+++ /dev/null
-/*
- * 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 <unistd.h> // 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
+++ /dev/null
-/*
- * 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
+++ /dev/null
-// 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
+++ /dev/null
-# libd0_blind_id.la - a libtool library file
-# Generated by libtool (GNU libtool) 2.4.6 Debian-2.4.6-15
-#
-# 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 cannot go in dependency_libs.
-inherited_linker_flags=''
-
-# Libraries that this one depends upon.
-dependency_libs=' -L/home/rpolzer/Games/xonotic/misc/builddeps/linux64/gmp/lib /home/rpolzer/Games/xonotic/misc/builddeps/linux64/gmp/lib/libgmp.la'
-
-# Names of additional weak libraries provided by this library
-weak_library_names=''
-
-# Version information for libd0_blind_id.
-current=7
-age=7
-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='/home/rpolzer/Games/xonotic/misc/builddeps/linux64/d0_blind_id/lib'
+++ /dev/null
-# libd0_rijndael.la - a libtool library file
-# Generated by libtool (GNU libtool) 2.4.6 Debian-2.4.6-15
-#
-# 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 cannot go in dependency_libs.
-inherited_linker_flags=''
-
-# Libraries that this one depends upon.
-dependency_libs=' -L/home/rpolzer/Games/xonotic/misc/builddeps/linux64/gmp/lib /home/rpolzer/Games/xonotic/misc/builddeps/linux64/gmp/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='/home/rpolzer/Games/xonotic/misc/builddeps/linux64/d0_blind_id/lib'
+++ /dev/null
-prefix=/home/rpolzer/Games/xonotic/misc/builddeps/linux64/d0_blind_id
-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${includedir}/d0_blind_id
+++ /dev/null
-prefix=/home/rpolzer/Games/xonotic/misc/builddeps/linux64/d0_blind_id
-exec_prefix=${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
+++ /dev/null
-/* Definitions for GNU multiple precision functions. -*- mode: c -*-
-
-Copyright 1991, 1993-1997, 1999-2016, 2020 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 either:
-
- * 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.
-
-or
-
- * the GNU General Public License as published by the Free Software
- Foundation; either version 2 of the License, or (at your option) any
- later version.
-
-or both in parallel, as here.
-
-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 General Public License
-for more details.
-
-You should have received copies of the GNU General Public License and the
-GNU Lesser General Public License along with the GNU MP Library. If not,
-see https://www.gnu.org/licenses/. */
-
-#ifndef __GMP_H__
-
-#if defined (__cplusplus)
-#include <iosfwd> /* for std::istream, std::ostream, std::string */
-#include <cstdio>
-#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)
-
-
-#ifndef __GNU_MP__
-#define __GNU_MP__ 6
-
-#include <stddef.h> /* for size_t */
-#include <limits.h>
-
-/* Instantiated by configure. */
-#if ! defined (__GMP_WITHIN_CONFIGURE)
-/* #undef _LONG_LONG_LIMB */
-#define __GMP_LIBGMP_DLL 0
-#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.
-
- 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
-#ifdef __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 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 const __mpz_struct *mpz_srcptr;
-typedef __mpz_struct *mpz_ptr;
-typedef const __mpf_struct *mpf_srcptr;
-typedef __mpf_struct *mpf_ptr;
-typedef const __mpq_struct *mpq_srcptr;
-typedef __mpq_struct *mpq_ptr;
-
-
-#if __GMP_LIBGMP_DLL
-#ifdef __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
-
-
-#ifndef __MPN
-#define __MPN(x) __gmpn_##x
-#endif
-
-/* For reference, "defined(EOF)" cannot be used here. In g++ 2.95.4,
- <iostream> 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++ */ \
- || defined (__STDIO_LOADED) /* VMS */ \
- || defined (__DEFINED_FILE) /* musl */
-#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 <obstack.h> */
-#define _GMP_H_HAVE_OBSTACK 1
-#endif
-
-/* The prototypes for gmp_vprintf etc are provided only if va_list is defined,
- via an application having included <stdarg.h>. Usually va_list is a typedef
- so can't be tested directly, but C99 specifies that va_start is a macro.
-
- <stdio.h> 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 <stdarg.h> 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<type> (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)
-#if __cplusplus >= 201103L
-#define __GMP_NOTHROW noexcept
-#else
-#define __GMP_NOTHROW throw ()
-#endif
-#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) \
- || (defined __GNUC_GNU_INLINE__ && defined __cplusplus)
-#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))
-
-
-/* __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 an 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 (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 (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 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 const char * const gmp_version;
-
-
-/**************** Random number routines. ****************/
-
-/* obsolete */
-#define gmp_randinit __gmp_randinit
-__GMP_DECLSPEC void gmp_randinit (gmp_randstate_t, gmp_randalg_t, ...);
-
-#define gmp_randinit_default __gmp_randinit_default
-__GMP_DECLSPEC void gmp_randinit_default (gmp_randstate_t);
-
-#define gmp_randinit_lc_2exp __gmp_randinit_lc_2exp
-__GMP_DECLSPEC void gmp_randinit_lc_2exp (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_randstate_t, mp_bitcnt_t);
-
-#define gmp_randinit_mt __gmp_randinit_mt
-__GMP_DECLSPEC void gmp_randinit_mt (gmp_randstate_t);
-
-#define gmp_randinit_set __gmp_randinit_set
-__GMP_DECLSPEC void gmp_randinit_set (gmp_randstate_t, const __gmp_randstate_struct *);
-
-#define gmp_randseed __gmp_randseed
-__GMP_DECLSPEC void gmp_randseed (gmp_randstate_t, mpz_srcptr);
-
-#define gmp_randseed_ui __gmp_randseed_ui
-__GMP_DECLSPEC void gmp_randseed_ui (gmp_randstate_t, unsigned long int);
-
-#define gmp_randclear __gmp_randclear
-__GMP_DECLSPEC void gmp_randclear (gmp_randstate_t);
-
-#define gmp_urandomb_ui __gmp_urandomb_ui
-__GMP_DECLSPEC unsigned long gmp_urandomb_ui (gmp_randstate_t, unsigned long);
-
-#define gmp_urandomm_ui __gmp_urandomm_ui
-__GMP_DECLSPEC unsigned long gmp_urandomm_ui (gmp_randstate_t, unsigned long);
-
-
-/**************** Formatted output routines. ****************/
-
-#define gmp_asprintf __gmp_asprintf
-__GMP_DECLSPEC int gmp_asprintf (char **, const char *, ...);
-
-#define gmp_fprintf __gmp_fprintf
-#ifdef _GMP_H_HAVE_FILE
-__GMP_DECLSPEC int gmp_fprintf (FILE *, const char *, ...);
-#endif
-
-#define gmp_obstack_printf __gmp_obstack_printf
-#if defined (_GMP_H_HAVE_OBSTACK)
-__GMP_DECLSPEC int gmp_obstack_printf (struct obstack *, 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 (struct obstack *, const char *, va_list);
-#endif
-
-#define gmp_printf __gmp_printf
-__GMP_DECLSPEC int gmp_printf (const char *, ...);
-
-#define gmp_snprintf __gmp_snprintf
-__GMP_DECLSPEC int gmp_snprintf (char *, size_t, const char *, ...);
-
-#define gmp_sprintf __gmp_sprintf
-__GMP_DECLSPEC int gmp_sprintf (char *, const char *, ...);
-
-#define gmp_vasprintf __gmp_vasprintf
-#if defined (_GMP_H_HAVE_VA_LIST)
-__GMP_DECLSPEC int gmp_vasprintf (char **, 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 (FILE *, const char *, va_list);
-#endif
-
-#define gmp_vprintf __gmp_vprintf
-#if defined (_GMP_H_HAVE_VA_LIST)
-__GMP_DECLSPEC int gmp_vprintf (const char *, va_list);
-#endif
-
-#define gmp_vsnprintf __gmp_vsnprintf
-#if defined (_GMP_H_HAVE_VA_LIST)
-__GMP_DECLSPEC int gmp_vsnprintf (char *, size_t, const char *, va_list);
-#endif
-
-#define gmp_vsprintf __gmp_vsprintf
-#if defined (_GMP_H_HAVE_VA_LIST)
-__GMP_DECLSPEC int gmp_vsprintf (char *, const char *, va_list);
-#endif
-
-
-/**************** Formatted input routines. ****************/
-
-#define gmp_fscanf __gmp_fscanf
-#ifdef _GMP_H_HAVE_FILE
-__GMP_DECLSPEC int gmp_fscanf (FILE *, const char *, ...);
-#endif
-
-#define gmp_scanf __gmp_scanf
-__GMP_DECLSPEC int gmp_scanf (const char *, ...);
-
-#define gmp_sscanf __gmp_sscanf
-__GMP_DECLSPEC int gmp_sscanf (const char *, const char *, ...);
-
-#define gmp_vfscanf __gmp_vfscanf
-#if defined (_GMP_H_HAVE_FILE) && defined (_GMP_H_HAVE_VA_LIST)
-__GMP_DECLSPEC int gmp_vfscanf (FILE *, const char *, va_list);
-#endif
-
-#define gmp_vscanf __gmp_vscanf
-#if defined (_GMP_H_HAVE_VA_LIST)
-__GMP_DECLSPEC int gmp_vscanf (const char *, va_list);
-#endif
-
-#define gmp_vsscanf __gmp_vsscanf
-#if defined (_GMP_H_HAVE_VA_LIST)
-__GMP_DECLSPEC int gmp_vsscanf (const char *, 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 (mpz_ptr, mp_size_t);
-
-#define mpz_abs __gmpz_abs
-#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpz_abs)
-__GMP_DECLSPEC void mpz_abs (mpz_ptr, mpz_srcptr);
-#endif
-
-#define mpz_add __gmpz_add
-__GMP_DECLSPEC void mpz_add (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_add_ui __gmpz_add_ui
-__GMP_DECLSPEC void mpz_add_ui (mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_addmul __gmpz_addmul
-__GMP_DECLSPEC void mpz_addmul (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_addmul_ui __gmpz_addmul_ui
-__GMP_DECLSPEC void mpz_addmul_ui (mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_and __gmpz_and
-__GMP_DECLSPEC void mpz_and (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_array_init __gmpz_array_init
-__GMP_DECLSPEC void mpz_array_init (mpz_ptr, mp_size_t, mp_size_t);
-
-#define mpz_bin_ui __gmpz_bin_ui
-__GMP_DECLSPEC void mpz_bin_ui (mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_bin_uiui __gmpz_bin_uiui
-__GMP_DECLSPEC void mpz_bin_uiui (mpz_ptr, unsigned long int, unsigned long int);
-
-#define mpz_cdiv_q __gmpz_cdiv_q
-__GMP_DECLSPEC void mpz_cdiv_q (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_cdiv_q_2exp __gmpz_cdiv_q_2exp
-__GMP_DECLSPEC void mpz_cdiv_q_2exp (mpz_ptr, mpz_srcptr, mp_bitcnt_t);
-
-#define mpz_cdiv_q_ui __gmpz_cdiv_q_ui
-__GMP_DECLSPEC unsigned long int mpz_cdiv_q_ui (mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_cdiv_qr __gmpz_cdiv_qr
-__GMP_DECLSPEC void mpz_cdiv_qr (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 (mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_cdiv_r __gmpz_cdiv_r
-__GMP_DECLSPEC void mpz_cdiv_r (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_cdiv_r_2exp __gmpz_cdiv_r_2exp
-__GMP_DECLSPEC void mpz_cdiv_r_2exp (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 (mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_cdiv_ui __gmpz_cdiv_ui
-__GMP_DECLSPEC unsigned long int mpz_cdiv_ui (mpz_srcptr, unsigned long int) __GMP_ATTRIBUTE_PURE;
-
-#define mpz_clear __gmpz_clear
-__GMP_DECLSPEC void mpz_clear (mpz_ptr);
-
-#define mpz_clears __gmpz_clears
-__GMP_DECLSPEC void mpz_clears (mpz_ptr, ...);
-
-#define mpz_clrbit __gmpz_clrbit
-__GMP_DECLSPEC void mpz_clrbit (mpz_ptr, mp_bitcnt_t);
-
-#define mpz_cmp __gmpz_cmp
-__GMP_DECLSPEC int mpz_cmp (mpz_srcptr, mpz_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpz_cmp_d __gmpz_cmp_d
-__GMP_DECLSPEC int mpz_cmp_d (mpz_srcptr, double) __GMP_ATTRIBUTE_PURE;
-
-#define _mpz_cmp_si __gmpz_cmp_si
-__GMP_DECLSPEC int _mpz_cmp_si (mpz_srcptr, signed long int) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define _mpz_cmp_ui __gmpz_cmp_ui
-__GMP_DECLSPEC int _mpz_cmp_ui (mpz_srcptr, unsigned long int) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpz_cmpabs __gmpz_cmpabs
-__GMP_DECLSPEC int mpz_cmpabs (mpz_srcptr, mpz_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpz_cmpabs_d __gmpz_cmpabs_d
-__GMP_DECLSPEC int mpz_cmpabs_d (mpz_srcptr, double) __GMP_ATTRIBUTE_PURE;
-
-#define mpz_cmpabs_ui __gmpz_cmpabs_ui
-__GMP_DECLSPEC int mpz_cmpabs_ui (mpz_srcptr, unsigned long int) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpz_com __gmpz_com
-__GMP_DECLSPEC void mpz_com (mpz_ptr, mpz_srcptr);
-
-#define mpz_combit __gmpz_combit
-__GMP_DECLSPEC void mpz_combit (mpz_ptr, mp_bitcnt_t);
-
-#define mpz_congruent_p __gmpz_congruent_p
-__GMP_DECLSPEC int mpz_congruent_p (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 (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 (mpz_srcptr, unsigned long, unsigned long) __GMP_ATTRIBUTE_PURE;
-
-#define mpz_divexact __gmpz_divexact
-__GMP_DECLSPEC void mpz_divexact (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_divexact_ui __gmpz_divexact_ui
-__GMP_DECLSPEC void mpz_divexact_ui (mpz_ptr, mpz_srcptr, unsigned long);
-
-#define mpz_divisible_p __gmpz_divisible_p
-__GMP_DECLSPEC int mpz_divisible_p (mpz_srcptr, mpz_srcptr) __GMP_ATTRIBUTE_PURE;
-
-#define mpz_divisible_ui_p __gmpz_divisible_ui_p
-__GMP_DECLSPEC int mpz_divisible_ui_p (mpz_srcptr, unsigned long) __GMP_ATTRIBUTE_PURE;
-
-#define mpz_divisible_2exp_p __gmpz_divisible_2exp_p
-__GMP_DECLSPEC int mpz_divisible_2exp_p (mpz_srcptr, mp_bitcnt_t) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpz_dump __gmpz_dump
-__GMP_DECLSPEC void mpz_dump (mpz_srcptr);
-
-#define mpz_export __gmpz_export
-__GMP_DECLSPEC void *mpz_export (void *, size_t *, int, size_t, int, size_t, mpz_srcptr);
-
-#define mpz_fac_ui __gmpz_fac_ui
-__GMP_DECLSPEC void mpz_fac_ui (mpz_ptr, unsigned long int);
-
-#define mpz_2fac_ui __gmpz_2fac_ui
-__GMP_DECLSPEC void mpz_2fac_ui (mpz_ptr, unsigned long int);
-
-#define mpz_mfac_uiui __gmpz_mfac_uiui
-__GMP_DECLSPEC void mpz_mfac_uiui (mpz_ptr, unsigned long int, unsigned long int);
-
-#define mpz_primorial_ui __gmpz_primorial_ui
-__GMP_DECLSPEC void mpz_primorial_ui (mpz_ptr, unsigned long int);
-
-#define mpz_fdiv_q __gmpz_fdiv_q
-__GMP_DECLSPEC void mpz_fdiv_q (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_fdiv_q_2exp __gmpz_fdiv_q_2exp
-__GMP_DECLSPEC void mpz_fdiv_q_2exp (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 (mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_fdiv_qr __gmpz_fdiv_qr
-__GMP_DECLSPEC void mpz_fdiv_qr (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 (mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_fdiv_r __gmpz_fdiv_r
-__GMP_DECLSPEC void mpz_fdiv_r (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_fdiv_r_2exp __gmpz_fdiv_r_2exp
-__GMP_DECLSPEC void mpz_fdiv_r_2exp (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 (mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_fdiv_ui __gmpz_fdiv_ui
-__GMP_DECLSPEC unsigned long int mpz_fdiv_ui (mpz_srcptr, unsigned long int) __GMP_ATTRIBUTE_PURE;
-
-#define mpz_fib_ui __gmpz_fib_ui
-__GMP_DECLSPEC void mpz_fib_ui (mpz_ptr, unsigned long int);
-
-#define mpz_fib2_ui __gmpz_fib2_ui
-__GMP_DECLSPEC void mpz_fib2_ui (mpz_ptr, mpz_ptr, unsigned long int);
-
-#define mpz_fits_sint_p __gmpz_fits_sint_p
-__GMP_DECLSPEC int mpz_fits_sint_p (mpz_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpz_fits_slong_p __gmpz_fits_slong_p
-__GMP_DECLSPEC int mpz_fits_slong_p (mpz_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpz_fits_sshort_p __gmpz_fits_sshort_p
-__GMP_DECLSPEC int mpz_fits_sshort_p (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 (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 (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 (mpz_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-#endif
-
-#define mpz_gcd __gmpz_gcd
-__GMP_DECLSPEC void mpz_gcd (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_gcd_ui __gmpz_gcd_ui
-__GMP_DECLSPEC unsigned long int mpz_gcd_ui (mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_gcdext __gmpz_gcdext
-__GMP_DECLSPEC void mpz_gcdext (mpz_ptr, mpz_ptr, mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_get_d __gmpz_get_d
-__GMP_DECLSPEC double mpz_get_d (mpz_srcptr) __GMP_ATTRIBUTE_PURE;
-
-#define mpz_get_d_2exp __gmpz_get_d_2exp
-__GMP_DECLSPEC double mpz_get_d_2exp (signed long int *, mpz_srcptr);
-
-#define mpz_get_si __gmpz_get_si
-__GMP_DECLSPEC /* signed */ long int mpz_get_si (mpz_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpz_get_str __gmpz_get_str
-__GMP_DECLSPEC char *mpz_get_str (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 (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 (mpz_srcptr, mp_size_t) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-#endif
-
-#define mpz_hamdist __gmpz_hamdist
-__GMP_DECLSPEC mp_bitcnt_t mpz_hamdist (mpz_srcptr, mpz_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpz_import __gmpz_import
-__GMP_DECLSPEC void mpz_import (mpz_ptr, size_t, int, size_t, int, size_t, const void *);
-
-#define mpz_init __gmpz_init
-__GMP_DECLSPEC void mpz_init (mpz_ptr) __GMP_NOTHROW;
-
-#define mpz_init2 __gmpz_init2
-__GMP_DECLSPEC void mpz_init2 (mpz_ptr, mp_bitcnt_t);
-
-#define mpz_inits __gmpz_inits
-__GMP_DECLSPEC void mpz_inits (mpz_ptr, ...) __GMP_NOTHROW;
-
-#define mpz_init_set __gmpz_init_set
-__GMP_DECLSPEC void mpz_init_set (mpz_ptr, mpz_srcptr);
-
-#define mpz_init_set_d __gmpz_init_set_d
-__GMP_DECLSPEC void mpz_init_set_d (mpz_ptr, double);
-
-#define mpz_init_set_si __gmpz_init_set_si
-__GMP_DECLSPEC void mpz_init_set_si (mpz_ptr, signed long int);
-
-#define mpz_init_set_str __gmpz_init_set_str
-__GMP_DECLSPEC int mpz_init_set_str (mpz_ptr, const char *, int);
-
-#define mpz_init_set_ui __gmpz_init_set_ui
-__GMP_DECLSPEC void mpz_init_set_ui (mpz_ptr, unsigned long int);
-
-#define mpz_inp_raw __gmpz_inp_raw
-#ifdef _GMP_H_HAVE_FILE
-__GMP_DECLSPEC size_t mpz_inp_raw (mpz_ptr, FILE *);
-#endif
-
-#define mpz_inp_str __gmpz_inp_str
-#ifdef _GMP_H_HAVE_FILE
-__GMP_DECLSPEC size_t mpz_inp_str (mpz_ptr, FILE *, int);
-#endif
-
-#define mpz_invert __gmpz_invert
-__GMP_DECLSPEC int mpz_invert (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_ior __gmpz_ior
-__GMP_DECLSPEC void mpz_ior (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_jacobi __gmpz_jacobi
-__GMP_DECLSPEC int mpz_jacobi (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 (mpz_srcptr, long) __GMP_ATTRIBUTE_PURE;
-
-#define mpz_kronecker_ui __gmpz_kronecker_ui
-__GMP_DECLSPEC int mpz_kronecker_ui (mpz_srcptr, unsigned long) __GMP_ATTRIBUTE_PURE;
-
-#define mpz_si_kronecker __gmpz_si_kronecker
-__GMP_DECLSPEC int mpz_si_kronecker (long, mpz_srcptr) __GMP_ATTRIBUTE_PURE;
-
-#define mpz_ui_kronecker __gmpz_ui_kronecker
-__GMP_DECLSPEC int mpz_ui_kronecker (unsigned long, mpz_srcptr) __GMP_ATTRIBUTE_PURE;
-
-#define mpz_lcm __gmpz_lcm
-__GMP_DECLSPEC void mpz_lcm (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_lcm_ui __gmpz_lcm_ui
-__GMP_DECLSPEC void mpz_lcm_ui (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 (mpz_ptr, unsigned long int);
-
-#define mpz_lucnum2_ui __gmpz_lucnum2_ui
-__GMP_DECLSPEC void mpz_lucnum2_ui (mpz_ptr, mpz_ptr, unsigned long int);
-
-#define mpz_millerrabin __gmpz_millerrabin
-__GMP_DECLSPEC int mpz_millerrabin (mpz_srcptr, int) __GMP_ATTRIBUTE_PURE;
-
-#define mpz_mod __gmpz_mod
-__GMP_DECLSPEC void mpz_mod (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 (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_mul_2exp __gmpz_mul_2exp
-__GMP_DECLSPEC void mpz_mul_2exp (mpz_ptr, mpz_srcptr, mp_bitcnt_t);
-
-#define mpz_mul_si __gmpz_mul_si
-__GMP_DECLSPEC void mpz_mul_si (mpz_ptr, mpz_srcptr, long int);
-
-#define mpz_mul_ui __gmpz_mul_ui
-__GMP_DECLSPEC void mpz_mul_ui (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 (mpz_ptr, mpz_srcptr);
-#endif
-
-#define mpz_nextprime __gmpz_nextprime
-__GMP_DECLSPEC void mpz_nextprime (mpz_ptr, mpz_srcptr);
-
-#define mpz_out_raw __gmpz_out_raw
-#ifdef _GMP_H_HAVE_FILE
-__GMP_DECLSPEC size_t mpz_out_raw (FILE *, mpz_srcptr);
-#endif
-
-#define mpz_out_str __gmpz_out_str
-#ifdef _GMP_H_HAVE_FILE
-__GMP_DECLSPEC size_t mpz_out_str (FILE *, int, mpz_srcptr);
-#endif
-
-#define mpz_perfect_power_p __gmpz_perfect_power_p
-__GMP_DECLSPEC int mpz_perfect_power_p (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 (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 (mpz_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-#endif
-
-#define mpz_pow_ui __gmpz_pow_ui
-__GMP_DECLSPEC void mpz_pow_ui (mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_powm __gmpz_powm
-__GMP_DECLSPEC void mpz_powm (mpz_ptr, mpz_srcptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_powm_sec __gmpz_powm_sec
-__GMP_DECLSPEC void mpz_powm_sec (mpz_ptr, mpz_srcptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_powm_ui __gmpz_powm_ui
-__GMP_DECLSPEC void mpz_powm_ui (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 (mpz_srcptr, int) __GMP_ATTRIBUTE_PURE;
-
-#define mpz_random __gmpz_random
-__GMP_DECLSPEC void mpz_random (mpz_ptr, mp_size_t);
-
-#define mpz_random2 __gmpz_random2
-__GMP_DECLSPEC void mpz_random2 (mpz_ptr, mp_size_t);
-
-#define mpz_realloc2 __gmpz_realloc2
-__GMP_DECLSPEC void mpz_realloc2 (mpz_ptr, mp_bitcnt_t);
-
-#define mpz_remove __gmpz_remove
-__GMP_DECLSPEC mp_bitcnt_t mpz_remove (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_root __gmpz_root
-__GMP_DECLSPEC int mpz_root (mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_rootrem __gmpz_rootrem
-__GMP_DECLSPEC void mpz_rootrem (mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_rrandomb __gmpz_rrandomb
-__GMP_DECLSPEC void mpz_rrandomb (mpz_ptr, gmp_randstate_t, mp_bitcnt_t);
-
-#define mpz_scan0 __gmpz_scan0
-__GMP_DECLSPEC mp_bitcnt_t mpz_scan0 (mpz_srcptr, mp_bitcnt_t) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpz_scan1 __gmpz_scan1
-__GMP_DECLSPEC mp_bitcnt_t mpz_scan1 (mpz_srcptr, mp_bitcnt_t) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpz_set __gmpz_set
-__GMP_DECLSPEC void mpz_set (mpz_ptr, mpz_srcptr);
-
-#define mpz_set_d __gmpz_set_d
-__GMP_DECLSPEC void mpz_set_d (mpz_ptr, double);
-
-#define mpz_set_f __gmpz_set_f
-__GMP_DECLSPEC void mpz_set_f (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 (mpz_ptr, mpq_srcptr);
-#endif
-
-#define mpz_set_si __gmpz_set_si
-__GMP_DECLSPEC void mpz_set_si (mpz_ptr, signed long int);
-
-#define mpz_set_str __gmpz_set_str
-__GMP_DECLSPEC int mpz_set_str (mpz_ptr, const char *, int);
-
-#define mpz_set_ui __gmpz_set_ui
-__GMP_DECLSPEC void mpz_set_ui (mpz_ptr, unsigned long int);
-
-#define mpz_setbit __gmpz_setbit
-__GMP_DECLSPEC void mpz_setbit (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 (mpz_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-#endif
-
-#define mpz_sizeinbase __gmpz_sizeinbase
-__GMP_DECLSPEC size_t mpz_sizeinbase (mpz_srcptr, int) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpz_sqrt __gmpz_sqrt
-__GMP_DECLSPEC void mpz_sqrt (mpz_ptr, mpz_srcptr);
-
-#define mpz_sqrtrem __gmpz_sqrtrem
-__GMP_DECLSPEC void mpz_sqrtrem (mpz_ptr, mpz_ptr, mpz_srcptr);
-
-#define mpz_sub __gmpz_sub
-__GMP_DECLSPEC void mpz_sub (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_sub_ui __gmpz_sub_ui
-__GMP_DECLSPEC void mpz_sub_ui (mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_ui_sub __gmpz_ui_sub
-__GMP_DECLSPEC void mpz_ui_sub (mpz_ptr, unsigned long int, mpz_srcptr);
-
-#define mpz_submul __gmpz_submul
-__GMP_DECLSPEC void mpz_submul (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_submul_ui __gmpz_submul_ui
-__GMP_DECLSPEC void mpz_submul_ui (mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_swap __gmpz_swap
-__GMP_DECLSPEC void mpz_swap (mpz_ptr, mpz_ptr) __GMP_NOTHROW;
-
-#define mpz_tdiv_ui __gmpz_tdiv_ui
-__GMP_DECLSPEC unsigned long int mpz_tdiv_ui (mpz_srcptr, unsigned long int) __GMP_ATTRIBUTE_PURE;
-
-#define mpz_tdiv_q __gmpz_tdiv_q
-__GMP_DECLSPEC void mpz_tdiv_q (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_tdiv_q_2exp __gmpz_tdiv_q_2exp
-__GMP_DECLSPEC void mpz_tdiv_q_2exp (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 (mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_tdiv_qr __gmpz_tdiv_qr
-__GMP_DECLSPEC void mpz_tdiv_qr (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 (mpz_ptr, mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_tdiv_r __gmpz_tdiv_r
-__GMP_DECLSPEC void mpz_tdiv_r (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_tdiv_r_2exp __gmpz_tdiv_r_2exp
-__GMP_DECLSPEC void mpz_tdiv_r_2exp (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 (mpz_ptr, mpz_srcptr, unsigned long int);
-
-#define mpz_tstbit __gmpz_tstbit
-__GMP_DECLSPEC int mpz_tstbit (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 (mpz_ptr, unsigned long int, unsigned long int);
-
-#define mpz_urandomb __gmpz_urandomb
-__GMP_DECLSPEC void mpz_urandomb (mpz_ptr, gmp_randstate_t, mp_bitcnt_t);
-
-#define mpz_urandomm __gmpz_urandomm
-__GMP_DECLSPEC void mpz_urandomm (mpz_ptr, gmp_randstate_t, mpz_srcptr);
-
-#define mpz_xor __gmpz_xor
-#define mpz_eor __gmpz_xor
-__GMP_DECLSPEC void mpz_xor (mpz_ptr, mpz_srcptr, mpz_srcptr);
-
-#define mpz_limbs_read __gmpz_limbs_read
-__GMP_DECLSPEC mp_srcptr mpz_limbs_read (mpz_srcptr);
-
-#define mpz_limbs_write __gmpz_limbs_write
-__GMP_DECLSPEC mp_ptr mpz_limbs_write (mpz_ptr, mp_size_t);
-
-#define mpz_limbs_modify __gmpz_limbs_modify
-__GMP_DECLSPEC mp_ptr mpz_limbs_modify (mpz_ptr, mp_size_t);
-
-#define mpz_limbs_finish __gmpz_limbs_finish
-__GMP_DECLSPEC void mpz_limbs_finish (mpz_ptr, mp_size_t);
-
-#define mpz_roinit_n __gmpz_roinit_n
-__GMP_DECLSPEC mpz_srcptr mpz_roinit_n (mpz_ptr, mp_srcptr, mp_size_t);
-
-#define MPZ_ROINIT_N(xp, xs) {{0, (xs),(xp) }}
-
-/**************** Rational (i.e. Q) routines. ****************/
-
-#define mpq_abs __gmpq_abs
-#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpq_abs)
-__GMP_DECLSPEC void mpq_abs (mpq_ptr, mpq_srcptr);
-#endif
-
-#define mpq_add __gmpq_add
-__GMP_DECLSPEC void mpq_add (mpq_ptr, mpq_srcptr, mpq_srcptr);
-
-#define mpq_canonicalize __gmpq_canonicalize
-__GMP_DECLSPEC void mpq_canonicalize (mpq_ptr);
-
-#define mpq_clear __gmpq_clear
-__GMP_DECLSPEC void mpq_clear (mpq_ptr);
-
-#define mpq_clears __gmpq_clears
-__GMP_DECLSPEC void mpq_clears (mpq_ptr, ...);
-
-#define mpq_cmp __gmpq_cmp
-__GMP_DECLSPEC int mpq_cmp (mpq_srcptr, mpq_srcptr) __GMP_ATTRIBUTE_PURE;
-
-#define _mpq_cmp_si __gmpq_cmp_si
-__GMP_DECLSPEC int _mpq_cmp_si (mpq_srcptr, long, unsigned long) __GMP_ATTRIBUTE_PURE;
-
-#define _mpq_cmp_ui __gmpq_cmp_ui
-__GMP_DECLSPEC int _mpq_cmp_ui (mpq_srcptr, unsigned long int, unsigned long int) __GMP_ATTRIBUTE_PURE;
-
-#define mpq_cmp_z __gmpq_cmp_z
-__GMP_DECLSPEC int mpq_cmp_z (mpq_srcptr, mpz_srcptr) __GMP_ATTRIBUTE_PURE;
-
-#define mpq_div __gmpq_div
-__GMP_DECLSPEC void mpq_div (mpq_ptr, mpq_srcptr, mpq_srcptr);
-
-#define mpq_div_2exp __gmpq_div_2exp
-__GMP_DECLSPEC void mpq_div_2exp (mpq_ptr, mpq_srcptr, mp_bitcnt_t);
-
-#define mpq_equal __gmpq_equal
-__GMP_DECLSPEC int mpq_equal (mpq_srcptr, mpq_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpq_get_num __gmpq_get_num
-__GMP_DECLSPEC void mpq_get_num (mpz_ptr, mpq_srcptr);
-
-#define mpq_get_den __gmpq_get_den
-__GMP_DECLSPEC void mpq_get_den (mpz_ptr, mpq_srcptr);
-
-#define mpq_get_d __gmpq_get_d
-__GMP_DECLSPEC double mpq_get_d (mpq_srcptr) __GMP_ATTRIBUTE_PURE;
-
-#define mpq_get_str __gmpq_get_str
-__GMP_DECLSPEC char *mpq_get_str (char *, int, mpq_srcptr);
-
-#define mpq_init __gmpq_init
-__GMP_DECLSPEC void mpq_init (mpq_ptr);
-
-#define mpq_inits __gmpq_inits
-__GMP_DECLSPEC void mpq_inits (mpq_ptr, ...);
-
-#define mpq_inp_str __gmpq_inp_str
-#ifdef _GMP_H_HAVE_FILE
-__GMP_DECLSPEC size_t mpq_inp_str (mpq_ptr, FILE *, int);
-#endif
-
-#define mpq_inv __gmpq_inv
-__GMP_DECLSPEC void mpq_inv (mpq_ptr, mpq_srcptr);
-
-#define mpq_mul __gmpq_mul
-__GMP_DECLSPEC void mpq_mul (mpq_ptr, mpq_srcptr, mpq_srcptr);
-
-#define mpq_mul_2exp __gmpq_mul_2exp
-__GMP_DECLSPEC void mpq_mul_2exp (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 (mpq_ptr, mpq_srcptr);
-#endif
-
-#define mpq_out_str __gmpq_out_str
-#ifdef _GMP_H_HAVE_FILE
-__GMP_DECLSPEC size_t mpq_out_str (FILE *, int, mpq_srcptr);
-#endif
-
-#define mpq_set __gmpq_set
-__GMP_DECLSPEC void mpq_set (mpq_ptr, mpq_srcptr);
-
-#define mpq_set_d __gmpq_set_d
-__GMP_DECLSPEC void mpq_set_d (mpq_ptr, double);
-
-#define mpq_set_den __gmpq_set_den
-__GMP_DECLSPEC void mpq_set_den (mpq_ptr, mpz_srcptr);
-
-#define mpq_set_f __gmpq_set_f
-__GMP_DECLSPEC void mpq_set_f (mpq_ptr, mpf_srcptr);
-
-#define mpq_set_num __gmpq_set_num
-__GMP_DECLSPEC void mpq_set_num (mpq_ptr, mpz_srcptr);
-
-#define mpq_set_si __gmpq_set_si
-__GMP_DECLSPEC void mpq_set_si (mpq_ptr, signed long int, unsigned long int);
-
-#define mpq_set_str __gmpq_set_str
-__GMP_DECLSPEC int mpq_set_str (mpq_ptr, const char *, int);
-
-#define mpq_set_ui __gmpq_set_ui
-__GMP_DECLSPEC void mpq_set_ui (mpq_ptr, unsigned long int, unsigned long int);
-
-#define mpq_set_z __gmpq_set_z
-__GMP_DECLSPEC void mpq_set_z (mpq_ptr, mpz_srcptr);
-
-#define mpq_sub __gmpq_sub
-__GMP_DECLSPEC void mpq_sub (mpq_ptr, mpq_srcptr, mpq_srcptr);
-
-#define mpq_swap __gmpq_swap
-__GMP_DECLSPEC void mpq_swap (mpq_ptr, mpq_ptr) __GMP_NOTHROW;
-
-
-/**************** Float (i.e. F) routines. ****************/
-
-#define mpf_abs __gmpf_abs
-__GMP_DECLSPEC void mpf_abs (mpf_ptr, mpf_srcptr);
-
-#define mpf_add __gmpf_add
-__GMP_DECLSPEC void mpf_add (mpf_ptr, mpf_srcptr, mpf_srcptr);
-
-#define mpf_add_ui __gmpf_add_ui
-__GMP_DECLSPEC void mpf_add_ui (mpf_ptr, mpf_srcptr, unsigned long int);
-#define mpf_ceil __gmpf_ceil
-__GMP_DECLSPEC void mpf_ceil (mpf_ptr, mpf_srcptr);
-
-#define mpf_clear __gmpf_clear
-__GMP_DECLSPEC void mpf_clear (mpf_ptr);
-
-#define mpf_clears __gmpf_clears
-__GMP_DECLSPEC void mpf_clears (mpf_ptr, ...);
-
-#define mpf_cmp __gmpf_cmp
-__GMP_DECLSPEC int mpf_cmp (mpf_srcptr, mpf_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_cmp_z __gmpf_cmp_z
-__GMP_DECLSPEC int mpf_cmp_z (mpf_srcptr, mpz_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_cmp_d __gmpf_cmp_d
-__GMP_DECLSPEC int mpf_cmp_d (mpf_srcptr, double) __GMP_ATTRIBUTE_PURE;
-
-#define mpf_cmp_si __gmpf_cmp_si
-__GMP_DECLSPEC int mpf_cmp_si (mpf_srcptr, signed long int) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_cmp_ui __gmpf_cmp_ui
-__GMP_DECLSPEC int mpf_cmp_ui (mpf_srcptr, unsigned long int) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_div __gmpf_div
-__GMP_DECLSPEC void mpf_div (mpf_ptr, mpf_srcptr, mpf_srcptr);
-
-#define mpf_div_2exp __gmpf_div_2exp
-__GMP_DECLSPEC void mpf_div_2exp (mpf_ptr, mpf_srcptr, mp_bitcnt_t);
-
-#define mpf_div_ui __gmpf_div_ui
-__GMP_DECLSPEC void mpf_div_ui (mpf_ptr, mpf_srcptr, unsigned long int);
-
-#define mpf_dump __gmpf_dump
-__GMP_DECLSPEC void mpf_dump (mpf_srcptr);
-
-#define mpf_eq __gmpf_eq
-__GMP_DECLSPEC int mpf_eq (mpf_srcptr, mpf_srcptr, mp_bitcnt_t) __GMP_ATTRIBUTE_PURE;
-
-#define mpf_fits_sint_p __gmpf_fits_sint_p
-__GMP_DECLSPEC int mpf_fits_sint_p (mpf_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_fits_slong_p __gmpf_fits_slong_p
-__GMP_DECLSPEC int mpf_fits_slong_p (mpf_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_fits_sshort_p __gmpf_fits_sshort_p
-__GMP_DECLSPEC int mpf_fits_sshort_p (mpf_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_fits_uint_p __gmpf_fits_uint_p
-__GMP_DECLSPEC int mpf_fits_uint_p (mpf_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_fits_ulong_p __gmpf_fits_ulong_p
-__GMP_DECLSPEC int mpf_fits_ulong_p (mpf_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_fits_ushort_p __gmpf_fits_ushort_p
-__GMP_DECLSPEC int mpf_fits_ushort_p (mpf_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_floor __gmpf_floor
-__GMP_DECLSPEC void mpf_floor (mpf_ptr, mpf_srcptr);
-
-#define mpf_get_d __gmpf_get_d
-__GMP_DECLSPEC double mpf_get_d (mpf_srcptr) __GMP_ATTRIBUTE_PURE;
-
-#define mpf_get_d_2exp __gmpf_get_d_2exp
-__GMP_DECLSPEC double mpf_get_d_2exp (signed long int *, mpf_srcptr);
-
-#define mpf_get_default_prec __gmpf_get_default_prec
-__GMP_DECLSPEC mp_bitcnt_t mpf_get_default_prec (void) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_get_prec __gmpf_get_prec
-__GMP_DECLSPEC mp_bitcnt_t mpf_get_prec (mpf_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_get_si __gmpf_get_si
-__GMP_DECLSPEC long mpf_get_si (mpf_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_get_str __gmpf_get_str
-__GMP_DECLSPEC char *mpf_get_str (char *, mp_exp_t *, int, size_t, mpf_srcptr);
-
-#define mpf_get_ui __gmpf_get_ui
-__GMP_DECLSPEC unsigned long mpf_get_ui (mpf_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_init __gmpf_init
-__GMP_DECLSPEC void mpf_init (mpf_ptr);
-
-#define mpf_init2 __gmpf_init2
-__GMP_DECLSPEC void mpf_init2 (mpf_ptr, mp_bitcnt_t);
-
-#define mpf_inits __gmpf_inits
-__GMP_DECLSPEC void mpf_inits (mpf_ptr, ...);
-
-#define mpf_init_set __gmpf_init_set
-__GMP_DECLSPEC void mpf_init_set (mpf_ptr, mpf_srcptr);
-
-#define mpf_init_set_d __gmpf_init_set_d
-__GMP_DECLSPEC void mpf_init_set_d (mpf_ptr, double);
-
-#define mpf_init_set_si __gmpf_init_set_si
-__GMP_DECLSPEC void mpf_init_set_si (mpf_ptr, signed long int);
-
-#define mpf_init_set_str __gmpf_init_set_str
-__GMP_DECLSPEC int mpf_init_set_str (mpf_ptr, const char *, int);
-
-#define mpf_init_set_ui __gmpf_init_set_ui
-__GMP_DECLSPEC void mpf_init_set_ui (mpf_ptr, unsigned long int);
-
-#define mpf_inp_str __gmpf_inp_str
-#ifdef _GMP_H_HAVE_FILE
-__GMP_DECLSPEC size_t mpf_inp_str (mpf_ptr, FILE *, int);
-#endif
-
-#define mpf_integer_p __gmpf_integer_p
-__GMP_DECLSPEC int mpf_integer_p (mpf_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_mul __gmpf_mul
-__GMP_DECLSPEC void mpf_mul (mpf_ptr, mpf_srcptr, mpf_srcptr);
-
-#define mpf_mul_2exp __gmpf_mul_2exp
-__GMP_DECLSPEC void mpf_mul_2exp (mpf_ptr, mpf_srcptr, mp_bitcnt_t);
-
-#define mpf_mul_ui __gmpf_mul_ui
-__GMP_DECLSPEC void mpf_mul_ui (mpf_ptr, mpf_srcptr, unsigned long int);
-
-#define mpf_neg __gmpf_neg
-__GMP_DECLSPEC void mpf_neg (mpf_ptr, mpf_srcptr);
-
-#define mpf_out_str __gmpf_out_str
-#ifdef _GMP_H_HAVE_FILE
-__GMP_DECLSPEC size_t mpf_out_str (FILE *, int, size_t, mpf_srcptr);
-#endif
-
-#define mpf_pow_ui __gmpf_pow_ui
-__GMP_DECLSPEC void mpf_pow_ui (mpf_ptr, mpf_srcptr, unsigned long int);
-
-#define mpf_random2 __gmpf_random2
-__GMP_DECLSPEC void mpf_random2 (mpf_ptr, mp_size_t, mp_exp_t);
-
-#define mpf_reldiff __gmpf_reldiff
-__GMP_DECLSPEC void mpf_reldiff (mpf_ptr, mpf_srcptr, mpf_srcptr);
-
-#define mpf_set __gmpf_set
-__GMP_DECLSPEC void mpf_set (mpf_ptr, mpf_srcptr);
-
-#define mpf_set_d __gmpf_set_d
-__GMP_DECLSPEC void mpf_set_d (mpf_ptr, double);
-
-#define mpf_set_default_prec __gmpf_set_default_prec
-__GMP_DECLSPEC void mpf_set_default_prec (mp_bitcnt_t) __GMP_NOTHROW;
-
-#define mpf_set_prec __gmpf_set_prec
-__GMP_DECLSPEC void mpf_set_prec (mpf_ptr, mp_bitcnt_t);
-
-#define mpf_set_prec_raw __gmpf_set_prec_raw
-__GMP_DECLSPEC void mpf_set_prec_raw (mpf_ptr, mp_bitcnt_t) __GMP_NOTHROW;
-
-#define mpf_set_q __gmpf_set_q
-__GMP_DECLSPEC void mpf_set_q (mpf_ptr, mpq_srcptr);
-
-#define mpf_set_si __gmpf_set_si
-__GMP_DECLSPEC void mpf_set_si (mpf_ptr, signed long int);
-
-#define mpf_set_str __gmpf_set_str
-__GMP_DECLSPEC int mpf_set_str (mpf_ptr, const char *, int);
-
-#define mpf_set_ui __gmpf_set_ui
-__GMP_DECLSPEC void mpf_set_ui (mpf_ptr, unsigned long int);
-
-#define mpf_set_z __gmpf_set_z
-__GMP_DECLSPEC void mpf_set_z (mpf_ptr, mpz_srcptr);
-
-#define mpf_size __gmpf_size
-__GMP_DECLSPEC size_t mpf_size (mpf_srcptr) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpf_sqrt __gmpf_sqrt
-__GMP_DECLSPEC void mpf_sqrt (mpf_ptr, mpf_srcptr);
-
-#define mpf_sqrt_ui __gmpf_sqrt_ui
-__GMP_DECLSPEC void mpf_sqrt_ui (mpf_ptr, unsigned long int);
-
-#define mpf_sub __gmpf_sub
-__GMP_DECLSPEC void mpf_sub (mpf_ptr, mpf_srcptr, mpf_srcptr);
-
-#define mpf_sub_ui __gmpf_sub_ui
-__GMP_DECLSPEC void mpf_sub_ui (mpf_ptr, mpf_srcptr, unsigned long int);
-
-#define mpf_swap __gmpf_swap
-__GMP_DECLSPEC void mpf_swap (mpf_ptr, mpf_ptr) __GMP_NOTHROW;
-
-#define mpf_trunc __gmpf_trunc
-__GMP_DECLSPEC void mpf_trunc (mpf_ptr, mpf_srcptr);
-
-#define mpf_ui_div __gmpf_ui_div
-__GMP_DECLSPEC void mpf_ui_div (mpf_ptr, unsigned long int, mpf_srcptr);
-
-#define mpf_ui_sub __gmpf_ui_sub
-__GMP_DECLSPEC void mpf_ui_sub (mpf_ptr, unsigned long int, mpf_srcptr);
-
-#define mpf_urandomb __gmpf_urandomb
-__GMP_DECLSPEC void mpf_urandomb (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 (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 (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 (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
-
-#define mpn_addmul_1 __MPN(addmul_1)
-__GMP_DECLSPEC mp_limb_t mpn_addmul_1 (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 (mp_srcptr, mp_srcptr, mp_size_t) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-#endif
-
-#define mpn_zero_p __MPN(zero_p)
-#if __GMP_INLINE_PROTOTYPES || defined (__GMP_FORCE_mpn_zero_p)
-__GMP_DECLSPEC int mpn_zero_p (mp_srcptr, mp_size_t) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-#endif
-
-#define mpn_divexact_1 __MPN(divexact_1)
-__GMP_DECLSPEC void mpn_divexact_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
-
-#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 (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 (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 (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 (mp_ptr, mp_size_t, mp_ptr, mp_size_t, mp_srcptr);
-
-#define mpn_div_qr_1 __MPN(div_qr_1)
-__GMP_DECLSPEC mp_limb_t mpn_div_qr_1 (mp_ptr, mp_limb_t *, mp_srcptr, mp_size_t, mp_limb_t);
-
-#define mpn_div_qr_2 __MPN(div_qr_2)
-__GMP_DECLSPEC mp_limb_t mpn_div_qr_2 (mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_srcptr);
-
-#define mpn_gcd __MPN(gcd)
-__GMP_DECLSPEC mp_size_t mpn_gcd (mp_ptr, mp_ptr, mp_size_t, mp_ptr, mp_size_t);
-
-#define mpn_gcd_11 __MPN(gcd_11)
-__GMP_DECLSPEC mp_limb_t mpn_gcd_11 (mp_limb_t, mp_limb_t) __GMP_ATTRIBUTE_PURE;
-
-#define mpn_gcd_1 __MPN(gcd_1)
-__GMP_DECLSPEC mp_limb_t mpn_gcd_1 (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 (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 (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 (unsigned char *, int, mp_ptr, mp_size_t);
-
-#define mpn_hamdist __MPN(hamdist)
-__GMP_DECLSPEC mp_bitcnt_t mpn_hamdist (mp_srcptr, mp_srcptr, mp_size_t) __GMP_NOTHROW __GMP_ATTRIBUTE_PURE;
-
-#define mpn_lshift __MPN(lshift)
-__GMP_DECLSPEC mp_limb_t mpn_lshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int);
-
-#define mpn_mod_1 __MPN(mod_1)
-__GMP_DECLSPEC mp_limb_t mpn_mod_1 (mp_srcptr, mp_size_t, mp_limb_t) __GMP_ATTRIBUTE_PURE;
-
-#define mpn_mul __MPN(mul)
-__GMP_DECLSPEC mp_limb_t mpn_mul (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 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
-
-#define mpn_mul_n __MPN(mul_n)
-__GMP_DECLSPEC void mpn_mul_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
-
-#define mpn_sqr __MPN(sqr)
-__GMP_DECLSPEC void mpn_sqr (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 (mp_ptr, mp_srcptr, mp_size_t);
-#endif
-
-#define mpn_com __MPN(com)
-__GMP_DECLSPEC void mpn_com (mp_ptr, mp_srcptr, mp_size_t);
-
-#define mpn_perfect_square_p __MPN(perfect_square_p)
-__GMP_DECLSPEC int mpn_perfect_square_p (mp_srcptr, mp_size_t) __GMP_ATTRIBUTE_PURE;
-
-#define mpn_perfect_power_p __MPN(perfect_power_p)
-__GMP_DECLSPEC int mpn_perfect_power_p (mp_srcptr, mp_size_t) __GMP_ATTRIBUTE_PURE;
-
-#define mpn_popcount __MPN(popcount)
-__GMP_DECLSPEC mp_bitcnt_t mpn_popcount (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 (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 (mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t) __GMP_ATTRIBUTE_PURE;
-
-#define mpn_random __MPN(random)
-__GMP_DECLSPEC void mpn_random (mp_ptr, mp_size_t);
-
-#define mpn_random2 __MPN(random2)
-__GMP_DECLSPEC void mpn_random2 (mp_ptr, mp_size_t);
-
-#define mpn_rshift __MPN(rshift)
-__GMP_DECLSPEC mp_limb_t mpn_rshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int);
-
-#define mpn_scan0 __MPN(scan0)
-__GMP_DECLSPEC mp_bitcnt_t mpn_scan0 (mp_srcptr, mp_bitcnt_t) __GMP_ATTRIBUTE_PURE;
-
-#define mpn_scan1 __MPN(scan1)
-__GMP_DECLSPEC mp_bitcnt_t mpn_scan1 (mp_srcptr, mp_bitcnt_t) __GMP_ATTRIBUTE_PURE;
-
-#define mpn_set_str __MPN(set_str)
-__GMP_DECLSPEC mp_size_t mpn_set_str (mp_ptr, const unsigned char *, size_t, int);
-
-#define mpn_sizeinbase __MPN(sizeinbase)
-__GMP_DECLSPEC size_t mpn_sizeinbase (mp_srcptr, mp_size_t, int);
-
-#define mpn_sqrtrem __MPN(sqrtrem)
-__GMP_DECLSPEC mp_size_t mpn_sqrtrem (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 (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 (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 (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
-
-#define mpn_submul_1 __MPN(submul_1)
-__GMP_DECLSPEC mp_limb_t mpn_submul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
-
-#define mpn_tdiv_qr __MPN(tdiv_qr)
-__GMP_DECLSPEC void mpn_tdiv_qr (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 (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
-#define mpn_andn_n __MPN(andn_n)
-__GMP_DECLSPEC void mpn_andn_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
-#define mpn_nand_n __MPN(nand_n)
-__GMP_DECLSPEC void mpn_nand_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
-#define mpn_ior_n __MPN(ior_n)
-__GMP_DECLSPEC void mpn_ior_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
-#define mpn_iorn_n __MPN(iorn_n)
-__GMP_DECLSPEC void mpn_iorn_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
-#define mpn_nior_n __MPN(nior_n)
-__GMP_DECLSPEC void mpn_nior_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
-#define mpn_xor_n __MPN(xor_n)
-__GMP_DECLSPEC void mpn_xor_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
-#define mpn_xnor_n __MPN(xnor_n)
-__GMP_DECLSPEC void mpn_xnor_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
-
-#define mpn_copyi __MPN(copyi)
-__GMP_DECLSPEC void mpn_copyi (mp_ptr, mp_srcptr, mp_size_t);
-#define mpn_copyd __MPN(copyd)
-__GMP_DECLSPEC void mpn_copyd (mp_ptr, mp_srcptr, mp_size_t);
-#define mpn_zero __MPN(zero)
-__GMP_DECLSPEC void mpn_zero (mp_ptr, mp_size_t);
-
-#define mpn_cnd_add_n __MPN(cnd_add_n)
-__GMP_DECLSPEC mp_limb_t mpn_cnd_add_n (mp_limb_t, mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
-#define mpn_cnd_sub_n __MPN(cnd_sub_n)
-__GMP_DECLSPEC mp_limb_t mpn_cnd_sub_n (mp_limb_t, mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
-
-#define mpn_sec_add_1 __MPN(sec_add_1)
-__GMP_DECLSPEC mp_limb_t mpn_sec_add_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_ptr);
-#define mpn_sec_add_1_itch __MPN(sec_add_1_itch)
-__GMP_DECLSPEC mp_size_t mpn_sec_add_1_itch (mp_size_t) __GMP_ATTRIBUTE_PURE;
-
-#define mpn_sec_sub_1 __MPN(sec_sub_1)
-__GMP_DECLSPEC mp_limb_t mpn_sec_sub_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t, mp_ptr);
-#define mpn_sec_sub_1_itch __MPN(sec_sub_1_itch)
-__GMP_DECLSPEC mp_size_t mpn_sec_sub_1_itch (mp_size_t) __GMP_ATTRIBUTE_PURE;
-
-#define mpn_cnd_swap __MPN(cnd_swap)
-__GMP_DECLSPEC void mpn_cnd_swap (mp_limb_t, volatile mp_limb_t *, volatile mp_limb_t *, mp_size_t);
-
-#define mpn_sec_mul __MPN(sec_mul)
-__GMP_DECLSPEC void mpn_sec_mul (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr);
-#define mpn_sec_mul_itch __MPN(sec_mul_itch)
-__GMP_DECLSPEC mp_size_t mpn_sec_mul_itch (mp_size_t, mp_size_t) __GMP_ATTRIBUTE_PURE;
-
-#define mpn_sec_sqr __MPN(sec_sqr)
-__GMP_DECLSPEC void mpn_sec_sqr (mp_ptr, mp_srcptr, mp_size_t, mp_ptr);
-#define mpn_sec_sqr_itch __MPN(sec_sqr_itch)
-__GMP_DECLSPEC mp_size_t mpn_sec_sqr_itch (mp_size_t) __GMP_ATTRIBUTE_PURE;
-
-#define mpn_sec_powm __MPN(sec_powm)
-__GMP_DECLSPEC void mpn_sec_powm (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_bitcnt_t, mp_srcptr, mp_size_t, mp_ptr);
-#define mpn_sec_powm_itch __MPN(sec_powm_itch)
-__GMP_DECLSPEC mp_size_t mpn_sec_powm_itch (mp_size_t, mp_bitcnt_t, mp_size_t) __GMP_ATTRIBUTE_PURE;
-
-#define mpn_sec_tabselect __MPN(sec_tabselect)
-__GMP_DECLSPEC void mpn_sec_tabselect (volatile mp_limb_t *, volatile const mp_limb_t *, mp_size_t, mp_size_t, mp_size_t);
-
-#define mpn_sec_div_qr __MPN(sec_div_qr)
-__GMP_DECLSPEC mp_limb_t mpn_sec_div_qr (mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr);
-#define mpn_sec_div_qr_itch __MPN(sec_div_qr_itch)
-__GMP_DECLSPEC mp_size_t mpn_sec_div_qr_itch (mp_size_t, mp_size_t) __GMP_ATTRIBUTE_PURE;
-#define mpn_sec_div_r __MPN(sec_div_r)
-__GMP_DECLSPEC void mpn_sec_div_r (mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_ptr);
-#define mpn_sec_div_r_itch __MPN(sec_div_r_itch)
-__GMP_DECLSPEC mp_size_t mpn_sec_div_r_itch (mp_size_t, mp_size_t) __GMP_ATTRIBUTE_PURE;
-
-#define mpn_sec_invert __MPN(sec_invert)
-__GMP_DECLSPEC int mpn_sec_invert (mp_ptr, mp_ptr, mp_srcptr, mp_size_t, mp_bitcnt_t, mp_ptr);
-#define mpn_sec_invert_itch __MPN(sec_invert_itch)
-__GMP_DECLSPEC mp_size_t mpn_sec_invert_itch (mp_size_t) __GMP_ATTRIBUTE_PURE;
-
-
-/**************** 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, 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, 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, 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
- "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_CAST (mp_bitcnt_t, 0) : __GMP_CAST (mp_bitcnt_t, 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_zero_p)
-#if ! defined (__GMP_FORCE_mpn_zero_p)
-__GMP_EXTERN_INLINE
-#endif
-int
-mpn_zero_p (mp_srcptr __gmp_p, mp_size_t __gmp_n) __GMP_NOTHROW
-{
- /* if (__GMP_LIKELY (__gmp_n > 0)) */
- do {
- if (__gmp_p[--__gmp_n] != 0)
- return 0;
- } while (__gmp_n != 0);
- return 1;
-}
-#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)
-{
- while (*__gmp_up == 0) /* Low zero limbs are unchanged by negation. */
- {
- *__gmp_rp = 0;
- if (!--__gmp_n) /* All zero */
- return 0;
- ++__gmp_up; ++__gmp_rp;
- }
-
- *__gmp_rp = (- *__gmp_up) & GMP_NUMB_MASK;
-
- if (--__gmp_n) /* Higher limbs get complemented. */
- mpn_com (++__gmp_rp, ++__gmp_up, __gmp_n);
-
- return 1;
-}
-#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) >= 0) && (SI) >= 0 \
- ? mpz_cmp_ui (Z, __GMP_CAST (unsigned long, SI)) \
- : _mpz_cmp_si (Z,SI))
-#define mpq_cmp_ui(Q,NUI,DUI) \
- (__builtin_constant_p (NUI) && (NUI) == 0 ? mpq_sgn (Q) \
- : __builtin_constant_p ((NUI) == (DUI)) && (NUI) == (DUI) \
- ? mpz_cmp (mpq_numref (Q), mpq_denref (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"
-#define __GMP_CFLAGS "-O2 -pedantic -fomit-frame-pointer -m64"
-
-/* Major version number is the value of __GNU_MP__ too, above. */
-#define __GNU_MP_VERSION 6
-#define __GNU_MP_VERSION_MINOR 2
-#define __GNU_MP_VERSION_PATCHLEVEL 1
-#define __GNU_MP_RELEASE (__GNU_MP_VERSION * 10000 + __GNU_MP_VERSION_MINOR * 100 + __GNU_MP_VERSION_PATCHLEVEL)
-
-#define __GMP_H__
-#endif /* __GMP_H__ */
+++ /dev/null
-# libgmp.la - a libtool library file
-# Generated by libtool (GNU libtool) 2.4.6
-#
-# 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 cannot 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=14
-age=4
-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='/home/rpolzer/Games/xonotic/misc/builddeps/linux64/gmp/lib'
+++ /dev/null
-prefix=/home/rpolzer/Games/xonotic/misc/builddeps/linux64/gmp
-exec_prefix=${prefix}
-includedir=${prefix}/include
-libdir=${exec_prefix}/lib
-
-Name: GNU MP
-Description: GNU Multiple Precision Arithmetic Library
-URL: https://gmplib.org
-Version: 6.2.1
-Cflags: -I${includedir}
-Libs: -L${libdir} -lgmp
+++ /dev/null
-This is gmp.info, produced by makeinfo version 6.7 from gmp.texi.
-
-This manual describes how to install and use the GNU multiple precision
-arithmetic library, version 6.2.1.
-
- Copyright 1991, 1993-2016, 2018-2020 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
-
-\1f
-Indirect:
-gmp.info-1: 863
-gmp.info-2: 303737
-\1f
-Tag Table:
-(Indirect)
-Node: Top\7f863
-Node: Copying\7f2941
-Node: Introduction to GMP\7f5288
-Node: Installing GMP\7f8004
-Node: Build Options\7f8736
-Node: ABI and ISA\7f24445
-Node: Notes for Package Builds\7f34286
-Node: Notes for Particular Systems\7f37373
-Node: Known Build Problems\7f45124
-Node: Performance optimization\7f48656
-Node: GMP Basics\7f49785
-Node: Headers and Libraries\7f50433
-Node: Nomenclature and Types\7f51838
-Node: Function Classes\7f53834
-Node: Variable Conventions\7f55369
-Node: Parameter Conventions\7f57609
-Node: Memory Management\7f59416
-Node: Reentrancy\7f60544
-Node: Useful Macros and Constants\7f62412
-Node: Compatibility with older versions\7f63403
-Node: Demonstration Programs\7f64313
-Node: Efficiency\7f66172
-Node: Debugging\7f73778
-Node: Profiling\7f80553
-Node: Autoconf\7f84544
-Node: Emacs\7f86325
-Node: Reporting Bugs\7f86931
-Node: Integer Functions\7f89557
-Node: Initializing Integers\7f90333
-Node: Assigning Integers\7f92709
-Node: Simultaneous Integer Init & Assign\7f94320
-Node: Converting Integers\7f95967
-Node: Integer Arithmetic\7f98907
-Node: Integer Division\7f100643
-Node: Integer Exponentiation\7f107402
-Node: Integer Roots\7f108899
-Node: Number Theoretic Functions\7f110616
-Node: Integer Comparisons\7f118111
-Node: Integer Logic and Bit Fiddling\7f119549
-Node: I/O of Integers\7f122189
-Node: Integer Random Numbers\7f125180
-Node: Integer Import and Export\7f127803
-Node: Miscellaneous Integer Functions\7f131819
-Node: Integer Special Functions\7f133733
-Node: Rational Number Functions\7f137906
-Node: Initializing Rationals\7f139099
-Node: Rational Conversions\7f141572
-Node: Rational Arithmetic\7f143594
-Node: Comparing Rationals\7f145006
-Node: Applying Integer Functions\7f146477
-Node: I/O of Rationals\7f147996
-Node: Floating-point Functions\7f150355
-Node: Initializing Floats\7f153400
-Node: Assigning Floats\7f157492
-Node: Simultaneous Float Init & Assign\7f160080
-Node: Converting Floats\7f161630
-Node: Float Arithmetic\7f164895
-Node: Float Comparison\7f167048
-Node: I/O of Floats\7f168619
-Node: Miscellaneous Float Functions\7f171308
-Node: Low-level Functions\7f173310
-Node: Random Number Functions\7f207558
-Node: Random State Initialization\7f208626
-Node: Random State Seeding\7f211491
-Node: Random State Miscellaneous\7f212896
-Node: Formatted Output\7f213538
-Node: Formatted Output Strings\7f213783
-Node: Formatted Output Functions\7f219178
-Node: C++ Formatted Output\7f223242
-Node: Formatted Input\7f225942
-Node: Formatted Input Strings\7f226178
-Node: Formatted Input Functions\7f230838
-Node: C++ Formatted Input\7f233807
-Node: C++ Class Interface\7f235710
-Node: C++ Interface General\7f236661
-Node: C++ Interface Integers\7f239730
-Node: C++ Interface Rationals\7f243963
-Node: C++ Interface Floats\7f247987
-Node: C++ Interface Random Numbers\7f254004
-Node: C++ Interface Limitations\7f256404
-Node: Custom Allocation\7f259979
-Node: Language Bindings\7f264198
-Node: Algorithms\7f267511
-Node: Multiplication Algorithms\7f268211
-Node: Basecase Multiplication\7f269300
-Node: Karatsuba Multiplication\7f271208
-Node: Toom 3-Way Multiplication\7f274832
-Node: Toom 4-Way Multiplication\7f281251
-Node: Higher degree Toom'n'half\7f282630
-Node: FFT Multiplication\7f283922
-Node: Other Multiplication\7f289258
-Node: Unbalanced Multiplication\7f291732
-Node: Division Algorithms\7f292520
-Node: Single Limb Division\7f292899
-Node: Basecase Division\7f295787
-Node: Divide and Conquer Division\7f296990
-Node: Block-Wise Barrett Division\7f299058
-Node: Exact Division\7f299710
-Node: Exact Remainder\7f303737
-Node: Small Quotient Division\7f305987
-Node: Greatest Common Divisor Algorithms\7f307585
-Node: Binary GCD\7f307882
-Node: Lehmer's Algorithm\7f310732
-Node: Subquadratic GCD\7f312962
-Node: Extended GCD\7f315431
-Node: Jacobi Symbol\7f316749
-Node: Powering Algorithms\7f318658
-Node: Normal Powering Algorithm\7f318921
-Node: Modular Powering Algorithm\7f319449
-Node: Root Extraction Algorithms\7f320231
-Node: Square Root Algorithm\7f320546
-Node: Nth Root Algorithm\7f322687
-Node: Perfect Square Algorithm\7f323472
-Node: Perfect Power Algorithm\7f325559
-Node: Radix Conversion Algorithms\7f326180
-Node: Binary to Radix\7f326556
-Node: Radix to Binary\7f330177
-Node: Other Algorithms\7f332265
-Node: Prime Testing Algorithm\7f332617
-Node: Factorial Algorithm\7f333801
-Node: Binomial Coefficients Algorithm\7f336201
-Node: Fibonacci Numbers Algorithm\7f337095
-Node: Lucas Numbers Algorithm\7f339569
-Node: Random Number Algorithms\7f340290
-Node: Assembly Coding\7f342410
-Node: Assembly Code Organisation\7f343370
-Node: Assembly Basics\7f344337
-Node: Assembly Carry Propagation\7f345487
-Node: Assembly Cache Handling\7f347317
-Node: Assembly Functional Units\7f349478
-Node: Assembly Floating Point\7f351091
-Node: Assembly SIMD Instructions\7f354870
-Node: Assembly Software Pipelining\7f355852
-Node: Assembly Loop Unrolling\7f356915
-Node: Assembly Writing Guide\7f359130
-Node: Internals\7f361895
-Node: Integer Internals\7f362407
-Node: Rational Internals\7f364871
-Node: Float Internals\7f366109
-Node: Raw Output Internals\7f373509
-Node: C++ Interface Internals\7f374703
-Node: Contributors\7f378024
-Node: References\7f384255
-Node: GNU Free Documentation License\7f390174
-Node: Concept Index\7f415316
-Node: Function Index\7f463130
-\1f
-End Tag Table
-
-\1f
-Local Variables:
-coding: iso-8859-1
-End:
+++ /dev/null
-This is gmp.info, produced by makeinfo version 6.7 from gmp.texi.
