream &, mpf_srcptr); -__GMP_DECLSPEC_XX std::istream& operator>> (std::istream &, mpz_ptr); -__GMP_DECLSPEC_XX std::istream& operator>> (std::istream &, mpq_ptr); -__GMP_DECLSPEC_XX std::istream& operator>> (std::istream &, mpf_ptr); -#endif - - -/* Source-level compatibility with GMP 2 and earlier. */ -#define mpn_divmod(qp,np,nsize,dp,dsize) \ - mpn_divrem (qp, __GMP_CAST (mp_size_t, 0), np, nsize, dp, dsize) - -/* Source-level compatibility with GMP 1. */ -#define mpz_mdiv mpz_fdiv_q -#define mpz_mdivmod mpz_fdiv_qr -#define mpz_mmod mpz_fdiv_r -#define mpz_mdiv_ui mpz_fdiv_q_ui -#define mpz_mdivmod_ui(q,r,n,d) \ - (((r) == 0) ? mpz_fdiv_q_ui (q,n,d) : mpz_fdiv_qr_ui (q,r,n,d)) -#define mpz_mmod_ui(r,n,d) \ - (((r) == 0) ? mpz_fdiv_ui (n,d) : mpz_fdiv_r_ui (r,n,d)) - -/* Useful synonyms, but not quite compatible with GMP 1. */ -#define mpz_div mpz_fdiv_q -#define mpz_divmod mpz_fdiv_qr -#define mpz_div_ui mpz_fdiv_q_ui -#define mpz_divmod_ui mpz_fdiv_qr_ui -#define mpz_div_2exp mpz_fdiv_q_2exp -#define mpz_mod_2exp mpz_fdiv_r_2exp - -enum -{ - GMP_ERROR_NONE = 0, - GMP_ERROR_UNSUPPORTED_ARGUMENT = 1, - GMP_ERROR_DIVISION_BY_ZERO = 2, - GMP_ERROR_SQRT_OF_NEGATIVE = 4, - GMP_ERROR_INVALID_ARGUMENT = 8 -}; - -/* Define CC and CFLAGS which were used to build this version of GMP */ -#define __GMP_CC "gcc -std=gnu99" -#define __GMP_CFLAGS "-m32 -O2 -pedantic -fomit-frame-pointer -mtune=pentiumpro -march=pentiumpro" - -/* Major version number is the value of __GNU_MP__ too, above and in mp.h. */ -#define __GNU_MP_VERSION 5 -#define __GNU_MP_VERSION_MINOR 0 -#define __GNU_MP_VERSION_PATCHLEVEL 1 -#define __GMP_MP_RELEASE (__GNU_MP_VERSION * 10000 + __GNU_MP_VERSION_MINOR * 100 + __GNU_MP_VERSION_PATCHLEVEL) - -#define __GMP_H__ -#endif /* __GMP_H__ */ diff --git a/misc/builddeps/linux32/gmp/lib/libgmp.a b/misc/builddeps/linux32/gmp/lib/libgmp.a deleted file mode 100644 index e61da303..00000000 Binary files a/misc/builddeps/linux32/gmp/lib/libgmp.a and /dev/null differ diff --git a/misc/builddeps/linux32/gmp/lib/libgmp.la b/misc/builddeps/linux32/gmp/lib/libgmp.la deleted file mode 100755 index b6124777..00000000 --- a/misc/builddeps/linux32/gmp/lib/libgmp.la +++ /dev/null @@ -1,41 +0,0 @@ -# libgmp.la - a libtool library file -# Generated by ltmain.sh (GNU libtool) 2.2.6b -# -# Please DO NOT delete this file! -# It is necessary for linking the library. - -# The name that we can dlopen(3). -dlname='' - -# Names of this library. -library_names='' - -# The name of the static archive. -old_library='libgmp.a' - -# Linker flags that can not go in dependency_libs. -inherited_linker_flags='' - -# Libraries that this one depends upon. -dependency_libs='' - -# Names of additional weak libraries provided by this library -weak_library_names='' - -# Version information for libgmp. -current=10 -age=0 -revision=1 - -# Is this an already installed library? -installed=yes - -# Should we warn about portability when linking against -modules? -shouldnotlink=no - -# Files to dlopen/dlpreopen -dlopen='' -dlpreopen='' - -# Directory that this library needs to be installed in: -libdir='/tmp/gg/lib' diff --git a/misc/builddeps/linux32/gmp/share/info/gmp.info b/misc/builddeps/linux32/gmp/share/info/gmp.info deleted file mode 100644 index d65ab795..00000000 --- a/misc/builddeps/linux32/gmp/share/info/gmp.info +++ /dev/null @@ -1,178 +0,0 @@ -This is ../../gmp/doc/gmp.info, produced by makeinfo version 4.8 from -../../gmp/doc/gmp.texi. - - This manual describes how to install and use the GNU multiple -precision arithmetic library, version 5.0.1. - - Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, -2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free -Software Foundation, Inc. - - Permission is granted to copy, distribute and/or modify this -document under the terms of the GNU Free Documentation License, Version -1.3 or any later version published by the Free Software Foundation; -with no Invariant Sections, with the Front-Cover Texts being "A GNU -Manual", and with the Back-Cover Texts being "You have freedom to copy -and modify this GNU Manual, like GNU software". A copy of the license -is included in *Note GNU Free Documentation License::. - -INFO-DIR-SECTION GNU libraries -START-INFO-DIR-ENTRY -* gmp: (gmp). GNU Multiple Precision Arithmetic Library. -END-INFO-DIR-ENTRY - - -Indirect: -gmp.info-1: 981 -gmp.info-2: 300864 - -Tag Table: -(Indirect) -Node: Top981 -Node: Copying3211 -Node: Introduction to GMP5062 -Node: Installing GMP7773 -Node: Build Options8505 -Node: ABI and ISA24573 -Node: Notes for Package Builds34251 -Node: Notes for Particular Systems37338 -Node: Known Build Problems43895 -Node: Performance optimization47429 -Node: GMP Basics48563 -Node: Headers and Libraries49211 -Node: Nomenclature and Types50635 -Node: Function Classes52632 -Node: Variable Conventions54325 -Node: Parameter Conventions55934 -Node: Memory Management57990 -Node: Reentrancy59118 -Node: Useful Macros and Constants60991 -Node: Compatibility with older versions61989 -Node: Demonstration Programs62950 -Node: Efficiency64815 -Node: Debugging72439 -Node: Profiling78997 -Node: Autoconf82988 -Node: Emacs84767 -Node: Reporting Bugs85373 -Node: Integer Functions87916 -Node: Initializing Integers88692 -Node: Assigning Integers90839 -Node: Simultaneous Integer Init & Assign92426 -Node: Converting Integers94051 -Node: Integer Arithmetic96973 -Node: Integer Division98559 -Node: Integer Exponentiation104869 -Node: Integer Roots106309 -Node: Number Theoretic Functions107983 -Node: Integer Comparisons114126 -Node: Integer Logic and Bit Fiddling115504 -Node: I/O of Integers118051 -Node: Integer Random Numbers120935 -Node: Integer Import and Export123546 -Node: Miscellaneous Integer Functions127556 -Node: Integer Special Functions129416 -Node: Rational Number Functions132503 -Node: Initializing Rationals133696 -Node: Rational Conversions136157 -Node: Rational Arithmetic137888 -Node: Comparing Rationals139192 -Node: Applying Integer Functions140559 -Node: I/O of Rationals142042 -Node: Floating-point Functions143902 -Node: Initializing Floats146787 -Node: Assigning Floats150874 -Node: Simultaneous Float Init & Assign153441 -Node: Converting Floats154969 -Node: Float Arithmetic158217 -Node: Float Comparison160230 -Node: I/O of Floats161811 -Node: Miscellaneous Float Functions164409 -Node: Low-level Functions166303 -Node: Random Number Functions190437 -Node: Random State Initialization191505 -Node: Random State Seeding194363 -Node: Random State Miscellaneous195752 -Node: Formatted Output196393 -Node: Formatted Output Strings196638 -Node: Formatted Output Functions201852 -Node: C++ Formatted Output205927 -Node: Formatted Input208609 -Node: Formatted Input Strings208845 -Node: Formatted Input Functions213497 -Node: C++ Formatted Input216466 -Node: C++ Class Interface218369 -Node: C++ Interface General219370 -Node: C++ Interface Integers222440 -Node: C++ Interface Rationals225871 -Node: C++ Interface Floats229548 -Node: C++ Interface Random Numbers234830 -Node: C++ Interface Limitations237236 -Node: BSD Compatible Functions240056 -Node: Custom Allocation244767 -Node: Language Bindings249085 -Node: Algorithms253038 -Node: Multiplication Algorithms253738 -Node: Basecase Multiplication254710 -Node: Karatsuba Multiplication256618 -Node: Toom 3-Way Multiplication260243 -Node: Toom 4-Way Multiplication266657 -Node: FFT Multiplication268029 -Node: Other Multiplication273365 -Node: Unbalanced Multiplication275839 -Node: Division Algorithms276627 -Node: Single Limb Division277006 -Node: Basecase Division279897 -Node: Divide and Conquer Division281100 -Node: Block-Wise Barrett Division283169 -Node: Exact Division283821 -Node: Exact Remainder286986 -Node: Small Quotient Division289213 -Node: Greatest Common Divisor Algorithms290811 -Node: Binary GCD291108 -Node: Lehmer's Algorithm293957 -Node: Subquadratic GCD296177 -Node: Extended GCD298636 -Node: Jacobi Symbol299948 -Node: Powering Algorithms300864 -Node: Normal Powering Algorithm301127 -Node: Modular Powering Algorithm301655 -Node: Root Extraction Algorithms302435 -Node: Square Root Algorithm302750 -Node: Nth Root Algorithm304891 -Node: Perfect Square Algorithm305676 -Node: Perfect Power Algorithm307762 -Node: Radix Conversion Algorithms308383 -Node: Binary to Radix308759 -Node: Radix to Binary312688 -Node: Other Algorithms314776 -Node: Prime Testing Algorithm315128 -Node: Factorial Algorithm316312 -Node: Binomial Coefficients Algorithm317715 -Node: Fibonacci Numbers Algorithm318609 -Node: Lucas Numbers Algorithm321083 -Node: Random Number Algorithms321804 -Node: Assembly Coding323925 -Node: Assembly Code Organisation324885 -Node: Assembly Basics325852 -Node: Assembly Carry Propagation327002 -Node: Assembly Cache Handling328833 -Node: Assembly Functional Units330994 -Node: Assembly Floating Point332607 -Node: Assembly SIMD Instructions336385 -Node: Assembly Software Pipelining337367 -Node: Assembly Loop Unrolling338429 -Node: Assembly Writing Guide340644 -Node: Internals343409 -Node: Integer Internals343921 -Node: Rational Internals346177 -Node: Float Internals347415 -Node: Raw Output Internals354829 -Node: C++ Interface Internals356023 -Node: Contributors359309 -Node: References364267 -Node: GNU Free Documentation License369925 -Node: Concept Index395094 -Node: Function Index441276 - -End Tag Table diff --git a/misc/builddeps/linux32/gmp/share/info/gmp.info-1 b/misc/builddeps/linux32/gmp/share/info/gmp.info-1 deleted file mode 100644 index d1360599..00000000 --- a/misc/builddeps/linux32/gmp/share/info/gmp.info-1 +++ /dev/null @@ -1,7084 +0,0 @@ -This is ../../gmp/doc/gmp.info, produced by makeinfo version 4.8 from -../../gmp/doc/gmp.texi. - - This manual describes how to install and use the GNU multiple -precision arithmetic library, version 5.0.1. - - Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, -2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free -Software Foundation, Inc. - - Permission is granted to copy, distribute and/or modify this -document under the terms of the GNU Free Documentation License, Version -1.3 or any later version published by the Free Software Foundation; -with no Invariant Sections, with the Front-Cover Texts being "A GNU -Manual", and with the Back-Cover Texts being "You have freedom to copy -and modify this GNU Manual, like GNU software". A copy of the license -is included in *Note GNU Free Documentation License::. - -INFO-DIR-SECTION GNU libraries -START-INFO-DIR-ENTRY -* gmp: (gmp). GNU Multiple Precision Arithmetic Library. -END-INFO-DIR-ENTRY - - -File: gmp.info, Node: Top, Next: Copying, Prev: (dir), Up: (dir) - -GNU MP -****** - - This manual describes how to install and use the GNU multiple -precision arithmetic library, version 5.0.1. - - Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, -2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free -Software Foundation, Inc. - - Permission is granted to copy, distribute and/or modify this -document under the terms of the GNU Free Documentation License, Version -1.3 or any later version published by the Free Software Foundation; -with no Invariant Sections, with the Front-Cover Texts being "A GNU -Manual", and with the Back-Cover Texts being "You have freedom to copy -and modify this GNU Manual, like GNU software". A copy of the license -is included in *Note GNU Free Documentation License::. - - -* Menu: - -* Copying:: GMP Copying Conditions (LGPL). -* Introduction to GMP:: Brief introduction to GNU MP. -* Installing GMP:: How to configure and compile the GMP library. -* GMP Basics:: What every GMP user should know. -* Reporting Bugs:: How to usefully report bugs. -* Integer Functions:: Functions for arithmetic on signed integers. -* Rational Number Functions:: Functions for arithmetic on rational numbers. -* Floating-point Functions:: Functions for arithmetic on floats. -* Low-level Functions:: Fast functions for natural numbers. -* Random Number Functions:: Functions for generating random numbers. -* Formatted Output:: `printf' style output. -* Formatted Input:: `scanf' style input. -* C++ Class Interface:: Class wrappers around GMP types. -* BSD Compatible Functions:: All functions found in BSD MP. -* Custom Allocation:: How to customize the internal allocation. -* Language Bindings:: Using GMP from other languages. -* Algorithms:: What happens behind the scenes. -* Internals:: How values are represented behind the scenes. - -* Contributors:: Who brings you this library? -* References:: Some useful papers and books to read. -* GNU Free Documentation License:: -* Concept Index:: -* Function Index:: - - -File: gmp.info, Node: Copying, Next: Introduction to GMP, Prev: Top, Up: Top - -GNU MP Copying Conditions -************************* - -This library is "free"; this means that everyone is free to use it and -free to redistribute it on a free basis. The library is not in the -public domain; it is copyrighted and there are restrictions on its -distribution, but these restrictions are designed to permit everything -that a good cooperating citizen would want to do. What is not allowed -is to try to prevent others from further sharing any version of this -library that they might get from you. - - Specifically, we want to make sure that you have the right to give -away copies of the library, that you receive source code or else can -get it if you want it, that you can change this library or use pieces -of it in new free programs, and that you know you can do these things. - - To make sure that everyone has such rights, we have to forbid you to -deprive anyone else of these rights. For example, if you distribute -copies of the GNU MP library, you must give the recipients all the -rights that you have. You must make sure that they, too, receive or -can get the source code. And you must tell them their rights. - - Also, for our own protection, we must make certain that everyone -finds out that there is no warranty for the GNU MP library. If it is -modified by someone else and passed on, we want their recipients to -know that what they have is not what we distributed, so that any -problems introduced by others will not reflect on our reputation. - - The precise conditions of the license for the GNU MP library are -found in the Lesser General Public License version 3 that accompanies -the source code, see `COPYING.LIB'. Certain demonstration programs are -provided under the terms of the plain General Public License version 3, -see `COPYING'. - - -File: gmp.info, Node: Introduction to GMP, Next: Installing GMP, Prev: Copying, Up: Top - -1 Introduction to GNU MP -************************ - -GNU MP is a portable library written in C for arbitrary precision -arithmetic on integers, rational numbers, and floating-point numbers. -It aims to provide the fastest possible arithmetic for all applications -that need higher precision than is directly supported by the basic C -types. - - Many applications use just a few hundred bits of precision; but some -applications may need thousands or even millions of bits. GMP is -designed to give good performance for both, by choosing algorithms -based on the sizes of the operands, and by carefully keeping the -overhead at a minimum. - - The speed of GMP is achieved by using fullwords as the basic -arithmetic type, by using sophisticated algorithms, by including -carefully optimized assembly code for the most common inner loops for -many different CPUs, and by a general emphasis on speed (as opposed to -simplicity or elegance). - - There is assembly code for these CPUs: ARM, DEC Alpha 21064, 21164, -and 21264, AMD 29000, AMD K6, K6-2, Athlon, and Athlon64, Hitachi -SuperH and SH-2, HPPA 1.0, 1.1 and 2.0, Intel Pentium, Pentium -Pro/II/III, Pentium 4, generic x86, Intel IA-64, i960, Motorola -MC68000, MC68020, MC88100, and MC88110, Motorola/IBM PowerPC 32 and 64, -National NS32000, IBM POWER, MIPS R3000, R4000, SPARCv7, SuperSPARC, -generic SPARCv8, UltraSPARC, DEC VAX, and Zilog Z8000. Some -optimizations also for Cray vector systems, Clipper, IBM ROMP (RT), and -Pyramid AP/XP. - -For up-to-date information on GMP, please see the GMP web pages at - - `http://gmplib.org/' - -The latest version of the library is available at - - `ftp://ftp.gnu.org/gnu/gmp/' - - Many sites around the world mirror `ftp.gnu.org', please use a mirror -near you, see `http://www.gnu.org/order/ftp.html' for a full list. - - There are three public mailing lists of interest. One for release -announcements, one for general questions and discussions about usage of -the GMP library and one for bug reports. For more information, see - - `http://gmplib.org/mailman/listinfo/'. - - The proper place for bug reports is . See -*Note Reporting Bugs:: for information about reporting bugs. - - -1.1 How to use this Manual -========================== - -Everyone should read *Note GMP Basics::. If you need to install the -library yourself, then read *Note Installing GMP::. If you have a -system with multiple ABIs, then read *Note ABI and ISA::, for the -compiler options that must be used on applications. - - The rest of the manual can be used for later reference, although it -is probably a good idea to glance through it. - - -File: gmp.info, Node: Installing GMP, Next: GMP Basics, Prev: Introduction to GMP, Up: Top - -2 Installing GMP -**************** - -GMP has an autoconf/automake/libtool based configuration system. On a -Unix-like system a basic build can be done with - - ./configure - make - -Some self-tests can be run with - - make check - -And you can install (under `/usr/local' by default) with - - make install - - If you experience problems, please report them to -. See *Note Reporting Bugs::, for information on -what to include in useful bug reports. - -* Menu: - -* Build Options:: -* ABI and ISA:: -* Notes for Package Builds:: -* Notes for Particular Systems:: -* Known Build Problems:: -* Performance optimization:: - - -File: gmp.info, Node: Build Options, Next: ABI and ISA, Prev: Installing GMP, Up: Installing GMP - -2.1 Build Options -================= - -All the usual autoconf configure options are available, run `./configure ---help' for a summary. The file `INSTALL.autoconf' has some generic -installation information too. - -Tools - `configure' requires various Unix-like tools. See *Note Notes for - Particular Systems::, for some options on non-Unix systems. - - It might be possible to build without the help of `configure', - certainly all the code is there, but unfortunately you'll be on - your own. - -Build Directory - To compile in a separate build directory, `cd' to that directory, - and prefix the configure command with the path to the GMP source - directory. For example - - cd /my/build/dir - /my/sources/gmp-5.0.1/configure - - Not all `make' programs have the necessary features (`VPATH') to - support this. In particular, SunOS and Slowaris `make' have bugs - that make them unable to build in a separate directory. Use GNU - `make' instead. - -`--prefix' and `--exec-prefix' - The `--prefix' option can be used in the normal way to direct GMP - to install under a particular tree. The default is `/usr/local'. - - `--exec-prefix' can be used to direct architecture-dependent files - like `libgmp.a' to a different location. This can be used to share - architecture-independent parts like the documentation, but - separate the dependent parts. Note however that `gmp.h' and - `mp.h' are architecture-dependent since they encode certain - aspects of `libgmp', so it will be necessary to ensure both - `$prefix/include' and `$exec_prefix/include' are available to the - compiler. - -`--disable-shared', `--disable-static' - By default both shared and static libraries are built (where - possible), but one or other can be disabled. Shared libraries - result in smaller executables and permit code sharing between - separate running processes, but on some CPUs are slightly slower, - having a small cost on each function call. - -Native Compilation, `--build=CPU-VENDOR-OS' - For normal native compilation, the system can be specified with - `--build'. By default `./configure' uses the output from running - `./config.guess'. On some systems `./config.guess' can determine - the exact CPU type, on others it will be necessary to give it - explicitly. For example, - - ./configure --build=ultrasparc-sun-solaris2.7 - - In all cases the `OS' part is important, since it controls how - libtool generates shared libraries. Running `./config.guess' is - the simplest way to see what it should be, if you don't know - already. - -Cross Compilation, `--host=CPU-VENDOR-OS' - When cross-compiling, the system used for compiling is given by - `--build' and the system where the library will run is given by - `--host'. For example when using a FreeBSD Athlon system to build - GNU/Linux m68k binaries, - - ./configure --build=athlon-pc-freebsd3.5 --host=m68k-mac-linux-gnu - - Compiler tools are sought first with the host system type as a - prefix. For example `m68k-mac-linux-gnu-ranlib' is tried, then - plain `ranlib'. This makes it possible for a set of - cross-compiling tools to co-exist with native tools. The prefix - is the argument to `--host', and this can be an alias, such as - `m68k-linux'. But note that tools don't have to be setup this - way, it's enough to just have a `PATH' with a suitable - cross-compiling `cc' etc. - - Compiling for a different CPU in the same family as the build - system is a form of cross-compilation, though very possibly this - would merely be special options on a native compiler. In any case - `./configure' avoids depending on being able to run code on the - build system, which is important when creating binaries for a - newer CPU since they very possibly won't run on the build system. - - In all cases the compiler must be able to produce an executable - (of whatever format) from a standard C `main'. Although only - object files will go to make up `libgmp', `./configure' uses - linking tests for various purposes, such as determining what - functions are available on the host system. - - Currently a warning is given unless an explicit `--build' is used - when cross-compiling, because it may not be possible to correctly - guess the build system type if the `PATH' has only a - cross-compiling `cc'. - - Note that the `--target' option is not appropriate for GMP. It's - for use when building compiler tools, with `--host' being where - they will run, and `--target' what they'll produce code for. - Ordinary programs or libraries like GMP are only interested in the - `--host' part, being where they'll run. (Some past versions of - GMP used `--target' incorrectly.) - -CPU types - In general, if you want a library that runs as fast as possible, - you should configure GMP for the exact CPU type your system uses. - However, this may mean the binaries won't run on older members of - the family, and might run slower on other members, older or newer. - The best idea is always to build GMP for the exact machine type - you intend to run it on. - - The following CPUs have specific support. See `configure.in' for - details of what code and compiler options they select. - - * Alpha: alpha, alphaev5, alphaev56, alphapca56, alphapca57, - alphaev6, alphaev67, alphaev68 alphaev7 - - * Cray: c90, j90, t90, sv1 - - * HPPA: hppa1.0, hppa1.1, hppa2.0, hppa2.0n, hppa2.0w, hppa64 - - * IA-64: ia64, itanium, itanium2 - - * MIPS: mips, mips3, mips64 - - * Motorola: m68k, m68000, m68010, m68020, m68030, m68040, - m68060, m68302, m68360, m88k, m88110 - - * POWER: power, power1, power2, power2sc - - * PowerPC: powerpc, powerpc64, powerpc401, powerpc403, - powerpc405, powerpc505, powerpc601, powerpc602, powerpc603, - powerpc603e, powerpc604, powerpc604e, powerpc620, powerpc630, - powerpc740, powerpc7400, powerpc7450, powerpc750, powerpc801, - powerpc821, powerpc823, powerpc860, powerpc970 - - * SPARC: sparc, sparcv8, microsparc, supersparc, sparcv9, - ultrasparc, ultrasparc2, ultrasparc2i, ultrasparc3, sparc64 - - * x86 family: i386, i486, i586, pentium, pentiummmx, pentiumpro, - pentium2, pentium3, pentium4, k6, k62, k63, athlon, amd64, - viac3, viac32 - - * Other: a29k, arm, clipper, i960, ns32k, pyramid, sh, sh2, vax, - z8k - - CPUs not listed will use generic C code. - -Generic C Build - If some of the assembly code causes problems, or if otherwise - desired, the generic C code can be selected with CPU `none'. For - example, - - ./configure --host=none-unknown-freebsd3.5 - - Note that this will run quite slowly, but it should be portable - and should at least make it possible to get something running if - all else fails. - -Fat binary, `--enable-fat' - Using `--enable-fat' selects a "fat binary" build on x86, where - optimized low level subroutines are chosen at runtime according to - the CPU detected. This means more code, but gives good - performance on all x86 chips. (This option might become available - for more architectures in the future.) - -`ABI' - On some systems GMP supports multiple ABIs (application binary - interfaces), meaning data type sizes and calling conventions. By - default GMP chooses the best ABI available, but a particular ABI - can be selected. For example - - ./configure --host=mips64-sgi-irix6 ABI=n32 - - See *Note ABI and ISA::, for the available choices on relevant - CPUs, and what applications need to do. - -`CC', `CFLAGS' - By default the C compiler used is chosen from among some likely - candidates, with `gcc' normally preferred if it's present. The - usual `CC=whatever' can be passed to `./configure' to choose - something different. - - For various systems, default compiler flags are set based on the - CPU and compiler. The usual `CFLAGS="-whatever"' can be passed to - `./configure' to use something different or to set good flags for - systems GMP doesn't otherwise know. - - The `CC' and `CFLAGS' used are printed during `./configure', and - can be found in each generated `Makefile'. This is the easiest way - to check the defaults when considering changing or adding - something. - - Note that when `CC' and `CFLAGS' are specified on a system - supporting multiple ABIs it's important to give an explicit - `ABI=whatever', since GMP can't determine the ABI just from the - flags and won't be able to select the correct assembly code. - - If just `CC' is selected then normal default `CFLAGS' for that - compiler will be used (if GMP recognises it). For example - `CC=gcc' can be used to force the use of GCC, with default flags - (and default ABI). - -`CPPFLAGS' - Any flags like `-D' defines or `-I' includes required by the - preprocessor should be set in `CPPFLAGS' rather than `CFLAGS'. - Compiling is done with both `CPPFLAGS' and `CFLAGS', but - preprocessing uses just `CPPFLAGS'. This distinction is because - most preprocessors won't accept all the flags the compiler does. - Preprocessing is done separately in some configure tests, and in - the `ansi2knr' support for K&R compilers. - -`CC_FOR_BUILD' - Some build-time programs are compiled and run to generate - host-specific data tables. `CC_FOR_BUILD' is the compiler used - for this. It doesn't need to be in any particular ABI or mode, it - merely needs to generate executables that can run. The default is - to try the selected `CC' and some likely candidates such as `cc' - and `gcc', looking for something that works. - - No flags are used with `CC_FOR_BUILD' because a simple invocation - like `cc foo.c' should be enough. If some particular options are - required they can be included as for instance `CC_FOR_BUILD="cc - -whatever"'. - -C++ Support, `--enable-cxx' - C++ support in GMP can be enabled with `--enable-cxx', in which - case a C++ compiler will be required. As a convenience - `--enable-cxx=detect' can be used to enable C++ support only if a - compiler can be found. The C++ support consists of a library - `libgmpxx.la' and header file `gmpxx.h' (*note Headers and - Libraries::). - - A separate `libgmpxx.la' has been adopted rather than having C++ - objects within `libgmp.la' in order to ensure dynamic linked C - programs aren't bloated by a dependency on the C++ standard - library, and to avoid any chance that the C++ compiler could be - required when linking plain C programs. - - `libgmpxx.la' will use certain internals from `libgmp.la' and can - only be expected to work with `libgmp.la' from the same GMP - version. Future changes to the relevant internals will be - accompanied by renaming, so a mismatch will cause unresolved - symbols rather than perhaps mysterious misbehaviour. - - In general `libgmpxx.la' will be usable only with the C++ compiler - that built it, since name mangling and runtime support are usually - incompatible between different compilers. - -`CXX', `CXXFLAGS' - When C++ support is enabled, the C++ compiler and its flags can be - set with variables `CXX' and `CXXFLAGS' in the usual way. The - default for `CXX' is the first compiler that works from a list of - likely candidates, with `g++' normally preferred when available. - The default for `CXXFLAGS' is to try `CFLAGS', `CFLAGS' without - `-g', then for `g++' either `-g -O2' or `-O2', or for other - compilers `-g' or nothing. Trying `CFLAGS' this way is convenient - when using `gcc' and `g++' together, since the flags for `gcc' will - usually suit `g++'. - - It's important that the C and C++ compilers match, meaning their - startup and runtime support routines are compatible and that they - generate code in the same ABI (if there's a choice of ABIs on the - system). `./configure' isn't currently able to check these things - very well itself, so for that reason `--disable-cxx' is the - default, to avoid a build failure due to a compiler mismatch. - Perhaps this will change in the future. - - Incidentally, it's normally not good enough to set `CXX' to the - same as `CC'. Although `gcc' for instance recognises `foo.cc' as - C++ code, only `g++' will invoke the linker the right way when - building an executable or shared library from C++ object files. - -Temporary Memory, `--enable-alloca=' - GMP allocates temporary workspace using one of the following three - methods, which can be selected with for instance - `--enable-alloca=malloc-reentrant'. - - * `alloca' - C library or compiler builtin. - - * `malloc-reentrant' - the heap, in a re-entrant fashion. - - * `malloc-notreentrant' - the heap, with global variables. - - For convenience, the following choices are also available. - `--disable-alloca' is the same as `no'. - - * `yes' - a synonym for `alloca'. - - * `no' - a synonym for `malloc-reentrant'. - - * `reentrant' - `alloca' if available, otherwise - `malloc-reentrant'. This is the default. - - * `notreentrant' - `alloca' if available, otherwise - `malloc-notreentrant'. - - `alloca' is reentrant and fast, and is recommended. It actually - allocates just small blocks on the stack; larger ones use - malloc-reentrant. - - `malloc-reentrant' is, as the name suggests, reentrant and thread - safe, but `malloc-notreentrant' is faster and should be used if - reentrancy is not required. - - The two malloc methods in fact use the memory allocation functions - selected by `mp_set_memory_functions', these being `malloc' and - friends by default. *Note Custom Allocation::. - - An additional choice `--enable-alloca=debug' is available, to help - when debugging memory related problems (*note Debugging::). - -FFT Multiplication, `--disable-fft' - By default multiplications are done using Karatsuba, 3-way Toom, - and Fermat FFT. The FFT is only used on large to very large - operands and can be disabled to save code size if desired. - -Berkeley MP, `--enable-mpbsd' - The Berkeley MP compatibility library (`libmp') and header file - (`mp.h') are built and installed only if `--enable-mpbsd' is used. - *Note BSD Compatible Functions::. - -Assertion Checking, `--enable-assert' - This option enables some consistency checking within the library. - This can be of use while debugging, *note Debugging::. - -Execution Profiling, `--enable-profiling=prof/gprof/instrument' - Enable profiling support, in one of various styles, *note - Profiling::. - -`MPN_PATH' - Various assembly versions of each mpn subroutines are provided. - For a given CPU, a search is made though a path to choose a - version of each. For example `sparcv8' has - - MPN_PATH="sparc32/v8 sparc32 generic" - - which means look first for v8 code, then plain sparc32 (which is - v7), and finally fall back on generic C. Knowledgeable users with - special requirements can specify a different path. Normally this - is completely unnecessary. - -Documentation - The source for the document you're now reading is `doc/gmp.texi', - in Texinfo format, see *Note Texinfo: (texinfo)Top. - - Info format `doc/gmp.info' is included in the distribution. The - usual automake targets are available to make PostScript, DVI, PDF - and HTML (these will require various TeX and Texinfo tools). - - DocBook and XML can be generated by the Texinfo `makeinfo' program - too, see *Note Options for `makeinfo': (texinfo)makeinfo options. - - Some supplementary notes can also be found in the `doc' - subdirectory. - - - -File: gmp.info, Node: ABI and ISA, Next: Notes for Package Builds, Prev: Build Options, Up: Installing GMP - -2.2 ABI and ISA -=============== - -ABI (Application Binary Interface) refers to the calling conventions -between functions, meaning what registers are used and what sizes the -various C data types are. ISA (Instruction Set Architecture) refers to -the instructions and registers a CPU has available. - - Some 64-bit ISA CPUs have both a 64-bit ABI and a 32-bit ABI -defined, the latter for compatibility with older CPUs in the family. -GMP supports some CPUs like this in both ABIs. In fact within GMP -`ABI' means a combination of chip ABI, plus how GMP chooses to use it. -For example in some 32-bit ABIs, GMP may support a limb as either a -32-bit `long' or a 64-bit `long long'. - - By default GMP chooses the best ABI available for a given system, -and this generally gives significantly greater speed. But an ABI can -be chosen explicitly to make GMP compatible with other libraries, or -particular application requirements. For example, - - ./configure ABI=32 - - In all cases it's vital that all object code used in a given program -is compiled for the same ABI. - - Usually a limb is implemented as a `long'. When a `long long' limb -is used this is encoded in the generated `gmp.h'. This is convenient -for applications, but it does mean that `gmp.h' will vary, and can't be -just copied around. `gmp.h' remains compiler independent though, since -all compilers for a particular ABI will be expected to use the same -limb type. - - Currently no attempt is made to follow whatever conventions a system -has for installing library or header files built for a particular ABI. -This will probably only matter when installing multiple builds of GMP, -and it might be as simple as configuring with a special `libdir', or it -might require more than that. Note that builds for different ABIs need -to done separately, with a fresh `./configure' and `make' each. - - -AMD64 (`x86_64') - On AMD64 systems supporting both 32-bit and 64-bit modes for - applications, the following ABI choices are available. - - `ABI=64' - The 64-bit ABI uses 64-bit limbs and pointers and makes full - use of the chip architecture. This is the default. - Applications will usually not need special compiler flags, - but for reference the option is - - gcc -m64 - - `ABI=32' - The 32-bit ABI is the usual i386 conventions. This will be - slower, and is not recommended except for inter-operating - with other code not yet 64-bit capable. Applications must be - compiled with - - gcc -m32 - - (In GCC 2.95 and earlier there's no `-m32' option, it's the - only mode.) - - -HPPA 2.0 (`hppa2.0*', `hppa64') - - `ABI=2.0w' - The 2.0w ABI uses 64-bit limbs and pointers and is available - on HP-UX 11 or up. Applications must be compiled with - - gcc [built for 2.0w] - cc +DD64 - - `ABI=2.0n' - The 2.0n ABI means the 32-bit HPPA 1.0 ABI and all its normal - calling conventions, but with 64-bit instructions permitted - within functions. GMP uses a 64-bit `long long' for a limb. - This ABI is available on hppa64 GNU/Linux and on HP-UX 10 or - higher. Applications must be compiled with - - gcc [built for 2.0n] - cc +DA2.0 +e - - Note that current versions of GCC (eg. 3.2) don't generate - 64-bit instructions for `long long' operations and so may be - slower than for 2.0w. (The GMP assembly code is the same - though.) - - `ABI=1.0' - HPPA 2.0 CPUs can run all HPPA 1.0 and 1.1 code in the 32-bit - HPPA 1.0 ABI. No special compiler options are needed for - applications. - - All three ABIs are available for CPU types `hppa2.0w', `hppa2.0' - and `hppa64', but for CPU type `hppa2.0n' only 2.0n or 1.0 are - considered. - - Note that GCC on HP-UX has no options to choose between 2.0n and - 2.0w modes, unlike HP `cc'. Instead it must be built for one or - the other ABI. GMP will detect how it was built, and skip to the - corresponding `ABI'. - - -IA-64 under HP-UX (`ia64*-*-hpux*', `itanium*-*-hpux*') - HP-UX supports two ABIs for IA-64. GMP performance is the same in - both. - - `ABI=32' - In the 32-bit ABI, pointers, `int's and `long's are 32 bits - and GMP uses a 64 bit `long long' for a limb. Applications - can be compiled without any special flags since this ABI is - the default in both HP C and GCC, but for reference the flags - are - - gcc -milp32 - cc +DD32 - - `ABI=64' - In the 64-bit ABI, `long's and pointers are 64 bits and GMP - uses a `long' for a limb. Applications must be compiled with - - gcc -mlp64 - cc +DD64 - - On other IA-64 systems, GNU/Linux for instance, `ABI=64' is the - only choice. - - -MIPS under IRIX 6 (`mips*-*-irix[6789]') - IRIX 6 always has a 64-bit MIPS 3 or better CPU, and supports ABIs - o32, n32, and 64. n32 or 64 are recommended, and GMP performance - will be the same in each. The default is n32. - - `ABI=o32' - The o32 ABI is 32-bit pointers and integers, and no 64-bit - operations. GMP will be slower than in n32 or 64, this - option only exists to support old compilers, eg. GCC 2.7.2. - Applications can be compiled with no special flags on an old - compiler, or on a newer compiler with - - gcc -mabi=32 - cc -32 - - `ABI=n32' - The n32 ABI is 32-bit pointers and integers, but with a - 64-bit limb using a `long long'. Applications must be - compiled with - - gcc -mabi=n32 - cc -n32 - - `ABI=64' - The 64-bit ABI is 64-bit pointers and integers. Applications - must be compiled with - - gcc -mabi=64 - cc -64 - - Note that MIPS GNU/Linux, as of kernel version 2.2, doesn't have - the necessary support for n32 or 64 and so only gets a 32-bit limb - and the MIPS 2 code. - - -PowerPC 64 (`powerpc64', `powerpc620', `powerpc630', `powerpc970', `power4', `power5') - - `ABI=aix64' - The AIX 64 ABI uses 64-bit limbs and pointers and is the - default on PowerPC 64 `*-*-aix*' systems. Applications must - be compiled with - - gcc -maix64 - xlc -q64 - - `ABI=mode64' - The `mode64' ABI uses 64-bit limbs and pointers, and is the - default on 64-bit GNU/Linux, BSD, and Mac OS X/Darwin - systems. Applications must be compiled with - - gcc -m64 - - `ABI=mode32' - The `mode32' ABI uses a 64-bit `long long' limb but with the - chip still in 32-bit mode and using 32-bit calling - conventions. This is the default on for systems where the - true 64-bit ABIs are unavailable. No special compiler - options are needed for applications. - - `ABI=32' - This is the basic 32-bit PowerPC ABI, with a 32-bit limb. No - special compiler options are needed for applications. - - GMP speed is greatest in `aix64' and `mode32'. In `ABI=32' only - the 32-bit ISA is used and this doesn't make full use of a 64-bit - chip. On a suitable system we could perhaps use more of the ISA, - but there are no plans to do so. - - -Sparc V9 (`sparc64', `sparcv9', `ultrasparc*') - - `ABI=64' - The 64-bit V9 ABI is available on the various BSD sparc64 - ports, recent versions of Sparc64 GNU/Linux, and Solaris 2.7 - and up (when the kernel is in 64-bit mode). GCC 3.2 or - higher, or Sun `cc' is required. On GNU/Linux, depending on - the default `gcc' mode, applications must be compiled with - - gcc -m64 - - On Solaris applications must be compiled with - - gcc -m64 -mptr64 -Wa,-xarch=v9 -mcpu=v9 - cc -xarch=v9 - - On the BSD sparc64 systems no special options are required, - since 64-bits is the only ABI available. - - `ABI=32' - For the basic 32-bit ABI, GMP still uses as much of the V9 - ISA as it can. In the Sun documentation this combination is - known as "v8plus". On GNU/Linux, depending on the default - `gcc' mode, applications may need to be compiled with - - gcc -m32 - - On Solaris, no special compiler options are required for - applications, though using something like the following is - recommended. (`gcc' 2.8 and earlier only support `-mv8' - though.) - - gcc -mv8plus - cc -xarch=v8plus - - GMP speed is greatest in `ABI=64', so it's the default where - available. The speed is partly because there are extra registers - available and partly because 64-bits is considered the more - important case and has therefore had better code written for it. - - Don't be confused by the names of the `-m' and `-x' compiler - options, they're called `arch' but effectively control both ABI - and ISA. - - On Solaris 2.6 and earlier, only `ABI=32' is available since the - kernel doesn't save all registers. - - On Solaris 2.7 with the kernel in 32-bit mode, a normal native - build will reject `ABI=64' because the resulting executables won't - run. `ABI=64' can still be built if desired by making it look - like a cross-compile, for example - - ./configure --build=none --host=sparcv9-sun-solaris2.7 ABI=64 - - -File: gmp.info, Node: Notes for Package Builds, Next: Notes for Particular Systems, Prev: ABI and ISA, Up: Installing GMP - -2.3 Notes for Package Builds -============================ - -GMP should present no great difficulties for packaging in a binary -distribution. - - Libtool is used to build the library and `-version-info' is set -appropriately, having started from `3:0:0' in GMP 3.0 (*note Library -interface versions: (libtool)Versioning.). - - The GMP 4 series will be upwardly binary compatible in each release -and will be upwardly binary compatible with all of the GMP 3 series. -Additional function interfaces may be added in each release, so on -systems where libtool versioning is not fully checked by the loader an -auxiliary mechanism may be needed to express that a dynamic linked -application depends on a new enough GMP. - - An auxiliary mechanism may also be needed to express that -`libgmpxx.la' (from `--enable-cxx', *note Build Options::) requires -`libgmp.la' from the same GMP version, since this is not done by the -libtool versioning, nor otherwise. A mismatch will result in -unresolved symbols from the linker, or perhaps the loader. - - When building a package for a CPU family, care should be taken to use -`--host' (or `--build') to choose the least common denominator among -the CPUs which might use the package. For example this might mean plain -`sparc' (meaning V7) for SPARCs. - - For x86s, `--enable-fat' sets things up for a fat binary build, -making a runtime selection of optimized low level routines. This is a -good choice for packaging to run on a range of x86 chips. - - Users who care about speed will want GMP built for their exact CPU -type, to make best use of the available optimizations. Providing a way -to suitably rebuild a package may be useful. This could be as simple -as making it possible for a user to omit `--build' (and `--host') so -`./config.guess' will detect the CPU. But a way to manually specify a -`--build' will be wanted for systems where `./config.guess' is inexact. - - On systems with multiple ABIs, a packaged build will need to decide -which among the choices is to be provided, see *Note ABI and ISA::. A -given run of `./configure' etc will only build one ABI. If a second -ABI is also required then a second run of `./configure' etc must be -made, starting from a clean directory tree (`make distclean'). - - As noted under "ABI and ISA", currently no attempt is made to follow -system conventions for install locations that vary with ABI, such as -`/usr/lib/sparcv9' for `ABI=64' as opposed to `/usr/lib' for `ABI=32'. -A package build can override `libdir' and other standard variables as -necessary. - - Note that `gmp.h' is a generated file, and will be architecture and -ABI dependent. When attempting to install two ABIs simultaneously it -will be important that an application compile gets the correct `gmp.h' -for its desired ABI. If compiler include paths don't vary with ABI -options then it might be necessary to create a `/usr/include/gmp.h' -which tests preprocessor symbols and chooses the correct actual `gmp.h'. - - -File: gmp.info, Node: Notes for Particular Systems, Next: Known Build Problems, Prev: Notes for Package Builds, Up: Installing GMP - -2.4 Notes for Particular Systems -================================ - -AIX 3 and 4 - On systems `*-*-aix[34]*' shared libraries are disabled by - default, since some versions of the native `ar' fail on the - convenience libraries used. A shared build can be attempted with - - ./configure --enable-shared --disable-static - - Note that the `--disable-static' is necessary because in a shared - build libtool makes `libgmp.a' a symlink to `libgmp.so', - apparently for the benefit of old versions of `ld' which only - recognise `.a', but unfortunately this is done even if a fully - functional `ld' is available. - -ARM - On systems `arm*-*-*', versions of GCC up to and including 2.95.3 - have a bug in unsigned division, giving wrong results for some - operands. GMP `./configure' will demand GCC 2.95.4 or later. - -Compaq C++ - Compaq C++ on OSF 5.1 has two flavours of `iostream', a standard - one and an old pre-standard one (see `man iostream_intro'). GMP - can only use the standard one, which unfortunately is not the - default but must be selected by defining `__USE_STD_IOSTREAM'. - Configure with for instance - - ./configure --enable-cxx CPPFLAGS=-D__USE_STD_IOSTREAM - -Floating Point Mode - On some systems, the hardware floating point has a control mode - which can set all operations to be done in a particular precision, - for instance single, double or extended on x86 systems (x87 - floating point). The GMP functions involving a `double' cannot be - expected to operate to their full precision when the hardware is - in single precision mode. Of course this affects all code, - including application code, not just GMP. - -MS-DOS and MS Windows - On an MS-DOS system DJGPP can be used to build GMP, and on an MS - Windows system Cygwin, DJGPP and MINGW can be used. All three are - excellent ports of GCC and the various GNU tools. - - `http://www.cygwin.com/' - `http://www.delorie.com/djgpp/' - `http://www.mingw.org/' - - Microsoft also publishes an Interix "Services for Unix" which can - be used to build GMP on Windows (with a normal `./configure'), but - it's not free software. - -MS Windows DLLs - On systems `*-*-cygwin*', `*-*-mingw*' and `*-*-pw32*' by default - GMP builds only a static library, but a DLL can be built instead - using - - ./configure --disable-static --enable-shared - - Static and DLL libraries can't both be built, since certain export - directives in `gmp.h' must be different. - - A MINGW DLL build of GMP can be used with Microsoft C. Libtool - doesn't install a `.lib' format import library, but it can be - created with MS `lib' as follows, and copied to the install - directory. Similarly for `libmp' and `libgmpxx'. - - cd .libs - lib /def:libgmp-3.dll.def /out:libgmp-3.lib - - MINGW uses the C runtime library `msvcrt.dll' for I/O, so - applications wanting to use the GMP I/O routines must be compiled - with `cl /MD' to do the same. If one of the other C runtime - library choices provided by MS C is desired then the suggestion is - to use the GMP string functions and confine I/O to the application. - -Motorola 68k CPU Types - `m68k' is taken to mean 68000. `m68020' or higher will give a - performance boost on applicable CPUs. `m68360' can be used for - CPU32 series chips. `m68302' can be used for "Dragonball" series - chips, though this is merely a synonym for `m68000'. - -OpenBSD 2.6 - `m4' in this release of OpenBSD has a bug in `eval' that makes it - unsuitable for `.asm' file processing. `./configure' will detect - the problem and either abort or choose another m4 in the `PATH'. - The bug is fixed in OpenBSD 2.7, so either upgrade or use GNU m4. - -Power CPU Types - In GMP, CPU types `power*' and `powerpc*' will each use - instructions not available on the other, so it's important to - choose the right one for the CPU that will be used. Currently GMP - has no assembly code support for using just the common instruction - subset. To get executables that run on both, the current - suggestion is to use the generic C code (CPU `none'), possibly - with appropriate compiler options (like `-mcpu=common' for `gcc'). - CPU `rs6000' (which is not a CPU but a family of workstations) is - accepted by `config.sub', but is currently equivalent to `none'. - -Sparc CPU Types - `sparcv8' or `supersparc' on relevant systems will give a - significant performance increase over the V7 code selected by plain - `sparc'. - -Sparc App Regs - The GMP assembly code for both 32-bit and 64-bit Sparc clobbers the - "application registers" `g2', `g3' and `g4', the same way that the - GCC default `-mapp-regs' does (*note SPARC Options: (gcc)SPARC - Options.). - - This makes that code unsuitable for use with the special V9 - `-mcmodel=embmedany' (which uses `g4' as a data segment pointer), - and for applications wanting to use those registers for special - purposes. In these cases the only suggestion currently is to - build GMP with CPU `none' to avoid the assembly code. - -SunOS 4 - `/usr/bin/m4' lacks various features needed to process `.asm' - files, and instead `./configure' will automatically use - `/usr/5bin/m4', which we believe is always available (if not then - use GNU m4). - -x86 CPU Types - `i586', `pentium' or `pentiummmx' code is good for its intended P5 - Pentium chips, but quite slow when run on Intel P6 class chips - (PPro, P-II, P-III). `i386' is a better choice when making - binaries that must run on both. - -x86 MMX and SSE2 Code - If the CPU selected has MMX code but the assembler doesn't support - it, a warning is given and non-MMX code is used instead. This - will be an inferior build, since the MMX code that's present is - there because it's faster than the corresponding plain integer - code. The same applies to SSE2. - - Old versions of `gas' don't support MMX instructions, in particular - version 1.92.3 that comes with FreeBSD 2.2.8 or the more recent - OpenBSD 3.1 doesn't. - - Solaris 2.6 and 2.7 `as' generate incorrect object code for - register to register `movq' instructions, and so can't be used for - MMX code. Install a recent `gas' if MMX code is wanted on these - systems. - - -File: gmp.info, Node: Known Build Problems, Next: Performance optimization, Prev: Notes for Particular Systems, Up: Installing GMP - -2.5 Known Build Problems -======================== - -You might find more up-to-date information at `http://gmplib.org/'. - -Compiler link options - The version of libtool currently in use rather aggressively strips - compiler options when linking a shared library. This will - hopefully be relaxed in the future, but for now if this is a - problem the suggestion is to create a little script to hide them, - and for instance configure with - - ./configure CC=gcc-with-my-options - -DJGPP (`*-*-msdosdjgpp*') - The DJGPP port of `bash' 2.03 is unable to run the `configure' - script, it exits silently, having died writing a preamble to - `config.log'. Use `bash' 2.04 or higher. - - `make all' was found to run out of memory during the final - `libgmp.la' link on one system tested, despite having 64Mb - available. Running `make libgmp.la' directly helped, perhaps - recursing into the various subdirectories uses up memory. - -GNU binutils `strip' prior to 2.12 - `strip' from GNU binutils 2.11 and earlier should not be used on - the static libraries `libgmp.a' and `libmp.a' since it will - discard all but the last of multiple archive members with the same - name, like the three versions of `init.o' in `libgmp.a'. Binutils - 2.12 or higher can be used successfully. - - The shared libraries `libgmp.so' and `libmp.so' are not affected by - this and any version of `strip' can be used on them. - -`make' syntax error - On certain versions of SCO OpenServer 5 and IRIX 6.5 the native - `make' is unable to handle the long dependencies list for - `libgmp.la'. The symptom is a "syntax error" on the following - line of the top-level `Makefile'. - - libgmp.la: $(libgmp_la_OBJECTS) $(libgmp_la_DEPENDENCIES) - - Either use GNU Make, or as a workaround remove - `$(libgmp_la_DEPENDENCIES)' from that line (which will make the - initial build work, but if any recompiling is done `libgmp.la' - might not be rebuilt). - -MacOS X (`*-*-darwin*') - Libtool currently only knows how to create shared libraries on - MacOS X using the native `cc' (which is a modified GCC), not a - plain GCC. A static-only build should work though - (`--disable-shared'). - -NeXT prior to 3.3 - The system compiler on old versions of NeXT was a massacred and - old GCC, even if it called itself `cc'. This compiler cannot be - used to build GMP, you need to get a real GCC, and install that. - (NeXT may have fixed this in release 3.3 of their system.) - -POWER and PowerPC - Bugs in GCC 2.7.2 (and 2.6.3) mean it can't be used to compile GMP - on POWER or PowerPC. If you want to use GCC for these machines, - get GCC 2.7.2.1 (or later). - -Sequent Symmetry - Use the GNU assembler instead of the system assembler, since the - latter has serious bugs. - -Solaris 2.6 - The system `sed' prints an error "Output line too long" when - libtool builds `libgmp.la'. This doesn't seem to cause any - obvious ill effects, but GNU `sed' is recommended, to avoid any - doubt. - -Sparc Solaris 2.7 with gcc 2.95.2 in `ABI=32' - A shared library build of GMP seems to fail in this combination, - it builds but then fails the tests, apparently due to some - incorrect data relocations within `gmp_randinit_lc_2exp_size'. - The exact cause is unknown, `--disable-shared' is recommended. - - -File: gmp.info, Node: Performance optimization, Prev: Known Build Problems, Up: Installing GMP - -2.6 Performance optimization -============================ - -For optimal performance, build GMP for the exact CPU type of the target -computer, see *Note Build Options::. - - Unlike what is the case for most other programs, the compiler -typically doesn't matter much, since GMP uses assembly language for the -most critical operation. - - In particular for long-running GMP applications, and applications -demanding extremely large numbers, building and running the `tuneup' -program in the `tune' subdirectory, can be important. For example, - - cd tune - make tuneup - ./tuneup - - will generate better contents for the `gmp-mparam.h' parameter file. - - To use the results, put the output in the file file indicated in the -`Parameters for ...' header. Then recompile from scratch. - - The `tuneup' program takes one useful parameter, `-f NNN', which -instructs the program how long to check FFT multiply parameters. If -you're going to use GMP for extremely large numbers, you may want to -run `tuneup' with a large NNN value. - - -File: gmp.info, Node: GMP Basics, Next: Reporting Bugs, Prev: Installing GMP, Up: Top - -3 GMP Basics -************ - -*Using functions, macros, data types, etc. not documented in this -manual is strongly discouraged. If you do so your application is -guaranteed to be incompatible with future versions of GMP.* - -* Menu: - -* Headers and Libraries:: -* Nomenclature and Types:: -* Function Classes:: -* Variable Conventions:: -* Parameter Conventions:: -* Memory Management:: -* Reentrancy:: -* Useful Macros and Constants:: -* Compatibility with older versions:: -* Demonstration Programs:: -* Efficiency:: -* Debugging:: -* Profiling:: -* Autoconf:: -* Emacs:: - - -File: gmp.info, Node: Headers and Libraries, Next: Nomenclature and Types, Prev: GMP Basics, Up: GMP Basics - -3.1 Headers and Libraries -========================= - -All declarations needed to use GMP are collected in the include file -`gmp.h'. It is designed to work with both C and C++ compilers. - - #include - - Note however that prototypes for GMP functions with `FILE *' -parameters are only provided if `' is included too. - - #include - #include - - Likewise `' (or `') is required for prototypes -with `va_list' parameters, such as `gmp_vprintf'. And `' -for prototypes with `struct obstack' parameters, such as -`gmp_obstack_printf', when available. - - All programs using GMP must link against the `libgmp' library. On a -typical Unix-like system this can be done with `-lgmp', for example - - gcc myprogram.c -lgmp - - GMP C++ functions are in a separate `libgmpxx' library. This is -built and installed if C++ support has been enabled (*note Build -Options::). For example, - - g++ mycxxprog.cc -lgmpxx -lgmp - - GMP is built using Libtool and an application can use that to link -if desired, *note GNU Libtool: (libtool)Top. - - If GMP has been installed to a non-standard location then it may be -necessary to use `-I' and `-L' compiler options to point to the right -directories, and some sort of run-time path for a shared library. - - -File: gmp.info, Node: Nomenclature and Types, Next: Function Classes, Prev: Headers and Libraries, Up: GMP Basics - -3.2 Nomenclature and Types -========================== - -In this manual, "integer" usually means a multiple precision integer, as -defined by the GMP library. The C data type for such integers is -`mpz_t'. Here are some examples of how to declare such integers: - - mpz_t sum; - - struct foo { mpz_t x, y; }; - - mpz_t vec[20]; - - "Rational number" means a multiple precision fraction. The C data -type for these fractions is `mpq_t'. For example: - - mpq_t quotient; - - "Floating point number" or "Float" for short, is an arbitrary -precision mantissa with a limited precision exponent. The C data type -for such objects is `mpf_t'. For example: - - mpf_t fp; - - The floating point functions accept and return exponents in the C -type `mp_exp_t'. Currently this is usually a `long', but on some -systems it's an `int' for efficiency. - - A "limb" means the part of a multi-precision number that fits in a -single machine word. (We chose this word because a limb of the human -body is analogous to a digit, only larger, and containing several -digits.) Normally a limb is 32 or 64 bits. The C data type for a limb -is `mp_limb_t'. - - Counts of limbs of a multi-precision number represented in the C type -`mp_size_t'. Currently this is normally a `long', but on some systems -it's an `int' for efficiency, and on some systems it will be `long -long' in the future. - - Counts of bits of a multi-precision number are represented in the C -type `mp_bitcnt_t'. Currently this is always an `unsigned long', but on -some systems it will be an `unsigned long long' in the future . - - "Random state" means an algorithm selection and current state data. -The C data type for such objects is `gmp_randstate_t'. For example: - - gmp_randstate_t rstate; - - Also, in general `mp_bitcnt_t' is used for bit counts and ranges, and -`size_t' is used for byte or character counts. - - -File: gmp.info, Node: Function Classes, Next: Variable Conventions, Prev: Nomenclature and Types, Up: GMP Basics - -3.3 Function Classes -==================== - -There are six classes of functions in the GMP library: - - 1. Functions for signed integer arithmetic, with names beginning with - `mpz_'. The associated type is `mpz_t'. There are about 150 - functions in this class. (*note Integer Functions::) - - 2. Functions for rational number arithmetic, with names beginning with - `mpq_'. The associated type is `mpq_t'. There are about 40 - functions in this class, but the integer functions can be used for - arithmetic on the numerator and denominator separately. (*note - Rational Number Functions::) - - 3. Functions for floating-point arithmetic, with names beginning with - `mpf_'. The associated type is `mpf_t'. There are about 60 - functions is this class. (*note Floating-point Functions::) - - 4. Functions compatible with Berkeley MP, such as `itom', `madd', and - `mult'. The associated type is `MINT'. (*note BSD Compatible - Functions::) - - 5. Fast low-level functions that operate on natural numbers. These - are used by the functions in the preceding groups, and you can - also call them directly from very time-critical user programs. - These functions' names begin with `mpn_'. The associated type is - array of `mp_limb_t'. There are about 30 (hard-to-use) functions - in this class. (*note Low-level Functions::) - - 6. Miscellaneous functions. Functions for setting up custom - allocation and functions for generating random numbers. (*note - Custom Allocation::, and *note Random Number Functions::) - - -File: gmp.info, Node: Variable Conventions, Next: Parameter Conventions, Prev: Function Classes, Up: GMP Basics - -3.4 Variable Conventions -======================== - -GMP functions generally have output arguments before input arguments. -This notation is by analogy with the assignment operator. The BSD MP -compatibility functions are exceptions, having the output arguments -last. - - GMP lets you use the same variable for both input and output in one -call. For example, the main function for integer multiplication, -`mpz_mul', can be used to square `x' and put the result back in `x' with - - mpz_mul (x, x, x); - - Before you can assign to a GMP variable, you need to initialize it -by calling one of the special initialization functions. When you're -done with a variable, you need to clear it out, using one of the -functions for that purpose. Which function to use depends on the type -of variable. See the chapters on integer functions, rational number -functions, and floating-point functions for details. - - A variable should only be initialized once, or at least cleared -between each initialization. After a variable has been initialized, it -may be assigned to any number of times. - - For efficiency reasons, avoid excessive initializing and clearing. -In general, initialize near the start of a function and clear near the -end. For example, - - void - foo (void) - { - mpz_t n; - int i; - mpz_init (n); - for (i = 1; i < 100; i++) - { - mpz_mul (n, ...); - mpz_fdiv_q (n, ...); - ... - } - mpz_clear (n); - } - - -File: gmp.info, Node: Parameter Conventions, Next: Memory Management, Prev: Variable Conventions, Up: GMP Basics - -3.5 Parameter Conventions -========================= - -When a GMP variable is used as a function parameter, it's effectively a -call-by-reference, meaning if the function stores a value there it will -change the original in the caller. Parameters which are input-only can -be designated `const' to provoke a compiler error or warning on -attempting to modify them. - - When a function is going to return a GMP result, it should designate -a parameter that it sets, like the library functions do. More than one -value can be returned by having more than one output parameter, again -like the library functions. A `return' of an `mpz_t' etc doesn't -return the object, only a pointer, and this is almost certainly not -what's wanted. - - Here's an example accepting an `mpz_t' parameter, doing a -calculation, and storing the result to the indicated parameter. - - void - foo (mpz_t result, const mpz_t param, unsigned long n) - { - unsigned long i; - mpz_mul_ui (result, param, n); - for (i = 1; i < n; i++) - mpz_add_ui (result, result, i*7); - } - - int - main (void) - { - mpz_t r, n; - mpz_init (r); - mpz_init_set_str (n, "123456", 0); - foo (r, n, 20L); - gmp_printf ("%Zd\n", r); - return 0; - } - - `foo' works even if the mainline passes the same variable for -`param' and `result', just like the library functions. But sometimes -it's tricky to make that work, and an application might not want to -bother supporting that sort of thing. - - For interest, the GMP types `mpz_t' etc are implemented as -one-element arrays of certain structures. This is why declaring a -variable creates an object with the fields GMP needs, but then using it -as a parameter passes a pointer to the object. Note that the actual -fields in each `mpz_t' etc are for internal use only and should not be -accessed directly by code that expects to be compatible with future GMP -releases. - - -File: gmp.info, Node: Memory Management, Next: Reentrancy, Prev: Parameter Conventions, Up: GMP Basics - -3.6 Memory Management -===================== - -The GMP types like `mpz_t' are small, containing only a couple of sizes, -and pointers to allocated data. Once a variable is initialized, GMP -takes care of all space allocation. Additional space is allocated -whenever a variable doesn't have enough. - - `mpz_t' and `mpq_t' variables never reduce their allocated space. -Normally this is the best policy, since it avoids frequent reallocation. -Applications that need to return memory to the heap at some particular -point can use `mpz_realloc2', or clear variables no longer needed. - - `mpf_t' variables, in the current implementation, use a fixed amount -of space, determined by the chosen precision and allocated at -initialization, so their size doesn't change. - - All memory is allocated using `malloc' and friends by default, but -this can be changed, see *Note Custom Allocation::. Temporary memory -on the stack is also used (via `alloca'), but this can be changed at -build-time if desired, see *Note Build Options::. - - -File: gmp.info, Node: Reentrancy, Next: Useful Macros and Constants, Prev: Memory Management, Up: GMP Basics - -3.7 Reentrancy -============== - -GMP is reentrant and thread-safe, with some exceptions: - - * If configured with `--enable-alloca=malloc-notreentrant' (or with - `--enable-alloca=notreentrant' when `alloca' is not available), - then naturally GMP is not reentrant. - - * `mpf_set_default_prec' and `mpf_init' use a global variable for the - selected precision. `mpf_init2' can be used instead, and in the - C++ interface an explicit precision to the `mpf_class' constructor. - - * `mpz_random' and the other old random number functions use a global - random state and are hence not reentrant. The newer random number - functions that accept a `gmp_randstate_t' parameter can be used - instead. - - * `gmp_randinit' (obsolete) returns an error indication through a - global variable, which is not thread safe. Applications are - advised to use `gmp_randinit_default' or `gmp_randinit_lc_2exp' - instead. - - * `mp_set_memory_functions' uses global variables to store the - selected memory allocation functions. - - * If the memory allocation functions set by a call to - `mp_set_memory_functions' (or `malloc' and friends by default) are - not reentrant, then GMP will not be reentrant either. - - * If the standard I/O functions such as `fwrite' are not reentrant - then the GMP I/O functions using them will not be reentrant either. - - * It's safe for two threads to read from the same GMP variable - simultaneously, but it's not safe for one to read while the - another might be writing, nor for two threads to write - simultaneously. It's not safe for two threads to generate a - random number from the same `gmp_randstate_t' simultaneously, - since this involves an update of that variable. - - -File: gmp.info, Node: Useful Macros and Constants, Next: Compatibility with older versions, Prev: Reentrancy, Up: GMP Basics - -3.8 Useful Macros and Constants -=============================== - - -- Global Constant: const int mp_bits_per_limb - The number of bits per limb. - - -- Macro: __GNU_MP_VERSION - -- Macro: __GNU_MP_VERSION_MINOR - -- Macro: __GNU_MP_VERSION_PATCHLEVEL - The major and minor GMP version, and patch level, respectively, as - integers. For GMP i.j, these numbers will be i, j, and 0, - respectively. For GMP i.j.k, these numbers will be i, j, and k, - respectively. - - -- Global Constant: const char * const gmp_version - The GMP version number, as a null-terminated string, in the form - "i.j.k". This release is "5.0.1". Note that the format "i.j" was - used when k was zero was used before version 4.3.0. - - -- Macro: __GMP_CC - -- Macro: __GMP_CFLAGS - The compiler and compiler flags, respectively, used when compiling - GMP, as strings. - - -File: gmp.info, Node: Compatibility with older versions, Next: Demonstration Programs, Prev: Useful Macros and Constants, Up: GMP Basics - -3.9 Compatibility with older versions -===================================== - -This version of GMP is upwardly binary compatible with all 4.x and 3.x -versions, and upwardly compatible at the source level with all 2.x -versions, with the following exceptions. - - * `mpn_gcd' had its source arguments swapped as of GMP 3.0, for - consistency with other `mpn' functions. - - * `mpf_get_prec' counted precision slightly differently in GMP 3.0 - and 3.0.1, but in 3.1 reverted to the 2.x style. - - There are a number of compatibility issues between GMP 1 and GMP 2 -that of course also apply when porting applications from GMP 1 to GMP -4. Please see the GMP 2 manual for details. - - The Berkeley MP compatibility library (*note BSD Compatible -Functions::) is source and binary compatible with the standard `libmp'. - - -File: gmp.info, Node: Demonstration Programs, Next: Efficiency, Prev: Compatibility with older versions, Up: GMP Basics - -3.10 Demonstration programs -=========================== - -The `demos' subdirectory has some sample programs using GMP. These -aren't built or installed, but there's a `Makefile' with rules for them. -For instance, - - make pexpr - ./pexpr 68^975+10 - -The following programs are provided - - * `pexpr' is an expression evaluator, the program used on the GMP - web page. - - * The `calc' subdirectory has a similar but simpler evaluator using - `lex' and `yacc'. - - * The `expr' subdirectory is yet another expression evaluator, a - library designed for ease of use within a C program. See - `demos/expr/README' for more information. - - * `factorize' is a Pollard-Rho factorization program. - - * `isprime' is a command-line interface to the `mpz_probab_prime_p' - function. - - * `primes' counts or lists primes in an interval, using a sieve. - - * `qcn' is an example use of `mpz_kronecker_ui' to estimate quadratic - class numbers. - - * The `perl' subdirectory is a comprehensive perl interface to GMP. - See `demos/perl/INSTALL' for more information. Documentation is - in POD format in `demos/perl/GMP.pm'. - - As an aside, consideration has been given at various times to some -sort of expression evaluation within the main GMP library. Going -beyond something minimal quickly leads to matters like user-defined -functions, looping, fixnums for control variables, etc, which are -considered outside the scope of GMP (much closer to language -interpreters or compilers, *Note Language Bindings::.) Something -simple for program input convenience may yet be a possibility, a -combination of the `expr' demo and the `pexpr' tree back-end perhaps. -But for now the above evaluators are offered as illustrations. - - -File: gmp.info, Node: Efficiency, Next: Debugging, Prev: Demonstration Programs, Up: GMP Basics - -3.11 Efficiency -=============== - -Small Operands - On small operands, the time for function call overheads and memory - allocation can be significant in comparison to actual calculation. - This is unavoidable in a general purpose variable precision - library, although GMP attempts to be as efficient as it can on - both large and small operands. - -Static Linking - On some CPUs, in particular the x86s, the static `libgmp.a' should - be used for maximum speed, since the PIC code in the shared - `libgmp.so' will have a small overhead on each function call and - global data address. For many programs this will be - insignificant, but for long calculations there's a gain to be had. - -Initializing and Clearing - Avoid excessive initializing and clearing of variables, since this - can be quite time consuming, especially in comparison to otherwise - fast operations like addition. - - A language interpreter might want to keep a free list or stack of - initialized variables ready for use. It should be possible to - integrate something like that with a garbage collector too. - -Reallocations - An `mpz_t' or `mpq_t' variable used to hold successively increasing - values will have its memory repeatedly `realloc'ed, which could be - quite slow or could fragment memory, depending on the C library. - If an application can estimate the final size then `mpz_init2' or - `mpz_realloc2' can be called to allocate the necessary space from - the beginning (*note Initializing Integers::). - - It doesn't matter if a size set with `mpz_init2' or `mpz_realloc2' - is too small, since all functions will do a further reallocation - if necessary. Badly overestimating memory required will waste - space though. - -`2exp' Functions - It's up to an application to call functions like `mpz_mul_2exp' - when appropriate. General purpose functions like `mpz_mul' make - no attempt to identify powers of two or other special forms, - because such inputs will usually be very rare and testing every - time would be wasteful. - -`ui' and `si' Functions - The `ui' functions and the small number of `si' functions exist for - convenience and should be used where applicable. But if for - example an `mpz_t' contains a value that fits in an `unsigned - long' there's no need extract it and call a `ui' function, just - use the regular `mpz' function. - -In-Place Operations - `mpz_abs', `mpq_abs', `mpf_abs', `mpz_neg', `mpq_neg' and - `mpf_neg' are fast when used for in-place operations like - `mpz_abs(x,x)', since in the current implementation only a single - field of `x' needs changing. On suitable compilers (GCC for - instance) this is inlined too. - - `mpz_add_ui', `mpz_sub_ui', `mpf_add_ui' and `mpf_sub_ui' benefit - from an in-place operation like `mpz_add_ui(x,x,y)', since usually - only one or two limbs of `x' will need to be changed. The same - applies to the full precision `mpz_add' etc if `y' is small. If - `y' is big then cache locality may be helped, but that's all. - - `mpz_mul' is currently the opposite, a separate destination is - slightly better. A call like `mpz_mul(x,x,y)' will, unless `y' is - only one limb, make a temporary copy of `x' before forming the - result. Normally that copying will only be a tiny fraction of the - time for the multiply, so this is not a particularly important - consideration. - - `mpz_set', `mpq_set', `mpq_set_num', `mpf_set', etc, make no - attempt to recognise a copy of something to itself, so a call like - `mpz_set(x,x)' will be wasteful. Naturally that would never be - written deliberately, but if it might arise from two pointers to - the same object then a test to avoid it might be desirable. - - if (x != y) - mpz_set (x, y); - - Note that it's never worth introducing extra `mpz_set' calls just - to get in-place operations. If a result should go to a particular - variable then just direct it there and let GMP take care of data - movement. - -Divisibility Testing (Small Integers) - `mpz_divisible_ui_p' and `mpz_congruent_ui_p' are the best - functions for testing whether an `mpz_t' is divisible by an - individual small integer. They use an algorithm which is faster - than `mpz_tdiv_ui', but which gives no useful information about - the actual remainder, only whether it's zero (or a particular - value). - - However when testing divisibility by several small integers, it's - best to take a remainder modulo their product, to save - multi-precision operations. For instance to test whether a number - is divisible by any of 23, 29 or 31 take a remainder modulo - 23*29*31 = 20677 and then test that. - - The division functions like `mpz_tdiv_q_ui' which give a quotient - as well as a remainder are generally a little slower than the - remainder-only functions like `mpz_tdiv_ui'. If the quotient is - only rarely wanted then it's probably best to just take a - remainder and then go back and calculate the quotient if and when - it's wanted (`mpz_divexact_ui' can be used if the remainder is - zero). - -Rational Arithmetic - The `mpq' functions operate on `mpq_t' values with no common - factors in the numerator and denominator. Common factors are - checked-for and cast out as necessary. In general, cancelling - factors every time is the best approach since it minimizes the - sizes for subsequent operations. - - However, applications that know something about the factorization - of the values they're working with might be able to avoid some of - the GCDs used for canonicalization, or swap them for divisions. - For example when multiplying by a prime it's enough to check for - factors of it in the denominator instead of doing a full GCD. Or - when forming a big product it might be known that very little - cancellation will be possible, and so canonicalization can be left - to the end. - - The `mpq_numref' and `mpq_denref' macros give access to the - numerator and denominator to do things outside the scope of the - supplied `mpq' functions. *Note Applying Integer Functions::. - - The canonical form for rationals allows mixed-type `mpq_t' and - integer additions or subtractions to be done directly with - multiples of the denominator. This will be somewhat faster than - `mpq_add'. For example, - - /* mpq increment */ - mpz_add (mpq_numref(q), mpq_numref(q), mpq_denref(q)); - - /* mpq += unsigned long */ - mpz_addmul_ui (mpq_numref(q), mpq_denref(q), 123UL); - - /* mpq -= mpz */ - mpz_submul (mpq_numref(q), mpq_denref(q), z); - -Number Sequences - Functions like `mpz_fac_ui', `mpz_fib_ui' and `mpz_bin_uiui' are - designed for calculating isolated values. If a range of values is - wanted it's probably best to call to get a starting point and - iterate from there. - -Text Input/Output - Hexadecimal or octal are suggested for input or output in text - form. Power-of-2 bases like these can be converted much more - efficiently than other bases, like decimal. For big numbers - there's usually nothing of particular interest to be seen in the - digits, so the base doesn't matter much. - - Maybe we can hope octal will one day become the normal base for - everyday use, as proposed by King Charles XII of Sweden and later - reformers. - - -File: gmp.info, Node: Debugging, Next: Profiling, Prev: Efficiency, Up: GMP Basics - -3.12 Debugging -============== - -Stack Overflow - Depending on the system, a segmentation violation or bus error - might be the only indication of stack overflow. See - `--enable-alloca' choices in *Note Build Options::, for how to - address this. - - In new enough versions of GCC, `-fstack-check' may be able to - ensure an overflow is recognised by the system before too much - damage is done, or `-fstack-limit-symbol' or - `-fstack-limit-register' may be able to add checking if the system - itself doesn't do any (*note Options for Code Generation: - (gcc)Code Gen Options.). These options must be added to the - `CFLAGS' used in the GMP build (*note Build Options::), adding - them just to an application will have no effect. Note also - they're a slowdown, adding overhead to each function call and each - stack allocation. - -Heap Problems - The most likely cause of application problems with GMP is heap - corruption. Failing to `init' GMP variables will have - unpredictable effects, and corruption arising elsewhere in a - program may well affect GMP. Initializing GMP variables more than - once or failing to clear them will cause memory leaks. - - In all such cases a `malloc' debugger is recommended. On a GNU or - BSD system the standard C library `malloc' has some diagnostic - facilities, see *Note Allocation Debugging: (libc)Allocation - Debugging, or `man 3 malloc'. Other possibilities, in no - particular order, include - - `http://www.inf.ethz.ch/personal/biere/projects/ccmalloc/' - `http://dmalloc.com/' - `http://www.perens.com/FreeSoftware/' (electric fence) - `http://packages.debian.org/stable/devel/fda' - `http://www.gnupdate.org/components/leakbug/' - `http://people.redhat.com/~otaylor/memprof/' - `http://www.cbmamiga.demon.co.uk/mpatrol/' - - The GMP default allocation routines in `memory.c' also have a - simple sentinel scheme which can be enabled with `#define DEBUG' - in that file. This is mainly designed for detecting buffer - overruns during GMP development, but might find other uses. - -Stack Backtraces - On some systems the compiler options GMP uses by default can - interfere with debugging. In particular on x86 and 68k systems - `-fomit-frame-pointer' is used and this generally inhibits stack - backtracing. Recompiling without such options may help while - debugging, though the usual caveats about it potentially moving a - memory problem or hiding a compiler bug will apply. - -GDB, the GNU Debugger - A sample `.gdbinit' is included in the distribution, showing how - to call some undocumented dump functions to print GMP variables - from within GDB. Note that these functions shouldn't be used in - final application code since they're undocumented and may be - subject to incompatible changes in future versions of GMP. - -Source File Paths - GMP has multiple source files with the same name, in different - directories. For example `mpz', `mpq' and `mpf' each have an - `init.c'. If the debugger can't already determine the right one - it may help to build with absolute paths on each C file. One way - to do that is to use a separate object directory with an absolute - path to the source directory. - - cd /my/build/dir - /my/source/dir/gmp-5.0.1/configure - - This works via `VPATH', and might require GNU `make'. Alternately - it might be possible to change the `.c.lo' rules appropriately. - -Assertion Checking - The build option `--enable-assert' is available to add some - consistency checks to the library (see *Note Build Options::). - These are likely to be of limited value to most applications. - Assertion failures are just as likely to indicate memory - corruption as a library or compiler bug. - - Applications using the low-level `mpn' functions, however, will - benefit from `--enable-assert' since it adds checks on the - parameters of most such functions, many of which have subtle - restrictions on their usage. Note however that only the generic C - code has checks, not the assembly code, so CPU `none' should be - used for maximum checking. - -Temporary Memory Checking - The build option `--enable-alloca=debug' arranges that each block - of temporary memory in GMP is allocated with a separate call to - `malloc' (or the allocation function set with - `mp_set_memory_functions'). - - This can help a malloc debugger detect accesses outside the - intended bounds, or detect memory not released. In a normal - build, on the other hand, temporary memory is allocated in blocks - which GMP divides up for its own use, or may be allocated with a - compiler builtin `alloca' which will go nowhere near any malloc - debugger hooks. - -Maximum Debuggability - To summarize the above, a GMP build for maximum debuggability - would be - - ./configure --disable-shared --enable-assert \ - --enable-alloca=debug --host=none CFLAGS=-g - - For C++, add `--enable-cxx CXXFLAGS=-g'. - -Checker - The GCC checker (`http://savannah.nongnu.org/projects/checker/') - can be used with GMP. It contains a stub library which means GMP - applications compiled with checker can use a normal GMP build. - - A build of GMP with checking within GMP itself can be made. This - will run very very slowly. On GNU/Linux for example, - - ./configure --host=none-pc-linux-gnu CC=checkergcc - - `--host=none' must be used, since the GMP assembly code doesn't - support the checking scheme. The GMP C++ features cannot be used, - since current versions of checker (0.9.9.1) don't yet support the - standard C++ library. - -Valgrind - The valgrind program (`http://valgrind.org/') is a memory checker - for x86s. It translates and emulates machine instructions to do - strong checks for uninitialized data (at the level of individual - bits), memory accesses through bad pointers, and memory leaks. - - Recent versions of Valgrind are getting support for MMX and - SSE/SSE2 instructions, for past versions GMP will need to be - configured not to use those, ie. for an x86 without them (for - instance plain `i486'). - -Other Problems - Any suspected bug in GMP itself should be isolated to make sure - it's not an application problem, see *Note Reporting Bugs::. - - -File: gmp.info, Node: Profiling, Next: Autoconf, Prev: Debugging, Up: GMP Basics - -3.13 Profiling -============== - -Running a program under a profiler is a good way to find where it's -spending most time and where improvements can be best sought. The -profiling choices for a GMP build are as follows. - -`--disable-profiling' - The default is to add nothing special for profiling. - - It should be possible to just compile the mainline of a program - with `-p' and use `prof' to get a profile consisting of - timer-based sampling of the program counter. Most of the GMP - assembly code has the necessary symbol information. - - This approach has the advantage of minimizing interference with - normal program operation, but on most systems the resolution of - the sampling is quite low (10 milliseconds for instance), - requiring long runs to get accurate information. - -`--enable-profiling=prof' - Build with support for the system `prof', which means `-p' added - to the `CFLAGS'. - - This provides call counting in addition to program counter - sampling, which allows the most frequently called routines to be - identified, and an average time spent in each routine to be - determined. - - The x86 assembly code has support for this option, but on other - processors the assembly routines will be as if compiled without - `-p' and therefore won't appear in the call counts. - - On some systems, such as GNU/Linux, `-p' in fact means `-pg' and in - this case `--enable-profiling=gprof' described below should be used - instead. - -`--enable-profiling=gprof' - Build with support for `gprof', which means `-pg' added to the - `CFLAGS'. - - This provides call graph construction in addition to call counting - and program counter sampling, which makes it possible to count - calls coming from different locations. For example the number of - calls to `mpn_mul' from `mpz_mul' versus the number from - `mpf_mul'. The program counter sampling is still flat though, so - only a total time in `mpn_mul' would be accumulated, not a - separate amount for each call site. - - The x86 assembly code has support for this option, but on other - processors the assembly routines will be as if compiled without - `-pg' and therefore not be included in the call counts. - - On x86 and m68k systems `-pg' and `-fomit-frame-pointer' are - incompatible, so the latter is omitted from the default flags in - that case, which might result in poorer code generation. - - Incidentally, it should be possible to use the `gprof' program - with a plain `--enable-profiling=prof' build. But in that case - only the `gprof -p' flat profile and call counts can be expected - to be valid, not the `gprof -q' call graph. - -`--enable-profiling=instrument' - Build with the GCC option `-finstrument-functions' added to the - `CFLAGS' (*note Options for Code Generation: (gcc)Code Gen - Options.). - - This inserts special instrumenting calls at the start and end of - each function, allowing exact timing and full call graph - construction. - - This instrumenting is not normally a standard system feature and - will require support from an external library, such as - - `http://sourceforge.net/projects/fnccheck/' - - This should be included in `LIBS' during the GMP configure so that - test programs will link. For example, - - ./configure --enable-profiling=instrument LIBS=-lfc - - On a GNU system the C library provides dummy instrumenting - functions, so programs compiled with this option will link. In - this case it's only necessary to ensure the correct library is - added when linking an application. - - The x86 assembly code supports this option, but on other - processors the assembly routines will be as if compiled without - `-finstrument-functions' meaning time spent in them will - effectively be attributed to their caller. - - -File: gmp.info, Node: Autoconf, Next: Emacs, Prev: Profiling, Up: GMP Basics - -3.14 Autoconf -============= - -Autoconf based applications can easily check whether GMP is installed. -The only thing to be noted is that GMP library symbols from version 3 -onwards have prefixes like `__gmpz'. The following therefore would be -a simple test, - - AC_CHECK_LIB(gmp, __gmpz_init) - - This just uses the default `AC_CHECK_LIB' actions for found or not -found, but an application that must have GMP would want to generate an -error if not found. For example, - - AC_CHECK_LIB(gmp, __gmpz_init, , - [AC_MSG_ERROR([GNU MP not found, see http://gmplib.org/])]) - - If functions added in some particular version of GMP are required, -then one of those can be used when checking. For example `mpz_mul_si' -was added in GMP 3.1, - - AC_CHECK_LIB(gmp, __gmpz_mul_si, , - [AC_MSG_ERROR( - [GNU MP not found, or not 3.1 or up, see http://gmplib.org/])]) - - An alternative would be to test the version number in `gmp.h' using -say `AC_EGREP_CPP'. That would make it possible to test the exact -version, if some particular sub-minor release is known to be necessary. - - In general it's recommended that applications should simply demand a -new enough GMP rather than trying to provide supplements for features -not available in past versions. - - Occasionally an application will need or want to know the size of a -type at configuration or preprocessing time, not just with `sizeof' in -the code. This can be done in the normal way with `mp_limb_t' etc, but -GMP 4.0 or up is best for this, since prior versions needed certain -`-D' defines on systems using a `long long' limb. The following would -suit Autoconf 2.50 or up, - - AC_CHECK_SIZEOF(mp_limb_t, , [#include ]) - - -File: gmp.info, Node: Emacs, Prev: Autoconf, Up: GMP Basics - -3.15 Emacs -========== - - (`info-lookup-symbol') is a good way to find documentation on -C functions while editing (*note Info Documentation Lookup: (emacs)Info -Lookup.). - - The GMP manual can be included in such lookups by putting the -following in your `.emacs', - - (eval-after-load "info-look" - '(let ((mode-value (assoc 'c-mode (assoc 'symbol info-lookup-alist)))) - (setcar (nthcdr 3 mode-value) - (cons '("(gmp)Function Index" nil "^ -.* " "\\>") - (nth 3 mode-value))))) - - -File: gmp.info, Node: Reporting Bugs, Next: Integer Functions, Prev: GMP Basics, Up: Top - -4 Reporting Bugs -**************** - -If you think you have found a bug in the GMP library, please -investigate it and report it. We have made this library available to -you, and it is not too much to ask you to report the bugs you find. - - Before you report a bug, check it's not already addressed in *Note -Known Build Problems::, or perhaps *Note Notes for Particular -Systems::. You may also want to check `http://gmplib.org/' for patches -for this release. - - Please include the following in any report, - - * The GMP version number, and if pre-packaged or patched then say so. - - * A test program that makes it possible for us to reproduce the bug. - Include instructions on how to run the program. - - * A description of what is wrong. If the results are incorrect, in - what way. If you get a crash, say so. - - * If you get a crash, include a stack backtrace from the debugger if - it's informative (`where' in `gdb', or `$C' in `adb'). - - * Please do not send core dumps, executables or `strace's. - - * The configuration options you used when building GMP, if any. - - * The name of the compiler and its version. For `gcc', get the - version with `gcc -v', otherwise perhaps `what `which cc`', or - similar. - - * The output from running `uname -a'. - - * The output from running `./config.guess', and from running - `./configfsf.guess' (might be the same). - - * If the bug is related to `configure', then the compressed contents - of `config.log'. - - * If the bug is related to an `asm' file not assembling, then the - contents of `config.m4' and the offending line or lines from the - temporary `mpn/tmp-.s'. - - Please make an effort to produce a self-contained report, with -something definite that can be tested or debugged. Vague queries or -piecemeal messages are difficult to act on and don't help the -development effort. - - It is not uncommon that an observed problem is actually due to a bug -in the compiler; the GMP code tends to explore interesting corners in -compilers. - - If your bug report is good, we will do our best to help you get a -corrected version of the library; if the bug report is poor, we won't -do anything about it (except maybe ask you to send a better report). - - Send your report to: . - - If you think something in this manual is unclear, or downright -incorrect, or if the language needs to be improved, please send a note -to the same address. - - -File: gmp.info, Node: Integer Functions, Next: Rational Number Functions, Prev: Reporting Bugs, Up: Top - -5 Integer Functions -******************* - -This chapter describes the GMP functions for performing integer -arithmetic. These functions start with the prefix `mpz_'. - - GMP integers are stored in objects of type `mpz_t'. - -* Menu: - -* Initializing Integers:: -* Assigning Integers:: -* Simultaneous Integer Init & Assign:: -* Converting Integers:: -* Integer Arithmetic:: -* Integer Division:: -* Integer Exponentiation:: -* Integer Roots:: -* Number Theoretic Functions:: -* Integer Comparisons:: -* Integer Logic and Bit Fiddling:: -* I/O of Integers:: -* Integer Random Numbers:: -* Integer Import and Export:: -* Miscellaneous Integer Functions:: -* Integer Special Functions:: - - -File: gmp.info, Node: Initializing Integers, Next: Assigning Integers, Prev: Integer Functions, Up: Integer Functions - -5.1 Initialization Functions -============================ - -The functions for integer arithmetic assume that all integer objects are -initialized. You do that by calling the function `mpz_init'. For -example, - - { - mpz_t integ; - mpz_init (integ); - ... - mpz_add (integ, ...); - ... - mpz_sub (integ, ...); - - /* Unless the program is about to exit, do ... */ - mpz_clear (integ); - } - - As you can see, you can store new values any number of times, once an -object is initialized. - - -- Function: void mpz_init (mpz_t X) - Initialize X, and set its value to 0. - - -- Function: void mpz_inits (mpz_t X, ...) - Initialize a NULL-terminated list of `mpz_t' variables, and set - their values to 0. - - -- Function: void mpz_init2 (mpz_t X, mp_bitcnt_t N) - Initialize X, with space for N-bit numbers, and set its value to 0. - Calling this function instead of `mpz_init' or `mpz_inits' is never - necessary; reallocation is handled automatically by GMP when - needed. - - N is only the initial space, X will grow automatically in the - normal way, if necessary, for subsequent values stored. - `mpz_init2' makes it possible to avoid such reallocations if a - maximum size is known in advance. - - -- Function: void mpz_clear (mpz_t X) - Free the space occupied by X. Call this function for all `mpz_t' - variables when you are done with them. - - -- Function: void mpz_clears (mpz_t X, ...) - Free the space occupied by a NULL-terminated list of `mpz_t' - variables. - - -- Function: void mpz_realloc2 (mpz_t X, mp_bitcnt_t N) - Change the space allocated for X to N bits. The value in X is - preserved if it fits, or is set to 0 if not. - - Calling this function is never necessary; reallocation is handled - automatically by GMP when needed. But this function can be used - to increase the space for a variable in order to avoid repeated - automatic reallocations, or to decrease it to give memory back to - the heap. - - -File: gmp.info, Node: Assigning Integers, Next: Simultaneous Integer Init & Assign, Prev: Initializing Integers, Up: Integer Functions - -5.2 Assignment Functions -======================== - -These functions assign new values to already initialized integers -(*note Initializing Integers::). - - -- Function: void mpz_set (mpz_t ROP, mpz_t OP) - -- Function: void mpz_set_ui (mpz_t ROP, unsigned long int OP) - -- Function: void mpz_set_si (mpz_t ROP, signed long int OP) - -- Function: void mpz_set_d (mpz_t ROP, double OP) - -- Function: void mpz_set_q (mpz_t ROP, mpq_t OP) - -- Function: void mpz_set_f (mpz_t ROP, mpf_t OP) - Set the value of ROP from OP. - - `mpz_set_d', `mpz_set_q' and `mpz_set_f' truncate OP to make it an - integer. - - -- Function: int mpz_set_str (mpz_t ROP, char *STR, int BASE) - Set the value of ROP from STR, a null-terminated C string in base - BASE. White space is allowed in the string, and is simply ignored. - - The BASE may vary from 2 to 62, or if BASE is 0, then the leading - characters are used: `0x' and `0X' for hexadecimal, `0b' and `0B' - for binary, `0' for octal, or decimal otherwise. - - For bases up to 36, case is ignored; upper-case and lower-case - letters have the same value. For bases 37 to 62, upper-case - letter represent the usual 10..35 while lower-case letter - represent 36..61. - - This function returns 0 if the entire string is a valid number in - base BASE. Otherwise it returns -1. - - -- Function: void mpz_swap (mpz_t ROP1, mpz_t ROP2) - Swap the values ROP1 and ROP2 efficiently. - - -File: gmp.info, Node: Simultaneous Integer Init & Assign, Next: Converting Integers, Prev: Assigning Integers, Up: Integer Functions - -5.3 Combined Initialization and Assignment Functions -==================================================== - -For convenience, GMP provides a parallel series of initialize-and-set -functions which initialize the output and then store the value there. -These functions' names have the form `mpz_init_set...' - - Here is an example of using one: - - { - mpz_t pie; - mpz_init_set_str (pie, "3141592653589793238462643383279502884", 10); - ... - mpz_sub (pie, ...); - ... - mpz_clear (pie); - } - -Once the integer has been initialized by any of the `mpz_init_set...' -functions, it can be used as the source or destination operand for the -ordinary integer functions. Don't use an initialize-and-set function -on a variable already initialized! - - -- Function: void mpz_init_set (mpz_t ROP, mpz_t OP) - -- Function: void mpz_init_set_ui (mpz_t ROP, unsigned long int OP) - -- Function: void mpz_init_set_si (mpz_t ROP, signed long int OP) - -- Function: void mpz_init_set_d (mpz_t ROP, double OP) - Initialize ROP with limb space and set the initial numeric value - from OP. - - -- Function: int mpz_init_set_str (mpz_t ROP, char *STR, int BASE) - Initialize ROP and set its value like `mpz_set_str' (see its - documentation above for details). - - If the string is a correct base BASE number, the function returns - 0; if an error occurs it returns -1. ROP is initialized even if - an error occurs. (I.e., you have to call `mpz_clear' for it.) - - -File: gmp.info, Node: Converting Integers, Next: Integer Arithmetic, Prev: Simultaneous Integer Init & Assign, Up: Integer Functions - -5.4 Conversion Functions -======================== - -This section describes functions for converting GMP integers to -standard C types. Functions for converting _to_ GMP integers are -described in *Note Assigning Integers:: and *Note I/O of Integers::. - - -- Function: unsigned long int mpz_get_ui (mpz_t OP) - Return the value of OP as an `unsigned long'. - - If OP is too big to fit an `unsigned long' then just the least - significant bits that do fit are returned. The sign of OP is - ignored, only the absolute value is used. - - -- Function: signed long int mpz_get_si (mpz_t OP) - If OP fits into a `signed long int' return the value of OP. - Otherwise return the least significant part of OP, with the same - sign as OP. - - If OP is too big to fit in a `signed long int', the returned - result is probably not very useful. To find out if the value will - fit, use the function `mpz_fits_slong_p'. - - -- Function: double mpz_get_d (mpz_t OP) - Convert OP to a `double', truncating if necessary (ie. rounding - towards zero). - - If the exponent from the conversion is too big, the result is - system dependent. An infinity is returned where available. A - hardware overflow trap may or may not occur. - - -- Function: double mpz_get_d_2exp (signed long int *EXP, mpz_t OP) - Convert OP to a `double', truncating if necessary (ie. rounding - towards zero), and returning the exponent separately. - - The return value is in the range 0.5<=abs(D)<1 and the exponent is - stored to `*EXP'. D * 2^EXP is the (truncated) OP value. If OP - is zero, the return is 0.0 and 0 is stored to `*EXP'. - - This is similar to the standard C `frexp' function (*note - Normalization Functions: (libc)Normalization Functions.). - - -- Function: char * mpz_get_str (char *STR, int BASE, mpz_t OP) - Convert OP to a string of digits in base BASE. The base argument - may vary from 2 to 62 or from -2 to -36. - - For BASE in the range 2..36, digits and lower-case letters are - used; for -2..-36, digits and upper-case letters are used; for - 37..62, digits, upper-case letters, and lower-case letters (in - that significance order) are used. - - If STR is `NULL', the result string is allocated using the current - allocation function (*note Custom Allocation::). The block will be - `strlen(str)+1' bytes, that being exactly enough for the string and - null-terminator. - - If STR is not `NULL', it should point to a block of storage large - enough for the result, that being `mpz_sizeinbase (OP, BASE) + 2'. - The two extra bytes are for a possible minus sign, and the - null-terminator. - - A pointer to the result string is returned, being either the - allocated block, or the given STR. - - -File: gmp.info, Node: Integer Arithmetic, Next: Integer Division, Prev: Converting Integers, Up: Integer Functions - -5.5 Arithmetic Functions -======================== - - -- Function: void mpz_add (mpz_t ROP, mpz_t OP1, mpz_t OP2) - -- Function: void mpz_add_ui (mpz_t ROP, mpz_t OP1, unsigned long int - OP2) - Set ROP to OP1 + OP2. - - -- Function: void mpz_sub (mpz_t ROP, mpz_t OP1, mpz_t OP2) - -- Function: void mpz_sub_ui (mpz_t ROP, mpz_t OP1, unsigned long int - OP2) - -- Function: void mpz_ui_sub (mpz_t ROP, unsigned long int OP1, mpz_t - OP2) - Set ROP to OP1 - OP2. - - -- Function: void mpz_mul (mpz_t ROP, mpz_t OP1, mpz_t OP2) - -- Function: void mpz_mul_si (mpz_t ROP, mpz_t OP1, long int OP2) - -- Function: void mpz_mul_ui (mpz_t ROP, mpz_t OP1, unsigned long int - OP2) - Set ROP to OP1 times OP2. - - -- Function: void mpz_addmul (mpz_t ROP, mpz_t OP1, mpz_t OP2) - -- Function: void mpz_addmul_ui (mpz_t ROP, mpz_t OP1, unsigned long - int OP2) - Set ROP to ROP + OP1 times OP2. - - -- Function: void mpz_submul (mpz_t ROP, mpz_t OP1, mpz_t OP2) - -- Function: void mpz_submul_ui (mpz_t ROP, mpz_t OP1, unsigned long - int OP2) - Set ROP to ROP - OP1 times OP2. - - -- Function: void mpz_mul_2exp (mpz_t ROP, mpz_t OP1, mp_bitcnt_t OP2) - Set ROP to OP1 times 2 raised to OP2. This operation can also be - defined as a left shift by OP2 bits. - - -- Function: void mpz_neg (mpz_t ROP, mpz_t OP) - Set ROP to -OP. - - -- Function: void mpz_abs (mpz_t ROP, mpz_t OP) - Set ROP to the absolute value of OP. - - -File: gmp.info, Node: Integer Division, Next: Integer Exponentiation, Prev: Integer Arithmetic, Up: Integer Functions - -5.6 Division Functions -====================== - -Division is undefined if the divisor is zero. Passing a zero divisor -to the division or modulo functions (including the modular powering -functions `mpz_powm' and `mpz_powm_ui'), will cause an intentional -division by zero. This lets a program handle arithmetic exceptions in -these functions the same way as for normal C `int' arithmetic. - - -- Function: void mpz_cdiv_q (mpz_t Q, mpz_t N, mpz_t D) - -- Function: void mpz_cdiv_r (mpz_t R, mpz_t N, mpz_t D) - -- Function: void mpz_cdiv_qr (mpz_t Q, mpz_t R, mpz_t N, mpz_t D) - -- Function: unsigned long int mpz_cdiv_q_ui (mpz_t Q, mpz_t N, - unsigned long int D) - -- Function: unsigned long int mpz_cdiv_r_ui (mpz_t R, mpz_t N, - unsigned long int D) - -- Function: unsigned long int mpz_cdiv_qr_ui (mpz_t Q, mpz_t R, - mpz_t N, unsigned long int D) - -- Function: unsigned long int mpz_cdiv_ui (mpz_t N, - unsigned long int D) - -- Function: void mpz_cdiv_q_2exp (mpz_t Q, mpz_t N, mp_bitcnt_t B) - -- Function: void mpz_cdiv_r_2exp (mpz_t R, mpz_t N, mp_bitcnt_t B) - - -- Function: void mpz_fdiv_q (mpz_t Q, mpz_t N, mpz_t D) - -- Function: void mpz_fdiv_r (mpz_t R, mpz_t N, mpz_t D) - -- Function: void mpz_fdiv_qr (mpz_t Q, mpz_t R, mpz_t N, mpz_t D) - -- Function: unsigned long int mpz_fdiv_q_ui (mpz_t Q, mpz_t N, - unsigned long int D) - -- Function: unsigned long int mpz_fdiv_r_ui (mpz_t R, mpz_t N, - unsigned long int D) - -- Function: unsigned long int mpz_fdiv_qr_ui (mpz_t Q, mpz_t R, - mpz_t N, unsigned long int D) - -- Function: unsigned long int mpz_fdiv_ui (mpz_t N, - unsigned long int D) - -- Function: void mpz_fdiv_q_2exp (mpz_t Q, mpz_t N, mp_bitcnt_t B) - -- Function: void mpz_fdiv_r_2exp (mpz_t R, mpz_t N, mp_bitcnt_t B) - - -- Function: void mpz_tdiv_q (mpz_t Q, mpz_t N, mpz_t D) - -- Function: void mpz_tdiv_r (mpz_t R, mpz_t N, mpz_t D) - -- Function: void mpz_tdiv_qr (mpz_t Q, mpz_t R, mpz_t N, mpz_t D) - -- Function: unsigned long int mpz_tdiv_q_ui (mpz_t Q, mpz_t N, - unsigned long int D) - -- Function: unsigned long int mpz_tdiv_r_ui (mpz_t R, mpz_t N, - unsigned long int D) - -- Function: unsigned long int mpz_tdiv_qr_ui (mpz_t Q, mpz_t R, - mpz_t N, unsigned long int D) - -- Function: unsigned long int mpz_tdiv_ui (mpz_t N, - unsigned long int D) - -- Function: void mpz_tdiv_q_2exp (mpz_t Q, mpz_t N, mp_bitcnt_t B) - -- Function: void mpz_tdiv_r_2exp (mpz_t R, mpz_t N, mp_bitcnt_t B) - - Divide N by D, forming a quotient Q and/or remainder R. For the - `2exp' functions, D=2^B. The rounding is in three styles, each - suiting different applications. - - * `cdiv' rounds Q up towards +infinity, and R will have the - opposite sign to D. The `c' stands for "ceil". - - * `fdiv' rounds Q down towards -infinity, and R will have the - same sign as D. The `f' stands for "floor". - - * `tdiv' rounds Q towards zero, and R will have the same sign - as N. The `t' stands for "truncate". - - In all cases Q and R will satisfy N=Q*D+R, and R will satisfy - 0<=abs(R) 0 and that MOD is odd. - - This function is designed to take the same time and have the same - cache access patterns for any two same-size arguments, assuming - that function arguments are placed at the same position and that - the machine state is identical upon function entry. This function - is intended for cryptographic purposes, where resilience to - side-channel attacks is desired. - - -- Function: void mpz_pow_ui (mpz_t ROP, mpz_t BASE, unsigned long int - EXP) - -- Function: void mpz_ui_pow_ui (mpz_t ROP, unsigned long int BASE, - unsigned long int EXP) - Set ROP to BASE raised to EXP. The case 0^0 yields 1. - - -File: gmp.info, Node: Integer Roots, Next: Number Theoretic Functions, Prev: Integer Exponentiation, Up: Integer Functions - -5.8 Root Extraction Functions -============================= - - -- Function: int mpz_root (mpz_t ROP, mpz_t OP, unsigned long int N) - Set ROP to the truncated integer part of the Nth root of OP. - Return non-zero if the computation was exact, i.e., if OP is ROP - to the Nth power. - - -- Function: void mpz_rootrem (mpz_t ROOT, mpz_t REM, mpz_t U, - unsigned long int N) - Set ROOT to the truncated integer part of the Nth root of U. Set - REM to the remainder, U-ROOT**N. - - -- Function: void mpz_sqrt (mpz_t ROP, mpz_t OP) - Set ROP to the truncated integer part of the square root of OP. - - -- Function: void mpz_sqrtrem (mpz_t ROP1, mpz_t ROP2, mpz_t OP) - Set ROP1 to the truncated integer part of the square root of OP, - like `mpz_sqrt'. Set ROP2 to the remainder OP-ROP1*ROP1, which - will be zero if OP is a perfect square. - - If ROP1 and ROP2 are the same variable, the results are undefined. - - -- Function: int mpz_perfect_power_p (mpz_t OP) - Return non-zero if OP is a perfect power, i.e., if there exist - integers A and B, with B>1, such that OP equals A raised to the - power B. - - Under this definition both 0 and 1 are considered to be perfect - powers. Negative values of OP are accepted, but of course can - only be odd perfect powers. - - -- Function: int mpz_perfect_square_p (mpz_t OP) - Return non-zero if OP is a perfect square, i.e., if the square - root of OP is an integer. Under this definition both 0 and 1 are - considered to be perfect squares. - - -File: gmp.info, Node: Number Theoretic Functions, Next: Integer Comparisons, Prev: Integer Roots, Up: Integer Functions - -5.9 Number Theoretic Functions -============================== - - -- Function: int mpz_probab_prime_p (mpz_t N, int REPS) - Determine whether N is prime. Return 2 if N is definitely prime, - return 1 if N is probably prime (without being certain), or return - 0 if N is definitely composite. - - This function does some trial divisions, then some Miller-Rabin - probabilistic primality tests. REPS controls how many such tests - are done, 5 to 10 is a reasonable number, more will reduce the - chances of a composite being returned as "probably prime". - - Miller-Rabin and similar tests can be more properly called - compositeness tests. Numbers which fail are known to be composite - but those which pass might be prime or might be composite. Only a - few composites pass, hence those which pass are considered - probably prime. - - -- Function: void mpz_nextprime (mpz_t ROP, mpz_t OP) - Set ROP to the next prime greater than OP. - - This function uses a probabilistic algorithm to identify primes. - For practical purposes it's adequate, the chance of a composite - passing will be extremely small. - - -- Function: void mpz_gcd (mpz_t ROP, mpz_t OP1, mpz_t OP2) - Set ROP to the greatest common divisor of OP1 and OP2. The result - is always positive even if one or both input operands are negative. - - -- Function: unsigned long int mpz_gcd_ui (mpz_t ROP, mpz_t OP1, - unsigned long int OP2) - Compute the greatest common divisor of OP1 and OP2. If ROP is not - `NULL', store the result there. - - If the result is small enough to fit in an `unsigned long int', it - is returned. If the result does not fit, 0 is returned, and the - result is equal to the argument OP1. Note that the result will - always fit if OP2 is non-zero. - - -- Function: void mpz_gcdext (mpz_t G, mpz_t S, mpz_t T, mpz_t A, - mpz_t B) - Set G to the greatest common divisor of A and B, and in addition - set S and T to coefficients satisfying A*S + B*T = G. The value - in G is always positive, even if one or both of A and B are - negative. The values in S and T are chosen such that abs(S) <= - abs(B) and abs(T) <= abs(A). - - If T is `NULL' then that value is not computed. - - -- Function: void mpz_lcm (mpz_t ROP, mpz_t OP1, mpz_t OP2) - -- Function: void mpz_lcm_ui (mpz_t ROP, mpz_t OP1, unsigned long OP2) - Set ROP to the least common multiple of OP1 and OP2. ROP is - always positive, irrespective of the signs of OP1 and OP2. ROP - will be zero if either OP1 or OP2 is zero. - - -- Function: int mpz_invert (mpz_t ROP, mpz_t OP1, mpz_t OP2) - Compute the inverse of OP1 modulo OP2 and put the result in ROP. - If the inverse exists, the return value is non-zero and ROP will - satisfy 0 <= ROP < OP2. If an inverse doesn't exist the return - value is zero and ROP is undefined. - - -- Function: int mpz_jacobi (mpz_t A, mpz_t B) - Calculate the Jacobi symbol (A/B). This is defined only for B odd. - - -- Function: int mpz_legendre (mpz_t A, mpz_t P) - Calculate the Legendre symbol (A/P). This is defined only for P - an odd positive prime, and for such P it's identical to the Jacobi - symbol. - - -- Function: int mpz_kronecker (mpz_t A, mpz_t B) - -- Function: int mpz_kronecker_si (mpz_t A, long B) - -- Function: int mpz_kronecker_ui (mpz_t A, unsigned long B) - -- Function: int mpz_si_kronecker (long A, mpz_t B) - -- Function: int mpz_ui_kronecker (unsigned long A, mpz_t B) - Calculate the Jacobi symbol (A/B) with the Kronecker extension - (a/2)=(2/a) when a odd, or (a/2)=0 when a even. - - When B is odd the Jacobi symbol and Kronecker symbol are - identical, so `mpz_kronecker_ui' etc can be used for mixed - precision Jacobi symbols too. - - For more information see Henri Cohen section 1.4.2 (*note - References::), or any number theory textbook. See also the - example program `demos/qcn.c' which uses `mpz_kronecker_ui'. - - -- Function: mp_bitcnt_t mpz_remove (mpz_t ROP, mpz_t OP, mpz_t F) - Remove all occurrences of the factor F from OP and store the - result in ROP. The return value is how many such occurrences were - removed. - - -- Function: void mpz_fac_ui (mpz_t ROP, unsigned long int OP) - Set ROP to OP!, the factorial of OP. - - -- Function: void mpz_bin_ui (mpz_t ROP, mpz_t N, unsigned long int K) - -- Function: void mpz_bin_uiui (mpz_t ROP, unsigned long int N, - unsigned long int K) - Compute the binomial coefficient N over K and store the result in - ROP. Negative values of N are supported by `mpz_bin_ui', using - the identity bin(-n,k) = (-1)^k * bin(n+k-1,k), see Knuth volume 1 - section 1.2.6 part G. - - -- Function: void mpz_fib_ui (mpz_t FN, unsigned long int N) - -- Function: void mpz_fib2_ui (mpz_t FN, mpz_t FNSUB1, unsigned long - int N) - `mpz_fib_ui' sets FN to to F[n], the N'th Fibonacci number. - `mpz_fib2_ui' sets FN to F[n], and FNSUB1 to F[n-1]. - - These functions are designed for calculating isolated Fibonacci - numbers. When a sequence of values is wanted it's best to start - with `mpz_fib2_ui' and iterate the defining F[n+1]=F[n]+F[n-1] or - similar. - - -- Function: void mpz_lucnum_ui (mpz_t LN, unsigned long int N) - -- Function: void mpz_lucnum2_ui (mpz_t LN, mpz_t LNSUB1, unsigned - long int N) - `mpz_lucnum_ui' sets LN to to L[n], the N'th Lucas number. - `mpz_lucnum2_ui' sets LN to L[n], and LNSUB1 to L[n-1]. - - These functions are designed for calculating isolated Lucas - numbers. When a sequence of values is wanted it's best to start - with `mpz_lucnum2_ui' and iterate the defining L[n+1]=L[n]+L[n-1] - or similar. - - The Fibonacci numbers and Lucas numbers are related sequences, so - it's never necessary to call both `mpz_fib2_ui' and - `mpz_lucnum2_ui'. The formulas for going from Fibonacci to Lucas - can be found in *Note Lucas Numbers Algorithm::, the reverse is - straightforward too. - - -File: gmp.info, Node: Integer Comparisons, Next: Integer Logic and Bit Fiddling, Prev: Number Theoretic Functions, Up: Integer Functions - -5.10 Comparison Functions -========================= - - -- Function: int mpz_cmp (mpz_t OP1, mpz_t OP2) - -- Function: int mpz_cmp_d (mpz_t OP1, double OP2) - -- Macro: int mpz_cmp_si (mpz_t OP1, signed long int OP2) - -- Macro: int mpz_cmp_ui (mpz_t OP1, unsigned long int OP2) - Compare OP1 and OP2. Return a positive value if OP1 > OP2, zero - if OP1 = OP2, or a negative value if OP1 < OP2. - - `mpz_cmp_ui' and `mpz_cmp_si' are macros and will evaluate their - arguments more than once. `mpz_cmp_d' can be called with an - infinity, but results are undefined for a NaN. - - -- Function: int mpz_cmpabs (mpz_t OP1, mpz_t OP2) - -- Function: int mpz_cmpabs_d (mpz_t OP1, double OP2) - -- Function: int mpz_cmpabs_ui (mpz_t OP1, unsigned long int OP2) - Compare the absolute values of OP1 and OP2. Return a positive - value if abs(OP1) > abs(OP2), zero if abs(OP1) = abs(OP2), or a - negative value if abs(OP1) < abs(OP2). - - `mpz_cmpabs_d' can be called with an infinity, but results are - undefined for a NaN. - - -- Macro: int mpz_sgn (mpz_t OP) - Return +1 if OP > 0, 0 if OP = 0, and -1 if OP < 0. - - This function is actually implemented as a macro. It evaluates - its argument multiple times. - - -File: gmp.info, Node: Integer Logic and Bit Fiddling, Next: I/O of Integers, Prev: Integer Comparisons, Up: Integer Functions - -5.11 Logical and Bit Manipulation Functions -=========================================== - -These functions behave as if twos complement arithmetic were used -(although sign-magnitude is the actual implementation). The least -significant bit is number 0. - - -- Function: void mpz_and (mpz_t ROP, mpz_t OP1, mpz_t OP2) - Set ROP to OP1 bitwise-and OP2. - - -- Function: void mpz_ior (mpz_t ROP, mpz_t OP1, mpz_t OP2) - Set ROP to OP1 bitwise inclusive-or OP2. - - -- Function: void mpz_xor (mpz_t ROP, mpz_t OP1, mpz_t OP2) - Set ROP to OP1 bitwise exclusive-or OP2. - - -- Function: void mpz_com (mpz_t ROP, mpz_t OP) - Set ROP to the one's complement of OP. - - -- Function: mp_bitcnt_t mpz_popcount (mpz_t OP) - If OP>=0, return the population count of OP, which is the number - of 1 bits in the binary representation. If OP<0, the number of 1s - is infinite, and the return value is the largest possible - `mp_bitcnt_t'. - - -- Function: mp_bitcnt_t mpz_hamdist (mpz_t OP1, mpz_t OP2) - If OP1 and OP2 are both >=0 or both <0, return the hamming - distance between the two operands, which is the number of bit - positions where OP1 and OP2 have different bit values. If one - operand is >=0 and the other <0 then the number of bits different - is infinite, and the return value is the largest possible - `mp_bitcnt_t'. - - -- Function: mp_bitcnt_t mpz_scan0 (mpz_t OP, mp_bitcnt_t STARTING_BIT) - -- Function: mp_bitcnt_t mpz_scan1 (mpz_t OP, mp_bitcnt_t STARTING_BIT) - Scan OP, starting from bit STARTING_BIT, towards more significant - bits, until the first 0 or 1 bit (respectively) is found. Return - the index of the found bit. - - If the bit at STARTING_BIT is already what's sought, then - STARTING_BIT is returned. - - If there's no bit found, then the largest possible `mp_bitcnt_t' is - returned. This will happen in `mpz_scan0' past the end of a - negative number, or `mpz_scan1' past the end of a nonnegative - number. - - -- Function: void mpz_setbit (mpz_t ROP, mp_bitcnt_t BIT_INDEX) - Set bit BIT_INDEX in ROP. - - -- Function: void mpz_clrbit (mpz_t ROP, mp_bitcnt_t BIT_INDEX) - Clear bit BIT_INDEX in ROP. - - -- Function: void mpz_combit (mpz_t ROP, mp_bitcnt_t BIT_INDEX) - Complement bit BIT_INDEX in ROP. - - -- Function: int mpz_tstbit (mpz_t OP, mp_bitcnt_t BIT_INDEX) - Test bit BIT_INDEX in OP and return 0 or 1 accordingly. - - -File: gmp.info, Node: I/O of Integers, Next: Integer Random Numbers, Prev: Integer Logic and Bit Fiddling, Up: Integer Functions - -5.12 Input and Output Functions -=============================== - -Functions that perform input from a stdio stream, and functions that -output to a stdio stream. Passing a `NULL' pointer for a STREAM -argument to any of these functions will make them read from `stdin' and -write to `stdout', respectively. - - When using any of these functions, it is a good idea to include -`stdio.h' before `gmp.h', since that will allow `gmp.h' to define -prototypes for these functions. - - -- Function: size_t mpz_out_str (FILE *STREAM, int BASE, mpz_t OP) - Output OP on stdio stream STREAM, as a string of digits in base - BASE. The base argument may vary from 2 to 62 or from -2 to -36. - - For BASE in the range 2..36, digits and lower-case letters are - used; for -2..