-
-This manual describes how to install and use the GNU multiple precision
-arithmetic library, version 6.2.1.
-
- Copyright 1991, 1993-2016, 2018-2020 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
-
-\1f
-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 6.2.1.
-
- Copyright 1991, 1993-2016, 2018-2020 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.
-* 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::
-
-\1f
-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.
-
- More precisely, the GNU MP library is dual licensed, under the
-conditions of the GNU Lesser General Public License version 3 (see
-'COPYING.LESSERv3'), or the GNU General Public License version 2 (see
-'COPYINGv2'). This is the recipient's choice, and the recipient also
-has the additional option of applying later versions of these licenses.
-(The reason for this dual licensing is to make it possible to use the
-library with programs which are licensed under GPL version 2, but which
-for historical or other reasons do not allow use under later versions of
-the GPL).
-
- Programs which are not part of the library itself, such as
-demonstration programs and the GMP testsuite, are licensed under the
-terms of the GNU General Public License version 3 (see 'COPYINGv3'), or
-any later version.
-
-\1f
-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 Cortex-A9, Cortex-A15, and
-generic ARM, DEC Alpha 21064, 21164, and 21264, AMD K8 and K10 (sold
-under many brands, e.g. Athlon64, Phenom, Opteron) Bulldozer, and
-Bobcat, Intel Pentium, Pentium Pro/II/III, Pentium 4, Core2, Nehalem,
-Sandy bridge, Haswell, generic x86, Intel IA-64, Motorola/IBM PowerPC 32
-and 64 such as POWER970, POWER5, POWER6, and POWER7, MIPS 32-bit and
-64-bit, SPARC 32-bit ad 64-bit with special support for all UltraSPARC
-models. There is also assembly code for many obsolete CPUs.
-
-For up-to-date information on GMP, please see the GMP web pages at
-
- <https://gmplib.org/>
-
-The latest version of the library is available at
-
- <https://ftp.gnu.org/gnu/gmp/>
-
- Many sites around the world mirror 'ftp.gnu.org', please use a mirror
-near you, see <https://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
-
- <https://gmplib.org/mailman/listinfo/>.
-
- The proper place for bug reports is <gmp-bugs@gmplib.org>. 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.
-
-\1f
-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
-<gmp-bugs@gmplib.org>. 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::
-
-\1f
-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-6.2.1/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' is
- architecture-dependent since it encodes 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.ac' 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: arm, sh, sh2, vax,
-
- 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 the configure
- '--disable-assembly'.
-
- 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.
-
-'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=<choice>'
- 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,
- higher degree 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.
-
-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.
-
-\1f
-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.)
-
- 'ABI=x32'
- The x32 ABI uses 64-bit limbs but 32-bit pointers. Like the
- 64-bit ABI, it makes full use of the chip's arithmetic
- capabilities. This ABI is not supported by all operating
- systems.
-
- gcc -mx32
-
-
-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=mode64'
- 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
-
- On 64-bit GNU/Linux, BSD, and Mac OS X/Darwin systems, the
- 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 for systems where the true
- 64-bit ABI is unavailable. No special compiler options are
- typically needed for applications. This ABI is not available
- under AIX.
-
- 'ABI=32'
- This is the basic 32-bit PowerPC ABI, with a 32-bit limb. No
- special compiler options are needed for applications.
-
- GMP's speed is greatest for the 'mode64' ABI, the 'mode32' ABI is
- 2nd best. In 'ABI=32' only the 32-bit ISA is used and this doesn't
- make full use of a 64-bit chip.
-
-
-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
-
-\1f
-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'.
-
-\1f
-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.
-
-FreeBSD 7.x, 8.x, 9.0, 9.1, 9.2
- 'm4' in these releases of FreeBSD has an eval function which
- ignores its 2nd and 3rd arguments, which 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 FreeBSD 9.3 and 10.0, so either upgrade or use GNU m4. Note
- that the FreeBSD package system installs GNU m4 under the name
- 'gm4', which GMP cannot guess.
-
-FreeBSD 7.x, 8.x, 9.x
- GMP releases starting with 6.0 do not support 'ABI=32' on
- FreeBSD/amd64 prior to release 10.0 of the system. The cause is a
- broken 'limits.h', which GMP no longer works around.
-
-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.
-
- <https://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'.
-
-NetBSD 5.x
- 'm4' in these releases of NetBSD has an eval function which ignores
- its 2nd and 3rd arguments, which 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
- NetBSD 6, so either upgrade or use GNU m4. Note that the NetBSD
- package system installs GNU m4 under the name 'gm4', which GMP
- cannot guess.
-
-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 ('--disable-assembly'),
- 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 '--disable-assembly'.
-
-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 '--disable-assembly' 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.
-
-\1f
-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 <https://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.
-
-\1f
-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 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.
-
-\1f
-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::
-
-\1f
-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 <gmp.h>
-
- Note however that prototypes for GMP functions with 'FILE *'
-parameters are only provided if '<stdio.h>' is included too.
-
- #include <stdio.h>
- #include <gmp.h>
-
- Likewise '<stdarg.h>' is required for prototypes with 'va_list'
-parameters, such as 'gmp_vprintf'. And '<obstack.h>' 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.
-
-\1f
-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.
-
-\1f
-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 35
- 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 70
- functions is this class. (*note Floating-point Functions::)
-
- 4. 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 60 (hard-to-use) functions in this
- class. (*note Low-level Functions::)
-
- 5. Miscellaneous functions. Functions for setting up custom
- allocation and functions for generating random numbers. (*note
- Custom Allocation::, and *note Random Number Functions::)
-
-\1f
-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.
-
- 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);
- }
-
- GMP types like 'mpz_t' are implemented as one-element arrays of
-certain structures. Declaring a variable creates an object with the
-fields GMP needs, but variables are normally manipulated by using the
-pointer to the object. For both behavior and efficiency reasons, it is
-discouraged to make copies of the GMP object itself (either directly or
-via aggregate objects containing such GMP objects). If copies are done,
-all of them must be used read-only; using a copy as the output of some
-function will invalidate all the other copies. 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.
-
-\1f
-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 that when 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;
- }
-
- Our function 'foo' works even if its caller 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.
-
- Since GMP types are implemented as one-element arrays, using a GMP
-variable as a parameter passes a pointer to the object. Hence the
-call-by-reference.
-
-\1f
-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::.
-
-\1f
-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 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.
-
-\1f
-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 "6.2.1". Note that the format "i.j" was
- used, before version 4.3.0, when k was zero.
-
- -- Macro: __GMP_CC
- -- Macro: __GMP_CFLAGS
- The compiler and compiler flags, respectively, used when compiling
- GMP, as strings.
-
-\1f
-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 5.x, 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.
-
- * 'mpn_bdivmod', documented as preliminary in GMP 4, has been
- removed.
-
- 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 5.
-Please see the GMP 2 manual for details.
-
-\1f
-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.
-
-\1f
-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 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.
-
-\1f
-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://cs.ecs.baylor.edu/~donahoo/tools/ccmalloc/>
- <http://dmalloc.com/>
- <https://wiki.gnome.org/Apps/MemProf>
-
- 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-6.2.1/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 '--disable-assembly'
- 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 --disable-assembly CFLAGS=-g
-
- For C++, add '--enable-cxx CXXFLAGS=-g'.
-
-Checker
- The GCC checker (<https://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 --disable-assembly CC=checkergcc
-
- '--disable-assembly' 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
- Valgrind (<http://valgrind.org/>) is a memory checker for x86, ARM,
- MIPS, PowerPC, and S/390. 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.
-
- Valgrind does not always support every possible instruction, in
- particular ones recently added to an ISA. Valgrind might therefore
- be incompatible with a recent GMP or even a less recent GMP which
- is compiled using a recent GCC.
-
- GMP's assembly code sometimes promotes a read of the limbs to some
- larger size, for efficiency. GMP will do this even at the start
- and end of a multilimb operand, using naturally aligned operations
- on the larger type. This may lead to benign reads outside of
- allocated areas, triggering complaints from Valgrind. Valgrind's
- option '--partial-loads-ok=yes' should help.
-
-Other Problems
- Any suspected bug in GMP itself should be isolated to make sure
- it's not an application problem, see *note Reporting Bugs::.
-
-\1f
-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
-
- <https://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.
-
-\1f
-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 https://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 https://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 <gmp.h>])
-
-\1f
-File: gmp.info, Node: Emacs, Prev: Autoconf, Up: GMP Basics
-
-3.15 Emacs
-==========
-
-<C-h C-i> ('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)))))
-
-\1f
-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 <https://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 'configure' options you used when building GMP, if any.
-
- * The output from 'configure', as printed to stdout, with any options
- used.
-
- * 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-<file>.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: <gmp-bugs@gmplib.org>.
-
- 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.
-
-\1f
-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::
-
-\1f
-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.
-
- While N defines 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.
-
- In preparation for an operation, GMP often allocates one limb more
- than ultimately needed. To make sure GMP will not perform
- reallocation for X, you need to add the number of bits in
- 'mp_limb_t' to N.
-
- -- 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.
-
-\1f
-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, const 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, const mpq_t OP)
- -- Function: void mpz_set_f (mpz_t ROP, const 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, const 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.
-
-\1f
-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, const 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, const 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.)
-
-\1f
-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 (const 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 (const 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 (const mpz_t OP)
- Convert OP to a 'double', truncating if necessary (i.e. 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, const mpz_t
- OP)
- Convert OP to a 'double', truncating if necessary (i.e. 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
- (libc)Normalization Functions::).
-
- -- Function: char * mpz_get_str (char *STR, int BASE, const 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.
-
-\1f
-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, const mpz_t OP1, const mpz_t OP2)
- -- Function: void mpz_add_ui (mpz_t ROP, const mpz_t OP1, unsigned long
- int OP2)
- Set ROP to OP1 + OP2.
-
- -- Function: void mpz_sub (mpz_t ROP, const mpz_t OP1, const mpz_t OP2)
- -- Function: void mpz_sub_ui (mpz_t ROP, const mpz_t OP1, unsigned long
- int OP2)
- -- Function: void mpz_ui_sub (mpz_t ROP, unsigned long int OP1, const
- mpz_t OP2)
- Set ROP to OP1 - OP2.
-
- -- Function: void mpz_mul (mpz_t ROP, const mpz_t OP1, const mpz_t OP2)
- -- Function: void mpz_mul_si (mpz_t ROP, const mpz_t OP1, long int OP2)
- -- Function: void mpz_mul_ui (mpz_t ROP, const mpz_t OP1, unsigned long
- int OP2)
- Set ROP to OP1 times OP2.
-
- -- Function: void mpz_addmul (mpz_t ROP, const mpz_t OP1, const mpz_t
- OP2)
- -- Function: void mpz_addmul_ui (mpz_t ROP, const mpz_t OP1, unsigned
- long int OP2)
- Set ROP to ROP + OP1 times OP2.
-
- -- Function: void mpz_submul (mpz_t ROP, const mpz_t OP1, const mpz_t
- OP2)
- -- Function: void mpz_submul_ui (mpz_t ROP, const mpz_t OP1, unsigned
- long int OP2)
- Set ROP to ROP - OP1 times OP2.
-
- -- Function: void mpz_mul_2exp (mpz_t ROP, const 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, const mpz_t OP)
- Set ROP to -OP.
-
- -- Function: void mpz_abs (mpz_t ROP, const mpz_t OP)
- Set ROP to the absolute value of OP.
-
-\1f
-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, const mpz_t N, const mpz_t D)
- -- Function: void mpz_cdiv_r (mpz_t R, const mpz_t N, const mpz_t D)
- -- Function: void mpz_cdiv_qr (mpz_t Q, mpz_t R, const mpz_t N, const
- mpz_t D)
-
- -- Function: unsigned long int mpz_cdiv_q_ui (mpz_t Q, const mpz_t N,
- unsigned long int D)
- -- Function: unsigned long int mpz_cdiv_r_ui (mpz_t R, const mpz_t N,
- unsigned long int D)
- -- Function: unsigned long int mpz_cdiv_qr_ui (mpz_t Q, mpz_t R,
- const mpz_t N, unsigned long int D)
- -- Function: unsigned long int mpz_cdiv_ui (const mpz_t N,
- unsigned long int D)
-
- -- Function: void mpz_cdiv_q_2exp (mpz_t Q, const mpz_t N,
- mp_bitcnt_t B)
- -- Function: void mpz_cdiv_r_2exp (mpz_t R, const mpz_t N,
- mp_bitcnt_t B)
-
- -- Function: void mpz_fdiv_q (mpz_t Q, const mpz_t N, const mpz_t D)
- -- Function: void mpz_fdiv_r (mpz_t R, const mpz_t N, const mpz_t D)
- -- Function: void mpz_fdiv_qr (mpz_t Q, mpz_t R, const mpz_t N, const
- mpz_t D)
-
- -- Function: unsigned long int mpz_fdiv_q_ui (mpz_t Q, const mpz_t N,
- unsigned long int D)
- -- Function: unsigned long int mpz_fdiv_r_ui (mpz_t R, const mpz_t N,
- unsigned long int D)
- -- Function: unsigned long int mpz_fdiv_qr_ui (mpz_t Q, mpz_t R,
- const mpz_t N, unsigned long int D)
- -- Function: unsigned long int mpz_fdiv_ui (const mpz_t N,
- unsigned long int D)
-
- -- Function: void mpz_fdiv_q_2exp (mpz_t Q, const mpz_t N,
- mp_bitcnt_t B)
- -- Function: void mpz_fdiv_r_2exp (mpz_t R, const mpz_t N,
- mp_bitcnt_t B)
-
- -- Function: void mpz_tdiv_q (mpz_t Q, const mpz_t N, const mpz_t D)
- -- Function: void mpz_tdiv_r (mpz_t R, const mpz_t N, const mpz_t D)
- -- Function: void mpz_tdiv_qr (mpz_t Q, mpz_t R, const mpz_t N, const
- mpz_t D)
-
- -- Function: unsigned long int mpz_tdiv_q_ui (mpz_t Q, const mpz_t N,
- unsigned long int D)
- -- Function: unsigned long int mpz_tdiv_r_ui (mpz_t R, const mpz_t N,
- unsigned long int D)
- -- Function: unsigned long int mpz_tdiv_qr_ui (mpz_t Q, mpz_t R,
- const mpz_t N, unsigned long int D)
- -- Function: unsigned long int mpz_tdiv_ui (const mpz_t N,
- unsigned long int D)
-
- -- Function: void mpz_tdiv_q_2exp (mpz_t Q, const mpz_t N,
- mp_bitcnt_t B)
- -- Function: void mpz_tdiv_r_2exp (mpz_t R, const 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)<abs(D).
-
- The 'q' functions calculate only the quotient, the 'r' functions
- only the remainder, and the 'qr' functions calculate both. Note
- that for 'qr' the same variable cannot be passed for both Q and R,
- or results will be unpredictable.
-
- For the 'ui' variants the return value is the remainder, and in
- fact returning the remainder is all the 'div_ui' functions do. For
- 'tdiv' and 'cdiv' the remainder can be negative, so for those the
- return value is the absolute value of the remainder.
-
- For the '2exp' variants the divisor is 2^B. These functions are
- implemented as right shifts and bit masks, but of course they round
- the same as the other functions.
-
- For positive N both 'mpz_fdiv_q_2exp' and 'mpz_tdiv_q_2exp' are
- simple bitwise right shifts. For negative N, 'mpz_fdiv_q_2exp' is
- effectively an arithmetic right shift treating N as twos complement
- the same as the bitwise logical functions do, whereas
- 'mpz_tdiv_q_2exp' effectively treats N as sign and magnitude.
-
- -- Function: void mpz_mod (mpz_t R, const mpz_t N, const mpz_t D)
- -- Function: unsigned long int mpz_mod_ui (mpz_t R, const mpz_t N,
- unsigned long int D)
- Set R to N 'mod' D. The sign of the divisor is ignored; the result
- is always non-negative.
-
- 'mpz_mod_ui' is identical to 'mpz_fdiv_r_ui' above, returning the
- remainder as well as setting R. See 'mpz_fdiv_ui' above if only
- the return value is wanted.
-
- -- Function: void mpz_divexact (mpz_t Q, const mpz_t N, const mpz_t D)
- -- Function: void mpz_divexact_ui (mpz_t Q, const mpz_t N, unsigned
- long D)
- Set Q to N/D. These functions produce correct results only when it
- is known in advance that D divides N.
-
- These routines are much faster than the other division functions,
- and are the best choice when exact division is known to occur, for
- example reducing a rational to lowest terms.
-
- -- Function: int mpz_divisible_p (const mpz_t N, const mpz_t D)
- -- Function: int mpz_divisible_ui_p (const mpz_t N, unsigned long int
- D)
- -- Function: int mpz_divisible_2exp_p (const mpz_t N, mp_bitcnt_t B)
- Return non-zero if N is exactly divisible by D, or in the case of
- 'mpz_divisible_2exp_p' by 2^B.
-
- N is divisible by D if there exists an integer Q satisfying N =
- Q*D. Unlike the other division functions, D=0 is accepted and
- following the rule it can be seen that only 0 is considered
- divisible by 0.
-
- -- Function: int mpz_congruent_p (const mpz_t N, const mpz_t C, const
- mpz_t D)
- -- Function: int mpz_congruent_ui_p (const mpz_t N, unsigned long int
- C, unsigned long int D)
- -- Function: int mpz_congruent_2exp_p (const mpz_t N, const mpz_t C,
- mp_bitcnt_t B)
- Return non-zero if N is congruent to C modulo D, or in the case of
- 'mpz_congruent_2exp_p' modulo 2^B.
-
- N is congruent to C mod D if there exists an integer Q satisfying N
- = C + Q*D. Unlike the other division functions, D=0 is accepted
- and following the rule it can be seen that N and C are considered
- congruent mod 0 only when exactly equal.
-
-\1f
-File: gmp.info, Node: Integer Exponentiation, Next: Integer Roots, Prev: Integer Division, Up: Integer Functions
-
-5.7 Exponentiation Functions
-============================
-
- -- Function: void mpz_powm (mpz_t ROP, const mpz_t BASE, const mpz_t
- EXP, const mpz_t MOD)
- -- Function: void mpz_powm_ui (mpz_t ROP, const mpz_t BASE, unsigned
- long int EXP, const mpz_t MOD)
- Set ROP to (BASE raised to EXP) modulo MOD.
-
- Negative EXP is supported if the inverse BASE^(-1) mod MOD exists
- (see 'mpz_invert' in *note Number Theoretic Functions::). If an
- inverse doesn't exist then a divide by zero is raised.
-
- -- Function: void mpz_powm_sec (mpz_t ROP, const mpz_t BASE, const
- mpz_t EXP, const mpz_t MOD)
- Set ROP to (BASE raised to EXP) modulo MOD.
-
- It is required that EXP > 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, const 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.
-
-\1f
-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, const 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, const 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, const 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, const 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 (const 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 (const 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.
-
-\1f
-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 (const 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 non-prime.
-
- This function performs some trial divisions, a Baillie-PSW probable
- prime test, then REPS-24 Miller-Rabin probabilistic primality
- tests. A higher REPS value will reduce the chances of a non-prime
- being identified as "probably prime". A composite number will be
- identified as a prime with an asymptotic probability of less than
- 4^(-REPS). Reasonable values of REPS are between 15 and 50.
-
- GMP versions up to and including 6.1.2 did not use the Baillie-PSW
- primality test. In those older versions of GMP, this function
- performed REPS Miller-Rabin tests.
-
- -- Function: void mpz_nextprime (mpz_t ROP, const 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, const mpz_t OP1, const 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.
- Except if both inputs are zero; then this function defines gcd(0,0)
- = 0.
-
- -- Function: unsigned long int mpz_gcd_ui (mpz_t ROP, const 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, const mpz_t A,
- const 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
- (or zero if both inputs are zero). The values in S and T are
- chosen such that normally, abs(S) < abs(B) / (2 G) and abs(T) <
- abs(A) / (2 G), and these relations define S and T uniquely. There
- are a few exceptional cases:
-
- If abs(A) = abs(B), then S = 0, T = sgn(B).
-
- Otherwise, S = sgn(A) if B = 0 or abs(B) = 2 G, and T = sgn(B) if A
- = 0 or abs(A) = 2 G.
-
- In all cases, S = 0 if and only if G = abs(B), i.e., if B divides A
- or A = B = 0.
-
- If T or G is 'NULL' then that value is not computed.
-
- -- Function: void mpz_lcm (mpz_t ROP, const mpz_t OP1, const mpz_t OP2)
- -- Function: void mpz_lcm_ui (mpz_t ROP, const 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, const mpz_t OP1, const 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 < abs(OP2) (with ROP = 0 possible only when
- abs(OP2) = 1, i.e., in the somewhat degenerate zero ring). If an
- inverse doesn't exist the return value is zero and ROP is
- undefined. The behaviour of this function is undefined when OP2 is
- zero.
-
- -- Function: int mpz_jacobi (const mpz_t A, const mpz_t B)
- Calculate the Jacobi symbol (A/B). This is defined only for B odd.
-
- -- Function: int mpz_legendre (const mpz_t A, const 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 (const mpz_t A, const mpz_t B)
- -- Function: int mpz_kronecker_si (const mpz_t A, long B)
- -- Function: int mpz_kronecker_ui (const mpz_t A, unsigned long B)
- -- Function: int mpz_si_kronecker (long A, const mpz_t B)
- -- Function: int mpz_ui_kronecker (unsigned long A, const 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, const mpz_t OP, const
- 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 N)
- -- Function: void mpz_2fac_ui (mpz_t ROP, unsigned long int N)
- -- Function: void mpz_mfac_uiui (mpz_t ROP, unsigned long int N,
- unsigned long int M)
- Set ROP to the factorial of N: 'mpz_fac_ui' computes the plain
- factorial N!, 'mpz_2fac_ui' computes the double-factorial N!!, and
- 'mpz_mfac_uiui' the M-multi-factorial N!^(M).
-
- -- Function: void mpz_primorial_ui (mpz_t ROP, unsigned long int N)
- Set ROP to the primorial of N, i.e. the product of all positive
- prime numbers <=N.
-
- -- Function: void mpz_bin_ui (mpz_t ROP, const 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.
-
-\1f
-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 (const mpz_t OP1, const mpz_t OP2)
- -- Function: int mpz_cmp_d (const mpz_t OP1, double OP2)
- -- Macro: int mpz_cmp_si (const mpz_t OP1, signed long int OP2)
- -- Macro: int mpz_cmp_ui (const 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 (const mpz_t OP1, const mpz_t OP2)
- -- Function: int mpz_cmpabs_d (const mpz_t OP1, double OP2)
- -- Function: int mpz_cmpabs_ui (const 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 (const 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.
-
-\1f
-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, const mpz_t OP1, const mpz_t OP2)
- Set ROP to OP1 bitwise-and OP2.
-
- -- Function: void mpz_ior (mpz_t ROP, const mpz_t OP1, const mpz_t OP2)
- Set ROP to OP1 bitwise inclusive-or OP2.
-
- -- Function: void mpz_xor (mpz_t ROP, const mpz_t OP1, const mpz_t OP2)
- Set ROP to OP1 bitwise exclusive-or OP2.
-
- -- Function: void mpz_com (mpz_t ROP, const mpz_t OP)
- Set ROP to the one's complement of OP.
-
- -- Function: mp_bitcnt_t mpz_popcount (const 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 (const mpz_t OP1, const 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 (const mpz_t OP, mp_bitcnt_t
- STARTING_BIT)
- -- Function: mp_bitcnt_t mpz_scan1 (const 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 (const mpz_t OP, mp_bitcnt_t BIT_INDEX)
- Test bit BIT_INDEX in OP and return 0 or 1 accordingly.
-
-\1f
-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, of 'mpz' numbers. 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.
-
- See also *note Formatted Output:: and *note Formatted Input::.
-
- -- Function: size_t mpz_out_str (FILE *STREAM, int BASE, const 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, const 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.
-
-\1f
-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, const
- 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 2^(N-1) 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.
-
-\1f
-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, const 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);
-
-\1f
-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 (const mpz_t OP)
- -- Function: int mpz_fits_slong_p (const mpz_t OP)
- -- Function: int mpz_fits_uint_p (const mpz_t OP)
- -- Function: int mpz_fits_sint_p (const mpz_t OP)
- -- Function: int mpz_fits_ushort_p (const mpz_t OP)
- -- Function: int mpz_fits_sshort_p (const 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 (const mpz_t OP)
- -- Macro: int mpz_even_p (const 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 (const 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.)
-
-\1f
-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 an obsolete function. Do not use it.*
-
- -- 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 (const 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 (const mpz_t OP)
- Return the size of OP measured in number of limbs. If OP is zero,
- the returned value will be zero.
-
- -- Function: const mp_limb_t * mpz_limbs_read (const mpz_t X)
- Return a pointer to the limb array representing the absolute value
- of X. The size of the array is 'mpz_size(X)'. Intended for read
- access only.
-
- -- Function: mp_limb_t * mpz_limbs_write (mpz_t X, mp_size_t N)
- -- Function: mp_limb_t * mpz_limbs_modify (mpz_t X, mp_size_t N)
- Return a pointer to the limb array, intended for write access. The
- array is reallocated as needed, to make room for N limbs. Requires
- N > 0. The 'mpz_limbs_modify' function returns an array that holds
- the old absolute value of X, while 'mpz_limbs_write' may destroy
- the old value and return an array with unspecified contents.
-
- -- Function: void mpz_limbs_finish (mpz_t X, mp_size_t S)
- Updates the internal size field of X. Used after writing to the
- limb array pointer returned by 'mpz_limbs_write' or
- 'mpz_limbs_modify' is completed. The array should contain abs(S)
- valid limbs, representing the new absolute value for X, and the
- sign of X is taken from the sign of S. This function never
- reallocates X, so the limb pointer remains valid.
-
- void foo (mpz_t x)
- {
- mp_size_t n, i;
- mp_limb_t *xp;
-
- n = mpz_size (x);
- xp = mpz_limbs_modify (x, 2*n);
- for (i = 0; i < n; i++)
- xp[n+i] = xp[n-1-i];
- mpz_limbs_finish (x, mpz_sgn (x) < 0 ? - 2*n : 2*n);
- }
-
- -- Function: mpz_srcptr mpz_roinit_n (mpz_t X, const mp_limb_t *XP,
- mp_size_t XS)
- Special initialization of X, using the given limb array and size.
- X should be treated as read-only: it can be passed safely as input
- to any mpz function, but not as an output. The array XP must point
- to at least a readable limb, its size is abs(XS), and the sign of X
- is the sign of XS. For convenience, the function returns X, but
- cast to a const pointer type.
-
- void foo (mpz_t x)
- {
- static const mp_limb_t y[3] = { 0x1, 0x2, 0x3 };
- mpz_t tmp;
- mpz_add (x, x, mpz_roinit_n (tmp, y, 3));
- }
-
- -- Macro: mpz_t MPZ_ROINIT_N (mp_limb_t *XP, mp_size_t XS)
- This macro expands to an initializer which can be assigned to an
- mpz_t variable. The limb array XP must point to at least a
- readable limb, moreover, unlike the 'mpz_roinit_n' function, the
- array must be normalized: if XS is non-zero, then 'XP[abs(XS)-1]'
- must be non-zero. Intended primarily for constant values. Using
- it for non-constant values requires a C compiler supporting C99.
-
- void foo (mpz_t x)
- {
- static const mp_limb_t ya[3] = { 0x1, 0x2, 0x3 };
- static const mpz_t y = MPZ_ROINIT_N ((mp_limb_t *) ya, 3);
-
- mpz_add (x, x, y);
- }
-
-\1f
-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 form 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::
-
-\1f
-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, const mpq_t OP)
- -- Function: void mpq_set_z (mpq_t ROP, const 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, const 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.
-
-\1f
-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 (const mpq_t OP)
- Convert OP to a 'double', truncating if necessary (i.e. 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, const 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, const mpq_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. The string will be of the
- form 'num/den', or if the denominator is 1 then just 'num'.
-
- 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 (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.
-
-\1f
-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, const mpq_t ADDEND1, const mpq_t
- ADDEND2)
- Set SUM to ADDEND1 + ADDEND2.
-
- -- Function: void mpq_sub (mpq_t DIFFERENCE, const mpq_t MINUEND, const
- mpq_t SUBTRAHEND)
- Set DIFFERENCE to MINUEND - SUBTRAHEND.
-
- -- Function: void mpq_mul (mpq_t PRODUCT, const mpq_t MULTIPLIER, const
- mpq_t MULTIPLICAND)
- Set PRODUCT to MULTIPLIER times MULTIPLICAND.
-
- -- Function: void mpq_mul_2exp (mpq_t ROP, const mpq_t OP1, mp_bitcnt_t
- OP2)
- Set ROP to OP1 times 2 raised to OP2.
-
- -- Function: void mpq_div (mpq_t QUOTIENT, const mpq_t DIVIDEND, const
- mpq_t DIVISOR)
- Set QUOTIENT to DIVIDEND/DIVISOR.
-
- -- Function: void mpq_div_2exp (mpq_t ROP, const 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, const mpq_t OPERAND)
- Set NEGATED_OPERAND to -OPERAND.
-
- -- Function: void mpq_abs (mpq_t ROP, const mpq_t OP)
- Set ROP to the absolute value of OP.
-
- -- Function: void mpq_inv (mpq_t INVERTED_NUMBER, const mpq_t NUMBER)
- Set INVERTED_NUMBER to 1/NUMBER. If the new denominator is zero,
- this routine will divide by zero.
-
-\1f
-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 (const mpq_t OP1, const mpq_t OP2)
- -- Function: int mpq_cmp_z (const mpq_t OP1, const mpz_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 (const mpq_t OP1, unsigned long int NUM2,
- unsigned long int DEN2)
- -- Macro: int mpq_cmp_si (const 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 (const 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
- argument multiple times.
-
- -- Function: int mpq_equal (const mpq_t OP1, const 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.
-
-\1f
-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 (const mpq_t OP)
- -- Macro: mpz_t mpq_denref (const 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, const mpq_t RATIONAL)
- -- Function: void mpq_get_den (mpz_t DENOMINATOR, const mpq_t RATIONAL)
- -- Function: void mpq_set_num (mpq_t RATIONAL, const mpz_t NUMERATOR)
- -- Function: void mpq_set_den (mpq_t RATIONAL, const 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.
-
-\1f
-File: gmp.info, Node: I/O of Rationals, Prev: Applying Integer Functions, Up: Rational Number Functions
-
-6.6 Input and Output Functions
-==============================
-
-Functions that perform input from a stdio stream, and functions that
-output to a stdio stream, of 'mpq' numbers. 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.
-
- See also *note Formatted Output:: and *note Formatted Input::.
-
- -- Function: size_t mpq_out_str (FILE *STREAM, int BASE, const mpq_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.
- Output is in the form 'num/den' or if the denominator is 1 then
- just 'num'.
-
- 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 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 62, or can be 0 in which case the
- leading characters of the string determine the base, '0x' or '0X'
- for hexadecimal, '0b' and '0B' for binary, '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.
-
-\1f
-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, in
-practice only limited by available memory. Each variable has its own
-precision, and that can be increased or decreased at any time. This
-selectable precision is a minimum value, GMP rounds it up to a whole
-limb.
-
- The accuracy of a calculation is determined by the priorly set
-precision of the destination variable and the numeric values of the
-input variables. Input variables' set precisions do not affect
-calculations (except indirectly as their values might have been affected
-when they were assigned).
-
- The exponent of each float has 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 much
-greater. Note however that '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 track of 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 variable's
-selected precision is high. This is a performance optimization; it does
-not affect the numeric results.
-
- Internally, GMP sometimes calculates with higher precision than that
-of the destination variable in order to limit errors. Final results are
-always truncated to the destination variable's precision.
-
- The mantissa is stored in binary. 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.)
-
- The '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.
-
- 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.
-
- New projects should consider using the GMP extension library MPFR
-(<http://mpfr.org>) instead. MPFR provides well-defined precision and
-accurate rounding, and thereby naturally extends IEEE P754.
-
-* Menu:
-
-* Initializing Floats::
-* Assigning Floats::
-* Simultaneous Float Init & Assign::
-* Converting Floats::
-* Float Arithmetic::
-* Float Comparison::
-* I/O of Floats::
-* Miscellaneous Float Functions::
-
-\1f
-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 (const 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.
-
-\1f
-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, const 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, const mpz_t OP)
- -- Function: void mpf_set_q (mpf_t ROP, const mpq_t OP)
- Set the value of ROP from OP.
-
- -- Function: int mpf_set_str (mpf_t ROP, const 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.
-
-\1f
-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, const 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, const 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'.
-
-\1f
-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 (const mpf_t OP)
- Convert OP to a 'double', truncating if necessary (i.e. 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, const mpf_t
- OP)
- Convert OP to a 'double', truncating if necessary (i.e. 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
- (libc)Normalization Functions::).
-
- -- Function: long mpf_get_si (const mpf_t OP)
- -- Function: unsigned long mpf_get_ui (const 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, const 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.
-
-\1f
-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, const mpf_t OP1, const mpf_t OP2)
- -- Function: void mpf_add_ui (mpf_t ROP, const mpf_t OP1, unsigned long
- int OP2)
- Set ROP to OP1 + OP2.
-
- -- Function: void mpf_sub (mpf_t ROP, const mpf_t OP1, const mpf_t OP2)
- -- Function: void mpf_ui_sub (mpf_t ROP, unsigned long int OP1, const
- mpf_t OP2)
- -- Function: void mpf_sub_ui (mpf_t ROP, const mpf_t OP1, unsigned long
- int OP2)
- Set ROP to OP1 - OP2.
-
- -- Function: void mpf_mul (mpf_t ROP, const mpf_t OP1, const mpf_t OP2)
- -- Function: void mpf_mul_ui (mpf_t ROP, const 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, const mpf_t OP1, const mpf_t OP2)
- -- Function: void mpf_ui_div (mpf_t ROP, unsigned long int OP1, const
- mpf_t OP2)
- -- Function: void mpf_div_ui (mpf_t ROP, const mpf_t OP1, unsigned long
- int OP2)
- Set ROP to OP1/OP2.
-
- -- Function: void mpf_sqrt (mpf_t ROP, const 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, const mpf_t OP1, unsigned long
- int OP2)
- Set ROP to OP1 raised to the power OP2.
-
- -- Function: void mpf_neg (mpf_t ROP, const mpf_t OP)
- Set ROP to -OP.
-
- -- Function: void mpf_abs (mpf_t ROP, const mpf_t OP)
- Set ROP to the absolute value of OP.
-
- -- Function: void mpf_mul_2exp (mpf_t ROP, const mpf_t OP1, mp_bitcnt_t
- OP2)
- Set ROP to OP1 times 2 raised to OP2.
-
- -- Function: void mpf_div_2exp (mpf_t ROP, const mpf_t OP1, mp_bitcnt_t
- OP2)
- Set ROP to OP1 divided by 2 raised to OP2.
-
-\1f
-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 (const mpf_t OP1, const mpf_t OP2)
- -- Function: int mpf_cmp_z (const mpf_t OP1, const mpz_t OP2)
- -- Function: int mpf_cmp_d (const mpf_t OP1, double OP2)
- -- Function: int mpf_cmp_ui (const mpf_t OP1, unsigned long int OP2)
- -- Function: int mpf_cmp_si (const 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 (const mpf_t OP1, const mpf_t OP2, mp_bitcnt_t
- op3)
- *This function is mathematically ill-defined and should not be
- used.*
-
- Return non-zero if the first OP3 bits of OP1 and OP2 are equal,
- zero otherwise. Note that numbers like e.g., 256 (binary
- 100000000) and 255 (binary 11111111) will never be equal by this
- function's measure, and furthermore that 0 will only be equal to
- itself.
-
- -- Function: void mpf_reldiff (mpf_t ROP, const mpf_t OP1, const 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 (const 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
- argument multiple times.
-
-\1f
-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, of 'mpf' numbers. 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.
-
- See also *note Formatted Output:: and *note Formatted Input::.
-
- -- Function: size_t mpf_out_str (FILE *STREAM, int BASE, size_t
- N_DIGITS, const 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.
-
-\1f
-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, const mpf_t OP)
- -- Function: void mpf_floor (mpf_t ROP, const mpf_t OP)
- -- Function: void mpf_trunc (mpf_t ROP, const 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 (const mpf_t OP)
- Return non-zero if OP is an integer.
-
- -- Function: int mpf_fits_ulong_p (const mpf_t OP)
- -- Function: int mpf_fits_slong_p (const mpf_t OP)
- -- Function: int mpf_fits_uint_p (const mpf_t OP)
- -- Function: int mpf_fits_sint_p (const mpf_t OP)
- -- Function: int mpf_fits_ushort_p (const mpf_t OP)
- -- Function: int mpf_fits_sshort_p (const 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 or less if
- the precision of ROP is smaller.
-
- 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.
-
-\1f
-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: mp_limb_t 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}.
- This is equivalent to calling 'mpn_sub_n' with a N-limb zero
- minuend and passing {SP, N} as subtrahend. Return borrow, either 0
- or 1.
-
- -- 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 2N 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. {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.
-
- -- 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. {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 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.]
-
- -- Function: void mpn_divexact_1 (mp_limb_t * RP, const mp_limb_t * SP,
- mp_size_t N, mp_limb_t D)
- Divide {SP, N} by D, expecting it to divide exactly, and writing
- the result to {RP, N}. If D doesn't divide exactly, the value
- written to {RP, N} is undefined. The areas at RP and SP have to be
- identical or completely separate, not partially overlapping.
-
- -- 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 (const 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: int mpn_zero_p (const mp_limb_t *SP, mp_size_t N)
- Test {SP, N} and return 1 if the operand is zero, 0 otherwise.
-
- -- 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.
-
- It is required that XN >= YN > 0, the most significant limb of {YP,
- YN} must be non-zero, and at least one of the two operands must be
- odd. 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 *UP, mp_size_t UN, mp_limb_t *VP,
- mp_size_t VN)
- Let U be defined by {UP, UN} and let V be defined by {VP, VN}.
-
- 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 UN >= VN > 0, and the
- most significant limb of {VP, VN} must be non-zero.
-
- 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 area at GP
- should have room for VN limbs and the area at SP should have room
- for VN+1 limbs.
-
- Both source operands are destroyed.
-
- Compatibility notes: GMP 4.3.0 and 4.3.1 defined S less strictly.
- Earlier as well as later GMP releases define S as described here.
- GMP releases before GMP 4.3.0 required additional space for both
- input and output areas. More precisely, the areas {UP, UN+1} and
- {VP, VN+1} were destroyed (i.e. the operands plus an extra limb
- past the end of each), and the areas pointed to by GP and SP should
- each have room for UN+1 limbs.
-
- -- 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
- 'mpn_perfect_square_p'.
-
- -- Function: size_t mpn_sizeinbase (const mp_limb_t *XP, mp_size_t N,
- int BASE)
- Return the size of {XP,N} measured in number of digits in the given
- BASE. BASE can vary from 2 to 62. Requires N > 0 and XP[N-1] > 0.
- The result will be either exact or 1 too big. If BASE is a power
- of 2, the result is always exact.
-
- -- 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 input byte and STR[STRSIZE-1] is the
- least significant input byte. 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 converted value is {RP,RN} where RN is the return value. If
- the most significant input byte STR[0] is non-zero, then RP[RN-1]
- will be non-zero, else RP[RN-1] and some number of subsequent limbs
- may be zero.
-
- The area at RP has to have space for the largest possible number
- with STRSIZE digits in the chosen base, plus one extra limb.
-
- The input must have at least one byte, 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. The most
- significant limb of the input {S1P, N} must be non-zero.
-
- -- 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 Low-level functions for cryptography
-========================================
-
-The functions prefixed with 'mpn_sec_' and 'mpn_cnd_' are designed to
-perform the exact same low-level operations 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. These functions are intended for
-cryptographic purposes, where resilience to side-channel attacks is
-desired.
-
- These functions are less efficient than their "leaky" counterparts;
-their performance for operands of the sizes typically used for
-cryptographic applications is between 15% and 100% worse. For larger
-operands, these functions might be inadequate, since they rely on
-asymptotically elementary algorithms.
-
- These functions do not make any explicit allocations. Those of these
-functions that need scratch space accept a scratch space operand. This
-convention allows callers to keep sensitive data in designated memory
-areas. Note however that compilers may choose to spill scalar values
-used within these functions to their stack frame and that such scalars
-may contain sensitive data.
-
- In addition to these specially crafted functions, the following 'mpn'
-functions are naturally side-channel resistant: 'mpn_add_n',
-'mpn_sub_n', 'mpn_lshift', 'mpn_rshift', 'mpn_zero', 'mpn_copyi',
-'mpn_copyd', 'mpn_com', and the logical function ('mpn_and_n', etc).
-
- There are some exceptions from the side-channel resilience: (1) Some
-assembly implementations of 'mpn_lshift' identify shift-by-one as a
-special case. This is a problem iff the shift count is a function of
-sensitive data. (2) Alpha ev6 and Pentium4 using 64-bit limbs have
-leaky 'mpn_add_n' and 'mpn_sub_n'. (3) Alpha ev6 has a leaky
-'mpn_mul_1' which also makes 'mpn_sec_mul' on those systems unsafe.
-
- -- Function: mp_limb_t mpn_cnd_add_n (mp_limb_t CND, mp_limb_t *RP,
- const mp_limb_t *S1P, const mp_limb_t *S2P, mp_size_t N)
- -- Function: mp_limb_t mpn_cnd_sub_n (mp_limb_t CND, mp_limb_t *RP,
- const mp_limb_t *S1P, const mp_limb_t *S2P, mp_size_t N)
- These functions do conditional addition and subtraction. If CND is
- non-zero, they produce the same result as a regular 'mpn_add_n' or
- 'mpn_sub_n', and if CND is zero, they copy {S1P,N} to the result
- area and return zero. The functions are designed to have timing
- and memory access patterns depending only on size and location of
- the data areas, but independent of the condition CND. Like for
- 'mpn_add_n' and 'mpn_sub_n', on most machines, the timing will also
- be independent of the actual limb values.
-
- -- Function: mp_limb_t mpn_sec_add_1 (mp_limb_t *RP, const mp_limb_t
- *AP, mp_size_t N, mp_limb_t B, mp_limb_t *TP)
- -- Function: mp_limb_t mpn_sec_sub_1 (mp_limb_t *RP, const mp_limb_t
- *AP, mp_size_t N, mp_limb_t B, mp_limb_t *TP)
- Set R to A + B or A - B, respectively, where R = {RP,N}, A =
- {AP,N}, and B is a single limb. Returns carry.
-
- These functions take O(N) time, unlike the leaky functions
- 'mpn_add_1' which are O(1) on average. They require scratch space
- of 'mpn_sec_add_1_itch(N)' and 'mpn_sec_sub_1_itch(N)' limbs,
- respectively, to be passed in the TP parameter. The scratch space
- requirements are guaranteed to be at most N limbs, and increase
- monotonously in the operand size.
-
- -- Function: void mpn_cnd_swap (mp_limb_t CND, volatile mp_limb_t *AP,
- volatile mp_limb_t *BP, mp_size_t N)
- If CND is non-zero, swaps the contents of the areas {AP,N} and
- {BP,N}. Otherwise, the areas are left unmodified. Implemented
- using logical operations on the limbs, with the same memory
- accesses independent of the value of CND.
-
- -- Function: void mpn_sec_mul (mp_limb_t *RP, const mp_limb_t *AP,
- mp_size_t AN, const mp_limb_t *BP, mp_size_t BN, mp_limb_t
- *TP)
- -- Function: mp_size_t mpn_sec_mul_itch (mp_size_t AN, mp_size_t BN)
- Set R to A * B, where A = {AP,AN}, B = {BP,BN}, and R = {RP,AN+BN}.
-
- It is required that AN >= BN > 0.
-
- No overlapping between R and the input operands is allowed. For A
- = B, use 'mpn_sec_sqr' for optimal performance.
-
- This function requires scratch space of 'mpn_sec_mul_itch(AN, BN)'
- limbs to be passed in the TP parameter. The scratch space
- requirements are guaranteed to increase monotonously in the operand
- sizes.
-
- -- Function: void mpn_sec_sqr (mp_limb_t *RP, const mp_limb_t *AP,
- mp_size_t AN, mp_limb_t *TP)
- -- Function: mp_size_t mpn_sec_sqr_itch (mp_size_t AN)
- Set R to A^2, where A = {AP,AN}, and R = {RP,2AN}.
-
- It is required that AN > 0.
-
- No overlapping between R and the input operands is allowed.
-
- This function requires scratch space of 'mpn_sec_sqr_itch(AN)'
- limbs to be passed in the TP parameter. The scratch space
- requirements are guaranteed to increase monotonously in the operand
- size.
-
- -- Function: void mpn_sec_powm (mp_limb_t *RP, const mp_limb_t *BP,
- mp_size_t BN, const mp_limb_t *EP, mp_bitcnt_t ENB, const
- mp_limb_t *MP, mp_size_t N, mp_limb_t *TP)
- -- Function: mp_size_t mpn_sec_powm_itch (mp_size_t BN, mp_bitcnt_t
- ENB, size_t N)
- Set R to (B raised to E) modulo M, where R = {RP,N}, M = {MP,N},
- and E = {EP,ceil(ENB / 'GMP\_NUMB\_BITS')}.
-
- It is required that B > 0, that M > 0 is odd, and that E < 2^ENB,
- with ENB > 0.
-
- No overlapping between R and the input operands is allowed.
-
- This function requires scratch space of 'mpn_sec_powm_itch(BN, ENB,
- N)' limbs to be passed in the TP parameter. The scratch space
- requirements are guaranteed to increase monotonously in the operand
- sizes.
-
- -- Function: void mpn_sec_tabselect (mp_limb_t *RP, const mp_limb_t
- *TAB, mp_size_t N, mp_size_t NENTS, mp_size_t WHICH)
- Select entry WHICH from table TAB, which has NENTS entries, each N
- limbs. Store the selected entry at RP.
-
- This function reads the entire table to avoid side-channel
- information leaks.
-
- -- Function: mp_limb_t mpn_sec_div_qr (mp_limb_t *QP, mp_limb_t *NP,
- mp_size_t NN, const mp_limb_t *DP, mp_size_t DN, mp_limb_t
- *TP)
- -- Function: mp_size_t mpn_sec_div_qr_itch (mp_size_t NN, mp_size_t DN)
-
- Set Q to the truncated quotient N / D and R to N modulo D, where N
- = {NP,NN}, D = {DP,DN}, Q's most significant limb is the function
- return value and the remaining limbs are {QP,NN-DN}, and R =
- {NP,DN}.
-
- It is required that NN >= DN >= 1, and that DP[DN-1] != 0. This
- does not imply that N >= D since N might be zero-padded.
-
- Note the overlapping between N and R. No other operand overlapping
- is allowed. The entire space occupied by N is overwritten.
-
- This function requires scratch space of 'mpn_sec_div_qr_itch(NN,
- DN)' limbs to be passed in the TP parameter.
-
- -- Function: void mpn_sec_div_r (mp_limb_t *NP, mp_size_t NN, const
- mp_limb_t *DP, mp_size_t DN, mp_limb_t *TP)
- -- Function: mp_size_t mpn_sec_div_r_itch (mp_size_t NN, mp_size_t DN)
-
- Set R to N modulo D, where N = {NP,NN}, D = {DP,DN}, and R =
- {NP,DN}.
-
- It is required that NN >= DN >= 1, and that DP[DN-1] != 0. This
- does not imply that N >= D since N might be zero-padded.
-
- Note the overlapping between N and R. No other operand overlapping
- is allowed. The entire space occupied by N is overwritten.
-
- This function requires scratch space of 'mpn_sec_div_r_itch(NN,
- DN)' limbs to be passed in the TP parameter.
-
- -- Function: int mpn_sec_invert (mp_limb_t *RP, mp_limb_t *AP, const
- mp_limb_t *MP, mp_size_t N, mp_bitcnt_t NBCNT, mp_limb_t *TP)
- -- Function: mp_size_t mpn_sec_invert_itch (mp_size_t N)
- Set R to the inverse of A modulo M, where R = {RP,N}, A = {AP,N},
- and M = {MP,N}. *This function's interface is preliminary.*
-
- If an inverse exists, return 1, otherwise return 0 and leave R
- undefined. In either case, the input A is destroyed.
-
- It is required that M is odd, and that NBCNT >= ceil(\log(A+1)) +
- ceil(\log(M+1)). A safe choice is NBCNT = 2 * N * GMP_NUMB_BITS,
- but a smaller value might improve performance if M or A are known
- to have leading zero bits.
-
- This function requires scratch space of 'mpn_sec_invert_itch(N)'
- limbs to be passed in the TP parameter.
-
-
-8.2 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.
-
-\1f
-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::
-
-\1f
-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, const
- 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, i.e.
- 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.
-
-\1f
-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, const 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.
-
-\1f
-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, i.e. 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.
-
-\1f
-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::
-
-\1f
-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 its 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. Without any dot and thus no
-precision field, a precision value of 6 will be used. Note that these
-rules mean that '%Ff', '%.Ff', and '%.0Ff' will all be different.
-
- 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.
-
-\1f
-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.
-
-\1f
-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 '<gmp.h>'.
-
- -- Function: ostream& operator<< (ostream& STREAM, const 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, const 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, const 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::.
-
-\1f
-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::
-
-\1f
-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 float
- G
- 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.
-
-\1f
-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'.
-
-\1f
-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 '<gmp.h>'.
-
- -- 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::.
-
-\1f
-File: gmp.info, Node: C++ Class Interface, Next: Custom Allocation, 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.
-
- *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::
-
-\1f
-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 <gmpxx.h>
-
- 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.
-
-\1f
-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: 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, although conversions from 'mpq_class' and 'mpf_class'
- are 'explicit'. Any necessary conversion follows the corresponding
- C function, for example 'double' follows 'mpz_set_d' (*note
- Assigning Integers::).
-
- -- Function: explicit mpz_class::mpz_class (const 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: explicit mpz_class::mpz_class (const char *S, int BASE =
- 0)
- -- Function: explicit 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 (const char *STR)
- With C++11 compilers, integers can be constructed with the syntax
- '123_mpz' which is equivalent to 'mpz_class("123")'.
-
- -- 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 OP)
- -- 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)
-
- -- Function: mpz_class gcd (mpz_class OP1, mpz_class OP2)
- -- Function: mpz_class lcm (mpz_class OP1, mpz_class OP2)
- -- Function: mpz_class mpz_class::factorial (type OP)
- -- Function: mpz_class factorial (mpz_class OP)
- -- Function: mpz_class mpz_class::primorial (type OP)
- -- Function: mpz_class primorial (mpz_class OP)
- -- Function: mpz_class mpz_class::fibonacci (type OP)
- -- Function: mpz_class fibonacci (mpz_class OP)
-
- -- Function: void mpz_class::swap (mpz_class& OP)
- -- Function: void swap (mpz_class& OP1, mpz_class& OP2)
- These functions provide a C++ class interface to the corresponding
- GMP C routines. Calling 'factorial' or 'primorial' on a negative
- number is undefined.
-
- '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'.
-
-\1f
-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: mpq_class::mpq_class (type OP)
- -- Function: mpq_class::mpq_class (integer NUM, integer DEN)
- Construct an 'mpq_class'. The initial value can be a single value
- of any type (conversion from 'mpf_class' is 'explicit'), 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: explicit mpq_class::mpq_class (const 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: explicit mpq_class::mpq_class (const char *S, int BASE =
- 0)
- -- Function: explicit 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: mpq_class operator"" _mpq (const char *STR)
- With C++11 compilers, integral rationals can be constructed with
- the syntax '123_mpq' which is equivalent to 'mpq_class(123_mpz)'.
- Other rationals can be built as '-1_mpq/2' or '0xb_mpq/123456_mpz'.
-
- -- 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)
-
- -- Function: void mpq_class::swap (mpq_class& OP)
- -- Function: void swap (mpq_class& OP1, mpq_class& OP2)
- 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.
-
-\1f
-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, mp_bitcnt_t 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: explicit mpf_class::mpf_class (const mpf_t F)
- -- Function: mpf_class::mpf_class (const mpf_t F, mp_bitcnt_t PREC)
- Construct an 'mpf_class' from an 'mpf_t'. The value in F is copied
- into the new 'mpf_class', there won't be any permanent association
- between it and F.
-
- If PREC is given, the initial precision is that value, in bits. If
- PREC is not given, then the initial precision is that of F.
-
- -- Function: explicit mpf_class::mpf_class (const char *S)
- -- Function: mpf_class::mpf_class (const char *S, mp_bitcnt_t PREC, int
- BASE = 0)
- -- Function: explicit mpf_class::mpf_class (const string& S)
- -- Function: mpf_class::mpf_class (const string& S, mp_bitcnt_t 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 operator"" _mpf (const char *STR)
- With C++11 compilers, floats can be constructed with the syntax
- '1.23e-1_mpf' which is equivalent to 'mpf_class("1.23e-1")'.
-
- -- 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: void mpf_class::swap (mpf_class& OP)
- -- Function: void swap (mpf_class& OP1, mpf_class& OP2)
- -- 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.
-
-\1f
-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 (mp_bitcnt_t 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 (mp_bitcnt_t 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
-
-\1f
-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 <gmp-bugs@gmplib.org>.
-
-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 <class T>
- 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 <class T>
- void fun (T f, T g)
- {
- fun2 (f, f+g); // Bad
- }
-
- template <class T>
- void fun (T f, T g)
- {
- fun2 (f, T(f+g)); // Good
- }
-
-C++11
- C++11 provides several new ways in which types can be inferred:
- 'auto', 'decltype', etc. While they can be very convenient, they
- don't mix well with expression templates. In this example, the
- addition is performed twice, as if we had defined 'sum' as a macro.
-
- mpz_class z = 33;
- auto sum = z + z;
- mpz_class prod = sum * sum;
-
- This other example may crash, though some compilers might make it
- look like it is working, because the expression 'z+z' goes out of
- scope before it is evaluated.
-
- mpz_class z = 33;
- auto sum = z + z + z;
- mpz_class prod = sum * 2;
-
- It is thus strongly recommended to avoid 'auto' anywhere a GMP C++
- expression may appear.
-
-\1f
-File: gmp.info, Node: Custom Allocation, Next: Language Bindings, Prev: C++ Class Interface, Up: Top
-
-13 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.
-
- -- 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 REALLOCATE_FUNCTION parameter OLD_SIZE and the FREE_FUNCTION
-parameter SIZE are passed for convenience, but of course they can be
-ignored if not needed by an implementation. 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);
-
-\1f
-File: gmp.info, Node: Language Bindings, Next: Algorithms, Prev: Custom Allocation, Up: Top
-
-14 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 <https://www-sop.inria.fr/saga/logiciels/ALP/>
- Linear algebra and polynomials using templates.
- * CLN <https://www.ginac.de/CLN/>
- High level classes for arithmetic.
- * Linbox <http://www.linalg.org/>
- Sparse vectors and matrices.
- * NTL <http://www.shoup.net/ntl/>
- A C++ number theory library.
-
-Eiffel
- * Eiffelroom <http://www.eiffelroom.org/node/442>
-
-Haskell
- * Glasgow Haskell Compiler <https://www.haskell.org/ghc/>
-
-Java
- * Kaffe <https://github.com/kaffe/kaffe>
-
-Lisp
- * GNU Common Lisp <https://www.gnu.org/software/gcl/gcl.html>
- * Librep <http://librep.sourceforge.net/>
- * XEmacs (21.5.18 beta and up) <https://www.xemacs.org>
- Optional big integers, rationals and floats using GMP.
-
-ML
- * MLton compiler <http://mlton.org/>
-
-Objective Caml
- * MLGMP <https://opam.ocaml.org/packages/mlgmp/>
- * Numerix <http://pauillac.inria.fr/~quercia/>
- Optionally using GMP.
-
-Oz
- * Mozart <https://mozart.github.io/>
-
-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 <https://www.cpan.org/>
- Compatible with Math::BigInt, but not as many functions as the
- GMP module above.
- * Math::BigInt::GMP <https://www.cpan.org/>
- Plug Math::GMP into normal Math::BigInt operations.
-
-Pike
- * pikempz module in the standard distribution,
- <https://pike.lysator.liu.se/>
-
-Prolog
- * SWI Prolog <http://www.swi-prolog.org/>
- Arbitrary precision floats.
-
-Python
- * GMPY <https://code.google.com/p/gmpy/>
-
-Ruby
- * <https://rubygems.org/gems/gmp>
-
-Scheme
- * GNU Guile <https://www.gnu.org/software/guile/guile.html>
- * RScheme <https://www.rscheme.org/>
- * STklos <http://www.stklos.net/>
-
-Smalltalk
- * GNU Smalltalk <http://smalltalk.gnu.org/>
-
-Other
- * Axiom <https://savannah.nongnu.org/projects/axiom>
- Computer algebra using GCL.
- * DrGenius <http://drgenius.seul.org/>
- Geometry system and mathematical programming language.
- * GiNaC <httsp://www.ginac.de/>
- C++ computer algebra using CLN.
- * GOO <https://www.eecs.berkeley.edu/~jrb/goo/>
- Dynamic object oriented language.
- * Maxima <https://www.ma.utexas.edu/users/wfs/maxima.html>
- Macsyma computer algebra using GCL.
- * Regina <http://regina.sourceforge.net/>
- Topological calculator.
- * Yacas <http://yacas.sourceforge.net>
- Yet another computer algebra system.
-
-\1f
-File: gmp.info, Node: Algorithms, Next: Internals, Prev: Language Bindings, Up: Top
-
-15 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::
-
-\1f
-File: gmp.info, Node: Multiplication Algorithms, Next: Division Algorithms, Prev: Algorithms, Up: Algorithms
-
-15.1 Multiplication
-===================
-
-NxN limb multiplications and squares are done using one of seven
-algorithms, as the size N increases.
-
- Algorithm Threshold
- Basecase (none)
- Karatsuba 'MUL_TOOM22_THRESHOLD'
- Toom-3 'MUL_TOOM33_THRESHOLD'
- Toom-4 'MUL_TOOM44_THRESHOLD'
- Toom-6.5 'MUL_TOOM6H_THRESHOLD'
- Toom-8.5 'MUL_TOOM8H_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::
-* Higher degree Toom'n'half::
-* FFT Multiplication::
-* Other Multiplication::
-* Unbalanced Multiplication::
-
-\1f
-File: gmp.info, Node: Basecase Multiplication, Next: Karatsuba Multiplication, Prev: Multiplication Algorithms, Up: Multiplication Algorithms
-
-15.1.1 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.
-
-\1f
-File: gmp.info, Node: Karatsuba Multiplication, Next: Toom 3-Way Multiplication, Prev: Basecase Multiplication, Up: Multiplication Algorithms
-
-15.1.2 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, i.e. 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.
-
-\1f
-File: gmp.info, Node: Toom 3-Way Multiplication, Next: Toom 4-Way Multiplication, Prev: Karatsuba Multiplication, Up: Multiplication Algorithms
-
-15.1.3 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, i.e. 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 'toom_interpolate_5pts' 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.
-
-\1f
-File: gmp.info, Node: Toom 4-Way Multiplication, Next: Higher degree Toom'n'half, Prev: Toom 3-Way Multiplication, Up: Multiplication Algorithms
-
-15.1.4 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.
-
-\1f
-File: gmp.info, Node: Higher degree Toom'n'half, Next: FFT Multiplication, Prev: Toom 4-Way Multiplication, Up: Multiplication Algorithms
-
-15.1.5 Higher degree Toom'n'half
---------------------------------
-
-The Toom algorithms described above (*note Toom 3-Way Multiplication::,
-*note Toom 4-Way Multiplication::) generalizes to split into an
-arbitrary number of pieces. In general a split of two equally long
-operands into r pieces leads to evaluations and pointwise
-multiplications done at 2*r-1 points. To fully exploit symmetries it
-would be better to have a multiple of 4 points, that's why for higher
-degree Toom'n'half is used.
-
- Toom'n'half means that the existence of one more piece is considered
-for a single operand. It can be virtual, i.e. zero, or real, when the
-two operand are not exactly balanced. By choosing an even r, Toom-r+1/2
-requires 2r points, a multiple of four.
-
- The quadruplets of points include 0, inf, +1, -1 and +-2^i, +-2^-i .
-Each of them giving shortcuts for the evaluation phase and for some
-steps in the interpolation phase. Further tricks are used to reduce the
-memory footprint of the whole multiplication algorithm to a memory
-buffer equal in size to the result of the product.
-
- Current GMP uses both Toom-6'n'half and Toom-8'n'half.
-
-\1f
-File: gmp.info, Node: FFT Multiplication, Next: Other Multiplication, Prev: Higher degree Toom'n'half, Up: Multiplication Algorithms
-
-15.1.6 FFT Multiplication
--------------------------
-
-At large to very large sizes a Fermat style FFT multiplication is used,
-following Schönhage 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.
-
-\1f
-File: gmp.info, Node: Other Multiplication, Next: Unbalanced Multiplication, Prev: FFT Multiplication, Up: Multiplication Algorithms
-
-15.1.7 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.
-
-\1f
-File: gmp.info, Node: Unbalanced Multiplication, Prev: Other Multiplication, Up: Multiplication Algorithms
-
-15.1.8 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.
-
-\1f
-File: gmp.info, Node: Division Algorithms, Next: Greatest Common Divisor Algorithms, Prev: Multiplication Algorithms, Up: Algorithms
-
-15.2 Division Algorithms
-========================
-
-* Menu:
-
-* Single Limb Division::
-* Basecase Division::
-* Divide and Conquer Division::
-* Block-Wise Barrett Division::
-* Exact Division::
-* Exact Remainder::
-* Small Quotient Division::
-
-\1f
-File: gmp.info, Node: Single Limb Division, Next: Basecase Division, Prev: Division Algorithms, Up: Division Algorithms
-
-15.2.1 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 Möller 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.