-36, digits and upper-case letters are used; for - 37..62, digits, upper-case letters, and lower-case letters (in - that significance order) are used. - - Return the number of bytes written, or if an error occurred, - return 0. - - -- Function: size_t mpz_inp_str (mpz_t ROP, FILE *STREAM, int BASE) - Input a possibly white-space preceded string in base BASE from - stdio stream STREAM, and put the read integer in ROP. - - The BASE may vary from 2 to 62, or if BASE is 0, then the leading - characters are used: `0x' and `0X' for hexadecimal, `0b' and `0B' - for binary, `0' for octal, or decimal otherwise. - - For bases up to 36, case is ignored; upper-case and lower-case - letters have the same value. For bases 37 to 62, upper-case - letter represent the usual 10..35 while lower-case letter - represent 36..61. - - Return the number of bytes read, or if an error occurred, return 0. - - -- Function: size_t mpz_out_raw (FILE *STREAM, mpz_t OP) - Output OP on stdio stream STREAM, in raw binary format. The - integer is written in a portable format, with 4 bytes of size - information, and that many bytes of limbs. Both the size and the - limbs are written in decreasing significance order (i.e., in - big-endian). - - The output can be read with `mpz_inp_raw'. - - Return the number of bytes written, or if an error occurred, - return 0. - - The output of this can not be read by `mpz_inp_raw' from GMP 1, - because of changes necessary for compatibility between 32-bit and - 64-bit machines. - - -- Function: size_t mpz_inp_raw (mpz_t ROP, FILE *STREAM) - Input from stdio stream STREAM in the format written by - `mpz_out_raw', and put the result in ROP. Return the number of - bytes read, or if an error occurred, return 0. - - This routine can read the output from `mpz_out_raw' also from GMP - 1, in spite of changes necessary for compatibility between 32-bit - and 64-bit machines. - - -File: gmp.info, Node: Integer Random Numbers, Next: Integer Import and Export, Prev: I/O of Integers, Up: Integer Functions - -5.13 Random Number Functions -============================ - -The random number functions of GMP come in two groups; older function -that rely on a global state, and newer functions that accept a state -parameter that is read and modified. Please see the *Note Random -Number Functions:: for more information on how to use and not to use -random number functions. - - -- Function: void mpz_urandomb (mpz_t ROP, gmp_randstate_t STATE, - mp_bitcnt_t N) - Generate a uniformly distributed random integer in the range 0 to - 2^N-1, inclusive. - - The variable STATE must be initialized by calling one of the - `gmp_randinit' functions (*Note Random State Initialization::) - before invoking this function. - - -- Function: void mpz_urandomm (mpz_t ROP, gmp_randstate_t STATE, - mpz_t N) - Generate a uniform random integer in the range 0 to N-1, inclusive. - - The variable STATE must be initialized by calling one of the - `gmp_randinit' functions (*Note Random State Initialization::) - before invoking this function. - - -- Function: void mpz_rrandomb (mpz_t ROP, gmp_randstate_t STATE, - mp_bitcnt_t N) - Generate a random integer with long strings of zeros and ones in - the binary representation. Useful for testing functions and - algorithms, since this kind of random numbers have proven to be - more likely to trigger corner-case bugs. The random number will - be in the range 0 to 2^N-1, inclusive. - - The variable STATE must be initialized by calling one of the - `gmp_randinit' functions (*Note Random State Initialization::) - before invoking this function. - - -- Function: void mpz_random (mpz_t ROP, mp_size_t MAX_SIZE) - Generate a random integer of at most MAX_SIZE limbs. The generated - random number doesn't satisfy any particular requirements of - randomness. Negative random numbers are generated when MAX_SIZE - is negative. - - This function is obsolete. Use `mpz_urandomb' or `mpz_urandomm' - instead. - - -- Function: void mpz_random2 (mpz_t ROP, mp_size_t MAX_SIZE) - Generate a random integer of at most MAX_SIZE limbs, with long - strings of zeros and ones in the binary representation. Useful - for testing functions and algorithms, since this kind of random - numbers have proven to be more likely to trigger corner-case bugs. - Negative random numbers are generated when MAX_SIZE is negative. - - This function is obsolete. Use `mpz_rrandomb' instead. - - -File: gmp.info, Node: Integer Import and Export, Next: Miscellaneous Integer Functions, Prev: Integer Random Numbers, Up: Integer Functions - -5.14 Integer Import and Export -============================== - -`mpz_t' variables can be converted to and from arbitrary words of binary -data with the following functions. - - -- Function: void mpz_import (mpz_t ROP, size_t COUNT, int ORDER, - size_t SIZE, int ENDIAN, size_t NAILS, const void *OP) - Set ROP from an array of word data at OP. - - The parameters specify the format of the data. COUNT many words - are read, each SIZE bytes. ORDER can be 1 for most significant - word first or -1 for least significant first. Within each word - ENDIAN can be 1 for most significant byte first, -1 for least - significant first, or 0 for the native endianness of the host CPU. - The most significant NAILS bits of each word are skipped, this - can be 0 to use the full words. - - There is no sign taken from the data, ROP will simply be a positive - integer. An application can handle any sign itself, and apply it - for instance with `mpz_neg'. - - There are no data alignment restrictions on OP, any address is - allowed. - - Here's an example converting an array of `unsigned long' data, most - significant element first, and host byte order within each value. - - unsigned long a[20]; - /* Initialize Z and A */ - mpz_import (z, 20, 1, sizeof(a[0]), 0, 0, a); - - This example assumes the full `sizeof' bytes are used for data in - the given type, which is usually true, and certainly true for - `unsigned long' everywhere we know of. However on Cray vector - systems it may be noted that `short' and `int' are always stored - in 8 bytes (and with `sizeof' indicating that) but use only 32 or - 46 bits. The NAILS feature can account for this, by passing for - instance `8*sizeof(int)-INT_BIT'. - - -- Function: void * mpz_export (void *ROP, size_t *COUNTP, int ORDER, - size_t SIZE, int ENDIAN, size_t NAILS, mpz_t OP) - Fill ROP with word data from OP. - - The parameters specify the format of the data produced. Each word - will be SIZE bytes and ORDER can be 1 for most significant word - first or -1 for least significant first. Within each word ENDIAN - can be 1 for most significant byte first, -1 for least significant - first, or 0 for the native endianness of the host CPU. The most - significant NAILS bits of each word are unused and set to zero, - this can be 0 to produce full words. - - The number of words produced is written to `*COUNTP', or COUNTP - can be `NULL' to discard the count. ROP must have enough space - for the data, or if ROP is `NULL' then a result array of the - necessary size is allocated using the current GMP allocation - function (*note Custom Allocation::). In either case the return - value is the destination used, either ROP or the allocated block. - - If OP is non-zero then the most significant word produced will be - non-zero. If OP is zero then the count returned will be zero and - nothing written to ROP. If ROP is `NULL' in this case, no block - is allocated, just `NULL' is returned. - - The sign of OP is ignored, just the absolute value is exported. An - application can use `mpz_sgn' to get the sign and handle it as - desired. (*note Integer Comparisons::) - - There are no data alignment restrictions on ROP, any address is - allowed. - - When an application is allocating space itself the required size - can be determined with a calculation like the following. Since - `mpz_sizeinbase' always returns at least 1, `count' here will be - at least one, which avoids any portability problems with - `malloc(0)', though if `z' is zero no space at all is actually - needed (or written). - - numb = 8*size - nail; - count = (mpz_sizeinbase (z, 2) + numb-1) / numb; - p = malloc (count * size); - - -File: gmp.info, Node: Miscellaneous Integer Functions, Next: Integer Special Functions, Prev: Integer Import and Export, Up: Integer Functions - -5.15 Miscellaneous Functions -============================ - - -- Function: int mpz_fits_ulong_p (mpz_t OP) - -- Function: int mpz_fits_slong_p (mpz_t OP) - -- Function: int mpz_fits_uint_p (mpz_t OP) - -- Function: int mpz_fits_sint_p (mpz_t OP) - -- Function: int mpz_fits_ushort_p (mpz_t OP) - -- Function: int mpz_fits_sshort_p (mpz_t OP) - Return non-zero iff the value of OP fits in an `unsigned long int', - `signed long int', `unsigned int', `signed int', `unsigned short - int', or `signed short int', respectively. Otherwise, return zero. - - -- Macro: int mpz_odd_p (mpz_t OP) - -- Macro: int mpz_even_p (mpz_t OP) - Determine whether OP is odd or even, respectively. Return - non-zero if yes, zero if no. These macros evaluate their argument - more than once. - - -- Function: size_t mpz_sizeinbase (mpz_t OP, int BASE) - Return the size of OP measured in number of digits in the given - BASE. BASE can vary from 2 to 62. The sign of OP is ignored, - just the absolute value is used. The result will be either exact - or 1 too big. If BASE is a power of 2, the result is always - exact. If OP is zero the return value is always 1. - - This function can be used to determine the space required when - converting OP to a string. The right amount of allocation is - normally two more than the value returned by `mpz_sizeinbase', one - extra for a minus sign and one for the null-terminator. - - It will be noted that `mpz_sizeinbase(OP,2)' can be used to locate - the most significant 1 bit in OP, counting from 1. (Unlike the - bitwise functions which start from 0, *Note Logical and Bit - Manipulation Functions: Integer Logic and Bit Fiddling.) - - -File: gmp.info, Node: Integer Special Functions, Prev: Miscellaneous Integer Functions, Up: Integer Functions - -5.16 Special Functions -====================== - -The functions in this section are for various special purposes. Most -applications will not need them. - - -- Function: void mpz_array_init (mpz_t INTEGER_ARRAY, mp_size_t - ARRAY_SIZE, mp_size_t FIXED_NUM_BITS) - This is a special type of initialization. *Fixed* space of - FIXED_NUM_BITS is allocated to each of the ARRAY_SIZE integers in - INTEGER_ARRAY. There is no way to free the storage allocated by - this function. Don't call `mpz_clear'! - - The INTEGER_ARRAY parameter is the first `mpz_t' in the array. For - example, - - mpz_t arr[20000]; - mpz_array_init (arr[0], 20000, 512); - - This function is only intended for programs that create a large - number of integers and need to reduce memory usage by avoiding the - overheads of allocating and reallocating lots of small blocks. In - normal programs this function is not recommended. - - The space allocated to each integer by this function will not be - automatically increased, unlike the normal `mpz_init', so an - application must ensure it is sufficient for any value stored. - The following space requirements apply to various routines, - - * `mpz_abs', `mpz_neg', `mpz_set', `mpz_set_si' and - `mpz_set_ui' need room for the value they store. - - * `mpz_add', `mpz_add_ui', `mpz_sub' and `mpz_sub_ui' need room - for the larger of the two operands, plus an extra - `mp_bits_per_limb'. - - * `mpz_mul', `mpz_mul_ui' and `mpz_mul_ui' need room for the sum - of the number of bits in their operands, but each rounded up - to a multiple of `mp_bits_per_limb'. - - * `mpz_swap' can be used between two array variables, but not - between an array and a normal variable. - - For other functions, or if in doubt, the suggestion is to - calculate in a regular `mpz_init' variable and copy the result to - an array variable with `mpz_set'. - - -- Function: void * _mpz_realloc (mpz_t INTEGER, mp_size_t NEW_ALLOC) - Change the space for INTEGER to NEW_ALLOC limbs. The value in - INTEGER is preserved if it fits, or is set to 0 if not. The return - value is not useful to applications and should be ignored. - - `mpz_realloc2' is the preferred way to accomplish allocation - changes like this. `mpz_realloc2' and `_mpz_realloc' are the same - except that `_mpz_realloc' takes its size in limbs. - - -- Function: mp_limb_t mpz_getlimbn (mpz_t OP, mp_size_t N) - Return limb number N from OP. The sign of OP is ignored, just the - absolute value is used. The least significant limb is number 0. - - `mpz_size' can be used to find how many limbs make up OP. - `mpz_getlimbn' returns zero if N is outside the range 0 to - `mpz_size(OP)-1'. - - -- Function: size_t mpz_size (mpz_t OP) - Return the size of OP measured in number of limbs. If OP is zero, - the returned value will be zero. - - -File: gmp.info, Node: Rational Number Functions, Next: Floating-point Functions, Prev: Integer Functions, Up: Top - -6 Rational Number Functions -*************************** - -This chapter describes the GMP functions for performing arithmetic on -rational numbers. These functions start with the prefix `mpq_'. - - Rational numbers are stored in objects of type `mpq_t'. - - All rational arithmetic functions assume operands have a canonical -form, and canonicalize their result. The canonical from means that the -denominator and the numerator have no common factors, and that the -denominator is positive. Zero has the unique representation 0/1. - - Pure assignment functions do not canonicalize the assigned variable. -It is the responsibility of the user to canonicalize the assigned -variable before any arithmetic operations are performed on that -variable. - - -- Function: void mpq_canonicalize (mpq_t OP) - Remove any factors that are common to the numerator and - denominator of OP, and make the denominator positive. - -* Menu: - -* Initializing Rationals:: -* Rational Conversions:: -* Rational Arithmetic:: -* Comparing Rationals:: -* Applying Integer Functions:: -* I/O of Rationals:: - - -File: gmp.info, Node: Initializing Rationals, Next: Rational Conversions, Prev: Rational Number Functions, Up: Rational Number Functions - -6.1 Initialization and Assignment Functions -=========================================== - - -- Function: void mpq_init (mpq_t X) - Initialize X and set it to 0/1. Each variable should normally - only be initialized once, or at least cleared out (using the - function `mpq_clear') between each initialization. - - -- Function: void mpq_inits (mpq_t X, ...) - Initialize a NULL-terminated list of `mpq_t' variables, and set - their values to 0/1. - - -- Function: void mpq_clear (mpq_t X) - Free the space occupied by X. Make sure to call this function for - all `mpq_t' variables when you are done with them. - - -- Function: void mpq_clears (mpq_t X, ...) - Free the space occupied by a NULL-terminated list of `mpq_t' - variables. - - -- Function: void mpq_set (mpq_t ROP, mpq_t OP) - -- Function: void mpq_set_z (mpq_t ROP, mpz_t OP) - Assign ROP from OP. - - -- Function: void mpq_set_ui (mpq_t ROP, unsigned long int OP1, - unsigned long int OP2) - -- Function: void mpq_set_si (mpq_t ROP, signed long int OP1, unsigned - long int OP2) - Set the value of ROP to OP1/OP2. Note that if OP1 and OP2 have - common factors, ROP has to be passed to `mpq_canonicalize' before - any operations are performed on ROP. - - -- Function: int mpq_set_str (mpq_t ROP, char *STR, int BASE) - Set ROP from a null-terminated string STR in the given BASE. - - The string can be an integer like "41" or a fraction like - "41/152". The fraction must be in canonical form (*note Rational - Number Functions::), or if not then `mpq_canonicalize' must be - called. - - The numerator and optional denominator are parsed the same as in - `mpz_set_str' (*note Assigning Integers::). White space is - allowed in the string, and is simply ignored. The BASE can vary - from 2 to 62, or if BASE is 0 then the leading characters are - used: `0x' or `0X' for hex, `0b' or `0B' for binary, `0' for - octal, or decimal otherwise. Note that this is done separately - for the numerator and denominator, so for instance `0xEF/100' is - 239/100, whereas `0xEF/0x100' is 239/256. - - The return value is 0 if the entire string is a valid number, or - -1 if not. - - -- Function: void mpq_swap (mpq_t ROP1, mpq_t ROP2) - Swap the values ROP1 and ROP2 efficiently. - - -File: gmp.info, Node: Rational Conversions, Next: Rational Arithmetic, Prev: Initializing Rationals, Up: Rational Number Functions - -6.2 Conversion Functions -======================== - - -- Function: double mpq_get_d (mpq_t OP) - Convert OP to a `double', truncating if necessary (ie. rounding - towards zero). - - If the exponent from the conversion is too big or too small to fit - a `double' then the result is system dependent. For too big an - infinity is returned when available. For too small 0.0 is - normally returned. Hardware overflow, underflow and denorm traps - may or may not occur. - - -- Function: void mpq_set_d (mpq_t ROP, double OP) - -- Function: void mpq_set_f (mpq_t ROP, mpf_t OP) - Set ROP to the value of OP. There is no rounding, this conversion - is exact. - - -- Function: char * mpq_get_str (char *STR, int BASE, mpq_t OP) - Convert OP to a string of digits in base BASE. The base may vary - from 2 to 36. The string will be of the form `num/den', or if the - denominator is 1 then just `num'. - - If STR is `NULL', the result string is allocated using the current - allocation function (*note Custom Allocation::). The block will be - `strlen(str)+1' bytes, that being exactly enough for the string and - null-terminator. - - If STR is not `NULL', it should point to a block of storage large - enough for the result, that being - - mpz_sizeinbase (mpq_numref(OP), BASE) - + mpz_sizeinbase (mpq_denref(OP), BASE) + 3 - - The three extra bytes are for a possible minus sign, possible - slash, and the null-terminator. - - A pointer to the result string is returned, being either the - allocated block, or the given STR. - - -File: gmp.info, Node: Rational Arithmetic, Next: Comparing Rationals, Prev: Rational Conversions, Up: Rational Number Functions - -6.3 Arithmetic Functions -======================== - - -- Function: void mpq_add (mpq_t SUM, mpq_t ADDEND1, mpq_t ADDEND2) - Set SUM to ADDEND1 + ADDEND2. - - -- Function: void mpq_sub (mpq_t DIFFERENCE, mpq_t MINUEND, mpq_t - SUBTRAHEND) - Set DIFFERENCE to MINUEND - SUBTRAHEND. - - -- Function: void mpq_mul (mpq_t PRODUCT, mpq_t MULTIPLIER, mpq_t - MULTIPLICAND) - Set PRODUCT to MULTIPLIER times MULTIPLICAND. - - -- Function: void mpq_mul_2exp (mpq_t ROP, mpq_t OP1, mp_bitcnt_t OP2) - Set ROP to OP1 times 2 raised to OP2. - - -- Function: void mpq_div (mpq_t QUOTIENT, mpq_t DIVIDEND, mpq_t - DIVISOR) - Set QUOTIENT to DIVIDEND/DIVISOR. - - -- Function: void mpq_div_2exp (mpq_t ROP, mpq_t OP1, mp_bitcnt_t OP2) - Set ROP to OP1 divided by 2 raised to OP2. - - -- Function: void mpq_neg (mpq_t NEGATED_OPERAND, mpq_t OPERAND) - Set NEGATED_OPERAND to -OPERAND. - - -- Function: void mpq_abs (mpq_t ROP, mpq_t OP) - Set ROP to the absolute value of OP. - - -- Function: void mpq_inv (mpq_t INVERTED_NUMBER, mpq_t NUMBER) - Set INVERTED_NUMBER to 1/NUMBER. If the new denominator is zero, - this routine will divide by zero. - - -File: gmp.info, Node: Comparing Rationals, Next: Applying Integer Functions, Prev: Rational Arithmetic, Up: Rational Number Functions - -6.4 Comparison Functions -======================== - - -- Function: int mpq_cmp (mpq_t OP1, mpq_t OP2) - Compare OP1 and OP2. Return a positive value if OP1 > OP2, zero - if OP1 = OP2, and a negative value if OP1 < OP2. - - To determine if two rationals are equal, `mpq_equal' is faster than - `mpq_cmp'. - - -- Macro: int mpq_cmp_ui (mpq_t OP1, unsigned long int NUM2, unsigned - long int DEN2) - -- Macro: int mpq_cmp_si (mpq_t OP1, long int NUM2, unsigned long int - DEN2) - Compare OP1 and NUM2/DEN2. Return a positive value if OP1 > - NUM2/DEN2, zero if OP1 = NUM2/DEN2, and a negative value if OP1 < - NUM2/DEN2. - - NUM2 and DEN2 are allowed to have common factors. - - These functions are implemented as a macros and evaluate their - arguments multiple times. - - -- Macro: int mpq_sgn (mpq_t OP) - Return +1 if OP > 0, 0 if OP = 0, and -1 if OP < 0. - - This function is actually implemented as a macro. It evaluates its - arguments multiple times. - - -- Function: int mpq_equal (mpq_t OP1, mpq_t OP2) - Return non-zero if OP1 and OP2 are equal, zero if they are - non-equal. Although `mpq_cmp' can be used for the same purpose, - this function is much faster. - - -File: gmp.info, Node: Applying Integer Functions, Next: I/O of Rationals, Prev: Comparing Rationals, Up: Rational Number Functions - -6.5 Applying Integer Functions to Rationals -=========================================== - -The set of `mpq' functions is quite small. In particular, there are few -functions for either input or output. The following functions give -direct access to the numerator and denominator of an `mpq_t'. - - Note that if an assignment to the numerator and/or denominator could -take an `mpq_t' out of the canonical form described at the start of -this chapter (*note Rational Number Functions::) then -`mpq_canonicalize' must be called before any other `mpq' functions are -applied to that `mpq_t'. - - -- Macro: mpz_t mpq_numref (mpq_t OP) - -- Macro: mpz_t mpq_denref (mpq_t OP) - Return a reference to the numerator and denominator of OP, - respectively. The `mpz' functions can be used on the result of - these macros. - - -- Function: void mpq_get_num (mpz_t NUMERATOR, mpq_t RATIONAL) - -- Function: void mpq_get_den (mpz_t DENOMINATOR, mpq_t RATIONAL) - -- Function: void mpq_set_num (mpq_t RATIONAL, mpz_t NUMERATOR) - -- Function: void mpq_set_den (mpq_t RATIONAL, mpz_t DENOMINATOR) - Get or set the numerator or denominator of a rational. These - functions are equivalent to calling `mpz_set' with an appropriate - `mpq_numref' or `mpq_denref'. Direct use of `mpq_numref' or - `mpq_denref' is recommended instead of these functions. - - -File: gmp.info, Node: I/O of Rationals, Prev: Applying Integer Functions, Up: Rational Number Functions - -6.6 Input and Output Functions -============================== - -When using any of these functions, it's a good idea to include `stdio.h' -before `gmp.h', since that will allow `gmp.h' to define prototypes for -these functions. - - Passing a `NULL' pointer for a STREAM argument to any of these -functions will make them read from `stdin' and write to `stdout', -respectively. - - -- Function: size_t mpq_out_str (FILE *STREAM, int BASE, mpq_t OP) - Output OP on stdio stream STREAM, as a string of digits in base - BASE. The base may vary from 2 to 36. Output is in the form - `num/den' or if the denominator is 1 then just `num'. - - Return the number of bytes written, or if an error occurred, - return 0. - - -- Function: size_t mpq_inp_str (mpq_t ROP, FILE *STREAM, int BASE) - Read a string of digits from STREAM and convert them to a rational - in ROP. Any initial white-space characters are read and - discarded. Return the number of characters read (including white - space), or 0 if a rational could not be read. - - The input can be a fraction like `17/63' or just an integer like - `123'. Reading stops at the first character not in this form, and - white space is not permitted within the string. If the input - might not be in canonical form, then `mpq_canonicalize' must be - called (*note Rational Number Functions::). - - The BASE can be between 2 and 36, or can be 0 in which case the - leading characters of the string determine the base, `0x' or `0X' - for hexadecimal, `0' for octal, or decimal otherwise. The leading - characters are examined separately for the numerator and - denominator of a fraction, so for instance `0x10/11' is 16/11, - whereas `0x10/0x11' is 16/17. - - -File: gmp.info, Node: Floating-point Functions, Next: Low-level Functions, Prev: Rational Number Functions, Up: Top - -7 Floating-point Functions -************************** - -GMP floating point numbers are stored in objects of type `mpf_t' and -functions operating on them have an `mpf_' prefix. - - The mantissa of each float has a user-selectable precision, limited -only by available memory. Each variable has its own precision, and -that can be increased or decreased at any time. - - The exponent of each float is a fixed precision, one machine word on -most systems. In the current implementation the exponent is a count of -limbs, so for example on a 32-bit system this means a range of roughly -2^-68719476768 to 2^68719476736, or on a 64-bit system this will be -greater. Note however `mpf_get_str' can only return an exponent which -fits an `mp_exp_t' and currently `mpf_set_str' doesn't accept exponents -bigger than a `long'. - - Each variable keeps a size for the mantissa data actually in use. -This means that if a float is exactly represented in only a few bits -then only those bits will be used in a calculation, even if the -selected precision is high. - - All calculations are performed to the precision of the destination -variable. Each function is defined to calculate with "infinite -precision" followed by a truncation to the destination precision, but -of course the work done is only what's needed to determine a result -under that definition. - - The precision selected for a variable is a minimum value, GMP may -increase it a little to facilitate efficient calculation. Currently -this means rounding up to a whole limb, and then sometimes having a -further partial limb, depending on the high limb of the mantissa. But -applications shouldn't be concerned by such details. - - The mantissa in stored in binary, as might be imagined from the fact -precisions are expressed in bits. One consequence of this is that -decimal fractions like 0.1 cannot be represented exactly. The same is -true of plain IEEE `double' floats. This makes both highly unsuitable -for calculations involving money or other values that should be exact -decimal fractions. (Suitably scaled integers, or perhaps rationals, -are better choices.) - - `mpf' functions and variables have no special notion of infinity or -not-a-number, and applications must take care not to overflow the -exponent or results will be unpredictable. This might change in a -future release. - - Note that the `mpf' functions are _not_ intended as a smooth -extension to IEEE P754 arithmetic. In particular results obtained on -one computer often differ from the results on a computer with a -different word size. - -* Menu: - -* Initializing Floats:: -* Assigning Floats:: -* Simultaneous Float Init & Assign:: -* Converting Floats:: -* Float Arithmetic:: -* Float Comparison:: -* I/O of Floats:: -* Miscellaneous Float Functions:: - - -File: gmp.info, Node: Initializing Floats, Next: Assigning Floats, Prev: Floating-point Functions, Up: Floating-point Functions - -7.1 Initialization Functions -============================ - - -- Function: void mpf_set_default_prec (mp_bitcnt_t PREC) - Set the default precision to be *at least* PREC bits. All - subsequent calls to `mpf_init' will use this precision, but - previously initialized variables are unaffected. - - -- Function: mp_bitcnt_t mpf_get_default_prec (void) - Return the default precision actually used. - - An `mpf_t' object must be initialized before storing the first value -in it. The functions `mpf_init' and `mpf_init2' are used for that -purpose. - - -- Function: void mpf_init (mpf_t X) - Initialize X to 0. Normally, a variable should be initialized - once only or at least be cleared, using `mpf_clear', between - initializations. The precision of X is undefined unless a default - precision has already been established by a call to - `mpf_set_default_prec'. - - -- Function: void mpf_init2 (mpf_t X, mp_bitcnt_t PREC) - Initialize X to 0 and set its precision to be *at least* PREC - bits. Normally, a variable should be initialized once only or at - least be cleared, using `mpf_clear', between initializations. - - -- Function: void mpf_inits (mpf_t X, ...) - Initialize a NULL-terminated list of `mpf_t' variables, and set - their values to 0. The precision of the initialized variables is - undefined unless a default precision has already been established - by a call to `mpf_set_default_prec'. - - -- Function: void mpf_clear (mpf_t X) - Free the space occupied by X. Make sure to call this function for - all `mpf_t' variables when you are done with them. - - -- Function: void mpf_clears (mpf_t X, ...) - Free the space occupied by a NULL-terminated list of `mpf_t' - variables. - - Here is an example on how to initialize floating-point variables: - { - mpf_t x, y; - mpf_init (x); /* use default precision */ - mpf_init2 (y, 256); /* precision _at least_ 256 bits */ - ... - /* Unless the program is about to exit, do ... */ - mpf_clear (x); - mpf_clear (y); - } - - The following three functions are useful for changing the precision -during a calculation. A typical use would be for adjusting the -precision gradually in iterative algorithms like Newton-Raphson, making -the computation precision closely match the actual accurate part of the -numbers. - - -- Function: mp_bitcnt_t mpf_get_prec (mpf_t OP) - Return the current precision of OP, in bits. - - -- Function: void mpf_set_prec (mpf_t ROP, mp_bitcnt_t PREC) - Set the precision of ROP to be *at least* PREC bits. The value in - ROP will be truncated to the new precision. - - This function requires a call to `realloc', and so should not be - used in a tight loop. - - -- Function: void mpf_set_prec_raw (mpf_t ROP, mp_bitcnt_t PREC) - Set the precision of ROP to be *at least* PREC bits, without - changing the memory allocated. - - PREC must be no more than the allocated precision for ROP, that - being the precision when ROP was initialized, or in the most recent - `mpf_set_prec'. - - The value in ROP is unchanged, and in particular if it had a higher - precision than PREC it will retain that higher precision. New - values written to ROP will use the new PREC. - - Before calling `mpf_clear' or the full `mpf_set_prec', another - `mpf_set_prec_raw' call must be made to restore ROP to its original - allocated precision. Failing to do so will have unpredictable - results. - - `mpf_get_prec' can be used before `mpf_set_prec_raw' to get the - original allocated precision. After `mpf_set_prec_raw' it - reflects the PREC value set. - - `mpf_set_prec_raw' is an efficient way to use an `mpf_t' variable - at different precisions during a calculation, perhaps to gradually - increase precision in an iteration, or just to use various - different precisions for different purposes during a calculation. - - -File: gmp.info, Node: Assigning Floats, Next: Simultaneous Float Init & Assign, Prev: Initializing Floats, Up: Floating-point Functions - -7.2 Assignment Functions -======================== - -These functions assign new values to already initialized floats (*note -Initializing Floats::). - - -- Function: void mpf_set (mpf_t ROP, mpf_t OP) - -- Function: void mpf_set_ui (mpf_t ROP, unsigned long int OP) - -- Function: void mpf_set_si (mpf_t ROP, signed long int OP) - -- Function: void mpf_set_d (mpf_t ROP, double OP) - -- Function: void mpf_set_z (mpf_t ROP, mpz_t OP) - -- Function: void mpf_set_q (mpf_t ROP, mpq_t OP) - Set the value of ROP from OP. - - -- Function: int mpf_set_str (mpf_t ROP, char *STR, int BASE) - Set the value of ROP from the string in STR. The string is of the - form `M@N' or, if the base is 10 or less, alternatively `MeN'. - `M' is the mantissa and `N' is the exponent. The mantissa is - always in the specified base. The exponent is either in the - specified base or, if BASE is negative, in decimal. The decimal - point expected is taken from the current locale, on systems - providing `localeconv'. - - The argument BASE may be in the ranges 2 to 62, or -62 to -2. - Negative values are used to specify that the exponent is in - decimal. - - For bases up to 36, case is ignored; upper-case and lower-case - letters have the same value; for bases 37 to 62, upper-case letter - represent the usual 10..35 while lower-case letter represent - 36..61. - - Unlike the corresponding `mpz' function, the base will not be - determined from the leading characters of the string if BASE is 0. - This is so that numbers like `0.23' are not interpreted as octal. - - White space is allowed in the string, and is simply ignored. - [This is not really true; white-space is ignored in the beginning - of the string and within the mantissa, but not in other places, - such as after a minus sign or in the exponent. We are considering - changing the definition of this function, making it fail when - there is any white-space in the input, since that makes a lot of - sense. Please tell us your opinion about this change. Do you - really want it to accept "3 14" as meaning 314 as it does now?] - - This function returns 0 if the entire string is a valid number in - base BASE. Otherwise it returns -1. - - -- Function: void mpf_swap (mpf_t ROP1, mpf_t ROP2) - Swap ROP1 and ROP2 efficiently. Both the values and the - precisions of the two variables are swapped. - - -File: gmp.info, Node: Simultaneous Float Init & Assign, Next: Converting Floats, Prev: Assigning Floats, Up: Floating-point Functions - -7.3 Combined Initialization and Assignment Functions -==================================================== - -For convenience, GMP provides a parallel series of initialize-and-set -functions which initialize the output and then store the value there. -These functions' names have the form `mpf_init_set...' - - Once the float has been initialized by any of the `mpf_init_set...' -functions, it can be used as the source or destination operand for the -ordinary float functions. Don't use an initialize-and-set function on -a variable already initialized! - - -- Function: void mpf_init_set (mpf_t ROP, mpf_t OP) - -- Function: void mpf_init_set_ui (mpf_t ROP, unsigned long int OP) - -- Function: void mpf_init_set_si (mpf_t ROP, signed long int OP) - -- Function: void mpf_init_set_d (mpf_t ROP, double OP) - Initialize ROP and set its value from OP. - - The precision of ROP will be taken from the active default - precision, as set by `mpf_set_default_prec'. - - -- Function: int mpf_init_set_str (mpf_t ROP, char *STR, int BASE) - Initialize ROP and set its value from the string in STR. See - `mpf_set_str' above for details on the assignment operation. - - Note that ROP is initialized even if an error occurs. (I.e., you - have to call `mpf_clear' for it.) - - The precision of ROP will be taken from the active default - precision, as set by `mpf_set_default_prec'. - - -File: gmp.info, Node: Converting Floats, Next: Float Arithmetic, Prev: Simultaneous Float Init & Assign, Up: Floating-point Functions - -7.4 Conversion Functions -======================== - - -- Function: double mpf_get_d (mpf_t OP) - Convert OP to a `double', truncating if necessary (ie. rounding - towards zero). - - If the exponent in OP is too big or too small to fit a `double' - then the result is system dependent. For too big an infinity is - returned when available. For too small 0.0 is normally returned. - Hardware overflow, underflow and denorm traps may or may not occur. - - -- Function: double mpf_get_d_2exp (signed long int *EXP, mpf_t OP) - Convert OP to a `double', truncating if necessary (ie. rounding - towards zero), and with an exponent returned separately. - - The return value is in the range 0.5<=abs(D)<1 and the exponent is - stored to `*EXP'. D * 2^EXP is the (truncated) OP value. If OP - is zero, the return is 0.0 and 0 is stored to `*EXP'. - - This is similar to the standard C `frexp' function (*note - Normalization Functions: (libc)Normalization Functions.). - - -- Function: long mpf_get_si (mpf_t OP) - -- Function: unsigned long mpf_get_ui (mpf_t OP) - Convert OP to a `long' or `unsigned long', truncating any fraction - part. If OP is too big for the return type, the result is - undefined. - - See also `mpf_fits_slong_p' and `mpf_fits_ulong_p' (*note - Miscellaneous Float Functions::). - - -- Function: char * mpf_get_str (char *STR, mp_exp_t *EXPPTR, int - BASE, size_t N_DIGITS, mpf_t OP) - Convert OP to a string of digits in base BASE. The base argument - may vary from 2 to 62 or from -2 to -36. Up to N_DIGITS digits - will be generated. Trailing zeros are not returned. No more - digits than can be accurately represented by OP are ever - generated. If N_DIGITS is 0 then that accurate maximum number of - digits are generated. - - For BASE in the range 2..36, digits and lower-case letters are - used; for -2..-36, digits and upper-case letters are used; for - 37..62, digits, upper-case letters, and lower-case letters (in - that significance order) are used. - - If STR is `NULL', the result string is allocated using the current - allocation function (*note Custom Allocation::). The block will be - `strlen(str)+1' bytes, that being exactly enough for the string and - null-terminator. - - If STR is not `NULL', it should point to a block of N_DIGITS + 2 - bytes, that being enough for the mantissa, a possible minus sign, - and a null-terminator. When N_DIGITS is 0 to get all significant - digits, an application won't be able to know the space required, - and STR should be `NULL' in that case. - - The generated string is a fraction, with an implicit radix point - immediately to the left of the first digit. The applicable - exponent is written through the EXPPTR pointer. For example, the - number 3.1416 would be returned as string "31416" and exponent 1. - - When OP is zero, an empty string is produced and the exponent - returned is 0. - - A pointer to the result string is returned, being either the - allocated block or the given STR. - - -File: gmp.info, Node: Float Arithmetic, Next: Float Comparison, Prev: Converting Floats, Up: Floating-point Functions - -7.5 Arithmetic Functions -======================== - - -- Function: void mpf_add (mpf_t ROP, mpf_t OP1, mpf_t OP2) - -- Function: void mpf_add_ui (mpf_t ROP, mpf_t OP1, unsigned long int - OP2) - Set ROP to OP1 + OP2. - - -- Function: void mpf_sub (mpf_t ROP, mpf_t OP1, mpf_t OP2) - -- Function: void mpf_ui_sub (mpf_t ROP, unsigned long int OP1, mpf_t - OP2) - -- Function: void mpf_sub_ui (mpf_t ROP, mpf_t OP1, unsigned long int - OP2) - Set ROP to OP1 - OP2. - - -- Function: void mpf_mul (mpf_t ROP, mpf_t OP1, mpf_t OP2) - -- Function: void mpf_mul_ui (mpf_t ROP, mpf_t OP1, unsigned long int - OP2) - Set ROP to OP1 times OP2. - - Division is undefined if the divisor is zero, and passing a zero -divisor to the divide functions will make these functions intentionally -divide by zero. This lets the user handle arithmetic exceptions in -these functions in the same manner as other arithmetic exceptions. - - -- Function: void mpf_div (mpf_t ROP, mpf_t OP1, mpf_t OP2) - -- Function: void mpf_ui_div (mpf_t ROP, unsigned long int OP1, mpf_t - OP2) - -- Function: void mpf_div_ui (mpf_t ROP, mpf_t OP1, unsigned long int - OP2) - Set ROP to OP1/OP2. - - -- Function: void mpf_sqrt (mpf_t ROP, mpf_t OP) - -- Function: void mpf_sqrt_ui (mpf_t ROP, unsigned long int OP) - Set ROP to the square root of OP. - - -- Function: void mpf_pow_ui (mpf_t ROP, mpf_t OP1, unsigned long int - OP2) - Set ROP to OP1 raised to the power OP2. - - -- Function: void mpf_neg (mpf_t ROP, mpf_t OP) - Set ROP to -OP. - - -- Function: void mpf_abs (mpf_t ROP, mpf_t OP) - Set ROP to the absolute value of OP. - - -- Function: void mpf_mul_2exp (mpf_t ROP, mpf_t OP1, mp_bitcnt_t OP2) - Set ROP to OP1 times 2 raised to OP2. - - -- Function: void mpf_div_2exp (mpf_t ROP, mpf_t OP1, mp_bitcnt_t OP2) - Set ROP to OP1 divided by 2 raised to OP2. - - -File: gmp.info, Node: Float Comparison, Next: I/O of Floats, Prev: Float Arithmetic, Up: Floating-point Functions - -7.6 Comparison Functions -======================== - - -- Function: int mpf_cmp (mpf_t OP1, mpf_t OP2) - -- Function: int mpf_cmp_d (mpf_t OP1, double OP2) - -- Function: int mpf_cmp_ui (mpf_t OP1, unsigned long int OP2) - -- Function: int mpf_cmp_si (mpf_t OP1, signed long int OP2) - Compare OP1 and OP2. Return a positive value if OP1 > OP2, zero - if OP1 = OP2, and a negative value if OP1 < OP2. - - `mpf_cmp_d' can be called with an infinity, but results are - undefined for a NaN. - - -- Function: int mpf_eq (mpf_t OP1, mpf_t OP2, mp_bitcnt_t op3) - Return non-zero if the first OP3 bits of OP1 and OP2 are equal, - zero otherwise. I.e., test if OP1 and OP2 are approximately equal. - - Caution 1: All version of GMP up to version 4.2.4 compared just - whole limbs, meaning sometimes more than OP3 bits, sometimes fewer. - - Caution 2: This function will consider XXX11...111 and XX100...000 - different, even if ... is replaced by a semi-infinite number of - bits. Such numbers are really just one ulp off, and should be - considered equal. - - -- Function: void mpf_reldiff (mpf_t ROP, mpf_t OP1, mpf_t OP2) - Compute the relative difference between OP1 and OP2 and store the - result in ROP. This is abs(OP1-OP2)/OP1. - - -- Macro: int mpf_sgn (mpf_t OP) - Return +1 if OP > 0, 0 if OP = 0, and -1 if OP < 0. - - This function is actually implemented as a macro. It evaluates - its arguments multiple times. - - -File: gmp.info, Node: I/O of Floats, Next: Miscellaneous Float Functions, Prev: Float Comparison, Up: Floating-point Functions - -7.7 Input and Output Functions -============================== - -Functions that perform input from a stdio stream, and functions that -output to a stdio stream. Passing a `NULL' pointer for a STREAM -argument to any of these functions will make them read from `stdin' and -write to `stdout', respectively. - - When using any of these functions, it is a good idea to include -`stdio.h' before `gmp.h', since that will allow `gmp.h' to define -prototypes for these functions. - - -- Function: size_t mpf_out_str (FILE *STREAM, int BASE, size_t - N_DIGITS, mpf_t OP) - Print OP to STREAM, as a string of digits. Return the number of - bytes written, or if an error occurred, return 0. - - The mantissa is prefixed with an `0.' and is in the given BASE, - which may vary from 2 to 62 or from -2 to -36. An exponent is - then printed, separated by an `e', or if the base is greater than - 10 then by an `@'. The exponent is always in decimal. The - decimal point follows the current locale, on systems providing - `localeconv'. - - For BASE in the range 2..36, digits and lower-case letters are - used; for -2..-36, digits and upper-case letters are used; for - 37..62, digits, upper-case letters, and lower-case letters (in - that significance order) are used. - - Up to N_DIGITS will be printed from the mantissa, except that no - more digits than are accurately representable by OP will be - printed. N_DIGITS can be 0 to select that accurate maximum. - - -- Function: size_t mpf_inp_str (mpf_t ROP, FILE *STREAM, int BASE) - Read a string in base BASE from STREAM, and put the read float in - ROP. The string is of the form `M@N' or, if the base is 10 or - less, alternatively `MeN'. `M' is the mantissa and `N' is the - exponent. The mantissa is always in the specified base. The - exponent is either in the specified base or, if BASE is negative, - in decimal. The decimal point expected is taken from the current - locale, on systems providing `localeconv'. - - The argument BASE may be in the ranges 2 to 36, or -36 to -2. - Negative values are used to specify that the exponent is in - decimal. - - Unlike the corresponding `mpz' function, the base will not be - determined from the leading characters of the string if BASE is 0. - This is so that numbers like `0.23' are not interpreted as octal. - - Return the number of bytes read, or if an error occurred, return 0. - - -File: gmp.info, Node: Miscellaneous Float Functions, Prev: I/O of Floats, Up: Floating-point Functions - -7.8 Miscellaneous Functions -=========================== - - -- Function: void mpf_ceil (mpf_t ROP, mpf_t OP) - -- Function: void mpf_floor (mpf_t ROP, mpf_t OP) - -- Function: void mpf_trunc (mpf_t ROP, mpf_t OP) - Set ROP to OP rounded to an integer. `mpf_ceil' rounds to the - next higher integer, `mpf_floor' to the next lower, and `mpf_trunc' - to the integer towards zero. - - -- Function: int mpf_integer_p (mpf_t OP) - Return non-zero if OP is an integer. - - -- Function: int mpf_fits_ulong_p (mpf_t OP) - -- Function: int mpf_fits_slong_p (mpf_t OP) - -- Function: int mpf_fits_uint_p (mpf_t OP) - -- Function: int mpf_fits_sint_p (mpf_t OP) - -- Function: int mpf_fits_ushort_p (mpf_t OP) - -- Function: int mpf_fits_sshort_p (mpf_t OP) - Return non-zero if OP would fit in the respective C data type, when - truncated to an integer. - - -- Function: void mpf_urandomb (mpf_t ROP, gmp_randstate_t STATE, - mp_bitcnt_t NBITS) - Generate a uniformly distributed random float in ROP, such that 0 - <= ROP < 1, with NBITS significant bits in the mantissa. - - The variable STATE must be initialized by calling one of the - `gmp_randinit' functions (*Note Random State Initialization::) - before invoking this function. - - -- Function: void mpf_random2 (mpf_t ROP, mp_size_t MAX_SIZE, mp_exp_t - EXP) - Generate a random float of at most MAX_SIZE limbs, with long - strings of zeros and ones in the binary representation. The - exponent of the number is in the interval -EXP to EXP (in limbs). - This function is useful for testing functions and algorithms, - since these kind of random numbers have proven to be more likely - to trigger corner-case bugs. Negative random numbers are - generated when MAX_SIZE is negative. - - -File: gmp.info, Node: Low-level Functions, Next: Random Number Functions, Prev: Floating-point Functions, Up: Top - -8 Low-level Functions -********************* - -This chapter describes low-level GMP functions, used to implement the -high-level GMP functions, but also intended for time-critical user code. - - These functions start with the prefix `mpn_'. - - The `mpn' functions are designed to be as fast as possible, *not* to -provide a coherent calling interface. The different functions have -somewhat similar interfaces, but there are variations that make them -hard to use. These functions do as little as possible apart from the -real multiple precision computation, so that no time is spent on things -that not all callers need. - - A source operand is specified by a pointer to the least significant -limb and a limb count. A destination operand is specified by just a -pointer. It is the responsibility of the caller to ensure that the -destination has enough space for storing the result. - - With this way of specifying operands, it is possible to perform -computations on subranges of an argument, and store the result into a -subrange of a destination. - - A common requirement for all functions is that each source area -needs at least one limb. No size argument may be zero. Unless -otherwise stated, in-place operations are allowed where source and -destination are the same, but not where they only partly overlap. - - The `mpn' functions are the base for the implementation of the -`mpz_', `mpf_', and `mpq_' functions. - - This example adds the number beginning at S1P and the number -beginning at S2P and writes the sum at DESTP. All areas have N limbs. - - cy = mpn_add_n (destp, s1p, s2p, n) - - It should be noted that the `mpn' functions make no attempt to -identify high or low zero limbs on their operands, or other special -forms. On random data such cases will be unlikely and it'd be wasteful -for every function to check every time. An application knowing -something about its data can take steps to trim or perhaps split its -calculations. - - -In the notation used below, a source operand is identified by the -pointer to the least significant limb, and the limb count in braces. -For example, {S1P, S1N}. - - -- Function: mp_limb_t mpn_add_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Add {S1P, N} and {S2P, N}, and write the N least significant limbs - of the result to RP. Return carry, either 0 or 1. - - This is the lowest-level function for addition. It is the - preferred function for addition, since it is written in assembly - for most CPUs. For addition of a variable to itself (i.e., S1P - equals S2P) use `mpn_lshift' with a count of 1 for optimal speed. - - -- Function: mp_limb_t mpn_add_1 (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t N, mp_limb_t S2LIMB) - Add {S1P, N} and S2LIMB, and write the N least significant limbs - of the result to RP. Return carry, either 0 or 1. - - -- Function: mp_limb_t mpn_add (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t S1N, const mp_limb_t *S2P, mp_size_t S2N) - Add {S1P, S1N} and {S2P, S2N}, and write the S1N least significant - limbs of the result to RP. Return carry, either 0 or 1. - - This function requires that S1N is greater than or equal to S2N. - - -- Function: mp_limb_t mpn_sub_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Subtract {S2P, N} from {S1P, N}, and write the N least significant - limbs of the result to RP. Return borrow, either 0 or 1. - - This is the lowest-level function for subtraction. It is the - preferred function for subtraction, since it is written in - assembly for most CPUs. - - -- Function: mp_limb_t mpn_sub_1 (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t N, mp_limb_t S2LIMB) - Subtract S2LIMB from {S1P, N}, and write the N least significant - limbs of the result to RP. Return borrow, either 0 or 1. - - -- Function: mp_limb_t mpn_sub (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t S1N, const mp_limb_t *S2P, mp_size_t S2N) - Subtract {S2P, S2N} from {S1P, S1N}, and write the S1N least - significant limbs of the result to RP. Return borrow, either 0 or - 1. - - This function requires that S1N is greater than or equal to S2N. - - -- Function: void mpn_neg (mp_limb_t *RP, const mp_limb_t *SP, - mp_size_t N) - Perform the negation of {SP, N}, and write the result to {RP, N}. - Return carry-out. - - -- Function: void mpn_mul_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Multiply {S1P, N} and {S2P, N}, and write the 2*N-limb result to - RP. - - The destination has to have space for 2*N limbs, even if the - product's most significant limb is zero. No overlap is permitted - between the destination and either source. - - If the two input operands are the same, use `mpn_sqr'. - - -- Function: mp_limb_t mpn_mul (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t S1N, const mp_limb_t *S2P, mp_size_t S2N) - Multiply {S1P, S1N} and {S2P, S2N}, and write the (S1N+S2N)-limb - result to RP. Return the most significant limb of the result. - - The destination has to have space for S1N + S2N limbs, even if the - product's most significant limb is zero. No overlap is permitted - between the destination and either source. - - This function requires that S1N is greater than or equal to S2N. - - -- Function: void mpn_sqr (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t N) - Compute the square of {S1P, N} and write the 2*N-limb result to RP. - - The destination has to have space for 2*N limbs, even if the - result's most significant limb is zero. No overlap is permitted - between the destination and the source. - - -- Function: mp_limb_t mpn_mul_1 (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t N, mp_limb_t S2LIMB) - Multiply {S1P, N} by S2LIMB, and write the N least significant - limbs of the product to RP. Return the most significant limb of - the product. {S1P, N} and {RP, N} are allowed to overlap provided - RP <= S1P. - - This is a low-level function that is a building block for general - multiplication as well as other operations in GMP. It is written - in assembly for most CPUs. - - Don't call this function if S2LIMB is a power of 2; use - `mpn_lshift' with a count equal to the logarithm of S2LIMB - instead, for optimal speed. - - -- Function: mp_limb_t mpn_addmul_1 (mp_limb_t *RP, const mp_limb_t - *S1P, mp_size_t N, mp_limb_t S2LIMB) - Multiply {S1P, N} and S2LIMB, and add the N least significant - limbs of the product to {RP, N} and write the result to RP. - Return the most significant limb of the product, plus carry-out - from the addition. - - This is a low-level function that is a building block for general - multiplication as well as other operations in GMP. It is written - in assembly for most CPUs. - - -- Function: mp_limb_t mpn_submul_1 (mp_limb_t *RP, const mp_limb_t - *S1P, mp_size_t N, mp_limb_t S2LIMB) - Multiply {S1P, N} and S2LIMB, and subtract the N least significant - limbs of the product from {RP, N} and write the result to RP. - Return the most significant limb of the product, plus borrow-out - from the subtraction. - - This is a low-level function that is a building block for general - multiplication and division as well as other operations in GMP. - It is written in assembly for most CPUs. - - -- Function: void mpn_tdiv_qr (mp_limb_t *QP, mp_limb_t *RP, mp_size_t - QXN, const mp_limb_t *NP, mp_size_t NN, const mp_limb_t *DP, - mp_size_t DN) - Divide {NP, NN} by {DP, DN} and put the quotient at {QP, NN-DN+1} - and the remainder at {RP, DN}. The quotient is rounded towards 0. - - No overlap is permitted between arguments, except that NP might - equal RP. The dividend size NN must be greater than or equal to - divisor size DN. The most significant limb of the divisor must be - non-zero. The QXN operand must be zero. - - -- Function: mp_limb_t mpn_divrem (mp_limb_t *R1P, mp_size_t QXN, - mp_limb_t *RS2P, mp_size_t RS2N, const mp_limb_t *S3P, - mp_size_t S3N) - [This function is obsolete. Please call `mpn_tdiv_qr' instead for - best performance.] - - Divide {RS2P, RS2N} by {S3P, S3N}, and write the quotient at R1P, - with the exception of the most significant limb, which is - returned. The remainder replaces the dividend at RS2P; it will be - S3N limbs long (i.e., as many limbs as the divisor). - - In addition to an integer quotient, QXN fraction limbs are - developed, and stored after the integral limbs. For most usages, - QXN will be zero. - - It is required that RS2N is greater than or equal to S3N. It is - required that the most significant bit of the divisor is set. - - If the quotient is not needed, pass RS2P + S3N as R1P. Aside from - that special case, no overlap between arguments is permitted. - - Return the most significant limb of the quotient, either 0 or 1. - - The area at R1P needs to be RS2N - S3N + QXN limbs large. - - -- Function: mp_limb_t mpn_divrem_1 (mp_limb_t *R1P, mp_size_t QXN, - mp_limb_t *S2P, mp_size_t S2N, mp_limb_t S3LIMB) - -- Macro: mp_limb_t mpn_divmod_1 (mp_limb_t *R1P, mp_limb_t *S2P, - mp_size_t S2N, mp_limb_t S3LIMB) - Divide {S2P, S2N} by S3LIMB, and write the quotient at R1P. - Return the remainder. - - The integer quotient is written to {R1P+QXN, S2N} and in addition - QXN fraction limbs are developed and written to {R1P, QXN}. - Either or both S2N and QXN can be zero. For most usages, QXN will - be zero. - - `mpn_divmod_1' exists for upward source compatibility and is - simply a macro calling `mpn_divrem_1' with a QXN of 0. - - The areas at R1P and S2P have to be identical or completely - separate, not partially overlapping. - - -- Function: mp_limb_t mpn_divmod (mp_limb_t *R1P, mp_limb_t *RS2P, - mp_size_t RS2N, const mp_limb_t *S3P, mp_size_t S3N) - [This function is obsolete. Please call `mpn_tdiv_qr' instead for - best performance.] - - -- Macro: mp_limb_t mpn_divexact_by3 (mp_limb_t *RP, mp_limb_t *SP, - mp_size_t N) - -- Function: mp_limb_t mpn_divexact_by3c (mp_limb_t *RP, mp_limb_t - *SP, mp_size_t N, mp_limb_t CARRY) - Divide {SP, N} by 3, expecting it to divide exactly, and writing - the result to {RP, N}. If 3 divides exactly, the return value is - zero and the result is the quotient. If not, the return value is - non-zero and the result won't be anything useful. - - `mpn_divexact_by3c' takes an initial carry parameter, which can be - the return value from a previous call, so a large calculation can - be done piece by piece from low to high. `mpn_divexact_by3' is - simply a macro calling `mpn_divexact_by3c' with a 0 carry - parameter. - - These routines use a multiply-by-inverse and will be faster than - `mpn_divrem_1' on CPUs with fast multiplication but slow division. - - The source a, result q, size n, initial carry i, and return value - c satisfy c*b^n + a-i = 3*q, where b=2^GMP_NUMB_BITS. The return - c is always 0, 1 or 2, and the initial carry i must also be 0, 1 - or 2 (these are both borrows really). When c=0 clearly q=(a-i)/3. - When c!=0, the remainder (a-i) mod 3 is given by 3-c, because b - == 1 mod 3 (when `mp_bits_per_limb' is even, which is always so - currently). - - -- Function: mp_limb_t mpn_mod_1 (mp_limb_t *S1P, mp_size_t S1N, - mp_limb_t S2LIMB) - Divide {S1P, S1N} by S2LIMB, and return the remainder. S1N can be - zero. - - -- Function: mp_limb_t mpn_lshift (mp_limb_t *RP, const mp_limb_t *SP, - mp_size_t N, unsigned int COUNT) - Shift {SP, N} left by COUNT bits, and write the result to {RP, N}. - The bits shifted out at the left are returned in the least - significant COUNT bits of the return value (the rest of the return - value is zero). - - COUNT must be in the range 1 to mp_bits_per_limb-1. The regions - {SP, N} and {RP, N} may overlap, provided RP >= SP. - - This function is written in assembly for most CPUs. - - -- Function: mp_limb_t mpn_rshift (mp_limb_t *RP, const mp_limb_t *SP, - mp_size_t N, unsigned int COUNT) - Shift {SP, N} right by COUNT bits, and write the result to {RP, - N}. The bits shifted out at the right are returned in the most - significant COUNT bits of the return value (the rest of the return - value is zero). - - COUNT must be in the range 1 to mp_bits_per_limb-1. The regions - {SP, N} and {RP, N} may overlap, provided RP <= SP. - - This function is written in assembly for most CPUs. - - -- Function: int mpn_cmp (const mp_limb_t *S1P, const mp_limb_t *S2P, - mp_size_t N) - Compare {S1P, N} and {S2P, N} and return a positive value if S1 > - S2, 0 if they are equal, or a negative value if S1 < S2. - - -- Function: mp_size_t mpn_gcd (mp_limb_t *RP, mp_limb_t *XP, - mp_size_t XN, mp_limb_t *YP, mp_size_t YN) - Set {RP, RETVAL} to the greatest common divisor of {XP, XN} and - {YP, YN}. The result can be up to YN limbs, the return value is - the actual number produced. Both source operands are destroyed. - - {XP, XN} must have at least as many bits as {YP, YN}. {YP, YN} - must be odd. Both operands must have non-zero most significant - limbs. No overlap is permitted between {XP, XN} and {YP, YN}. - - -- Function: mp_limb_t mpn_gcd_1 (const mp_limb_t *XP, mp_size_t XN, - mp_limb_t YLIMB) - Return the greatest common divisor of {XP, XN} and YLIMB. Both - operands must be non-zero. - - -- Function: mp_size_t mpn_gcdext (mp_limb_t *GP, mp_limb_t *SP, - mp_size_t *SN, mp_limb_t *XP, mp_size_t XN, mp_limb_t *YP, - mp_size_t YN) - Let U be defined by {XP, XN} and let V be defined by {YP, YN}. - - Compute the greatest common divisor G of U and V. Compute a - cofactor S such that G = US + VT. The second cofactor T is not - computed but can easily be obtained from (G - U*S) / V (the - division will be exact). It is required that U >= V > 0. - - S satisfies S = 1 or abs(S) < V / (2 G). S = 0 if and only if V - divides U (i.e., G = V). - - Store G at GP and let the return value define its limb count. - Store S at SP and let |*SN| define its limb count. S can be - negative; when this happens *SN will be negative. The areas at GP - and SP should each have room for XN+1 limbs. - - The areas {XP, XN+1} and {YP, YN+1} are destroyed (i.e. the input - operands plus an extra limb past the end of each). - - Compatibility note: GMP 4.3.0 and 4.3.1 defined S less strictly. - Earlier as well as later GMP releases define S as described here. - - -- Function: mp_size_t mpn_sqrtrem (mp_limb_t *R1P, mp_limb_t *R2P, - const mp_limb_t *SP, mp_size_t N) - Compute the square root of {SP, N} and put the result at {R1P, - ceil(N/2)} and the remainder at {R2P, RETVAL}. R2P needs space - for N limbs, but the return value indicates how many are produced. - - The most significant limb of {SP, N} must be non-zero. The areas - {R1P, ceil(N/2)} and {SP, N} must be completely separate. The - areas {R2P, N} and {SP, N} must be either identical or completely - separate. - - If the remainder is not wanted then R2P can be `NULL', and in this - case the return value is zero or non-zero according to whether the - remainder would have been zero or non-zero. - - A return value of zero indicates a perfect square. See also - `mpz_perfect_square_p'. - - -- Function: mp_size_t mpn_get_str (unsigned char *STR, int BASE, - mp_limb_t *S1P, mp_size_t S1N) - Convert {S1P, S1N} to a raw unsigned char array at STR in base - BASE, and return the number of characters produced. There may be - leading zeros in the string. The string is not in ASCII; to - convert it to printable format, add the ASCII codes for `0' or - `A', depending on the base and range. BASE can vary from 2 to 256. - - The most significant limb of the input {S1P, S1N} must be - non-zero. The input {S1P, S1N} is clobbered, except when BASE is - a power of 2, in which case it's unchanged. - - The area at STR has to have space for the largest possible number - represented by a S1N long limb array, plus one extra character. - - -- Function: mp_size_t mpn_set_str (mp_limb_t *RP, const unsigned char - *STR, size_t STRSIZE, int BASE) - Convert bytes {STR,STRSIZE} in the given BASE to limbs at RP. - - STR[0] is the most significant byte and STR[STRSIZE-1] is the - least significant. Each byte should be a value in the range 0 to - BASE-1, not an ASCII character. BASE can vary from 2 to 256. - - The return value is the number of limbs written to RP. If the most - significant input byte is non-zero then the high limb at RP will be - non-zero, and only that exact number of limbs will be required - there. - - If the most significant input byte is zero then there may be high - zero limbs written to RP and included in the return value. - - STRSIZE must be at least 1, and no overlap is permitted between - {STR,STRSIZE} and the result at RP. - - -- Function: mp_bitcnt_t mpn_scan0 (const mp_limb_t *S1P, mp_bitcnt_t - BIT) - Scan S1P from bit position BIT for the next clear bit. - - It is required that there be a clear bit within the area at S1P at - or beyond bit position BIT, so that the function has something to - return. - - -- Function: mp_bitcnt_t mpn_scan1 (const mp_limb_t *S1P, mp_bitcnt_t - BIT) - Scan S1P from bit position BIT for the next set bit. - - It is required that there be a set bit within the area at S1P at or - beyond bit position BIT, so that the function has something to - return. - - -- Function: void mpn_random (mp_limb_t *R1P, mp_size_t R1N) - -- Function: void mpn_random2 (mp_limb_t *R1P, mp_size_t R1N) - Generate a random number of length R1N and store it at R1P. The - most significant limb is always non-zero. `mpn_random' generates - uniformly distributed limb data, `mpn_random2' generates long - strings of zeros and ones in the binary representation. - - `mpn_random2' is intended for testing the correctness of the `mpn' - routines. - - -- Function: mp_bitcnt_t mpn_popcount (const mp_limb_t *S1P, mp_size_t - N) - Count the number of set bits in {S1P, N}. - - -- Function: mp_bitcnt_t mpn_hamdist (const mp_limb_t *S1P, const - mp_limb_t *S2P, mp_size_t N) - Compute the hamming distance between {S1P, N} and {S2P, N}, which - is the number of bit positions where the two operands have - different bit values. - - -- Function: int mpn_perfect_square_p (const mp_limb_t *S1P, mp_size_t - N) - Return non-zero iff {S1P, N} is a perfect square. - - -- Function: void mpn_and_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical and of {S1P, N} and {S2P, N}, and - write the result to {RP, N}. - - -- Function: void mpn_ior_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical inclusive or of {S1P, N} and {S2P, N}, - and write the result to {RP, N}. - - -- Function: void mpn_xor_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical exclusive or of {S1P, N} and {S2P, N}, - and write the result to {RP, N}. - - -- Function: void mpn_andn_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical and of {S1P, N} and the bitwise - complement of {S2P, N}, and write the result to {RP, N}. - - -- Function: void mpn_iorn_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical inclusive or of {S1P, N} and the - bitwise complement of {S2P, N}, and write the result to {RP, N}. - - -- Function: void mpn_nand_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical and of {S1P, N} and {S2P, N}, and - write the bitwise complement of the result to {RP, N}. - - -- Function: void mpn_nior_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical inclusive or of {S1P, N} and {S2P, N}, - and write the bitwise complement of the result to {RP, N}. - - -- Function: void mpn_xnor_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical exclusive or of {S1P, N} and {S2P, N}, - and write the bitwise complement of the result to {RP, N}. - - -- Function: void mpn_com (mp_limb_t *RP, const mp_limb_t *SP, - mp_size_t N) - Perform the bitwise complement of {SP, N}, and write the result to - {RP, N}. - - -- Function: void mpn_copyi (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t N) - Copy from {S1P, N} to {RP, N}, increasingly. - - -- Function: void mpn_copyd (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t N) - Copy from {S1P, N} to {RP, N}, decreasingly. - - -- Function: void mpn_zero (mp_limb_t *RP, mp_size_t N) - Zero {RP, N}. - - -8.1 Nails -========= - -*Everything in this section is highly experimental and may disappear or -be subject to incompatible changes in a future version of GMP.* - - Nails are an experimental feature whereby a few bits are left unused -at the top of each `mp_limb_t'. This can significantly improve carry -handling on some processors. - - All the `mpn' functions accepting limb data will expect the nail -bits to be zero on entry, and will return data with the nails similarly -all zero. This applies both to limb vectors and to single limb -arguments. - - Nails can be enabled by configuring with `--enable-nails'. By -default the number of bits will be chosen according to what suits the -host processor, but a particular number can be selected with -`--enable-nails=N'. - - At the mpn level, a nail build is neither source nor binary -compatible with a non-nail build, strictly speaking. But programs -acting on limbs only through the mpn functions are likely to work -equally well with either build, and judicious use of the definitions -below should make any program compatible with either build, at the -source level. - - For the higher level routines, meaning `mpz' etc, a nail build -should be fully source and binary compatible with a non-nail build. - - -- Macro: GMP_NAIL_BITS - -- Macro: GMP_NUMB_BITS - -- Macro: GMP_LIMB_BITS - `GMP_NAIL_BITS' is the number of nail bits, or 0 when nails are - not in use. `GMP_NUMB_BITS' is the number of data bits in a limb. - `GMP_LIMB_BITS' is the total number of bits in an `mp_limb_t'. In - all cases - - GMP_LIMB_BITS == GMP_NAIL_BITS + GMP_NUMB_BITS - - -- Macro: GMP_NAIL_MASK - -- Macro: GMP_NUMB_MASK - Bit masks for the nail and number parts of a limb. - `GMP_NAIL_MASK' is 0 when nails are not in use. - - `GMP_NAIL_MASK' is not often needed, since the nail part can be - obtained with `x >> GMP_NUMB_BITS', and that means one less large - constant, which can help various RISC chips. - - -- Macro: GMP_NUMB_MAX - The maximum value that can be stored in the number part of a limb. - This is the same as `GMP_NUMB_MASK', but can be used for clarity - when doing comparisons rather than bit-wise operations. - - The term "nails" comes from finger or toe nails, which are at the -ends of a limb (arm or leg). "numb" is short for number, but is also -how the developers felt after trying for a long time to come up with -sensible names for these things. - - In the future (the distant future most likely) a non-zero nail might -be permitted, giving non-unique representations for numbers in a limb -vector. This would help vector processors since carries would only -ever need to propagate one or two limbs. - - -File: gmp.info, Node: Random Number Functions, Next: Formatted Output, Prev: Low-level Functions, Up: Top - -9 Random Number Functions -************************* - -Sequences of pseudo-random numbers in GMP are generated using a -variable of type `gmp_randstate_t', which holds an algorithm selection -and a current state. Such a variable must be initialized by a call to -one of the `gmp_randinit' functions, and can be seeded with one of the -`gmp_randseed' functions. - - The functions actually generating random numbers are described in -*Note Integer Random Numbers::, and *Note Miscellaneous Float -Functions::. - - The older style random number functions don't accept a -`gmp_randstate_t' parameter but instead share a global variable of that -type. They use a default algorithm and are currently not seeded -(though perhaps that will change in the future). The new functions -accepting a `gmp_randstate_t' are recommended for applications that -care about randomness. - -* Menu: - -* Random State Initialization:: -* Random State Seeding:: -* Random State Miscellaneous:: - - -File: gmp.info, Node: Random State Initialization, Next: Random State Seeding, Prev: Random Number Functions, Up: Random Number Functions - -9.1 Random State Initialization -=============================== - - -- Function: void gmp_randinit_default (gmp_randstate_t STATE) - Initialize STATE with a default algorithm. This will be a - compromise between speed and randomness, and is recommended for - applications with no special requirements. Currently this is - `gmp_randinit_mt'. - - -- Function: void gmp_randinit_mt (gmp_randstate_t STATE) - Initialize STATE for a Mersenne Twister algorithm. This algorithm - is fast and has good randomness properties. - - -- Function: void gmp_randinit_lc_2exp (gmp_randstate_t STATE, mpz_t - A, unsigned long C, mp_bitcnt_t M2EXP) - Initialize STATE with a linear congruential algorithm X = (A*X + - C) mod 2^M2EXP. - - The low bits of X in this algorithm are not very random. The least - significant bit will have a period no more than 2, and the second - bit no more than 4, etc. For this reason only the high half of - each X is actually used. - - When a random number of more than M2EXP/2 bits is to be generated, - multiple iterations of the recurrence are used and the results - concatenated. - - -- Function: int gmp_randinit_lc_2exp_size (gmp_randstate_t STATE, - mp_bitcnt_t SIZE) - Initialize STATE for a linear congruential algorithm as per - `gmp_randinit_lc_2exp'. A, C and M2EXP are selected from a table, - chosen so that SIZE bits (or more) of each X will be used, ie. - M2EXP/2 >= SIZE. - - If successful the return value is non-zero. If SIZE is bigger - than the table data provides then the return value is zero. The - maximum SIZE currently supported is 128. - - -- Function: void gmp_randinit_set (gmp_randstate_t ROP, - gmp_randstate_t OP) - Initialize ROP with a copy of the algorithm and state from OP. - - -- Function: void gmp_randinit (gmp_randstate_t STATE, - gmp_randalg_t ALG, ...) - *This function is obsolete.* - - Initialize STATE with an algorithm selected by ALG. The only - choice is `GMP_RAND_ALG_LC', which is `gmp_randinit_lc_2exp_size' - described above. A third parameter of type `unsigned long' is - required, this is the SIZE for that function. - `GMP_RAND_ALG_DEFAULT' or 0 are the same as `GMP_RAND_ALG_LC'. - - `gmp_randinit' sets bits in the global variable `gmp_errno' to - indicate an error. `GMP_ERROR_UNSUPPORTED_ARGUMENT' if ALG is - unsupported, or `GMP_ERROR_INVALID_ARGUMENT' if the SIZE parameter - is too big. It may be noted this error reporting is not thread - safe (a good reason to use `gmp_randinit_lc_2exp_size' instead). - - -- Function: void gmp_randclear (gmp_randstate_t STATE) - Free all memory occupied by STATE. - - -File: gmp.info, Node: Random State Seeding, Next: Random State Miscellaneous, Prev: Random State Initialization, Up: Random Number Functions - -9.2 Random State Seeding -======================== - - -- Function: void gmp_randseed (gmp_randstate_t STATE, mpz_t SEED) - -- Function: void gmp_randseed_ui (gmp_randstate_t STATE, - unsigned long int SEED) - Set an initial seed value into STATE. - - The size of a seed determines how many different sequences of - random numbers that it's possible to generate. The "quality" of - the seed is the randomness of a given seed compared to the - previous seed used, and this affects the randomness of separate - number sequences. The method for choosing a seed is critical if - the generated numbers are to be used for important applications, - such as generating cryptographic keys. - - Traditionally the system time has been used to seed, but care - needs to be taken with this. If an application seeds often and - the resolution of the system clock is low, then the same sequence - of numbers might be repeated. Also, the system time is quite easy - to guess, so if unpredictability is required then it should - definitely not be the only source for the seed value. On some - systems there's a special device `/dev/random' which provides - random data better suited for use as a seed. - - -File: gmp.info, Node: Random State Miscellaneous, Prev: Random State Seeding, Up: Random Number Functions - -9.3 Random State Miscellaneous -============================== - - -- Function: unsigned long gmp_urandomb_ui (gmp_randstate_t STATE, - unsigned long N) - Return a uniformly distributed random number of N bits, ie. in the - range 0 to 2^N-1 inclusive. N must be less than or equal to the - number of bits in an `unsigned long'. - - -- Function: unsigned long gmp_urandomm_ui (gmp_randstate_t STATE, - unsigned long N) - Return a uniformly distributed random number in the range 0 to - N-1, inclusive. - - -File: gmp.info, Node: Formatted Output, Next: Formatted Input, Prev: Random Number Functions, Up: Top - -10 Formatted Output -******************* - -* Menu: - -* Formatted Output Strings:: -* Formatted Output Functions:: -* C++ Formatted Output:: - - -File: gmp.info, Node: Formatted Output Strings, Next: Formatted Output Functions, Prev: Formatted Output, Up: Formatted Output - -10.1 Format Strings -=================== - -`gmp_printf' and friends accept format strings similar to the standard C -`printf' (*note Formatted Output: (libc)Formatted Output.). A format -specification is of the form - - % [flags] [width] [.[precision]] [type] conv - - GMP adds types `Z', `Q' and `F' for `mpz_t', `mpq_t' and `mpf_t' -respectively, `M' for `mp_limb_t', and `N' for an `mp_limb_t' array. -`Z', `Q', `M' and `N' behave like integers. `Q' will print a `/' and a -denominator, if needed. `F' behaves like a float. For example, - - mpz_t z; - gmp_printf ("%s is an mpz %Zd\n", "here", z); - - mpq_t q; - gmp_printf ("a hex rational: %#40Qx\n", q); - - mpf_t f; - int n; - gmp_printf ("fixed point mpf %.*Ff with %d digits\n", n, f, n); - - mp_limb_t l; - gmp_printf ("limb %Mu\n", l); - - const mp_limb_t *ptr; - mp_size_t size; - gmp_printf ("limb array %Nx\n", ptr, size); - - For `N' the limbs are expected least significant first, as per the -`mpn' functions (*note Low-level Functions::). A negative size can be -given to print the value as a negative. - - All the standard C `printf' types behave the same as the C library -`printf', and can be freely intermixed with the GMP extensions. In the -current implementation the standard parts of the format string are -simply handed to `printf' and only the GMP extensions handled directly. - - The flags accepted are as follows. GLIBC style ' is only for the -standard C types (not the GMP types), and only if the C library -supports it. - - 0 pad with zeros (rather than spaces) - # show the base with `0x', `0X' or `0' - + always show a sign - (space) show a space or a `-' sign - ' group digits, GLIBC style (not GMP types) - - The optional width and precision can be given as a number within the -format string, or as a `*' to take an extra parameter of type `int', the -same as the standard `printf'. - - The standard types accepted are as follows. `h' and `l' are -portable, the rest will depend on the compiler (or include files) for -the type and the C library for the output. - - h short - hh char - j intmax_t or uintmax_t - l long or wchar_t - ll long long - L long double - q quad_t or u_quad_t - t ptrdiff_t - z size_t - -The GMP types are - - F mpf_t, float conversions - Q mpq_t, integer conversions - M mp_limb_t, integer conversions - N mp_limb_t array, integer conversions - Z mpz_t, integer conversions - - The conversions accepted are as follows. `a' and `A' are always -supported for `mpf_t' but depend on the C library for standard C float -types. `m' and `p' depend on the C library. - - a A hex floats, C99 style - c character - d decimal integer - e E scientific format float - f fixed point float - i same as d - g G fixed or scientific float - m `strerror' string, GLIBC style - n store characters written so far - o octal integer - p pointer - s string - u unsigned integer - x X hex integer - - `o', `x' and `X' are unsigned for the standard C types, but for -types `Z', `Q' and `N' they are signed. `u' is not meaningful for `Z', -`Q' and `N'. - - `M' is a proxy for the C library `l' or `L', according to the size -of `mp_limb_t'. Unsigned conversions will be usual, but a signed -conversion can be used and will interpret the value as a twos complement -negative. - - `n' can be used with any type, even the GMP types. - - Other types or conversions that might be accepted by the C library -`printf' cannot be used through `gmp_printf', this includes for -instance extensions registered with GLIBC `register_printf_function'. -Also currently there's no support for POSIX `$' style numbered arguments -(perhaps this will be added in the future). - - The precision field has it's usual meaning for integer `Z' and float -`F' types, but is currently undefined for `Q' and should not be used -with that. - - `mpf_t' conversions only ever generate as many digits as can be -accurately represented by the operand, the same as `mpf_get_str' does. -Zeros will be used if necessary to pad to the requested precision. This -happens even for an `f' conversion of an `mpf_t' which is an integer, -for instance 2^1024 in an `mpf_t' of 128 bits precision will only -produce about 40 digits, then pad with zeros to the decimal point. An -empty precision field like `%.Fe' or `%.Ff' can be used to specifically -request just the significant digits. - - The decimal point character (or string) is taken from the current -locale settings on systems which provide `localeconv' (*note Locales -and Internationalization: (libc)Locales.). The C library will normally -do the same for standard float output. - - The format string is only interpreted as plain `char's, multibyte -characters are not recognised. Perhaps this will change in the future. - - -File: gmp.info, Node: Formatted Output Functions, Next: C++ Formatted Output, Prev: Formatted Output Strings, Up: Formatted Output - -10.2 Functions -============== - -Each of the following functions is similar to the corresponding C -library function. The basic `printf' forms take a variable argument -list. The `vprintf' forms take an argument pointer, see *Note Variadic -Functions: (libc)Variadic Functions, or `man 3 va_start'. - - It should be emphasised that if a format string is invalid, or the -arguments don't match what the format specifies, then the behaviour of -any of these functions will be unpredictable. GCC format string -checking is not available, since it doesn't recognise the GMP -extensions. - - The file based functions `gmp_printf' and `gmp_fprintf' will return --1 to indicate a write error. Output is not "atomic", so partial -output may be produced if a write error occurs. All the functions can -return -1 if the C library `printf' variant in use returns -1, but this -shouldn't normally occur. - - -- Function: int gmp_printf (const char *FMT, ...) - -- Function: int gmp_vprintf (const char *FMT, va_list AP) - Print to the standard output `stdout'. Return the number of - characters written, or -1 if an error occurred. - - -- Function: int gmp_fprintf (FILE *FP, const char *FMT, ...) - -- Function: int gmp_vfprintf (FILE *FP, const char *FMT, va_list AP) - Print to the stream FP. Return the number of characters written, - or -1 if an error occurred. - - -- Function: int gmp_sprintf (char *BUF, const char *FMT, ...) - -- Function: int gmp_vsprintf (char *BUF, const char *FMT, va_list AP) - Form a null-terminated string in BUF. Return the number of - characters written, excluding the terminating null. - - No overlap is permitted between the space at BUF and the string - FMT. - - These functions are not recommended, since there's no protection - against exceeding the space available at BUF. - - -- Function: int gmp_snprintf (char *BUF, size_t SIZE, const char - *FMT, ...) - -- Function: int gmp_vsnprintf (char *BUF, size_t SIZE, const char - *FMT, va_list AP) - Form a null-terminated string in BUF. No more than SIZE bytes - will be written. To get the full output, SIZE must be enough for - the string and null-terminator. - - The return value is the total number of characters which ought to - have been produced, excluding the terminating null. If RETVAL >= - SIZE then the actual output has been truncated to the first SIZE-1 - characters, and a null appended. - - No overlap is permitted between the region {BUF,SIZE} and the FMT - string. - - Notice the return value is in ISO C99 `snprintf' style. This is - so even if the C library `vsnprintf' is the older GLIBC 2.0.x - style. - - -- Function: int gmp_asprintf (char **PP, const char *FMT, ...) - -- Function: int gmp_vasprintf (char **PP, const char *FMT, va_list AP) - Form a null-terminated string in a block of memory obtained from - the current memory allocation function (*note Custom - Allocation::). The block will be the size of the string and - null-terminator. The address of the block in stored to *PP. The - return value is the number of characters produced, excluding the - null-terminator. - - Unlike the C library `asprintf', `gmp_asprintf' doesn't return -1 - if there's no more memory available, it lets the current allocation - function handle that. - - -- Function: int gmp_obstack_printf (struct obstack *OB, const char - *FMT, ...) - -- Function: int gmp_obstack_vprintf (struct obstack *OB, const char - *FMT, va_list AP) - Append to the current object in OB. The return value is the - number of characters written. A null-terminator is not written. - - FMT cannot be within the current object in OB, since that object - might move as it grows. - - These functions are available only when the C library provides the - obstack feature, which probably means only on GNU systems, see - *Note Obstacks: (libc)Obstacks. - - -File: gmp.info, Node: C++ Formatted Output, Prev: Formatted Output Functions, Up: Formatted Output - -10.3 C++ Formatted Output -========================= - -The following functions are provided in `libgmpxx' (*note Headers and -Libraries::), which is built if C++ support is enabled (*note Build -Options::). Prototypes are available from `'. - - -- Function: ostream& operator<< (ostream& STREAM, mpz_t OP) - Print OP to STREAM, using its `ios' formatting settings. - `ios::width' is reset to 0 after output, the same as the standard - `ostream operator<<' routines do. - - In hex or octal, OP is printed as a signed number, the same as for - decimal. This is unlike the standard `operator<<' routines on - `int' etc, which instead give twos complement. - - -- Function: ostream& operator<< (ostream& STREAM, mpq_t OP) - Print OP to STREAM, using its `ios' formatting settings. - `ios::width' is reset to 0 after output, the same as the standard - `ostream operator<<' routines do. - - Output will be a fraction like `5/9', or if the denominator is 1 - then just a plain integer like `123'. - - In hex or octal, OP is printed as a signed value, the same as for - decimal. If `ios::showbase' is set then a base indicator is shown - on both the numerator and denominator (if the denominator is - required). - - -- Function: ostream& operator<< (ostream& STREAM, mpf_t OP) - Print OP to STREAM, using its `ios' formatting settings. - `ios::width' is reset to 0 after output, the same as the standard - `ostream operator<<' routines do. - - The decimal point follows the standard library float `operator<<', - which on recent systems means the `std::locale' imbued on STREAM. - - Hex and octal are supported, unlike the standard `operator<<' on - `double'. The mantissa will be in hex or octal, the exponent will - be in decimal. For hex the exponent delimiter is an `@'. This is - as per `mpf_out_str'. - - `ios::showbase' is supported, and will put a base on the mantissa, - for example hex `0x1.8' or `0x0.8', or octal `01.4' or `00.4'. - This last form is slightly strange, but at least differentiates - itself from decimal. - - These operators mean that GMP types can be printed in the usual C++ -way, for example, - - mpz_t z; - int n; - ... - cout << "iteration " << n << " value " << z << "\n"; - - But note that `ostream' output (and `istream' input, *note C++ -Formatted Input::) is the only overloading available for the GMP types -and that for instance using `+' with an `mpz_t' will have unpredictable -results. For classes with overloading, see *Note C++ Class Interface::. - - -File: gmp.info, Node: Formatted Input, Next: C++ Class Interface, Prev: Formatted Output, Up: Top - -11 Formatted Input -****************** - -* Menu: - -* Formatted Input Strings:: -* Formatted Input Functions:: -* C++ Formatted Input:: - - -File: gmp.info, Node: Formatted Input Strings, Next: Formatted Input Functions, Prev: Formatted Input, Up: Formatted Input - -11.1 Formatted Input Strings -============================ - -`gmp_scanf' and friends accept format strings similar to the standard C -`scanf' (*note Formatted Input: (libc)Formatted Input.). A format -specification is of the form - - % [flags] [width] [type] conv - - GMP adds types `Z', `Q' and `F' for `mpz_t', `mpq_t' and `mpf_t' -respectively. `Z' and `Q' behave like integers. `Q' will read a `/' -and a denominator, if present. `F' behaves like a float. - - GMP variables don't require an `&' when passed to `gmp_scanf', since -they're already "call-by-reference". For example, - - /* to read say "a(5) = 1234" */ - int n; - mpz_t z; - gmp_scanf ("a(%d) = %Zd\n", &n, z); - - mpq_t q1, q2; - gmp_sscanf ("0377 + 0x10/0x11", "%Qi + %Qi", q1, q2); - - /* to read say "topleft (1.55,-2.66)" */ - mpf_t x, y; - char buf[32]; - gmp_scanf ("%31s (%Ff,%Ff)", buf, x, y); - - All the standard C `scanf' types behave the same as in the C library -`scanf', and can be freely intermixed with the GMP extensions. In the -current implementation the standard parts of the format string are -simply handed to `scanf' and only the GMP extensions handled directly. - - The flags accepted are as follows. `a' and `'' will depend on -support from the C library, and `'' cannot be used with GMP types. - - * read but don't store - a allocate a buffer (string conversions) - ' grouped digits, GLIBC style (not GMP - types) - - The standard types accepted are as follows. `h' and `l' are -portable, the rest will depend on the compiler (or include files) for -the type and the C library for the input. - - h short - hh char - j intmax_t or uintmax_t - l long int, double or wchar_t - ll long long - L long double - q quad_t or u_quad_t - t ptrdiff_t - z size_t - -The GMP types are - - F mpf_t, float conversions - Q mpq_t, integer conversions - Z mpz_t, integer conversions - - The conversions accepted are as follows. `p' and `[' will depend on -support from the C library, the rest are standard. - - c character or characters - d decimal integer - e E f g G float - i integer with base indicator - n characters read so far - o octal integer - p pointer - s string of non-whitespace characters - u decimal integer - x X hex integer - [ string of characters in a set - - `e', `E', `f', `g' and `G' are identical, they all read either fixed -point or scientific format, and either upper or lower case `e' for the -exponent in scientific format. - - C99 style hex float format (`printf %a', *note Formatted Output -Strings::) is always accepted for `mpf_t', but for the standard float -types it will depend on the C library. - - `x' and `X' are identical, both accept both upper and lower case -hexadecimal. - - `o', `u', `x' and `X' all read positive or negative values. For the -standard C types these are described as "unsigned" conversions, but -that merely affects certain overflow handling, negatives are still -allowed (per `strtoul', *note Parsing of Integers: (libc)Parsing of -Integers.). For GMP types there are no overflows, so `d' and `u' are -identical. - - `Q' type reads the numerator and (optional) denominator as given. -If the value might not be in canonical form then `mpq_canonicalize' -must be called before using it in any calculations (*note Rational -Number Functions::). - - `Qi' will read a base specification separately for the numerator and -denominator. For example `0x10/11' would be 16/11, whereas `0x10/0x11' -would be 16/17. - - `n' can be used with any of the types above, even the GMP types. -`*' to suppress assignment is allowed, though in that case it would do -nothing at all. - - Other conversions or types that might be accepted by the C library -`scanf' cannot be used through `gmp_scanf'. - - Whitespace is read and discarded before a field, except for `c' and -`[' conversions. - - For float conversions, the decimal point character (or string) -expected is taken from the current locale settings on systems which -provide `localeconv' (*note Locales and Internationalization: -(libc)Locales.). The C library will normally do the same for standard -float input. - - The format string is only interpreted as plain `char's, multibyte -characters are not recognised. Perhaps this will change in the future. - - -File: gmp.info, Node: Formatted Input Functions, Next: C++ Formatted Input, Prev: Formatted Input Strings, Up: Formatted Input - -11.2 Formatted Input Functions -============================== - -Each of the following functions is similar to the corresponding C -library function. The plain `scanf' forms take a variable argument -list. The `vscanf' forms take an argument pointer, see *Note Variadic -Functions: (libc)Variadic Functions, or `man 3 va_start'. - - It should be emphasised that if a format string is invalid, or the -arguments don't match what the format specifies, then the behaviour of -any of these functions will be unpredictable. GCC format string -checking is not available, since it doesn't recognise the GMP -extensions. - - No overlap is permitted between the FMT string and any of the results -produced. - - -- Function: int gmp_scanf (const char *FMT, ...) - -- Function: int gmp_vscanf (const char *FMT, va_list AP) - Read from the standard input `stdin'. - - -- Function: int gmp_fscanf (FILE *FP, const char *FMT, ...) - -- Function: int gmp_vfscanf (FILE *FP, const char *FMT, va_list AP) - Read from the stream FP. - - -- Function: int gmp_sscanf (const char *S, const char *FMT, ...) - -- Function: int gmp_vsscanf (const char *S, const char *FMT, va_list - AP) - Read from a null-terminated string S. - - The return value from each of these functions is the same as the -standard C99 `scanf', namely the number of fields successfully parsed -and stored. `%n' fields and fields read but suppressed by `*' don't -count towards the return value. - - If end of input (or a file error) is reached before a character for -a field or a literal, and if no previous non-suppressed fields have -matched, then the return value is `EOF' instead of 0. A whitespace -character in the format string is only an optional match and doesn't -induce an `EOF' in this fashion. Leading whitespace read and discarded -for a field don't count as characters for that field. - - For the GMP types, input parsing follows C99 rules, namely one -character of lookahead is used and characters are read while they -continue to meet the format requirements. If this doesn't provide a -complete number then the function terminates, with that field not -stored nor counted towards the return value. For instance with `mpf_t' -an input `1.23e-XYZ' would be read up to the `X' and that character -pushed back since it's not a digit. The string `1.23e-' would then be -considered invalid since an `e' must be followed by at least one digit. - - For the standard C types, in the current implementation GMP calls -the C library `scanf' functions, which might have looser rules about -what constitutes a valid input. - - Note that `gmp_sscanf' is the same as `gmp_fscanf' and only does one -character of lookahead when parsing. Although clearly it could look at -its entire input, it is deliberately made identical to `gmp_fscanf', -the same way C99 `sscanf' is the same as `fscanf'. - - -File: gmp.info, Node: C++ Formatted Input, Prev: Formatted Input Functions, Up: Formatted Input - -11.3 C++ Formatted Input -======================== - -The following functions are provided in `libgmpxx' (*note Headers and -Libraries::), which is built only if C++ support is enabled (*note -Build Options::). Prototypes are available from `'. - - -- Function: istream& operator>> (istream& STREAM, mpz_t ROP) - Read ROP from STREAM, using its `ios' formatting settings. - - -- Function: istream& operator>> (istream& STREAM, mpq_t ROP) - An integer like `123' will be read, or a fraction like `5/9'. No - whitespace is allowed around the `/'. If the fraction is not in - canonical form then `mpq_canonicalize' must be called (*note - Rational Number Functions::) before operating on it. - - As per integer input, an `0' or `0x' base indicator is read when - none of `ios::dec', `ios::oct' or `ios::hex' are set. This is - done separately for numerator and denominator, so that for instance - `0x10/11' is 16/11 and `0x10/0x11' is 16/17. - - -- Function: istream& operator>> (istream& STREAM, mpf_t ROP) - Read ROP from STREAM, using its `ios' formatting settings. - - Hex or octal floats are not supported, but might be in the future, - or perhaps it's best to accept only what the standard float - `operator>>' does. - - Note that digit grouping specified by the `istream' locale is -currently not accepted. Perhaps this will change in the future. - - - These operators mean that GMP types can be read in the usual C++ -way, for example, - - mpz_t z; - ... - cin >> z; - - But note that `istream' input (and `ostream' output, *note C++ -Formatted Output::) is the only overloading available for the GMP types -and that for instance using `+' with an `mpz_t' will have unpredictable -results. For classes with overloading, see *Note C++ Class Interface::. - - -File: gmp.info, Node: C++ Class Interface, Next: BSD Compatible Functions, Prev: Formatted Input, Up: Top - -12 C++ Class Interface -********************** - -This chapter describes the C++ class based interface to GMP. - - All GMP C language types and functions can be used in C++ programs, -since `gmp.h' has `extern "C"' qualifiers, but the class interface -offers overloaded functions and operators which may be more convenient. - - Due to the implementation of this interface, a reasonably recent C++ -compiler is required, one supporting namespaces, partial specialization -of templates and member templates. For GCC this means version 2.91 or -later. - - *Everything described in this chapter is to be considered preliminary -and might be subject to incompatible changes if some unforeseen -difficulty reveals itself.* - -* Menu: - -* C++ Interface General:: -* C++ Interface Integers:: -* C++ Interface Rationals:: -* C++ Interface Floats:: -* C++ Interface Random Numbers:: -* C++ Interface Limitations:: - - -File: gmp.info, Node: C++ Interface General, Next: C++ Interface Integers, Prev: C++ Class Interface, Up: C++ Class Interface - -12.1 C++ Interface General -========================== - -All the C++ classes and functions are available with - - #include - - Programs should be linked with the `libgmpxx' and `libgmp' -libraries. For example, - - g++ mycxxprog.cc -lgmpxx -lgmp - -The classes defined are - - -- Class: mpz_class - -- Class: mpq_class - -- Class: mpf_class - - The standard operators and various standard functions are overloaded -to allow arithmetic with these classes. For example, - - int - main (void) - { - mpz_class a, b, c; - - a = 1234; - b = "-5678"; - c = a+b; - cout << "sum is " << c << "\n"; - cout << "absolute value is " << abs(c) << "\n"; - - return 0; - } - - An important feature of the implementation is that an expression like -`a=b+c' results in a single call to the corresponding `mpz_add', -without using a temporary for the `b+c' part. Expressions which by -their nature imply intermediate values, like `a=b*c+d*e', still use -temporaries though. - - The classes can be freely intermixed in expressions, as can the -classes and the standard types `long', `unsigned long' and `double'. -Smaller types like `int' or `float' can also be intermixed, since C++ -will promote them. - - Note that `bool' is not accepted directly, but must be explicitly -cast to an `int' first. This is because C++ will automatically convert -any pointer to a `bool', so if GMP accepted `bool' it would make all -sorts of invalid class and pointer combinations compile but almost -certainly not do anything sensible. - - Conversions back from the classes to standard C++ types aren't done -automatically, instead member functions like `get_si' are provided (see -the following sections for details). - - Also there are no automatic conversions from the classes to the -corresponding GMP C types, instead a reference to the underlying C -object can be obtained with the following functions, - - -- Function: mpz_t mpz_class::get_mpz_t () - -- Function: mpq_t mpq_class::get_mpq_t () - -- Function: mpf_t mpf_class::get_mpf_t () - - These can be used to call a C function which doesn't have a C++ class -interface. For example to set `a' to the GCD of `b' and `c', - - mpz_class a, b, c; - ... - mpz_gcd (a.get_mpz_t(), b.get_mpz_t(), c.get_mpz_t()); - - In the other direction, a class can be initialized from the -corresponding GMP C type, or assigned to if an explicit constructor is -used. In both cases this makes a copy of the value, it doesn't create -any sort of association. For example, - - mpz_t z; - // ... init and calculate z ... - mpz_class x(z); - mpz_class y; - y = mpz_class (z); - - There are no namespace setups in `gmpxx.h', all types and functions -are simply put into the global namespace. This is what `gmp.h' has -done in the past, and continues to do for compatibility. The extras -provided by `gmpxx.h' follow GMP naming conventions and are unlikely to -clash with anything. - - -File: gmp.info, Node: C++ Interface Integers, Next: C++ Interface Rationals, Prev: C++ Interface General, Up: C++ Class Interface - -12.2 C++ Interface Integers -=========================== - - -- Function: void mpz_class::mpz_class (type N) - Construct an `mpz_class'. All the standard C++ types may be used, - except `long long' and `long double', and all the GMP C++ classes - can be used. Any necessary conversion follows the corresponding C - function, for example `double' follows `mpz_set_d' (*note - Assigning Integers::). - - -- Function: void mpz_class::mpz_class (mpz_t Z) - Construct an `mpz_class' from an `mpz_t'. The value in Z is - copied into the new `mpz_class', there won't be any permanent - association between it and Z. - - -- Function: void mpz_class::mpz_class (const char *S) - -- Function: void mpz_class::mpz_class (const char *S, int BASE = 0) - -- Function: void mpz_class::mpz_class (const string& S) - -- Function: void mpz_class::mpz_class (const string& S, int BASE = 0) - Construct an `mpz_class' converted from a string using - `mpz_set_str' (*note Assigning Integers::). - - If the string is not a valid integer, an `std::invalid_argument' - exception is thrown. The same applies to `operator='. - - -- Function: mpz_class operator/ (mpz_class A, mpz_class D) - -- Function: mpz_class operator% (mpz_class A, mpz_class D) - Divisions involving `mpz_class' round towards zero, as per the - `mpz_tdiv_q' and `mpz_tdiv_r' functions (*note Integer Division::). - This is the same as the C99 `/' and `%' operators. - - The `mpz_fdiv...' or `mpz_cdiv...' functions can always be called - directly if desired. For example, - - mpz_class q, a, d; - ... - mpz_fdiv_q (q.get_mpz_t(), a.get_mpz_t(), d.get_mpz_t()); - - -- Function: mpz_class abs (mpz_class OP1) - -- Function: int cmp (mpz_class OP1, type OP2) - -- Function: int cmp (type OP1, mpz_class OP2) - -- Function: bool mpz_class::fits_sint_p (void) - -- Function: bool mpz_class::fits_slong_p (void) - -- Function: bool mpz_class::fits_sshort_p (void) - -- Function: bool mpz_class::fits_uint_p (void) - -- Function: bool mpz_class::fits_ulong_p (void) - -- Function: bool mpz_class::fits_ushort_p (void) - -- Function: double mpz_class::get_d (void) - -- Function: long mpz_class::get_si (void) - -- Function: string mpz_class::get_str (int BASE = 10) - -- Function: unsigned long mpz_class::get_ui (void) - -- Function: int mpz_class::set_str (const char *STR, int BASE) - -- Function: int mpz_class::set_str (const string& STR, int BASE) - -- Function: int sgn (mpz_class OP) - -- Function: mpz_class sqrt (mpz_class OP) - These functions provide a C++ class interface to the corresponding - GMP C routines. - - `cmp' can be used with any of the classes or the standard C++ - types, except `long long' and `long double'. - - - Overloaded operators for combinations of `mpz_class' and `double' -are provided for completeness, but it should be noted that if the given -`double' is not an integer then the way any rounding is done is -currently unspecified. The rounding might take place at the start, in -the middle, or at the end of the operation, and it might change in the -future. - - Conversions between `mpz_class' and `double', however, are defined -to follow the corresponding C functions `mpz_get_d' and `mpz_set_d'. -And comparisons are always made exactly, as per `mpz_cmp_d'. - - -File: gmp.info, Node: C++ Interface Rationals, Next: C++ Interface Floats, Prev: C++ Interface Integers, Up: C++ Class Interface - -12.3 C++ Interface Rationals -============================ - -In all the following constructors, if a fraction is given then it -should be in canonical form, or if not then `mpq_class::canonicalize' -called. - - -- Function: void mpq_class::mpq_class (type OP) - -- Function: void mpq_class::mpq_class (integer NUM, integer DEN) - Construct an `mpq_class'. The initial value can be a single value - of any type, or a pair of integers (`mpz_class' or standard C++ - integer types) representing a fraction, except that `long long' - and `long double' are not supported. For example, - - mpq_class q (99); - mpq_class q (1.75); - mpq_class q (1, 3); - - -- Function: void mpq_class::mpq_class (mpq_t Q) - Construct an `mpq_class' from an `mpq_t'. The value in Q is - copied into the new `mpq_class', there won't be any permanent - association between it and Q. - - -- Function: void mpq_class::mpq_class (const char *S) - -- Function: void mpq_class::mpq_class (const char *S, int BASE = 0) - -- Function: void mpq_class::mpq_class (const string& S) - -- Function: void mpq_class::mpq_class (const string& S, int BASE = 0) - Construct an `mpq_class' converted from a string using - `mpq_set_str' (*note Initializing Rationals::). - - If the string is not a valid rational, an `std::invalid_argument' - exception is thrown. The same applies to `operator='. - - -- Function: void mpq_class::canonicalize () - Put an `mpq_class' into canonical form, as per *Note Rational - Number Functions::. All arithmetic operators require their - operands in canonical form, and will return results in canonical - form. - - -- Function: mpq_class abs (mpq_class OP) - -- Function: int cmp (mpq_class OP1, type OP2) - -- Function: int cmp (type OP1, mpq_class OP2) - -- Function: double mpq_class::get_d (void) - -- Function: string mpq_class::get_str (int BASE = 10) - -- Function: int mpq_class::set_str (const char *STR, int BASE) - -- Function: int mpq_class::set_str (const string& STR, int BASE) - -- Function: int sgn (mpq_class OP) - These functions provide a C++ class interface to the corresponding - GMP C routines. - - `cmp' can be used with any of the classes or the standard C++ - types, except `long long' and `long double'. - - -- Function: mpz_class& mpq_class::get_num () - -- Function: mpz_class& mpq_class::get_den () - Get a reference to an `mpz_class' which is the numerator or - denominator of an `mpq_class'. This can be used both for read and - write access. If the object returned is modified, it modifies the - original `mpq_class'. - - If direct manipulation might produce a non-canonical value, then - `mpq_class::canonicalize' must be called before further operations. - - -- Function: mpz_t mpq_class::get_num_mpz_t () - -- Function: mpz_t mpq_class::get_den_mpz_t () - Get a reference to the underlying `mpz_t' numerator or denominator - of an `mpq_class'. This can be passed to C functions expecting an - `mpz_t'. Any modifications made to the `mpz_t' will modify the - original `mpq_class'. - - If direct manipulation might produce a non-canonical value, then - `mpq_class::canonicalize' must be called before further operations. - - -- Function: istream& operator>> (istream& STREAM, mpq_class& ROP); - Read ROP from STREAM, using its `ios' formatting settings, the - same as `mpq_t operator>>' (*note C++ Formatted Input::). - - If the ROP read might not be in canonical form then - `mpq_class::canonicalize' must be called. - - -File: gmp.info, Node: C++ Interface Floats, Next: C++ Interface Random Numbers, Prev: C++ Interface Rationals, Up: C++ Class Interface - -12.4 C++ Interface Floats -========================= - -When an expression requires the use of temporary intermediate -`mpf_class' values, like `f=g*h+x*y', those temporaries will have the -same precision as the destination `f'. Explicit constructors can be -used if this doesn't suit. - - -- Function: mpf_class::mpf_class (type OP) - -- Function: mpf_class::mpf_class (type OP, unsigned long PREC) - Construct an `mpf_class'. Any standard C++ type can be used, - except `long long' and `long double', and any of the GMP C++ - classes can be used. - - If PREC is given, the initial precision is that value, in bits. If - PREC is not given, then the initial precision is determined by the - type of OP given. An `mpz_class', `mpq_class', or C++ builtin - type will give the default `mpf' precision (*note Initializing - Floats::). An `mpf_class' or expression will give the precision - of that value. The precision of a binary expression is the higher - of the two operands. - - mpf_class f(1.5); // default precision - mpf_class f(1.5, 500); // 500 bits (at least) - mpf_class f(x); // precision of x - mpf_class f(abs(x)); // precision of x - mpf_class f(-g, 1000); // 1000 bits (at least) - mpf_class f(x+y); // greater of precisions of x and y - - -- Function: void mpf_class::mpf_class (const char *S) - -- Function: void mpf_class::mpf_class (const char *S, unsigned long - PREC, int BASE = 0) - -- Function: void mpf_class::mpf_class (const string& S) - -- Function: void mpf_class::mpf_class (const string& S, unsigned long - PREC, int BASE = 0) - Construct an `mpf_class' converted from a string using - `mpf_set_str' (*note Assigning Floats::). If PREC is given, the - initial precision is that value, in bits. If not, the default - `mpf' precision (*note Initializing Floats::) is used. - - If the string is not a valid float, an `std::invalid_argument' - exception is thrown. The same applies to `operator='. - - -- Function: mpf_class& mpf_class::operator= (type OP) - Convert and store the given OP value to an `mpf_class' object. The - same types are accepted as for the constructors above. - - Note that `operator=' only stores a new value, it doesn't copy or - change the precision of the destination, instead the value is - truncated if necessary. This is the same as `mpf_set' etc. Note - in particular this means for `mpf_class' a copy constructor is not - the same as a default constructor plus assignment. - - mpf_class x (y); // x created with precision of y - - mpf_class x; // x created with default precision - x = y; // value truncated to that precision - - Applications using templated code may need to be careful about the - assumptions the code makes in this area, when working with - `mpf_class' values of various different or non-default precisions. - For instance implementations of the standard `complex' template - have been seen in both styles above, though of course `complex' is - normally only actually specified for use with the builtin float - types. - - -- Function: mpf_class abs (mpf_class OP) - -- Function: mpf_class ceil (mpf_class OP) - -- Function: int cmp (mpf_class OP1, type OP2) - -- Function: int cmp (type OP1, mpf_class OP2) - -- Function: bool mpf_class::fits_sint_p (void) - -- Function: bool mpf_class::fits_slong_p (void) - -- Function: bool mpf_class::fits_sshort_p (void) - -- Function: bool mpf_class::fits_uint_p (void) - -- Function: bool mpf_class::fits_ulong_p (void) - -- Function: bool mpf_class::fits_ushort_p (void) - -- Function: mpf_class floor (mpf_class OP) - -- Function: mpf_class hypot (mpf_class OP1, mpf_class OP2) - -- Function: double mpf_class::get_d (void) - -- Function: long mpf_class::get_si (void) - -- Function: string mpf_class::get_str (mp_exp_t& EXP, int BASE = 10, - size_t DIGITS = 0) - -- Function: unsigned long mpf_class::get_ui (void) - -- Function: int mpf_class::set_str (const char *STR, int BASE) - -- Function: int mpf_class::set_str (const string& STR, int BASE) - -- Function: int sgn (mpf_class OP) - -- Function: mpf_class sqrt (mpf_class OP) - -- Function: mpf_class trunc (mpf_class OP) - These functions provide a C++ class interface to the corresponding - GMP C routines. - - `cmp' can be used with any of the classes or the standard C++ - types, except `long long' and `long double'. - - The accuracy provided by `hypot' is not currently guaranteed. - - -- Function: mp_bitcnt_t mpf_class::get_prec () - -- Function: void mpf_class::set_prec (mp_bitcnt_t PREC) - -- Function: void mpf_class::set_prec_raw (mp_bitcnt_t PREC) - Get or set the current precision of an `mpf_class'. - - The restrictions described for `mpf_set_prec_raw' (*note - Initializing Floats::) apply to `mpf_class::set_prec_raw'. Note - in particular that the `mpf_class' must be restored to it's - allocated precision before being destroyed. This must be done by - application code, there's no automatic mechanism for it. - - -File: gmp.info, Node: C++ Interface Random Numbers, Next: C++ Interface Limitations, Prev: C++ Interface Floats, Up: C++ Class Interface - -12.5 C++ Interface Random Numbers -================================= - - -- Class: gmp_randclass - The C++ class interface to the GMP random number functions uses - `gmp_randclass' to hold an algorithm selection and current state, - as per `gmp_randstate_t'. - - -- Function: gmp_randclass::gmp_randclass (void (*RANDINIT) - (gmp_randstate_t, ...), ...) - Construct a `gmp_randclass', using a call to the given RANDINIT - function (*note Random State Initialization::). The arguments - expected are the same as RANDINIT, but with `mpz_class' instead of - `mpz_t'. For example, - - gmp_randclass r1 (gmp_randinit_default); - gmp_randclass r2 (gmp_randinit_lc_2exp_size, 32); - gmp_randclass r3 (gmp_randinit_lc_2exp, a, c, m2exp); - gmp_randclass r4 (gmp_randinit_mt); - - `gmp_randinit_lc_2exp_size' will fail if the size requested is too - big, an `std::length_error' exception is thrown in that case. - - -- Function: gmp_randclass::gmp_randclass (gmp_randalg_t ALG, ...) - Construct a `gmp_randclass' using the same parameters as - `gmp_randinit' (*note Random State Initialization::). This - function is obsolete and the above RANDINIT style should be - preferred. - - -- Function: void gmp_randclass::seed (unsigned long int S) - -- Function: void gmp_randclass::seed (mpz_class S) - Seed a random number generator. See *note Random Number - Functions::, for how to choose a good seed. - - -- Function: mpz_class gmp_randclass::get_z_bits (unsigned long BITS) - -- Function: mpz_class gmp_randclass::get_z_bits (mpz_class BITS) - Generate a random integer with a specified number of bits. - - -- Function: mpz_class gmp_randclass::get_z_range (mpz_class N) - Generate a random integer in the range 0 to N-1 inclusive. - - -- Function: mpf_class gmp_randclass::get_f () - -- Function: mpf_class gmp_randclass::get_f (unsigned long PREC) - Generate a random float F in the range 0 <= F < 1. F will be to - PREC bits precision, or if PREC is not given then to the precision - of the destination. For example, - - gmp_randclass r; - ... - mpf_class f (0, 512); // 512 bits precision - f = r.get_f(); // random number, 512 bits - - -File: gmp.info, Node: C++ Interface Limitations, Prev: C++ Interface Random Numbers, Up: C++ Class Interface - -12.6 C++ Interface Limitations -============================== - -`mpq_class' and Templated Reading - A generic piece of template code probably won't know that - `mpq_class' requires a `canonicalize' call if inputs read with - `operator>>' might be non-canonical. This can lead to incorrect - results. - - `operator>>' behaves as it does for reasons of efficiency. A - canonicalize can be quite time consuming on large operands, and is - best avoided if it's not necessary. - - But this potential difficulty reduces the usefulness of - `mpq_class'. Perhaps a mechanism to tell `operator>>' what to do - will be adopted in the future, maybe a preprocessor define, a - global flag, or an `ios' flag pressed into service. Or maybe, at - the risk of inconsistency, the `mpq_class' `operator>>' could - canonicalize and leave `mpq_t' `operator>>' not doing so, for use - on those occasions when that's acceptable. Send feedback or - alternate ideas to . - -Subclassing - Subclassing the GMP C++ classes works, but is not currently - recommended. - - Expressions involving subclasses resolve correctly (or seem to), - but in normal C++ fashion the subclass doesn't inherit - constructors and assignments. There's many of those in the GMP - classes, and a good way to reestablish them in a subclass is not - yet provided. - -Templated Expressions - A subtle difficulty exists when using expressions together with - application-defined template functions. Consider the following, - with `T' intended to be some numeric type, - - template - T fun (const T &, const T &); - - When used with, say, plain `mpz_class' variables, it works fine: - `T' is resolved as `mpz_class'. - - mpz_class f(1), g(2); - fun (f, g); // Good - - But when one of the arguments is an expression, it doesn't work. - - mpz_class f(1), g(2), h(3); - fun (f, g+h); // Bad - - This is because `g+h' ends up being a certain expression template - type internal to `gmpxx.h', which the C++ template resolution - rules are unable to automatically convert to `mpz_class'. The - workaround is simply to add an explicit cast. - - mpz_class f(1), g(2), h(3); - fun (f, mpz_class(g+h)); // Good - - Similarly, within `fun' it may be necessary to cast an expression - to type `T' when calling a templated `fun2'. - - template - void fun (T f, T g) - { - fun2 (f, f+g); // Bad - } - - template - void fun (T f, T g) - { - fun2 (f, T(f+g)); // Good - } - - -File: gmp.info, Node: BSD Compatible Functions, Next: Custom Allocation, Prev: C++ Class Interface, Up: Top - -13 Berkeley MP Compatible Functions -*********************************** - -These functions are intended to be fully compatible with the Berkeley MP -library which is available on many BSD derived U*ix systems. The -`--enable-mpbsd' option must be used when building GNU MP to make these -available (*note Installing GMP::). - - The original Berkeley MP library has a usage restriction: you cannot -use the same variable as both source and destination in a single -function call. The compatible functions in GNU MP do not share this -restriction--inputs and outputs may overlap. - - It is not recommended that new programs are written using these -functions. Apart from the incomplete set of functions, the interface -for initializing `MINT' objects is more error prone, and the `pow' -function collides with `pow' in `libm.a'. - - Include the header `mp.h' to get the definition of the necessary -types and functions. If you are on a BSD derived system, make sure to -include GNU `mp.h' if you are going to link the GNU `libmp.a' to your -program. This means that you probably need to give the `-I' -option to the compiler, where `' is the directory where you have -GNU `mp.h'. - - -- Function: MINT * itom (signed short int INITIAL_VALUE) - Allocate an integer consisting of a `MINT' object and dynamic limb - space. Initialize the integer to INITIAL_VALUE. Return a pointer - to the `MINT' object. - - -- Function: MINT * xtom (char *INITIAL_VALUE) - Allocate an integer consisting of a `MINT' object and dynamic limb - space. Initialize the integer from INITIAL_VALUE, a hexadecimal, - null-terminated C string. Return a pointer to the `MINT' object. - - -- Function: void move (MINT *SRC, MINT *DEST) - Set DEST to SRC by copying. Both variables must be previously - initialized. - - -- Function: void madd (MINT *SRC_1, MINT *SRC_2, MINT *DESTINATION) - Add SRC_1 and SRC_2 and put the sum in DESTINATION. - - -- Function: void msub (MINT *SRC_1, MINT *SRC_2, MINT *DESTINATION) - Subtract SRC_2 from SRC_1 and put the difference in DESTINATION. - - -- Function: void mult (MINT *SRC_1, MINT *SRC_2, MINT *DESTINATION) - Multiply SRC_1 and SRC_2 and put the product in DESTINATION. - - -- Function: void mdiv (MINT *DIVIDEND, MINT *DIVISOR, MINT *QUOTIENT, - MINT *REMAINDER) - -- Function: void sdiv (MINT *DIVIDEND, signed short int DIVISOR, MINT - *QUOTIENT, signed short int *REMAINDER) - Set QUOTIENT to DIVIDEND/DIVISOR, and REMAINDER to DIVIDEND mod - DIVISOR. The quotient is rounded towards zero; the remainder has - the same sign as the dividend unless it is zero. - - Some implementations of these functions work differently--or not - at all--for negative arguments. - - -- Function: void msqrt (MINT *OP, MINT *ROOT, MINT *REMAINDER) - Set ROOT to the truncated integer part of the square root of OP, - like `mpz_sqrt'. Set REMAINDER to OP-ROOT*ROOT, i.e. zero if OP - is a perfect square. - - If ROOT and REMAINDER are the same variable, the results are - undefined. - - -- Function: void pow (MINT *BASE, MINT *EXP, MINT *MOD, MINT *DEST) - Set DEST to (BASE raised to EXP) modulo MOD. - - Note that the name `pow' clashes with `pow' from the standard C - math library (*note Exponentiation and Logarithms: (libc)Exponents - and Logarithms.). An application will only be able to use one or - the other. - - -- Function: void rpow (MINT *BASE, signed short int EXP, MINT *DEST) - Set DEST to BASE raised to EXP. - - -- Function: void gcd (MINT *OP1, MINT *OP2, MINT *RES) - Set RES to the greatest common divisor of OP1 and OP2. - - -- Function: int mcmp (MINT *OP1, MINT *OP2) - Compare OP1 and OP2. Return a positive value if OP1 > OP2, zero - if OP1 = OP2, and a negative value if OP1 < OP2. - - -- Function: void min (MINT *DEST) - Input a decimal string from `stdin', and put the read integer in - DEST. SPC and TAB are allowed in the number string, and are - ignored. - - -- Function: void mout (MINT *SRC) - Output SRC to `stdout', as a decimal string. Also output a - newline. - - -- Function: char * mtox (MINT *OP) - Convert OP to a hexadecimal string, and return a pointer to the - string. The returned string is allocated using the default memory - allocation function, `malloc' by default. It will be - `strlen(str)+1' bytes, that being exactly enough for the string - and null-terminator. - - -- Function: void mfree (MINT *OP) - De-allocate, the space used by OP. *This function should only be - passed a value returned by `itom' or `xtom'.