-
-\1f
-File: gmp.info, Node: Basecase Division, Next: Divide and Conquer Division, Prev: Single Limb Division, Up: Division Algorithms
-
-15.2.2 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.
-
-\1f
-File: gmp.info, Node: Divide and Conquer Division, Next: Block-Wise Barrett Division, Prev: Basecase Division, Up: Division Algorithms
-
-15.2.3 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.
-
-\1f
-File: gmp.info, Node: Block-Wise Barrett Division, Next: Exact Division, Prev: Divide and Conquer Division, Up: Division Algorithms
-
-15.2.4 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.
-
-\1f
-File: gmp.info, Node: Exact Division, Next: Exact Remainder, Prev: Block-Wise Barrett Division, Up: Division Algorithms
-
-15.2.5 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.
-
+++ /dev/null
-This is gmp.info, produced by makeinfo version 6.7 from gmp.texi.
-
-This manual describes how to install and use the GNU multiple precision
-arithmetic library, version 6.2.1.
-
- Copyright 1991, 1993-2016, 2018-2020 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
-
-\1f
-File: gmp.info, Node: Exact Remainder, Next: Small Quotient Division, Prev: Exact Division, Up: Division Algorithms
-
-15.2.6 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<=r<d and can be viewed as a remainder, but one shifted up by a factor
-of b^n.
-
- Carrying out full subtractions at each stage means the same number of
-cross products must be done as a normal division, but there's still some
-single limb divisions saved. When d is a single limb some
-simplifications arise, providing good speedups on a number of
-processors.
-
- The functions 'mpn_divexact_by3', 'mpn_modexact_1_odd' and the
-internal 'mpn_redc_X' functions differ subtly in how they return r,
-leading to some negations in the above formula, but all are essentially
-the same.
-
- Clearly r is zero when a is a multiple of d, and this leads to
-divisibility or congruence tests which are potentially more efficient
-than a normal division.
-
- The factor of b^n on r can be ignored in a GCD when d is odd, hence
-the use of 'mpn_modexact_1_odd' by 'mpn_gcd_1' and 'mpz_kronecker_ui'
-etc (*note Greatest Common Divisor Algorithms::).
-
- Montgomery's REDC method for modular multiplications uses operands of
-the form of x*b^-n and y*b^-n and on calculating (x*b^-n)*(y*b^-n) uses
-the factor of b^n in the exact remainder to reach a product in the same
-form (x*y)*b^-n (*note Modular Powering Algorithm::).
-
- Notice that r generally gives no useful information about the
-ordinary remainder a mod d since b^n mod d could be anything. If
-however b^n == 1 mod d, then r is the negative of the ordinary
-remainder. This occurs whenever d is a factor of b^n-1, as for example
-with 3 in 'mpn_divexact_by3'. For a 32 or 64 bit limb other such
-factors include 5, 17 and 257, but no particular use has been found for
-this.
-
-\1f
-File: gmp.info, Node: Small Quotient Division, Prev: Exact Remainder, Up: Division Algorithms
-
-15.2.7 Small Quotient Division
-------------------------------
-
-An NxM division where the number of quotient limbs Q=N-M is small can be
-optimized somewhat.
-
- An ordinary basecase division normalizes the divisor by shifting it
-to make the high bit set, shifting the dividend accordingly, and
-shifting the remainder back down at the end of the calculation. This is
-wasteful if only a few quotient limbs are to be formed. Instead a
-division of just the top 2*Q limbs of the dividend by the top Q limbs of
-the divisor can be used to form a trial quotient. This requires only
-those limbs normalized, not the whole of the divisor and dividend.
-
- A multiply and subtract then applies the trial quotient to the M-Q
-unused limbs of the divisor and N-Q dividend limbs (which includes Q
-limbs remaining from the trial quotient division). The starting trial
-quotient can be 1 or 2 too big, but all cases of 2 too big and most
-cases of 1 too big are detected by first comparing the most significant
-limbs that will arise from the subtraction. An addback is done if the
-quotient still turns out to be 1 too big.
-
- This whole procedure is essentially the same as one step of the
-basecase algorithm done in a Q limb base, though with the trial quotient
-test done only with the high limbs, not an entire Q limb "digit"
-product. The correctness of this weaker test can be established by
-following the argument of Knuth section 4.3.1 exercise 20 but with the
-v2*q>b*r+u2 condition appropriately relaxed.
-
-\1f
-File: gmp.info, Node: Greatest Common Divisor Algorithms, Next: Powering Algorithms, Prev: Division Algorithms, Up: Algorithms
-
-15.3 Greatest Common Divisor
-============================
-
-* Menu:
-
-* Binary GCD::
-* Lehmer's Algorithm::
-* Subquadratic GCD::
-* Extended GCD::
-* Jacobi Symbol::
-
-\1f
-File: gmp.info, Node: Binary GCD, Next: Lehmer's Algorithm, Prev: Greatest Common Divisor Algorithms, Up: Greatest Common Divisor Algorithms
-
-15.3.1 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.
-
-\1f
-File: gmp.info, Node: Lehmer's Algorithm, Next: Subquadratic GCD, Prev: Binary GCD, Up: Greatest Common Divisor Algorithms
-
-15.3.2 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 computed 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.
-
-\1f
-File: gmp.info, Node: Subquadratic GCD, Next: Extended GCD, Prev: Lehmer's Algorithm, Up: Greatest Common Divisor Algorithms
-
-15.3.3 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 Schönhage's algorithm and subquadratic integer
-GCD computation" by Möller (*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
-sub-quadratic 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.
-
-\1f
-File: gmp.info, Node: Extended GCD, Next: Jacobi Symbol, Prev: Subquadratic GCD, Up: Greatest Common Divisor Algorithms
-
-15.3.4 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.
-
-\1f
-File: gmp.info, Node: Jacobi Symbol, Prev: Extended GCD, Up: Greatest Common Divisor Algorithms
-
-15.3.5 Jacobi Symbol
---------------------
-
-Jacobi symbol (A/B)
-
- Initially if either operand fits in a single limb, a 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.
-
- For inputs larger than 'GCD_DC_THRESHOLD', 'mpz_jacobi',
-'mpz_legendre' and 'mpz_kronecker' are computed via the HGCD (Half GCD)
-function, as a generalization to Lehmer's algorithm.
-
- Most GCD algorithms reduce a and b by repeatatily computing the
-quotient q = floor(a/b) and iteratively replacing
-
- a, b = b, a - q * b
-
- Different algorithms use different methods for calculating q, but the
-core algorithm is the same if we use *note Lehmer's Algorithm:: or *note
-HGCD: Subquadratic GCD.
-
- At each step it is possible to compute if the reduction inverts the
-Jacobi symbol based on the two least significant bits of A and B. For
-more details see "Efficient computation of the Jacobi symbol" by Möller
-(*note References::).
-
- A small set of bits is thus used to track state
- * current sign of result (1 bit)
-
- * two least significant bits of A and B (4 bits)
-
- * a pointer to which input is currently the denominator (1 bit)
-
- In all the routines sign changes for the result are accumulated using
-fast bit twiddling which avoids conditional jumps.
-
- The final result is calculated after verifying the inputs are coprime
-(GCD = 1) by raising (-1)^e
-
- Much of the HGCD code is shared directly with the HGCD
-implementations, such as the 2x2 matrix calculation, *Note Lehmer's
-Algorithm:: basecase and 'GCD_DC_THRESHOLD'.
-
- The asymptotic running time is O(M(N)*log(N)), where M(N) is the time
-for multiplying two N-limb numbers.
-
-\1f
-File: gmp.info, Node: Powering Algorithms, Next: Root Extraction Algorithms, Prev: Greatest Common Divisor Algorithms, Up: Algorithms
-
-15.4 Powering Algorithms
-========================
-
-* Menu:
-
-* Normal Powering Algorithm::
-* Modular Powering Algorithm::
-
-\1f
-File: gmp.info, Node: Normal Powering Algorithm, Next: Modular Powering Algorithm, Prev: Powering Algorithms, Up: Powering Algorithms
-
-15.4.1 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.
-
-\1f
-File: gmp.info, Node: Modular Powering Algorithm, Prev: Normal Powering Algorithm, Up: Powering Algorithms
-
-15.4.2 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 squarings 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::).
-
-\1f
-File: gmp.info, Node: Root Extraction Algorithms, Next: Radix Conversion Algorithms, Prev: Powering Algorithms, Up: Algorithms
-
-15.5 Root Extraction Algorithms
-===============================
-
-* Menu:
-
-* Square Root Algorithm::
-* Nth Root Algorithm::
-* Perfect Square Algorithm::
-* Perfect Power Algorithm::
-
-\1f
-File: gmp.info, Node: Square Root Algorithm, Next: Nth Root Algorithm, Prev: Root Extraction Algorithms, Up: Root Extraction Algorithms
-
-15.5.1 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.
-
-\1f
-File: gmp.info, Node: Nth Root Algorithm, Next: Perfect Square Algorithm, Prev: Square Root Algorithm, Up: Root Extraction Algorithms
-
-15.5.2 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.
-
-\1f
-File: gmp.info, Node: Perfect Square Algorithm, Next: Perfect Power Algorithm, Prev: Nth Root Algorithm, Up: Root Extraction Algorithms
-
-15.5.3 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 (i.e. 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.
-
-\1f
-File: gmp.info, Node: Perfect Power Algorithm, Prev: Perfect Square Algorithm, Up: Root Extraction Algorithms
-
-15.5.4 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.
-
-\1f
-File: gmp.info, Node: Radix Conversion Algorithms, Next: Other Algorithms, Prev: Root Extraction Algorithms, Up: Algorithms
-
-15.6 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::
-
-\1f
-File: gmp.info, Node: Binary to Radix, Next: Radix to Binary, Prev: Radix Conversion Algorithms, Up: Radix Conversion Algorithms
-
-15.6.1 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.
-
- 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, i.e. 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.
-
-\1f
-File: gmp.info, Node: Radix to Binary, Prev: Binary to Radix, Up: Radix Conversion Algorithms
-
-15.6.2 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).
-
-\1f
-File: gmp.info, Node: Other Algorithms, Next: Assembly Coding, Prev: Radix Conversion Algorithms, Up: Algorithms
-
-15.7 Other Algorithms
-=====================
-
-* Menu:
-
-* Prime Testing Algorithm::
-* Factorial Algorithm::
-* Binomial Coefficients Algorithm::
-* Fibonacci Numbers Algorithm::
-* Lucas Numbers Algorithm::
-* Random Number Algorithms::
-
-\1f
-File: gmp.info, Node: Prime Testing Algorithm, Next: Factorial Algorithm, Prev: Other Algorithms, Up: Other Algorithms
-
-15.7.1 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.
-
-\1f
-File: gmp.info, Node: Factorial Algorithm, Next: Binomial Coefficients Algorithm, Prev: Prime Testing Algorithm, Up: Other Algorithms
-
-15.7.2 Factorial
-----------------
-
-Factorials are calculated by a combination of two algorithms. An idea
-is shared among them: to compute the odd part of the factorial; a final
-step takes account of the power of 2 term, by shifting.
-
- For small n, the odd factor of n! is computed with the simple
-observation that it is equal to the product of all positive odd numbers
-smaller than n times the odd factor of [n/2]!, where [x] is the integer
-part of x, and so on recursively. The procedure can be best illustrated
-with an example,
-
- 23! = (23.21.19.17.15.13.11.9.7.5.3)(11.9.7.5.3)(5.3)2^{19}
-
- Current code collects all the factors in a single list, with a loop
-and no recursion, and compute the product, with no special care for
-repeated chunks.
-
- When n is larger, computation pass trough prime sieving. An helper
-function is used, as suggested by Peter Luschny:
-
- n
- -----
- n! | | L(p,n)
- msf(n) = -------------- = | | p
- [n/2]!^2.2^k p=3
-
- Where p ranges on odd prime numbers. The exponent k is chosen to
-obtain an odd integer number: k is the number of 1 bits in the binary
-representation of [n/2]. The function L(p,n) can be defined as zero
-when p is composite, and, for any prime p, it is computed with:
-
- ---
- \ n
- L(p,n) = / [---] mod 2 <= log (n) .
- --- p^i p
- i>0
-
- With this helper function, we are able to compute the odd part of n!
-using the recursion implied by n!=[n/2]!^2*msf(n)*2^k. The recursion
-stops using the small-n algorithm on some [n/2^i].
-
- Both the above algorithms use binary splitting to compute the product
-of many small factors. At first as many products as possible are
-accumulated in a single register, generating a list of factors that fit
-in a machine word. This list is then split into halves, and the product
-is computed recursively.
-
- 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.
-
-\1f
-File: gmp.info, Node: Binomial Coefficients Algorithm, Next: Fibonacci Numbers Algorithm, Prev: Factorial Algorithm, Up: Other Algorithms
-
-15.7.3 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.
-
-\1f
-File: gmp.info, Node: Fibonacci Numbers Algorithm, Next: Lucas Numbers Algorithm, Prev: Binomial Coefficients Algorithm, Up: Other Algorithms
-
-15.7.4 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.
-
-\1f
-File: gmp.info, Node: Lucas Numbers Algorithm, Next: Random Number Algorithms, Prev: Fibonacci Numbers Algorithm, Up: Other Algorithms
-
-15.7.5 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
-
-\1f
-File: gmp.info, Node: Random Number Algorithms, Prev: Lucas Numbers Algorithm, Up: Other Algorithms
-
-15.7.6 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<=R<N are
-generated by taking values R of ceil(log2(N)) bits each until one
-satisfies R<N. This will normally require only one or two attempts, but
-the attempts are limited in case the generator is somehow degenerate and
-produces only 1 bits or similar.
-
- The Mersenne Twister generator is by Matsumoto and Nishimura (*note
-References::). It has a non-repeating period of 2^19937-1, which is a
-Mersenne prime, hence the name of the generator. The state is 624 words
-of 32-bits each, which is iterated with one XOR and shift for each
-32-bit word generated, making the algorithm very fast. Randomness
-properties are also very good and this is the default algorithm used by
-GMP.
-
- Linear congruential generators are described in many text books, for
-instance Knuth volume 2 (*note References::). With a modulus M and
-parameters A and C, an integer state S is iterated by the formula S <-
-A*S+C mod M. At each step the new state is a linear function of the
-previous, mod M, hence the name of the generator.
-
- In GMP only moduli of the form 2^N are supported, and the current
-implementation is not as well optimized as it could be. Overheads are
-significant when N is small, and when N is large clearly the multiply at
-each step will become slow. This is not a big concern, since the
-Mersenne Twister generator is better in every respect and is therefore
-recommended for all normal applications.
-
- For both generators the current state can be deduced by observing
-enough output and applying some linear algebra (over GF(2) in the case
-of the Mersenne Twister). This generally means raw output is unsuitable
-for cryptographic applications without further hashing or the like.
-
-\1f
-File: gmp.info, Node: Assembly Coding, Prev: Other Algorithms, Up: Algorithms
-
-15.8 Assembly Coding
-====================
-
-The assembly subroutines in GMP are the most significant source of speed
-at small to moderate sizes. At larger sizes algorithm selection becomes
-more important, but of course speedups in low level routines will still
-speed up everything proportionally.
-
- Carry handling and widening multiplies that are important for GMP
-can't be easily expressed in C. GCC 'asm' blocks help a lot and are
-provided in 'longlong.h', but hand coding low level routines invariably
-offers a speedup over generic C by a factor of anything from 2 to 10.
-
-* Menu:
-
-* Assembly Code Organisation::
-* Assembly Basics::
-* Assembly Carry Propagation::
-* Assembly Cache Handling::
-* Assembly Functional Units::
-* Assembly Floating Point::
-* Assembly SIMD Instructions::
-* Assembly Software Pipelining::
-* Assembly Loop Unrolling::
-* Assembly Writing Guide::
-
-\1f
-File: gmp.info, Node: Assembly Code Organisation, Next: Assembly Basics, Prev: Assembly Coding, Up: Assembly Coding
-
-15.8.1 Code Organisation
-------------------------
-
-The various 'mpn' subdirectories contain machine-dependent code, written
-in C or assembly. The 'mpn/generic' subdirectory contains default code,
-used when there's no machine-specific version of a particular file.
-
- Each 'mpn' subdirectory is for an ISA family. Generally 32-bit and
-64-bit variants in a family cannot share code and have separate
-directories. Within a family further subdirectories may exist for CPU
-variants.
-
- In each directory a 'nails' subdirectory may exist, holding code with
-nails support for that CPU variant. A 'NAILS_SUPPORT' directive in each
-file indicates the nails values the code handles. Nails code only
-exists where it's faster, or promises to be faster, than plain code.
-There's no effort put into nails if they're not going to enhance a given
-CPU.
-
-\1f
-File: gmp.info, Node: Assembly Basics, Next: Assembly Carry Propagation, Prev: Assembly Code Organisation, Up: Assembly Coding
-
-15.8.2 Assembly Basics
-----------------------
-
-'mpn_addmul_1' and 'mpn_submul_1' are the most important routines for
-overall GMP performance. All multiplications and divisions come down to
-repeated calls to these. 'mpn_add_n', 'mpn_sub_n', 'mpn_lshift' and
-'mpn_rshift' are next most important.
-
- On some CPUs assembly versions of the internal functions
-'mpn_mul_basecase' and 'mpn_sqr_basecase' give significant speedups,
-mainly through avoiding function call overheads. They can also
-potentially make better use of a wide superscalar processor, as can
-bigger primitives like 'mpn_addmul_2' or 'mpn_addmul_4'.
-
- The restrictions on overlaps between sources and destinations (*note
-Low-level Functions::) are designed to facilitate a variety of
-implementations. For example, knowing 'mpn_add_n' won't have partly
-overlapping sources and destination means reading can be done far ahead
-of writing on superscalar processors, and loops can be vectorized on a
-vector processor, depending on the carry handling.
-
-\1f
-File: gmp.info, Node: Assembly Carry Propagation, Next: Assembly Cache Handling, Prev: Assembly Basics, Up: Assembly Coding
-
-15.8.3 Carry Propagation
-------------------------
-
-The problem that presents most challenges in GMP is propagating carries
-from one limb to the next. In functions like 'mpn_addmul_1' and
-'mpn_add_n', carries are the only dependencies between limb operations.
-
- On processors with carry flags, a straightforward CISC style 'adc' is
-generally best. AMD K6 'mpn_addmul_1' however is an example of an
-unusual set of circumstances where a branch works out better.
-
- On RISC processors generally an add and compare for overflow is used.
-This sort of thing can be seen in 'mpn/generic/aors_n.c'. Some carry
-propagation schemes require 4 instructions, meaning at least 4 cycles
-per limb, but other schemes may use just 1 or 2. On wide superscalar
-processors performance may be completely determined by the number of
-dependent instructions between carry-in and carry-out for each limb.
-
- On vector processors good use can be made of the fact that a carry
-bit only very rarely propagates more than one limb. When adding a
-single bit to a limb, there's only a carry out if that limb was
-'0xFF...FF' which on random data will be only 1 in 2^mp_bits_per_limb.
-'mpn/cray/add_n.c' is an example of this, it adds all limbs in parallel,
-adds one set of carry bits in parallel and then only rarely needs to
-fall through to a loop propagating further carries.
-
- On the x86s, GCC (as of version 2.95.2) doesn't generate particularly
-good code for the RISC style idioms that are necessary to handle carry
-bits in C. Often conditional jumps are generated where 'adc' or 'sbb'
-forms would be better. And so unfortunately almost any loop involving
-carry bits needs to be coded in assembly for best results.
-
-\1f
-File: gmp.info, Node: Assembly Cache Handling, Next: Assembly Functional Units, Prev: Assembly Carry Propagation, Up: Assembly Coding
-
-15.8.4 Cache Handling
----------------------
-
-GMP aims to perform well both on operands that fit entirely in L1 cache
-and those which don't.
-
- Basic routines like 'mpn_add_n' or 'mpn_lshift' are often used on
-large operands, so L2 and main memory performance is important for them.
-'mpn_mul_1' and 'mpn_addmul_1' are mostly used for multiply and square
-basecases, so L1 performance matters most for them, unless assembly
-versions of 'mpn_mul_basecase' and 'mpn_sqr_basecase' exist, in which
-case the remaining uses are mostly for larger operands.
-
- For L2 or main memory operands, memory access times will almost
-certainly be more than the calculation time. The aim therefore is to
-maximize memory throughput, by starting a load of the next cache line
-while processing the contents of the previous one. Clearly this is only
-possible if the chip has a lock-up free cache or some sort of prefetch
-instruction. Most current chips have both these features.
-
- Prefetching sources combines well with loop unrolling, since a
-prefetch can be initiated once per unrolled loop (or more than once if
-the loop covers more than one cache line).
-
- On CPUs without write-allocate caches, prefetching destinations will
-ensure individual stores don't go further down the cache hierarchy,
-limiting bandwidth. Of course for calculations which are slow anyway,
-like 'mpn_divrem_1', write-throughs might be fine.
-
- The distance ahead to prefetch will be determined by memory latency
-versus throughput. The aim of course is to have data arriving
-continuously, at peak throughput. Some CPUs have limits on the number
-of fetches or prefetches in progress.
-
- If a special prefetch instruction doesn't exist then a plain load can
-be used, but in that case care must be taken not to attempt to read past
-the end of an operand, since that might produce a segmentation
-violation.
-
- Some CPUs or systems have hardware that detects sequential memory
-accesses and initiates suitable cache movements automatically, making
-life easy.
-
-\1f
-File: gmp.info, Node: Assembly Functional Units, Next: Assembly Floating Point, Prev: Assembly Cache Handling, Up: Assembly Coding
-
-15.8.5 Functional Units
------------------------
-
-When choosing an approach for an assembly loop, consideration is given
-to what operations can execute simultaneously and what throughput can
-thereby be achieved. In some cases an algorithm can be tweaked to
-accommodate available resources.
-
- Loop control will generally require a counter and pointer updates,
-costing as much as 5 instructions, plus any delays a branch introduces.
-CPU addressing modes might reduce pointer updates, perhaps by allowing
-just one updating pointer and others expressed as offsets from it, or on
-CISC chips with all addressing done with the loop counter as a scaled
-index.
-
- The final loop control cost can be amortised by processing several
-limbs in each iteration (*note Assembly Loop Unrolling::). This at
-least ensures loop control isn't a big fraction the work done.
-
- Memory throughput is always a limit. If perhaps only one load or one
-store can be done per cycle then 3 cycles/limb will the top speed for
-"binary" operations like 'mpn_add_n', and any code achieving that is
-optimal.
-
- Integer resources can be freed up by having the loop counter in a
-float register, or by pressing the float units into use for some
-multiplying, perhaps doing every second limb on the float side (*note
-Assembly Floating Point::).
-
- Float resources can be freed up by doing carry propagation on the
-integer side, or even by doing integer to float conversions in integers
-using bit twiddling.
-
-\1f
-File: gmp.info, Node: Assembly Floating Point, Next: Assembly SIMD Instructions, Prev: Assembly Functional Units, Up: Assembly Coding
-
-15.8.6 Floating Point
----------------------
-
-Floating point arithmetic is used in GMP for multiplications on CPUs
-with poor integer multipliers. It's mostly useful for 'mpn_mul_1',
-'mpn_addmul_1' and 'mpn_submul_1' on 64-bit machines, and
-'mpn_mul_basecase' on both 32-bit and 64-bit machines.
-
- With IEEE 53-bit double precision floats, integer multiplications
-producing up to 53 bits will give exact results. Breaking a 64x64
-multiplication into eight 16x32->48 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).
-
-\1f
-File: gmp.info, Node: Assembly SIMD Instructions, Next: Assembly Software Pipelining, Prev: Assembly Floating Point, Up: Assembly Coding
-
-15.8.7 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'.
-
-\1f
-File: gmp.info, Node: Assembly Software Pipelining, Next: Assembly Loop Unrolling, Prev: Assembly SIMD Instructions, Up: Assembly Coding
-
-15.8.8 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::).
-
-\1f
-File: gmp.info, Node: Assembly Loop Unrolling, Next: Assembly Writing Guide, Prev: Assembly Software Pipelining, Up: Assembly Coding
-
-15.8.9 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.
-
-\1f
-File: gmp.info, Node: Assembly Writing Guide, Prev: Assembly Loop Unrolling, Up: Assembly Coding
-
-15.8.10 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.
-
-\1f
-File: gmp.info, Node: Internals, Next: Contributors, Prev: Algorithms, Up: Top
-
-16 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::
-
-\1f
-File: gmp.info, Node: Integer Internals, Next: Rational Internals, Prev: Internals, Up: Internals
-
-16.1 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 undefined.
-
-'_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 readable limb, so for
- instance 'mpz_get_ui' can fetch '_mp_d[0]' unconditionally (though
- its value is undefined if '_mp_size' is zero).
-
-'_mp_alloc'
- '_mp_alloc' is the number of limbs currently allocated at '_mp_d',
- and normally '_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.
-
- 'mpz_t' variables initialised with the 'mpz_roinit_n' function or
- the 'MPZ_ROINIT_N' macro have '_mp_alloc = 0' but can have a
- non-zero '_mp_size'. They can only be used as read-only constants.
- See *note Integer Special Functions:: for details.
-
- 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.
-
-\1f
-File: gmp.info, Node: Rational Internals, Next: Float Internals, Prev: Integer Internals, Up: Internals
-
-16.2 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.
-
-\1f
-File: gmp.info, Node: Float Internals, Next: Raw Output Internals, Prev: Rational Internals, Up: Internals
-
-16.3 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.
-
-\1f
-File: gmp.info, Node: Raw Output Internals, Next: C++ Interface Internals, Prev: Float Internals, Up: Internals
-
-16.4 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'.
-
-\1f
-File: gmp.info, Node: C++ Interface Internals, Prev: Raw Output Internals, Up: Internals
-
-16.5 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, const mpf_t g, const mpf_t h)
- {
- mpf_add(f, g, h);
- }
- };
-
-And an "additive expression" object,
-
- __gmp_expr<__gmp_binary_expr<mpf_class, mpf_class, __gmp_binary_plus> >
- operator+(const mpf_class &f, const mpf_class &g)
- {
- return __gmp_expr
- <__gmp_binary_expr<mpf_class, mpf_class, __gmp_binary_plus> >(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 <class T>
- mpf_class & mpf_class::operator=(const __gmp_expr<T> &expr)
- {
- expr.eval(this->get_mpf_t(), this->precision());
- return *this;
- }
-
- template <class Op>
- void __gmp_expr<__gmp_binary_expr<mpf_class, mpf_class, Op> >::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 <class T, class U>
- __gmp_expr
- <__gmp_binary_expr<__gmp_expr<T>, __gmp_expr<U>, __gmp_binary_plus> >
- operator+(const __gmp_expr<T> &expr1, const __gmp_expr<U> &expr2)
- {
- return __gmp_expr
- <__gmp_binary_expr<__gmp_expr<T>, __gmp_expr<U>, __gmp_binary_plus> >
- (expr1, expr2);
- }
-
- And the corresponding specializations of '__gmp_expr::eval':
-
- template <class T, class U, class Op>
- void __gmp_expr
- <__gmp_binary_expr<__gmp_expr<T>, __gmp_expr<U>, 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'.
-
-\1f
-File: gmp.info, Node: Contributors, Next: References, Prev: Internals, Up: Top
-
-Appendix A Contributors
-***********************
-
-Torbjörn Granlund wrote the original GMP library and is still the main
-developer. Code not explicitly attributed to others, was contributed by
-Torbjörn. Several other individuals and organizations have contributed
-GMP. Here is a list in chronological order on first contribution:
-
- Gunnar Sjödin 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
-Schönhage-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 Torbjörn).
-
- 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 Möller wrote the sub-quadratic GCD, extended GCD and jacobi
-code, the quadratic Hensel division code, and (with Torbjörn) 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, and he is the main author of the
-mini-gmp package used for gmp bootstrapping.
-
- 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, mpn_mullo_n, and
-mpn_sqrlo. Marco also wrote the functions mpn_invert and
-mpn_invertappr, and improved the speed of integer root extraction. He
-is the author of mini-mpq, an additional layer to mini-gmp; of most of
-the combinatorial functions and the BPSW primality testing
-implementation, for both the main library and the mini-gmp package.
-
- 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'. He wrote the internal middle product functions
-'mpn_mulmid_basecase', 'mpn_toom42_mulmid', 'mpn_mulmid_n' and related
-helper routines.
-
- Martin Boij wrote 'mpn_perfect_power_p'.
-
- Marc Glisse improved 'gmpxx.h': use fewer temporaries (faster),
-specializations of 'numeric_limits' and 'common_type', C++11 features
-(move constructors, explicit bool conversion, UDL), make the conversion
-from 'mpq_class' to 'mpz_class' explicit, optimize operations where one
-argument is a small compile-time constant, replace some heap allocations
-by stack allocations. He also fixed the eofbit handling of C++ streams,
-and removed one division from 'mpq/aors.c'.
-
- David S Miller wrote assembly code for SPARC T3 and T4.
-
- Mark Sofroniou cleaned up the types of mul_fft.c, letting it work for
-huge operands.
-
- Ulrich Weigand ported GMP to the powerpc64le ABI.
-
- (This list is chronological, not ordered after significance. If you
-have contributed to GMP but are not listed above, please tell
-<gmp-devel@gmplib.org> 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 4.0 was supported in part by the IDA
-Center for Computing Sciences.
-
- The development of GMP 4.3, 5.0, and 5.1 was supported in part by the
-Swedish Foundation for Strategic Research.
-
- Thanks go to Hans Thorsen for donating an SGI system for the GMP test
-system environment.
-
-\1f
-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.
- <https://www.math.dartmouth.edu/~carlp/>
-
- * Henri Cohen, "A Course in Computational Algebraic Number Theory",
- Graduate Texts in Mathematics number 138, Springer-Verlag, 1993.
- <https://www.math.u-bordeaux.fr/~cohen/>
-
- * Donald E. Knuth, "The Art of Computer Programming", volume 2,
- "Seminumerical Algorithms", 3rd edition, Addison-Wesley, 1998.
- <https://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 <https://gcc.gnu.org/onlinedocs/>, and in the GCC package
- <https://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
- 2002, <https://hal.inria.fr/docs/00/07/21/13/PDF/RR-4475.pdf>
-
- * Christoph Burnikel and Joachim Ziegler, "Fast Recursive Division",
- Max-Planck-Institut fuer Informatik Research Report MPI-I-98-1-022,
- <https://www.mpi-inf.mpg.de/~ziegler/TechRep.ps.gz>
-
- * Torbjörn Granlund and Peter L. Montgomery, "Division by Invariant
- Integers using Multiplication", in Proceedings of the SIGPLAN
- PLDI'94 Conference, June 1994. Also available
- <https://gmplib.org/~tege/divcnst-pldi94.pdf>.
-
- * Niels Möller and Torbjörn Granlund, "Improved division by invariant
- integers", IEEE Transactions on Computers, 11 June 2010.
- <https://gmplib.org/~tege/division-paper.pdf>
-
- * Torbjörn Granlund and Niels Möller, "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.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 Möller, "On Schönhage's algorithm and subquadratic integer
- GCD computation", in Mathematics of Computation, volume 77, January
- 2008, pp. 589-607,
- <https://www.ams.org/journals/mcom/2008-77-261/S0025-5718-07-02017-0/home.html>
-
- * Peter L. Montgomery, "Modular Multiplication Without Trial
- Division", in Mathematics of Computation, volume 44, number 170,
- April 1985.
-
- * Arnold Schönhage 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,
- <https://hal.inria.fr/inria-00072854/PDF/RR-3805.pdf>
-
- * Paul Zimmermann, "A Proof of GMP Fast Division and Square Root
- Implementations",
- <https://homepages.loria.fr/PZimmermann/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.
-
- * Niels Möller, "Efficient computation of the Jacobi symbol",
- <https://arxiv.org/abs/1907.07795>
-
-\1f
-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 © 2000-2002, 2007, 2008 Free Software Foundation, Inc.
- <http://fsf.org/>
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- Everyone is permitted to copy and distribute verbatim copies
- of this license document, but changing it is not allowed.
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- 0. PREAMBLE
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- assure everyone the effective freedom to copy and redistribute it,
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- recommend this License principally for works whose purpose is
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-ADDENDUM: How to use this License for your documents
-====================================================
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-To use this License in a document you have written, include a copy of
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- Copyright (C) YEAR YOUR NAME.
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- or any later version published by the Free Software Foundation;
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-Texts, replace the "with...Texts." line with this:
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-recommend releasing these examples in parallel under your choice of free
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-their use in free software.
-
-\1f
-File: gmp.info, Node: Concept Index, Next: Function Index, Prev: GNU Free Documentation License, Up: Top
-
-Concept Index
-*************
-
-\0\b[index\0\b]
-* Menu:
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-* --build: Build Options. (line 51)
-* --disable-fft: Build Options. (line 307)
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-* -finstrument-functions: Profiling. (line 66)
-* 2exp functions: Efficiency. (line 43)
-* 68000: Notes for Particular Systems.
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-* 80x86: Notes for Particular Systems.
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-* ABI: Build Options. (line 167)
-* ABI <1>: ABI and ISA. (line 6)
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-* Application Binary Interface: ABI and ISA. (line 6)
-* Arithmetic functions: Integer Arithmetic. (line 6)
-* Arithmetic functions <1>: Rational Arithmetic. (line 6)
-* Arithmetic functions <2>: Float Arithmetic. (line 6)
-* ARM: Notes for Particular Systems.
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-* Assembly cache handling: Assembly Cache Handling.
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-* Assembly carry propagation: Assembly Carry Propagation.
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-* Bit manipulation functions: Integer Logic and Bit Fiddling.
- (line 6)
-* Bit scanning functions: Integer Logic and Bit Fiddling.
- (line 39)
-* Bit shift left: Integer Arithmetic. (line 38)
-* Bit shift right: Integer Division. (line 74)
-* Bits per limb: Useful Macros and Constants.
- (line 7)
-* 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 51)
-* Building GMP: Installing GMP. (line 6)
-* Bus error: Debugging. (line 7)
-* C compiler: Build Options. (line 178)
-* C++ compiler: Build Options. (line 249)
-* 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 225)
-* CC: Build Options. (line 178)
-* CC_FOR_BUILD: Build Options. (line 212)
-* CFLAGS: Build Options. (line 178)
-* Checker: Debugging. (line 110)
-* checkergcc: Debugging. (line 117)
-* Code organisation: Assembly Code Organisation.
- (line 6)
-* Compaq C++: Notes for Particular Systems.
- (line 25)
-* Comparison functions: Integer Comparisons. (line 6)
-* Comparison functions <1>: Comparing Rationals. (line 6)
-* Comparison functions <2>: 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 30)
-* Congruence functions: Integer Division. (line 150)
-* 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: Converting Integers. (line 6)
-* Conversion functions <1>: Rational Conversions.
- (line 6)
-* Conversion functions <2>: Converting Floats. (line 6)
-* Copying conditions: Copying. (line 6)
-* CPPFLAGS: Build Options. (line 204)
-* CPU types: Introduction to GMP. (line 24)
-* CPU types <1>: Build Options. (line 107)
-* Cross compiling: Build Options. (line 65)
-* Cryptography functions, low-level: Low-level Functions. (line 507)
-* Custom allocation: Custom Allocation. (line 6)
-* CXX: Build Options. (line 249)
-* CXXFLAGS: Build Options. (line 249)
-* Cygwin: Notes for Particular Systems.
- (line 57)
-* 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 30)
-* Divisibility functions: Integer Division. (line 136)
-* Divisibility functions <1>: Integer Division. (line 150)
-* Divisibility testing: Efficiency. (line 91)
-* Division algorithms: Division Algorithms. (line 6)
-* Division functions: Integer Division. (line 6)
-* Division functions <1>: Rational Arithmetic. (line 24)
-* Division functions <2>: Float Arithmetic. (line 33)
-* DJGPP: Notes for Particular Systems.
- (line 57)
-* DJGPP <1>: Known Build Problems.
- (line 18)
-* DLLs: Notes for Particular Systems.
- (line 70)
-* DocBook: Build Options. (line 340)
-* Documentation formats: Build Options. (line 333)
-* Documentation license: GNU Free Documentation License.
- (line 6)
-* DVI: Build Options. (line 336)
-* Efficiency: Efficiency. (line 6)
-* Emacs: Emacs. (line 6)
-* Exact division functions: Integer Division. (line 125)
-* Exact remainder: Exact Remainder. (line 6)
-* Example programs: Demonstration Programs.
- (line 6)
-* Exec prefix: Build Options. (line 32)
-* Execution profiling: Build Options. (line 317)
-* Execution profiling <1>: Profiling. (line 6)
-* Exponentiation functions: Integer Exponentiation.
- (line 6)
-* Exponentiation functions <1>: Float Arithmetic. (line 41)
-* Export: Integer Import and Export.
- (line 45)
-* Expression parsing demo: Demonstration Programs.
- (line 15)
-* Expression parsing demo <1>: Demonstration Programs.
- (line 17)
-* Expression parsing demo <2>: Demonstration Programs.
- (line 19)
-* Extended GCD: Number Theoretic Functions.
- (line 47)
-* Factor removal functions: Number Theoretic Functions.
- (line 108)
-* Factorial algorithm: Factorial Algorithm. (line 6)
-* Factorial functions: Number Theoretic Functions.
- (line 116)
-* Factorization demo: Demonstration Programs.
- (line 22)
-* Fast Fourier Transform: FFT Multiplication. (line 6)
-* Fat binary: Build Options. (line 160)
-* FFT multiplication: Build Options. (line 307)
-* FFT multiplication <1>: FFT Multiplication. (line 6)
-* Fibonacci number algorithm: Fibonacci Numbers Algorithm.
- (line 6)
-* Fibonacci sequence functions: Number Theoretic Functions.
- (line 136)
-* Float arithmetic functions: Float Arithmetic. (line 6)
-* Float assignment functions: Assigning Floats. (line 6)
-* Float assignment functions <1>: Simultaneous Float Init & Assign.
- (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: Initializing Floats. (line 6)
-* Float initialization functions <1>: Simultaneous Float Init & Assign.
- (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 34)
-* 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)
-* FreeBSD: Notes for Particular Systems.
- (line 43)
-* FreeBSD <1>: Notes for Particular Systems.
- (line 52)
-* frexp: Converting Integers. (line 43)
-* frexp <1>: Converting Floats. (line 24)
-* FTP of latest version: Introduction to GMP. (line 37)
-* Function classes: Function Classes. (line 6)
-* FunctionCheck: Profiling. (line 77)
-* GCC Checker: Debugging. (line 110)
-* GCD algorithms: Greatest Common Divisor Algorithms.
- (line 6)
-* GCD extended: Number Theoretic Functions.
- (line 47)
-* GCD functions: Number Theoretic Functions.
- (line 30)
-* GDB: Debugging. (line 53)
-* Generic C: Build Options. (line 151)
-* GMP Perl module: Demonstration Programs.
- (line 28)
-* 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 53)
-* 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 23)
-* Home page: Introduction to GMP. (line 33)
-* Host system: Build Options. (line 65)
-* HP-UX: ABI and ISA. (line 76)
-* HP-UX <1>: ABI and ISA. (line 114)
-* HPPA: ABI and ISA. (line 76)
-* I/O functions: I/O of Integers. (line 6)
-* I/O functions <1>: I/O of Rationals. (line 6)
-* I/O functions <2>: I/O of Floats. (line 6)
-* i386: Notes for Particular Systems.
- (line 150)
-* IA-64: ABI and ISA. (line 114)
-* 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: Initializing Integers.
- (line 6)
-* Initialization functions <1>: Simultaneous Integer Init & Assign.
- (line 6)
-* Initialization functions <2>: Initializing Rationals.
- (line 6)
-* Initialization functions <3>: Initializing Floats. (line 6)
-* Initialization functions <4>: Simultaneous Float Init & Assign.
- (line 6)
-* Initialization functions <5>: Random State Initialization.
- (line 6)
-* Initializing and clearing: Efficiency. (line 21)
-* Input functions: I/O of Integers. (line 6)
-* Input functions <1>: I/O of Rationals. (line 6)
-* Input functions <2>: I/O of Floats. (line 6)
-* Input functions <3>: 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: Assigning Integers. (line 6)
-* Integer assignment functions <1>: Simultaneous Integer Init & Assign.
- (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: Initializing Integers.
- (line 6)
-* Integer initialization functions <1>: Simultaneous Integer Init & Assign.
- (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 65)
-* Internals: Internals. (line 6)
-* Introduction: Introduction to GMP. (line 6)
-* Inverse modulo functions: Number Theoretic Functions.
- (line 74)
-* IRIX: ABI and ISA. (line 139)
-* IRIX <1>: Known Build Problems.
- (line 38)
-* 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 83)
-* Karatsuba multiplication: Karatsuba Multiplication.
- (line 6)
-* Karatsuba square root algorithm: Square Root Algorithm.
- (line 6)
-* Kronecker symbol functions: Number Theoretic Functions.
- (line 95)
-* Language bindings: Language Bindings. (line 6)
-* Latest version of GMP: Introduction to GMP. (line 37)
-* LCM functions: Number Theoretic Functions.
- (line 68)
-* Least common multiple functions: Number Theoretic Functions.
- (line 68)
-* Legendre symbol functions: Number Theoretic Functions.
- (line 86)
-* 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 18)
-* Linear congruential random numbers <1>: 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)
-* Low-level functions for cryptography: Low-level Functions. (line 507)
-* Lucas number algorithm: Lucas Numbers Algorithm.
- (line 6)
-* Lucas number functions: Number Theoretic Functions.
- (line 147)
-* MacOS X: Known Build Problems.
- (line 51)
-* Mailing lists: Introduction to GMP. (line 44)
-* Malloc debugger: Debugging. (line 29)
-* Malloc problems: Debugging. (line 23)
-* 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 57)
-* MIPS: ABI and ISA. (line 139)
-* Miscellaneous float functions: Miscellaneous Float Functions.
- (line 6)
-* Miscellaneous integer functions: Miscellaneous Integer Functions.
- (line 6)
-* MMX: Notes for Particular Systems.
- (line 156)
-* Modular inverse functions: Number Theoretic Functions.
- (line 74)
-* Most significant bit: Miscellaneous Integer Functions.
- (line 34)
-* MPN_PATH: Build Options. (line 321)
-* MS Windows: Notes for Particular Systems.
- (line 57)
-* MS Windows <1>: Notes for Particular Systems.
- (line 70)
-* MS-DOS: Notes for Particular Systems.
- (line 57)
-* Multi-threading: Reentrancy. (line 6)
-* Multiplication algorithms: Multiplication Algorithms.
- (line 6)
-* Nails: Low-level Functions. (line 686)
-* Native compilation: Build Options. (line 51)
-* NetBSD: Notes for Particular Systems.
- (line 100)
-* 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 145)
-* Number theoretic functions: Number Theoretic Functions.
- (line 6)
-* Numerator and denominator: Applying Integer Functions.
- (line 6)
-* obstack output: Formatted Output Functions.
- (line 79)
-* OpenBSD: Notes for Particular Systems.
- (line 109)
-* Optimizing performance: Performance optimization.
- (line 6)
-* ostream output: C++ Formatted Output.
- (line 6)
-* Other languages: Language Bindings. (line 6)
-* Output functions: I/O of Integers. (line 6)
-* Output functions <1>: I/O of Rationals. (line 6)
-* Output functions <2>: I/O of Floats. (line 6)
-* Output functions <3>: Formatted Output Functions.
- (line 6)
-* Packaged builds: Notes for Package Builds.
- (line 6)
-* Parameter conventions: Parameter Conventions.
- (line 6)
-* Parsing expressions demo: Demonstration Programs.
- (line 15)
-* Parsing expressions demo <1>: Demonstration Programs.
- (line 17)
-* Parsing expressions demo <2>: Demonstration Programs.
- (line 19)
-* Particular systems: Notes for Particular Systems.
- (line 6)
-* Past GMP versions: Compatibility with older versions.
- (line 6)
-* PDF: Build Options. (line 336)
-* Perfect power algorithm: Perfect Power Algorithm.
- (line 6)
-* Perfect power functions: Integer Roots. (line 28)
-* Perfect square algorithm: Perfect Square Algorithm.
- (line 6)
-* Perfect square functions: Integer Roots. (line 37)
-* perl: Demonstration Programs.
- (line 28)
-* Perl module: Demonstration Programs.
- (line 28)
-* Postscript: Build Options. (line 336)
-* Power/PowerPC: Notes for Particular Systems.
- (line 115)
-* Power/PowerPC <1>: Known Build Problems.
- (line 63)
-* Powering algorithms: Powering Algorithms. (line 6)
-* Powering functions: Integer Exponentiation.
- (line 6)
-* Powering functions <1>: Float Arithmetic. (line 41)
-* PowerPC: ABI and ISA. (line 173)
-* 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)
-* Primorial functions: Number Theoretic Functions.
- (line 121)
-* 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: Integer Random Numbers.
- (line 6)
-* Random number functions <1>: Miscellaneous Float Functions.
- (line 27)
-* Random number functions <2>: 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 111)
-* 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 28)
-* Raw output internals: Raw Output Internals.
- (line 6)
-* Reallocations: Efficiency. (line 30)
-* Reentrancy: Reentrancy. (line 6)
-* References: References. (line 5)
-* Remove factor functions: Number Theoretic Functions.
- (line 108)
-* 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: Integer Roots. (line 6)
-* Root extraction functions <1>: Float Arithmetic. (line 37)
-* Root testing functions: Integer Roots. (line 28)
-* Root testing functions <1>: Integer Roots. (line 37)
-* Rounding functions: Miscellaneous Float Functions.
- (line 9)
-* Sample programs: Demonstration Programs.
- (line 6)
-* Scan bit functions: Integer Logic and Bit Fiddling.
- (line 39)
-* 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 65)
-* Shared library versioning: Notes for Package Builds.
- (line 9)
-* Sign tests: Integer Comparisons. (line 28)
-* Sign tests <1>: Comparing Rationals. (line 28)
-* Sign tests <2>: Float Comparison. (line 34)
-* Size in digits: Miscellaneous Integer Functions.
- (line 23)
-* Small operands: Efficiency. (line 7)
-* Solaris: ABI and ISA. (line 204)
-* Solaris <1>: Known Build Problems.
- (line 72)
-* Solaris <2>: Known Build Problems.
- (line 77)
-* Sparc: Notes for Particular Systems.
- (line 127)
-* Sparc <1>: Notes for Particular Systems.
- (line 132)
-* Sparc V9: ABI and ISA. (line 204)
-* Special integer functions: Integer Special Functions.
- (line 6)
-* Square root algorithm: Square Root Algorithm.
- (line 6)
-* SSE2: Notes for Particular Systems.
- (line 156)
-* Stack backtrace: Debugging. (line 45)
-* Stack overflow: Build Options. (line 273)
-* Stack overflow <1>: Debugging. (line 7)
-* 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 204)
-* SunOS: Notes for Particular Systems.
- (line 144)
-* Systems: Notes for Particular Systems.
- (line 6)
-* Temporary memory: Build Options. (line 273)
-* Texinfo: Build Options. (line 333)
-* Text input/output: Efficiency. (line 151)
-* Thread safety: Reentrancy. (line 6)
-* Toom multiplication: Toom 3-Way Multiplication.
- (line 6)
-* Toom multiplication <1>: Toom 4-Way Multiplication.
- (line 6)
-* Toom multiplication <2>: Higher degree Toom'n'half.
- (line 6)
-* Toom multiplication <3>: Other 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 125)
-* Variable conventions: Variable Conventions.
- (line 6)
-* Version number: Useful Macros and Constants.
- (line 12)
-* Web page: Introduction to GMP. (line 33)
-* Windows: Notes for Particular Systems.
- (line 57)
-* Windows <1>: Notes for Particular Systems.
- (line 70)
-* x86: Notes for Particular Systems.
- (line 150)
-* x87: Notes for Particular Systems.
- (line 34)
-* XML: Build Options. (line 340)
-
-\1f
-File: gmp.info, Node: Function Index, Prev: Concept Index, Up: Top
-
-Function and Type Index
-***********************
-
-\0\b[index\0\b]
-* Menu:
-
-* _mpz_realloc: Integer Special Functions.
- (line 13)
-* __GMP_CC: Useful Macros and Constants.
- (line 22)
-* __GMP_CFLAGS: Useful Macros and Constants.
- (line 23)
-* __GNU_MP_VERSION: Useful Macros and Constants.
- (line 9)
-* __GNU_MP_VERSION_MINOR: Useful Macros and Constants.
- (line 10)
-* __GNU_MP_VERSION_PATCHLEVEL: Useful Macros and Constants.
- (line 11)
-* abs: C++ Interface Integers.
- (line 46)
-* abs <1>: C++ Interface Rationals.
- (line 47)
-* abs <2>: C++ Interface Floats.
- (line 82)
-* ceil: C++ Interface Floats.
- (line 83)
-* cmp: C++ Interface Integers.
- (line 47)
-* cmp <1>: C++ Interface Integers.
- (line 48)
-* cmp <2>: C++ Interface Rationals.
- (line 48)
-* cmp <3>: C++ Interface Rationals.
- (line 49)
-* cmp <4>: C++ Interface Floats.
- (line 84)
-* cmp <5>: C++ Interface Floats.
- (line 85)
-* factorial: C++ Interface Integers.
- (line 71)
-* fibonacci: C++ Interface Integers.
- (line 75)
-* floor: C++ Interface Floats.
- (line 95)
-* gcd: C++ Interface Integers.
- (line 68)
-* gmp_asprintf: Formatted Output Functions.
- (line 63)
-* gmp_errno: Random State Initialization.
- (line 56)
-* GMP_ERROR_INVALID_ARGUMENT: Random State Initialization.
- (line 56)
-* GMP_ERROR_UNSUPPORTED_ARGUMENT: Random State Initialization.
- (line 56)
-* gmp_fprintf: Formatted Output Functions.
- (line 28)
-* gmp_fscanf: Formatted Input Functions.
- (line 24)
-* GMP_LIMB_BITS: Low-level Functions. (line 714)
-* GMP_NAIL_BITS: Low-level Functions. (line 712)
-* GMP_NAIL_MASK: Low-level Functions. (line 722)
-* GMP_NUMB_BITS: Low-level Functions. (line 713)
-* GMP_NUMB_MASK: Low-level Functions. (line 723)
-* GMP_NUMB_MAX: Low-level Functions. (line 731)
-* gmp_obstack_printf: Formatted Output Functions.
- (line 75)
-* gmp_obstack_vprintf: Formatted Output Functions.
- (line 77)
-* gmp_printf: Formatted Output Functions.
- (line 23)
-* gmp_randclass: C++ Interface Random Numbers.
- (line 6)
-* gmp_randclass::get_f: C++ Interface Random Numbers.
- (line 44)
-* gmp_randclass::get_f <1>: C++ Interface Random Numbers.
- (line 45)
-* gmp_randclass::get_z_bits: C++ Interface Random Numbers.
- (line 37)
-* gmp_randclass::get_z_bits <1>: C++ Interface Random Numbers.
- (line 38)
-* gmp_randclass::get_z_range: C++ Interface Random Numbers.
- (line 41)
-* gmp_randclass::gmp_randclass: C++ Interface Random Numbers.
- (line 11)
-* gmp_randclass::gmp_randclass <1>: C++ Interface Random Numbers.
- (line 26)
-* gmp_randclass::seed: C++ Interface Random Numbers.
- (line 32)
-* gmp_randclass::seed <1>: C++ Interface Random Numbers.
- (line 33)
-* gmp_randclear: Random State Initialization.
- (line 62)
-* gmp_randinit: Random State Initialization.
- (line 45)
-* gmp_randinit_default: Random State Initialization.
- (line 6)
-* gmp_randinit_lc_2exp: Random State Initialization.
- (line 16)
-* gmp_randinit_lc_2exp_size: Random State Initialization.
- (line 30)
-* gmp_randinit_mt: Random State Initialization.
- (line 12)
-* gmp_randinit_set: Random State Initialization.
- (line 41)
-* gmp_randseed: Random State Seeding.
- (line 6)
-* gmp_randseed_ui: Random State Seeding.
- (line 8)
-* gmp_randstate_t: Nomenclature and Types.
- (line 46)
-* GMP_RAND_ALG_DEFAULT: Random State Initialization.
- (line 50)
-* GMP_RAND_ALG_LC: Random State Initialization.
- (line 50)
-* gmp_scanf: Formatted Input Functions.
- (line 20)
-* gmp_snprintf: Formatted Output Functions.
- (line 44)
-* gmp_sprintf: Formatted Output Functions.
- (line 33)
-* gmp_sscanf: Formatted Input Functions.
- (line 28)
-* gmp_urandomb_ui: Random State Miscellaneous.
- (line 6)
-* gmp_urandomm_ui: Random State Miscellaneous.
- (line 12)
-* gmp_vasprintf: Formatted Output Functions.
- (line 64)
-* gmp_version: Useful Macros and Constants.
- (line 18)
-* gmp_vfprintf: Formatted Output Functions.
- (line 29)
-* gmp_vfscanf: Formatted Input Functions.
- (line 25)
-* gmp_vprintf: Formatted Output Functions.
- (line 24)
-* gmp_vscanf: Formatted Input Functions.
- (line 21)
-* gmp_vsnprintf: Formatted Output Functions.
- (line 46)
-* gmp_vsprintf: Formatted Output Functions.
- (line 34)
-* gmp_vsscanf: Formatted Input Functions.
- (line 29)
-* hypot: C++ Interface Floats.
- (line 96)
-* lcm: C++ Interface Integers.
- (line 69)
-* mpf_abs: Float Arithmetic. (line 46)
-* mpf_add: Float Arithmetic. (line 6)
-* mpf_add_ui: Float Arithmetic. (line 7)
-* mpf_ceil: Miscellaneous Float Functions.
- (line 6)
-* mpf_class: C++ Interface General.
- (line 19)
-* mpf_class::fits_sint_p: C++ Interface Floats.
- (line 87)
-* mpf_class::fits_slong_p: C++ Interface Floats.
- (line 88)
-* mpf_class::fits_sshort_p: C++ Interface Floats.
- (line 89)
-* mpf_class::fits_uint_p: C++ Interface Floats.
- (line 91)
-* mpf_class::fits_ulong_p: C++ Interface Floats.
- (line 92)
-* mpf_class::fits_ushort_p: C++ Interface Floats.
- (line 93)
-* mpf_class::get_d: C++ Interface Floats.
- (line 98)
-* mpf_class::get_mpf_t: C++ Interface General.
- (line 65)
-* mpf_class::get_prec: C++ Interface Floats.
- (line 120)
-* mpf_class::get_si: C++ Interface Floats.
- (line 99)
-* mpf_class::get_str: C++ Interface Floats.
- (line 100)
-* mpf_class::get_ui: C++ Interface Floats.
- (line 102)
-* mpf_class::mpf_class: C++ Interface Floats.
- (line 11)
-* mpf_class::mpf_class <1>: C++ Interface Floats.
- (line 12)
-* mpf_class::mpf_class <2>: C++ Interface Floats.
- (line 32)
-* mpf_class::mpf_class <3>: C++ Interface Floats.
- (line 33)
-* mpf_class::mpf_class <4>: C++ Interface Floats.
- (line 41)
-* mpf_class::mpf_class <5>: C++ Interface Floats.
- (line 42)
-* mpf_class::mpf_class <6>: C++ Interface Floats.
- (line 44)
-* mpf_class::mpf_class <7>: C++ Interface Floats.
- (line 45)
-* mpf_class::operator=: C++ Interface Floats.
- (line 59)
-* mpf_class::set_prec: C++ Interface Floats.
- (line 121)
-* mpf_class::set_prec_raw: C++ Interface Floats.
- (line 122)
-* mpf_class::set_str: C++ Interface Floats.
- (line 104)
-* mpf_class::set_str <1>: C++ Interface Floats.
- (line 105)
-* mpf_class::swap: C++ Interface Floats.
- (line 109)
-* mpf_clear: Initializing Floats. (line 36)
-* mpf_clears: Initializing Floats. (line 40)
-* mpf_cmp: Float Comparison. (line 6)
-* mpf_cmp_d: Float Comparison. (line 8)
-* mpf_cmp_si: Float Comparison. (line 10)
-* mpf_cmp_ui: Float Comparison. (line 9)
-* mpf_cmp_z: Float Comparison. (line 7)
-* mpf_div: Float Arithmetic. (line 28)
-* mpf_div_2exp: Float Arithmetic. (line 53)
-* mpf_div_ui: Float Arithmetic. (line 31)
-* mpf_eq: Float Comparison. (line 17)
-* mpf_fits_sint_p: Miscellaneous Float Functions.
- (line 19)
-* mpf_fits_slong_p: Miscellaneous Float Functions.
- (line 17)
-* mpf_fits_sshort_p: Miscellaneous Float Functions.
- (line 21)
-* mpf_fits_uint_p: Miscellaneous Float Functions.
- (line 18)
-* mpf_fits_ulong_p: Miscellaneous Float Functions.
- (line 16)
-* mpf_fits_ushort_p: Miscellaneous Float Functions.
- (line 20)
-* mpf_floor: Miscellaneous Float Functions.
- (line 7)
-* mpf_get_d: Converting Floats. (line 6)
-* mpf_get_default_prec: Initializing Floats. (line 11)
-* mpf_get_d_2exp: Converting Floats. (line 15)
-* mpf_get_prec: Initializing Floats. (line 61)
-* mpf_get_si: Converting Floats. (line 27)
-* mpf_get_str: Converting Floats. (line 36)
-* mpf_get_ui: Converting Floats. (line 28)
-* mpf_init: Initializing Floats. (line 18)
-* mpf_init2: Initializing Floats. (line 25)
-* mpf_inits: Initializing Floats. (line 30)
-* mpf_init_set: Simultaneous Float Init & Assign.
- (line 15)
-* mpf_init_set_d: Simultaneous Float Init & Assign.
- (line 18)
-* mpf_init_set_si: Simultaneous Float Init & Assign.
- (line 17)
-* mpf_init_set_str: Simultaneous Float Init & Assign.
- (line 24)
-* mpf_init_set_ui: Simultaneous Float Init & Assign.
- (line 16)
-* mpf_inp_str: I/O of Floats. (line 38)
-* mpf_integer_p: Miscellaneous Float Functions.
- (line 13)
-* mpf_mul: Float Arithmetic. (line 18)
-* mpf_mul_2exp: Float Arithmetic. (line 49)
-* mpf_mul_ui: Float Arithmetic. (line 19)
-* mpf_neg: Float Arithmetic. (line 43)
-* mpf_out_str: I/O of Floats. (line 17)
-* mpf_pow_ui: Float Arithmetic. (line 39)
-* mpf_random2: Miscellaneous Float Functions.
- (line 35)
-* mpf_reldiff: Float Comparison. (line 28)
-* mpf_set: Assigning Floats. (line 9)
-* mpf_set_d: Assigning Floats. (line 12)
-* mpf_set_default_prec: Initializing Floats. (line 6)
-* mpf_set_prec: Initializing Floats. (line 64)
-* mpf_set_prec_raw: Initializing Floats. (line 71)
-* mpf_set_q: Assigning Floats. (line 14)
-* mpf_set_si: Assigning Floats. (line 11)
-* mpf_set_str: Assigning Floats. (line 17)
-* mpf_set_ui: Assigning Floats. (line 10)
-* mpf_set_z: Assigning Floats. (line 13)
-* mpf_sgn: Float Comparison. (line 33)
-* mpf_sqrt: Float Arithmetic. (line 35)
-* mpf_sqrt_ui: Float Arithmetic. (line 36)
-* mpf_sub: Float Arithmetic. (line 11)
-* mpf_sub_ui: Float Arithmetic. (line 14)
-* mpf_swap: Assigning Floats. (line 50)
-* mpf_t: Nomenclature and Types.
- (line 21)
-* mpf_trunc: Miscellaneous Float Functions.
- (line 8)
-* mpf_ui_div: Float Arithmetic. (line 29)
-* mpf_ui_sub: Float Arithmetic. (line 12)
-* mpf_urandomb: Miscellaneous Float Functions.
- (line 25)
-* mpn_add: Low-level Functions. (line 67)
-* mpn_addmul_1: Low-level Functions. (line 148)
-* mpn_add_1: Low-level Functions. (line 62)
-* mpn_add_n: Low-level Functions. (line 52)
-* mpn_andn_n: Low-level Functions. (line 462)
-* mpn_and_n: Low-level Functions. (line 447)
-* mpn_cmp: Low-level Functions. (line 293)
-* mpn_cnd_add_n: Low-level Functions. (line 540)
-* mpn_cnd_sub_n: Low-level Functions. (line 542)
-* mpn_cnd_swap: Low-level Functions. (line 567)
-* mpn_com: Low-level Functions. (line 487)
-* mpn_copyd: Low-level Functions. (line 496)
-* mpn_copyi: Low-level Functions. (line 492)
-* mpn_divexact_1: Low-level Functions. (line 231)
-* mpn_divexact_by3: Low-level Functions. (line 238)
-* mpn_divexact_by3c: Low-level Functions. (line 240)
-* mpn_divmod: Low-level Functions. (line 226)
-* mpn_divmod_1: Low-level Functions. (line 210)
-* mpn_divrem: Low-level Functions. (line 183)
-* mpn_divrem_1: Low-level Functions. (line 208)
-* mpn_gcd: Low-level Functions. (line 301)
-* mpn_gcdext: Low-level Functions. (line 316)
-* mpn_gcd_1: Low-level Functions. (line 311)
-* mpn_get_str: Low-level Functions. (line 371)
-* mpn_hamdist: Low-level Functions. (line 436)
-* mpn_iorn_n: Low-level Functions. (line 467)
-* mpn_ior_n: Low-level Functions. (line 452)
-* mpn_lshift: Low-level Functions. (line 269)
-* mpn_mod_1: Low-level Functions. (line 264)
-* 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 472)
-* mpn_neg: Low-level Functions. (line 96)
-* mpn_nior_n: Low-level Functions. (line 477)
-* mpn_perfect_square_p: Low-level Functions. (line 442)
-* mpn_popcount: Low-level Functions. (line 432)
-* mpn_random: Low-level Functions. (line 422)
-* mpn_random2: Low-level Functions. (line 423)
-* mpn_rshift: Low-level Functions. (line 281)
-* mpn_scan0: Low-level Functions. (line 406)
-* mpn_scan1: Low-level Functions. (line 414)
-* mpn_sec_add_1: Low-level Functions. (line 553)
-* mpn_sec_div_qr: Low-level Functions. (line 630)
-* mpn_sec_div_qr_itch: Low-level Functions. (line 633)
-* mpn_sec_div_r: Low-level Functions. (line 649)
-* mpn_sec_div_r_itch: Low-level Functions. (line 651)
-* mpn_sec_invert: Low-level Functions. (line 665)
-* mpn_sec_invert_itch: Low-level Functions. (line 667)
-* mpn_sec_mul: Low-level Functions. (line 574)
-* mpn_sec_mul_itch: Low-level Functions. (line 577)
-* mpn_sec_powm: Low-level Functions. (line 604)
-* mpn_sec_powm_itch: Low-level Functions. (line 607)
-* mpn_sec_sqr: Low-level Functions. (line 590)
-* mpn_sec_sqr_itch: Low-level Functions. (line 592)
-* mpn_sec_sub_1: Low-level Functions. (line 555)
-* mpn_sec_tabselect: Low-level Functions. (line 622)
-* mpn_set_str: Low-level Functions. (line 386)
-* mpn_sizeinbase: Low-level Functions. (line 364)
-* mpn_sqr: Low-level Functions. (line 125)
-* mpn_sqrtrem: Low-level Functions. (line 346)
-* mpn_sub: Low-level Functions. (line 88)
-* mpn_submul_1: Low-level Functions. (line 160)
-* mpn_sub_1: Low-level Functions. (line 83)
-* mpn_sub_n: Low-level Functions. (line 74)
-* mpn_tdiv_qr: Low-level Functions. (line 172)
-* mpn_xnor_n: Low-level Functions. (line 482)
-* mpn_xor_n: Low-level Functions. (line 457)
-* mpn_zero: Low-level Functions. (line 500)
-* mpn_zero_p: Low-level Functions. (line 298)
-* mpq_abs: Rational Arithmetic. (line 33)
-* mpq_add: Rational Arithmetic. (line 6)
-* mpq_canonicalize: Rational Number Functions.