* - - -File: gmp.info, Node: Custom Allocation, Next: Language Bindings, Prev: BSD Compatible Functions, Up: Top - -14 Custom Allocation -******************** - -By default GMP uses `malloc', `realloc' and `free' for memory -allocation, and if they fail GMP prints a message to the standard error -output and terminates the program. - - Alternate functions can be specified, to allocate memory in a -different way or to have a different error action on running out of -memory. - - This feature is available in the Berkeley compatibility library -(*note BSD Compatible Functions::) as well as the main GMP library. - - -- Function: void mp_set_memory_functions ( - void *(*ALLOC_FUNC_PTR) (size_t), - void *(*REALLOC_FUNC_PTR) (void *, size_t, size_t), - void (*FREE_FUNC_PTR) (void *, size_t)) - Replace the current allocation functions from the arguments. If - an argument is `NULL', the corresponding default function is used. - - These functions will be used for all memory allocation done by - GMP, apart from temporary space from `alloca' if that function is - available and GMP is configured to use it (*note Build Options::). - - *Be sure to call `mp_set_memory_functions' only when there are no - active GMP objects allocated using the previous memory functions! - Usually that means calling it before any other GMP function.* - - The functions supplied should fit the following declarations: - - -- Function: void * allocate_function (size_t ALLOC_SIZE) - Return a pointer to newly allocated space with at least ALLOC_SIZE - bytes. - - -- Function: void * reallocate_function (void *PTR, size_t OLD_SIZE, - size_t NEW_SIZE) - Resize a previously allocated block PTR of OLD_SIZE bytes to be - NEW_SIZE bytes. - - The block may be moved if necessary or if desired, and in that - case the smaller of OLD_SIZE and NEW_SIZE bytes must be copied to - the new location. The return value is a pointer to the resized - block, that being the new location if moved or just PTR if not. - - PTR is never `NULL', it's always a previously allocated block. - NEW_SIZE may be bigger or smaller than OLD_SIZE. - - -- Function: void free_function (void *PTR, size_t SIZE) - De-allocate the space pointed to by PTR. - - PTR is never `NULL', it's always a previously allocated block of - SIZE bytes. - - A "byte" here means the unit used by the `sizeof' operator. - - The OLD_SIZE parameters to REALLOCATE_FUNCTION and FREE_FUNCTION are -passed for convenience, but of course can be ignored if not needed. -The default functions using `malloc' and friends for instance don't use -them. - - No error return is allowed from any of these functions, if they -return then they must have performed the specified operation. In -particular note that ALLOCATE_FUNCTION or REALLOCATE_FUNCTION mustn't -return `NULL'. - - Getting a different fatal error action is a good use for custom -allocation functions, for example giving a graphical dialog rather than -the default print to `stderr'. How much is possible when genuinely out -of memory is another question though. - - There's currently no defined way for the allocation functions to -recover from an error such as out of memory, they must terminate -program execution. A `longjmp' or throwing a C++ exception will have -undefined results. This may change in the future. - - GMP may use allocated blocks to hold pointers to other allocated -blocks. This will limit the assumptions a conservative garbage -collection scheme can make. - - Since the default GMP allocation uses `malloc' and friends, those -functions will be linked in even if the first thing a program does is an -`mp_set_memory_functions'. It's necessary to change the GMP sources if -this is a problem. - - - -- Function: void mp_get_memory_functions ( - void *(**ALLOC_FUNC_PTR) (size_t), - void *(**REALLOC_FUNC_PTR) (void *, size_t, size_t), - void (**FREE_FUNC_PTR) (void *, size_t)) - Get the current allocation functions, storing function pointers to - the locations given by the arguments. If an argument is `NULL', - that function pointer is not stored. - - For example, to get just the current free function, - - void (*freefunc) (void *, size_t); - - mp_get_memory_functions (NULL, NULL, &freefunc); - - -File: gmp.info, Node: Language Bindings, Next: Algorithms, Prev: Custom Allocation, Up: Top - -15 Language Bindings -******************** - -The following packages and projects offer access to GMP from languages -other than C, though perhaps with varying levels of functionality and -efficiency. - - -C++ - * GMP C++ class interface, *note C++ Class Interface:: - Straightforward interface, expression templates to eliminate - temporaries. - - * ALP `http://www-sop.inria.fr/saga/logiciels/ALP/' - Linear algebra and polynomials using templates. - - * Arithmos `http://www.win.ua.ac.be/~cant/arithmos/' - Rationals with infinities and square roots. - - * CLN `http://www.ginac.de/CLN/' - High level classes for arithmetic. - - * LiDIA `http://www.cdc.informatik.tu-darmstadt.de/TI/LiDIA/' - A C++ library for computational number theory. - - * Linbox `http://www.linalg.org/' - Sparse vectors and matrices. - - * NTL `http://www.shoup.net/ntl/' - A C++ number theory library. - -Fortran - * Omni F77 `http://phase.hpcc.jp/Omni/home.html' - Arbitrary precision floats. - -Haskell - * Glasgow Haskell Compiler `http://www.haskell.org/ghc/' - -Java - * Kaffe `http://www.kaffe.org/' - - * Kissme `http://kissme.sourceforge.net/' - -Lisp - * GNU Common Lisp `http://www.gnu.org/software/gcl/gcl.html' - - * Librep `http://librep.sourceforge.net/' - - * XEmacs (21.5.18 beta and up) `http://www.xemacs.org' - Optional big integers, rationals and floats using GMP. - -M4 - * GNU m4 betas `http://www.seindal.dk/rene/gnu/' - Optionally provides an arbitrary precision `mpeval'. - -ML - * MLton compiler `http://mlton.org/' - -Objective Caml - * MLGMP `http://www.di.ens.fr/~monniaux/programmes.html.en' - - * Numerix `http://pauillac.inria.fr/~quercia/' - Optionally using GMP. - -Oz - * Mozart `http://www.mozart-oz.org/' - -Pascal - * GNU Pascal Compiler `http://www.gnu-pascal.de/' - GMP unit. - - * Numerix `http://pauillac.inria.fr/~quercia/' - For Free Pascal, optionally using GMP. - -Perl - * GMP module, see `demos/perl' in the GMP sources (*note - Demonstration Programs::). - - * Math::GMP `http://www.cpan.org/' - Compatible with Math::BigInt, but not as many functions as - the GMP module above. - - * Math::BigInt::GMP `http://www.cpan.org/' - Plug Math::GMP into normal Math::BigInt operations. - -Pike - * mpz module in the standard distribution, - `http://pike.ida.liu.se/' - -Prolog - * SWI Prolog `http://www.swi-prolog.org/' - Arbitrary precision floats. - -Python - * mpz module in the standard distribution, - `http://www.python.org/' - - * GMPY `http://gmpy.sourceforge.net/' - -Scheme - * GNU Guile (upcoming 1.8) - `http://www.gnu.org/software/guile/guile.html' - - * RScheme `http://www.rscheme.org/' - - * STklos `http://www.stklos.org/' - -Smalltalk - * GNU Smalltalk - `http://www.smalltalk.org/versions/GNUSmalltalk.html' - -Other - * Axiom `http://savannah.nongnu.org/projects/axiom' - Computer algebra using GCL. - - * DrGenius `http://drgenius.seul.org/' - Geometry system and mathematical programming language. - - * GiNaC `http://www.ginac.de/' - C++ computer algebra using CLN. - - * GOO `http://www.googoogaga.org/' - Dynamic object oriented language. - - * Maxima `http://www.ma.utexas.edu/users/wfs/maxima.html' - Macsyma computer algebra using GCL. - - * Q `http://q-lang.sourceforge.net/' - Equational programming system. - - * Regina `http://regina.sourceforge.net/' - Topological calculator. - - * Yacas `http://www.xs4all.nl/~apinkus/yacas.html' - Yet another computer algebra system. - - - -File: gmp.info, Node: Algorithms, Next: Internals, Prev: Language Bindings, Up: Top - -16 Algorithms -************* - -This chapter is an introduction to some of the algorithms used for -various GMP operations. The code is likely to be hard to understand -without knowing something about the algorithms. - - Some GMP internals are mentioned, but applications that expect to be -compatible with future GMP releases should take care to use only the -documented functions. - -* Menu: - -* Multiplication Algorithms:: -* Division Algorithms:: -* Greatest Common Divisor Algorithms:: -* Powering Algorithms:: -* Root Extraction Algorithms:: -* Radix Conversion Algorithms:: -* Other Algorithms:: -* Assembly Coding:: - - -File: gmp.info, Node: Multiplication Algorithms, Next: Division Algorithms, Prev: Algorithms, Up: Algorithms - -16.1 Multiplication -=================== - -NxN limb multiplications and squares are done using one of five -algorithms, as the size N increases. - - Algorithm Threshold - Basecase (none) - Karatsuba `MUL_TOOM22_THRESHOLD' - Toom-3 `MUL_TOOM33_THRESHOLD' - Toom-4 `MUL_TOOM44_THRESHOLD' - FFT `MUL_FFT_THRESHOLD' - - Similarly for squaring, with the `SQR' thresholds. - - NxM multiplications of operands with different sizes above -`MUL_TOOM22_THRESHOLD' are currently done by special Toom-inspired -algorithms or directly with FFT, depending on operand size (*note -Unbalanced Multiplication::). - -* Menu: - -* Basecase Multiplication:: -* Karatsuba Multiplication:: -* Toom 3-Way Multiplication:: -* Toom 4-Way Multiplication:: -* FFT Multiplication:: -* Other Multiplication:: -* Unbalanced Multiplication:: - - -File: gmp.info, Node: Basecase Multiplication, Next: Karatsuba Multiplication, Prev: Multiplication Algorithms, Up: Multiplication Algorithms - -16.1.1 Basecase Multiplication ------------------------------- - -Basecase NxM multiplication is a straightforward rectangular set of -cross-products, the same as long multiplication done by hand and for -that reason sometimes known as the schoolbook or grammar school method. -This is an O(N*M) algorithm. See Knuth section 4.3.1 algorithm M -(*note References::), and the `mpn/generic/mul_basecase.c' code. - - Assembly implementations of `mpn_mul_basecase' are essentially the -same as the generic C code, but have all the usual assembly tricks and -obscurities introduced for speed. - - A square can be done in roughly half the time of a multiply, by -using the fact that the cross products above and below the diagonal are -the same. A triangle of products below the diagonal is formed, doubled -(left shift by one bit), and then the products on the diagonal added. -This can be seen in `mpn/generic/sqr_basecase.c'. Again the assembly -implementations take essentially the same approach. - - u0 u1 u2 u3 u4 - +---+---+---+---+---+ - u0 | d | | | | | - +---+---+---+---+---+ - u1 | | d | | | | - +---+---+---+---+---+ - u2 | | | d | | | - +---+---+---+---+---+ - u3 | | | | d | | - +---+---+---+---+---+ - u4 | | | | | d | - +---+---+---+---+---+ - - In practice squaring isn't a full 2x faster than multiplying, it's -usually around 1.5x. Less than 1.5x probably indicates -`mpn_sqr_basecase' wants improving on that CPU. - - On some CPUs `mpn_mul_basecase' can be faster than the generic C -`mpn_sqr_basecase' on some small sizes. `SQR_BASECASE_THRESHOLD' is -the size at which to use `mpn_sqr_basecase', this will be zero if that -routine should be used always. - - -File: gmp.info, Node: Karatsuba Multiplication, Next: Toom 3-Way Multiplication, Prev: Basecase Multiplication, Up: Multiplication Algorithms - -16.1.2 Karatsuba Multiplication -------------------------------- - -The Karatsuba multiplication algorithm is described in Knuth section -4.3.3 part A, and various other textbooks. A brief description is -given here. - - The inputs x and y are treated as each split into two parts of equal -length (or the most significant part one limb shorter if N is odd). - - high low - +----------+----------+ - | x1 | x0 | - +----------+----------+ - - +----------+----------+ - | y1 | y0 | - +----------+----------+ - - Let b be the power of 2 where the split occurs, ie. if x0 is k limbs -(y0 the same) then b=2^(k*mp_bits_per_limb). With that x=x1*b+x0 and -y=y1*b+y0, and the following holds, - - x*y = (b^2+b)*x1*y1 - b*(x1-x0)*(y1-y0) + (b+1)*x0*y0 - - This formula means doing only three multiplies of (N/2)x(N/2) limbs, -whereas a basecase multiply of NxN limbs is equivalent to four -multiplies of (N/2)x(N/2). The factors (b^2+b) etc represent the -positions where the three products must be added. - - high low - +--------+--------+ +--------+--------+ - | x1*y1 | | x0*y0 | - +--------+--------+ +--------+--------+ - +--------+--------+ - add | x1*y1 | - +--------+--------+ - +--------+--------+ - add | x0*y0 | - +--------+--------+ - +--------+--------+ - sub | (x1-x0)*(y1-y0) | - +--------+--------+ - - The term (x1-x0)*(y1-y0) is best calculated as an absolute value, -and the sign used to choose to add or subtract. Notice the sum -high(x0*y0)+low(x1*y1) occurs twice, so it's possible to do 5*k limb -additions, rather than 6*k, but in GMP extra function call overheads -outweigh the saving. - - Squaring is similar to multiplying, but with x=y the formula reduces -to an equivalent with three squares, - - x^2 = (b^2+b)*x1^2 - b*(x1-x0)^2 + (b+1)*x0^2 - - The final result is accumulated from those three squares the same -way as for the three multiplies above. The middle term (x1-x0)^2 is now -always positive. - - A similar formula for both multiplying and squaring can be -constructed with a middle term (x1+x0)*(y1+y0). But those sums can -exceed k limbs, leading to more carry handling and additions than the -form above. - - Karatsuba multiplication is asymptotically an O(N^1.585) algorithm, -the exponent being log(3)/log(2), representing 3 multiplies each 1/2 -the size of the inputs. This is a big improvement over the basecase -multiply at O(N^2) and the advantage soon overcomes the extra additions -Karatsuba performs. `MUL_TOOM22_THRESHOLD' can be as little as 10 -limbs. The `SQR' threshold is usually about twice the `MUL'. - - The basecase algorithm will take a time of the form M(N) = a*N^2 + -b*N + c and the Karatsuba algorithm K(N) = 3*M(N/2) + d*N + e, which -expands to K(N) = 3/4*a*N^2 + 3/2*b*N + 3*c + d*N + e. The factor 3/4 -for a means per-crossproduct speedups in the basecase code will -increase the threshold since they benefit M(N) more than K(N). And -conversely the 3/2 for b means linear style speedups of b will increase -the threshold since they benefit K(N) more than M(N). The latter can -be seen for instance when adding an optimized `mpn_sqr_diagonal' to -`mpn_sqr_basecase'. Of course all speedups reduce total time, and in -that sense the algorithm thresholds are merely of academic interest. - - -File: gmp.info, Node: Toom 3-Way Multiplication, Next: Toom 4-Way Multiplication, Prev: Karatsuba Multiplication, Up: Multiplication Algorithms - -16.1.3 Toom 3-Way Multiplication --------------------------------- - -The Karatsuba formula is the simplest case of a general approach to -splitting inputs that leads to both Toom and FFT algorithms. A -description of Toom can be found in Knuth section 4.3.3, with an -example 3-way calculation after Theorem A. The 3-way form used in GMP -is described here. - - The operands are each considered split into 3 pieces of equal length -(or the most significant part 1 or 2 limbs shorter than the other two). - - high low - +----------+----------+----------+ - | x2 | x1 | x0 | - +----------+----------+----------+ - - +----------+----------+----------+ - | y2 | y1 | y0 | - +----------+----------+----------+ - -These parts are treated as the coefficients of two polynomials - - X(t) = x2*t^2 + x1*t + x0 - Y(t) = y2*t^2 + y1*t + y0 - - Let b equal the power of 2 which is the size of the x0, x1, y0 and -y1 pieces, ie. if they're k limbs each then b=2^(k*mp_bits_per_limb). -With this x=X(b) and y=Y(b). - - Let a polynomial W(t)=X(t)*Y(t) and suppose its coefficients are - - W(t) = w4*t^4 + w3*t^3 + w2*t^2 + w1*t + w0 - - The w[i] are going to be determined, and when they are they'll give -the final result using w=W(b), since x*y=X(b)*Y(b)=W(b). The -coefficients will be roughly b^2 each, and the final W(b) will be an -addition like, - - high low - +-------+-------+ - | w4 | - +-------+-------+ - +--------+-------+ - | w3 | - +--------+-------+ - +--------+-------+ - | w2 | - +--------+-------+ - +--------+-------+ - | w1 | - +--------+-------+ - +-------+-------+ - | w0 | - +-------+-------+ - - The w[i] coefficients could be formed by a simple set of cross -products, like w4=x2*y2, w3=x2*y1+x1*y2, w2=x2*y0+x1*y1+x0*y2 etc, but -this would need all nine x[i]*y[j] for i,j=0,1,2, and would be -equivalent merely to a basecase multiply. Instead the following -approach is used. - - X(t) and Y(t) are evaluated and multiplied at 5 points, giving -values of W(t) at those points. In GMP the following points are used, - - Point Value - t=0 x0 * y0, which gives w0 immediately - t=1 (x2+x1+x0) * (y2+y1+y0) - t=-1 (x2-x1+x0) * (y2-y1+y0) - t=2 (4*x2+2*x1+x0) * (4*y2+2*y1+y0) - t=inf x2 * y2, which gives w4 immediately - - At t=-1 the values can be negative and that's handled using the -absolute values and tracking the sign separately. At t=inf the value -is actually X(t)*Y(t)/t^4 in the limit as t approaches infinity, but -it's much easier to think of as simply x2*y2 giving w4 immediately -(much like x0*y0 at t=0 gives w0 immediately). - - Each of the points substituted into W(t)=w4*t^4+...+w0 gives a -linear combination of the w[i] coefficients, and the value of those -combinations has just been calculated. - - W(0) = w0 - W(1) = w4 + w3 + w2 + w1 + w0 - W(-1) = w4 - w3 + w2 - w1 + w0 - W(2) = 16*w4 + 8*w3 + 4*w2 + 2*w1 + w0 - W(inf) = w4 - - This is a set of five equations in five unknowns, and some -elementary linear algebra quickly isolates each w[i]. This involves -adding or subtracting one W(t) value from another, and a couple of -divisions by powers of 2 and one division by 3, the latter using the -special `mpn_divexact_by3' (*note Exact Division::). - - The conversion of W(t) values to the coefficients is interpolation. -A polynomial of degree 4 like W(t) is uniquely determined by values -known at 5 different points. The points are arbitrary and can be -chosen to make the linear equations come out with a convenient set of -steps for quickly isolating the w[i]. - - Squaring follows the same procedure as multiplication, but there's -only one X(t) and it's evaluated at the 5 points, and those values -squared to give values of W(t). The interpolation is then identical, -and in fact the same `toom3_interpolate' subroutine is used for both -squaring and multiplying. - - Toom-3 is asymptotically O(N^1.465), the exponent being -log(5)/log(3), representing 5 recursive multiplies of 1/3 the original -size each. This is an improvement over Karatsuba at O(N^1.585), though -Toom does more work in the evaluation and interpolation and so it only -realizes its advantage above a certain size. - - Near the crossover between Toom-3 and Karatsuba there's generally a -range of sizes where the difference between the two is small. -`MUL_TOOM33_THRESHOLD' is a somewhat arbitrary point in that range and -successive runs of the tune program can give different values due to -small variations in measuring. A graph of time versus size for the two -shows the effect, see `tune/README'. - - At the fairly small sizes where the Toom-3 thresholds occur it's -worth remembering that the asymptotic behaviour for Karatsuba and -Toom-3 can't be expected to make accurate predictions, due of course to -the big influence of all sorts of overheads, and the fact that only a -few recursions of each are being performed. Even at large sizes -there's a good chance machine dependent effects like cache architecture -will mean actual performance deviates from what might be predicted. - - The formula given for the Karatsuba algorithm (*note Karatsuba -Multiplication::) has an equivalent for Toom-3 involving only five -multiplies, but this would be complicated and unenlightening. - - An alternate view of Toom-3 can be found in Zuras (*note -References::), using a vector to represent the x and y splits and a -matrix multiplication for the evaluation and interpolation stages. The -matrix inverses are not meant to be actually used, and they have -elements with values much greater than in fact arise in the -interpolation steps. The diagram shown for the 3-way is attractive, -but again doesn't have to be implemented that way and for example with -a bit of rearrangement just one division by 6 can be done. - - -File: gmp.info, Node: Toom 4-Way Multiplication, Next: FFT Multiplication, Prev: Toom 3-Way Multiplication, Up: Multiplication Algorithms - -16.1.4 Toom 4-Way Multiplication --------------------------------- - -Karatsuba and Toom-3 split the operands into 2 and 3 coefficients, -respectively. Toom-4 analogously splits the operands into 4 -coefficients. Using the notation from the section on Toom-3 -multiplication, we form two polynomials: - - X(t) = x3*t^3 + x2*t^2 + x1*t + x0 - Y(t) = y3*t^3 + y2*t^2 + y1*t + y0 - - X(t) and Y(t) are evaluated and multiplied at 7 points, giving -values of W(t) at those points. In GMP the following points are used, - - Point Value - t=0 x0 * y0, which gives w0 immediately - t=1/2 (x3+2*x2+4*x1+8*x0) * (y3+2*y2+4*y1+8*y0) - t=-1/2 (-x3+2*x2-4*x1+8*x0) * (-y3+2*y2-4*y1+8*y0) - t=1 (x3+x2+x1+x0) * (y3+y2+y1+y0) - t=-1 (-x3+x2-x1+x0) * (-y3+y2-y1+y0) - t=2 (8*x3+4*x2+2*x1+x0) * (8*y3+4*y2+2*y1+y0) - t=inf x3 * y3, which gives w6 immediately - - The number of additions and subtractions for Toom-4 is much larger -than for Toom-3. But several subexpressions occur multiple times, for -example x2+x0, occurs for both t=1 and t=-1. - - Toom-4 is asymptotically O(N^1.404), the exponent being -log(7)/log(4), representing 7 recursive multiplies of 1/4 the original -size each. - - -File: gmp.info, Node: FFT Multiplication, Next: Other Multiplication, Prev: Toom 4-Way Multiplication, Up: Multiplication Algorithms - -16.1.5 FFT Multiplication -------------------------- - -At large to very large sizes a Fermat style FFT multiplication is used, -following Scho"nhage and Strassen (*note References::). Descriptions -of FFTs in various forms can be found in many textbooks, for instance -Knuth section 4.3.3 part C or Lipson chapter IX. A brief description -of the form used in GMP is given here. - - The multiplication done is x*y mod 2^N+1, for a given N. A full -product x*y is obtained by choosing N>=bits(x)+bits(y) and padding x -and y with high zero limbs. The modular product is the native form for -the algorithm, so padding to get a full product is unavoidable. - - The algorithm follows a split, evaluate, pointwise multiply, -interpolate and combine similar to that described above for Karatsuba -and Toom-3. A k parameter controls the split, with an FFT-k splitting -into 2^k pieces of M=N/2^k bits each. N must be a multiple of -(2^k)*mp_bits_per_limb so the split falls on limb boundaries, avoiding -bit shifts in the split and combine stages. - - The evaluations, pointwise multiplications, and interpolation, are -all done modulo 2^N'+1 where N' is 2M+k+3 rounded up to a multiple of -2^k and of `mp_bits_per_limb'. The results of interpolation will be -the following negacyclic convolution of the input pieces, and the -choice of N' ensures these sums aren't truncated. - - --- - \ b - w[n] = / (-1) * x[i] * y[j] - --- - i+j==b*2^k+n - b=0,1 - - The points used for the evaluation are g^i for i=0 to 2^k-1 where -g=2^(2N'/2^k). g is a 2^k'th root of unity mod 2^N'+1, which produces -necessary cancellations at the interpolation stage, and it's also a -power of 2 so the fast Fourier transforms used for the evaluation and -interpolation do only shifts, adds and negations. - - The pointwise multiplications are done modulo 2^N'+1 and either -recurse into a further FFT or use a plain multiplication (Toom-3, -Karatsuba or basecase), whichever is optimal at the size N'. The -interpolation is an inverse fast Fourier transform. The resulting set -of sums of x[i]*y[j] are added at appropriate offsets to give the final -result. - - Squaring is the same, but x is the only input so it's one transform -at the evaluate stage and the pointwise multiplies are squares. The -interpolation is the same. - - For a mod 2^N+1 product, an FFT-k is an O(N^(k/(k-1))) algorithm, -the exponent representing 2^k recursed modular multiplies each -1/2^(k-1) the size of the original. Each successive k is an asymptotic -improvement, but overheads mean each is only faster at bigger and -bigger sizes. In the code, `MUL_FFT_TABLE' and `SQR_FFT_TABLE' are the -thresholds where each k is used. Each new k effectively swaps some -multiplying for some shifts, adds and overheads. - - A mod 2^N+1 product can be formed with a normal NxN->2N bit multiply -plus a subtraction, so an FFT and Toom-3 etc can be compared directly. -A k=4 FFT at O(N^1.333) can be expected to be the first faster than -Toom-3 at O(N^1.465). In practice this is what's found, with -`MUL_FFT_MODF_THRESHOLD' and `SQR_FFT_MODF_THRESHOLD' being between 300 -and 1000 limbs, depending on the CPU. So far it's been found that only -very large FFTs recurse into pointwise multiplies above these sizes. - - When an FFT is to give a full product, the change of N to 2N doesn't -alter the theoretical complexity for a given k, but for the purposes of -considering where an FFT might be first used it can be assumed that the -FFT is recursing into a normal multiply and that on that basis it's -doing 2^k recursed multiplies each 1/2^(k-2) the size of the inputs, -making it O(N^(k/(k-2))). This would mean k=7 at O(N^1.4) would be the -first FFT faster than Toom-3. In practice `MUL_FFT_THRESHOLD' and -`SQR_FFT_THRESHOLD' have been found to be in the k=8 range, somewhere -between 3000 and 10000 limbs. - - The way N is split into 2^k pieces and then 2M+k+3 is rounded up to -a multiple of 2^k and `mp_bits_per_limb' means that when -2^k>=mp_bits_per_limb the effective N is a multiple of 2^(2k-1) bits. -The +k+3 means some values of N just under such a multiple will be -rounded to the next. The complexity calculations above assume that a -favourable size is used, meaning one which isn't padded through -rounding, and it's also assumed that the extra +k+3 bits are negligible -at typical FFT sizes. - - The practical effect of the 2^(2k-1) constraint is to introduce a -step-effect into measured speeds. For example k=8 will round N up to a -multiple of 32768 bits, so for a 32-bit limb there'll be 512 limb -groups of sizes for which `mpn_mul_n' runs at the same speed. Or for -k=9 groups of 2048 limbs, k=10 groups of 8192 limbs, etc. In practice -it's been found each k is used at quite small multiples of its size -constraint and so the step effect is quite noticeable in a time versus -size graph. - - The threshold determinations currently measure at the mid-points of -size steps, but this is sub-optimal since at the start of a new step it -can happen that it's better to go back to the previous k for a while. -Something more sophisticated for `MUL_FFT_TABLE' and `SQR_FFT_TABLE' -will be needed. - - -File: gmp.info, Node: Other Multiplication, Next: Unbalanced Multiplication, Prev: FFT Multiplication, Up: Multiplication Algorithms - -16.1.6 Other Multiplication ---------------------------- - -The Toom algorithms described above (*note Toom 3-Way Multiplication::, -*note Toom 4-Way Multiplication::) generalizes to split into an -arbitrary number of pieces, as per Knuth section 4.3.3 algorithm C. -This is not currently used. The notes here are merely for interest. - - In general a split into r+1 pieces is made, and evaluations and -pointwise multiplications done at 2*r+1 points. A 4-way split does 7 -pointwise multiplies, 5-way does 9, etc. Asymptotically an (r+1)-way -algorithm is O(N^(log(2*r+1)/log(r+1))). Only the pointwise -multiplications count towards big-O complexity, but the time spent in -the evaluate and interpolate stages grows with r and has a significant -practical impact, with the asymptotic advantage of each r realized only -at bigger and bigger sizes. The overheads grow as O(N*r), whereas in -an r=2^k FFT they grow only as O(N*log(r)). - - Knuth algorithm C evaluates at points 0,1,2,...,2*r, but exercise 4 -uses -r,...,0,...,r and the latter saves some small multiplies in the -evaluate stage (or rather trades them for additions), and has a further -saving of nearly half the interpolate steps. The idea is to separate -odd and even final coefficients and then perform algorithm C steps C7 -and C8 on them separately. The divisors at step C7 become j^2 and the -multipliers at C8 become 2*t*j-j^2. - - Splitting odd and even parts through positive and negative points -can be thought of as using -1 as a square root of unity. If a 4th root -of unity was available then a further split and speedup would be -possible, but no such root exists for plain integers. Going to complex -integers with i=sqrt(-1) doesn't help, essentially because in Cartesian -form it takes three real multiplies to do a complex multiply. The -existence of 2^k'th roots of unity in a suitable ring or field lets the -fast Fourier transform keep splitting and get to O(N*log(r)). - - Floating point FFTs use complex numbers approximating Nth roots of -unity. Some processors have special support for such FFTs. But these -are not used in GMP since it's very difficult to guarantee an exact -result (to some number of bits). An occasional difference of 1 in the -last bit might not matter to a typical signal processing algorithm, but -is of course of vital importance to GMP. - - -File: gmp.info, Node: Unbalanced Multiplication, Prev: Other Multiplication, Up: Multiplication Algorithms - -16.1.7 Unbalanced Multiplication --------------------------------- - -Multiplication of operands with different sizes, both below -`MUL_TOOM22_THRESHOLD' are done with plain schoolbook multiplication -(*note Basecase Multiplication::). - - For really large operands, we invoke FFT directly. - - For operands between these sizes, we use Toom inspired algorithms -suggested by Alberto Zanoni and Marco Bodrato. The idea is to split -the operands into polynomials of different degree. GMP currently -splits the smaller operand onto 2 coefficients, i.e., a polynomial of -degree 1, but the larger operand can be split into 2, 3, or 4 -coefficients, i.e., a polynomial of degree 1 to 3. - - -File: gmp.info, Node: Division Algorithms, Next: Greatest Common Divisor Algorithms, Prev: Multiplication Algorithms, Up: Algorithms - -16.2 Division Algorithms -======================== - -* Menu: - -* Single Limb Division:: -* Basecase Division:: -* Divide and Conquer Division:: -* Block-Wise Barrett Division:: -* Exact Division:: -* Exact Remainder:: -* Small Quotient Division:: - - -File: gmp.info, Node: Single Limb Division, Next: Basecase Division, Prev: Division Algorithms, Up: Division Algorithms - -16.2.1 Single Limb Division ---------------------------- - -Nx1 division is implemented using repeated 2x1 divisions from high to -low, either with a hardware divide instruction or a multiplication by -inverse, whichever is best on a given CPU. - - The multiply by inverse follows "Improved division by invariant -integers" by Mo"ller and Granlund (*note References::) and is -implemented as `udiv_qrnnd_preinv' in `gmp-impl.h'. The idea is to -have a fixed-point approximation to 1/d (see `invert_limb') and then -multiply by the high limb (plus one bit) of the dividend to get a -quotient q. With d normalized (high bit set), q is no more than 1 too -small. Subtracting q*d from the dividend gives a remainder, and -reveals whether q or q-1 is correct. - - The result is a division done with two multiplications and four or -five arithmetic operations. On CPUs with low latency multipliers this -can be much faster than a hardware divide, though the cost of -calculating the inverse at the start may mean it's only better on -inputs bigger than say 4 or 5 limbs. - - When a divisor must be normalized, either for the generic C -`__udiv_qrnnd_c' or the multiply by inverse, the division performed is -actually a*2^k by d*2^k where a is the dividend and k is the power -necessary to have the high bit of d*2^k set. The bit shifts for the -dividend are usually accomplished "on the fly" meaning by extracting -the appropriate bits at each step. Done this way the quotient limbs -come out aligned ready to store. When only the remainder is wanted, an -alternative is to take the dividend limbs unshifted and calculate r = a -mod d*2^k followed by an extra final step r*2^k mod d*2^k. This can -help on CPUs with poor bit shifts or few registers. - - The multiply by inverse can be done two limbs at a time. The -calculation is basically the same, but the inverse is two limbs and the -divisor treated as if padded with a low zero limb. This means more -work, since the inverse will need a 2x2 multiply, but the four 1x1s to -do that are independent and can therefore be done partly or wholly in -parallel. Likewise for a 2x1 calculating q*d. The net effect is to -process two limbs with roughly the same two multiplies worth of latency -that one limb at a time gives. This extends to 3 or 4 limbs at a time, -though the extra work to apply the inverse will almost certainly soon -reach the limits of multiplier throughput. - - A similar approach in reverse can be taken to process just half a -limb at a time if the divisor is only a half limb. In this case the -1x1 multiply for the inverse effectively becomes two (1/2)x1 for each -limb, which can be a saving on CPUs with a fast half limb multiply, or -in fact if the only multiply is a half limb, and especially if it's not -pipelined. - - -File: gmp.info, Node: Basecase Division, Next: Divide and Conquer Division, Prev: Single Limb Division, Up: Division Algorithms - -16.2.2 Basecase Division ------------------------- - -Basecase NxM division is like long division done by hand, but in base -2^mp_bits_per_limb. See Knuth section 4.3.1 algorithm D, and -`mpn/generic/sb_divrem_mn.c'. - - Briefly stated, while the dividend remains larger than the divisor, -a high quotient limb is formed and the Nx1 product q*d subtracted at -the top end of the dividend. With a normalized divisor (most -significant bit set), each quotient limb can be formed with a 2x1 -division and a 1x1 multiplication plus some subtractions. The 2x1 -division is by the high limb of the divisor and is done either with a -hardware divide or a multiply by inverse (the same as in *Note Single -Limb Division::) whichever is faster. Such a quotient is sometimes one -too big, requiring an addback of the divisor, but that happens rarely. - - With Q=N-M being the number of quotient limbs, this is an O(Q*M) -algorithm and will run at a speed similar to a basecase QxM -multiplication, differing in fact only in the extra multiply and divide -for each of the Q quotient limbs. - - -File: gmp.info, Node: Divide and Conquer Division, Next: Block-Wise Barrett Division, Prev: Basecase Division, Up: Division Algorithms - -16.2.3 Divide and Conquer Division ----------------------------------- - -For divisors larger than `DC_DIV_QR_THRESHOLD', division is done by -dividing. Or to be precise by a recursive divide and conquer algorithm -based on work by Moenck and Borodin, Jebelean, and Burnikel and Ziegler -(*note References::). - - The algorithm consists essentially of recognising that a 2NxN -division can be done with the basecase division algorithm (*note -Basecase Division::), but using N/2 limbs as a base, not just a single -limb. This way the multiplications that arise are (N/2)x(N/2) and can -take advantage of Karatsuba and higher multiplication algorithms (*note -Multiplication Algorithms::). The two "digits" of the quotient are -formed by recursive Nx(N/2) divisions. - - If the (N/2)x(N/2) multiplies are done with a basecase multiplication -then the work is about the same as a basecase division, but with more -function call overheads and with some subtractions separated from the -multiplies. These overheads mean that it's only when N/2 is above -`MUL_TOOM22_THRESHOLD' that divide and conquer is of use. - - `DC_DIV_QR_THRESHOLD' is based on the divisor size N, so it will be -somewhere above twice `MUL_TOOM22_THRESHOLD', but how much above -depends on the CPU. An optimized `mpn_mul_basecase' can lower -`DC_DIV_QR_THRESHOLD' a little by offering a ready-made advantage over -repeated `mpn_submul_1' calls. - - Divide and conquer is asymptotically O(M(N)*log(N)) where M(N) is -the time for an NxN multiplication done with FFTs. The actual time is -a sum over multiplications of the recursed sizes, as can be seen near -the end of section 2.2 of Burnikel and Ziegler. For example, within -the Toom-3 range, divide and conquer is 2.63*M(N). With higher -algorithms the M(N) term improves and the multiplier tends to log(N). -In practice, at moderate to large sizes, a 2NxN division is about 2 to -4 times slower than an NxN multiplication. - - -File: gmp.info, Node: Block-Wise Barrett Division, Next: Exact Division, Prev: Divide and Conquer Division, Up: Division Algorithms - -16.2.4 Block-Wise Barrett Division ----------------------------------- - -For the largest divisions, a block-wise Barrett division algorithm is -used. Here, the divisor is inverted to a precision determined by the -relative size of the dividend and divisor. Blocks of quotient limbs -are then generated by multiplying blocks from the dividend by the -inverse. - - Our block-wise algorithm computes a smaller inverse than in the -plain Barrett algorithm. For a 2n/n division, the inverse will be just -ceil(n/2) limbs. - - -File: gmp.info, Node: Exact Division, Next: Exact Remainder, Prev: Block-Wise Barrett Division, Up: Division Algorithms - -16.2.5 Exact Division ---------------------- - -A so-called exact division is when the dividend is known to be an exact -multiple of the divisor. Jebelean's exact division algorithm uses this -knowledge to make some significant optimizations (*note References::). - - The idea can be illustrated in decimal for example with 368154 -divided by 543. Because the low digit of the dividend is 4, the low -digit of the quotient must be 8. This is arrived at from 4*7 mod 10, -using the fact 7 is the modular inverse of 3 (the low digit of the -divisor), since 3*7 == 1 mod 10. So 8*543=4344 can be subtracted from -the dividend leaving 363810. Notice the low digit has become zero. - - The procedure is repeated at the second digit, with the next -quotient digit 7 (7 == 1*7 mod 10), subtracting 7*543=3801, leaving -325800. And finally at the third digit with quotient digit 6 (8*7 mod -10), subtracting 6*543=3258 leaving 0. So the quotient is 678. - - Notice however that the multiplies and subtractions don't need to -extend past the low three digits of the dividend, since that's enough -to determine the three quotient digits. For the last quotient digit no -subtraction is needed at all. On a 2NxN division like this one, only -about half the work of a normal basecase division is necessary. - - For an NxM exact division producing Q=N-M quotient limbs, the saving -over a normal basecase division is in two parts. Firstly, each of the -Q quotient limbs needs only one multiply, not a 2x1 divide and -multiply. Secondly, the crossproducts are reduced when Q>M to -Q*M-M*(M+1)/2, or when Q<=M to Q*(Q-1)/2. Notice the savings are -complementary. If Q is big then many divisions are saved, or if Q is -small then the crossproducts reduce to a small number. - - The modular inverse used is calculated efficiently by `binvert_limb' -in `gmp-impl.h'. This does four multiplies for a 32-bit limb, or six -for a 64-bit limb. `tune/modlinv.c' has some alternate implementations -that might suit processors better at bit twiddling than multiplying. - - The sub-quadratic exact division described by Jebelean in "Exact -Division with Karatsuba Complexity" is not currently implemented. It -uses a rearrangement similar to the divide and conquer for normal -division (*note Divide and Conquer Division::), but operating from low -to high. A further possibility not currently implemented is -"Bidirectional Exact Integer Division" by Krandick and Jebelean which -forms quotient limbs from both the high and low ends of the dividend, -and can halve once more the number of crossproducts needed in a 2NxN -division. - - A special case exact division by 3 exists in `mpn_divexact_by3', -supporting Toom-3 multiplication and `mpq' canonicalizations. It forms -quotient digits with a multiply by the modular inverse of 3 (which is -`0xAA..AAB') and uses two comparisons to determine a borrow for the next -limb. The multiplications don't need to be on the dependent chain, as -long as the effect of the borrows is applied, which can help chips with -pipelined multipliers. - - -File: gmp.info, Node: Exact Remainder, Next: Small Quotient Division, Prev: Exact Division, Up: Division Algorithms - -16.2.6 Exact Remainder ----------------------- - -If the exact division algorithm is done with a full subtraction at each -stage and the dividend isn't a multiple of the divisor, then low zero -limbs are produced but with a remainder in the high limbs. For -dividend a, divisor d, quotient q, and b = 2^mp_bits_per_limb, this -remainder r is of the form - - a = q*d + r*b^n - - n represents the number of zero limbs produced by the subtractions, -that being the number of limbs produced for q. r will be in the range -0<=rb*r+u2 condition appropriately relaxed. - - -File: gmp.info, Node: Greatest Common Divisor Algorithms, Next: Powering Algorithms, Prev: Division Algorithms, Up: Algorithms - -16.3 Greatest Common Divisor -============================ - -* Menu: - -* Binary GCD:: -* Lehmer's Algorithm:: -* Subquadratic GCD:: -* Extended GCD:: -* Jacobi Symbol:: - - -File: gmp.info, Node: Binary GCD, Next: Lehmer's Algorithm, Prev: Greatest Common Divisor Algorithms, Up: Greatest Common Divisor Algorithms - -16.3.1 Binary GCD ------------------ - -At small sizes GMP uses an O(N^2) binary style GCD. This is described -in many textbooks, for example Knuth section 4.5.2 algorithm B. It -simply consists of successively reducing odd operands a and b using - - a,b = abs(a-b),min(a,b) - strip factors of 2 from a - - The Euclidean GCD algorithm, as per Knuth algorithms E and A, -repeatedly computes the quotient q = floor(a/b) and replaces a,b by v, -u - q v. The binary algorithm has so far been found to be faster than -the Euclidean algorithm everywhere. One reason the binary method does -well is that the implied quotient at each step is usually small, so -often only one or two subtractions are needed to get the same effect as -a division. Quotients 1, 2 and 3 for example occur 67.7% of the time, -see Knuth section 4.5.3 Theorem E. - - When the implied quotient is large, meaning b is much smaller than -a, then a division is worthwhile. This is the basis for the initial a -mod b reductions in `mpn_gcd' and `mpn_gcd_1' (the latter for both Nx1 -and 1x1 cases). But after that initial reduction, big quotients occur -too rarely to make it worth checking for them. - - - The final 1x1 GCD in `mpn_gcd_1' is done in the generic C code as -described above. For two N-bit operands, the algorithm takes about -0.68 iterations per bit. For optimum performance some attention needs -to be paid to the way the factors of 2 are stripped from a. - - Firstly it may be noted that in twos complement the number of low -zero bits on a-b is the same as b-a, so counting or testing can begin on -a-b without waiting for abs(a-b) to be determined. - - A loop stripping low zero bits tends not to branch predict well, -since the condition is data dependent. But on average there's only a -few low zeros, so an option is to strip one or two bits arithmetically -then loop for more (as done for AMD K6). Or use a lookup table to get -a count for several bits then loop for more (as done for AMD K7). An -alternative approach is to keep just one of a or b odd and iterate - - a,b = abs(a-b), min(a,b) - a = a/2 if even - b = b/2 if even - - This requires about 1.25 iterations per bit, but stripping of a -single bit at each step avoids any branching. Repeating the bit strip -reduces to about 0.9 iterations per bit, which may be a worthwhile -tradeoff. - - Generally with the above approaches a speed of perhaps 6 cycles per -bit can be achieved, which is still not terribly fast with for instance -a 64-bit GCD taking nearly 400 cycles. It's this sort of time which -means it's not usually advantageous to combine a set of divisibility -tests into a GCD. - - Currently, the binary algorithm is used for GCD only when N < 3. - - -File: gmp.info, Node: Lehmer's Algorithm, Next: Subquadratic GCD, Prev: Binary GCD, Up: Greatest Common Divisor Algorithms - -16.3.2 Lehmer's algorithm -------------------------- - -Lehmer's improvement of the Euclidean algorithms is based on the -observation that the initial part of the quotient sequence depends only -on the most significant parts of the inputs. The variant of Lehmer's -algorithm used in GMP splits off the most significant two limbs, as -suggested, e.g., in "A Double-Digit Lehmer-Euclid Algorithm" by -Jebelean (*note References::). The quotients of two double-limb inputs -are collected as a 2 by 2 matrix with single-limb elements. This is -done by the function `mpn_hgcd2'. The resulting matrix is applied to -the inputs using `mpn_mul_1' and `mpn_submul_1'. Each iteration usually -reduces the inputs by almost one limb. In the rare case of a large -quotient, no progress can be made by examining just the most -significant two limbs, and the quotient is computing using plain -division. - - The resulting algorithm is asymptotically O(N^2), just as the -Euclidean algorithm and the binary algorithm. The quadratic part of the -work are the calls to `mpn_mul_1' and `mpn_submul_1'. For small sizes, -the linear work is also significant. There are roughly N calls to the -`mpn_hgcd2' function. This function uses a couple of important -optimizations: - - * It uses the same relaxed notion of correctness as `mpn_hgcd' (see - next section). This means that when called with the most - significant two limbs of two large numbers, the returned matrix - does not always correspond exactly to the initial quotient - sequence for the two large numbers; the final quotient may - sometimes be one off. - - * It takes advantage of the fact the quotients are usually small. - The division operator is not used, since the corresponding - assembler instruction is very slow on most architectures. (This - code could probably be improved further, it uses many branches - that are unfriendly to prediction). - - * It switches from double-limb calculations to single-limb - calculations half-way through, when the input numbers have been - reduced in size from two limbs to one and a half. - - - -File: gmp.info, Node: Subquadratic GCD, Next: Extended GCD, Prev: Lehmer's Algorithm, Up: Greatest Common Divisor Algorithms - -16.3.3 Subquadratic GCD ------------------------ - -For inputs larger than `GCD_DC_THRESHOLD', GCD is computed via the HGCD -(Half GCD) function, as a generalization to Lehmer's algorithm. - - Let the inputs a,b be of size N limbs each. Put S = floor(N/2) + 1. -Then HGCD(a,b) returns a transformation matrix T with non-negative -elements, and reduced numbers (c;d) = T^-1 (a;b). The reduced numbers -c,d must be larger than S limbs, while their difference abs(c-d) must -fit in S limbs. The matrix elements will also be of size roughly N/2. - - The HGCD base case uses Lehmer's algorithm, but with the above stop -condition that returns reduced numbers and the corresponding -transformation matrix half-way through. For inputs larger than -`HGCD_THRESHOLD', HGCD is computed recursively, using the divide and -conquer algorithm in "On Scho"nhage's algorithm and subquadratic -integer GCD computation" by Mo"ller (*note References::). The recursive -algorithm consists of these main steps. - - * Call HGCD recursively, on the most significant N/2 limbs. Apply the - resulting matrix T_1 to the full numbers, reducing them to a size - just above 3N/2. - - * Perform a small number of division or subtraction steps to reduce - the numbers to size below 3N/2. This is essential mainly for the - unlikely case of large quotients. - - * Call HGCD recursively, on the most significant N/2 limbs of the - reduced numbers. Apply the resulting matrix T_2 to the full - numbers, reducing them to a size just above N/2. - - * Compute T = T_1 T_2. - - * Perform a small number of division and subtraction steps to - satisfy the requirements, and return. - - GCD is then implemented as a loop around HGCD, similarly to Lehmer's -algorithm. Where Lehmer repeatedly chops off the top two limbs, calls -`mpn_hgcd2', and applies the resulting matrix to the full numbers, the -subquadratic GCD chops off the most significant third of the limbs (the -proportion is a tuning parameter, and 1/3 seems to be more efficient -than, e.g, 1/2), calls `mpn_hgcd', and applies the resulting matrix. -Once the input numbers are reduced to size below `GCD_DC_THRESHOLD', -Lehmer's algorithm is used for the rest of the work. - - The asymptotic running time of both HGCD and GCD is O(M(N)*log(N)), -where M(N) is the time for multiplying two N-limb numbers. - - -File: gmp.info, Node: Extended GCD, Next: Jacobi Symbol, Prev: Subquadratic GCD, Up: Greatest Common Divisor Algorithms - -16.3.4 Extended GCD -------------------- - -The extended GCD function, or GCDEXT, calculates gcd(a,b) and also -cofactors x and y satisfying a*x+b*y=gcd(a,b). All the algorithms used -for plain GCD are extended to handle this case. The binary algorithm is -used only for single-limb GCDEXT. Lehmer's algorithm is used for sizes -up to `GCDEXT_DC_THRESHOLD'. Above this threshold, GCDEXT is -implemented as a loop around HGCD, but with more book-keeping to keep -track of the cofactors. This gives the same asymptotic running time as -for GCD and HGCD, O(M(N)*log(N)) - - One difference to plain GCD is that while the inputs a and b are -reduced as the algorithm proceeds, the cofactors x and y grow in size. -This makes the tuning of the chopping-point more difficult. The current -code chops off the most significant half of the inputs for the call to -HGCD in the first iteration, and the most significant two thirds for -the remaining calls. This strategy could surely be improved. Also the -stop condition for the loop, where Lehmer's algorithm is invoked once -the inputs are reduced below `GCDEXT_DC_THRESHOLD', could maybe be -improved by taking into account the current size of the cofactors. - - -File: gmp.info, Node: Jacobi Symbol, Prev: Extended GCD, Up: Greatest Common Divisor Algorithms - -16.3.5 Jacobi Symbol --------------------- - -`mpz_jacobi' and `mpz_kronecker' are currently implemented with a -simple binary algorithm similar to that described for the GCDs (*note -Binary GCD::). They're not very fast when both inputs are large. -Lehmer's multi-step improvement or a binary based multi-step algorithm -is likely to be better. - - When one operand fits a single limb, and that includes -`mpz_kronecker_ui' and friends, an initial reduction is done with -either `mpn_mod_1' or `mpn_modexact_1_odd', followed by the binary -algorithm on a single limb. The binary algorithm is well suited to a -single limb, and the whole calculation in this case is quite efficient. - - In all the routines sign changes for the result are accumulated -using some bit twiddling, avoiding table lookups or conditional jumps. - diff --git a/misc/builddeps/linux32/gmp/share/info/gmp.info-2 b/misc/builddeps/linux32/gmp/share/info/gmp.info-2 deleted file mode 100644 index 45846232..00000000 --- a/misc/builddeps/linux32/gmp/share/info/gmp.info-2 +++ /dev/null @@ -1,3489 +0,0 @@ -This is ../../gmp/doc/gmp.info, produced by makeinfo version 4.8 from -../../gmp/doc/gmp.texi. - - This manual describes how to install and use the GNU multiple -precision arithmetic library, version 5.0.1. - - Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, -2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free -Software Foundation, Inc. - - Permission is granted to copy, distribute and/or modify this -document under the terms of the GNU Free Documentation License, Version -1.3 or any later version published by the Free Software Foundation; -with no Invariant Sections, with the Front-Cover Texts being "A GNU -Manual", and with the Back-Cover Texts being "You have freedom to copy -and modify this GNU Manual, like GNU software". A copy of the license -is included in *Note GNU Free Documentation License::. - -INFO-DIR-SECTION GNU libraries -START-INFO-DIR-ENTRY -* gmp: (gmp). GNU Multiple Precision Arithmetic Library. -END-INFO-DIR-ENTRY - - -File: gmp.info, Node: Powering Algorithms, Next: Root Extraction Algorithms, Prev: Greatest Common Divisor Algorithms, Up: Algorithms - -16.4 Powering Algorithms -======================== - -* Menu: - -* Normal Powering Algorithm:: -* Modular Powering Algorithm:: - - -File: gmp.info, Node: Normal Powering Algorithm, Next: Modular Powering Algorithm, Prev: Powering Algorithms, Up: Powering Algorithms - -16.4.1 Normal Powering ----------------------- - -Normal `mpz' or `mpf' powering uses a simple binary algorithm, -successively squaring and then multiplying by the base when a 1 bit is -seen in the exponent, as per Knuth section 4.6.3. The "left to right" -variant described there is used rather than algorithm A, since it's -just as easy and can be done with somewhat less temporary memory. - - -File: gmp.info, Node: Modular Powering Algorithm, Prev: Normal Powering Algorithm, Up: Powering Algorithms - -16.4.2 Modular Powering ------------------------ - -Modular powering is implemented using a 2^k-ary sliding window -algorithm, as per "Handbook of Applied Cryptography" algorithm 14.85 -(*note References::). k is chosen according to the size of the -exponent. Larger exponents use larger values of k, the choice being -made to minimize the average number of multiplications that must -supplement the squaring. - - The modular multiplies and squares use either a simple division or -the REDC method by Montgomery (*note References::). REDC is a little -faster, essentially saving N single limb divisions in a fashion similar -to an exact remainder (*note Exact Remainder::). - - -File: gmp.info, Node: Root Extraction Algorithms, Next: Radix Conversion Algorithms, Prev: Powering Algorithms, Up: Algorithms - -16.5 Root Extraction Algorithms -=============================== - -* Menu: - -* Square Root Algorithm:: -* Nth Root Algorithm:: -* Perfect Square Algorithm:: -* Perfect Power Algorithm:: - - -File: gmp.info, Node: Square Root Algorithm, Next: Nth Root Algorithm, Prev: Root Extraction Algorithms, Up: Root Extraction Algorithms - -16.5.1 Square Root ------------------- - -Square roots are taken using the "Karatsuba Square Root" algorithm by -Paul Zimmermann (*note References::). - - An input n is split into four parts of k bits each, so with b=2^k we -have n = a3*b^3 + a2*b^2 + a1*b + a0. Part a3 must be "normalized" so -that either the high or second highest bit is set. In GMP, k is kept -on a limb boundary and the input is left shifted (by an even number of -bits) to normalize. - - The square root of the high two parts is taken, by recursive -application of the algorithm (bottoming out in a one-limb Newton's -method), - - s1,r1 = sqrtrem (a3*b + a2) - - This is an approximation to the desired root and is extended by a -division to give s,r, - - q,u = divrem (r1*b + a1, 2*s1) - s = s1*b + q - r = u*b + a0 - q^2 - - The normalization requirement on a3 means at this point s is either -correct or 1 too big. r is negative in the latter case, so - - if r < 0 then - r = r + 2*s - 1 - s = s - 1 - - The algorithm is expressed in a divide and conquer form, but as -noted in the paper it can also be viewed as a discrete variant of -Newton's method, or as a variation on the schoolboy method (no longer -taught) for square roots two digits at a time. - - If the remainder r is not required then usually only a few high limbs -of r and u need to be calculated to determine whether an adjustment to -s is required. This optimization is not currently implemented. - - In the Karatsuba multiplication range this algorithm is -O(1.5*M(N/2)), where M(n) is the time to multiply two numbers of n -limbs. In the FFT multiplication range this grows to a bound of -O(6*M(N/2)). In practice a factor of about 1.5 to 1.8 is found in the -Karatsuba and Toom-3 ranges, growing to 2 or 3 in the FFT range. - - The algorithm does all its calculations in integers and the resulting -`mpn_sqrtrem' is used for both `mpz_sqrt' and `mpf_sqrt'. The extended -precision given by `mpf_sqrt_ui' is obtained by padding with zero limbs. - - -File: gmp.info, Node: Nth Root Algorithm, Next: Perfect Square Algorithm, Prev: Square Root Algorithm, Up: Root Extraction Algorithms - -16.5.2 Nth Root ---------------- - -Integer Nth roots are taken using Newton's method with the following -iteration, where A is the input and n is the root to be taken. - - 1 A - a[i+1] = - * ( --------- + (n-1)*a[i] ) - n a[i]^(n-1) - - The initial approximation a[1] is generated bitwise by successively -powering a trial root with or without new 1 bits, aiming to be just -above the true root. The iteration converges quadratically when -started from a good approximation. When n is large more initial bits -are needed to get good convergence. The current implementation is not -particularly well optimized. - - -File: gmp.info, Node: Perfect Square Algorithm, Next: Perfect Power Algorithm, Prev: Nth Root Algorithm, Up: Root Extraction Algorithms - -16.5.3 Perfect Square ---------------------- - -A significant fraction of non-squares can be quickly identified by -checking whether the input is a quadratic residue modulo small integers. - - `mpz_perfect_square_p' first tests the input mod 256, which means -just examining the low byte. Only 44 different values occur for -squares mod 256, so 82.8% of inputs can be immediately identified as -non-squares. - - On a 32-bit system similar tests are done mod 9, 5, 7, 13 and 17, -for a total 99.25% of inputs identified as non-squares. On a 64-bit -system 97 is tested too, for a total 99.62%. - - These moduli are chosen because they're factors of 2^24-1 (or 2^48-1 -for 64-bits), and such a remainder can be quickly taken just using -additions (see `mpn_mod_34lsub1'). - - When nails are in use moduli are instead selected by the `gen-psqr.c' -program and applied with an `mpn_mod_1'. The same 2^24-1 or 2^48-1 -could be done with nails using some extra bit shifts, but this is not -currently implemented. - - In any case each modulus is applied to the `mpn_mod_34lsub1' or -`mpn_mod_1' remainder and a table lookup identifies non-squares. By -using a "modexact" style calculation, and suitably permuted tables, -just one multiply each is required, see the code for details. Moduli -are also combined to save operations, so long as the lookup tables -don't become too big. `gen-psqr.c' does all the pre-calculations. - - A square root must still be taken for any value that passes these -tests, to verify it's really a square and not one of the small fraction -of non-squares that get through (ie. a pseudo-square to all the tested -bases). - - Clearly more residue tests could be done, `mpz_perfect_square_p' only -uses a compact and efficient set. Big inputs would probably benefit -from more residue testing, small inputs might be better off with less. -The assumed distribution of squares versus non-squares in the input -would affect such considerations. - - -File: gmp.info, Node: Perfect Power Algorithm, Prev: Perfect Square Algorithm, Up: Root Extraction Algorithms - -16.5.4 Perfect Power --------------------- - -Detecting perfect powers is required by some factorization algorithms. -Currently `mpz_perfect_power_p' is implemented using repeated Nth root -extractions, though naturally only prime roots need to be considered. -(*Note Nth Root Algorithm::.) - - If a prime divisor p with multiplicity e can be found, then only -roots which are divisors of e need to be considered, much reducing the -work necessary. To this end divisibility by a set of small primes is -checked. - - -File: gmp.info, Node: Radix Conversion Algorithms, Next: Other Algorithms, Prev: Root Extraction Algorithms, Up: Algorithms - -16.6 Radix Conversion -===================== - -Radix conversions are less important than other algorithms. A program -dominated by conversions should probably use a different data -representation. - -* Menu: - -* Binary to Radix:: -* Radix to Binary:: - - -File: gmp.info, Node: Binary to Radix, Next: Radix to Binary, Prev: Radix Conversion Algorithms, Up: Radix Conversion Algorithms - -16.6.1 Binary to Radix ----------------------- - -Conversions from binary to a power-of-2 radix use a simple and fast -O(N) bit extraction algorithm. - - Conversions from binary to other radices use one of two algorithms. -Sizes below `GET_STR_PRECOMPUTE_THRESHOLD' use a basic O(N^2) method. -Repeated divisions by b^n are made, where b is the radix and n is the -biggest power that fits in a limb. But instead of simply using the -remainder r from such divisions, an extra divide step is done to give a -fractional limb representing r/b^n. The digits of r can then be -extracted using multiplications by b rather than divisions. Special -case code is provided for decimal, allowing multiplications by 10 to -optimize to shifts and adds. - - Above `GET_STR_PRECOMPUTE_THRESHOLD' a sub-quadratic algorithm is -used. For an input t, powers b^(n*2^i) of the radix are calculated, -until a power between t and sqrt(t) is reached. t is then divided by -that largest power, giving a quotient which is the digits above that -power, and a remainder which is those below. These two parts are in -turn divided by the second highest power, and so on recursively. When -a piece has been divided down to less than `GET_STR_DC_THRESHOLD' -limbs, the basecase algorithm described above is used. - - The advantage of this algorithm is that big divisions can make use -of the sub-quadratic divide and conquer division (*note Divide and -Conquer Division::), and big divisions tend to have less overheads than -lots of separate single limb divisions anyway. But in any case the -cost of calculating the powers b^(n*2^i) must first be overcome. - - `GET_STR_PRECOMPUTE_THRESHOLD' and `GET_STR_DC_THRESHOLD' represent -the same basic thing, the point where it becomes worth doing a big -division to cut the input in half. `GET_STR_PRECOMPUTE_THRESHOLD' -includes the cost of calculating the radix power required, whereas -`GET_STR_DC_THRESHOLD' assumes that's already available, which is the -case when recursing. - - Since the base case produces digits from least to most significant -but they want to be stored from most to least, it's necessary to -calculate in advance how many digits there will be, or at least be sure -not to underestimate that. For GMP the number of input bits is -multiplied by `chars_per_bit_exactly' from `mp_bases', rounding up. -The result is either correct or one too big. - - Examining some of the high bits of the input could increase the -chance of getting the exact number of digits, but an exact result every -time would not be practical, since in general the difference between -numbers 100... and 99... is only in the last few bits and the work to -identify 99... might well be almost as much as a full conversion. - - `mpf_get_str' doesn't currently use the algorithm described here, it -multiplies or divides by a power of b to move the radix point to the -just above the highest non-zero digit (or at worst one above that -location), then multiplies by b^n to bring out digits. This is O(N^2) -and is certainly not optimal. - - The r/b^n scheme described above for using multiplications to bring -out digits might be useful for more than a single limb. Some brief -experiments with it on the base case when recursing didn't give a -noticeable improvement, but perhaps that was only due to the -implementation. Something similar would work for the sub-quadratic -divisions too, though there would be the cost of calculating a bigger -radix power. - - Another possible improvement for the sub-quadratic part would be to -arrange for radix powers that balanced the sizes of quotient and -remainder produced, ie. the highest power would be an b^(n*k) -approximately equal to sqrt(t), not restricted to a 2^i factor. That -ought to smooth out a graph of times against sizes, but may or may not -be a net speedup. - - -File: gmp.info, Node: Radix to Binary, Prev: Binary to Radix, Up: Radix Conversion Algorithms - -16.6.2 Radix to Binary ----------------------- - -*This section needs to be rewritten, it currently describes the -algorithms used before GMP 4.3.* - - Conversions from a power-of-2 radix into binary use a simple and fast -O(N) bitwise concatenation algorithm. - - Conversions from other radices use one of two algorithms. Sizes -below `SET_STR_PRECOMPUTE_THRESHOLD' use a basic O(N^2) method. Groups -of n digits are converted to limbs, where n is the biggest power of the -base b which will fit in a limb, then those groups are accumulated into -the result by multiplying by b^n and adding. This saves -multi-precision operations, as per Knuth section 4.4 part E (*note -References::). Some special case code is provided for decimal, giving -the compiler a chance to optimize multiplications by 10. - - Above `SET_STR_PRECOMPUTE_THRESHOLD' a sub-quadratic algorithm is -used. First groups of n digits are converted into limbs. Then adjacent -limbs are combined into limb pairs with x*b^n+y, where x and y are the -limbs. Adjacent limb pairs are combined into quads similarly with -x*b^(2n)+y. This continues until a single block remains, that being -the result. - - The advantage of this method is that the multiplications for each x -are big blocks, allowing Karatsuba and higher algorithms to be used. -But the cost of calculating the powers b^(n*2^i) must be overcome. -`SET_STR_PRECOMPUTE_THRESHOLD' usually ends up quite big, around 5000 -digits, and on some processors much bigger still. - - `SET_STR_PRECOMPUTE_THRESHOLD' is based on the input digits (and -tuned for decimal), though it might be better based on a limb count, so -as to be independent of the base. But that sort of count isn't used by -the base case and so would need some sort of initial calculation or -estimate. - - The main reason `SET_STR_PRECOMPUTE_THRESHOLD' is so much bigger -than the corresponding `GET_STR_PRECOMPUTE_THRESHOLD' is that -`mpn_mul_1' is much faster than `mpn_divrem_1' (often by a factor of 5, -or more). - - -File: gmp.info, Node: Other Algorithms, Next: Assembly Coding, Prev: Radix Conversion Algorithms, Up: Algorithms - -16.7 Other Algorithms -===================== - -* Menu: - -* Prime Testing Algorithm:: -* Factorial Algorithm:: -* Binomial Coefficients Algorithm:: -* Fibonacci Numbers Algorithm:: -* Lucas Numbers Algorithm:: -* Random Number Algorithms:: - - -File: gmp.info, Node: Prime Testing Algorithm, Next: Factorial Algorithm, Prev: Other Algorithms, Up: Other Algorithms - -16.7.1 Prime Testing --------------------- - -The primality testing in `mpz_probab_prime_p' (*note Number Theoretic -Functions::) first does some trial division by small factors and then -uses the Miller-Rabin probabilistic primality testing algorithm, as -described in Knuth section 4.5.4 algorithm P (*note References::). - - For an odd input n, and with n = q*2^k+1 where q is odd, this -algorithm selects a random base x and tests whether x^q mod n is 1 or --1, or an x^(q*2^j) mod n is 1, for 1<=j<=k. If so then n is probably -prime, if not then n is definitely composite. - - Any prime n will pass the test, but some composites do too. Such -composites are known as strong pseudoprimes to base x. No n is a -strong pseudoprime to more than 1/4 of all bases (see Knuth exercise -22), hence with x chosen at random there's no more than a 1/4 chance a -"probable prime" will in fact be composite. - - In fact strong pseudoprimes are quite rare, making the test much more -powerful than this analysis would suggest, but 1/4 is all that's proven -for an arbitrary n. - - -File: gmp.info, Node: Factorial Algorithm, Next: Binomial Coefficients Algorithm, Prev: Prime Testing Algorithm, Up: Other Algorithms - -16.7.2 Factorial ----------------- - -Factorials are calculated by a combination of removal of twos, -powering, and binary splitting. The procedure can be best illustrated -with an example, - - 23! = 1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23 - -has factors of two removed, - - 23! = 2^19.1.1.3.1.5.3.7.1.9.5.11.3.13.7.15.1.17.9.19.5.21.11.23 - -and the resulting terms collected up according to their multiplicity, - - 23! = 2^19.(3.5)^3.(7.9.11)^2.(13.15.17.19.21.23) - - Each sequence such as 13.15.17.19.21.23 is evaluated by splitting -into every second term, as for instance (13.17.21).(15.19.23), and the -same recursively on each half. This is implemented iteratively using -some bit twiddling. - - Such splitting is more efficient than repeated Nx1 multiplies since -it forms big multiplies, allowing Karatsuba and higher algorithms to be -used. And even below the Karatsuba threshold a big block of work can -be more efficient for the basecase algorithm. - - Splitting into subsequences of every second term keeps the resulting -products more nearly equal in size than would the simpler approach of -say taking the first half and second half of the sequence. Nearly -equal products are more efficient for the current multiply -implementation. - - -File: gmp.info, Node: Binomial Coefficients Algorithm, Next: Fibonacci Numbers Algorithm, Prev: Factorial Algorithm, Up: Other Algorithms - -16.7.3 Binomial Coefficients ----------------------------- - -Binomial coefficients C(n,k) are calculated by first arranging k <= n/2 -using C(n,k) = C(n,n-k) if necessary, and then evaluating the following -product simply from i=2 to i=k. - - k (n-k+i) - C(n,k) = (n-k+1) * prod ------- - i=2 i - - It's easy to show that each denominator i will divide the product so -far, so the exact division algorithm is used (*note Exact Division::). - - The numerators n-k+i and denominators i are first accumulated into -as many fit a limb, to save multi-precision operations, though for -`mpz_bin_ui' this applies only to the divisors, since n is an `mpz_t' -and n-k+i in general won't fit in a limb at all. - - -File: gmp.info, Node: Fibonacci Numbers Algorithm, Next: Lucas Numbers Algorithm, Prev: Binomial Coefficients Algorithm, Up: Other Algorithms - -16.7.4 Fibonacci Numbers ------------------------- - -The Fibonacci functions `mpz_fib_ui' and `mpz_fib2_ui' are designed for -calculating isolated F[n] or F[n],F[n-1] values efficiently. - - For small n, a table of single limb values in `__gmp_fib_table' is -used. On a 32-bit limb this goes up to F[47], or on a 64-bit limb up -to F[93]. For convenience the table starts at F[-1]. - - Beyond the table, values are generated with a binary powering -algorithm, calculating a pair F[n] and F[n-1] working from high to low -across the bits of n. The formulas used are - - F[2k+1] = 4*F[k]^2 - F[k-1]^2 + 2*(-1)^k - F[2k-1] = F[k]^2 + F[k-1]^2 - - F[2k] = F[2k+1] - F[2k-1] - - At each step, k is the high b bits of n. If the next bit of n is 0 -then F[2k],F[2k-1] is used, or if it's a 1 then F[2k+1],F[2k] is used, -and the process repeated until all bits of n are incorporated. Notice -these formulas require just two squares per bit of n. - - It'd be possible to handle the first few n above the single limb -table with simple additions, using the defining Fibonacci recurrence -F[k+1]=F[k]+F[k-1], but this is not done since it usually turns out to -be faster for only about 10 or 20 values of n, and including a block of -code for just those doesn't seem worthwhile. If they really mattered -it'd be better to extend the data table. - - Using a table avoids lots of calculations on small numbers, and -makes small n go fast. A bigger table would make more small n go fast, -it's just a question of balancing size against desired speed. For GMP -the code is kept compact, with the emphasis primarily on a good -powering algorithm. - - `mpz_fib2_ui' returns both F[n] and F[n-1], but `mpz_fib_ui' is only -interested in F[n]. In this case the last step of the algorithm can -become one multiply instead of two squares. One of the following two -formulas is used, according as n is odd or even. - - F[2k] = F[k]*(F[k]+2F[k-1]) - - F[2k+1] = (2F[k]+F[k-1])*(2F[k]-F[k-1]) + 2*(-1)^k - - F[2k+1] here is the same as above, just rearranged to be a multiply. -For interest, the 2*(-1)^k term both here and above can be applied -just to the low limb of the calculation, without a carry or borrow into -further limbs, which saves some code size. See comments with -`mpz_fib_ui' and the internal `mpn_fib2_ui' for how this is done. - - -File: gmp.info, Node: Lucas Numbers Algorithm, Next: Random Number Algorithms, Prev: Fibonacci Numbers Algorithm, Up: Other Algorithms - -16.7.5 Lucas Numbers --------------------- - -`mpz_lucnum2_ui' derives a pair of Lucas numbers from a pair of -Fibonacci numbers with the following simple formulas. - - L[k] = F[k] + 2*F[k-1] - L[k-1] = 2*F[k] - F[k-1] - - `mpz_lucnum_ui' is only interested in L[n], and some work can be -saved. Trailing zero bits on n can be handled with a single square -each. - - L[2k] = L[k]^2 - 2*(-1)^k - - And the lowest 1 bit can be handled with one multiply of a pair of -Fibonacci numbers, similar to what `mpz_fib_ui' does. - - L[2k+1] = 5*F[k-1]*(2*F[k]+F[k-1]) - 4*(-1)^k - - -File: gmp.info, Node: Random Number Algorithms, Prev: Lucas Numbers Algorithm, Up: Other Algorithms - -16.7.6 Random Numbers ---------------------- - -For the `urandomb' functions, random numbers are generated simply by -concatenating bits produced by the generator. As long as the generator -has good randomness properties this will produce well-distributed N bit -numbers. - - For the `urandomm' functions, random numbers in a range 0<=R48 bit pieces is convenient. With -some care though six 21x32->53 bit products can be used, if one of the -lower two 21-bit pieces also uses the sign bit. - - For the `mpn_mul_1' family of functions on a 64-bit machine, the -invariant single limb is split at the start, into 3 or 4 pieces. -Inside the loop, the bignum operand is split into 32-bit pieces. Fast -conversion of these unsigned 32-bit pieces to floating point is highly -machine-dependent. In some cases, reading the data into the integer -unit, zero-extending to 64-bits, then transferring to the floating -point unit back via memory is the only option. - - Converting partial products back to 64-bit limbs is usually best -done as a signed conversion. Since all values are smaller than 2^53, -signed and unsigned are the same, but most processors lack unsigned -conversions. - - - - Here is a diagram showing 16x32 bit products for an `mpn_mul_1' or -`mpn_addmul_1' with a 64-bit limb. The single limb operand V is split -into four 16-bit parts. The multi-limb operand U is split in the loop -into two 32-bit parts. - - +---+---+---+---+ - |v48|v32|v16|v00| V operand - +---+---+---+---+ - - +-------+---+---+ - x | u32 | u00 | U operand (one limb) - +---------------+ - - --------------------------------- - - +-----------+ - | u00 x v00 | p00 48-bit products - +-----------+ - +-----------+ - | u00 x v16 | p16 - +-----------+ - +-----------+ - | u00 x v32 | p32 - +-----------+ - +-----------+ - | u00 x v48 | p48 - +-----------+ - +-----------+ - | u32 x v00 | r32 - +-----------+ - +-----------+ - | u32 x v16 | r48 - +-----------+ - +-----------+ - | u32 x v32 | r64 - +-----------+ - +-----------+ - | u32 x v48 | r80 - +-----------+ - - p32 and r32 can be summed using floating-point addition, and -likewise p48 and r48. p00 and p16 can be summed with r64 and r80 from -the previous iteration. - - For each loop then, four 49-bit quantities are transferred to the -integer unit, aligned as follows, - - |-----64bits----|-----64bits----| - +------------+ - | p00 + r64' | i00 - +------------+ - +------------+ - | p16 + r80' | i16 - +------------+ - +------------+ - | p32 + r32 | i32 - +------------+ - +------------+ - | p48 + r48 | i48 - +------------+ - - The challenge then is to sum these efficiently and add in a carry -limb, generating a low 64-bit result limb and a high 33-bit carry limb -(i48 extends 33 bits into the high half). - - -File: gmp.info, Node: Assembly SIMD Instructions, Next: Assembly Software Pipelining, Prev: Assembly Floating Point, Up: Assembly Coding - -16.8.7 SIMD Instructions ------------------------- - -The single-instruction multiple-data support in current microprocessors -is aimed at signal processing algorithms where each data point can be -treated more or less independently. There's generally not much support -for propagating the sort of carries that arise in GMP. - - SIMD multiplications of say four 16x16 bit multiplies only do as much -work as one 32x32 from GMP's point of view, and need some shifts and -adds besides. But of course if say the SIMD form is fully pipelined -and uses less instruction decoding then it may still be worthwhile. - - On the x86 chips, MMX has so far found a use in `mpn_rshift' and -`mpn_lshift', and is used in a special case for 16-bit multipliers in -the P55 `mpn_mul_1'. SSE2 is used for Pentium 4 `mpn_mul_1', -`mpn_addmul_1', and `mpn_submul_1'. - - -File: gmp.info, Node: Assembly Software Pipelining, Next: Assembly Loop Unrolling, Prev: Assembly SIMD Instructions, Up: Assembly Coding - -16.8.8 Software Pipelining --------------------------- - -Software pipelining consists of scheduling instructions around the -branch point in a loop. For example a loop might issue a load not for -use in the present iteration but the next, thereby allowing extra -cycles for the data to arrive from memory. - - Naturally this is wanted only when doing things like loads or -multiplies that take several cycles to complete, and only where a CPU -has multiple functional units so that other work can be done in the -meantime. - - A pipeline with several stages will have a data value in progress at -each stage and each loop iteration moves them along one stage. This is -like juggling. - - If the latency of some instruction is greater than the loop time -then it will be necessary to unroll, so one register has a result ready -to use while another (or multiple others) are still in progress. -(*note Assembly Loop Unrolling::). - - -File: gmp.info, Node: Assembly Loop Unrolling, Next: Assembly Writing Guide, Prev: Assembly Software Pipelining, Up: Assembly Coding - -16.8.9 Loop Unrolling ---------------------- - -Loop unrolling consists of replicating code so that several limbs are -processed in each loop. At a minimum this reduces loop overheads by a -corresponding factor, but it can also allow better register usage, for -example alternately using one register combination and then another. -Judicious use of `m4' macros can help avoid lots of duplication in the -source code. - - Any amount of unrolling can be handled with a loop counter that's -decremented by N each time, stopping when the remaining count is less -than the further N the loop will process. Or by subtracting N at the -start, the termination condition becomes when the counter C is less -than 0 (and the count of remaining limbs is C+N). - - Alternately for a power of 2 unroll the loop count and remainder can -be established with a shift and mask. This is convenient if also -making a computed jump into the middle of a large loop. - - The limbs not a multiple of the unrolling can be handled in various -ways, for example - - * A simple loop at the end (or the start) to process the excess. - Care will be wanted that it isn't too much slower than the - unrolled part. - - * A set of binary tests, for example after an 8-limb unrolling, test - for 4 more limbs to process, then a further 2 more or not, and - finally 1 more or not. This will probably take more code space - than a simple loop. - - * A `switch' statement, providing separate code for each possible - excess, for example an 8-limb unrolling would have separate code - for 0 remaining, 1 remaining, etc, up to 7 remaining. This might - take a lot of code, but may be the best way to optimize all cases - in combination with a deep pipelined loop. - - * A computed jump into the middle of the loop, thus making the first - iteration handle the excess. This should make times smoothly - increase with size, which is attractive, but setups for the jump - and adjustments for pointers can be tricky and could become quite - difficult in combination with deep pipelining. - - -File: gmp.info, Node: Assembly Writing Guide, Prev: Assembly Loop Unrolling, Up: Assembly Coding - -16.8.10 Writing Guide ---------------------- - -This is a guide to writing software pipelined loops for processing limb -vectors in assembly. - - First determine the algorithm and which instructions are needed. -Code it without unrolling or scheduling, to make sure it works. On a -3-operand CPU try to write each new value to a new register, this will -greatly simplify later steps. - - Then note for each instruction the functional unit and/or issue port -requirements. If an instruction can use either of two units, like U0 -or U1 then make a category "U0/U1". Count the total using each unit -(or combined unit), and count all instructions. - - Figure out from those counts the best possible loop time. The goal -will be to find a perfect schedule where instruction latencies are -completely hidden. The total instruction count might be the limiting -factor, or perhaps a particular functional unit. It might be possible -to tweak the instructions to help the limiting factor. - - Suppose the loop time is N, then make N issue buckets, with the -final loop branch at the end of the last. Now fill the buckets with -dummy instructions using the functional units desired. Run this to -make sure the intended speed is reached. - - Now replace the dummy instructions with the real instructions from -the slow but correct loop you started with. The first will typically -be a load instruction. Then the instruction using that value is placed -in a bucket an appropriate distance down. Run the loop again, to check -it still runs at target speed. - - Keep placing instructions, frequently measuring the loop. After a -few you will need to wrap around from the last bucket back to the top -of the loop. If you used the new-register for new-value strategy above -then there will be no register conflicts. If not then take care not to -clobber something already in use. Changing registers at this time is -very error prone. - - The loop will overlap two or more of the original loop iterations, -and the computation of one vector element result will be started in one -iteration of the new loop, and completed one or several iterations -later. - - The final step is to create feed-in and wind-down code for the loop. -A good way to do this is to make a copy (or copies) of the loop at the -start and delete those instructions which don't have valid antecedents, -and at the end replicate and delete those whose results are unwanted -(including any further loads). - - The loop will have a minimum number of limbs loaded and processed, -so the feed-in code must test if the request size is smaller and skip -either to a suitable part of the wind-down or to special code for small -sizes. - - -File: gmp.info, Node: Internals, Next: Contributors, Prev: Algorithms, Up: Top - -17 Internals -************ - -*This chapter is provided only for informational purposes and the -various internals described here may change in future GMP releases. -Applications expecting to be compatible with future releases should use -only the documented interfaces described in previous chapters.* - -* Menu: - -* Integer Internals:: -* Rational Internals:: -* Float Internals:: -* Raw Output Internals:: -* C++ Interface Internals:: - - -File: gmp.info, Node: Integer Internals, Next: Rational Internals, Prev: Internals, Up: Internals - -17.1 Integer Internals -====================== - -`mpz_t' variables represent integers using sign and magnitude, in space -dynamically allocated and reallocated. The fields are as follows. - -`_mp_size' - The number of limbs, or the negative of that when representing a - negative integer. Zero is represented by `_mp_size' set to zero, - in which case the `_mp_d' data is unused. - -`_mp_d' - A pointer to an array of limbs which is the magnitude. These are - stored "little endian" as per the `mpn' functions, so `_mp_d[0]' - is the least significant limb and `_mp_d[ABS(_mp_size)-1]' is the - most significant. Whenever `_mp_size' is non-zero, the most - significant limb is non-zero. - - Currently there's always at least one limb allocated, so for - instance `mpz_set_ui' never needs to reallocate, and `mpz_get_ui' - can fetch `_mp_d[0]' unconditionally (though its value is then - only wanted if `_mp_size' is non-zero). - -`_mp_alloc' - `_mp_alloc' is the number of limbs currently allocated at `_mp_d', - and naturally `_mp_alloc >= ABS(_mp_size)'. When an `mpz' routine - is about to (or might be about to) increase `_mp_size', it checks - `_mp_alloc' to see whether there's enough space, and reallocates - if not. `MPZ_REALLOC' is generally used for this. - - The various bitwise logical functions like `mpz_and' behave as if -negative values were twos complement. But sign and magnitude is always -used internally, and necessary adjustments are made during the -calculations. Sometimes this isn't pretty, but sign and magnitude are -best for other routines. - - Some internal temporary variables are setup with `MPZ_TMP_INIT' and -these have `_mp_d' space obtained from `TMP_ALLOC' rather than the -memory allocation functions. Care is taken to ensure that these are -big enough that no reallocation is necessary (since it would have -unpredictable consequences). - - `_mp_size' and `_mp_alloc' are `int', although `mp_size_t' is -usually a `long'. This is done to make the fields just 32 bits on some -64 bits systems, thereby saving a few bytes of data space but still -providing plenty of range. - - -File: gmp.info, Node: Rational Internals, Next: Float Internals, Prev: Integer Internals, Up: Internals - -17.2 Rational Internals -======================= - -`mpq_t' variables represent rationals using an `mpz_t' numerator and -denominator (*note Integer Internals::). - - The canonical form adopted is denominator positive (and non-zero), -no common factors between numerator and denominator, and zero uniquely -represented as 0/1. - - It's believed that casting out common factors at each stage of a -calculation is best in general. A GCD is an O(N^2) operation so it's -better to do a few small ones immediately than to delay and have to do -a big one later. Knowing the numerator and denominator have no common -factors can be used for example in `mpq_mul' to make only two cross -GCDs necessary, not four. - - This general approach to common factors is badly sub-optimal in the -presence of simple factorizations or little prospect for cancellation, -but GMP has no way to know when this will occur. As per *Note -Efficiency::, that's left to applications. The `mpq_t' framework might -still suit, with `mpq_numref' and `mpq_denref' for direct access to the -numerator and denominator, or of course `mpz_t' variables can be used -directly. - - -File: gmp.info, Node: Float Internals, Next: Raw Output Internals, Prev: Rational Internals, Up: Internals - -17.3 Float Internals -==================== - -Efficient calculation is the primary aim of GMP floats and the use of -whole limbs and simple rounding facilitates this. - - `mpf_t' floats have a variable precision mantissa and a single -machine word signed exponent. The mantissa is represented using sign -and magnitude. - - most least - significant significant - limb limb - - _mp_d - |---- _mp_exp ---> | - _____ _____ _____ _____ _____ - |_____|_____|_____|_____|_____| - . <------------ radix point - - <-------- _mp_size ---------> - -The fields are as follows. - -`_mp_size' - The number of limbs currently in use, or the negative of that when - representing a negative value. Zero is represented by `_mp_size' - and `_mp_exp' both set to zero, and in that case the `_mp_d' data - is unused. (In the future `_mp_exp' might be undefined when - representing zero.) - -`_mp_prec' - The precision of the mantissa, in limbs. In any calculation the - aim is to produce `_mp_prec' limbs of result (the most significant - being non-zero). - -`_mp_d' - A pointer to the array of limbs which is the absolute value of the - mantissa. These are stored "little endian" as per the `mpn' - functions, so `_mp_d[0]' is the least significant limb and - `_mp_d[ABS(_mp_size)-1]' the most significant. - - The most significant limb is always non-zero, but there are no - other restrictions on its value, in particular the highest 1 bit - can be anywhere within the limb. - - `_mp_prec+1' limbs are allocated to `_mp_d', the extra limb being - for convenience (see below). There are no reallocations during a - calculation, only in a change of precision with `mpf_set_prec'. - -`_mp_exp' - The exponent, in limbs, determining the location of the implied - radix point. Zero means the radix point is just above the most - significant limb. Positive values mean a radix point offset - towards the lower limbs and hence a value >= 1, as for example in - the diagram above. Negative exponents mean a radix point further - above the highest limb. - - Naturally the exponent can be any value, it doesn't have to fall - within the limbs as the diagram shows, it can be a long way above - or a long way below. Limbs other than those included in the - `{_mp_d,_mp_size}' data are treated as zero. - - The `_mp_size' and `_mp_prec' fields are `int', although the -`mp_size_t' type is usually a `long'. The `_mp_exp' field is usually -`long'. This is done to make some fields just 32 bits on some 64 bits -systems, thereby saving a few bytes of data space but still providing -plenty of precision and a very large range. - - -The following various points should be noted. - -Low Zeros - The least significant limbs `_mp_d[0]' etc can be zero, though - such low zeros can always be ignored. Routines likely to produce - low zeros check and avoid them to save time in subsequent - calculations, but for most routines they're quite unlikely and - aren't checked. - -Mantissa Size Range - The `_mp_size' count of limbs in use can be less than `_mp_prec' if - the value can be represented in less. This means low precision - values or small integers stored in a high precision `mpf_t' can - still be operated on efficiently. - - `_mp_size' can also be greater than `_mp_prec'. Firstly a value is - allowed to use all of the `_mp_prec+1' limbs available at `_mp_d', - and secondly when `mpf_set_prec_raw' lowers `_mp_prec' it leaves - `_mp_size' unchanged and so the size can be arbitrarily bigger than - `_mp_prec'. - -Rounding - All rounding is done on limb boundaries. Calculating `_mp_prec' - limbs with the high non-zero will ensure the application requested - minimum precision is obtained. - - The use of simple "trunc" rounding towards zero is efficient, - since there's no need to examine extra limbs and increment or - decrement. - -Bit Shifts - Since the exponent is in limbs, there are no bit shifts in basic - operations like `mpf_add' and `mpf_mul'. When differing exponents - are encountered all that's needed is to adjust pointers to line up - the relevant limbs. - - Of course `mpf_mul_2exp' and `mpf_div_2exp' will require bit - shifts, but the choice is between an exponent in limbs which - requires shifts there, or one in bits which requires them almost - everywhere else. - -Use of `_mp_prec+1' Limbs - The extra limb on `_mp_d' (`_mp_prec+1' rather than just - `_mp_prec') helps when an `mpf' routine might get a carry from its - operation. `mpf_add' for instance will do an `mpn_add' of - `_mp_prec' limbs. If there's no carry then that's the result, but - if there is a carry then it's stored in the extra limb of space and - `_mp_size' becomes `_mp_prec+1'. - - Whenever `_mp_prec+1' limbs are held in a variable, the low limb - is not needed for the intended precision, only the `_mp_prec' high - limbs. But zeroing it out or moving the rest down is unnecessary. - Subsequent routines reading the value will simply take the high - limbs they need, and this will be `_mp_prec' if their target has - that same precision. This is no more than a pointer adjustment, - and must be checked anyway since the destination precision can be - different from the sources. - - Copy functions like `mpf_set' will retain a full `_mp_prec+1' limbs - if available. This ensures that a variable which has `_mp_size' - equal to `_mp_prec+1' will get its full exact value copied. - Strictly speaking this is unnecessary since only `_mp_prec' limbs - are needed for the application's requested precision, but it's - considered that an `mpf_set' from one variable into another of the - same precision ought to produce an exact copy. - -Application Precisions - `__GMPF_BITS_TO_PREC' converts an application requested precision - to an `_mp_prec'. The value in bits is rounded up to a whole limb - then an extra limb is added since the most significant limb of - `_mp_d' is only non-zero and therefore might contain only one bit. - - `__GMPF_PREC_TO_BITS' does the reverse conversion, and removes the - extra limb from `_mp_prec' before converting to bits. The net - effect of reading back with `mpf_get_prec' is simply the precision - rounded up to a multiple of `mp_bits_per_limb'. - - Note that the extra limb added here for the high only being - non-zero is in addition to the extra limb allocated to `_mp_d'. - For example with a 32-bit limb, an application request for 250 - bits will be rounded up to 8 limbs, then an extra added for the - high being only non-zero, giving an `_mp_prec' of 9. `_mp_d' then - gets 10 limbs allocated. Reading back with `mpf_get_prec' will - take `_mp_prec' subtract 1 limb and multiply by 32, giving 256 - bits. - - Strictly speaking, the fact the high limb has at least one bit - means that a float with, say, 3 limbs of 32-bits each will be - holding at least 65 bits, but for the purposes of `mpf_t' it's - considered simply to be 64 bits, a nice multiple of the limb size. - - -File: gmp.info, Node: Raw Output Internals, Next: C++ Interface Internals, Prev: Float Internals, Up: Internals - -17.4 Raw Output Internals -========================= - -`mpz_out_raw' uses the following format. - - +------+------------------------+ - | size | data bytes | - +------+------------------------+ - - The size is 4 bytes written most significant byte first, being the -number of subsequent data bytes, or the twos complement negative of -that when a negative integer is represented. The data bytes are the -absolute value of the integer, written most significant byte first. - - The most significant data byte is always non-zero, so the output is -the same on all systems, irrespective of limb size. - - In GMP 1, leading zero bytes were written to pad the data bytes to a -multiple of the limb size. `mpz_inp_raw' will still accept this, for -compatibility. - - The use of "big endian" for both the size and data fields is -deliberate, it makes the data easy to read in a hex dump of a file. -Unfortunately it also means that the limb data must be reversed when -reading or writing, so neither a big endian nor little endian system -can just read and write `_mp_d'. - - -File: gmp.info, Node: C++ Interface Internals, Prev: Raw Output Internals, Up: Internals - -17.5 C++ Interface Internals -============================ - -A system of expression templates is used to ensure something like -`a=b+c' turns into a simple call to `mpz_add' etc. For `mpf_class' the -scheme also ensures the precision of the final destination is used for -any temporaries within a statement like `f=w*x+y*z'. These are -important features which a naive implementation cannot provide. - - A simplified description of the scheme follows. The true scheme is -complicated by the fact that expressions have different return types. -For detailed information, refer to the source code. - - To perform an operation, say, addition, we first define a "function -object" evaluating it, - - struct __gmp_binary_plus - { - static void eval(mpf_t f, mpf_t g, mpf_t h) { mpf_add(f, g, h); } - }; - -And an "additive expression" object, - - __gmp_expr<__gmp_binary_expr > - operator+(const mpf_class &f, const mpf_class &g) - { - return __gmp_expr - <__gmp_binary_expr >(f, g); - } - - The seemingly redundant `__gmp_expr<__gmp_binary_expr<...>>' is used -to encapsulate any possible kind of expression into a single template -type. In fact even `mpf_class' etc are `typedef' specializations of -`__gmp_expr'. - - Next we define assignment of `__gmp_expr' to `mpf_class'. - - template - mpf_class & mpf_class::operator=(const __gmp_expr &expr) - { - expr.eval(this->get_mpf_t(), this->precision()); - return *this; - } - - template - void __gmp_expr<__gmp_binary_expr >::eval - (mpf_t f, mp_bitcnt_t precision) - { - Op::eval(f, expr.val1.get_mpf_t(), expr.val2.get_mpf_t()); - } - - where `expr.val1' and `expr.val2' are references to the expression's -operands (here `expr' is the `__gmp_binary_expr' stored within the -`__gmp_expr'). - - This way, the expression is actually evaluated only at the time of -assignment, when the required precision (that of `f') is known. -Furthermore the target `mpf_t' is now available, thus we can call -`mpf_add' directly with `f' as the output argument. - - Compound expressions are handled by defining operators taking -subexpressions as their arguments, like this: - - template - __gmp_expr - <__gmp_binary_expr<__gmp_expr, __gmp_expr, __gmp_binary_plus> > - operator+(const __gmp_expr &expr1, const __gmp_expr &expr2) - { - return __gmp_expr - <__gmp_binary_expr<__gmp_expr, __gmp_expr, __gmp_binary_plus> > - (expr1, expr2); - } - - And the corresponding specializations of `__gmp_expr::eval': - - template - void __gmp_expr - <__gmp_binary_expr<__gmp_expr, __gmp_expr, Op> >::eval - (mpf_t f, mp_bitcnt_t precision) - { - // declare two temporaries - mpf_class temp1(expr.val1, precision), temp2(expr.val2, precision); - Op::eval(f, temp1.get_mpf_t(), temp2.get_mpf_t()); - } - - The expression is thus recursively evaluated to any level of -complexity and all subexpressions are evaluated to the precision of `f'. - - -File: gmp.info, Node: Contributors, Next: References, Prev: Internals, Up: Top - -Appendix A Contributors -*********************** - -Torbjo"rn Granlund wrote the original GMP library and is still the main -developer. Code not explicitly attributed to others, was contributed by -Torbjo"rn. Several other individuals and organizations have contributed -GMP. Here is a list in chronological order on first contribution: - - Gunnar Sjo"din and Hans Riesel helped with mathematical problems in -early versions of the library. - - Richard Stallman helped with the interface design and revised the -first version of this manual. - - Brian Beuning and Doug Lea helped with testing of early versions of -the library and made creative suggestions. - - John Amanatides of York University in Canada contributed the function -`mpz_probab_prime_p'. - - Paul Zimmermann wrote the REDC-based mpz_powm code, the -Scho"nhage-Strassen FFT multiply code, and the Karatsuba square root -code. He also improved the Toom3 code for GMP 4.2. Paul sparked the -development of GMP 2, with his comparisons between bignum packages. -The ECMNET project Paul is organizing was a driving force behind many -of the optimizations in GMP 3. Paul also wrote the new GMP 4.3 nth -root code (with Torbjo"rn). - - Ken Weber (Kent State University, Universidade Federal do Rio Grande -do Sul) contributed now defunct versions of `mpz_gcd', `mpz_divexact', -`mpn_gcd', and `mpn_bdivmod', partially supported by CNPq (Brazil) -grant 301314194-2. - - Per Bothner of Cygnus Support helped to set up GMP to use Cygnus' -configure. He has also made valuable suggestions and tested numerous -intermediary releases. - - Joachim Hollman was involved in the design of the `mpf' interface, -and in the `mpz' design revisions for version 2. - - Bennet Yee contributed the initial versions of `mpz_jacobi' and -`mpz_legendre'. - - Andreas Schwab contributed the files `mpn/m68k/lshift.S' and -`mpn/m68k/rshift.S' (now in `.asm' form). - - Robert Harley of Inria, France and David Seal of ARM, England, -suggested clever improvements for population count. Robert also wrote -highly optimized Karatsuba and 3-way Toom multiplication functions for -GMP 3, and contributed the ARM assembly code. - - Torsten Ekedahl of the Mathematical department of Stockholm -University provided significant inspiration during several phases of -the GMP development. His mathematical expertise helped improve several -algorithms. - - Linus Nordberg wrote the new configure system based on autoconf and -implemented the new random functions. - - Kevin Ryde worked on a large number of things: optimized x86 code, -m4 asm macros, parameter tuning, speed measuring, the configure system, -function inlining, divisibility tests, bit scanning, Jacobi symbols, -Fibonacci and Lucas number functions, printf and scanf functions, perl -interface, demo expression parser, the algorithms chapter in the -manual, `gmpasm-mode.el', and various miscellaneous improvements -elsewhere. - - Kent Boortz made the Mac OS 9 port. - - Steve Root helped write the optimized alpha 21264 assembly code. - - Gerardo Ballabio wrote the `gmpxx.h' C++ class interface and the C++ -`istream' input routines. - - Jason Moxham rewrote `mpz_fac_ui'. - - Pedro Gimeno implemented the Mersenne Twister and made other random -number improvements. - - Niels Mo"ller wrote the sub-quadratic GCD and extended GCD code, the -quadratic Hensel division code, and (with Torbjo"rn) the new divide and -conquer division code for GMP 4.3. Niels also helped implement the new -Toom multiply code for GMP 4.3 and implemented helper functions to -simplify Toom evaluations for GMP 5.0. He wrote the original version -of mpn_mulmod_bnm1. - - Alberto Zanoni and Marco Bodrato suggested the unbalanced multiply -strategy, and found the optimal strategies for evaluation and -interpolation in Toom multiplication. - - Marco Bodrato helped implement the new Toom multiply code for GMP -4.3 and implemented most of the new Toom multiply and squaring code for -5.0. He is the main author of the current mpn_mulmod_bnm1 and -mpn_mullo_n. Marco also wrote the functions mpn_invert and -mpn_invertappr. - - David Harvey suggested the internal function `mpn_bdiv_dbm1', -implementing division relevant to Toom multiplication. He also worked -on fast assembly sequences, in particular on a fast AMD64 -`mpn_mul_basecase'. - - Martin Boij wrote `mpn_perfect_power_p'. - - (This list is chronological, not ordered after significance. If you -have contributed to GMP but are not listed above, please tell - about the omission!) - - The development of floating point functions of GNU MP 2, were -supported in part by the ESPRIT-BRA (Basic Research Activities) 6846 -project POSSO (POlynomial System SOlving). - - The development of GMP 2, 3, and 4 was supported in part by the IDA -Center for Computing Sciences. - - Thanks go to Hans Thorsen for donating an SGI system for the GMP -test system environment. - - -File: gmp.info, Node: References, Next: GNU Free Documentation License, Prev: Contributors, Up: Top - -Appendix B References -********************* - -B.1 Books -========= - - * Jonathan M. Borwein and Peter B. Borwein, "Pi and the AGM: A Study - in Analytic Number Theory and Computational Complexity", Wiley, - 1998. - - * Richard Crandall and Carl Pomerance, "Prime Numbers: A - Computational Perspective", 2nd edition, Springer-Verlag, 2005. - `http://math.dartmouth.edu/~carlp/' - - * Henri Cohen, "A Course in Computational Algebraic Number Theory", - Graduate Texts in Mathematics number 138, Springer-Verlag, 1993. - `http://www.math.u-bordeaux.fr/~cohen/' - - * Donald E. Knuth, "The Art of Computer Programming", volume 2, - "Seminumerical Algorithms", 3rd edition, Addison-Wesley, 1998. - `http://www-cs-faculty.stanford.edu/~knuth/taocp.html' - - * John D. Lipson, "Elements of Algebra and Algebraic Computing", The - Benjamin Cummings Publishing Company Inc, 1981. - - * Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone, - "Handbook of Applied Cryptography", - `http://www.cacr.math.uwaterloo.ca/hac/' - - * Richard M. Stallman and the GCC Developer Community, "Using the - GNU Compiler Collection", Free Software Foundation, 2008, - available online `http://gcc.gnu.org/onlinedocs/', and in the GCC - package `ftp://ftp.gnu.org/gnu/gcc/' - -B.2 Papers -========== - - * Yves Bertot, Nicolas Magaud and Paul Zimmermann, "A Proof of GMP - Square Root", Journal of Automated Reasoning, volume 29, 2002, pp. - 225-252. Also available online as INRIA Research Report 4475, - June 2001, `http://www.inria.fr/rrrt/rr-4475.html' - - * Christoph Burnikel and Joachim Ziegler, "Fast Recursive Division", - Max-Planck-Institut fuer Informatik Research Report MPI-I-98-1-022, - `http://data.mpi-sb.mpg.de/internet/reports.nsf/NumberView/1998-1-022' - - * Torbjo"rn Granlund and Peter L. Montgomery, "Division by Invariant - Integers using Multiplication", in Proceedings of the SIGPLAN - PLDI'94 Conference, June 1994. Also available - `ftp://ftp.cwi.nl/pub/pmontgom/divcnst.psa4.gz' (and .psl.gz). - - * Niels Mo"ller and Torbjo"rn Granlund, "Improved division by - invariant integers", to appear. - - * Torbjo"rn Granlund and Niels Mo"ller, "Division of integers large - and small", to appear. - - * Tudor Jebelean, "An algorithm for exact division", Journal of - Symbolic Computation, volume 15, 1993, pp. 169-180. Research - report version available - `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1992/92-35.ps.gz' - - * Tudor Jebelean, "Exact Division with Karatsuba Complexity - - Extended Abstract", RISC-Linz technical report 96-31, - `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1996/96-31.ps.gz' - - * Tudor Jebelean, "Practical Integer Division with Karatsuba - Complexity", ISSAC 97, pp. 339-341. Technical report available - `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1996/96-29.ps.gz' - - * Tudor Jebelean, "A Generalization of the Binary GCD Algorithm", - ISSAC 93, pp. 111-116. Technical report version available - `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1993/93-01.ps.gz' - - * Tudor Jebelean, "A Double-Digit Lehmer-Euclid Algorithm for - Finding the GCD of Long Integers", Journal of Symbolic - Computation, volume 19, 1995, pp. 145-157. Technical report - version also available - `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1992/92-69.ps.gz' - - * Werner Krandick and Tudor Jebelean, "Bidirectional Exact Integer - Division", Journal of Symbolic Computation, volume 21, 1996, pp. - 441-455. Early technical report version also available - `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1994/94-50.ps.gz' - - * Makoto Matsumoto and Takuji Nishimura, "Mersenne Twister: A - 623-dimensionally equidistributed uniform pseudorandom number - generator", ACM Transactions on Modelling and Computer Simulation, - volume 8, January 1998, pp. 3-30. Available online - `http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.ps.gz' - (or .pdf) - - * R. Moenck and A. Borodin, "Fast Modular Transforms via Division", - Proceedings of the 13th Annual IEEE Symposium on Switching and - Automata Theory, October 1972, pp. 90-96. Reprinted as "Fast - Modular Transforms", Journal of Computer and System Sciences, - volume 8, number 3, June 1974, pp. 366-386. - - * Niels Mo"ller, "On Scho"nhage's algorithm and subquadratic integer - GCD computation", in Mathematics of Computation, volume 77, - January 2008, pp. 589-607. - - * Peter L. Montgomery, "Modular Multiplication Without Trial - Division", in Mathematics of Computation, volume 44, number 170, - April 1985. - - * Arnold Scho"nhage and Volker Strassen, "Schnelle Multiplikation - grosser Zahlen", Computing 7, 1971, pp. 281-292. - - * Kenneth Weber, "The accelerated integer GCD algorithm", ACM - Transactions on Mathematical Software, volume 21, number 1, March - 1995, pp. 111-122. - - * Paul Zimmermann, "Karatsuba Square Root", INRIA Research Report - 3805, November 1999, `http://www.inria.fr/rrrt/rr-3805.html' - - * Paul Zimmermann, "A Proof of GMP Fast Division and Square Root - Implementations", - `http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz' - - * Dan Zuras, "On Squaring and Multiplying Large Integers", ARITH-11: - IEEE Symposium on Computer Arithmetic, 1993, pp. 260 to 271. - Reprinted as "More on Multiplying and Squaring Large Integers", - IEEE Transactions on Computers, volume 43, number 8, August 1994, - pp. 899-908. - - -File: gmp.info, Node: GNU Free Documentation License, Next: Concept Index, Prev: References, Up: Top - -Appendix C GNU Free Documentation License -***************************************** - - Version 1.3, 3 November 2008 - - Copyright (C) 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc. - `http://fsf.org/' - - Everyone is permitted to copy and distribute verbatim copies - of this license document, but changing it is not allowed. - - 0. 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A - copy that is not "Transparent" is called "Opaque". - - Examples of suitable formats for Transparent copies include plain - ASCII without markup, Texinfo input format, LaTeX input format, - SGML or XML using a publicly available DTD, and - standard-conforming simple HTML, PostScript or PDF designed for - human modification. Examples of transparent image formats include - PNG, XCF and JPG. Opaque formats include proprietary formats that - can be read and edited only by proprietary word processors, SGML or - XML for which the DTD and/or processing tools are not generally - available, and the machine-generated HTML, PostScript or PDF - produced by some word processors for output purposes only. - - The "Title Page" means, for a printed book, the title page itself, - plus such following pages as are needed to hold, legibly, the - material this License requires to appear in the title page. For - works in formats which do not have any title page as such, "Title - Page" means the text near the most prominent appearance of the - work's title, preceding the beginning of the body of the text. - - The "publisher" means any person or entity that distributes copies - of the Document to the public. - - A section "Entitled XYZ" means a named subunit of the Document - whose title either is precisely XYZ or contains XYZ in parentheses - following text that translates XYZ in another language. (Here XYZ - stands for a specific section name mentioned below, such as - "Acknowledgements", "Dedications", "Endorsements", or "History".) - To "Preserve the Title" of such a section when you modify the - Document means that it remains a section "Entitled XYZ" according - to this definition. - - The Document may include Warranty Disclaimers next to the notice - which states that this License applies to the Document. These - Warranty Disclaimers are considered to be included by reference in - this License, but only as regards disclaiming warranties: any other - implication that these Warranty Disclaimers may have is void and - has no effect on the meaning of this License. - - 2. VERBATIM COPYING - - You may copy and distribute the Document in any medium, either - commercially or noncommercially, provided that this License, the - copyright notices, and the license notice saying this License - applies to the Document are reproduced in all copies, and that you - add no other conditions whatsoever to those of this License. You - may not use technical measures to obstruct or control the reading - or further copying of the copies you make or distribute. However, - you may accept compensation in exchange for copies. If you - distribute a large enough number of copies you must also follow - the conditions in section 3. - - You may also lend copies, under the same conditions stated above, - and you may publicly display copies. - - 3. COPYING IN QUANTITY - - If you publish printed copies (or copies in media that commonly - have printed covers) of the Document, numbering more than 100, and - the Document's license notice requires Cover Texts, you must - enclose the copies in covers that carry, clearly and legibly, all - these Cover Texts: Front-Cover Texts on the front cover, and - Back-Cover Texts on the back cover. Both covers must also clearly - and legibly identify you as the publisher of these copies. The - front cover must present the full title with all words of the - title equally prominent and visible. You may add other material - on the covers in addition. Copying with changes limited to the - covers, as long as they preserve the title of the Document and - satisfy these conditions, can be treated as verbatim copying in - other respects. - - If the required texts for either cover are too voluminous to fit - legibly, you should put the first ones listed (as many as fit - reasonably) on the actual cover, and continue the rest onto - adjacent pages. - - If you publish or distribute Opaque copies of the Document - numbering more than 100, you must either include a - machine-readable Transparent copy along with each Opaque copy, or - state in or with each Opaque copy a computer-network location from - which the general network-using public has access to download - using public-standard network protocols a complete Transparent - copy of the Document, free of added material. If you use the - latter option, you must take reasonably prudent steps, when you - begin distribution of Opaque copies in quantity, to ensure that - this Transparent copy will remain thus accessible at the stated - location until at least one year after the last time you - distribute an Opaque copy (directly or through your agents or - retailers) of that edition to the public. - - It is requested, but not required, that you contact the authors of - the Document well before redistributing any large number of - copies, to give them a chance to provide you with an updated - version of the Document. - - 4. MODIFICATIONS - - You may copy and distribute a Modified Version of the Document - under the conditions of sections 2 and 3 above, provided that you - release the Modified Version under precisely this License, with - the Modified Version filling the role of the Document, thus - licensing distribution and modification of the Modified Version to - whoever possesses a copy of it. In addition, you must do these - things in the Modified Version: - - A. Use in the Title Page (and on the covers, if any) a title - distinct from that of the Document, and from those of - previous versions (which should, if there were any, be listed - in the History section of the Document). You may use the - same title as a previous version if the original publisher of - that version gives permission. - - B. List on the Title Page, as authors, one or more persons or - entities responsible for authorship of the modifications in - the Modified Version, together with at least five of the - principal authors of the Document (all of its principal - authors, if it has fewer than five), unless they release you - from this requirement. - - C. State on the Title page the name of the publisher of the - Modified Version, as the publisher. - - D. Preserve all the copyright notices of the Document. - - E. Add an appropriate copyright notice for your modifications - adjacent to the other copyright notices. - - F. Include, immediately after the copyright notices, a license - notice giving the public permission to use the Modified - Version under the terms of this License, in the form shown in - the Addendum below. - - G. Preserve in that license notice the full lists of Invariant - Sections and required Cover Texts given in the Document's - license notice. - - H. Include an unaltered copy of this License. - - I. Preserve the section Entitled "History", Preserve its Title, - and add to it an item stating at least the title, year, new - authors, and publisher of the Modified Version as given on - the Title Page. If there is no section Entitled "History" in - the Document, create one stating the title, year, authors, - and publisher of the Document as given on its Title Page, - then add an item describing the Modified Version as stated in - the previous sentence. - - J. Preserve the network location, if any, given in the Document - for public access to a Transparent copy of the Document, and - likewise the network locations given in the Document for - previous versions it was based on. These may be placed in - the "History" section. You may omit a network location for a - work that was published at least four years before the - Document itself, or if the original publisher of the version - it refers to gives permission. - - K. For any section Entitled "Acknowledgements" or "Dedications", - Preserve the Title of the section, and preserve in the - section all the substance and tone of each of the contributor - acknowledgements and/or dedications given therein. - - L. Preserve all the Invariant Sections of the Document, - unaltered in their text and in their titles. Section numbers - or the equivalent are not considered part of the section - titles. - - M. Delete any section Entitled "Endorsements". Such a section - may not be included in the Modified Version. - - N. Do not retitle any existing section to be Entitled - "Endorsements" or to conflict in title with any Invariant - Section. - - O. Preserve any Warranty Disclaimers. - - If the Modified Version includes new front-matter sections or - appendices that qualify as Secondary Sections and contain no - material copied from the Document, you may at your option - designate some or all of these sections as invariant. To do this, - add their titles to the list of Invariant Sections in the Modified - Version's license notice. These titles must be distinct from any - other section titles. - - You may add a section Entitled "Endorsements", provided it contains - nothing but endorsements of your Modified Version by various - parties--for example, statements of peer review or that the text - has been approved by an organization as the authoritative - definition of a standard. - - You may add a passage of up to five words as a Front-Cover Text, - and a passage of up to 25 words as a Back-Cover Text, to the end - of the list of Cover Texts in the Modified Version. Only one - passage of Front-Cover Text and one of Back-Cover Text may be - added by (or through arrangements made by) any one entity. If the - Document already includes a cover text for the same cover, - previously added by you or by arrangement made by the same entity - you are acting on behalf of, you may not add another; but you may - replace the old one, on explicit permission from the previous - publisher that added the old one. - - The author(s) and publisher(s) of the Document do not by this - License give permission to use their names for publicity for or to - assert or imply endorsement of any Modified Version. - - 5. COMBINING DOCUMENTS - - You may combine the Document with other documents released under - this License, under the terms defined in section 4 above for - modified versions, provided that you include in the combination - all of the Invariant Sections of all of the original documents, - unmodified, and list them all as Invariant Sections of your - combined work in its license notice, and that you preserve all - their Warranty Disclaimers. - - The combined work need only contain one copy of this License, and - multiple identical Invariant Sections may be replaced with a single - copy. If there are multiple Invariant Sections with the same name - but different contents, make the title of each such section unique - by adding at the end of it, in parentheses, the name of the - original author or publisher of that section if known, or else a - unique number. Make the same adjustment to the section titles in - the list of Invariant Sections in the license notice of the - combined work. - - In the combination, you must combine any sections Entitled - "History" in the various original documents, forming one section - Entitled "History"; likewise combine any sections Entitled - "Acknowledgements", and any sections Entitled "Dedications". You - must delete all sections Entitled "Endorsements." - - 6. COLLECTIONS OF DOCUMENTS - - You may make a collection consisting of the Document and other - documents released under this License, and replace the individual - copies of this License in the various documents with a single copy - that is included in the collection, provided that you follow the - rules of this License for verbatim copying of each of the - documents in all other respects. - - You may extract a single document from such a collection, and - distribute it individually under this License, provided you insert - a copy of this License into the extracted document, and follow - this License in all other respects regarding verbatim copying of - that document. - - 7. AGGREGATION WITH INDEPENDENT WORKS - - A compilation of the Document or its derivatives with other - separate and independent documents or works, in or on a volume of - a storage or distribution medium, is called an "aggregate" if the - copyright resulting from the compilation is not used to limit the - legal rights of the compilation's users beyond what the individual - works permit. When the Document is included in an aggregate, this - License does not apply to the other works in the aggregate which - are not themselves derivative works of the Document. - - If the Cover Text requirement of section 3 is applicable to these - copies of the Document, then if the Document is less than one half - of the entire aggregate, the Document's Cover Texts may be placed - on covers that bracket the Document within the aggregate, or the - electronic equivalent of covers if the Document is in electronic - form. Otherwise they must appear on printed covers that bracket - the whole aggregate. - - 8. TRANSLATION - - Translation is considered a kind of modification, so you may - distribute translations of the Document under the terms of section - 4. Replacing Invariant Sections with translations requires special - permission from their copyright holders, but you may include - translations of some or all Invariant Sections in addition to the - original versions of these Invariant Sections. You may include a - translation of this License, and all the license notices in the - Document, and any Warranty Disclaimers, provided that you also - include the original English version of this License and the - original versions of those notices and disclaimers. In case of a - disagreement between the translation and the original version of - this License or a notice or disclaimer, the original version will - prevail. - - If a section in the Document is Entitled "Acknowledgements", - "Dedications", or "History", the requirement (section 4) to - Preserve its Title (section 1) will typically require changing the - actual title. - - 9. TERMINATION - - You may not copy, modify, sublicense, or distribute the Document - except as expressly provided under this License. Any attempt - otherwise to copy, modify, sublicense, or distribute it is void, - and will automatically terminate your rights under this License. - - However, if you cease all violation of this License, then your - license from a particular copyright holder is reinstated (a) - provisionally, unless and until the copyright holder explicitly - and finally terminates your license, and (b) permanently, if the - copyright holder fails to notify you of the violation by some - reasonable means prior to 60 days after the cessation. - - Moreover, your license from a particular copyright holder is - reinstated permanently if the copyright holder notifies you of the - violation by some reasonable means, this is the first time you have - received notice of violation of this License (for any work) from - that copyright holder, and you cure the violation prior to 30 days - after your receipt of the notice. - - Termination of your rights under this section does not terminate - the licenses of parties who have received copies or rights from - you under this License. If your rights have been terminated and - not permanently reinstated, receipt of a copy of some or all of - the same material does not give you any rights to use it. - - 10. FUTURE REVISIONS OF THIS LICENSE - - The Free Software Foundation may publish new, revised versions of - the GNU Free Documentation License from time to time. Such new - versions will be similar in spirit to the present version, but may - differ in detail to address new problems or concerns. See - `http://www.gnu.org/copyleft/'. - - Each version of the License is given a distinguishing version - number. If the Document specifies that a particular numbered - version of this License "or any later version" applies to it, you - have the option of following the terms and conditions either of - that specified version or of any later version that has been - published (not as a draft) by the Free Software Foundation. If - the Document does not specify a version number of this License, - you may choose any version ever published (not as a draft) by the - Free Software Foundation. If the Document specifies that a proxy - can decide which future versions of this License can be used, that - proxy's public statement of acceptance of a version permanently - authorizes you to choose that version for the Document. - - 11. RELICENSING - - "Massive Multiauthor Collaboration Site" (or "MMC Site") means any - World Wide Web server that publishes copyrightable works and also - provides prominent facilities for anybody to edit those works. A - public wiki that anybody can edit is an example of such a server. - A "Massive Multiauthor Collaboration" (or "MMC") contained in the - site means any set of copyrightable works thus published on the MMC - site. - - "CC-BY-SA" means the Creative Commons Attribution-Share Alike 3.0 - license published by Creative Commons Corporation, a not-for-profit - corporation with a principal place of business in San Francisco, - California, as well as future copyleft versions of that license - published by that same organization. - - "Incorporate" means to publish or republish a Document, in whole or - in part, as part of another Document. - - An MMC is "eligible for relicensing" if it is licensed under this - License, and if all works that were first published under this - License somewhere other than this MMC, and subsequently - incorporated in whole or in part into the MMC, (1) had no cover - texts or invariant sections, and (2) were thus incorporated prior - to November 1, 2008. - - The operator of an MMC Site may republish an MMC contained in the - site under CC-BY-SA on the same site at any time before August 1, - 2009, provided the MMC is eligible for relicensing. - - -ADDENDUM: How to use this License for your documents -==================================================== - -To use this License in a document you have written, include a copy of -the License in the document and put the following copyright and license -notices just after the title page: - - Copyright (C) YEAR YOUR NAME. - Permission is granted to copy, distribute and/or modify this document - under the terms of the GNU Free Documentation License, Version 1.3 - or any later version published by the Free Software Foundation; - with no Invariant Sections, no Front-Cover Texts, and no Back-Cover - Texts. A copy of the license is included in the section entitled ``GNU - Free Documentation License''. - - If you have Invariant Sections, Front-Cover Texts and Back-Cover -Texts, replace the "with...Texts." line with this: - - with the Invariant Sections being LIST THEIR TITLES, with - the Front-Cover Texts being LIST, and with the Back-Cover Texts - being LIST. - - If you have Invariant Sections without Cover Texts, or some other -combination of the three, merge those two alternatives to suit the -situation. - - If your document contains nontrivial examples of program code, we -recommend releasing these examples in parallel under your choice of -free software license, such as the GNU General Public License, to -permit their use in free software. - - -File: gmp.info, Node: Concept Index, Next: Function Index, Prev: GNU Free Documentation License, Up: Top - -Concept Index -************* - -[index] -* Menu: - -* #include: Headers and Libraries. - (line 6) -* --build: Build Options. (line 52) -* --disable-fft: Build Options. (line 317) -* --disable-shared: Build Options. (line 45) -* --disable-static: Build Options. (line 45) -* --enable-alloca: Build Options. (line 278) -* --enable-assert: Build Options. (line 327) -* --enable-cxx: Build Options. (line 230) -* --enable-fat: Build Options. (line 164) -* --enable-mpbsd: Build Options. (line 322) -* --enable-profiling <1>: Profiling. (line 6) -* --enable-profiling: Build Options. (line 331) -* --exec-prefix: Build Options. (line 32) -* --host: Build Options. (line 66) -* --prefix: Build Options. (line 32) -* -finstrument-functions: Profiling. (line 66) -* 2exp functions: Efficiency. (line 43) -* 68000: Notes for Particular Systems. - (line 80) -* 80x86: Notes for Particular Systems. - (line 126) -* ABI <1>: Build Options. (line 171) -* ABI: ABI and ISA. (line 6) -* About this manual: Introduction to GMP. (line 58) -* AC_CHECK_LIB: Autoconf. (line 11) -* AIX <1>: ABI and ISA. (line 184) -* AIX <2>: Notes for Particular Systems. - (line 7) -* AIX: ABI and ISA. (line 169) -* Algorithms: Algorithms. (line 6) -* alloca: Build Options. (line 278) -* Allocation of memory: Custom Allocation. (line 6) -* AMD64: ABI and ISA. (line 44) -* Anonymous FTP of latest version: Introduction to GMP. (line 38) -* Application Binary Interface: ABI and ISA. (line 6) -* Arithmetic functions <1>: Float Arithmetic. (line 6) -* Arithmetic functions <2>: Integer Arithmetic. (line 6) -* Arithmetic functions: Rational Arithmetic. (line 6) -* ARM: Notes for Particular Systems. - (line 20) -* Assembly cache handling: Assembly Cache Handling. - (line 6) -* Assembly carry propagation: Assembly Carry Propagation. - (line 6) -* Assembly code organisation: Assembly Code Organisation. - (line 6) -* Assembly coding: Assembly Coding. (line 6) -* Assembly floating Point: Assembly Floating Point. - (line 6) -* Assembly loop unrolling: Assembly Loop Unrolling. - (line 6) -* Assembly SIMD: Assembly SIMD Instructions. - (line 6) -* Assembly software pipelining: Assembly Software Pipelining. - (line 6) -* Assembly writing guide: Assembly Writing Guide. - (line 6) -* Assertion checking <1>: Debugging. (line 79) -* Assertion checking: Build Options. (line 327) -* Assignment functions <1>: Assigning Floats. (line 6) -* Assignment functions <2>: Initializing Rationals. - (line 6) -* Assignment functions <3>: Simultaneous Integer Init & Assign. - (line 6) -* Assignment functions <4>: Simultaneous Float Init & Assign. - (line 6) -* Assignment functions: Assigning Integers. (line 6) -* Autoconf: Autoconf. (line 6) -* Basics: GMP Basics. (line 6) -* Berkeley MP compatible functions <1>: Build Options. (line 322) -* Berkeley MP compatible functions: BSD Compatible Functions. - (line 6) -* Binomial coefficient algorithm: Binomial Coefficients Algorithm. - (line 6) -* Binomial coefficient functions: Number Theoretic Functions. - (line 100) -* Binutils strip: Known Build Problems. - (line 28) -* Bit manipulation functions: Integer Logic and Bit Fiddling. - (line 6) -* Bit scanning functions: Integer Logic and Bit Fiddling. - (line 38) -* Bit shift left: Integer Arithmetic. (line 35) -* Bit shift right: Integer Division. (line 53) -* Bits per limb: Useful Macros and Constants. - (line 7) -* BSD MP compatible functions <1>: Build Options. (line 322) -* BSD MP compatible functions: BSD Compatible Functions. - (line 6) -* Bug reporting: Reporting Bugs. (line 6) -* Build directory: Build Options. (line 19) -* Build notes for binary packaging: Notes for Package Builds. - (line 6) -* Build notes for particular systems: Notes for Particular Systems. - (line 6) -* Build options: Build Options. (line 6) -* Build problems known: Known Build Problems. - (line 6) -* Build system: Build Options. (line 52) -* Building GMP: Installing GMP. (line 6) -* Bus error: Debugging. (line 7) -* C compiler: Build Options. (line 182) -* C++ compiler: Build Options. (line 254) -* C++ interface: C++ Class Interface. (line 6) -* C++ interface internals: C++ Interface Internals. - (line 6) -* C++ istream input: C++ Formatted Input. (line 6) -* C++ ostream output: C++ Formatted Output. - (line 6) -* C++ support: Build Options. (line 230) -* CC: Build Options. (line 182) -* CC_FOR_BUILD: Build Options. (line 217) -* CFLAGS: Build Options. (line 182) -* Checker: Debugging. (line 115) -* checkergcc: Debugging. (line 122) -* Code organisation: Assembly Code Organisation. - (line 6) -* Compaq C++: Notes for Particular Systems. - (line 25) -* Comparison functions <1>: Integer Comparisons. (line 6) -* Comparison functions <2>: Comparing Rationals. (line 6) -* Comparison functions: Float Comparison. (line 6) -* Compatibility with older versions: Compatibility with older versions. - (line 6) -* Conditions for copying GNU MP: Copying. (line 6) -* Configuring GMP: Installing GMP. (line 6) -* Congruence algorithm: Exact Remainder. (line 29) -* Congruence functions: Integer Division. (line 124) -* Constants: Useful Macros and Constants. - (line 6) -* Contributors: Contributors. (line 6) -* Conventions for parameters: Parameter Conventions. - (line 6) -* Conventions for variables: Variable Conventions. - (line 6) -* Conversion functions <1>: Converting Integers. (line 6) -* Conversion functions <2>: Converting Floats. (line 6) -* Conversion functions: Rational Conversions. - (line 6) -* Copying conditions: Copying. (line 6) -* CPPFLAGS: Build Options. (line 208) -* CPU types <1>: Introduction to GMP. (line 24) -* CPU types: Build Options. (line 108) -* Cross compiling: Build Options. (line 66) -* Custom allocation: Custom Allocation. (line 6) -* CXX: Build Options. (line 254) -* CXXFLAGS: Build Options. (line 254) -* Cygwin: Notes for Particular Systems. - (line 43) -* Darwin: Known Build Problems. - (line 51) -* Debugging: Debugging. (line 6) -* Demonstration programs: Demonstration Programs. - (line 6) -* Digits in an integer: Miscellaneous Integer Functions. - (line 23) -* Divisibility algorithm: Exact Remainder. (line 29) -* Divisibility functions: Integer Division. (line 124) -* Divisibility testing: Efficiency. (line 91) -* Division algorithms: Division Algorithms. (line 6) -* Division functions <1>: Rational Arithmetic. (line 22) -* Division functions <2>: Integer Division. (line 6) -* Division functions: Float Arithmetic. (line 33) -* DJGPP <1>: Notes for Particular Systems. - (line 43) -* DJGPP: Known Build Problems. - (line 18) -* DLLs: Notes for Particular Systems. - (line 56) -* DocBook: Build Options. (line 354) -* Documentation formats: Build Options. (line 347) -* Documentation license: GNU Free Documentation License. - (line 6) -* DVI: Build Options. (line 350) -* Efficiency: Efficiency. (line 6) -* Emacs: Emacs. (line 6) -* Exact division functions: Integer Division. (line 102) -* Exact remainder: Exact Remainder. (line 6) -* Example programs: Demonstration Programs. - (line 6) -* Exec prefix: Build Options. (line 32) -* Execution profiling <1>: Profiling. (line 6) -* Execution profiling: Build Options. (line 331) -* Exponentiation functions <1>: Integer Exponentiation. - (line 6) -* Exponentiation functions: Float Arithmetic. (line 41) -* Export: Integer Import and Export. - (line 45) -* Expression parsing demo: Demonstration Programs. - (line 18) -* Extended GCD: Number Theoretic Functions. - (line 45) -* Factor removal functions: Number Theoretic Functions. - (line 90) -* Factorial algorithm: Factorial Algorithm. (line 6) -* Factorial functions: Number Theoretic Functions. - (line 95) -* Factorization demo: Demonstration Programs. - (line 25) -* Fast Fourier Transform: FFT Multiplication. (line 6) -* Fat binary: Build Options. (line 164) -* FFT multiplication <1>: FFT Multiplication. (line 6) -* FFT multiplication: Build Options. (line 317) -* Fibonacci number algorithm: Fibonacci Numbers Algorithm. - (line 6) -* Fibonacci sequence functions: Number Theoretic Functions. - (line 108) -* Float arithmetic functions: Float Arithmetic. (line 6) -* Float assignment functions <1>: Simultaneous Float Init & Assign. - (line 6) -* Float assignment functions: Assigning Floats. (line 6) -* Float comparison functions: Float Comparison. (line 6) -* Float conversion functions: Converting Floats. (line 6) -* Float functions: Floating-point Functions. - (line 6) -* Float initialization functions <1>: Simultaneous Float Init & Assign. - (line 6) -* Float initialization functions: Initializing Floats. (line 6) -* Float input and output functions: I/O of Floats. (line 6) -* Float internals: Float Internals. (line 6) -* Float miscellaneous functions: Miscellaneous Float Functions. - (line 6) -* Float random number functions: Miscellaneous Float Functions. - (line 27) -* Float rounding functions: Miscellaneous Float Functions. - (line 9) -* Float sign tests: Float Comparison. (line 33) -* Floating point mode: Notes for Particular Systems. - (line 34) -* Floating-point functions: Floating-point Functions. - (line 6) -* Floating-point number: Nomenclature and Types. - (line 21) -* fnccheck: Profiling. (line 77) -* Formatted input: Formatted Input. (line 6) -* Formatted output: Formatted Output. (line 6) -* Free Documentation License: GNU Free Documentation License. - (line 6) -* frexp <1>: Converting Floats. (line 23) -* frexp: Converting Integers. (line 42) -* FTP of latest version: Introduction to GMP. (line 38) -* Function classes: Function Classes. (line 6) -* FunctionCheck: Profiling. (line 77) -* GCC Checker: Debugging. (line 115) -* GCD algorithms: Greatest Common Divisor Algorithms. - (line 6) -* GCD extended: Number Theoretic Functions. - (line 45) -* GCD functions: Number Theoretic Functions. - (line 30) -* GDB: Debugging. (line 58) -* Generic C: Build Options. (line 153) -* GMP Perl module: Demonstration Programs. - (line 35) -* GMP version number: Useful Macros and Constants. - (line 12) -* gmp.h: Headers and Libraries. - (line 6) -* gmpxx.h: C++ Interface General. - (line 8) -* GNU Debugger: Debugging. (line 58) -* GNU Free Documentation License: GNU Free Documentation License. - (line 6) -* GNU strip: Known Build Problems. - (line 28) -* gprof: Profiling. (line 41) -* Greatest common divisor algorithms: Greatest Common Divisor Algorithms. - (line 6) -* Greatest common divisor functions: Number Theoretic Functions. - (line 30) -* Hardware floating point mode: Notes for Particular Systems. - (line 34) -* Headers: Headers and Libraries. - (line 6) -* Heap problems: Debugging. (line 24) -* Home page: Introduction to GMP. (line 34) -* Host system: Build Options. (line 66) -* HP-UX: ABI and ISA. (line 107) -* HPPA: ABI and ISA. (line 68) -* I/O functions <1>: I/O of Integers. (line 6) -* I/O functions <2>: I/O of Rationals. (line 6) -* I/O functions: I/O of Floats. (line 6) -* i386: Notes for Particular Systems. - (line 126) -* IA-64: ABI and ISA. (line 107) -* Import: Integer Import and Export. - (line 11) -* In-place operations: Efficiency. (line 57) -* Include files: Headers and Libraries. - (line 6) -* info-lookup-symbol: Emacs. (line 6) -* Initialization functions <1>: Initializing Integers. - (line 6) -* Initialization functions <2>: Initializing Rationals. - (line 6) -* Initialization functions <3>: Random State Initialization. - (line 6) -* Initialization functions <4>: Simultaneous Float Init & Assign. - (line 6) -* Initialization functions <5>: Simultaneous Integer Init & Assign. - (line 6) -* Initialization functions: Initializing Floats. (line 6) -* Initializing and clearing: Efficiency. (line 21) -* Input functions <1>: I/O of Integers. (line 6) -* Input functions <2>: I/O of Rationals. (line 6) -* Input functions <3>: I/O of Floats. (line 6) -* Input functions: Formatted Input Functions. - (line 6) -* Install prefix: Build Options. (line 32) -* Installing GMP: Installing GMP. (line 6) -* Instruction Set Architecture: ABI and ISA. (line 6) -* instrument-functions: Profiling. (line 66) -* Integer: Nomenclature and Types. - (line 6) -* Integer arithmetic functions: Integer Arithmetic. (line 6) -* Integer assignment functions <1>: Simultaneous Integer Init & Assign. - (line 6) -* Integer assignment functions: Assigning Integers. (line 6) -* Integer bit manipulation functions: Integer Logic and Bit Fiddling. - (line 6) -* Integer comparison functions: Integer Comparisons. (line 6) -* Integer conversion functions: Converting Integers. (line 6) -* Integer division functions: Integer Division. (line 6) -* Integer exponentiation functions: Integer Exponentiation. - (line 6) -* Integer export: Integer Import and Export. - (line 45) -* Integer functions: Integer Functions. (line 6) -* Integer import: Integer Import and Export. - (line 11) -* Integer initialization functions <1>: Simultaneous Integer Init & Assign. - (line 6) -* Integer initialization functions: Initializing Integers. - (line 6) -* Integer input and output functions: I/O of Integers. (line 6) -* Integer internals: Integer Internals. (line 6) -* Integer logical functions: Integer Logic and Bit Fiddling. - (line 6) -* Integer miscellaneous functions: Miscellaneous Integer Functions. - (line 6) -* Integer random number functions: Integer Random Numbers. - (line 6) -* Integer root functions: Integer Roots. (line 6) -* Integer sign tests: Integer Comparisons. (line 28) -* Integer special functions: Integer Special Functions. - (line 6) -* Interix: Notes for Particular Systems. - (line 51) -* Internals: Internals. (line 6) -* Introduction: Introduction to GMP. (line 6) -* Inverse modulo functions: Number Theoretic Functions. - (line 60) -* IRIX <1>: Known Build Problems. - (line 38) -* IRIX: ABI and ISA. (line 132) -* ISA: ABI and ISA. (line 6) -* istream input: C++ Formatted Input. (line 6) -* Jacobi symbol algorithm: Jacobi Symbol. (line 6) -* Jacobi symbol functions: Number Theoretic Functions. - (line 66) -* Karatsuba multiplication: Karatsuba Multiplication. - (line 6) -* Karatsuba square root algorithm: Square Root Algorithm. - (line 6) -* Kronecker symbol functions: Number Theoretic Functions. - (line 78) -* Language bindings: Language Bindings. (line 6) -* Latest version of GMP: Introduction to GMP. (line 38) -* LCM functions: Number Theoretic Functions. - (line 55) -* Least common multiple functions: Number Theoretic Functions. - (line 55) -* Legendre symbol functions: Number Theoretic Functions. - (line 69) -* libgmp: Headers and Libraries. - (line 22) -* libgmpxx: Headers and Libraries. - (line 27) -* Libraries: Headers and Libraries. - (line 22) -* Libtool: Headers and Libraries. - (line 33) -* Libtool versioning: Notes for Package Builds. - (line 9) -* License conditions: Copying. (line 6) -* Limb: Nomenclature and Types. - (line 31) -* Limb size: Useful Macros and Constants. - (line 7) -* Linear congruential algorithm: Random Number Algorithms. - (line 25) -* Linear congruential random numbers: Random State Initialization. - (line 32) -* Linking: Headers and Libraries. - (line 22) -* Logical functions: Integer Logic and Bit Fiddling. - (line 6) -* Low-level functions: Low-level Functions. (line 6) -* Lucas number algorithm: Lucas Numbers Algorithm. - (line 6) -* Lucas number functions: Number Theoretic Functions. - (line 119) -* MacOS X: Known Build Problems. - (line 51) -* Mailing lists: Introduction to GMP. (line 45) -* Malloc debugger: Debugging. (line 30) -* Malloc problems: Debugging. (line 24) -* Memory allocation: Custom Allocation. (line 6) -* Memory management: Memory Management. (line 6) -* Mersenne twister algorithm: Random Number Algorithms. - (line 17) -* Mersenne twister random numbers: Random State Initialization. - (line 13) -* MINGW: Notes for Particular Systems. - (line 43) -* MIPS: ABI and ISA. (line 132) -* Miscellaneous float functions: Miscellaneous Float Functions. - (line 6) -* Miscellaneous integer functions: Miscellaneous Integer Functions. - (line 6) -* MMX: Notes for Particular Systems. - (line 132) -* Modular inverse functions: Number Theoretic Functions. - (line 60) -* Most significant bit: Miscellaneous Integer Functions. - (line 34) -* mp.h: BSD Compatible Functions. - (line 21) -* MPN_PATH: Build Options. (line 335) -* MS Windows: Notes for Particular Systems. - (line 56) -* MS-DOS: Notes for Particular Systems. - (line 43) -* Multi-threading: Reentrancy. (line 6) -* Multiplication algorithms: Multiplication Algorithms. - (line 6) -* Nails: Low-level Functions. (line 478) -* Native compilation: Build Options. (line 52) -* NeXT: Known Build Problems. - (line 57) -* Next prime function: Number Theoretic Functions. - (line 23) -* Nomenclature: Nomenclature and Types. - (line 6) -* Non-Unix systems: Build Options. (line 11) -* Nth root algorithm: Nth Root Algorithm. (line 6) -* Number sequences: Efficiency. (line 147) -* Number theoretic functions: Number Theoretic Functions. - (line 6) -* Numerator and denominator: Applying Integer Functions. - (line 6) -* obstack output: Formatted Output Functions. - (line 81) -* OpenBSD: Notes for Particular Systems. - (line 86) -* Optimizing performance: Performance optimization. - (line 6) -* ostream output: C++ Formatted Output. - (line 6) -* Other languages: Language Bindings. (line 6) -* Output functions <1>: I/O of Floats. (line 6) -* Output functions <2>: I/O of Rationals. (line 6) -* Output functions <3>: Formatted Output Functions. - (line 6) -* Output functions: I/O of Integers. (line 6) -* Packaged builds: Notes for Package Builds. - (line 6) -* Parameter conventions: Parameter Conventions. - (line 6) -* Parsing expressions demo: Demonstration Programs. - (line 21) -* Particular systems: Notes for Particular Systems. - (line 6) -* Past GMP versions: Compatibility with older versions. - (line 6) -* PDF: Build Options. (line 350) -* Perfect power algorithm: Perfect Power Algorithm. - (line 6) -* Perfect power functions: Integer Roots. (line 27) -* Perfect square algorithm: Perfect Square Algorithm. - (line 6) -* Perfect square functions: Integer Roots. (line 36) -* perl: Demonstration Programs. - (line 35) -* Perl module: Demonstration Programs. - (line 35) -* Postscript: Build Options. (line 350) -* Power/PowerPC <1>: Known Build Problems. - (line 63) -* Power/PowerPC: Notes for Particular Systems. - (line 92) -* Powering algorithms: Powering Algorithms. (line 6) -* Powering functions <1>: Float Arithmetic. (line 41) -* Powering functions: Integer Exponentiation. - (line 6) -* PowerPC: ABI and ISA. (line 167) -* Precision of floats: Floating-point Functions. - (line 6) -* Precision of hardware floating point: Notes for Particular Systems. - (line 34) -* Prefix: Build Options. (line 32) -* Prime testing algorithms: Prime Testing Algorithm. - (line 6) -* Prime testing functions: Number Theoretic Functions. - (line 7) -* printf formatted output: Formatted Output. (line 6) -* Probable prime testing functions: Number Theoretic Functions. - (line 7) -* prof: Profiling. (line 24) -* Profiling: Profiling. (line 6) -* Radix conversion algorithms: Radix Conversion Algorithms. - (line 6) -* Random number algorithms: Random Number Algorithms. - (line 6) -* Random number functions <1>: Integer Random Numbers. - (line 6) -* Random number functions <2>: Miscellaneous Float Functions. - (line 27) -* Random number functions: Random Number Functions. - (line 6) -* Random number seeding: Random State Seeding. - (line 6) -* Random number state: Random State Initialization. - (line 6) -* Random state: Nomenclature and Types. - (line 46) -* Rational arithmetic: Efficiency. (line 113) -* Rational arithmetic functions: Rational Arithmetic. (line 6) -* Rational assignment functions: Initializing Rationals. - (line 6) -* Rational comparison functions: Comparing Rationals. (line 6) -* Rational conversion functions: Rational Conversions. - (line 6) -* Rational initialization functions: Initializing Rationals. - (line 6) -* Rational input and output functions: I/O of Rationals. (line 6) -* Rational internals: Rational Internals. (line 6) -* Rational number: Nomenclature and Types. - (line 16) -* Rational number functions: Rational Number Functions. - (line 6) -* Rational numerator and denominator: Applying Integer Functions. - (line 6) -* Rational sign tests: Comparing Rationals. (line 27) -* Raw output internals: Raw Output Internals. - (line 6) -* Reallocations: Efficiency. (line 30) -* Reentrancy: Reentrancy. (line 6) -* References: References. (line 6) -* Remove factor functions: Number Theoretic Functions. - (line 90) -* Reporting bugs: Reporting Bugs. (line 6) -* Root extraction algorithm: Nth Root Algorithm. (line 6) -* Root extraction algorithms: Root Extraction Algorithms. - (line 6) -* Root extraction functions <1>: Float Arithmetic. (line 37) -* Root extraction functions: Integer Roots. (line 6) -* Root testing functions: Integer Roots. (line 36) -* Rounding functions: Miscellaneous Float Functions. - (line 9) -* Sample programs: Demonstration Programs. - (line 6) -* Scan bit functions: Integer Logic and Bit Fiddling. - (line 38) -* scanf formatted input: Formatted Input. (line 6) -* SCO: Known Build Problems. - (line 38) -* Seeding random numbers: Random State Seeding. - (line 6) -* Segmentation violation: Debugging. (line 7) -* Sequent Symmetry: Known Build Problems. - (line 68) -* Services for Unix: Notes for Particular Systems. - (line 51) -* Shared library versioning: Notes for Package Builds. - (line 9) -* Sign tests <1>: Float Comparison. (line 33) -* Sign tests <2>: Integer Comparisons. (line 28) -* Sign tests: Comparing Rationals. (line 27) -* Size in digits: Miscellaneous Integer Functions. - (line 23) -* Small operands: Efficiency. (line 7) -* Solaris <1>: ABI and ISA. (line 201) -* Solaris: Known Build Problems. - (line 78) -* Sparc: Notes for Particular Systems. - (line 108) -* Sparc V9: ABI and ISA. (line 201) -* Special integer functions: Integer Special Functions. - (line 6) -* Square root algorithm: Square Root Algorithm. - (line 6) -* SSE2: Notes for Particular Systems. - (line 132) -* Stack backtrace: Debugging. (line 50) -* Stack overflow <1>: Debugging. (line 7) -* Stack overflow: Build Options. (line 278) -* Static linking: Efficiency. (line 14) -* stdarg.h: Headers and Libraries. - (line 17) -* stdio.h: Headers and Libraries. - (line 11) -* Stripped libraries: Known Build Problems. - (line 28) -* Sun: ABI and ISA. (line 201) -* SunOS: Notes for Particular Systems. - (line 120) -* Systems: Notes for Particular Systems. - (line 6) -* Temporary memory: Build Options. (line 278) -* Texinfo: Build Options. (line 347) -* Text input/output: Efficiency. (line 153) -* Thread safety: Reentrancy. (line 6) -* Toom multiplication <1>: Other Multiplication. - (line 6) -* Toom multiplication <2>: Toom 4-Way Multiplication. - (line 6) -* Toom multiplication: Toom 3-Way Multiplication. - (line 6) -* Types: Nomenclature and Types. - (line 6) -* ui and si functions: Efficiency. (line 50) -* Unbalanced multiplication: Unbalanced Multiplication. - (line 6) -* Upward compatibility: Compatibility with older versions. - (line 6) -* Useful macros and constants: Useful Macros and Constants. - (line 6) -* User-defined precision: Floating-point Functions. - (line 6) -* Valgrind: Debugging. (line 130) -* Variable conventions: Variable Conventions. - (line 6) -* Version number: Useful Macros and Constants. - (line 12) -* Web page: Introduction to GMP. (line 34) -* Windows: Notes for Particular Systems. - (line 56) -* x86: Notes for Particular Systems. - (line 126) -* x87: Notes for Particular Systems. - (line 34) -* XML: Build Options. (line 354) - - -File: gmp.info, Node: Function Index, Prev: Concept Index, Up: Top - -Function and Type Index -*********************** - -[index] -* Menu: - -* __GMP_CC: Useful Macros and Constants. - (line 23) -* __GMP_CFLAGS: Useful Macros and Constants. - (line 24) -* __GNU_MP_VERSION: Useful Macros and Constants. - (line 10) -* __GNU_MP_VERSION_MINOR: Useful Macros and Constants. - (line 11) -* __GNU_MP_VERSION_PATCHLEVEL: Useful Macros and Constants. - (line 12) -* _mpz_realloc: Integer Special Functions. - (line 51) -* abs <1>: C++ Interface Rationals. - (line 43) -* abs <2>: C++ Interface Integers. - (line 42) -* abs: C++ Interface Floats. - (line 70) -* ceil: C++ Interface Floats. - (line 71) -* cmp <1>: C++ Interface Floats. - (line 72) -* cmp <2>: C++ Interface Rationals. - (line 44) -* cmp <3>: C++ Interface Integers. - (line 44) -* cmp: C++ Interface Rationals. - (line 45) -* floor: C++ Interface Floats. - (line 80) -* gcd: BSD Compatible Functions. - (line 82) -* gmp_asprintf: Formatted Output Functions. - (line 65) -* gmp_errno: Random State Initialization. - (line 55) -* GMP_ERROR_INVALID_ARGUMENT: Random State Initialization. - (line 55) -* GMP_ERROR_UNSUPPORTED_ARGUMENT: Random State Initialization. - (line 55) -* gmp_fprintf: Formatted Output Functions. - (line 29) -* gmp_fscanf: Formatted Input Functions. - (line 25) -* GMP_LIMB_BITS: Low-level Functions. (line 508) -* GMP_NAIL_BITS: Low-level Functions. (line 506) -* GMP_NAIL_MASK: Low-level Functions. (line 516) -* GMP_NUMB_BITS: Low-level Functions. (line 507) -* GMP_NUMB_MASK: Low-level Functions. (line 517) -* GMP_NUMB_MAX: Low-level Functions. (line 525) -* gmp_obstack_printf: Formatted Output Functions. - (line 79) -* gmp_obstack_vprintf: Formatted Output Functions. - (line 81) -* gmp_printf: Formatted Output Functions. - (line 24) -* GMP_RAND_ALG_DEFAULT: Random State Initialization. - (line 49) -* GMP_RAND_ALG_LC: Random State Initialization. - (line 49) -* gmp_randclass: C++ Interface Random Numbers. - (line 7) -* gmp_randclass::get_f: C++ Interface Random Numbers. - (line 45) -* gmp_randclass::get_z_bits: C++ Interface Random Numbers. - (line 39) -* gmp_randclass::get_z_range: C++ Interface Random Numbers. - (line 42) -* gmp_randclass::gmp_randclass: C++ Interface Random Numbers. - (line 13) -* gmp_randclass::seed: C++ Interface Random Numbers. - (line 33) -* gmp_randclear: Random State Initialization. - (line 62) -* gmp_randinit: Random State Initialization. - (line 47) -* gmp_randinit_default: Random State Initialization. - (line 7) -* gmp_randinit_lc_2exp: Random State Initialization. - (line 18) -* gmp_randinit_lc_2exp_size: Random State Initialization. - (line 32) -* gmp_randinit_mt: Random State Initialization. - (line 13) -* gmp_randinit_set: Random State Initialization. - (line 43) -* gmp_randseed: Random State Seeding. - (line 7) -* gmp_randseed_ui: Random State Seeding. - (line 9) -* gmp_randstate_t: Nomenclature and Types. - (line 46) -* gmp_scanf: Formatted Input Functions. - (line 21) -* gmp_snprintf: Formatted Output Functions. - (line 46) -* gmp_sprintf: Formatted Output Functions. - (line 34) -* gmp_sscanf: Formatted Input Functions. - (line 29) -* gmp_urandomb_ui: Random State Miscellaneous. - (line 8) -* gmp_urandomm_ui: Random State Miscellaneous. - (line 14) -* gmp_vasprintf: Formatted Output Functions. - (line 66) -* gmp_version: Useful Macros and Constants. - (line 18) -* gmp_vfprintf: Formatted Output Functions. - (line 30) -* gmp_vfscanf: Formatted Input Functions. - (line 26) -* gmp_vprintf: Formatted Output Functions. - (line 25) -* gmp_vscanf: Formatted Input Functions. - (line 22) -* gmp_vsnprintf: Formatted Output Functions. - (line 48) -* gmp_vsprintf: Formatted Output Functions. - (line 35) -* gmp_vsscanf: Formatted Input Functions. - (line 31) -* hypot: C++ Interface Floats. - (line 81) -* itom: BSD Compatible Functions. - (line 29) -* madd: BSD Compatible Functions. - (line 43) -* mcmp: BSD Compatible Functions. - (line 85) -* mdiv: BSD Compatible Functions. - (line 53) -* mfree: BSD Compatible Functions. - (line 105) -* min: BSD Compatible Functions. - (line 89) -* MINT: BSD Compatible Functions. - (line 21) -* mout: BSD Compatible Functions. - (line 94) -* move: BSD Compatible Functions. - (line 39) -* mp_bitcnt_t: Nomenclature and Types. - (line 42) -* mp_bits_per_limb: Useful Macros and Constants. - (line 7) -* mp_exp_t: Nomenclature and Types. - (line 27) -* mp_get_memory_functions: Custom Allocation. (line 93) -* mp_limb_t: Nomenclature and Types. - (line 31) -* mp_set_memory_functions: Custom Allocation. (line 21) -* mp_size_t: Nomenclature and Types. - (line 37) -* mpf_abs: Float Arithmetic. (line 47) -* mpf_add: Float Arithmetic. (line 7) -* mpf_add_ui: Float Arithmetic. (line 9) -* mpf_ceil: Miscellaneous Float Functions. - (line 7) -* mpf_class: C++ Interface General. - (line 20) -* mpf_class::fits_sint_p: C++ Interface Floats. - (line 74) -* mpf_class::fits_slong_p: C++ Interface Floats. - (line 75) -* mpf_class::fits_sshort_p: C++ Interface Floats. - (line 76) -* mpf_class::fits_uint_p: C++ Interface Floats. - (line 77) -* mpf_class::fits_ulong_p: C++ Interface Floats. - (line 78) -* mpf_class::fits_ushort_p: C++ Interface Floats. - (line 79) -* mpf_class::get_d: C++ Interface Floats. - (line 82) -* mpf_class::get_mpf_t: C++ Interface General. - (line 66) -* mpf_class::get_prec: C++ Interface Floats. - (line 100) -* mpf_class::get_si: C++ Interface Floats. - (line 83) -* mpf_class::get_str: C++ Interface Floats. - (line 85) -* mpf_class::get_ui: C++ Interface Floats. - (line 86) -* mpf_class::mpf_class: C++ Interface Floats. - (line 38) -* mpf_class::operator=: C++ Interface Floats. - (line 47) -* mpf_class::set_prec: C++ Interface Floats. - (line 101) -* mpf_class::set_prec_raw: C++ Interface Floats. - (line 102) -* mpf_class::set_str: C++ Interface Floats. - (line 88) -* mpf_clear: Initializing Floats. (line 37) -* mpf_clears: Initializing Floats. (line 41) -* mpf_cmp: Float Comparison. (line 7) -* mpf_cmp_d: Float Comparison. (line 8) -* mpf_cmp_si: Float Comparison. (line 10) -* mpf_cmp_ui: Float Comparison. (line 9) -* mpf_div: Float Arithmetic. (line 29) -* mpf_div_2exp: Float Arithmetic. (line 53) -* mpf_div_ui: Float Arithmetic. (line 33) -* mpf_eq: Float Comparison. (line 17) -* mpf_fits_sint_p: Miscellaneous Float Functions. - (line 20) -* mpf_fits_slong_p: Miscellaneous Float Functions. - (line 18) -* mpf_fits_sshort_p: Miscellaneous Float Functions. - (line 22) -* mpf_fits_uint_p: Miscellaneous Float Functions. - (line 19) -* mpf_fits_ulong_p: Miscellaneous Float Functions. - (line 17) -* mpf_fits_ushort_p: Miscellaneous Float Functions. - (line 21) -* mpf_floor: Miscellaneous Float Functions. - (line 8) -* mpf_get_d: Converting Floats. (line 7) -* mpf_get_d_2exp: Converting Floats. (line 16) -* mpf_get_default_prec: Initializing Floats. (line 12) -* mpf_get_prec: Initializing Floats. (line 62) -* mpf_get_si: Converting Floats. (line 27) -* mpf_get_str: Converting Floats. (line 37) -* mpf_get_ui: Converting Floats. (line 28) -* mpf_init: Initializing Floats. (line 19) -* mpf_init2: Initializing Floats. (line 26) -* mpf_init_set: Simultaneous Float Init & Assign. - (line 16) -* mpf_init_set_d: Simultaneous Float Init & Assign. - (line 19) -* mpf_init_set_si: Simultaneous Float Init & Assign. - (line 18) -* mpf_init_set_str: Simultaneous Float Init & Assign. - (line 25) -* mpf_init_set_ui: Simultaneous Float Init & Assign. - (line 17) -* mpf_inits: Initializing Floats. (line 31) -* mpf_inp_str: I/O of Floats. (line 37) -* mpf_integer_p: Miscellaneous Float Functions. - (line 14) -* mpf_mul: Float Arithmetic. (line 19) -* mpf_mul_2exp: Float Arithmetic. (line 50) -* mpf_mul_ui: Float Arithmetic. (line 21) -* mpf_neg: Float Arithmetic. (line 44) -* mpf_out_str: I/O of Floats. (line 17) -* mpf_pow_ui: Float Arithmetic. (line 41) -* mpf_random2: Miscellaneous Float Functions. - (line 36) -* mpf_reldiff: Float Comparison. (line 29) -* mpf_set: Assigning Floats. (line 10) -* mpf_set_d: Assigning Floats. (line 13) -* mpf_set_default_prec: Initializing Floats. (line 7) -* mpf_set_prec: Initializing Floats. (line 65) -* mpf_set_prec_raw: Initializing Floats. (line 72) -* mpf_set_q: Assigning Floats. (line 15) -* mpf_set_si: Assigning Floats. (line 12) -* mpf_set_str: Assigning Floats. (line 18) -* mpf_set_ui: Assigning Floats. (line 11) -* mpf_set_z: Assigning Floats. (line 14) -* mpf_sgn: Float Comparison. (line 33) -* mpf_sqrt: Float Arithmetic. (line 36) -* mpf_sqrt_ui: Float Arithmetic. (line 37) -* mpf_sub: Float Arithmetic. (line 12) -* mpf_sub_ui: Float Arithmetic. (line 16) -* mpf_swap: Assigning Floats. (line 52) -* mpf_t: Nomenclature and Types. - (line 21) -* mpf_trunc: Miscellaneous Float Functions. - (line 9) -* mpf_ui_div: Float Arithmetic. (line 31) -* mpf_ui_sub: Float Arithmetic. (line 14) -* mpf_urandomb: Miscellaneous Float Functions. - (line 27) -* mpn_add: Low-level Functions. (line 69) -* mpn_add_1: Low-level Functions. (line 64) -* mpn_add_n: Low-level Functions. (line 54) -* mpn_addmul_1: Low-level Functions. (line 148) -* mpn_and_n: Low-level Functions. (line 420) -* mpn_andn_n: Low-level Functions. (line 435) -* mpn_cmp: Low-level Functions. (line 284) -* mpn_com: Low-level Functions. (line 460) -* mpn_copyd: Low-level Functions. (line 469) -* mpn_copyi: Low-level Functions. (line 465) -* mpn_divexact_by3: Low-level Functions. (line 229) -* mpn_divexact_by3c: Low-level Functions. (line 231) -* mpn_divmod: Low-level Functions. (line 224) -* mpn_divmod_1: Low-level Functions. (line 208) -* mpn_divrem: Low-level Functions. (line 182) -* mpn_divrem_1: Low-level Functions. (line 206) -* mpn_gcd: Low-level Functions. (line 289) -* mpn_gcd_1: Low-level Functions. (line 299) -* mpn_gcdext: Low-level Functions. (line 305) -* mpn_get_str: Low-level Functions. (line 346) -* mpn_hamdist: Low-level Functions. (line 410) -* mpn_ior_n: Low-level Functions. (line 425) -* mpn_iorn_n: Low-level Functions. (line 440) -* mpn_lshift: Low-level Functions. (line 260) -* mpn_mod_1: Low-level Functions. (line 255) -* mpn_mul: Low-level Functions. (line 114) -* mpn_mul_1: Low-level Functions. (line 133) -* mpn_mul_n: Low-level Functions. (line 103) -* mpn_nand_n: Low-level Functions. (line 445) -* mpn_neg: Low-level Functions. (line 98) -* mpn_nior_n: Low-level Functions. (line 450) -* mpn_perfect_square_p: Low-level Functions. (line 416) -* mpn_popcount: Low-level Functions. (line 406) -* mpn_random: Low-level Functions. (line 395) -* mpn_random2: Low-level Functions. (line 396) -* mpn_rshift: Low-level Functions. (line 272) -* mpn_scan0: Low-level Functions. (line 380) -* mpn_scan1: Low-level Functions. (line 388) -* mpn_set_str: Low-level Functions. (line 361) -* mpn_sqr: Low-level Functions. (line 125) -* mpn_sqrtrem: Low-level Functions. (line 328) -* mpn_sub: Low-level Functions. (line 90) -* mpn_sub_1: Low-level Functions. (line 85) -* mpn_sub_n: Low-level Functions. (line 76) -* mpn_submul_1: Low-level Functions. (line 159) -* mpn_tdiv_qr: Low-level Functions. (line 171) -* mpn_xnor_n: Low-level Functions. (line 455) -* mpn_xor_n: Low-level Functions. (line 430) -* mpn_zero: Low-level Functions. (line 472) -* mpq_abs: Rational Arithmetic. (line 31) -* mpq_add: Rational Arithmetic. (line 7) -* mpq_canonicalize: Rational Number Functions. - (line 22) -* mpq_class: C++ Interface General. - (line 19) -* mpq_class::canonicalize: C++ Interface Rationals. - (line 37) -* mpq_class::get_d: C++ Interface Rationals. - (line 46) -* mpq_class::get_den: C++ Interface Rationals. - (line 58) -* mpq_class::get_den_mpz_t: C++ Interface Rationals. - (line 68) -* mpq_class::get_mpq_t: C++ Interface General. - (line 65) -* mpq_class::get_num: C++ Interface Rationals. - (line 57) -* mpq_class::get_num_mpz_t: C++ Interface Rationals. - (line 67) -* mpq_class::get_str: C++ Interface Rationals. - (line 47) -* mpq_class::mpq_class: C++ Interface Rationals. - (line 22) -* mpq_class::set_str: C++ Interface Rationals. - (line 49) -* mpq_clear: Initializing Rationals. - (line 16) -* mpq_clears: Initializing Rationals. - (line 20) -* mpq_cmp: Comparing Rationals. (line 7) -* mpq_cmp_si: Comparing Rationals. (line 17) -* mpq_cmp_ui: Comparing Rationals. (line 15) -* mpq_denref: Applying Integer Functions. - (line 18) -* mpq_div: Rational Arithmetic. (line 22) -* mpq_div_2exp: Rational Arithmetic. (line 25) -* mpq_equal: Comparing Rationals. (line 33) -* mpq_get_d: Rational Conversions. - (line 7) -* mpq_get_den: Applying Integer Functions. - (line 24) -* mpq_get_num: Applying Integer Functions. - (line 23) -* mpq_get_str: Rational Conversions. - (line 22) -* mpq_init: Initializing Rationals. - (line 7) -* mpq_inits: Initializing Rationals. - (line 12) -* mpq_inp_str: I/O of Rationals. (line 23) -* mpq_inv: Rational Arithmetic. (line 34) -* mpq_mul: Rational Arithmetic. (line 15) -* mpq_mul_2exp: Rational Arithmetic. (line 18) -* mpq_neg: Rational Arithmetic. (line 28) -* mpq_numref: Applying Integer Functions. - (line 17) -* mpq_out_str: I/O of Rationals. (line 15) -* mpq_set: Initializing Rationals. - (line 24) -* mpq_set_d: Rational Conversions. - (line 17) -* mpq_set_den: Applying Integer Functions. - (line 26) -* mpq_set_f: Rational Conversions. - (line 18) -* mpq_set_num: Applying Integer Functions. - (line 25) -* mpq_set_si: Initializing Rationals. - (line 31) -* mpq_set_str: Initializing Rationals. - (line 36) -* mpq_set_ui: Initializing Rationals. - (line 29) -* mpq_set_z: Initializing Rationals. - (line 25) -* mpq_sgn: Comparing Rationals. (line 27) -* mpq_sub: Rational Arithmetic. (line 11) -* mpq_swap: Initializing Rationals. - (line 56) -* mpq_t: Nomenclature and Types. - (line 16) -* mpz_abs: Integer Arithmetic. (line 42) -* mpz_add: Integer Arithmetic. (line 7) -* mpz_add_ui: Integer Arithmetic. (line 9) -* mpz_addmul: Integer Arithmetic. (line 25) -* mpz_addmul_ui: Integer Arithmetic. (line 27) -* mpz_and: Integer Logic and Bit Fiddling. - (line 11) -* mpz_array_init: Integer Special Functions. - (line 11) -* mpz_bin_ui: Number Theoretic Functions. - (line 98) -* mpz_bin_uiui: Number Theoretic Functions. - (line 100) -* mpz_cdiv_q: Integer Division. (line 13) -* mpz_cdiv_q_2exp: Integer Division. (line 24) -* mpz_cdiv_q_ui: Integer Division. (line 17) -* mpz_cdiv_qr: Integer Division. (line 15) -* mpz_cdiv_qr_ui: Integer Division. (line 21) -* mpz_cdiv_r: Integer Division. (line 14) -* mpz_cdiv_r_2exp: Integer Division. (line 25) -* mpz_cdiv_r_ui: Integer Division. (line 19) -* mpz_cdiv_ui: Integer Division. (line 23) -* mpz_class: C++ Interface General. - (line 18) -* mpz_class::fits_sint_p: C++ Interface Integers. - (line 45) -* mpz_class::fits_slong_p: C++ Interface Integers. - (line 46) -* mpz_class::fits_sshort_p: C++ Interface Integers. - (line 47) -* mpz_class::fits_uint_p: C++ Interface Integers. - (line 48) -* mpz_class::fits_ulong_p: C++ Interface Integers. - (line 49) -* mpz_class::fits_ushort_p: C++ Interface Integers. - (line 50) -* mpz_class::get_d: C++ Interface Integers. - (line 51) -* mpz_class::get_mpz_t: C++ Interface General. - (line 64) -* mpz_class::get_si: C++ Interface Integers. - (line 52) -* mpz_class::get_str: C++ Interface Integers. - (line 53) -* mpz_class::get_ui: C++ Interface Integers. - (line 54) -* mpz_class::mpz_class: C++ Interface Integers. - (line 7) -* mpz_class::set_str: C++ Interface Integers. - (line 56) -* mpz_clear: Initializing Integers. - (line 44) -* mpz_clears: Initializing Integers. - (line 48) -* mpz_clrbit: Integer Logic and Bit Fiddling. - (line 54) -* mpz_cmp: Integer Comparisons. (line 7) -* mpz_cmp_d: Integer Comparisons. (line 8) -* mpz_cmp_si: Integer Comparisons. (line 9) -* mpz_cmp_ui: Integer Comparisons. (line 10) -* mpz_cmpabs: Integer Comparisons. (line 18) -* mpz_cmpabs_d: Integer Comparisons. (line 19) -* mpz_cmpabs_ui: Integer Comparisons. (line 20) -* mpz_com: Integer Logic and Bit Fiddling. - (line 20) -* mpz_combit: Integer Logic and Bit Fiddling. - (line 57) -* mpz_congruent_2exp_p: Integer Division. (line 124) -* mpz_congruent_p: Integer Division. (line 121) -* mpz_congruent_ui_p: Integer Division. (line 123) -* mpz_divexact: Integer Division. (line 101) -* mpz_divexact_ui: Integer Division. (line 102) -* mpz_divisible_2exp_p: Integer Division. (line 112) -* mpz_divisible_p: Integer Division. (line 110) -* mpz_divisible_ui_p: Integer Division. (line 111) -* mpz_even_p: Miscellaneous Integer Functions. - (line 18) -* mpz_export: Integer Import and Export. - (line 45) -* mpz_fac_ui: Number Theoretic Functions. - (line 95) -* mpz_fdiv_q: Integer Division. (line 27) -* mpz_fdiv_q_2exp: Integer Division. (line 38) -* mpz_fdiv_q_ui: Integer Division. (line 31) -* mpz_fdiv_qr: Integer Division. (line 29) -* mpz_fdiv_qr_ui: Integer Division. (line 35) -* mpz_fdiv_r: Integer Division. (line 28) -* mpz_fdiv_r_2exp: Integer Division. (line 39) -* mpz_fdiv_r_ui: Integer Division. (line 33) -* mpz_fdiv_ui: Integer Division. (line 37) -* mpz_fib2_ui: Number Theoretic Functions. - (line 108) -* mpz_fib_ui: Number Theoretic Functions. - (line 106) -* mpz_fits_sint_p: Miscellaneous Integer Functions. - (line 10) -* mpz_fits_slong_p: Miscellaneous Integer Functions. - (line 8) -* mpz_fits_sshort_p: Miscellaneous Integer Functions. - (line 12) -* mpz_fits_uint_p: Miscellaneous Integer Functions. - (line 9) -* mpz_fits_ulong_p: Miscellaneous Integer Functions. - (line 7) -* mpz_fits_ushort_p: Miscellaneous Integer Functions. - (line 11) -* mpz_gcd: Number Theoretic Functions. - (line 30) -* mpz_gcd_ui: Number Theoretic Functions. - (line 35) -* mpz_gcdext: Number Theoretic Functions. - (line 45) -* mpz_get_d: Converting Integers. (line 27) -* mpz_get_d_2exp: Converting Integers. (line 35) -* mpz_get_si: Converting Integers. (line 18) -* mpz_get_str: Converting Integers. (line 46) -* mpz_get_ui: Converting Integers. (line 11) -* mpz_getlimbn: Integer Special Functions. - (line 60) -* mpz_hamdist: Integer Logic and Bit Fiddling. - (line 29) -* mpz_import: Integer Import and Export. - (line 11) -* mpz_init: Initializing Integers. - (line 26) -* mpz_init2: Initializing Integers. - (line 33) -* mpz_init_set: Simultaneous Integer Init & Assign. - (line 27) -* mpz_init_set_d: Simultaneous Integer Init & Assign. - (line 30) -* mpz_init_set_si: Simultaneous Integer Init & Assign. - (line 29) -* mpz_init_set_str: Simultaneous Integer Init & Assign. - (line 34) -* mpz_init_set_ui: Simultaneous Integer Init & Assign. - (line 28) -* mpz_inits: Initializing Integers. - (line 29) -* mpz_inp_raw: I/O of Integers. (line 59) -* mpz_inp_str: I/O of Integers. (line 28) -* mpz_invert: Number Theoretic Functions. - (line 60) -* mpz_ior: Integer Logic and Bit Fiddling. - (line 14) -* mpz_jacobi: Number Theoretic Functions. - (line 66) -* mpz_kronecker: Number Theoretic Functions. - (line 74) -* mpz_kronecker_si: Number Theoretic Functions. - (line 75) -* mpz_kronecker_ui: Number Theoretic Functions. - (line 76) -* mpz_lcm: Number Theoretic Functions. - (line 54) -* mpz_lcm_ui: Number Theoretic Functions. - (line 55) -* mpz_legendre: Number Theoretic Functions. - (line 69) -* mpz_lucnum2_ui: Number Theoretic Functions. - (line 119) -* mpz_lucnum_ui: Number Theoretic Functions. - (line 117) -* mpz_mod: Integer Division. (line 91) -* mpz_mod_ui: Integer Division. (line 93) -* mpz_mul: Integer Arithmetic. (line 19) -* mpz_mul_2exp: Integer Arithmetic. (line 35) -* mpz_mul_si: Integer Arithmetic. (line 20) -* mpz_mul_ui: Integer Arithmetic. (line 22) -* mpz_neg: Integer Arithmetic. (line 39) -* mpz_nextprime: Number Theoretic Functions. - (line 23) -* mpz_odd_p: Miscellaneous Integer Functions. - (line 17) -* mpz_out_raw: I/O of Integers. (line 43) -* mpz_out_str: I/O of Integers. (line 16) -* mpz_perfect_power_p: Integer Roots. (line 27) -* mpz_perfect_square_p: Integer Roots. (line 36) -* mpz_popcount: Integer Logic and Bit Fiddling. - (line 23) -* mpz_pow_ui: Integer Exponentiation. - (line 31) -* mpz_powm: Integer Exponentiation. - (line 8) -* mpz_powm_sec: Integer Exponentiation. - (line 18) -* mpz_powm_ui: Integer Exponentiation. - (line 10) -* mpz_probab_prime_p: Number Theoretic Functions. - (line 7) -* mpz_random: Integer Random Numbers. - (line 42) -* mpz_random2: Integer Random Numbers. - (line 51) -* mpz_realloc2: Initializing Integers. - (line 52) -* mpz_remove: Number Theoretic Functions. - (line 90) -* mpz_root: Integer Roots. (line 7) -* mpz_rootrem: Integer Roots. (line 13) -* mpz_rrandomb: Integer Random Numbers. - (line 31) -* mpz_scan0: Integer Logic and Bit Fiddling. - (line 37) -* mpz_scan1: Integer Logic and Bit Fiddling. - (line 38) -* mpz_set: Assigning Integers. (line 10) -* mpz_set_d: Assigning Integers. (line 13) -* mpz_set_f: Assigning Integers. (line 15) -* mpz_set_q: Assigning Integers. (line 14) -* mpz_set_si: Assigning Integers. (line 12) -* mpz_set_str: Assigning Integers. (line 21) -* mpz_set_ui: Assigning Integers. (line 11) -* mpz_setbit: Integer Logic and Bit Fiddling. - (line 51) -* mpz_sgn: Integer Comparisons. (line 28) -* mpz_si_kronecker: Number Theoretic Functions. - (line 77) -* mpz_size: Integer Special Functions. - (line 68) -* mpz_sizeinbase: Miscellaneous Integer Functions. - (line 23) -* mpz_sqrt: Integer Roots. (line 17) -* mpz_sqrtrem: Integer Roots. (line 20) -* mpz_sub: Integer Arithmetic. (line 12) -* mpz_sub_ui: Integer Arithmetic. (line 14) -* mpz_submul: Integer Arithmetic. (line 30) -* mpz_submul_ui: Integer Arithmetic. (line 32) -* mpz_swap: Assigning Integers. (line 37) -* mpz_t: Nomenclature and Types. - (line 6) -* mpz_tdiv_q: Integer Division. (line 41) -* mpz_tdiv_q_2exp: Integer Division. (line 52) -* mpz_tdiv_q_ui: Integer Division. (line 45) -* mpz_tdiv_qr: Integer Division. (line 43) -* mpz_tdiv_qr_ui: Integer Division. (line 49) -* mpz_tdiv_r: Integer Division. (line 42) -* mpz_tdiv_r_2exp: Integer Division. (line 53) -* mpz_tdiv_r_ui: Integer Division. (line 47) -* mpz_tdiv_ui: Integer Division. (line 51) -* mpz_tstbit: Integer Logic and Bit Fiddling. - (line 60) -* mpz_ui_kronecker: Number Theoretic Functions. - (line 78) -* mpz_ui_pow_ui: Integer Exponentiation. - (line 33) -* mpz_ui_sub: Integer Arithmetic. (line 16) -* mpz_urandomb: Integer Random Numbers. - (line 14) -* mpz_urandomm: Integer Random Numbers. - (line 23) -* mpz_xor: Integer Logic and Bit Fiddling. - (line 17) -* msqrt: BSD Compatible Functions. - (line 63) -* msub: BSD Compatible Functions. - (line 46) -* mtox: BSD Compatible Functions. - (line 98) -* mult: BSD Compatible Functions. - (line 49) -* operator%: C++ Interface Integers. - (line 30) -* operator/: C++ Interface Integers. - (line 29) -* operator<<: C++ Formatted Output. - (line 20) -* operator>> <1>: C++ Formatted Input. (line 11) -* operator>>: C++ Interface Rationals. - (line 77) -* pow: BSD Compatible Functions. - (line 71) -* rpow: BSD Compatible Functions. - (line 79) -* sdiv: BSD Compatible Functions. - (line 55) -* sgn <1>: C++ Interface Rationals. - (line 50) -* sgn <2>: C++ Interface Integers. - (line 57) -* sgn: C++ Interface Floats. - (line 89) -* sqrt <1>: C++ Interface Integers. - (line 58) -* sqrt: C++ Interface Floats. - (line 90) -* trunc: C++ Interface Floats. - (line 91) -* xtom: BSD Compatible Functions. - (line 34) - - diff --git a/misc/builddeps/linux64/d0_blind_id/bin/blind_id b/misc/builddeps/linux64/d0_blind_id/bin/blind_id deleted file mode 100755 index 775836cd..00000000 Binary files a/misc/builddeps/linux64/d0_blind_id/bin/blind_id and /dev/null differ diff --git a/misc/builddeps/linux64/d0_blind_id/include/d0_blind_id/d0.h b/misc/builddeps/linux64/d0_blind_id/include/d0_blind_id/d0.h deleted file mode 100644 index 4c8708e3..00000000 --- a/misc/builddeps/linux64/d0_blind_id/include/d0_blind_id/d0.h +++ /dev/null @@ -1,66 +0,0 @@ -/* - * FILE: d0.h - * AUTHOR: Rudolf Polzer - divVerent@xonotic.org - * - * Copyright (c) 2010, Rudolf Polzer - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * 3. Neither the name of the copyright holder nor the names of contributors - * may be used to endorse or promote products derived from this software - * without specific prior written permission. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTOR(S) ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTOR(S) BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - * - * $Format:commit %H$ - * $Id: 6c55afeb50f24bd316079ae46582e65f8020b19b $ - */ - -#ifndef __D0_H__ -#define __D0_H__ - -#include // size_t - -#define D0_EXPORT __attribute__((__visibility__("default"))) -#define D0_USED __attribute__((used)) -#define D0_WARN_UNUSED_RESULT __attribute__((warn_unused_result)) -#define D0_BOOL int - -typedef void *(d0_malloc_t)(size_t len); -typedef void (d0_free_t)(void *p); -typedef void *(d0_createmutex_t)(void); -typedef void (d0_destroymutex_t)(void *); -typedef int (d0_lockmutex_t)(void *); // zero on success -typedef int (d0_unlockmutex_t)(void *); // zero on success - -extern d0_malloc_t *d0_malloc; -extern d0_free_t *d0_free; -extern d0_createmutex_t *d0_createmutex; -extern d0_destroymutex_t *d0_destroymutex; -extern d0_lockmutex_t *d0_lockmutex; -extern d0_unlockmutex_t *d0_unlockmutex; - -void d0_setmallocfuncs(d0_malloc_t *m, d0_free_t *f); -void d0_setmutexfuncs(d0_createmutex_t *c, d0_destroymutex_t *d, d0_lockmutex_t *l, d0_unlockmutex_t *u); -void d0_initfuncs(void); // initializes them, this needs to be only called internally once - -extern const char *d0_bsd_license_notice; - -#endif diff --git a/misc/builddeps/linux64/d0_blind_id/include/d0_blind_id/d0_blind_id.h b/misc/builddeps/linux64/d0_blind_id/include/d0_blind_id/d0_blind_id.h deleted file mode 100644 index f546b679..00000000 --- a/misc/builddeps/linux64/d0_blind_id/include/d0_blind_id/d0_blind_id.h +++ /dev/null @@ -1,91 +0,0 @@ -/* - * FILE: d0_blind_id.h - * AUTHOR: Rudolf Polzer - divVerent@xonotic.org - * - * Copyright (c) 2010, Rudolf Polzer - * All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in the - * documentation and/or other materials provided with the distribution. - * 3. Neither the name of the copyright holder nor the names of contributors - * may be used to endorse or promote products derived from this software - * without specific prior written permission. - * - * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTOR(S) ``AS IS'' AND - * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE - * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTOR(S) BE LIABLE - * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL - * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS - * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT - * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY - * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF - * SUCH DAMAGE. - * - * $Format:commit %H$ - * $Id: bf838f43093aceadcd2d20071684f1e7148a4332 $ - */ - -#ifndef __D0_BLIND_ID_H__ -#define __D0_BLIND_ID_H__ - -#include "d0.h" - -typedef struct d0_blind_id_s d0_blind_id_t; -typedef D0_BOOL (*d0_fastreject_function) (const d0_blind_id_t *ctx, void *pass); - -D0_EXPORT D0_WARN_UNUSED_RESULT d0_blind_id_t *d0_blind_id_new(void); -D0_EXPORT void d0_blind_id_free(d0_blind_id_t *a); -D0_EXPORT void d0_blind_id_clear(d0_blind_id_t *ctx); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_copy(d0_blind_id_t *ctx, const d0_blind_id_t *src); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_generate_private_key(d0_blind_id_t *ctx, int k); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_generate_private_key_fastreject(d0_blind_id_t *ctx, int k, d0_fastreject_function reject, void *pass); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_read_private_key(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_read_public_key(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_write_private_key(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_write_public_key(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_fingerprint64_public_key(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_generate_private_id_modulus(d0_blind_id_t *ctx); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_read_private_id_modulus(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_write_private_id_modulus(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_generate_private_id_start(d0_blind_id_t *ctx); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_generate_private_id_request(d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_answer_private_id_request(const d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_finish_private_id_request(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_read_private_id_request_camouflage(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_write_private_id_request_camouflage(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_read_private_id(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_read_public_id(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_write_private_id(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_write_public_id(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_authenticate_with_private_id_start(d0_blind_id_t *ctx, D0_BOOL is_first, D0_BOOL send_modulus, const char *message, size_t msglen, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_authenticate_with_private_id_challenge(d0_blind_id_t *ctx, D0_BOOL is_first, D0_BOOL recv_modulus, const char *inbuf, size_t inbuflen, char *outbuf, size_t *outbuflen, D0_BOOL *status); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_authenticate_with_private_id_response(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_authenticate_with_private_id_verify(d0_blind_id_t *ctx, const char *inbuf, size_t inbuflen, char *msg, size_t *msglen, D0_BOOL *status); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_authenticate_with_private_id_generate_missing_signature(d0_blind_id_t *ctx); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_sign_with_private_id_sign(d0_blind_id_t *ctx, D0_BOOL is_first, D0_BOOL send_modulus, const char *message, size_t msglen, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_sign_with_private_id_sign_detached(d0_blind_id_t *ctx, D0_BOOL is_first, D0_BOOL send_modulus, const char *message, size_t msglen, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_sign_with_private_id_verify(d0_blind_id_t *ctx, D0_BOOL is_first, D0_BOOL recv_modulus, const char *inbuf, size_t inbuflen, char *msg, size_t *msglen, D0_BOOL *status); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_sign_with_private_id_verify_detached(d0_blind_id_t *ctx, D0_BOOL is_first, D0_BOOL recv_modulus, const char *inbuf, size_t inbuflen, const char *msg, size_t msglen, D0_BOOL *status); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_fingerprint64_public_id(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_verify_public_id(const d0_blind_id_t *ctx, D0_BOOL *status); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_verify_private_id(const d0_blind_id_t *ctx); -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_sessionkey_public_id(const d0_blind_id_t *ctx, char *outbuf, size_t *outbuflen); // can only be done after successful key exchange, this performs a modpow; key length is limited by SHA_DIGESTSIZE for now; also ONLY valid after successful d0_blind_id_authenticate_with_private_id_verify/d0_blind_id_fingerprint64_public_id - -D0_EXPORT D0_WARN_UNUSED_RESULT D0_BOOL d0_blind_id_INITIALIZE(void); -D0_EXPORT void d0_blind_id_SHUTDOWN(void); - -D0_EXPORT void d0_blind_id_util_sha256(char *out, const char *in, size_t n); - -// for exporting -D0_EXPORT void d0_blind_id_setmallocfuncs(d0_malloc_t *m, d0_free_t *f); -D0_EXPORT void d0_blind_id_setmutexfuncs(d0_createmutex_t *c, d0_destroymutex_t *d, d0_lockmutex_t *l, d0_unlockmutex_t *u); - -#endif diff --git a/misc/builddeps/linux64/d0_blind_id/include/d0_blind_id/d0_rijndael.h b/misc/builddeps/linux64/d0_blind_id/include/d0_blind_id/d0_rijndael.h deleted file mode 100644 index e1c8f71b..00000000 --- a/misc/builddeps/linux64/d0_blind_id/include/d0_blind_id/d0_rijndael.h +++ /dev/null @@ -1,21 +0,0 @@ -// from http://www.efgh.com/software/rijndael.htm (public domain) - -#ifndef H__RIJNDAEL -#define H__RIJNDAEL - -#include "d0.h" - -D0_EXPORT int d0_rijndael_setup_encrypt(unsigned long *rk, const unsigned char *key, - int keybits); -D0_EXPORT int d0_rijndael_setup_decrypt(unsigned long *rk, const unsigned char *key, - int keybits); -D0_EXPORT void d0_rijndael_encrypt(const unsigned long *rk, int nrounds, - const unsigned char plaintext[16], unsigned char ciphertext[16]); -D0_EXPORT void d0_rijndael_decrypt(const unsigned long *rk, int nrounds, - const unsigned char ciphertext[16], unsigned char plaintext[16]); - -#define D0_RIJNDAEL_KEYLENGTH(keybits) ((keybits)/8) -#define D0_RIJNDAEL_RKLENGTH(keybits) ((keybits)/8+28) -#define D0_RIJNDAEL_NROUNDS(keybits) ((keybits)/32+6) - -#endif diff --git a/misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.a b/misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.a deleted file mode 100644 index 4f0fedab..00000000 Binary files a/misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.a and /dev/null differ diff --git a/misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.la b/misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.la deleted file mode 100755 index 34767d3b..00000000 --- a/misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.la +++ /dev/null @@ -1,41 +0,0 @@ -# libd0_blind_id.la - a libtool library file -# Generated by ltmain.sh (GNU libtool) 2.2.6b Debian-2.2.6b-2ubuntu1 -# -# Please DO NOT delete this file! -# It is necessary for linking the library. - -# The name that we can dlopen(3). -dlname='' - -# Names of this library. -library_names='' - -# The name of the static archive. -old_library='libd0_blind_id.a' - -# Linker flags that can not go in dependency_libs. -inherited_linker_flags='' - -# Libraries that this one depends upon. -dependency_libs=' -L/tmp/d0_blind_id.deps/lib/ /tmp/g/lib/libgmp.la' - -# Names of additional weak libraries provided by this library -weak_library_names='' - -# Version information for libd0_blind_id. -current=0 -age=0 -revision=0 - -# Is this an already installed library? -installed=yes - -# Should we warn about portability when linking against -modules? -shouldnotlink=no - -# Files to dlopen/dlpreopen -dlopen='' -dlpreopen='' - -# Directory that this library needs to be installed in: -libdir='/usr/local/lib' diff --git a/misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.so b/misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.so deleted file mode 120000 index 6adf4aa9..00000000 --- a/misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.so +++ /dev/null @@ -1 +0,0 @@ -libd0_blind_id.so.0.0.0 \ No newline at end of file diff --git a/misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.so.0 b/misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.so.0 deleted file mode 120000 index 6adf4aa9..00000000 --- a/misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.so.0 +++ /dev/null @@ -1 +0,0 @@ -libd0_blind_id.so.0.0.0 \ No newline at end of file diff --git a/misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.so.0.0.0 b/misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.so.0.0.0 deleted file mode 100755 index 11fb746a..00000000 Binary files a/misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.so.0.0.0 and /dev/null differ diff --git a/misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.a b/misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.a deleted file mode 100644 index 4e593022..00000000 Binary files a/misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.a and /dev/null differ diff --git a/misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.la b/misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.la deleted file mode 100755 index f0bab29d..00000000 --- a/misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.la +++ /dev/null @@ -1,41 +0,0 @@ -# libd0_rijndael.la - a libtool library file -# Generated by ltmain.sh (GNU libtool) 2.2.6b Debian-2.2.6b-2ubuntu1 -# -# Please DO NOT delete this file! -# It is necessary for linking the library. - -# The name that we can dlopen(3). -dlname='' - -# Names of this library. -library_names='' - -# The name of the static archive. -old_library='libd0_rijndael.a' - -# Linker flags that can not go in dependency_libs. -inherited_linker_flags='' - -# Libraries that this one depends upon. -dependency_libs=' -L/tmp/d0_blind_id.deps/lib/ /tmp/g/lib/libgmp.la' - -# Names of additional weak libraries provided by this library -weak_library_names='' - -# Version information for libd0_rijndael. -current=0 -age=0 -revision=0 - -# Is this an already installed library? -installed=yes - -# Should we warn about portability when linking against -modules? -shouldnotlink=no - -# Files to dlopen/dlpreopen -dlopen='' -dlpreopen='' - -# Directory that this library needs to be installed in: -libdir='/usr/local/lib' diff --git a/misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.so b/misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.so deleted file mode 120000 index 01dce017..00000000 --- a/misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.so +++ /dev/null @@ -1 +0,0 @@ -libd0_rijndael.so.0.0.0 \ No newline at end of file diff --git a/misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.so.0 b/misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.so.0 deleted file mode 120000 index 01dce017..00000000 --- a/misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.so.0 +++ /dev/null @@ -1 +0,0 @@ -libd0_rijndael.so.0.0.0 \ No newline at end of file diff --git a/misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.so.0.0.0 b/misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.so.0.0.0 deleted file mode 100755 index 16e0840a..00000000 Binary files a/misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.so.0.0.0 and /dev/null differ diff --git a/misc/builddeps/linux64/d0_blind_id/lib/pkgconfig/d0_blind_id.pc b/misc/builddeps/linux64/d0_blind_id/lib/pkgconfig/d0_blind_id.pc deleted file mode 100644 index 8c9bb32b..00000000 --- a/misc/builddeps/linux64/d0_blind_id/lib/pkgconfig/d0_blind_id.pc +++ /dev/null @@ -1,11 +0,0 @@ -prefix=/usr/local -exec_prefix=${prefix} -libdir=${exec_prefix}/lib -includedir=${prefix}/include - -Name: Blind-ID -Description: Library for user identification using RSA blind signatures -Requires: -Version: 0.5 -Libs: -L${libdir} -ld0_blind_id -Cflags: -I${includedir}/d0_blind_id diff --git a/misc/builddeps/linux64/d0_blind_id/lib/pkgconfig/d0_rijndael.pc b/misc/builddeps/linux64/d0_blind_id/lib/pkgconfig/d0_rijndael.pc deleted file mode 100644 index 1040d658..00000000 --- a/misc/builddeps/linux64/d0_blind_id/lib/pkgconfig/d0_rijndael.pc +++ /dev/null @@ -1,11 +0,0 @@ -prefix=/usr/local -exec_prefix=${prefix} -libdir=${exec_prefix}/lib -includedir=${prefix}/include - -Name: Rijndael -Description: Library for Rijndael encryption -Requires: -Version: 0.5 -Libs: -L${libdir} -ld0_rijndael -Cflags: -I${includedir}/d0_blind_id diff --git a/misc/builddeps/linux64/gmp/include/gmp.h b/misc/builddeps/linux64/gmp/include/gmp.h deleted file mode 100644 index e8cc9b39..00000000 --- a/misc/builddeps/linux64/gmp/include/gmp.h +++ /dev/null @@ -1,2280 +0,0 @@ -/* Definitions for GNU multiple precision functions. -*- mode: c -*- - -Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1999, 2000, 2001, 2002, 2003, -2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc. - -This file is part of the GNU MP Library. - -The GNU MP Library is free software; you can redistribute it and/or modify -it under the terms of the GNU Lesser General Public License as published by -the Free Software Foundation; either version 3 of the License, or (at your -option) any later version. - -The GNU MP Library is distributed in the hope that it will be useful, but -WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY -or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public -License for more details. - -You should have received a copy of the GNU Lesser General Public License -along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */ - -#ifndef __GMP_H__ - -#if defined (__cplusplus) -#include /* for std::istream, std::ostream, std::string */ -#include -#endif - - -/* Instantiated by configure. */ -#if ! defined (__GMP_WITHIN_CONFIGURE) -#define __GMP_HAVE_HOST_CPU_FAMILY_power 0 -#define __GMP_HAVE_HOST_CPU_FAMILY_powerpc 0 -#define GMP_LIMB_BITS 64 -#define GMP_NAIL_BITS 0 -#endif -#define GMP_NUMB_BITS (GMP_LIMB_BITS - GMP_NAIL_BITS) -#define GMP_NUMB_MASK ((~ __GMP_CAST (mp_limb_t, 0)) >> GMP_NAIL_BITS) -#define GMP_NUMB_MAX GMP_NUMB_MASK -#define GMP_NAIL_MASK (~ GMP_NUMB_MASK) - - -/* The following (everything under ifndef __GNU_MP__) must be identical in - gmp.h and mp.h to allow both to be included in an application or during - the library build. */ -#ifndef __GNU_MP__ -#define __GNU_MP__ 5 - -#define __need_size_t /* tell gcc stddef.h we only want size_t */ -#if defined (__cplusplus) -#include /* for size_t */ -#else -#include /* for size_t */ -#endif -#undef __need_size_t - -/* Instantiated by configure. */ -#if ! defined (__GMP_WITHIN_CONFIGURE) -/* #undef _LONG_LONG_LIMB */ -#define __GMP_LIBGMP_DLL 0 -#endif - - -/* __STDC__ - some ANSI compilers define this only to 0, hence the use of - "defined" and not "__STDC__-0". In particular Sun workshop C 5.0 - sets __STDC__ to 0, but requires "##" for token pasting. - - _AIX - gnu ansidecl.h asserts that all known AIX compilers are ANSI but - don't always define __STDC__. - - __DECC - current versions of DEC C (5.9 for instance) for alpha are ANSI, - but don't define __STDC__ in their default mode. Don't know if old - versions might have been K&R, but let's not worry about that unless - someone is still using one. - - _mips - gnu ansidecl.h says the RISC/OS MIPS compiler is ANSI in SVR4 - mode, but doesn't define __STDC__. - - _MSC_VER - Microsoft C is ANSI, but __STDC__ is undefined unless the /Za - option is given (in which case it's 1). - - _WIN32 - tested for by gnu ansidecl.h, no doubt on the assumption that - all w32 compilers are ansi. - - Note: This same set of tests is used by gen-psqr.c and - demos/expr/expr-impl.h, so if anything needs adding, then be sure to - update those too. */ - -#if defined (__STDC__) \ - || defined (__cplusplus) \ - || defined (_AIX) \ - || defined (__DECC) \ - || (defined (__mips) && defined (_SYSTYPE_SVR4)) \ - || defined (_MSC_VER) \ - || defined (_WIN32) -#define __GMP_HAVE_CONST 1 -#define __GMP_HAVE_PROTOTYPES 1 -#define __GMP_HAVE_TOKEN_PASTE 1 -#else -#define __GMP_HAVE_CONST 0 -#define __GMP_HAVE_PROTOTYPES 0 -#define __GMP_HAVE_TOKEN_PASTE 0 -#endif - - -#if __GMP_HAVE_CONST -#define __gmp_const const -#define __gmp_signed signed -#else -#define __gmp_const -#define __gmp_signed -#endif - - -/* __GMP_DECLSPEC supports Windows DLL versions of libgmp, and is empty in - all other circumstances. - - When compiling objects for libgmp, __GMP_DECLSPEC is an export directive, - or when compiling for an application it's an import directive. The two - cases are differentiated by __GMP_WITHIN_GMP defined by the GMP Makefiles - (and not defined from an application). - - __GMP_DECLSPEC_XX is similarly used for libgmpxx. __GMP_WITHIN_GMPXX - indicates when building libgmpxx, and in that case libgmpxx functions are - exports, but libgmp functions which might get called are imports. - - libmp.la uses __GMP_DECLSPEC, just as if it were libgmp.la. libgmp and - libmp don't call each other, so there's no conflict or confusion. - - Libtool DLL_EXPORT define is not used. - - There's no attempt to support GMP built both static and DLL. Doing so - would mean applications would have to tell us which of the two is going - to be used when linking, and that seems very tedious and error prone if - using GMP by hand, and equally tedious from a package since autoconf and - automake don't give much help. - - __GMP_DECLSPEC is required on all documented global functions and - variables, the various internals in gmp-impl.h etc can be left unadorned. - But internals used by the test programs or speed measuring programs - should have __GMP_DECLSPEC, and certainly constants or variables must - have it or the wrong address will be resolved. - - In gcc __declspec can go at either the start or end of a prototype. - - In Microsoft C __declspec must go at the start, or after the type like - void __declspec(...) *foo()". There's no __dllexport or anything to - guard against someone foolish #defining dllexport. _export used to be - available, but no longer. - - In Borland C _export still exists, but needs to go after the type, like - "void _export foo();". Would have to change the __GMP_DECLSPEC syntax to - make use of that. Probably more trouble than it's worth. */ - -#if defined (__GNUC__) -#define __GMP_DECLSPEC_EXPORT __declspec(__dllexport__) -#define __GMP_DECLSPEC_IMPORT __declspec(__dllimport__) -#endif -#if defined (_MSC_VER) || defined (__BORLANDC__) -#define __GMP_DECLSPEC_EXPORT __declspec(dllexport) -#define __GMP_DECLSPEC_IMPORT __declspec(dllimport) -#endif -#ifdef __WATCOMC__ -#define __GMP_DECLSPEC_EXPORT __export -#define __GMP_DECLSPEC_IMPORT __import -#endif -#ifdef __IBMC__ -#define __GMP_DECLSPEC_EXPORT _Export -#define __GMP_DECLSPEC_IMPORT _Import -#endif - -#if __GMP_LIBGMP_DLL -#if __GMP_WITHIN_GMP -/* compiling to go into a DLL libgmp */ -#define __GMP_DECLSPEC __GMP_DECLSPEC_EXPORT -#else -/* compiling to go into an application which will link to a DLL libgmp */ -#define __GMP_DECLSPEC __GMP_DECLSPEC_IMPORT -#endif -#else -/* all other cases */ -#define __GMP_DECLSPEC -#endif - - -#ifdef __GMP_SHORT_LIMB -typedef unsigned int mp_limb_t; -typedef int mp_limb_signed_t; -#else -#ifdef _LONG_LONG_LIMB -typedef unsigned long long int mp_limb_t; -typedef long long int mp_limb_signed_t; -#else -typedef unsigned long int mp_limb_t; -typedef long int mp_limb_signed_t; -#endif -#endif -typedef unsigned long int mp_bitcnt_t; - -/* For reference, note that the name __mpz_struct gets into C++ mangled - function names, which means although the "__" suggests an internal, we - must leave this name for binary compatibility. */ -typedef struct -{ - int _mp_alloc; /* Number of *limbs* allocated and pointed - to by the _mp_d field. */ - int _mp_size; /* abs(_mp_size) is the number of limbs the - last field points to. If _mp_size is - negative this is a negative number. */ - mp_limb_t *_mp_d; /* Pointer to the limbs. */ -} __mpz_struct; - -#endif /* __GNU_MP__ */ - - -typedef __mpz_struct MP_INT; /* gmp 1 source compatibility */ -typedef __mpz_struct mpz_t[1]; - -typedef mp_limb_t * mp_ptr; -typedef __gmp_const mp_limb_t * mp_srcptr; -#if defined (_CRAY) && ! defined (_CRAYMPP) -/* plain `int' is much faster (48 bits) */ -#define __GMP_MP_SIZE_T_INT 1 -typedef int mp_size_t; -typedef int mp_exp_t; -#else -#define __GMP_MP_SIZE_T_INT 0 -typedef long int mp_size_t; -typedef long int mp_exp_t; -#endif - -typedef struct -{ - __mpz_struct _mp_num; - __mpz_struct _mp_den; -} __mpq_struct; - -typedef __mpq_struct MP_RAT; /* gmp 1 source compatibility */ -typedef __mpq_struct mpq_t[1]; - -typedef struct -{ - int _mp_prec; /* Max precision, in number of `mp_limb_t's. - Set by mpf_init and modified by - mpf_set_prec. The area pointed to by the - _mp_d field contains `prec' + 1 limbs. */ - int _mp_size; /* abs(_mp_size) is the number of limbs the - last field points to. If _mp_size is - negative this is a negative number. */ - mp_exp_t _mp_exp; /* Exponent, in the base of `mp_limb_t'. */ - mp_limb_t *_mp_d; /* Pointer to the limbs. */ -} __mpf_struct; - -/* typedef __mpf_struct MP_FLOAT; */ -typedef __mpf_struct mpf_t[1]; - -/* Available random number generation algorithms. */ -typedef enum -{ - GMP_RAND_ALG_DEFAULT = 0, - GMP_RAND_ALG_LC = GMP_RAND_ALG_DEFAULT /* Linear congruential. */ -} gmp_randalg_t; - -/* Random state struct. */ -typedef struct -{ - mpz_t _mp_seed; /* _mp_d member points to state of the generator. */ - gmp_randalg_t _mp_alg; /* Currently unused. */ - union { - void *_mp_lc; /* Pointer to function pointers structure. */ - } _mp_algdata; -} __gmp_randstate_struct; -typedef __gmp_randstate_struct gmp_randstate_t[1]; - -/* Types for function declarations in gmp files. */ -/* ??? Should not pollute user name space with these ??? */ -typedef __gmp_const __mpz_struct *mpz_srcptr; -typedef __mpz_struct *mpz_ptr; -typedef __gmp_const __mpf_struct *mpf_srcptr; -typedef __mpf_struct *mpf_ptr; -typedef __gmp_const __mpq_struct *mpq_srcptr; -typedef __mpq_struct *mpq_ptr; - - -/* This is not wanted in mp.h, so put it outside the __GNU_MP__ common - section. */ -#if __GMP_LIBGMP_DLL -#if __GMP_WITHIN_GMPXX -/* compiling to go into a DLL libgmpxx */ -#define __GMP_DECLSPEC_XX __GMP_DECLSPEC_EXPORT -#else -/* compiling to go into a application which will link to a DLL libgmpxx */ -#define __GMP_DECLSPEC_XX __GMP_DECLSPEC_IMPORT -#endif -#else -/* all other cases */ -#define __GMP_DECLSPEC_XX -#endif - - -#if __GMP_HAVE_PROTOTYPES -#define __GMP_PROTO(x) x -#else -#define __GMP_PROTO(x) () -#endif - -#ifndef __MPN -#if __GMP_HAVE_TOKEN_PASTE -#define __MPN(x) __gmpn_##x -#else -#define __MPN(x) __gmpn_/**/x -#endif -#endif - -/* For reference, "defined(EOF)" cannot be used here. In g++ 2.95.4, - defines EOF but not FILE. */ -#if defined (FILE) \ - || defined (H_STDIO) \ - || defined (_H_STDIO) /* AIX */ \ - || defined (_STDIO_H) /* glibc, Sun, SCO */ \ - || defined (_STDIO_H_) /* BSD, OSF */ \ - || defined (__STDIO_H) /* Borland */ \ - || defined (__STDIO_H__) /* IRIX */ \ - || defined (_STDIO_INCLUDED) /* HPUX */ \ - || defined (__dj_include_stdio_h_) /* DJGPP */ \ - || defined (_FILE_DEFINED) /* Microsoft */ \ - || defined (__STDIO__) /* Apple MPW MrC */ \ - || defined (_MSL_STDIO_H) /* Metrowerks */ \ - || defined (_STDIO_H_INCLUDED) /* QNX4 */ \ - || defined (_ISO_STDIO_ISO_H) /* Sun C++ */ -#define _GMP_H_HAVE_FILE 1 -#endif - -/* In ISO C, if a prototype involving "struct obstack *" is given without - that structure defined, then the struct is scoped down to just the - prototype, causing a conflict if it's subsequently defined for real. So - only give prototypes if we've got obstack.h. */ -#if defined (_OBSTACK_H) /* glibc */ -#define _GMP_H_HAVE_OBSTACK 1 -#endif - -/* The prototypes for gmp_vprintf etc are provided only if va_list is - available, via an application having included or . - Usually va_list is a typedef so can't be tested directly, but C99 - specifies that va_start is a macro (and it was normally a macro on past - systems too), so look for that. - - will define some sort of va_list for vprintf and vfprintf, but - let's not bother trying to use that since it's not standard and since - application uses for gmp_vprintf etc will almost certainly require the - whole or anyway. */ - -#ifdef va_start -#define _GMP_H_HAVE_VA_LIST 1 -#endif - -/* Test for gcc >= maj.min, as per __GNUC_PREREQ in glibc */ -#if defined (__GNUC__) && defined (__GNUC_MINOR__) -#define __GMP_GNUC_PREREQ(maj, min) \ - ((__GNUC__ << 16) + __GNUC_MINOR__ >= ((maj) << 16) + (min)) -#else -#define __GMP_GNUC_PREREQ(maj, min) 0 -#endif - -/* "pure" is in gcc 2.96 and up, see "(gcc)Function Attributes". Basically - it means a function does nothing but examine its arguments and memory - (global or via arguments) to generate a return value, but changes nothing - and has no side-effects. __GMP_NO_ATTRIBUTE_CONST_PURE lets - tune/common.c etc turn this off when trying to write timing loops. */ -#if __GMP_GNUC_PREREQ (2,96) && ! defined (__GMP_NO_ATTRIBUTE_CONST_PURE) -#define __GMP_ATTRIBUTE_PURE __attribute__ ((__pure__)) -#else -#define __GMP_ATTRIBUTE_PURE -#endif - - -/* __GMP_CAST allows us to use static_cast in C++, so our macros are clean - to "g++ -Wold-style-cast". - - Casts in "extern inline" code within an extern "C" block don't induce - these warnings, so __GMP_CAST only needs to be used on documented - macros. */ - -#ifdef __cplusplus -#define __GMP_CAST(type, expr) (static_cast (expr)) -#else -#define __GMP_CAST(type, expr) ((type) (expr)) -#endif - - -/* An empty "throw ()" means the function doesn't throw any C++ exceptions, - this can save some stack frame info in applications. - - Currently it's given only on functions which never divide-by-zero etc, - don't allocate memory, and are expected to never need to allocate memory. - This leaves open the possibility of a C++ throw from a future GMP - exceptions scheme. - - mpz_set_ui etc are omitted to leave open the lazy allocation scheme - described in doc/tasks.html. mpz_get_d etc are omitted to leave open - exceptions for float overflows. - - Note that __GMP_NOTHROW must be given on any inlines the same as on their - prototypes (for g++ at least, where they're used together). Note also - that g++ 3.0 demands that __GMP_NOTHROW is before other attributes like - __GMP_ATTRIBUTE_PURE. */ - -#if defined (__cplusplus) -#define __GMP_NOTHROW throw () -#else -#define __GMP_NOTHROW -#endif - - -/* PORTME: What other compilers have a useful "extern inline"? "static - inline" would be an acceptable substitute if the compiler (or linker) - discards unused statics. */ - - /* gcc has __inline__ in all modes, including strict ansi. Give a prototype - for an inline too, so as to correctly specify "dllimport" on windows, in - case the function is called rather than inlined. - GCC 4.3 and above with -std=c99 or -std=gnu99 implements ISO C99 - inline semantics, unless -fgnu89-inline is used. */ -#ifdef __GNUC__ -#if (defined __GNUC_STDC_INLINE__) || (__GNUC__ == 4 && __GNUC_MINOR__ == 2) -#define __GMP_EXTERN_INLINE extern __inline__ __attribute__ ((__gnu_inline__)) -#else -#define __GMP_EXTERN_INLINE extern __inline__ -#endif -#define __GMP_INLINE_PROTOTYPES 1 -#endif - -/* DEC C (eg. version 5.9) supports "static __inline foo()", even in -std1 - strict ANSI mode. Inlining is done even when not optimizing (ie. -O0 - mode, which is the default), but an unnecessary local copy of foo is - emitted unless -O is used. "extern __inline" is accepted, but the - "extern" appears to be ignored, ie. it becomes a plain global function - but which is inlined within its file. Don't know if all old versions of - DEC C supported __inline, but as a start let's do the right thing for - current versions. */ -#ifdef __DECC -#define __GMP_EXTERN_INLINE static __inline -#endif - -/* SCO OpenUNIX 8 cc supports "static inline foo()" but not in -Xc strict - ANSI mode (__STDC__ is 1 in that mode). Inlining only actually takes - place under -O. Without -O "foo" seems to be emitted whether it's used - or not, which is wasteful. "extern inline foo()" isn't useful, the - "extern" is apparently ignored, so foo is inlined if possible but also - emitted as a global, which causes multiple definition errors when - building a shared libgmp. */ -#ifdef __SCO_VERSION__ -#if __SCO_VERSION__ > 400000000 && __STDC__ != 1 \ - && ! defined (__GMP_EXTERN_INLINE) -#define __GMP_EXTERN_INLINE static inline -#endif -#endif - -/* Microsoft's C compiler accepts __inline */ -#ifdef _MSC_VER -#define __GMP_EXTERN_INLINE __inline -#endif - -/* Recent enough Sun C compilers want "inline" */ -#if defined (__SUNPRO_C) && __SUNPRO_C >= 0x560 \ - && ! defined (__GMP_EXTERN_INLINE) -#define __GMP_EXTERN_INLINE inline -#endif - -/* Somewhat older Sun C compilers want "static inline" */ -#if defined (__SUNPRO_C) && __SUNPRO_C >= 0x540 \ - && ! defined (__GMP_EXTERN_INLINE) -#define __GMP_EXTERN_INLINE static inline -#endif - - -/* C++ always has "inline" and since it's a normal feature the linker should - discard duplicate non-inlined copies, or if it doesn't then that's a - problem for everyone, not just GMP. */ -#if defined (__cplusplus) && ! defined (__GMP_EXTERN_INLINE) -#define __GMP_EXTERN_INLINE inline -#endif - -/* Don't do any inlining within a configure run, since if the compiler ends - up emitting copies of the code into the object file it can end up - demanding the various support routines (like mpn_popcount) for linking, - making the "alloca" test and perhaps others fail. And on hppa ia64 a - pre-release gcc 3.2 was seen not respecting the "extern" in "extern - __inline__", triggering this problem too. */ -#if defined (__GMP_WITHIN_CONFIGURE) && ! __GMP_WITHIN_CONFIGURE_INLINE -#undef __GMP_EXTERN_INLINE -#endif - -/* By default, don't give a prototype when there's going to be an inline - version. Note in particular that Cray C++ objects to the combination of - prototype and inline. */ -#ifdef __GMP_EXTERN_INLINE -#ifndef __GMP_INLINE_PROTOTYPES -#define __GMP_INLINE_PROTOTYPES 0 -#endif -#else -#define __GMP_INLINE_PROTOTYPES 1 -#endif - - -#define __GMP_ABS(x) ((x) >= 0 ? (x) : -(x)) -#define __GMP_MAX(h,i) ((h) > (i) ? (h) : (i)) - -/* __GMP_USHRT_MAX is not "~ (unsigned short) 0" because short is promoted - to int by "~". */ -#define __GMP_UINT_MAX (~ (unsigned) 0) -#define __GMP_ULONG_MAX (~ (unsigned long) 0) -#define __GMP_USHRT_MAX ((unsigned short) ~0) - - -/* __builtin_expect is in gcc 3.0, and not in 2.95. */ -#if __GMP_GNUC_PREREQ (3,0) -#define __GMP_LIKELY(cond) __builtin_expect ((cond) != 0, 1) -#define __GMP_UNLIKELY(cond) __builtin_expect ((cond) != 0, 0) -#else -#define __GMP_LIKELY(cond) (cond) -#define __GMP_UNLIKELY(cond) (cond) -#endif - -#ifdef _CRAY -#define __GMP_CRAY_Pragma(str) _Pragma (str) -#else -#define __GMP_CRAY_Pragma(str) -#endif - - -/* Allow direct user access to numerator and denominator of a mpq_t object. */ -#define mpq_numref(Q) (&((Q)->_mp_num)) -#define mpq_denref(Q) (&((Q)->_mp_den)) - - -#if defined (__cplusplus) -extern "C" { -using std::FILE; -#endif - -#define mp_set_memory_functions __gmp_set_memory_functions -__GMP_DECLSPEC void mp_set_memory_functions __GMP_PROTO ((void *(*) (size_t), - void *(*) (void *, size_t, size_t), - void (*) (void *, size_t))) __GMP_NOTHROW; - -#define mp_get_memory_functions __gmp_get_memory_functions -__GMP_DECLSPEC void mp_get_memory_functions __GMP_PROTO ((void *(**) (size_t), - void *(**) (void *, size_t, size_t), - void (**) (void *, size_t))) __GMP_NOTHROW; - -#define mp_bits_per_limb __gmp_bits_per_limb -__GMP_DECLSPEC extern __gmp_const int mp_bits_per_limb; - -#define gmp_errno __gmp_errno -__GMP_DECLSPEC extern int gmp_errno; - -#define gmp_version __gmp_version -__GMP_DECLSPEC extern __gmp_const char * __gmp_const gmp_version; - - -/**************** Random number routines. ****************/ - -/* obsolete */ -#define gmp_randinit __gmp_randinit -__GMP_DECLSPEC void gmp_randinit __GMP_PROTO ((gmp_randstate_t, gmp_randalg_t, ...)); - -#define gmp_randinit_default __gmp_randinit_default -__GMP_DECLSPEC void gmp_randinit_default __GMP_PROTO ((gmp_randstate_t)); - -#define gmp_randinit_lc_2exp __gmp_randinit_lc_2exp -__GMP_DECLSPEC void gmp_randinit_lc_2exp __GMP_PROTO ((gmp_randstate_t, - mpz_srcptr, unsigned long int, - mp_bitcnt_t)); - -#define gmp_randinit_lc_2exp_size __gmp_randinit_lc_2exp_size -__GMP_DECLSPEC int gmp_randinit_lc_2exp_size __GMP_PROTO ((gmp_randstate_t, mp_bitcnt_t)); - -#define gmp_randinit_mt __gmp_randinit_mt -__GMP_DECLSPEC void gmp_randinit_mt __GMP_PROTO ((gmp_randstate_t)); - -#define gmp_randinit_set __gmp_randinit_set -__GMP_DECLSPEC void gmp_randinit_set __GMP_PROTO ((gmp_randstate_t, __gmp_const __gmp_randstate_struct *)); - -#define gmp_randseed __gmp_randseed -__GMP_DECLSPEC void gmp_randseed __GMP_PROTO ((gmp_randstate_t, mpz_srcptr)); - -#define gmp_randseed_ui __gmp_randseed_ui -__GMP_DECLSPEC void gmp_randseed_ui __GMP_PROTO ((gmp_randstate_t, unsigned long int)); - -#define gmp_randclear __gmp_randclear -__GMP_DECLSPEC void gmp_randclear __GMP_PROTO ((gmp_randstate_t)); - -#define gmp_urandomb_ui __gmp_urandomb_ui -__GMP_DECLSPEC unsigned long gmp_urandomb_ui __GMP_PROTO ((gmp_randstate_t, unsigned long)); - -#define gmp_urandomm_ui __gmp_urandomm_ui -__GMP_DECLSPEC unsigned long gmp_urandomm_ui __GMP_PROTO ((gmp_randstate_t, unsigned long)); - - -/**************** Formatted output routines. ****************/ - -#define gmp_asprintf __gmp_asprintf -__GMP_DECLSPEC int gmp_asprintf __GMP_PROTO ((char **, __gmp_const char *, ...)); - -#define gmp_fprintf __gmp_fprintf -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC int gmp_fprintf __GMP_PROTO ((FILE *, __gmp_const char *, ...)); -#endif - -#define gmp_obstack_printf __gmp_obstack_printf -#if defined (_GMP_H_HAVE_OBSTACK) -__GMP_DECLSPEC int gmp_obstack_printf __GMP_PROTO ((struct obstack *, __gmp_const char *, ...)); -#endif - -#define gmp_obstack_vprintf __gmp_obstack_vprintf -#if defined (_GMP_H_HAVE_OBSTACK) && defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_obstack_vprintf __GMP_PROTO ((struct obstack *, __gmp_const char *, va_list)); -#endif - -#define gmp_printf __gmp_printf -__GMP_DECLSPEC int gmp_printf __GMP_PROTO ((__gmp_const char *, ...)); - -#define gmp_snprintf __gmp_snprintf -__GMP_DECLSPEC int gmp_snprintf __GMP_PROTO ((char *, size_t, __gmp_const char *, ...)); - -#define gmp_sprintf __gmp_sprintf -__GMP_DECLSPEC int gmp_sprintf __GMP_PROTO ((char *, __gmp_const char *, ...)); - -#define gmp_vasprintf __gmp_vasprintf -#if defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vasprintf __GMP_PROTO ((char **, __gmp_const char *, va_list)); -#endif - -#define gmp_vfprintf __gmp_vfprintf -#if defined (_GMP_H_HAVE_FILE) && defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vfprintf __GMP_PROTO ((FILE *, __gmp_const char *, va_list)); -#endif - -#define gmp_vprintf __gmp_vprintf -#if defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vprintf __GMP_PROTO ((__gmp_const char *, va_list)); -#endif - -#define gmp_vsnprintf __gmp_vsnprintf -#if defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vsnprintf __GMP_PROTO ((char *, size_t, __gmp_const char *, va_list)); -#endif - -#define gmp_vsprintf __gmp_vsprintf -#if defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vsprintf __GMP_PROTO ((char *, __gmp_const char *, va_list)); -#endif - - -/**************** Formatted input routines. ****************/ - -#define gmp_fscanf __gmp_fscanf -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC int gmp_fscanf __GMP_PROTO ((FILE *, __gmp_const char *, ...)); -#endif - -#define gmp_scanf __gmp_scanf -__GMP_DECLSPEC int gmp_scanf __GMP_PROTO ((__gmp_const char *, ...)); - -#define gmp_sscanf __gmp_sscanf -__GMP_DECLSPEC int gmp_sscanf __GMP_PROTO ((__gmp_const char *, __gmp_const char *, ...)); - -#define gmp_vfscanf __gmp_vfscanf -#if defined (_GMP_H_HAVE_FILE) && defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vfscanf __GMP_PROTO ((FILE *, __gmp_const char *, va_list)); -#endif - -#define gmp_vscanf __gmp_vscanf -#if defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vscanf __GMP_PROTO ((__gmp_const char *, va_list)); -#endif - -#define gmp_vsscanf __gmp_vsscanf -#if defined (_GMP_H_HAVE_VA_LIST) -__GMP_DECLSPEC int gmp_vsscanf __GMP_PROTO ((__gmp_const char *, __gmp_const char *, va_list)); -#endif - - -/**************** Integer (i.e. Z) routines. ****************/ - -#define _mpz_realloc __gmpz_realloc -#define mpz_realloc __gmpz_realloc -__GMP_DECLSPEC void *_mpz_realloc __GMP_PROTO ((mpz_ptr, mp_size_t)); - -#define mpz_abs __gmpz_abs -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_abs) -__GMP_DECLSPEC void mpz_abs __GMP_PROTO ((mpz_ptr, mpz_srcptr)); -#endif - -#define mpz_add __gmpz_add -__GMP_DECLSPEC void mpz_add __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_add_ui __gmpz_add_ui -__GMP_DECLSPEC void mpz_add_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_addmul __gmpz_addmul -__GMP_DECLSPEC void mpz_addmul __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_addmul_ui __gmpz_addmul_ui -__GMP_DECLSPEC void mpz_addmul_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_and __gmpz_and -__GMP_DECLSPEC void mpz_and __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_array_init __gmpz_array_init -__GMP_DECLSPEC void mpz_array_init __GMP_PROTO ((mpz_ptr, mp_size_t, mp_size_t)); - -#define mpz_bin_ui __gmpz_bin_ui -__GMP_DECLSPEC void mpz_bin_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_bin_uiui __gmpz_bin_uiui -__GMP_DECLSPEC void mpz_bin_uiui __GMP_PROTO ((mpz_ptr, unsigned long int, unsigned long int)); - -#define mpz_cdiv_q __gmpz_cdiv_q -__GMP_DECLSPEC void mpz_cdiv_q __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_cdiv_q_2exp __gmpz_cdiv_q_2exp -__GMP_DECLSPEC void mpz_cdiv_q_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long)); - -#define mpz_cdiv_q_ui __gmpz_cdiv_q_ui -__GMP_DECLSPEC unsigned long int mpz_cdiv_q_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_cdiv_qr __gmpz_cdiv_qr -__GMP_DECLSPEC void mpz_cdiv_qr __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_cdiv_qr_ui __gmpz_cdiv_qr_ui -__GMP_DECLSPEC unsigned long int mpz_cdiv_qr_ui __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_cdiv_r __gmpz_cdiv_r -__GMP_DECLSPEC void mpz_cdiv_r __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_cdiv_r_2exp __gmpz_cdiv_r_2exp -__GMP_DECLSPEC void mpz_cdiv_r_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, mp_bitcnt_t)); - -#define mpz_cdiv_r_ui __gmpz_cdiv_r_ui -__GMP_DECLSPEC unsigned long int mpz_cdiv_r_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_cdiv_ui __gmpz_cdiv_ui -__GMP_DECLSPEC unsigned long int mpz_cdiv_ui __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_ATTRIBUTE_PURE; - -#define mpz_clear __gmpz_clear -__GMP_DECLSPEC void mpz_clear __GMP_PROTO ((mpz_ptr)); - -#define mpz_clears __gmpz_clears -__GMP_DECLSPEC void mpz_clears __GMP_PROTO ((mpz_ptr, ...)); - -#define mpz_clrbit __gmpz_clrbit -__GMP_DECLSPEC void mpz_clrbit __GMP_PROTO ((mpz_ptr, mp_bitcnt_t)); - -#define mpz_cmp __gmpz_cmp -__GMP_DECLSPEC int mpz_cmp __GMP_PROTO ((mpz_srcptr, mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_cmp_d __gmpz_cmp_d -__GMP_DECLSPEC int mpz_cmp_d __GMP_PROTO ((mpz_srcptr, double)) __GMP_ATTRIBUTE_PURE; - -#define _mpz_cmp_si __gmpz_cmp_si -__GMP_DECLSPEC int _mpz_cmp_si __GMP_PROTO ((mpz_srcptr, signed long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define _mpz_cmp_ui __gmpz_cmp_ui -__GMP_DECLSPEC int _mpz_cmp_ui __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_cmpabs __gmpz_cmpabs -__GMP_DECLSPEC int mpz_cmpabs __GMP_PROTO ((mpz_srcptr, mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_cmpabs_d __gmpz_cmpabs_d -__GMP_DECLSPEC int mpz_cmpabs_d __GMP_PROTO ((mpz_srcptr, double)) __GMP_ATTRIBUTE_PURE; - -#define mpz_cmpabs_ui __gmpz_cmpabs_ui -__GMP_DECLSPEC int mpz_cmpabs_ui __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_com __gmpz_com -__GMP_DECLSPEC void mpz_com __GMP_PROTO ((mpz_ptr, mpz_srcptr)); - -#define mpz_combit __gmpz_combit -__GMP_DECLSPEC void mpz_combit __GMP_PROTO ((mpz_ptr, mp_bitcnt_t)); - -#define mpz_congruent_p __gmpz_congruent_p -__GMP_DECLSPEC int mpz_congruent_p __GMP_PROTO ((mpz_srcptr, mpz_srcptr, mpz_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpz_congruent_2exp_p __gmpz_congruent_2exp_p -__GMP_DECLSPEC int mpz_congruent_2exp_p __GMP_PROTO ((mpz_srcptr, mpz_srcptr, mp_bitcnt_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_congruent_ui_p __gmpz_congruent_ui_p -__GMP_DECLSPEC int mpz_congruent_ui_p __GMP_PROTO ((mpz_srcptr, unsigned long, unsigned long)) __GMP_ATTRIBUTE_PURE; - -#define mpz_divexact __gmpz_divexact -__GMP_DECLSPEC void mpz_divexact __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_divexact_ui __gmpz_divexact_ui -__GMP_DECLSPEC void mpz_divexact_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long)); - -#define mpz_divisible_p __gmpz_divisible_p -__GMP_DECLSPEC int mpz_divisible_p __GMP_PROTO ((mpz_srcptr, mpz_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpz_divisible_ui_p __gmpz_divisible_ui_p -__GMP_DECLSPEC int mpz_divisible_ui_p __GMP_PROTO ((mpz_srcptr, unsigned long)) __GMP_ATTRIBUTE_PURE; - -#define mpz_divisible_2exp_p __gmpz_divisible_2exp_p -__GMP_DECLSPEC int mpz_divisible_2exp_p __GMP_PROTO ((mpz_srcptr, mp_bitcnt_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_dump __gmpz_dump -__GMP_DECLSPEC void mpz_dump __GMP_PROTO ((mpz_srcptr)); - -#define mpz_export __gmpz_export -__GMP_DECLSPEC void *mpz_export __GMP_PROTO ((void *, size_t *, int, size_t, int, size_t, mpz_srcptr)); - -#define mpz_fac_ui __gmpz_fac_ui -__GMP_DECLSPEC void mpz_fac_ui __GMP_PROTO ((mpz_ptr, unsigned long int)); - -#define mpz_fdiv_q __gmpz_fdiv_q -__GMP_DECLSPEC void mpz_fdiv_q __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_fdiv_q_2exp __gmpz_fdiv_q_2exp -__GMP_DECLSPEC void mpz_fdiv_q_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, mp_bitcnt_t)); - -#define mpz_fdiv_q_ui __gmpz_fdiv_q_ui -__GMP_DECLSPEC unsigned long int mpz_fdiv_q_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_fdiv_qr __gmpz_fdiv_qr -__GMP_DECLSPEC void mpz_fdiv_qr __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_fdiv_qr_ui __gmpz_fdiv_qr_ui -__GMP_DECLSPEC unsigned long int mpz_fdiv_qr_ui __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_fdiv_r __gmpz_fdiv_r -__GMP_DECLSPEC void mpz_fdiv_r __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_fdiv_r_2exp __gmpz_fdiv_r_2exp -__GMP_DECLSPEC void mpz_fdiv_r_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, mp_bitcnt_t)); - -#define mpz_fdiv_r_ui __gmpz_fdiv_r_ui -__GMP_DECLSPEC unsigned long int mpz_fdiv_r_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_fdiv_ui __gmpz_fdiv_ui -__GMP_DECLSPEC unsigned long int mpz_fdiv_ui __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_ATTRIBUTE_PURE; - -#define mpz_fib_ui __gmpz_fib_ui -__GMP_DECLSPEC void mpz_fib_ui __GMP_PROTO ((mpz_ptr, unsigned long int)); - -#define mpz_fib2_ui __gmpz_fib2_ui -__GMP_DECLSPEC void mpz_fib2_ui __GMP_PROTO ((mpz_ptr, mpz_ptr, unsigned long int)); - -#define mpz_fits_sint_p __gmpz_fits_sint_p -__GMP_DECLSPEC int mpz_fits_sint_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_fits_slong_p __gmpz_fits_slong_p -__GMP_DECLSPEC int mpz_fits_slong_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_fits_sshort_p __gmpz_fits_sshort_p -__GMP_DECLSPEC int mpz_fits_sshort_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_fits_uint_p __gmpz_fits_uint_p -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_fits_uint_p) -__GMP_DECLSPEC int mpz_fits_uint_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_fits_ulong_p __gmpz_fits_ulong_p -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_fits_ulong_p) -__GMP_DECLSPEC int mpz_fits_ulong_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_fits_ushort_p __gmpz_fits_ushort_p -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_fits_ushort_p) -__GMP_DECLSPEC int mpz_fits_ushort_p __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_gcd __gmpz_gcd -__GMP_DECLSPEC void mpz_gcd __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_gcd_ui __gmpz_gcd_ui -__GMP_DECLSPEC unsigned long int mpz_gcd_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_gcdext __gmpz_gcdext -__GMP_DECLSPEC void mpz_gcdext __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_get_d __gmpz_get_d -__GMP_DECLSPEC double mpz_get_d __GMP_PROTO ((mpz_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpz_get_d_2exp __gmpz_get_d_2exp -__GMP_DECLSPEC double mpz_get_d_2exp __GMP_PROTO ((signed long int *, mpz_srcptr)); - -#define mpz_get_si __gmpz_get_si -__GMP_DECLSPEC /* signed */ long int mpz_get_si __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_get_str __gmpz_get_str -__GMP_DECLSPEC char *mpz_get_str __GMP_PROTO ((char *, int, mpz_srcptr)); - -#define mpz_get_ui __gmpz_get_ui -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_get_ui) -__GMP_DECLSPEC unsigned long int mpz_get_ui __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_getlimbn __gmpz_getlimbn -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_getlimbn) -__GMP_DECLSPEC mp_limb_t mpz_getlimbn __GMP_PROTO ((mpz_srcptr, mp_size_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_hamdist __gmpz_hamdist -__GMP_DECLSPEC mp_bitcnt_t mpz_hamdist __GMP_PROTO ((mpz_srcptr, mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_import __gmpz_import -__GMP_DECLSPEC void mpz_import __GMP_PROTO ((mpz_ptr, size_t, int, size_t, int, size_t, __gmp_const void *)); - -#define mpz_init __gmpz_init -__GMP_DECLSPEC void mpz_init __GMP_PROTO ((mpz_ptr)); - -#define mpz_init2 __gmpz_init2 -__GMP_DECLSPEC void mpz_init2 __GMP_PROTO ((mpz_ptr, mp_bitcnt_t)); - -#define mpz_inits __gmpz_inits -__GMP_DECLSPEC void mpz_inits __GMP_PROTO ((mpz_ptr, ...)); - -#define mpz_init_set __gmpz_init_set -__GMP_DECLSPEC void mpz_init_set __GMP_PROTO ((mpz_ptr, mpz_srcptr)); - -#define mpz_init_set_d __gmpz_init_set_d -__GMP_DECLSPEC void mpz_init_set_d __GMP_PROTO ((mpz_ptr, double)); - -#define mpz_init_set_si __gmpz_init_set_si -__GMP_DECLSPEC void mpz_init_set_si __GMP_PROTO ((mpz_ptr, signed long int)); - -#define mpz_init_set_str __gmpz_init_set_str -__GMP_DECLSPEC int mpz_init_set_str __GMP_PROTO ((mpz_ptr, __gmp_const char *, int)); - -#define mpz_init_set_ui __gmpz_init_set_ui -__GMP_DECLSPEC void mpz_init_set_ui __GMP_PROTO ((mpz_ptr, unsigned long int)); - -#define mpz_inp_raw __gmpz_inp_raw -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpz_inp_raw __GMP_PROTO ((mpz_ptr, FILE *)); -#endif - -#define mpz_inp_str __gmpz_inp_str -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpz_inp_str __GMP_PROTO ((mpz_ptr, FILE *, int)); -#endif - -#define mpz_invert __gmpz_invert -__GMP_DECLSPEC int mpz_invert __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_ior __gmpz_ior -__GMP_DECLSPEC void mpz_ior __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_jacobi __gmpz_jacobi -__GMP_DECLSPEC int mpz_jacobi __GMP_PROTO ((mpz_srcptr, mpz_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpz_kronecker mpz_jacobi /* alias */ - -#define mpz_kronecker_si __gmpz_kronecker_si -__GMP_DECLSPEC int mpz_kronecker_si __GMP_PROTO ((mpz_srcptr, long)) __GMP_ATTRIBUTE_PURE; - -#define mpz_kronecker_ui __gmpz_kronecker_ui -__GMP_DECLSPEC int mpz_kronecker_ui __GMP_PROTO ((mpz_srcptr, unsigned long)) __GMP_ATTRIBUTE_PURE; - -#define mpz_si_kronecker __gmpz_si_kronecker -__GMP_DECLSPEC int mpz_si_kronecker __GMP_PROTO ((long, mpz_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpz_ui_kronecker __gmpz_ui_kronecker -__GMP_DECLSPEC int mpz_ui_kronecker __GMP_PROTO ((unsigned long, mpz_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpz_lcm __gmpz_lcm -__GMP_DECLSPEC void mpz_lcm __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_lcm_ui __gmpz_lcm_ui -__GMP_DECLSPEC void mpz_lcm_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long)); - -#define mpz_legendre mpz_jacobi /* alias */ - -#define mpz_lucnum_ui __gmpz_lucnum_ui -__GMP_DECLSPEC void mpz_lucnum_ui __GMP_PROTO ((mpz_ptr, unsigned long int)); - -#define mpz_lucnum2_ui __gmpz_lucnum2_ui -__GMP_DECLSPEC void mpz_lucnum2_ui __GMP_PROTO ((mpz_ptr, mpz_ptr, unsigned long int)); - -#define mpz_millerrabin __gmpz_millerrabin -__GMP_DECLSPEC int mpz_millerrabin __GMP_PROTO ((mpz_srcptr, int)) __GMP_ATTRIBUTE_PURE; - -#define mpz_mod __gmpz_mod -__GMP_DECLSPEC void mpz_mod __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_mod_ui mpz_fdiv_r_ui /* same as fdiv_r because divisor unsigned */ - -#define mpz_mul __gmpz_mul -__GMP_DECLSPEC void mpz_mul __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_mul_2exp __gmpz_mul_2exp -__GMP_DECLSPEC void mpz_mul_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, mp_bitcnt_t)); - -#define mpz_mul_si __gmpz_mul_si -__GMP_DECLSPEC void mpz_mul_si __GMP_PROTO ((mpz_ptr, mpz_srcptr, long int)); - -#define mpz_mul_ui __gmpz_mul_ui -__GMP_DECLSPEC void mpz_mul_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_neg __gmpz_neg -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_neg) -__GMP_DECLSPEC void mpz_neg __GMP_PROTO ((mpz_ptr, mpz_srcptr)); -#endif - -#define mpz_nextprime __gmpz_nextprime -__GMP_DECLSPEC void mpz_nextprime __GMP_PROTO ((mpz_ptr, mpz_srcptr)); - -#define mpz_out_raw __gmpz_out_raw -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpz_out_raw __GMP_PROTO ((FILE *, mpz_srcptr)); -#endif - -#define mpz_out_str __gmpz_out_str -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpz_out_str __GMP_PROTO ((FILE *, int, mpz_srcptr)); -#endif - -#define mpz_perfect_power_p __gmpz_perfect_power_p -__GMP_DECLSPEC int mpz_perfect_power_p __GMP_PROTO ((mpz_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpz_perfect_square_p __gmpz_perfect_square_p -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_perfect_square_p) -__GMP_DECLSPEC int mpz_perfect_square_p __GMP_PROTO ((mpz_srcptr)) __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_popcount __gmpz_popcount -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_popcount) -__GMP_DECLSPEC mp_bitcnt_t mpz_popcount __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_pow_ui __gmpz_pow_ui -__GMP_DECLSPEC void mpz_pow_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_powm __gmpz_powm -__GMP_DECLSPEC void mpz_powm __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_powm_sec __gmpz_powm_sec -__GMP_DECLSPEC void mpz_powm_sec __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_powm_ui __gmpz_powm_ui -__GMP_DECLSPEC void mpz_powm_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int, mpz_srcptr)); - -#define mpz_probab_prime_p __gmpz_probab_prime_p -__GMP_DECLSPEC int mpz_probab_prime_p __GMP_PROTO ((mpz_srcptr, int)) __GMP_ATTRIBUTE_PURE; - -#define mpz_random __gmpz_random -__GMP_DECLSPEC void mpz_random __GMP_PROTO ((mpz_ptr, mp_size_t)); - -#define mpz_random2 __gmpz_random2 -__GMP_DECLSPEC void mpz_random2 __GMP_PROTO ((mpz_ptr, mp_size_t)); - -#define mpz_realloc2 __gmpz_realloc2 -__GMP_DECLSPEC void mpz_realloc2 __GMP_PROTO ((mpz_ptr, mp_bitcnt_t)); - -#define mpz_remove __gmpz_remove -__GMP_DECLSPEC unsigned long int mpz_remove __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_root __gmpz_root -__GMP_DECLSPEC int mpz_root __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_rootrem __gmpz_rootrem -__GMP_DECLSPEC void mpz_rootrem __GMP_PROTO ((mpz_ptr,mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_rrandomb __gmpz_rrandomb -__GMP_DECLSPEC void mpz_rrandomb __GMP_PROTO ((mpz_ptr, gmp_randstate_t, mp_bitcnt_t)); - -#define mpz_scan0 __gmpz_scan0 -__GMP_DECLSPEC mp_bitcnt_t mpz_scan0 __GMP_PROTO ((mpz_srcptr, mp_bitcnt_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_scan1 __gmpz_scan1 -__GMP_DECLSPEC mp_bitcnt_t mpz_scan1 __GMP_PROTO ((mpz_srcptr, mp_bitcnt_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_set __gmpz_set -__GMP_DECLSPEC void mpz_set __GMP_PROTO ((mpz_ptr, mpz_srcptr)); - -#define mpz_set_d __gmpz_set_d -__GMP_DECLSPEC void mpz_set_d __GMP_PROTO ((mpz_ptr, double)); - -#define mpz_set_f __gmpz_set_f -__GMP_DECLSPEC void mpz_set_f __GMP_PROTO ((mpz_ptr, mpf_srcptr)); - -#define mpz_set_q __gmpz_set_q -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_set_q) -__GMP_DECLSPEC void mpz_set_q __GMP_PROTO ((mpz_ptr, mpq_srcptr)); -#endif - -#define mpz_set_si __gmpz_set_si -__GMP_DECLSPEC void mpz_set_si __GMP_PROTO ((mpz_ptr, signed long int)); - -#define mpz_set_str __gmpz_set_str -__GMP_DECLSPEC int mpz_set_str __GMP_PROTO ((mpz_ptr, __gmp_const char *, int)); - -#define mpz_set_ui __gmpz_set_ui -__GMP_DECLSPEC void mpz_set_ui __GMP_PROTO ((mpz_ptr, unsigned long int)); - -#define mpz_setbit __gmpz_setbit -__GMP_DECLSPEC void mpz_setbit __GMP_PROTO ((mpz_ptr, mp_bitcnt_t)); - -#define mpz_size __gmpz_size -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_size) -__GMP_DECLSPEC size_t mpz_size __GMP_PROTO ((mpz_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpz_sizeinbase __gmpz_sizeinbase -__GMP_DECLSPEC size_t mpz_sizeinbase __GMP_PROTO ((mpz_srcptr, int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_sqrt __gmpz_sqrt -__GMP_DECLSPEC void mpz_sqrt __GMP_PROTO ((mpz_ptr, mpz_srcptr)); - -#define mpz_sqrtrem __gmpz_sqrtrem -__GMP_DECLSPEC void mpz_sqrtrem __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr)); - -#define mpz_sub __gmpz_sub -__GMP_DECLSPEC void mpz_sub __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_sub_ui __gmpz_sub_ui -__GMP_DECLSPEC void mpz_sub_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_ui_sub __gmpz_ui_sub -__GMP_DECLSPEC void mpz_ui_sub __GMP_PROTO ((mpz_ptr, unsigned long int, mpz_srcptr)); - -#define mpz_submul __gmpz_submul -__GMP_DECLSPEC void mpz_submul __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_submul_ui __gmpz_submul_ui -__GMP_DECLSPEC void mpz_submul_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_swap __gmpz_swap -__GMP_DECLSPEC void mpz_swap __GMP_PROTO ((mpz_ptr, mpz_ptr)) __GMP_NOTHROW; - -#define mpz_tdiv_ui __gmpz_tdiv_ui -__GMP_DECLSPEC unsigned long int mpz_tdiv_ui __GMP_PROTO ((mpz_srcptr, unsigned long int)) __GMP_ATTRIBUTE_PURE; - -#define mpz_tdiv_q __gmpz_tdiv_q -__GMP_DECLSPEC void mpz_tdiv_q __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_tdiv_q_2exp __gmpz_tdiv_q_2exp -__GMP_DECLSPEC void mpz_tdiv_q_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, mp_bitcnt_t)); - -#define mpz_tdiv_q_ui __gmpz_tdiv_q_ui -__GMP_DECLSPEC unsigned long int mpz_tdiv_q_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_tdiv_qr __gmpz_tdiv_qr -__GMP_DECLSPEC void mpz_tdiv_qr __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_tdiv_qr_ui __gmpz_tdiv_qr_ui -__GMP_DECLSPEC unsigned long int mpz_tdiv_qr_ui __GMP_PROTO ((mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_tdiv_r __gmpz_tdiv_r -__GMP_DECLSPEC void mpz_tdiv_r __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - -#define mpz_tdiv_r_2exp __gmpz_tdiv_r_2exp -__GMP_DECLSPEC void mpz_tdiv_r_2exp __GMP_PROTO ((mpz_ptr, mpz_srcptr, mp_bitcnt_t)); - -#define mpz_tdiv_r_ui __gmpz_tdiv_r_ui -__GMP_DECLSPEC unsigned long int mpz_tdiv_r_ui __GMP_PROTO ((mpz_ptr, mpz_srcptr, unsigned long int)); - -#define mpz_tstbit __gmpz_tstbit -__GMP_DECLSPEC int mpz_tstbit __GMP_PROTO ((mpz_srcptr, mp_bitcnt_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpz_ui_pow_ui __gmpz_ui_pow_ui -__GMP_DECLSPEC void mpz_ui_pow_ui __GMP_PROTO ((mpz_ptr, unsigned long int, unsigned long int)); - -#define mpz_urandomb __gmpz_urandomb -__GMP_DECLSPEC void mpz_urandomb __GMP_PROTO ((mpz_ptr, gmp_randstate_t, mp_bitcnt_t)); - -#define mpz_urandomm __gmpz_urandomm -__GMP_DECLSPEC void mpz_urandomm __GMP_PROTO ((mpz_ptr, gmp_randstate_t, mpz_srcptr)); - -#define mpz_xor __gmpz_xor -#define mpz_eor __gmpz_xor -__GMP_DECLSPEC void mpz_xor __GMP_PROTO ((mpz_ptr, mpz_srcptr, mpz_srcptr)); - - -/**************** Rational (i.e. Q) routines. ****************/ - -#define mpq_abs __gmpq_abs -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpq_abs) -__GMP_DECLSPEC void mpq_abs __GMP_PROTO ((mpq_ptr, mpq_srcptr)); -#endif - -#define mpq_add __gmpq_add -__GMP_DECLSPEC void mpq_add __GMP_PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr)); - -#define mpq_canonicalize __gmpq_canonicalize -__GMP_DECLSPEC void mpq_canonicalize __GMP_PROTO ((mpq_ptr)); - -#define mpq_clear __gmpq_clear -__GMP_DECLSPEC void mpq_clear __GMP_PROTO ((mpq_ptr)); - -#define mpq_clears __gmpq_clears -__GMP_DECLSPEC void mpq_clears __GMP_PROTO ((mpq_ptr, ...)); - -#define mpq_cmp __gmpq_cmp -__GMP_DECLSPEC int mpq_cmp __GMP_PROTO ((mpq_srcptr, mpq_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define _mpq_cmp_si __gmpq_cmp_si -__GMP_DECLSPEC int _mpq_cmp_si __GMP_PROTO ((mpq_srcptr, long, unsigned long)) __GMP_ATTRIBUTE_PURE; - -#define _mpq_cmp_ui __gmpq_cmp_ui -__GMP_DECLSPEC int _mpq_cmp_ui __GMP_PROTO ((mpq_srcptr, unsigned long int, unsigned long int)) __GMP_ATTRIBUTE_PURE; - -#define mpq_div __gmpq_div -__GMP_DECLSPEC void mpq_div __GMP_PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr)); - -#define mpq_div_2exp __gmpq_div_2exp -__GMP_DECLSPEC void mpq_div_2exp __GMP_PROTO ((mpq_ptr, mpq_srcptr, mp_bitcnt_t)); - -#define mpq_equal __gmpq_equal -__GMP_DECLSPEC int mpq_equal __GMP_PROTO ((mpq_srcptr, mpq_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpq_get_num __gmpq_get_num -__GMP_DECLSPEC void mpq_get_num __GMP_PROTO ((mpz_ptr, mpq_srcptr)); - -#define mpq_get_den __gmpq_get_den -__GMP_DECLSPEC void mpq_get_den __GMP_PROTO ((mpz_ptr, mpq_srcptr)); - -#define mpq_get_d __gmpq_get_d -__GMP_DECLSPEC double mpq_get_d __GMP_PROTO ((mpq_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpq_get_str __gmpq_get_str -__GMP_DECLSPEC char *mpq_get_str __GMP_PROTO ((char *, int, mpq_srcptr)); - -#define mpq_init __gmpq_init -__GMP_DECLSPEC void mpq_init __GMP_PROTO ((mpq_ptr)); - -#define mpq_inits __gmpq_inits -__GMP_DECLSPEC void mpq_inits __GMP_PROTO ((mpq_ptr, ...)); - -#define mpq_inp_str __gmpq_inp_str -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpq_inp_str __GMP_PROTO ((mpq_ptr, FILE *, int)); -#endif - -#define mpq_inv __gmpq_inv -__GMP_DECLSPEC void mpq_inv __GMP_PROTO ((mpq_ptr, mpq_srcptr)); - -#define mpq_mul __gmpq_mul -__GMP_DECLSPEC void mpq_mul __GMP_PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr)); - -#define mpq_mul_2exp __gmpq_mul_2exp -__GMP_DECLSPEC void mpq_mul_2exp __GMP_PROTO ((mpq_ptr, mpq_srcptr, mp_bitcnt_t)); - -#define mpq_neg __gmpq_neg -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpq_neg) -__GMP_DECLSPEC void mpq_neg __GMP_PROTO ((mpq_ptr, mpq_srcptr)); -#endif - -#define mpq_out_str __gmpq_out_str -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpq_out_str __GMP_PROTO ((FILE *, int, mpq_srcptr)); -#endif - -#define mpq_set __gmpq_set -__GMP_DECLSPEC void mpq_set __GMP_PROTO ((mpq_ptr, mpq_srcptr)); - -#define mpq_set_d __gmpq_set_d -__GMP_DECLSPEC void mpq_set_d __GMP_PROTO ((mpq_ptr, double)); - -#define mpq_set_den __gmpq_set_den -__GMP_DECLSPEC void mpq_set_den __GMP_PROTO ((mpq_ptr, mpz_srcptr)); - -#define mpq_set_f __gmpq_set_f -__GMP_DECLSPEC void mpq_set_f __GMP_PROTO ((mpq_ptr, mpf_srcptr)); - -#define mpq_set_num __gmpq_set_num -__GMP_DECLSPEC void mpq_set_num __GMP_PROTO ((mpq_ptr, mpz_srcptr)); - -#define mpq_set_si __gmpq_set_si -__GMP_DECLSPEC void mpq_set_si __GMP_PROTO ((mpq_ptr, signed long int, unsigned long int)); - -#define mpq_set_str __gmpq_set_str -__GMP_DECLSPEC int mpq_set_str __GMP_PROTO ((mpq_ptr, __gmp_const char *, int)); - -#define mpq_set_ui __gmpq_set_ui -__GMP_DECLSPEC void mpq_set_ui __GMP_PROTO ((mpq_ptr, unsigned long int, unsigned long int)); - -#define mpq_set_z __gmpq_set_z -__GMP_DECLSPEC void mpq_set_z __GMP_PROTO ((mpq_ptr, mpz_srcptr)); - -#define mpq_sub __gmpq_sub -__GMP_DECLSPEC void mpq_sub __GMP_PROTO ((mpq_ptr, mpq_srcptr, mpq_srcptr)); - -#define mpq_swap __gmpq_swap -__GMP_DECLSPEC void mpq_swap __GMP_PROTO ((mpq_ptr, mpq_ptr)) __GMP_NOTHROW; - - -/**************** Float (i.e. F) routines. ****************/ - -#define mpf_abs __gmpf_abs -__GMP_DECLSPEC void mpf_abs __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_add __gmpf_add -__GMP_DECLSPEC void mpf_add __GMP_PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr)); - -#define mpf_add_ui __gmpf_add_ui -__GMP_DECLSPEC void mpf_add_ui __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int)); -#define mpf_ceil __gmpf_ceil -__GMP_DECLSPEC void mpf_ceil __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_clear __gmpf_clear -__GMP_DECLSPEC void mpf_clear __GMP_PROTO ((mpf_ptr)); - -#define mpf_clears __gmpf_clears -__GMP_DECLSPEC void mpf_clears __GMP_PROTO ((mpf_ptr, ...)); - -#define mpf_cmp __gmpf_cmp -__GMP_DECLSPEC int mpf_cmp __GMP_PROTO ((mpf_srcptr, mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_cmp_d __gmpf_cmp_d -__GMP_DECLSPEC int mpf_cmp_d __GMP_PROTO ((mpf_srcptr, double)) __GMP_ATTRIBUTE_PURE; - -#define mpf_cmp_si __gmpf_cmp_si -__GMP_DECLSPEC int mpf_cmp_si __GMP_PROTO ((mpf_srcptr, signed long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_cmp_ui __gmpf_cmp_ui -__GMP_DECLSPEC int mpf_cmp_ui __GMP_PROTO ((mpf_srcptr, unsigned long int)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_div __gmpf_div -__GMP_DECLSPEC void mpf_div __GMP_PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr)); - -#define mpf_div_2exp __gmpf_div_2exp -__GMP_DECLSPEC void mpf_div_2exp __GMP_PROTO ((mpf_ptr, mpf_srcptr, mp_bitcnt_t)); - -#define mpf_div_ui __gmpf_div_ui -__GMP_DECLSPEC void mpf_div_ui __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int)); - -#define mpf_dump __gmpf_dump -__GMP_DECLSPEC void mpf_dump __GMP_PROTO ((mpf_srcptr)); - -#define mpf_eq __gmpf_eq -__GMP_DECLSPEC int mpf_eq __GMP_PROTO ((mpf_srcptr, mpf_srcptr, unsigned long int)) __GMP_ATTRIBUTE_PURE; - -#define mpf_fits_sint_p __gmpf_fits_sint_p -__GMP_DECLSPEC int mpf_fits_sint_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_fits_slong_p __gmpf_fits_slong_p -__GMP_DECLSPEC int mpf_fits_slong_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_fits_sshort_p __gmpf_fits_sshort_p -__GMP_DECLSPEC int mpf_fits_sshort_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_fits_uint_p __gmpf_fits_uint_p -__GMP_DECLSPEC int mpf_fits_uint_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_fits_ulong_p __gmpf_fits_ulong_p -__GMP_DECLSPEC int mpf_fits_ulong_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_fits_ushort_p __gmpf_fits_ushort_p -__GMP_DECLSPEC int mpf_fits_ushort_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_floor __gmpf_floor -__GMP_DECLSPEC void mpf_floor __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_get_d __gmpf_get_d -__GMP_DECLSPEC double mpf_get_d __GMP_PROTO ((mpf_srcptr)) __GMP_ATTRIBUTE_PURE; - -#define mpf_get_d_2exp __gmpf_get_d_2exp -__GMP_DECLSPEC double mpf_get_d_2exp __GMP_PROTO ((signed long int *, mpf_srcptr)); - -#define mpf_get_default_prec __gmpf_get_default_prec -__GMP_DECLSPEC mp_bitcnt_t mpf_get_default_prec __GMP_PROTO ((void)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_get_prec __gmpf_get_prec -__GMP_DECLSPEC mp_bitcnt_t mpf_get_prec __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_get_si __gmpf_get_si -__GMP_DECLSPEC long mpf_get_si __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_get_str __gmpf_get_str -__GMP_DECLSPEC char *mpf_get_str __GMP_PROTO ((char *, mp_exp_t *, int, size_t, mpf_srcptr)); - -#define mpf_get_ui __gmpf_get_ui -__GMP_DECLSPEC unsigned long mpf_get_ui __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_init __gmpf_init -__GMP_DECLSPEC void mpf_init __GMP_PROTO ((mpf_ptr)); - -#define mpf_init2 __gmpf_init2 -__GMP_DECLSPEC void mpf_init2 __GMP_PROTO ((mpf_ptr, mp_bitcnt_t)); - -#define mpf_inits __gmpf_inits -__GMP_DECLSPEC void mpf_inits __GMP_PROTO ((mpf_ptr, ...)); - -#define mpf_init_set __gmpf_init_set -__GMP_DECLSPEC void mpf_init_set __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_init_set_d __gmpf_init_set_d -__GMP_DECLSPEC void mpf_init_set_d __GMP_PROTO ((mpf_ptr, double)); - -#define mpf_init_set_si __gmpf_init_set_si -__GMP_DECLSPEC void mpf_init_set_si __GMP_PROTO ((mpf_ptr, signed long int)); - -#define mpf_init_set_str __gmpf_init_set_str -__GMP_DECLSPEC int mpf_init_set_str __GMP_PROTO ((mpf_ptr, __gmp_const char *, int)); - -#define mpf_init_set_ui __gmpf_init_set_ui -__GMP_DECLSPEC void mpf_init_set_ui __GMP_PROTO ((mpf_ptr, unsigned long int)); - -#define mpf_inp_str __gmpf_inp_str -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpf_inp_str __GMP_PROTO ((mpf_ptr, FILE *, int)); -#endif - -#define mpf_integer_p __gmpf_integer_p -__GMP_DECLSPEC int mpf_integer_p __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_mul __gmpf_mul -__GMP_DECLSPEC void mpf_mul __GMP_PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr)); - -#define mpf_mul_2exp __gmpf_mul_2exp -__GMP_DECLSPEC void mpf_mul_2exp __GMP_PROTO ((mpf_ptr, mpf_srcptr, mp_bitcnt_t)); - -#define mpf_mul_ui __gmpf_mul_ui -__GMP_DECLSPEC void mpf_mul_ui __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int)); - -#define mpf_neg __gmpf_neg -__GMP_DECLSPEC void mpf_neg __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_out_str __gmpf_out_str -#ifdef _GMP_H_HAVE_FILE -__GMP_DECLSPEC size_t mpf_out_str __GMP_PROTO ((FILE *, int, size_t, mpf_srcptr)); -#endif - -#define mpf_pow_ui __gmpf_pow_ui -__GMP_DECLSPEC void mpf_pow_ui __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int)); - -#define mpf_random2 __gmpf_random2 -__GMP_DECLSPEC void mpf_random2 __GMP_PROTO ((mpf_ptr, mp_size_t, mp_exp_t)); - -#define mpf_reldiff __gmpf_reldiff -__GMP_DECLSPEC void mpf_reldiff __GMP_PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr)); - -#define mpf_set __gmpf_set -__GMP_DECLSPEC void mpf_set __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_set_d __gmpf_set_d -__GMP_DECLSPEC void mpf_set_d __GMP_PROTO ((mpf_ptr, double)); - -#define mpf_set_default_prec __gmpf_set_default_prec -__GMP_DECLSPEC void mpf_set_default_prec __GMP_PROTO ((mp_bitcnt_t)) __GMP_NOTHROW; - -#define mpf_set_prec __gmpf_set_prec -__GMP_DECLSPEC void mpf_set_prec __GMP_PROTO ((mpf_ptr, mp_bitcnt_t)); - -#define mpf_set_prec_raw __gmpf_set_prec_raw -__GMP_DECLSPEC void mpf_set_prec_raw __GMP_PROTO ((mpf_ptr, mp_bitcnt_t)) __GMP_NOTHROW; - -#define mpf_set_q __gmpf_set_q -__GMP_DECLSPEC void mpf_set_q __GMP_PROTO ((mpf_ptr, mpq_srcptr)); - -#define mpf_set_si __gmpf_set_si -__GMP_DECLSPEC void mpf_set_si __GMP_PROTO ((mpf_ptr, signed long int)); - -#define mpf_set_str __gmpf_set_str -__GMP_DECLSPEC int mpf_set_str __GMP_PROTO ((mpf_ptr, __gmp_const char *, int)); - -#define mpf_set_ui __gmpf_set_ui -__GMP_DECLSPEC void mpf_set_ui __GMP_PROTO ((mpf_ptr, unsigned long int)); - -#define mpf_set_z __gmpf_set_z -__GMP_DECLSPEC void mpf_set_z __GMP_PROTO ((mpf_ptr, mpz_srcptr)); - -#define mpf_size __gmpf_size -__GMP_DECLSPEC size_t mpf_size __GMP_PROTO ((mpf_srcptr)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpf_sqrt __gmpf_sqrt -__GMP_DECLSPEC void mpf_sqrt __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_sqrt_ui __gmpf_sqrt_ui -__GMP_DECLSPEC void mpf_sqrt_ui __GMP_PROTO ((mpf_ptr, unsigned long int)); - -#define mpf_sub __gmpf_sub -__GMP_DECLSPEC void mpf_sub __GMP_PROTO ((mpf_ptr, mpf_srcptr, mpf_srcptr)); - -#define mpf_sub_ui __gmpf_sub_ui -__GMP_DECLSPEC void mpf_sub_ui __GMP_PROTO ((mpf_ptr, mpf_srcptr, unsigned long int)); - -#define mpf_swap __gmpf_swap -__GMP_DECLSPEC void mpf_swap __GMP_PROTO ((mpf_ptr, mpf_ptr)) __GMP_NOTHROW; - -#define mpf_trunc __gmpf_trunc -__GMP_DECLSPEC void mpf_trunc __GMP_PROTO ((mpf_ptr, mpf_srcptr)); - -#define mpf_ui_div __gmpf_ui_div -__GMP_DECLSPEC void mpf_ui_div __GMP_PROTO ((mpf_ptr, unsigned long int, mpf_srcptr)); - -#define mpf_ui_sub __gmpf_ui_sub -__GMP_DECLSPEC void mpf_ui_sub __GMP_PROTO ((mpf_ptr, unsigned long int, mpf_srcptr)); - -#define mpf_urandomb __gmpf_urandomb -__GMP_DECLSPEC void mpf_urandomb __GMP_PROTO ((mpf_t, gmp_randstate_t, mp_bitcnt_t)); - - -/************ Low level positive-integer (i.e. N) routines. ************/ - -/* This is ugly, but we need to make user calls reach the prefixed function. */ - -#define mpn_add __MPN(add) -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_add) -__GMP_DECLSPEC mp_limb_t mpn_add __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr,mp_size_t)); -#endif - -#define mpn_add_1 __MPN(add_1) -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_add_1) -__GMP_DECLSPEC mp_limb_t mpn_add_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t)) __GMP_NOTHROW; -#endif - -#define mpn_add_n __MPN(add_n) -__GMP_DECLSPEC mp_limb_t mpn_add_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); - -#define mpn_addmul_1 __MPN(addmul_1) -__GMP_DECLSPEC mp_limb_t mpn_addmul_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t)); - -#define mpn_cmp __MPN(cmp) -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_cmp) -__GMP_DECLSPEC int mpn_cmp __GMP_PROTO ((mp_srcptr, mp_srcptr, mp_size_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; -#endif - -#define mpn_divexact_by3(dst,src,size) \ - mpn_divexact_by3c (dst, src, size, __GMP_CAST (mp_limb_t, 0)) - -#define mpn_divexact_by3c __MPN(divexact_by3c) -__GMP_DECLSPEC mp_limb_t mpn_divexact_by3c __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t)); - -#define mpn_divmod_1(qp,np,nsize,dlimb) \ - mpn_divrem_1 (qp, __GMP_CAST (mp_size_t, 0), np, nsize, dlimb) - -#define mpn_divrem __MPN(divrem) -__GMP_DECLSPEC mp_limb_t mpn_divrem __GMP_PROTO ((mp_ptr, mp_size_t, mp_ptr, mp_size_t, mp_srcptr, mp_size_t)); - -#define mpn_divrem_1 __MPN(divrem_1) -__GMP_DECLSPEC mp_limb_t mpn_divrem_1 __GMP_PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t)); - -#define mpn_divrem_2 __MPN(divrem_2) -__GMP_DECLSPEC mp_limb_t mpn_divrem_2 __GMP_PROTO ((mp_ptr, mp_size_t, mp_ptr, mp_size_t, mp_srcptr)); - -#define mpn_gcd __MPN(gcd) -__GMP_DECLSPEC mp_size_t mpn_gcd __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_ptr, mp_size_t)); - -#define mpn_gcd_1 __MPN(gcd_1) -__GMP_DECLSPEC mp_limb_t mpn_gcd_1 __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE; - -#define mpn_gcdext_1 __MPN(gcdext_1) -__GMP_DECLSPEC mp_limb_t mpn_gcdext_1 __GMP_PROTO ((mp_limb_signed_t *, mp_limb_signed_t *, mp_limb_t, mp_limb_t)); - -#define mpn_gcdext __MPN(gcdext) -__GMP_DECLSPEC mp_size_t mpn_gcdext __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t *, mp_ptr, mp_size_t, mp_ptr, mp_size_t)); - -#define mpn_get_str __MPN(get_str) -__GMP_DECLSPEC size_t mpn_get_str __GMP_PROTO ((unsigned char *, int, mp_ptr, mp_size_t)); - -#define mpn_hamdist __MPN(hamdist) -__GMP_DECLSPEC mp_bitcnt_t mpn_hamdist __GMP_PROTO ((mp_srcptr, mp_srcptr, mp_size_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpn_lshift __MPN(lshift) -__GMP_DECLSPEC mp_limb_t mpn_lshift __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, unsigned int)); - -#define mpn_mod_1 __MPN(mod_1) -__GMP_DECLSPEC mp_limb_t mpn_mod_1 __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE; - -#define mpn_mul __MPN(mul) -__GMP_DECLSPEC mp_limb_t mpn_mul __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t)); - -#define mpn_mul_1 __MPN(mul_1) -__GMP_DECLSPEC mp_limb_t mpn_mul_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t)); - -#define mpn_mul_n __MPN(mul_n) -__GMP_DECLSPEC void mpn_mul_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); - -#define mpn_sqr __MPN(sqr) -__GMP_DECLSPEC void mpn_sqr __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t)); - -#define mpn_neg __MPN(neg) -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_neg) -__GMP_DECLSPEC mp_limb_t mpn_neg __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t)); -#endif - -#define mpn_com __MPN(com) -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_com) -__GMP_DECLSPEC void mpn_com __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t)); -#endif - -#define mpn_perfect_square_p __MPN(perfect_square_p) -__GMP_DECLSPEC int mpn_perfect_square_p __GMP_PROTO ((mp_srcptr, mp_size_t)) __GMP_ATTRIBUTE_PURE; - -#define mpn_perfect_power_p __MPN(perfect_power_p) -__GMP_DECLSPEC int mpn_perfect_power_p __GMP_PROTO ((mp_srcptr, mp_size_t)) __GMP_ATTRIBUTE_PURE; - -#define mpn_popcount __MPN(popcount) -__GMP_DECLSPEC mp_bitcnt_t mpn_popcount __GMP_PROTO ((mp_srcptr, mp_size_t)) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE; - -#define mpn_pow_1 __MPN(pow_1) -__GMP_DECLSPEC mp_size_t mpn_pow_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_ptr)); - -/* undocumented now, but retained here for upward compatibility */ -#define mpn_preinv_mod_1 __MPN(preinv_mod_1) -__GMP_DECLSPEC mp_limb_t mpn_preinv_mod_1 __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE; - -#define mpn_random __MPN(random) -__GMP_DECLSPEC void mpn_random __GMP_PROTO ((mp_ptr, mp_size_t)); - -#define mpn_random2 __MPN(random2) -__GMP_DECLSPEC void mpn_random2 __GMP_PROTO ((mp_ptr, mp_size_t)); - -#define mpn_rshift __MPN(rshift) -__GMP_DECLSPEC mp_limb_t mpn_rshift __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, unsigned int)); - -#define mpn_scan0 __MPN(scan0) -__GMP_DECLSPEC mp_bitcnt_t mpn_scan0 __GMP_PROTO ((mp_srcptr, mp_bitcnt_t)) __GMP_ATTRIBUTE_PURE; - -#define mpn_scan1 __MPN(scan1) -__GMP_DECLSPEC mp_bitcnt_t mpn_scan1 __GMP_PROTO ((mp_srcptr, mp_bitcnt_t)) __GMP_ATTRIBUTE_PURE; - -#define mpn_set_str __MPN(set_str) -__GMP_DECLSPEC mp_size_t mpn_set_str __GMP_PROTO ((mp_ptr, __gmp_const unsigned char *, size_t, int)); - -#define mpn_sqrtrem __MPN(sqrtrem) -__GMP_DECLSPEC mp_size_t mpn_sqrtrem __GMP_PROTO ((mp_ptr, mp_ptr, mp_srcptr, mp_size_t)); - -#define mpn_sub __MPN(sub) -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_sub) -__GMP_DECLSPEC mp_limb_t mpn_sub __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_srcptr,mp_size_t)); -#endif - -#define mpn_sub_1 __MPN(sub_1) -#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_sub_1) -__GMP_DECLSPEC mp_limb_t mpn_sub_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t)) __GMP_NOTHROW; -#endif - -#define mpn_sub_n __MPN(sub_n) -__GMP_DECLSPEC mp_limb_t mpn_sub_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); - -#define mpn_submul_1 __MPN(submul_1) -__GMP_DECLSPEC mp_limb_t mpn_submul_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t)); - -#define mpn_tdiv_qr __MPN(tdiv_qr) -__GMP_DECLSPEC void mpn_tdiv_qr __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t)); - -#define mpn_and_n __MPN(and_n) -__GMP_DECLSPEC void mpn_and_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); -#define mpn_andn_n __MPN(andn_n) -__GMP_DECLSPEC void mpn_andn_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); -#define mpn_nand_n __MPN(nand_n) -__GMP_DECLSPEC void mpn_nand_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); -#define mpn_ior_n __MPN(ior_n) -__GMP_DECLSPEC void mpn_ior_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); -#define mpn_iorn_n __MPN(iorn_n) -__GMP_DECLSPEC void mpn_iorn_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); -#define mpn_nior_n __MPN(nior_n) -__GMP_DECLSPEC void mpn_nior_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); -#define mpn_xor_n __MPN(xor_n) -__GMP_DECLSPEC void mpn_xor_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); -#define mpn_xnor_n __MPN(xnor_n) -__GMP_DECLSPEC void mpn_xnor_n __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t)); - -#define mpn_copyi __MPN(copyi) -__GMP_DECLSPEC void mpn_copyi __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t)); -#define mpn_copyd __MPN(copyd) -__GMP_DECLSPEC void mpn_copyd __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t)); -#define mpn_zero __MPN(zero) -__GMP_DECLSPEC void mpn_zero __GMP_PROTO ((mp_ptr, mp_size_t)); - -/**************** mpz inlines ****************/ - -/* The following are provided as inlines where possible, but always exist as - library functions too, for binary compatibility. - - Within gmp itself this inlining generally isn't relied on, since it - doesn't get done for all compilers, whereas if something is worth - inlining then it's worth arranging always. - - There are two styles of inlining here. When the same bit of code is - wanted for the inline as for the library version, then __GMP_FORCE_foo - arranges for that code to be emitted and the __GMP_EXTERN_INLINE - directive suppressed, eg. mpz_fits_uint_p. When a different bit of code - is wanted for the inline than for the library version, then - __GMP_FORCE_foo arranges the inline to be suppressed, eg. mpz_abs. */ - -#if defined (__GMP_EXTERN_INLINE) && ! defined (__GMP_FORCE_mpz_abs) -__GMP_EXTERN_INLINE void -mpz_abs (mpz_ptr __gmp_w, mpz_srcptr __gmp_u) -{ - if (__gmp_w != __gmp_u) - mpz_set (__gmp_w, __gmp_u); - __gmp_w->_mp_size = __GMP_ABS (__gmp_w->_mp_size); -} -#endif - -#if GMP_NAIL_BITS == 0 -#define __GMPZ_FITS_UTYPE_P(z,maxval) \ - mp_size_t __gmp_n = z->_mp_size; \ - mp_ptr __gmp_p = z->_mp_d; \ - return (__gmp_n == 0 || (__gmp_n == 1 && __gmp_p[0] <= maxval)); -#else -#define __GMPZ_FITS_UTYPE_P(z,maxval) \ - mp_size_t __gmp_n = z->_mp_size; \ - mp_ptr __gmp_p = z->_mp_d; \ - return (__gmp_n == 0 || (__gmp_n == 1 && __gmp_p[0] <= maxval) \ - || (__gmp_n == 2 && __gmp_p[1] <= ((mp_limb_t) maxval >> GMP_NUMB_BITS))); -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_fits_uint_p) -#if ! defined (__GMP_FORCE_mpz_fits_uint_p) -__GMP_EXTERN_INLINE -#endif -int -mpz_fits_uint_p (mpz_srcptr __gmp_z) __GMP_NOTHROW -{ - __GMPZ_FITS_UTYPE_P (__gmp_z, __GMP_UINT_MAX); -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_fits_ulong_p) -#if ! defined (__GMP_FORCE_mpz_fits_ulong_p) -__GMP_EXTERN_INLINE -#endif -int -mpz_fits_ulong_p (mpz_srcptr __gmp_z) __GMP_NOTHROW -{ - __GMPZ_FITS_UTYPE_P (__gmp_z, __GMP_ULONG_MAX); -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_fits_ushort_p) -#if ! defined (__GMP_FORCE_mpz_fits_ushort_p) -__GMP_EXTERN_INLINE -#endif -int -mpz_fits_ushort_p (mpz_srcptr __gmp_z) __GMP_NOTHROW -{ - __GMPZ_FITS_UTYPE_P (__gmp_z, __GMP_USHRT_MAX); -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_get_ui) -#if ! defined (__GMP_FORCE_mpz_get_ui) -__GMP_EXTERN_INLINE -#endif -unsigned long -mpz_get_ui (mpz_srcptr __gmp_z) __GMP_NOTHROW -{ - mp_ptr __gmp_p = __gmp_z->_mp_d; - mp_size_t __gmp_n = __gmp_z->_mp_size; - mp_limb_t __gmp_l = __gmp_p[0]; - /* This is a "#if" rather than a plain "if" so as to avoid gcc warnings - about "<< GMP_NUMB_BITS" exceeding the type size, and to avoid Borland - C++ 6.0 warnings about condition always true for something like - "__GMP_ULONG_MAX < GMP_NUMB_MASK". */ -#if GMP_NAIL_BITS == 0 || defined (_LONG_LONG_LIMB) - /* limb==long and no nails, or limb==longlong, one limb is enough */ - return (__gmp_n != 0 ? __gmp_l : 0); -#else - /* limb==long and nails, need two limbs when available */ - __gmp_n = __GMP_ABS (__gmp_n); - if (__gmp_n <= 1) - return (__gmp_n != 0 ? __gmp_l : 0); - else - return __gmp_l + (__gmp_p[1] << GMP_NUMB_BITS); -#endif -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_getlimbn) -#if ! defined (__GMP_FORCE_mpz_getlimbn) -__GMP_EXTERN_INLINE -#endif -mp_limb_t -mpz_getlimbn (mpz_srcptr __gmp_z, mp_size_t __gmp_n) __GMP_NOTHROW -{ - mp_limb_t __gmp_result = 0; - if (__GMP_LIKELY (__gmp_n >= 0 && __gmp_n < __GMP_ABS (__gmp_z->_mp_size))) - __gmp_result = __gmp_z->_mp_d[__gmp_n]; - return __gmp_result; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) && ! defined (__GMP_FORCE_mpz_neg) -__GMP_EXTERN_INLINE void -mpz_neg (mpz_ptr __gmp_w, mpz_srcptr __gmp_u) -{ - if (__gmp_w != __gmp_u) - mpz_set (__gmp_w, __gmp_u); - __gmp_w->_mp_size = - __gmp_w->_mp_size; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_perfect_square_p) -#if ! defined (__GMP_FORCE_mpz_perfect_square_p) -__GMP_EXTERN_INLINE -#endif -int -mpz_perfect_square_p (mpz_srcptr __gmp_a) -{ - mp_size_t __gmp_asize; - int __gmp_result; - - __gmp_asize = __gmp_a->_mp_size; - __gmp_result = (__gmp_asize >= 0); /* zero is a square, negatives are not */ - if (__GMP_LIKELY (__gmp_asize > 0)) - __gmp_result = mpn_perfect_square_p (__gmp_a->_mp_d, __gmp_asize); - return __gmp_result; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_popcount) -#if ! defined (__GMP_FORCE_mpz_popcount) -__GMP_EXTERN_INLINE -#endif -mp_bitcnt_t -mpz_popcount (mpz_srcptr __gmp_u) __GMP_NOTHROW -{ - mp_size_t __gmp_usize; - mp_bitcnt_t __gmp_result; - - __gmp_usize = __gmp_u->_mp_size; - __gmp_result = (__gmp_usize < 0 ? __GMP_ULONG_MAX : 0); - if (__GMP_LIKELY (__gmp_usize > 0)) - __gmp_result = mpn_popcount (__gmp_u->_mp_d, __gmp_usize); - return __gmp_result; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_set_q) -#if ! defined (__GMP_FORCE_mpz_set_q) -__GMP_EXTERN_INLINE -#endif -void -mpz_set_q (mpz_ptr __gmp_w, mpq_srcptr __gmp_u) -{ - mpz_tdiv_q (__gmp_w, mpq_numref (__gmp_u), mpq_denref (__gmp_u)); -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpz_size) -#if ! defined (__GMP_FORCE_mpz_size) -__GMP_EXTERN_INLINE -#endif -size_t -mpz_size (mpz_srcptr __gmp_z) __GMP_NOTHROW -{ - return __GMP_ABS (__gmp_z->_mp_size); -} -#endif - - -/**************** mpq inlines ****************/ - -#if defined (__GMP_EXTERN_INLINE) && ! defined (__GMP_FORCE_mpq_abs) -__GMP_EXTERN_INLINE void -mpq_abs (mpq_ptr __gmp_w, mpq_srcptr __gmp_u) -{ - if (__gmp_w != __gmp_u) - mpq_set (__gmp_w, __gmp_u); - __gmp_w->_mp_num._mp_size = __GMP_ABS (__gmp_w->_mp_num._mp_size); -} -#endif - -#if defined (__GMP_EXTERN_INLINE) && ! defined (__GMP_FORCE_mpq_neg) -__GMP_EXTERN_INLINE void -mpq_neg (mpq_ptr __gmp_w, mpq_srcptr __gmp_u) -{ - if (__gmp_w != __gmp_u) - mpq_set (__gmp_w, __gmp_u); - __gmp_w->_mp_num._mp_size = - __gmp_w->_mp_num._mp_size; -} -#endif - - -/**************** mpn inlines ****************/ - -/* The comments with __GMPN_ADD_1 below apply here too. - - The test for FUNCTION returning 0 should predict well. If it's assumed - {yp,ysize} will usually have a random number of bits then the high limb - won't be full and a carry out will occur a good deal less than 50% of the - time. - - ysize==0 isn't a documented feature, but is used internally in a few - places. - - Producing cout last stops it using up a register during the main part of - the calculation, though gcc (as of 3.0) on an "if (mpn_add (...))" - doesn't seem able to move the true and false legs of the conditional up - to the two places cout is generated. */ - -#define __GMPN_AORS(cout, wp, xp, xsize, yp, ysize, FUNCTION, TEST) \ - do { \ - mp_size_t __gmp_i; \ - mp_limb_t __gmp_x; \ - \ - /* ASSERT ((ysize) >= 0); */ \ - /* ASSERT ((xsize) >= (ysize)); */ \ - /* ASSERT (MPN_SAME_OR_SEPARATE2_P (wp, xsize, xp, xsize)); */ \ - /* ASSERT (MPN_SAME_OR_SEPARATE2_P (wp, xsize, yp, ysize)); */ \ - \ - __gmp_i = (ysize); \ - if (__gmp_i != 0) \ - { \ - if (FUNCTION (wp, xp, yp, __gmp_i)) \ - { \ - do \ - { \ - if (__gmp_i >= (xsize)) \ - { \ - (cout) = 1; \ - goto __gmp_done; \ - } \ - __gmp_x = (xp)[__gmp_i]; \ - } \ - while (TEST); \ - } \ - } \ - if ((wp) != (xp)) \ - __GMPN_COPY_REST (wp, xp, xsize, __gmp_i); \ - (cout) = 0; \ - __gmp_done: \ - ; \ - } while (0) - -#define __GMPN_ADD(cout, wp, xp, xsize, yp, ysize) \ - __GMPN_AORS (cout, wp, xp, xsize, yp, ysize, mpn_add_n, \ - (((wp)[__gmp_i++] = (__gmp_x + 1) & GMP_NUMB_MASK) == 0)) -#define __GMPN_SUB(cout, wp, xp, xsize, yp, ysize) \ - __GMPN_AORS (cout, wp, xp, xsize, yp, ysize, mpn_sub_n, \ - (((wp)[__gmp_i++] = (__gmp_x - 1) & GMP_NUMB_MASK), __gmp_x == 0)) - - -/* The use of __gmp_i indexing is designed to ensure a compile time src==dst - remains nice and clear to the compiler, so that __GMPN_COPY_REST can - disappear, and the load/add/store gets a chance to become a - read-modify-write on CISC CPUs. - - Alternatives: - - Using a pair of pointers instead of indexing would be possible, but gcc - isn't able to recognise compile-time src==dst in that case, even when the - pointers are incremented more or less together. Other compilers would - very likely have similar difficulty. - - gcc could use "if (__builtin_constant_p(src==dst) && src==dst)" or - similar to detect a compile-time src==dst. This works nicely on gcc - 2.95.x, it's not good on gcc 3.0 where __builtin_constant_p(p==p) seems - to be always false, for a pointer p. But the current code form seems - good enough for src==dst anyway. - - gcc on x86 as usual doesn't give particularly good flags handling for the - carry/borrow detection. It's tempting to want some multi instruction asm - blocks to help it, and this was tried, but in truth there's only a few - instructions to save and any gain is all too easily lost by register - juggling setting up for the asm. */ - -#if GMP_NAIL_BITS == 0 -#define __GMPN_AORS_1(cout, dst, src, n, v, OP, CB) \ - do { \ - mp_size_t __gmp_i; \ - mp_limb_t __gmp_x, __gmp_r; \ - \ - /* ASSERT ((n) >= 1); */ \ - /* ASSERT (MPN_SAME_OR_SEPARATE_P (dst, src, n)); */ \ - \ - __gmp_x = (src)[0]; \ - __gmp_r = __gmp_x OP (v); \ - (dst)[0] = __gmp_r; \ - if (CB (__gmp_r, __gmp_x, (v))) \ - { \ - (cout) = 1; \ - for (__gmp_i = 1; __gmp_i < (n);) \ - { \ - __gmp_x = (src)[__gmp_i]; \ - __gmp_r = __gmp_x OP 1; \ - (dst)[__gmp_i] = __gmp_r; \ - ++__gmp_i; \ - if (!CB (__gmp_r, __gmp_x, 1)) \ - { \ - if ((src) != (dst)) \ - __GMPN_COPY_REST (dst, src, n, __gmp_i); \ - (cout) = 0; \ - break; \ - } \ - } \ - } \ - else \ - { \ - if ((src) != (dst)) \ - __GMPN_COPY_REST (dst, src, n, 1); \ - (cout) = 0; \ - } \ - } while (0) -#endif - -#if GMP_NAIL_BITS >= 1 -#define __GMPN_AORS_1(cout, dst, src, n, v, OP, CB) \ - do { \ - mp_size_t __gmp_i; \ - mp_limb_t __gmp_x, __gmp_r; \ - \ - /* ASSERT ((n) >= 1); */ \ - /* ASSERT (MPN_SAME_OR_SEPARATE_P (dst, src, n)); */ \ - \ - __gmp_x = (src)[0]; \ - __gmp_r = __gmp_x OP (v); \ - (dst)[0] = __gmp_r & GMP_NUMB_MASK; \ - if (__gmp_r >> GMP_NUMB_BITS != 0) \ - { \ - (cout) = 1; \ - for (__gmp_i = 1; __gmp_i < (n);) \ - { \ - __gmp_x = (src)[__gmp_i]; \ - __gmp_r = __gmp_x OP 1; \ - (dst)[__gmp_i] = __gmp_r & GMP_NUMB_MASK; \ - ++__gmp_i; \ - if (__gmp_r >> GMP_NUMB_BITS == 0) \ - { \ - if ((src) != (dst)) \ - __GMPN_COPY_REST (dst, src, n, __gmp_i); \ - (cout) = 0; \ - break; \ - } \ - } \ - } \ - else \ - { \ - if ((src) != (dst)) \ - __GMPN_COPY_REST (dst, src, n, 1); \ - (cout) = 0; \ - } \ - } while (0) -#endif - -#define __GMPN_ADDCB(r,x,y) ((r) < (y)) -#define __GMPN_SUBCB(r,x,y) ((x) < (y)) - -#define __GMPN_ADD_1(cout, dst, src, n, v) \ - __GMPN_AORS_1(cout, dst, src, n, v, +, __GMPN_ADDCB) -#define __GMPN_SUB_1(cout, dst, src, n, v) \ - __GMPN_AORS_1(cout, dst, src, n, v, -, __GMPN_SUBCB) - - -/* Compare {xp,size} and {yp,size}, setting "result" to positive, zero or - negative. size==0 is allowed. On random data usually only one limb will - need to be examined to get a result, so it's worth having it inline. */ -#define __GMPN_CMP(result, xp, yp, size) \ - do { \ - mp_size_t __gmp_i; \ - mp_limb_t __gmp_x, __gmp_y; \ - \ - /* ASSERT ((size) >= 0); */ \ - \ - (result) = 0; \ - __gmp_i = (size); \ - while (--__gmp_i >= 0) \ - { \ - __gmp_x = (xp)[__gmp_i]; \ - __gmp_y = (yp)[__gmp_i]; \ - if (__gmp_x != __gmp_y) \ - { \ - /* Cannot use __gmp_x - __gmp_y, may overflow an "int" */ \ - (result) = (__gmp_x > __gmp_y ? 1 : -1); \ - break; \ - } \ - } \ - } while (0) - - -#if defined (__GMPN_COPY) && ! defined (__GMPN_COPY_REST) -#define __GMPN_COPY_REST(dst, src, size, start) \ - do { \ - /* ASSERT ((start) >= 0); */ \ - /* ASSERT ((start) <= (size)); */ \ - __GMPN_COPY ((dst)+(start), (src)+(start), (size)-(start)); \ - } while (0) -#endif - -/* Copy {src,size} to {dst,size}, starting at "start". This is designed to - keep the indexing dst[j] and src[j] nice and simple for __GMPN_ADD_1, - __GMPN_ADD, etc. */ -#if ! defined (__GMPN_COPY_REST) -#define __GMPN_COPY_REST(dst, src, size, start) \ - do { \ - mp_size_t __gmp_j; \ - /* ASSERT ((size) >= 0); */ \ - /* ASSERT ((start) >= 0); */ \ - /* ASSERT ((start) <= (size)); */ \ - /* ASSERT (MPN_SAME_OR_SEPARATE_P (dst, src, size)); */ \ - __GMP_CRAY_Pragma ("_CRI ivdep"); \ - for (__gmp_j = (start); __gmp_j < (size); __gmp_j++) \ - (dst)[__gmp_j] = (src)[__gmp_j]; \ - } while (0) -#endif - -/* Enhancement: Use some of the smarter code from gmp-impl.h. Maybe use - mpn_copyi if there's a native version, and if we don't mind demanding - binary compatibility for it (on targets which use it). */ - -#if ! defined (__GMPN_COPY) -#define __GMPN_COPY(dst, src, size) __GMPN_COPY_REST (dst, src, size, 0) -#endif - - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_add) -#if ! defined (__GMP_FORCE_mpn_add) -__GMP_EXTERN_INLINE -#endif -mp_limb_t -mpn_add (mp_ptr __gmp_wp, mp_srcptr __gmp_xp, mp_size_t __gmp_xsize, mp_srcptr __gmp_yp, mp_size_t __gmp_ysize) -{ - mp_limb_t __gmp_c; - __GMPN_ADD (__gmp_c, __gmp_wp, __gmp_xp, __gmp_xsize, __gmp_yp, __gmp_ysize); - return __gmp_c; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_add_1) -#if ! defined (__GMP_FORCE_mpn_add_1) -__GMP_EXTERN_INLINE -#endif -mp_limb_t -mpn_add_1 (mp_ptr __gmp_dst, mp_srcptr __gmp_src, mp_size_t __gmp_size, mp_limb_t __gmp_n) __GMP_NOTHROW -{ - mp_limb_t __gmp_c; - __GMPN_ADD_1 (__gmp_c, __gmp_dst, __gmp_src, __gmp_size, __gmp_n); - return __gmp_c; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_cmp) -#if ! defined (__GMP_FORCE_mpn_cmp) -__GMP_EXTERN_INLINE -#endif -int -mpn_cmp (mp_srcptr __gmp_xp, mp_srcptr __gmp_yp, mp_size_t __gmp_size) __GMP_NOTHROW -{ - int __gmp_result; - __GMPN_CMP (__gmp_result, __gmp_xp, __gmp_yp, __gmp_size); - return __gmp_result; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_sub) -#if ! defined (__GMP_FORCE_mpn_sub) -__GMP_EXTERN_INLINE -#endif -mp_limb_t -mpn_sub (mp_ptr __gmp_wp, mp_srcptr __gmp_xp, mp_size_t __gmp_xsize, mp_srcptr __gmp_yp, mp_size_t __gmp_ysize) -{ - mp_limb_t __gmp_c; - __GMPN_SUB (__gmp_c, __gmp_wp, __gmp_xp, __gmp_xsize, __gmp_yp, __gmp_ysize); - return __gmp_c; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_sub_1) -#if ! defined (__GMP_FORCE_mpn_sub_1) -__GMP_EXTERN_INLINE -#endif -mp_limb_t -mpn_sub_1 (mp_ptr __gmp_dst, mp_srcptr __gmp_src, mp_size_t __gmp_size, mp_limb_t __gmp_n) __GMP_NOTHROW -{ - mp_limb_t __gmp_c; - __GMPN_SUB_1 (__gmp_c, __gmp_dst, __gmp_src, __gmp_size, __gmp_n); - return __gmp_c; -} -#endif - -#if defined (__GMP_EXTERN_INLINE) || defined (__GMP_FORCE_mpn_neg) -#if ! defined (__GMP_FORCE_mpn_neg) -__GMP_EXTERN_INLINE -#endif -mp_limb_t -mpn_neg (mp_ptr __gmp_rp, mp_srcptr __gmp_up, mp_size_t __gmp_n) -{ - mp_limb_t __gmp_ul, __gmp_cy; - __gmp_cy = 0; - do { - __gmp_ul = *__gmp_up++; - *__gmp_rp++ = -__gmp_ul - __gmp_cy; - __gmp_cy |= __gmp_ul != 0; - } while (--__gmp_n != 0); - return __gmp_cy; -} -#endif - -#if defined (__cplusplus) -} -#endif - - -/* Allow faster testing for negative, zero, and positive. */ -#define mpz_sgn(Z) ((Z)->_mp_size < 0 ? -1 : (Z)->_mp_size > 0) -#define mpf_sgn(F) ((F)->_mp_size < 0 ? -1 : (F)->_mp_size > 0) -#define mpq_sgn(Q) ((Q)->_mp_num._mp_size < 0 ? -1 : (Q)->_mp_num._mp_size > 0) - -/* When using GCC, optimize certain common comparisons. */ -#if defined (__GNUC__) && __GNUC__ >= 2 -#define mpz_cmp_ui(Z,UI) \ - (__builtin_constant_p (UI) && (UI) == 0 \ - ? mpz_sgn (Z) : _mpz_cmp_ui (Z,UI)) -#define mpz_cmp_si(Z,SI) \ - (__builtin_constant_p (SI) && (SI) == 0 ? mpz_sgn (Z) \ - : __builtin_constant_p (SI) && (SI) > 0 \ - ? _mpz_cmp_ui (Z, __GMP_CAST (unsigned long int, SI)) \ - : _mpz_cmp_si (Z,SI)) -#define mpq_cmp_ui(Q,NUI,DUI) \ - (__builtin_constant_p (NUI) && (NUI) == 0 \ - ? mpq_sgn (Q) : _mpq_cmp_ui (Q,NUI,DUI)) -#define mpq_cmp_si(q,n,d) \ - (__builtin_constant_p ((n) >= 0) && (n) >= 0 \ - ? mpq_cmp_ui (q, __GMP_CAST (unsigned long, n), d) \ - : _mpq_cmp_si (q, n, d)) -#else -#define mpz_cmp_ui(Z,UI) _mpz_cmp_ui (Z,UI) -#define mpz_cmp_si(Z,UI) _mpz_cmp_si (Z,UI) -#define mpq_cmp_ui(Q,NUI,DUI) _mpq_cmp_ui (Q,NUI,DUI) -#define mpq_cmp_si(q,n,d) _mpq_cmp_si(q,n,d) -#endif - - -/* Using "&" rather than "&&" means these can come out branch-free. Every - mpz_t has at least one limb allocated, so fetching the low limb is always - allowed. */ -#define mpz_odd_p(z) (((z)->_mp_size != 0) & __GMP_CAST (int, (z)->_mp_d[0])) -#define mpz_even_p(z) (! mpz_odd_p (z)) - - -/**************** C++ routines ****************/ - -#ifdef __cplusplus -__GMP_DECLSPEC_XX std::ostream& operator<< (std::ostream &, mpz_srcptr); -__GMP_DECLSPEC_XX std::ostream& operator<< (std::ostream &, mpq_srcptr); -__GMP_DECLSPEC_XX std::ostream& operator<< (std::ostream &, mpf_srcptr); -__GMP_DECLSPEC_XX std::istream& operator>> (std::istream &, mpz_ptr); -__GMP_DECLSPEC_XX std::istream& operator>> (std::istream &, mpq_ptr); -__GMP_DECLSPEC_XX std::istream& operator>> (std::istream &, mpf_ptr); -#endif - - -/* Source-level compatibility with GMP 2 and earlier. */ -#define mpn_divmod(qp,np,nsize,dp,dsize) \ - mpn_divrem (qp, __GMP_CAST (mp_size_t, 0), np, nsize, dp, dsize) - -/* Source-level compatibility with GMP 1. */ -#define mpz_mdiv mpz_fdiv_q -#define mpz_mdivmod mpz_fdiv_qr -#define mpz_mmod mpz_fdiv_r -#define mpz_mdiv_ui mpz_fdiv_q_ui -#define mpz_mdivmod_ui(q,r,n,d) \ - (((r) == 0) ? mpz_fdiv_q_ui (q,n,d) : mpz_fdiv_qr_ui (q,r,n,d)) -#define mpz_mmod_ui(r,n,d) \ - (((r) == 0) ? mpz_fdiv_ui (n,d) : mpz_fdiv_r_ui (r,n,d)) - -/* Useful synonyms, but not quite compatible with GMP 1. */ -#define mpz_div mpz_fdiv_q -#define mpz_divmod mpz_fdiv_qr -#define mpz_div_ui mpz_fdiv_q_ui -#define mpz_divmod_ui mpz_fdiv_qr_ui -#define mpz_div_2exp mpz_fdiv_q_2exp -#define mpz_mod_2exp mpz_fdiv_r_2exp - -enum -{ - GMP_ERROR_NONE = 0, - GMP_ERROR_UNSUPPORTED_ARGUMENT = 1, - GMP_ERROR_DIVISION_BY_ZERO = 2, - GMP_ERROR_SQRT_OF_NEGATIVE = 4, - GMP_ERROR_INVALID_ARGUMENT = 8 -}; - -/* Define CC and CFLAGS which were used to build this version of GMP */ -#define __GMP_CC "gcc -std=gnu99" -#define __GMP_CFLAGS "-O2 -pedantic -m64 -mtune=k8 -march=k8" - -/* Major version number is the value of __GNU_MP__ too, above and in mp.h. */ -#define __GNU_MP_VERSION 5 -#define __GNU_MP_VERSION_MINOR 0 -#define __GNU_MP_VERSION_PATCHLEVEL 1 -#define __GMP_MP_RELEASE (__GNU_MP_VERSION * 10000 + __GNU_MP_VERSION_MINOR * 100 + __GNU_MP_VERSION_PATCHLEVEL) - -#define __GMP_H__ -#endif /* __GMP_H__ */ diff --git a/misc/builddeps/linux64/gmp/lib/libgmp.a b/misc/builddeps/linux64/gmp/lib/libgmp.a deleted file mode 100644 index abac8d22..00000000 Binary files a/misc/builddeps/linux64/gmp/lib/libgmp.a and /dev/null differ diff --git a/misc/builddeps/linux64/gmp/lib/libgmp.la b/misc/builddeps/linux64/gmp/lib/libgmp.la deleted file mode 100755 index 34fab8f3..00000000 --- a/misc/builddeps/linux64/gmp/lib/libgmp.la +++ /dev/null @@ -1,41 +0,0 @@ -# libgmp.la - a libtool library file -# Generated by ltmain.sh (GNU libtool) 2.2.6b -# -# Please DO NOT delete this file! -# It is necessary for linking the library. - -# The name that we can dlopen(3). -dlname='' - -# Names of this library. -library_names='' - -# The name of the static archive. -old_library='libgmp.a' - -# Linker flags that can not go in dependency_libs. -inherited_linker_flags='' - -# Libraries that this one depends upon. -dependency_libs='' - -# Names of additional weak libraries provided by this library -weak_library_names='' - -# Version information for libgmp. -current=10 -age=0 -revision=1 - -# Is this an already installed library? -installed=yes - -# Should we warn about portability when linking against -modules? -shouldnotlink=no - -# Files to dlopen/dlpreopen -dlopen='' -dlpreopen='' - -# Directory that this library needs to be installed in: -libdir='/tmp/g/lib' diff --git a/misc/builddeps/linux64/gmp/share/info/gmp.info b/misc/builddeps/linux64/gmp/share/info/gmp.info deleted file mode 100644 index d65ab795..00000000 --- a/misc/builddeps/linux64/gmp/share/info/gmp.info +++ /dev/null @@ -1,178 +0,0 @@ -This is ../../gmp/doc/gmp.info, produced by makeinfo version 4.8 from -../../gmp/doc/gmp.texi. - - This manual describes how to install and use the GNU multiple -precision arithmetic library, version 5.0.1. - - Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, -2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free -Software Foundation, Inc. - - Permission is granted to copy, distribute and/or modify this -document under the terms of the GNU Free Documentation License, Version -1.3 or any later version published by the Free Software Foundation; -with no Invariant Sections, with the Front-Cover Texts being "A GNU -Manual", and with the Back-Cover Texts being "You have freedom to copy -and modify this GNU Manual, like GNU software". A copy of the license -is included in *Note GNU Free Documentation License::. - -INFO-DIR-SECTION GNU libraries -START-INFO-DIR-ENTRY -* gmp: (gmp). GNU Multiple Precision Arithmetic Library. -END-INFO-DIR-ENTRY - - -Indirect: -gmp.info-1: 981 -gmp.info-2: 300864 - -Tag Table: -(Indirect) -Node: Top981 -Node: Copying3211 -Node: Introduction to GMP5062 -Node: Installing GMP7773 -Node: Build Options8505 -Node: ABI and ISA24573 -Node: Notes for Package Builds34251 -Node: Notes for Particular Systems37338 -Node: Known Build Problems43895 -Node: Performance optimization47429 -Node: GMP Basics48563 -Node: Headers and Libraries49211 -Node: Nomenclature and Types50635 -Node: Function Classes52632 -Node: Variable Conventions54325 -Node: Parameter Conventions55934 -Node: Memory Management57990 -Node: Reentrancy59118 -Node: Useful Macros and Constants60991 -Node: Compatibility with older versions61989 -Node: Demonstration Programs62950 -Node: Efficiency64815 -Node: Debugging72439 -Node: Profiling78997 -Node: Autoconf82988 -Node: Emacs84767 -Node: Reporting Bugs85373 -Node: Integer Functions87916 -Node: Initializing Integers88692 -Node: Assigning Integers90839 -Node: Simultaneous Integer Init & Assign92426 -Node: Converting Integers94051 -Node: Integer Arithmetic96973 -Node: Integer Division98559 -Node: Integer Exponentiation104869 -Node: Integer Roots106309 -Node: Number Theoretic Functions107983 -Node: Integer Comparisons114126 -Node: Integer Logic and Bit Fiddling115504 -Node: I/O of Integers118051 -Node: Integer Random Numbers120935 -Node: Integer Import and Export123546 -Node: Miscellaneous Integer Functions127556 -Node: Integer Special Functions129416 -Node: Rational Number Functions132503 -Node: Initializing Rationals133696 -Node: Rational Conversions136157 -Node: Rational Arithmetic137888 -Node: Comparing Rationals139192 -Node: Applying Integer Functions140559 -Node: I/O of Rationals142042 -Node: Floating-point Functions143902 -Node: Initializing Floats146787 -Node: Assigning Floats150874 -Node: Simultaneous Float Init & Assign153441 -Node: Converting Floats154969 -Node: Float Arithmetic158217 -Node: Float Comparison160230 -Node: I/O of Floats161811 -Node: Miscellaneous Float Functions164409 -Node: Low-level Functions166303 -Node: Random Number Functions190437 -Node: Random State Initialization191505 -Node: Random State Seeding194363 -Node: Random State Miscellaneous195752 -Node: Formatted Output196393 -Node: Formatted Output Strings196638 -Node: Formatted Output Functions201852 -Node: C++ Formatted Output205927 -Node: Formatted Input208609 -Node: Formatted Input Strings208845 -Node: Formatted Input Functions213497 -Node: C++ Formatted Input216466 -Node: C++ Class Interface218369 -Node: C++ Interface General219370 -Node: C++ Interface Integers222440 -Node: C++ Interface Rationals225871 -Node: C++ Interface Floats229548 -Node: C++ Interface Random Numbers234830 -Node: C++ Interface Limitations237236 -Node: BSD Compatible Functions240056 -Node: Custom Allocation244767 -Node: Language Bindings249085 -Node: Algorithms253038 -Node: Multiplication Algorithms253738 -Node: Basecase Multiplication254710 -Node: Karatsuba Multiplication256618 -Node: Toom 3-Way Multiplication260243 -Node: Toom 4-Way Multiplication266657 -Node: FFT Multiplication268029 -Node: Other Multiplication273365 -Node: Unbalanced Multiplication275839 -Node: Division Algorithms276627 -Node: Single Limb Division277006 -Node: Basecase Division279897 -Node: Divide and Conquer Division281100 -Node: Block-Wise Barrett Division283169 -Node: Exact Division283821 -Node: Exact Remainder286986 -Node: Small Quotient Division289213 -Node: Greatest Common Divisor Algorithms290811 -Node: Binary GCD291108 -Node: Lehmer's Algorithm293957 -Node: Subquadratic GCD296177 -Node: Extended GCD298636 -Node: Jacobi Symbol299948 -Node: Powering Algorithms300864 -Node: Normal Powering Algorithm301127 -Node: Modular Powering Algorithm301655 -Node: Root Extraction Algorithms302435 -Node: Square Root Algorithm302750 -Node: Nth Root Algorithm304891 -Node: Perfect Square Algorithm305676 -Node: Perfect Power Algorithm307762 -Node: Radix Conversion Algorithms308383 -Node: Binary to Radix308759 -Node: Radix to Binary312688 -Node: Other Algorithms314776 -Node: Prime Testing Algorithm315128 -Node: Factorial Algorithm316312 -Node: Binomial Coefficients Algorithm317715 -Node: Fibonacci Numbers Algorithm318609 -Node: Lucas Numbers Algorithm321083 -Node: Random Number Algorithms321804 -Node: Assembly Coding323925 -Node: Assembly Code Organisation324885 -Node: Assembly Basics325852 -Node: Assembly Carry Propagation327002 -Node: Assembly Cache Handling328833 -Node: Assembly Functional Units330994 -Node: Assembly Floating Point332607 -Node: Assembly SIMD Instructions336385 -Node: Assembly Software Pipelining337367 -Node: Assembly Loop Unrolling338429 -Node: Assembly Writing Guide340644 -Node: Internals343409 -Node: Integer Internals343921 -Node: Rational Internals346177 -Node: Float Internals347415 -Node: Raw Output Internals354829 -Node: C++ Interface Internals356023 -Node: Contributors359309 -Node: References364267 -Node: GNU Free Documentation License369925 -Node: Concept Index395094 -Node: Function Index441276 - -End Tag Table diff --git a/misc/builddeps/linux64/gmp/share/info/gmp.info-1 b/misc/builddeps/linux64/gmp/share/info/gmp.info-1 deleted file mode 100644 index d1360599..00000000 --- a/misc/builddeps/linux64/gmp/share/info/gmp.info-1 +++ /dev/null @@ -1,7084 +0,0 @@ -This is ../../gmp/doc/gmp.info, produced by makeinfo version 4.8 from -../../gmp/doc/gmp.texi. - - This manual describes how to install and use the GNU multiple -precision arithmetic library, version 5.0.1. - - Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, -2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free -Software Foundation, Inc. - - Permission is granted to copy, distribute and/or modify this -document under the terms of the GNU Free Documentation License, Version -1.3 or any later version published by the Free Software Foundation; -with no Invariant Sections, with the Front-Cover Texts being "A GNU -Manual", and with the Back-Cover Texts being "You have freedom to copy -and modify this GNU Manual, like GNU software". A copy of the license -is included in *Note GNU Free Documentation License::. - -INFO-DIR-SECTION GNU libraries -START-INFO-DIR-ENTRY -* gmp: (gmp). GNU Multiple Precision Arithmetic Library. -END-INFO-DIR-ENTRY - - -File: gmp.info, Node: Top, Next: Copying, Prev: (dir), Up: (dir) - -GNU MP -****** - - This manual describes how to install and use the GNU multiple -precision arithmetic library, version 5.0.1. - - Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, -2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free -Software Foundation, Inc. - - Permission is granted to copy, distribute and/or modify this -document under the terms of the GNU Free Documentation License, Version -1.3 or any later version published by the Free Software Foundation; -with no Invariant Sections, with the Front-Cover Texts being "A GNU -Manual", and with the Back-Cover Texts being "You have freedom to copy -and modify this GNU Manual, like GNU software". A copy of the license -is included in *Note GNU Free Documentation License::. - - -* Menu: - -* Copying:: GMP Copying Conditions (LGPL). -* Introduction to GMP:: Brief introduction to GNU MP. -* Installing GMP:: How to configure and compile the GMP library. -* GMP Basics:: What every GMP user should know. -* Reporting Bugs:: How to usefully report bugs. -* Integer Functions:: Functions for arithmetic on signed integers. -* Rational Number Functions:: Functions for arithmetic on rational numbers. -* Floating-point Functions:: Functions for arithmetic on floats. -* Low-level Functions:: Fast functions for natural numbers. -* Random Number Functions:: Functions for generating random numbers. -* Formatted Output:: `printf' style output. -* Formatted Input:: `scanf' style input. -* C++ Class Interface:: Class wrappers around GMP types. -* BSD Compatible Functions:: All functions found in BSD MP. -* Custom Allocation:: How to customize the internal allocation. -* Language Bindings:: Using GMP from other languages. -* Algorithms:: What happens behind the scenes. -* Internals:: How values are represented behind the scenes. - -* Contributors:: Who brings you this library? -* References:: Some useful papers and books to read. -* GNU Free Documentation License:: -* Concept Index:: -* Function Index:: - - -File: gmp.info, Node: Copying, Next: Introduction to GMP, Prev: Top, Up: Top - -GNU MP Copying Conditions -************************* - -This library is "free"; this means that everyone is free to use it and -free to redistribute it on a free basis. The library is not in the -public domain; it is copyrighted and there are restrictions on its -distribution, but these restrictions are designed to permit everything -that a good cooperating citizen would want to do. What is not allowed -is to try to prevent others from further sharing any version of this -library that they might get from you. - - Specifically, we want to make sure that you have the right to give -away copies of the library, that you receive source code or else can -get it if you want it, that you can change this library or use pieces -of it in new free programs, and that you know you can do these things. - - To make sure that everyone has such rights, we have to forbid you to -deprive anyone else of these rights. For example, if you distribute -copies of the GNU MP library, you must give the recipients all the -rights that you have. You must make sure that they, too, receive or -can get the source code. And you must tell them their rights. - - Also, for our own protection, we must make certain that everyone -finds out that there is no warranty for the GNU MP library. If it is -modified by someone else and passed on, we want their recipients to -know that what they have is not what we distributed, so that any -problems introduced by others will not reflect on our reputation. - - The precise conditions of the license for the GNU MP library are -found in the Lesser General Public License version 3 that accompanies -the source code, see `COPYING.LIB'. Certain demonstration programs are -provided under the terms of the plain General Public License version 3, -see `COPYING'. - - -File: gmp.info, Node: Introduction to GMP, Next: Installing GMP, Prev: Copying, Up: Top - -1 Introduction to GNU MP -************************ - -GNU MP is a portable library written in C for arbitrary precision -arithmetic on integers, rational numbers, and floating-point numbers. -It aims to provide the fastest possible arithmetic for all applications -that need higher precision than is directly supported by the basic C -types. - - Many applications use just a few hundred bits of precision; but some -applications may need thousands or even millions of bits. GMP is -designed to give good performance for both, by choosing algorithms -based on the sizes of the operands, and by carefully keeping the -overhead at a minimum. - - The speed of GMP is achieved by using fullwords as the basic -arithmetic type, by using sophisticated algorithms, by including -carefully optimized assembly code for the most common inner loops for -many different CPUs, and by a general emphasis on speed (as opposed to -simplicity or elegance). - - There is assembly code for these CPUs: ARM, DEC Alpha 21064, 21164, -and 21264, AMD 29000, AMD K6, K6-2, Athlon, and Athlon64, Hitachi -SuperH and SH-2, HPPA 1.0, 1.1 and 2.0, Intel Pentium, Pentium -Pro/II/III, Pentium 4, generic x86, Intel IA-64, i960, Motorola -MC68000, MC68020, MC88100, and MC88110, Motorola/IBM PowerPC 32 and 64, -National NS32000, IBM POWER, MIPS R3000, R4000, SPARCv7, SuperSPARC, -generic SPARCv8, UltraSPARC, DEC VAX, and Zilog Z8000. Some -optimizations also for Cray vector systems, Clipper, IBM ROMP (RT), and -Pyramid AP/XP. - -For up-to-date information on GMP, please see the GMP web pages at - - `http://gmplib.org/' - -The latest version of the library is available at - - `ftp://ftp.gnu.org/gnu/gmp/' - - Many sites around the world mirror `ftp.gnu.org', please use a mirror -near you, see `http://www.gnu.org/order/ftp.html' for a full list. - - There are three public mailing lists of interest. One for release -announcements, one for general questions and discussions about usage of -the GMP library and one for bug reports. For more information, see - - `http://gmplib.org/mailman/listinfo/'. - - The proper place for bug reports is . See -*Note Reporting Bugs:: for information about reporting bugs. - - -1.1 How to use this Manual -========================== - -Everyone should read *Note GMP Basics::. If you need to install the -library yourself, then read *Note Installing GMP::. If you have a -system with multiple ABIs, then read *Note ABI and ISA::, for the -compiler options that must be used on applications. - - The rest of the manual can be used for later reference, although it -is probably a good idea to glance through it. - - -File: gmp.info, Node: Installing GMP, Next: GMP Basics, Prev: Introduction to GMP, Up: Top - -2 Installing GMP -**************** - -GMP has an autoconf/automake/libtool based configuration system. On a -Unix-like system a basic build can be done with - - ./configure - make - -Some self-tests can be run with - - make check - -And you can install (under `/usr/local' by default) with - - make install - - If you experience problems, please report them to -. See *Note Reporting Bugs::, for information on -what to include in useful bug reports. - -* Menu: - -* Build Options:: -* ABI and ISA:: -* Notes for Package Builds:: -* Notes for Particular Systems:: -* Known Build Problems:: -* Performance optimization:: - - -File: gmp.info, Node: Build Options, Next: ABI and ISA, Prev: Installing GMP, Up: Installing GMP - -2.1 Build Options -================= - -All the usual autoconf configure options are available, run `./configure ---help' for a summary. The file `INSTALL.autoconf' has some generic -installation information too. - -Tools - `configure' requires various Unix-like tools. See *Note Notes for - Particular Systems::, for some options on non-Unix systems. - - It might be possible to build without the help of `configure', - certainly all the code is there, but unfortunately you'll be on - your own. - -Build Directory - To compile in a separate build directory, `cd' to that directory, - and prefix the configure command with the path to the GMP source - directory. For example - - cd /my/build/dir - /my/sources/gmp-5.0.1/configure - - Not all `make' programs have the necessary features (`VPATH') to - support this. In particular, SunOS and Slowaris `make' have bugs - that make them unable to build in a separate directory. Use GNU - `make' instead. - -`--prefix' and `--exec-prefix' - The `--prefix' option can be used in the normal way to direct GMP - to install under a particular tree. The default is `/usr/local'. - - `--exec-prefix' can be used to direct architecture-dependent files - like `libgmp.a' to a different location. This can be used to share - architecture-independent parts like the documentation, but - separate the dependent parts. Note however that `gmp.h' and - `mp.h' are architecture-dependent since they encode certain - aspects of `libgmp', so it will be necessary to ensure both - `$prefix/include' and `$exec_prefix/include' are available to the - compiler. - -`--disable-shared', `--disable-static' - By default both shared and static libraries are built (where - possible), but one or other can be disabled. Shared libraries - result in smaller executables and permit code sharing between - separate running processes, but on some CPUs are slightly slower, - having a small cost on each function call. - -Native Compilation, `--build=CPU-VENDOR-OS' - For normal native compilation, the system can be specified with - `--build'. By default `./configure' uses the output from running - `./config.guess'. On some systems `./config.guess' can determine - the exact CPU type, on others it will be necessary to give it - explicitly. For example, - - ./configure --build=ultrasparc-sun-solaris2.7 - - In all cases the `OS' part is important, since it controls how - libtool generates shared libraries. Running `./config.guess' is - the simplest way to see what it should be, if you don't know - already. - -Cross Compilation, `--host=CPU-VENDOR-OS' - When cross-compiling, the system used for compiling is given by - `--build' and the system where the library will run is given by - `--host'. For example when using a FreeBSD Athlon system to build - GNU/Linux m68k binaries, - - ./configure --build=athlon-pc-freebsd3.5 --host=m68k-mac-linux-gnu - - Compiler tools are sought first with the host system type as a - prefix. For example `m68k-mac-linux-gnu-ranlib' is tried, then - plain `ranlib'. This makes it possible for a set of - cross-compiling tools to co-exist with native tools. The prefix - is the argument to `--host', and this can be an alias, such as - `m68k-linux'. But note that tools don't have to be setup this - way, it's enough to just have a `PATH' with a suitable - cross-compiling `cc' etc. - - Compiling for a different CPU in the same family as the build - system is a form of cross-compilation, though very possibly this - would merely be special options on a native compiler. In any case - `./configure' avoids depending on being able to run code on the - build system, which is important when creating binaries for a - newer CPU since they very possibly won't run on the build system. - - In all cases the compiler must be able to produce an executable - (of whatever format) from a standard C `main'. Although only - object files will go to make up `libgmp', `./configure' uses - linking tests for various purposes, such as determining what - functions are available on the host system. - - Currently a warning is given unless an explicit `--build' is used - when cross-compiling, because it may not be possible to correctly - guess the build system type if the `PATH' has only a - cross-compiling `cc'. - - Note that the `--target' option is not appropriate for GMP. It's - for use when building compiler tools, with `--host' being where - they will run, and `--target' what they'll produce code for. - Ordinary programs or libraries like GMP are only interested in the - `--host' part, being where they'll run. (Some past versions of - GMP used `--target' incorrectly.) - -CPU types - In general, if you want a library that runs as fast as possible, - you should configure GMP for the exact CPU type your system uses. - However, this may mean the binaries won't run on older members of - the family, and might run slower on other members, older or newer. - The best idea is always to build GMP for the exact machine type - you intend to run it on. - - The following CPUs have specific support. See `configure.in' for - details of what code and compiler options they select. - - * Alpha: alpha, alphaev5, alphaev56, alphapca56, alphapca57, - alphaev6, alphaev67, alphaev68 alphaev7 - - * Cray: c90, j90, t90, sv1 - - * HPPA: hppa1.0, hppa1.1, hppa2.0, hppa2.0n, hppa2.0w, hppa64 - - * IA-64: ia64, itanium, itanium2 - - * MIPS: mips, mips3, mips64 - - * Motorola: m68k, m68000, m68010, m68020, m68030, m68040, - m68060, m68302, m68360, m88k, m88110 - - * POWER: power, power1, power2, power2sc - - * PowerPC: powerpc, powerpc64, powerpc401, powerpc403, - powerpc405, powerpc505, powerpc601, powerpc602, powerpc603, - powerpc603e, powerpc604, powerpc604e, powerpc620, powerpc630, - powerpc740, powerpc7400, powerpc7450, powerpc750, powerpc801, - powerpc821, powerpc823, powerpc860, powerpc970 - - * SPARC: sparc, sparcv8, microsparc, supersparc, sparcv9, - ultrasparc, ultrasparc2, ultrasparc2i, ultrasparc3, sparc64 - - * x86 family: i386, i486, i586, pentium, pentiummmx, pentiumpro, - pentium2, pentium3, pentium4, k6, k62, k63, athlon, amd64, - viac3, viac32 - - * Other: a29k, arm, clipper, i960, ns32k, pyramid, sh, sh2, vax, - z8k - - CPUs not listed will use generic C code. - -Generic C Build - If some of the assembly code causes problems, or if otherwise - desired, the generic C code can be selected with CPU `none'. For - example, - - ./configure --host=none-unknown-freebsd3.5 - - Note that this will run quite slowly, but it should be portable - and should at least make it possible to get something running if - all else fails. - -Fat binary, `--enable-fat' - Using `--enable-fat' selects a "fat binary" build on x86, where - optimized low level subroutines are chosen at runtime according to - the CPU detected. This means more code, but gives good - performance on all x86 chips. (This option might become available - for more architectures in the future.) - -`ABI' - On some systems GMP supports multiple ABIs (application binary - interfaces), meaning data type sizes and calling conventions. By - default GMP chooses the best ABI available, but a particular ABI - can be selected. For example - - ./configure --host=mips64-sgi-irix6 ABI=n32 - - See *Note ABI and ISA::, for the available choices on relevant - CPUs, and what applications need to do. - -`CC', `CFLAGS' - By default the C compiler used is chosen from among some likely - candidates, with `gcc' normally preferred if it's present. The - usual `CC=whatever' can be passed to `./configure' to choose - something different. - - For various systems, default compiler flags are set based on the - CPU and compiler. The usual `CFLAGS="-whatever"' can be passed to - `./configure' to use something different or to set good flags for - systems GMP doesn't otherwise know. - - The `CC' and `CFLAGS' used are printed during `./configure', and - can be found in each generated `Makefile'. This is the easiest way - to check the defaults when considering changing or adding - something. - - Note that when `CC' and `CFLAGS' are specified on a system - supporting multiple ABIs it's important to give an explicit - `ABI=whatever', since GMP can't determine the ABI just from the - flags and won't be able to select the correct assembly code. - - If just `CC' is selected then normal default `CFLAGS' for that - compiler will be used (if GMP recognises it). For example - `CC=gcc' can be used to force the use of GCC, with default flags - (and default ABI). - -`CPPFLAGS' - Any flags like `-D' defines or `-I' includes required by the - preprocessor should be set in `CPPFLAGS' rather than `CFLAGS'. - Compiling is done with both `CPPFLAGS' and `CFLAGS', but - preprocessing uses just `CPPFLAGS'. This distinction is because - most preprocessors won't accept all the flags the compiler does. - Preprocessing is done separately in some configure tests, and in - the `ansi2knr' support for K&R compilers. - -`CC_FOR_BUILD' - Some build-time programs are compiled and run to generate - host-specific data tables. `CC_FOR_BUILD' is the compiler used - for this. It doesn't need to be in any particular ABI or mode, it - merely needs to generate executables that can run. The default is - to try the selected `CC' and some likely candidates such as `cc' - and `gcc', looking for something that works. - - No flags are used with `CC_FOR_BUILD' because a simple invocation - like `cc foo.c' should be enough. If some particular options are - required they can be included as for instance `CC_FOR_BUILD="cc - -whatever"'. - -C++ Support, `--enable-cxx' - C++ support in GMP can be enabled with `--enable-cxx', in which - case a C++ compiler will be required. As a convenience - `--enable-cxx=detect' can be used to enable C++ support only if a - compiler can be found. The C++ support consists of a library - `libgmpxx.la' and header file `gmpxx.h' (*note Headers and - Libraries::). - - A separate `libgmpxx.la' has been adopted rather than having C++ - objects within `libgmp.la' in order to ensure dynamic linked C - programs aren't bloated by a dependency on the C++ standard - library, and to avoid any chance that the C++ compiler could be - required when linking plain C programs. - - `libgmpxx.la' will use certain internals from `libgmp.la' and can - only be expected to work with `libgmp.la' from the same GMP - version. Future changes to the relevant internals will be - accompanied by renaming, so a mismatch will cause unresolved - symbols rather than perhaps mysterious misbehaviour. - - In general `libgmpxx.la' will be usable only with the C++ compiler - that built it, since name mangling and runtime support are usually - incompatible between different compilers. - -`CXX', `CXXFLAGS' - When C++ support is enabled, the C++ compiler and its flags can be - set with variables `CXX' and `CXXFLAGS' in the usual way. The - default for `CXX' is the first compiler that works from a list of - likely candidates, with `g++' normally preferred when available. - The default for `CXXFLAGS' is to try `CFLAGS', `CFLAGS' without - `-g', then for `g++' either `-g -O2' or `-O2', or for other - compilers `-g' or nothing. Trying `CFLAGS' this way is convenient - when using `gcc' and `g++' together, since the flags for `gcc' will - usually suit `g++'. - - It's important that the C and C++ compilers match, meaning their - startup and runtime support routines are compatible and that they - generate code in the same ABI (if there's a choice of ABIs on the - system). `./configure' isn't currently able to check these things - very well itself, so for that reason `--disable-cxx' is the - default, to avoid a build failure due to a compiler mismatch. - Perhaps this will change in the future. - - Incidentally, it's normally not good enough to set `CXX' to the - same as `CC'. Although `gcc' for instance recognises `foo.cc' as - C++ code, only `g++' will invoke the linker the right way when - building an executable or shared library from C++ object files. - -Temporary Memory, `--enable-alloca=' - GMP allocates temporary workspace using one of the following three - methods, which can be selected with for instance - `--enable-alloca=malloc-reentrant'. - - * `alloca' - C library or compiler builtin. - - * `malloc-reentrant' - the heap, in a re-entrant fashion. - - * `malloc-notreentrant' - the heap, with global variables. - - For convenience, the following choices are also available. - `--disable-alloca' is the same as `no'. - - * `yes' - a synonym for `alloca'. - - * `no' - a synonym for `malloc-reentrant'. - - * `reentrant' - `alloca' if available, otherwise - `malloc-reentrant'. This is the default. - - * `notreentrant' - `alloca' if available, otherwise - `malloc-notreentrant'. - - `alloca' is reentrant and fast, and is recommended. It actually - allocates just small blocks on the stack; larger ones use - malloc-reentrant. - - `malloc-reentrant' is, as the name suggests, reentrant and thread - safe, but `malloc-notreentrant' is faster and should be used if - reentrancy is not required. - - The two malloc methods in fact use the memory allocation functions - selected by `mp_set_memory_functions', these being `malloc' and - friends by default. *Note Custom Allocation::. - - An additional choice `--enable-alloca=debug' is available, to help - when debugging memory related problems (*note Debugging::). - -FFT Multiplication, `--disable-fft' - By default multiplications are done using Karatsuba, 3-way Toom, - and Fermat FFT. The FFT is only used on large to very large - operands and can be disabled to save code size if desired. - -Berkeley MP, `--enable-mpbsd' - The Berkeley MP compatibility library (`libmp') and header file - (`mp.h') are built and installed only if `--enable-mpbsd' is used. - *Note BSD Compatible Functions::. - -Assertion Checking, `--enable-assert' - This option enables some consistency checking within the library. - This can be of use while debugging, *note Debugging::. - -Execution Profiling, `--enable-profiling=prof/gprof/instrument' - Enable profiling support, in one of various styles, *note - Profiling::. - -`MPN_PATH' - Various assembly versions of each mpn subroutines are provided. - For a given CPU, a search is made though a path to choose a - version of each. For example `sparcv8' has - - MPN_PATH="sparc32/v8 sparc32 generic" - - which means look first for v8 code, then plain sparc32 (which is - v7), and finally fall back on generic C. Knowledgeable users with - special requirements can specify a different path. Normally this - is completely unnecessary. - -Documentation - The source for the document you're now reading is `doc/gmp.texi', - in Texinfo format, see *Note Texinfo: (texinfo)Top. - - Info format `doc/gmp.info' is included in the distribution. The - usual automake targets are available to make PostScript, DVI, PDF - and HTML (these will require various TeX and Texinfo tools). - - DocBook and XML can be generated by the Texinfo `makeinfo' program - too, see *Note Options for `makeinfo': (texinfo)makeinfo options. - - Some supplementary notes can also be found in the `doc' - subdirectory. - - - -File: gmp.info, Node: ABI and ISA, Next: Notes for Package Builds, Prev: Build Options, Up: Installing GMP - -2.2 ABI and ISA -=============== - -ABI (Application Binary Interface) refers to the calling conventions -between functions, meaning what registers are used and what sizes the -various C data types are. ISA (Instruction Set Architecture) refers to -the instructions and registers a CPU has available. - - Some 64-bit ISA CPUs have both a 64-bit ABI and a 32-bit ABI -defined, the latter for compatibility with older CPUs in the family. -GMP supports some CPUs like this in both ABIs. In fact within GMP -`ABI' means a combination of chip ABI, plus how GMP chooses to use it. -For example in some 32-bit ABIs, GMP may support a limb as either a -32-bit `long' or a 64-bit `long long'. - - By default GMP chooses the best ABI available for a given system, -and this generally gives significantly greater speed. But an ABI can -be chosen explicitly to make GMP compatible with other libraries, or -particular application requirements. For example, - - ./configure ABI=32 - - In all cases it's vital that all object code used in a given program -is compiled for the same ABI. - - Usually a limb is implemented as a `long'. When a `long long' limb -is used this is encoded in the generated `gmp.h'. This is convenient -for applications, but it does mean that `gmp.h' will vary, and can't be -just copied around. `gmp.h' remains compiler independent though, since -all compilers for a particular ABI will be expected to use the same -limb type. - - Currently no attempt is made to follow whatever conventions a system -has for installing library or header files built for a particular ABI. -This will probably only matter when installing multiple builds of GMP, -and it might be as simple as configuring with a special `libdir', or it -might require more than that. Note that builds for different ABIs need -to done separately, with a fresh `./configure' and `make' each. - - -AMD64 (`x86_64') - On AMD64 systems supporting both 32-bit and 64-bit modes for - applications, the following ABI choices are available. - - `ABI=64' - The 64-bit ABI uses 64-bit limbs and pointers and makes full - use of the chip architecture. This is the default. - Applications will usually not need special compiler flags, - but for reference the option is - - gcc -m64 - - `ABI=32' - The 32-bit ABI is the usual i386 conventions. This will be - slower, and is not recommended except for inter-operating - with other code not yet 64-bit capable. Applications must be - compiled with - - gcc -m32 - - (In GCC 2.95 and earlier there's no `-m32' option, it's the - only mode.) - - -HPPA 2.0 (`hppa2.0*', `hppa64') - - `ABI=2.0w' - The 2.0w ABI uses 64-bit limbs and pointers and is available - on HP-UX 11 or up. Applications must be compiled with - - gcc [built for 2.0w] - cc +DD64 - - `ABI=2.0n' - The 2.0n ABI means the 32-bit HPPA 1.0 ABI and all its normal - calling conventions, but with 64-bit instructions permitted - within functions. GMP uses a 64-bit `long long' for a limb. - This ABI is available on hppa64 GNU/Linux and on HP-UX 10 or - higher. Applications must be compiled with - - gcc [built for 2.0n] - cc +DA2.0 +e - - Note that current versions of GCC (eg. 3.2) don't generate - 64-bit instructions for `long long' operations and so may be - slower than for 2.0w. (The GMP assembly code is the same - though.) - - `ABI=1.0' - HPPA 2.0 CPUs can run all HPPA 1.0 and 1.1 code in the 32-bit - HPPA 1.0 ABI. No special compiler options are needed for - applications. - - All three ABIs are available for CPU types `hppa2.0w', `hppa2.0' - and `hppa64', but for CPU type `hppa2.0n' only 2.0n or 1.0 are - considered. - - Note that GCC on HP-UX has no options to choose between 2.0n and - 2.0w modes, unlike HP `cc'. Instead it must be built for one or - the other ABI. GMP will detect how it was built, and skip to the - corresponding `ABI'. - - -IA-64 under HP-UX (`ia64*-*-hpux*', `itanium*-*-hpux*') - HP-UX supports two ABIs for IA-64. GMP performance is the same in - both. - - `ABI=32' - In the 32-bit ABI, pointers, `int's and `long's are 32 bits - and GMP uses a 64 bit `long long' for a limb. Applications - can be compiled without any special flags since this ABI is - the default in both HP C and GCC, but for reference the flags - are - - gcc -milp32 - cc +DD32 - - `ABI=64' - In the 64-bit ABI, `long's and pointers are 64 bits and GMP - uses a `long' for a limb. Applications must be compiled with - - gcc -mlp64 - cc +DD64 - - On other IA-64 systems, GNU/Linux for instance, `ABI=64' is the - only choice. - - -MIPS under IRIX 6 (`mips*-*-irix[6789]') - IRIX 6 always has a 64-bit MIPS 3 or better CPU, and supports ABIs - o32, n32, and 64. n32 or 64 are recommended, and GMP performance - will be the same in each. The default is n32. - - `ABI=o32' - The o32 ABI is 32-bit pointers and integers, and no 64-bit - operations. GMP will be slower than in n32 or 64, this - option only exists to support old compilers, eg. GCC 2.7.2. - Applications can be compiled with no special flags on an old - compiler, or on a newer compiler with - - gcc -mabi=32 - cc -32 - - `ABI=n32' - The n32 ABI is 32-bit pointers and integers, but with a - 64-bit limb using a `long long'. Applications must be - compiled with - - gcc -mabi=n32 - cc -n32 - - `ABI=64' - The 64-bit ABI is 64-bit pointers and integers. Applications - must be compiled with - - gcc -mabi=64 - cc -64 - - Note that MIPS GNU/Linux, as of kernel version 2.2, doesn't have - the necessary support for n32 or 64 and so only gets a 32-bit limb - and the MIPS 2 code. - - -PowerPC 64 (`powerpc64', `powerpc620', `powerpc630', `powerpc970', `power4', `power5') - - `ABI=aix64' - The AIX 64 ABI uses 64-bit limbs and pointers and is the - default on PowerPC 64 `*-*-aix*' systems. Applications must - be compiled with - - gcc -maix64 - xlc -q64 - - `ABI=mode64' - The `mode64' ABI uses 64-bit limbs and pointers, and is the - default on 64-bit GNU/Linux, BSD, and Mac OS X/Darwin - systems. Applications must be compiled with - - gcc -m64 - - `ABI=mode32' - The `mode32' ABI uses a 64-bit `long long' limb but with the - chip still in 32-bit mode and using 32-bit calling - conventions. This is the default on for systems where the - true 64-bit ABIs are unavailable. No special compiler - options are needed for applications. - - `ABI=32' - This is the basic 32-bit PowerPC ABI, with a 32-bit limb. No - special compiler options are needed for applications. - - GMP speed is greatest in `aix64' and `mode32'. In `ABI=32' only - the 32-bit ISA is used and this doesn't make full use of a 64-bit - chip. On a suitable system we could perhaps use more of the ISA, - but there are no plans to do so. - - -Sparc V9 (`sparc64', `sparcv9', `ultrasparc*') - - `ABI=64' - The 64-bit V9 ABI is available on the various BSD sparc64 - ports, recent versions of Sparc64 GNU/Linux, and Solaris 2.7 - and up (when the kernel is in 64-bit mode). GCC 3.2 or - higher, or Sun `cc' is required. On GNU/Linux, depending on - the default `gcc' mode, applications must be compiled with - - gcc -m64 - - On Solaris applications must be compiled with - - gcc -m64 -mptr64 -Wa,-xarch=v9 -mcpu=v9 - cc -xarch=v9 - - On the BSD sparc64 systems no special options are required, - since 64-bits is the only ABI available. - - `ABI=32' - For the basic 32-bit ABI, GMP still uses as much of the V9 - ISA as it can. In the Sun documentation this combination is - known as "v8plus". On GNU/Linux, depending on the default - `gcc' mode, applications may need to be compiled with - - gcc -m32 - - On Solaris, no special compiler options are required for - applications, though using something like the following is - recommended. (`gcc' 2.8 and earlier only support `-mv8' - though.) - - gcc -mv8plus - cc -xarch=v8plus - - GMP speed is greatest in `ABI=64', so it's the default where - available. The speed is partly because there are extra registers - available and partly because 64-bits is considered the more - important case and has therefore had better code written for it. - - Don't be confused by the names of the `-m' and `-x' compiler - options, they're called `arch' but effectively control both ABI - and ISA. - - On Solaris 2.6 and earlier, only `ABI=32' is available since the - kernel doesn't save all registers. - - On Solaris 2.7 with the kernel in 32-bit mode, a normal native - build will reject `ABI=64' because the resulting executables won't - run. `ABI=64' can still be built if desired by making it look - like a cross-compile, for example - - ./configure --build=none --host=sparcv9-sun-solaris2.7 ABI=64 - - -File: gmp.info, Node: Notes for Package Builds, Next: Notes for Particular Systems, Prev: ABI and ISA, Up: Installing GMP - -2.3 Notes for Package Builds -============================ - -GMP should present no great difficulties for packaging in a binary -distribution. - - Libtool is used to build the library and `-version-info' is set -appropriately, having started from `3:0:0' in GMP 3.0 (*note Library -interface versions: (libtool)Versioning.). - - The GMP 4 series will be upwardly binary compatible in each release -and will be upwardly binary compatible with all of the GMP 3 series. -Additional function interfaces may be added in each release, so on -systems where libtool versioning is not fully checked by the loader an -auxiliary mechanism may be needed to express that a dynamic linked -application depends on a new enough GMP. - - An auxiliary mechanism may also be needed to express that -`libgmpxx.la' (from `--enable-cxx', *note Build Options::) requires -`libgmp.la' from the same GMP version, since this is not done by the -libtool versioning, nor otherwise. A mismatch will result in -unresolved symbols from the linker, or perhaps the loader. - - When building a package for a CPU family, care should be taken to use -`--host' (or `--build') to choose the least common denominator among -the CPUs which might use the package. For example this might mean plain -`sparc' (meaning V7) for SPARCs. - - For x86s, `--enable-fat' sets things up for a fat binary build, -making a runtime selection of optimized low level routines. This is a -good choice for packaging to run on a range of x86 chips. - - Users who care about speed will want GMP built for their exact CPU -type, to make best use of the available optimizations. Providing a way -to suitably rebuild a package may be useful. This could be as simple -as making it possible for a user to omit `--build' (and `--host') so -`./config.guess' will detect the CPU. But a way to manually specify a -`--build' will be wanted for systems where `./config.guess' is inexact. - - On systems with multiple ABIs, a packaged build will need to decide -which among the choices is to be provided, see *Note ABI and ISA::. A -given run of `./configure' etc will only build one ABI. If a second -ABI is also required then a second run of `./configure' etc must be -made, starting from a clean directory tree (`make distclean'). - - As noted under "ABI and ISA", currently no attempt is made to follow -system conventions for install locations that vary with ABI, such as -`/usr/lib/sparcv9' for `ABI=64' as opposed to `/usr/lib' for `ABI=32'. -A package build can override `libdir' and other standard variables as -necessary. - - Note that `gmp.h' is a generated file, and will be architecture and -ABI dependent. When attempting to install two ABIs simultaneously it -will be important that an application compile gets the correct `gmp.h' -for its desired ABI. If compiler include paths don't vary with ABI -options then it might be necessary to create a `/usr/include/gmp.h' -which tests preprocessor symbols and chooses the correct actual `gmp.h'. - - -File: gmp.info, Node: Notes for Particular Systems, Next: Known Build Problems, Prev: Notes for Package Builds, Up: Installing GMP - -2.4 Notes for Particular Systems -================================ - -AIX 3 and 4 - On systems `*-*-aix[34]*' shared libraries are disabled by - default, since some versions of the native `ar' fail on the - convenience libraries used. A shared build can be attempted with - - ./configure --enable-shared --disable-static - - Note that the `--disable-static' is necessary because in a shared - build libtool makes `libgmp.a' a symlink to `libgmp.so', - apparently for the benefit of old versions of `ld' which only - recognise `.a', but unfortunately this is done even if a fully - functional `ld' is available. - -ARM - On systems `arm*-*-*', versions of GCC up to and including 2.95.3 - have a bug in unsigned division, giving wrong results for some - operands. GMP `./configure' will demand GCC 2.95.4 or later. - -Compaq C++ - Compaq C++ on OSF 5.1 has two flavours of `iostream', a standard - one and an old pre-standard one (see `man iostream_intro'). GMP - can only use the standard one, which unfortunately is not the - default but must be selected by defining `__USE_STD_IOSTREAM'. - Configure with for instance - - ./configure --enable-cxx CPPFLAGS=-D__USE_STD_IOSTREAM - -Floating Point Mode - On some systems, the hardware floating point has a control mode - which can set all operations to be done in a particular precision, - for instance single, double or extended on x86 systems (x87 - floating point). The GMP functions involving a `double' cannot be - expected to operate to their full precision when the hardware is - in single precision mode. Of course this affects all code, - including application code, not just GMP. - -MS-DOS and MS Windows - On an MS-DOS system DJGPP can be used to build GMP, and on an MS - Windows system Cygwin, DJGPP and MINGW can be used. All three are - excellent ports of GCC and the various GNU tools. - - `http://www.cygwin.com/' - `http://www.delorie.com/djgpp/' - `http://www.mingw.org/' - - Microsoft also publishes an Interix "Services for Unix" which can - be used to build GMP on Windows (with a normal `./configure'), but - it's not free software. - -MS Windows DLLs - On systems `*-*-cygwin*', `*-*-mingw*' and `*-*-pw32*' by default - GMP builds only a static library, but a DLL can be built instead - using - - ./configure --disable-static --enable-shared - - Static and DLL libraries can't both be built, since certain export - directives in `gmp.h' must be different. - - A MINGW DLL build of GMP can be used with Microsoft C. Libtool - doesn't install a `.lib' format import library, but it can be - created with MS `lib' as follows, and copied to the install - directory. Similarly for `libmp' and `libgmpxx'. - - cd .libs - lib /def:libgmp-3.dll.def /out:libgmp-3.lib - - MINGW uses the C runtime library `msvcrt.dll' for I/O, so - applications wanting to use the GMP I/O routines must be compiled - with `cl /MD' to do the same. If one of the other C runtime - library choices provided by MS C is desired then the suggestion is - to use the GMP string functions and confine I/O to the application. - -Motorola 68k CPU Types - `m68k' is taken to mean 68000. `m68020' or higher will give a - performance boost on applicable CPUs. `m68360' can be used for - CPU32 series chips. `m68302' can be used for "Dragonball" series - chips, though this is merely a synonym for `m68000'. - -OpenBSD 2.6 - `m4' in this release of OpenBSD has a bug in `eval' that makes it - unsuitable for `.asm' file processing. `./configure' will detect - the problem and either abort or choose another m4 in the `PATH'. - The bug is fixed in OpenBSD 2.7, so either upgrade or use GNU m4. - -Power CPU Types - In GMP, CPU types `power*' and `powerpc*' will each use - instructions not available on the other, so it's important to - choose the right one for the CPU that will be used. Currently GMP - has no assembly code support for using just the common instruction - subset. To get executables that run on both, the current - suggestion is to use the generic C code (CPU `none'), possibly - with appropriate compiler options (like `-mcpu=common' for `gcc'). - CPU `rs6000' (which is not a CPU but a family of workstations) is - accepted by `config.sub', but is currently equivalent to `none'. - -Sparc CPU Types - `sparcv8' or `supersparc' on relevant systems will give a - significant performance increase over the V7 code selected by plain - `sparc'. - -Sparc App Regs - The GMP assembly code for both 32-bit and 64-bit Sparc clobbers the - "application registers" `g2', `g3' and `g4', the same way that the - GCC default `-mapp-regs' does (*note SPARC Options: (gcc)SPARC - Options.). - - This makes that code unsuitable for use with the special V9 - `-mcmodel=embmedany' (which uses `g4' as a data segment pointer), - and for applications wanting to use those registers for special - purposes. In these cases the only suggestion currently is to - build GMP with CPU `none' to avoid the assembly code. - -SunOS 4 - `/usr/bin/m4' lacks various features needed to process `.asm' - files, and instead `./configure' will automatically use - `/usr/5bin/m4', which we believe is always available (if not then - use GNU m4). - -x86 CPU Types - `i586', `pentium' or `pentiummmx' code is good for its intended P5 - Pentium chips, but quite slow when run on Intel P6 class chips - (PPro, P-II, P-III). `i386' is a better choice when making - binaries that must run on both. - -x86 MMX and SSE2 Code - If the CPU selected has MMX code but the assembler doesn't support - it, a warning is given and non-MMX code is used instead. This - will be an inferior build, since the MMX code that's present is - there because it's faster than the corresponding plain integer - code. The same applies to SSE2. - - Old versions of `gas' don't support MMX instructions, in particular - version 1.92.3 that comes with FreeBSD 2.2.8 or the more recent - OpenBSD 3.1 doesn't. - - Solaris 2.6 and 2.7 `as' generate incorrect object code for - register to register `movq' instructions, and so can't be used for - MMX code. Install a recent `gas' if MMX code is wanted on these - systems. - - -File: gmp.info, Node: Known Build Problems, Next: Performance optimization, Prev: Notes for Particular Systems, Up: Installing GMP - -2.5 Known Build Problems -======================== - -You might find more up-to-date information at `http://gmplib.org/'. - -Compiler link options - The version of libtool currently in use rather aggressively strips - compiler options when linking a shared library. This will - hopefully be relaxed in the future, but for now if this is a - problem the suggestion is to create a little script to hide them, - and for instance configure with - - ./configure CC=gcc-with-my-options - -DJGPP (`*-*-msdosdjgpp*') - The DJGPP port of `bash' 2.03 is unable to run the `configure' - script, it exits silently, having died writing a preamble to - `config.log'. Use `bash' 2.04 or higher. - - `make all' was found to run out of memory during the final - `libgmp.la' link on one system tested, despite having 64Mb - available. Running `make libgmp.la' directly helped, perhaps - recursing into the various subdirectories uses up memory. - -GNU binutils `strip' prior to 2.12 - `strip' from GNU binutils 2.11 and earlier should not be used on - the static libraries `libgmp.a' and `libmp.a' since it will - discard all but the last of multiple archive members with the same - name, like the three versions of `init.o' in `libgmp.a'. Binutils - 2.12 or higher can be used successfully. - - The shared libraries `libgmp.so' and `libmp.so' are not affected by - this and any version of `strip' can be used on them. - -`make' syntax error - On certain versions of SCO OpenServer 5 and IRIX 6.5 the native - `make' is unable to handle the long dependencies list for - `libgmp.la'. The symptom is a "syntax error" on the following - line of the top-level `Makefile'. - - libgmp.la: $(libgmp_la_OBJECTS) $(libgmp_la_DEPENDENCIES) - - Either use GNU Make, or as a workaround remove - `$(libgmp_la_DEPENDENCIES)' from that line (which will make the - initial build work, but if any recompiling is done `libgmp.la' - might not be rebuilt). - -MacOS X (`*-*-darwin*') - Libtool currently only knows how to create shared libraries on - MacOS X using the native `cc' (which is a modified GCC), not a - plain GCC. A static-only build should work though - (`--disable-shared'). - -NeXT prior to 3.3 - The system compiler on old versions of NeXT was a massacred and - old GCC, even if it called itself `cc'. This compiler cannot be - used to build GMP, you need to get a real GCC, and install that. - (NeXT may have fixed this in release 3.3 of their system.) - -POWER and PowerPC - Bugs in GCC 2.7.2 (and 2.6.3) mean it can't be used to compile GMP - on POWER or PowerPC. If you want to use GCC for these machines, - get GCC 2.7.2.1 (or later). - -Sequent Symmetry - Use the GNU assembler instead of the system assembler, since the - latter has serious bugs. - -Solaris 2.6 - The system `sed' prints an error "Output line too long" when - libtool builds `libgmp.la'. This doesn't seem to cause any - obvious ill effects, but GNU `sed' is recommended, to avoid any - doubt. - -Sparc Solaris 2.7 with gcc 2.95.2 in `ABI=32' - A shared library build of GMP seems to fail in this combination, - it builds but then fails the tests, apparently due to some - incorrect data relocations within `gmp_randinit_lc_2exp_size'. - The exact cause is unknown, `--disable-shared' is recommended. - - -File: gmp.info, Node: Performance optimization, Prev: Known Build Problems, Up: Installing GMP - -2.6 Performance optimization -============================ - -For optimal performance, build GMP for the exact CPU type of the target -computer, see *Note Build Options::. - - Unlike what is the case for most other programs, the compiler -typically doesn't matter much, since GMP uses assembly language for the -most critical operation. - - In particular for long-running GMP applications, and applications -demanding extremely large numbers, building and running the `tuneup' -program in the `tune' subdirectory, can be important. For example, - - cd tune - make tuneup - ./tuneup - - will generate better contents for the `gmp-mparam.h' parameter file. - - To use the results, put the output in the file file indicated in the -`Parameters for ...' header. Then recompile from scratch. - - The `tuneup' program takes one useful parameter, `-f NNN', which -instructs the program how long to check FFT multiply parameters. If -you're going to use GMP for extremely large numbers, you may want to -run `tuneup' with a large NNN value. - - -File: gmp.info, Node: GMP Basics, Next: Reporting Bugs, Prev: Installing GMP, Up: Top - -3 GMP Basics -************ - -*Using functions, macros, data types, etc. not documented in this -manual is strongly discouraged. If you do so your application is -guaranteed to be incompatible with future versions of GMP.