- (line 21)
-* mpq_class: C++ Interface General.
- (line 18)
-* mpq_class::canonicalize: C++ Interface Rationals.
- (line 41)
-* mpq_class::get_d: C++ Interface Rationals.
- (line 51)
-* mpq_class::get_den: C++ Interface Rationals.
- (line 67)
-* mpq_class::get_den_mpz_t: C++ Interface Rationals.
- (line 77)
-* mpq_class::get_mpq_t: C++ Interface General.
- (line 64)
-* mpq_class::get_num: C++ Interface Rationals.
- (line 66)
-* mpq_class::get_num_mpz_t: C++ Interface Rationals.
- (line 76)
-* mpq_class::get_str: C++ Interface Rationals.
- (line 52)
-* mpq_class::mpq_class: C++ Interface Rationals.
- (line 9)
-* mpq_class::mpq_class <1>: C++ Interface Rationals.
- (line 10)
-* mpq_class::mpq_class <2>: C++ Interface Rationals.
- (line 21)
-* mpq_class::mpq_class <3>: C++ Interface Rationals.
- (line 26)
-* mpq_class::mpq_class <4>: C++ Interface Rationals.
- (line 28)
-* mpq_class::set_str: C++ Interface Rationals.
- (line 54)
-* mpq_class::set_str <1>: C++ Interface Rationals.
- (line 55)
-* mpq_class::swap: C++ Interface Rationals.
- (line 58)
-* mpq_clear: Initializing Rationals.
- (line 15)
-* mpq_clears: Initializing Rationals.
- (line 19)
-* mpq_cmp: Comparing Rationals. (line 6)
-* mpq_cmp_si: Comparing Rationals. (line 16)
-* mpq_cmp_ui: Comparing Rationals. (line 14)
-* mpq_cmp_z: Comparing Rationals. (line 7)
-* mpq_denref: Applying Integer Functions.
- (line 16)
-* mpq_div: Rational Arithmetic. (line 22)
-* mpq_div_2exp: Rational Arithmetic. (line 26)
-* mpq_equal: Comparing Rationals. (line 33)
-* mpq_get_d: Rational Conversions.
- (line 6)
-* mpq_get_den: Applying Integer Functions.
- (line 22)
-* mpq_get_num: Applying Integer Functions.
- (line 21)
-* mpq_get_str: Rational Conversions.
- (line 21)
-* mpq_init: Initializing Rationals.
- (line 6)
-* mpq_inits: Initializing Rationals.
- (line 11)
-* mpq_inp_str: I/O of Rationals. (line 32)
-* mpq_inv: Rational Arithmetic. (line 36)
-* mpq_mul: Rational Arithmetic. (line 14)
-* mpq_mul_2exp: Rational Arithmetic. (line 18)
-* mpq_neg: Rational Arithmetic. (line 30)
-* mpq_numref: Applying Integer Functions.
- (line 15)
-* mpq_out_str: I/O of Rationals. (line 17)
-* mpq_set: Initializing Rationals.
- (line 23)
-* mpq_set_d: Rational Conversions.
- (line 16)
-* mpq_set_den: Applying Integer Functions.
- (line 24)
-* mpq_set_f: Rational Conversions.
- (line 17)
-* mpq_set_num: Applying Integer Functions.
- (line 23)
-* mpq_set_si: Initializing Rationals.
- (line 29)
-* mpq_set_str: Initializing Rationals.
- (line 35)
-* mpq_set_ui: Initializing Rationals.
- (line 27)
-* mpq_set_z: Initializing Rationals.
- (line 24)
-* mpq_sgn: Comparing Rationals. (line 27)
-* mpq_sub: Rational Arithmetic. (line 10)
-* mpq_swap: Initializing Rationals.
- (line 54)
-* mpq_t: Nomenclature and Types.
- (line 16)
-* mpz_2fac_ui: Number Theoretic Functions.
- (line 113)
-* mpz_abs: Integer Arithmetic. (line 44)
-* mpz_add: Integer Arithmetic. (line 6)
-* mpz_addmul: Integer Arithmetic. (line 24)
-* mpz_addmul_ui: Integer Arithmetic. (line 26)
-* mpz_add_ui: Integer Arithmetic. (line 7)
-* mpz_and: Integer Logic and Bit Fiddling.
- (line 10)
-* mpz_array_init: Integer Special Functions.
- (line 9)
-* mpz_bin_ui: Number Theoretic Functions.
- (line 124)
-* mpz_bin_uiui: Number Theoretic Functions.
- (line 126)
-* mpz_cdiv_q: Integer Division. (line 12)
-* mpz_cdiv_qr: Integer Division. (line 14)
-* mpz_cdiv_qr_ui: Integer Division. (line 21)
-* mpz_cdiv_q_2exp: Integer Division. (line 26)
-* mpz_cdiv_q_ui: Integer Division. (line 17)
-* mpz_cdiv_r: Integer Division. (line 13)
-* mpz_cdiv_r_2exp: Integer Division. (line 29)
-* mpz_cdiv_r_ui: Integer Division. (line 19)
-* mpz_cdiv_ui: Integer Division. (line 23)
-* mpz_class: C++ Interface General.
- (line 17)
-* mpz_class::factorial: C++ Interface Integers.
- (line 70)
-* mpz_class::fibonacci: C++ Interface Integers.
- (line 74)
-* mpz_class::fits_sint_p: C++ Interface Integers.
- (line 50)
-* mpz_class::fits_slong_p: C++ Interface Integers.
- (line 51)
-* mpz_class::fits_sshort_p: C++ Interface Integers.
- (line 52)
-* mpz_class::fits_uint_p: C++ Interface Integers.
- (line 54)
-* mpz_class::fits_ulong_p: C++ Interface Integers.
- (line 55)
-* mpz_class::fits_ushort_p: C++ Interface Integers.
- (line 56)
-* mpz_class::get_d: C++ Interface Integers.
- (line 58)
-* mpz_class::get_mpz_t: C++ Interface General.
- (line 63)
-* mpz_class::get_si: C++ Interface Integers.
- (line 59)
-* mpz_class::get_str: C++ Interface Integers.
- (line 60)
-* mpz_class::get_ui: C++ Interface Integers.
- (line 61)
-* mpz_class::mpz_class: C++ Interface Integers.
- (line 6)
-* mpz_class::mpz_class <1>: C++ Interface Integers.
- (line 14)
-* mpz_class::mpz_class <2>: C++ Interface Integers.
- (line 19)
-* mpz_class::mpz_class <3>: C++ Interface Integers.
- (line 21)
-* mpz_class::primorial: C++ Interface Integers.
- (line 72)
-* mpz_class::set_str: C++ Interface Integers.
- (line 63)
-* mpz_class::set_str <1>: C++ Interface Integers.
- (line 64)
-* mpz_class::swap: C++ Interface Integers.
- (line 77)
-* mpz_clear: Initializing Integers.
- (line 48)
-* mpz_clears: Initializing Integers.
- (line 52)
-* mpz_clrbit: Integer Logic and Bit Fiddling.
- (line 54)
-* mpz_cmp: Integer Comparisons. (line 6)
-* mpz_cmpabs: Integer Comparisons. (line 17)
-* mpz_cmpabs_d: Integer Comparisons. (line 18)
-* mpz_cmpabs_ui: Integer Comparisons. (line 19)
-* mpz_cmp_d: Integer Comparisons. (line 7)
-* mpz_cmp_si: Integer Comparisons. (line 8)
-* mpz_cmp_ui: Integer Comparisons. (line 9)
-* mpz_com: Integer Logic and Bit Fiddling.
- (line 19)
-* mpz_combit: Integer Logic and Bit Fiddling.
- (line 57)
-* mpz_congruent_2exp_p: Integer Division. (line 148)
-* mpz_congruent_p: Integer Division. (line 144)
-* mpz_congruent_ui_p: Integer Division. (line 146)
-* mpz_divexact: Integer Division. (line 122)
-* mpz_divexact_ui: Integer Division. (line 123)
-* mpz_divisible_2exp_p: Integer Division. (line 135)
-* mpz_divisible_p: Integer Division. (line 132)
-* mpz_divisible_ui_p: Integer Division. (line 133)
-* mpz_even_p: Miscellaneous Integer Functions.
- (line 17)
-* mpz_export: Integer Import and Export.
- (line 43)
-* mpz_fac_ui: Number Theoretic Functions.
- (line 112)
-* mpz_fdiv_q: Integer Division. (line 33)
-* mpz_fdiv_qr: Integer Division. (line 35)
-* mpz_fdiv_qr_ui: Integer Division. (line 42)
-* mpz_fdiv_q_2exp: Integer Division. (line 47)
-* mpz_fdiv_q_ui: Integer Division. (line 38)
-* mpz_fdiv_r: Integer Division. (line 34)
-* mpz_fdiv_r_2exp: Integer Division. (line 50)
-* mpz_fdiv_r_ui: Integer Division. (line 40)
-* mpz_fdiv_ui: Integer Division. (line 44)
-* mpz_fib2_ui: Number Theoretic Functions.
- (line 134)
-* mpz_fib_ui: Number Theoretic Functions.
- (line 133)
-* mpz_fits_sint_p: Miscellaneous Integer Functions.
- (line 9)
-* mpz_fits_slong_p: Miscellaneous Integer Functions.
- (line 7)
-* mpz_fits_sshort_p: Miscellaneous Integer Functions.
- (line 11)
-* mpz_fits_uint_p: Miscellaneous Integer Functions.
- (line 8)
-* mpz_fits_ulong_p: Miscellaneous Integer Functions.
- (line 6)
-* mpz_fits_ushort_p: Miscellaneous Integer Functions.
- (line 10)
-* mpz_gcd: Number Theoretic Functions.
- (line 29)
-* mpz_gcdext: Number Theoretic Functions.
- (line 45)
-* mpz_gcd_ui: Number Theoretic Functions.
- (line 35)
-* mpz_getlimbn: Integer Special Functions.
- (line 22)
-* mpz_get_d: Converting Integers. (line 26)
-* mpz_get_d_2exp: Converting Integers. (line 34)
-* mpz_get_si: Converting Integers. (line 17)
-* mpz_get_str: Converting Integers. (line 46)
-* mpz_get_ui: Converting Integers. (line 10)
-* mpz_hamdist: Integer Logic and Bit Fiddling.
- (line 28)
-* mpz_import: Integer Import and Export.
- (line 9)
-* mpz_init: Initializing Integers.
- (line 25)
-* mpz_init2: Initializing Integers.
- (line 32)
-* mpz_inits: Initializing Integers.
- (line 28)
-* mpz_init_set: Simultaneous Integer Init & Assign.
- (line 26)
-* mpz_init_set_d: Simultaneous Integer Init & Assign.
- (line 29)
-* mpz_init_set_si: Simultaneous Integer Init & Assign.
- (line 28)
-* mpz_init_set_str: Simultaneous Integer Init & Assign.
- (line 33)
-* mpz_init_set_ui: Simultaneous Integer Init & Assign.
- (line 27)
-* mpz_inp_raw: I/O of Integers. (line 61)
-* mpz_inp_str: I/O of Integers. (line 30)
-* mpz_invert: Number Theoretic Functions.
- (line 72)
-* mpz_ior: Integer Logic and Bit Fiddling.
- (line 13)
-* mpz_jacobi: Number Theoretic Functions.
- (line 82)
-* mpz_kronecker: Number Theoretic Functions.
- (line 90)
-* mpz_kronecker_si: Number Theoretic Functions.
- (line 91)
-* mpz_kronecker_ui: Number Theoretic Functions.
- (line 92)
-* mpz_lcm: Number Theoretic Functions.
- (line 65)
-* mpz_lcm_ui: Number Theoretic Functions.
- (line 66)
-* mpz_legendre: Number Theoretic Functions.
- (line 85)
-* mpz_limbs_finish: Integer Special Functions.
- (line 47)
-* mpz_limbs_modify: Integer Special Functions.
- (line 40)
-* mpz_limbs_read: Integer Special Functions.
- (line 34)
-* mpz_limbs_write: Integer Special Functions.
- (line 39)
-* mpz_lucnum2_ui: Number Theoretic Functions.
- (line 145)
-* mpz_lucnum_ui: Number Theoretic Functions.
- (line 144)
-* mpz_mfac_uiui: Number Theoretic Functions.
- (line 114)
-* mpz_mod: Integer Division. (line 112)
-* mpz_mod_ui: Integer Division. (line 113)
-* mpz_mul: Integer Arithmetic. (line 18)
-* mpz_mul_2exp: Integer Arithmetic. (line 36)
-* mpz_mul_si: Integer Arithmetic. (line 19)
-* mpz_mul_ui: Integer Arithmetic. (line 20)
-* mpz_neg: Integer Arithmetic. (line 41)
-* mpz_nextprime: Number Theoretic Functions.
- (line 22)
-* mpz_odd_p: Miscellaneous Integer Functions.
- (line 16)
-* mpz_out_raw: I/O of Integers. (line 45)
-* mpz_out_str: I/O of Integers. (line 17)
-* mpz_perfect_power_p: Integer Roots. (line 27)
-* mpz_perfect_square_p: Integer Roots. (line 36)
-* mpz_popcount: Integer Logic and Bit Fiddling.
- (line 22)
-* mpz_powm: Integer Exponentiation.
- (line 6)
-* mpz_powm_sec: Integer Exponentiation.
- (line 16)
-* mpz_powm_ui: Integer Exponentiation.
- (line 8)
-* mpz_pow_ui: Integer Exponentiation.
- (line 29)
-* mpz_primorial_ui: Number Theoretic Functions.
- (line 120)
-* mpz_probab_prime_p: Number Theoretic Functions.
- (line 6)
-* mpz_random: Integer Random Numbers.
- (line 41)
-* mpz_random2: Integer Random Numbers.
- (line 50)
-* mpz_realloc2: Initializing Integers.
- (line 56)
-* mpz_remove: Number Theoretic Functions.
- (line 106)
-* mpz_roinit_n: Integer Special Functions.
- (line 67)
-* MPZ_ROINIT_N: Integer Special Functions.
- (line 83)
-* mpz_root: Integer Roots. (line 6)
-* mpz_rootrem: Integer Roots. (line 12)
-* mpz_rrandomb: Integer Random Numbers.
- (line 29)
-* mpz_scan0: Integer Logic and Bit Fiddling.
- (line 35)
-* mpz_scan1: Integer Logic and Bit Fiddling.
- (line 37)
-* mpz_set: Assigning Integers. (line 9)
-* mpz_setbit: Integer Logic and Bit Fiddling.
- (line 51)
-* mpz_set_d: Assigning Integers. (line 12)
-* mpz_set_f: Assigning Integers. (line 14)
-* mpz_set_q: Assigning Integers. (line 13)
-* mpz_set_si: Assigning Integers. (line 11)
-* mpz_set_str: Assigning Integers. (line 20)
-* mpz_set_ui: Assigning Integers. (line 10)
-* mpz_sgn: Integer Comparisons. (line 27)
-* mpz_size: Integer Special Functions.
- (line 30)
-* mpz_sizeinbase: Miscellaneous Integer Functions.
- (line 22)
-* mpz_si_kronecker: Number Theoretic Functions.
- (line 93)
-* mpz_sqrt: Integer Roots. (line 17)
-* mpz_sqrtrem: Integer Roots. (line 20)
-* mpz_sub: Integer Arithmetic. (line 11)
-* mpz_submul: Integer Arithmetic. (line 30)
-* mpz_submul_ui: Integer Arithmetic. (line 32)
-* mpz_sub_ui: Integer Arithmetic. (line 12)
-* mpz_swap: Assigning Integers. (line 36)
-* mpz_t: Nomenclature and Types.
- (line 6)
-* mpz_tdiv_q: Integer Division. (line 54)
-* mpz_tdiv_qr: Integer Division. (line 56)
-* mpz_tdiv_qr_ui: Integer Division. (line 63)
-* mpz_tdiv_q_2exp: Integer Division. (line 68)
-* mpz_tdiv_q_ui: Integer Division. (line 59)
-* mpz_tdiv_r: Integer Division. (line 55)
-* mpz_tdiv_r_2exp: Integer Division. (line 71)
-* mpz_tdiv_r_ui: Integer Division. (line 61)
-* mpz_tdiv_ui: Integer Division. (line 65)
-* mpz_tstbit: Integer Logic and Bit Fiddling.
- (line 60)
-* mpz_ui_kronecker: Number Theoretic Functions.
- (line 94)
-* mpz_ui_pow_ui: Integer Exponentiation.
- (line 31)
-* mpz_ui_sub: Integer Arithmetic. (line 14)
-* mpz_urandomb: Integer Random Numbers.
- (line 12)
-* mpz_urandomm: Integer Random Numbers.
- (line 21)
-* mpz_xor: Integer Logic and Bit Fiddling.
- (line 16)
-* 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 86)
-* mp_limb_t: Nomenclature and Types.
- (line 31)
-* mp_set_memory_functions: Custom Allocation. (line 14)
-* mp_size_t: Nomenclature and Types.
- (line 37)
-* operator"": C++ Interface Integers.
- (line 29)
-* operator"" <1>: C++ Interface Rationals.
- (line 36)
-* operator"" <2>: C++ Interface Floats.
- (line 55)
-* operator%: C++ Interface Integers.
- (line 34)
-* operator/: C++ Interface Integers.
- (line 33)
-* operator<<: C++ Formatted Output.
- (line 10)
-* operator<< <1>: C++ Formatted Output.
- (line 19)
-* operator<< <2>: C++ Formatted Output.
- (line 32)
-* operator>>: C++ Formatted Input. (line 10)
-* operator>> <1>: C++ Formatted Input. (line 13)
-* operator>> <2>: C++ Formatted Input. (line 24)
-* operator>> <3>: C++ Interface Rationals.
- (line 86)
-* primorial: C++ Interface Integers.
- (line 73)
-* sgn: C++ Interface Integers.
- (line 65)
-* sgn <1>: C++ Interface Rationals.
- (line 56)
-* sgn <2>: C++ Interface Floats.
- (line 106)
-* sqrt: C++ Interface Integers.
- (line 66)
-* sqrt <1>: C++ Interface Floats.
- (line 107)
-* swap: C++ Interface Integers.
- (line 78)
-* swap <1>: C++ Interface Rationals.
- (line 59)
-* swap <2>: C++ Interface Floats.
- (line 110)
-* trunc: C++ Interface Floats.
- (line 111)
-
+++ /dev/null
-#!/bin/sh
-
-prefix=/tmp/ode
-exec_prefix=${prefix}
-exec_prefix_set=no
-
-usage="\
-Usage: ode-config [--prefix[=DIR]] [--exec-prefix[=DIR]] [--version] [--cflags] [--libs]"
-
-if test $# -eq 0; then
- echo "${usage}" 1>&2
- exit 1
-fi
-
-while test $# -gt 0; do
- case "$1" in
- -*=*) optarg=`echo "$1" | sed 's/[-_a-zA-Z0-9]*=//'` ;;
- *) optarg= ;;
- esac
-
- case $1 in
- --prefix=*)
- prefix=$optarg
- if test $exec_prefix_set = no ; then
- exec_prefix=$optarg
- fi
- ;;
- --prefix)
- echo $prefix
- ;;
- --exec-prefix=*)
- exec_prefix=$optarg
- exec_prefix_set=yes
- ;;
- --exec-prefix)
- echo $exec_prefix
- ;;
- --version)
- echo 0.16.2
- ;;
- --cflags)
- echo -I${prefix}/include
- ;;
- --libs)
- echo -L${exec_prefix}/lib -lode
- ;;
- *)
- echo "${usage}" 1>&2
- exit 1
- ;;
- esac
- shift
-done
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001-2003 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_COLLISION_H_
-#define _ODE_COLLISION_H_
-
-#include <ode/common.h>
-#include <ode/collision_space.h>
-#include <ode/contact.h>
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-/**
- * @defgroup collide Collision Detection
- *
- * ODE has two main components: a dynamics simulation engine and a collision
- * detection engine. The collision engine is given information about the
- * shape of each body. At each time step it figures out which bodies touch
- * each other and passes the resulting contact point information to the user.
- * The user in turn creates contact joints between bodies.
- *
- * Using ODE's collision detection is optional - an alternative collision
- * detection system can be used as long as it can supply the right kinds of
- * contact information.
- */
-
-
-/* ************************************************************************ */
-/* general functions */
-
-/**
- * @brief Destroy a geom, removing it from any space.
- *
- * Destroy a geom, removing it from any space it is in first. This one
- * function destroys a geom of any type, but to create a geom you must call
- * a creation function for that type.
- *
- * When a space is destroyed, if its cleanup mode is 1 (the default) then all
- * the geoms in that space are automatically destroyed as well.
- *
- * @param geom the geom to be destroyed.
- * @ingroup collide
- */
-ODE_API void dGeomDestroy (dGeomID geom);
-
-
-/**
- * @brief Set the user-defined data pointer stored in the geom.
- *
- * @param geom the geom to hold the data
- * @param data the data pointer to be stored
- * @ingroup collide
- */
-ODE_API void dGeomSetData (dGeomID geom, void* data);
-
-
-/**
- * @brief Get the user-defined data pointer stored in the geom.
- *
- * @param geom the geom containing the data
- * @ingroup collide
- */
-ODE_API void *dGeomGetData (dGeomID geom);
-
-
-/**
- * @brief Set the body associated with a placeable geom.
- *
- * Setting a body on a geom automatically combines the position vector and
- * rotation matrix of the body and geom, so that setting the position or
- * orientation of one will set the value for both objects. Setting a body
- * ID of zero gives the geom its own position and rotation, independent
- * from any body. If the geom was previously connected to a body then its
- * new independent position/rotation is set to the current position/rotation
- * of the body.
- *
- * Calling these functions on a non-placeable geom results in a runtime
- * error in the debug build of ODE.
- *
- * @param geom the geom to connect
- * @param body the body to attach to the geom
- * @ingroup collide
- */
-ODE_API void dGeomSetBody (dGeomID geom, dBodyID body);
-
-
-/**
- * @brief Get the body associated with a placeable geom.
- * @param geom the geom to query.
- * @sa dGeomSetBody
- * @ingroup collide
- */
-ODE_API dBodyID dGeomGetBody (dGeomID geom);
-
-
-/**
- * @brief Set the position vector of a placeable geom.
- *
- * If the geom is attached to a body, the body's position will also be changed.
- * Calling this function on a non-placeable geom results in a runtime error in
- * the debug build of ODE.
- *
- * @param geom the geom to set.
- * @param x the new X coordinate.
- * @param y the new Y coordinate.
- * @param z the new Z coordinate.
- * @sa dBodySetPosition
- * @ingroup collide
- */
-ODE_API void dGeomSetPosition (dGeomID geom, dReal x, dReal y, dReal z);
-
-
-/**
- * @brief Set the rotation matrix of a placeable geom.
- *
- * If the geom is attached to a body, the body's rotation will also be changed.
- * Calling this function on a non-placeable geom results in a runtime error in
- * the debug build of ODE.
- *
- * @param geom the geom to set.
- * @param R the new rotation matrix.
- * @sa dBodySetRotation
- * @ingroup collide
- */
-ODE_API void dGeomSetRotation (dGeomID geom, const dMatrix3 R);
-
-
-/**
- * @brief Set the rotation of a placeable geom.
- *
- * If the geom is attached to a body, the body's rotation will also be changed.
- *
- * Calling this function on a non-placeable geom results in a runtime error in
- * the debug build of ODE.
- *
- * @param geom the geom to set.
- * @param Q the new rotation.
- * @sa dBodySetQuaternion
- * @ingroup collide
- */
-ODE_API void dGeomSetQuaternion (dGeomID geom, const dQuaternion Q);
-
-
-/**
- * @brief Get the position vector of a placeable geom.
- *
- * If the geom is attached to a body, the body's position will be returned.
- *
- * Calling this function on a non-placeable geom results in a runtime error in
- * the debug build of ODE.
- *
- * @param geom the geom to query.
- * @returns A pointer to the geom's position vector.
- * @remarks The returned value is a pointer to the geom's internal
- * data structure. It is valid until any changes are made
- * to the geom.
- * @sa dBodyGetPosition
- * @ingroup collide
- */
-ODE_API const dReal * dGeomGetPosition (dGeomID geom);
-
-
-/**
- * @brief Copy the position of a geom into a vector.
- * @ingroup collide
- * @param geom the geom to query
- * @param pos a copy of the geom position
- * @sa dGeomGetPosition
- */
-ODE_API void dGeomCopyPosition (dGeomID geom, dVector3 pos);
-
-
-/**
- * @brief Get the rotation matrix of a placeable geom.
- *
- * If the geom is attached to a body, the body's rotation will be returned.
- *
- * Calling this function on a non-placeable geom results in a runtime error in
- * the debug build of ODE.
- *
- * @param geom the geom to query.
- * @returns A pointer to the geom's rotation matrix.
- * @remarks The returned value is a pointer to the geom's internal
- * data structure. It is valid until any changes are made
- * to the geom.
- * @sa dBodyGetRotation
- * @ingroup collide
- */
-ODE_API const dReal * dGeomGetRotation (dGeomID geom);
-
-
-/**
- * @brief Get the rotation matrix of a placeable geom.
- *
- * If the geom is attached to a body, the body's rotation will be returned.
- *
- * Calling this function on a non-placeable geom results in a runtime error in
- * the debug build of ODE.
- *
- * @param geom the geom to query.
- * @param R a copy of the geom rotation
- * @sa dGeomGetRotation
- * @ingroup collide
- */
-ODE_API void dGeomCopyRotation(dGeomID geom, dMatrix3 R);
-
-
-/**
- * @brief Get the rotation quaternion of a placeable geom.
- *
- * If the geom is attached to a body, the body's quaternion will be returned.
- *
- * Calling this function on a non-placeable geom results in a runtime error in
- * the debug build of ODE.
- *
- * @param geom the geom to query.
- * @param result a copy of the rotation quaternion.
- * @sa dBodyGetQuaternion
- * @ingroup collide
- */
-ODE_API void dGeomGetQuaternion (dGeomID geom, dQuaternion result);
-
-
-/**
- * @brief Return the axis-aligned bounding box.
- *
- * Return in aabb an axis aligned bounding box that surrounds the given geom.
- * The aabb array has elements (minx, maxx, miny, maxy, minz, maxz). If the
- * geom is a space, a bounding box that surrounds all contained geoms is
- * returned.
- *
- * This function may return a pre-computed cached bounding box, if it can
- * determine that the geom has not moved since the last time the bounding
- * box was computed.
- *
- * @param geom the geom to query
- * @param aabb the returned bounding box
- * @ingroup collide
- */
-ODE_API void dGeomGetAABB (dGeomID geom, dReal aabb[6]);
-
-
-/**
- * @brief Determing if a geom is a space.
- * @param geom the geom to query
- * @returns Non-zero if the geom is a space, zero otherwise.
- * @ingroup collide
- */
-ODE_API int dGeomIsSpace (dGeomID geom);
-
-
-/**
- * @brief Query for the space containing a particular geom.
- * @param geom the geom to query
- * @returns The space that contains the geom, or NULL if the geom is
- * not contained by a space.
- * @ingroup collide
- */
-ODE_API dSpaceID dGeomGetSpace (dGeomID);
-
-
-/**
- * @brief Given a geom, this returns its class.
- *
- * The ODE classes are:
- * @li dSphereClass
- * @li dBoxClass
- * @li dCylinderClass
- * @li dPlaneClass
- * @li dRayClass
- * @li dConvexClass
- * @li dGeomTransformClass
- * @li dTriMeshClass
- * @li dSimpleSpaceClass
- * @li dHashSpaceClass
- * @li dQuadTreeSpaceClass
- * @li dFirstUserClass
- * @li dLastUserClass
- *
- * User-defined class will return their own number.
- *
- * @param geom the geom to query
- * @returns The geom class ID.
- * @ingroup collide
- */
-ODE_API int dGeomGetClass (dGeomID geom);
-
-
-/**
- * @brief Set the "category" bitfield for the given geom.
- *
- * The category bitfield is used by spaces to govern which geoms will
- * interact with each other. The bitfield is guaranteed to be at least
- * 32 bits wide. The default category values for newly created geoms
- * have all bits set.
- *
- * @param geom the geom to set
- * @param bits the new bitfield value
- * @ingroup collide
- */
-ODE_API void dGeomSetCategoryBits (dGeomID geom, unsigned long bits);
-
-
-/**
- * @brief Set the "collide" bitfield for the given geom.
- *
- * The collide bitfield is used by spaces to govern which geoms will
- * interact with each other. The bitfield is guaranteed to be at least
- * 32 bits wide. The default category values for newly created geoms
- * have all bits set.
- *
- * @param geom the geom to set
- * @param bits the new bitfield value
- * @ingroup collide
- */
-ODE_API void dGeomSetCollideBits (dGeomID geom, unsigned long bits);
-
-
-/**
- * @brief Get the "category" bitfield for the given geom.
- *
- * @param geom the geom to set
- * @param bits the new bitfield value
- * @sa dGeomSetCategoryBits
- * @ingroup collide
- */
-ODE_API unsigned long dGeomGetCategoryBits (dGeomID);
-
-
-/**
- * @brief Get the "collide" bitfield for the given geom.
- *
- * @param geom the geom to set
- * @param bits the new bitfield value
- * @sa dGeomSetCollideBits
- * @ingroup collide
- */
-ODE_API unsigned long dGeomGetCollideBits (dGeomID);
-
-
-/**
- * @brief Enable a geom.
- *
- * Disabled geoms are completely ignored by dSpaceCollide and dSpaceCollide2,
- * although they can still be members of a space. New geoms are created in
- * the enabled state.
- *
- * @param geom the geom to enable
- * @sa dGeomDisable
- * @sa dGeomIsEnabled
- * @ingroup collide
- */
-ODE_API void dGeomEnable (dGeomID geom);
-
-
-/**
- * @brief Disable a geom.
- *
- * Disabled geoms are completely ignored by dSpaceCollide and dSpaceCollide2,
- * although they can still be members of a space. New geoms are created in
- * the enabled state.
- *
- * @param geom the geom to disable
- * @sa dGeomDisable
- * @sa dGeomIsEnabled
- * @ingroup collide
- */
-ODE_API void dGeomDisable (dGeomID geom);
-
-
-/**
- * @brief Check to see if a geom is enabled.
- *
- * Disabled geoms are completely ignored by dSpaceCollide and dSpaceCollide2,
- * although they can still be members of a space. New geoms are created in
- * the enabled state.
- *
- * @param geom the geom to query
- * @returns Non-zero if the geom is enabled, zero otherwise.
- * @sa dGeomDisable
- * @sa dGeomIsEnabled
- * @ingroup collide
- */
-ODE_API int dGeomIsEnabled (dGeomID geom);
-
-
-enum
-{
- dGeomCommonControlClass = 0,
- dGeomColliderControlClass = 1
-};
-
-enum
-{
- dGeomCommonAnyControlCode = 0,
-
- dGeomColliderSetMergeSphereContactsControlCode = 1,
- dGeomColliderGetMergeSphereContactsControlCode = 2
-};
-
-enum
-{
- dGeomColliderMergeContactsValue__Default = 0, /* Used with Set... to restore default value*/
- dGeomColliderMergeContactsValue_None = 1,
- dGeomColliderMergeContactsValue_Normals = 2,
- dGeomColliderMergeContactsValue_Full = 3
-};
-
-/**
- * @brief Execute low level control operation for geometry.
- *
- * The variable the dataSize points to must be initialized before the call.
- * If the size does not match the one expected for the control class/code function
- * changes it to the size expected and returns failure. This implies the function
- * can be called with NULL data and zero size to test if control class/code is supported
- * and obtain required data size for it.
- *
- * dGeomCommonAnyControlCode applies to any control class and returns success if
- * at least one control code is available for the given class with given geom.
- *
- * Currently there are the folliwing control classes supported:
- * @li dGeomColliderControlClass
- *
- * For dGeomColliderControlClass there are the following codes available:
- * @li dGeomColliderSetMergeSphereContactsControlCode (arg of type int, dGeomColliderMergeContactsValue_*)
- * @li dGeomColliderGetMergeSphereContactsControlCode (arg of type int, dGeomColliderMergeContactsValue_*)
- *
- * @param geom the geom to control
- * @param controlClass the control class
- * @param controlCode the control code for the class
- * @param dataValue the control argument pointer
- * @param dataSize the control argument size provided or expected
- * @returns Boolean execution status
- * @ingroup collide
- */
-ODE_API int dGeomLowLevelControl (dGeomID geom, int controlClass, int controlCode, void *dataValue, int *dataSize);
-
-
-/**
- * @brief Get world position of a relative point on geom.
- *
- * Calling this function on a non-placeable geom results in the same point being
- * returned.
- *
- * @ingroup collide
- * @param result will contain the result.
- */
-ODE_API void dGeomGetRelPointPos
-(
- dGeomID geom, dReal px, dReal py, dReal pz,
- dVector3 result
-);
-
-/**
- * @brief takes a point in global coordinates and returns
- * the point's position in geom-relative coordinates.
- *
- * Calling this function on a non-placeable geom results in the same point being
- * returned.
- *
- * @remarks
- * This is the inverse of dGeomGetRelPointPos()
- * @ingroup collide
- * @param result will contain the result.
- */
-ODE_API void dGeomGetPosRelPoint
-(
- dGeomID geom, dReal px, dReal py, dReal pz,
- dVector3 result
-);
-
-/**
- * @brief Convert from geom-local to world coordinates.
- *
- * Calling this function on a non-placeable geom results in the same vector being
- * returned.
- *
- * @ingroup collide
- * @param result will contain the result.
- */
-ODE_API void dGeomVectorToWorld
-(
- dGeomID geom, dReal px, dReal py, dReal pz,
- dVector3 result
-);
-
-/**
- * @brief Convert from world to geom-local coordinates.
- *
- * Calling this function on a non-placeable geom results in the same vector being
- * returned.
- *
- * @ingroup collide
- * @param result will contain the result.
- */
-ODE_API void dGeomVectorFromWorld
-(
- dGeomID geom, dReal px, dReal py, dReal pz,
- dVector3 result
-);
-
-
-/* ************************************************************************ */
-/* geom offset from body */
-
-/**
- * @brief Set the local offset position of a geom from its body.
- *
- * Sets the geom's positional offset in local coordinates.
- * After this call, the geom will be at a new position determined from the
- * body's position and the offset.
- * The geom must be attached to a body.
- * If the geom did not have an offset, it is automatically created.
- *
- * @param geom the geom to set.
- * @param x the new X coordinate.
- * @param y the new Y coordinate.
- * @param z the new Z coordinate.
- * @ingroup collide
- */
-ODE_API void dGeomSetOffsetPosition (dGeomID geom, dReal x, dReal y, dReal z);
-
-
-/**
- * @brief Set the local offset rotation matrix of a geom from its body.
- *
- * Sets the geom's rotational offset in local coordinates.
- * After this call, the geom will be at a new position determined from the
- * body's position and the offset.
- * The geom must be attached to a body.
- * If the geom did not have an offset, it is automatically created.
- *
- * @param geom the geom to set.
- * @param R the new rotation matrix.
- * @ingroup collide
- */
-ODE_API void dGeomSetOffsetRotation (dGeomID geom, const dMatrix3 R);
-
-
-/**
- * @brief Set the local offset rotation of a geom from its body.
- *
- * Sets the geom's rotational offset in local coordinates.
- * After this call, the geom will be at a new position determined from the
- * body's position and the offset.
- * The geom must be attached to a body.
- * If the geom did not have an offset, it is automatically created.
- *
- * @param geom the geom to set.
- * @param Q the new rotation.
- * @ingroup collide
- */
-ODE_API void dGeomSetOffsetQuaternion (dGeomID geom, const dQuaternion Q);
-
-
-/**
- * @brief Set the offset position of a geom from its body.
- *
- * Sets the geom's positional offset to move it to the new world
- * coordinates.
- * After this call, the geom will be at the world position passed in,
- * and the offset will be the difference from the current body position.
- * The geom must be attached to a body.
- * If the geom did not have an offset, it is automatically created.
- *
- * @param geom the geom to set.
- * @param x the new X coordinate.
- * @param y the new Y coordinate.
- * @param z the new Z coordinate.
- * @ingroup collide
- */
-ODE_API void dGeomSetOffsetWorldPosition (dGeomID geom, dReal x, dReal y, dReal z);
-
-
-/**
- * @brief Set the offset rotation of a geom from its body.
- *
- * Sets the geom's rotational offset to orient it to the new world
- * rotation matrix.
- * After this call, the geom will be at the world orientation passed in,
- * and the offset will be the difference from the current body orientation.
- * The geom must be attached to a body.
- * If the geom did not have an offset, it is automatically created.
- *
- * @param geom the geom to set.
- * @param R the new rotation matrix.
- * @ingroup collide
- */
-ODE_API void dGeomSetOffsetWorldRotation (dGeomID geom, const dMatrix3 R);
-
-
-/**
- * @brief Set the offset rotation of a geom from its body.
- *
- * Sets the geom's rotational offset to orient it to the new world
- * rotation matrix.
- * After this call, the geom will be at the world orientation passed in,
- * and the offset will be the difference from the current body orientation.
- * The geom must be attached to a body.
- * If the geom did not have an offset, it is automatically created.
- *
- * @param geom the geom to set.
- * @param Q the new rotation.
- * @ingroup collide
- */
-ODE_API void dGeomSetOffsetWorldQuaternion (dGeomID geom, const dQuaternion);
-
-
-/**
- * @brief Clear any offset from the geom.
- *
- * If the geom has an offset, it is eliminated and the geom is
- * repositioned at the body's position. If the geom has no offset,
- * this function does nothing.
- * This is more efficient than calling dGeomSetOffsetPosition(zero)
- * and dGeomSetOffsetRotation(identiy), because this function actually
- * eliminates the offset, rather than leaving it as the identity transform.
- *
- * @param geom the geom to have its offset destroyed.
- * @ingroup collide
- */
-ODE_API void dGeomClearOffset(dGeomID geom);
-
-
-/**
- * @brief Check to see whether the geom has an offset.
- *
- * This function will return non-zero if the offset has been created.
- * Note that there is a difference between a geom with no offset,
- * and a geom with an offset that is the identity transform.
- * In the latter case, although the observed behaviour is identical,
- * there is a unnecessary computation involved because the geom will
- * be applying the transform whenever it needs to recalculate its world
- * position.
- *
- * @param geom the geom to query.
- * @returns Non-zero if the geom has an offset, zero otherwise.
- * @ingroup collide
- */
-ODE_API int dGeomIsOffset(dGeomID geom);
-
-
-/**
- * @brief Get the offset position vector of a geom.
- *
- * Returns the positional offset of the geom in local coordinates.
- * If the geom has no offset, this function returns the zero vector.
- *
- * @param geom the geom to query.
- * @returns A pointer to the geom's offset vector.
- * @remarks The returned value is a pointer to the geom's internal
- * data structure. It is valid until any changes are made
- * to the geom.
- * @ingroup collide
- */
-ODE_API const dReal * dGeomGetOffsetPosition (dGeomID geom);
-
-
-/**
- * @brief Copy the offset position vector of a geom.
- *
- * Returns the positional offset of the geom in local coordinates.
- * If the geom has no offset, this function returns the zero vector.
- *
- * @param geom the geom to query.
- * @param pos returns the offset position
- * @ingroup collide
- */
-ODE_API void dGeomCopyOffsetPosition (dGeomID geom, dVector3 pos);
-
-
-/**
- * @brief Get the offset rotation matrix of a geom.
- *
- * Returns the rotational offset of the geom in local coordinates.
- * If the geom has no offset, this function returns the identity
- * matrix.
- *
- * @param geom the geom to query.
- * @returns A pointer to the geom's offset rotation matrix.
- * @remarks The returned value is a pointer to the geom's internal
- * data structure. It is valid until any changes are made
- * to the geom.
- * @ingroup collide
- */
-ODE_API const dReal * dGeomGetOffsetRotation (dGeomID geom);
-
-
-/**
- * @brief Copy the offset rotation matrix of a geom.
- *
- * Returns the rotational offset of the geom in local coordinates.
- * If the geom has no offset, this function returns the identity
- * matrix.
- *
- * @param geom the geom to query.
- * @param R returns the rotation matrix.
- * @ingroup collide
- */
-ODE_API void dGeomCopyOffsetRotation (dGeomID geom, dMatrix3 R);
-
-
-/**
- * @brief Get the offset rotation quaternion of a geom.
- *
- * Returns the rotation offset of the geom as a quaternion.
- * If the geom has no offset, the identity quaternion is returned.
- *
- * @param geom the geom to query.
- * @param result a copy of the rotation quaternion.
- * @ingroup collide
- */
-ODE_API void dGeomGetOffsetQuaternion (dGeomID geom, dQuaternion result);
-
-
-/* ************************************************************************ */
-/* collision detection */
-
-/*
- * Just generate any contacts (disables any contact refining).
- */
-#define CONTACTS_UNIMPORTANT 0x80000000
-
-/**
- *
- * @brief Given two geoms o1 and o2 that potentially intersect,
- * generate contact information for them.
- *
- * Internally, this just calls the correct class-specific collision
- * functions for o1 and o2.
- *
- * @param o1 The first geom to test.
- * @param o2 The second geom to test.
- *
- * @param flags The flags specify how contacts should be generated if
- * the geoms touch. The lower 16 bits of flags is an integer that
- * specifies the maximum number of contact points to generate. You must
- * ask for at least one contact.
- * Additionally, following bits may be set:
- * CONTACTS_UNIMPORTANT -- just generate any contacts (skip contact refining).
- * All other bits in flags must be set to zero. In the future the other bits
- * may be used to select from different contact generation strategies.
- *
- * @param contact Points to an array of dContactGeom structures. The array
- * must be able to hold at least the maximum number of contacts. These
- * dContactGeom structures may be embedded within larger structures in the
- * array -- the skip parameter is the byte offset from one dContactGeom to
- * the next in the array. If skip is sizeof(dContactGeom) then contact
- * points to a normal (C-style) array. It is an error for skip to be smaller
- * than sizeof(dContactGeom).
- *
- * @returns If the geoms intersect, this function returns the number of contact
- * points generated (and updates the contact array), otherwise it returns 0
- * (and the contact array is not touched).
- *
- * @remarks If a space is passed as o1 or o2 then this function will collide
- * all objects contained in o1 with all objects contained in o2, and return
- * the resulting contact points. This method for colliding spaces with geoms
- * (or spaces with spaces) provides no user control over the individual
- * collisions. To get that control, use dSpaceCollide or dSpaceCollide2 instead.
- *
- * @remarks If o1 and o2 are the same geom then this function will do nothing
- * and return 0. Technically speaking an object intersects with itself, but it
- * is not useful to find contact points in this case.
- *
- * @remarks This function does not care if o1 and o2 are in the same space or not
- * (or indeed if they are in any space at all).
- *
- * @ingroup collide
- */
-ODE_API int dCollide (dGeomID o1, dGeomID o2, int flags, dContactGeom *contact,
- int skip);
-
-/**
- * @brief Determines which pairs of geoms in a space may potentially intersect,
- * and calls the callback function for each candidate pair.
- *
- * @param space The space to test.
- *
- * @param data Passed from dSpaceCollide directly to the callback
- * function. Its meaning is user defined. The o1 and o2 arguments are the
- * geoms that may be near each other.
- *
- * @param callback A callback function is of type @ref dNearCallback.
- *
- * @remarks Other spaces that are contained within the colliding space are
- * not treated specially, i.e. they are not recursed into. The callback
- * function may be passed these contained spaces as one or both geom
- * arguments.
- *
- * @remarks dSpaceCollide() is guaranteed to pass all intersecting geom
- * pairs to the callback function, but may also pass close but
- * non-intersecting pairs. The number of these calls depends on the
- * internal algorithms used by the space. Thus you should not expect
- * that dCollide will return contacts for every pair passed to the
- * callback.
- *
- * @sa dSpaceCollide2
- * @ingroup collide
- */
-ODE_API void dSpaceCollide (dSpaceID space, void *data, dNearCallback *callback);
-
-
-/**
- * @brief Determines which geoms from one space may potentially intersect with
- * geoms from another space, and calls the callback function for each candidate
- * pair.
- *
- * @param space1 The first space to test.
- *
- * @param space2 The second space to test.
- *
- * @param data Passed from dSpaceCollide directly to the callback
- * function. Its meaning is user defined. The o1 and o2 arguments are the
- * geoms that may be near each other.
- *
- * @param callback A callback function is of type @ref dNearCallback.
- *
- * @remarks This function can also test a single non-space geom against a
- * space. This function is useful when there is a collision hierarchy, i.e.
- * when there are spaces that contain other spaces.
- *
- * @remarks Other spaces that are contained within the colliding space are
- * not treated specially, i.e. they are not recursed into. The callback
- * function may be passed these contained spaces as one or both geom
- * arguments.
- *
- * @remarks Sublevel value of space affects how the spaces are iterated.
- * Both spaces are recursed only if their sublevels match. Otherwise, only
- * the space with greater sublevel is recursed and the one with lesser sublevel
- * is used as a geom itself.
- *
- * @remarks dSpaceCollide2() is guaranteed to pass all intersecting geom
- * pairs to the callback function, but may also pass close but
- * non-intersecting pairs. The number of these calls depends on the
- * internal algorithms used by the space. Thus you should not expect
- * that dCollide will return contacts for every pair passed to the
- * callback.
- *
- * @sa dSpaceCollide
- * @sa dSpaceSetSublevel
- * @ingroup collide
- */
-ODE_API void dSpaceCollide2 (dGeomID space1, dGeomID space2, void *data, dNearCallback *callback);
-
-
-/* ************************************************************************ */
-/* standard classes */
-
-/* the maximum number of user classes that are supported */
-enum {
- dMaxUserClasses = 4
-};
-
-/* class numbers - each geometry object needs a unique number */
-enum {
- dSphereClass = 0,
- dBoxClass,
- dCapsuleClass,
- dCylinderClass,
- dPlaneClass,
- dRayClass,
- dConvexClass,
- dGeomTransformClass,
- dTriMeshClass,
- dHeightfieldClass,
-
- dFirstSpaceClass,
- dSimpleSpaceClass = dFirstSpaceClass,
- dHashSpaceClass,
- dSweepAndPruneSpaceClass, /* SAP */
- dQuadTreeSpaceClass,
- dLastSpaceClass = dQuadTreeSpaceClass,
-
- dFirstUserClass,
- dLastUserClass = dFirstUserClass + dMaxUserClasses - 1,
- dGeomNumClasses
-};
-
-
-/**
- * @defgroup collide_sphere Sphere Class
- * @ingroup collide
- */
-
-/**
- * @brief Create a sphere geom of the given radius, and return its ID.
- *
- * @param space a space to contain the new geom. May be null.
- * @param radius the radius of the sphere.
- *
- * @returns A new sphere geom.
- *
- * @remarks The point of reference for a sphere is its center.
- *
- * @sa dGeomDestroy
- * @sa dGeomSphereSetRadius
- * @ingroup collide_sphere
- */
-ODE_API dGeomID dCreateSphere (dSpaceID space, dReal radius);
-
-
-/**
- * @brief Set the radius of a sphere geom.
- *
- * @param sphere the sphere to set.
- * @param radius the new radius.
- *
- * @sa dGeomSphereGetRadius
- * @ingroup collide_sphere
- */
-ODE_API void dGeomSphereSetRadius (dGeomID sphere, dReal radius);
-
-
-/**
- * @brief Retrieves the radius of a sphere geom.
- *
- * @param sphere the sphere to query.
- *
- * @sa dGeomSphereSetRadius
- * @ingroup collide_sphere
- */
-ODE_API dReal dGeomSphereGetRadius (dGeomID sphere);
-
-
-/**
- * @brief Calculate the depth of the a given point within a sphere.
- *
- * @param sphere the sphere to query.
- * @param x the X coordinate of the point.
- * @param y the Y coordinate of the point.
- * @param z the Z coordinate of the point.
- *
- * @returns The depth of the point. Points inside the sphere will have a
- * positive depth, points outside it will have a negative depth, and points
- * on the surface will have a depth of zero.
- *
- * @ingroup collide_sphere
- */
-ODE_API dReal dGeomSpherePointDepth (dGeomID sphere, dReal x, dReal y, dReal z);
-
-
-/*--> Convex Functions*/
-ODE_API dGeomID dCreateConvex (dSpaceID space,
- const dReal *_planes,
- unsigned int _planecount,
- const dReal *_points,
- unsigned int _pointcount,
- const unsigned int *_polygons);
-
-ODE_API void dGeomSetConvex (dGeomID g,
- const dReal *_planes,
- unsigned int _count,
- const dReal *_points,
- unsigned int _pointcount,
- const unsigned int *_polygons);
-/*<-- Convex Functions*/
-
-/**
- * @defgroup collide_box Box Class
- * @ingroup collide
- */
-
-/**
- * @brief Create a box geom with the provided side lengths.
- *
- * @param space a space to contain the new geom. May be null.
- * @param lx the length of the box along the X axis
- * @param ly the length of the box along the Y axis
- * @param lz the length of the box along the Z axis
- *
- * @returns A new box geom.
- *
- * @remarks The point of reference for a box is its center.
- *
- * @sa dGeomDestroy
- * @sa dGeomBoxSetLengths
- * @ingroup collide_box
- */
-ODE_API dGeomID dCreateBox (dSpaceID space, dReal lx, dReal ly, dReal lz);
-
-
-/**
- * @brief Set the side lengths of the given box.
- *
- * @param box the box to set
- * @param lx the length of the box along the X axis
- * @param ly the length of the box along the Y axis
- * @param lz the length of the box along the Z axis
- *
- * @sa dGeomBoxGetLengths
- * @ingroup collide_box
- */
-ODE_API void dGeomBoxSetLengths (dGeomID box, dReal lx, dReal ly, dReal lz);
-
-
-/**
- * @brief Get the side lengths of a box.
- *
- * @param box the box to query
- * @param result the returned side lengths
- *
- * @sa dGeomBoxSetLengths
- * @ingroup collide_box
- */
-ODE_API void dGeomBoxGetLengths (dGeomID box, dVector3 result);
-
-
-/**
- * @brief Return the depth of a point in a box.
- *
- * @param box the box to query
- * @param x the X coordinate of the point to test.
- * @param y the Y coordinate of the point to test.
- * @param z the Z coordinate of the point to test.
- *
- * @returns The depth of the point. Points inside the box will have a
- * positive depth, points outside it will have a negative depth, and points
- * on the surface will have a depth of zero.
- */
-ODE_API dReal dGeomBoxPointDepth (dGeomID box, dReal x, dReal y, dReal z);
-
-
-ODE_API dGeomID dCreatePlane (dSpaceID space, dReal a, dReal b, dReal c, dReal d);
-ODE_API void dGeomPlaneSetParams (dGeomID plane, dReal a, dReal b, dReal c, dReal d);
-ODE_API void dGeomPlaneGetParams (dGeomID plane, dVector4 result);
-ODE_API dReal dGeomPlanePointDepth (dGeomID plane, dReal x, dReal y, dReal z);
-
-ODE_API dGeomID dCreateCapsule (dSpaceID space, dReal radius, dReal length);
-ODE_API void dGeomCapsuleSetParams (dGeomID ccylinder, dReal radius, dReal length);
-ODE_API void dGeomCapsuleGetParams (dGeomID ccylinder, dReal *radius, dReal *length);
-ODE_API dReal dGeomCapsulePointDepth (dGeomID ccylinder, dReal x, dReal y, dReal z);
-
-/* For now we want to have a backwards compatible C-API, note: C++ API is not.*/
-#define dCreateCCylinder dCreateCapsule
-#define dGeomCCylinderSetParams dGeomCapsuleSetParams
-#define dGeomCCylinderGetParams dGeomCapsuleGetParams
-#define dGeomCCylinderPointDepth dGeomCapsulePointDepth
-#define dCCylinderClass dCapsuleClass
-
-ODE_API dGeomID dCreateCylinder (dSpaceID space, dReal radius, dReal length);
-ODE_API void dGeomCylinderSetParams (dGeomID cylinder, dReal radius, dReal length);
-ODE_API void dGeomCylinderGetParams (dGeomID cylinder, dReal *radius, dReal *length);
-
-ODE_API dGeomID dCreateRay (dSpaceID space, dReal length);
-ODE_API void dGeomRaySetLength (dGeomID ray, dReal length);
-ODE_API dReal dGeomRayGetLength (dGeomID ray);
-ODE_API void dGeomRaySet (dGeomID ray, dReal px, dReal py, dReal pz,
- dReal dx, dReal dy, dReal dz);
-ODE_API void dGeomRayGet (dGeomID ray, dVector3 start, dVector3 dir);
-
-/*
- * Set/get ray flags that influence ray collision detection.
- * These flags are currently only noticed by the trimesh collider, because
- * they can make a major differences there.
- */
-ODE_API_DEPRECATED ODE_API void dGeomRaySetParams (dGeomID g, int FirstContact, int BackfaceCull);
-ODE_API_DEPRECATED ODE_API void dGeomRayGetParams (dGeomID g, int *FirstContact, int *BackfaceCull);
-ODE_API void dGeomRaySetFirstContact (dGeomID g, int firstContact);
-ODE_API int dGeomRayGetFirstContact (dGeomID g);
-ODE_API void dGeomRaySetBackfaceCull (dGeomID g, int backfaceCull);
-ODE_API int dGeomRayGetBackfaceCull (dGeomID g);
-ODE_API void dGeomRaySetClosestHit (dGeomID g, int closestHit);
-ODE_API int dGeomRayGetClosestHit (dGeomID g);
-
-#include "collision_trimesh.h"
-
-ODE_API_DEPRECATED ODE_API dGeomID dCreateGeomTransform (dSpaceID space);
-ODE_API_DEPRECATED ODE_API void dGeomTransformSetGeom (dGeomID g, dGeomID obj);
-ODE_API_DEPRECATED ODE_API dGeomID dGeomTransformGetGeom (dGeomID g);
-ODE_API_DEPRECATED ODE_API void dGeomTransformSetCleanup (dGeomID g, int mode);
-ODE_API_DEPRECATED ODE_API int dGeomTransformGetCleanup (dGeomID g);
-ODE_API_DEPRECATED ODE_API void dGeomTransformSetInfo (dGeomID g, int mode);
-ODE_API_DEPRECATED ODE_API int dGeomTransformGetInfo (dGeomID g);
-
-
-/* ************************************************************************ */
-/* heightfield functions */
-
-
-/* Data storage for heightfield data.*/
-struct dxHeightfieldData;
-typedef struct dxHeightfieldData* dHeightfieldDataID;
-
-
-/**
- * @brief Callback prototype
- *
- * Used by the callback heightfield data type to sample a height for a
- * given cell position.
- *
- * @param p_user_data User data specified when creating the dHeightfieldDataID
- * @param x The index of a sample in the local x axis. It is a value
- * in the range zero to ( nWidthSamples - 1 ).
- * @param x The index of a sample in the local z axis. It is a value
- * in the range zero to ( nDepthSamples - 1 ).
- *
- * @return The sample height which is then scaled and offset using the
- * values specified when the heightfield data was created.
- *
- * @ingroup collide
- */
-typedef dReal dHeightfieldGetHeight( void* p_user_data, int x, int z );
-
-
-
-/**
- * @brief Creates a heightfield geom.
- *
- * Uses the information in the given dHeightfieldDataID to construct
- * a geom representing a heightfield in a collision space.
- *
- * @param space The space to add the geom to.
- * @param data The dHeightfieldDataID created by dGeomHeightfieldDataCreate and
- * setup by dGeomHeightfieldDataBuildCallback, dGeomHeightfieldDataBuildByte,
- * dGeomHeightfieldDataBuildShort or dGeomHeightfieldDataBuildFloat.
- * @param bPlaceable If non-zero this geom can be transformed in the world using the
- * usual functions such as dGeomSetPosition and dGeomSetRotation. If the geom is
- * not set as placeable, then it uses a fixed orientation where the global y axis
- * represents the dynamic 'height' of the heightfield.
- *
- * @return A geom id to reference this geom in other calls.
- *
- * @ingroup collide
- */
-ODE_API dGeomID dCreateHeightfield( dSpaceID space,
- dHeightfieldDataID data, int bPlaceable );
-
-
-/**
- * @brief Creates a new empty dHeightfieldDataID.
- *
- * Allocates a new dHeightfieldDataID and returns it. You must call
- * dGeomHeightfieldDataDestroy to destroy it after the geom has been removed.
- * The dHeightfieldDataID value is used when specifying a data format type.
- *
- * @return A dHeightfieldDataID for use with dGeomHeightfieldDataBuildCallback,
- * dGeomHeightfieldDataBuildByte, dGeomHeightfieldDataBuildShort or
- * dGeomHeightfieldDataBuildFloat.
- * @ingroup collide
- */
-ODE_API dHeightfieldDataID dGeomHeightfieldDataCreate(void);
-
-
-/**
- * @brief Destroys a dHeightfieldDataID.
- *
- * Deallocates a given dHeightfieldDataID and all managed resources.
- *
- * @param d A dHeightfieldDataID created by dGeomHeightfieldDataCreate
- * @ingroup collide
- */
-ODE_API void dGeomHeightfieldDataDestroy( dHeightfieldDataID d );
-
-
-
-/**
- * @brief Configures a dHeightfieldDataID to use a callback to
- * retrieve height data.
- *
- * Before a dHeightfieldDataID can be used by a geom it must be
- * configured to specify the format of the height data.
- * This call specifies that the heightfield data is computed by
- * the user and it should use the given callback when determining
- * the height of a given element of it's shape.
- *
- * @param d A new dHeightfieldDataID created by dGeomHeightfieldDataCreate
- *
- * @param width Specifies the total 'width' of the heightfield along
- * the geom's local x axis.
- * @param depth Specifies the total 'depth' of the heightfield along
- * the geom's local z axis.
- *
- * @param widthSamples Specifies the number of vertices to sample
- * along the width of the heightfield. Each vertex has a corresponding
- * height value which forms the overall shape.
- * Naturally this value must be at least two or more.
- * @param depthSamples Specifies the number of vertices to sample
- * along the depth of the heightfield.
- *
- * @param scale A uniform scale applied to all raw height data.
- * @param offset An offset applied to the scaled height data.
- *
- * @param thickness A value subtracted from the lowest height
- * value which in effect adds an additional cuboid to the base of the
- * heightfield. This is used to prevent geoms from looping under the
- * desired terrain and not registering as a collision. Note that the
- * thickness is not affected by the scale or offset parameters.
- *
- * @param bWrap If non-zero the heightfield will infinitely tile in both
- * directions along the local x and z axes. If zero the heightfield is
- * bounded from zero to width in the local x axis, and zero to depth in
- * the local z axis.
- *
- * @ingroup collide
- */
-ODE_API void dGeomHeightfieldDataBuildCallback( dHeightfieldDataID d,
- void* pUserData, dHeightfieldGetHeight* pCallback,
- dReal width, dReal depth, int widthSamples, int depthSamples,
- dReal scale, dReal offset, dReal thickness, int bWrap );
-
-/**
- * @brief Configures a dHeightfieldDataID to use height data in byte format.
- *
- * Before a dHeightfieldDataID can be used by a geom it must be
- * configured to specify the format of the height data.
- * This call specifies that the heightfield data is stored as a rectangular
- * array of bytes (8 bit unsigned) representing the height at each sample point.
- *
- * @param d A new dHeightfieldDataID created by dGeomHeightfieldDataCreate
- *
- * @param pHeightData A pointer to the height data.
- * @param bCopyHeightData When non-zero the height data is copied to an
- * internal store. When zero the height data is accessed by reference and
- * so must persist throughout the lifetime of the heightfield.
- *
- * @param width Specifies the total 'width' of the heightfield along
- * the geom's local x axis.
- * @param depth Specifies the total 'depth' of the heightfield along
- * the geom's local z axis.
- *
- * @param widthSamples Specifies the number of vertices to sample
- * along the width of the heightfield. Each vertex has a corresponding
- * height value which forms the overall shape.
- * Naturally this value must be at least two or more.
- * @param depthSamples Specifies the number of vertices to sample
- * along the depth of the heightfield.
- *
- * @param scale A uniform scale applied to all raw height data.
- * @param offset An offset applied to the scaled height data.
- *
- * @param thickness A value subtracted from the lowest height
- * value which in effect adds an additional cuboid to the base of the
- * heightfield. This is used to prevent geoms from looping under the
- * desired terrain and not registering as a collision. Note that the
- * thickness is not affected by the scale or offset parameters.
- *
- * @param bWrap If non-zero the heightfield will infinitely tile in both
- * directions along the local x and z axes. If zero the heightfield is
- * bounded from zero to width in the local x axis, and zero to depth in
- * the local z axis.
- *
- * @ingroup collide
- */
-ODE_API void dGeomHeightfieldDataBuildByte( dHeightfieldDataID d,
- const unsigned char* pHeightData, int bCopyHeightData,
- dReal width, dReal depth, int widthSamples, int depthSamples,
- dReal scale, dReal offset, dReal thickness, int bWrap );
-
-/**
- * @brief Configures a dHeightfieldDataID to use height data in short format.
- *
- * Before a dHeightfieldDataID can be used by a geom it must be
- * configured to specify the format of the height data.
- * This call specifies that the heightfield data is stored as a rectangular
- * array of shorts (16 bit signed) representing the height at each sample point.
- *
- * @param d A new dHeightfieldDataID created by dGeomHeightfieldDataCreate
- *
- * @param pHeightData A pointer to the height data.
- * @param bCopyHeightData When non-zero the height data is copied to an
- * internal store. When zero the height data is accessed by reference and
- * so must persist throughout the lifetime of the heightfield.
- *
- * @param width Specifies the total 'width' of the heightfield along
- * the geom's local x axis.
- * @param depth Specifies the total 'depth' of the heightfield along
- * the geom's local z axis.
- *
- * @param widthSamples Specifies the number of vertices to sample
- * along the width of the heightfield. Each vertex has a corresponding
- * height value which forms the overall shape.
- * Naturally this value must be at least two or more.
- * @param depthSamples Specifies the number of vertices to sample
- * along the depth of the heightfield.
- *
- * @param scale A uniform scale applied to all raw height data.
- * @param offset An offset applied to the scaled height data.
- *
- * @param thickness A value subtracted from the lowest height
- * value which in effect adds an additional cuboid to the base of the
- * heightfield. This is used to prevent geoms from looping under the
- * desired terrain and not registering as a collision. Note that the
- * thickness is not affected by the scale or offset parameters.
- *
- * @param bWrap If non-zero the heightfield will infinitely tile in both
- * directions along the local x and z axes. If zero the heightfield is
- * bounded from zero to width in the local x axis, and zero to depth in
- * the local z axis.
- *
- * @ingroup collide
- */
-ODE_API void dGeomHeightfieldDataBuildShort( dHeightfieldDataID d,
- const short* pHeightData, int bCopyHeightData,
- dReal width, dReal depth, int widthSamples, int depthSamples,
- dReal scale, dReal offset, dReal thickness, int bWrap );
-
-/**
- * @brief Configures a dHeightfieldDataID to use height data in
- * single precision floating point format.
- *
- * Before a dHeightfieldDataID can be used by a geom it must be
- * configured to specify the format of the height data.
- * This call specifies that the heightfield data is stored as a rectangular
- * array of single precision floats representing the height at each
- * sample point.
- *
- * @param d A new dHeightfieldDataID created by dGeomHeightfieldDataCreate
- *
- * @param pHeightData A pointer to the height data.
- * @param bCopyHeightData When non-zero the height data is copied to an
- * internal store. When zero the height data is accessed by reference and
- * so must persist throughout the lifetime of the heightfield.
- *
- * @param width Specifies the total 'width' of the heightfield along
- * the geom's local x axis.
- * @param depth Specifies the total 'depth' of the heightfield along
- * the geom's local z axis.
- *
- * @param widthSamples Specifies the number of vertices to sample
- * along the width of the heightfield. Each vertex has a corresponding
- * height value which forms the overall shape.
- * Naturally this value must be at least two or more.
- * @param depthSamples Specifies the number of vertices to sample
- * along the depth of the heightfield.
- *
- * @param scale A uniform scale applied to all raw height data.
- * @param offset An offset applied to the scaled height data.