* - -* Menu: - -* Headers and Libraries:: -* Nomenclature and Types:: -* Function Classes:: -* Variable Conventions:: -* Parameter Conventions:: -* Memory Management:: -* Reentrancy:: -* Useful Macros and Constants:: -* Compatibility with older versions:: -* Demonstration Programs:: -* Efficiency:: -* Debugging:: -* Profiling:: -* Autoconf:: -* Emacs:: - - -File: gmp.info, Node: Headers and Libraries, Next: Nomenclature and Types, Prev: GMP Basics, Up: GMP Basics - -3.1 Headers and Libraries -========================= - -All declarations needed to use GMP are collected in the include file -`gmp.h'. It is designed to work with both C and C++ compilers. - - #include - - Note however that prototypes for GMP functions with `FILE *' -parameters are only provided if `' is included too. - - #include - #include - - Likewise `' (or `') is required for prototypes -with `va_list' parameters, such as `gmp_vprintf'. And `' -for prototypes with `struct obstack' parameters, such as -`gmp_obstack_printf', when available. - - All programs using GMP must link against the `libgmp' library. On a -typical Unix-like system this can be done with `-lgmp', for example - - gcc myprogram.c -lgmp - - GMP C++ functions are in a separate `libgmpxx' library. This is -built and installed if C++ support has been enabled (*note Build -Options::). For example, - - g++ mycxxprog.cc -lgmpxx -lgmp - - GMP is built using Libtool and an application can use that to link -if desired, *note GNU Libtool: (libtool)Top. - - If GMP has been installed to a non-standard location then it may be -necessary to use `-I' and `-L' compiler options to point to the right -directories, and some sort of run-time path for a shared library. - - -File: gmp.info, Node: Nomenclature and Types, Next: Function Classes, Prev: Headers and Libraries, Up: GMP Basics - -3.2 Nomenclature and Types -========================== - -In this manual, "integer" usually means a multiple precision integer, as -defined by the GMP library. The C data type for such integers is -`mpz_t'. Here are some examples of how to declare such integers: - - mpz_t sum; - - struct foo { mpz_t x, y; }; - - mpz_t vec[20]; - - "Rational number" means a multiple precision fraction. The C data -type for these fractions is `mpq_t'. For example: - - mpq_t quotient; - - "Floating point number" or "Float" for short, is an arbitrary -precision mantissa with a limited precision exponent. The C data type -for such objects is `mpf_t'. For example: - - mpf_t fp; - - The floating point functions accept and return exponents in the C -type `mp_exp_t'. Currently this is usually a `long', but on some -systems it's an `int' for efficiency. - - A "limb" means the part of a multi-precision number that fits in a -single machine word. (We chose this word because a limb of the human -body is analogous to a digit, only larger, and containing several -digits.) Normally a limb is 32 or 64 bits. The C data type for a limb -is `mp_limb_t'. - - Counts of limbs of a multi-precision number represented in the C type -`mp_size_t'. Currently this is normally a `long', but on some systems -it's an `int' for efficiency, and on some systems it will be `long -long' in the future. - - Counts of bits of a multi-precision number are represented in the C -type `mp_bitcnt_t'. Currently this is always an `unsigned long', but on -some systems it will be an `unsigned long long' in the future . - - "Random state" means an algorithm selection and current state data. -The C data type for such objects is `gmp_randstate_t'. For example: - - gmp_randstate_t rstate; - - Also, in general `mp_bitcnt_t' is used for bit counts and ranges, and -`size_t' is used for byte or character counts. - - -File: gmp.info, Node: Function Classes, Next: Variable Conventions, Prev: Nomenclature and Types, Up: GMP Basics - -3.3 Function Classes -==================== - -There are six classes of functions in the GMP library: - - 1. Functions for signed integer arithmetic, with names beginning with - `mpz_'. The associated type is `mpz_t'. There are about 150 - functions in this class. (*note Integer Functions::) - - 2. Functions for rational number arithmetic, with names beginning with - `mpq_'. The associated type is `mpq_t'. There are about 40 - functions in this class, but the integer functions can be used for - arithmetic on the numerator and denominator separately. (*note - Rational Number Functions::) - - 3. Functions for floating-point arithmetic, with names beginning with - `mpf_'. The associated type is `mpf_t'. There are about 60 - functions is this class. (*note Floating-point Functions::) - - 4. Functions compatible with Berkeley MP, such as `itom', `madd', and - `mult'. The associated type is `MINT'. (*note BSD Compatible - Functions::) - - 5. Fast low-level functions that operate on natural numbers. These - are used by the functions in the preceding groups, and you can - also call them directly from very time-critical user programs. - These functions' names begin with `mpn_'. The associated type is - array of `mp_limb_t'. There are about 30 (hard-to-use) functions - in this class. (*note Low-level Functions::) - - 6. Miscellaneous functions. Functions for setting up custom - allocation and functions for generating random numbers. (*note - Custom Allocation::, and *note Random Number Functions::) - - -File: gmp.info, Node: Variable Conventions, Next: Parameter Conventions, Prev: Function Classes, Up: GMP Basics - -3.4 Variable Conventions -======================== - -GMP functions generally have output arguments before input arguments. -This notation is by analogy with the assignment operator. The BSD MP -compatibility functions are exceptions, having the output arguments -last. - - GMP lets you use the same variable for both input and output in one -call. For example, the main function for integer multiplication, -`mpz_mul', can be used to square `x' and put the result back in `x' with - - mpz_mul (x, x, x); - - Before you can assign to a GMP variable, you need to initialize it -by calling one of the special initialization functions. When you're -done with a variable, you need to clear it out, using one of the -functions for that purpose. Which function to use depends on the type -of variable. See the chapters on integer functions, rational number -functions, and floating-point functions for details. - - A variable should only be initialized once, or at least cleared -between each initialization. After a variable has been initialized, it -may be assigned to any number of times. - - For efficiency reasons, avoid excessive initializing and clearing. -In general, initialize near the start of a function and clear near the -end. For example, - - void - foo (void) - { - mpz_t n; - int i; - mpz_init (n); - for (i = 1; i < 100; i++) - { - mpz_mul (n, ...); - mpz_fdiv_q (n, ...); - ... - } - mpz_clear (n); - } - - -File: gmp.info, Node: Parameter Conventions, Next: Memory Management, Prev: Variable Conventions, Up: GMP Basics - -3.5 Parameter Conventions -========================= - -When a GMP variable is used as a function parameter, it's effectively a -call-by-reference, meaning if the function stores a value there it will -change the original in the caller. Parameters which are input-only can -be designated `const' to provoke a compiler error or warning on -attempting to modify them. - - When a function is going to return a GMP result, it should designate -a parameter that it sets, like the library functions do. More than one -value can be returned by having more than one output parameter, again -like the library functions. A `return' of an `mpz_t' etc doesn't -return the object, only a pointer, and this is almost certainly not -what's wanted. - - Here's an example accepting an `mpz_t' parameter, doing a -calculation, and storing the result to the indicated parameter. - - void - foo (mpz_t result, const mpz_t param, unsigned long n) - { - unsigned long i; - mpz_mul_ui (result, param, n); - for (i = 1; i < n; i++) - mpz_add_ui (result, result, i*7); - } - - int - main (void) - { - mpz_t r, n; - mpz_init (r); - mpz_init_set_str (n, "123456", 0); - foo (r, n, 20L); - gmp_printf ("%Zd\n", r); - return 0; - } - - `foo' works even if the mainline passes the same variable for -`param' and `result', just like the library functions. But sometimes -it's tricky to make that work, and an application might not want to -bother supporting that sort of thing. - - For interest, the GMP types `mpz_t' etc are implemented as -one-element arrays of certain structures. This is why declaring a -variable creates an object with the fields GMP needs, but then using it -as a parameter passes a pointer to the object. Note that the actual -fields in each `mpz_t' etc are for internal use only and should not be -accessed directly by code that expects to be compatible with future GMP -releases. - - -File: gmp.info, Node: Memory Management, Next: Reentrancy, Prev: Parameter Conventions, Up: GMP Basics - -3.6 Memory Management -===================== - -The GMP types like `mpz_t' are small, containing only a couple of sizes, -and pointers to allocated data. Once a variable is initialized, GMP -takes care of all space allocation. Additional space is allocated -whenever a variable doesn't have enough. - - `mpz_t' and `mpq_t' variables never reduce their allocated space. -Normally this is the best policy, since it avoids frequent reallocation. -Applications that need to return memory to the heap at some particular -point can use `mpz_realloc2', or clear variables no longer needed. - - `mpf_t' variables, in the current implementation, use a fixed amount -of space, determined by the chosen precision and allocated at -initialization, so their size doesn't change. - - All memory is allocated using `malloc' and friends by default, but -this can be changed, see *Note Custom Allocation::. Temporary memory -on the stack is also used (via `alloca'), but this can be changed at -build-time if desired, see *Note Build Options::. - - -File: gmp.info, Node: Reentrancy, Next: Useful Macros and Constants, Prev: Memory Management, Up: GMP Basics - -3.7 Reentrancy -============== - -GMP is reentrant and thread-safe, with some exceptions: - - * If configured with `--enable-alloca=malloc-notreentrant' (or with - `--enable-alloca=notreentrant' when `alloca' is not available), - then naturally GMP is not reentrant. - - * `mpf_set_default_prec' and `mpf_init' use a global variable for the - selected precision. `mpf_init2' can be used instead, and in the - C++ interface an explicit precision to the `mpf_class' constructor. - - * `mpz_random' and the other old random number functions use a global - random state and are hence not reentrant. The newer random number - functions that accept a `gmp_randstate_t' parameter can be used - instead. - - * `gmp_randinit' (obsolete) returns an error indication through a - global variable, which is not thread safe. Applications are - advised to use `gmp_randinit_default' or `gmp_randinit_lc_2exp' - instead. - - * `mp_set_memory_functions' uses global variables to store the - selected memory allocation functions. - - * If the memory allocation functions set by a call to - `mp_set_memory_functions' (or `malloc' and friends by default) are - not reentrant, then GMP will not be reentrant either. - - * If the standard I/O functions such as `fwrite' are not reentrant - then the GMP I/O functions using them will not be reentrant either. - - * It's safe for two threads to read from the same GMP variable - simultaneously, but it's not safe for one to read while the - another might be writing, nor for two threads to write - simultaneously. It's not safe for two threads to generate a - random number from the same `gmp_randstate_t' simultaneously, - since this involves an update of that variable. - - -File: gmp.info, Node: Useful Macros and Constants, Next: Compatibility with older versions, Prev: Reentrancy, Up: GMP Basics - -3.8 Useful Macros and Constants -=============================== - - -- Global Constant: const int mp_bits_per_limb - The number of bits per limb. - - -- Macro: __GNU_MP_VERSION - -- Macro: __GNU_MP_VERSION_MINOR - -- Macro: __GNU_MP_VERSION_PATCHLEVEL - The major and minor GMP version, and patch level, respectively, as - integers. For GMP i.j, these numbers will be i, j, and 0, - respectively. For GMP i.j.k, these numbers will be i, j, and k, - respectively. - - -- Global Constant: const char * const gmp_version - The GMP version number, as a null-terminated string, in the form - "i.j.k". This release is "5.0.1". Note that the format "i.j" was - used when k was zero was used before version 4.3.0. - - -- Macro: __GMP_CC - -- Macro: __GMP_CFLAGS - The compiler and compiler flags, respectively, used when compiling - GMP, as strings. - - -File: gmp.info, Node: Compatibility with older versions, Next: Demonstration Programs, Prev: Useful Macros and Constants, Up: GMP Basics - -3.9 Compatibility with older versions -===================================== - -This version of GMP is upwardly binary compatible with all 4.x and 3.x -versions, and upwardly compatible at the source level with all 2.x -versions, with the following exceptions. - - * `mpn_gcd' had its source arguments swapped as of GMP 3.0, for - consistency with other `mpn' functions. - - * `mpf_get_prec' counted precision slightly differently in GMP 3.0 - and 3.0.1, but in 3.1 reverted to the 2.x style. - - There are a number of compatibility issues between GMP 1 and GMP 2 -that of course also apply when porting applications from GMP 1 to GMP -4. Please see the GMP 2 manual for details. - - The Berkeley MP compatibility library (*note BSD Compatible -Functions::) is source and binary compatible with the standard `libmp'. - - -File: gmp.info, Node: Demonstration Programs, Next: Efficiency, Prev: Compatibility with older versions, Up: GMP Basics - -3.10 Demonstration programs -=========================== - -The `demos' subdirectory has some sample programs using GMP. These -aren't built or installed, but there's a `Makefile' with rules for them. -For instance, - - make pexpr - ./pexpr 68^975+10 - -The following programs are provided - - * `pexpr' is an expression evaluator, the program used on the GMP - web page. - - * The `calc' subdirectory has a similar but simpler evaluator using - `lex' and `yacc'. - - * The `expr' subdirectory is yet another expression evaluator, a - library designed for ease of use within a C program. See - `demos/expr/README' for more information. - - * `factorize' is a Pollard-Rho factorization program. - - * `isprime' is a command-line interface to the `mpz_probab_prime_p' - function. - - * `primes' counts or lists primes in an interval, using a sieve. - - * `qcn' is an example use of `mpz_kronecker_ui' to estimate quadratic - class numbers. - - * The `perl' subdirectory is a comprehensive perl interface to GMP. - See `demos/perl/INSTALL' for more information. Documentation is - in POD format in `demos/perl/GMP.pm'. - - As an aside, consideration has been given at various times to some -sort of expression evaluation within the main GMP library. Going -beyond something minimal quickly leads to matters like user-defined -functions, looping, fixnums for control variables, etc, which are -considered outside the scope of GMP (much closer to language -interpreters or compilers, *Note Language Bindings::.) Something -simple for program input convenience may yet be a possibility, a -combination of the `expr' demo and the `pexpr' tree back-end perhaps. -But for now the above evaluators are offered as illustrations. - - -File: gmp.info, Node: Efficiency, Next: Debugging, Prev: Demonstration Programs, Up: GMP Basics - -3.11 Efficiency -=============== - -Small Operands - On small operands, the time for function call overheads and memory - allocation can be significant in comparison to actual calculation. - This is unavoidable in a general purpose variable precision - library, although GMP attempts to be as efficient as it can on - both large and small operands. - -Static Linking - On some CPUs, in particular the x86s, the static `libgmp.a' should - be used for maximum speed, since the PIC code in the shared - `libgmp.so' will have a small overhead on each function call and - global data address. For many programs this will be - insignificant, but for long calculations there's a gain to be had. - -Initializing and Clearing - Avoid excessive initializing and clearing of variables, since this - can be quite time consuming, especially in comparison to otherwise - fast operations like addition. - - A language interpreter might want to keep a free list or stack of - initialized variables ready for use. It should be possible to - integrate something like that with a garbage collector too. - -Reallocations - An `mpz_t' or `mpq_t' variable used to hold successively increasing - values will have its memory repeatedly `realloc'ed, which could be - quite slow or could fragment memory, depending on the C library. - If an application can estimate the final size then `mpz_init2' or - `mpz_realloc2' can be called to allocate the necessary space from - the beginning (*note Initializing Integers::). - - It doesn't matter if a size set with `mpz_init2' or `mpz_realloc2' - is too small, since all functions will do a further reallocation - if necessary. Badly overestimating memory required will waste - space though. - -`2exp' Functions - It's up to an application to call functions like `mpz_mul_2exp' - when appropriate. General purpose functions like `mpz_mul' make - no attempt to identify powers of two or other special forms, - because such inputs will usually be very rare and testing every - time would be wasteful. - -`ui' and `si' Functions - The `ui' functions and the small number of `si' functions exist for - convenience and should be used where applicable. But if for - example an `mpz_t' contains a value that fits in an `unsigned - long' there's no need extract it and call a `ui' function, just - use the regular `mpz' function. - -In-Place Operations - `mpz_abs', `mpq_abs', `mpf_abs', `mpz_neg', `mpq_neg' and - `mpf_neg' are fast when used for in-place operations like - `mpz_abs(x,x)', since in the current implementation only a single - field of `x' needs changing. On suitable compilers (GCC for - instance) this is inlined too. - - `mpz_add_ui', `mpz_sub_ui', `mpf_add_ui' and `mpf_sub_ui' benefit - from an in-place operation like `mpz_add_ui(x,x,y)', since usually - only one or two limbs of `x' will need to be changed. The same - applies to the full precision `mpz_add' etc if `y' is small. If - `y' is big then cache locality may be helped, but that's all. - - `mpz_mul' is currently the opposite, a separate destination is - slightly better. A call like `mpz_mul(x,x,y)' will, unless `y' is - only one limb, make a temporary copy of `x' before forming the - result. Normally that copying will only be a tiny fraction of the - time for the multiply, so this is not a particularly important - consideration. - - `mpz_set', `mpq_set', `mpq_set_num', `mpf_set', etc, make no - attempt to recognise a copy of something to itself, so a call like - `mpz_set(x,x)' will be wasteful. Naturally that would never be - written deliberately, but if it might arise from two pointers to - the same object then a test to avoid it might be desirable. - - if (x != y) - mpz_set (x, y); - - Note that it's never worth introducing extra `mpz_set' calls just - to get in-place operations. If a result should go to a particular - variable then just direct it there and let GMP take care of data - movement. - -Divisibility Testing (Small Integers) - `mpz_divisible_ui_p' and `mpz_congruent_ui_p' are the best - functions for testing whether an `mpz_t' is divisible by an - individual small integer. They use an algorithm which is faster - than `mpz_tdiv_ui', but which gives no useful information about - the actual remainder, only whether it's zero (or a particular - value). - - However when testing divisibility by several small integers, it's - best to take a remainder modulo their product, to save - multi-precision operations. For instance to test whether a number - is divisible by any of 23, 29 or 31 take a remainder modulo - 23*29*31 = 20677 and then test that. - - The division functions like `mpz_tdiv_q_ui' which give a quotient - as well as a remainder are generally a little slower than the - remainder-only functions like `mpz_tdiv_ui'. If the quotient is - only rarely wanted then it's probably best to just take a - remainder and then go back and calculate the quotient if and when - it's wanted (`mpz_divexact_ui' can be used if the remainder is - zero). - -Rational Arithmetic - The `mpq' functions operate on `mpq_t' values with no common - factors in the numerator and denominator. Common factors are - checked-for and cast out as necessary. In general, cancelling - factors every time is the best approach since it minimizes the - sizes for subsequent operations. - - However, applications that know something about the factorization - of the values they're working with might be able to avoid some of - the GCDs used for canonicalization, or swap them for divisions. - For example when multiplying by a prime it's enough to check for - factors of it in the denominator instead of doing a full GCD. Or - when forming a big product it might be known that very little - cancellation will be possible, and so canonicalization can be left - to the end. - - The `mpq_numref' and `mpq_denref' macros give access to the - numerator and denominator to do things outside the scope of the - supplied `mpq' functions. *Note Applying Integer Functions::. - - The canonical form for rationals allows mixed-type `mpq_t' and - integer additions or subtractions to be done directly with - multiples of the denominator. This will be somewhat faster than - `mpq_add'. For example, - - /* mpq increment */ - mpz_add (mpq_numref(q), mpq_numref(q), mpq_denref(q)); - - /* mpq += unsigned long */ - mpz_addmul_ui (mpq_numref(q), mpq_denref(q), 123UL); - - /* mpq -= mpz */ - mpz_submul (mpq_numref(q), mpq_denref(q), z); - -Number Sequences - Functions like `mpz_fac_ui', `mpz_fib_ui' and `mpz_bin_uiui' are - designed for calculating isolated values. If a range of values is - wanted it's probably best to call to get a starting point and - iterate from there. - -Text Input/Output - Hexadecimal or octal are suggested for input or output in text - form. Power-of-2 bases like these can be converted much more - efficiently than other bases, like decimal. For big numbers - there's usually nothing of particular interest to be seen in the - digits, so the base doesn't matter much. - - Maybe we can hope octal will one day become the normal base for - everyday use, as proposed by King Charles XII of Sweden and later - reformers. - - -File: gmp.info, Node: Debugging, Next: Profiling, Prev: Efficiency, Up: GMP Basics - -3.12 Debugging -============== - -Stack Overflow - Depending on the system, a segmentation violation or bus error - might be the only indication of stack overflow. See - `--enable-alloca' choices in *Note Build Options::, for how to - address this. - - In new enough versions of GCC, `-fstack-check' may be able to - ensure an overflow is recognised by the system before too much - damage is done, or `-fstack-limit-symbol' or - `-fstack-limit-register' may be able to add checking if the system - itself doesn't do any (*note Options for Code Generation: - (gcc)Code Gen Options.). These options must be added to the - `CFLAGS' used in the GMP build (*note Build Options::), adding - them just to an application will have no effect. Note also - they're a slowdown, adding overhead to each function call and each - stack allocation. - -Heap Problems - The most likely cause of application problems with GMP is heap - corruption. Failing to `init' GMP variables will have - unpredictable effects, and corruption arising elsewhere in a - program may well affect GMP. Initializing GMP variables more than - once or failing to clear them will cause memory leaks. - - In all such cases a `malloc' debugger is recommended. On a GNU or - BSD system the standard C library `malloc' has some diagnostic - facilities, see *Note Allocation Debugging: (libc)Allocation - Debugging, or `man 3 malloc'. Other possibilities, in no - particular order, include - - `http://www.inf.ethz.ch/personal/biere/projects/ccmalloc/' - `http://dmalloc.com/' - `http://www.perens.com/FreeSoftware/' (electric fence) - `http://packages.debian.org/stable/devel/fda' - `http://www.gnupdate.org/components/leakbug/' - `http://people.redhat.com/~otaylor/memprof/' - `http://www.cbmamiga.demon.co.uk/mpatrol/' - - The GMP default allocation routines in `memory.c' also have a - simple sentinel scheme which can be enabled with `#define DEBUG' - in that file. This is mainly designed for detecting buffer - overruns during GMP development, but might find other uses. - -Stack Backtraces - On some systems the compiler options GMP uses by default can - interfere with debugging. In particular on x86 and 68k systems - `-fomit-frame-pointer' is used and this generally inhibits stack - backtracing. Recompiling without such options may help while - debugging, though the usual caveats about it potentially moving a - memory problem or hiding a compiler bug will apply. - -GDB, the GNU Debugger - A sample `.gdbinit' is included in the distribution, showing how - to call some undocumented dump functions to print GMP variables - from within GDB. Note that these functions shouldn't be used in - final application code since they're undocumented and may be - subject to incompatible changes in future versions of GMP. - -Source File Paths - GMP has multiple source files with the same name, in different - directories. For example `mpz', `mpq' and `mpf' each have an - `init.c'. If the debugger can't already determine the right one - it may help to build with absolute paths on each C file. One way - to do that is to use a separate object directory with an absolute - path to the source directory. - - cd /my/build/dir - /my/source/dir/gmp-5.0.1/configure - - This works via `VPATH', and might require GNU `make'. Alternately - it might be possible to change the `.c.lo' rules appropriately. - -Assertion Checking - The build option `--enable-assert' is available to add some - consistency checks to the library (see *Note Build Options::). - These are likely to be of limited value to most applications. - Assertion failures are just as likely to indicate memory - corruption as a library or compiler bug. - - Applications using the low-level `mpn' functions, however, will - benefit from `--enable-assert' since it adds checks on the - parameters of most such functions, many of which have subtle - restrictions on their usage. Note however that only the generic C - code has checks, not the assembly code, so CPU `none' should be - used for maximum checking. - -Temporary Memory Checking - The build option `--enable-alloca=debug' arranges that each block - of temporary memory in GMP is allocated with a separate call to - `malloc' (or the allocation function set with - `mp_set_memory_functions'). - - This can help a malloc debugger detect accesses outside the - intended bounds, or detect memory not released. In a normal - build, on the other hand, temporary memory is allocated in blocks - which GMP divides up for its own use, or may be allocated with a - compiler builtin `alloca' which will go nowhere near any malloc - debugger hooks. - -Maximum Debuggability - To summarize the above, a GMP build for maximum debuggability - would be - - ./configure --disable-shared --enable-assert \ - --enable-alloca=debug --host=none CFLAGS=-g - - For C++, add `--enable-cxx CXXFLAGS=-g'. - -Checker - The GCC checker (`http://savannah.nongnu.org/projects/checker/') - can be used with GMP. It contains a stub library which means GMP - applications compiled with checker can use a normal GMP build. - - A build of GMP with checking within GMP itself can be made. This - will run very very slowly. On GNU/Linux for example, - - ./configure --host=none-pc-linux-gnu CC=checkergcc - - `--host=none' must be used, since the GMP assembly code doesn't - support the checking scheme. The GMP C++ features cannot be used, - since current versions of checker (0.9.9.1) don't yet support the - standard C++ library. - -Valgrind - The valgrind program (`http://valgrind.org/') is a memory checker - for x86s. It translates and emulates machine instructions to do - strong checks for uninitialized data (at the level of individual - bits), memory accesses through bad pointers, and memory leaks. - - Recent versions of Valgrind are getting support for MMX and - SSE/SSE2 instructions, for past versions GMP will need to be - configured not to use those, ie. for an x86 without them (for - instance plain `i486'). - -Other Problems - Any suspected bug in GMP itself should be isolated to make sure - it's not an application problem, see *Note Reporting Bugs::. - - -File: gmp.info, Node: Profiling, Next: Autoconf, Prev: Debugging, Up: GMP Basics - -3.13 Profiling -============== - -Running a program under a profiler is a good way to find where it's -spending most time and where improvements can be best sought. The -profiling choices for a GMP build are as follows. - -`--disable-profiling' - The default is to add nothing special for profiling. - - It should be possible to just compile the mainline of a program - with `-p' and use `prof' to get a profile consisting of - timer-based sampling of the program counter. Most of the GMP - assembly code has the necessary symbol information. - - This approach has the advantage of minimizing interference with - normal program operation, but on most systems the resolution of - the sampling is quite low (10 milliseconds for instance), - requiring long runs to get accurate information. - -`--enable-profiling=prof' - Build with support for the system `prof', which means `-p' added - to the `CFLAGS'. - - This provides call counting in addition to program counter - sampling, which allows the most frequently called routines to be - identified, and an average time spent in each routine to be - determined. - - The x86 assembly code has support for this option, but on other - processors the assembly routines will be as if compiled without - `-p' and therefore won't appear in the call counts. - - On some systems, such as GNU/Linux, `-p' in fact means `-pg' and in - this case `--enable-profiling=gprof' described below should be used - instead. - -`--enable-profiling=gprof' - Build with support for `gprof', which means `-pg' added to the - `CFLAGS'. - - This provides call graph construction in addition to call counting - and program counter sampling, which makes it possible to count - calls coming from different locations. For example the number of - calls to `mpn_mul' from `mpz_mul' versus the number from - `mpf_mul'. The program counter sampling is still flat though, so - only a total time in `mpn_mul' would be accumulated, not a - separate amount for each call site. - - The x86 assembly code has support for this option, but on other - processors the assembly routines will be as if compiled without - `-pg' and therefore not be included in the call counts. - - On x86 and m68k systems `-pg' and `-fomit-frame-pointer' are - incompatible, so the latter is omitted from the default flags in - that case, which might result in poorer code generation. - - Incidentally, it should be possible to use the `gprof' program - with a plain `--enable-profiling=prof' build. But in that case - only the `gprof -p' flat profile and call counts can be expected - to be valid, not the `gprof -q' call graph. - -`--enable-profiling=instrument' - Build with the GCC option `-finstrument-functions' added to the - `CFLAGS' (*note Options for Code Generation: (gcc)Code Gen - Options.). - - This inserts special instrumenting calls at the start and end of - each function, allowing exact timing and full call graph - construction. - - This instrumenting is not normally a standard system feature and - will require support from an external library, such as - - `http://sourceforge.net/projects/fnccheck/' - - This should be included in `LIBS' during the GMP configure so that - test programs will link. For example, - - ./configure --enable-profiling=instrument LIBS=-lfc - - On a GNU system the C library provides dummy instrumenting - functions, so programs compiled with this option will link. In - this case it's only necessary to ensure the correct library is - added when linking an application. - - The x86 assembly code supports this option, but on other - processors the assembly routines will be as if compiled without - `-finstrument-functions' meaning time spent in them will - effectively be attributed to their caller. - - -File: gmp.info, Node: Autoconf, Next: Emacs, Prev: Profiling, Up: GMP Basics - -3.14 Autoconf -============= - -Autoconf based applications can easily check whether GMP is installed. -The only thing to be noted is that GMP library symbols from version 3 -onwards have prefixes like `__gmpz'. The following therefore would be -a simple test, - - AC_CHECK_LIB(gmp, __gmpz_init) - - This just uses the default `AC_CHECK_LIB' actions for found or not -found, but an application that must have GMP would want to generate an -error if not found. For example, - - AC_CHECK_LIB(gmp, __gmpz_init, , - [AC_MSG_ERROR([GNU MP not found, see http://gmplib.org/])]) - - If functions added in some particular version of GMP are required, -then one of those can be used when checking. For example `mpz_mul_si' -was added in GMP 3.1, - - AC_CHECK_LIB(gmp, __gmpz_mul_si, , - [AC_MSG_ERROR( - [GNU MP not found, or not 3.1 or up, see http://gmplib.org/])]) - - An alternative would be to test the version number in `gmp.h' using -say `AC_EGREP_CPP'. That would make it possible to test the exact -version, if some particular sub-minor release is known to be necessary. - - In general it's recommended that applications should simply demand a -new enough GMP rather than trying to provide supplements for features -not available in past versions. - - Occasionally an application will need or want to know the size of a -type at configuration or preprocessing time, not just with `sizeof' in -the code. This can be done in the normal way with `mp_limb_t' etc, but -GMP 4.0 or up is best for this, since prior versions needed certain -`-D' defines on systems using a `long long' limb. The following would -suit Autoconf 2.50 or up, - - AC_CHECK_SIZEOF(mp_limb_t, , [#include ]) - - -File: gmp.info, Node: Emacs, Prev: Autoconf, Up: GMP Basics - -3.15 Emacs -========== - - (`info-lookup-symbol') is a good way to find documentation on -C functions while editing (*note Info Documentation Lookup: (emacs)Info -Lookup.). - - The GMP manual can be included in such lookups by putting the -following in your `.emacs', - - (eval-after-load "info-look" - '(let ((mode-value (assoc 'c-mode (assoc 'symbol info-lookup-alist)))) - (setcar (nthcdr 3 mode-value) - (cons '("(gmp)Function Index" nil "^ -.* " "\\>") - (nth 3 mode-value))))) - - -File: gmp.info, Node: Reporting Bugs, Next: Integer Functions, Prev: GMP Basics, Up: Top - -4 Reporting Bugs -**************** - -If you think you have found a bug in the GMP library, please -investigate it and report it. We have made this library available to -you, and it is not too much to ask you to report the bugs you find. - - Before you report a bug, check it's not already addressed in *Note -Known Build Problems::, or perhaps *Note Notes for Particular -Systems::. You may also want to check `http://gmplib.org/' for patches -for this release. - - Please include the following in any report, - - * The GMP version number, and if pre-packaged or patched then say so. - - * A test program that makes it possible for us to reproduce the bug. - Include instructions on how to run the program. - - * A description of what is wrong. If the results are incorrect, in - what way. If you get a crash, say so. - - * If you get a crash, include a stack backtrace from the debugger if - it's informative (`where' in `gdb', or `$C' in `adb'). - - * Please do not send core dumps, executables or `strace's. - - * The configuration options you used when building GMP, if any. - - * The name of the compiler and its version. For `gcc', get the - version with `gcc -v', otherwise perhaps `what `which cc`', or - similar. - - * The output from running `uname -a'. - - * The output from running `./config.guess', and from running - `./configfsf.guess' (might be the same). - - * If the bug is related to `configure', then the compressed contents - of `config.log'. - - * If the bug is related to an `asm' file not assembling, then the - contents of `config.m4' and the offending line or lines from the - temporary `mpn/tmp-.s'. - - Please make an effort to produce a self-contained report, with -something definite that can be tested or debugged. Vague queries or -piecemeal messages are difficult to act on and don't help the -development effort. - - It is not uncommon that an observed problem is actually due to a bug -in the compiler; the GMP code tends to explore interesting corners in -compilers. - - If your bug report is good, we will do our best to help you get a -corrected version of the library; if the bug report is poor, we won't -do anything about it (except maybe ask you to send a better report). - - Send your report to: . - - If you think something in this manual is unclear, or downright -incorrect, or if the language needs to be improved, please send a note -to the same address. - - -File: gmp.info, Node: Integer Functions, Next: Rational Number Functions, Prev: Reporting Bugs, Up: Top - -5 Integer Functions -******************* - -This chapter describes the GMP functions for performing integer -arithmetic. These functions start with the prefix `mpz_'. - - GMP integers are stored in objects of type `mpz_t'. - -* Menu: - -* Initializing Integers:: -* Assigning Integers:: -* Simultaneous Integer Init & Assign:: -* Converting Integers:: -* Integer Arithmetic:: -* Integer Division:: -* Integer Exponentiation:: -* Integer Roots:: -* Number Theoretic Functions:: -* Integer Comparisons:: -* Integer Logic and Bit Fiddling:: -* I/O of Integers:: -* Integer Random Numbers:: -* Integer Import and Export:: -* Miscellaneous Integer Functions:: -* Integer Special Functions:: - - -File: gmp.info, Node: Initializing Integers, Next: Assigning Integers, Prev: Integer Functions, Up: Integer Functions - -5.1 Initialization Functions -============================ - -The functions for integer arithmetic assume that all integer objects are -initialized. You do that by calling the function `mpz_init'. For -example, - - { - mpz_t integ; - mpz_init (integ); - ... - mpz_add (integ, ...); - ... - mpz_sub (integ, ...); - - /* Unless the program is about to exit, do ... */ - mpz_clear (integ); - } - - As you can see, you can store new values any number of times, once an -object is initialized. - - -- Function: void mpz_init (mpz_t X) - Initialize X, and set its value to 0. - - -- Function: void mpz_inits (mpz_t X, ...) - Initialize a NULL-terminated list of `mpz_t' variables, and set - their values to 0. - - -- Function: void mpz_init2 (mpz_t X, mp_bitcnt_t N) - Initialize X, with space for N-bit numbers, and set its value to 0. - Calling this function instead of `mpz_init' or `mpz_inits' is never - necessary; reallocation is handled automatically by GMP when - needed. - - N is only the initial space, X will grow automatically in the - normal way, if necessary, for subsequent values stored. - `mpz_init2' makes it possible to avoid such reallocations if a - maximum size is known in advance. - - -- Function: void mpz_clear (mpz_t X) - Free the space occupied by X. Call this function for all `mpz_t' - variables when you are done with them. - - -- Function: void mpz_clears (mpz_t X, ...) - Free the space occupied by a NULL-terminated list of `mpz_t' - variables. - - -- Function: void mpz_realloc2 (mpz_t X, mp_bitcnt_t N) - Change the space allocated for X to N bits. The value in X is - preserved if it fits, or is set to 0 if not. - - Calling this function is never necessary; reallocation is handled - automatically by GMP when needed. But this function can be used - to increase the space for a variable in order to avoid repeated - automatic reallocations, or to decrease it to give memory back to - the heap. - - -File: gmp.info, Node: Assigning Integers, Next: Simultaneous Integer Init & Assign, Prev: Initializing Integers, Up: Integer Functions - -5.2 Assignment Functions -======================== - -These functions assign new values to already initialized integers -(*note Initializing Integers::). - - -- Function: void mpz_set (mpz_t ROP, mpz_t OP) - -- Function: void mpz_set_ui (mpz_t ROP, unsigned long int OP) - -- Function: void mpz_set_si (mpz_t ROP, signed long int OP) - -- Function: void mpz_set_d (mpz_t ROP, double OP) - -- Function: void mpz_set_q (mpz_t ROP, mpq_t OP) - -- Function: void mpz_set_f (mpz_t ROP, mpf_t OP) - Set the value of ROP from OP. - - `mpz_set_d', `mpz_set_q' and `mpz_set_f' truncate OP to make it an - integer. - - -- Function: int mpz_set_str (mpz_t ROP, char *STR, int BASE) - Set the value of ROP from STR, a null-terminated C string in base - BASE. White space is allowed in the string, and is simply ignored. - - The BASE may vary from 2 to 62, or if BASE is 0, then the leading - characters are used: `0x' and `0X' for hexadecimal, `0b' and `0B' - for binary, `0' for octal, or decimal otherwise. - - For bases up to 36, case is ignored; upper-case and lower-case - letters have the same value. For bases 37 to 62, upper-case - letter represent the usual 10..35 while lower-case letter - represent 36..61. - - This function returns 0 if the entire string is a valid number in - base BASE. Otherwise it returns -1. - - -- Function: void mpz_swap (mpz_t ROP1, mpz_t ROP2) - Swap the values ROP1 and ROP2 efficiently. - - -File: gmp.info, Node: Simultaneous Integer Init & Assign, Next: Converting Integers, Prev: Assigning Integers, Up: Integer Functions - -5.3 Combined Initialization and Assignment Functions -==================================================== - -For convenience, GMP provides a parallel series of initialize-and-set -functions which initialize the output and then store the value there. -These functions' names have the form `mpz_init_set...' - - Here is an example of using one: - - { - mpz_t pie; - mpz_init_set_str (pie, "3141592653589793238462643383279502884", 10); - ... - mpz_sub (pie, ...); - ... - mpz_clear (pie); - } - -Once the integer has been initialized by any of the `mpz_init_set...' -functions, it can be used as the source or destination operand for the -ordinary integer functions. Don't use an initialize-and-set function -on a variable already initialized! - - -- Function: void mpz_init_set (mpz_t ROP, mpz_t OP) - -- Function: void mpz_init_set_ui (mpz_t ROP, unsigned long int OP) - -- Function: void mpz_init_set_si (mpz_t ROP, signed long int OP) - -- Function: void mpz_init_set_d (mpz_t ROP, double OP) - Initialize ROP with limb space and set the initial numeric value - from OP. - - -- Function: int mpz_init_set_str (mpz_t ROP, char *STR, int BASE) - Initialize ROP and set its value like `mpz_set_str' (see its - documentation above for details). - - If the string is a correct base BASE number, the function returns - 0; if an error occurs it returns -1. ROP is initialized even if - an error occurs. (I.e., you have to call `mpz_clear' for it.) - - -File: gmp.info, Node: Converting Integers, Next: Integer Arithmetic, Prev: Simultaneous Integer Init & Assign, Up: Integer Functions - -5.4 Conversion Functions -======================== - -This section describes functions for converting GMP integers to -standard C types. Functions for converting _to_ GMP integers are -described in *Note Assigning Integers:: and *Note I/O of Integers::. - - -- Function: unsigned long int mpz_get_ui (mpz_t OP) - Return the value of OP as an `unsigned long'. - - If OP is too big to fit an `unsigned long' then just the least - significant bits that do fit are returned. The sign of OP is - ignored, only the absolute value is used. - - -- Function: signed long int mpz_get_si (mpz_t OP) - If OP fits into a `signed long int' return the value of OP. - Otherwise return the least significant part of OP, with the same - sign as OP. - - If OP is too big to fit in a `signed long int', the returned - result is probably not very useful. To find out if the value will - fit, use the function `mpz_fits_slong_p'. - - -- Function: double mpz_get_d (mpz_t OP) - Convert OP to a `double', truncating if necessary (ie. rounding - towards zero). - - If the exponent from the conversion is too big, the result is - system dependent. An infinity is returned where available. A - hardware overflow trap may or may not occur. - - -- Function: double mpz_get_d_2exp (signed long int *EXP, mpz_t OP) - Convert OP to a `double', truncating if necessary (ie. rounding - towards zero), and returning the exponent separately. - - The return value is in the range 0.5<=abs(D)<1 and the exponent is - stored to `*EXP'. D * 2^EXP is the (truncated) OP value. If OP - is zero, the return is 0.0 and 0 is stored to `*EXP'. - - This is similar to the standard C `frexp' function (*note - Normalization Functions: (libc)Normalization Functions.). - - -- Function: char * mpz_get_str (char *STR, int BASE, mpz_t OP) - Convert OP to a string of digits in base BASE. The base argument - may vary from 2 to 62 or from -2 to -36. - - For BASE in the range 2..36, digits and lower-case letters are - used; for -2..-36, digits and upper-case letters are used; for - 37..62, digits, upper-case letters, and lower-case letters (in - that significance order) are used. - - If STR is `NULL', the result string is allocated using the current - allocation function (*note Custom Allocation::). The block will be - `strlen(str)+1' bytes, that being exactly enough for the string and - null-terminator. - - If STR is not `NULL', it should point to a block of storage large - enough for the result, that being `mpz_sizeinbase (OP, BASE) + 2'. - The two extra bytes are for a possible minus sign, and the - null-terminator. - - A pointer to the result string is returned, being either the - allocated block, or the given STR. - - -File: gmp.info, Node: Integer Arithmetic, Next: Integer Division, Prev: Converting Integers, Up: Integer Functions - -5.5 Arithmetic Functions -======================== - - -- Function: void mpz_add (mpz_t ROP, mpz_t OP1, mpz_t OP2) - -- Function: void mpz_add_ui (mpz_t ROP, mpz_t OP1, unsigned long int - OP2) - Set ROP to OP1 + OP2. - - -- Function: void mpz_sub (mpz_t ROP, mpz_t OP1, mpz_t OP2) - -- Function: void mpz_sub_ui (mpz_t ROP, mpz_t OP1, unsigned long int - OP2) - -- Function: void mpz_ui_sub (mpz_t ROP, unsigned long int OP1, mpz_t - OP2) - Set ROP to OP1 - OP2. - - -- Function: void mpz_mul (mpz_t ROP, mpz_t OP1, mpz_t OP2) - -- Function: void mpz_mul_si (mpz_t ROP, mpz_t OP1, long int OP2) - -- Function: void mpz_mul_ui (mpz_t ROP, mpz_t OP1, unsigned long int - OP2) - Set ROP to OP1 times OP2. - - -- Function: void mpz_addmul (mpz_t ROP, mpz_t OP1, mpz_t OP2) - -- Function: void mpz_addmul_ui (mpz_t ROP, mpz_t OP1, unsigned long - int OP2) - Set ROP to ROP + OP1 times OP2. - - -- Function: void mpz_submul (mpz_t ROP, mpz_t OP1, mpz_t OP2) - -- Function: void mpz_submul_ui (mpz_t ROP, mpz_t OP1, unsigned long - int OP2) - Set ROP to ROP - OP1 times OP2. - - -- Function: void mpz_mul_2exp (mpz_t ROP, mpz_t OP1, mp_bitcnt_t OP2) - Set ROP to OP1 times 2 raised to OP2. This operation can also be - defined as a left shift by OP2 bits. - - -- Function: void mpz_neg (mpz_t ROP, mpz_t OP) - Set ROP to -OP. - - -- Function: void mpz_abs (mpz_t ROP, mpz_t OP) - Set ROP to the absolute value of OP. - - -File: gmp.info, Node: Integer Division, Next: Integer Exponentiation, Prev: Integer Arithmetic, Up: Integer Functions - -5.6 Division Functions -====================== - -Division is undefined if the divisor is zero. Passing a zero divisor -to the division or modulo functions (including the modular powering -functions `mpz_powm' and `mpz_powm_ui'), will cause an intentional -division by zero. This lets a program handle arithmetic exceptions in -these functions the same way as for normal C `int' arithmetic. - - -- Function: void mpz_cdiv_q (mpz_t Q, mpz_t N, mpz_t D) - -- Function: void mpz_cdiv_r (mpz_t R, mpz_t N, mpz_t D) - -- Function: void mpz_cdiv_qr (mpz_t Q, mpz_t R, mpz_t N, mpz_t D) - -- Function: unsigned long int mpz_cdiv_q_ui (mpz_t Q, mpz_t N, - unsigned long int D) - -- Function: unsigned long int mpz_cdiv_r_ui (mpz_t R, mpz_t N, - unsigned long int D) - -- Function: unsigned long int mpz_cdiv_qr_ui (mpz_t Q, mpz_t R, - mpz_t N, unsigned long int D) - -- Function: unsigned long int mpz_cdiv_ui (mpz_t N, - unsigned long int D) - -- Function: void mpz_cdiv_q_2exp (mpz_t Q, mpz_t N, mp_bitcnt_t B) - -- Function: void mpz_cdiv_r_2exp (mpz_t R, mpz_t N, mp_bitcnt_t B) - - -- Function: void mpz_fdiv_q (mpz_t Q, mpz_t N, mpz_t D) - -- Function: void mpz_fdiv_r (mpz_t R, mpz_t N, mpz_t D) - -- Function: void mpz_fdiv_qr (mpz_t Q, mpz_t R, mpz_t N, mpz_t D) - -- Function: unsigned long int mpz_fdiv_q_ui (mpz_t Q, mpz_t N, - unsigned long int D) - -- Function: unsigned long int mpz_fdiv_r_ui (mpz_t R, mpz_t N, - unsigned long int D) - -- Function: unsigned long int mpz_fdiv_qr_ui (mpz_t Q, mpz_t R, - mpz_t N, unsigned long int D) - -- Function: unsigned long int mpz_fdiv_ui (mpz_t N, - unsigned long int D) - -- Function: void mpz_fdiv_q_2exp (mpz_t Q, mpz_t N, mp_bitcnt_t B) - -- Function: void mpz_fdiv_r_2exp (mpz_t R, mpz_t N, mp_bitcnt_t B) - - -- Function: void mpz_tdiv_q (mpz_t Q, mpz_t N, mpz_t D) - -- Function: void mpz_tdiv_r (mpz_t R, mpz_t N, mpz_t D) - -- Function: void mpz_tdiv_qr (mpz_t Q, mpz_t R, mpz_t N, mpz_t D) - -- Function: unsigned long int mpz_tdiv_q_ui (mpz_t Q, mpz_t N, - unsigned long int D) - -- Function: unsigned long int mpz_tdiv_r_ui (mpz_t R, mpz_t N, - unsigned long int D) - -- Function: unsigned long int mpz_tdiv_qr_ui (mpz_t Q, mpz_t R, - mpz_t N, unsigned long int D) - -- Function: unsigned long int mpz_tdiv_ui (mpz_t N, - unsigned long int D) - -- Function: void mpz_tdiv_q_2exp (mpz_t Q, mpz_t N, mp_bitcnt_t B) - -- Function: void mpz_tdiv_r_2exp (mpz_t R, mpz_t N, mp_bitcnt_t B) - - Divide N by D, forming a quotient Q and/or remainder R. For the - `2exp' functions, D=2^B. The rounding is in three styles, each - suiting different applications. - - * `cdiv' rounds Q up towards +infinity, and R will have the - opposite sign to D. The `c' stands for "ceil". - - * `fdiv' rounds Q down towards -infinity, and R will have the - same sign as D. The `f' stands for "floor". - - * `tdiv' rounds Q towards zero, and R will have the same sign - as N. The `t' stands for "truncate". - - In all cases Q and R will satisfy N=Q*D+R, and R will satisfy - 0<=abs(R) 0 and that MOD is odd. - - This function is designed to take the same time and have the same - cache access patterns for any two same-size arguments, assuming - that function arguments are placed at the same position and that - the machine state is identical upon function entry. This function - is intended for cryptographic purposes, where resilience to - side-channel attacks is desired. - - -- Function: void mpz_pow_ui (mpz_t ROP, mpz_t BASE, unsigned long int - EXP) - -- Function: void mpz_ui_pow_ui (mpz_t ROP, unsigned long int BASE, - unsigned long int EXP) - Set ROP to BASE raised to EXP. The case 0^0 yields 1. - - -File: gmp.info, Node: Integer Roots, Next: Number Theoretic Functions, Prev: Integer Exponentiation, Up: Integer Functions - -5.8 Root Extraction Functions -============================= - - -- Function: int mpz_root (mpz_t ROP, mpz_t OP, unsigned long int N) - Set ROP to the truncated integer part of the Nth root of OP. - Return non-zero if the computation was exact, i.e., if OP is ROP - to the Nth power. - - -- Function: void mpz_rootrem (mpz_t ROOT, mpz_t REM, mpz_t U, - unsigned long int N) - Set ROOT to the truncated integer part of the Nth root of U. Set - REM to the remainder, U-ROOT**N. - - -- Function: void mpz_sqrt (mpz_t ROP, mpz_t OP) - Set ROP to the truncated integer part of the square root of OP. - - -- Function: void mpz_sqrtrem (mpz_t ROP1, mpz_t ROP2, mpz_t OP) - Set ROP1 to the truncated integer part of the square root of OP, - like `mpz_sqrt'. Set ROP2 to the remainder OP-ROP1*ROP1, which - will be zero if OP is a perfect square. - - If ROP1 and ROP2 are the same variable, the results are undefined. - - -- Function: int mpz_perfect_power_p (mpz_t OP) - Return non-zero if OP is a perfect power, i.e., if there exist - integers A and B, with B>1, such that OP equals A raised to the - power B. - - Under this definition both 0 and 1 are considered to be perfect - powers. Negative values of OP are accepted, but of course can - only be odd perfect powers. - - -- Function: int mpz_perfect_square_p (mpz_t OP) - Return non-zero if OP is a perfect square, i.e., if the square - root of OP is an integer. Under this definition both 0 and 1 are - considered to be perfect squares. - - -File: gmp.info, Node: Number Theoretic Functions, Next: Integer Comparisons, Prev: Integer Roots, Up: Integer Functions - -5.9 Number Theoretic Functions -============================== - - -- Function: int mpz_probab_prime_p (mpz_t N, int REPS) - Determine whether N is prime. Return 2 if N is definitely prime, - return 1 if N is probably prime (without being certain), or return - 0 if N is definitely composite. - - This function does some trial divisions, then some Miller-Rabin - probabilistic primality tests. REPS controls how many such tests - are done, 5 to 10 is a reasonable number, more will reduce the - chances of a composite being returned as "probably prime". - - Miller-Rabin and similar tests can be more properly called - compositeness tests. Numbers which fail are known to be composite - but those which pass might be prime or might be composite. Only a - few composites pass, hence those which pass are considered - probably prime. - - -- Function: void mpz_nextprime (mpz_t ROP, mpz_t OP) - Set ROP to the next prime greater than OP. - - This function uses a probabilistic algorithm to identify primes. - For practical purposes it's adequate, the chance of a composite - passing will be extremely small. - - -- Function: void mpz_gcd (mpz_t ROP, mpz_t OP1, mpz_t OP2) - Set ROP to the greatest common divisor of OP1 and OP2. The result - is always positive even if one or both input operands are negative. - - -- Function: unsigned long int mpz_gcd_ui (mpz_t ROP, mpz_t OP1, - unsigned long int OP2) - Compute the greatest common divisor of OP1 and OP2. If ROP is not - `NULL', store the result there. - - If the result is small enough to fit in an `unsigned long int', it - is returned. If the result does not fit, 0 is returned, and the - result is equal to the argument OP1. Note that the result will - always fit if OP2 is non-zero. - - -- Function: void mpz_gcdext (mpz_t G, mpz_t S, mpz_t T, mpz_t A, - mpz_t B) - Set G to the greatest common divisor of A and B, and in addition - set S and T to coefficients satisfying A*S + B*T = G. The value - in G is always positive, even if one or both of A and B are - negative. The values in S and T are chosen such that abs(S) <= - abs(B) and abs(T) <= abs(A). - - If T is `NULL' then that value is not computed. - - -- Function: void mpz_lcm (mpz_t ROP, mpz_t OP1, mpz_t OP2) - -- Function: void mpz_lcm_ui (mpz_t ROP, mpz_t OP1, unsigned long OP2) - Set ROP to the least common multiple of OP1 and OP2. ROP is - always positive, irrespective of the signs of OP1 and OP2. ROP - will be zero if either OP1 or OP2 is zero. - - -- Function: int mpz_invert (mpz_t ROP, mpz_t OP1, mpz_t OP2) - Compute the inverse of OP1 modulo OP2 and put the result in ROP. - If the inverse exists, the return value is non-zero and ROP will - satisfy 0 <= ROP < OP2. If an inverse doesn't exist the return - value is zero and ROP is undefined. - - -- Function: int mpz_jacobi (mpz_t A, mpz_t B) - Calculate the Jacobi symbol (A/B). This is defined only for B odd. - - -- Function: int mpz_legendre (mpz_t A, mpz_t P) - Calculate the Legendre symbol (A/P). This is defined only for P - an odd positive prime, and for such P it's identical to the Jacobi - symbol. - - -- Function: int mpz_kronecker (mpz_t A, mpz_t B) - -- Function: int mpz_kronecker_si (mpz_t A, long B) - -- Function: int mpz_kronecker_ui (mpz_t A, unsigned long B) - -- Function: int mpz_si_kronecker (long A, mpz_t B) - -- Function: int mpz_ui_kronecker (unsigned long A, mpz_t B) - Calculate the Jacobi symbol (A/B) with the Kronecker extension - (a/2)=(2/a) when a odd, or (a/2)=0 when a even. - - When B is odd the Jacobi symbol and Kronecker symbol are - identical, so `mpz_kronecker_ui' etc can be used for mixed - precision Jacobi symbols too. - - For more information see Henri Cohen section 1.4.2 (*note - References::), or any number theory textbook. See also the - example program `demos/qcn.c' which uses `mpz_kronecker_ui'. - - -- Function: mp_bitcnt_t mpz_remove (mpz_t ROP, mpz_t OP, mpz_t F) - Remove all occurrences of the factor F from OP and store the - result in ROP. The return value is how many such occurrences were - removed. - - -- Function: void mpz_fac_ui (mpz_t ROP, unsigned long int OP) - Set ROP to OP!, the factorial of OP. - - -- Function: void mpz_bin_ui (mpz_t ROP, mpz_t N, unsigned long int K) - -- Function: void mpz_bin_uiui (mpz_t ROP, unsigned long int N, - unsigned long int K) - Compute the binomial coefficient N over K and store the result in - ROP. Negative values of N are supported by `mpz_bin_ui', using - the identity bin(-n,k) = (-1)^k * bin(n+k-1,k), see Knuth volume 1 - section 1.2.6 part G. - - -- Function: void mpz_fib_ui (mpz_t FN, unsigned long int N) - -- Function: void mpz_fib2_ui (mpz_t FN, mpz_t FNSUB1, unsigned long - int N) - `mpz_fib_ui' sets FN to to F[n], the N'th Fibonacci number. - `mpz_fib2_ui' sets FN to F[n], and FNSUB1 to F[n-1]. - - These functions are designed for calculating isolated Fibonacci - numbers. When a sequence of values is wanted it's best to start - with `mpz_fib2_ui' and iterate the defining F[n+1]=F[n]+F[n-1] or - similar. - - -- Function: void mpz_lucnum_ui (mpz_t LN, unsigned long int N) - -- Function: void mpz_lucnum2_ui (mpz_t LN, mpz_t LNSUB1, unsigned - long int N) - `mpz_lucnum_ui' sets LN to to L[n], the N'th Lucas number. - `mpz_lucnum2_ui' sets LN to L[n], and LNSUB1 to L[n-1]. - - These functions are designed for calculating isolated Lucas - numbers. When a sequence of values is wanted it's best to start - with `mpz_lucnum2_ui' and iterate the defining L[n+1]=L[n]+L[n-1] - or similar. - - The Fibonacci numbers and Lucas numbers are related sequences, so - it's never necessary to call both `mpz_fib2_ui' and - `mpz_lucnum2_ui'. The formulas for going from Fibonacci to Lucas - can be found in *Note Lucas Numbers Algorithm::, the reverse is - straightforward too. - - -File: gmp.info, Node: Integer Comparisons, Next: Integer Logic and Bit Fiddling, Prev: Number Theoretic Functions, Up: Integer Functions - -5.10 Comparison Functions -========================= - - -- Function: int mpz_cmp (mpz_t OP1, mpz_t OP2) - -- Function: int mpz_cmp_d (mpz_t OP1, double OP2) - -- Macro: int mpz_cmp_si (mpz_t OP1, signed long int OP2) - -- Macro: int mpz_cmp_ui (mpz_t OP1, unsigned long int OP2) - Compare OP1 and OP2. Return a positive value if OP1 > OP2, zero - if OP1 = OP2, or a negative value if OP1 < OP2. - - `mpz_cmp_ui' and `mpz_cmp_si' are macros and will evaluate their - arguments more than once. `mpz_cmp_d' can be called with an - infinity, but results are undefined for a NaN. - - -- Function: int mpz_cmpabs (mpz_t OP1, mpz_t OP2) - -- Function: int mpz_cmpabs_d (mpz_t OP1, double OP2) - -- Function: int mpz_cmpabs_ui (mpz_t OP1, unsigned long int OP2) - Compare the absolute values of OP1 and OP2. Return a positive - value if abs(OP1) > abs(OP2), zero if abs(OP1) = abs(OP2), or a - negative value if abs(OP1) < abs(OP2). - - `mpz_cmpabs_d' can be called with an infinity, but results are - undefined for a NaN. - - -- Macro: int mpz_sgn (mpz_t OP) - Return +1 if OP > 0, 0 if OP = 0, and -1 if OP < 0. - - This function is actually implemented as a macro. It evaluates - its argument multiple times. - - -File: gmp.info, Node: Integer Logic and Bit Fiddling, Next: I/O of Integers, Prev: Integer Comparisons, Up: Integer Functions - -5.11 Logical and Bit Manipulation Functions -=========================================== - -These functions behave as if twos complement arithmetic were used -(although sign-magnitude is the actual implementation). The least -significant bit is number 0. - - -- Function: void mpz_and (mpz_t ROP, mpz_t OP1, mpz_t OP2) - Set ROP to OP1 bitwise-and OP2. - - -- Function: void mpz_ior (mpz_t ROP, mpz_t OP1, mpz_t OP2) - Set ROP to OP1 bitwise inclusive-or OP2. - - -- Function: void mpz_xor (mpz_t ROP, mpz_t OP1, mpz_t OP2) - Set ROP to OP1 bitwise exclusive-or OP2. - - -- Function: void mpz_com (mpz_t ROP, mpz_t OP) - Set ROP to the one's complement of OP. - - -- Function: mp_bitcnt_t mpz_popcount (mpz_t OP) - If OP>=0, return the population count of OP, which is the number - of 1 bits in the binary representation. If OP<0, the number of 1s - is infinite, and the return value is the largest possible - `mp_bitcnt_t'. - - -- Function: mp_bitcnt_t mpz_hamdist (mpz_t OP1, mpz_t OP2) - If OP1 and OP2 are both >=0 or both <0, return the hamming - distance between the two operands, which is the number of bit - positions where OP1 and OP2 have different bit values. If one - operand is >=0 and the other <0 then the number of bits different - is infinite, and the return value is the largest possible - `mp_bitcnt_t'. - - -- Function: mp_bitcnt_t mpz_scan0 (mpz_t OP, mp_bitcnt_t STARTING_BIT) - -- Function: mp_bitcnt_t mpz_scan1 (mpz_t OP, mp_bitcnt_t STARTING_BIT) - Scan OP, starting from bit STARTING_BIT, towards more significant - bits, until the first 0 or 1 bit (respectively) is found. Return - the index of the found bit. - - If the bit at STARTING_BIT is already what's sought, then - STARTING_BIT is returned. - - If there's no bit found, then the largest possible `mp_bitcnt_t' is - returned. This will happen in `mpz_scan0' past the end of a - negative number, or `mpz_scan1' past the end of a nonnegative - number. - - -- Function: void mpz_setbit (mpz_t ROP, mp_bitcnt_t BIT_INDEX) - Set bit BIT_INDEX in ROP. - - -- Function: void mpz_clrbit (mpz_t ROP, mp_bitcnt_t BIT_INDEX) - Clear bit BIT_INDEX in ROP. - - -- Function: void mpz_combit (mpz_t ROP, mp_bitcnt_t BIT_INDEX) - Complement bit BIT_INDEX in ROP. - - -- Function: int mpz_tstbit (mpz_t OP, mp_bitcnt_t BIT_INDEX) - Test bit BIT_INDEX in OP and return 0 or 1 accordingly. - - -File: gmp.info, Node: I/O of Integers, Next: Integer Random Numbers, Prev: Integer Logic and Bit Fiddling, Up: Integer Functions - -5.12 Input and Output Functions -=============================== - -Functions that perform input from a stdio stream, and functions that -output to a stdio stream. Passing a `NULL' pointer for a STREAM -argument to any of these functions will make them read from `stdin' and -write to `stdout', respectively. - - When using any of these functions, it is a good idea to include -`stdio.h' before `gmp.h', since that will allow `gmp.h' to define -prototypes for these functions. - - -- Function: size_t mpz_out_str (FILE *STREAM, int BASE, mpz_t OP) - Output OP on stdio stream STREAM, as a string of digits in base - BASE. The base argument may vary from 2 to 62 or from -2 to -36. - - For BASE in the range 2..36, digits and lower-case letters are - used; for -2..-36, digits and upper-case letters are used; for - 37..62, digits, upper-case letters, and lower-case letters (in - that significance order) are used. - - Return the number of bytes written, or if an error occurred, - return 0. - - -- Function: size_t mpz_inp_str (mpz_t ROP, FILE *STREAM, int BASE) - Input a possibly white-space preceded string in base BASE from - stdio stream STREAM, and put the read integer in ROP. - - The BASE may vary from 2 to 62, or if BASE is 0, then the leading - characters are used: `0x' and `0X' for hexadecimal, `0b' and `0B' - for binary, `0' for octal, or decimal otherwise. - - For bases up to 36, case is ignored; upper-case and lower-case - letters have the same value. For bases 37 to 62, upper-case - letter represent the usual 10..35 while lower-case letter - represent 36..61. - - Return the number of bytes read, or if an error occurred, return 0. - - -- Function: size_t mpz_out_raw (FILE *STREAM, mpz_t OP) - Output OP on stdio stream STREAM, in raw binary format. The - integer is written in a portable format, with 4 bytes of size - information, and that many bytes of limbs. Both the size and the - limbs are written in decreasing significance order (i.e., in - big-endian). - - The output can be read with `mpz_inp_raw'. - - Return the number of bytes written, or if an error occurred, - return 0. - - The output of this can not be read by `mpz_inp_raw' from GMP 1, - because of changes necessary for compatibility between 32-bit and - 64-bit machines. - - -- Function: size_t mpz_inp_raw (mpz_t ROP, FILE *STREAM) - Input from stdio stream STREAM in the format written by - `mpz_out_raw', and put the result in ROP. Return the number of - bytes read, or if an error occurred, return 0. - - This routine can read the output from `mpz_out_raw' also from GMP - 1, in spite of changes necessary for compatibility between 32-bit - and 64-bit machines. - - -File: gmp.info, Node: Integer Random Numbers, Next: Integer Import and Export, Prev: I/O of Integers, Up: Integer Functions - -5.13 Random Number Functions -============================ - -The random number functions of GMP come in two groups; older function -that rely on a global state, and newer functions that accept a state -parameter that is read and modified. Please see the *Note Random -Number Functions:: for more information on how to use and not to use -random number functions. - - -- Function: void mpz_urandomb (mpz_t ROP, gmp_randstate_t STATE, - mp_bitcnt_t N) - Generate a uniformly distributed random integer in the range 0 to - 2^N-1, inclusive. - - The variable STATE must be initialized by calling one of the - `gmp_randinit' functions (*Note Random State Initialization::) - before invoking this function. - - -- Function: void mpz_urandomm (mpz_t ROP, gmp_randstate_t STATE, - mpz_t N) - Generate a uniform random integer in the range 0 to N-1, inclusive. - - The variable STATE must be initialized by calling one of the - `gmp_randinit' functions (*Note Random State Initialization::) - before invoking this function. - - -- Function: void mpz_rrandomb (mpz_t ROP, gmp_randstate_t STATE, - mp_bitcnt_t N) - Generate a random integer with long strings of zeros and ones in - the binary representation. Useful for testing functions and - algorithms, since this kind of random numbers have proven to be - more likely to trigger corner-case bugs. The random number will - be in the range 0 to 2^N-1, inclusive. - - The variable STATE must be initialized by calling one of the - `gmp_randinit' functions (*Note Random State Initialization::) - before invoking this function. - - -- Function: void mpz_random (mpz_t ROP, mp_size_t MAX_SIZE) - Generate a random integer of at most MAX_SIZE limbs. The generated - random number doesn't satisfy any particular requirements of - randomness. Negative random numbers are generated when MAX_SIZE - is negative. - - This function is obsolete. Use `mpz_urandomb' or `mpz_urandomm' - instead. - - -- Function: void mpz_random2 (mpz_t ROP, mp_size_t MAX_SIZE) - Generate a random integer of at most MAX_SIZE limbs, with long - strings of zeros and ones in the binary representation. Useful - for testing functions and algorithms, since this kind of random - numbers have proven to be more likely to trigger corner-case bugs. - Negative random numbers are generated when MAX_SIZE is negative. - - This function is obsolete. Use `mpz_rrandomb' instead. - - -File: gmp.info, Node: Integer Import and Export, Next: Miscellaneous Integer Functions, Prev: Integer Random Numbers, Up: Integer Functions - -5.14 Integer Import and Export -============================== - -`mpz_t' variables can be converted to and from arbitrary words of binary -data with the following functions. - - -- Function: void mpz_import (mpz_t ROP, size_t COUNT, int ORDER, - size_t SIZE, int ENDIAN, size_t NAILS, const void *OP) - Set ROP from an array of word data at OP. - - The parameters specify the format of the data. COUNT many words - are read, each SIZE bytes. ORDER can be 1 for most significant - word first or -1 for least significant first. Within each word - ENDIAN can be 1 for most significant byte first, -1 for least - significant first, or 0 for the native endianness of the host CPU. - The most significant NAILS bits of each word are skipped, this - can be 0 to use the full words. - - There is no sign taken from the data, ROP will simply be a positive - integer. An application can handle any sign itself, and apply it - for instance with `mpz_neg'. - - There are no data alignment restrictions on OP, any address is - allowed. - - Here's an example converting an array of `unsigned long' data, most - significant element first, and host byte order within each value. - - unsigned long a[20]; - /* Initialize Z and A */ - mpz_import (z, 20, 1, sizeof(a[0]), 0, 0, a); - - This example assumes the full `sizeof' bytes are used for data in - the given type, which is usually true, and certainly true for - `unsigned long' everywhere we know of. However on Cray vector - systems it may be noted that `short' and `int' are always stored - in 8 bytes (and with `sizeof' indicating that) but use only 32 or - 46 bits. The NAILS feature can account for this, by passing for - instance `8*sizeof(int)-INT_BIT'. - - -- Function: void * mpz_export (void *ROP, size_t *COUNTP, int ORDER, - size_t SIZE, int ENDIAN, size_t NAILS, mpz_t OP) - Fill ROP with word data from OP. - - The parameters specify the format of the data produced. Each word - will be SIZE bytes and ORDER can be 1 for most significant word - first or -1 for least significant first. Within each word ENDIAN - can be 1 for most significant byte first, -1 for least significant - first, or 0 for the native endianness of the host CPU. The most - significant NAILS bits of each word are unused and set to zero, - this can be 0 to produce full words. - - The number of words produced is written to `*COUNTP', or COUNTP - can be `NULL' to discard the count. ROP must have enough space - for the data, or if ROP is `NULL' then a result array of the - necessary size is allocated using the current GMP allocation - function (*note Custom Allocation::). In either case the return - value is the destination used, either ROP or the allocated block. - - If OP is non-zero then the most significant word produced will be - non-zero. If OP is zero then the count returned will be zero and - nothing written to ROP. If ROP is `NULL' in this case, no block - is allocated, just `NULL' is returned. - - The sign of OP is ignored, just the absolute value is exported. An - application can use `mpz_sgn' to get the sign and handle it as - desired. (*note Integer Comparisons::) - - There are no data alignment restrictions on ROP, any address is - allowed. - - When an application is allocating space itself the required size - can be determined with a calculation like the following. Since - `mpz_sizeinbase' always returns at least 1, `count' here will be - at least one, which avoids any portability problems with - `malloc(0)', though if `z' is zero no space at all is actually - needed (or written). - - numb = 8*size - nail; - count = (mpz_sizeinbase (z, 2) + numb-1) / numb; - p = malloc (count * size); - - -File: gmp.info, Node: Miscellaneous Integer Functions, Next: Integer Special Functions, Prev: Integer Import and Export, Up: Integer Functions - -5.15 Miscellaneous Functions -============================ - - -- Function: int mpz_fits_ulong_p (mpz_t OP) - -- Function: int mpz_fits_slong_p (mpz_t OP) - -- Function: int mpz_fits_uint_p (mpz_t OP) - -- Function: int mpz_fits_sint_p (mpz_t OP) - -- Function: int mpz_fits_ushort_p (mpz_t OP) - -- Function: int mpz_fits_sshort_p (mpz_t OP) - Return non-zero iff the value of OP fits in an `unsigned long int', - `signed long int', `unsigned int', `signed int', `unsigned short - int', or `signed short int', respectively. Otherwise, return zero. - - -- Macro: int mpz_odd_p (mpz_t OP) - -- Macro: int mpz_even_p (mpz_t OP) - Determine whether OP is odd or even, respectively. Return - non-zero if yes, zero if no. These macros evaluate their argument - more than once. - - -- Function: size_t mpz_sizeinbase (mpz_t OP, int BASE) - Return the size of OP measured in number of digits in the given - BASE. BASE can vary from 2 to 62. The sign of OP is ignored, - just the absolute value is used. The result will be either exact - or 1 too big. If BASE is a power of 2, the result is always - exact. If OP is zero the return value is always 1. - - This function can be used to determine the space required when - converting OP to a string. The right amount of allocation is - normally two more than the value returned by `mpz_sizeinbase', one - extra for a minus sign and one for the null-terminator. - - It will be noted that `mpz_sizeinbase(OP,2)' can be used to locate - the most significant 1 bit in OP, counting from 1. (Unlike the - bitwise functions which start from 0, *Note Logical and Bit - Manipulation Functions: Integer Logic and Bit Fiddling.) - - -File: gmp.info, Node: Integer Special Functions, Prev: Miscellaneous Integer Functions, Up: Integer Functions - -5.16 Special Functions -====================== - -The functions in this section are for various special purposes. Most -applications will not need them. - - -- Function: void mpz_array_init (mpz_t INTEGER_ARRAY, mp_size_t - ARRAY_SIZE, mp_size_t FIXED_NUM_BITS) - This is a special type of initialization. *Fixed* space of - FIXED_NUM_BITS is allocated to each of the ARRAY_SIZE integers in - INTEGER_ARRAY. There is no way to free the storage allocated by - this function. Don't call `mpz_clear'! - - The INTEGER_ARRAY parameter is the first `mpz_t' in the array. For - example, - - mpz_t arr[20000]; - mpz_array_init (arr[0], 20000, 512); - - This function is only intended for programs that create a large - number of integers and need to reduce memory usage by avoiding the - overheads of allocating and reallocating lots of small blocks. In - normal programs this function is not recommended. - - The space allocated to each integer by this function will not be - automatically increased, unlike the normal `mpz_init', so an - application must ensure it is sufficient for any value stored. - The following space requirements apply to various routines, - - * `mpz_abs', `mpz_neg', `mpz_set', `mpz_set_si' and - `mpz_set_ui' need room for the value they store. - - * `mpz_add', `mpz_add_ui', `mpz_sub' and `mpz_sub_ui' need room - for the larger of the two operands, plus an extra - `mp_bits_per_limb'. - - * `mpz_mul', `mpz_mul_ui' and `mpz_mul_ui' need room for the sum - of the number of bits in their operands, but each rounded up - to a multiple of `mp_bits_per_limb'. - - * `mpz_swap' can be used between two array variables, but not - between an array and a normal variable. - - For other functions, or if in doubt, the suggestion is to - calculate in a regular `mpz_init' variable and copy the result to - an array variable with `mpz_set'. - - -- Function: void * _mpz_realloc (mpz_t INTEGER, mp_size_t NEW_ALLOC) - Change the space for INTEGER to NEW_ALLOC limbs. The value in - INTEGER is preserved if it fits, or is set to 0 if not. The return - value is not useful to applications and should be ignored. - - `mpz_realloc2' is the preferred way to accomplish allocation - changes like this. `mpz_realloc2' and `_mpz_realloc' are the same - except that `_mpz_realloc' takes its size in limbs. - - -- Function: mp_limb_t mpz_getlimbn (mpz_t OP, mp_size_t N) - Return limb number N from OP. The sign of OP is ignored, just the - absolute value is used. The least significant limb is number 0. - - `mpz_size' can be used to find how many limbs make up OP. - `mpz_getlimbn' returns zero if N is outside the range 0 to - `mpz_size(OP)-1'. - - -- Function: size_t mpz_size (mpz_t OP) - Return the size of OP measured in number of limbs. If OP is zero, - the returned value will be zero. - - -File: gmp.info, Node: Rational Number Functions, Next: Floating-point Functions, Prev: Integer Functions, Up: Top - -6 Rational Number Functions -*************************** - -This chapter describes the GMP functions for performing arithmetic on -rational numbers. These functions start with the prefix `mpq_'. - - Rational numbers are stored in objects of type `mpq_t'. - - All rational arithmetic functions assume operands have a canonical -form, and canonicalize their result. The canonical from means that the -denominator and the numerator have no common factors, and that the -denominator is positive. Zero has the unique representation 0/1. - - Pure assignment functions do not canonicalize the assigned variable. -It is the responsibility of the user to canonicalize the assigned -variable before any arithmetic operations are performed on that -variable. - - -- Function: void mpq_canonicalize (mpq_t OP) - Remove any factors that are common to the numerator and - denominator of OP, and make the denominator positive. - -* Menu: - -* Initializing Rationals:: -* Rational Conversions:: -* Rational Arithmetic:: -* Comparing Rationals:: -* Applying Integer Functions:: -* I/O of Rationals:: - - -File: gmp.info, Node: Initializing Rationals, Next: Rational Conversions, Prev: Rational Number Functions, Up: Rational Number Functions - -6.1 Initialization and Assignment Functions -=========================================== - - -- Function: void mpq_init (mpq_t X) - Initialize X and set it to 0/1. Each variable should normally - only be initialized once, or at least cleared out (using the - function `mpq_clear') between each initialization. - - -- Function: void mpq_inits (mpq_t X, ...) - Initialize a NULL-terminated list of `mpq_t' variables, and set - their values to 0/1. - - -- Function: void mpq_clear (mpq_t X) - Free the space occupied by X. Make sure to call this function for - all `mpq_t' variables when you are done with them. - - -- Function: void mpq_clears (mpq_t X, ...) - Free the space occupied by a NULL-terminated list of `mpq_t' - variables. - - -- Function: void mpq_set (mpq_t ROP, mpq_t OP) - -- Function: void mpq_set_z (mpq_t ROP, mpz_t OP) - Assign ROP from OP. - - -- Function: void mpq_set_ui (mpq_t ROP, unsigned long int OP1, - unsigned long int OP2) - -- Function: void mpq_set_si (mpq_t ROP, signed long int OP1, unsigned - long int OP2) - Set the value of ROP to OP1/OP2. Note that if OP1 and OP2 have - common factors, ROP has to be passed to `mpq_canonicalize' before - any operations are performed on ROP. - - -- Function: int mpq_set_str (mpq_t ROP, char *STR, int BASE) - Set ROP from a null-terminated string STR in the given BASE. - - The string can be an integer like "41" or a fraction like - "41/152". The fraction must be in canonical form (*note Rational - Number Functions::), or if not then `mpq_canonicalize' must be - called. - - The numerator and optional denominator are parsed the same as in - `mpz_set_str' (*note Assigning Integers::). White space is - allowed in the string, and is simply ignored. The BASE can vary - from 2 to 62, or if BASE is 0 then the leading characters are - used: `0x' or `0X' for hex, `0b' or `0B' for binary, `0' for - octal, or decimal otherwise. Note that this is done separately - for the numerator and denominator, so for instance `0xEF/100' is - 239/100, whereas `0xEF/0x100' is 239/256. - - The return value is 0 if the entire string is a valid number, or - -1 if not. - - -- Function: void mpq_swap (mpq_t ROP1, mpq_t ROP2) - Swap the values ROP1 and ROP2 efficiently. - - -File: gmp.info, Node: Rational Conversions, Next: Rational Arithmetic, Prev: Initializing Rationals, Up: Rational Number Functions - -6.2 Conversion Functions -======================== - - -- Function: double mpq_get_d (mpq_t OP) - Convert OP to a `double', truncating if necessary (ie. rounding - towards zero). - - If the exponent from the conversion is too big or too small to fit - a `double' then the result is system dependent. For too big an - infinity is returned when available. For too small 0.0 is - normally returned. Hardware overflow, underflow and denorm traps - may or may not occur. - - -- Function: void mpq_set_d (mpq_t ROP, double OP) - -- Function: void mpq_set_f (mpq_t ROP, mpf_t OP) - Set ROP to the value of OP. There is no rounding, this conversion - is exact. - - -- Function: char * mpq_get_str (char *STR, int BASE, mpq_t OP) - Convert OP to a string of digits in base BASE. The base may vary - from 2 to 36. The string will be of the form `num/den', or if the - denominator is 1 then just `num'. - - If STR is `NULL', the result string is allocated using the current - allocation function (*note Custom Allocation::). The block will be - `strlen(str)+1' bytes, that being exactly enough for the string and - null-terminator. - - If STR is not `NULL', it should point to a block of storage large - enough for the result, that being - - mpz_sizeinbase (mpq_numref(OP), BASE) - + mpz_sizeinbase (mpq_denref(OP), BASE) + 3 - - The three extra bytes are for a possible minus sign, possible - slash, and the null-terminator. - - A pointer to the result string is returned, being either the - allocated block, or the given STR. - - -File: gmp.info, Node: Rational Arithmetic, Next: Comparing Rationals, Prev: Rational Conversions, Up: Rational Number Functions - -6.3 Arithmetic Functions -======================== - - -- Function: void mpq_add (mpq_t SUM, mpq_t ADDEND1, mpq_t ADDEND2) - Set SUM to ADDEND1 + ADDEND2. - - -- Function: void mpq_sub (mpq_t DIFFERENCE, mpq_t MINUEND, mpq_t - SUBTRAHEND) - Set DIFFERENCE to MINUEND - SUBTRAHEND. - - -- Function: void mpq_mul (mpq_t PRODUCT, mpq_t MULTIPLIER, mpq_t - MULTIPLICAND) - Set PRODUCT to MULTIPLIER times MULTIPLICAND. - - -- Function: void mpq_mul_2exp (mpq_t ROP, mpq_t OP1, mp_bitcnt_t OP2) - Set ROP to OP1 times 2 raised to OP2. - - -- Function: void mpq_div (mpq_t QUOTIENT, mpq_t DIVIDEND, mpq_t - DIVISOR) - Set QUOTIENT to DIVIDEND/DIVISOR. - - -- Function: void mpq_div_2exp (mpq_t ROP, mpq_t OP1, mp_bitcnt_t OP2) - Set ROP to OP1 divided by 2 raised to OP2. - - -- Function: void mpq_neg (mpq_t NEGATED_OPERAND, mpq_t OPERAND) - Set NEGATED_OPERAND to -OPERAND. - - -- Function: void mpq_abs (mpq_t ROP, mpq_t OP) - Set ROP to the absolute value of OP. - - -- Function: void mpq_inv (mpq_t INVERTED_NUMBER, mpq_t NUMBER) - Set INVERTED_NUMBER to 1/NUMBER. If the new denominator is zero, - this routine will divide by zero. - - -File: gmp.info, Node: Comparing Rationals, Next: Applying Integer Functions, Prev: Rational Arithmetic, Up: Rational Number Functions - -6.4 Comparison Functions -======================== - - -- Function: int mpq_cmp (mpq_t OP1, mpq_t OP2) - Compare OP1 and OP2. Return a positive value if OP1 > OP2, zero - if OP1 = OP2, and a negative value if OP1 < OP2. - - To determine if two rationals are equal, `mpq_equal' is faster than - `mpq_cmp'. - - -- Macro: int mpq_cmp_ui (mpq_t OP1, unsigned long int NUM2, unsigned - long int DEN2) - -- Macro: int mpq_cmp_si (mpq_t OP1, long int NUM2, unsigned long int - DEN2) - Compare OP1 and NUM2/DEN2. Return a positive value if OP1 > - NUM2/DEN2, zero if OP1 = NUM2/DEN2, and a negative value if OP1 < - NUM2/DEN2. - - NUM2 and DEN2 are allowed to have common factors. - - These functions are implemented as a macros and evaluate their - arguments multiple times. - - -- Macro: int mpq_sgn (mpq_t OP) - Return +1 if OP > 0, 0 if OP = 0, and -1 if OP < 0. - - This function is actually implemented as a macro. It evaluates its - arguments multiple times. - - -- Function: int mpq_equal (mpq_t OP1, mpq_t OP2) - Return non-zero if OP1 and OP2 are equal, zero if they are - non-equal. Although `mpq_cmp' can be used for the same purpose, - this function is much faster. - - -File: gmp.info, Node: Applying Integer Functions, Next: I/O of Rationals, Prev: Comparing Rationals, Up: Rational Number Functions - -6.5 Applying Integer Functions to Rationals -=========================================== - -The set of `mpq' functions is quite small. In particular, there are few -functions for either input or output. The following functions give -direct access to the numerator and denominator of an `mpq_t'. - - Note that if an assignment to the numerator and/or denominator could -take an `mpq_t' out of the canonical form described at the start of -this chapter (*note Rational Number Functions::) then -`mpq_canonicalize' must be called before any other `mpq' functions are -applied to that `mpq_t'. - - -- Macro: mpz_t mpq_numref (mpq_t OP) - -- Macro: mpz_t mpq_denref (mpq_t OP) - Return a reference to the numerator and denominator of OP, - respectively. The `mpz' functions can be used on the result of - these macros. - - -- Function: void mpq_get_num (mpz_t NUMERATOR, mpq_t RATIONAL) - -- Function: void mpq_get_den (mpz_t DENOMINATOR, mpq_t RATIONAL) - -- Function: void mpq_set_num (mpq_t RATIONAL, mpz_t NUMERATOR) - -- Function: void mpq_set_den (mpq_t RATIONAL, mpz_t DENOMINATOR) - Get or set the numerator or denominator of a rational. These - functions are equivalent to calling `mpz_set' with an appropriate - `mpq_numref' or `mpq_denref'. Direct use of `mpq_numref' or - `mpq_denref' is recommended instead of these functions. - - -File: gmp.info, Node: I/O of Rationals, Prev: Applying Integer Functions, Up: Rational Number Functions - -6.6 Input and Output Functions -============================== - -When using any of these functions, it's a good idea to include `stdio.h' -before `gmp.h', since that will allow `gmp.h' to define prototypes for -these functions. - - Passing a `NULL' pointer for a STREAM argument to any of these -functions will make them read from `stdin' and write to `stdout', -respectively. - - -- Function: size_t mpq_out_str (FILE *STREAM, int BASE, mpq_t OP) - Output OP on stdio stream STREAM, as a string of digits in base - BASE. The base may vary from 2 to 36. Output is in the form - `num/den' or if the denominator is 1 then just `num'. - - Return the number of bytes written, or if an error occurred, - return 0. - - -- Function: size_t mpq_inp_str (mpq_t ROP, FILE *STREAM, int BASE) - Read a string of digits from STREAM and convert them to a rational - in ROP. Any initial white-space characters are read and - discarded. Return the number of characters read (including white - space), or 0 if a rational could not be read. - - The input can be a fraction like `17/63' or just an integer like - `123'. Reading stops at the first character not in this form, and - white space is not permitted within the string. If the input - might not be in canonical form, then `mpq_canonicalize' must be - called (*note Rational Number Functions::). - - The BASE can be between 2 and 36, or can be 0 in which case the - leading characters of the string determine the base, `0x' or `0X' - for hexadecimal, `0' for octal, or decimal otherwise. The leading - characters are examined separately for the numerator and - denominator of a fraction, so for instance `0x10/11' is 16/11, - whereas `0x10/0x11' is 16/17. - - -File: gmp.info, Node: Floating-point Functions, Next: Low-level Functions, Prev: Rational Number Functions, Up: Top - -7 Floating-point Functions -************************** - -GMP floating point numbers are stored in objects of type `mpf_t' and -functions operating on them have an `mpf_' prefix. - - The mantissa of each float has a user-selectable precision, limited -only by available memory. Each variable has its own precision, and -that can be increased or decreased at any time. - - The exponent of each float is a fixed precision, one machine word on -most systems. In the current implementation the exponent is a count of -limbs, so for example on a 32-bit system this means a range of roughly -2^-68719476768 to 2^68719476736, or on a 64-bit system this will be -greater. Note however `mpf_get_str' can only return an exponent which -fits an `mp_exp_t' and currently `mpf_set_str' doesn't accept exponents -bigger than a `long'. - - Each variable keeps a size for the mantissa data actually in use. -This means that if a float is exactly represented in only a few bits -then only those bits will be used in a calculation, even if the -selected precision is high. - - All calculations are performed to the precision of the destination -variable. Each function is defined to calculate with "infinite -precision" followed by a truncation to the destination precision, but -of course the work done is only what's needed to determine a result -under that definition. - - The precision selected for a variable is a minimum value, GMP may -increase it a little to facilitate efficient calculation. Currently -this means rounding up to a whole limb, and then sometimes having a -further partial limb, depending on the high limb of the mantissa. But -applications shouldn't be concerned by such details. - - The mantissa in stored in binary, as might be imagined from the fact -precisions are expressed in bits. One consequence of this is that -decimal fractions like 0.1 cannot be represented exactly. The same is -true of plain IEEE `double' floats. This makes both highly unsuitable -for calculations involving money or other values that should be exact -decimal fractions. (Suitably scaled integers, or perhaps rationals, -are better choices.) - - `mpf' functions and variables have no special notion of infinity or -not-a-number, and applications must take care not to overflow the -exponent or results will be unpredictable. This might change in a -future release. - - Note that the `mpf' functions are _not_ intended as a smooth -extension to IEEE P754 arithmetic. In particular results obtained on -one computer often differ from the results on a computer with a -different word size. - -* Menu: - -* Initializing Floats:: -* Assigning Floats:: -* Simultaneous Float Init & Assign:: -* Converting Floats:: -* Float Arithmetic:: -* Float Comparison:: -* I/O of Floats:: -* Miscellaneous Float Functions:: - - -File: gmp.info, Node: Initializing Floats, Next: Assigning Floats, Prev: Floating-point Functions, Up: Floating-point Functions - -7.1 Initialization Functions -============================ - - -- Function: void mpf_set_default_prec (mp_bitcnt_t PREC) - Set the default precision to be *at least* PREC bits. All - subsequent calls to `mpf_init' will use this precision, but - previously initialized variables are unaffected. - - -- Function: mp_bitcnt_t mpf_get_default_prec (void) - Return the default precision actually used. - - An `mpf_t' object must be initialized before storing the first value -in it. The functions `mpf_init' and `mpf_init2' are used for that -purpose. - - -- Function: void mpf_init (mpf_t X) - Initialize X to 0. Normally, a variable should be initialized - once only or at least be cleared, using `mpf_clear', between - initializations. The precision of X is undefined unless a default - precision has already been established by a call to - `mpf_set_default_prec'. - - -- Function: void mpf_init2 (mpf_t X, mp_bitcnt_t PREC) - Initialize X to 0 and set its precision to be *at least* PREC - bits. Normally, a variable should be initialized once only or at - least be cleared, using `mpf_clear', between initializations. - - -- Function: void mpf_inits (mpf_t X, ...) - Initialize a NULL-terminated list of `mpf_t' variables, and set - their values to 0. The precision of the initialized variables is - undefined unless a default precision has already been established - by a call to `mpf_set_default_prec'. - - -- Function: void mpf_clear (mpf_t X) - Free the space occupied by X. Make sure to call this function for - all `mpf_t' variables when you are done with them. - - -- Function: void mpf_clears (mpf_t X, ...) - Free the space occupied by a NULL-terminated list of `mpf_t' - variables. - - Here is an example on how to initialize floating-point variables: - { - mpf_t x, y; - mpf_init (x); /* use default precision */ - mpf_init2 (y, 256); /* precision _at least_ 256 bits */ - ... - /* Unless the program is about to exit, do ... */ - mpf_clear (x); - mpf_clear (y); - } - - The following three functions are useful for changing the precision -during a calculation. A typical use would be for adjusting the -precision gradually in iterative algorithms like Newton-Raphson, making -the computation precision closely match the actual accurate part of the -numbers. - - -- Function: mp_bitcnt_t mpf_get_prec (mpf_t OP) - Return the current precision of OP, in bits. - - -- Function: void mpf_set_prec (mpf_t ROP, mp_bitcnt_t PREC) - Set the precision of ROP to be *at least* PREC bits. The value in - ROP will be truncated to the new precision. - - This function requires a call to `realloc', and so should not be - used in a tight loop. - - -- Function: void mpf_set_prec_raw (mpf_t ROP, mp_bitcnt_t PREC) - Set the precision of ROP to be *at least* PREC bits, without - changing the memory allocated. - - PREC must be no more than the allocated precision for ROP, that - being the precision when ROP was initialized, or in the most recent - `mpf_set_prec'. - - The value in ROP is unchanged, and in particular if it had a higher - precision than PREC it will retain that higher precision. New - values written to ROP will use the new PREC. - - Before calling `mpf_clear' or the full `mpf_set_prec', another - `mpf_set_prec_raw' call must be made to restore ROP to its original - allocated precision. Failing to do so will have unpredictable - results. - - `mpf_get_prec' can be used before `mpf_set_prec_raw' to get the - original allocated precision. After `mpf_set_prec_raw' it - reflects the PREC value set. - - `mpf_set_prec_raw' is an efficient way to use an `mpf_t' variable - at different precisions during a calculation, perhaps to gradually - increase precision in an iteration, or just to use various - different precisions for different purposes during a calculation. - - -File: gmp.info, Node: Assigning Floats, Next: Simultaneous Float Init & Assign, Prev: Initializing Floats, Up: Floating-point Functions - -7.2 Assignment Functions -======================== - -These functions assign new values to already initialized floats (*note -Initializing Floats::). - - -- Function: void mpf_set (mpf_t ROP, mpf_t OP) - -- Function: void mpf_set_ui (mpf_t ROP, unsigned long int OP) - -- Function: void mpf_set_si (mpf_t ROP, signed long int OP) - -- Function: void mpf_set_d (mpf_t ROP, double OP) - -- Function: void mpf_set_z (mpf_t ROP, mpz_t OP) - -- Function: void mpf_set_q (mpf_t ROP, mpq_t OP) - Set the value of ROP from OP. - - -- Function: int mpf_set_str (mpf_t ROP, char *STR, int BASE) - Set the value of ROP from the string in STR. The string is of the - form `M@N' or, if the base is 10 or less, alternatively `MeN'. - `M' is the mantissa and `N' is the exponent. The mantissa is - always in the specified base. The exponent is either in the - specified base or, if BASE is negative, in decimal. The decimal - point expected is taken from the current locale, on systems - providing `localeconv'. - - The argument BASE may be in the ranges 2 to 62, or -62 to -2. - Negative values are used to specify that the exponent is in - decimal. - - For bases up to 36, case is ignored; upper-case and lower-case - letters have the same value; for bases 37 to 62, upper-case letter - represent the usual 10..35 while lower-case letter represent - 36..61. - - Unlike the corresponding `mpz' function, the base will not be - determined from the leading characters of the string if BASE is 0. - This is so that numbers like `0.23' are not interpreted as octal. - - White space is allowed in the string, and is simply ignored. - [This is not really true; white-space is ignored in the beginning - of the string and within the mantissa, but not in other places, - such as after a minus sign or in the exponent. We are considering - changing the definition of this function, making it fail when - there is any white-space in the input, since that makes a lot of - sense. Please tell us your opinion about this change. Do you - really want it to accept "3 14" as meaning 314 as it does now?] - - This function returns 0 if the entire string is a valid number in - base BASE. Otherwise it returns -1. - - -- Function: void mpf_swap (mpf_t ROP1, mpf_t ROP2) - Swap ROP1 and ROP2 efficiently. Both the values and the - precisions of the two variables are swapped. - - -File: gmp.info, Node: Simultaneous Float Init & Assign, Next: Converting Floats, Prev: Assigning Floats, Up: Floating-point Functions - -7.3 Combined Initialization and Assignment Functions -==================================================== - -For convenience, GMP provides a parallel series of initialize-and-set -functions which initialize the output and then store the value there. -These functions' names have the form `mpf_init_set...' - - Once the float has been initialized by any of the `mpf_init_set...' -functions, it can be used as the source or destination operand for the -ordinary float functions. Don't use an initialize-and-set function on -a variable already initialized! - - -- Function: void mpf_init_set (mpf_t ROP, mpf_t OP) - -- Function: void mpf_init_set_ui (mpf_t ROP, unsigned long int OP) - -- Function: void mpf_init_set_si (mpf_t ROP, signed long int OP) - -- Function: void mpf_init_set_d (mpf_t ROP, double OP) - Initialize ROP and set its value from OP. - - The precision of ROP will be taken from the active default - precision, as set by `mpf_set_default_prec'. - - -- Function: int mpf_init_set_str (mpf_t ROP, char *STR, int BASE) - Initialize ROP and set its value from the string in STR. See - `mpf_set_str' above for details on the assignment operation. - - Note that ROP is initialized even if an error occurs. (I.e., you - have to call `mpf_clear' for it.) - - The precision of ROP will be taken from the active default - precision, as set by `mpf_set_default_prec'. - - -File: gmp.info, Node: Converting Floats, Next: Float Arithmetic, Prev: Simultaneous Float Init & Assign, Up: Floating-point Functions - -7.4 Conversion Functions -======================== - - -- Function: double mpf_get_d (mpf_t OP) - Convert OP to a `double', truncating if necessary (ie. rounding - towards zero). - - If the exponent in OP is too big or too small to fit a `double' - then the result is system dependent. For too big an infinity is - returned when available. For too small 0.0 is normally returned. - Hardware overflow, underflow and denorm traps may or may not occur. - - -- Function: double mpf_get_d_2exp (signed long int *EXP, mpf_t OP) - Convert OP to a `double', truncating if necessary (ie. rounding - towards zero), and with an exponent returned separately. - - The return value is in the range 0.5<=abs(D)<1 and the exponent is - stored to `*EXP'. D * 2^EXP is the (truncated) OP value. If OP - is zero, the return is 0.0 and 0 is stored to `*EXP'. - - This is similar to the standard C `frexp' function (*note - Normalization Functions: (libc)Normalization Functions.). - - -- Function: long mpf_get_si (mpf_t OP) - -- Function: unsigned long mpf_get_ui (mpf_t OP) - Convert OP to a `long' or `unsigned long', truncating any fraction - part. If OP is too big for the return type, the result is - undefined. - - See also `mpf_fits_slong_p' and `mpf_fits_ulong_p' (*note - Miscellaneous Float Functions::). - - -- Function: char * mpf_get_str (char *STR, mp_exp_t *EXPPTR, int - BASE, size_t N_DIGITS, mpf_t OP) - Convert OP to a string of digits in base BASE. The base argument - may vary from 2 to 62 or from -2 to -36. Up to N_DIGITS digits - will be generated. Trailing zeros are not returned. No more - digits than can be accurately represented by OP are ever - generated. If N_DIGITS is 0 then that accurate maximum number of - digits are generated. - - For BASE in the range 2..36, digits and lower-case letters are - used; for -2..-36, digits and upper-case letters are used; for - 37..62, digits, upper-case letters, and lower-case letters (in - that significance order) are used. - - If STR is `NULL', the result string is allocated using the current - allocation function (*note Custom Allocation::). The block will be - `strlen(str)+1' bytes, that being exactly enough for the string and - null-terminator. - - If STR is not `NULL', it should point to a block of N_DIGITS + 2 - bytes, that being enough for the mantissa, a possible minus sign, - and a null-terminator. When N_DIGITS is 0 to get all significant - digits, an application won't be able to know the space required, - and STR should be `NULL' in that case. - - The generated string is a fraction, with an implicit radix point - immediately to the left of the first digit. The applicable - exponent is written through the EXPPTR pointer. For example, the - number 3.1416 would be returned as string "31416" and exponent 1. - - When OP is zero, an empty string is produced and the exponent - returned is 0. - - A pointer to the result string is returned, being either the - allocated block or the given STR. - - -File: gmp.info, Node: Float Arithmetic, Next: Float Comparison, Prev: Converting Floats, Up: Floating-point Functions - -7.5 Arithmetic Functions -======================== - - -- Function: void mpf_add (mpf_t ROP, mpf_t OP1, mpf_t OP2) - -- Function: void mpf_add_ui (mpf_t ROP, mpf_t OP1, unsigned long int - OP2) - Set ROP to OP1 + OP2. - - -- Function: void mpf_sub (mpf_t ROP, mpf_t OP1, mpf_t OP2) - -- Function: void mpf_ui_sub (mpf_t ROP, unsigned long int OP1, mpf_t - OP2) - -- Function: void mpf_sub_ui (mpf_t ROP, mpf_t OP1, unsigned long int - OP2) - Set ROP to OP1 - OP2. - - -- Function: void mpf_mul (mpf_t ROP, mpf_t OP1, mpf_t OP2) - -- Function: void mpf_mul_ui (mpf_t ROP, mpf_t OP1, unsigned long int - OP2) - Set ROP to OP1 times OP2. - - Division is undefined if the divisor is zero, and passing a zero -divisor to the divide functions will make these functions intentionally -divide by zero. This lets the user handle arithmetic exceptions in -these functions in the same manner as other arithmetic exceptions. - - -- Function: void mpf_div (mpf_t ROP, mpf_t OP1, mpf_t OP2) - -- Function: void mpf_ui_div (mpf_t ROP, unsigned long int OP1, mpf_t - OP2) - -- Function: void mpf_div_ui (mpf_t ROP, mpf_t OP1, unsigned long int - OP2) - Set ROP to OP1/OP2. - - -- Function: void mpf_sqrt (mpf_t ROP, mpf_t OP) - -- Function: void mpf_sqrt_ui (mpf_t ROP, unsigned long int OP) - Set ROP to the square root of OP. - - -- Function: void mpf_pow_ui (mpf_t ROP, mpf_t OP1, unsigned long int - OP2) - Set ROP to OP1 raised to the power OP2. - - -- Function: void mpf_neg (mpf_t ROP, mpf_t OP) - Set ROP to -OP. - - -- Function: void mpf_abs (mpf_t ROP, mpf_t OP) - Set ROP to the absolute value of OP. - - -- Function: void mpf_mul_2exp (mpf_t ROP, mpf_t OP1, mp_bitcnt_t OP2) - Set ROP to OP1 times 2 raised to OP2. - - -- Function: void mpf_div_2exp (mpf_t ROP, mpf_t OP1, mp_bitcnt_t OP2) - Set ROP to OP1 divided by 2 raised to OP2. - - -File: gmp.info, Node: Float Comparison, Next: I/O of Floats, Prev: Float Arithmetic, Up: Floating-point Functions - -7.6 Comparison Functions -======================== - - -- Function: int mpf_cmp (mpf_t OP1, mpf_t OP2) - -- Function: int mpf_cmp_d (mpf_t OP1, double OP2) - -- Function: int mpf_cmp_ui (mpf_t OP1, unsigned long int OP2) - -- Function: int mpf_cmp_si (mpf_t OP1, signed long int OP2) - Compare OP1 and OP2. Return a positive value if OP1 > OP2, zero - if OP1 = OP2, and a negative value if OP1 < OP2. - - `mpf_cmp_d' can be called with an infinity, but results are - undefined for a NaN. - - -- Function: int mpf_eq (mpf_t OP1, mpf_t OP2, mp_bitcnt_t op3) - Return non-zero if the first OP3 bits of OP1 and OP2 are equal, - zero otherwise. I.e., test if OP1 and OP2 are approximately equal. - - Caution 1: All version of GMP up to version 4.2.4 compared just - whole limbs, meaning sometimes more than OP3 bits, sometimes fewer. - - Caution 2: This function will consider XXX11...111 and XX100...000 - different, even if ... is replaced by a semi-infinite number of - bits. Such numbers are really just one ulp off, and should be - considered equal. - - -- Function: void mpf_reldiff (mpf_t ROP, mpf_t OP1, mpf_t OP2) - Compute the relative difference between OP1 and OP2 and store the - result in ROP. This is abs(OP1-OP2)/OP1. - - -- Macro: int mpf_sgn (mpf_t OP) - Return +1 if OP > 0, 0 if OP = 0, and -1 if OP < 0. - - This function is actually implemented as a macro. It evaluates - its arguments multiple times. - - -File: gmp.info, Node: I/O of Floats, Next: Miscellaneous Float Functions, Prev: Float Comparison, Up: Floating-point Functions - -7.7 Input and Output Functions -============================== - -Functions that perform input from a stdio stream, and functions that -output to a stdio stream. Passing a `NULL' pointer for a STREAM -argument to any of these functions will make them read from `stdin' and -write to `stdout', respectively. - - When using any of these functions, it is a good idea to include -`stdio.h' before `gmp.h', since that will allow `gmp.h' to define -prototypes for these functions. - - -- Function: size_t mpf_out_str (FILE *STREAM, int BASE, size_t - N_DIGITS, mpf_t OP) - Print OP to STREAM, as a string of digits. Return the number of - bytes written, or if an error occurred, return 0. - - The mantissa is prefixed with an `0.' and is in the given BASE, - which may vary from 2 to 62 or from -2 to -36. An exponent is - then printed, separated by an `e', or if the base is greater than - 10 then by an `@'. The exponent is always in decimal. The - decimal point follows the current locale, on systems providing - `localeconv'. - - For BASE in the range 2..36, digits and lower-case letters are - used; for -2..-36, digits and upper-case letters are used; for - 37..62, digits, upper-case letters, and lower-case letters (in - that significance order) are used. - - Up to N_DIGITS will be printed from the mantissa, except that no - more digits than are accurately representable by OP will be - printed. N_DIGITS can be 0 to select that accurate maximum. - - -- Function: size_t mpf_inp_str (mpf_t ROP, FILE *STREAM, int BASE) - Read a string in base BASE from STREAM, and put the read float in - ROP. The string is of the form `M@N' or, if the base is 10 or - less, alternatively `MeN'. `M' is the mantissa and `N' is the - exponent. The mantissa is always in the specified base. The - exponent is either in the specified base or, if BASE is negative, - in decimal. The decimal point expected is taken from the current - locale, on systems providing `localeconv'. - - The argument BASE may be in the ranges 2 to 36, or -36 to -2. - Negative values are used to specify that the exponent is in - decimal. - - Unlike the corresponding `mpz' function, the base will not be - determined from the leading characters of the string if BASE is 0. - This is so that numbers like `0.23' are not interpreted as octal. - - Return the number of bytes read, or if an error occurred, return 0. - - -File: gmp.info, Node: Miscellaneous Float Functions, Prev: I/O of Floats, Up: Floating-point Functions - -7.8 Miscellaneous Functions -=========================== - - -- Function: void mpf_ceil (mpf_t ROP, mpf_t OP) - -- Function: void mpf_floor (mpf_t ROP, mpf_t OP) - -- Function: void mpf_trunc (mpf_t ROP, mpf_t OP) - Set ROP to OP rounded to an integer. `mpf_ceil' rounds to the - next higher integer, `mpf_floor' to the next lower, and `mpf_trunc' - to the integer towards zero. - - -- Function: int mpf_integer_p (mpf_t OP) - Return non-zero if OP is an integer. - - -- Function: int mpf_fits_ulong_p (mpf_t OP) - -- Function: int mpf_fits_slong_p (mpf_t OP) - -- Function: int mpf_fits_uint_p (mpf_t OP) - -- Function: int mpf_fits_sint_p (mpf_t OP) - -- Function: int mpf_fits_ushort_p (mpf_t OP) - -- Function: int mpf_fits_sshort_p (mpf_t OP) - Return non-zero if OP would fit in the respective C data type, when - truncated to an integer. - - -- Function: void mpf_urandomb (mpf_t ROP, gmp_randstate_t STATE, - mp_bitcnt_t NBITS) - Generate a uniformly distributed random float in ROP, such that 0 - <= ROP < 1, with NBITS significant bits in the mantissa. - - The variable STATE must be initialized by calling one of the - `gmp_randinit' functions (*Note Random State Initialization::) - before invoking this function. - - -- Function: void mpf_random2 (mpf_t ROP, mp_size_t MAX_SIZE, mp_exp_t - EXP) - Generate a random float of at most MAX_SIZE limbs, with long - strings of zeros and ones in the binary representation. The - exponent of the number is in the interval -EXP to EXP (in limbs). - This function is useful for testing functions and algorithms, - since these kind of random numbers have proven to be more likely - to trigger corner-case bugs. Negative random numbers are - generated when MAX_SIZE is negative. - - -File: gmp.info, Node: Low-level Functions, Next: Random Number Functions, Prev: Floating-point Functions, Up: Top - -8 Low-level Functions -********************* - -This chapter describes low-level GMP functions, used to implement the -high-level GMP functions, but also intended for time-critical user code. - - These functions start with the prefix `mpn_'. - - The `mpn' functions are designed to be as fast as possible, *not* to -provide a coherent calling interface. The different functions have -somewhat similar interfaces, but there are variations that make them -hard to use. These functions do as little as possible apart from the -real multiple precision computation, so that no time is spent on things -that not all callers need. - - A source operand is specified by a pointer to the least significant -limb and a limb count. A destination operand is specified by just a -pointer. It is the responsibility of the caller to ensure that the -destination has enough space for storing the result. - - With this way of specifying operands, it is possible to perform -computations on subranges of an argument, and store the result into a -subrange of a destination. - - A common requirement for all functions is that each source area -needs at least one limb. No size argument may be zero. Unless -otherwise stated, in-place operations are allowed where source and -destination are the same, but not where they only partly overlap. - - The `mpn' functions are the base for the implementation of the -`mpz_', `mpf_', and `mpq_' functions. - - This example adds the number beginning at S1P and the number -beginning at S2P and writes the sum at DESTP. All areas have N limbs. - - cy = mpn_add_n (destp, s1p, s2p, n) - - It should be noted that the `mpn' functions make no attempt to -identify high or low zero limbs on their operands, or other special -forms. On random data such cases will be unlikely and it'd be wasteful -for every function to check every time. An application knowing -something about its data can take steps to trim or perhaps split its -calculations. - - -In the notation used below, a source operand is identified by the -pointer to the least significant limb, and the limb count in braces. -For example, {S1P, S1N}. - - -- Function: mp_limb_t mpn_add_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Add {S1P, N} and {S2P, N}, and write the N least significant limbs - of the result to RP. Return carry, either 0 or 1. - - This is the lowest-level function for addition. It is the - preferred function for addition, since it is written in assembly - for most CPUs. For addition of a variable to itself (i.e., S1P - equals S2P) use `mpn_lshift' with a count of 1 for optimal speed. - - -- Function: mp_limb_t mpn_add_1 (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t N, mp_limb_t S2LIMB) - Add {S1P, N} and S2LIMB, and write the N least significant limbs - of the result to RP. Return carry, either 0 or 1. - - -- Function: mp_limb_t mpn_add (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t S1N, const mp_limb_t *S2P, mp_size_t S2N) - Add {S1P, S1N} and {S2P, S2N}, and write the S1N least significant - limbs of the result to RP. Return carry, either 0 or 1. - - This function requires that S1N is greater than or equal to S2N. - - -- Function: mp_limb_t mpn_sub_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Subtract {S2P, N} from {S1P, N}, and write the N least significant - limbs of the result to RP. Return borrow, either 0 or 1. - - This is the lowest-level function for subtraction. It is the - preferred function for subtraction, since it is written in - assembly for most CPUs. - - -- Function: mp_limb_t mpn_sub_1 (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t N, mp_limb_t S2LIMB) - Subtract S2LIMB from {S1P, N}, and write the N least significant - limbs of the result to RP. Return borrow, either 0 or 1. - - -- Function: mp_limb_t mpn_sub (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t S1N, const mp_limb_t *S2P, mp_size_t S2N) - Subtract {S2P, S2N} from {S1P, S1N}, and write the S1N least - significant limbs of the result to RP. Return borrow, either 0 or - 1. - - This function requires that S1N is greater than or equal to S2N. - - -- Function: void mpn_neg (mp_limb_t *RP, const mp_limb_t *SP, - mp_size_t N) - Perform the negation of {SP, N}, and write the result to {RP, N}. - Return carry-out. - - -- Function: void mpn_mul_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Multiply {S1P, N} and {S2P, N}, and write the 2*N-limb result to - RP. - - The destination has to have space for 2*N limbs, even if the - product's most significant limb is zero. No overlap is permitted - between the destination and either source. - - If the two input operands are the same, use `mpn_sqr'. - - -- Function: mp_limb_t mpn_mul (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t S1N, const mp_limb_t *S2P, mp_size_t S2N) - Multiply {S1P, S1N} and {S2P, S2N}, and write the (S1N+S2N)-limb - result to RP. Return the most significant limb of the result. - - The destination has to have space for S1N + S2N limbs, even if the - product's most significant limb is zero. No overlap is permitted - between the destination and either source. - - This function requires that S1N is greater than or equal to S2N. - - -- Function: void mpn_sqr (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t N) - Compute the square of {S1P, N} and write the 2*N-limb result to RP. - - The destination has to have space for 2*N limbs, even if the - result's most significant limb is zero. No overlap is permitted - between the destination and the source. - - -- Function: mp_limb_t mpn_mul_1 (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t N, mp_limb_t S2LIMB) - Multiply {S1P, N} by S2LIMB, and write the N least significant - limbs of the product to RP. Return the most significant limb of - the product. {S1P, N} and {RP, N} are allowed to overlap provided - RP <= S1P. - - This is a low-level function that is a building block for general - multiplication as well as other operations in GMP. It is written - in assembly for most CPUs. - - Don't call this function if S2LIMB is a power of 2; use - `mpn_lshift' with a count equal to the logarithm of S2LIMB - instead, for optimal speed. - - -- Function: mp_limb_t mpn_addmul_1 (mp_limb_t *RP, const mp_limb_t - *S1P, mp_size_t N, mp_limb_t S2LIMB) - Multiply {S1P, N} and S2LIMB, and add the N least significant - limbs of the product to {RP, N} and write the result to RP. - Return the most significant limb of the product, plus carry-out - from the addition. - - This is a low-level function that is a building block for general - multiplication as well as other operations in GMP. It is written - in assembly for most CPUs. - - -- Function: mp_limb_t mpn_submul_1 (mp_limb_t *RP, const mp_limb_t - *S1P, mp_size_t N, mp_limb_t S2LIMB) - Multiply {S1P, N} and S2LIMB, and subtract the N least significant - limbs of the product from {RP, N} and write the result to RP. - Return the most significant limb of the product, plus borrow-out - from the subtraction. - - This is a low-level function that is a building block for general - multiplication and division as well as other operations in GMP. - It is written in assembly for most CPUs. - - -- Function: void mpn_tdiv_qr (mp_limb_t *QP, mp_limb_t *RP, mp_size_t - QXN, const mp_limb_t *NP, mp_size_t NN, const mp_limb_t *DP, - mp_size_t DN) - Divide {NP, NN} by {DP, DN} and put the quotient at {QP, NN-DN+1} - and the remainder at {RP, DN}. The quotient is rounded towards 0. - - No overlap is permitted between arguments, except that NP might - equal RP. The dividend size NN must be greater than or equal to - divisor size DN. The most significant limb of the divisor must be - non-zero. The QXN operand must be zero. - - -- Function: mp_limb_t mpn_divrem (mp_limb_t *R1P, mp_size_t QXN, - mp_limb_t *RS2P, mp_size_t RS2N, const mp_limb_t *S3P, - mp_size_t S3N) - [This function is obsolete. Please call `mpn_tdiv_qr' instead for - best performance.] - - Divide {RS2P, RS2N} by {S3P, S3N}, and write the quotient at R1P, - with the exception of the most significant limb, which is - returned. The remainder replaces the dividend at RS2P; it will be - S3N limbs long (i.e., as many limbs as the divisor). - - In addition to an integer quotient, QXN fraction limbs are - developed, and stored after the integral limbs. For most usages, - QXN will be zero. - - It is required that RS2N is greater than or equal to S3N. It is - required that the most significant bit of the divisor is set. - - If the quotient is not needed, pass RS2P + S3N as R1P. Aside from - that special case, no overlap between arguments is permitted. - - Return the most significant limb of the quotient, either 0 or 1. - - The area at R1P needs to be RS2N - S3N + QXN limbs large. - - -- Function: mp_limb_t mpn_divrem_1 (mp_limb_t *R1P, mp_size_t QXN, - mp_limb_t *S2P, mp_size_t S2N, mp_limb_t S3LIMB) - -- Macro: mp_limb_t mpn_divmod_1 (mp_limb_t *R1P, mp_limb_t *S2P, - mp_size_t S2N, mp_limb_t S3LIMB) - Divide {S2P, S2N} by S3LIMB, and write the quotient at R1P. - Return the remainder. - - The integer quotient is written to {R1P+QXN, S2N} and in addition - QXN fraction limbs are developed and written to {R1P, QXN}. - Either or both S2N and QXN can be zero. For most usages, QXN will - be zero. - - `mpn_divmod_1' exists for upward source compatibility and is - simply a macro calling `mpn_divrem_1' with a QXN of 0. - - The areas at R1P and S2P have to be identical or completely - separate, not partially overlapping. - - -- Function: mp_limb_t mpn_divmod (mp_limb_t *R1P, mp_limb_t *RS2P, - mp_size_t RS2N, const mp_limb_t *S3P, mp_size_t S3N) - [This function is obsolete. Please call `mpn_tdiv_qr' instead for - best performance.] - - -- Macro: mp_limb_t mpn_divexact_by3 (mp_limb_t *RP, mp_limb_t *SP, - mp_size_t N) - -- Function: mp_limb_t mpn_divexact_by3c (mp_limb_t *RP, mp_limb_t - *SP, mp_size_t N, mp_limb_t CARRY) - Divide {SP, N} by 3, expecting it to divide exactly, and writing - the result to {RP, N}. If 3 divides exactly, the return value is - zero and the result is the quotient. If not, the return value is - non-zero and the result won't be anything useful. - - `mpn_divexact_by3c' takes an initial carry parameter, which can be - the return value from a previous call, so a large calculation can - be done piece by piece from low to high. `mpn_divexact_by3' is - simply a macro calling `mpn_divexact_by3c' with a 0 carry - parameter. - - These routines use a multiply-by-inverse and will be faster than - `mpn_divrem_1' on CPUs with fast multiplication but slow division. - - The source a, result q, size n, initial carry i, and return value - c satisfy c*b^n + a-i = 3*q, where b=2^GMP_NUMB_BITS. The return - c is always 0, 1 or 2, and the initial carry i must also be 0, 1 - or 2 (these are both borrows really). When c=0 clearly q=(a-i)/3. - When c!=0, the remainder (a-i) mod 3 is given by 3-c, because b - == 1 mod 3 (when `mp_bits_per_limb' is even, which is always so - currently). - - -- Function: mp_limb_t mpn_mod_1 (mp_limb_t *S1P, mp_size_t S1N, - mp_limb_t S2LIMB) - Divide {S1P, S1N} by S2LIMB, and return the remainder. S1N can be - zero. - - -- Function: mp_limb_t mpn_lshift (mp_limb_t *RP, const mp_limb_t *SP, - mp_size_t N, unsigned int COUNT) - Shift {SP, N} left by COUNT bits, and write the result to {RP, N}. - The bits shifted out at the left are returned in the least - significant COUNT bits of the return value (the rest of the return - value is zero). - - COUNT must be in the range 1 to mp_bits_per_limb-1. The regions - {SP, N} and {RP, N} may overlap, provided RP >= SP. - - This function is written in assembly for most CPUs. - - -- Function: mp_limb_t mpn_rshift (mp_limb_t *RP, const mp_limb_t *SP, - mp_size_t N, unsigned int COUNT) - Shift {SP, N} right by COUNT bits, and write the result to {RP, - N}. The bits shifted out at the right are returned in the most - significant COUNT bits of the return value (the rest of the return - value is zero). - - COUNT must be in the range 1 to mp_bits_per_limb-1. The regions - {SP, N} and {RP, N} may overlap, provided RP <= SP. - - This function is written in assembly for most CPUs. - - -- Function: int mpn_cmp (const mp_limb_t *S1P, const mp_limb_t *S2P, - mp_size_t N) - Compare {S1P, N} and {S2P, N} and return a positive value if S1 > - S2, 0 if they are equal, or a negative value if S1 < S2. - - -- Function: mp_size_t mpn_gcd (mp_limb_t *RP, mp_limb_t *XP, - mp_size_t XN, mp_limb_t *YP, mp_size_t YN) - Set {RP, RETVAL} to the greatest common divisor of {XP, XN} and - {YP, YN}. The result can be up to YN limbs, the return value is - the actual number produced. Both source operands are destroyed. - - {XP, XN} must have at least as many bits as {YP, YN}. {YP, YN} - must be odd. Both operands must have non-zero most significant - limbs. No overlap is permitted between {XP, XN} and {YP, YN}. - - -- Function: mp_limb_t mpn_gcd_1 (const mp_limb_t *XP, mp_size_t XN, - mp_limb_t YLIMB) - Return the greatest common divisor of {XP, XN} and YLIMB. Both - operands must be non-zero. - - -- Function: mp_size_t mpn_gcdext (mp_limb_t *GP, mp_limb_t *SP, - mp_size_t *SN, mp_limb_t *XP, mp_size_t XN, mp_limb_t *YP, - mp_size_t YN) - Let U be defined by {XP, XN} and let V be defined by {YP, YN}. - - Compute the greatest common divisor G of U and V. Compute a - cofactor S such that G = US + VT. The second cofactor T is not - computed but can easily be obtained from (G - U*S) / V (the - division will be exact). It is required that U >= V > 0. - - S satisfies S = 1 or abs(S) < V / (2 G). S = 0 if and only if V - divides U (i.e., G = V). - - Store G at GP and let the return value define its limb count. - Store S at SP and let |*SN| define its limb count. S can be - negative; when this happens *SN will be negative. The areas at GP - and SP should each have room for XN+1 limbs. - - The areas {XP, XN+1} and {YP, YN+1} are destroyed (i.e. the input - operands plus an extra limb past the end of each). - - Compatibility note: GMP 4.3.0 and 4.3.1 defined S less strictly. - Earlier as well as later GMP releases define S as described here. - - -- Function: mp_size_t mpn_sqrtrem (mp_limb_t *R1P, mp_limb_t *R2P, - const mp_limb_t *SP, mp_size_t N) - Compute the square root of {SP, N} and put the result at {R1P, - ceil(N/2)} and the remainder at {R2P, RETVAL}. R2P needs space - for N limbs, but the return value indicates how many are produced. - - The most significant limb of {SP, N} must be non-zero. The areas - {R1P, ceil(N/2)} and {SP, N} must be completely separate. The - areas {R2P, N} and {SP, N} must be either identical or completely - separate. - - If the remainder is not wanted then R2P can be `NULL', and in this - case the return value is zero or non-zero according to whether the - remainder would have been zero or non-zero. - - A return value of zero indicates a perfect square. See also - `mpz_perfect_square_p'. - - -- Function: mp_size_t mpn_get_str (unsigned char *STR, int BASE, - mp_limb_t *S1P, mp_size_t S1N) - Convert {S1P, S1N} to a raw unsigned char array at STR in base - BASE, and return the number of characters produced. There may be - leading zeros in the string. The string is not in ASCII; to - convert it to printable format, add the ASCII codes for `0' or - `A', depending on the base and range. BASE can vary from 2 to 256. - - The most significant limb of the input {S1P, S1N} must be - non-zero. The input {S1P, S1N} is clobbered, except when BASE is - a power of 2, in which case it's unchanged. - - The area at STR has to have space for the largest possible number - represented by a S1N long limb array, plus one extra character. - - -- Function: mp_size_t mpn_set_str (mp_limb_t *RP, const unsigned char - *STR, size_t STRSIZE, int BASE) - Convert bytes {STR,STRSIZE} in the given BASE to limbs at RP. - - STR[0] is the most significant byte and STR[STRSIZE-1] is the - least significant. Each byte should be a value in the range 0 to - BASE-1, not an ASCII character. BASE can vary from 2 to 256. - - The return value is the number of limbs written to RP. If the most - significant input byte is non-zero then the high limb at RP will be - non-zero, and only that exact number of limbs will be required - there. - - If the most significant input byte is zero then there may be high - zero limbs written to RP and included in the return value. - - STRSIZE must be at least 1, and no overlap is permitted between - {STR,STRSIZE} and the result at RP. - - -- Function: mp_bitcnt_t mpn_scan0 (const mp_limb_t *S1P, mp_bitcnt_t - BIT) - Scan S1P from bit position BIT for the next clear bit. - - It is required that there be a clear bit within the area at S1P at - or beyond bit position BIT, so that the function has something to - return. - - -- Function: mp_bitcnt_t mpn_scan1 (const mp_limb_t *S1P, mp_bitcnt_t - BIT) - Scan S1P from bit position BIT for the next set bit. - - It is required that there be a set bit within the area at S1P at or - beyond bit position BIT, so that the function has something to - return. - - -- Function: void mpn_random (mp_limb_t *R1P, mp_size_t R1N) - -- Function: void mpn_random2 (mp_limb_t *R1P, mp_size_t R1N) - Generate a random number of length R1N and store it at R1P. The - most significant limb is always non-zero. `mpn_random' generates - uniformly distributed limb data, `mpn_random2' generates long - strings of zeros and ones in the binary representation. - - `mpn_random2' is intended for testing the correctness of the `mpn' - routines. - - -- Function: mp_bitcnt_t mpn_popcount (const mp_limb_t *S1P, mp_size_t - N) - Count the number of set bits in {S1P, N}. - - -- Function: mp_bitcnt_t mpn_hamdist (const mp_limb_t *S1P, const - mp_limb_t *S2P, mp_size_t N) - Compute the hamming distance between {S1P, N} and {S2P, N}, which - is the number of bit positions where the two operands have - different bit values. - - -- Function: int mpn_perfect_square_p (const mp_limb_t *S1P, mp_size_t - N) - Return non-zero iff {S1P, N} is a perfect square. - - -- Function: void mpn_and_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical and of {S1P, N} and {S2P, N}, and - write the result to {RP, N}. - - -- Function: void mpn_ior_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical inclusive or of {S1P, N} and {S2P, N}, - and write the result to {RP, N}. - - -- Function: void mpn_xor_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical exclusive or of {S1P, N} and {S2P, N}, - and write the result to {RP, N}. - - -- Function: void mpn_andn_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical and of {S1P, N} and the bitwise - complement of {S2P, N}, and write the result to {RP, N}. - - -- Function: void mpn_iorn_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical inclusive or of {S1P, N} and the - bitwise complement of {S2P, N}, and write the result to {RP, N}. - - -- Function: void mpn_nand_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical and of {S1P, N} and {S2P, N}, and - write the bitwise complement of the result to {RP, N}. - - -- Function: void mpn_nior_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical inclusive or of {S1P, N} and {S2P, N}, - and write the bitwise complement of the result to {RP, N}. - - -- Function: void mpn_xnor_n (mp_limb_t *RP, const mp_limb_t *S1P, - const mp_limb_t *S2P, mp_size_t N) - Perform the bitwise logical exclusive or of {S1P, N} and {S2P, N}, - and write the bitwise complement of the result to {RP, N}. - - -- Function: void mpn_com (mp_limb_t *RP, const mp_limb_t *SP, - mp_size_t N) - Perform the bitwise complement of {SP, N}, and write the result to - {RP, N}. - - -- Function: void mpn_copyi (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t N) - Copy from {S1P, N} to {RP, N}, increasingly. - - -- Function: void mpn_copyd (mp_limb_t *RP, const mp_limb_t *S1P, - mp_size_t N) - Copy from {S1P, N} to {RP, N}, decreasingly. - - -- Function: void mpn_zero (mp_limb_t *RP, mp_size_t N) - Zero {RP, N}. - - -8.1 Nails -========= - -*Everything in this section is highly experimental and may disappear or -be subject to incompatible changes in a future version of GMP.* - - Nails are an experimental feature whereby a few bits are left unused -at the top of each `mp_limb_t'. This can significantly improve carry -handling on some processors. - - All the `mpn' functions accepting limb data will expect the nail -bits to be zero on entry, and will return data with the nails similarly -all zero. This applies both to limb vectors and to single limb -arguments. - - Nails can be enabled by configuring with `--enable-nails'. By -default the number of bits will be chosen according to what suits the -host processor, but a particular number can be selected with -`--enable-nails=N'. - - At the mpn level, a nail build is neither source nor binary -compatible with a non-nail build, strictly speaking. But programs -acting on limbs only through the mpn functions are likely to work -equally well with either build, and judicious use of the definitions -below should make any program compatible with either build, at the -source level. - - For the higher level routines, meaning `mpz' etc, a nail build -should be fully source and binary compatible with a non-nail build. - - -- Macro: GMP_NAIL_BITS - -- Macro: GMP_NUMB_BITS - -- Macro: GMP_LIMB_BITS - `GMP_NAIL_BITS' is the number of nail bits, or 0 when nails are - not in use. `GMP_NUMB_BITS' is the number of data bits in a limb. - `GMP_LIMB_BITS' is the total number of bits in an `mp_limb_t'. In - all cases - - GMP_LIMB_BITS == GMP_NAIL_BITS + GMP_NUMB_BITS - - -- Macro: GMP_NAIL_MASK - -- Macro: GMP_NUMB_MASK - Bit masks for the nail and number parts of a limb. - `GMP_NAIL_MASK' is 0 when nails are not in use. - - `GMP_NAIL_MASK' is not often needed, since the nail part can be - obtained with `x >> GMP_NUMB_BITS', and that means one less large - constant, which can help various RISC chips. - - -- Macro: GMP_NUMB_MAX - The maximum value that can be stored in the number part of a limb. - This is the same as `GMP_NUMB_MASK', but can be used for clarity - when doing comparisons rather than bit-wise operations. - - The term "nails" comes from finger or toe nails, which are at the -ends of a limb (arm or leg). "numb" is short for number, but is also -how the developers felt after trying for a long time to come up with -sensible names for these things. - - In the future (the distant future most likely) a non-zero nail might -be permitted, giving non-unique representations for numbers in a limb -vector. This would help vector processors since carries would only -ever need to propagate one or two limbs. - - -File: gmp.info, Node: Random Number Functions, Next: Formatted Output, Prev: Low-level Functions, Up: Top - -9 Random Number Functions -************************* - -Sequences of pseudo-random numbers in GMP are generated using a -variable of type `gmp_randstate_t', which holds an algorithm selection -and a current state. Such a variable must be initialized by a call to -one of the `gmp_randinit' functions, and can be seeded with one of the -`gmp_randseed' functions. - - The functions actually generating random numbers are described in -*Note Integer Random Numbers::, and *Note Miscellaneous Float -Functions::. - - The older style random number functions don't accept a -`gmp_randstate_t' parameter but instead share a global variable of that -type. They use a default algorithm and are currently not seeded -(though perhaps that will change in the future). The new functions -accepting a `gmp_randstate_t' are recommended for applications that -care about randomness. - -* Menu: - -* Random State Initialization:: -* Random State Seeding:: -* Random State Miscellaneous:: - - -File: gmp.info, Node: Random State Initialization, Next: Random State Seeding, Prev: Random Number Functions, Up: Random Number Functions - -9.1 Random State Initialization -=============================== - - -- Function: void gmp_randinit_default (gmp_randstate_t STATE) - Initialize STATE with a default algorithm. This will be a - compromise between speed and randomness, and is recommended for - applications with no special requirements. Currently this is - `gmp_randinit_mt'. - - -- Function: void gmp_randinit_mt (gmp_randstate_t STATE) - Initialize STATE for a Mersenne Twister algorithm. This algorithm - is fast and has good randomness properties. - - -- Function: void gmp_randinit_lc_2exp (gmp_randstate_t STATE, mpz_t - A, unsigned long C, mp_bitcnt_t M2EXP) - Initialize STATE with a linear congruential algorithm X = (A*X + - C) mod 2^M2EXP. - - The low bits of X in this algorithm are not very random. The least - significant bit will have a period no more than 2, and the second - bit no more than 4, etc. For this reason only the high half of - each X is actually used. - - When a random number of more than M2EXP/2 bits is to be generated, - multiple iterations of the recurrence are used and the results - concatenated. - - -- Function: int gmp_randinit_lc_2exp_size (gmp_randstate_t STATE, - mp_bitcnt_t SIZE) - Initialize STATE for a linear congruential algorithm as per - `gmp_randinit_lc_2exp'. A, C and M2EXP are selected from a table, - chosen so that SIZE bits (or more) of each X will be used, ie. - M2EXP/2 >= SIZE. - - If successful the return value is non-zero. If SIZE is bigger - than the table data provides then the return value is zero. The - maximum SIZE currently supported is 128. - - -- Function: void gmp_randinit_set (gmp_randstate_t ROP, - gmp_randstate_t OP) - Initialize ROP with a copy of the algorithm and state from OP. - - -- Function: void gmp_randinit (gmp_randstate_t STATE, - gmp_randalg_t ALG, ...) - *This function is obsolete.* - - Initialize STATE with an algorithm selected by ALG. The only - choice is `GMP_RAND_ALG_LC', which is `gmp_randinit_lc_2exp_size' - described above. A third parameter of type `unsigned long' is - required, this is the SIZE for that function. - `GMP_RAND_ALG_DEFAULT' or 0 are the same as `GMP_RAND_ALG_LC'. - - `gmp_randinit' sets bits in the global variable `gmp_errno' to - indicate an error. `GMP_ERROR_UNSUPPORTED_ARGUMENT' if ALG is - unsupported, or `GMP_ERROR_INVALID_ARGUMENT' if the SIZE parameter - is too big. It may be noted this error reporting is not thread - safe (a good reason to use `gmp_randinit_lc_2exp_size' instead). - - -- Function: void gmp_randclear (gmp_randstate_t STATE) - Free all memory occupied by STATE. - - -File: gmp.info, Node: Random State Seeding, Next: Random State Miscellaneous, Prev: Random State Initialization, Up: Random Number Functions - -9.2 Random State Seeding -======================== - - -- Function: void gmp_randseed (gmp_randstate_t STATE, mpz_t SEED) - -- Function: void gmp_randseed_ui (gmp_randstate_t STATE, - unsigned long int SEED) - Set an initial seed value into STATE. - - The size of a seed determines how many different sequences of - random numbers that it's possible to generate. The "quality" of - the seed is the randomness of a given seed compared to the - previous seed used, and this affects the randomness of separate - number sequences. The method for choosing a seed is critical if - the generated numbers are to be used for important applications, - such as generating cryptographic keys. - - Traditionally the system time has been used to seed, but care - needs to be taken with this. If an application seeds often and - the resolution of the system clock is low, then the same sequence - of numbers might be repeated. Also, the system time is quite easy - to guess, so if unpredictability is required then it should - definitely not be the only source for the seed value. On some - systems there's a special device `/dev/random' which provides - random data better suited for use as a seed. - - -File: gmp.info, Node: Random State Miscellaneous, Prev: Random State Seeding, Up: Random Number Functions - -9.3 Random State Miscellaneous -============================== - - -- Function: unsigned long gmp_urandomb_ui (gmp_randstate_t STATE, - unsigned long N) - Return a uniformly distributed random number of N bits, ie. in the - range 0 to 2^N-1 inclusive. N must be less than or equal to the - number of bits in an `unsigned long'. - - -- Function: unsigned long gmp_urandomm_ui (gmp_randstate_t STATE, - unsigned long N) - Return a uniformly distributed random number in the range 0 to - N-1, inclusive. - - -File: gmp.info, Node: Formatted Output, Next: Formatted Input, Prev: Random Number Functions, Up: Top - -10 Formatted Output -******************* - -* Menu: - -* Formatted Output Strings:: -* Formatted Output Functions:: -* C++ Formatted Output:: - - -File: gmp.info, Node: Formatted Output Strings, Next: Formatted Output Functions, Prev: Formatted Output, Up: Formatted Output - -10.1 Format Strings -=================== - -`gmp_printf' and friends accept format strings similar to the standard C -`printf' (*note Formatted Output: (libc)Formatted Output.). A format -specification is of the form - - % [flags] [width] [.[precision]] [type] conv - - GMP adds types `Z', `Q' and `F' for `mpz_t', `mpq_t' and `mpf_t' -respectively, `M' for `mp_limb_t', and `N' for an `mp_limb_t' array. -`Z', `Q', `M' and `N' behave like integers. `Q' will print a `/' and a -denominator, if needed. `F' behaves like a float. For example, - - mpz_t z; - gmp_printf ("%s is an mpz %Zd\n", "here", z); - - mpq_t q; - gmp_printf ("a hex rational: %#40Qx\n", q); - - mpf_t f; - int n; - gmp_printf ("fixed point mpf %.*Ff with %d digits\n", n, f, n); - - mp_limb_t l; - gmp_printf ("limb %Mu\n", l); - - const mp_limb_t *ptr; - mp_size_t size; - gmp_printf ("limb array %Nx\n", ptr, size); - - For `N' the limbs are expected least significant first, as per the -`mpn' functions (*note Low-level Functions::). A negative size can be -given to print the value as a negative. - - All the standard C `printf' types behave the same as the C library -`printf', and can be freely intermixed with the GMP extensions. In the -current implementation the standard parts of the format string are -simply handed to `printf' and only the GMP extensions handled directly. - - The flags accepted are as follows. GLIBC style ' is only for the -standard C types (not the GMP types), and only if the C library -supports it. - - 0 pad with zeros (rather than spaces) - # show the base with `0x', `0X' or `0' - + always show a sign - (space) show a space or a `-' sign - ' group digits, GLIBC style (not GMP types) - - The optional width and precision can be given as a number within the -format string, or as a `*' to take an extra parameter of type `int', the -same as the standard `printf'. - - The standard types accepted are as follows. `h' and `l' are -portable, the rest will depend on the compiler (or include files) for -the type and the C library for the output. - - h short - hh char - j intmax_t or uintmax_t - l long or wchar_t - ll long long - L long double - q quad_t or u_quad_t - t ptrdiff_t - z size_t - -The GMP types are - - F mpf_t, float conversions - Q mpq_t, integer conversions - M mp_limb_t, integer conversions - N mp_limb_t array, integer conversions - Z mpz_t, integer conversions - - The conversions accepted are as follows. `a' and `A' are always -supported for `mpf_t' but depend on the C library for standard C float -types. `m' and `p' depend on the C library. - - a A hex floats, C99 style - c character - d decimal integer - e E scientific format float - f fixed point float - i same as d - g G fixed or scientific float - m `strerror' string, GLIBC style - n store characters written so far - o octal integer - p pointer - s string - u unsigned integer - x X hex integer - - `o', `x' and `X' are unsigned for the standard C types, but for -types `Z', `Q' and `N' they are signed. `u' is not meaningful for `Z', -`Q' and `N'. - - `M' is a proxy for the C library `l' or `L', according to the size -of `mp_limb_t'. Unsigned conversions will be usual, but a signed -conversion can be used and will interpret the value as a twos complement -negative. - - `n' can be used with any type, even the GMP types. - - Other types or conversions that might be accepted by the C library -`printf' cannot be used through `gmp_printf', this includes for -instance extensions registered with GLIBC `register_printf_function'. -Also currently there's no support for POSIX `$' style numbered arguments -(perhaps this will be added in the future). - - The precision field has it's usual meaning for integer `Z' and float -`F' types, but is currently undefined for `Q' and should not be used -with that. - - `mpf_t' conversions only ever generate as many digits as can be -accurately represented by the operand, the same as `mpf_get_str' does. -Zeros will be used if necessary to pad to the requested precision. This -happens even for an `f' conversion of an `mpf_t' which is an integer, -for instance 2^1024 in an `mpf_t' of 128 bits precision will only -produce about 40 digits, then pad with zeros to the decimal point. An -empty precision field like `%.Fe' or `%.Ff' can be used to specifically -request just the significant digits. - - The decimal point character (or string) is taken from the current -locale settings on systems which provide `localeconv' (*note Locales -and Internationalization: (libc)Locales.). The C library will normally -do the same for standard float output. - - The format string is only interpreted as plain `char's, multibyte -characters are not recognised. Perhaps this will change in the future. - - -File: gmp.info, Node: Formatted Output Functions, Next: C++ Formatted Output, Prev: Formatted Output Strings, Up: Formatted Output - -10.2 Functions -============== - -Each of the following functions is similar to the corresponding C -library function. The basic `printf' forms take a variable argument -list. The `vprintf' forms take an argument pointer, see *Note Variadic -Functions: (libc)Variadic Functions, or `man 3 va_start'. - - It should be emphasised that if a format string is invalid, or the -arguments don't match what the format specifies, then the behaviour of -any of these functions will be unpredictable. GCC format string -checking is not available, since it doesn't recognise the GMP -extensions. - - The file based functions `gmp_printf' and `gmp_fprintf' will return --1 to indicate a write error. Output is not "atomic", so partial -output may be produced if a write error occurs. All the functions can -return -1 if the C library `printf' variant in use returns -1, but this -shouldn't normally occur. - - -- Function: int gmp_printf (const char *FMT, ...) - -- Function: int gmp_vprintf (const char *FMT, va_list AP) - Print to the standard output `stdout'. Return the number of - characters written, or -1 if an error occurred. - - -- Function: int gmp_fprintf (FILE *FP, const char *FMT, ...) - -- Function: int gmp_vfprintf (FILE *FP, const char *FMT, va_list AP) - Print to the stream FP. Return the number of characters written, - or -1 if an error occurred. - - -- Function: int gmp_sprintf (char *BUF, const char *FMT, ...) - -- Function: int gmp_vsprintf (char *BUF, const char *FMT, va_list AP) - Form a null-terminated string in BUF. Return the number of - characters written, excluding the terminating null. - - No overlap is permitted between the space at BUF and the string - FMT. - - These functions are not recommended, since there's no protection - against exceeding the space available at BUF. - - -- Function: int gmp_snprintf (char *BUF, size_t SIZE, const char - *FMT, ...) - -- Function: int gmp_vsnprintf (char *BUF, size_t SIZE, const char - *FMT, va_list AP) - Form a null-terminated string in BUF. No more than SIZE bytes - will be written. To get the full output, SIZE must be enough for - the string and null-terminator. - - The return value is the total number of characters which ought to - have been produced, excluding the terminating null. If RETVAL >= - SIZE then the actual output has been truncated to the first SIZE-1 - characters, and a null appended. - - No overlap is permitted between the region {BUF,SIZE} and the FMT - string. - - Notice the return value is in ISO C99 `snprintf' style. This is - so even if the C library `vsnprintf' is the older GLIBC 2.0.x - style. - - -- Function: int gmp_asprintf (char **PP, const char *FMT, ...) - -- Function: int gmp_vasprintf (char **PP, const char *FMT, va_list AP) - Form a null-terminated string in a block of memory obtained from - the current memory allocation function (*note Custom - Allocation::). The block will be the size of the string and - null-terminator. The address of the block in stored to *PP. The - return value is the number of characters produced, excluding the - null-terminator. - - Unlike the C library `asprintf', `gmp_asprintf' doesn't return -1 - if there's no more memory available, it lets the current allocation - function handle that. - - -- Function: int gmp_obstack_printf (struct obstack *OB, const char - *FMT, ...) - -- Function: int gmp_obstack_vprintf (struct obstack *OB, const char - *FMT, va_list AP) - Append to the current object in OB. The return value is the - number of characters written. A null-terminator is not written. - - FMT cannot be within the current object in OB, since that object - might move as it grows. - - These functions are available only when the C library provides the - obstack feature, which probably means only on GNU systems, see - *Note Obstacks: (libc)Obstacks. - - -File: gmp.info, Node: C++ Formatted Output, Prev: Formatted Output Functions, Up: Formatted Output - -10.3 C++ Formatted Output -========================= - -The following functions are provided in `libgmpxx' (*note Headers and -Libraries::), which is built if C++ support is enabled (*note Build -Options::). Prototypes are available from `'. - - -- Function: ostream& operator<< (ostream& STREAM, mpz_t OP) - Print OP to STREAM, using its `ios' formatting settings. - `ios::width' is reset to 0 after output, the same as the standard - `ostream operator<<' routines do. - - In hex or octal, OP is printed as a signed number, the same as for - decimal. This is unlike the standard `operator<<' routines on - `int' etc, which instead give twos complement. - - -- Function: ostream& operator<< (ostream& STREAM, mpq_t OP) - Print OP to STREAM, using its `ios' formatting settings. - `ios::width' is reset to 0 after output, the same as the standard - `ostream operator<<' routines do. - - Output will be a fraction like `5/9', or if the denominator is 1 - then just a plain integer like `123'. - - In hex or octal, OP is printed as a signed value, the same as for - decimal. If `ios::showbase' is set then a base indicator is shown - on both the numerator and denominator (if the denominator is - required). - - -- Function: ostream& operator<< (ostream& STREAM, mpf_t OP) - Print OP to STREAM, using its `ios' formatting settings. - `ios::width' is reset to 0 after output, the same as the standard - `ostream operator<<' routines do. - - The decimal point follows the standard library float `operator<<', - which on recent systems means the `std::locale' imbued on STREAM. - - Hex and octal are supported, unlike the standard `operator<<' on - `double'. The mantissa will be in hex or octal, the exponent will - be in decimal. For hex the exponent delimiter is an `@'. This is - as per `mpf_out_str'. - - `ios::showbase' is supported, and will put a base on the mantissa, - for example hex `0x1.8' or `0x0.8', or octal `01.4' or `00.4'. - This last form is slightly strange, but at least differentiates - itself from decimal. - - These operators mean that GMP types can be printed in the usual C++ -way, for example, - - mpz_t z; - int n; - ... - cout << "iteration " << n << " value " << z << "\n"; - - But note that `ostream' output (and `istream' input, *note C++ -Formatted Input::) is the only overloading available for the GMP types -and that for instance using `+' with an `mpz_t' will have unpredictable -results. For classes with overloading, see *Note C++ Class Interface::. - - -File: gmp.info, Node: Formatted Input, Next: C++ Class Interface, Prev: Formatted Output, Up: Top - -11 Formatted Input -****************** - -* Menu: - -* Formatted Input Strings:: -* Formatted Input Functions:: -* C++ Formatted Input:: - - -File: gmp.info, Node: Formatted Input Strings, Next: Formatted Input Functions, Prev: Formatted Input, Up: Formatted Input - -11.1 Formatted Input Strings -============================ - -`gmp_scanf' and friends accept format strings similar to the standard C -`scanf' (*note Formatted Input: (libc)Formatted Input.). A format -specification is of the form - - % [flags] [width] [type] conv - - GMP adds types `Z', `Q' and `F' for `mpz_t', `mpq_t' and `mpf_t' -respectively. `Z' and `Q' behave like integers. `Q' will read a `/' -and a denominator, if present. `F' behaves like a float. - - GMP variables don't require an `&' when passed to `gmp_scanf', since -they're already "call-by-reference". For example, - - /* to read say "a(5) = 1234" */ - int n; - mpz_t z; - gmp_scanf ("a(%d) = %Zd\n", &n, z); - - mpq_t q1, q2; - gmp_sscanf ("0377 + 0x10/0x11", "%Qi + %Qi", q1, q2); - - /* to read say "topleft (1.55,-2.66)" */ - mpf_t x, y; - char buf[32]; - gmp_scanf ("%31s (%Ff,%Ff)", buf, x, y); - - All the standard C `scanf' types behave the same as in the C library -`scanf', and can be freely intermixed with the GMP extensions. In the -current implementation the standard parts of the format string are -simply handed to `scanf' and only the GMP extensions handled directly. - - The flags accepted are as follows. `a' and `'' will depend on -support from the C library, and `'' cannot be used with GMP types. - - * read but don't store - a allocate a buffer (string conversions) - ' grouped digits, GLIBC style (not GMP - types) - - The standard types accepted are as follows. `h' and `l' are -portable, the rest will depend on the compiler (or include files) for -the type and the C library for the input. - - h short - hh char - j intmax_t or uintmax_t - l long int, double or wchar_t - ll long long - L long double - q quad_t or u_quad_t - t ptrdiff_t - z size_t - -The GMP types are - - F mpf_t, float conversions - Q mpq_t, integer conversions - Z mpz_t, integer conversions - - The conversions accepted are as follows. `p' and `[' will depend on -support from the C library, the rest are standard. - - c character or characters - d decimal integer - e E f g G float - i integer with base indicator - n characters read so far - o octal integer - p pointer - s string of non-whitespace characters - u decimal integer - x X hex integer - [ string of characters in a set - - `e', `E', `f', `g' and `G' are identical, they all read either fixed -point or scientific format, and either upper or lower case `e' for the -exponent in scientific format. - - C99 style hex float format (`printf %a', *note Formatted Output -Strings::) is always accepted for `mpf_t', but for the standard float -types it will depend on the C library. - - `x' and `X' are identical, both accept both upper and lower case -hexadecimal. - - `o', `u', `x' and `X' all read positive or negative values. For the -standard C types these are described as "unsigned" conversions, but -that merely affects certain overflow handling, negatives are still -allowed (per `strtoul', *note Parsing of Integers: (libc)Parsing of -Integers.). For GMP types there are no overflows, so `d' and `u' are -identical. - - `Q' type reads the numerator and (optional) denominator as given. -If the value might not be in canonical form then `mpq_canonicalize' -must be called before using it in any calculations (*note Rational -Number Functions::). - - `Qi' will read a base specification separately for the numerator and -denominator. For example `0x10/11' would be 16/11, whereas `0x10/0x11' -would be 16/17. - - `n' can be used with any of the types above, even the GMP types. -`*' to suppress assignment is allowed, though in that case it would do -nothing at all. - - Other conversions or types that might be accepted by the C library -`scanf' cannot be used through `gmp_scanf'. - - Whitespace is read and discarded before a field, except for `c' and -`[' conversions. - - For float conversions, the decimal point character (or string) -expected is taken from the current locale settings on systems which -provide `localeconv' (*note Locales and Internationalization: -(libc)Locales.). The C library will normally do the same for standard -float input. - - The format string is only interpreted as plain `char's, multibyte -characters are not recognised. Perhaps this will change in the future. - - -File: gmp.info, Node: Formatted Input Functions, Next: C++ Formatted Input, Prev: Formatted Input Strings, Up: Formatted Input - -11.2 Formatted Input Functions -============================== - -Each of the following functions is similar to the corresponding C -library function. The plain `scanf' forms take a variable argument -list. The `vscanf' forms take an argument pointer, see *Note Variadic -Functions: (libc)Variadic Functions, or `man 3 va_start'. - - It should be emphasised that if a format string is invalid, or the -arguments don't match what the format specifies, then the behaviour of -any of these functions will be unpredictable. GCC format string -checking is not available, since it doesn't recognise the GMP -extensions. - - No overlap is permitted between the FMT string and any of the results -produced. - - -- Function: int gmp_scanf (const char *FMT, ...) - -- Function: int gmp_vscanf (const char *FMT, va_list AP) - Read from the standard input `stdin'. - - -- Function: int gmp_fscanf (FILE *FP, const char *FMT, ...) - -- Function: int gmp_vfscanf (FILE *FP, const char *FMT, va_list AP) - Read from the stream FP. - - -- Function: int gmp_sscanf (const char *S, const char *FMT, ...) - -- Function: int gmp_vsscanf (const char *S, const char *FMT, va_list - AP) - Read from a null-terminated string S. - - The return value from each of these functions is the same as the -standard C99 `scanf', namely the number of fields successfully parsed -and stored. `%n' fields and fields read but suppressed by `*' don't -count towards the return value. - - If end of input (or a file error) is reached before a character for -a field or a literal, and if no previous non-suppressed fields have -matched, then the return value is `EOF' instead of 0. A whitespace -character in the format string is only an optional match and doesn't -induce an `EOF' in this fashion. Leading whitespace read and discarded -for a field don't count as characters for that field. - - For the GMP types, input parsing follows C99 rules, namely one -character of lookahead is used and characters are read while they -continue to meet the format requirements. If this doesn't provide a -complete number then the function terminates, with that field not -stored nor counted towards the return value. For instance with `mpf_t' -an input `1.23e-XYZ' would be read up to the `X' and that character -pushed back since it's not a digit. The string `1.23e-' would then be -considered invalid since an `e' must be followed by at least one digit. - - For the standard C types, in the current implementation GMP calls -the C library `scanf' functions, which might have looser rules about -what constitutes a valid input. - - Note that `gmp_sscanf' is the same as `gmp_fscanf' and only does one -character of lookahead when parsing. Although clearly it could look at -its entire input, it is deliberately made identical to `gmp_fscanf', -the same way C99 `sscanf' is the same as `fscanf'. - - -File: gmp.info, Node: C++ Formatted Input, Prev: Formatted Input Functions, Up: Formatted Input - -11.3 C++ Formatted Input -======================== - -The following functions are provided in `libgmpxx' (*note Headers and -Libraries::), which is built only if C++ support is enabled (*note -Build Options::). Prototypes are available from `'. - - -- Function: istream& operator>> (istream& STREAM, mpz_t ROP) - Read ROP from STREAM, using its `ios' formatting settings. - - -- Function: istream& operator>> (istream& STREAM, mpq_t ROP) - An integer like `123' will be read, or a fraction like `5/9'. No - whitespace is allowed around the `/'. If the fraction is not in - canonical form then `mpq_canonicalize' must be called (*note - Rational Number Functions::) before operating on it. - - As per integer input, an `0' or `0x' base indicator is read when - none of `ios::dec', `ios::oct' or `ios::hex' are set. This is - done separately for numerator and denominator, so that for instance - `0x10/11' is 16/11 and `0x10/0x11' is 16/17. - - -- Function: istream& operator>> (istream& STREAM, mpf_t ROP) - Read ROP from STREAM, using its `ios' formatting settings. - - Hex or octal floats are not supported, but might be in the future, - or perhaps it's best to accept only what the standard float - `operator>>' does. - - Note that digit grouping specified by the `istream' locale is -currently not accepted. Perhaps this will change in the future. - - - These operators mean that GMP types can be read in the usual C++ -way, for example, - - mpz_t z; - ... - cin >> z; - - But note that `istream' input (and `ostream' output, *note C++ -Formatted Output::) is the only overloading available for the GMP types -and that for instance using `+' with an `mpz_t' will have unpredictable -results. For classes with overloading, see *Note C++ Class Interface::. - - -File: gmp.info, Node: C++ Class Interface, Next: BSD Compatible Functions, Prev: Formatted Input, Up: Top - -12 C++ Class Interface -********************** - -This chapter describes the C++ class based interface to GMP. - - All GMP C language types and functions can be used in C++ programs, -since `gmp.h' has `extern "C"' qualifiers, but the class interface -offers overloaded functions and operators which may be more convenient. - - Due to the implementation of this interface, a reasonably recent C++ -compiler is required, one supporting namespaces, partial specialization -of templates and member templates. For GCC this means version 2.91 or -later. - - *Everything described in this chapter is to be considered preliminary -and might be subject to incompatible changes if some unforeseen -difficulty reveals itself.* - -* Menu: - -* C++ Interface General:: -* C++ Interface Integers:: -* C++ Interface Rationals:: -* C++ Interface Floats:: -* C++ Interface Random Numbers:: -* C++ Interface Limitations:: - - -File: gmp.info, Node: C++ Interface General, Next: C++ Interface Integers, Prev: C++ Class Interface, Up: C++ Class Interface - -12.1 C++ Interface General -========================== - -All the C++ classes and functions are available with - - #include - - Programs should be linked with the `libgmpxx' and `libgmp' -libraries. For example, - - g++ mycxxprog.cc -lgmpxx -lgmp - -The classes defined are - - -- Class: mpz_class - -- Class: mpq_class - -- Class: mpf_class - - The standard operators and various standard functions are overloaded -to allow arithmetic with these classes. For example, - - int - main (void) - { - mpz_class a, b, c; - - a = 1234; - b = "-5678"; - c = a+b; - cout << "sum is " << c << "\n"; - cout << "absolute value is " << abs(c) << "\n"; - - return 0; - } - - An important feature of the implementation is that an expression like -`a=b+c' results in a single call to the corresponding `mpz_add', -without using a temporary for the `b+c' part. Expressions which by -their nature imply intermediate values, like `a=b*c+d*e', still use -temporaries though. - - The classes can be freely intermixed in expressions, as can the -classes and the standard types `long', `unsigned long' and `double'. -Smaller types like `int' or `float' can also be intermixed, since C++ -will promote them. - - Note that `bool' is not accepted directly, but must be explicitly -cast to an `int' first. This is because C++ will automatically convert -any pointer to a `bool', so if GMP accepted `bool' it would make all -sorts of invalid class and pointer combinations compile but almost -certainly not do anything sensible. - - Conversions back from the classes to standard C++ types aren't done -automatically, instead member functions like `get_si' are provided (see -the following sections for details). - - Also there are no automatic conversions from the classes to the -corresponding GMP C types, instead a reference to the underlying C -object can be obtained with the following functions, - - -- Function: mpz_t mpz_class::get_mpz_t () - -- Function: mpq_t mpq_class::get_mpq_t () - -- Function: mpf_t mpf_class::get_mpf_t () - - These can be used to call a C function which doesn't have a C++ class -interface. For example to set `a' to the GCD of `b' and `c', - - mpz_class a, b, c; - ... - mpz_gcd (a.get_mpz_t(), b.get_mpz_t(), c.get_mpz_t()); - - In the other direction, a class can be initialized from the -corresponding GMP C type, or assigned to if an explicit constructor is -used. In both cases this makes a copy of the value, it doesn't create -any sort of association. For example, - - mpz_t z; - // ... init and calculate z ... - mpz_class x(z); - mpz_class y; - y = mpz_class (z); - - There are no namespace setups in `gmpxx.h', all types and functions -are simply put into the global namespace. This is what `gmp.h' has -done in the past, and continues to do for compatibility. The extras -provided by `gmpxx.h' follow GMP naming conventions and are unlikely to -clash with anything. - - -File: gmp.info, Node: C++ Interface Integers, Next: C++ Interface Rationals, Prev: C++ Interface General, Up: C++ Class Interface - -12.2 C++ Interface Integers -=========================== - - -- Function: void mpz_class::mpz_class (type N) - Construct an `mpz_class'. All the standard C++ types may be used, - except `long long' and `long double', and all the GMP C++ classes - can be used. Any necessary conversion follows the corresponding C - function, for example `double' follows `mpz_set_d' (*note - Assigning Integers::). - - -- Function: void mpz_class::mpz_class (mpz_t Z) - Construct an `mpz_class' from an `mpz_t'. The value in Z is - copied into the new `mpz_class', there won't be any permanent - association between it and Z. - - -- Function: void mpz_class::mpz_class (const char *S) - -- Function: void mpz_class::mpz_class (const char *S, int BASE = 0) - -- Function: void mpz_class::mpz_class (const string& S) - -- Function: void mpz_class::mpz_class (const string& S, int BASE = 0) - Construct an `mpz_class' converted from a string using - `mpz_set_str' (*note Assigning Integers::). - - If the string is not a valid integer, an `std::invalid_argument' - exception is thrown. The same applies to `operator='. - - -- Function: mpz_class operator/ (mpz_class A, mpz_class D) - -- Function: mpz_class operator% (mpz_class A, mpz_class D) - Divisions involving `mpz_class' round towards zero, as per the - `mpz_tdiv_q' and `mpz_tdiv_r' functions (*note Integer Division::). - This is the same as the C99 `/' and `%' operators. - - The `mpz_fdiv...' or `mpz_cdiv...' functions can always be called - directly if desired. For example, - - mpz_class q, a, d; - ... - mpz_fdiv_q (q.get_mpz_t(), a.get_mpz_t(), d.get_mpz_t()); - - -- Function: mpz_class abs (mpz_class OP1) - -- Function: int cmp (mpz_class OP1, type OP2) - -- Function: int cmp (type OP1, mpz_class OP2) - -- Function: bool mpz_class::fits_sint_p (void) - -- Function: bool mpz_class::fits_slong_p (void) - -- Function: bool mpz_class::fits_sshort_p (void) - -- Function: bool mpz_class::fits_uint_p (void) - -- Function: bool mpz_class::fits_ulong_p (void) - -- Function: bool mpz_class::fits_ushort_p (void) - -- Function: double mpz_class::get_d (void) - -- Function: long mpz_class::get_si (void) - -- Function: string mpz_class::get_str (int BASE = 10) - -- Function: unsigned long mpz_class::get_ui (void) - -- Function: int mpz_class::set_str (const char *STR, int BASE) - -- Function: int mpz_class::set_str (const string& STR, int BASE) - -- Function: int sgn (mpz_class OP) - -- Function: mpz_class sqrt (mpz_class OP) - These functions provide a C++ class interface to the corresponding - GMP C routines. - - `cmp' can be used with any of the classes or the standard C++ - types, except `long long' and `long double'. - - - Overloaded operators for combinations of `mpz_class' and `double' -are provided for completeness, but it should be noted that if the given -`double' is not an integer then the way any rounding is done is -currently unspecified. The rounding might take place at the start, in -the middle, or at the end of the operation, and it might change in the -future. - - Conversions between `mpz_class' and `double', however, are defined -to follow the corresponding C functions `mpz_get_d' and `mpz_set_d'. -And comparisons are always made exactly, as per `mpz_cmp_d'. - - -File: gmp.info, Node: C++ Interface Rationals, Next: C++ Interface Floats, Prev: C++ Interface Integers, Up: C++ Class Interface - -12.3 C++ Interface Rationals -============================ - -In all the following constructors, if a fraction is given then it -should be in canonical form, or if not then `mpq_class::canonicalize' -called. - - -- Function: void mpq_class::mpq_class (type OP) - -- Function: void mpq_class::mpq_class (integer NUM, integer DEN) - Construct an `mpq_class'. The initial value can be a single value - of any type, or a pair of integers (`mpz_class' or standard C++ - integer types) representing a fraction, except that `long long' - and `long double' are not supported. For example, - - mpq_class q (99); - mpq_class q (1.75); - mpq_class q (1, 3); - - -- Function: void mpq_class::mpq_class (mpq_t Q) - Construct an `mpq_class' from an `mpq_t'. The value in Q is - copied into the new `mpq_class', there won't be any permanent - association between it and Q. - - -- Function: void mpq_class::mpq_class (const char *S) - -- Function: void mpq_class::mpq_class (const char *S, int BASE = 0) - -- Function: void mpq_class::mpq_class (const string& S) - -- Function: void mpq_class::mpq_class (const string& S, int BASE = 0) - Construct an `mpq_class' converted from a string using - `mpq_set_str' (*note Initializing Rationals::). - - If the string is not a valid rational, an `std::invalid_argument' - exception is thrown. The same applies to `operator='. - - -- Function: void mpq_class::canonicalize () - Put an `mpq_class' into canonical form, as per *Note Rational - Number Functions::. All arithmetic operators require their - operands in canonical form, and will return results in canonical - form. - - -- Function: mpq_class abs (mpq_class OP) - -- Function: int cmp (mpq_class OP1, type OP2) - -- Function: int cmp (type OP1, mpq_class OP2) - -- Function: double mpq_class::get_d (void) - -- Function: string mpq_class::get_str (int BASE = 10) - -- Function: int mpq_class::set_str (const char *STR, int BASE) - -- Function: int mpq_class::set_str (const string& STR, int BASE) - -- Function: int sgn (mpq_class OP) - These functions provide a C++ class interface to the corresponding - GMP C routines. - - `cmp' can be used with any of the classes or the standard C++ - types, except `long long' and `long double'. - - -- Function: mpz_class& mpq_class::get_num () - -- Function: mpz_class& mpq_class::get_den () - Get a reference to an `mpz_class' which is the numerator or - denominator of an `mpq_class'. This can be used both for read and - write access. If the object returned is modified, it modifies the - original `mpq_class'. - - If direct manipulation might produce a non-canonical value, then - `mpq_class::canonicalize' must be called before further operations. - - -- Function: mpz_t mpq_class::get_num_mpz_t () - -- Function: mpz_t mpq_class::get_den_mpz_t () - Get a reference to the underlying `mpz_t' numerator or denominator - of an `mpq_class'. This can be passed to C functions expecting an - `mpz_t'. Any modifications made to the `mpz_t' will modify the - original `mpq_class'. - - If direct manipulation might produce a non-canonical value, then - `mpq_class::canonicalize' must be called before further operations. - - -- Function: istream& operator>> (istream& STREAM, mpq_class& ROP); - Read ROP from STREAM, using its `ios' formatting settings, the - same as `mpq_t operator>>' (*note C++ Formatted Input::). - - If the ROP read might not be in canonical form then - `mpq_class::canonicalize' must be called. - - -File: gmp.info, Node: C++ Interface Floats, Next: C++ Interface Random Numbers, Prev: C++ Interface Rationals, Up: C++ Class Interface - -12.4 C++ Interface Floats -========================= - -When an expression requires the use of temporary intermediate -`mpf_class' values, like `f=g*h+x*y', those temporaries will have the -same precision as the destination `f'. Explicit constructors can be -used if this doesn't suit. - - -- Function: mpf_class::mpf_class (type OP) - -- Function: mpf_class::mpf_class (type OP, unsigned long PREC) - Construct an `mpf_class'. Any standard C++ type can be used, - except `long long' and `long double', and any of the GMP C++ - classes can be used. - - If PREC is given, the initial precision is that value, in bits. If - PREC is not given, then the initial precision is determined by the - type of OP given. An `mpz_class', `mpq_class', or C++ builtin - type will give the default `mpf' precision (*note Initializing - Floats::). An `mpf_class' or expression will give the precision - of that value. The precision of a binary expression is the higher - of the two operands. - - mpf_class f(1.5); // default precision - mpf_class f(1.5, 500); // 500 bits (at least) - mpf_class f(x); // precision of x - mpf_class f(abs(x)); // precision of x - mpf_class f(-g, 1000); // 1000 bits (at least) - mpf_class f(x+y); // greater of precisions of x and y - - -- Function: void mpf_class::mpf_class (const char *S) - -- Function: void mpf_class::mpf_class (const char *S, unsigned long - PREC, int BASE = 0) - -- Function: void mpf_class::mpf_class (const string& S) - -- Function: void mpf_class::mpf_class (const string& S, unsigned long - PREC, int BASE = 0) - Construct an `mpf_class' converted from a string using - `mpf_set_str' (*note Assigning Floats::). If PREC is given, the - initial precision is that value, in bits. If not, the default - `mpf' precision (*note Initializing Floats::) is used. - - If the string is not a valid float, an `std::invalid_argument' - exception is thrown. The same applies to `operator='. - - -- Function: mpf_class& mpf_class::operator= (type OP) - Convert and store the given OP value to an `mpf_class' object. The - same types are accepted as for the constructors above. - - Note that `operator=' only stores a new value, it doesn't copy or - change the precision of the destination, instead the value is - truncated if necessary. This is the same as `mpf_set' etc. Note - in particular this means for `mpf_class' a copy constructor is not - the same as a default constructor plus assignment. - - mpf_class x (y); // x created with precision of y - - mpf_class x; // x created with default precision - x = y; // value truncated to that precision - - Applications using templated code may need to be careful about the - assumptions the code makes in this area, when working with - `mpf_class' values of various different or non-default precisions. - For instance implementations of the standard `complex' template - have been seen in both styles above, though of course `complex' is - normally only actually specified for use with the builtin float - types. - - -- Function: mpf_class abs (mpf_class OP) - -- Function: mpf_class ceil (mpf_class OP) - -- Function: int cmp (mpf_class OP1, type OP2) - -- Function: int cmp (type OP1, mpf_class OP2) - -- Function: bool mpf_class::fits_sint_p (void) - -- Function: bool mpf_class::fits_slong_p (void) - -- Function: bool mpf_class::fits_sshort_p (void) - -- Function: bool mpf_class::fits_uint_p (void) - -- Function: bool mpf_class::fits_ulong_p (void) - -- Function: bool mpf_class::fits_ushort_p (void) - -- Function: mpf_class floor (mpf_class OP) - -- Function: mpf_class hypot (mpf_class OP1, mpf_class OP2) - -- Function: double mpf_class::get_d (void) - -- Function: long mpf_class::get_si (void) - -- Function: string mpf_class::get_str (mp_exp_t& EXP, int BASE = 10, - size_t DIGITS = 0) - -- Function: unsigned long mpf_class::get_ui (void) - -- Function: int mpf_class::set_str (const char *STR, int BASE) - -- Function: int mpf_class::set_str (const string& STR, int BASE) - -- Function: int sgn (mpf_class OP) - -- Function: mpf_class sqrt (mpf_class OP) - -- Function: mpf_class trunc (mpf_class OP) - These functions provide a C++ class interface to the corresponding - GMP C routines. - - `cmp' can be used with any of the classes or the standard C++ - types, except `long long' and `long double'. - - The accuracy provided by `hypot' is not currently guaranteed. - - -- Function: mp_bitcnt_t mpf_class::get_prec () - -- Function: void mpf_class::set_prec (mp_bitcnt_t PREC) - -- Function: void mpf_class::set_prec_raw (mp_bitcnt_t PREC) - Get or set the current precision of an `mpf_class'. - - The restrictions described for `mpf_set_prec_raw' (*note - Initializing Floats::) apply to `mpf_class::set_prec_raw'. Note - in particular that the `mpf_class' must be restored to it's - allocated precision before being destroyed. This must be done by - application code, there's no automatic mechanism for it. - - -File: gmp.info, Node: C++ Interface Random Numbers, Next: C++ Interface Limitations, Prev: C++ Interface Floats, Up: C++ Class Interface - -12.5 C++ Interface Random Numbers -================================= - - -- Class: gmp_randclass - The C++ class interface to the GMP random number functions uses - `gmp_randclass' to hold an algorithm selection and current state, - as per `gmp_randstate_t'. - - -- Function: gmp_randclass::gmp_randclass (void (*RANDINIT) - (gmp_randstate_t, ...), ...) - Construct a `gmp_randclass', using a call to the given RANDINIT - function (*note Random State Initialization::). The arguments - expected are the same as RANDINIT, but with `mpz_class' instead of - `mpz_t'. For example, - - gmp_randclass r1 (gmp_randinit_default); - gmp_randclass r2 (gmp_randinit_lc_2exp_size, 32); - gmp_randclass r3 (gmp_randinit_lc_2exp, a, c, m2exp); - gmp_randclass r4 (gmp_randinit_mt); - - `gmp_randinit_lc_2exp_size' will fail if the size requested is too - big, an `std::length_error' exception is thrown in that case. - - -- Function: gmp_randclass::gmp_randclass (gmp_randalg_t ALG, ...) - Construct a `gmp_randclass' using the same parameters as - `gmp_randinit' (*note Random State Initialization::). This - function is obsolete and the above RANDINIT style should be - preferred. - - -- Function: void gmp_randclass::seed (unsigned long int S) - -- Function: void gmp_randclass::seed (mpz_class S) - Seed a random number generator. See *note Random Number - Functions::, for how to choose a good seed. - - -- Function: mpz_class gmp_randclass::get_z_bits (unsigned long BITS) - -- Function: mpz_class gmp_randclass::get_z_bits (mpz_class BITS) - Generate a random integer with a specified number of bits. - - -- Function: mpz_class gmp_randclass::get_z_range (mpz_class N) - Generate a random integer in the range 0 to N-1 inclusive. - - -- Function: mpf_class gmp_randclass::get_f () - -- Function: mpf_class gmp_randclass::get_f (unsigned long PREC) - Generate a random float F in the range 0 <= F < 1. F will be to - PREC bits precision, or if PREC is not given then to the precision - of the destination. For example, - - gmp_randclass r; - ... - mpf_class f (0, 512); // 512 bits precision - f = r.get_f(); // random number, 512 bits - - -File: gmp.info, Node: C++ Interface Limitations, Prev: C++ Interface Random Numbers, Up: C++ Class Interface - -12.6 C++ Interface Limitations -============================== - -`mpq_class' and Templated Reading - A generic piece of template code probably won't know that - `mpq_class' requires a `canonicalize' call if inputs read with - `operator>>' might be non-canonical. This can lead to incorrect - results. - - `operator>>' behaves as it does for reasons of efficiency. A - canonicalize can be quite time consuming on large operands, and is - best avoided if it's not necessary. - - But this potential difficulty reduces the usefulness of - `mpq_class'. Perhaps a mechanism to tell `operator>>' what to do - will be adopted in the future, maybe a preprocessor define, a - global flag, or an `ios' flag pressed into service. Or maybe, at - the risk of inconsistency, the `mpq_class' `operator>>' could - canonicalize and leave `mpq_t' `operator>>' not doing so, for use - on those occasions when that's acceptable. Send feedback or - alternate ideas to . - -Subclassing - Subclassing the GMP C++ classes works, but is not currently - recommended. - - Expressions involving subclasses resolve correctly (or seem to), - but in normal C++ fashion the subclass doesn't inherit - constructors and assignments. There's many of those in the GMP - classes, and a good way to reestablish them in a subclass is not - yet provided. - -Templated Expressions - A subtle difficulty exists when using expressions together with - application-defined template functions. Consider the following, - with `T' intended to be some numeric type, - - template - T fun (const T &, const T &); - - When used with, say, plain `mpz_class' variables, it works fine: - `T' is resolved as `mpz_class'. - - mpz_class f(1), g(2); - fun (f, g); // Good - - But when one of the arguments is an expression, it doesn't work. - - mpz_class f(1), g(2), h(3); - fun (f, g+h); // Bad - - This is because `g+h' ends up being a certain expression template - type internal to `gmpxx.h', which the C++ template resolution - rules are unable to automatically convert to `mpz_class'. The - workaround is simply to add an explicit cast. - - mpz_class f(1), g(2), h(3); - fun (f, mpz_class(g+h)); // Good - - Similarly, within `fun' it may be necessary to cast an expression - to type `T' when calling a templated `fun2'. - - template - void fun (T f, T g) - { - fun2 (f, f+g); // Bad - } - - template - void fun (T f, T g) - { - fun2 (f, T(f+g)); // Good - } - - -File: gmp.info, Node: BSD Compatible Functions, Next: Custom Allocation, Prev: C++ Class Interface, Up: Top - -13 Berkeley MP Compatible Functions -*********************************** - -These functions are intended to be fully compatible with the Berkeley MP -library which is available on many BSD derived U*ix systems. The -`--enable-mpbsd' option must be used when building GNU MP to make these -available (*note Installing GMP::). - - The original Berkeley MP library has a usage restriction: you cannot -use the same variable as both source and destination in a single -function call. The compatible functions in GNU MP do not share this -restriction--inputs and outputs may overlap. - - It is not recommended that new programs are written using these -functions. Apart from the incomplete set of functions, the interface -for initializing `MINT' objects is more error prone, and the `pow' -function collides with `pow' in `libm.a'. - - Include the header `mp.h' to get the definition of the necessary -types and functions. If you are on a BSD derived system, make sure to -include GNU `mp.h' if you are going to link the GNU `libmp.a' to your -program. This means that you probably need to give the `-I' -option to the compiler, where `' is the directory where you have -GNU `mp.h'. - - -- Function: MINT * itom (signed short int INITIAL_VALUE) - Allocate an integer consisting of a `MINT' object and dynamic limb - space. Initialize the integer to INITIAL_VALUE. Return a pointer - to the `MINT' object. - - -- Function: MINT * xtom (char *INITIAL_VALUE) - Allocate an integer consisting of a `MINT' object and dynamic limb - space. Initialize the integer from INITIAL_VALUE, a hexadecimal, - null-terminated C string. Return a pointer to the `MINT' object. - - -- Function: void move (MINT *SRC, MINT *DEST) - Set DEST to SRC by copying. Both variables must be previously - initialized. - - -- Function: void madd (MINT *SRC_1, MINT *SRC_2, MINT *DESTINATION) - Add SRC_1 and SRC_2 and put the sum in DESTINATION. - - -- Function: void msub (MINT *SRC_1, MINT *SRC_2, MINT *DESTINATION) - Subtract SRC_2 from SRC_1 and put the difference in DESTINATION. - - -- Function: void mult (MINT *SRC_1, MINT *SRC_2, MINT *DESTINATION) - Multiply SRC_1 and SRC_2 and put the product in DESTINATION. - - -- Function: void mdiv (MINT *DIVIDEND, MINT *DIVISOR, MINT *QUOTIENT, - MINT *REMAINDER) - -- Function: void sdiv (MINT *DIVIDEND, signed short int DIVISOR, MINT - *QUOTIENT, signed short int *REMAINDER) - Set QUOTIENT to DIVIDEND/DIVISOR, and REMAINDER to DIVIDEND mod - DIVISOR. The quotient is rounded towards zero; the remainder has - the same sign as the dividend unless it is zero. - - Some implementations of these functions work differently--or not - at all--for negative arguments. - - -- Function: void msqrt (MINT *OP, MINT *ROOT, MINT *REMAINDER) - Set ROOT to the truncated integer part of the square root of OP, - like `mpz_sqrt'. Set REMAINDER to OP-ROOT*ROOT, i.e. zero if OP - is a perfect square. - - If ROOT and REMAINDER are the same variable, the results are - undefined. - - -- Function: void pow (MINT *BASE, MINT *EXP, MINT *MOD, MINT *DEST) - Set DEST to (BASE raised to EXP) modulo MOD. - - Note that the name `pow' clashes with `pow' from the standard C - math library (*note Exponentiation and Logarithms: (libc)Exponents - and Logarithms.). An application will only be able to use one or - the other. - - -- Function: void rpow (MINT *BASE, signed short int EXP, MINT *DEST) - Set DEST to BASE raised to EXP. - - -- Function: void gcd (MINT *OP1, MINT *OP2, MINT *RES) - Set RES to the greatest common divisor of OP1 and OP2. - - -- Function: int mcmp (MINT *OP1, MINT *OP2) - Compare OP1 and OP2. Return a positive value if OP1 > OP2, zero - if OP1 = OP2, and a negative value if OP1 < OP2. - - -- Function: void min (MINT *DEST) - Input a decimal string from `stdin', and put the read integer in - DEST. SPC and TAB are allowed in the number string, and are - ignored. - - -- Function: void mout (MINT *SRC) - Output SRC to `stdout', as a decimal string. Also output a - newline. - - -- Function: char * mtox (MINT *OP) - Convert OP to a hexadecimal string, and return a pointer to the - string. The returned string is allocated using the default memory - allocation function, `malloc' by default. It will be - `strlen(str)+1' bytes, that being exactly enough for the string - and null-terminator. - - -- Function: void mfree (MINT *OP) - De-allocate, the space used by OP. *This function should only be - passed a value returned by `itom' or `xtom'.* - - -File: gmp.info, Node: Custom Allocation, Next: Language Bindings, Prev: BSD Compatible Functions, Up: Top - -14 Custom Allocation -******************** - -By default GMP uses `malloc', `realloc' and `free' for memory -allocation, and if they fail GMP prints a message to the standard error -output and terminates the program. - - Alternate functions can be specified, to allocate memory in a -different way or to have a different error action on running out of -memory. - - This feature is available in the Berkeley compatibility library -(*note BSD Compatible Functions::) as well as the main GMP library. - - -- Function: void mp_set_memory_functions ( - void *(*ALLOC_FUNC_PTR) (size_t), - void *(*REALLOC_FUNC_PTR) (void *, size_t, size_t), - void (*FREE_FUNC_PTR) (void *, size_t)) - Replace the current allocation functions from the arguments. If - an argument is `NULL', the corresponding default function is used. - - These functions will be used for all memory allocation done by - GMP, apart from temporary space from `alloca' if that function is - available and GMP is configured to use it (*note Build Options::). - - *Be sure to call `mp_set_memory_functions' only when there are no - active GMP objects allocated using the previous memory functions! - Usually that means calling it before any other GMP function.* - - The functions supplied should fit the following declarations: - - -- Function: void * allocate_function (size_t ALLOC_SIZE) - Return a pointer to newly allocated space with at least ALLOC_SIZE - bytes. - - -- Function: void * reallocate_function (void *PTR, size_t OLD_SIZE, - size_t NEW_SIZE) - Resize a previously allocated block PTR of OLD_SIZE bytes to be - NEW_SIZE bytes. - - The block may be moved if necessary or if desired, and in that - case the smaller of OLD_SIZE and NEW_SIZE bytes must be copied to - the new location. The return value is a pointer to the resized - block, that being the new location if moved or just PTR if not. - - PTR is never `NULL', it's always a previously allocated block. - NEW_SIZE may be bigger or smaller than OLD_SIZE. - - -- Function: void free_function (void *PTR, size_t SIZE) - De-allocate the space pointed to by PTR. - - PTR is never `NULL', it's always a previously allocated block of - SIZE bytes. - - A "byte" here means the unit used by the `sizeof' operator. - - The OLD_SIZE parameters to REALLOCATE_FUNCTION and FREE_FUNCTION are -passed for convenience, but of course can be ignored if not needed. -The default functions using `malloc' and friends for instance don't use -them. - - No error return is allowed from any of these functions, if they -return then they must have performed the specified operation. In -particular note that ALLOCATE_FUNCTION or REALLOCATE_FUNCTION mustn't -return `NULL'. - - Getting a different fatal error action is a good use for custom -allocation functions, for example giving a graphical dialog rather than -the default print to `stderr'. How much is possible when genuinely out -of memory is another question though. - - There's currently no defined way for the allocation functions to -recover from an error such as out of memory, they must terminate -program execution. A `longjmp' or throwing a C++ exception will have -undefined results. This may change in the future. - - GMP may use allocated blocks to hold pointers to other allocated -blocks. This will limit the assumptions a conservative garbage -collection scheme can make. - - Since the default GMP allocation uses `malloc' and friends, those -functions will be linked in even if the first thing a program does is an -`mp_set_memory_functions'. It's necessary to change the GMP sources if -this is a problem. - - - -- Function: void mp_get_memory_functions ( - void *(**ALLOC_FUNC_PTR) (size_t), - void *(**REALLOC_FUNC_PTR) (void *, size_t, size_t), - void (**FREE_FUNC_PTR) (void *, size_t)) - Get the current allocation functions, storing function pointers to - the locations given by the arguments. If an argument is `NULL', - that function pointer is not stored. - - For example, to get just the current free function, - - void (*freefunc) (void *, size_t); - - mp_get_memory_functions (NULL, NULL, &freefunc); - - -File: gmp.info, Node: Language Bindings, Next: Algorithms, Prev: Custom Allocation, Up: Top - -15 Language Bindings -******************** - -The following packages and projects offer access to GMP from languages -other than C, though perhaps with varying levels of functionality and -efficiency. - - -C++ - * GMP C++ class interface, *note C++ Class Interface:: - Straightforward interface, expression templates to eliminate - temporaries. - - * ALP `http://www-sop.inria.fr/saga/logiciels/ALP/' - Linear algebra and polynomials using templates. - - * Arithmos `http://www.win.ua.ac.be/~cant/arithmos/' - Rationals with infinities and square roots. - - * CLN `http://www.ginac.de/CLN/' - High level classes for arithmetic. - - * LiDIA `http://www.cdc.informatik.tu-darmstadt.de/TI/LiDIA/' - A C++ library for computational number theory. - - * Linbox `http://www.linalg.org/' - Sparse vectors and matrices. - - * NTL `http://www.shoup.net/ntl/' - A C++ number theory library. - -Fortran - * Omni F77 `http://phase.hpcc.jp/Omni/home.html' - Arbitrary precision floats. - -Haskell - * Glasgow Haskell Compiler `http://www.haskell.org/ghc/' - -Java - * Kaffe `http://www.kaffe.org/' - - * Kissme `http://kissme.sourceforge.net/' - -Lisp - * GNU Common Lisp `http://www.gnu.org/software/gcl/gcl.html' - - * Librep `http://librep.sourceforge.net/' - - * XEmacs (21.5.18 beta and up) `http://www.xemacs.org' - Optional big integers, rationals and floats using GMP. - -M4 - * GNU m4 betas `http://www.seindal.dk/rene/gnu/' - Optionally provides an arbitrary precision `mpeval'. - -ML - * MLton compiler `http://mlton.org/' - -Objective Caml - * MLGMP `http://www.di.ens.fr/~monniaux/programmes.html.en' - - * Numerix `http://pauillac.inria.fr/~quercia/' - Optionally using GMP. - -Oz - * Mozart `http://www.mozart-oz.org/' - -Pascal - * GNU Pascal Compiler `http://www.gnu-pascal.de/' - GMP unit. - - * Numerix `http://pauillac.inria.fr/~quercia/' - For Free Pascal, optionally using GMP. - -Perl - * GMP module, see `demos/perl' in the GMP sources (*note - Demonstration Programs::). - - * Math::GMP `http://www.cpan.org/' - Compatible with Math::BigInt, but not as many functions as - the GMP module above. - - * Math::BigInt::GMP `http://www.cpan.org/' - Plug Math::GMP into normal Math::BigInt operations. - -Pike - * mpz module in the standard distribution, - `http://pike.ida.liu.se/' - -Prolog - * SWI Prolog `http://www.swi-prolog.org/' - Arbitrary precision floats. - -Python - * mpz module in the standard distribution, - `http://www.python.org/' - - * GMPY `http://gmpy.sourceforge.net/' - -Scheme - * GNU Guile (upcoming 1.8) - `http://www.gnu.org/software/guile/guile.html' - - * RScheme `http://www.rscheme.org/' - - * STklos `http://www.stklos.org/' - -Smalltalk - * GNU Smalltalk - `http://www.smalltalk.org/versions/GNUSmalltalk.html' - -Other - * Axiom `http://savannah.nongnu.org/projects/axiom' - Computer algebra using GCL. - - * DrGenius `http://drgenius.seul.org/' - Geometry system and mathematical programming language. - - * GiNaC `http://www.ginac.de/' - C++ computer algebra using CLN. - - * GOO `http://www.googoogaga.org/' - Dynamic object oriented language. - - * Maxima `http://www.ma.utexas.edu/users/wfs/maxima.html' - Macsyma computer algebra using GCL. - - * Q `http://q-lang.sourceforge.net/' - Equational programming system. - - * Regina `http://regina.sourceforge.net/' - Topological calculator. - - * Yacas `http://www.xs4all.nl/~apinkus/yacas.html' - Yet another computer algebra system. - - - -File: gmp.info, Node: Algorithms, Next: Internals, Prev: Language Bindings, Up: Top - -16 Algorithms -************* - -This chapter is an introduction to some of the algorithms used for -various GMP operations. The code is likely to be hard to understand -without knowing something about the algorithms. - - Some GMP internals are mentioned, but applications that expect to be -compatible with future GMP releases should take care to use only the -documented functions. - -* Menu: - -* Multiplication Algorithms:: -* Division Algorithms:: -* Greatest Common Divisor Algorithms:: -* Powering Algorithms:: -* Root Extraction Algorithms:: -* Radix Conversion Algorithms:: -* Other Algorithms:: -* Assembly Coding:: - - -File: gmp.info, Node: Multiplication Algorithms, Next: Division Algorithms, Prev: Algorithms, Up: Algorithms - -16.1 Multiplication -=================== - -NxN limb multiplications and squares are done using one of five -algorithms, as the size N increases. - - Algorithm Threshold - Basecase (none) - Karatsuba `MUL_TOOM22_THRESHOLD' - Toom-3 `MUL_TOOM33_THRESHOLD' - Toom-4 `MUL_TOOM44_THRESHOLD' - FFT `MUL_FFT_THRESHOLD' - - Similarly for squaring, with the `SQR' thresholds. - - NxM multiplications of operands with different sizes above -`MUL_TOOM22_THRESHOLD' are currently done by special Toom-inspired -algorithms or directly with FFT, depending on operand size (*note -Unbalanced Multiplication::). - -* Menu: - -* Basecase Multiplication:: -* Karatsuba Multiplication:: -* Toom 3-Way Multiplication:: -* Toom 4-Way Multiplication:: -* FFT Multiplication:: -* Other Multiplication:: -* Unbalanced Multiplication:: - - -File: gmp.info, Node: Basecase Multiplication, Next: Karatsuba Multiplication, Prev: Multiplication Algorithms, Up: Multiplication Algorithms - -16.1.1 Basecase Multiplication ------------------------------- - -Basecase NxM multiplication is a straightforward rectangular set of -cross-products, the same as long multiplication done by hand and for -that reason sometimes known as the schoolbook or grammar school method. -This is an O(N*M) algorithm. See Knuth section 4.3.1 algorithm M -(*note References::), and the `mpn/generic/mul_basecase.c' code. - - Assembly implementations of `mpn_mul_basecase' are essentially the -same as the generic C code, but have all the usual assembly tricks and -obscurities introduced for speed. - - A square can be done in roughly half the time of a multiply, by -using the fact that the cross products above and below the diagonal are -the same. A triangle of products below the diagonal is formed, doubled -(left shift by one bit), and then the products on the diagonal added. -This can be seen in `mpn/generic/sqr_basecase.c'. Again the assembly -implementations take essentially the same approach. - - u0 u1 u2 u3 u4 - +---+---+---+---+---+ - u0 | d | | | | | - +---+---+---+---+---+ - u1 | | d | | | | - +---+---+---+---+---+ - u2 | | | d | | | - +---+---+---+---+---+ - u3 | | | | d | | - +---+---+---+---+---+ - u4 | | | | | d | - +---+---+---+---+---+ - - In practice squaring isn't a full 2x faster than multiplying, it's -usually around 1.5x. Less than 1.5x probably indicates -`mpn_sqr_basecase' wants improving on that CPU. - - On some CPUs `mpn_mul_basecase' can be faster than the generic C -`mpn_sqr_basecase' on some small sizes. `SQR_BASECASE_THRESHOLD' is -the size at which to use `mpn_sqr_basecase', this will be zero if that -routine should be used always. - - -File: gmp.info, Node: Karatsuba Multiplication, Next: Toom 3-Way Multiplication, Prev: Basecase Multiplication, Up: Multiplication Algorithms - -16.1.2 Karatsuba Multiplication -------------------------------- - -The Karatsuba multiplication algorithm is described in Knuth section -4.3.3 part A, and various other textbooks. A brief description is -given here. - - The inputs x and y are treated as each split into two parts of equal -length (or the most significant part one limb shorter if N is odd). - - high low - +----------+----------+ - | x1 | x0 | - +----------+----------+ - - +----------+----------+ - | y1 | y0 | - +----------+----------+ - - Let b be the power of 2 where the split occurs, ie. if x0 is k limbs -(y0 the same) then b=2^(k*mp_bits_per_limb). With that x=x1*b+x0 and -y=y1*b+y0, and the following holds, - - x*y = (b^2+b)*x1*y1 - b*(x1-x0)*(y1-y0) + (b+1)*x0*y0 - - This formula means doing only three multiplies of (N/2)x(N/2) limbs, -whereas a basecase multiply of NxN limbs is equivalent to four -multiplies of (N/2)x(N/2). The factors (b^2+b) etc represent the -positions where the three products must be added. - - high low - +--------+--------+ +--------+--------+ - | x1*y1 | | x0*y0 | - +--------+--------+ +--------+--------+ - +--------+--------+ - add | x1*y1 | - +--------+--------+ - +--------+--------+ - add | x0*y0 | - +--------+--------+ - +--------+--------+ - sub | (x1-x0)*(y1-y0) | - +--------+--------+ - - The term (x1-x0)*(y1-y0) is best calculated as an absolute value, -and the sign used to choose to add or subtract. Notice the sum -high(x0*y0)+low(x1*y1) occurs twice, so it's possible to do 5*k limb -additions, rather than 6*k, but in GMP extra function call overheads -outweigh the saving. - - Squaring is similar to multiplying, but with x=y the formula reduces -to an equivalent with three squares, - - x^2 = (b^2+b)*x1^2 - b*(x1-x0)^2 + (b+1)*x0^2 - - The final result is accumulated from those three squares the same -way as for the three multiplies above. The middle term (x1-x0)^2 is now -always positive. - - A similar formula for both multiplying and squaring can be -constructed with a middle term (x1+x0)*(y1+y0). But those sums can -exceed k limbs, leading to more carry handling and additions than the -form above. - - Karatsuba multiplication is asymptotically an O(N^1.585) algorithm, -the exponent being log(3)/log(2), representing 3 multiplies each 1/2 -the size of the inputs. This is a big improvement over the basecase -multiply at O(N^2) and the advantage soon overcomes the extra additions -Karatsuba performs. `MUL_TOOM22_THRESHOLD' can be as little as 10 -limbs. The `SQR' threshold is usually about twice the `MUL'. - - The basecase algorithm will take a time of the form M(N) = a*N^2 + -b*N + c and the Karatsuba algorithm K(N) = 3*M(N/2) + d*N + e, which -expands to K(N) = 3/4*a*N^2 + 3/2*b*N + 3*c + d*N + e. The factor 3/4 -for a means per-crossproduct speedups in the basecase code will -increase the threshold since they benefit M(N) more than K(N). And -conversely the 3/2 for b means linear style speedups of b will increase -the threshold since they benefit K(N) more than M(N). The latter can -be seen for instance when adding an optimized `mpn_sqr_diagonal' to -`mpn_sqr_basecase'. Of course all speedups reduce total time, and in -that sense the algorithm thresholds are merely of academic interest. - - -File: gmp.info, Node: Toom 3-Way Multiplication, Next: Toom 4-Way Multiplication, Prev: Karatsuba Multiplication, Up: Multiplication Algorithms - -16.1.3 Toom 3-Way Multiplication --------------------------------- - -The Karatsuba formula is the simplest case of a general approach to -splitting inputs that leads to both Toom and FFT algorithms. A -description of Toom can be found in Knuth section 4.3.3, with an -example 3-way calculation after Theorem A. The 3-way form used in GMP -is described here. - - The operands are each considered split into 3 pieces of equal length -(or the most significant part 1 or 2 limbs shorter than the other two). - - high low - +----------+----------+----------+ - | x2 | x1 | x0 | - +----------+----------+----------+ - - +----------+----------+----------+ - | y2 | y1 | y0 | - +----------+----------+----------+ - -These parts are treated as the coefficients of two polynomials - - X(t) = x2*t^2 + x1*t + x0 - Y(t) = y2*t^2 + y1*t + y0 - - Let b equal the power of 2 which is the size of the x0, x1, y0 and -y1 pieces, ie. if they're k limbs each then b=2^(k*mp_bits_per_limb). -With this x=X(b) and y=Y(b). - - Let a polynomial W(t)=X(t)*Y(t) and suppose its coefficients are - - W(t) = w4*t^4 + w3*t^3 + w2*t^2 + w1*t + w0 - - The w[i] are going to be determined, and when they are they'll give -the final result using w=W(b), since x*y=X(b)*Y(b)=W(b). The -coefficients will be roughly b^2 each, and the final W(b) will be an -addition like, - - high low - +-------+-------+ - | w4 | - +-------+-------+ - +--------+-------+ - | w3 | - +--------+-------+ - +--------+-------+ - | w2 | - +--------+-------+ - +--------+-------+ - | w1 | - +--------+-------+ - +-------+-------+ - | w0 | - +-------+-------+ - - The w[i] coefficients could be formed by a simple set of cross -products, like w4=x2*y2, w3=x2*y1+x1*y2, w2=x2*y0+x1*y1+x0*y2 etc, but -this would need all nine x[i]*y[j] for i,j=0,1,2, and would be -equivalent merely to a basecase multiply. Instead the following -approach is used. - - X(t) and Y(t) are evaluated and multiplied at 5 points, giving -values of W(t) at those points. In GMP the following points are used, - - Point Value - t=0 x0 * y0, which gives w0 immediately - t=1 (x2+x1+x0) * (y2+y1+y0) - t=-1 (x2-x1+x0) * (y2-y1+y0) - t=2 (4*x2+2*x1+x0) * (4*y2+2*y1+y0) - t=inf x2 * y2, which gives w4 immediately - - At t=-1 the values can be negative and that's handled using the -absolute values and tracking the sign separately. At t=inf the value -is actually X(t)*Y(t)/t^4 in the limit as t approaches infinity, but -it's much easier to think of as simply x2*y2 giving w4 immediately -(much like x0*y0 at t=0 gives w0 immediately). - - Each of the points substituted into W(t)=w4*t^4+...+w0 gives a -linear combination of the w[i] coefficients, and the value of those -combinations has just been calculated. - - W(0) = w0 - W(1) = w4 + w3 + w2 + w1 + w0 - W(-1) = w4 - w3 + w2 - w1 + w0 - W(2) = 16*w4 + 8*w3 + 4*w2 + 2*w1 + w0 - W(inf) = w4 - - This is a set of five equations in five unknowns, and some -elementary linear algebra quickly isolates each w[i]. This involves -adding or subtracting one W(t) value from another, and a couple of -divisions by powers of 2 and one division by 3, the latter using the -special `mpn_divexact_by3' (*note Exact Division::). - - The conversion of W(t) values to the coefficients is interpolation. -A polynomial of degree 4 like W(t) is uniquely determined by values -known at 5 different points. The points are arbitrary and can be -chosen to make the linear equations come out with a convenient set of -steps for quickly isolating the w[i]. - - Squaring follows the same procedure as multiplication, but there's -only one X(t) and it's evaluated at the 5 points, and those values -squared to give values of W(t). The interpolation is then identical, -and in fact the same `toom3_interpolate' subroutine is used for both -squaring and multiplying. - - Toom-3 is asymptotically O(N^1.465), the exponent being -log(5)/log(3), representing 5 recursive multiplies of 1/3 the original -size each. This is an improvement over Karatsuba at O(N^1.585), though -Toom does more work in the evaluation and interpolation and so it only -realizes its advantage above a certain size. - - Near the crossover between Toom-3 and Karatsuba there's generally a -range of sizes where the difference between the two is small. -`MUL_TOOM33_THRESHOLD' is a somewhat arbitrary point in that range and -successive runs of the tune program can give different values due to -small variations in measuring. A graph of time versus size for the two -shows the effect, see `tune/README'. - - At the fairly small sizes where the Toom-3 thresholds occur it's -worth remembering that the asymptotic behaviour for Karatsuba and -Toom-3 can't be expected to make accurate predictions, due of course to -the big influence of all sorts of overheads, and the fact that only a -few recursions of each are being performed. Even at large sizes -there's a good chance machine dependent effects like cache architecture -will mean actual performance deviates from what might be predicted. - - The formula given for the Karatsuba algorithm (*note Karatsuba -Multiplication::) has an equivalent for Toom-3 involving only five -multiplies, but this would be complicated and unenlightening. - - An alternate view of Toom-3 can be found in Zuras (*note -References::), using a vector to represent the x and y splits and a -matrix multiplication for the evaluation and interpolation stages. The -matrix inverses are not meant to be actually used, and they have -elements with values much greater than in fact arise in the -interpolation steps. The diagram shown for the 3-way is attractive, -but again doesn't have to be implemented that way and for example with -a bit of rearrangement just one division by 6 can be done. - - -File: gmp.info, Node: Toom 4-Way Multiplication, Next: FFT Multiplication, Prev: Toom 3-Way Multiplication, Up: Multiplication Algorithms - -16.1.4 Toom 4-Way Multiplication --------------------------------- - -Karatsuba and Toom-3 split the operands into 2 and 3 coefficients, -respectively. Toom-4 analogously splits the operands into 4 -coefficients. Using the notation from the section on Toom-3 -multiplication, we form two polynomials: - - X(t) = x3*t^3 + x2*t^2 + x1*t + x0 - Y(t) = y3*t^3 + y2*t^2 + y1*t + y0 - - X(t) and Y(t) are evaluated and multiplied at 7 points, giving -values of W(t) at those points. In GMP the following points are used, - - Point Value - t=0 x0 * y0, which gives w0 immediately - t=1/2 (x3+2*x2+4*x1+8*x0) * (y3+2*y2+4*y1+8*y0) - t=-1/2 (-x3+2*x2-4*x1+8*x0) * (-y3+2*y2-4*y1+8*y0) - t=1 (x3+x2+x1+x0) * (y3+y2+y1+y0) - t=-1 (-x3+x2-x1+x0) * (-y3+y2-y1+y0) - t=2 (8*x3+4*x2+2*x1+x0) * (8*y3+4*y2+2*y1+y0) - t=inf x3 * y3, which gives w6 immediately - - The number of additions and subtractions for Toom-4 is much larger -than for Toom-3. But several subexpressions occur multiple times, for -example x2+x0, occurs for both t=1 and t=-1. - - Toom-4 is asymptotically O(N^1.404), the exponent being -log(7)/log(4), representing 7 recursive multiplies of 1/4 the original -size each. - - -File: gmp.info, Node: FFT Multiplication, Next: Other Multiplication, Prev: Toom 4-Way Multiplication, Up: Multiplication Algorithms - -16.1.5 FFT Multiplication -------------------------- - -At large to very large sizes a Fermat style FFT multiplication is used, -following Scho"nhage and Strassen (*note References::). Descriptions -of FFTs in various forms can be found in many textbooks, for instance -Knuth section 4.3.3 part C or Lipson chapter IX. A brief description -of the form used in GMP is given here. - - The multiplication done is x*y mod 2^N+1, for a given N. A full -product x*y is obtained by choosing N>=bits(x)+bits(y) and padding x -and y with high zero limbs. The modular product is the native form for -the algorithm, so padding to get a full product is unavoidable. - - The algorithm follows a split, evaluate, pointwise multiply, -interpolate and combine similar to that described above for Karatsuba -and Toom-3. A k parameter controls the split, with an FFT-k splitting -into 2^k pieces of M=N/2^k bits each. N must be a multiple of -(2^k)*mp_bits_per_limb so the split falls on limb boundaries, avoiding -bit shifts in the split and combine stages. - - The evaluations, pointwise multiplications, and interpolation, are -all done modulo 2^N'+1 where N' is 2M+k+3 rounded up to a multiple of -2^k and of `mp_bits_per_limb'. The results of interpolation will be -the following negacyclic convolution of the input pieces, and the -choice of N' ensures these sums aren't truncated. - - --- - \ b - w[n] = / (-1) * x[i] * y[j] - --- - i+j==b*2^k+n - b=0,1 - - The points used for the evaluation are g^i for i=0 to 2^k-1 where -g=2^(2N'/2^k). g is a 2^k'th root of unity mod 2^N'+1, which produces -necessary cancellations at the interpolation stage, and it's also a -power of 2 so the fast Fourier transforms used for the evaluation and -interpolation do only shifts, adds and negations. - - The pointwise multiplications are done modulo 2^N'+1 and either -recurse into a further FFT or use a plain multiplication (Toom-3, -Karatsuba or basecase), whichever is optimal at the size N'. The -interpolation is an inverse fast Fourier transform. The resulting set -of sums of x[i]*y[j] are added at appropriate offsets to give the final -result. - - Squaring is the same, but x is the only input so it's one transform -at the evaluate stage and the pointwise multiplies are squares. The -interpolation is the same. - - For a mod 2^N+1 product, an FFT-k is an O(N^(k/(k-1))) algorithm, -the exponent representing 2^k recursed modular multiplies each -1/2^(k-1) the size of the original. Each successive k is an asymptotic -improvement, but overheads mean each is only faster at bigger and -bigger sizes. In the code, `MUL_FFT_TABLE' and `SQR_FFT_TABLE' are the -thresholds where each k is used. Each new k effectively swaps some -multiplying for some shifts, adds and overheads. - - A mod 2^N+1 product can be formed with a normal NxN->2N bit multiply -plus a subtraction, so an FFT and Toom-3 etc can be compared directly. -A k=4 FFT at O(N^1.333) can be expected to be the first faster than -Toom-3 at O(N^1.465). In practice this is what's found, with -`MUL_FFT_MODF_THRESHOLD' and `SQR_FFT_MODF_THRESHOLD' being between 300 -and 1000 limbs, depending on the CPU. So far it's been found that only -very large FFTs recurse into pointwise multiplies above these sizes. - - When an FFT is to give a full product, the change of N to 2N doesn't -alter the theoretical complexity for a given k, but for the purposes of -considering where an FFT might be first used it can be assumed that the -FFT is recursing into a normal multiply and that on that basis it's -doing 2^k recursed multiplies each 1/2^(k-2) the size of the inputs, -making it O(N^(k/(k-2))). This would mean k=7 at O(N^1.4) would be the -first FFT faster than Toom-3. In practice `MUL_FFT_THRESHOLD' and -`SQR_FFT_THRESHOLD' have been found to be in the k=8 range, somewhere -between 3000 and 10000 limbs. - - The way N is split into 2^k pieces and then 2M+k+3 is rounded up to -a multiple of 2^k and `mp_bits_per_limb' means that when -2^k>=mp_bits_per_limb the effective N is a multiple of 2^(2k-1) bits. -The +k+3 means some values of N just under such a multiple will be -rounded to the next. The complexity calculations above assume that a -favourable size is used, meaning one which isn't padded through -rounding, and it's also assumed that the extra +k+3 bits are negligible -at typical FFT sizes. - - The practical effect of the 2^(2k-1) constraint is to introduce a -step-effect into measured speeds. For example k=8 will round N up to a -multiple of 32768 bits, so for a 32-bit limb there'll be 512 limb -groups of sizes for which `mpn_mul_n' runs at the same speed. Or for -k=9 groups of 2048 limbs, k=10 groups of 8192 limbs, etc. In practice -it's been found each k is used at quite small multiples of its size -constraint and so the step effect is quite noticeable in a time versus -size graph. - - The threshold determinations currently measure at the mid-points of -size steps, but this is sub-optimal since at the start of a new step it -can happen that it's better to go back to the previous k for a while. -Something more sophisticated for `MUL_FFT_TABLE' and `SQR_FFT_TABLE' -will be needed. - - -File: gmp.info, Node: Other Multiplication, Next: Unbalanced Multiplication, Prev: FFT Multiplication, Up: Multiplication Algorithms - -16.1.6 Other Multiplication ---------------------------- - -The Toom algorithms described above (*note Toom 3-Way Multiplication::, -*note Toom 4-Way Multiplication::) generalizes to split into an -arbitrary number of pieces, as per Knuth section 4.3.3 algorithm C. -This is not currently used. The notes here are merely for interest. - - In general a split into r+1 pieces is made, and evaluations and -pointwise multiplications done at 2*r+1 points. A 4-way split does 7 -pointwise multiplies, 5-way does 9, etc. Asymptotically an (r+1)-way -algorithm is O(N^(log(2*r+1)/log(r+1))). Only the pointwise -multiplications count towards big-O complexity, but the time spent in -the evaluate and interpolate stages grows with r and has a significant -practical impact, with the asymptotic advantage of each r realized only -at bigger and bigger sizes. The overheads grow as O(N*r), whereas in -an r=2^k FFT they grow only as O(N*log(r)). - - Knuth algorithm C evaluates at points 0,1,2,...,2*r, but exercise 4 -uses -r,...,0,...,r and the latter saves some small multiplies in the -evaluate stage (or rather trades them for additions), and has a further -saving of nearly half the interpolate steps. The idea is to separate -odd and even final coefficients and then perform algorithm C steps C7 -and C8 on them separately. The divisors at step C7 become j^2 and the -multipliers at C8 become 2*t*j-j^2. - - Splitting odd and even parts through positive and negative points -can be thought of as using -1 as a square root of unity. If a 4th root -of unity was available then a further split and speedup would be -possible, but no such root exists for plain integers. Going to complex -integers with i=sqrt(-1) doesn't help, essentially because in Cartesian -form it takes three real multiplies to do a complex multiply. The -existence of 2^k'th roots of unity in a suitable ring or field lets the -fast Fourier transform keep splitting and get to O(N*log(r)). - - Floating point FFTs use complex numbers approximating Nth roots of -unity. Some processors have special support for such FFTs. But these -are not used in GMP since it's very difficult to guarantee an exact -result (to some number of bits). An occasional difference of 1 in the -last bit might not matter to a typical signal processing algorithm, but -is of course of vital importance to GMP. - - -File: gmp.info, Node: Unbalanced Multiplication, Prev: Other Multiplication, Up: Multiplication Algorithms - -16.1.7 Unbalanced Multiplication --------------------------------- - -Multiplication of operands with different sizes, both below -`MUL_TOOM22_THRESHOLD' are done with plain schoolbook multiplication -(*note Basecase Multiplication::). - - For really large operands, we invoke FFT directly. - - For operands between these sizes, we use Toom inspired algorithms -suggested by Alberto Zanoni and Marco Bodrato. The idea is to split -the operands into polynomials of different degree. GMP currently -splits the smaller operand onto 2 coefficients, i.e., a polynomial of -degree 1, but the larger operand can be split into 2, 3, or 4 -coefficients, i.e., a polynomial of degree 1 to 3. - - -File: gmp.info, Node: Division Algorithms, Next: Greatest Common Divisor Algorithms, Prev: Multiplication Algorithms, Up: Algorithms - -16.2 Division Algorithms -======================== - -* Menu: - -* Single Limb Division:: -* Basecase Division:: -* Divide and Conquer Division:: -* Block-Wise Barrett Division:: -* Exact Division:: -* Exact Remainder:: -* Small Quotient Division:: - - -File: gmp.info, Node: Single Limb Division, Next: Basecase Division, Prev: Division Algorithms, Up: Division Algorithms - -16.2.1 Single Limb Division ---------------------------- - -Nx1 division is implemented using repeated 2x1 divisions from high to -low, either with a hardware divide instruction or a multiplication by -inverse, whichever is best on a given CPU. - - The multiply by inverse follows "Improved division by invariant -integers" by Mo"ller and Granlund (*note References::) and is -implemented as `udiv_qrnnd_preinv' in `gmp-impl.h'. The idea is to -have a fixed-point approximation to 1/d (see `invert_limb') and then -multiply by the high limb (plus one bit) of the dividend to get a -quotient q. With d normalized (high bit set), q is no more than 1 too -small. Subtracting q*d from the dividend gives a remainder, and -reveals whether q or q-1 is correct. - - The result is a division done with two multiplications and four or -five arithmetic operations. On CPUs with low latency multipliers this -can be much faster than a hardware divide, though the cost of -calculating the inverse at the start may mean it's only better on -inputs bigger than say 4 or 5 limbs. - - When a divisor must be normalized, either for the generic C -`__udiv_qrnnd_c' or the multiply by inverse, the division performed is -actually a*2^k by d*2^k where a is the dividend and k is the power -necessary to have the high bit of d*2^k set. The bit shifts for the -dividend are usually accomplished "on the fly" meaning by extracting -the appropriate bits at each step. Done this way the quotient limbs -come out aligned ready to store. When only the remainder is wanted, an -alternative is to take the dividend limbs unshifted and calculate r = a -mod d*2^k followed by an extra final step r*2^k mod d*2^k. This can -help on CPUs with poor bit shifts or few registers. - - The multiply by inverse can be done two limbs at a time. The -calculation is basically the same, but the inverse is two limbs and the -divisor treated as if padded with a low zero limb. This means more -work, since the inverse will need a 2x2 multiply, but the four 1x1s to -do that are independent and can therefore be done partly or wholly in -parallel. Likewise for a 2x1 calculating q*d. The net effect is to -process two limbs with roughly the same two multiplies worth of latency -that one limb at a time gives. This extends to 3 or 4 limbs at a time, -though the extra work to apply the inverse will almost certainly soon -reach the limits of multiplier throughput. - - A similar approach in reverse can be taken to process just half a -limb at a time if the divisor is only a half limb. In this case the -1x1 multiply for the inverse effectively becomes two (1/2)x1 for each -limb, which can be a saving on CPUs with a fast half limb multiply, or -in fact if the only multiply is a half limb, and especially if it's not -pipelined. - - -File: gmp.info, Node: Basecase Division, Next: Divide and Conquer Division, Prev: Single Limb Division, Up: Division Algorithms - -16.2.2 Basecase Division ------------------------- - -Basecase NxM division is like long division done by hand, but in base -2^mp_bits_per_limb. See Knuth section 4.3.1 algorithm D, and -`mpn/generic/sb_divrem_mn.c'. - - Briefly stated, while the dividend remains larger than the divisor, -a high quotient limb is formed and the Nx1 product q*d subtracted at -the top end of the dividend. With a normalized divisor (most -significant bit set), each quotient limb can be formed with a 2x1 -division and a 1x1 multiplication plus some subtractions. The 2x1 -division is by the high limb of the divisor and is done either with a -hardware divide or a multiply by inverse (the same as in *Note Single -Limb Division::) whichever is faster. Such a quotient is sometimes one -too big, requiring an addback of the divisor, but that happens rarely. - - With Q=N-M being the number of quotient limbs, this is an O(Q*M) -algorithm and will run at a speed similar to a basecase QxM -multiplication, differing in fact only in the extra multiply and divide -for each of the Q quotient limbs. - - -File: gmp.info, Node: Divide and Conquer Division, Next: Block-Wise Barrett Division, Prev: Basecase Division, Up: Division Algorithms - -16.2.3 Divide and Conquer Division ----------------------------------- - -For divisors larger than `DC_DIV_QR_THRESHOLD', division is done by -dividing. Or to be precise by a recursive divide and conquer algorithm -based on work by Moenck and Borodin, Jebelean, and Burnikel and Ziegler -(*note References::). - - The algorithm consists essentially of recognising that a 2NxN -division can be done with the basecase division algorithm (*note -Basecase Division::), but using N/2 limbs as a base, not just a single -limb. This way the multiplications that arise are (N/2)x(N/2) and can -take advantage of Karatsuba and higher multiplication algorithms (*note -Multiplication Algorithms::). The two "digits" of the quotient are -formed by recursive Nx(N/2) divisions. - - If the (N/2)x(N/2) multiplies are done with a basecase multiplication -then the work is about the same as a basecase division, but with more -function call overheads and with some subtractions separated from the -multiplies. These overheads mean that it's only when N/2 is above -`MUL_TOOM22_THRESHOLD' that divide and conquer is of use. - - `DC_DIV_QR_THRESHOLD' is based on the divisor size N, so it will be -somewhere above twice `MUL_TOOM22_THRESHOLD', but how much above -depends on the CPU. An optimized `mpn_mul_basecase' can lower -`DC_DIV_QR_THRESHOLD' a little by offering a ready-made advantage over -repeated `mpn_submul_1' calls. - - Divide and conquer is asymptotically O(M(N)*log(N)) where M(N) is -the time for an NxN multiplication done with FFTs. The actual time is -a sum over multiplications of the recursed sizes, as can be seen near -the end of section 2.2 of Burnikel and Ziegler. For example, within -the Toom-3 range, divide and conquer is 2.63*M(N). With higher -algorithms the M(N) term improves and the multiplier tends to log(N). -In practice, at moderate to large sizes, a 2NxN division is about 2 to -4 times slower than an NxN multiplication. - - -File: gmp.info, Node: Block-Wise Barrett Division, Next: Exact Division, Prev: Divide and Conquer Division, Up: Division Algorithms - -16.2.4 Block-Wise Barrett Division ----------------------------------- - -For the largest divisions, a block-wise Barrett division algorithm is -used. Here, the divisor is inverted to a precision determined by the -relative size of the dividend and divisor. Blocks of quotient limbs -are then generated by multiplying blocks from the dividend by the -inverse. - - Our block-wise algorithm computes a smaller inverse than in the -plain Barrett algorithm. For a 2n/n division, the inverse will be just -ceil(n/2) limbs. - - -File: gmp.info, Node: Exact Division, Next: Exact Remainder, Prev: Block-Wise Barrett Division, Up: Division Algorithms - -16.2.5 Exact Division ---------------------- - -A so-called exact division is when the dividend is known to be an exact -multiple of the divisor. Jebelean's exact division algorithm uses this -knowledge to make some significant optimizations (*note References::). - - The idea can be illustrated in decimal for example with 368154 -divided by 543. Because the low digit of the dividend is 4, the low -digit of the quotient must be 8. This is arrived at from 4*7 mod 10, -using the fact 7 is the modular inverse of 3 (the low digit of the -divisor), since 3*7 == 1 mod 10. So 8*543=4344 can be subtracted from -the dividend leaving 363810. Notice the low digit has become zero. - - The procedure is repeated at the second digit, with the next -quotient digit 7 (7 == 1*7 mod 10), subtracting 7*543=3801, leaving -325800. And finally at the third digit with quotient digit 6 (8*7 mod -10), subtracting 6*543=3258 leaving 0. So the quotient is 678. - - Notice however that the multiplies and subtractions don't need to -extend past the low three digits of the dividend, since that's enough -to determine the three quotient digits. For the last quotient digit no -subtraction is needed at all. On a 2NxN division like this one, only -about half the work of a normal basecase division is necessary. - - For an NxM exact division producing Q=N-M quotient limbs, the saving -over a normal basecase division is in two parts. Firstly, each of the -Q quotient limbs needs only one multiply, not a 2x1 divide and -multiply. Secondly, the crossproducts are reduced when Q>M to -Q*M-M*(M+1)/2, or when Q<=M to Q*(Q-1)/2. Notice the savings are -complementary. If Q is big then many divisions are saved, or if Q is -small then the crossproducts reduce to a small number. - - The modular inverse used is calculated efficiently by `binvert_limb' -in `gmp-impl.h'. This does four multiplies for a 32-bit limb, or six -for a 64-bit limb. `tune/modlinv.c' has some alternate implementations -that might suit processors better at bit twiddling than multiplying. - - The sub-quadratic exact division described by Jebelean in "Exact -Division with Karatsuba Complexity" is not currently implemented. It -uses a rearrangement similar to the divide and conquer for normal -division (*note Divide and Conquer Division::), but operating from low -to high. A further possibility not currently implemented is -"Bidirectional Exact Integer Division" by Krandick and Jebelean which -forms quotient limbs from both the high and low ends of the dividend, -and can halve once more the number of crossproducts needed in a 2NxN -division. - - A special case exact division by 3 exists in `mpn_divexact_by3', -supporting Toom-3 multiplication and `mpq' canonicalizations. It forms -quotient digits with a multiply by the modular inverse of 3 (which is -`0xAA..AAB') and uses two comparisons to determine a borrow for the next -limb. The multiplications don't need to be on the dependent chain, as -long as the effect of the borrows is applied, which can help chips with -pipelined multipliers. - - -File: gmp.info, Node: Exact Remainder, Next: Small Quotient Division, Prev: Exact Division, Up: Division Algorithms - -16.2.6 Exact Remainder ----------------------- - -If the exact division algorithm is done with a full subtraction at each -stage and the dividend isn't a multiple of the divisor, then low zero -limbs are produced but with a remainder in the high limbs. For -dividend a, divisor d, quotient q, and b = 2^mp_bits_per_limb, this -remainder r is of the form - - a = q*d + r*b^n - - n represents the number of zero limbs produced by the subtractions, -that being the number of limbs produced for q. r will be in the range -0<=rb*r+u2 condition appropriately relaxed. - - -File: gmp.info, Node: Greatest Common Divisor Algorithms, Next: Powering Algorithms, Prev: Division Algorithms, Up: Algorithms - -16.3 Greatest Common Divisor -============================ - -* Menu: - -* Binary GCD:: -* Lehmer's Algorithm:: -* Subquadratic GCD:: -* Extended GCD:: -* Jacobi Symbol:: - - -File: gmp.info, Node: Binary GCD, Next: Lehmer's Algorithm, Prev: Greatest Common Divisor Algorithms, Up: Greatest Common Divisor Algorithms - -16.3.1 Binary GCD ------------------ - -At small sizes GMP uses an O(N^2) binary style GCD. This is described -in many textbooks, for example Knuth section 4.5.2 algorithm B. It -simply consists of successively reducing odd operands a and b using - - a,b = abs(a-b),min(a,b) - strip factors of 2 from a - - The Euclidean GCD algorithm, as per Knuth algorithms E and A, -repeatedly computes the quotient q = floor(a/b) and replaces a,b by v, -u - q v. The binary algorithm has so far been found to be faster than -the Euclidean algorithm everywhere. One reason the binary method does -well is that the implied quotient at each step is usually small, so -often only one or two subtractions are needed to get the same effect as -a division. Quotients 1, 2 and 3 for example occur 67.7% of the time, -see Knuth section 4.5.3 Theorem E. - - When the implied quotient is large, meaning b is much smaller than -a, then a division is worthwhile. This is the basis for the initial a -mod b reductions in `mpn_gcd' and `mpn_gcd_1' (the latter for both Nx1 -and 1x1 cases). But after that initial reduction, big quotients occur -too rarely to make it worth checking for them. - - - The final 1x1 GCD in `mpn_gcd_1' is done in the generic C code as -described above. For two N-bit operands, the algorithm takes about -0.68 iterations per bit. For optimum performance some attention needs -to be paid to the way the factors of 2 are stripped from a. - - Firstly it may be noted that in twos complement the number of low -zero bits on a-b is the same as b-a, so counting or testing can begin on -a-b without waiting for abs(a-b) to be determined. - - A loop stripping low zero bits tends not to branch predict well, -since the condition is data dependent. But on average there's only a -few low zeros, so an option is to strip one or two bits arithmetically -then loop for more (as done for AMD K6). Or use a lookup table to get -a count for several bits then loop for more (as done for AMD K7). An -alternative approach is to keep just one of a or b odd and iterate - - a,b = abs(a-b), min(a,b) - a = a/2 if even - b = b/2 if even - - This requires about 1.25 iterations per bit, but stripping of a -single bit at each step avoids any branching. Repeating the bit strip -reduces to about 0.9 iterations per bit, which may be a worthwhile -tradeoff. - - Generally with the above approaches a speed of perhaps 6 cycles per -bit can be achieved, which is still not terribly fast with for instance -a 64-bit GCD taking nearly 400 cycles. It's this sort of time which -means it's not usually advantageous to combine a set of divisibility -tests into a GCD. - - Currently, the binary algorithm is used for GCD only when N < 3. - - -File: gmp.info, Node: Lehmer's Algorithm, Next: Subquadratic GCD, Prev: Binary GCD, Up: Greatest Common Divisor Algorithms - -16.3.2 Lehmer's algorithm -------------------------- - -Lehmer's improvement of the Euclidean algorithms is based on the -observation that the initial part of the quotient sequence depends only -on the most significant parts of the inputs. The variant of Lehmer's -algorithm used in GMP splits off the most significant two limbs, as -suggested, e.g., in "A Double-Digit Lehmer-Euclid Algorithm" by -Jebelean (*note References::). The quotients of two double-limb inputs -are collected as a 2 by 2 matrix with single-limb elements. This is -done by the function `mpn_hgcd2'. The resulting matrix is applied to -the inputs using `mpn_mul_1' and `mpn_submul_1'. Each iteration usually -reduces the inputs by almost one limb. In the rare case of a large -quotient, no progress can be made by examining just the most -significant two limbs, and the quotient is computing using plain -division. - - The resulting algorithm is asymptotically O(N^2), just as the -Euclidean algorithm and the binary algorithm. The quadratic part of the -work are the calls to `mpn_mul_1' and `mpn_submul_1'. For small sizes, -the linear work is also significant. There are roughly N calls to the -`mpn_hgcd2' function. This function uses a couple of important -optimizations: - - * It uses the same relaxed notion of correctness as `mpn_hgcd' (see - next section). This means that when called with the most - significant two limbs of two large numbers, the returned matrix - does not always correspond exactly to the initial quotient - sequence for the two large numbers; the final quotient may - sometimes be one off. - - * It takes advantage of the fact the quotients are usually small. - The division operator is not used, since the corresponding - assembler instruction is very slow on most architectures. (This - code could probably be improved further, it uses many branches - that are unfriendly to prediction). - - * It switches from double-limb calculations to single-limb - calculations half-way through, when the input numbers have been - reduced in size from two limbs to one and a half. - - - -File: gmp.info, Node: Subquadratic GCD, Next: Extended GCD, Prev: Lehmer's Algorithm, Up: Greatest Common Divisor Algorithms - -16.3.3 Subquadratic GCD ------------------------ - -For inputs larger than `GCD_DC_THRESHOLD', GCD is computed via the HGCD -(Half GCD) function, as a generalization to Lehmer's algorithm. - - Let the inputs a,b be of size N limbs each. Put S = floor(N/2) + 1. -Then HGCD(a,b) returns a transformation matrix T with non-negative -elements, and reduced numbers (c;d) = T^-1 (a;b). The reduced numbers -c,d must be larger than S limbs, while their difference abs(c-d) must -fit in S limbs. The matrix elements will also be of size roughly N/2. - - The HGCD base case uses Lehmer's algorithm, but with the above stop -condition that returns reduced numbers and the corresponding -transformation matrix half-way through. For inputs larger than -`HGCD_THRESHOLD', HGCD is computed recursively, using the divide and -conquer algorithm in "On Scho"nhage's algorithm and subquadratic -integer GCD computation" by Mo"ller (*note References::). The recursive -algorithm consists of these main steps. - - * Call HGCD recursively, on the most significant N/2 limbs. Apply the - resulting matrix T_1 to the full numbers, reducing them to a size - just above 3N/2. - - * Perform a small number of division or subtraction steps to reduce - the numbers to size below 3N/2. This is essential mainly for the - unlikely case of large quotients. - - * Call HGCD recursively, on the most significant N/2 limbs of the - reduced numbers. Apply the resulting matrix T_2 to the full - numbers, reducing them to a size just above N/2. - - * Compute T = T_1 T_2. - - * Perform a small number of division and subtraction steps to - satisfy the requirements, and return. - - GCD is then implemented as a loop around HGCD, similarly to Lehmer's -algorithm. Where Lehmer repeatedly chops off the top two limbs, calls -`mpn_hgcd2', and applies the resulting matrix to the full numbers, the -subquadratic GCD chops off the most significant third of the limbs (the -proportion is a tuning parameter, and 1/3 seems to be more efficient -than, e.g, 1/2), calls `mpn_hgcd', and applies the resulting matrix. -Once the input numbers are reduced to size below `GCD_DC_THRESHOLD', -Lehmer's algorithm is used for the rest of the work. - - The asymptotic running time of both HGCD and GCD is O(M(N)*log(N)), -where M(N) is the time for multiplying two N-limb numbers. - - -File: gmp.info, Node: Extended GCD, Next: Jacobi Symbol, Prev: Subquadratic GCD, Up: Greatest Common Divisor Algorithms - -16.3.4 Extended GCD -------------------- - -The extended GCD function, or GCDEXT, calculates gcd(a,b) and also -cofactors x and y satisfying a*x+b*y=gcd(a,b). All the algorithms used -for plain GCD are extended to handle this case. The binary algorithm is -used only for single-limb GCDEXT. Lehmer's algorithm is used for sizes -up to `GCDEXT_DC_THRESHOLD'. Above this threshold, GCDEXT is -implemented as a loop around HGCD, but with more book-keeping to keep -track of the cofactors. This gives the same asymptotic running time as -for GCD and HGCD, O(M(N)*log(N)) - - One difference to plain GCD is that while the inputs a and b are -reduced as the algorithm proceeds, the cofactors x and y grow in size. -This makes the tuning of the chopping-point more difficult. The current -code chops off the most significant half of the inputs for the call to -HGCD in the first iteration, and the most significant two thirds for -the remaining calls. This strategy could surely be improved. Also the -stop condition for the loop, where Lehmer's algorithm is invoked once -the inputs are reduced below `GCDEXT_DC_THRESHOLD', could maybe be -improved by taking into account the current size of the cofactors. - - -File: gmp.info, Node: Jacobi Symbol, Prev: Extended GCD, Up: Greatest Common Divisor Algorithms - -16.3.5 Jacobi Symbol --------------------- - -`mpz_jacobi' and `mpz_kronecker' are currently implemented with a -simple binary algorithm similar to that described for the GCDs (*note -Binary GCD::). They're not very fast when both inputs are large. -Lehmer's multi-step improvement or a binary based multi-step algorithm -is likely to be better. - - When one operand fits a single limb, and that includes -`mpz_kronecker_ui' and friends, an initial reduction is done with -either `mpn_mod_1' or `mpn_modexact_1_odd', followed by the binary -algorithm on a single limb. The binary algorithm is well suited to a -single limb, and the whole calculation in this case is quite efficient. - - In all the routines sign changes for the result are accumulated -using some bit twiddling, avoiding table lookups or conditional jumps. - diff --git a/misc/builddeps/linux64/gmp/share/info/gmp.info-2 b/misc/builddeps/linux64/gmp/share/info/gmp.info-2 deleted file mode 100644 index 45846232..00000000 --- a/misc/builddeps/linux64/gmp/share/info/gmp.info-2 +++ /dev/null @@ -1,3489 +0,0 @@ -This is ../../gmp/doc/gmp.info, produced by makeinfo version 4.8 from -../../gmp/doc/gmp.texi. - - This manual describes how to install and use the GNU multiple -precision arithmetic library, version 5.0.1. - - Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, -2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free -Software Foundation, Inc. - - Permission is granted to copy, distribute and/or modify this -document under the terms of the GNU Free Documentation License, Version -1.3 or any later version published by the Free Software Foundation; -with no Invariant Sections, with the Front-Cover Texts being "A GNU -Manual", and with the Back-Cover Texts being "You have freedom to copy -and modify this GNU Manual, like GNU software". A copy of the license -is included in *Note GNU Free Documentation License::. - -INFO-DIR-SECTION GNU libraries -START-INFO-DIR-ENTRY -* gmp: (gmp). GNU Multiple Precision Arithmetic Library. -END-INFO-DIR-ENTRY - - -File: gmp.info, Node: Powering Algorithms, Next: Root Extraction Algorithms, Prev: Greatest Common Divisor Algorithms, Up: Algorithms - -16.4 Powering Algorithms -======================== - -* Menu: - -* Normal Powering Algorithm:: -* Modular Powering Algorithm:: - - -File: gmp.info, Node: Normal Powering Algorithm, Next: Modular Powering Algorithm, Prev: Powering Algorithms, Up: Powering Algorithms - -16.4.1 Normal Powering ----------------------- - -Normal `mpz' or `mpf' powering uses a simple binary algorithm, -successively squaring and then multiplying by the base when a 1 bit is -seen in the exponent, as per Knuth section 4.6.3. The "left to right" -variant described there is used rather than algorithm A, since it's -just as easy and can be done with somewhat less temporary memory. - - -File: gmp.info, Node: Modular Powering Algorithm, Prev: Normal Powering Algorithm, Up: Powering Algorithms - -16.4.2 Modular Powering ------------------------ - -Modular powering is implemented using a 2^k-ary sliding window -algorithm, as per "Handbook of Applied Cryptography" algorithm 14.85 -(*note References::). k is chosen according to the size of the -exponent. Larger exponents use larger values of k, the choice being -made to minimize the average number of multiplications that must -supplement the squaring. - - The modular multiplies and squares use either a simple division or -the REDC method by Montgomery (*note References::). REDC is a little -faster, essentially saving N single limb divisions in a fashion similar -to an exact remainder (*note Exact Remainder::). - - -File: gmp.info, Node: Root Extraction Algorithms, Next: Radix Conversion Algorithms, Prev: Powering Algorithms, Up: Algorithms - -16.5 Root Extraction Algorithms -=============================== - -* Menu: - -* Square Root Algorithm:: -* Nth Root Algorithm:: -* Perfect Square Algorithm:: -* Perfect Power Algorithm:: - - -File: gmp.info, Node: Square Root Algorithm, Next: Nth Root Algorithm, Prev: Root Extraction Algorithms, Up: Root Extraction Algorithms - -16.5.1 Square Root ------------------- - -Square roots are taken using the "Karatsuba Square Root" algorithm by -Paul Zimmermann (*note References::). - - An input n is split into four parts of k bits each, so with b=2^k we -have n = a3*b^3 + a2*b^2 + a1*b + a0. Part a3 must be "normalized" so -that either the high or second highest bit is set. In GMP, k is kept -on a limb boundary and the input is left shifted (by an even number of -bits) to normalize. - - The square root of the high two parts is taken, by recursive -application of the algorithm (bottoming out in a one-limb Newton's -method), - - s1,r1 = sqrtrem (a3*b + a2) - - This is an approximation to the desired root and is extended by a -division to give s,r, - - q,u = divrem (r1*b + a1, 2*s1) - s = s1*b + q - r = u*b + a0 - q^2 - - The normalization requirement on a3 means at this point s is either -correct or 1 too big. r is negative in the latter case, so - - if r < 0 then - r = r + 2*s - 1 - s = s - 1 - - The algorithm is expressed in a divide and conquer form, but as -noted in the paper it can also be viewed as a discrete variant of -Newton's method, or as a variation on the schoolboy method (no longer -taught) for square roots two digits at a time. - - If the remainder r is not required then usually only a few high limbs -of r and u need to be calculated to determine whether an adjustment to -s is required. This optimization is not currently implemented. - - In the Karatsuba multiplication range this algorithm is -O(1.5*M(N/2)), where M(n) is the time to multiply two numbers of n -limbs. In the FFT multiplication range this grows to a bound of -O(6*M(N/2)). In practice a factor of about 1.5 to 1.8 is found in the -Karatsuba and Toom-3 ranges, growing to 2 or 3 in the FFT range. - - The algorithm does all its calculations in integers and the resulting -`mpn_sqrtrem' is used for both `mpz_sqrt' and `mpf_sqrt'. The extended -precision given by `mpf_sqrt_ui' is obtained by padding with zero limbs. - - -File: gmp.info, Node: Nth Root Algorithm, Next: Perfect Square Algorithm, Prev: Square Root Algorithm, Up: Root Extraction Algorithms - -16.5.2 Nth Root ---------------- - -Integer Nth roots are taken using Newton's method with the following -iteration, where A is the input and n is the root to be taken. - - 1 A - a[i+1] = - * ( --------- + (n-1)*a[i] ) - n a[i]^(n-1) - - The initial approximation a[1] is generated bitwise by successively -powering a trial root with or without new 1 bits, aiming to be just -above the true root. The iteration converges quadratically when -started from a good approximation. When n is large more initial bits -are needed to get good convergence. The current implementation is not -particularly well optimized. - - -File: gmp.info, Node: Perfect Square Algorithm, Next: Perfect Power Algorithm, Prev: Nth Root Algorithm, Up: Root Extraction Algorithms - -16.5.3 Perfect Square ---------------------- - -A significant fraction of non-squares can be quickly identified by -checking whether the input is a quadratic residue modulo small integers. - - `mpz_perfect_square_p' first tests the input mod 256, which means -just examining the low byte. Only 44 different values occur for -squares mod 256, so 82.8% of inputs can be immediately identified as -non-squares. - - On a 32-bit system similar tests are done mod 9, 5, 7, 13 and 17, -for a total 99.25% of inputs identified as non-squares. On a 64-bit -system 97 is tested too, for a total 99.62%. - - These moduli are chosen because they're factors of 2^24-1 (or 2^48-1 -for 64-bits), and such a remainder can be quickly taken just using -additions (see `mpn_mod_34lsub1'). - - When nails are in use moduli are instead selected by the `gen-psqr.c' -program and applied with an `mpn_mod_1'. The same 2^24-1 or 2^48-1 -could be done with nails using some extra bit shifts, but this is not -currently implemented. - - In any case each modulus is applied to the `mpn_mod_34lsub1' or -`mpn_mod_1' remainder and a table lookup identifies non-squares. By -using a "modexact" style calculation, and suitably permuted tables, -just one multiply each is required, see the code for details. Moduli -are also combined to save operations, so long as the lookup tables -don't become too big. `gen-psqr.c' does all the pre-calculations. - - A square root must still be taken for any value that passes these -tests, to verify it's really a square and not one of the small fraction -of non-squares that get through (ie. a pseudo-square to all the tested -bases). - - Clearly more residue tests could be done, `mpz_perfect_square_p' only -uses a compact and efficient set. Big inputs would probably benefit -from more residue testing, small inputs might be better off with less. -The assumed distribution of squares versus non-squares in the input -would affect such considerations. - - -File: gmp.info, Node: Perfect Power Algorithm, Prev: Perfect Square Algorithm, Up: Root Extraction Algorithms - -16.5.4 Perfect Power --------------------- - -Detecting perfect powers is required by some factorization algorithms. -Currently `mpz_perfect_power_p' is implemented using repeated Nth root -extractions, though naturally only prime roots need to be considered. -(*Note Nth Root Algorithm::.) - - If a prime divisor p with multiplicity e can be found, then only -roots which are divisors of e need to be considered, much reducing the -work necessary. To this end divisibility by a set of small primes is -checked. - - -File: gmp.info, Node: Radix Conversion Algorithms, Next: Other Algorithms, Prev: Root Extraction Algorithms, Up: Algorithms - -16.6 Radix Conversion -===================== - -Radix conversions are less important than other algorithms. A program -dominated by conversions should probably use a different data -representation. - -* Menu: - -* Binary to Radix:: -* Radix to Binary:: - - -File: gmp.info, Node: Binary to Radix, Next: Radix to Binary, Prev: Radix Conversion Algorithms, Up: Radix Conversion Algorithms - -16.6.1 Binary to Radix ----------------------- - -Conversions from binary to a power-of-2 radix use a simple and fast -O(N) bit extraction algorithm. - - Conversions from binary to other radices use one of two algorithms. -Sizes below `GET_STR_PRECOMPUTE_THRESHOLD' use a basic O(N^2) method. -Repeated divisions by b^n are made, where b is the radix and n is the -biggest power that fits in a limb. But instead of simply using the -remainder r from such divisions, an extra divide step is done to give a -fractional limb representing r/b^n. The digits of r can then be -extracted using multiplications by b rather than divisions. Special -case code is provided for decimal, allowing multiplications by 10 to -optimize to shifts and adds. - - Above `GET_STR_PRECOMPUTE_THRESHOLD' a sub-quadratic algorithm is -used. For an input t, powers b^(n*2^i) of the radix are calculated, -until a power between t and sqrt(t) is reached. t is then divided by -that largest power, giving a quotient which is the digits above that -power, and a remainder which is those below. These two parts are in -turn divided by the second highest power, and so on recursively. When -a piece has been divided down to less than `GET_STR_DC_THRESHOLD' -limbs, the basecase algorithm described above is used. - - The advantage of this algorithm is that big divisions can make use -of the sub-quadratic divide and conquer division (*note Divide and -Conquer Division::), and big divisions tend to have less overheads than -lots of separate single limb divisions anyway. But in any case the -cost of calculating the powers b^(n*2^i) must first be overcome. - - `GET_STR_PRECOMPUTE_THRESHOLD' and `GET_STR_DC_THRESHOLD' represent -the same basic thing, the point where it becomes worth doing a big -division to cut the input in half. `GET_STR_PRECOMPUTE_THRESHOLD' -includes the cost of calculating the radix power required, whereas -`GET_STR_DC_THRESHOLD' assumes that's already available, which is the -case when recursing. - - Since the base case produces digits from least to most significant -but they want to be stored from most to least, it's necessary to -calculate in advance how many digits there will be, or at least be sure -not to underestimate that. For GMP the number of input bits is -multiplied by `chars_per_bit_exactly' from `mp_bases', rounding up. -The result is either correct or one too big. - - Examining some of the high bits of the input could increase the -chance of getting the exact number of digits, but an exact result every -time would not be practical, since in general the difference between -numbers 100... and 99... is only in the last few bits and the work to -identify 99... might well be almost as much as a full conversion. - - `mpf_get_str' doesn't currently use the algorithm described here, it -multiplies or divides by a power of b to move the radix point to the -just above the highest non-zero digit (or at worst one above that -location), then multiplies by b^n to bring out digits. This is O(N^2) -and is certainly not optimal. - - The r/b^n scheme described above for using multiplications to bring -out digits might be useful for more than a single limb. Some brief -experiments with it on the base case when recursing didn't give a -noticeable improvement, but perhaps that was only due to the -implementation. Something similar would work for the sub-quadratic -divisions too, though there would be the cost of calculating a bigger -radix power. - - Another possible improvement for the sub-quadratic part would be to -arrange for radix powers that balanced the sizes of quotient and -remainder produced, ie. the highest power would be an b^(n*k) -approximately equal to sqrt(t), not restricted to a 2^i factor. That -ought to smooth out a graph of times against sizes, but may or may not -be a net speedup. - - -File: gmp.info, Node: Radix to Binary, Prev: Binary to Radix, Up: Radix Conversion Algorithms - -16.6.2 Radix to Binary ----------------------- - -*This section needs to be rewritten, it currently describes the -algorithms used before GMP 4.3.* - - Conversions from a power-of-2 radix into binary use a simple and fast -O(N) bitwise concatenation algorithm. - - Conversions from other radices use one of two algorithms. Sizes -below `SET_STR_PRECOMPUTE_THRESHOLD' use a basic O(N^2) method. Groups -of n digits are converted to limbs, where n is the biggest power of the -base b which will fit in a limb, then those groups are accumulated into -the result by multiplying by b^n and adding. This saves -multi-precision operations, as per Knuth section 4.4 part E (*note -References::). Some special case code is provided for decimal, giving -the compiler a chance to optimize multiplications by 10. - - Above `SET_STR_PRECOMPUTE_THRESHOLD' a sub-quadratic algorithm is -used. First groups of n digits are converted into limbs. Then adjacent -limbs are combined into limb pairs with x*b^n+y, where x and y are the -limbs. Adjacent limb pairs are combined into quads similarly with -x*b^(2n)+y. This continues until a single block remains, that being -the result. - - The advantage of this method is that the multiplications for each x -are big blocks, allowing Karatsuba and higher algorithms to be used. -But the cost of calculating the powers b^(n*2^i) must be overcome. -`SET_STR_PRECOMPUTE_THRESHOLD' usually ends up quite big, around 5000 -digits, and on some processors much bigger still. - - `SET_STR_PRECOMPUTE_THRESHOLD' is based on the input digits (and -tuned for decimal), though it might be better based on a limb count, so -as to be independent of the base. But that sort of count isn't used by -the base case and so would need some sort of initial calculation or -estimate. - - The main reason `SET_STR_PRECOMPUTE_THRESHOLD' is so much bigger -than the corresponding `GET_STR_PRECOMPUTE_THRESHOLD' is that -`mpn_mul_1' is much faster than `mpn_divrem_1' (often by a factor of 5, -or more). - - -File: gmp.info, Node: Other Algorithms, Next: Assembly Coding, Prev: Radix Conversion Algorithms, Up: Algorithms - -16.7 Other Algorithms -===================== - -* Menu: - -* Prime Testing Algorithm:: -* Factorial Algorithm:: -* Binomial Coefficients Algorithm:: -* Fibonacci Numbers Algorithm:: -* Lucas Numbers Algorithm:: -* Random Number Algorithms:: - - -File: gmp.info, Node: Prime Testing Algorithm, Next: Factorial Algorithm, Prev: Other Algorithms, Up: Other Algorithms - -16.7.1 Prime Testing --------------------- - -The primality testing in `mpz_probab_prime_p' (*note Number Theoretic -Functions::) first does some trial division by small factors and then -uses the Miller-Rabin probabilistic primality testing algorithm, as -described in Knuth section 4.5.4 algorithm P (*note References::). - - For an odd input n, and with n = q*2^k+1 where q is odd, this -algorithm selects a random base x and tests whether x^q mod n is 1 or --1, or an x^(q*2^j) mod n is 1, for 1<=j<=k. If so then n is probably -prime, if not then n is definitely composite. - - Any prime n will pass the test, but some composites do too. Such -composites are known as strong pseudoprimes to base x. No n is a -strong pseudoprime to more than 1/4 of all bases (see Knuth exercise -22), hence with x chosen at random there's no more than a 1/4 chance a -"probable prime" will in fact be composite. - - In fact strong pseudoprimes are quite rare, making the test much more -powerful than this analysis would suggest, but 1/4 is all that's proven -for an arbitrary n. - - -File: gmp.info, Node: Factorial Algorithm, Next: Binomial Coefficients Algorithm, Prev: Prime Testing Algorithm, Up: Other Algorithms - -16.7.2 Factorial ----------------- - -Factorials are calculated by a combination of removal of twos, -powering, and binary splitting. The procedure can be best illustrated -with an example, - - 23! = 1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23 - -has factors of two removed, - - 23! = 2^19.1.1.3.1.5.3.7.1.9.5.11.3.13.7.15.1.17.9.19.5.21.11.23 - -and the resulting terms collected up according to their multiplicity, - - 23! = 2^19.(3.5)^3.(7.9.11)^2.(13.15.17.19.21.23) - - Each sequence such as 13.15.17.19.21.23 is evaluated by splitting -into every second term, as for instance (13.17.21).(15.19.23), and the -same recursively on each half. This is implemented iteratively using -some bit twiddling. - - Such splitting is more efficient than repeated Nx1 multiplies since -it forms big multiplies, allowing Karatsuba and higher algorithms to be -used. And even below the Karatsuba threshold a big block of work can -be more efficient for the basecase algorithm. - - Splitting into subsequences of every second term keeps the resulting -products more nearly equal in size than would the simpler approach of -say taking the first half and second half of the sequence. Nearly -equal products are more efficient for the current multiply -implementation. - - -File: gmp.info, Node: Binomial Coefficients Algorithm, Next: Fibonacci Numbers Algorithm, Prev: Factorial Algorithm, Up: Other Algorithms - -16.7.3 Binomial Coefficients ----------------------------- - -Binomial coefficients C(n,k) are calculated by first arranging k <= n/2 -using C(n,k) = C(n,n-k) if necessary, and then evaluating the following -product simply from i=2 to i=k. - - k (n-k+i) - C(n,k) = (n-k+1) * prod ------- - i=2 i - - It's easy to show that each denominator i will divide the product so -far, so the exact division algorithm is used (*note Exact Division::). - - The numerators n-k+i and denominators i are first accumulated into -as many fit a limb, to save multi-precision operations, though for -`mpz_bin_ui' this applies only to the divisors, since n is an `mpz_t' -and n-k+i in general won't fit in a limb at all. - - -File: gmp.info, Node: Fibonacci Numbers Algorithm, Next: Lucas Numbers Algorithm, Prev: Binomial Coefficients Algorithm, Up: Other Algorithms - -16.7.4 Fibonacci Numbers ------------------------- - -The Fibonacci functions `mpz_fib_ui' and `mpz_fib2_ui' are designed for -calculating isolated F[n] or F[n],F[n-1] values efficiently. - - For small n, a table of single limb values in `__gmp_fib_table' is -used. On a 32-bit limb this goes up to F[47], or on a 64-bit limb up -to F[93]. For convenience the table starts at F[-1]. - - Beyond the table, values are generated with a binary powering -algorithm, calculating a pair F[n] and F[n-1] working from high to low -across the bits of n. The formulas used are - - F[2k+1] = 4*F[k]^2 - F[k-1]^2 + 2*(-1)^k - F[2k-1] = F[k]^2 + F[k-1]^2 - - F[2k] = F[2k+1] - F[2k-1] - - At each step, k is the high b bits of n. If the next bit of n is 0 -then F[2k],F[2k-1] is used, or if it's a 1 then F[2k+1],F[2k] is used, -and the process repeated until all bits of n are incorporated. Notice -these formulas require just two squares per bit of n. - - It'd be possible to handle the first few n above the single limb -table with simple additions, using the defining Fibonacci recurrence -F[k+1]=F[k]+F[k-1], but this is not done since it usually turns out to -be faster for only about 10 or 20 values of n, and including a block of -code for just those doesn't seem worthwhile. If they really mattered -it'd be better to extend the data table. - - Using a table avoids lots of calculations on small numbers, and -makes small n go fast. A bigger table would make more small n go fast, -it's just a question of balancing size against desired speed. For GMP -the code is kept compact, with the emphasis primarily on a good -powering algorithm. - - `mpz_fib2_ui' returns both F[n] and F[n-1], but `mpz_fib_ui' is only -interested in F[n]. In this case the last step of the algorithm can -become one multiply instead of two squares. One of the following two -formulas is used, according as n is odd or even. - - F[2k] = F[k]*(F[k]+2F[k-1]) - - F[2k+1] = (2F[k]+F[k-1])*(2F[k]-F[k-1]) + 2*(-1)^k - - F[2k+1] here is the same as above, just rearranged to be a multiply. -For interest, the 2*(-1)^k term both here and above can be applied -just to the low limb of the calculation, without a carry or borrow into -further limbs, which saves some code size. See comments with -`mpz_fib_ui' and the internal `mpn_fib2_ui' for how this is done. - - -File: gmp.info, Node: Lucas Numbers Algorithm, Next: Random Number Algorithms, Prev: Fibonacci Numbers Algorithm, Up: Other Algorithms - -16.7.5 Lucas Numbers --------------------- - -`mpz_lucnum2_ui' derives a pair of Lucas numbers from a pair of -Fibonacci numbers with the following simple formulas. - - L[k] = F[k] + 2*F[k-1] - L[k-1] = 2*F[k] - F[k-1] - - `mpz_lucnum_ui' is only interested in L[n], and some work can be -saved. Trailing zero bits on n can be handled with a single square -each. - - L[2k] = L[k]^2 - 2*(-1)^k - - And the lowest 1 bit can be handled with one multiply of a pair of -Fibonacci numbers, similar to what `mpz_fib_ui' does. - - L[2k+1] = 5*F[k-1]*(2*F[k]+F[k-1]) - 4*(-1)^k - - -File: gmp.info, Node: Random Number Algorithms, Prev: Lucas Numbers Algorithm, Up: Other Algorithms - -16.7.6 Random Numbers ---------------------- - -For the `urandomb' functions, random numbers are generated simply by -concatenating bits produced by the generator. As long as the generator -has good randomness properties this will produce well-distributed N bit -numbers. - - For the `urandomm' functions, random numbers in a range 0<=R48 bit pieces is convenient. With -some care though six 21x32->53 bit products can be used, if one of the -lower two 21-bit pieces also uses the sign bit. - - For the `mpn_mul_1' family of functions on a 64-bit machine, the -invariant single limb is split at the start, into 3 or 4 pieces. -Inside the loop, the bignum operand is split into 32-bit pieces. Fast -conversion of these unsigned 32-bit pieces to floating point is highly -machine-dependent. In some cases, reading the data into the integer -unit, zero-extending to 64-bits, then transferring to the floating -point unit back via memory is the only option. - - Converting partial products back to 64-bit limbs is usually best -done as a signed conversion. Since all values are smaller than 2^53, -signed and unsigned are the same, but most processors lack unsigned -conversions. - - - - Here is a diagram showing 16x32 bit products for an `mpn_mul_1' or -`mpn_addmul_1' with a 64-bit limb. The single limb operand V is split -into four 16-bit parts. The multi-limb operand U is split in the loop -into two 32-bit parts. - - +---+---+---+---+ - |v48|v32|v16|v00| V operand - +---+---+---+---+ - - +-------+---+---+ - x | u32 | u00 | U operand (one limb) - +---------------+ - - --------------------------------- - - +-----------+ - | u00 x v00 | p00 48-bit products - +-----------+ - +-----------+ - | u00 x v16 | p16 - +-----------+ - +-----------+ - | u00 x v32 | p32 - +-----------+ - +-----------+ - | u00 x v48 | p48 - +-----------+ - +-----------+ - | u32 x v00 | r32 - +-----------+ - +-----------+ - | u32 x v16 | r48 - +-----------+ - +-----------+ - | u32 x v32 | r64 - +-----------+ - +-----------+ - | u32 x v48 | r80 - +-----------+ - - p32 and r32 can be summed using floating-point addition, and -likewise p48 and r48. p00 and p16 can be summed with r64 and r80 from -the previous iteration. - - For each loop then, four 49-bit quantities are transferred to the -integer unit, aligned as follows, - - |-----64bits----|-----64bits----| - +------------+ - | p00 + r64' | i00 - +------------+ - +------------+ - | p16 + r80' | i16 - +------------+ - +------------+ - | p32 + r32 | i32 - +------------+ - +------------+ - | p48 + r48 | i48 - +------------+ - - The challenge then is to sum these efficiently and add in a carry -limb, generating a low 64-bit result limb and a high 33-bit carry limb -(i48 extends 33 bits into the high half). - - -File: gmp.info, Node: Assembly SIMD Instructions, Next: Assembly Software Pipelining, Prev: Assembly Floating Point, Up: Assembly Coding - -16.8.7 SIMD Instructions ------------------------- - -The single-instruction multiple-data support in current microprocessors -is aimed at signal processing algorithms where each data point can be -treated more or less independently. There's generally not much support -for propagating the sort of carries that arise in GMP. - - SIMD multiplications of say four 16x16 bit multiplies only do as much -work as one 32x32 from GMP's point of view, and need some shifts and -adds besides. But of course if say the SIMD form is fully pipelined -and uses less instruction decoding then it may still be worthwhile. - - On the x86 chips, MMX has so far found a use in `mpn_rshift' and -`mpn_lshift', and is used in a special case for 16-bit multipliers in -the P55 `mpn_mul_1'. SSE2 is used for Pentium 4 `mpn_mul_1', -`mpn_addmul_1', and `mpn_submul_1'. - - -File: gmp.info, Node: Assembly Software Pipelining, Next: Assembly Loop Unrolling, Prev: Assembly SIMD Instructions, Up: Assembly Coding - -16.8.8 Software Pipelining --------------------------- - -Software pipelining consists of scheduling instructions around the -branch point in a loop. For example a loop might issue a load not for -use in the present iteration but the next, thereby allowing extra -cycles for the data to arrive from memory. - - Naturally this is wanted only when doing things like loads or -multiplies that take several cycles to complete, and only where a CPU -has multiple functional units so that other work can be done in the -meantime. - - A pipeline with several stages will have a data value in progress at -each stage and each loop iteration moves them along one stage. This is -like juggling. - - If the latency of some instruction is greater than the loop time -then it will be necessary to unroll, so one register has a result ready -to use while another (or multiple others) are still in progress. -(*note Assembly Loop Unrolling::). - - -File: gmp.info, Node: Assembly Loop Unrolling, Next: Assembly Writing Guide, Prev: Assembly Software Pipelining, Up: Assembly Coding - -16.8.9 Loop Unrolling ---------------------- - -Loop unrolling consists of replicating code so that several limbs are -processed in each loop. At a minimum this reduces loop overheads by a -corresponding factor, but it can also allow better register usage, for -example alternately using one register combination and then another. -Judicious use of `m4' macros can help avoid lots of duplication in the -source code. - - Any amount of unrolling can be handled with a loop counter that's -decremented by N each time, stopping when the remaining count is less -than the further N the loop will process. Or by subtracting N at the -start, the termination condition becomes when the counter C is less -than 0 (and the count of remaining limbs is C+N). - - Alternately for a power of 2 unroll the loop count and remainder can -be established with a shift and mask. This is convenient if also -making a computed jump into the middle of a large loop. - - The limbs not a multiple of the unrolling can be handled in various -ways, for example - - * A simple loop at the end (or the start) to process the excess. - Care will be wanted that it isn't too much slower than the - unrolled part. - - * A set of binary tests, for example after an 8-limb unrolling, test - for 4 more limbs to process, then a further 2 more or not, and - finally 1 more or not. This will probably take more code space - than a simple loop. - - * A `switch' statement, providing separate code for each possible - excess, for example an 8-limb unrolling would have separate code - for 0 remaining, 1 remaining, etc, up to 7 remaining. This might - take a lot of code, but may be the best way to optimize all cases - in combination with a deep pipelined loop. - - * A computed jump into the middle of the loop, thus making the first - iteration handle the excess. This should make times smoothly - increase with size, which is attractive, but setups for the jump - and adjustments for pointers can be tricky and could become quite - difficult in combination with deep pipelining. - - -File: gmp.info, Node: Assembly Writing Guide, Prev: Assembly Loop Unrolling, Up: Assembly Coding - -16.8.10 Writing Guide ---------------------- - -This is a guide to writing software pipelined loops for processing limb -vectors in assembly. - - First determine the algorithm and which instructions are needed. -Code it without unrolling or scheduling, to make sure it works. On a -3-operand CPU try to write each new value to a new register, this will -greatly simplify later steps. - - Then note for each instruction the functional unit and/or issue port -requirements. If an instruction can use either of two units, like U0 -or U1 then make a category "U0/U1". Count the total using each unit -(or combined unit), and count all instructions. - - Figure out from those counts the best possible loop time. The goal -will be to find a perfect schedule where instruction latencies are -completely hidden. The total instruction count might be the limiting -factor, or perhaps a particular functional unit. It might be possible -to tweak the instructions to help the limiting factor. - - Suppose the loop time is N, then make N issue buckets, with the -final loop branch at the end of the last. Now fill the buckets with -dummy instructions using the functional units desired. Run this to -make sure the intended speed is reached. - - Now replace the dummy instructions with the real instructions from -the slow but correct loop you started with. The first will typically -be a load instruction. Then the instruction using that value is placed -in a bucket an appropriate distance down. Run the loop again, to check -it still runs at target speed. - - Keep placing instructions, frequently measuring the loop. After a -few you will need to wrap around from the last bucket back to the top -of the loop. If you used the new-register for new-value strategy above -then there will be no register conflicts. If not then take care not to -clobber something already in use. Changing registers at this time is -very error prone. - - The loop will overlap two or more of the original loop iterations, -and the computation of one vector element result will be started in one -iteration of the new loop, and completed one or several iterations -later. - - The final step is to create feed-in and wind-down code for the loop. -A good way to do this is to make a copy (or copies) of the loop at the -start and delete those instructions which don't have valid antecedents, -and at the end replicate and delete those whose results are unwanted -(including any further loads). - - The loop will have a minimum number of limbs loaded and processed, -so the feed-in code must test if the request size is smaller and skip -either to a suitable part of the wind-down or to special code for small -sizes. - - -File: gmp.info, Node: Internals, Next: Contributors, Prev: Algorithms, Up: Top - -17 Internals -************ - -*This chapter is provided only for informational purposes and the -various internals described here may change in future GMP releases. -Applications expecting to be compatible with future releases should use -only the documented interfaces described in previous chapters.* - -* Menu: - -* Integer Internals:: -* Rational Internals:: -* Float Internals:: -* Raw Output Internals:: -* C++ Interface Internals:: - - -File: gmp.info, Node: Integer Internals, Next: Rational Internals, Prev: Internals, Up: Internals - -17.1 Integer Internals -====================== - -`mpz_t' variables represent integers using sign and magnitude, in space -dynamically allocated and reallocated. The fields are as follows. - -`_mp_size' - The number of limbs, or the negative of that when representing a - negative integer. Zero is represented by `_mp_size' set to zero, - in which case the `_mp_d' data is unused. - -`_mp_d' - A pointer to an array of limbs which is the magnitude. These are - stored "little endian" as per the `mpn' functions, so `_mp_d[0]' - is the least significant limb and `_mp_d[ABS(_mp_size)-1]' is the - most significant. Whenever `_mp_size' is non-zero, the most - significant limb is non-zero. - - Currently there's always at least one limb allocated, so for - instance `mpz_set_ui' never needs to reallocate, and `mpz_get_ui' - can fetch `_mp_d[0]' unconditionally (though its value is then - only wanted if `_mp_size' is non-zero). - -`_mp_alloc' - `_mp_alloc' is the number of limbs currently allocated at `_mp_d', - and naturally `_mp_alloc >= ABS(_mp_size)'. When an `mpz' routine - is about to (or might be about to) increase `_mp_size', it checks - `_mp_alloc' to see whether there's enough space, and reallocates - if not. `MPZ_REALLOC' is generally used for this. - - The various bitwise logical functions like `mpz_and' behave as if -negative values were twos complement. But sign and magnitude is always -used internally, and necessary adjustments are made during the -calculations. Sometimes this isn't pretty, but sign and magnitude are -best for other routines. - - Some internal temporary variables are setup with `MPZ_TMP_INIT' and -these have `_mp_d' space obtained from `TMP_ALLOC' rather than the -memory allocation functions. Care is taken to ensure that these are -big enough that no reallocation is necessary (since it would have -unpredictable consequences). - - `_mp_size' and `_mp_alloc' are `int', although `mp_size_t' is -usually a `long'. This is done to make the fields just 32 bits on some -64 bits systems, thereby saving a few bytes of data space but still -providing plenty of range. - - -File: gmp.info, Node: Rational Internals, Next: Float Internals, Prev: Integer Internals, Up: Internals - -17.2 Rational Internals -======================= - -`mpq_t' variables represent rationals using an `mpz_t' numerator and -denominator (*note Integer Internals::). - - The canonical form adopted is denominator positive (and non-zero), -no common factors between numerator and denominator, and zero uniquely -represented as 0/1. - - It's believed that casting out common factors at each stage of a -calculation is best in general. A GCD is an O(N^2) operation so it's -better to do a few small ones immediately than to delay and have to do -a big one later. Knowing the numerator and denominator have no common -factors can be used for example in `mpq_mul' to make only two cross -GCDs necessary, not four. - - This general approach to common factors is badly sub-optimal in the -presence of simple factorizations or little prospect for cancellation, -but GMP has no way to know when this will occur. As per *Note -Efficiency::, that's left to applications. The `mpq_t' framework might -still suit, with `mpq_numref' and `mpq_denref' for direct access to the -numerator and denominator, or of course `mpz_t' variables can be used -directly. - - -File: gmp.info, Node: Float Internals, Next: Raw Output Internals, Prev: Rational Internals, Up: Internals - -17.3 Float Internals -==================== - -Efficient calculation is the primary aim of GMP floats and the use of -whole limbs and simple rounding facilitates this. - - `mpf_t' floats have a variable precision mantissa and a single -machine word signed exponent. The mantissa is represented using sign -and magnitude. - - most least - significant significant - limb limb - - _mp_d - |---- _mp_exp ---> | - _____ _____ _____ _____ _____ - |_____|_____|_____|_____|_____| - . <------------ radix point - - <-------- _mp_size ---------> - -The fields are as follows. - -`_mp_size' - The number of limbs currently in use, or the negative of that when - representing a negative value. Zero is represented by `_mp_size' - and `_mp_exp' both set to zero, and in that case the `_mp_d' data - is unused. (In the future `_mp_exp' might be undefined when - representing zero.) - -`_mp_prec' - The precision of the mantissa, in limbs. In any calculation the - aim is to produce `_mp_prec' limbs of result (the most significant - being non-zero). - -`_mp_d' - A pointer to the array of limbs which is the absolute value of the - mantissa. These are stored "little endian" as per the `mpn' - functions, so `_mp_d[0]' is the least significant limb and - `_mp_d[ABS(_mp_size)-1]' the most significant. - - The most significant limb is always non-zero, but there are no - other restrictions on its value, in particular the highest 1 bit - can be anywhere within the limb. - - `_mp_prec+1' limbs are allocated to `_mp_d', the extra limb being - for convenience (see below). There are no reallocations during a - calculation, only in a change of precision with `mpf_set_prec'. - -`_mp_exp' - The exponent, in limbs, determining the location of the implied - radix point. Zero means the radix point is just above the most - significant limb. Positive values mean a radix point offset - towards the lower limbs and hence a value >= 1, as for example in - the diagram above. Negative exponents mean a radix point further - above the highest limb. - - Naturally the exponent can be any value, it doesn't have to fall - within the limbs as the diagram shows, it can be a long way above - or a long way below. Limbs other than those included in the - `{_mp_d,_mp_size}' data are treated as zero. - - The `_mp_size' and `_mp_prec' fields are `int', although the -`mp_size_t' type is usually a `long'. The `_mp_exp' field is usually -`long'. This is done to make some fields just 32 bits on some 64 bits -systems, thereby saving a few bytes of data space but still providing -plenty of precision and a very large range. - - -The following various points should be noted. - -Low Zeros - The least significant limbs `_mp_d[0]' etc can be zero, though - such low zeros can always be ignored. Routines likely to produce - low zeros check and avoid them to save time in subsequent - calculations, but for most routines they're quite unlikely and - aren't checked. - -Mantissa Size Range - The `_mp_size' count of limbs in use can be less than `_mp_prec' if - the value can be represented in less. This means low precision - values or small integers stored in a high precision `mpf_t' can - still be operated on efficiently. - - `_mp_size' can also be greater than `_mp_prec'. Firstly a value is - allowed to use all of the `_mp_prec+1' limbs available at `_mp_d', - and secondly when `mpf_set_prec_raw' lowers `_mp_prec' it leaves - `_mp_size' unchanged and so the size can be arbitrarily bigger than - `_mp_prec'. - -Rounding - All rounding is done on limb boundaries. Calculating `_mp_prec' - limbs with the high non-zero will ensure the application requested - minimum precision is obtained. - - The use of simple "trunc" rounding towards zero is efficient, - since there's no need to examine extra limbs and increment or - decrement. - -Bit Shifts - Since the exponent is in limbs, there are no bit shifts in basic - operations like `mpf_add' and `mpf_mul'. When differing exponents - are encountered all that's needed is to adjust pointers to line up - the relevant limbs. - - Of course `mpf_mul_2exp' and `mpf_div_2exp' will require bit - shifts, but the choice is between an exponent in limbs which - requires shifts there, or one in bits which requires them almost - everywhere else. - -Use of `_mp_prec+1' Limbs - The extra limb on `_mp_d' (`_mp_prec+1' rather than just - `_mp_prec') helps when an `mpf' routine might get a carry from its - operation. `mpf_add' for instance will do an `mpn_add' of - `_mp_prec' limbs. If there's no carry then that's the result, but - if there is a carry then it's stored in the extra limb of space and - `_mp_size' becomes `_mp_prec+1'. - - Whenever `_mp_prec+1' limbs are held in a variable, the low limb - is not needed for the intended precision, only the `_mp_prec' high - limbs. But zeroing it out or moving the rest down is unnecessary. - Subsequent routines reading the value will simply take the high - limbs they need, and this will be `_mp_prec' if their target has - that same precision. This is no more than a pointer adjustment, - and must be checked anyway since the destination precision can be - different from the sources. - - Copy functions like `mpf_set' will retain a full `_mp_prec+1' limbs - if available. This ensures that a variable which has `_mp_size' - equal to `_mp_prec+1' will get its full exact value copied. - Strictly speaking this is unnecessary since only `_mp_prec' limbs - are needed for the application's requested precision, but it's - considered that an `mpf_set' from one variable into another of the - same precision ought to produce an exact copy. - -Application Precisions - `__GMPF_BITS_TO_PREC' converts an application requested precision - to an `_mp_prec'. The value in bits is rounded up to a whole limb - then an extra limb is added since the most significant limb of - `_mp_d' is only non-zero and therefore might contain only one bit. - - `__GMPF_PREC_TO_BITS' does the reverse conversion, and removes the - extra limb from `_mp_prec' before converting to bits. The net - effect of reading back with `mpf_get_prec' is simply the precision - rounded up to a multiple of `mp_bits_per_limb'. - - Note that the extra limb added here for the high only being - non-zero is in addition to the extra limb allocated to `_mp_d'. - For example with a 32-bit limb, an application request for 250 - bits will be rounded up to 8 limbs, then an extra added for the - high being only non-zero, giving an `_mp_prec' of 9. `_mp_d' then - gets 10 limbs allocated. Reading back with `mpf_get_prec' will - take `_mp_prec' subtract 1 limb and multiply by 32, giving 256 - bits. - - Strictly speaking, the fact the high limb has at least one bit - means that a float with, say, 3 limbs of 32-bits each will be - holding at least 65 bits, but for the purposes of `mpf_t' it's - considered simply to be 64 bits, a nice multiple of the limb size. - - -File: gmp.info, Node: Raw Output Internals, Next: C++ Interface Internals, Prev: Float Internals, Up: Internals - -17.4 Raw Output Internals -========================= - -`mpz_out_raw' uses the following format. - - +------+------------------------+ - | size | data bytes | - +------+------------------------+ - - The size is 4 bytes written most significant byte first, being the -number of subsequent data bytes, or the twos complement negative of -that when a negative integer is represented. The data bytes are the -absolute value of the integer, written most significant byte first. - - The most significant data byte is always non-zero, so the output is -the same on all systems, irrespective of limb size. - - In GMP 1, leading zero bytes were written to pad the data bytes to a -multiple of the limb size. `mpz_inp_raw' will still accept this, for -compatibility. - - The use of "big endian" for both the size and data fields is -deliberate, it makes the data easy to read in a hex dump of a file. -Unfortunately it also means that the limb data must be reversed when -reading or writing, so neither a big endian nor little endian system -can just read and write `_mp_d'. - - -File: gmp.info, Node: C++ Interface Internals, Prev: Raw Output Internals, Up: Internals - -17.5 C++ Interface Internals -============================ - -A system of expression templates is used to ensure something like -`a=b+c' turns into a simple call to `mpz_add' etc. For `mpf_class' the -scheme also ensures the precision of the final destination is used for -any temporaries within a statement like `f=w*x+y*z'. These are -important features which a naive implementation cannot provide. - - A simplified description of the scheme follows. The true scheme is -complicated by the fact that expressions have different return types. -For detailed information, refer to the source code. - - To perform an operation, say, addition, we first define a "function -object" evaluating it, - - struct __gmp_binary_plus - { - static void eval(mpf_t f, mpf_t g, mpf_t h) { mpf_add(f, g, h); } - }; - -And an "additive expression" object, - - __gmp_expr<__gmp_binary_expr > - operator+(const mpf_class &f, const mpf_class &g) - { - return __gmp_expr - <__gmp_binary_expr >(f, g); - } - - The seemingly redundant `__gmp_expr<__gmp_binary_expr<...>>' is used -to encapsulate any possible kind of expression into a single template -type. In fact even `mpf_class' etc are `typedef' specializations of -`__gmp_expr'. - - Next we define assignment of `__gmp_expr' to `mpf_class'. - - template - mpf_class & mpf_class::operator=(const __gmp_expr &expr) - { - expr.eval(this->get_mpf_t(), this->precision()); - return *this; - } - - template - void __gmp_expr<__gmp_binary_expr >::eval - (mpf_t f, mp_bitcnt_t precision) - { - Op::eval(f, expr.val1.get_mpf_t(), expr.val2.get_mpf_t()); - } - - where `expr.val1' and `expr.val2' are references to the expression's -operands (here `expr' is the `__gmp_binary_expr' stored within the -`__gmp_expr'). - - This way, the expression is actually evaluated only at the time of -assignment, when the required precision (that of `f') is known. -Furthermore the target `mpf_t' is now available, thus we can call -`mpf_add' directly with `f' as the output argument. - - Compound expressions are handled by defining operators taking -subexpressions as their arguments, like this: - - template - __gmp_expr - <__gmp_binary_expr<__gmp_expr, __gmp_expr, __gmp_binary_plus> > - operator+(const __gmp_expr &expr1, const __gmp_expr &expr2) - { - return __gmp_expr - <__gmp_binary_expr<__gmp_expr, __gmp_expr, __gmp_binary_plus> > - (expr1, expr2); - } - - And the corresponding specializations of `__gmp_expr::eval': - - template - void __gmp_expr - <__gmp_binary_expr<__gmp_expr, __gmp_expr, Op> >::eval - (mpf_t f, mp_bitcnt_t precision) - { - // declare two temporaries - mpf_class temp1(expr.val1, precision), temp2(expr.val2, precision); - Op::eval(f, temp1.get_mpf_t(), temp2.get_mpf_t()); - } - - The expression is thus recursively evaluated to any level of -complexity and all subexpressions are evaluated to the precision of `f'. - - -File: gmp.info, Node: Contributors, Next: References, Prev: Internals, Up: Top - -Appendix A Contributors -*********************** - -Torbjo"rn Granlund wrote the original GMP library and is still the main -developer. Code not explicitly attributed to others, was contributed by -Torbjo"rn. Several other individuals and organizations have contributed -GMP. Here is a list in chronological order on first contribution: - - Gunnar Sjo"din and Hans Riesel helped with mathematical problems in -early versions of the library. - - Richard Stallman helped with the interface design and revised the -first version of this manual. - - Brian Beuning and Doug Lea helped with testing of early versions of -the library and made creative suggestions. - - John Amanatides of York University in Canada contributed the function -`mpz_probab_prime_p'. - - Paul Zimmermann wrote the REDC-based mpz_powm code, the -Scho"nhage-Strassen FFT multiply code, and the Karatsuba square root -code. He also improved the Toom3 code for GMP 4.2. Paul sparked the -development of GMP 2, with his comparisons between bignum packages. -The ECMNET project Paul is organizing was a driving force behind many -of the optimizations in GMP 3. Paul also wrote the new GMP 4.3 nth -root code (with Torbjo"rn). - - Ken Weber (Kent State University, Universidade Federal do Rio Grande -do Sul) contributed now defunct versions of `mpz_gcd', `mpz_divexact', -`mpn_gcd', and `mpn_bdivmod', partially supported by CNPq (Brazil) -grant 301314194-2. - - Per Bothner of Cygnus Support helped to set up GMP to use Cygnus' -configure. He has also made valuable suggestions and tested numerous -intermediary releases. - - Joachim Hollman was involved in the design of the `mpf' interface, -and in the `mpz' design revisions for version 2. - - Bennet Yee contributed the initial versions of `mpz_jacobi' and -`mpz_legendre'. - - Andreas Schwab contributed the files `mpn/m68k/lshift.S' and -`mpn/m68k/rshift.S' (now in `.asm' form). - - Robert Harley of Inria, France and David Seal of ARM, England, -suggested clever improvements for population count. Robert also wrote -highly optimized Karatsuba and 3-way Toom multiplication functions for -GMP 3, and contributed the ARM assembly code. - - Torsten Ekedahl of the Mathematical department of Stockholm -University provided significant inspiration during several phases of -the GMP development. His mathematical expertise helped improve several -algorithms. - - Linus Nordberg wrote the new configure system based on autoconf and -implemented the new random functions. - - Kevin Ryde worked on a large number of things: optimized x86 code, -m4 asm macros, parameter tuning, speed measuring, the configure system, -function inlining, divisibility tests, bit scanning, Jacobi symbols, -Fibonacci and Lucas number functions, printf and scanf functions, perl -interface, demo expression parser, the algorithms chapter in the -manual, `gmpasm-mode.el', and various miscellaneous improvements -elsewhere. - - Kent Boortz made the Mac OS 9 port. - - Steve Root helped write the optimized alpha 21264 assembly code. - - Gerardo Ballabio wrote the `gmpxx.h' C++ class interface and the C++ -`istream' input routines. - - Jason Moxham rewrote `mpz_fac_ui'. - - Pedro Gimeno implemented the Mersenne Twister and made other random -number improvements. - - Niels Mo"ller wrote the sub-quadratic GCD and extended GCD code, the -quadratic Hensel division code, and (with Torbjo"rn) the new divide and -conquer division code for GMP 4.3. Niels also helped implement the new -Toom multiply code for GMP 4.3 and implemented helper functions to -simplify Toom evaluations for GMP 5.0. He wrote the original version -of mpn_mulmod_bnm1. - - Alberto Zanoni and Marco Bodrato suggested the unbalanced multiply -strategy, and found the optimal strategies for evaluation and -interpolation in Toom multiplication. - - Marco Bodrato helped implement the new Toom multiply code for GMP -4.3 and implemented most of the new Toom multiply and squaring code for -5.0. He is the main author of the current mpn_mulmod_bnm1 and -mpn_mullo_n. Marco also wrote the functions mpn_invert and -mpn_invertappr. - - David Harvey suggested the internal function `mpn_bdiv_dbm1', -implementing division relevant to Toom multiplication. He also worked -on fast assembly sequences, in particular on a fast AMD64 -`mpn_mul_basecase'. - - Martin Boij wrote `mpn_perfect_power_p'. - - (This list is chronological, not ordered after significance. If you -have contributed to GMP but are not listed above, please tell - about the omission!) - - The development of floating point functions of GNU MP 2, were -supported in part by the ESPRIT-BRA (Basic Research Activities) 6846 -project POSSO (POlynomial System SOlving). - - The development of GMP 2, 3, and 4 was supported in part by the IDA -Center for Computing Sciences. - - Thanks go to Hans Thorsen for donating an SGI system for the GMP -test system environment. - - -File: gmp.info, Node: References, Next: GNU Free Documentation License, Prev: Contributors, Up: Top - -Appendix B References -********************* - -B.1 Books -========= - - * Jonathan M. Borwein and Peter B. Borwein, "Pi and the AGM: A Study - in Analytic Number Theory and Computational Complexity", Wiley, - 1998. - - * Richard Crandall and Carl Pomerance, "Prime Numbers: A - Computational Perspective", 2nd edition, Springer-Verlag, 2005. - `http://math.dartmouth.edu/~carlp/' - - * Henri Cohen, "A Course in Computational Algebraic Number Theory", - Graduate Texts in Mathematics number 138, Springer-Verlag, 1993. - `http://www.math.u-bordeaux.fr/~cohen/' - - * Donald E. Knuth, "The Art of Computer Programming", volume 2, - "Seminumerical Algorithms", 3rd edition, Addison-Wesley, 1998. - `http://www-cs-faculty.stanford.edu/~knuth/taocp.html' - - * John D. Lipson, "Elements of Algebra and Algebraic Computing", The - Benjamin Cummings Publishing Company Inc, 1981. - - * Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone, - "Handbook of Applied Cryptography", - `http://www.cacr.math.uwaterloo.ca/hac/' - - * Richard M. Stallman and the GCC Developer Community, "Using the - GNU Compiler Collection", Free Software Foundation, 2008, - available online `http://gcc.gnu.org/onlinedocs/', and in the GCC - package `ftp://ftp.gnu.org/gnu/gcc/' - -B.2 Papers -========== - - * Yves Bertot, Nicolas Magaud and Paul Zimmermann, "A Proof of GMP - Square Root", Journal of Automated Reasoning, volume 29, 2002, pp. - 225-252. Also available online as INRIA Research Report 4475, - June 2001, `http://www.inria.fr/rrrt/rr-4475.html' - - * Christoph Burnikel and Joachim Ziegler, "Fast Recursive Division", - Max-Planck-Institut fuer Informatik Research Report MPI-I-98-1-022, - `http://data.mpi-sb.mpg.de/internet/reports.nsf/NumberView/1998-1-022' - - * Torbjo"rn Granlund and Peter L. Montgomery, "Division by Invariant - Integers using Multiplication", in Proceedings of the SIGPLAN - PLDI'94 Conference, June 1994. Also available - `ftp://ftp.cwi.nl/pub/pmontgom/divcnst.psa4.gz' (and .psl.gz). - - * Niels Mo"ller and Torbjo"rn Granlund, "Improved division by - invariant integers", to appear. - - * Torbjo"rn Granlund and Niels Mo"ller, "Division of integers large - and small", to appear. - - * Tudor Jebelean, "An algorithm for exact division", Journal of - Symbolic Computation, volume 15, 1993, pp. 169-180. Research - report version available - `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1992/92-35.ps.gz' - - * Tudor Jebelean, "Exact Division with Karatsuba Complexity - - Extended Abstract", RISC-Linz technical report 96-31, - `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1996/96-31.ps.gz' - - * Tudor Jebelean, "Practical Integer Division with Karatsuba - Complexity", ISSAC 97, pp. 339-341. Technical report available - `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1996/96-29.ps.gz' - - * Tudor Jebelean, "A Generalization of the Binary GCD Algorithm", - ISSAC 93, pp. 111-116. Technical report version available - `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1993/93-01.ps.gz' - - * Tudor Jebelean, "A Double-Digit Lehmer-Euclid Algorithm for - Finding the GCD of Long Integers", Journal of Symbolic - Computation, volume 19, 1995, pp. 145-157. Technical report - version also available - `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1992/92-69.ps.gz' - - * Werner Krandick and Tudor Jebelean, "Bidirectional Exact Integer - Division", Journal of Symbolic Computation, volume 21, 1996, pp. - 441-455. Early technical report version also available - `ftp://ftp.risc.uni-linz.ac.at/pub/techreports/1994/94-50.ps.gz' - - * Makoto Matsumoto and Takuji Nishimura, "Mersenne Twister: A - 623-dimensionally equidistributed uniform pseudorandom number - generator", ACM Transactions on Modelling and Computer Simulation, - volume 8, January 1998, pp. 3-30. Available online - `http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.ps.gz' - (or .pdf) - - * R. Moenck and A. Borodin, "Fast Modular Transforms via Division", - Proceedings of the 13th Annual IEEE Symposium on Switching and - Automata Theory, October 1972, pp. 90-96. Reprinted as "Fast - Modular Transforms", Journal of Computer and System Sciences, - volume 8, number 3, June 1974, pp. 366-386. - - * Niels Mo"ller, "On Scho"nhage's algorithm and subquadratic integer - GCD computation", in Mathematics of Computation, volume 77, - January 2008, pp. 589-607. - - * Peter L. Montgomery, "Modular Multiplication Without Trial - Division", in Mathematics of Computation, volume 44, number 170, - April 1985. - - * Arnold Scho"nhage and Volker Strassen, "Schnelle Multiplikation - grosser Zahlen", Computing 7, 1971, pp. 281-292. - - * Kenneth Weber, "The accelerated integer GCD algorithm", ACM - Transactions on Mathematical Software, volume 21, number 1, March - 1995, pp. 111-122. - - * Paul Zimmermann, "Karatsuba Square Root", INRIA Research Report - 3805, November 1999, `http://www.inria.fr/rrrt/rr-3805.html' - - * Paul Zimmermann, "A Proof of GMP Fast Division and Square Root - Implementations", - `http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz' - - * Dan Zuras, "On Squaring and Multiplying Large Integers", ARITH-11: - IEEE Symposium on Computer Arithmetic, 1993, pp. 260 to 271. - Reprinted as "More on Multiplying and Squaring Large Integers", - IEEE Transactions on Computers, volume 43, number 8, August 1994, - pp. 899-908. - - -File: gmp.info, Node: GNU Free Documentation License, Next: Concept Index, Prev: References, Up: Top - -Appendix C GNU Free Documentation License -***************************************** - - Version 1.3, 3 November 2008 - - Copyright (C) 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc. - `http://fsf.org/' - - Everyone is permitted to copy and distribute verbatim copies - of this license document, but changing it is not allowed. - - 0. 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In case of a - disagreement between the translation and the original version of - this License or a notice or disclaimer, the original version will - prevail. - - If a section in the Document is Entitled "Acknowledgements", - "Dedications", or "History", the requirement (section 4) to - Preserve its Title (section 1) will typically require changing the - actual title. - - 9. TERMINATION - - You may not copy, modify, sublicense, or distribute the Document - except as expressly provided under this License. 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If your rights have been terminated and - not permanently reinstated, receipt of a copy of some or all of - the same material does not give you any rights to use it. - - 10. FUTURE REVISIONS OF THIS LICENSE - - The Free Software Foundation may publish new, revised versions of - the GNU Free Documentation License from time to time. Such new - versions will be similar in spirit to the present version, but may - differ in detail to address new problems or concerns. See - `http://www.gnu.org/copyleft/'. - - Each version of the License is given a distinguishing version - number. If the Document specifies that a particular numbered - version of this License "or any later version" applies to it, you - have the option of following the terms and conditions either of - that specified version or of any later version that has been - published (not as a draft) by the Free Software Foundation. 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A copy of the license is included in the section entitled ``GNU - Free Documentation License''. - - If you have Invariant Sections, Front-Cover Texts and Back-Cover -Texts, replace the "with...Texts." line with this: - - with the Invariant Sections being LIST THEIR TITLES, with - the Front-Cover Texts being LIST, and with the Back-Cover Texts - being LIST. - - If you have Invariant Sections without Cover Texts, or some other -combination of the three, merge those two alternatives to suit the -situation. - - If your document contains nontrivial examples of program code, we -recommend releasing these examples in parallel under your choice of -free software license, such as the GNU General Public License, to -permit their use in free software. - - -File: gmp.info, Node: Concept Index, Next: Function Index, Prev: GNU Free Documentation License, Up: Top - -Concept Index -************* - -[index] -* Menu: - -* #include: Headers and Libraries. - (line 6) -* --build: Build Options. (line 52) -* --disable-fft: Build Options. (line 317) -* --disable-shared: Build Options. (line 45) -* --disable-static: Build Options. (line 45) -* --enable-alloca: Build Options. (line 278) -* --enable-assert: Build Options. (line 327) -* --enable-cxx: Build Options. (line 230) -* --enable-fat: Build Options. (line 164) -* --enable-mpbsd: Build Options. (line 322) -* --enable-profiling <1>: Profiling. (line 6) -* --enable-profiling: Build Options. (line 331) -* --exec-prefix: Build Options. (line 32) -* --host: Build Options. (line 66) -* --prefix: Build Options. (line 32) -* -finstrument-functions: Profiling. (line 66) -* 2exp functions: Efficiency. (line 43) -* 68000: Notes for Particular Systems. - (line 80) -* 80x86: Notes for Particular Systems. - (line 126) -* ABI <1>: Build Options. (line 171) -* ABI: ABI and ISA. (line 6) -* About this manual: Introduction to GMP. (line 58) -* AC_CHECK_LIB: Autoconf. (line 11) -* AIX <1>: ABI and ISA. (line 184) -* AIX <2>: Notes for Particular Systems. - (line 7) -* AIX: ABI and ISA. (line 169) -* Algorithms: Algorithms. (line 6) -* alloca: Build Options. (line 278) -* Allocation of memory: Custom Allocation. (line 6) -* AMD64: ABI and ISA. (line 44) -* Anonymous FTP of latest version: Introduction to GMP. (line 38) -* Application Binary Interface: ABI and ISA. (line 6) -* Arithmetic functions <1>: Float Arithmetic. (line 6) -* Arithmetic functions <2>: Integer Arithmetic. (line 6) -* Arithmetic functions: Rational Arithmetic. (line 6) -* ARM: Notes for Particular Systems. - (line 20) -* Assembly cache handling: Assembly Cache Handling. - (line 6) -* Assembly carry propagation: Assembly Carry Propagation. - (line 6) -* Assembly code organisation: Assembly Code Organisation. - (line 6) -* Assembly coding: Assembly Coding. (line 6) -* Assembly floating Point: Assembly Floating Point. - (line 6) -* Assembly loop unrolling: Assembly Loop Unrolling. - (line 6) -* Assembly SIMD: Assembly SIMD Instructions. - (line 6) -* Assembly software pipelining: Assembly Software Pipelining. - (line 6) -* Assembly writing guide: Assembly Writing Guide. - (line 6) -* Assertion checking <1>: Debugging. (line 79) -* Assertion checking: Build Options. (line 327) -* Assignment functions <1>: Assigning Floats. (line 6) -* Assignment functions <2>: Initializing Rationals. - (line 6) -* Assignment functions <3>: Simultaneous Integer Init & Assign. - (line 6) -* Assignment functions <4>: Simultaneous Float Init & Assign. - (line 6) -* Assignment functions: Assigning Integers. (line 6) -* Autoconf: Autoconf. (line 6) -* Basics: GMP Basics. (line 6) -* Berkeley MP compatible functions <1>: Build Options. (line 322) -* Berkeley MP compatible functions: BSD Compatible Functions. - (line 6) -* Binomial coefficient algorithm: Binomial Coefficients Algorithm. - (line 6) -* Binomial coefficient functions: Number Theoretic Functions. - (line 100) -* Binutils strip: Known Build Problems. - (line 28) -* Bit manipulation functions: Integer Logic and Bit Fiddling. - (line 6) -* Bit scanning functions: Integer Logic and Bit Fiddling. - (line 38) -* Bit shift left: Integer Arithmetic. (line 35) -* Bit shift right: Integer Division. (line 53) -* Bits per limb: Useful Macros and Constants. - (line 7) -* BSD MP compatible functions <1>: Build Options. (line 322) -* BSD MP compatible functions: BSD Compatible Functions. - (line 6) -* Bug reporting: Reporting Bugs. (line 6) -* Build directory: Build Options. (line 19) -* Build notes for binary packaging: Notes for Package Builds. - (line 6) -* Build notes for particular systems: Notes for Particular Systems. - (line 6) -* Build options: Build Options. (line 6) -* Build problems known: Known Build Problems. - (line 6) -* Build system: Build Options. (line 52) -* Building GMP: Installing GMP. (line 6) -* Bus error: Debugging. (line 7) -* C compiler: Build Options. (line 182) -* C++ compiler: Build Options. (line 254) -* C++ interface: C++ Class Interface. (line 6) -* C++ interface internals: C++ Interface Internals. - (line 6) -* C++ istream input: C++ Formatted Input. (line 6) -* C++ ostream output: C++ Formatted Output. - (line 6) -* C++ support: Build Options. (line 230) -* CC: Build Options. (line 182) -* CC_FOR_BUILD: Build Options. (line 217) -* CFLAGS: Build Options. (line 182) -* Checker: Debugging. (line 115) -* checkergcc: Debugging. (line 122) -* Code organisation: Assembly Code Organisation. - (line 6) -* Compaq C++: Notes for Particular Systems. - (line 25) -* Comparison functions <1>: Integer Comparisons. (line 6) -* Comparison functions <2>: Comparing Rationals. (line 6) -* Comparison functions: Float Comparison. (line 6) -* Compatibility with older versions: Compatibility with older versions. - (line 6) -* Conditions for copying GNU MP: Copying. (line 6) -* Configuring GMP: Installing GMP. (line 6) -* Congruence algorithm: Exact Remainder. (line 29) -* Congruence functions: Integer Division. (line 124) -* Constants: Useful Macros and Constants. - (line 6) -* Contributors: Contributors. (line 6) -* Conventions for parameters: Parameter Conventions. - (line 6) -* Conventions for variables: Variable Conventions. - (line 6) -* Conversion functions <1>: Converting Integers. (line 6) -* Conversion functions <2>: Converting Floats. (line 6) -* Conversion functions: Rational Conversions. - (line 6) -* Copying conditions: Copying. (line 6) -* CPPFLAGS: Build Options. (line 208) -* CPU types <1>: Introduction to GMP. (line 24) -* CPU types: Build Options. (line 108) -* Cross compiling: Build Options. (line 66) -* Custom allocation: Custom Allocation. (line 6) -* CXX: Build Options. (line 254) -* CXXFLAGS: Build Options. (line 254) -* Cygwin: Notes for Particular Systems. - (line 43) -* Darwin: Known Build Problems. - (line 51) -* Debugging: Debugging. (line 6) -* Demonstration programs: Demonstration Programs. - (line 6) -* Digits in an integer: Miscellaneous Integer Functions. - (line 23) -* Divisibility algorithm: Exact Remainder. (line 29) -* Divisibility functions: Integer Division. (line 124) -* Divisibility testing: Efficiency. (line 91) -* Division algorithms: Division Algorithms. (line 6) -* Division functions <1>: Rational Arithmetic. (line 22) -* Division functions <2>: Integer Division. (line 6) -* Division functions: Float Arithmetic. (line 33) -* DJGPP <1>: Notes for Particular Systems. - (line 43) -* DJGPP: Known Build Problems. - (line 18) -* DLLs: Notes for Particular Systems. - (line 56) -* DocBook: Build Options. (line 354) -* Documentation formats: Build Options. (line 347) -* Documentation license: GNU Free Documentation License. - (line 6) -* DVI: Build Options. (line 350) -* Efficiency: Efficiency. (line 6) -* Emacs: Emacs. (line 6) -* Exact division functions: Integer Division. (line 102) -* Exact remainder: Exact Remainder. (line 6) -* Example programs: Demonstration Programs. - (line 6) -* Exec prefix: Build Options. (line 32) -* Execution profiling <1>: Profiling. (line 6) -* Execution profiling: Build Options. (line 331) -* Exponentiation functions <1>: Integer Exponentiation. - (line 6) -* Exponentiation functions: Float Arithmetic. (line 41) -* Export: Integer Import and Export. - (line 45) -* Expression parsing demo: Demonstration Programs. - (line 18) -* Extended GCD: Number Theoretic Functions. - (line 45) -* Factor removal functions: Number Theoretic Functions. - (line 90) -* Factorial algorithm: Factorial Algorithm. (line 6) -* Factorial functions: Number Theoretic Functions. - (line 95) -* Factorization demo: Demonstration Programs. - (line 25) -* Fast Fourier Transform: FFT Multiplication. (line 6) -* Fat binary: Build Options. (line 164) -* FFT multiplication <1>: FFT Multiplication. (line 6) -* FFT multiplication: Build Options. (line 317) -* Fibonacci number algorithm: Fibonacci Numbers Algorithm. - (line 6) -* Fibonacci sequence functions: Number Theoretic Functions. - (line 108) -* Float arithmetic functions: Float Arithmetic. (line 6) -* Float assignment functions <1>: Simultaneous Float Init & Assign. - (line 6) -* Float assignment functions: Assigning Floats. (line 6) -* Float comparison functions: Float Comparison. (line 6) -* Float conversion functions: Converting Floats. (line 6) -* Float functions: Floating-point Functions. - (line 6) -* Float initialization functions <1>: Simultaneous Float Init & Assign. - (line 6) -* Float initialization functions: Initializing Floats. (line 6) -* Float input and output functions: I/O of Floats. (line 6) -* Float internals: Float Internals. (line 6) -* Float miscellaneous functions: Miscellaneous Float Functions. - (line 6) -* Float random number functions: Miscellaneous Float Functions. - (line 27) -* Float rounding functions: Miscellaneous Float Functions. - (line 9) -* Float sign tests: Float Comparison. (line 33) -* Floating point mode: Notes for Particular Systems. - (line 34) -* Floating-point functions: Floating-point Functions. - (line 6) -* Floating-point number: Nomenclature and Types. - (line 21) -* fnccheck: Profiling. (line 77) -* Formatted input: Formatted Input. (line 6) -* Formatted output: Formatted Output. (line 6) -* Free Documentation License: GNU Free Documentation License. - (line 6) -* frexp <1>: Converting Floats. (line 23) -* frexp: Converting Integers. (line 42) -* FTP of latest version: Introduction to GMP. (line 38) -* Function classes: Function Classes. (line 6) -* FunctionCheck: Profiling. (line 77) -* GCC Checker: Debugging. (line 115) -* GCD algorithms: Greatest Common Divisor Algorithms. - (line 6) -* GCD extended: Number Theoretic Functions. - (line 45) -* GCD functions: Number Theoretic Functions. - (line 30) -* GDB: Debugging. (line 58) -* Generic C: Build Options. (line 153) -* GMP Perl module: Demonstration Programs. - (line 35) -* GMP version number: Useful Macros and Constants. - (line 12) -* gmp.h: Headers and Libraries. - (line 6) -* gmpxx.h: C++ Interface General. - (line 8) -* GNU Debugger: Debugging. (line 58) -* GNU Free Documentation License: GNU Free Documentation License. - (line 6) -* GNU strip: Known Build Problems. - (line 28) -* gprof: Profiling. (line 41) -* Greatest common divisor algorithms: Greatest Common Divisor Algorithms. - (line 6) -* Greatest common divisor functions: Number Theoretic Functions. - (line 30) -* Hardware floating point mode: Notes for Particular Systems. - (line 34) -* Headers: Headers and Libraries. - (line 6) -* Heap problems: Debugging. (line 24) -* Home page: Introduction to GMP. (line 34) -* Host system: Build Options. (line 66) -* HP-UX: ABI and ISA. (line 107) -* HPPA: ABI and ISA. (line 68) -* I/O functions <1>: I/O of Integers. (line 6) -* I/O functions <2>: I/O of Rationals. (line 6) -* I/O functions: I/O of Floats. (line 6) -* i386: Notes for Particular Systems. - (line 126) -* IA-64: ABI and ISA. (line 107) -* Import: Integer Import and Export. - (line 11) -* In-place operations: Efficiency. (line 57) -* Include files: Headers and Libraries. - (line 6) -* info-lookup-symbol: Emacs. (line 6) -* Initialization functions <1>: Initializing Integers. - (line 6) -* Initialization functions <2>: Initializing Rationals. - (line 6) -* Initialization functions <3>: Random State Initialization. - (line 6) -* Initialization functions <4>: Simultaneous Float Init & Assign. - (line 6) -* Initialization functions <5>: Simultaneous Integer Init & Assign. - (line 6) -* Initialization functions: Initializing Floats. (line 6) -* Initializing and clearing: Efficiency. (line 21) -* Input functions <1>: I/O of Integers. (line 6) -* Input functions <2>: I/O of Rationals. (line 6) -* Input functions <3>: I/O of Floats. (line 6) -* Input functions: Formatted Input Functions. - (line 6) -* Install prefix: Build Options. (line 32) -* Installing GMP: Installing GMP. (line 6) -* Instruction Set Architecture: ABI and ISA. (line 6) -* instrument-functions: Profiling. (line 66) -* Integer: Nomenclature and Types. - (line 6) -* Integer arithmetic functions: Integer Arithmetic. (line 6) -* Integer assignment functions <1>: Simultaneous Integer Init & Assign. - (line 6) -* Integer assignment functions: Assigning Integers. (line 6) -* Integer bit manipulation functions: Integer Logic and Bit Fiddling. - (line 6) -* Integer comparison functions: Integer Comparisons. (line 6) -* Integer conversion functions: Converting Integers. (line 6) -* Integer division functions: Integer Division. (line 6) -* Integer exponentiation functions: Integer Exponentiation. - (line 6) -* Integer export: Integer Import and Export. - (line 45) -* Integer functions: Integer Functions. (line 6) -* Integer import: Integer Import and Export. - (line 11) -* Integer initialization functions <1>: Simultaneous Integer Init & Assign. - (line 6) -* Integer initialization functions: Initializing Integers. - (line 6) -* Integer input and output functions: I/O of Integers. (line 6) -* Integer internals: Integer Internals. (line 6) -* Integer logical functions: Integer Logic and Bit Fiddling. - (line 6) -* Integer miscellaneous functions: Miscellaneous Integer Functions. - (line 6) -* Integer random number functions: Integer Random Numbers. - (line 6) -* Integer root functions: Integer Roots. (line 6) -* Integer sign tests: Integer Comparisons. (line 28) -* Integer special functions: Integer Special Functions. - (line 6) -* Interix: Notes for Particular Systems. - (line 51) -* Internals: Internals. (line 6) -* Introduction: Introduction to GMP. (line 6) -* Inverse modulo functions: Number Theoretic Functions. - (line 60) -* IRIX <1>: Known Build Problems. - (line 38) -* IRIX: ABI and ISA. (line 132) -* ISA: ABI and ISA. (line 6) -* istream input: C++ Formatted Input. (line 6) -* Jacobi symbol algorithm: Jacobi Symbol. (line 6) -* Jacobi symbol functions: Number Theoretic Functions. - (line 66) -* Karatsuba multiplication: Karatsuba Multiplication. - (line 6) -* Karatsuba square root algorithm: Square Root Algorithm. - (line 6) -* Kronecker symbol functions: Number Theoretic Functions. - (line 78) -* Language bindings: Language Bindings. (line 6) -* Latest version of GMP: Introduction to GMP. (line 38) -* LCM functions: Number Theoretic Functions. - (line 55) -* Least common multiple functions: Number Theoretic Functions. - (line 55) -* Legendre symbol functions: Number Theoretic Functions. - (line 69) -* libgmp: Headers and Libraries. - (line 22) -* libgmpxx: Headers and Libraries. - (line 27) -* Libraries: Headers and Libraries. - (line 22) -* Libtool: Headers and Libraries. - (line 33) -* Libtool versioning: Notes for Package Builds. - (line 9) -* License conditions: Copying. (line 6) -* Limb: Nomenclature and Types. - (line 31) -* Limb size: Useful Macros and Constants. - (line 7) -* Linear congruential algorithm: Random Number Algorithms. - (line 25) -* Linear congruential random numbers: Random State Initialization. - (line 32) -* Linking: Headers and Libraries. - (line 22) -* Logical functions: Integer Logic and Bit Fiddling. - (line 6) -* Low-level functions: Low-level Functions. (line 6) -* Lucas number algorithm: Lucas Numbers Algorithm. - (line 6) -* Lucas number functions: Number Theoretic Functions. - (line 119) -* MacOS X: Known Build Problems. - (line 51) -* Mailing lists: Introduction to GMP. (line 45) -* Malloc debugger: Debugging. (line 30) -* Malloc problems: Debugging. (line 24) -* Memory allocation: Custom Allocation. (line 6) -* Memory management: Memory Management. (line 6) -* Mersenne twister algorithm: Random Number Algorithms. - (line 17) -* Mersenne twister random numbers: Random State Initialization. - (line 13) -* MINGW: Notes for Particular Systems. - (line 43) -* MIPS: ABI and ISA. (line 132) -* Miscellaneous float functions: Miscellaneous Float Functions. - (line 6) -* Miscellaneous integer functions: Miscellaneous Integer Functions. - (line 6) -* MMX: Notes for Particular Systems. - (line 132) -* Modular inverse functions: Number Theoretic Functions. - (line 60) -* Most significant bit: Miscellaneous Integer Functions. - (line 34) -* mp.h: BSD Compatible Functions. - (line 21) -* MPN_PATH: Build Options. (line 335) -* MS Windows: Notes for Particular Systems. - (line 56) -* MS-DOS: Notes for Particular Systems. - (line 43) -* Multi-threading: Reentrancy. (line 6) -* Multiplication algorithms: Multiplication Algorithms. - (line 6) -* Nails: Low-level Functions. (line 478) -* Native compilation: Build Options. (line 52) -* NeXT: Known Build Problems. - (line 57) -* Next prime function: Number Theoretic Functions. - (line 23) -* Nomenclature: Nomenclature and Types. - (line 6) -* Non-Unix systems: Build Options. (line 11) -* Nth root algorithm: Nth Root Algorithm. (line 6) -* Number sequences: Efficiency. (line 147) -* Number theoretic functions: Number Theoretic Functions. - (line 6) -* Numerator and denominator: Applying Integer Functions. - (line 6) -* obstack output: Formatted Output Functions. - (line 81) -* OpenBSD: Notes for Particular Systems. - (line 86) -* Optimizing performance: Performance optimization. - (line 6) -* ostream output: C++ Formatted Output. - (line 6) -* Other languages: Language Bindings. (line 6) -* Output functions <1>: I/O of Floats. (line 6) -* Output functions <2>: I/O of Rationals. (line 6) -* Output functions <3>: Formatted Output Functions. - (line 6) -* Output functions: I/O of Integers. (line 6) -* Packaged builds: Notes for Package Builds. - (line 6) -* Parameter conventions: Parameter Conventions. - (line 6) -* Parsing expressions demo: Demonstration Programs. - (line 21) -* Particular systems: Notes for Particular Systems. - (line 6) -* Past GMP versions: Compatibility with older versions. - (line 6) -* PDF: Build Options. (line 350) -* Perfect power algorithm: Perfect Power Algorithm. - (line 6) -* Perfect power functions: Integer Roots. (line 27) -* Perfect square algorithm: Perfect Square Algorithm. - (line 6) -* Perfect square functions: Integer Roots. (line 36) -* perl: Demonstration Programs. - (line 35) -* Perl module: Demonstration Programs. - (line 35) -* Postscript: Build Options. (line 350) -* Power/PowerPC <1>: Known Build Problems. - (line 63) -* Power/PowerPC: Notes for Particular Systems. - (line 92) -* Powering algorithms: Powering Algorithms. (line 6) -* Powering functions <1>: Float Arithmetic. (line 41) -* Powering functions: Integer Exponentiation. - (line 6) -* PowerPC: ABI and ISA. (line 167) -* Precision of floats: Floating-point Functions. - (line 6) -* Precision of hardware floating point: Notes for Particular Systems. - (line 34) -* Prefix: Build Options. (line 32) -* Prime testing algorithms: Prime Testing Algorithm. - (line 6) -* Prime testing functions: Number Theoretic Functions. - (line 7) -* printf formatted output: Formatted Output. (line 6) -* Probable prime testing functions: Number Theoretic Functions. - (line 7) -* prof: Profiling. (line 24) -* Profiling: Profiling. (line 6) -* Radix conversion algorithms: Radix Conversion Algorithms. - (line 6) -* Random number algorithms: Random Number Algorithms. - (line 6) -* Random number functions <1>: Integer Random Numbers. - (line 6) -* Random number functions <2>: Miscellaneous Float Functions. - (line 27) -* Random number functions: Random Number Functions. - (line 6) -* Random number seeding: Random State Seeding. - (line 6) -* Random number state: Random State Initialization. - (line 6) -* Random state: Nomenclature and Types. - (line 46) -* Rational arithmetic: Efficiency. (line 113) -* Rational arithmetic functions: Rational Arithmetic. (line 6) -* Rational assignment functions: Initializing Rationals. - (line 6) -* Rational comparison functions: Comparing Rationals. (line 6) -* Rational conversion functions: Rational Conversions. - (line 6) -* Rational initialization functions: Initializing Rationals. - (line 6) -* Rational input and output functions: I/O of Rationals. (line 6) -* Rational internals: Rational Internals. (line 6) -* Rational number: Nomenclature and Types. - (line 16) -* Rational number functions: Rational Number Functions. - (line 6) -* Rational numerator and denominator: Applying Integer Functions. - (line 6) -* Rational sign tests: Comparing Rationals. (line 27) -* Raw output internals: Raw Output Internals. - (line 6) -* Reallocations: Efficiency. (line 30) -* Reentrancy: Reentrancy. (line 6) -* References: References. (line 6) -* Remove factor functions: Number Theoretic Functions. - (line 90) -* Reporting bugs: Reporting Bugs. (line 6) -* Root extraction algorithm: Nth Root Algorithm. (line 6) -* Root extraction algorithms: Root Extraction Algorithms. - (line 6) -* Root extraction functions <1>: Float Arithmetic. (line 37) -* Root extraction functions: Integer Roots. (line 6) -* Root testing functions: Integer Roots. (line 36) -* Rounding functions: Miscellaneous Float Functions. - (line 9) -* Sample programs: Demonstration Programs. - (line 6) -* Scan bit functions: Integer Logic and Bit Fiddling. - (line 38) -* scanf formatted input: Formatted Input. (line 6) -* SCO: Known Build Problems. - (line 38) -* Seeding random numbers: Random State Seeding. - (line 6) -* Segmentation violation: Debugging. (line 7) -* Sequent Symmetry: Known Build Problems. - (line 68) -* Services for Unix: Notes for Particular Systems. - (line 51) -* Shared library versioning: Notes for Package Builds. - (line 9) -* Sign tests <1>: Float Comparison. (line 33) -* Sign tests <2>: Integer Comparisons. (line 28) -* Sign tests: Comparing Rationals. (line 27) -* Size in digits: Miscellaneous Integer Functions. - (line 23) -* Small operands: Efficiency. (line 7) -* Solaris <1>: ABI and ISA. (line 201) -* Solaris: Known Build Problems. - (line 78) -* Sparc: Notes for Particular Systems. - (line 108) -* Sparc V9: ABI and ISA. (line 201) -* Special integer functions: Integer Special Functions. - (line 6) -* Square root algorithm: Square Root Algorithm. - (line 6) -* SSE2: Notes for Particular Systems. - (line 132) -* Stack backtrace: Debugging. (line 50) -* Stack overflow <1>: Debugging. (line 7) -* Stack overflow: Build Options. (line 278) -* Static linking: Efficiency. (line 14) -* stdarg.h: Headers and Libraries. - (line 17) -* stdio.h: Headers and Libraries. - (line 11) -* Stripped libraries: Known Build Problems. - (line 28) -* Sun: ABI and ISA. (line 201) -* SunOS: Notes for Particular Systems. - (line 120) -* Systems: Notes for Particular Systems. - (line 6) -* Temporary memory: Build Options. (line 278) -* Texinfo: Build Options. (line 347) -* Text input/output: Efficiency. (line 153) -* Thread safety: Reentrancy. (line 6) -* Toom multiplication <1>: Other Multiplication. - (line 6) -* Toom multiplication <2>: Toom 4-Way Multiplication. - (line 6) -* Toom multiplication: Toom 3-Way Multiplication. - (line 6) -* Types: Nomenclature and Types. - (line 6) -* ui and si functions: Efficiency. (line 50) -* Unbalanced multiplication: Unbalanced Multiplication. - (line 6) -* Upward compatibility: Compatibility with older versions. - (line 6) -* Useful macros and constants: Useful Macros and Constants. - (line 6) -* User-defined precision: Floating-point Functions. - (line 6) -* Valgrind: Debugging. (line 130) -* Variable conventions: Variable Conventions. - (line 6) -* Version number: Useful Macros and Constants. - (line 12) -* Web page: Introduction to GMP. (line 34) -* Windows: Notes for Particular Systems. - (line 56) -* x86: Notes for Particular Systems. - (line 126) -* x87: Notes for Particular Systems. - (line 34) -* XML: Build Options. (line 354) - - -File: gmp.info, Node: Function Index, Prev: Concept Index, Up: Top - -Function and Type Index -*********************** - -[index] -* Menu: - -* __GMP_CC: Useful Macros and Constants. - (line 23) -* __GMP_CFLAGS: Useful Macros and Constants. - (line 24) -* __GNU_MP_VERSION: Useful Macros and Constants. - (line 10) -* __GNU_MP_VERSION_MINOR: Useful Macros and Constants. - (line 11) -* __GNU_MP_VERSION_PATCHLEVEL: Useful Macros and Constants. - (line 12) -* _mpz_realloc: Integer Special Functions. - (line 51) -* abs <1>: C++ Interface Rationals. - (line 43) -* abs <2>: C++ Interface Integers. - (line 42) -* abs: C++ Interface Floats. - (line 70) -* ceil: C++ Interface Floats. - (line 71) -* cmp <1>: C++ Interface Floats. - (line 72) -* cmp <2>: C++ Interface Rationals. - (line 44) -* cmp <3>: C++ Interface Integers. - (line 44) -* cmp: C++ Interface Rationals. - (line 45) -* floor: C++ Interface Floats. - (line 80) -* gcd: BSD Compatible Functions. - (line 82) -* gmp_asprintf: Formatted Output Functions. - (line 65) -* gmp_errno: Random State Initialization. - (line 55) -* GMP_ERROR_INVALID_ARGUMENT: Random State Initialization. - (line 55) -* GMP_ERROR_UNSUPPORTED_ARGUMENT: Random State Initialization. - (line 55) -* gmp_fprintf: Formatted Output Functions. - (line 29) -* gmp_fscanf: Formatted Input Functions. - (line 25) -* GMP_LIMB_BITS: Low-level Functions. (line 508) -* GMP_NAIL_BITS: Low-level Functions. (line 506) -* GMP_NAIL_MASK: Low-level Functions. (line 516) -* GMP_NUMB_BITS: Low-level Functions. (line 507) -* GMP_NUMB_MASK: Low-level Functions. (line 517) -* GMP_NUMB_MAX: Low-level Functions. (line 525) -* gmp_obstack_printf: Formatted Output Functions. - (line 79) -* gmp_obstack_vprintf: Formatted Output Functions. - (line 81) -* gmp_printf: Formatted Output Functions. - (line 24) -* GMP_RAND_ALG_DEFAULT: Random State Initialization. - (line 49) -* GMP_RAND_ALG_LC: Random State Initialization. - (line 49) -* gmp_randclass: C++ Interface Random Numbers. - (line 7) -* gmp_randclass::get_f: C++ Interface Random Numbers. - (line 45) -* gmp_randclass::get_z_bits: C++ Interface Random Numbers. - (line 39) -* gmp_randclass::get_z_range: C++ Interface Random Numbers. - (line 42) -* gmp_randclass::gmp_randclass: C++ Interface Random Numbers. - (line 13) -* gmp_randclass::seed: C++ Interface Random Numbers. - (line 33) -* gmp_randclear: Random State Initialization. - (line 62) -* gmp_randinit: Random State Initialization. - (line 47) -* gmp_randinit_default: Random State Initialization. - (line 7) -* gmp_randinit_lc_2exp: Random State Initialization. - (line 18) -* gmp_randinit_lc_2exp_size: Random State Initialization. - (line 32) -* gmp_randinit_mt: Random State Initialization. - (line 13) -* gmp_randinit_set: Random State Initialization. - (line 43) -* gmp_randseed: Random State Seeding. - (line 7) -* gmp_randseed_ui: Random State Seeding. - (line 9) -* gmp_randstate_t: Nomenclature and Types. - (line 46) -* gmp_scanf: Formatted Input Functions. - (line 21) -* gmp_snprintf: Formatted Output Functions. - (line 46) -* gmp_sprintf: Formatted Output Functions. - (line 34) -* gmp_sscanf: Formatted Input Functions. - (line 29) -* gmp_urandomb_ui: Random State Miscellaneous. - (line 8) -* gmp_urandomm_ui: Random State Miscellaneous. - (line 14) -* gmp_vasprintf: Formatted Output Functions. - (line 66) -* gmp_version: Useful Macros and Constants. - (line 18) -* gmp_vfprintf: Formatted Output Functions. - (line 30) -* gmp_vfscanf: Formatted Input Functions. - (line 26) -* gmp_vprintf: Formatted Output Functions. - (line 25) -* gmp_vscanf: Formatted Input Functions. - (line 22) -* gmp_vsnprintf: Formatted Output Functions. - (line 48) -* gmp_vsprintf: Formatted Output Functions. - (line 35) -* gmp_vsscanf: Formatted Input Functions. - (line 31) -* hypot: C++ Interface Floats. - (line 81) -* itom: BSD Compatible Functions. - (line 29) -* madd: BSD Compatible Functions. - (line 43) -* mcmp: BSD Compatible Functions. - (line 85) -* mdiv: BSD Compatible Functions. - (line 53) -* mfree: BSD Compatible Functions. - (line 105) -* min: BSD Compatible Functions. - (line 89) -* MINT: BSD Compatible Functions. - (line 21) -* mout: BSD Compatible Functions. - (line 94) -* move: BSD Compatible Functions. - (line 39) -* mp_bitcnt_t: Nomenclature and Types. - (line 42) -* mp_bits_per_limb: Useful Macros and Constants. - (line 7) -* mp_exp_t: Nomenclature and Types. - (line 27) -* mp_get_memory_functions: Custom Allocation. (line 93) -* mp_limb_t: Nomenclature and Types. - (line 31) -* mp_set_memory_functions: Custom Allocation. (line 21) -* mp_size_t: Nomenclature and Types. - (line 37) -* mpf_abs: Float Arithmetic. (line 47) -* mpf_add: Float Arithmetic. (line 7) -* mpf_add_ui: Float Arithmetic. (line 9) -* mpf_ceil: Miscellaneous Float Functions. - (line 7) -* mpf_class: C++ Interface General. - (line 20) -* mpf_class::fits_sint_p: C++ Interface Floats. - (line 74) -* mpf_class::fits_slong_p: C++ Interface Floats. - (line 75) -* mpf_class::fits_sshort_p: C++ Interface Floats. - (line 76) -* mpf_class::fits_uint_p: C++ Interface Floats. - (line 77) -* mpf_class::fits_ulong_p: C++ Interface Floats. - (line 78) -* mpf_class::fits_ushort_p: C++ Interface Floats. - (line 79) -* mpf_class::get_d: C++ Interface Floats. - (line 82) -* mpf_class::get_mpf_t: C++ Interface General. - (line 66) -* mpf_class::get_prec: C++ Interface Floats. - (line 100) -* mpf_class::get_si: C++ Interface Floats. - (line 83) -* mpf_class::get_str: C++ Interface Floats. - (line 85) -* mpf_class::get_ui: C++ Interface Floats. - (line 86) -* mpf_class::mpf_class: C++ Interface Floats. - (line 38) -* mpf_class::operator=: C++ Interface Floats. - (line 47) -* mpf_class::set_prec: C++ Interface Floats. - (line 101) -* mpf_class::set_prec_raw: C++ Interface Floats. - (line 102) -* mpf_class::set_str: C++ Interface Floats. - (line 88) -* mpf_clear: Initializing Floats. (line 37) -* mpf_clears: Initializing Floats. (line 41) -* mpf_cmp: Float Comparison. (line 7) -* mpf_cmp_d: Float Comparison. (line 8) -* mpf_cmp_si: Float Comparison. (line 10) -* mpf_cmp_ui: Float Comparison. (line 9) -* mpf_div: Float Arithmetic. (line 29) -* mpf_div_2exp: Float Arithmetic. (line 53) -* mpf_div_ui: Float Arithmetic. (line 33) -* mpf_eq: Float Comparison. (line 17) -* mpf_fits_sint_p: Miscellaneous Float Functions. - (line 20) -* mpf_fits_slong_p: Miscellaneous Float Functions. - (line 18) -* mpf_fits_sshort_p: Miscellaneous Float Functions. - (line 22) -* mpf_fits_uint_p: Miscellaneous Float Functions. - (line 19) -* mpf_fits_ulong_p: Miscellaneous Float Functions. - (line 17) -* mpf_fits_ushort_p: Miscellaneous Float Functions. - (line 21) -* mpf_floor: Miscellaneous Float Functions. - (line 8) -* mpf_get_d: Converting Floats. (line 7) -* mpf_get_d_2exp: Converting Floats. (line 16) -* mpf_get_default_prec: Initializing Floats. (line 12) -* mpf_get_prec: Initializing Floats. (line 62) -* mpf_get_si: Converting Floats. (line 27) -* mpf_get_str: Converting Floats. (line 37) -* mpf_get_ui: Converting Floats. (line 28) -* mpf_init: Initializing Floats. (line 19) -* mpf_init2: Initializing Floats. (line 26) -* mpf_init_set: Simultaneous Float Init & Assign. - (line 16) -* mpf_init_set_d: Simultaneous Float Init & Assign. - (line 19) -* mpf_init_set_si: Simultaneous Float Init & Assign. - (line 18) -* mpf_init_set_str: Simultaneous Float Init & Assign. - (line 25) -* mpf_init_set_ui: Simultaneous Float Init & Assign. - (line 17) -* mpf_inits: Initializing Floats. (line 31) -* mpf_inp_str: I/O of Floats. (line 37) -* mpf_integer_p: Miscellaneous Float Functions. - (line 14) -* mpf_mul: Float Arithmetic. (line 19) -* mpf_mul_2exp: Float Arithmetic. (line 50) -* mpf_mul_ui: Float Arithmetic. (line 21) -* mpf_neg: Float Arithmetic. (line 44) -* mpf_out_str: I/O of Floats. (line 17) -* mpf_pow_ui: Float Arithmetic. (line 41) -* mpf_random2: Miscellaneous Float Functions. - (line 36) -* mpf_reldiff: Float Comparison. (line 29) -* mpf_set: Assigning Floats. (line 10) -* mpf_set_d: Assigning Floats. (line 13) -* mpf_set_default_prec: Initializing Floats. (line 7) -* mpf_set_prec: Initializing Floats. (line 65) -* mpf_set_prec_raw: Initializing Floats. (line 72) -* mpf_set_q: Assigning Floats. (line 15) -* mpf_set_si: Assigning Floats. (line 12) -* mpf_set_str: Assigning Floats. (line 18) -* mpf_set_ui: Assigning Floats. (line 11) -* mpf_set_z: Assigning Floats. (line 14) -* mpf_sgn: Float Comparison. (line 33) -* mpf_sqrt: Float Arithmetic. (line 36) -* mpf_sqrt_ui: Float Arithmetic. (line 37) -* mpf_sub: Float Arithmetic. (line 12) -* mpf_sub_ui: Float Arithmetic. (line 16) -* mpf_swap: Assigning Floats. (line 52) -* mpf_t: Nomenclature and Types. - (line 21) -* mpf_trunc: Miscellaneous Float Functions. - (line 9) -* mpf_ui_div: Float Arithmetic. (line 31) -* mpf_ui_sub: Float Arithmetic. (line 14) -* mpf_urandomb: Miscellaneous Float Functions. - (line 27) -* mpn_add: Low-level Functions. (line 69) -* mpn_add_1: Low-level Functions. (line 64) -* mpn_add_n: Low-level Functions. (line 54) -* mpn_addmul_1: Low-level Functions. (line 148) -* mpn_and_n: Low-level Functions. (line 420) -* mpn_andn_n: Low-level Functions. (line 435) -* mpn_cmp: Low-level Functions. (line 284) -* mpn_com: Low-level Functions. (line 460) -* mpn_copyd: Low-level Functions. (line 469) -* mpn_copyi: Low-level Functions. (line 465) -* mpn_divexact_by3: Low-level Functions. (line 229) -* mpn_divexact_by3c: Low-level Functions. (line 231) -* mpn_divmod: Low-level Functions. (line 224) -* mpn_divmod_1: Low-level Functions. (line 208) -* mpn_divrem: Low-level Functions. (line 182) -* mpn_divrem_1: Low-level Functions. (line 206) -* mpn_gcd: Low-level Functions. (line 289) -* mpn_gcd_1: Low-level Functions. (line 299) -* mpn_gcdext: Low-level Functions. (line 305) -* mpn_get_str: Low-level Functions. (line 346) -* mpn_hamdist: Low-level Functions. (line 410) -* mpn_ior_n: Low-level Functions. (line 425) -* mpn_iorn_n: Low-level Functions. (line 440) -* mpn_lshift: Low-level Functions. (line 260) -* mpn_mod_1: Low-level Functions. (line 255) -* mpn_mul: Low-level Functions. (line 114) -* mpn_mul_1: Low-level Functions. (line 133) -* mpn_mul_n: Low-level Functions. (line 103) -* mpn_nand_n: Low-level Functions. (line 445) -* mpn_neg: Low-level Functions. (line 98) -* mpn_nior_n: Low-level Functions. (line 450) -* mpn_perfect_square_p: Low-level Functions. (line 416) -* mpn_popcount: Low-level Functions. (line 406) -* mpn_random: Low-level Functions. (line 395) -* mpn_random2: Low-level Functions. (line 396) -* mpn_rshift: Low-level Functions. (line 272) -* mpn_scan0: Low-level Functions. (line 380) -* mpn_scan1: Low-level Functions. (line 388) -* mpn_set_str: Low-level Functions. (line 361) -* mpn_sqr: Low-level Functions. (line 125) -* mpn_sqrtrem: Low-level Functions. (line 328) -* mpn_sub: Low-level Functions. (line 90) -* mpn_sub_1: Low-level Functions. (line 85) -* mpn_sub_n: Low-level Functions. (line 76) -* mpn_submul_1: Low-level Functions. (line 159) -* mpn_tdiv_qr: Low-level Functions. (line 171) -* mpn_xnor_n: Low-level Functions. (line 455) -* mpn_xor_n: Low-level Functions. (line 430) -* mpn_zero: Low-level Functions. (line 472) -* mpq_abs: Rational Arithmetic. (line 31) -* mpq_add: Rational Arithmetic. (line 7) -* mpq_canonicalize: Rational Number Functions. - (line 22) -* mpq_class: C++ Interface General. - (line 19) -* mpq_class::canonicalize: C++ Interface Rationals. - (line 37) -* mpq_class::get_d: C++ Interface Rationals. - (line 46) -* mpq_class::get_den: C++ Interface Rationals. - (line 58) -* mpq_class::get_den_mpz_t: C++ Interface Rationals. - (line 68) -* mpq_class::get_mpq_t: C++ Interface General. - (line 65) -* mpq_class::get_num: C++ Interface Rationals. - (line 57) -* mpq_class::get_num_mpz_t: C++ Interface Rationals. - (line 67) -* mpq_class::get_str: C++ Interface Rationals. - (line 47) -* mpq_class::mpq_class: C++ Interface Rationals. - (line 22) -* mpq_class::set_str: C++ Interface Rationals. - (line 49) -* mpq_clear: Initializing Rationals. - (line 16) -* mpq_clears: Initializing Rationals. - (line 20) -* mpq_cmp: Comparing Rationals. (line 7) -* mpq_cmp_si: Comparing Rationals. (line 17) -* mpq_cmp_ui: Comparing Rationals. (line 15) -* mpq_denref: Applying Integer Functions. - (line 18) -* mpq_div: Rational Arithmetic. (line 22) -* mpq_div_2exp: Rational Arithmetic. (line 25) -* mpq_equal: Comparing Rationals. (line 33) -* mpq_get_d: Rational Conversions. - (line 7) -* mpq_get_den: Applying Integer Functions. - (line 24) -* mpq_get_num: Applying Integer Functions. - (line 23) -* mpq_get_str: Rational Conversions. - (line 22) -* mpq_init: Initializing Rationals. - (line 7) -* mpq_inits: Initializing Rationals. - (line 12) -* mpq_inp_str: I/O of Rationals. (line 23) -* mpq_inv: Rational Arithmetic. (line 34) -* mpq_mul: Rational Arithmetic. (line 15) -* mpq_mul_2exp: Rational Arithmetic. (line 18) -* mpq_neg: Rational Arithmetic. (line 28) -* mpq_numref: Applying Integer Functions. - (line 17) -* mpq_out_str: I/O of Rationals. (line 15) -* mpq_set: Initializing Rationals. - (line 24) -* mpq_set_d: Rational Conversions. - (line 17) -* mpq_set_den: Applying Integer Functions. - (line 26) -* mpq_set_f: Rational Conversions. - (line 18) -* mpq_set_num: Applying Integer Functions. - (line 25) -* mpq_set_si: Initializing Rationals. - (line 31) -* mpq_set_str: Initializing Rationals. - (line 36) -* mpq_set_ui: Initializing Rationals. - (line 29) -* mpq_set_z: Initializing Rationals. - (line 25) -* mpq_sgn: Comparing Rationals. (line 27) -* mpq_sub: Rational Arithmetic. (line 11) -* mpq_swap: Initializing Rationals. - (line 56) -* mpq_t: Nomenclature and Types. - (line 16) -* mpz_abs: Integer Arithmetic. (line 42) -* mpz_add: Integer Arithmetic. (line 7) -* mpz_add_ui: Integer Arithmetic. (line 9) -* mpz_addmul: Integer Arithmetic. (line 25) -* mpz_addmul_ui: Integer Arithmetic. (line 27) -* mpz_and: Integer Logic and Bit Fiddling. - (line 11) -* mpz_array_init: Integer Special Functions. - (line 11) -* mpz_bin_ui: Number Theoretic Functions. - (line 98) -* mpz_bin_uiui: Number Theoretic Functions. - (line 100) -* mpz_cdiv_q: Integer Division. (line 13) -* mpz_cdiv_q_2exp: Integer Division. (line 24) -* mpz_cdiv_q_ui: Integer Division. (line 17) -* mpz_cdiv_qr: Integer Division. (line 15) -* mpz_cdiv_qr_ui: Integer Division. (line 21) -* mpz_cdiv_r: Integer Division. (line 14) -* mpz_cdiv_r_2exp: Integer Division. (line 25) -* mpz_cdiv_r_ui: Integer Division. (line 19) -* mpz_cdiv_ui: Integer Division. (line 23) -* mpz_class: C++ Interface General. - (line 18) -* mpz_class::fits_sint_p: C++ Interface Integers. - (line 45) -* mpz_class::fits_slong_p: C++ Interface Integers. - (line 46) -* mpz_class::fits_sshort_p: C++ Interface Integers. - (line 47) -* mpz_class::fits_uint_p: C++ Interface Integers. - (line 48) -* mpz_class::fits_ulong_p: C++ Interface Integers. - (line 49) -* mpz_class::fits_ushort_p: C++ Interface Integers. - (line 50) -* mpz_class::get_d: C++ Interface Integers. - (line 51) -* mpz_class::get_mpz_t: C++ Interface General. - (line 64) -* mpz_class::get_si: C++ Interface Integers. - (line 52) -* mpz_class::get_str: C++ Interface Integers. - (line 53) -* mpz_class::get_ui: C++ Interface Integers. - (line 54) -* mpz_class::mpz_class: C++ Interface Integers. - (line 7) -* mpz_class::set_str: C++ Interface Integers. - (line 56) -* mpz_clear: Initializing Integers. - (line 44) -* mpz_clears: Initializing Integers. - (line 48) -* mpz_clrbit: Integer Logic and Bit Fiddling. - (line 54) -* mpz_cmp: Integer Comparisons. (line 7) -* mpz_cmp_d: Integer Comparisons. (line 8) -* mpz_cmp_si: Integer Comparisons. (line 9) -* mpz_cmp_ui: Integer Comparisons. (line 10) -* mpz_cmpabs: Integer Comparisons. (line 18) -* mpz_cmpabs_d: Integer Comparisons. (line 19) -* mpz_cmpabs_ui: Integer Comparisons. (line 20) -* mpz_com: Integer Logic and Bit Fiddling. - (line 20) -* mpz_combit: Integer Logic and Bit Fiddling. - (line 57) -* mpz_congruent_2exp_p: Integer Division. (line 124) -* mpz_congruent_p: Integer Division. (line 121) -* mpz_congruent_ui_p: Integer Division. (line 123) -* mpz_divexact: Integer Division. (line 101) -* mpz_divexact_ui: Integer Division. (line 102) -* mpz_divisible_2exp_p: Integer Division. (line 112) -* mpz_divisible_p: Integer Division. (line 110) -* mpz_divisible_ui_p: Integer Division. (line 111) -* mpz_even_p: Miscellaneous Integer Functions. - (line 18) -* mpz_export: Integer Import and Export. - (line 45) -* mpz_fac_ui: Number Theoretic Functions. - (line 95) -* mpz_fdiv_q: Integer Division. (line 27) -* mpz_fdiv_q_2exp: Integer Division. (line 38) -* mpz_fdiv_q_ui: Integer Division. (line 31) -* mpz_fdiv_qr: Integer Division. (line 29) -* mpz_fdiv_qr_ui: Integer Division. (line 35) -* mpz_fdiv_r: Integer Division. (line 28) -* mpz_fdiv_r_2exp: Integer Division. (line 39) -* mpz_fdiv_r_ui: Integer Division. (line 33) -* mpz_fdiv_ui: Integer Division. (line 37) -* mpz_fib2_ui: Number Theoretic Functions. - (line 108) -* mpz_fib_ui: Number Theoretic Functions. - (line 106) -* mpz_fits_sint_p: Miscellaneous Integer Functions. - (line 10) -* mpz_fits_slong_p: Miscellaneous Integer Functions. - (line 8) -* mpz_fits_sshort_p: Miscellaneous Integer Functions. - (line 12) -* mpz_fits_uint_p: Miscellaneous Integer Functions. - (line 9) -* mpz_fits_ulong_p: Miscellaneous Integer Functions. - (line 7) -* mpz_fits_ushort_p: Miscellaneous Integer Functions. - (line 11) -* mpz_gcd: Number Theoretic Functions. - (line 30) -* mpz_gcd_ui: Number Theoretic Functions. - (line 35) -* mpz_gcdext: Number Theoretic Functions. - (line 45) -* mpz_get_d: Converting Integers. (line 27) -* mpz_get_d_2exp: Converting Integers. (line 35) -* mpz_get_si: Converting Integers. (line 18) -* mpz_get_str: Converting Integers. (line 46) -* mpz_get_ui: Converting Integers. (line 11) -* mpz_getlimbn: Integer Special Functions. - (line 60) -* mpz_hamdist: Integer Logic and Bit Fiddling. - (line 29) -* mpz_import: Integer Import and Export. - (line 11) -* mpz_init: Initializing Integers. - (line 26) -* mpz_init2: Initializing Integers. - (line 33) -* mpz_init_set: Simultaneous Integer Init & Assign. - (line 27) -* mpz_init_set_d: Simultaneous Integer Init & Assign. - (line 30) -* mpz_init_set_si: Simultaneous Integer Init & Assign. - (line 29) -* mpz_init_set_str: Simultaneous Integer Init & Assign. - (line 34) -* mpz_init_set_ui: Simultaneous Integer Init & Assign. - (line 28) -* mpz_inits: Initializing Integers. - (line 29) -* mpz_inp_raw: I/O of Integers. (line 59) -* mpz_inp_str: I/O of Integers. (line 28) -* mpz_invert: Number Theoretic Functions. - (line 60) -* mpz_ior: Integer Logic and Bit Fiddling. - (line 14) -* mpz_jacobi: Number Theoretic Functions. - (line 66) -* mpz_kronecker: Number Theoretic Functions. - (line 74) -* mpz_kronecker_si: Number Theoretic Functions. - (line 75) -* mpz_kronecker_ui: Number Theoretic Functions. - (line 76) -* mpz_lcm: Number Theoretic Functions. - (line 54) -* mpz_lcm_ui: Number Theoretic Functions. - (line 55) -* mpz_legendre: Number Theoretic Functions. - (line 69) -* mpz_lucnum2_ui: Number Theoretic Functions. - (line 119) -* mpz_lucnum_ui: Number Theoretic Functions. - (line 117) -* mpz_mod: Integer Division. (line 91) -* mpz_mod_ui: Integer Division. (line 93) -* mpz_mul: Integer Arithmetic. (line 19) -* mpz_mul_2exp: Integer Arithmetic. (line 35) -* mpz_mul_si: Integer Arithmetic. (line 20) -* mpz_mul_ui: Integer Arithmetic. (line 22) -* mpz_neg: Integer Arithmetic. (line 39) -* mpz_nextprime: Number Theoretic Functions. - (line 23) -* mpz_odd_p: Miscellaneous Integer Functions. - (line 17) -* mpz_out_raw: I/O of Integers. (line 43) -* mpz_out_str: I/O of Integers. (line 16) -* mpz_perfect_power_p: Integer Roots. (line 27) -* mpz_perfect_square_p: Integer Roots. (line 36) -* mpz_popcount: Integer Logic and Bit Fiddling. - (line 23) -* mpz_pow_ui: Integer Exponentiation. - (line 31) -* mpz_powm: Integer Exponentiation. - (line 8) -* mpz_powm_sec: Integer Exponentiation. - (line 18) -* mpz_powm_ui: Integer Exponentiation. - (line 10) -* mpz_probab_prime_p: Number Theoretic Functions. - (line 7) -* mpz_random: Integer Random Numbers. - (line 42) -* mpz_random2: Integer Random Numbers. - (line 51) -* mpz_realloc2: Initializing Integers. - (line 52) -* mpz_remove: Number Theoretic Functions. - (line 90) -* mpz_root: Integer Roots. (line 7) -* mpz_rootrem: Integer Roots. (line 13) -* mpz_rrandomb: Integer Random Numbers. - (line 31) -* mpz_scan0: Integer Logic and Bit Fiddling. - (line 37) -* mpz_scan1: Integer Logic and Bit Fiddling. - (line 38) -* mpz_set: Assigning Integers. (line 10) -* mpz_set_d: Assigning Integers. (line 13) -* mpz_set_f: Assigning Integers. (line 15) -* mpz_set_q: Assigning Integers. (line 14) -* mpz_set_si: Assigning Integers. (line 12) -* mpz_set_str: Assigning Integers. (line 21) -* mpz_set_ui: Assigning Integers. (line 11) -* mpz_setbit: Integer Logic and Bit Fiddling. - (line 51) -* mpz_sgn: Integer Comparisons. (line 28) -* mpz_si_kronecker: Number Theoretic Functions. - (line 77) -* mpz_size: Integer Special Functions. - (line 68) -* mpz_sizeinbase: Miscellaneous Integer Functions. - (line 23) -* mpz_sqrt: Integer Roots. (line 17) -* mpz_sqrtrem: Integer Roots. (line 20) -* mpz_sub: Integer Arithmetic. (line 12) -* mpz_sub_ui: Integer Arithmetic. (line 14) -* mpz_submul: Integer Arithmetic. (line 30) -* mpz_submul_ui: Integer Arithmetic. (line 32) -* mpz_swap: Assigning Integers. (line 37) -* mpz_t: Nomenclature and Types. - (line 6) -* mpz_tdiv_q: Integer Division. (line 41) -* mpz_tdiv_q_2exp: Integer Division. (line 52) -* mpz_tdiv_q_ui: Integer Division. (line 45) -* mpz_tdiv_qr: Integer Division. (line 43) -* mpz_tdiv_qr_ui: Integer Division. (line 49) -* mpz_tdiv_r: Integer Division. (line 42) -* mpz_tdiv_r_2exp: Integer Division. (line 53) -* mpz_tdiv_r_ui: Integer Division. (line 47) -* mpz_tdiv_ui: Integer Division. (line 51) -* mpz_tstbit: Integer Logic and Bit Fiddling. - (line 60) -* mpz_ui_kronecker: Number Theoretic Functions. - (line 78) -* mpz_ui_pow_ui: Integer Exponentiation. - (line 33) -* mpz_ui_sub: Integer Arithmetic. (line 16) -* mpz_urandomb: Integer Random Numbers. - (line 14) -* mpz_urandomm: Integer Random Numbers. - (line 23) -* mpz_xor: Integer Logic and Bit Fiddling. - (line 17) -* msqrt: BSD Compatible Functions. - (line 63) -* msub: BSD Compatible Functions. - (line 46) -* mtox: BSD Compatible Functions. - (line 98) -* mult: BSD Compatible Functions. - (line 49) -* operator%: C++ Interface Integers. - (line 30) -* operator/: C++ Interface Integers. - (line 29) -* operator<<: C++ Formatted Output. - (line 20) -* operator>> <1>: C++ Formatted Input. (line 11) -* operator>>: C++ Interface Rationals. - (line 77) -* pow: BSD Compatible Functions. - (line 71) -* rpow: BSD Compatible Functions. - (line 79) -* sdiv: BSD Compatible Functions. - (line 55) -* sgn <1>: C++ Interface Rationals. - (line 50) -* sgn <2>: C++ Interface Integers. - (line 57) -* sgn: C++ Interface Floats. - (line 89) -* sqrt <1>: C++ Interface Integers. - (line 58) -* sqrt: C++ Interface Floats. - (line 90) -* trunc: C++ Interface Floats. - (line 91) -* xtom: BSD Compatible Functions. - (line 34) - - diff --git a/misc/tools/all/xonotic.subr b/misc/tools/all/xonotic.subr index 570305f8..08c570c3 100644 --- a/misc/tools/all/xonotic.subr +++ b/misc/tools/all/xonotic.subr @@ -197,23 +197,17 @@ case "$cmd" in case `uname -m` in x86_64) # No cp commands, we want to use static linking instead. - export CC="$CC -I../../../../misc/builddeps/linux64/d0_blind_id/include" - export CC="$CC -L../../../../misc/builddeps/linux64/d0_blind_id/lib" - export CC="$CC -Wl,-rpath,../../../../misc/builddeps/linux64/d0_blind_id/lib" - export CC="$CC -I../../../../misc/builddeps/linux64/gmp/include" - export CC="$CC -L../../../../misc/builddeps/linux64/gmp/lib" - export CC="$CC -Wl,-rpath,../../../../misc/builddeps/linux64/gmp/lib" - MAKEFLAGS="$MAKEFLAGS DP_LINK_CRYPTO=shared DP_LINK_CRYPTO_RIJNDAEL=shared LIB_CRYPTO=../../../../misc/builddeps/linux64/d0_blind_id/lib/libd0_blind_id.a LIB_CRYPTO+=../../../../misc/builddeps/linux64/gmp/lib/libgmp.a LIB_CRYPTO_RIJNDAEL=../../../../misc/builddeps/linux64/d0_blind_id/lib/libd0_rijndael.a" + MAKEFLAGS="$MAKEFLAGS DP_LINK_CRYPTO=shared DP_LINK_CRYPTO_RIJNDAEL=shared" + export CC="$CC -I../../../../" + export CC="$CC -L../../../../d0_blind_id/.libs" + export CC="$CC -Wl,-rpath,./d0_blind_id/.libs" ;; *86) # No cp commands, we want to use static linking instead. - export CC="$CC -I../../../../misc/builddeps/linux32/d0_blind_id/include" - export CC="$CC -L../../../../misc/builddeps/linux32/d0_blind_id/lib" - export CC="$CC -Wl,-rpath,../../../../misc/builddeps/linux32/d0_blind_id/lib" - export CC="$CC -I../../../../misc/builddeps/linux32/gmp/include" - export CC="$CC -L../../../../misc/builddeps/linux32/gmp/lib" - export CC="$CC -Wl,-rpath,../../../../misc/builddeps/linux32/gmp/lib" - MAKEFLAGS="$MAKEFLAGS DP_LINK_CRYPTO=shared DP_LINK_CRYPTO_RIJNDAEL=shared LIB_CRYPTO=../../../../misc/builddeps/linux32/d0_blind_id/lib/libd0_blind_id.a LIB_CRYPTO+=../../../../misc/builddeps/linux32/gmp/lib/libgmp.a LIB_CRYPTO_RIJNDAEL=../../../../misc/builddeps/linux32/d0_blind_id/lib/libd0_rijndael.a" + export CC="$CC -I../../../../" + export CC="$CC -L../../../../d0_blind_id/.libs" + export CC="$CC -Wl,-rpath,./d0_blind_id/.libs" + MAKEFLAGS="$MAKEFLAGS DP_LINK_CRYPTO=shared DP_LINK_CRYPTO_RIJNDAEL=shared" ;; *) compiled0=true