- *
- * @param thickness A value subtracted from the lowest height
- * value which in effect adds an additional cuboid to the base of the
- * heightfield. This is used to prevent geoms from looping under the
- * desired terrain and not registering as a collision. Note that the
- * thickness is not affected by the scale or offset parameters.
- *
- * @param bWrap If non-zero the heightfield will infinitely tile in both
- * directions along the local x and z axes. If zero the heightfield is
- * bounded from zero to width in the local x axis, and zero to depth in
- * the local z axis.
- *
- * @ingroup collide
- */
-ODE_API void dGeomHeightfieldDataBuildSingle( dHeightfieldDataID d,
- const float* pHeightData, int bCopyHeightData,
- dReal width, dReal depth, int widthSamples, int depthSamples,
- dReal scale, dReal offset, dReal thickness, int bWrap );
-
-/**
- * @brief Configures a dHeightfieldDataID to use height data in
- * double precision floating point format.
- *
- * Before a dHeightfieldDataID can be used by a geom it must be
- * configured to specify the format of the height data.
- * This call specifies that the heightfield data is stored as a rectangular
- * array of double precision floats representing the height at each
- * sample point.
- *
- * @param d A new dHeightfieldDataID created by dGeomHeightfieldDataCreate
- *
- * @param pHeightData A pointer to the height data.
- * @param bCopyHeightData When non-zero the height data is copied to an
- * internal store. When zero the height data is accessed by reference and
- * so must persist throughout the lifetime of the heightfield.
- *
- * @param width Specifies the total 'width' of the heightfield along
- * the geom's local x axis.
- * @param depth Specifies the total 'depth' of the heightfield along
- * the geom's local z axis.
- *
- * @param widthSamples Specifies the number of vertices to sample
- * along the width of the heightfield. Each vertex has a corresponding
- * height value which forms the overall shape.
- * Naturally this value must be at least two or more.
- * @param depthSamples Specifies the number of vertices to sample
- * along the depth of the heightfield.
- *
- * @param scale A uniform scale applied to all raw height data.
- * @param offset An offset applied to the scaled height data.
- *
- * @param thickness A value subtracted from the lowest height
- * value which in effect adds an additional cuboid to the base of the
- * heightfield. This is used to prevent geoms from looping under the
- * desired terrain and not registering as a collision. Note that the
- * thickness is not affected by the scale or offset parameters.
- *
- * @param bWrap If non-zero the heightfield will infinitely tile in both
- * directions along the local x and z axes. If zero the heightfield is
- * bounded from zero to width in the local x axis, and zero to depth in
- * the local z axis.
- *
- * @ingroup collide
- */
-ODE_API void dGeomHeightfieldDataBuildDouble( dHeightfieldDataID d,
- const double* pHeightData, int bCopyHeightData,
- dReal width, dReal depth, int widthSamples, int depthSamples,
- dReal scale, dReal offset, dReal thickness, int bWrap );
-
-/**
- * @brief Manually set the minimum and maximum height bounds.
- *
- * This call allows you to set explicit min / max values after initial
- * creation typically for callback heightfields which default to +/- infinity,
- * or those whose data has changed. This must be set prior to binding with a
- * geom, as the the AABB is not recomputed after it's first generation.
- *
- * @remarks The minimum and maximum values are used to compute the AABB
- * for the heightfield which is used for early rejection of collisions.
- * A close fit will yield a more efficient collision check.
- *
- * @param d A dHeightfieldDataID created by dGeomHeightfieldDataCreate
- * @param min_height The new minimum height value. Scale, offset and thickness is then applied.
- * @param max_height The new maximum height value. Scale and offset is then applied.
- * @ingroup collide
- */
-ODE_API void dGeomHeightfieldDataSetBounds( dHeightfieldDataID d,
- dReal minHeight, dReal maxHeight );
-
-
-/**
- * @brief Assigns a dHeightfieldDataID to a heightfield geom.
- *
- * Associates the given dHeightfieldDataID with a heightfield geom.
- * This is done without affecting the GEOM_PLACEABLE flag.
- *
- * @param g A geom created by dCreateHeightfield
- * @param d A dHeightfieldDataID created by dGeomHeightfieldDataCreate
- * @ingroup collide
- */
-ODE_API void dGeomHeightfieldSetHeightfieldData( dGeomID g, dHeightfieldDataID d );
-
-
-/**
- * @brief Gets the dHeightfieldDataID bound to a heightfield geom.
- *
- * Returns the dHeightfieldDataID associated with a heightfield geom.
- *
- * @param g A geom created by dCreateHeightfield
- * @return The dHeightfieldDataID which may be NULL if none was assigned.
- * @ingroup collide
- */
-ODE_API dHeightfieldDataID dGeomHeightfieldGetHeightfieldData( dGeomID g );
-
-
-
-/* ************************************************************************ */
-/* utility functions */
-
-ODE_API void dClosestLineSegmentPoints (const dVector3 a1, const dVector3 a2,
- const dVector3 b1, const dVector3 b2,
- dVector3 cp1, dVector3 cp2);
-
-ODE_API int dBoxTouchesBox (const dVector3 _p1, const dMatrix3 R1,
- const dVector3 side1, const dVector3 _p2,
- const dMatrix3 R2, const dVector3 side2);
-
-/* The meaning of flags parameter is the same as in dCollide()*/
-ODE_API int dBoxBox (const dVector3 p1, const dMatrix3 R1,
- const dVector3 side1, const dVector3 p2,
- const dMatrix3 R2, const dVector3 side2,
- dVector3 normal, dReal *depth, int *return_code,
- int flags, dContactGeom *contact, int skip);
-
-ODE_API void dInfiniteAABB (dGeomID geom, dReal aabb[6]);
-
-
-/* ************************************************************************ */
-/* custom classes */
-
-typedef void dGetAABBFn (dGeomID, dReal aabb[6]);
-typedef int dColliderFn (dGeomID o1, dGeomID o2,
- int flags, dContactGeom *contact, int skip);
-typedef dColliderFn * dGetColliderFnFn (int num);
-typedef void dGeomDtorFn (dGeomID o);
-typedef int dAABBTestFn (dGeomID o1, dGeomID o2, dReal aabb[6]);
-
-typedef struct dGeomClass {
- int bytes;
- dGetColliderFnFn *collider;
- dGetAABBFn *aabb;
- dAABBTestFn *aabb_test;
- dGeomDtorFn *dtor;
-} dGeomClass;
-
-ODE_API int dCreateGeomClass (const dGeomClass *classptr);
-ODE_API void * dGeomGetClassData (dGeomID);
-ODE_API dGeomID dCreateGeom (int classnum);
-
-/**
- * @brief Sets a custom collider function for two geom classes.
- *
- * @param i The first geom class handled by this collider
- * @param j The second geom class handled by this collider
- * @param fn The collider function to use to determine collisions.
- * @ingroup collide
- */
-ODE_API void dSetColliderOverride (int i, int j, dColliderFn *fn);
-
-
-/* ************************************************************************ */
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001-2003 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_COLLISION_SPACE_H_
-#define _ODE_COLLISION_SPACE_H_
-
-#include <ode/common.h>
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-struct dContactGeom;
-
-/**
- * @brief User callback for geom-geom collision testing.
- *
- * @param data The user data object, as passed to dSpaceCollide.
- * @param o1 The first geom being tested.
- * @param o2 The second geom being test.
- *
- * @remarks The callback function can call dCollide on o1 and o2 to generate
- * contact points between each pair. Then these contact points may be added
- * to the simulation as contact joints. The user's callback function can of
- * course chose not to call dCollide for any pair, e.g. if the user decides
- * that those pairs should not interact.
- *
- * @ingroup collide
- */
-typedef void dNearCallback (void *data, dGeomID o1, dGeomID o2);
-
-
-ODE_API dSpaceID dSimpleSpaceCreate (dSpaceID space);
-ODE_API dSpaceID dHashSpaceCreate (dSpaceID space);
-ODE_API dSpaceID dQuadTreeSpaceCreate (dSpaceID space, const dVector3 Center, const dVector3 Extents, int Depth);
-
-
-/* SAP */
-/* Order XZY or ZXY usually works best, if your Y is up. */
-#define dSAP_AXES_XYZ ((0)|(1<<2)|(2<<4))
-#define dSAP_AXES_XZY ((0)|(2<<2)|(1<<4))
-#define dSAP_AXES_YXZ ((1)|(0<<2)|(2<<4))
-#define dSAP_AXES_YZX ((1)|(2<<2)|(0<<4))
-#define dSAP_AXES_ZXY ((2)|(0<<2)|(1<<4))
-#define dSAP_AXES_ZYX ((2)|(1<<2)|(0<<4))
-
-ODE_API dSpaceID dSweepAndPruneSpaceCreate( dSpaceID space, int axisorder );
-
-
-
-ODE_API void dSpaceDestroy (dSpaceID);
-
-ODE_API void dHashSpaceSetLevels (dSpaceID space, int minlevel, int maxlevel);
-ODE_API void dHashSpaceGetLevels (dSpaceID space, int *minlevel, int *maxlevel);
-
-ODE_API void dSpaceSetCleanup (dSpaceID space, int mode);
-ODE_API int dSpaceGetCleanup (dSpaceID space);
-
-/**
-* @brief Sets sublevel value for a space.
-*
-* Sublevel affects how the space is handled in dSpaceCollide2 when it is collided
-* with another space. If sublevels of both spaces match, the function iterates
-* geometries of both spaces and collides them with each other. If sublevel of one
-* space is greater than the sublevel of another one, only the geometries of the
-* space with greater sublevel are iterated, another space is passed into
-* collision callback as a geometry itself. By default all the spaces are assigned
-* zero sublevel.
-*
-* @note
-* The space sublevel @e IS @e NOT automatically updated when one space is inserted
-* into another or removed from one. It is a client's responsibility to update sublevel
-* value if necessary.
-*
-* @param space the space to modify
-* @param sublevel the sublevel value to be assigned
-* @ingroup collide
-* @see dSpaceGetSublevel
-* @see dSpaceCollide2
-*/
-ODE_API void dSpaceSetSublevel (dSpaceID space, int sublevel);
-
-/**
-* @brief Gets sublevel value of a space.
-*
-* Sublevel affects how the space is handled in dSpaceCollide2 when it is collided
-* with another space. See @c dSpaceSetSublevel for more details.
-*
-* @param space the space to query
-* @returns the sublevel value of the space
-* @ingroup collide
-* @see dSpaceSetSublevel
-* @see dSpaceCollide2
-*/
-ODE_API int dSpaceGetSublevel (dSpaceID space);
-
-
-/**
-* @brief Sets manual cleanup flag for a space.
-*
-* Manual cleanup flag marks a space as eligible for manual thread data cleanup.
-* This function should be called for every space object right after creation in
-* case if ODE has been initialized with @c dInitFlagManualThreadCleanup flag.
-*
-* Failure to set manual cleanup flag for a space may lead to some resources
-* remaining leaked until the program exit.
-*
-* @param space the space to modify
-* @param mode 1 for manual cleanup mode and 0 for default cleanup mode
-* @ingroup collide
-* @see dSpaceGetManualCleanup
-* @see dInitODE2
-*/
-ODE_API void dSpaceSetManualCleanup (dSpaceID space, int mode);
-
-/**
-* @brief Get manual cleanup flag of a space.
-*
-* Manual cleanup flag marks a space space as eligible for manual thread data cleanup.
-* See @c dSpaceSetManualCleanup for more details.
-*
-* @param space the space to query
-* @returns 1 for manual cleanup mode and 0 for default cleanup mode of the space
-* @ingroup collide
-* @see dSpaceSetManualCleanup
-* @see dInitODE2
-*/
-ODE_API int dSpaceGetManualCleanup (dSpaceID space);
-
-ODE_API void dSpaceAdd (dSpaceID, dGeomID);
-ODE_API void dSpaceRemove (dSpaceID, dGeomID);
-ODE_API int dSpaceQuery (dSpaceID, dGeomID);
-ODE_API void dSpaceClean (dSpaceID);
-ODE_API int dSpaceGetNumGeoms (dSpaceID);
-ODE_API dGeomID dSpaceGetGeom (dSpaceID, int i);
-
-/**
- * @brief Given a space, this returns its class.
- *
- * The ODE classes are:
- * @li dSimpleSpaceClass
- * @li dHashSpaceClass
- * @li dSweepAndPruneSpaceClass
- * @li dQuadTreeSpaceClass
- * @li dFirstUserClass
- * @li dLastUserClass
- *
- * The class id not defined by the user should be between
- * dFirstSpaceClass and dLastSpaceClass.
- *
- * User-defined class will return their own number.
- *
- * @param space the space to query
- * @returns The space class ID.
- * @ingroup collide
- */
-ODE_API int dSpaceGetClass(dSpaceID space);
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001-2003 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-/*
- * TriMesh code by Erwin de Vries.
- *
- * Trimesh data.
- * This is where the actual vertexdata (pointers), and BV tree is stored.
- * Vertices should be single precision!
- * This should be more sophisticated, so that the user can easyly implement
- * another collision library, but this is a lot of work, and also costs some
- * performance because some data has to be copied.
- */
-
-#ifndef _ODE_COLLISION_TRIMESH_H_
-#define _ODE_COLLISION_TRIMESH_H_
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-/*
- * Data storage for triangle meshes.
- */
-struct dxTriMeshData;
-typedef struct dxTriMeshData* dTriMeshDataID;
-
-
-typedef enum
-{
- dMTV__MIN,
-
- dMTV_FIRST = dMTV__MIN,
- dMTV_SECOND,
- dMTV_THIRD,
-
- dMTV__MAX,
-
-} dMeshTriangleVertex;
-
-/*
- * These don't make much sense now, but they will later when we add more
- * features.
- */
-ODE_API dTriMeshDataID dGeomTriMeshDataCreate(void);
-ODE_API void dGeomTriMeshDataDestroy(dTriMeshDataID g);
-
-
-/*
- * The values of data_id that can be used with dGeomTriMeshDataSet/dGeomTriMeshDataGet
- */
-enum
-{
- dTRIMESHDATA__MIN,
-
- dTRIMESHDATA_FACE_NORMALS = dTRIMESHDATA__MIN,
- dTRIMESHDATA_USE_FLAGS,
-
- dTRIMESHDATA__MAX,
-
-#ifndef TRIMESH_FACE_NORMALS // Define this name during the header inclusion if you need it for something else
- // Included for backward compatibility -- please use the corrected name above. Sorry.
- TRIMESH_FACE_NORMALS = dTRIMESHDATA_FACE_NORMALS,
-#endif
-};
-
-/*
- * The flags of the dTRIMESHDATA_USE_FLAGS data elements
- */
-enum
-{
- dMESHDATAUSE_EDGE1 = 0x01,
- dMESHDATAUSE_EDGE2 = 0x02,
- dMESHDATAUSE_EDGE3 = 0x04,
- dMESHDATAUSE_VERTEX1 = 0x08,
- dMESHDATAUSE_VERTEX2 = 0x10,
- dMESHDATAUSE_VERTEX3 = 0x20,
-};
-
-/*
- * Set and get the TriMeshData additional data
- * Note: The data is NOT COPIED on assignment
- */
-ODE_API void dGeomTriMeshDataSet(dTriMeshDataID g, int data_id, void *in_data);
-ODE_API void *dGeomTriMeshDataGet(dTriMeshDataID g, int data_id);
-ODE_API void *dGeomTriMeshDataGet2(dTriMeshDataID g, int data_id, dsizeint *pout_size/*=NULL*/);
-
-
-
-/**
- * We need to set the last transform after each time step for
- * accurate collision response. These functions get and set that transform.
- * It is stored per geom instance, rather than per dTriMeshDataID.
- */
-ODE_API void dGeomTriMeshSetLastTransform( dGeomID g, const dMatrix4 last_trans );
-ODE_API const dReal* dGeomTriMeshGetLastTransform( dGeomID g );
-
-/*
- * Build a TriMesh data object with single precision vertex data.
- */
-ODE_API void dGeomTriMeshDataBuildSingle(dTriMeshDataID g,
- const void* Vertices, int VertexStride, int VertexCount,
- const void* Indices, int IndexCount, int TriStride);
-/* same again with a normals array (used as trimesh-trimesh optimization) */
-ODE_API void dGeomTriMeshDataBuildSingle1(dTriMeshDataID g,
- const void* Vertices, int VertexStride, int VertexCount,
- const void* Indices, int IndexCount, int TriStride,
- const void* Normals);
-/*
-* Build a TriMesh data object with double precision vertex data.
-*/
-ODE_API void dGeomTriMeshDataBuildDouble(dTriMeshDataID g,
- const void* Vertices, int VertexStride, int VertexCount,
- const void* Indices, int IndexCount, int TriStride);
-/* same again with a normals array (used as trimesh-trimesh optimization) */
-ODE_API void dGeomTriMeshDataBuildDouble1(dTriMeshDataID g,
- const void* Vertices, int VertexStride, int VertexCount,
- const void* Indices, int IndexCount, int TriStride,
- const void* Normals);
-
-/*
- * Simple build. Single/double precision based on dSINGLE/dDOUBLE!
- */
-ODE_API void dGeomTriMeshDataBuildSimple(dTriMeshDataID g,
- const dReal* Vertices, int VertexCount,
- const dTriIndex* Indices, int IndexCount);
-/* same again with a normals array (used as trimesh-trimesh optimization) */
-ODE_API void dGeomTriMeshDataBuildSimple1(dTriMeshDataID g,
- const dReal* Vertices, int VertexCount,
- const dTriIndex* Indices, int IndexCount,
- const int* Normals);
-
-
-/*
- * Data preprocessing build request flags.
- */
-enum
-{
- dTRIDATAPREPROCESS_BUILD__MIN,
-
- dTRIDATAPREPROCESS_BUILD_CONCAVE_EDGES = dTRIDATAPREPROCESS_BUILD__MIN, // Used to optimize OPCODE trimesh-capsule collisions; allocates 1 byte per triangle; no extra data associated
- dTRIDATAPREPROCESS_BUILD_FACE_ANGLES, // Used to aid trimesh-convex collisions; memory requirements depend on extra data
-
- dTRIDATAPREPROCESS_BUILD__MAX,
-};
-
-/*
- * Data preprocessing extra values for dTRIDATAPREPROCESS_BUILD_FACE_ANGLES.
- */
-enum
-{
- dTRIDATAPREPROCESS_FACE_ANGLES_EXTRA__MIN,
-
- dTRIDATAPREPROCESS_FACE_ANGLES_EXTRA_BYTE_POSITIVE = dTRIDATAPREPROCESS_FACE_ANGLES_EXTRA__MIN, // Build angles for convex edges only and store as bytes; allocates 3 bytes per triangle; stores angles (0..180] in 1/254 fractions leaving two values for the flat and all the concaves
- dTRIDATAPREPROCESS_FACE_ANGLES_EXTRA_BYTE_ALL, // Build angles for all the edges and store in bytes; allocates 3 bytes per triangle; stores angles [-180..0) and (0..180] in 1/127 fractions plus a value for the flat angle
- dTRIDATAPREPROCESS_FACE_ANGLES_EXTRA_WORD_ALL, // Build angles for all the edges and store in words; allocates 6 bytes per triangle; stores angles [-180..0) and (0..180] in 1/32767 fractions plus a value for the flat angle
-
- dTRIDATAPREPROCESS_FACE_ANGLES_EXTRA__MAX,
-
- dTRIDATAPREPROCESS_FACE_ANGLES_EXTRA__DEFAULT = dTRIDATAPREPROCESS_FACE_ANGLES_EXTRA_BYTE_POSITIVE, // The default value assumed if the extra data is not provided
-};
-
-
-/*
- * Pre-process the trimesh data according to the request flags.
- *
- * buildRequestFlags is a bitmask of 1U << dTRIDATAPREPROCESS_BUILD_...
- * It is allowed to call the function multiple times provided the bitmasks are different each time.
- *
- * requestExtraData is an optional pointer to array of extra parameters per bitmask bits
- * (only the elements indexed by positions of raised bits are examined;
- * defaults are assumed if the pointer is NULL)
- *
- * The function returns a boolean status the only failure reason being insufficient memory.
- */
-ODE_API int dGeomTriMeshDataPreprocess2(dTriMeshDataID g, unsigned int buildRequestFlags, const dintptr *requestExtraData/*=NULL | const dintptr (*)[dTRIDATAPREPROCESS_BUILD__MAX]*/);
-
-/*
- * Obsolete. Equivalent to calling dGeomTriMeshDataPreprocess2(g, (1U << dTRIDATAPREPROCESS_BUILD_CONCAVE_EDGES), NULL)
- */
-ODE_API int dGeomTriMeshDataPreprocess(dTriMeshDataID g);
-
-
-
-/*
- * Get and set the internal preprocessed trimesh data buffer (see the enumerated type above), for loading and saving
- * These functions are deprecated. Use dGeomTriMeshDataSet/dGeomTriMeshDataGet2 with dTRIMESHDATA_USE_FLAGS instead.
- */
-ODE_API_DEPRECATED ODE_API void dGeomTriMeshDataGetBuffer(dTriMeshDataID g, unsigned char** buf, int* bufLen);
-ODE_API_DEPRECATED ODE_API void dGeomTriMeshDataSetBuffer(dTriMeshDataID g, unsigned char* buf);
-
-
-/*
- * Per triangle callback. Allows the user to say if he wants a collision with
- * a particular triangle.
- */
-typedef int dTriCallback(dGeomID TriMesh, dGeomID RefObject, int TriangleIndex);
-ODE_API void dGeomTriMeshSetCallback(dGeomID g, dTriCallback* Callback);
-ODE_API dTriCallback* dGeomTriMeshGetCallback(dGeomID g);
-
-/*
- * Per object callback. Allows the user to get the list of triangles in 1
- * shot. Maybe we should remove this one.
- */
-typedef void dTriArrayCallback(dGeomID TriMesh, dGeomID RefObject, const int* TriIndices, int TriCount);
-ODE_API void dGeomTriMeshSetArrayCallback(dGeomID g, dTriArrayCallback* ArrayCallback);
-ODE_API dTriArrayCallback* dGeomTriMeshGetArrayCallback(dGeomID g);
-
-/*
- * Ray callback.
- * Allows the user to say if a ray collides with a triangle on barycentric
- * coords. The user can for example sample a texture with alpha transparency
- * to determine if a collision should occur.
- */
-typedef int dTriRayCallback(dGeomID TriMesh, dGeomID Ray, int TriangleIndex, dReal u, dReal v);
-ODE_API void dGeomTriMeshSetRayCallback(dGeomID g, dTriRayCallback* Callback);
-ODE_API dTriRayCallback* dGeomTriMeshGetRayCallback(dGeomID g);
-
-/*
- * Triangle merging callback.
- * Allows the user to generate a fake triangle index for a new contact generated
- * from merging of two other contacts. That index could later be used by the
- * user to determine attributes of original triangles used as sources for a
- * merged contact.
- */
-typedef int dTriTriMergeCallback(dGeomID TriMesh, int FirstTriangleIndex, int SecondTriangleIndex);
-ODE_API void dGeomTriMeshSetTriMergeCallback(dGeomID g, dTriTriMergeCallback* Callback);
-ODE_API dTriTriMergeCallback* dGeomTriMeshGetTriMergeCallback(dGeomID g);
-
-/*
- * Trimesh class
- * Construction. Callbacks are optional.
- */
-ODE_API dGeomID dCreateTriMesh(dSpaceID space, dTriMeshDataID Data, dTriCallback* Callback, dTriArrayCallback* ArrayCallback, dTriRayCallback* RayCallback);
-
-ODE_API void dGeomTriMeshSetData(dGeomID g, dTriMeshDataID Data);
-ODE_API dTriMeshDataID dGeomTriMeshGetData(dGeomID g);
-
-
-/* enable/disable/check temporal coherence*/
-ODE_API void dGeomTriMeshEnableTC(dGeomID g, int geomClass, int enable);
-ODE_API int dGeomTriMeshIsTCEnabled(dGeomID g, int geomClass);
-
-/*
- * Clears the internal temporal coherence caches. When a geom has its
- * collision checked with a trimesh once, data is stored inside the trimesh.
- * With large worlds with lots of seperate objects this list could get huge.
- * We should be able to do this automagically.
- */
-ODE_API void dGeomTriMeshClearTCCache(dGeomID g);
-
-
-/*
- * returns the TriMeshDataID
- */
-ODE_API dTriMeshDataID dGeomTriMeshGetTriMeshDataID(dGeomID g);
-
-/*
- * Gets a triangle.
- */
-ODE_API void dGeomTriMeshGetTriangle(dGeomID g, int Index, dVector3* v0, dVector3* v1, dVector3* v2);
-
-/*
- * Gets the point on the requested triangle and the given barycentric
- * coordinates.
- */
-ODE_API void dGeomTriMeshGetPoint(dGeomID g, int Index, dReal u, dReal v, dVector3 Out);
-
-/*
-
-This is how the strided data works:
-
-struct StridedVertex{
- dVector3 Vertex;
- // Userdata
-};
-int VertexStride = sizeof(StridedVertex);
-
-struct StridedTri{
- int Indices[3];
- // Userdata
-};
-int TriStride = sizeof(StridedTri);
-
-*/
-
-
-ODE_API int dGeomTriMeshGetTriangleCount (dGeomID g);
-
-ODE_API void dGeomTriMeshDataUpdate(dTriMeshDataID g);
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif /* _ODE_COLLISION_TRIMESH_H_ */
-
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_COMMON_H_
-#define _ODE_COMMON_H_
-
-#include <ode/odeconfig.h>
-#include <ode/error.h>
-
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-
-/* configuration stuff */
-
-/* constants */
-
-/* pi and 1/sqrt(2) are defined here if necessary because they don't get
- * defined in <math.h> on some platforms (like MS-Windows)
- */
-
-#ifndef M_PI
-#define M_PI REAL(3.1415926535897932384626433832795029)
-#endif
-#ifndef M_PI_2
-#define M_PI_2 REAL(1.5707963267948966192313216916398)
-#endif
-#ifndef M_SQRT1_2
-#define M_SQRT1_2 REAL(0.7071067811865475244008443621048490)
-#endif
-
-
-/* floating point data type, vector, matrix and quaternion types */
-
-#if defined(dSINGLE)
-typedef float dReal;
-#ifdef dDOUBLE
-#error You can only #define dSINGLE or dDOUBLE, not both.
-#endif /* dDOUBLE */
-#elif defined(dDOUBLE)
-typedef double dReal;
-#else
-#error You must #define dSINGLE or dDOUBLE
-#endif
-
-/* Detect if we've got both trimesh engines enabled. */
-#if dTRIMESH_ENABLED
-#if dTRIMESH_OPCODE && dTRIMESH_GIMPACT
-#error You can only #define dTRIMESH_OPCODE or dTRIMESH_GIMPACT, not both.
-#endif
-#endif /* dTRIMESH_ENABLED */
-
-/*
- * Define a type for indices, either 16 or 32 bit, based on build option
- * TODO: Currently GIMPACT only supports 32 bit indices.
- */
-#if dTRIMESH_16BIT_INDICES
-#if dTRIMESH_GIMPACT
-typedef duint32 dTriIndex;
-#else /* dTRIMESH_GIMPACT */
-typedef duint16 dTriIndex;
-#endif /* dTRIMESH_GIMPACT */
-#else /* dTRIMESH_16BIT_INDICES */
-typedef duint32 dTriIndex;
-#endif /* dTRIMESH_16BIT_INDICES */
-
-/* round an integer up to a multiple of 4, except that 0 and 1 are unmodified
- * (used to compute matrix leading dimensions)
- */
-#define dPAD(a) (((a) > 1) ? (((a) + 3) & (int)(~3)) : (a))
-
-typedef enum {
- dSA__MIN,
-
- dSA_X = dSA__MIN,
- dSA_Y,
- dSA_Z,
-
- dSA__MAX,
-} dSpaceAxis;
-
-typedef enum {
- dMD__MIN,
-
- dMD_LINEAR = dMD__MIN,
- dMD_ANGULAR,
-
- dMD__MAX,
-} dMotionDynamics;
-
-typedef enum {
- dDA__MIN,
-
- dDA__L_MIN = dDA__MIN + dMD_LINEAR * dSA__MAX,
-
- dDA_LX = dDA__L_MIN + dSA_X,
- dDA_LY = dDA__L_MIN + dSA_Y,
- dDA_LZ = dDA__L_MIN + dSA_Z,
-
- dDA__L_MAX = dDA__L_MIN + dSA__MAX,
-
- dDA__A_MIN = dDA__MIN + dMD_ANGULAR * dSA__MAX,
-
- dDA_AX = dDA__A_MIN + dSA_X,
- dDA_AY = dDA__A_MIN + dSA_Y,
- dDA_AZ = dDA__A_MIN + dSA_Z,
-
- dDA__A_MAX = dDA__A_MIN + dSA__MAX,
-
- dDA__MAX = dDA__MIN + dMD__MAX * dSA__MAX,
-} dDynamicsAxis;
-
-typedef enum {
- dV3E__MIN,
-
- dV3E__AXES_MIN = dV3E__MIN,
-
- dV3E_X = dV3E__AXES_MIN + dSA_X,
- dV3E_Y = dV3E__AXES_MIN + dSA_Y,
- dV3E_Z = dV3E__AXES_MIN + dSA_Z,
-
- dV3E__AXES_MAX = dV3E__AXES_MIN + dSA__MAX,
-
- dV3E_PAD = dV3E__AXES_MAX,
-
- dV3E__MAX,
-
- dV3E__AXES_COUNT = dV3E__AXES_MAX - dV3E__AXES_MIN,
-} dVec3Element;
-
-typedef enum {
- dV4E__MIN,
-
- dV4E_X = dV4E__MIN + dSA_X,
- dV4E_Y = dV4E__MIN + dSA_Y,
- dV4E_Z = dV4E__MIN + dSA_Z,
- dV4E_O = dV4E__MIN + dSA__MAX,
-
- dV4E__MAX,
-} dVec4Element;
-
-typedef enum {
- dM3E__MIN,
-
- dM3E__X_MIN = dM3E__MIN + dSA_X * dV3E__MAX,
-
- dM3E__X_AXES_MIN = dM3E__X_MIN + dV3E__AXES_MIN,
-
- dM3E_XX = dM3E__X_MIN + dV3E_X,
- dM3E_XY = dM3E__X_MIN + dV3E_Y,
- dM3E_XZ = dM3E__X_MIN + dV3E_Z,
-
- dM3E__X_AXES_MAX = dM3E__X_MIN + dV3E__AXES_MAX,
-
- dM3E_XPAD = dM3E__X_MIN + dV3E_PAD,
-
- dM3E__X_MAX = dM3E__X_MIN + dV3E__MAX,
-
- dM3E__Y_MIN = dM3E__MIN + dSA_Y * dV3E__MAX,
-
- dM3E__Y_AXES_MIN = dM3E__Y_MIN + dV3E__AXES_MIN,
-
- dM3E_YX = dM3E__Y_MIN + dV3E_X,
- dM3E_YY = dM3E__Y_MIN + dV3E_Y,
- dM3E_YZ = dM3E__Y_MIN + dV3E_Z,
-
- dM3E__Y_AXES_MAX = dM3E__Y_MIN + dV3E__AXES_MAX,
-
- dM3E_YPAD = dM3E__Y_MIN + dV3E_PAD,
-
- dM3E__Y_MAX = dM3E__Y_MIN + dV3E__MAX,
-
- dM3E__Z_MIN = dM3E__MIN + dSA_Z * dV3E__MAX,
-
- dM3E__Z_AXES_MIN = dM3E__Z_MIN + dV3E__AXES_MIN,
-
- dM3E_ZX = dM3E__Z_MIN + dV3E_X,
- dM3E_ZY = dM3E__Z_MIN + dV3E_Y,
- dM3E_ZZ = dM3E__Z_MIN + dV3E_Z,
-
- dM3E__Z_AXES_MAX = dM3E__Z_MIN + dV3E__AXES_MAX,
-
- dM3E_ZPAD = dM3E__Z_MIN + dV3E_PAD,
-
- dM3E__Z_MAX = dM3E__Z_MIN + dV3E__MAX,
-
- dM3E__MAX = dM3E__MIN + dSA__MAX * dV3E__MAX,
-} dMat3Element;
-
-typedef enum {
- dM4E__MIN,
-
- dM4E__X_MIN = dM4E__MIN + dV4E_X * dV4E__MAX,
-
- dM4E_XX = dM4E__X_MIN + dV4E_X,
- dM4E_XY = dM4E__X_MIN + dV4E_Y,
- dM4E_XZ = dM4E__X_MIN + dV4E_Z,
- dM4E_XO = dM4E__X_MIN + dV4E_O,
-
- dM4E__X_MAX = dM4E__X_MIN + dV4E__MAX,
-
- dM4E__Y_MIN = dM4E__MIN + dV4E_Y * dV4E__MAX,
-
- dM4E_YX = dM4E__Y_MIN + dV4E_X,
- dM4E_YY = dM4E__Y_MIN + dV4E_Y,
- dM4E_YZ = dM4E__Y_MIN + dV4E_Z,
- dM4E_YO = dM4E__Y_MIN + dV4E_O,
-
- dM4E__Y_MAX = dM4E__Y_MIN + dV4E__MAX,
-
- dM4E__Z_MIN = dM4E__MIN + dV4E_Z * dV4E__MAX,
-
- dM4E_ZX = dM4E__Z_MIN + dV4E_X,
- dM4E_ZY = dM4E__Z_MIN + dV4E_Y,
- dM4E_ZZ = dM4E__Z_MIN + dV4E_Z,
- dM4E_ZO = dM4E__Z_MIN + dV4E_O,
-
- dM4E__Z_MAX = dM4E__Z_MIN + dV4E__MAX,
-
- dM4E__O_MIN = dM4E__MIN + dV4E_O * dV4E__MAX,
-
- dM4E_OX = dM4E__O_MIN + dV4E_X,
- dM4E_OY = dM4E__O_MIN + dV4E_Y,
- dM4E_OZ = dM4E__O_MIN + dV4E_Z,
- dM4E_OO = dM4E__O_MIN + dV4E_O,
-
- dM4E__O_MAX = dM4E__O_MIN + dV4E__MAX,
-
- dM4E__MAX = dM4E__MIN + dV4E__MAX * dV4E__MAX,
-} dMat4Element;
-
-typedef enum {
- dQUE__MIN,
-
- dQUE_R = dQUE__MIN,
-
- dQUE__AXIS_MIN,
-
- dQUE_I = dQUE__AXIS_MIN + dSA_X,
- dQUE_J = dQUE__AXIS_MIN + dSA_Y,
- dQUE_K = dQUE__AXIS_MIN + dSA_Z,
-
- dQUE__AXIS_MAX = dQUE__AXIS_MIN + dSA__MAX,
-
- dQUE__MAX = dQUE__AXIS_MAX,
-} dQuatElement;
-
-/* these types are mainly just used in headers */
-typedef dReal dVector3[dV3E__MAX];
-typedef dReal dVector4[dV4E__MAX];
-typedef dReal dMatrix3[dM3E__MAX];
-typedef dReal dMatrix4[dM4E__MAX];
-typedef dReal dMatrix6[(dMD__MAX * dV3E__MAX) * (dMD__MAX * dSA__MAX)];
-typedef dReal dQuaternion[dQUE__MAX];
-
-
-/* precision dependent scalar math functions */
-
-#if defined(dSINGLE)
-
-#define REAL(x) (x##f) /* form a constant */
-#define dRecip(x) ((1.0f/(x))) /* reciprocal */
-#define dSqrt(x) (sqrtf(x)) /* square root */
-#define dRecipSqrt(x) ((1.0f/sqrtf(x))) /* reciprocal square root */
-#define dSin(x) (sinf(x)) /* sine */
-#define dCos(x) (cosf(x)) /* cosine */
-#define dFabs(x) (fabsf(x)) /* absolute value */
-#define dAtan2(y,x) (atan2f(y,x)) /* arc tangent with 2 args */
-#define dAsin(x) (asinf(x))
-#define dAcos(x) (acosf(x))
-#define dFMod(a,b) (fmodf(a,b)) /* modulo */
-#define dFloor(x) floorf(x) /* floor */
-#define dCeil(x) ceilf(x) /* ceil */
-#define dCopySign(a,b) _ode_copysignf(a, b) /* copy value sign */
-#define dNextAfter(x, y) _ode_nextafterf(x, y) /* next value after */
-
-#ifdef HAVE___ISNANF
-#define dIsNan(x) (__isnanf(x))
-#elif defined(HAVE__ISNANF)
-#define dIsNan(x) (_isnanf(x))
-#elif defined(HAVE_ISNANF)
-#define dIsNan(x) (isnanf(x))
-#else
- /*
- fall back to _isnan which is the VC way,
- this may seem redundant since we already checked
- for _isnan before, but if isnan is detected by
- configure but is not found during compilation
- we should always make sure we check for __isnanf,
- _isnanf and isnanf in that order before falling
- back to a default
- */
-#define dIsNan(x) (_isnan(x))
-#endif
-
-#elif defined(dDOUBLE)
-
-#define REAL(x) (x)
-#define dRecip(x) (1.0/(x))
-#define dSqrt(x) sqrt(x)
-#define dRecipSqrt(x) (1.0/sqrt(x))
-#define dSin(x) sin(x)
-#define dCos(x) cos(x)
-#define dFabs(x) fabs(x)
-#define dAtan2(y,x) atan2((y),(x))
-#define dAsin(x) asin(x)
-#define dAcos(x) acos(x)
-#define dFMod(a,b) (fmod((a),(b)))
-#define dFloor(x) floor(x)
-#define dCeil(x) ceil(x)
-#define dCopySign(a,b) _ode_copysign(a, b)
-#define dNextAfter(x, y) _ode_nextafter(x, y)
-
-#ifdef HAVE___ISNAN
-#define dIsNan(x) (__isnan(x))
-#elif defined(HAVE__ISNAN)
-#define dIsNan(x) (_isnan(x))
-#elif defined(HAVE_ISNAN)
-#define dIsNan(x) (isnan(x))
-#else
-#define dIsNan(x) (_isnan(x))
-#endif
-
-#else
-#error You must #define dSINGLE or dDOUBLE
-#endif
-
-ODE_PURE_INLINE dReal dMin(dReal x, dReal y) { return x <= y ? x : y; }
-ODE_PURE_INLINE dReal dMax(dReal x, dReal y) { return x <= y ? y : x; }
-
-
-/* internal object types (all prefixed with `dx') */
-
-struct dxWorld; /* dynamics world */
-struct dxSpace; /* collision space */
-struct dxBody; /* rigid body (dynamics object) */
-struct dxGeom; /* geometry (collision object) */
-struct dxJoint; /* joint */
-struct dxJointGroup;/* joint group */
-
-
-typedef struct dxWorld *dWorldID;
-typedef struct dxSpace *dSpaceID;
-typedef struct dxBody *dBodyID;
-typedef struct dxGeom *dGeomID;
-typedef struct dxJoint *dJointID;
-typedef struct dxJointGroup *dJointGroupID;
-
-
-/* error numbers */
-
-enum {
- d_ERR_UNKNOWN = 0, /* unknown error */
- d_ERR_IASSERT, /* internal assertion failed */
- d_ERR_UASSERT, /* user assertion failed */
- d_ERR_LCP /* user assertion failed */
-};
-
-
-/* joint type numbers */
-
-typedef enum {
- dJointTypeNone = 0, /* or "unknown" */
- dJointTypeBall,
- dJointTypeHinge,
- dJointTypeSlider,
- dJointTypeContact,
- dJointTypeUniversal,
- dJointTypeHinge2,
- dJointTypeFixed,
- dJointTypeNull,
- dJointTypeAMotor,
- dJointTypeLMotor,
- dJointTypePlane2D,
- dJointTypePR,
- dJointTypePU,
- dJointTypePiston,
- dJointTypeDBall,
- dJointTypeDHinge,
- dJointTypeTransmission,
-} dJointType;
-
-
-/* an alternative way of setting joint parameters, using joint parameter
- * structures and member constants. we don't actually do this yet.
- */
-
-/*
-typedef struct dLimot {
- int mode;
- dReal lostop, histop;
- dReal vel, fmax;
- dReal fudge_factor;
- dReal bounce, soft;
- dReal suspension_erp, suspension_cfm;
-} dLimot;
-
-enum {
- dLimotLoStop = 0x0001,
- dLimotHiStop = 0x0002,
- dLimotVel = 0x0004,
- dLimotFMax = 0x0008,
- dLimotFudgeFactor = 0x0010,
- dLimotBounce = 0x0020,
- dLimotSoft = 0x0040
-};
-*/
-
-
-/* standard joint parameter names. why are these here? - because we don't want
- * to include all the joint function definitions in joint.cpp. hmmmm.
- * MSVC complains if we call D_ALL_PARAM_NAMES_X with a blank second argument,
- * which is why we have the D_ALL_PARAM_NAMES macro as well. please copy and
- * paste between these two.
- */
-
-#define D_ALL_PARAM_NAMES(start) \
- /* parameters for limits and motors */ \
- dParamLoStop = start, \
- dParamHiStop, \
- dParamVel, \
- dParamLoVel, \
- dParamHiVel, \
- dParamFMax, \
- dParamFudgeFactor, \
- dParamBounce, \
- dParamCFM, \
- dParamStopERP, \
- dParamStopCFM, \
- /* parameters for suspension */ \
- dParamSuspensionERP, \
- dParamSuspensionCFM, \
- dParamERP, \
-
- /*
- * \enum D_ALL_PARAM_NAMES_X
- *
- * \var dParamGroup This is the starting value of the different group
- * (i.e. dParamGroup1, dParamGroup2, dParamGroup3)
- * It also helps in the use of parameter
- * (dParamGroup2 | dParamFMax) == dParamFMax2
- */
-#define D_ALL_PARAM_NAMES_X(start,x) \
- dParamGroup ## x = start, \
- /* parameters for limits and motors */ \
- dParamLoStop ## x = start, \
- dParamHiStop ## x, \
- dParamVel ## x, \
- dParamLoVel ## x, \
- dParamHiVel ## x, \
- dParamFMax ## x, \
- dParamFudgeFactor ## x, \
- dParamBounce ## x, \
- dParamCFM ## x, \
- dParamStopERP ## x, \
- dParamStopCFM ## x, \
- /* parameters for suspension */ \
- dParamSuspensionERP ## x, \
- dParamSuspensionCFM ## x, \
- dParamERP ## x,
-
-enum {
- D_ALL_PARAM_NAMES(0)
- dParamsInGroup, /* < Number of parameter in a group */
- D_ALL_PARAM_NAMES_X(0x000,1)
- D_ALL_PARAM_NAMES_X(0x100,2)
- D_ALL_PARAM_NAMES_X(0x200,3)
-
- /* add a multiple of this constant to the basic parameter numbers to get
- * the parameters for the second, third etc axes.
- */
- dParamGroup=0x100
-};
-
-
-/* angular motor mode numbers */
-
-enum {
- dAMotorUser = 0,
- dAMotorEuler = 1
-};
-
-/* transmission joint mode numbers */
-
-enum {
- dTransmissionParallelAxes = 0,
- dTransmissionIntersectingAxes = 1,
- dTransmissionChainDrive = 2
-};
-
-
-/* joint force feedback information */
-
-typedef struct dJointFeedback {
- dVector3 f1; /* force applied to body 1 */
- dVector3 t1; /* torque applied to body 1 */
- dVector3 f2; /* force applied to body 2 */
- dVector3 t2; /* torque applied to body 2 */
-} dJointFeedback;
-
-
-/* private functions that must be implemented by the collision library:
- * (1) indicate that a geom has moved, (2) get the next geom in a body list.
- * these functions are called whenever the position of geoms connected to a
- * body have changed, e.g. with dBodySetPosition(), dBodySetRotation(), or
- * when the ODE step function updates the body state.
- */
-
-void dGeomMoved (dGeomID);
-dGeomID dGeomGetBodyNext (dGeomID);
-
-/**
- * dGetConfiguration returns the specific ODE build configuration as
- * a string of tokens. The string can be parsed in a similar way to
- * the OpenGL extension mechanism, the naming convention should be
- * familiar too. The following extensions are reported:
- *
- * ODE
- * ODE_single_precision
- * ODE_double_precision
- * ODE_EXT_no_debug
- * ODE_EXT_trimesh
- * ODE_EXT_opcode
- * ODE_EXT_gimpact
- * ODE_OPC_16bit_indices
- * ODE_OPC_new_collider
- * ODE_EXT_mt_collisions
- * ODE_EXT_threading
- * ODE_THR_builtin_impl
- */
-ODE_API const char* dGetConfiguration (void);
-
-/**
- * Helper to check for a token in the ODE configuration string.
- * Caution, this function is case sensitive.
- *
- * @param token A configuration token, see dGetConfiguration for details
- *
- * @return 1 if exact token is present, 0 if not present
- */
-ODE_API int dCheckConfiguration( const char* token );
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_COMPATIBILITY_H_
-#define _ODE_COMPATIBILITY_H_
-
-/*
- * ODE's backward compatibility system ensures that as ODE's API
- * evolves, user code will not break.
- */
-
-/*
- * These new rotation function names are more consistent with the
- * rest of the API.
- */
-#define dQtoR(q,R) dRfromQ((R),(q))
-#define dRtoQ(R,q) dQfromR((q),(R))
-#define dWtoDQ(w,q,dq) dDQfromW((dq),(w),(q))
-
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_CONTACT_H_
-#define _ODE_CONTACT_H_
-
-#include <ode/common.h>
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-
-enum {
- dContactMu2 = 0x001, /**< Use axis dependent friction */
- dContactAxisDep = 0x001, /**< Same as above */
- dContactFDir1 = 0x002, /**< Use FDir for the first friction value */
- dContactBounce = 0x004, /**< Restore collision energy anti-parallel to the normal */
- dContactSoftERP = 0x008, /**< Don't use global erp for penetration reduction */
- dContactSoftCFM = 0x010, /**< Don't use global cfm for penetration constraint */
- dContactMotion1 = 0x020, /**< Use a non-zero target velocity for the constraint */
- dContactMotion2 = 0x040,
- dContactMotionN = 0x080,
- dContactSlip1 = 0x100, /**< Force-dependent slip. */
- dContactSlip2 = 0x200,
- dContactRolling = 0x400, /**< Rolling/Angular friction */
-
- dContactApprox0 = 0x0000,
- dContactApprox1_1 = 0x1000,
- dContactApprox1_2 = 0x2000,
- dContactApprox1_N = 0x4000, /**< For rolling friction */
- dContactApprox1 = 0x7000
-};
-
-
-typedef struct dSurfaceParameters {
- /* must always be defined */
- int mode;
- dReal mu;
-
- /* only defined if the corresponding flag is set in mode */
- dReal mu2;
- dReal rho; /**< Rolling friction */
- dReal rho2;
- dReal rhoN; /**< Spinning friction */
- dReal bounce; /**< Coefficient of restitution */
- dReal bounce_vel; /**< Bouncing threshold */
- dReal soft_erp;
- dReal soft_cfm;
- dReal motion1,motion2,motionN;
- dReal slip1,slip2;
-} dSurfaceParameters;
-
-
-/**
- * @brief Describe the contact point between two geoms.
- *
- * If two bodies touch, or if a body touches a static feature in its
- * environment, the contact is represented by one or more "contact
- * points", described by dContactGeom.
- *
- * The convention is that if body 1 is moved along the normal vector by
- * a distance depth (or equivalently if body 2 is moved the same distance
- * in the opposite direction) then the contact depth will be reduced to
- * zero. This means that the normal vector points "in" to body 1.
- *
- * @ingroup collide
- */
-typedef struct dContactGeom {
- dVector3 pos; /*< contact position*/
- dVector3 normal; /*< normal vector*/
- dReal depth; /*< penetration depth*/
- dGeomID g1,g2; /*< the colliding geoms*/
- int side1,side2; /*< (to be documented)*/
-} dContactGeom;
-
-
-/* contact info used by contact joint */
-
-typedef struct dContact {
- dSurfaceParameters surface;
- dContactGeom geom;
- dVector3 fdir1;
-} dContact;
-
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001-2003 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_COOPERATIVE_H_
-#define _ODE_COOPERATIVE_H_
-
-
-#include <ode/common.h>
-#include <ode/threading.h>
-
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-/**
- * @defgroup coop Cooperative Algorithms
- *
- * Algorithms implemented as multiple threads doing work cooperatively.
- */
-
-
-struct dxCooperative;
-struct dxResourceRequirements;
-struct dxResourceContainer;
-
-/**
- * @brief A container for cooperative algorithms shared context
- *
- * The Cooperative is a container for cooperative algorithms shared context.
- * At present it contains threading object (either a real one or a defaulted
- * self-threading).
- *
- * Cooperative use in functions performing computations must be serialized. That is,
- * functions referring to a single instance of Cooperative object must not be called in
- * parallel.
- */
-typedef struct dxCooperative *dCooperativeID;
-
-
-/**
- * @brief A container for resource requirements information
- *
- * The ResourceRequirements object is a container for descriptive information
- * regarding what resources (memory, synchronization objects, etc.) need to be
- * allocated for particular computations. The object can be used for accumulating
- * resource requirement maxima over multiple functions and then allocating resources
- * that would suffice for any of those function calls.
- *
- * ResourceRequirements objects maintain relations to Cooperative objects since
- * amounts of resources that could be required can depend on characteristics of
- * shared context, e.g. on maximal number of threads in the threading object.
- *
- * @ingroup coop
- * @see dCooperativeID
- * @see dResourceContainerID
- */
-typedef struct dxResourceRequirements *dResourceRequirementsID;
-
-/**
- * @brief A container for algorithm allocated resources
- *
- * The ResourceContainer object can contain resources allocated according to information
- * in a ResourceRequirements. The resources inherit link to the threading object
- * from the requirements they are allocated according to.
- *
- * @ingroup coop
- * @see dResourceRequirementsID
- * @see dCooperativeID
- */
-typedef struct dxResourceContainer *dResourceContainerID;
-
-
- /**
- * @brief Creates a Cooperative object related to the specified threading.
- *
- * NULL's are allowed for the threading. In this case the default (global) self-threading
- * object will be used.
- *
- * Use @c dCooperativeDestroy to destroy the object. The Cooperative object must exist
- * until after all the objects referencing it are destroyed.
- *
- * @param functionInfo The threading functions to use
- * @param threadingImpl The threading implementation object to use
- * @returns The Cooperative object instance or NULL if allocation fails.
- * @ingroup coop
- * @see dCooperativeDestroy
- */
-ODE_API dCooperativeID dCooperativeCreate(const dThreadingFunctionsInfo *functionInfo/*=NULL*/, dThreadingImplementationID threadingImpl/*=NULL*/);
-
- /**
- * @brief Destroys Cooperative object.
- *
- * The Cooperative object can only be destroyed after all the objects referencing it.
- *
- * @param cooperative A Cooperative object to be deleted (NULL is allowed)
- * @ingroup coop
- * @see dCooperativeCreate
- */
-ODE_API void dCooperativeDestroy(dCooperativeID cooperative);
-
-
- /**
- * @brief Creates a ResourceRequirements object related to a Cooperative.
- *
- * The object is purely descriptive and does not contain any resources by itself.
- * The actual resources are allocated by means of ResourceContainer object.
- *
- * The object is created with empty requirements. It can be then used to accumulate
- * requirements for one or more function calls and can be cloned or merged with others.
- * The actual requirements information is added to the object by computation related
- * functions.
- *
- * Use @c dResourceRequirementsDestroy to delete the object when it is no longer needed.
- *
- * @param cooperative A Cooperative object to be used
- * @returns The ResourceRequirements object instance or NULL if allocation fails
- * @ingroup coop
- * @see dResourceRequirementsDestroy
- * @see dResourceRequirementsClone
- * @see dResourceRequirementsMergeIn
- * @see dCooperativeCreate
- * @see dResourceContainerAcquire
- */
-ODE_API dResourceRequirementsID dResourceRequirementsCreate(dCooperativeID cooperative);
-
- /**
- * @brief Destroys ResourceRequirements object.
- *
- * The ResourceRequirements object can be destroyed at any time with no regards
- * to other objects' lifetime.
- *
- * @param requirements A ResourceRequirements object to be deleted (NULL is allowed)
- * @ingroup coop
- * @see dResourceRequirementsCreate
- */
-ODE_API void dResourceRequirementsDestroy(dResourceRequirementsID requirements);
-
- /**
- * @brief Clones ResourceRequirements object.
- *
- * The function creates a copy of the ResourceRequirements object with all the
- * contents and the relation to Cooperative matching. The object passed in
- * the parameter is not changed.
- *
- * The object created with the function must later be destroyed with @c dResourceRequirementsDestroy.
- *
- * @param requirements A ResourceRequirements object to be cloned
- * @returns A handle to the new object or NULL if allocation fails
- * @ingroup coop
- * @see dResourceRequirementsCreate
- * @see dResourceRequirementsDestroy
- * @see dResourceRequirementsMergeIn
- */
-ODE_API dResourceRequirementsID dResourceRequirementsClone(/*const */dResourceRequirementsID requirements);
-
- /**
- * @brief Merges one ResourceRequirements object into another ResourceRequirements object.
- *
- * The function updates @a summaryRequirements requirements to be also sufficient
- * for the purposes @a extraRequirements could be used for. The @a extraRequirements
- * object is not changed. The both objects should normally have had been created
- * with the same Cooperative object.
- *
- * @param summaryRequirements A ResourceRequirements object to be changed
- * @param extraRequirements A ResourceRequirements the requirements to be taken from
- * @ingroup coop
- * @see dResourceRequirementsCreate
- * @see dResourceRequirementsDestroy
- * @see dResourceRequirementsClone
- */
-ODE_API void dResourceRequirementsMergeIn(dResourceRequirementsID summaryRequirements, /*const */dResourceRequirementsID extraRequirements);
-
-
- /**
- * @brief Allocates resources as specified in ResourceRequirements object.
- *
- * The ResourceContainer object can be used in cooperative computation algorithms.
- *
- * The same @a requirements object can be passed to many resource allocations
- * (with or without modifications) and can be deleted immediately, without waiting
- * for the ResourceContainer object destruction.
- *
- * Use @c dResourceContainerDestroy to delete the object and release the resources
- * when they are no longer needed.
- *
- * @param requirements The ResourceRequirements object to allocate resources according to
- * @returns A ResourceContainer object instance with the resources allocated or NULL if allocation fails
- * @ingroup coop
- * @see dResourceContainerDestroy
- * @see dResourceRequirementsCreate
- */
-ODE_API dResourceContainerID dResourceContainerAcquire(/*const */dResourceRequirementsID requirements);
-
- /**
- * @brief Destroys ResourceContainer object and releases resources allocated in it.
- *
- * @param resources A ResourceContainer object to be deleted (NULL is allowed)
- * @ingroup coop
- * @see dResourceContainerAcquire
- */
-ODE_API void dResourceContainerDestroy(dResourceContainerID resources);
-
-
-#ifdef __cplusplus
-} // extern "C"
-#endif
-
-
-#endif // #ifndef _ODE_COOPERATIVE_H_
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-/* this comes from the `reuse' library. copy any changes back to the source */
-
-#ifndef _ODE_ERROR_H_
-#define _ODE_ERROR_H_
-
-#include <ode/odeconfig.h>
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-/* all user defined error functions have this type. error and debug functions
- * should not return.
- */
-typedef void dMessageFunction (int errnum, const char *msg, va_list ap);
-
-/* set a new error, debug or warning handler. if fn is 0, the default handlers
- * are used.
- */
-ODE_API void dSetErrorHandler (dMessageFunction *fn);
-ODE_API void dSetDebugHandler (dMessageFunction *fn);
-ODE_API void dSetMessageHandler (dMessageFunction *fn);
-
-/* return the current error, debug or warning handler. if the return value is
- * 0, the default handlers are in place.
- */
-ODE_API dMessageFunction *dGetErrorHandler(void);
-ODE_API dMessageFunction *dGetDebugHandler(void);
-ODE_API dMessageFunction *dGetMessageHandler(void);
-
-/* generate a fatal error, debug trap or a message. */
-ODE_API void ODE_NORETURN dError (int num, const char *msg, ...);
-ODE_API void ODE_NORETURN dDebug (int num, const char *msg, ...);
-ODE_API void dMessage (int num, const char *msg, ...);
-
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_EXPORT_DIF_
-#define _ODE_EXPORT_DIF_
-
-#include <ode/common.h>
-
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-ODE_API void dWorldExportDIF (dWorldID w, FILE *file, const char *world_name);
-
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_MASS_H_
-#define _ODE_MASS_H_
-
-#include <ode/common.h>
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-struct dMass;
-typedef struct dMass dMass;
-
-/**
- * Check if a mass structure has valid value.
- * The function check if the mass and innertia matrix are positive definits
- *
- * @param m A mass structure to check
- *
- * @return 1 if both codition are met
- */
-ODE_API int dMassCheck(const dMass *m);
-
-ODE_API void dMassSetZero (dMass *);
-
-ODE_API void dMassSetParameters (dMass *, dReal themass,
- dReal cgx, dReal cgy, dReal cgz,
- dReal I11, dReal I22, dReal I33,
- dReal I12, dReal I13, dReal I23);
-
-ODE_API void dMassSetSphere (dMass *, dReal density, dReal radius);
-ODE_API void dMassSetSphereTotal (dMass *, dReal total_mass, dReal radius);
-
-ODE_API void dMassSetCapsule (dMass *, dReal density, int direction,
- dReal radius, dReal length);
-ODE_API void dMassSetCapsuleTotal (dMass *, dReal total_mass, int direction,
- dReal radius, dReal length);
-
-ODE_API void dMassSetCylinder (dMass *, dReal density, int direction,
- dReal radius, dReal length);
-ODE_API void dMassSetCylinderTotal (dMass *, dReal total_mass, int direction,
- dReal radius, dReal length);
-
-ODE_API void dMassSetBox (dMass *, dReal density,
- dReal lx, dReal ly, dReal lz);
-ODE_API void dMassSetBoxTotal (dMass *, dReal total_mass,
- dReal lx, dReal ly, dReal lz);
-
-ODE_API void dMassSetTrimesh (dMass *, dReal density, dGeomID g);
-
-ODE_API void dMassSetTrimeshTotal (dMass *m, dReal total_mass, dGeomID g);
-
-ODE_API void dMassAdjust (dMass *, dReal newmass);
-
-ODE_API void dMassTranslate (dMass *, dReal x, dReal y, dReal z);
-
-ODE_API void dMassRotate (dMass *, const dMatrix3 R);
-
-ODE_API void dMassAdd (dMass *a, const dMass *b);
-
-
-/* Backwards compatible API */
-ODE_API_DEPRECATED ODE_API void dMassSetCappedCylinder(dMass *a, dReal b, int c, dReal d, dReal e);
-ODE_API_DEPRECATED ODE_API void dMassSetCappedCylinderTotal(dMass *a, dReal b, int c, dReal d, dReal e);
-
-
-struct dMass {
- dReal mass;
- dVector3 c;
- dMatrix3 I;
-
-#ifdef __cplusplus
- dMass()
- { dMassSetZero (this); }
- void setZero()
- { dMassSetZero (this); }
- void setParameters (dReal themass, dReal cgx, dReal cgy, dReal cgz,
- dReal I11, dReal I22, dReal I33,
- dReal I12, dReal I13, dReal I23)
- { dMassSetParameters (this,themass,cgx,cgy,cgz,I11,I22,I33,I12,I13,I23); }
-
- void setSphere (dReal density, dReal radius)
- { dMassSetSphere (this,density,radius); }
- void setSphereTotal (dReal total, dReal radius)
- { dMassSetSphereTotal (this,total,radius); }
-
- void setCapsule (dReal density, int direction, dReal radius, dReal length)
- { dMassSetCapsule (this,density,direction,radius,length); }
- void setCapsuleTotal (dReal total, int direction, dReal radius, dReal length)
- { dMassSetCapsule (this,total,direction,radius,length); }
-
- void setCylinder(dReal density, int direction, dReal radius, dReal length)
- { dMassSetCylinder (this,density,direction,radius,length); }
- void setCylinderTotal(dReal total, int direction, dReal radius, dReal length)
- { dMassSetCylinderTotal (this,total,direction,radius,length); }
-
- void setBox (dReal density, dReal lx, dReal ly, dReal lz)
- { dMassSetBox (this,density,lx,ly,lz); }
- void setBoxTotal (dReal total, dReal lx, dReal ly, dReal lz)
- { dMassSetBoxTotal (this,total,lx,ly,lz); }
-
- void setTrimesh(dReal density, dGeomID g)
- { dMassSetTrimesh (this, density, g); }
- void setTrimeshTotal(dReal total, dGeomID g)
- { dMassSetTrimeshTotal (this, total, g); }
-
- void adjust (dReal newmass)
- { dMassAdjust (this,newmass); }
- void translate (dReal x, dReal y, dReal z)
- { dMassTranslate (this,x,y,z); }
- void rotate (const dMatrix3 R)
- { dMassRotate (this,R); }
- void add (const dMass *b)
- { dMassAdd (this,b); }
-#endif
-};
-
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-/* optimized and unoptimized vector and matrix functions */
-
-#ifndef _ODE_MATRIX_H_
-#define _ODE_MATRIX_H_
-
-#include <ode/common.h>
-
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-
-/* set a vector/matrix of size n to all zeros, or to a specific value. */
-
-ODE_API void dSetZero (dReal *a, int n);
-ODE_API void dSetValue (dReal *a, int n, dReal value);
-
-
-/* get the dot product of two n*1 vectors. if n <= 0 then
- * zero will be returned (in which case a and b need not be valid).
- */
-
-ODE_API dReal dDot (const dReal *a, const dReal *b, int n);
-
-
-/* get the dot products of (a0,b), (a1,b), etc and return them in outsum.
- * all vectors are n*1. if n <= 0 then zeroes will be returned (in which case
- * the input vectors need not be valid). this function is somewhat faster
- * than calling dDot() for all of the combinations separately.
- */
-
-/* NOT INCLUDED in the library for now.
-void dMultidot2 (const dReal *a0, const dReal *a1,
- const dReal *b, dReal *outsum, int n);
-*/
-
-
-/* matrix multiplication. all matrices are stored in standard row format.
- * the digit refers to the argument that is transposed:
- * 0: A = B * C (sizes: A:p*r B:p*q C:q*r)
- * 1: A = B' * C (sizes: A:p*r B:q*p C:q*r)
- * 2: A = B * C' (sizes: A:p*r B:p*q C:r*q)
- * case 1,2 are equivalent to saying that the operation is A=B*C but
- * B or C are stored in standard column format.
- */
-
-ODE_API void dMultiply0 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
-ODE_API void dMultiply1 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
-ODE_API void dMultiply2 (dReal *A, const dReal *B, const dReal *C, int p,int q,int r);
-
-
-/* do an in-place cholesky decomposition on the lower triangle of the n*n
- * symmetric matrix A (which is stored by rows). the resulting lower triangle
- * will be such that L*L'=A. return 1 on success and 0 on failure (on failure
- * the matrix is not positive definite).
- */
-
-ODE_API int dFactorCholesky (dReal *A, int n);
-
-
-/* solve for x: L*L'*x = b, and put the result back into x.
- * L is size n*n, b is size n*1. only the lower triangle of L is considered.
- */
-
-ODE_API void dSolveCholesky (const dReal *L, dReal *b, int n);
-
-
-/* compute the inverse of the n*n positive definite matrix A and put it in
- * Ainv. this is not especially fast. this returns 1 on success (A was
- * positive definite) or 0 on failure (not PD).
- */
-
-ODE_API int dInvertPDMatrix (const dReal *A, dReal *Ainv, int n);
-
-
-/* check whether an n*n matrix A is positive definite, return 1/0 (yes/no).
- * positive definite means that x'*A*x > 0 for any x. this performs a
- * cholesky decomposition of A. if the decomposition fails then the matrix
- * is not positive definite. A is stored by rows. A is not altered.
- */
-
-ODE_API int dIsPositiveDefinite (const dReal *A, int n);
-
-
-/* factorize a matrix A into L*D*L', where L is lower triangular with ones on
- * the diagonal, and D is diagonal.
- * A is an n*n matrix stored by rows, with a leading dimension of n rounded
- * up to 4. L is written into the strict lower triangle of A (the ones are not
- * written) and the reciprocal of the diagonal elements of D are written into
- * d.
- */
-ODE_API void dFactorLDLT (dReal *A, dReal *d, int n, int nskip);
-
-
-/* solve L*x=b, where L is n*n lower triangular with ones on the diagonal,
- * and x,b are n*1. b is overwritten with x.
- * the leading dimension of L is `nskip'.
- */
-ODE_API void dSolveL1 (const dReal *L, dReal *b, int n, int nskip);
-
-
-/* solve L'*x=b, where L is n*n lower triangular with ones on the diagonal,
- * and x,b are n*1. b is overwritten with x.
- * the leading dimension of L is `nskip'.
- */
-ODE_API void dSolveL1T (const dReal *L, dReal *b, int n, int nskip);
-
-
-/* in matlab syntax: a(1:n) = a(1:n) .* d(1:n)
- */
-
-ODE_API void dScaleVector (dReal *a, const dReal *d, int n);
-
-/* The function is an alias for @c dScaleVector.
- * It has been deprecated because of a wrong naming schema used.
- */
-ODE_API_DEPRECATED ODE_API void dVectorScale (dReal *a, const dReal *d, int n);
-
-
-/* given `L', a n*n lower triangular matrix with ones on the diagonal,
- * and `d', a n*1 vector of the reciprocal diagonal elements of an n*n matrix
- * D, solve L*D*L'*x=b where x,b are n*1. x overwrites b.
- * the leading dimension of L is `nskip'.
- */
-
-ODE_API void dSolveLDLT (const dReal *L, const dReal *d, dReal *b, int n, int nskip);
-
-
-/* given an L*D*L' factorization of an n*n matrix A, return the updated
- * factorization L2*D2*L2' of A plus the following "top left" matrix:
- *
- * [ b a' ] <-- b is a[0]
- * [ a 0 ] <-- a is a[1..n-1]
- *
- * - L has size n*n, its leading dimension is nskip. L is lower triangular
- * with ones on the diagonal. only the lower triangle of L is referenced.
- * - d has size n. d contains the reciprocal diagonal elements of D.
- * - a has size n.
- * the result is written into L, except that the left column of L and d[0]
- * are not actually modified. see ldltaddTL.m for further comments.
- */
-ODE_API void dLDLTAddTL (dReal *L, dReal *d, const dReal *a, int n, int nskip);
-
-
-/* given an L*D*L' factorization of a permuted matrix A, produce a new
- * factorization for row and column `r' removed.
- * - A has size n1*n1, its leading dimension in nskip. A is symmetric and
- * positive definite. only the lower triangle of A is referenced.
- * A itself may actually be an array of row pointers.
- * - L has size n2*n2, its leading dimension in nskip. L is lower triangular
- * with ones on the diagonal. only the lower triangle of L is referenced.
- * - d has size n2. d contains the reciprocal diagonal elements of D.
- * - p is a permutation vector. it contains n2 indexes into A. each index
- * must be in the range 0..n1-1.
- * - r is the row/column of L to remove.
- * the new L will be written within the old L, i.e. will have the same leading
- * dimension. the last row and column of L, and the last element of d, are
- * undefined on exit.
- *
- * a fast O(n^2) algorithm is used. see ldltremove.m for further comments.
- */
-ODE_API void dLDLTRemove (dReal **A, const int *p, dReal *L, dReal *d,
- int n1, int n2, int r, int nskip);
-
-
-/* given an n*n matrix A (with leading dimension nskip), remove the r'th row
- * and column by moving elements. the new matrix will have the same leading
- * dimension. the last row and column of A are untouched on exit.
- */
-ODE_API void dRemoveRowCol (dReal *A, int n, int nskip, int r);
-
-#ifdef __cplusplus
-}
-#endif
-
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001-2003 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_MATRIX_COOP_H_
-#define _ODE_MATRIX_COOP_H_
-
-
-#include <ode/common.h>
-#include <ode/cooperative.h>
-#include <ode/threading.h>
-
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-/**
- * @defgroup matrix_coop Matrix Cooperative Algorithms
- *
- * Cooperative algorithms operating on matrices and vectors.
- *
- * @ingroup coop
- */
-
-
-/**
- * @brief Estimates resource requirements for a @c dCooperativelyFactorLDLT call
- *
- * The function updates the contents of @a requirements to also suffice for calling
- * @c dCooperativelyFactorLDLT with the given parameters.
- *
- * Note: The requirements that could have already been in the @a requirements parameter
- * are never decreased.
- *
- * @param requirements The ResourceRequirements object to update
- * @param maximalAllowedThreadCount Maximal value of allowedThreadCount parameter that is going to be used
- * @param maximalRowCount Maximal value of rowCount parameter that is going to be used
- * @ingroup matrix_coop
- * @see dCooperativelyFactorLDLT
- * @see dResourceRequirementsCreate
- */
-ODE_API void dEstimateCooperativelyFactorLDLTResourceRequirements(dResourceRequirementsID requirements,
- unsigned maximalAllowedThreadCount, unsigned maximalRowCount);
-
-/**
- * @brief Cooperatively factorizes a matrix `A' into L*D*L'
- *
- * The function factorizes a matrix `A' into L*D*L', where `L' is lower triangular with ones on
- * the diagonal, and `D' is diagonal.
- * @a A is a rowCount*rowCount matrix stored by rows, with a leading dimension of @a rowCount rounded
- * up at least to 4 elements. `L; is written into the strict lower triangle of @a A
- * (the ones are not written) and the reciprocal of the diagonal elements of `D' are written into @a d.
- *
- * The @a resources must have had been allocated from a ResourceRequirements object
- * estimated in @c dEstimateCooperativelyFactorLDLTResourceRequirements.
- *
- * The operation is performed cooperatively by up to @a allowedThreadCount threads
- * from thread pool available in @a resources. The threading must must not be simultaneously
- * used (via other @c dResourceContainerID instances) in other calls that employ its features.
- *
- * @param resources The resources allocated for the function
- * @param allowedThreadCount Maximum thread count to use (the actual thread count could be less, depending on other parameters)
- * @param A The `A' matrix
- * @param d The `d' vector
- * @param rowCount The row count in @a A and @a d
- * @param rowskip The actual number of elements to be added to skip to next row in @a A
- * @ingroup matrix_coop
- * @see dEstimateCooperativelyFactorLDLTResourceRequirements
- * @see dResourceContainerAcquire
- * @see dCooperativelySolveLDLT
- */
-ODE_API void dCooperativelyFactorLDLT(dResourceContainerID resources, unsigned allowedThreadCount,
- dReal *A, dReal *d, unsigned rowCount, unsigned rowSkip);
-
-
-/**
- * @brief Estimates resource requirements for a @c dCooperativelySolveLDLT call
- *
- * The function updates the contents of @a requirements to also suffice for calling
- * @c dCooperativelySolveLDLT with the given parameters.
- *
- * Note: The requirements that could have already been in the @a requirements parameter
- * are never decreased.
- *
- * @param requirements The ResourceRequirements object to update
- * @param maximalAllowedThreadCount Maximal value of allowedThreadCount parameter that is going to be used
- * @param maximalRowCount Maximal value of rowCount parameter that is going to be used
- * @ingroup matrix_coop
- * @see dCooperativelySolveLDLT
- * @see dResourceRequirementsCreate
- */
-ODE_API void dEstimateCooperativelySolveLDLTResourceRequirements(dResourceRequirementsID requirements,
- unsigned maximalAllowedThreadCount, unsigned maximalRowCount);
-
-/**
- * @brief Cooperatively solves L*D*L'*x=b
- *
- * Given `L', a rowCount*rowCount lower triangular matrix with ones on the diagonal,
- * and `d', a rowCount*1 vector of the reciprocal diagonal elements of a rowCount*rowCount matrix
- * D, the function solves L*D*L'*x=b where `x' and `b' are rowCount*1.
- * The leading dimension of @a L is @a rowSkip. The resulting vector `x' overwrites @a b.
- *
- * The @a resources must have had been allocated from a ResourceRequirements object
- * estimated in @c dEstimateCooperativelySolveLDLTResourceRequirements.
- *
- * The operation is performed cooperatively by up to @a allowedThreadCount threads
- * from thread pool available in @a resources. The threading must must not be simultaneously
- * used (via other @c dResourceContainerID instances) in other calls that employ its features.
- *
- * @param resources The resources allocated for the function
- * @param allowedThreadCount Maximum thread count to use (the actual thread count could be less, depending on other parameters)
- * @param L The `L' matrix
- * @param d The `d' vector
- * @param b The `b' vector; also the result is stored here
- * @param rowCount The row count in @a L, @a d and @a b
- * @param rowskip The actual number of elements to be added to skip to next row in @a L
- * @ingroup matrix_coop
- * @see dEstimateCooperativelySolveLDLTResourceRequirements
- * @see dResourceContainerAcquire
- * @see dCooperativelyFactorLDLT
- */
-ODE_API void dCooperativelySolveLDLT(dResourceContainerID resources, unsigned allowedThreadCount,
- const dReal *L, const dReal *d, dReal *b, unsigned rowCount, unsigned rowSkip);
-
-
-/**
- * @brief Estimates resource requirements for a @c dCooperativelySolveL1Straight call
- *
- * The function updates the contents of @a requirements to also suffice for calling
- * @c dCooperativelySolveL1Straight with the given parameters.
- *
- * Note: The requirements that could have already been in the @a requirements parameter
- * are never decreased.
- *
- * @param requirements The ResourceRequirements object to update
- * @param maximalAllowedThreadCount Maximal value of allowedThreadCount parameter that is going to be used
- * @param maximalRowCount Maximal value of rowCount parameter that is going to be used
- * @ingroup matrix_coop
- * @see dCooperativelySolveL1Straight
- * @see dResourceRequirementsCreate
- */
-ODE_API void dEstimateCooperativelySolveL1StraightResourceRequirements(dResourceRequirementsID requirements,
- unsigned maximalAllowedThreadCount, unsigned maximalRowCount);
-
-/**
- * @brief Cooperatively solves L*x=b
- *
- * The function solves L*x=b, where `L' is rowCount*rowCount lower triangular with ones on the diagonal,
- * and `x', `b' are rowCount*1. The leading dimension of @a L is @a rowSkip.
- * @a b is overwritten with `x'.
- *
- * The @a resources must have had been allocated from a ResourceRequirements object
- * estimated in @c dEstimateCooperativelySolveL1StraightResourceRequirements.
- *
- * The operation is performed cooperatively by up to @a allowedThreadCount threads
- * from thread pool available in @a resources. The threading must must not be simultaneously
- * used (via other @c dResourceContainerID instances) in other calls that employ its features.
- *
- * @param resources The resources allocated for the function
- * @param allowedThreadCount Maximum thread count to use (the actual thread count could be less, depending on other parameters)
- * @param L The `L' matrix
- * @param b The `b' vector; also the result is stored here
- * @param rowCount The row count in @a L and @a b
- * @param rowskip The actual number of elements to be added to skip to next row in @a L
- * @ingroup matrix_coop
- * @see dEstimateCooperativelySolveL1StraightResourceRequirements
- * @see dResourceContainerAcquire
- * @see dCooperativelyFactorLDLT
- */
-ODE_API void dCooperativelySolveL1Straight(dResourceContainerID resources, unsigned allowedThreadCount,
- const dReal *L, dReal *b, unsigned rowCount, unsigned rowSkip);
-
-
-/**
- * @brief Estimates resource requirements for a @c dCooperativelySolveL1Transposed call
- *
- * The function updates the contents of @a requirements to also suffice for calling
- * @c dCooperativelySolveL1Transposed with the given parameters.
- *
- * Note: The requirements that could have already been in the @a requirements parameter
- * are never decreased.
- *
- * @param requirements The ResourceRequirements object to update
- * @param maximalAllowedThreadCount Maximal value of allowedThreadCount parameter that is going to be used
- * @param maximalRowCount Maximal value of rowCount parameter that is going to be used
- * @ingroup matrix_coop
- * @see dCooperativelySolveL1Transposed
- * @see dResourceRequirementsCreate
- */
-ODE_API void dEstimateCooperativelySolveL1TransposedResourceRequirements(dResourceRequirementsID requirements,
- unsigned maximalAllowedThreadCount, unsigned maximalRowCount);
-
-/**
- * @brief Cooperatively solves L'*x=b
- *
- * The function solves L'*x=b, where `L' is rowCount*rowCount lower triangular with ones on the diagonal,
- * and `x', b are rowCount*1. The leading dimension of @a L is @a rowSkip.
- * @a b is overwritten with `x'.
- *
- * The @a resources must have had been allocated from a ResourceRequirements object
- * estimated in @c dEstimateCooperativelySolveL1TransposedResourceRequirements.
- *
- * The operation is performed cooperatively by up to @a allowedThreadCount threads
- * from thread pool available in @a resources. The threading must must not be simultaneously
- * used (via other @c dResourceContainerID instances) in other calls that employ its features.
- *
- * @param resources The resources allocated for the function
- * @param allowedThreadCount Maximum thread count to use (the actual thread count could be less, depending on other parameters)
- * @param L The `L' matrix
- * @param b The `b' vector; also the result is stored here
- * @param rowCount The row count in @a L and @a b
- * @param rowskip The actual number of elements to be added to skip to next row in @a L
- * @ingroup matrix_coop
- * @see dEstimateCooperativelySolveL1TransposedResourceRequirements
- * @see dResourceContainerAcquire
- * @see dCooperativelyFactorLDLT
- */
-ODE_API void dCooperativelySolveL1Transposed(dResourceContainerID resources, unsigned allowedThreadCount,
- const dReal *L, dReal *b, unsigned rowCount, unsigned rowSkip);
-
-
-/**
- * @brief Estimates resource requirements for a @c dCooperativelyScaleVector call
- *
- * The function updates the contents of @a requirements to also suffice for calling
- * @c dCooperativelyScaleVector with the given parameters.
- *
- * Note: The requirements that could have already been in the @a requirements parameter
- * are never decreased.
- *
- * @param requirements The ResourceRequirements object to update
- * @param maximalAllowedThreadCount Maximal value of allowedThreadCount parameter that is going to be used
- * @param maximalElementCount Maximal value of elementCount parameter that is going to be used
- * @ingroup matrix_coop
- * @see dCooperativelyScaleVector
- * @see dResourceRequirementsCreate
- */
-ODE_API void dEstimateCooperativelyScaleVectorResourceRequirements(dResourceRequirementsID requirements,
- unsigned maximalAllowedThreadCount, unsigned maximalElementCount);
-
-/**
- * @brief Multiplies elements of one vector by corresponding element of another one
- *
- * In matlab syntax, the operation performed is: dataVector(1:elementCount) = dataVector(1:elementCount) .* scaleVector(1:elementCount)
- *
- * The @a resources must have had been allocated from a ResourceRequirements object
- * estimated in @c dEstimateCooperativelyScaleVectorResourceRequirements.
- *
- * The operation is performed cooperatively by up to @a allowedThreadCount threads
- * from thread pool available in @a resources. The threading must must not be simultaneously
- * used (via other @c dResourceContainerID instances) in other calls that employ its features.
- *
- * @param resources The resources allocated for the function
- * @param allowedThreadCount Maximum thread count to use (the actual thread count could be less, depending on other parameters)
- * @param dataVector The vector to be scaled in place
- * @param scaleVector The scale vector
- * @param elementCount The number of elements in @a dataVector and @a scaleVector
- * @ingroup matrix_coop
- * @see dEstimateCooperativelyScaleVectorResourceRequirements
- * @see dResourceContainerAcquire
- * @see dCooperativelyFactorLDLT
- */
-ODE_API void dCooperativelyScaleVector(dResourceContainerID resources, unsigned allowedThreadCount,
- dReal *dataVector, const dReal *scaleVector, unsigned elementCount);
-
-
-#ifdef __cplusplus
-} // extern "C"
-#endif
-
-
-#endif // #ifndef _ODE_MATRIX_COOP_H_
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-/* this comes from the `reuse' library. copy any changes back to the source */
-
-#ifndef _ODE_MEMORY_H_
-#define _ODE_MEMORY_H_
-
-#include <ode/odeconfig.h>
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-/* function types to allocate and free memory */
-typedef void * dAllocFunction (dsizeint size);
-typedef void * dReallocFunction (void *ptr, dsizeint oldsize, dsizeint newsize);
-typedef void dFreeFunction (void *ptr, dsizeint size);
-
-/* set new memory management functions. if fn is 0, the default handlers are
- * used. */
-ODE_API void dSetAllocHandler (dAllocFunction *fn);
-ODE_API void dSetReallocHandler (dReallocFunction *fn);
-ODE_API void dSetFreeHandler (dFreeFunction *fn);
-
-/* get current memory management functions */
-ODE_API dAllocFunction *dGetAllocHandler (void);
-ODE_API dReallocFunction *dGetReallocHandler (void);
-ODE_API dFreeFunction *dGetFreeHandler (void);
-
-/* allocate and free memory. */
-ODE_API void * dAlloc (dsizeint size);
-ODE_API void * dRealloc (void *ptr, dsizeint oldsize, dsizeint newsize);
-ODE_API void dFree (void *ptr, dsizeint size);
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-/* miscellaneous math functions. these are mostly useful for testing */
-
-#ifndef _ODE_MISC_H_
-#define _ODE_MISC_H_
-
-#include <ode/common.h>
-
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-
-/* return 1 if the random number generator is working. */
-ODE_API int dTestRand(void);
-
-/* return next 32 bit random number. this uses a not-very-random linear
- * congruential method.
- */
-ODE_API unsigned long dRand(void);
-
-/* get and set the current random number seed. */
-ODE_API unsigned long dRandGetSeed(void);
-ODE_API void dRandSetSeed (unsigned long s);
-
-/* return a random integer between 0..n-1. the distribution will get worse
- * as n approaches 2^32.
- */
-ODE_API int dRandInt (int n);
-
-/* return a random real number between 0..1 */
-ODE_API dReal dRandReal(void);
-
-/* print out a matrix */
-ODE_API void dPrintMatrix (const dReal *A, int n, int m, const char *fmt, FILE *f);
-
-/* make a random vector with entries between +/- range. A has n elements. */
-ODE_API void dMakeRandomVector (dReal *A, int n, dReal range);
-
-/* make a random matrix with entries between +/- range. A has size n*m. */
-ODE_API void dMakeRandomMatrix (dReal *A, int n, int m, dReal range);
-
-/* clear the upper triangle of a square matrix */
-ODE_API void dClearUpperTriangle (dReal *A, int n);
-
-/* return the maximum element difference between the two n*m matrices */
-ODE_API dReal dMaxDifference (const dReal *A, const dReal *B, int n, int m);
-
-/* return the maximum element difference between the lower triangle of two
- * n*n matrices */
-ODE_API dReal dMaxDifferenceLowerTriangle (const dReal *A, const dReal *B, int n);
-
-
-#ifdef __cplusplus
-}
-#endif
-
-
-#ifdef __cplusplus
-static inline void dPrintMatrix (const dReal *A, int n, int m, const char *fmt="%10.4f ") { dPrintMatrix(A, n, m, fmt, stdout); }
-#endif
-
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_OBJECTS_H_
-#define _ODE_OBJECTS_H_
-
-#include <ode/common.h>
-#include <ode/mass.h>
-#include <ode/contact.h>
-#include <ode/threading.h>
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-/**
- * @defgroup world World
- *
- * The world object is a container for rigid bodies and joints. Objects in
- * different worlds can not interact, for example rigid bodies from two
- * different worlds can not collide.
- *
- * All the objects in a world exist at the same point in time, thus one
- * reason to use separate worlds is to simulate systems at different rates.
- * Most applications will only need one world.
- */
-
-/**
- * @brief Create a new, empty world and return its ID number.
- * @return an identifier
- * @ingroup world
- */
-ODE_API dWorldID dWorldCreate(void);
-
-
-/**
- * @brief Destroy a world and everything in it.
- *
- * This includes all bodies, and all joints that are not part of a joint
- * group. Joints that are part of a joint group will be deactivated, and
- * can be destroyed by calling, for example, dJointGroupEmpty().
- * @ingroup world
- * @param world the identifier for the world the be destroyed.
- */
-ODE_API void dWorldDestroy (dWorldID world);
-
-
-/**
- * @brief Set the user-data pointer
- * @param world the world to set the data on
- * @param data
- * @ingroup world
- */
-ODE_API void dWorldSetData (dWorldID world, void* data);
-
-
-/**
- * @brief Get the user-data pointer
- * @param world the world to set the data on
- * @param data
- * @ingroup world
- */
-ODE_API void* dWorldGetData (dWorldID world);
-
-
-/**
- * @brief Set the world's global gravity vector.
- *
- * The units are m/s^2, so Earth's gravity vector would be (0,0,-9.81),
- * assuming that +z is up. The default is no gravity, i.e. (0,0,0).
- *
- * @ingroup world
- */
-ODE_API void dWorldSetGravity (dWorldID, dReal x, dReal y, dReal z);
-
-
-/**
- * @brief Get the gravity vector for a given world.
- * @ingroup world
- */
-ODE_API void dWorldGetGravity (dWorldID, dVector3 gravity);
-
-
-/**
- * @brief Set the global ERP value, that controls how much error
- * correction is performed in each time step.
- * @ingroup world
- * @param dWorldID the identifier of the world.
- * @param erp Typical values are in the range 0.1--0.8. The default is 0.2.
- */
-ODE_API void dWorldSetERP (dWorldID, dReal erp);
-
-/**
- * @brief Get the error reduction parameter.
- * @ingroup world
- * @return ERP value
- */
-ODE_API dReal dWorldGetERP (dWorldID);
-
-
-/**
- * @brief Set the global CFM (constraint force mixing) value.
- * @ingroup world
- * @param cfm Typical values are in the range @m{10^{-9}} -- 1.
- * The default is 10^-5 if single precision is being used, or 10^-10
- * if double precision is being used.
- */
-ODE_API void dWorldSetCFM (dWorldID, dReal cfm);
-
-/**
- * @brief Get the constraint force mixing value.
- * @ingroup world
- * @return CFM value
- */
-ODE_API dReal dWorldGetCFM (dWorldID);
-
-
-#define dWORLDSTEP_THREADCOUNT_UNLIMITED dTHREADING_THREAD_COUNT_UNLIMITED
-
-/**
- * @brief Set maximum threads to be used for island stepping
- *
- * The actual number of threads that is going to be used will be the minimum
- * of this limit and number of threads in the threading pool. By default
- * there is no limit (@c dWORLDSTEP_THREADCOUNT_UNLIMITED).
- *
- * @warning
- * WARNING! Running island stepping in multiple threads requires allocating
- * individual stepping memory buffer for each of those threads. The size of buffers
- * allocated is the size needed to handle the largest island in the world.
- *
- * Note: Setting a limit for island stepping does not affect threading at lower
- * levels in stepper functions. The sub-calls scheduled from them can be executed
- * in as many threads as there are available in the pool.
- *
- * @param w The world affected
- * @param count Thread count limit value for island stepping
- * @ingroup world
- * @see dWorldGetStepIslandsProcessingMaxThreadCount
- */
-ODE_API void dWorldSetStepIslandsProcessingMaxThreadCount(dWorldID w, unsigned count);
-/**
- * @brief Get maximum threads that are allowed to be used for island stepping.
- *
- * Please read commentaries to @c dWorldSetStepIslandsProcessingMaxThreadCount for
- * important information regarding the value returned.
- *
- * @param w The world queried
- * @returns Current thread count limit value for island stepping
- * @ingroup world
- * @see dWorldSetStepIslandsProcessingMaxThreadCount
- */
-ODE_API unsigned dWorldGetStepIslandsProcessingMaxThreadCount(dWorldID w);
-
-/**
- * @brief Set the world to use shared working memory along with another world.
- *
- * The worlds allocate working memory internally for simulation stepping. This
- * memory is cached among the calls to @c dWordStep and @c dWorldQuickStep.
- * Similarly, several worlds can be set up to share this memory caches thus
- * reducing overall memory usage by cost of making worlds inappropriate for
- * simultaneous simulation in multiple threads.
- *
- * If null value is passed for @a from_world parameter the world is detached from
- * sharing and returns to defaults for working memory, reservation policy and
- * memory manager as if just created. This can also be used to enable use of shared
- * memory for a world that has already had working memory allocated privately.
- * Normally using shared memory after a world has its private working memory allocated
- * is prohibited.
- *
- * Allocation policy used can only increase world's internal reserved memory size
- * and never decreases it. @c dWorldCleanupWorkingMemory can be used to release
- * working memory for a world in case if number of objects/joint decreases
- * significantly in it.
- *
- * With sharing working memory worlds also automatically share memory reservation
- * policy and memory manager. Thus, these parameters need to be customized for
- * initial world to be used as sharing source only.
- *
- * If worlds share working memory they must also use compatible threading implementations
- * (i.e. it is illegal for one world to perform stepping with self-threaded implementation
- * when the other world is assigned a multi-threaded implementation).
- * For more information read section about threading approaches in ODE.
- *
- * Failure result status means a memory allocation failure.
- *
- * @param w The world to use the shared memory with.
- * @param from_world Null or the world the shared memory is to be used from.
- * @returns 1 for success and 0 for failure.
- *
- * @ingroup world
- * @see dWorldCleanupWorkingMemory
- * @see dWorldSetStepMemoryReservationPolicy
- * @see dWorldSetStepMemoryManager
- */
-ODE_API int dWorldUseSharedWorkingMemory(dWorldID w, dWorldID from_world/*=NULL*/);
-
-/**
- * @brief Release internal working memory allocated for world
- *
- * The worlds allocate working memory internally for simulation stepping. This
- * function can be used to free world's internal memory cache in case if number of
- * objects/joints in the world decreases significantly. By default, internal
- * allocation policy is used to only increase cache size as necessary and never
- * decrease it.
- *
- * If a world shares its working memory with other worlds the cache deletion
- * affects all the linked worlds. However the shared status itself remains intact.
- *
- * The function call does affect neither memory reservation policy nor memory manager.
- *
- * @param w The world to release working memory for.
- *
- * @ingroup world
- * @see dWorldUseSharedWorkingMemory
- * @see dWorldSetStepMemoryReservationPolicy
- * @see dWorldSetStepMemoryManager
- */
-ODE_API void dWorldCleanupWorkingMemory(dWorldID w);
-
-
-#define dWORLDSTEP_RESERVEFACTOR_DEFAULT 1.2f
-#define dWORLDSTEP_RESERVESIZE_DEFAULT 65536U
-
-/**
- * @struct dWorldStepReserveInfo
- * @brief Memory reservation policy descriptor structure for world stepping functions.
- *
- * @c struct_size should be assigned the size of the structure.
- *
- * @c reserve_factor is a quotient that is multiplied by required memory size
- * to allocate extra reserve whenever reallocation is needed.
- *
- * @c reserve_minimum is a minimum size that is checked against whenever reallocation
- * is needed to allocate expected working memory minimum at once without extra
- * reallocations as number of bodies/joints grows.
- *
- * @ingroup world
- * @see dWorldSetStepMemoryReservationPolicy
- */
-typedef struct
-{
- unsigned struct_size;
- float reserve_factor; /* Use float as precision does not matter here*/
- unsigned reserve_minimum;
-
-} dWorldStepReserveInfo;
-
-/**
- * @brief Set memory reservation policy for world to be used with simulation stepping functions
- *
- * The function allows to customize reservation policy to be used for internal
- * memory which is allocated to aid simulation for a world. By default, values
- * of @c dWORLDSTEP_RESERVEFACTOR_DEFAULT and @c dWORLDSTEP_RESERVESIZE_DEFAULT
- * are used.
- *
- * Passing @a policyinfo argument as NULL results in reservation policy being
- * reset to defaults as if the world has been just created. The content of
- * @a policyinfo structure is copied internally and does not need to remain valid
- * after the call returns.
- *
- * If the world uses working memory sharing, changing memory reservation policy
- * affects all the worlds linked together.
- *
- * Failure result status means a memory allocation failure.
- *
- * @param w The world to change memory reservation policy for.
- * @param policyinfo Null or a pointer to policy descriptor structure.
- * @returns 1 for success and 0 for failure.
- *
- * @ingroup world
- * @see dWorldUseSharedWorkingMemory
- */
-ODE_API int dWorldSetStepMemoryReservationPolicy(dWorldID w, const dWorldStepReserveInfo *policyinfo/*=NULL*/);
-
-/**
-* @struct dWorldStepMemoryFunctionsInfo
-* @brief World stepping memory manager descriptor structure
-*
-* This structure is intended to define the functions of memory manager to be used
-* with world stepping functions.
-*
-* @c struct_size should be assigned the size of the structure
-*
-* @c alloc_block is a function to allocate memory block of given size.
-*
-* @c shrink_block is a function to shrink existing memory block to a smaller size.
-* It must preserve the contents of block head while shrinking. The new block size
-* is guaranteed to be always less than the existing one.
-*
-* @c free_block is a function to delete existing memory block.
-*
-* @ingroup init
-* @see dWorldSetStepMemoryManager
-*/
-typedef struct
-{
- unsigned struct_size;
- void *(*alloc_block)(dsizeint block_size);
- void *(*shrink_block)(void *block_pointer, dsizeint block_current_size, dsizeint block_smaller_size);
- void (*free_block)(void *block_pointer, dsizeint block_current_size);
-
-} dWorldStepMemoryFunctionsInfo;
-
-/**
-* @brief Set memory manager for world to be used with simulation stepping functions
-*
-* The function allows to customize memory manager to be used for internal
-* memory allocation during simulation for a world. By default, @c dAlloc/@c dRealloc/@c dFree
-* based memory manager is used.
-*
-* Passing @a memfuncs argument as NULL results in memory manager being
-* reset to default one as if the world has been just created. The content of
-* @a memfuncs structure is copied internally and does not need to remain valid
-* after the call returns.
-*
-* If the world uses working memory sharing, changing memory manager
-* affects all the worlds linked together.
-*
-* Failure result status means a memory allocation failure.
-*
-* @param w The world to change memory reservation policy for.
-* @param memfuncs Null or a pointer to memory manager descriptor structure.
-* @returns 1 for success and 0 for failure.
-*
-* @ingroup world
-* @see dWorldUseSharedWorkingMemory
-*/
-ODE_API int dWorldSetStepMemoryManager(dWorldID w, const dWorldStepMemoryFunctionsInfo *memfuncs);
-
-/**
- * @brief Assign threading implementation to be used for [quick]stepping the world.
- *
- * @warning It is not recommended to assign the same threading implementation to
- * different worlds if they are going to be called in parallel. In particular this
- * makes resources preallocation for threaded calls to lose its sense.
- * Built-in threading implementation is likely to crash if misused this way.
- *
- * @param w The world to change threading implementation for.
- * @param functions_info Pointer to threading functions structure
- * @param threading_impl ID of threading implementation object
- *
- * @ingroup world
- */
-ODE_API void dWorldSetStepThreadingImplementation(dWorldID w, const dThreadingFunctionsInfo *functions_info, dThreadingImplementationID threading_impl);
-
-/**
- * @brief Step the world.
- *
- * This uses a "big matrix" method that takes time on the order of m^3
- * and memory on the order of m^2, where m is the total number of constraint
- * rows. For large systems this will use a lot of memory and can be very slow,
- * but this is currently the most accurate method.
- *
- * Failure result status means that the memory allocation has failed for operation.
- * In such a case all the objects remain in unchanged state and simulation can be
- * retried as soon as more memory is available.
- *
- * @param w The world to be stepped
- * @param stepsize The number of seconds that the simulation has to advance.
- * @returns 1 for success and 0 for failure
- *
- * @ingroup world
- */
-ODE_API int dWorldStep (dWorldID w, dReal stepsize);
-
-/**
- * @brief Quick-step the world.
- *
- * This uses an iterative method that takes time on the order of m*N
- * and memory on the order of m, where m is the total number of constraint
- * rows N is the number of iterations.
- * For large systems this is a lot faster than dWorldStep(),
- * but it is less accurate.
- *
- * QuickStep is great for stacks of objects especially when the
- * auto-disable feature is used as well.
- * However, it has poor accuracy for near-singular systems.
- * Near-singular systems can occur when using high-friction contacts, motors,
- * or certain articulated structures. For example, a robot with multiple legs
- * sitting on the ground may be near-singular.
- *
- * There are ways to help overcome QuickStep's inaccuracy problems:
- *
- * \li Increase CFM.
- * \li Reduce the number of contacts in your system (e.g. use the minimum
- * number of contacts for the feet of a robot or creature).
- * \li Don't use excessive friction in the contacts.
- * \li Use contact slip if appropriate
- * \li Avoid kinematic loops (however, kinematic loops are inevitable in
- * legged creatures).
- * \li Don't use excessive motor strength.
- * \liUse force-based motors instead of velocity-based motors.
- *
- * Increasing the number of QuickStep iterations may help a little bit, but
- * it is not going to help much if your system is really near singular.
- *
- * Failure result status means that the memory allocation has failed for operation.
- * In such a case all the objects remain in unchanged state and simulation can be
- * retried as soon as more memory is available.
- *
- * @param w The world to be stepped
- * @param stepsize The number of seconds that the simulation has to advance.
- * @returns 1 for success and 0 for failure
- *
- * @ingroup world
- */
-ODE_API int dWorldQuickStep (dWorldID w, dReal stepsize);
-
-
-/**
-* @brief Converts an impulse to a force.
-* @ingroup world
-* @remarks
-* If you want to apply a linear or angular impulse to a rigid body,
-* instead of a force or a torque, then you can use this function to convert
-* the desired impulse into a force/torque vector before calling the
-* BodyAdd... function.
-* The current algorithm simply scales the impulse by 1/stepsize,
-* where stepsize is the step size for the next step that will be taken.
-* This function is given a dWorldID because, in the future, the force
-* computation may depend on integrator parameters that are set as
-* properties of the world.
-*/
-ODE_API void dWorldImpulseToForce
-(
- dWorldID, dReal stepsize,
- dReal ix, dReal iy, dReal iz, dVector3 force
- );
-
-
-/**
- * @brief Set the number of iterations that the QuickStep method performs per
- * step.
- * @ingroup world
- * @remarks
- * More iterations will give a more accurate solution, but will take
- * longer to compute.
- * @param num The default is 20 iterations.
- */
-ODE_API void dWorldSetQuickStepNumIterations (dWorldID, int num);
-
-
-/**
- * @brief Get the number of iterations that the QuickStep method performs per
- * step.
- * @ingroup world
- * @return nr of iterations
- */
-ODE_API int dWorldGetQuickStepNumIterations (dWorldID);
-
-/**
- * @brief Set the SOR over-relaxation parameter
- * @ingroup world
- * @param over_relaxation value to use by SOR
- */
-ODE_API void dWorldSetQuickStepW (dWorldID, dReal over_relaxation);
-
-/**
- * @brief Get the SOR over-relaxation parameter
- * @ingroup world
- * @returns the over-relaxation setting
- */
-ODE_API dReal dWorldGetQuickStepW (dWorldID);
-
-/* World contact parameter functions */
-
-/**
- * @brief Set the maximum correcting velocity that contacts are allowed
- * to generate.
- * @ingroup world
- * @param vel The default value is infinity (i.e. no limit).
- * @remarks
- * Reducing this value can help prevent "popping" of deeply embedded objects.
- */
-ODE_API void dWorldSetContactMaxCorrectingVel (dWorldID, dReal vel);
-
-/**
- * @brief Get the maximum correcting velocity that contacts are allowed
- * to generated.
- * @ingroup world
- */
-ODE_API dReal dWorldGetContactMaxCorrectingVel (dWorldID);
-
-/**
- * @brief Set the depth of the surface layer around all geometry objects.
- * @ingroup world
- * @remarks
- * Contacts are allowed to sink into the surface layer up to the given
- * depth before coming to rest.
- * @param depth The default value is zero.
- * @remarks
- * Increasing this to some small value (e.g. 0.001) can help prevent
- * jittering problems due to contacts being repeatedly made and broken.
- */
-ODE_API void dWorldSetContactSurfaceLayer (dWorldID, dReal depth);
-
-/**
- * @brief Get the depth of the surface layer around all geometry objects.
- * @ingroup world
- * @returns the depth
- */
-ODE_API dReal dWorldGetContactSurfaceLayer (dWorldID);
-
-
-/**
- * @defgroup disable Automatic Enabling and Disabling
- * @ingroup world bodies
- *
- * Every body can be enabled or disabled. Enabled bodies participate in the
- * simulation, while disabled bodies are turned off and do not get updated
- * during a simulation step. New bodies are always created in the enabled state.
- *
- * A disabled body that is connected through a joint to an enabled body will be
- * automatically re-enabled at the next simulation step.
- *
- * Disabled bodies do not consume CPU time, therefore to speed up the simulation
- * bodies should be disabled when they come to rest. This can be done automatically
- * with the auto-disable feature.
- *
- * If a body has its auto-disable flag turned on, it will automatically disable
- * itself when
- * @li It has been idle for a given number of simulation steps.
- * @li It has also been idle for a given amount of simulation time.
- *
- * A body is considered to be idle when the magnitudes of both its
- * linear average velocity and angular average velocity are below given thresholds.
- * The sample size for the average defaults to one and can be disabled by setting
- * to zero with
- *
- * Thus, every body has six auto-disable parameters: an enabled flag, a idle step
- * count, an idle time, linear/angular average velocity thresholds, and the
- * average samples count.
- *
- * Newly created bodies get these parameters from world.
- */
-
-/**
- * @brief Get auto disable linear average threshold for newly created bodies.
- * @ingroup disable
- * @return the threshold
- */
-ODE_API dReal dWorldGetAutoDisableLinearThreshold (dWorldID);
-
-/**
- * @brief Set auto disable linear average threshold for newly created bodies.
- * @param linear_average_threshold default is 0.01
- * @ingroup disable
- */
-ODE_API void dWorldSetAutoDisableLinearThreshold (dWorldID, dReal linear_average_threshold);
-
-/**
- * @brief Get auto disable angular average threshold for newly created bodies.
- * @ingroup disable
- * @return the threshold
- */
-ODE_API dReal dWorldGetAutoDisableAngularThreshold (dWorldID);
-
-/**
- * @brief Set auto disable angular average threshold for newly created bodies.
- * @param linear_average_threshold default is 0.01
- * @ingroup disable
- */
-ODE_API void dWorldSetAutoDisableAngularThreshold (dWorldID, dReal angular_average_threshold);
-
-/**
- * @brief Get auto disable sample count for newly created bodies.
- * @ingroup disable
- * @return number of samples used
- */
-ODE_API int dWorldGetAutoDisableAverageSamplesCount (dWorldID);
-
-/**
- * @brief Set auto disable average sample count for newly created bodies.
- * @ingroup disable
- * @param average_samples_count Default is 1, meaning only instantaneous velocity is used.
- * Set to zero to disable sampling and thus prevent any body from auto-disabling.
- */
-ODE_API void dWorldSetAutoDisableAverageSamplesCount (dWorldID, unsigned int average_samples_count );
-
-/**
- * @brief Get auto disable steps for newly created bodies.
- * @ingroup disable
- * @return nr of steps
- */
-ODE_API int dWorldGetAutoDisableSteps (dWorldID);
-
-/**
- * @brief Set auto disable steps for newly created bodies.
- * @ingroup disable
- * @param steps default is 10
- */
-ODE_API void dWorldSetAutoDisableSteps (dWorldID, int steps);
-
-/**
- * @brief Get auto disable time for newly created bodies.
- * @ingroup disable
- * @return nr of seconds
- */
-ODE_API dReal dWorldGetAutoDisableTime (dWorldID);
-
-/**
- * @brief Set auto disable time for newly created bodies.
- * @ingroup disable
- * @param time default is 0 seconds
- */
-ODE_API void dWorldSetAutoDisableTime (dWorldID, dReal time);
-
-/**
- * @brief Get auto disable flag for newly created bodies.
- * @ingroup disable
- * @return 0 or 1
- */
-ODE_API int dWorldGetAutoDisableFlag (dWorldID);
-
-/**
- * @brief Set auto disable flag for newly created bodies.
- * @ingroup disable
- * @param do_auto_disable default is false.
- */
-ODE_API void dWorldSetAutoDisableFlag (dWorldID, int do_auto_disable);
-
-
-/**
- * @defgroup damping Damping
- * @ingroup bodies world
- *
- * Damping serves two purposes: reduce simulation instability, and to allow
- * the bodies to come to rest (and possibly auto-disabling them).
- *
- * Bodies are constructed using the world's current damping parameters. Setting
- * the scales to 0 disables the damping.
- *
- * Here is how it is done: after every time step linear and angular
- * velocities are tested against the corresponding thresholds. If they
- * are above, they are multiplied by (1 - scale). So a negative scale value
- * will actually increase the speed, and values greater than one will
- * make the object oscillate every step; both can make the simulation unstable.
- *
- * To disable damping just set the damping scale to zero.
- *
- * You can also limit the maximum angular velocity. In contrast to the damping
- * functions, the angular velocity is affected before the body is moved.
- * This means that it will introduce errors in joints that are forcing the body
- * to rotate too fast. Some bodies have naturally high angular velocities
- * (like cars' wheels), so you may want to give them a very high (like the default,
- * dInfinity) limit.
- *
- * @note The velocities are damped after the stepper function has moved the
- * object. Otherwise the damping could introduce errors in joints. First the
- * joint constraints are processed by the stepper (moving the body), then
- * the damping is applied.
- *
- * @note The damping happens right after the moved callback is called; this way
- * it still possible use the exact velocities the body has acquired during the
- * step. You can even use the callback to create your own customized damping.
- */
-
-/**
- * @brief Get the world's linear damping threshold.
- * @ingroup damping
- */
-ODE_API dReal dWorldGetLinearDampingThreshold (dWorldID w);
-
-/**
- * @brief Set the world's linear damping threshold.
- * @param threshold The damping won't be applied if the linear speed is
- * below this threshold. Default is 0.01.
- * @ingroup damping
- */
-ODE_API void dWorldSetLinearDampingThreshold(dWorldID w, dReal threshold);
-
-/**
- * @brief Get the world's angular damping threshold.
- * @ingroup damping
- */
-ODE_API dReal dWorldGetAngularDampingThreshold (dWorldID w);
-
-/**
- * @brief Set the world's angular damping threshold.
- * @param threshold The damping won't be applied if the angular speed is
- * below this threshold. Default is 0.01.
- * @ingroup damping
- */
-ODE_API void dWorldSetAngularDampingThreshold(dWorldID w, dReal threshold);
-
-/**
- * @brief Get the world's linear damping scale.
- * @ingroup damping
- */
-ODE_API dReal dWorldGetLinearDamping (dWorldID w);
-
-/**
- * @brief Set the world's linear damping scale.
- * @param scale The linear damping scale that is to be applied to bodies.
- * Default is 0 (no damping). Should be in the interval [0, 1].
- * @ingroup damping
- */
-ODE_API void dWorldSetLinearDamping (dWorldID w, dReal scale);
-
-/**
- * @brief Get the world's angular damping scale.
- * @ingroup damping
- */
-ODE_API dReal dWorldGetAngularDamping (dWorldID w);
-
-/**
- * @brief Set the world's angular damping scale.
- * @param scale The angular damping scale that is to be applied to bodies.
- * Default is 0 (no damping). Should be in the interval [0, 1].
- * @ingroup damping
- */
-ODE_API void dWorldSetAngularDamping(dWorldID w, dReal scale);
-
-/**
- * @brief Convenience function to set body linear and angular scales.
- * @param linear_scale The linear damping scale that is to be applied to bodies.
- * @param angular_scale The angular damping scale that is to be applied to bodies.
- * @ingroup damping
- */
-ODE_API void dWorldSetDamping(dWorldID w,
- dReal linear_scale,
- dReal angular_scale);
-
-/**
- * @brief Get the default maximum angular speed.
- * @ingroup damping
- * @sa dBodyGetMaxAngularSpeed()
- */
-ODE_API dReal dWorldGetMaxAngularSpeed (dWorldID w);
-
-
-/**
- * @brief Set the default maximum angular speed for new bodies.
- * @ingroup damping
- * @sa dBodySetMaxAngularSpeed()
- */
-ODE_API void dWorldSetMaxAngularSpeed (dWorldID w, dReal max_speed);
-
-
-
-/**
- * @defgroup bodies Rigid Bodies
- *
- * A rigid body has various properties from the point of view of the
- * simulation. Some properties change over time:
- *
- * @li Position vector (x,y,z) of the body's point of reference.
- * Currently the point of reference must correspond to the body's center of mass.
- * @li Linear velocity of the point of reference, a vector (vx,vy,vz).
- * @li Orientation of a body, represented by a quaternion (qs,qx,qy,qz) or
- * a 3x3 rotation matrix.
- * @li Angular velocity vector (wx,wy,wz) which describes how the orientation
- * changes over time.
- *
- * Other body properties are usually constant over time:
- *
- * @li Mass of the body.
- * @li Position of the center of mass with respect to the point of reference.
- * In the current implementation the center of mass and the point of
- * reference must coincide.
- * @li Inertia matrix. This is a 3x3 matrix that describes how the body's mass
- * is distributed around the center of mass. Conceptually each body has an
- * x-y-z coordinate frame embedded in it that moves and rotates with the body.
- *
- * The origin of this coordinate frame is the body's point of reference. Some values
- * in ODE (vectors, matrices etc) are relative to the body coordinate frame, and others
- * are relative to the global coordinate frame.
- *
- * Note that the shape of a rigid body is not a dynamical property (except insofar as
- * it influences the various mass properties). It is only collision detection that cares
- * about the detailed shape of the body.
- */
-
-
-/**
- * @brief Get auto disable linear average threshold.
- * @ingroup bodies disable
- * @return the threshold
- */
-ODE_API dReal dBodyGetAutoDisableLinearThreshold (dBodyID);
-
-/**
- * @brief Set auto disable linear average threshold.
- * @ingroup bodies disable
- * @return the threshold
- */
-ODE_API void dBodySetAutoDisableLinearThreshold (dBodyID, dReal linear_average_threshold);
-
-/**
- * @brief Get auto disable angular average threshold.
- * @ingroup bodies disable
- * @return the threshold
- */
-ODE_API dReal dBodyGetAutoDisableAngularThreshold (dBodyID);
-
-/**
- * @brief Set auto disable angular average threshold.
- * @ingroup bodies disable
- * @return the threshold
- */
-ODE_API void dBodySetAutoDisableAngularThreshold (dBodyID, dReal angular_average_threshold);
-
-/**
- * @brief Get auto disable average size (samples count).
- * @ingroup bodies disable
- * @return the nr of steps/size.
- */
-ODE_API int dBodyGetAutoDisableAverageSamplesCount (dBodyID);
-
-/**
- * @brief Set auto disable average buffer size (average steps).
- * @ingroup bodies disable
- * @param average_samples_count the nr of samples to review.
- */
-ODE_API void dBodySetAutoDisableAverageSamplesCount (dBodyID, unsigned int average_samples_count);
-
-
-/**
- * @brief Get auto steps a body must be thought of as idle to disable
- * @ingroup bodies disable
- * @return the nr of steps
- */
-ODE_API int dBodyGetAutoDisableSteps (dBodyID);
-
-/**
- * @brief Set auto disable steps.
- * @ingroup bodies disable
- * @param steps the nr of steps.
- */
-ODE_API void dBodySetAutoDisableSteps (dBodyID, int steps);
-
-/**
- * @brief Get auto disable time.
- * @ingroup bodies disable
- * @return nr of seconds
- */
-ODE_API dReal dBodyGetAutoDisableTime (dBodyID);
-
-/**
- * @brief Set auto disable time.
- * @ingroup bodies disable
- * @param time nr of seconds.
- */
-ODE_API void dBodySetAutoDisableTime (dBodyID, dReal time);
-
-/**
- * @brief Get auto disable flag.
- * @ingroup bodies disable
- * @return 0 or 1
- */
-ODE_API int dBodyGetAutoDisableFlag (dBodyID);
-
-/**
- * @brief Set auto disable flag.
- * @ingroup bodies disable
- * @param do_auto_disable 0 or 1
- */
-ODE_API void dBodySetAutoDisableFlag (dBodyID, int do_auto_disable);
-
-/**
- * @brief Set auto disable defaults.
- * @remarks
- * Set the values for the body to those set as default for the world.
- * @ingroup bodies disable
- */
-ODE_API void dBodySetAutoDisableDefaults (dBodyID);
-
-
-/**
- * @brief Retrieves the world attached to te given body.
- * @remarks
- *
- * @ingroup bodies
- */
-ODE_API dWorldID dBodyGetWorld (dBodyID);
-
-/**
- * @brief Create a body in given world.
- * @remarks
- * Default mass parameters are at position (0,0,0).
- * @ingroup bodies
- */
-ODE_API dBodyID dBodyCreate (dWorldID);
-
-/**
- * @brief Destroy a body.
- * @remarks
- * All joints that are attached to this body will be put into limbo:
- * i.e. unattached and not affecting the simulation, but they will NOT be
- * deleted.
- * @ingroup bodies
- */
-ODE_API void dBodyDestroy (dBodyID);
-
-/**
- * @brief Set the body's user-data pointer.
- * @ingroup bodies
- * @param data arbitraty pointer
- */
-ODE_API void dBodySetData (dBodyID, void *data);
-
-/**
- * @brief Get the body's user-data pointer.
- * @ingroup bodies
- * @return a pointer to the user's data.
- */
-ODE_API void *dBodyGetData (dBodyID);
-
-/**
- * @brief Set position of a body.
- * @remarks
- * After setting, the outcome of the simulation is undefined
- * if the new configuration is inconsistent with the joints/constraints
- * that are present.
- * @ingroup bodies
- */
-ODE_API void dBodySetPosition (dBodyID, dReal x, dReal y, dReal z);
-
-/**
- * @brief Set the orientation of a body.
- * @ingroup bodies
- * @remarks
- * After setting, the outcome of the simulation is undefined
- * if the new configuration is inconsistent with the joints/constraints
- * that are present.
- */
-ODE_API void dBodySetRotation (dBodyID, const dMatrix3 R);
-
-/**
- * @brief Set the orientation of a body.
- * @ingroup bodies
- * @remarks
- * After setting, the outcome of the simulation is undefined
- * if the new configuration is inconsistent with the joints/constraints
- * that are present.
- */
-ODE_API void dBodySetQuaternion (dBodyID, const dQuaternion q);
-
-/**
- * @brief Set the linear velocity of a body.
- * @ingroup bodies
- */
-ODE_API void dBodySetLinearVel (dBodyID, dReal x, dReal y, dReal z);
-
-/**
- * @brief Set the angular velocity of a body.
- * @ingroup bodies
- */
-ODE_API void dBodySetAngularVel (dBodyID, dReal x, dReal y, dReal z);
-
-/**
- * @brief Get the position of a body.
- * @ingroup bodies
- * @remarks
- * When getting, the returned values are pointers to internal data structures,
- * so the vectors are valid until any changes are made to the rigid body
- * system structure.
- * @sa dBodyCopyPosition
- */
-ODE_API const dReal * dBodyGetPosition (dBodyID);
-
-
-/**
- * @brief Copy the position of a body into a vector.
- * @ingroup bodies
- * @param body the body to query
- * @param pos a copy of the body position
- * @sa dBodyGetPosition
- */
-ODE_API void dBodyCopyPosition (dBodyID body, dVector3 pos);
-
-
-/**
- * @brief Get the rotation of a body.
- * @ingroup bodies
- * @return pointer to a 4x3 rotation matrix.
- */
-ODE_API const dReal * dBodyGetRotation (dBodyID);
-
-
-/**
- * @brief Copy the rotation of a body.
- * @ingroup bodies
- * @param body the body to query
- * @param R a copy of the rotation matrix
- * @sa dBodyGetRotation
- */
-ODE_API void dBodyCopyRotation (dBodyID, dMatrix3 R);
-
-
-/**
- * @brief Get the rotation of a body.
- * @ingroup bodies
- * @return pointer to 4 scalars that represent the quaternion.
- */
-ODE_API const dReal * dBodyGetQuaternion (dBodyID);
-
-
-/**
- * @brief Copy the orientation of a body into a quaternion.
- * @ingroup bodies
- * @param body the body to query
- * @param quat a copy of the orientation quaternion
- * @sa dBodyGetQuaternion
- */
-ODE_API void dBodyCopyQuaternion(dBodyID body, dQuaternion quat);
-
-
-/**
- * @brief Get the linear velocity of a body.
- * @ingroup bodies
- */
-ODE_API const dReal * dBodyGetLinearVel (dBodyID);
-
-/**
- * @brief Get the angular velocity of a body.
- * @ingroup bodies
- */
-ODE_API const dReal * dBodyGetAngularVel (dBodyID);
-
-/**
- * @brief Set the mass of a body.
- * @ingroup bodies
- */
-ODE_API void dBodySetMass (dBodyID, const dMass *mass);
-
-/**
- * @brief Get the mass of a body.
- * @ingroup bodies
- */
-ODE_API void dBodyGetMass (dBodyID, dMass *mass);
-
-/**
- * @brief Add force at centre of mass of body in absolute coordinates.
- * @ingroup bodies
- */
-ODE_API void dBodyAddForce (dBodyID, dReal fx, dReal fy, dReal fz);
-
-/**
- * @brief Add torque at centre of mass of body in absolute coordinates.
- * @ingroup bodies
- */
-ODE_API void dBodyAddTorque (dBodyID, dReal fx, dReal fy, dReal fz);
-
-/**
- * @brief Add force at centre of mass of body in coordinates relative to body.
- * @ingroup bodies
- */
-ODE_API void dBodyAddRelForce (dBodyID, dReal fx, dReal fy, dReal fz);
-
-/**
- * @brief Add torque at centre of mass of body in coordinates relative to body.
- * @ingroup bodies
- */
-ODE_API void dBodyAddRelTorque (dBodyID, dReal fx, dReal fy, dReal fz);
-
-/**
- * @brief Add force at specified point in body in global coordinates.
- * @ingroup bodies
- */
-ODE_API void dBodyAddForceAtPos (dBodyID, dReal fx, dReal fy, dReal fz,
- dReal px, dReal py, dReal pz);
-/**
- * @brief Add force at specified point in body in local coordinates.
- * @ingroup bodies
- */
-ODE_API void dBodyAddForceAtRelPos (dBodyID, dReal fx, dReal fy, dReal fz,
- dReal px, dReal py, dReal pz);
-/**
- * @brief Add force at specified point in body in global coordinates.
- * @ingroup bodies
- */
-ODE_API void dBodyAddRelForceAtPos (dBodyID, dReal fx, dReal fy, dReal fz,
- dReal px, dReal py, dReal pz);
-/**
- * @brief Add force at specified point in body in local coordinates.
- * @ingroup bodies
- */
-ODE_API void dBodyAddRelForceAtRelPos (dBodyID, dReal fx, dReal fy, dReal fz,
- dReal px, dReal py, dReal pz);
-
-/**
- * @brief Return the current accumulated force vector.
- * @return points to an array of 3 reals.
- * @remarks
- * The returned values are pointers to internal data structures, so
- * the vectors are only valid until any changes are made to the rigid
- * body system.
- * @ingroup bodies
- */
-ODE_API const dReal * dBodyGetForce (dBodyID);
-
-/**
- * @brief Return the current accumulated torque vector.
- * @return points to an array of 3 reals.
- * @remarks
- * The returned values are pointers to internal data structures, so
- * the vectors are only valid until any changes are made to the rigid
- * body system.
- * @ingroup bodies
- */
-ODE_API const dReal * dBodyGetTorque (dBodyID);
-
-/**
- * @brief Set the body force accumulation vector.
- * @remarks
- * This is mostly useful to zero the force and torque for deactivated bodies
- * before they are reactivated, in the case where the force-adding functions
- * were called on them while they were deactivated.
- * @ingroup bodies
- */
-ODE_API void dBodySetForce (dBodyID b, dReal x, dReal y, dReal z);
-
-/**
- * @brief Set the body torque accumulation vector.
- * @remarks
- * This is mostly useful to zero the force and torque for deactivated bodies
- * before they are reactivated, in the case where the force-adding functions
- * were called on them while they were deactivated.
- * @ingroup bodies
- */
-ODE_API void dBodySetTorque (dBodyID b, dReal x, dReal y, dReal z);
-
-/**
- * @brief Get world position of a relative point on body.
- * @ingroup bodies
- * @param result will contain the result.
- */
-ODE_API void dBodyGetRelPointPos
-(
- dBodyID, dReal px, dReal py, dReal pz,
- dVector3 result
-);
-
-/**
- * @brief Get velocity vector in global coords of a relative point on body.
- * @ingroup bodies
- * @param result will contain the result.
- */
-ODE_API void dBodyGetRelPointVel
-(
- dBodyID, dReal px, dReal py, dReal pz,
- dVector3 result
-);
-
-/**
- * @brief Get velocity vector in global coords of a globally
- * specified point on a body.
- * @ingroup bodies
- * @param result will contain the result.
- */
-ODE_API void dBodyGetPointVel
-(
- dBodyID, dReal px, dReal py, dReal pz,
- dVector3 result
-);
-
-/**
- * @brief takes a point in global coordinates and returns
- * the point's position in body-relative coordinates.
- * @remarks
- * This is the inverse of dBodyGetRelPointPos()
- * @ingroup bodies
- * @param result will contain the result.
- */
-ODE_API void dBodyGetPosRelPoint
-(
- dBodyID, dReal px, dReal py, dReal pz,
- dVector3 result
-);
-
-/**
- * @brief Convert from local to world coordinates.
- * @ingroup bodies
- * @param result will contain the result.
- */
-ODE_API void dBodyVectorToWorld
-(
- dBodyID, dReal px, dReal py, dReal pz,
- dVector3 result
-);
-
-/**
- * @brief Convert from world to local coordinates.
- * @ingroup bodies
- * @param result will contain the result.
- */
-ODE_API void dBodyVectorFromWorld
-(
- dBodyID, dReal px, dReal py, dReal pz,
- dVector3 result
-);
-
-/**
- * @brief controls the way a body's orientation is updated at each timestep.
- * @ingroup bodies
- * @param mode can be 0 or 1:
- * \li 0: An ``infinitesimal'' orientation update is used.
- * This is fast to compute, but it can occasionally cause inaccuracies
- * for bodies that are rotating at high speed, especially when those
- * bodies are joined to other bodies.
- * This is the default for every new body that is created.
- * \li 1: A ``finite'' orientation update is used.
- * This is more costly to compute, but will be more accurate for high
- * speed rotations.
- * @remarks
- * Note however that high speed rotations can result in many types of
- * error in a simulation, and the finite mode will only fix one of those
- * sources of error.
- */
-ODE_API void dBodySetFiniteRotationMode (dBodyID, int mode);
-
-/**
- * @brief sets the finite rotation axis for a body.
- * @ingroup bodies
- * @remarks
- * This is axis only has meaning when the finite rotation mode is set
- * If this axis is zero (0,0,0), full finite rotations are performed on
- * the body.
- * If this axis is nonzero, the body is rotated by performing a partial finite
- * rotation along the axis direction followed by an infinitesimal rotation
- * along an orthogonal direction.
- * @remarks
- * This can be useful to alleviate certain sources of error caused by quickly
- * spinning bodies. For example, if a car wheel is rotating at high speed
- * you can call this function with the wheel's hinge axis as the argument to
- * try and improve its behavior.
- */
-ODE_API void dBodySetFiniteRotationAxis (dBodyID, dReal x, dReal y, dReal z);
-
-/**
- * @brief Get the way a body's orientation is updated each timestep.
- * @ingroup bodies
- * @return the mode 0 (infitesimal) or 1 (finite).
- */
-ODE_API int dBodyGetFiniteRotationMode (dBodyID);
-
-/**
- * @brief Get the finite rotation axis.
- * @param result will contain the axis.
- * @ingroup bodies
- */
-ODE_API void dBodyGetFiniteRotationAxis (dBodyID, dVector3 result);
-
-/**
- * @brief Get the number of joints that are attached to this body.
- * @ingroup bodies
- * @return nr of joints
- */
-ODE_API int dBodyGetNumJoints (dBodyID b);
-
-/**
- * @brief Return a joint attached to this body, given by index.
- * @ingroup bodies
- * @param index valid range is 0 to n-1 where n is the value returned by
- * dBodyGetNumJoints().
- */
-ODE_API dJointID dBodyGetJoint (dBodyID, int index);
-
-
-
-
-/**
- * @brief Set rigid body to dynamic state (default).
- * @param dBodyID identification of body.
- * @ingroup bodies
- */
-ODE_API void dBodySetDynamic (dBodyID);
-
-/**
- * @brief Set rigid body to kinematic state.
- * When in kinematic state the body isn't simulated as a dynamic
- * body (it's "unstoppable", doesn't respond to forces),
- * but can still affect dynamic bodies (e.g. in joints).
- * Kinematic bodies can be controlled by position and velocity.
- * @note A kinematic body has infinite mass. If you set its mass
- * to something else, it loses the kinematic state and behaves
- * as a normal dynamic body.
- * @param dBodyID identification of body.
- * @ingroup bodies
- */
-ODE_API void dBodySetKinematic (dBodyID);
-
-/**
- * @brief Check wether a body is in kinematic state.
- * @ingroup bodies
- * @return 1 if a body is kinematic or 0 if it is dynamic.
- */
-ODE_API int dBodyIsKinematic (dBodyID);
-
-/**
- * @brief Manually enable a body.
- * @param dBodyID identification of body.
- * @ingroup bodies
- */
-ODE_API void dBodyEnable (dBodyID);
-
-/**
- * @brief Manually disable a body.
- * @ingroup bodies
- * @remarks
- * A disabled body that is connected through a joint to an enabled body will
- * be automatically re-enabled at the next simulation step.
- */
-ODE_API void dBodyDisable (dBodyID);
-
-/**
- * @brief Check wether a body is enabled.
- * @ingroup bodies
- * @return 1 if a body is currently enabled or 0 if it is disabled.
- */
-ODE_API int dBodyIsEnabled (dBodyID);
-
-/**
- * @brief Set whether the body is influenced by the world's gravity or not.
- * @ingroup bodies
- * @param mode when nonzero gravity affects this body.
- * @remarks
- * Newly created bodies are always influenced by the world's gravity.
- */
-ODE_API void dBodySetGravityMode (dBodyID b, int mode);
-
-/**
- * @brief Get whether the body is influenced by the world's gravity or not.
- * @ingroup bodies
- * @return nonzero means gravity affects this body.
- */
-ODE_API int dBodyGetGravityMode (dBodyID b);
-
-/**
- * @brief Set the 'moved' callback of a body.
- *
- * Whenever a body has its position or rotation changed during the
- * timestep, the callback will be called (with body as the argument).
- * Use it to know which body may need an update in an external
- * structure (like a 3D engine).
- *
- * @param b the body that needs to be watched.
- * @param callback the callback to be invoked when the body moves. Set to zero
- * to disable.
- * @ingroup bodies
- */
-ODE_API void dBodySetMovedCallback(dBodyID b, void (*callback)(dBodyID));
-
-
-/**
- * @brief Return the first geom associated with the body.
- *
- * You can traverse through the geoms by repeatedly calling
- * dBodyGetNextGeom().
- *
- * @return the first geom attached to this body, or 0.
- * @ingroup bodies
- */
-ODE_API dGeomID dBodyGetFirstGeom (dBodyID b);
-
-
-/**
- * @brief returns the next geom associated with the same body.
- * @param g a geom attached to some body.
- * @return the next geom attached to the same body, or 0.
- * @sa dBodyGetFirstGeom
- * @ingroup bodies
- */
-ODE_API dGeomID dBodyGetNextGeom (dGeomID g);
-
-
-/**
- * @brief Resets the damping settings to the current world's settings.
- * @ingroup bodies damping
- */
-ODE_API void dBodySetDampingDefaults(dBodyID b);
-
-/**
- * @brief Get the body's linear damping scale.
- * @ingroup bodies damping
- */
-ODE_API dReal dBodyGetLinearDamping (dBodyID b);
-
-/**
- * @brief Set the body's linear damping scale.
- * @param scale The linear damping scale. Should be in the interval [0, 1].
- * @ingroup bodies damping
- * @remarks From now on the body will not use the world's linear damping
- * scale until dBodySetDampingDefaults() is called.
- * @sa dBodySetDampingDefaults()
- */
-ODE_API void dBodySetLinearDamping(dBodyID b, dReal scale);
-
-/**
- * @brief Get the body's angular damping scale.
- * @ingroup bodies damping
- * @remarks If the body's angular damping scale was not set, this function
- * returns the world's angular damping scale.
- */
-ODE_API dReal dBodyGetAngularDamping (dBodyID b);
-
-/**
- * @brief Set the body's angular damping scale.
- * @param scale The angular damping scale. Should be in the interval [0, 1].
- * @ingroup bodies damping
- * @remarks From now on the body will not use the world's angular damping
- * scale until dBodyResetAngularDamping() is called.
- * @sa dBodyResetAngularDamping()
- */
-ODE_API void dBodySetAngularDamping(dBodyID b, dReal scale);
-
-/**
- * @brief Convenience function to set linear and angular scales at once.
- * @param linear_scale The linear damping scale. Should be in the interval [0, 1].
- * @param angular_scale The angular damping scale. Should be in the interval [0, 1].
- * @ingroup bodies damping
- * @sa dBodySetLinearDamping() dBodySetAngularDamping()
- */
-ODE_API void dBodySetDamping(dBodyID b, dReal linear_scale, dReal angular_scale);
-
-/**
- * @brief Get the body's linear damping threshold.
- * @ingroup bodies damping
- */
-ODE_API dReal dBodyGetLinearDampingThreshold (dBodyID b);
-
-/**
- * @brief Set the body's linear damping threshold.
- * @param threshold The linear threshold to be used. Damping
- * is only applied if the linear speed is above this limit.
- * @ingroup bodies damping
- */
-ODE_API void dBodySetLinearDampingThreshold(dBodyID b, dReal threshold);
-
-/**
- * @brief Get the body's angular damping threshold.
- * @ingroup bodies damping
- */
-ODE_API dReal dBodyGetAngularDampingThreshold (dBodyID b);
-
-/**
- * @brief Set the body's angular damping threshold.
- * @param threshold The angular threshold to be used. Damping is
- * only used if the angular speed is above this limit.
- * @ingroup bodies damping
- */
-ODE_API void dBodySetAngularDampingThreshold(dBodyID b, dReal threshold);
-
-/**
- * @brief Get the body's maximum angular speed.
- * @ingroup damping bodies
- * @sa dWorldGetMaxAngularSpeed()
- */
-ODE_API dReal dBodyGetMaxAngularSpeed (dBodyID b);
-
-/**
- * @brief Set the body's maximum angular speed.
- * @ingroup damping bodies
- * @sa dWorldSetMaxAngularSpeed() dBodyResetMaxAngularSpeed()
- * The default value is dInfinity, but it's a good idea to limit
- * it at less than 500 if the body has the gyroscopic term
- * enabled.
- */
-ODE_API void dBodySetMaxAngularSpeed(dBodyID b, dReal max_speed);
-
-
-
-/**
- * @brief Get the body's gyroscopic state.
- *
- * @return nonzero if gyroscopic term computation is enabled (default),
- * zero otherwise.
- * @ingroup bodies
- */
-ODE_API int dBodyGetGyroscopicMode(dBodyID b);
-
-
-/**
- * @brief Enable/disable the body's gyroscopic term.
- *
- * Disabling the gyroscopic term of a body usually improves
- * stability. It also helps turning spining objects, like cars'
- * wheels.
- *
- * @param enabled nonzero (default) to enable gyroscopic term, 0
- * to disable.
- * @ingroup bodies
- */
-ODE_API void dBodySetGyroscopicMode(dBodyID b, int enabled);
-
-
-
-
-/**
- * @defgroup joints Joints
- *
- * In real life a joint is something like a hinge, that is used to connect two
- * objects.
- * In ODE a joint is very similar: It is a relationship that is enforced between
- * two bodies so that they can only have certain positions and orientations
- * relative to each other.
- * This relationship is called a constraint -- the words joint and
- * constraint are often used interchangeably.
- *
- * A joint has a set of parameters that can be set. These include:
- *
- *
- * \li dParamLoStop Low stop angle or position. Setting this to
- * -dInfinity (the default value) turns off the low stop.
- * For rotational joints, this stop must be greater than -pi to be
- * effective.
- * \li dParamHiStop High stop angle or position. Setting this to
- * dInfinity (the default value) turns off the high stop.
- * For rotational joints, this stop must be less than pi to be
- * effective.
- * If the high stop is less than the low stop then both stops will
- * be ineffective.
- * \li dParamVel Desired motor velocity (this will be an angular or
- * linear velocity).
- * \li dParamFMax The maximum force or torque that the motor will use to
- * achieve the desired velocity.
- * This must always be greater than or equal to zero.
- * Setting this to zero (the default value) turns off the motor.
- * \li dParamFudgeFactor The current joint stop/motor implementation has
- * a small problem:
- * when the joint is at one stop and the motor is set to move it away
- * from the stop, too much force may be applied for one time step,
- * causing a ``jumping'' motion.
- * This fudge factor is used to scale this excess force.
- * It should have a value between zero and one (the default value).
- * If the jumping motion is too visible in a joint, the value can be
- * reduced.
- * Making this value too small can prevent the motor from being able to
- * move the joint away from a stop.
- * \li dParamBounce The bouncyness of the stops.
- * This is a restitution parameter in the range 0..1.
- * 0 means the stops are not bouncy at all, 1 means maximum bouncyness.
- * \li dParamCFM The constraint force mixing (CFM) value used when not
- * at a stop.
- * \li dParamStopERP The error reduction parameter (ERP) used by the
- * stops.
- * \li dParamStopCFM The constraint force mixing (CFM) value used by the
- * stops. Together with the ERP value this can be used to get spongy or
- * soft stops.
- * Note that this is intended for unpowered joints, it does not really
- * work as expected when a powered joint reaches its limit.
- * \li dParamSuspensionERP Suspension error reduction parameter (ERP).
- * Currently this is only implemented on the hinge-2 joint.
- * \li dParamSuspensionCFM Suspension constraint force mixing (CFM) value.
- * Currently this is only implemented on the hinge-2 joint.
- *
- * If a particular parameter is not implemented by a given joint, setting it
- * will have no effect.
- * These parameter names can be optionally followed by a digit (2 or 3)
- * to indicate the second or third set of parameters, e.g. for the second axis
- * in a hinge-2 joint, or the third axis in an AMotor joint.
- */
-
-
-/**
- * @brief Create a new joint of the ball type.
- * @ingroup joints
- * @remarks
- * The joint is initially in "limbo" (i.e. it has no effect on the simulation)
- * because it does not connect to any bodies.
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given joint group.
- */
-ODE_API dJointID dJointCreateBall (dWorldID, dJointGroupID);
-
-/**
- * @brief Create a new joint of the hinge type.
- * @ingroup joints
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given joint group.
- */
-ODE_API dJointID dJointCreateHinge (dWorldID, dJointGroupID);
-
-/**
- * @brief Create a new joint of the slider type.
- * @ingroup joints
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given joint group.
- */
-ODE_API dJointID dJointCreateSlider (dWorldID, dJointGroupID);
-
-/**
- * @brief Create a new joint of the contact type.
- * @ingroup joints
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given joint group.
- */
-ODE_API dJointID dJointCreateContact (dWorldID, dJointGroupID, const dContact *);
-
-/**
- * @brief Create a new joint of the hinge2 type.
- * @ingroup joints
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given joint group.
- */
-ODE_API dJointID dJointCreateHinge2 (dWorldID, dJointGroupID);
-
-/**
- * @brief Create a new joint of the universal type.
- * @ingroup joints
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given joint group.
- */
-ODE_API dJointID dJointCreateUniversal (dWorldID, dJointGroupID);
-
-/**
- * @brief Create a new joint of the PR (Prismatic and Rotoide) type.
- * @ingroup joints
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given joint group.
- */
-ODE_API dJointID dJointCreatePR (dWorldID, dJointGroupID);
-
-/**
- * @brief Create a new joint of the PU (Prismatic and Universal) type.
- * @ingroup joints
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given joint group.
- */
-ODE_API dJointID dJointCreatePU (dWorldID, dJointGroupID);
-
-/**
- * @brief Create a new joint of the Piston type.
- * @ingroup joints
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given
- * joint group.
- */
-ODE_API dJointID dJointCreatePiston (dWorldID, dJointGroupID);
-
-/**
- * @brief Create a new joint of the fixed type.
- * @ingroup joints
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given joint group.
- */
-ODE_API dJointID dJointCreateFixed (dWorldID, dJointGroupID);
-
-ODE_API dJointID dJointCreateNull (dWorldID, dJointGroupID);
-
-/**
- * @brief Create a new joint of the A-motor type.
- * @ingroup joints
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given joint group.
- */
-ODE_API dJointID dJointCreateAMotor (dWorldID, dJointGroupID);
-
-/**
- * @brief Create a new joint of the L-motor type.
- * @ingroup joints
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given joint group.
- */
-ODE_API dJointID dJointCreateLMotor (dWorldID, dJointGroupID);
-
-/**
- * @brief Create a new joint of the plane-2d type.
- * @ingroup joints
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given joint group.
- */
-ODE_API dJointID dJointCreatePlane2D (dWorldID, dJointGroupID);
-
-/**
- * @brief Create a new joint of the double ball type.
- * @ingroup joints
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given joint group.
- */
-ODE_API dJointID dJointCreateDBall (dWorldID, dJointGroupID);
-
-/**
- * @brief Create a new joint of the double hinge type.
- * @ingroup joints
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given joint group.
- */
-ODE_API dJointID dJointCreateDHinge (dWorldID, dJointGroupID);
-
-/**
- * @brief Create a new joint of the Transmission type.
- * @ingroup joints
- * @param dJointGroupID set to 0 to allocate the joint normally.
- * If it is nonzero the joint is allocated in the given joint group.
- */
-ODE_API dJointID dJointCreateTransmission (dWorldID, dJointGroupID);
-
-
-/**
- * @brief Destroy a joint.
- * @ingroup joints
- *
- * disconnects it from its attached bodies and removing it from the world.
- * However, if the joint is a member of a group then this function has no
- * effect - to destroy that joint the group must be emptied or destroyed.
- */
-ODE_API void dJointDestroy (dJointID);
-
-
-/**
- * @brief Create a joint group
- * @ingroup joints
- * @param max_size deprecated. Set to 0.
- */
-ODE_API dJointGroupID dJointGroupCreate (int max_size);
-
-/**
- * @brief Destroy a joint group.
- * @ingroup joints
- *
- * All joints in the joint group will be destroyed.
- */
-ODE_API void dJointGroupDestroy (dJointGroupID);
-
-/**
- * @brief Empty a joint group.
- * @ingroup joints
- *
- * All joints in the joint group will be destroyed,
- * but the joint group itself will not be destroyed.
- */
-ODE_API void dJointGroupEmpty (dJointGroupID);
-
-/**
- * @brief Return the number of bodies attached to the joint
- * @ingroup joints
- */
-ODE_API int dJointGetNumBodies(dJointID);
-
-/**
- * @brief Attach the joint to some new bodies.
- * @ingroup joints
- *
- * If the joint is already attached, it will be detached from the old bodies
- * first.
- * To attach this joint to only one body, set body1 or body2 to zero - a zero
- * body refers to the static environment.
- * Setting both bodies to zero puts the joint into "limbo", i.e. it will
- * have no effect on the simulation.
- * @remarks
- * Some joints, like hinge-2 need to be attached to two bodies to work.
- */
-ODE_API void dJointAttach (dJointID, dBodyID body1, dBodyID body2);
-
-/**
- * @brief Manually enable a joint.
- * @param dJointID identification of joint.
- * @ingroup joints
- */
-ODE_API void dJointEnable (dJointID);
-
-/**
- * @brief Manually disable a joint.
- * @ingroup joints
- * @remarks
- * A disabled joint will not affect the simulation, but will maintain the anchors and
- * axes so it can be enabled later.
- */
-ODE_API void dJointDisable (dJointID);
-
-/**
- * @brief Check wether a joint is enabled.
- * @ingroup joints
- * @return 1 if a joint is currently enabled or 0 if it is disabled.
- */
-ODE_API int dJointIsEnabled (dJointID);
-
-/**
- * @brief Set the user-data pointer
- * @ingroup joints
- */
-ODE_API void dJointSetData (dJointID, void *data);
-
-/**
- * @brief Get the user-data pointer
- * @ingroup joints
- */
-ODE_API void *dJointGetData (dJointID);
-
-/**
- * @brief Get the type of the joint
- * @ingroup joints
- * @return the type, being one of these:
- * \li dJointTypeBall
- * \li dJointTypeHinge
- * \li dJointTypeSlider
- * \li dJointTypeContact
- * \li dJointTypeUniversal
- * \li dJointTypeHinge2
- * \li dJointTypeFixed
- * \li dJointTypeNull
- * \li dJointTypeAMotor
- * \li dJointTypeLMotor
- * \li dJointTypePlane2D
- * \li dJointTypePR
- * \li dJointTypePU
- * \li dJointTypePiston
- */
-ODE_API dJointType dJointGetType (dJointID);
-
-/**
- * @brief Return the bodies that this joint connects.
- * @ingroup joints
- * @param index return the first (0) or second (1) body.
- * @remarks
- * If one of these returned body IDs is zero, the joint connects the other body
- * to the static environment.
- * If both body IDs are zero, the joint is in ``limbo'' and has no effect on
- * the simulation.
- */
-ODE_API dBodyID dJointGetBody (dJointID, int index);
-
-/**
- * @brief Sets the datastructure that is to receive the feedback.
- *
- * The feedback can be used by the user, so that it is known how
- * much force an individual joint exerts.
- * @ingroup joints
- */
-ODE_API void dJointSetFeedback (dJointID, dJointFeedback *);
-
-/**
- * @brief Gets the datastructure that is to receive the feedback.
- * @ingroup joints
- */
-ODE_API dJointFeedback *dJointGetFeedback (dJointID);
-
-/**
- * @brief Set the joint anchor point.
- * @ingroup joints
- *
- * The joint will try to keep this point on each body
- * together. The input is specified in world coordinates.
- */
-ODE_API void dJointSetBallAnchor (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief Set the joint anchor point.
- * @ingroup joints
- */
-ODE_API void dJointSetBallAnchor2 (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief Param setting for Ball joints
- * @ingroup joints
- */
-ODE_API void dJointSetBallParam (dJointID, int parameter, dReal value);
-
-/**
- * @brief Set hinge anchor parameter.
- * @ingroup joints
- */
-ODE_API void dJointSetHingeAnchor (dJointID, dReal x, dReal y, dReal z);
-
-ODE_API void dJointSetHingeAnchorDelta (dJointID, dReal x, dReal y, dReal z, dReal ax, dReal ay, dReal az);
-
-/**
- * @brief Set hinge axis.
- * @ingroup joints
- */
-ODE_API void dJointSetHingeAxis (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief Set the Hinge axis as if the 2 bodies were already at angle appart.
- * @ingroup joints
- *
- * This function initialize the Axis and the relative orientation of each body
- * as if body1 was rotated around the axis by the angle value. \br
- * Ex:
- * <PRE>
- * dJointSetHingeAxis(jId, 1, 0, 0);
- * // If you request the position you will have: dJointGetHingeAngle(jId) == 0
- * dJointSetHingeAxisDelta(jId, 1, 0, 0, 0.23);
- * // If you request the position you will have: dJointGetHingeAngle(jId) == 0.23
- * </PRE>
-
- * @param j The Hinge joint ID for which the axis will be set
- * @param x The X component of the axis in world frame
- * @param y The Y component of the axis in world frame
- * @param z The Z component of the axis in world frame
- * @param angle The angle for the offset of the relative orientation.
- * As if body1 was rotated by angle when the Axis was set (see below).
- * The rotation is around the new Hinge axis.
- *
- * @note Usually the function dJointSetHingeAxis set the current position of body1
- * and body2 as the zero angle position. This function set the current position
- * as the if the 2 bodies where \b angle appart.
- * @warning Calling dJointSetHingeAnchor or dJointSetHingeAxis will reset the "zero"
- * angle position.
- */
-ODE_API void dJointSetHingeAxisOffset (dJointID j, dReal x, dReal y, dReal z, dReal angle);
-
-/**
- * @brief set joint parameter
- * @ingroup joints
- */
-ODE_API void dJointSetHingeParam (dJointID, int parameter, dReal value);
-
-/**
- * @brief Applies the torque about the hinge axis.
- *
- * That is, it applies a torque with specified magnitude in the direction
- * of the hinge axis, to body 1, and with the same magnitude but in opposite
- * direction to body 2. This function is just a wrapper for dBodyAddTorque()}
- * @ingroup joints
- */
-ODE_API void dJointAddHingeTorque(dJointID joint, dReal torque);
-
-/**
- * @brief set the joint axis
- * @ingroup joints
- */
-ODE_API void dJointSetSliderAxis (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @ingroup joints
- */
-ODE_API void dJointSetSliderAxisDelta (dJointID, dReal x, dReal y, dReal z, dReal ax, dReal ay, dReal az);
-
-/**
- * @brief set joint parameter
- * @ingroup joints
- */
-ODE_API void dJointSetSliderParam (dJointID, int parameter, dReal value);
-
-/**
- * @brief Applies the given force in the slider's direction.
- *
- * That is, it applies a force with specified magnitude, in the direction of
- * slider's axis, to body1, and with the same magnitude but opposite
- * direction to body2. This function is just a wrapper for dBodyAddForce().
- * @ingroup joints
- */
-ODE_API void dJointAddSliderForce(dJointID joint, dReal force);
-
-/**
- * @brief set anchor
- * @ingroup joints
- */
-ODE_API void dJointSetHinge2Anchor (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief set both axes (optionally)
- *
- * This can change both axes at once avoiding transitions via invalid states
- * while changing axes one by one and having the first changed axis coincide
- * with the other axis existing direction.
- *
- * At least one of the axes must be not NULL. If NULL is passed, the corresponding
- * axis retains its existing value.
- *
- * @ingroup joints
- */
-ODE_API void dJointSetHinge2Axes (dJointID j, const dReal *axis1/*=[dSA__MAX],=NULL*/, const dReal *axis2/*=[dSA__MAX],=NULL*/);
-
-/**
- * @brief set axis
- *
- * Deprecated. Use @fn dJointSetHinge2Axes instead.
- *
- * @ingroup joints
- * @see dJointSetHinge2Axes
- */
-ODE_API_DEPRECATED ODE_API void dJointSetHinge2Axis1 (dJointID j, dReal x, dReal y, dReal z);
-
-/**
- * @brief set axis
- *
- * Deprecated. Use @fn dJointSetHinge2Axes instead.
- *
- * @ingroup joints
- * @see dJointSetHinge2Axes
- */
-ODE_API_DEPRECATED ODE_API void dJointSetHinge2Axis2 (dJointID j, dReal x, dReal y, dReal z);
-
-/**
- * @brief set joint parameter
- * @ingroup joints
- */
-ODE_API void dJointSetHinge2Param (dJointID, int parameter, dReal value);
-
-/**
- * @brief Applies torque1 about the hinge2's axis 1, torque2 about the
- * hinge2's axis 2.
- * @remarks This function is just a wrapper for dBodyAddTorque().
- * @ingroup joints
- */
-ODE_API void dJointAddHinge2Torques(dJointID joint, dReal torque1, dReal torque2);
-
-/**
- * @brief set anchor
- * @ingroup joints
- */
-ODE_API void dJointSetUniversalAnchor (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief set axis
- * @ingroup joints
- */
-ODE_API void dJointSetUniversalAxis1 (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief Set the Universal axis1 as if the 2 bodies were already at
- * offset1 and offset2 appart with respect to axis1 and axis2.
- * @ingroup joints
- *
- * This function initialize the axis1 and the relative orientation of
- * each body as if body1 was rotated around the new axis1 by the offset1
- * value and as if body2 was rotated around the axis2 by offset2. \br
- * Ex:
-* <PRE>
- * dJointSetHuniversalAxis1(jId, 1, 0, 0);
- * // If you request the position you will have: dJointGetUniversalAngle1(jId) == 0
- * // If you request the position you will have: dJointGetUniversalAngle2(jId) == 0
- * dJointSetHuniversalAxis1Offset(jId, 1, 0, 0, 0.2, 0.17);
- * // If you request the position you will have: dJointGetUniversalAngle1(jId) == 0.2
- * // If you request the position you will have: dJointGetUniversalAngle2(jId) == 0.17
- * </PRE>
- *
- * @param j The Hinge joint ID for which the axis will be set
- * @param x The X component of the axis in world frame
- * @param y The Y component of the axis in world frame
- * @param z The Z component of the axis in world frame
- * @param angle The angle for the offset of the relative orientation.
- * As if body1 was rotated by angle when the Axis was set (see below).
- * The rotation is around the new Hinge axis.
- *
- * @note Usually the function dJointSetHingeAxis set the current position of body1
- * and body2 as the zero angle position. This function set the current position
- * as the if the 2 bodies where \b offsets appart.
- *
- * @note Any previous offsets are erased.
- *
- * @warning Calling dJointSetUniversalAnchor, dJointSetUnivesalAxis1,
- * dJointSetUniversalAxis2, dJointSetUniversalAxis2Offset
- * will reset the "zero" angle position.
- */
-ODE_API void dJointSetUniversalAxis1Offset (dJointID, dReal x, dReal y, dReal z,
- dReal offset1, dReal offset2);
-
-/**
- * @brief set axis
- * @ingroup joints
- */
-ODE_API void dJointSetUniversalAxis2 (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief Set the Universal axis2 as if the 2 bodies were already at
- * offset1 and offset2 appart with respect to axis1 and axis2.
- * @ingroup joints
- *
- * This function initialize the axis2 and the relative orientation of
- * each body as if body1 was rotated around the axis1 by the offset1
- * value and as if body2 was rotated around the new axis2 by offset2. \br
- * Ex:
- * <PRE>
- * dJointSetHuniversalAxis2(jId, 0, 1, 0);
- * // If you request the position you will have: dJointGetUniversalAngle1(jId) == 0
- * // If you request the position you will have: dJointGetUniversalAngle2(jId) == 0
- * dJointSetHuniversalAxis2Offset(jId, 0, 1, 0, 0.2, 0.17);
- * // If you request the position you will have: dJointGetUniversalAngle1(jId) == 0.2
- * // If you request the position you will have: dJointGetUniversalAngle2(jId) == 0.17
- * </PRE>
-
- * @param j The Hinge joint ID for which the axis will be set
- * @param x The X component of the axis in world frame
- * @param y The Y component of the axis in world frame
- * @param z The Z component of the axis in world frame
- * @param angle The angle for the offset of the relative orientation.
- * As if body1 was rotated by angle when the Axis was set (see below).
- * The rotation is around the new Hinge axis.
- *
- * @note Usually the function dJointSetHingeAxis set the current position of body1
- * and body2 as the zero angle position. This function set the current position
- * as the if the 2 bodies where \b offsets appart.
- *
- * @note Any previous offsets are erased.
- *
- * @warning Calling dJointSetUniversalAnchor, dJointSetUnivesalAxis1,
- * dJointSetUniversalAxis2, dJointSetUniversalAxis2Offset
- * will reset the "zero" angle position.
- */
-
-
-ODE_API void dJointSetUniversalAxis2Offset (dJointID, dReal x, dReal y, dReal z,
- dReal offset1, dReal offset2);
-
-/**
- * @brief set joint parameter
- * @ingroup joints
- */
-ODE_API void dJointSetUniversalParam (dJointID, int parameter, dReal value);
-
-/**
- * @brief Applies torque1 about the universal's axis 1, torque2 about the
- * universal's axis 2.
- * @remarks This function is just a wrapper for dBodyAddTorque().
- * @ingroup joints
- */
-ODE_API void dJointAddUniversalTorques(dJointID joint, dReal torque1, dReal torque2);
-
-
-/**
- * @brief set anchor
- * @ingroup joints
- */
-ODE_API void dJointSetPRAnchor (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief set the axis for the prismatic articulation
- * @ingroup joints
- */
-ODE_API void dJointSetPRAxis1 (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief set the axis for the rotoide articulation
- * @ingroup joints
- */
-ODE_API void dJointSetPRAxis2 (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief set joint parameter
- * @ingroup joints
- *
- * @note parameterX where X equal 2 refer to parameter for the rotoide articulation
- */
-ODE_API void dJointSetPRParam (dJointID, int parameter, dReal value);
-
-/**
- * @brief Applies the torque about the rotoide axis of the PR joint
- *
- * That is, it applies a torque with specified magnitude in the direction
- * of the rotoide axis, to body 1, and with the same magnitude but in opposite
- * direction to body 2. This function is just a wrapper for dBodyAddTorque()}
- * @ingroup joints
- */
-ODE_API void dJointAddPRTorque (dJointID j, dReal torque);
-
-
-/**
-* @brief set anchor
-* @ingroup joints
-*/
-ODE_API void dJointSetPUAnchor (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief set anchor
- * @ingroup joints
- */
-ODE_API_DEPRECATED ODE_API void dJointSetPUAnchorDelta (dJointID, dReal x, dReal y, dReal z,
- dReal dx, dReal dy, dReal dz);
-
-/**
- * @brief Set the PU anchor as if the 2 bodies were already at [dx, dy, dz] appart.
- * @ingroup joints
- *
- * This function initialize the anchor and the relative position of each body
- * as if the position between body1 and body2 was already the projection of [dx, dy, dz]
- * along the Piston axis. (i.e as if the body1 was at its current position - [dx,dy,dy] when the
- * axis is set).
- * Ex:
- * <PRE>
- * dReal offset = 3;
- * dVector3 axis;
- * dJointGetPUAxis(jId, axis);
- * dJointSetPUAnchor(jId, 0, 0, 0);
- * // If you request the position you will have: dJointGetPUPosition(jId) == 0
- * dJointSetPUAnchorOffset(jId, 0, 0, 0, axis[X]*offset, axis[Y]*offset, axis[Z]*offset);
- * // If you request the position you will have: dJointGetPUPosition(jId) == offset
- * </PRE>
- * @param j The PU joint for which the anchor point will be set
- * @param x The X position of the anchor point in world frame
- * @param y The Y position of the anchor point in world frame
- * @param z The Z position of the anchor point in world frame
- * @param dx A delta to be substracted to the X position as if the anchor was set
- * when body1 was at current_position[X] - dx
- * @param dx A delta to be substracted to the Y position as if the anchor was set
- * when body1 was at current_position[Y] - dy
- * @param dx A delta to be substracted to the Z position as if the anchor was set
- * when body1 was at current_position[Z] - dz
- */
-ODE_API void dJointSetPUAnchorOffset (dJointID, dReal x, dReal y, dReal z,
- dReal dx, dReal dy, dReal dz);
-
-/**
- * @brief set the axis for the first axis or the universal articulation
- * @ingroup joints
- */
-ODE_API void dJointSetPUAxis1 (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief set the axis for the second axis or the universal articulation
- * @ingroup joints
- */
-ODE_API void dJointSetPUAxis2 (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief set the axis for the prismatic articulation
- * @ingroup joints
- */
-ODE_API void dJointSetPUAxis3 (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief set the axis for the prismatic articulation
- * @ingroup joints
- * @note This function was added for convenience it is the same as
- * dJointSetPUAxis3
- */
-ODE_API void dJointSetPUAxisP (dJointID id, dReal x, dReal y, dReal z);
-
-
-
-/**
- * @brief set joint parameter
- * @ingroup joints
- *
- * @note parameterX where X equal 2 refer to parameter for second axis of the
- * universal articulation
- * @note parameterX where X equal 3 refer to parameter for prismatic
- * articulation
- */
-ODE_API void dJointSetPUParam (dJointID, int parameter, dReal value);
-
-/**
- * @brief Applies the torque about the rotoide axis of the PU joint
- *
- * That is, it applies a torque with specified magnitude in the direction
- * of the rotoide axis, to body 1, and with the same magnitude but in opposite
- * direction to body 2. This function is just a wrapper for dBodyAddTorque()}
- * @ingroup joints
- */
-ODE_API void dJointAddPUTorque (dJointID j, dReal torque);
-
-
-
-
-/**
- * @brief set the joint anchor
- * @ingroup joints
- */
-ODE_API void dJointSetPistonAnchor (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief Set the Piston anchor as if the 2 bodies were already at [dx,dy, dz] appart.
- * @ingroup joints
- *
- * This function initialize the anchor and the relative position of each body
- * as if the position between body1 and body2 was already the projection of [dx, dy, dz]
- * along the Piston axis. (i.e as if the body1 was at its current position - [dx,dy,dy] when the
- * axis is set).
- * Ex:
- * <PRE>
- * dReal offset = 3;
- * dVector3 axis;
- * dJointGetPistonAxis(jId, axis);
- * dJointSetPistonAnchor(jId, 0, 0, 0);
- * // If you request the position you will have: dJointGetPistonPosition(jId) == 0
- * dJointSetPistonAnchorOffset(jId, 0, 0, 0, axis[X]*offset, axis[Y]*offset, axis[Z]*offset);
- * // If you request the position you will have: dJointGetPistonPosition(jId) == offset
- * </PRE>
- * @param j The Piston joint for which the anchor point will be set
- * @param x The X position of the anchor point in world frame
- * @param y The Y position of the anchor point in world frame
- * @param z The Z position of the anchor point in world frame
- * @param dx A delta to be substracted to the X position as if the anchor was set
- * when body1 was at current_position[X] - dx
- * @param dx A delta to be substracted to the Y position as if the anchor was set
- * when body1 was at current_position[Y] - dy
- * @param dx A delta to be substracted to the Z position as if the anchor was set
- * when body1 was at current_position[Z] - dz
- */
-ODE_API void dJointSetPistonAnchorOffset(dJointID j, dReal x, dReal y, dReal z,
- dReal dx, dReal dy, dReal dz);
-
- /**
- * @brief set the joint axis
- * @ingroup joints
- */
-ODE_API void dJointSetPistonAxis (dJointID, dReal x, dReal y, dReal z);
-
-/**
- * This function set prismatic axis of the joint and also set the position
- * of the joint.
- *
- * @ingroup joints
- * @param j The joint affected by this function
- * @param x The x component of the axis
- * @param y The y component of the axis
- * @param z The z component of the axis
- * @param dx The Initial position of the prismatic join in the x direction
- * @param dy The Initial position of the prismatic join in the y direction
- * @param dz The Initial position of the prismatic join in the z direction
- */
-ODE_API_DEPRECATED ODE_API void dJointSetPistonAxisDelta (dJointID j, dReal x, dReal y, dReal z, dReal ax, dReal ay, dReal az);
-
-/**
- * @brief set joint parameter
- * @ingroup joints
- */
-ODE_API void dJointSetPistonParam (dJointID, int parameter, dReal value);
-
-/**
- * @brief Applies the given force in the slider's direction.
- *
- * That is, it applies a force with specified magnitude, in the direction of
- * prismatic's axis, to body1, and with the same magnitude but opposite
- * direction to body2. This function is just a wrapper for dBodyAddForce().
- * @ingroup joints
- */
-ODE_API void dJointAddPistonForce (dJointID joint, dReal force);
-
-
-/**
- * @brief Call this on the fixed joint after it has been attached to
- * remember the current desired relative offset and desired relative
- * rotation between the bodies.
- * @ingroup joints
- */
-ODE_API void dJointSetFixed (dJointID);
-
-/*
- * @brief Sets joint parameter
- *
- * @ingroup joints
- */
-ODE_API void dJointSetFixedParam (dJointID, int parameter, dReal value);
-
-/**
- * @brief set the nr of axes
- * @param num 0..3
- * @ingroup joints
- */
-ODE_API void dJointSetAMotorNumAxes (dJointID, int num);
-
-/**
- * @brief set axis
- * @ingroup joints
- */
-ODE_API void dJointSetAMotorAxis (dJointID, int anum, int rel,
- dReal x, dReal y, dReal z);
-
-/**
- * @brief Tell the AMotor what the current angle is along axis anum.
- *
- * This function should only be called in dAMotorUser mode, because in this
- * mode the AMotor has no other way of knowing the joint angles.
- * The angle information is needed if stops have been set along the axis,
- * but it is not needed for axis motors.
- * @ingroup joints
- */
-ODE_API void dJointSetAMotorAngle (dJointID, int anum, dReal angle);
-
-/**
- * @brief set joint parameter
- * @ingroup joints
- */
-ODE_API void dJointSetAMotorParam (dJointID, int parameter, dReal value);
-
-/**
- * @brief set mode
- * @ingroup joints
- */
-ODE_API void dJointSetAMotorMode (dJointID, int mode);
-
-/**
- * @brief Applies torque0 about the AMotor's axis 0, torque1 about the
- * AMotor's axis 1, and torque2 about the AMotor's axis 2.
- * @remarks
- * If the motor has fewer than three axes, the higher torques are ignored.
- * This function is just a wrapper for dBodyAddTorque().
- * @ingroup joints
- */
-ODE_API void dJointAddAMotorTorques (dJointID, dReal torque1, dReal torque2, dReal torque3);
-
-/**
- * @brief Set the number of axes that will be controlled by the LMotor.
- * @param num can range from 0 (which effectively deactivates the joint) to 3.
- * @ingroup joints
- */
-ODE_API void dJointSetLMotorNumAxes (dJointID, int num);
-
-/**
- * @brief Set the AMotor axes.
- * @param anum selects the axis to change (0,1 or 2).
- * @param rel Each axis can have one of three ``relative orientation'' modes
- * \li 0: The axis is anchored to the global frame.
- * \li 1: The axis is anchored to the first body.
- * \li 2: The axis is anchored to the second body.
- * @remarks The axis vector is always specified in global coordinates
- * regardless of the setting of rel.
- * @ingroup joints
- */
-ODE_API void dJointSetLMotorAxis (dJointID, int anum, int rel, dReal x, dReal y, dReal z);
-
-/**
- * @brief set joint parameter
- * @ingroup joints
- */
-ODE_API void dJointSetLMotorParam (dJointID, int parameter, dReal value);
-
-/**
- * @ingroup joints
- */
-ODE_API void dJointSetPlane2DXParam (dJointID, int parameter, dReal value);
-
-/**
- * @ingroup joints
- */
-
-ODE_API void dJointSetPlane2DYParam (dJointID, int parameter, dReal value);
-
-/**
- * @ingroup joints
- */
-ODE_API void dJointSetPlane2DAngleParam (dJointID, int parameter, dReal value);
-
-/**
- * @brief Get the joint anchor point, in world coordinates.
- *
- * This returns the point on body 1. If the joint is perfectly satisfied,
- * this will be the same as the point on body 2.
- */
-ODE_API void dJointGetBallAnchor (dJointID, dVector3 result);
-
-/**
- * @brief Get the joint anchor point, in world coordinates.
- *
- * This returns the point on body 2. You can think of a ball and socket
- * joint as trying to keep the result of dJointGetBallAnchor() and
- * dJointGetBallAnchor2() the same. If the joint is perfectly satisfied,
- * this function will return the same value as dJointGetBallAnchor() to
- * within roundoff errors. dJointGetBallAnchor2() can be used, along with
- * dJointGetBallAnchor(), to see how far the joint has come apart.
- */
-ODE_API void dJointGetBallAnchor2 (dJointID, dVector3 result);
-
-/**
- * @brief get joint parameter
- * @ingroup joints
- */
-ODE_API dReal dJointGetBallParam (dJointID, int parameter);
-
-/**
- * @brief Get the hinge anchor point, in world coordinates.
- *
- * This returns the point on body 1. If the joint is perfectly satisfied,
- * this will be the same as the point on body 2.
- * @ingroup joints
- */
-ODE_API void dJointGetHingeAnchor (dJointID, dVector3 result);
-
-/**
- * @brief Get the joint anchor point, in world coordinates.
- * @return The point on body 2. If the joint is perfectly satisfied,
- * this will return the same value as dJointGetHingeAnchor().
- * If not, this value will be slightly different.
- * This can be used, for example, to see how far the joint has come apart.
- * @ingroup joints
- */
-ODE_API void dJointGetHingeAnchor2 (dJointID, dVector3 result);
-
-/**
- * @brief get axis
- * @ingroup joints
- */
-ODE_API void dJointGetHingeAxis (dJointID, dVector3 result);
-
-/**
- * @brief get joint parameter
- * @ingroup joints
- */
-ODE_API dReal dJointGetHingeParam (dJointID, int parameter);
-
-/**
- * @brief Get the hinge angle.
- *
- * The angle is measured between the two bodies, or between the body and
- * the static environment.
- * The angle will be between -pi..pi.
- * Give the relative rotation with respect to the Hinge axis of Body 1 with
- * respect to Body 2.
- * When the hinge anchor or axis is set, the current position of the attached
- * bodies is examined and that position will be the zero angle.
- * @ingroup joints
- */
-ODE_API dReal dJointGetHingeAngle (dJointID);
-
-/**
- * @brief Get the hinge angle time derivative.
- * @ingroup joints
- */
-ODE_API dReal dJointGetHingeAngleRate (dJointID);
-
-/**
- * @brief Get the slider linear position (i.e. the slider's extension)
- *
- * When the axis is set, the current position of the attached bodies is
- * examined and that position will be the zero position.
-
- * The position is the distance, with respect to the zero position,
- * along the slider axis of body 1 with respect to
- * body 2. (A NULL body is replaced by the world).
- * @ingroup joints
- */
-ODE_API dReal dJointGetSliderPosition (dJointID);
-
-/**
- * @brief Get the slider linear position's time derivative.
- * @ingroup joints
- */
-ODE_API dReal dJointGetSliderPositionRate (dJointID);
-
-/**
- * @brief Get the slider axis
- * @ingroup joints
- */
-ODE_API void dJointGetSliderAxis (dJointID, dVector3 result);
-
-/**
- * @brief get joint parameter
- * @ingroup joints
- */
-ODE_API dReal dJointGetSliderParam (dJointID, int parameter);
-
-/**
- * @brief Get the joint anchor point, in world coordinates.
- * @return the point on body 1. If the joint is perfectly satisfied,
- * this will be the same as the point on body 2.
- * @ingroup joints
- */
-ODE_API void dJointGetHinge2Anchor (dJointID, dVector3 result);
-
-/**
- * @brief Get the joint anchor point, in world coordinates.
- * This returns the point on body 2. If the joint is perfectly satisfied,
- * this will return the same value as dJointGetHinge2Anchor.
- * If not, this value will be slightly different.
- * This can be used, for example, to see how far the joint has come apart.
- * @ingroup joints
- */
-ODE_API void dJointGetHinge2Anchor2 (dJointID, dVector3 result);
-
-/**
- * @brief Get joint axis
- * @ingroup joints
- */
-ODE_API void dJointGetHinge2Axis1 (dJointID, dVector3 result);
-
-/**
- * @brief Get joint axis
- * @ingroup joints
- */
-ODE_API void dJointGetHinge2Axis2 (dJointID, dVector3 result);
-
-/**
- * @brief get joint parameter
- * @ingroup joints
- */
-ODE_API dReal dJointGetHinge2Param (dJointID, int parameter);
-
-/**
- * @brief Get angle
- * @ingroup joints
- */
-ODE_API dReal dJointGetHinge2Angle1 (dJointID);
-
-/**
- * @brief Get angle
- * @ingroup joints
- */
-ODE_API dReal dJointGetHinge2Angle2 (dJointID);
-
-/**
- * @brief Get time derivative of angle
- * @ingroup joints
- */
-ODE_API dReal dJointGetHinge2Angle1Rate (dJointID);
-
-/**
- * @brief Get time derivative of angle
- * @ingroup joints
- */
-ODE_API dReal dJointGetHinge2Angle2Rate (dJointID);
-
-/**
- * @brief Get the joint anchor point, in world coordinates.
- * @return the point on body 1. If the joint is perfectly satisfied,
- * this will be the same as the point on body 2.
- * @ingroup joints
- */
-ODE_API void dJointGetUniversalAnchor (dJointID, dVector3 result);
-
-/**
- * @brief Get the joint anchor point, in world coordinates.
- * @return This returns the point on body 2.
- * @remarks
- * You can think of the ball and socket part of a universal joint as
- * trying to keep the result of dJointGetBallAnchor() and
- * dJointGetBallAnchor2() the same. If the joint is
- * perfectly satisfied, this function will return the same value
- * as dJointGetUniversalAnchor() to within roundoff errors.
- * dJointGetUniversalAnchor2() can be used, along with
- * dJointGetUniversalAnchor(), to see how far the joint has come apart.
- * @ingroup joints
- */
-ODE_API void dJointGetUniversalAnchor2 (dJointID, dVector3 result);
-
-/**
- * @brief Get axis
- * @ingroup joints
- */
-ODE_API void dJointGetUniversalAxis1 (dJointID, dVector3 result);
-
-/**
- * @brief Get axis
- * @ingroup joints
- */
-ODE_API void dJointGetUniversalAxis2 (dJointID, dVector3 result);
-
-
-/**
- * @brief get joint parameter
- * @ingroup joints
- */
-ODE_API dReal dJointGetUniversalParam (dJointID, int parameter);
-
-/**
- * @brief Get both angles at the same time.
- * @ingroup joints
- *
- * @param joint The universal joint for which we want to calculate the angles
- * @param angle1 The angle between the body1 and the axis 1
- * @param angle2 The angle between the body2 and the axis 2
- *
- * @note This function combine getUniversalAngle1 and getUniversalAngle2 together
- * and try to avoid redundant calculation
- */
-ODE_API void dJointGetUniversalAngles (dJointID, dReal *angle1, dReal *angle2);
-
-/**
- * @brief Get angle
- * @ingroup joints
- */
-ODE_API dReal dJointGetUniversalAngle1 (dJointID);
-
-/**
- * @brief Get angle
- * @ingroup joints
- */
-ODE_API dReal dJointGetUniversalAngle2 (dJointID);
-
-/**
- * @brief Get time derivative of angle
- * @ingroup joints
- */
-ODE_API dReal dJointGetUniversalAngle1Rate (dJointID);
-
-/**
- * @brief Get time derivative of angle
- * @ingroup joints
- */
-ODE_API dReal dJointGetUniversalAngle2Rate (dJointID);
-
-
-
-/**
- * @brief Get the joint anchor point, in world coordinates.
- * @return the point on body 1. If the joint is perfectly satisfied,
- * this will be the same as the point on body 2.
- * @ingroup joints
- */
-ODE_API void dJointGetPRAnchor (dJointID, dVector3 result);
-
-/**
- * @brief Get the PR linear position (i.e. the prismatic's extension)
- *
- * When the axis is set, the current position of the attached bodies is
- * examined and that position will be the zero position.
- *
- * The position is the "oriented" length between the
- * position = (Prismatic axis) dot_product [(body1 + offset) - (body2 + anchor2)]
- *
- * @ingroup joints
- */
-ODE_API dReal dJointGetPRPosition (dJointID);
-
-/**
- * @brief Get the PR linear position's time derivative
- *
- * @ingroup joints
- */
-ODE_API dReal dJointGetPRPositionRate (dJointID);
-
-
-/**
- * @brief Get the PR angular position (i.e. the twist between the 2 bodies)
- *
- * When the axis is set, the current position of the attached bodies is
- * examined and that position will be the zero position.
- * @ingroup joints
- */
-ODE_API dReal dJointGetPRAngle (dJointID);
-
-/**
- * @brief Get the PR angular position's time derivative
- *
- * @ingroup joints
- */
-ODE_API dReal dJointGetPRAngleRate (dJointID);
-
-
-/**
- * @brief Get the prismatic axis
- * @ingroup joints
- */
-ODE_API void dJointGetPRAxis1 (dJointID, dVector3 result);
-
-/**
- * @brief Get the Rotoide axis
- * @ingroup joints
- */
-ODE_API void dJointGetPRAxis2 (dJointID, dVector3 result);
-
-/**
- * @brief get joint parameter
- * @ingroup joints
- */
-ODE_API dReal dJointGetPRParam (dJointID, int parameter);
-
-
-
-/**
- * @brief Get the joint anchor point, in world coordinates.
- * @return the point on body 1. If the joint is perfectly satisfied,
- * this will be the same as the point on body 2.
- * @ingroup joints
- */
-ODE_API void dJointGetPUAnchor (dJointID, dVector3 result);
-
-/**
- * @brief Get the PU linear position (i.e. the prismatic's extension)
- *
- * When the axis is set, the current position of the attached bodies is
- * examined and that position will be the zero position.
- *
- * The position is the "oriented" length between the
- * position = (Prismatic axis) dot_product [(body1 + offset) - (body2 + anchor2)]
- *
- * @ingroup joints
- */
-ODE_API dReal dJointGetPUPosition (dJointID);
-
-/**
- * @brief Get the PR linear position's time derivative
- *
- * @ingroup joints
- */
-ODE_API dReal dJointGetPUPositionRate (dJointID);
-
-/**
- * @brief Get the first axis of the universal component of the joint
- * @ingroup joints
- */
-ODE_API void dJointGetPUAxis1 (dJointID, dVector3 result);
-
-/**
- * @brief Get the second axis of the Universal component of the joint
- * @ingroup joints
- */
-ODE_API void dJointGetPUAxis2 (dJointID, dVector3 result);
-
-/**
- * @brief Get the prismatic axis
- * @ingroup joints
- */
-ODE_API void dJointGetPUAxis3 (dJointID, dVector3 result);
-
-/**
- * @brief Get the prismatic axis
- * @ingroup joints
- *
- * @note This function was added for convenience it is the same as
- * dJointGetPUAxis3
- */
-ODE_API void dJointGetPUAxisP (dJointID id, dVector3 result);
-
-
-
-
-/**
- * @brief Get both angles at the same time.
- * @ingroup joints
- *
- * @param joint The Prismatic universal joint for which we want to calculate the angles
- * @param angle1 The angle between the body1 and the axis 1
- * @param angle2 The angle between the body2 and the axis 2
- *
- * @note This function combine dJointGetPUAngle1 and dJointGetPUAngle2 together
- * and try to avoid redundant calculation
- */
-ODE_API void dJointGetPUAngles (dJointID, dReal *angle1, dReal *angle2);
-
-/**
- * @brief Get angle
- * @ingroup joints
- */
-ODE_API dReal dJointGetPUAngle1 (dJointID);
-
-/**
- * @brief * @brief Get time derivative of angle1
- *
- * @ingroup joints
- */
-ODE_API dReal dJointGetPUAngle1Rate (dJointID);
-
-
-/**
- * @brief Get angle
- * @ingroup joints
- */
-ODE_API dReal dJointGetPUAngle2 (dJointID);
-
-/**
- * @brief * @brief Get time derivative of angle2
- *
- * @ingroup joints
- */
-ODE_API dReal dJointGetPUAngle2Rate (dJointID);
-
- /**
- * @brief get joint parameter
- * @ingroup joints
- */
-ODE_API dReal dJointGetPUParam (dJointID, int parameter);
-
-
-
-
-
-/**
- * @brief Get the Piston linear position (i.e. the piston's extension)
- *
- * When the axis is set, the current position of the attached bodies is
- * examined and that position will be the zero position.
- * @ingroup joints
- */
-ODE_API dReal dJointGetPistonPosition (dJointID);
-
-/**
- * @brief Get the piston linear position's time derivative.
- * @ingroup joints
- */
-ODE_API dReal dJointGetPistonPositionRate (dJointID);
-
-/**
- * @brief Get the Piston angular position (i.e. the twist between the 2 bodies)
- *
- * When the axis is set, the current position of the attached bodies is
- * examined and that position will be the zero position.
- * @ingroup joints
- */
-ODE_API dReal dJointGetPistonAngle (dJointID);
-
-/**
- * @brief Get the piston angular position's time derivative.
- * @ingroup joints
- */
-ODE_API dReal dJointGetPistonAngleRate (dJointID);
-
-
-/**
- * @brief Get the joint anchor
- *
- * This returns the point on body 1. If the joint is perfectly satisfied,
- * this will be the same as the point on body 2 in direction perpendicular
- * to the prismatic axis.
- *
- * @ingroup joints
- */
-ODE_API void dJointGetPistonAnchor (dJointID, dVector3 result);
-
-/**
- * @brief Get the joint anchor w.r.t. body 2
- *
- * This returns the point on body 2. You can think of a Piston
- * joint as trying to keep the result of dJointGetPistonAnchor() and
- * dJointGetPistonAnchor2() the same in the direction perpendicular to the
- * pirsmatic axis. If the joint is perfectly satisfied,
- * this function will return the same value as dJointGetPistonAnchor() to
- * within roundoff errors. dJointGetPistonAnchor2() can be used, along with
- * dJointGetPistonAnchor(), to see how far the joint has come apart.
- *
- * @ingroup joints
- */
-ODE_API void dJointGetPistonAnchor2 (dJointID, dVector3 result);
-
-/**
- * @brief Get the prismatic axis (This is also the rotoide axis.
- * @ingroup joints
- */
-ODE_API void dJointGetPistonAxis (dJointID, dVector3 result);
-
-/**
- * @brief get joint parameter
- * @ingroup joints
- */
-ODE_API dReal dJointGetPistonParam (dJointID, int parameter);
-
-
-/**
- * @brief Get the number of angular axes that will be controlled by the
- * AMotor.
- * @param num can range from 0 (which effectively deactivates the
- * joint) to 3.
- * This is automatically set to 3 in dAMotorEuler mode.
- * @ingroup joints
- */
-ODE_API int dJointGetAMotorNumAxes (dJointID);
-
-/**
- * @brief Get the AMotor axes.
- * @param anum selects the axis to change (0,1 or 2).
- * @param rel Each axis can have one of three ``relative orientation'' modes.
- * \li 0: The axis is anchored to the global frame.
- * \li 1: The axis is anchored to the first body.
- * \li 2: The axis is anchored to the second body.
- * @ingroup joints
- */
-ODE_API void dJointGetAMotorAxis (dJointID, int anum, dVector3 result);
-
-/**
- * @brief Get axis
- * @remarks
- * The axis vector is always specified in global coordinates regardless
- * of the setting of rel.
- * There are two GetAMotorAxis functions, one to return the axis and one to
- * return the relative mode.
- *
- * For dAMotorEuler mode:
- * \li Only axes 0 and 2 need to be set. Axis 1 will be determined
- automatically at each time step.
- * \li Axes 0 and 2 must be perpendicular to each other.
- * \li Axis 0 must be anchored to the first body, axis 2 must be anchored
- to the second body.
- * @ingroup joints
- */
-ODE_API int dJointGetAMotorAxisRel (dJointID, int anum);
-
-/**
- * @brief Get the current angle for axis.
- * @remarks
- * In dAMotorUser mode this is simply the value that was set with
- * dJointSetAMotorAngle().
- * In dAMotorEuler mode this is the corresponding euler angle.
- * @ingroup joints
- */
-ODE_API dReal dJointGetAMotorAngle (dJointID, int anum);
-
-/**
- * @brief Get the current angle rate for axis anum.
- * @remarks
- * In dAMotorUser mode this is always zero, as not enough information is
- * available.
- * In dAMotorEuler mode this is the corresponding euler angle rate.
- * @ingroup joints
- */
-ODE_API dReal dJointGetAMotorAngleRate (dJointID, int anum);
-
-/**
- * @brief get joint parameter
- * @ingroup joints
- */
-ODE_API dReal dJointGetAMotorParam (dJointID, int parameter);
-
-/**
- * @brief Get the angular motor mode.
- * @param mode must be one of the following constants:
- * \li dAMotorUser The AMotor axes and joint angle settings are entirely
- * controlled by the user. This is the default mode.
- * \li dAMotorEuler Euler angles are automatically computed.
- * The axis a1 is also automatically computed.
- * The AMotor axes must be set correctly when in this mode,
- * as described below.
- * When this mode is initially set the current relative orientations
- * of the bodies will correspond to all euler angles at zero.
- * @ingroup joints
- */
-ODE_API int dJointGetAMotorMode (dJointID);
-
-/**
- * @brief Get nr of axes.
- * @ingroup joints
- */
-ODE_API int dJointGetLMotorNumAxes (dJointID);
-
-/**
- * @brief Get axis.
- * @ingroup joints
- */
-ODE_API void dJointGetLMotorAxis (dJointID, int anum, dVector3 result);
-
-/**
- * @brief get joint parameter
- * @ingroup joints
- */
-ODE_API dReal dJointGetLMotorParam (dJointID, int parameter);
-
-/**
- * @brief get joint parameter
- * @ingroup joints
- */
-ODE_API dReal dJointGetFixedParam (dJointID, int parameter);
-
-
-/**
- * @brief get the contact point of the first wheel of the Transmission joint.
- * @ingroup joints
- */
-ODE_API void dJointGetTransmissionContactPoint1(dJointID, dVector3 result);
-
-/**
- * @brief get contact point of the second wheel of the Transmission joint.
- * @ingroup joints
- */
-ODE_API void dJointGetTransmissionContactPoint2(dJointID, dVector3 result);
-
-/**
- * @brief set the first axis for the Transmission joint
- * @remarks This is the axis around which the first body is allowed to
- * revolve and is attached to it. It is given in global coordinates
- * and can only be set explicitly in intersecting-axes mode. For the
- * parallel-axes and chain modes which share one common axis of
- * revolution for both gears dJointSetTransmissionAxis should be used.
- * @ingroup joints
- */
-ODE_API void dJointSetTransmissionAxis1(dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief get first axis for the Transmission joint
- * @remarks In parallel-axes and chain mode the common axis with
- * respect to the first body is returned. If the joint constraint is
- * satisfied it should be the same as the axis return with
- * dJointGetTransmissionAxis2 or dJointGetTransmissionAxis.
- * @ingroup joints
- */
-ODE_API void dJointGetTransmissionAxis1(dJointID, dVector3 result);
-
-/**
- * @brief set second axis for the Transmission joint
- * @remarks This is the axis around which the second body is allowed
- * to revolve and is attached to it. It is given in global
- * coordinates and can only be set explicitly in intersecting-axes
- * mode. For the parallel-axes and chain modes which share one common
- * axis of revolution for both gears dJointSetTransmissionAxis should
- * be used.
- * @ingroup joints
- */
-ODE_API void dJointSetTransmissionAxis2(dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief get second axis for the Transmission joint
- * @remarks In parallel-axes and chain mode the common axis with
- * respect to the second body is returned. If the joint constraint is
- * satisfied it should be the same as the axis return with
- * dJointGetTransmissionAxis1 or dJointGetTransmissionAxis.
- * @ingroup joints
- */
-ODE_API void dJointGetTransmissionAxis2(dJointID, dVector3 result);
-
-/**
- * @brief set the first anchor for the Transmission joint
- * @remarks This is the point of attachment of the wheel on the
- * first body. It is given in global coordinates.
- * @ingroup joints
- */
-ODE_API void dJointSetTransmissionAnchor1(dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief get the first anchor of the Transmission joint
- * @ingroup joints
- */
-ODE_API void dJointGetTransmissionAnchor1(dJointID, dVector3 result);
-
-/**
- * @brief set the second anchor for the Transmission joint
- * @remarks This is the point of attachment of the wheel on the
- * second body. It is given in global coordinates.
- * @ingroup joints
- */
-ODE_API void dJointSetTransmissionAnchor2(dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief get the second anchor for the Transmission joint
- * @ingroup joints
- */
-ODE_API void dJointGetTransmissionAnchor2(dJointID, dVector3 result);
-
-/**
- * @brief set a Transmission joint parameter
- * @ingroup joints
- */
-ODE_API void dJointSetTransmissionParam(dJointID, int parameter, dReal value);
-
-/**
- * @brief get a Transmission joint parameter
- * @ingroup joints
- */
-ODE_API dReal dJointGetTransmissionParam(dJointID, int parameter);
-
-/**
- * @brief set the Transmission joint mode
- * @remarks The mode can be one of dTransmissionParallelAxes,
- * dTransmissionIntersectingAxes and dTransmissionChainDrive simulating a
- * set of parallel-axes gears, intersecting-axes beveled gears or
- * chain and sprockets respectively.
- * @ingroup joints
- */
-ODE_API void dJointSetTransmissionMode( dJointID j, int mode );
-
-/**
- * @brief get the Transmission joint mode
- * @ingroup joints
- */
-ODE_API int dJointGetTransmissionMode( dJointID j );
-
-/**
- * @brief set the Transmission ratio
- * @remarks This is the ratio of the angular speed of the first gear
- * to that of the second gear. It can only be set explicitly in
- * parallel-axes mode. In intersecting-axes mode the ratio is defined
- * implicitly by the initial configuration of the wheels and in chain
- * mode it is defined implicitly be the wheel radii.
- * @ingroup joints
- */
-ODE_API void dJointSetTransmissionRatio( dJointID j, dReal ratio );
-
-/**
- * @brief get the Transmission joint ratio
- * @ingroup joints
- */
-ODE_API dReal dJointGetTransmissionRatio( dJointID j );
-
-/**
- * @brief set the common axis for both wheels of the Transmission joint
- * @remarks This sets the common axis of revolution for both wheels
- * and should only be used in parallel-axes or chain mode. For
- * intersecting-axes mode where each wheel axis needs to be specified
- * individually dJointSetTransmissionAxis1 and
- * dJointSetTransmissionAxis2 should be used. The axis is given in
- * global coordinates
- * @ingroup joints
- */
-ODE_API void dJointSetTransmissionAxis( dJointID j, dReal x, dReal y, dReal z );
-
-/**
- * @brief get the common axis for both wheels of the Transmission joint
- * @ingroup joints
- */
-ODE_API void dJointGetTransmissionAxis( dJointID j, dVector3 result );
-
-/**
- * @brief get the phase, that is the traversed angle for the first
- * wheel of the Transmission joint
- * @ingroup joints
- */
-ODE_API dReal dJointGetTransmissionAngle1( dJointID j );
-
-/**
- * @brief get the phase, that is the traversed angle for the second
- * wheel of the Transmission joint
- * @ingroup joints
- */
-ODE_API dReal dJointGetTransmissionAngle2( dJointID j );
-
-/**
- * @brief get the radius of the first wheel of the Transmission joint
- * @ingroup joints
- */
-ODE_API dReal dJointGetTransmissionRadius1( dJointID j );
-
-/**
- * @brief get the radius of the second wheel of the Transmission joint
- * @ingroup joints
- */
-ODE_API dReal dJointGetTransmissionRadius2( dJointID j );
-
-/**
- * @brief set the radius of the first wheel of the Transmission joint
- * @remarks The wheel radii can only be set explicitly in chain mode.
- * In the other modes they're defined implicitly by the initial
- * configuration and ratio of the wheels.
- * @ingroup joints
- */
-ODE_API void dJointSetTransmissionRadius1( dJointID j, dReal radius );
-
-/**
- * @brief set the radius of the second wheel of the Transmission joint
- * @remarks The wheel radii can only be set explicitly in chain mode.
- * In the other modes they're defined implicitly by the initial
- * configuration and ratio of the wheels.
- * @ingroup joints
- */
-ODE_API void dJointSetTransmissionRadius2( dJointID j, dReal radius );
-
-/**
- * @brief get the backlash of the Transmission joint
- * @ingroup joints
- */
-ODE_API dReal dJointGetTransmissionBacklash( dJointID j );
-
-/**
- * @brief set the backlash of the Transmission joint
- * @remarks Backlash is the clearance in the mesh of the wheels of the
- * transmission and is defined as the maximum distance that the
- * geometric contact point can travel without any actual contact or
- * transfer of power between the wheels. This can be converted in
- * degrees of revolution for each wheel by dividing by the wheel's
- * radius. To further illustrate this consider the situation where a
- * wheel of radius r_1 is driving another wheel of radius r_2 and
- * there is an amount of backlash equal to b in their mesh. If the
- * driving wheel were to instantaneously stop there would be no
- * contact and hence the driven wheel would continue to turn for
- * another b / r_2 radians until all the backlash in the mesh was take
- * up and contact restored with the relationship of driving and driven
- * wheel reversed. The backlash is therefore given in untis of
- * length.
- * @ingroup joints
- */
-ODE_API void dJointSetTransmissionBacklash( dJointID j, dReal backlash );
-
-/**
- * @brief set anchor1 for double ball joint
- * @ingroup joints
- */
-ODE_API void dJointSetDBallAnchor1(dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief set anchor2 for double ball joint
- * @ingroup joints
- */
-ODE_API void dJointSetDBallAnchor2(dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief get anchor1 from double ball joint
- * @ingroup joints
- */
-ODE_API void dJointGetDBallAnchor1(dJointID, dVector3 result);
-
-/**
- * @brief get anchor2 from double ball joint
- * @ingroup joints
- */
-ODE_API void dJointGetDBallAnchor2(dJointID, dVector3 result);
-
-/**
- * @brief get the target distance from double ball joint
- * @ingroup joints
- */
-ODE_API dReal dJointGetDBallDistance(dJointID);
-
-/**
- * @brief set the target distance for the double ball joint
- * @ingroup joints
- */
-ODE_API void dJointSetDBallDistance(dJointID, dReal dist);
-
-/**
- * @brief set double ball joint parameter
- * @ingroup joints
- */
-ODE_API void dJointSetDBallParam(dJointID, int parameter, dReal value);
-
-/**
- * @brief get double ball joint parameter
- * @ingroup joints
- */
-ODE_API dReal dJointGetDBallParam(dJointID, int parameter);
-
-/**
- * @brief set axis for double hinge joint
- * @ingroup joints
- */
-ODE_API void dJointSetDHingeAxis(dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief get axis for double hinge joint
- * @ingroup joints
- */
-ODE_API void dJointGetDHingeAxis(dJointID, dVector3 result);
-
-/**
- * @brief set anchor1 for double hinge joint
- * @ingroup joints
- */
-ODE_API void dJointSetDHingeAnchor1(dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief set anchor2 for double hinge joint
- * @ingroup joints
- */
-ODE_API void dJointSetDHingeAnchor2(dJointID, dReal x, dReal y, dReal z);
-
-/**
- * @brief get anchor1 from double hinge joint
- * @ingroup joints
- */
-ODE_API void dJointGetDHingeAnchor1(dJointID, dVector3 result);
-
-/**
- * @brief get anchor2 from double hinge joint
- * @ingroup joints
- */
-ODE_API void dJointGetDHingeAnchor2(dJointID, dVector3 result);
-
-/**
- * @brief get the set distance from double hinge joint
- * @ingroup joints
- */
-ODE_API dReal dJointGetDHingeDistance(dJointID);
-
-/**
- * @brief set double hinge joint parameter
- * @ingroup joints
- */
-ODE_API void dJointSetDHingeParam(dJointID, int parameter, dReal value);
-
-/**
- * @brief get double hinge joint parameter
- * @ingroup joints
- */
-ODE_API dReal dJointGetDHingeParam(dJointID, int parameter);
-
-
-
-
-/**
- * @ingroup joints
- */
-ODE_API dJointID dConnectingJoint (dBodyID, dBodyID);
-
-/**
- * @ingroup joints
- */
-ODE_API int dConnectingJointList (dBodyID, dBodyID, dJointID*);
-
-/**
- * @brief Utility function
- * @return 1 if the two bodies are connected together by
- * a joint, otherwise return 0.
- * @ingroup joints
- */
-ODE_API int dAreConnected (dBodyID, dBodyID);
-
-/**
- * @brief Utility function
- * @return 1 if the two bodies are connected together by
- * a joint that does not have type @arg{joint_type}, otherwise return 0.
- * @param body1 A body to check.
- * @param body2 A body to check.
- * @param joint_type is a dJointTypeXXX constant.
- * This is useful for deciding whether to add contact joints between two bodies:
- * if they are already connected by non-contact joints then it may not be
- * appropriate to add contacts, however it is okay to add more contact between-
- * bodies that already have contacts.
- * @ingroup joints
- */
-ODE_API int dAreConnectedExcluding (dBodyID body1, dBodyID body2, int joint_type);
-
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_ODE_H_
-#define _ODE_ODE_H_
-
-/* include *everything* here */
-
-#include <ode/odeconfig.h>
-#include <ode/compatibility.h>
-#include <ode/common.h>
-#include <ode/odeinit.h>
-#include <ode/contact.h>
-#include <ode/error.h>
-#include <ode/memory.h>
-#include <ode/odemath.h>
-#include <ode/matrix.h>
-#include <ode/matrix_coop.h>
-#include <ode/timer.h>
-#include <ode/rotation.h>
-#include <ode/mass.h>
-#include <ode/misc.h>
-#include <ode/objects.h>
-#include <ode/collision_space.h>
-#include <ode/collision.h>
-#include <ode/threading.h>
-#include <ode/threading_impl.h>
-#include <ode/cooperative.h>
-#include <ode/export-dif.h>
-#include <ode/version.h>
-
-#ifdef __cplusplus
-# include <ode/odecpp.h>
-# include <ode/odecpp_collision.h>
-#endif
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_ODECONFIG_H_
-#define _ODE_ODECONFIG_H_
-
-/* Pull in the standard headers */
-#include <stddef.h>
-#include <limits.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <stdarg.h>
-#include <math.h>
-#include <string.h>
-#include <float.h>
-
-
-#include <ode/precision.h>
-
-
-#if defined(ODE_DLL) || defined(ODE_LIB)
-#define __ODE__
-#endif
-
-/* Define a DLL export symbol for those platforms that need it */
-#if defined(_MSC_VER) || (defined(__GNUC__) && defined(_WIN32))
- #if defined(ODE_DLL)
- #define ODE_API __declspec(dllexport)
- #else
- #define ODE_API
- #endif
-#endif
-
-#if !defined(ODE_API)
- #define ODE_API
-#endif
-
-#if defined(_MSC_VER)
-# define ODE_API_DEPRECATED __declspec(deprecated)
-#elif defined (__GNUC__) && ( (__GNUC__ > 3) || ((__GNUC__ == 3) && (__GNUC_MINOR__ >= 1)) )
-# define ODE_API_DEPRECATED __attribute__((__deprecated__))
-#else
-# define ODE_API_DEPRECATED
-#endif
-
-#define ODE_PURE_INLINE static __inline
-#define ODE_INLINE __inline
-
-#if defined(__cplusplus)
- #define ODE_EXTERN_C extern "C"
-#else
- #define ODE_EXTERN_C
-#endif
-
-#if defined(__GNUC__)
-#define ODE_NORETURN __attribute__((noreturn))
-#elif defined(_MSC_VER)
-#define ODE_NORETURN __declspec(noreturn)
-#else // #if !defined(_MSC_VER)
-#define ODE_NORETURN
-#endif // #if !defined(__GNUC__)
-
-
-/* Well-defined common data types...need to be defined for 64 bit systems */
-#if defined(__aarch64__) || defined(__alpha__) || defined(__ppc64__) \
- || defined(__s390__) || defined(__s390x__) || defined(__zarch__) \
- || defined(__mips__) || defined(__powerpc64__) || defined(__riscv) \
- || (defined(__sparc__) && defined(__arch64__))
- #include <stdint.h>
- typedef int64_t dint64;
- typedef uint64_t duint64;
- typedef int32_t dint32;
- typedef uint32_t duint32;
- typedef int16_t dint16;
- typedef uint16_t duint16;
- typedef int8_t dint8;
- typedef uint8_t duint8;
-
- typedef intptr_t dintptr;
- typedef uintptr_t duintptr;
- typedef ptrdiff_t ddiffint;
- typedef size_t dsizeint;
-
-#elif (defined(_M_IA64) || defined(__ia64__) || defined(_M_AMD64) || defined(__x86_64__)) && !defined(__ILP32__) && !defined(_ILP32)
- #define X86_64_SYSTEM 1
-#if defined(_MSC_VER)
- typedef __int64 dint64;
- typedef unsigned __int64 duint64;
-#else
-#if defined(_LP64) || defined(__LP64__)
-typedef long dint64;
-typedef unsigned long duint64;
-#else
- typedef long long dint64;
- typedef unsigned long long duint64;
-#endif
-#endif
- typedef int dint32;
- typedef unsigned int duint32;
- typedef short dint16;
- typedef unsigned short duint16;
- typedef signed char dint8;
- typedef unsigned char duint8;
-
- typedef dint64 dintptr;
- typedef duint64 duintptr;
- typedef dint64 ddiffint;
- typedef duint64 dsizeint;
-
-#else
-#if defined(_MSC_VER)
- typedef __int64 dint64;
- typedef unsigned __int64 duint64;
-#else
- typedef long long dint64;
- typedef unsigned long long duint64;
-#endif
- typedef int dint32;
- typedef unsigned int duint32;
- typedef short dint16;
- typedef unsigned short duint16;
- typedef signed char dint8;
- typedef unsigned char duint8;
-
- typedef dint32 dintptr;
- typedef duint32 duintptr;
- typedef dint32 ddiffint;
- typedef duint32 dsizeint;
-
-#endif
-
-
-/* Define the dInfinity macro */
-#ifdef INFINITY
- #ifdef dSINGLE
- #define dInfinity ((float)INFINITY)
- #else
- #define dInfinity ((double)INFINITY)
- #endif
-#elif defined(HUGE_VAL)
- #ifdef dSINGLE
- #ifdef HUGE_VALF
- #define dInfinity HUGE_VALF
- #else
- #define dInfinity ((float)HUGE_VAL)
- #endif
- #else
- #define dInfinity HUGE_VAL
- #endif
-#else
- #ifdef dSINGLE
- #define dInfinity ((float)(1.0/0.0))
- #else
- #define dInfinity (1.0/0.0)
- #endif
-#endif
-
-
-/* Define the dNaN macro */
-#if defined(NAN)
- #define dNaN NAN
-#elif defined(__GNUC__)
- #define dNaN ({ union { duint32 m_ui; float m_f; } un; un.m_ui = 0x7FC00000; un.m_f; })
-#elif defined(__cplusplus)
- union _dNaNUnion
- {
- _dNaNUnion(): m_ui(0x7FC00000) {}
- duint32 m_ui;
- float m_f;
- };
- #define dNaN (_dNaNUnion().m_f)
-#else
- #ifdef dSINGLE
- #define dNaN ((float)(dInfinity - dInfinity))
- #else
- #define dNaN (dInfinity - dInfinity)
- #endif
-#endif
-
-
- /* Visual C does not define these functions */
-#if defined(_MSC_VER)
- #define _ode_copysignf(x, y) ((float)_copysign(x, y))
- #define _ode_copysign(x, y) _copysign(x, y)
- #define _ode_nextafterf(x, y) _nextafterf(x, y)
- #define _ode_nextafter(x, y) _nextafter(x, y)
- #if !defined(_WIN64) && defined(dSINGLE)
- #define _ODE__NEXTAFTERF_REQUIRED
- ODE_EXTERN_C float _nextafterf(float x, float y);
- #endif
-#else
- #define _ode_copysignf(x, y) copysignf(x, y)
- #define _ode_copysign(x, y) copysign(x, y)
- #define _ode_nextafterf(x, y) nextafterf(x, y)
- #define _ode_nextafter(x, y) nextafter(x, y)
-#endif
-
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-/* C++ interface for non-collision stuff */
-
-
-#ifndef _ODE_ODECPP_H_
-#define _ODE_ODECPP_H_
-#ifdef __cplusplus
-
-
-
-
-//namespace ode {
-
-
-class dWorldSimpleIDContainer {
-protected:
- dWorldID _id;
-
- dWorldSimpleIDContainer(): _id(0) {}
- ~dWorldSimpleIDContainer() { destroy(); }
-
- void destroy() {
- if (_id) {
- dWorldDestroy(_id);
- _id = 0;
- }
- }
-};
-
-class dWorldDynamicIDContainer: public dWorldSimpleIDContainer {
-protected:
- virtual ~dWorldDynamicIDContainer() {}
-};
-
-template <class dWorldTemplateBase>
-class dWorldTemplate: public dWorldTemplateBase {
- // intentionally undefined, don't use these
- dWorldTemplate (const dWorldTemplate<dWorldTemplateBase> &);
- void operator= (const dWorldTemplate<dWorldTemplateBase> &);
-
-protected:
- dWorldID get_id() const { return dWorldTemplateBase::_id; }
- void set_id(dWorldID value) { dWorldTemplateBase::_id = value; }
-
-public:
- dWorldTemplate()
- { set_id(dWorldCreate()); }
-
- dWorldID id() const
- { return get_id(); }
- operator dWorldID() const
- { return get_id(); }
-
- void setGravity (dReal x, dReal y, dReal z)
- { dWorldSetGravity (get_id(), x, y, z); }
- void setGravity (const dVector3 g)
- { setGravity (g[0], g[1], g[2]); }
- void getGravity (dVector3 g) const
- { dWorldGetGravity (get_id(), g); }
-
- void setERP (dReal erp)
- { dWorldSetERP(get_id(), erp); }
- dReal getERP() const
- { return dWorldGetERP(get_id()); }
-
- void setCFM (dReal cfm)
- { dWorldSetCFM(get_id(), cfm); }
- dReal getCFM() const
- { return dWorldGetCFM(get_id()); }
-
- void step (dReal stepsize)
- { dWorldStep (get_id(), stepsize); }
-
- void quickStep(dReal stepsize)
- { dWorldQuickStep (get_id(), stepsize); }
- void setQuickStepNumIterations(int num)
- { dWorldSetQuickStepNumIterations (get_id(), num); }
- int getQuickStepNumIterations() const
- { return dWorldGetQuickStepNumIterations (get_id()); }
- void setQuickStepW(dReal over_relaxation)
- { dWorldSetQuickStepW (get_id(), over_relaxation); }
- dReal getQuickStepW() const
- { return dWorldGetQuickStepW (get_id()); }
-
- void setAutoDisableLinearThreshold (dReal threshold)
- { dWorldSetAutoDisableLinearThreshold (get_id(), threshold); }
- dReal getAutoDisableLinearThreshold() const
- { return dWorldGetAutoDisableLinearThreshold (get_id()); }
- void setAutoDisableAngularThreshold (dReal threshold)
- { dWorldSetAutoDisableAngularThreshold (get_id(), threshold); }
- dReal getAutoDisableAngularThreshold() const
- { return dWorldGetAutoDisableAngularThreshold (get_id()); }
- void setAutoDisableSteps (int steps)
- { dWorldSetAutoDisableSteps (get_id(), steps); }
- int getAutoDisableSteps() const
- { return dWorldGetAutoDisableSteps (get_id()); }
- void setAutoDisableTime (dReal time)
- { dWorldSetAutoDisableTime (get_id(), time); }
- dReal getAutoDisableTime() const
- { return dWorldGetAutoDisableTime (get_id()); }
- void setAutoDisableFlag (int do_auto_disable)
- { dWorldSetAutoDisableFlag (get_id(), do_auto_disable); }
- int getAutoDisableFlag() const
- { return dWorldGetAutoDisableFlag (get_id()); }
-
- dReal getLinearDampingThreshold() const
- { return dWorldGetLinearDampingThreshold(get_id()); }
- void setLinearDampingThreshold(dReal threshold)
- { dWorldSetLinearDampingThreshold(get_id(), threshold); }
- dReal getAngularDampingThreshold() const
- { return dWorldGetAngularDampingThreshold(get_id()); }
- void setAngularDampingThreshold(dReal threshold)
- { dWorldSetAngularDampingThreshold(get_id(), threshold); }
- dReal getLinearDamping() const
- { return dWorldGetLinearDamping(get_id()); }
- void setLinearDamping(dReal scale)
- { dWorldSetLinearDamping(get_id(), scale); }
- dReal getAngularDamping() const
- { return dWorldGetAngularDamping(get_id()); }
- void setAngularDamping(dReal scale)
- { dWorldSetAngularDamping(get_id(), scale); }
- void setDamping(dReal linear_scale, dReal angular_scale)
- { dWorldSetDamping(get_id(), linear_scale, angular_scale); }
-
- dReal getMaxAngularSpeed() const
- { return dWorldGetMaxAngularSpeed(get_id()); }
- void setMaxAngularSpeed(dReal max_speed)
- { dWorldSetMaxAngularSpeed(get_id(), max_speed); }
-
- void setContactSurfaceLayer(dReal depth)
- { dWorldSetContactSurfaceLayer (get_id(), depth); }
- dReal getContactSurfaceLayer() const
- { return dWorldGetContactSurfaceLayer (get_id()); }
-
- void impulseToForce (dReal stepsize, dReal ix, dReal iy, dReal iz,
- dVector3 force)
- { dWorldImpulseToForce (get_id(), stepsize, ix, iy, iz, force); }
-};
-
-
-class dBodySimpleIDContainer {
-protected:
- dBodyID _id;
-
- dBodySimpleIDContainer(): _id(0) {}
- ~dBodySimpleIDContainer() { destroy(); }
-
- void destroy() {
- if (_id) {
- dBodyDestroy(_id);
- _id = 0;
- }
- }
-};
-
-class dBodyDynamicIDContainer: public dBodySimpleIDContainer {
-protected:
- virtual ~dBodyDynamicIDContainer() {}
-};
-
-template <class dBodyTemplateBase, class dWorldTemplateBase>
-class dBodyTemplate: public dBodyTemplateBase {
- // intentionally undefined, don't use these
- dBodyTemplate (const dBodyTemplate<dBodyTemplateBase, dWorldTemplateBase> &);
- void operator= (const dBodyTemplate<dBodyTemplateBase, dWorldTemplateBase> &);
-
-protected:
- dBodyID get_id() const { return dBodyTemplateBase::_id; }
- void set_id(dBodyID value) { dBodyTemplateBase::_id = value; }
-
- void destroy() { dBodyTemplateBase::destroy(); }
-
-public:
- dBodyTemplate()
- { }
- dBodyTemplate (dWorldID world)
- { set_id(dBodyCreate(world)); }
- dBodyTemplate (dWorldTemplate<dWorldTemplateBase>& world)
- { set_id(dBodyCreate(world.id())); }
-
- void create (dWorldID world) {
- destroy();
- set_id(dBodyCreate(world));
- }
- void create (dWorldTemplate<dWorldTemplateBase>& world) {
- create(world.id());
- }
-
- dBodyID id() const
- { return get_id(); }
- operator dBodyID() const
- { return get_id(); }
-
- void setData (void *data)
- { dBodySetData (get_id(), data); }
- void *getData() const
- { return dBodyGetData (get_id()); }
-
- void setPosition (dReal x, dReal y, dReal z)
- { dBodySetPosition (get_id(), x, y, z); }
- void setPosition (const dVector3 p)
- { setPosition(p[0], p[1], p[2]); }
-
- void setRotation (const dMatrix3 R)
- { dBodySetRotation (get_id(), R); }
- void setQuaternion (const dQuaternion q)
- { dBodySetQuaternion (get_id(), q); }
- void setLinearVel (dReal x, dReal y, dReal z)
- { dBodySetLinearVel (get_id(), x, y, z); }
- void setLinearVel (const dVector3 v)
- { setLinearVel(v[0], v[1], v[2]); }
- void setAngularVel (dReal x, dReal y, dReal z)
- { dBodySetAngularVel (get_id(), x, y, z); }
- void setAngularVel (const dVector3 v)
- { setAngularVel (v[0], v[1], v[2]); }
-
- const dReal * getPosition() const
- { return dBodyGetPosition (get_id()); }
- const dReal * getRotation() const
- { return dBodyGetRotation (get_id()); }
- const dReal * getQuaternion() const
- { return dBodyGetQuaternion (get_id()); }
- const dReal * getLinearVel() const
- { return dBodyGetLinearVel (get_id()); }
- const dReal * getAngularVel() const
- { return dBodyGetAngularVel (get_id()); }
-
- void setMass (const dMass *mass)
- { dBodySetMass (get_id(), mass); }
- void setMass (const dMass &mass)
- { setMass (&mass); }
- dMass getMass () const
- { dMass mass; dBodyGetMass (get_id(), &mass); return mass; }
-
- void addForce (dReal fx, dReal fy, dReal fz)
- { dBodyAddForce (get_id(), fx, fy, fz); }
- void addForce (const dVector3 f)
- { addForce (f[0], f[1], f[2]); }
- void addTorque (dReal fx, dReal fy, dReal fz)
- { dBodyAddTorque (get_id(), fx, fy, fz); }
- void addTorque (const dVector3 t)
- { addTorque(t[0], t[1], t[2]); }
-
- void addRelForce (dReal fx, dReal fy, dReal fz)
- { dBodyAddRelForce (get_id(), fx, fy, fz); }
- void addRelForce (const dVector3 f)
- { addRelForce (f[0], f[1], f[2]); }
- void addRelTorque (dReal fx, dReal fy, dReal fz)
- { dBodyAddRelTorque (get_id(), fx, fy, fz); }
- void addRelTorque (const dVector3 t)
- { addRelTorque (t[0], t[1], t[2]); }
-
- void addForceAtPos (dReal fx, dReal fy, dReal fz,
- dReal px, dReal py, dReal pz)
- { dBodyAddForceAtPos (get_id(), fx, fy, fz, px, py, pz); }
- void addForceAtPos (const dVector3 f, const dVector3 p)
- { addForceAtPos (f[0], f[1], f[2], p[0], p[1], p[2]); }
-
- void addForceAtRelPos (dReal fx, dReal fy, dReal fz,
- dReal px, dReal py, dReal pz)
- { dBodyAddForceAtRelPos (get_id(), fx, fy, fz, px, py, pz); }
- void addForceAtRelPos (const dVector3 f, const dVector3 p)
- { addForceAtRelPos (f[0], f[1], f[2], p[0], p[1], p[2]); }
-
- void addRelForceAtPos (dReal fx, dReal fy, dReal fz,
- dReal px, dReal py, dReal pz)
- { dBodyAddRelForceAtPos (get_id(), fx, fy, fz, px, py, pz); }
- void addRelForceAtPos (const dVector3 f, const dVector3 p)
- { addRelForceAtPos (f[0], f[1], f[2], p[0], p[1], p[2]); }
-
- void addRelForceAtRelPos (dReal fx, dReal fy, dReal fz,
- dReal px, dReal py, dReal pz)
- { dBodyAddRelForceAtRelPos (get_id(), fx, fy, fz, px, py, pz); }
- void addRelForceAtRelPos (const dVector3 f, const dVector3 p)
- { addRelForceAtRelPos (f[0], f[1], f[2], p[0], p[1], p[2]); }
-
- const dReal * getForce() const
- { return dBodyGetForce(get_id()); }
- const dReal * getTorque() const
- { return dBodyGetTorque(get_id()); }
- void setForce (dReal x, dReal y, dReal z)
- { dBodySetForce (get_id(), x, y, z); }
- void setForce (const dVector3 f)
- { setForce (f[0], f[1], f[2]); }
- void setTorque (dReal x, dReal y, dReal z)
- { dBodySetTorque (get_id(), x, y, z); }
- void setTorque (const dVector3 t)
- { setTorque (t[0], t[1], t[2]); }
-
- void setDynamic()
- { dBodySetDynamic (get_id()); }
- void setKinematic()
- { dBodySetKinematic (get_id()); }
- bool isKinematic() const
- { return dBodyIsKinematic (get_id()) != 0; }
-
- void enable()
- { dBodyEnable (get_id()); }
- void disable()
- { dBodyDisable (get_id()); }
- bool isEnabled() const
- { return dBodyIsEnabled (get_id()) != 0; }
-
- void getRelPointPos (dReal px, dReal py, dReal pz, dVector3 result) const
- { dBodyGetRelPointPos (get_id(), px, py, pz, result); }
- void getRelPointPos (const dVector3 p, dVector3 result) const
- { getRelPointPos (p[0], p[1], p[2], result); }
-
- void getRelPointVel (dReal px, dReal py, dReal pz, dVector3 result) const
- { dBodyGetRelPointVel (get_id(), px, py, pz, result); }
- void getRelPointVel (const dVector3 p, dVector3 result) const
- { getRelPointVel (p[0], p[1], p[2], result); }
-
- void getPointVel (dReal px, dReal py, dReal pz, dVector3 result) const
- { dBodyGetPointVel (get_id(), px, py, pz, result); }
- void getPointVel (const dVector3 p, dVector3 result) const
- { getPointVel (p[0], p[1], p[2], result); }
-
- void getPosRelPoint (dReal px, dReal py, dReal pz, dVector3 result) const
- { dBodyGetPosRelPoint (get_id(), px, py, pz, result); }
- void getPosRelPoint (const dVector3 p, dVector3 result) const
- { getPosRelPoint (p[0], p[1], p[2], result); }
-
- void vectorToWorld (dReal px, dReal py, dReal pz, dVector3 result) const
- { dBodyVectorToWorld (get_id(), px, py, pz, result); }
- void vectorToWorld (const dVector3 p, dVector3 result) const
- { vectorToWorld (p[0], p[1], p[2], result); }
-
- void vectorFromWorld (dReal px, dReal py, dReal pz, dVector3 result) const
- { dBodyVectorFromWorld (get_id(), px, py, pz, result); }
- void vectorFromWorld (const dVector3 p, dVector3 result) const
- { vectorFromWorld (p[0], p[1], p[2], result); }
-
- void setFiniteRotationMode (bool mode)
- { dBodySetFiniteRotationMode (get_id(), mode); }
-
- void setFiniteRotationAxis (dReal x, dReal y, dReal z)
- { dBodySetFiniteRotationAxis (get_id(), x, y, z); }
- void setFiniteRotationAxis (const dVector3 a)
- { setFiniteRotationAxis (a[0], a[1], a[2]); }
-
- bool getFiniteRotationMode() const
- { return dBodyGetFiniteRotationMode (get_id()) != 0; }
- void getFiniteRotationAxis (dVector3 result) const
- { dBodyGetFiniteRotationAxis (get_id(), result); }
-
- int getNumJoints() const
- { return dBodyGetNumJoints (get_id()); }
- dJointID getJoint (int index) const
- { return dBodyGetJoint (get_id(), index); }
-
- void setGravityMode (bool mode)
- { dBodySetGravityMode (get_id(), mode); }
- bool getGravityMode() const
- { return dBodyGetGravityMode (get_id()) != 0; }
-
- bool isConnectedTo (dBodyID body) const
- { return dAreConnected (get_id(), body) != 0; }
-
- void setAutoDisableLinearThreshold (dReal threshold)
- { dBodySetAutoDisableLinearThreshold (get_id(), threshold); }
- dReal getAutoDisableLinearThreshold() const
- { return dBodyGetAutoDisableLinearThreshold (get_id()); }
- void setAutoDisableAngularThreshold (dReal threshold)
- { dBodySetAutoDisableAngularThreshold (get_id(), threshold); }
- dReal getAutoDisableAngularThreshold() const
- { return dBodyGetAutoDisableAngularThreshold (get_id()); }
- void setAutoDisableSteps (int steps)
- { dBodySetAutoDisableSteps (get_id(), steps); }
- int getAutoDisableSteps() const
- { return dBodyGetAutoDisableSteps (get_id()); }
- void setAutoDisableTime (dReal time)
- { dBodySetAutoDisableTime (get_id(), time); }
- dReal getAutoDisableTime() const
- { return dBodyGetAutoDisableTime (get_id()); }
- void setAutoDisableFlag (bool do_auto_disable)
- { dBodySetAutoDisableFlag (get_id(), do_auto_disable); }
- bool getAutoDisableFlag() const
- { return dBodyGetAutoDisableFlag (get_id()) != 0; }
-
- dReal getLinearDamping() const
- { return dBodyGetLinearDamping(get_id()); }
- void setLinearDamping(dReal scale)
- { dBodySetLinearDamping(get_id(), scale); }
- dReal getAngularDamping() const
- { return dBodyGetAngularDamping(get_id()); }
- void setAngularDamping(dReal scale)
- { dBodySetAngularDamping(get_id(), scale); }
- void setDamping(dReal linear_scale, dReal angular_scale)
- { dBodySetDamping(get_id(), linear_scale, angular_scale); }
- dReal getLinearDampingThreshold() const
- { return dBodyGetLinearDampingThreshold(get_id()); }
- void setLinearDampingThreshold(dReal threshold) const
- { dBodySetLinearDampingThreshold(get_id(), threshold); }
- dReal getAngularDampingThreshold() const
- { return dBodyGetAngularDampingThreshold(get_id()); }
- void setAngularDampingThreshold(dReal threshold)
- { dBodySetAngularDampingThreshold(get_id(), threshold); }
- void setDampingDefaults()
- { dBodySetDampingDefaults(get_id()); }
-
- dReal getMaxAngularSpeed() const
- { return dBodyGetMaxAngularSpeed(get_id()); }
- void setMaxAngularSpeed(dReal max_speed)
- { dBodySetMaxAngularSpeed(get_id(), max_speed); }
-
- bool getGyroscopicMode() const
- { return dBodyGetGyroscopicMode(get_id()) != 0; }
- void setGyroscopicMode(bool mode)
- { dBodySetGyroscopicMode(get_id(), mode); }
-
-};
-
-
-class dJointGroupSimpleIDContainer {
-protected:
- dJointGroupID _id;
-
- dJointGroupSimpleIDContainer(): _id(0) {}
- ~dJointGroupSimpleIDContainer() { destroy(); }
-
- void destroy() {
- if (_id) {
- dJointGroupDestroy(_id);
- _id = 0;
- }
- }
-};
-
-class dJointGroupDynamicIDContainer: public dJointGroupSimpleIDContainer {
-protected:
- virtual ~dJointGroupDynamicIDContainer() {}
-};
-
-template <class dJointGroupTemplateBase>
-class dJointGroupTemplate: public dJointGroupTemplateBase {
- // intentionally undefined, don't use these
- dJointGroupTemplate (const dJointGroupTemplate<dJointGroupTemplateBase> &);
- void operator= (const dJointGroupTemplate<dJointGroupTemplateBase> &);
-
-protected:
- dJointGroupID get_id() const { return dJointGroupTemplateBase::_id; }
- void set_id(dJointGroupID value) { dJointGroupTemplateBase::_id = value; }
-
- void destroy() { dJointGroupTemplateBase::destroy(); }
-
-public:
- dJointGroupTemplate ()
- { set_id(dJointGroupCreate(0)); }
-
- void create () {
- destroy();
- set_id(dJointGroupCreate(0));
- }
-
- dJointGroupID id() const
- { return get_id(); }
- operator dJointGroupID() const
- { return get_id(); }
-
- void empty()
- { dJointGroupEmpty (get_id()); }
- void clear()
- { empty(); }
-};
-
-
-class dJointSimpleIDContainer {
-protected:
- dJointID _id;
-
- dJointSimpleIDContainer(): _id(0) {}
- ~dJointSimpleIDContainer() { destroy(); }
-
- void destroy() {
- if (_id) {
- dJointDestroy (_id);
- _id = 0;
- }
- }
-};
-
-class dJointDynamicIDContainer: public dJointSimpleIDContainer {
-protected:
- virtual ~dJointDynamicIDContainer() {}
-};
-
-template <class dJointTemplateBase, class dWorldTemplateBase, class dBodyTemplateBase>
-class dJointTemplate: public dJointTemplateBase {
-private:
- // intentionally undefined, don't use these
- dJointTemplate (const dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &) ;
- void operator= (const dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
-
-protected:
- dJointID get_id() const { return dJointTemplateBase::_id; }
- void set_id(dJointID value) { dJointTemplateBase::_id = value; }
-
- void destroy() { dJointTemplateBase::destroy(); }
-
-protected:
- dJointTemplate() // don't let user construct pure dJointTemplate objects
- { }
-
-public:
- dJointID id() const
- { return get_id(); }
- operator dJointID() const
- { return get_id(); }
-
- int getNumBodies() const
- { return dJointGetNumBodies(get_id()); }
-
- void attach (dBodyID body1, dBodyID body2)
- { dJointAttach (get_id(), body1, body2); }
- void attach (dBodyTemplate<dBodyTemplateBase, dWorldTemplateBase>& body1, dBodyTemplate<dBodyTemplateBase, dWorldTemplateBase>& body2)
- { attach(body1.id(), body2.id()); }
-
- void enable()
- { dJointEnable (get_id()); }
- void disable()
- { dJointDisable (get_id()); }
- bool isEnabled() const
- { return dJointIsEnabled (get_id()) != 0; }
-
- void setData (void *data)
- { dJointSetData (get_id(), data); }
- void *getData() const
- { return dJointGetData (get_id()); }
-
- dJointType getType() const
- { return dJointGetType (get_id()); }
-
- dBodyID getBody (int index) const
- { return dJointGetBody (get_id(), index); }
-
- void setFeedback(dJointFeedback *fb)
- { dJointSetFeedback(get_id(), fb); }
- dJointFeedback *getFeedback() const
- { return dJointGetFeedback(get_id()); }
-
- // If not implemented it will do nothing as describe in the doc
- virtual void setParam (int, dReal) {};
- virtual dReal getParam (int) const { return 0; }
-};
-
-
-template <class dJointTemplateBase, class dWorldTemplateBase, class dBodyTemplateBase>
-class dBallJointTemplate : public dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> {
-private:
- // intentionally undefined, don't use these
- dBallJointTemplate (const dBallJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
- void operator= (const dBallJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
-
-protected:
- typedef dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> dBaseTemplate;
-
- dJointID get_id() const { return dBaseTemplate::get_id(); }
- void set_id(dJointID value) { dBaseTemplate::set_id(value); }
-
- void destroy() { dBaseTemplate::destroy(); }
-
-public:
- dBallJointTemplate() { }
- dBallJointTemplate (dWorldID world, dJointGroupID group=0)
- { set_id(dJointCreateBall(world, group)); }
- dBallJointTemplate (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { set_id(dJointCreateBall(world.id(), group)); }
-
- void create (dWorldID world, dJointGroupID group=0) {
- destroy();
- set_id(dJointCreateBall(world, group));
- }
- void create (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { create(world.id(), group); }
-
- void setAnchor (dReal x, dReal y, dReal z)
- { dJointSetBallAnchor (get_id(), x, y, z); }
- void setAnchor (const dVector3 a)
- { setAnchor (a[0], a[1], a[2]); }
- void getAnchor (dVector3 result) const
- { dJointGetBallAnchor (get_id(), result); }
- void getAnchor2 (dVector3 result) const
- { dJointGetBallAnchor2 (get_id(), result); }
- virtual void setParam (int parameter, dReal value)
- { dJointSetBallParam (get_id(), parameter, value); }
- virtual dReal getParam (int parameter) const
- { return dJointGetBallParam (get_id(), parameter); }
- // TODO: expose params through methods
-} ;
-
-
-template <class dJointTemplateBase, class dWorldTemplateBase, class dBodyTemplateBase>
-class dHingeJointTemplate : public dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> {
-private:
- // intentionally undefined, don't use these
- dHingeJointTemplate (const dHingeJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
- void operator = (const dHingeJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
-
-protected:
- typedef dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> dBaseTemplate;
-
- dJointID get_id() const { return dBaseTemplate::get_id(); }
- void set_id(dJointID value) { dBaseTemplate::set_id(value); }
-
- void destroy() { dBaseTemplate::destroy(); }
-
-public:
- dHingeJointTemplate() { }
- dHingeJointTemplate (dWorldID world, dJointGroupID group=0)
- { set_id(dJointCreateHinge(world, group)); }
- dHingeJointTemplate (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { set_id(dJointCreateHinge(world.id(), group)); }
-
- void create (dWorldID world, dJointGroupID group=0) {
- destroy();
- set_id(dJointCreateHinge (world, group));
- }
- void create (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { create(world.id(), group); }
-
- void setAnchor (dReal x, dReal y, dReal z)
- { dJointSetHingeAnchor (get_id(), x, y, z); }
- void setAnchor (const dVector3 a)
- { setAnchor (a[0], a[1], a[2]); }
- void getAnchor (dVector3 result) const
- { dJointGetHingeAnchor (get_id(), result); }
- void getAnchor2 (dVector3 result) const
- { dJointGetHingeAnchor2 (get_id(), result); }
-
- void setAxis (dReal x, dReal y, dReal z)
- { dJointSetHingeAxis (get_id(), x, y, z); }
- void setAxis (const dVector3 a)
- { setAxis(a[0], a[1], a[2]); }
- void getAxis (dVector3 result) const
- { dJointGetHingeAxis (get_id(), result); }
-
- dReal getAngle() const
- { return dJointGetHingeAngle (get_id()); }
- dReal getAngleRate() const
- { return dJointGetHingeAngleRate (get_id()); }
-
- virtual void setParam (int parameter, dReal value)
- { dJointSetHingeParam (get_id(), parameter, value); }
- virtual dReal getParam (int parameter) const
- { return dJointGetHingeParam (get_id(), parameter); }
- // TODO: expose params through methods
-
- void addTorque (dReal torque)
- { dJointAddHingeTorque(get_id(), torque); }
-};
-
-
-template <class dJointTemplateBase, class dWorldTemplateBase, class dBodyTemplateBase>
-class dSliderJointTemplate : public dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> {
-private:
- // intentionally undefined, don't use these
- dSliderJointTemplate (const dSliderJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
- void operator = (const dSliderJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
-
-protected:
- typedef dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> dBaseTemplate;
-
- dJointID get_id() const { return dBaseTemplate::get_id(); }
- void set_id(dJointID value) { dBaseTemplate::set_id(value); }
-
- void destroy() { dBaseTemplate::destroy(); }
-
-public:
- dSliderJointTemplate() { }
- dSliderJointTemplate (dWorldID world, dJointGroupID group=0)
- { set_id(dJointCreateSlider(world, group)); }
- dSliderJointTemplate (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { set_id(dJointCreateSlider(world.id(), group)); }
-
- void create (dWorldID world, dJointGroupID group=0) {
- destroy();
- set_id(dJointCreateSlider(world, group));
- }
- void create (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { create(world.id(), group); }
-
- void setAxis (dReal x, dReal y, dReal z)
- { dJointSetSliderAxis (get_id(), x, y, z); }
- void setAxis (const dVector3 a)
- { setAxis (a[0], a[1], a[2]); }
- void getAxis (dVector3 result) const
- { dJointGetSliderAxis (get_id(), result); }
-
- dReal getPosition() const
- { return dJointGetSliderPosition (get_id()); }
- dReal getPositionRate() const
- { return dJointGetSliderPositionRate (get_id()); }
-
- virtual void setParam (int parameter, dReal value)
- { dJointSetSliderParam (get_id(), parameter, value); }
- virtual dReal getParam (int parameter) const
- { return dJointGetSliderParam (get_id(), parameter); }
- // TODO: expose params through methods
-
- void addForce (dReal force)
- { dJointAddSliderForce(get_id(), force); }
-};
-
-
-template <class dJointTemplateBase, class dWorldTemplateBase, class dBodyTemplateBase>
-class dUniversalJointTemplate : public dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> {
-private:
- // intentionally undefined, don't use these
- dUniversalJointTemplate (const dUniversalJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
- void operator = (const dUniversalJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
-
-protected:
- typedef dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> dBaseTemplate;
-
- dJointID get_id() const { return dBaseTemplate::get_id(); }
- void set_id(dJointID value) { dBaseTemplate::set_id(value); }
-
- void destroy() { dBaseTemplate::destroy(); }
-
-public:
- dUniversalJointTemplate() { }
- dUniversalJointTemplate (dWorldID world, dJointGroupID group=0)
- { set_id(dJointCreateUniversal(world, group)); }
- dUniversalJointTemplate (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { set_id(dJointCreateUniversal(world.id(), group)); }
-
- void create (dWorldID world, dJointGroupID group=0) {
- destroy();
- set_id(dJointCreateUniversal(world, group));
- }
- void create (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { create(world.id(), group); }
-
- void setAnchor (dReal x, dReal y, dReal z)
- { dJointSetUniversalAnchor (get_id(), x, y, z); }
- void setAnchor (const dVector3 a)
- { setAnchor(a[0], a[1], a[2]); }
- void setAxis1 (dReal x, dReal y, dReal z)
- { dJointSetUniversalAxis1 (get_id(), x, y, z); }
- void setAxis1 (const dVector3 a)
- { setAxis1 (a[0], a[1], a[2]); }
- void setAxis2 (dReal x, dReal y, dReal z)
- { dJointSetUniversalAxis2 (get_id(), x, y, z); }
- void setAxis2 (const dVector3 a)
- { setAxis2 (a[0], a[1], a[2]); }
-
- void getAnchor (dVector3 result) const
- { dJointGetUniversalAnchor (get_id(), result); }
- void getAnchor2 (dVector3 result) const
- { dJointGetUniversalAnchor2 (get_id(), result); }
- void getAxis1 (dVector3 result) const
- { dJointGetUniversalAxis1 (get_id(), result); }
- void getAxis2 (dVector3 result) const
- { dJointGetUniversalAxis2 (get_id(), result); }
-
- virtual void setParam (int parameter, dReal value)
- { dJointSetUniversalParam (get_id(), parameter, value); }
- virtual dReal getParam (int parameter) const
- { return dJointGetUniversalParam (get_id(), parameter); }
- // TODO: expose params through methods
-
- void getAngles(dReal *angle1, dReal *angle2) const
- { dJointGetUniversalAngles (get_id(), angle1, angle2); }
-
- dReal getAngle1() const
- { return dJointGetUniversalAngle1 (get_id()); }
- dReal getAngle1Rate() const
- { return dJointGetUniversalAngle1Rate (get_id()); }
- dReal getAngle2() const
- { return dJointGetUniversalAngle2 (get_id()); }
- dReal getAngle2Rate() const
- { return dJointGetUniversalAngle2Rate (get_id()); }
-
- void addTorques (dReal torque1, dReal torque2)
- { dJointAddUniversalTorques(get_id(), torque1, torque2); }
-};
-
-
-template <class dJointTemplateBase, class dWorldTemplateBase, class dBodyTemplateBase>
-class dHinge2JointTemplate : public dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> {
-private:
- // intentionally undefined, don't use these
- dHinge2JointTemplate (const dHinge2JointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
- void operator = (const dHinge2JointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
-
-protected:
- typedef dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> dBaseTemplate;
-
- dJointID get_id() const { return dBaseTemplate::get_id(); }
- void set_id(dJointID value) { dBaseTemplate::set_id(value); }
-
- void destroy() { dBaseTemplate::destroy(); }
-
-public:
- dHinge2JointTemplate() { }
- dHinge2JointTemplate (dWorldID world, dJointGroupID group=0)
- { set_id(dJointCreateHinge2(world, group)); }
- dHinge2JointTemplate (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { set_id(dJointCreateHinge2(world.id(), group)); }
-
- void create (dWorldID world, dJointGroupID group=0) {
- destroy();
- set_id(dJointCreateHinge2(world, group));
- }
- void create (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { create(world.id(), group); }
-
- void setAnchor (dReal x, dReal y, dReal z)
- { dJointSetHinge2Anchor (get_id(), x, y, z); }
- void setAnchor (const dVector3 a)
- { setAnchor(a[0], a[1], a[2]); }
- void setAxes (const dReal *axis1/*=NULL*/, const dReal *axis2/*=NULL*/)
- { dJointSetHinge2Axes (get_id(), axis1, axis2); }
- ODE_API_DEPRECATED void setAxis1 (dReal x, dReal y, dReal z)
- { dVector3 a = { x, y, z }; dJointSetHinge2Axes (get_id(), a, NULL); }
- ODE_API_DEPRECATED void setAxis1 (const dVector3 a)
- { dJointSetHinge2Axes (get_id(), a, NULL); }
- ODE_API_DEPRECATED void setAxis2 (dReal x, dReal y, dReal z)
- { dVector3 a = { x, y, z }; dJointSetHinge2Axes (get_id(), NULL, a); }
- ODE_API_DEPRECATED void setAxis2 (const dVector3 a)
- { dJointSetHinge2Axes (get_id(), NULL, a); }
-
- void getAnchor (dVector3 result) const
- { dJointGetHinge2Anchor (get_id(), result); }
- void getAnchor2 (dVector3 result) const
- { dJointGetHinge2Anchor2 (get_id(), result); }
- void getAxis1 (dVector3 result) const
- { dJointGetHinge2Axis1 (get_id(), result); }
- void getAxis2 (dVector3 result) const
- { dJointGetHinge2Axis2 (get_id(), result); }
-
- dReal getAngle1() const
- { return dJointGetHinge2Angle1 (get_id()); }
- dReal getAngle1Rate() const
- { return dJointGetHinge2Angle1Rate (get_id()); }
- dReal getAngle2Rate() const
- { return dJointGetHinge2Angle2Rate (get_id()); }
-
- virtual void setParam (int parameter, dReal value)
- { dJointSetHinge2Param (get_id(), parameter, value); }
- virtual dReal getParam (int parameter) const
- { return dJointGetHinge2Param (get_id(), parameter); }
- // TODO: expose params through methods
-
- void addTorques(dReal torque1, dReal torque2)
- { dJointAddHinge2Torques(get_id(), torque1, torque2); }
-};
-
-
-template <class dJointTemplateBase, class dWorldTemplateBase, class dBodyTemplateBase>
-class dPRJointTemplate : public dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> {
-private:
- // intentionally undefined, don't use these
- dPRJointTemplate (const dPRJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
- void operator = (const dPRJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
-
-protected:
- typedef dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> dBaseTemplate;
-
- dJointID get_id() const { return dBaseTemplate::get_id(); }
- void set_id(dJointID value) { dBaseTemplate::set_id(value); }
-
- void destroy() { dBaseTemplate::destroy(); }
-
-public:
- dPRJointTemplate() { }
- dPRJointTemplate (dWorldID world, dJointGroupID group=0)
- { set_id(dJointCreatePR(world, group)); }
- dPRJointTemplate (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { set_id(dJointCreatePR(world.id(), group)); }
-
- void create (dWorldID world, dJointGroupID group=0) {
- destroy();
- set_id(dJointCreatePR(world, group));
- }
- void create (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { create(world.id(), group); }
-
- void setAnchor (dReal x, dReal y, dReal z)
- { dJointSetPRAnchor (get_id(), x, y, z); }
- void setAnchor (const dVector3 a)
- { setAnchor (a[0], a[1], a[2]); }
- void setAxis1 (dReal x, dReal y, dReal z)
- { dJointSetPRAxis1 (get_id(), x, y, z); }
- void setAxis1 (const dVector3 a)
- { setAxis1(a[0], a[1], a[2]); }
- void setAxis2 (dReal x, dReal y, dReal z)
- { dJointSetPRAxis2 (get_id(), x, y, z); }
- void setAxis2 (const dVector3 a)
- { setAxis2(a[0], a[1], a[2]); }
-
- void getAnchor (dVector3 result) const
- { dJointGetPRAnchor (get_id(), result); }
- void getAxis1 (dVector3 result) const
- { dJointGetPRAxis1 (get_id(), result); }
- void getAxis2 (dVector3 result) const
- { dJointGetPRAxis2 (get_id(), result); }
-
- dReal getPosition() const
- { return dJointGetPRPosition (get_id()); }
- dReal getPositionRate() const
- { return dJointGetPRPositionRate (get_id()); }
-
- dReal getAngle() const
- { return dJointGetPRAngle (get_id()); }
- dReal getAngleRate() const
- { return dJointGetPRAngleRate (get_id()); }
-
- virtual void setParam (int parameter, dReal value)
- { dJointSetPRParam (get_id(), parameter, value); }
- virtual dReal getParam (int parameter) const
- { return dJointGetPRParam (get_id(), parameter); }
-};
-
-
-
-template <class dJointTemplateBase, class dWorldTemplateBase, class dBodyTemplateBase>
-class dPUJointTemplate : public dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase>
-{
-private:
- // intentionally undefined, don't use these
- dPUJointTemplate (const dPUJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
- void operator = (const dPUJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
-
-protected:
- typedef dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> dBaseTemplate;
-
- dJointID get_id() const { return dBaseTemplate::get_id(); }
- void set_id(dJointID value) { dBaseTemplate::set_id(value); }
-
- void destroy() { dBaseTemplate::destroy(); }
-
-public:
- dPUJointTemplate() { }
- dPUJointTemplate (dWorldID world, dJointGroupID group=0)
- { set_id(dJointCreatePU(world, group)); }
- dPUJointTemplate (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { set_id(dJointCreatePU(world.id(), group)); }
-
- void create (dWorldID world, dJointGroupID group=0)
- {
- destroy();
- set_id(dJointCreatePU(world, group));
- }
- void create (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { create(world.id(), group); }
-
- void setAnchor (dReal x, dReal y, dReal z)
- { dJointSetPUAnchor (get_id(), x, y, z); }
- void setAnchor (const dVector3 a)
- { setAnchor (a[0], a[1], a[2]); }
- void setAxis1 (dReal x, dReal y, dReal z)
- { dJointSetPUAxis1 (get_id(), x, y, z); }
- void setAxis1 (const dVector3 a)
- { setAxis1(a[0], a[1], a[2]); }
- void setAxis2 (dReal x, dReal y, dReal z)
- { dJointSetPUAxis2 (get_id(), x, y, z); }
- void setAxis3 (dReal x, dReal y, dReal z)
- { dJointSetPUAxis3 (get_id(), x, y, z); }
- void setAxis3 (const dVector3 a)
- { setAxis3(a[0], a[1], a[2]); }
- void setAxisP (dReal x, dReal y, dReal z)
- { dJointSetPUAxis3 (get_id(), x, y, z); }
- void setAxisP (const dVector3 a)
- { setAxisP(a[0], a[1], a[2]); }
-
- virtual void getAnchor (dVector3 result) const
- { dJointGetPUAnchor (get_id(), result); }
- void getAxis1 (dVector3 result) const
- { dJointGetPUAxis1 (get_id(), result); }
- void getAxis2 (dVector3 result) const
- { dJointGetPUAxis2 (get_id(), result); }
- void getAxis3 (dVector3 result) const
- { dJointGetPUAxis3 (get_id(), result); }
- void getAxisP (dVector3 result) const
- { dJointGetPUAxis3 (get_id(), result); }
-
- dReal getAngle1() const
- { return dJointGetPUAngle1 (get_id()); }
- dReal getAngle1Rate() const
- { return dJointGetPUAngle1Rate (get_id()); }
- dReal getAngle2() const
- { return dJointGetPUAngle2 (get_id()); }
- dReal getAngle2Rate() const
- { return dJointGetPUAngle2Rate (get_id()); }
-
- dReal getPosition() const
- { return dJointGetPUPosition (get_id()); }
- dReal getPositionRate() const
- { return dJointGetPUPositionRate (get_id()); }
-
- virtual void setParam (int parameter, dReal value)
- { dJointSetPUParam (get_id(), parameter, value); }
- virtual dReal getParam (int parameter) const
- { return dJointGetPUParam (get_id(), parameter); }
- // TODO: expose params through methods
-};
-
-
-
-
-
-template <class dJointTemplateBase, class dWorldTemplateBase, class dBodyTemplateBase>
-class dPistonJointTemplate : public dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase>
-{
-private:
- // intentionally undefined, don't use these
- dPistonJointTemplate (const dPistonJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
- void operator = (const dPistonJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
-
-protected:
- typedef dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> dBaseTemplate;
-
- dJointID get_id() const { return dBaseTemplate::get_id(); }
- void set_id(dJointID value) { dBaseTemplate::set_id(value); }
-
- void destroy() { dBaseTemplate::destroy(); }
-
-public:
- dPistonJointTemplate() { }
- dPistonJointTemplate (dWorldID world, dJointGroupID group=0)
- { set_id(dJointCreatePiston(world, group)); }
- dPistonJointTemplate (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { set_id(dJointCreatePiston(world, group)); }
-
- void create (dWorldID world, dJointGroupID group=0)
- {
- destroy();
- set_id(dJointCreatePiston(world, group));
- }
- void create (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { create(world.id(), group); }
-
- void setAnchor (dReal x, dReal y, dReal z)
- { dJointSetPistonAnchor (get_id(), x, y, z); }
- void setAnchor (const dVector3 a)
- { setAnchor (a[0], a[1], a[2]); }
- void getAnchor (dVector3 result) const
- { dJointGetPistonAnchor (get_id(), result); }
- void getAnchor2 (dVector3 result) const
- { dJointGetPistonAnchor2 (get_id(), result); }
-
- void setAxis (dReal x, dReal y, dReal z)
- { dJointSetPistonAxis (get_id(), x, y, z); }
- void setAxis (const dVector3 a)
- { setAxis(a[0], a[1], a[2]); }
- void getAxis (dVector3 result) const
- { dJointGetPistonAxis (get_id(), result); }
-
- dReal getPosition() const
- { return dJointGetPistonPosition (get_id()); }
- dReal getPositionRate() const
- { return dJointGetPistonPositionRate (get_id()); }
-
- virtual void setParam (int parameter, dReal value)
- { dJointSetPistonParam (get_id(), parameter, value); }
- virtual dReal getParam (int parameter) const
- { return dJointGetPistonParam (get_id(), parameter); }
- // TODO: expose params through methods
-
- void addForce (dReal force)
- { dJointAddPistonForce (get_id(), force); }
-};
-
-
-
-template <class dJointTemplateBase, class dWorldTemplateBase, class dBodyTemplateBase>
-class dFixedJointTemplate : public dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase>
-{
-private:
- // intentionally undefined, don't use these
- dFixedJointTemplate (const dFixedJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
- void operator = (const dFixedJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
-
-protected:
- typedef dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> dBaseTemplate;
-
- dJointID get_id() const { return dBaseTemplate::get_id(); }
- void set_id(dJointID value) { dBaseTemplate::set_id(value); }
-
- void destroy() { dBaseTemplate::destroy(); }
-
-public:
- dFixedJointTemplate() { }
- dFixedJointTemplate (dWorldID world, dJointGroupID group=0)
- { set_id(dJointCreateFixed(world, group)); }
- dFixedJointTemplate (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { set_id(dJointCreateFixed(world, group)); }
-
- void create (dWorldID world, dJointGroupID group=0) {
- destroy();
- set_id(dJointCreateFixed(world, group));
- }
- void create (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { create(world.id(), group); }
-
- void set()
- { dJointSetFixed (get_id()); }
-
- virtual void setParam (int parameter, dReal value)
- { dJointSetFixedParam (get_id(), parameter, value); }
-
- virtual dReal getParam (int parameter) const
- { return dJointGetFixedParam (get_id(), parameter); }
- // TODO: expose params through methods
-};
-
-
-template <class dJointTemplateBase, class dWorldTemplateBase, class dBodyTemplateBase>
-class dContactJointTemplate : public dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> {
-private:
- // intentionally undefined, don't use these
- dContactJointTemplate (const dContactJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
- void operator = (const dContactJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
-
-protected:
- typedef dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> dBaseTemplate;
-
- dJointID get_id() const { return dBaseTemplate::get_id(); }
- void set_id(dJointID value) { dBaseTemplate::set_id(value); }
-
- void destroy() { dBaseTemplate::destroy(); }
-
-public:
- dContactJointTemplate() { }
- dContactJointTemplate (dWorldID world, dJointGroupID group, dContact *contact)
- { set_id(dJointCreateContact(world, group, contact)); }
- dContactJointTemplate (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group, dContact *contact)
- { set_id(dJointCreateContact(world.id(), group, contact)); }
-
- void create (dWorldID world, dJointGroupID group, dContact *contact) {
- destroy();
- set_id(dJointCreateContact(world, group, contact));
- }
-
- void create (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group, dContact *contact)
- { create(world.id(), group, contact); }
-};
-
-
-template <class dJointTemplateBase, class dWorldTemplateBase, class dBodyTemplateBase>
-class dNullJointTemplate : public dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> {
-private:
- // intentionally undefined, don't use these
- dNullJointTemplate (const dNullJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
- void operator = (const dNullJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
-
-protected:
- typedef dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> dBaseTemplate;
-
- dJointID get_id() const { return dBaseTemplate::get_id(); }
- void set_id(dJointID value) { dBaseTemplate::set_id(value); }
-
- void destroy() { dBaseTemplate::destroy(); }
-
-public:
- dNullJointTemplate() { }
- dNullJointTemplate (dWorldID world, dJointGroupID group=0)
- { set_id(dJointCreateNull(world, group)); }
- dNullJointTemplate (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { set_id(dJointCreateNull (world.id(), group)); }
-
- void create (dWorldID world, dJointGroupID group=0) {
- destroy();
- set_id(dJointCreateNull(world, group));
- }
- void create (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { create(world.id(), group); }
-};
-
-
-template <class dJointTemplateBase, class dWorldTemplateBase, class dBodyTemplateBase>
-class dAMotorJointTemplate : public dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> {
-private:
- // intentionally undefined, don't use these
- dAMotorJointTemplate (const dAMotorJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
- void operator = (const dAMotorJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
-
-protected:
- typedef dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> dBaseTemplate;
-
- dJointID get_id() const { return dBaseTemplate::get_id(); }
- void set_id(dJointID value) { dBaseTemplate::set_id(value); }
-
- void destroy() { dBaseTemplate::destroy(); }
-
-public:
- dAMotorJointTemplate() { }
- dAMotorJointTemplate (dWorldID world, dJointGroupID group=0)
- { set_id(dJointCreateAMotor(world, group)); }
- dAMotorJointTemplate (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { set_id(dJointCreateAMotor(world.id(), group)); }
-
- void create (dWorldID world, dJointGroupID group=0) {
- destroy();
- set_id(dJointCreateAMotor(world, group));
- }
- void create (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { create(world.id(), group); }
-
- void setMode (int mode)
- { dJointSetAMotorMode (get_id(), mode); }
- int getMode() const
- { return dJointGetAMotorMode (get_id()); }
-
- void setNumAxes (int num)
- { dJointSetAMotorNumAxes (get_id(), num); }
- int getNumAxes() const
- { return dJointGetAMotorNumAxes (get_id()); }
-
- void setAxis (int anum, int rel, dReal x, dReal y, dReal z)
- { dJointSetAMotorAxis (get_id(), anum, rel, x, y, z); }
- void setAxis (int anum, int rel, const dVector3 a)
- { setAxis(anum, rel, a[0], a[1], a[2]); }
- void getAxis (int anum, dVector3 result) const
- { dJointGetAMotorAxis (get_id(), anum, result); }
- int getAxisRel (int anum) const
- { return dJointGetAMotorAxisRel (get_id(), anum); }
-
- void setAngle (int anum, dReal angle)
- { dJointSetAMotorAngle (get_id(), anum, angle); }
- dReal getAngle (int anum) const
- { return dJointGetAMotorAngle (get_id(), anum); }
- dReal getAngleRate (int anum)
- { return dJointGetAMotorAngleRate (get_id(), anum); }
-
- void setParam (int parameter, dReal value)
- { dJointSetAMotorParam (get_id(), parameter, value); }
- dReal getParam (int parameter) const
- { return dJointGetAMotorParam (get_id(), parameter); }
- // TODO: expose params through methods
-
- void addTorques(dReal torque1, dReal torque2, dReal torque3)
- { dJointAddAMotorTorques(get_id(), torque1, torque2, torque3); }
-};
-
-
-template <class dJointTemplateBase, class dWorldTemplateBase, class dBodyTemplateBase>
-class dLMotorJointTemplate : public dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> {
-private:
- // intentionally undefined, don't use these
- dLMotorJointTemplate (const dLMotorJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
- void operator = (const dLMotorJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> &);
-
-protected:
- typedef dJointTemplate<dJointTemplateBase, dWorldTemplateBase, dBodyTemplateBase> dBaseTemplate;
-
- dJointID get_id() const { return dBaseTemplate::get_id(); }
- void set_id(dJointID value) { dBaseTemplate::set_id(value); }
-
- void destroy() { dBaseTemplate::destroy(); }
-
-public:
- dLMotorJointTemplate() { }
- dLMotorJointTemplate (dWorldID world, dJointGroupID group=0)
- { set_id(dJointCreateLMotor(world, group)); }
- dLMotorJointTemplate (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { set_id(dJointCreateLMotor(world.id(), group)); }
-
- void create (dWorldID world, dJointGroupID group=0) {
- destroy();
- set_id(dJointCreateLMotor(world, group));
- }
- void create (dWorldTemplate<dWorldTemplateBase>& world, dJointGroupID group=0)
- { create(world.id(), group); }
-
- void setNumAxes (int num)
- { dJointSetLMotorNumAxes (get_id(), num); }
- int getNumAxes() const
- { return dJointGetLMotorNumAxes (get_id()); }
-
- void setAxis (int anum, int rel, dReal x, dReal y, dReal z)
- { dJointSetLMotorAxis (get_id(), anum, rel, x, y, z); }
- void setAxis (int anum, int rel, const dVector3 a)
- { setAxis(anum, rel, a[0], a[1], a[2]); }
- void getAxis (int anum, dVector3 result) const
- { dJointGetLMotorAxis (get_id(), anum, result); }
-
- void setParam (int parameter, dReal value)
- { dJointSetLMotorParam (get_id(), parameter, value); }
- dReal getParam (int parameter) const
- { return dJointGetLMotorParam (get_id(), parameter); }
- // TODO: expose params through methods
-};
-
-//}
-
-#if !defined(dODECPP_WORLD_TEMPLATE_BASE)
-
-#if defined(dODECPP_BODY_TEMPLATE_BASE) || defined(dODECPP_JOINTGROUP_TEMPLATE_BASE) || defined(dODECPP_JOINT_TEMPLATE_BASE)
-#error All the odecpp template bases must be defined or not defined together
-#endif
-
-#define dODECPP_WORLD_TEMPLATE_BASE dWorldDynamicIDContainer
-#define dODECPP_BODY_TEMPLATE_BASE dBodyDynamicIDContainer
-#define dODECPP_JOINTGROUP_TEMPLATE_BASE dJointGroupDynamicIDContainer
-#define dODECPP_JOINT_TEMPLATE_BASE dJointDynamicIDContainer
-
-#else // #if defined(dODECPP_WORLD_TEMPLATE_BASE)
-
-#if !defined(dODECPP_BODY_TEMPLATE_BASE) || !defined(dODECPP_JOINTGROUP_TEMPLATE_BASE) || !defined(dODECPP_JOINT_TEMPLATE_BASE)
-#error All the odecpp template bases must be defined or not defined together
-#endif
-
-#endif // #if defined(dODECPP_WORLD_TEMPLATE_BASE)
-
-
-typedef dWorldTemplate<dODECPP_WORLD_TEMPLATE_BASE> dWorld;
-typedef dBodyTemplate<dODECPP_BODY_TEMPLATE_BASE, dODECPP_WORLD_TEMPLATE_BASE> dBody;
-typedef dJointGroupTemplate<dODECPP_JOINTGROUP_TEMPLATE_BASE> dJointGroup;
-typedef dJointTemplate<dODECPP_JOINT_TEMPLATE_BASE, dODECPP_WORLD_TEMPLATE_BASE, dODECPP_BODY_TEMPLATE_BASE> dJoint;
-typedef dBallJointTemplate<dODECPP_JOINT_TEMPLATE_BASE, dODECPP_WORLD_TEMPLATE_BASE, dODECPP_BODY_TEMPLATE_BASE> dBallJoint;
-typedef dHingeJointTemplate<dODECPP_JOINT_TEMPLATE_BASE, dODECPP_WORLD_TEMPLATE_BASE, dODECPP_BODY_TEMPLATE_BASE> dHingeJoint;
-typedef dSliderJointTemplate<dODECPP_JOINT_TEMPLATE_BASE, dODECPP_WORLD_TEMPLATE_BASE, dODECPP_BODY_TEMPLATE_BASE> dSliderJoint;
-typedef dUniversalJointTemplate<dODECPP_JOINT_TEMPLATE_BASE, dODECPP_WORLD_TEMPLATE_BASE, dODECPP_BODY_TEMPLATE_BASE> dUniversalJoint;
-typedef dHinge2JointTemplate<dODECPP_JOINT_TEMPLATE_BASE, dODECPP_WORLD_TEMPLATE_BASE, dODECPP_BODY_TEMPLATE_BASE> dHinge2Joint;
-typedef dPRJointTemplate<dODECPP_JOINT_TEMPLATE_BASE, dODECPP_WORLD_TEMPLATE_BASE, dODECPP_BODY_TEMPLATE_BASE> dPRJoint;
-typedef dPUJointTemplate<dODECPP_JOINT_TEMPLATE_BASE, dODECPP_WORLD_TEMPLATE_BASE, dODECPP_BODY_TEMPLATE_BASE> dPUJoint;
-typedef dPistonJointTemplate<dODECPP_JOINT_TEMPLATE_BASE, dODECPP_WORLD_TEMPLATE_BASE, dODECPP_BODY_TEMPLATE_BASE> dPistonJoint;
-typedef dFixedJointTemplate<dODECPP_JOINT_TEMPLATE_BASE, dODECPP_WORLD_TEMPLATE_BASE, dODECPP_BODY_TEMPLATE_BASE> dFixedJoint;
-typedef dContactJointTemplate<dODECPP_JOINT_TEMPLATE_BASE, dODECPP_WORLD_TEMPLATE_BASE, dODECPP_BODY_TEMPLATE_BASE> dContactJoint;
-typedef dNullJointTemplate<dODECPP_JOINT_TEMPLATE_BASE, dODECPP_WORLD_TEMPLATE_BASE, dODECPP_BODY_TEMPLATE_BASE> dNullJoint;
-typedef dAMotorJointTemplate<dODECPP_JOINT_TEMPLATE_BASE, dODECPP_WORLD_TEMPLATE_BASE, dODECPP_BODY_TEMPLATE_BASE> dAMotorJoint;
-typedef dLMotorJointTemplate<dODECPP_JOINT_TEMPLATE_BASE, dODECPP_WORLD_TEMPLATE_BASE, dODECPP_BODY_TEMPLATE_BASE> dLMotorJoint;
-
-
-#endif
-#endif
-
-// Local variables:
-// mode:c++
-// c-basic-offset:2
-// End:
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-/* C++ interface for new collision API */
-
-
-#ifndef _ODE_ODECPP_COLLISION_H_
-#define _ODE_ODECPP_COLLISION_H_
-#ifdef __cplusplus
-
-//#include <ode/error.h>
-
-//namespace ode {
-
-class dGeom {
- // intentionally undefined, don't use these
- dGeom (dGeom &);
- void operator= (dGeom &);
-
-protected:
- dGeomID _id;
-
- dGeom()
- { _id = 0; }
-public:
- ~dGeom()
- { if (_id) dGeomDestroy (_id); }
-
- dGeomID id() const
- { return _id; }
- operator dGeomID() const
- { return _id; }
-
- void destroy() {
- if (_id) dGeomDestroy (_id);
- _id = 0;
- }
-
- int getClass() const
- { return dGeomGetClass (_id); }
-
- dSpaceID getSpace() const
- { return dGeomGetSpace (_id); }
-
- void setData (void *data)
- { dGeomSetData (_id,data); }
- void *getData() const
- { return dGeomGetData (_id); }
-
- void setBody (dBodyID b)
- { dGeomSetBody (_id,b); }
- dBodyID getBody() const
- { return dGeomGetBody (_id); }
-
- void setPosition (dReal x, dReal y, dReal z)
- { dGeomSetPosition (_id,x,y,z); }
- const dReal * getPosition() const
- { return dGeomGetPosition (_id); }
-
- void setRotation (const dMatrix3 R)
- { dGeomSetRotation (_id,R); }
- const dReal * getRotation() const
- { return dGeomGetRotation (_id); }
-
- void setQuaternion (const dQuaternion quat)
- { dGeomSetQuaternion (_id,quat); }
- void getQuaternion (dQuaternion quat) const
- { dGeomGetQuaternion (_id,quat); }
-
- void getAABB (dReal aabb[6]) const
- { dGeomGetAABB (_id, aabb); }
-
- int isSpace()
- { return dGeomIsSpace (_id); }
-
- void setCategoryBits (unsigned long bits)
- { dGeomSetCategoryBits (_id, bits); }
- void setCollideBits (unsigned long bits)
- { dGeomSetCollideBits (_id, bits); }
- unsigned long getCategoryBits()
- { return dGeomGetCategoryBits (_id); }
- unsigned long getCollideBits()
- { return dGeomGetCollideBits (_id); }
-
- void enable()
- { dGeomEnable (_id); }
- void disable()
- { dGeomDisable (_id); }
- int isEnabled()
- { return dGeomIsEnabled (_id); }
-
- void getRelPointPos (dReal px, dReal py, dReal pz, dVector3 result) const
- { dGeomGetRelPointPos (_id, px, py, pz, result); }
- void getRelPointPos (const dVector3 p, dVector3 result) const
- { getRelPointPos (p[0], p[1], p[2], result); }
-
- void getPosRelPoint (dReal px, dReal py, dReal pz, dVector3 result) const
- { dGeomGetPosRelPoint (_id, px, py, pz, result); }
- void getPosRelPoint (const dVector3 p, dVector3 result) const
- { getPosRelPoint (p[0], p[1], p[2], result); }
-
- void vectorToWorld (dReal px, dReal py, dReal pz, dVector3 result) const
- { dGeomVectorToWorld (_id, px, py, pz, result); }
- void vectorToWorld (const dVector3 p, dVector3 result) const
- { vectorToWorld (p[0], p[1], p[2], result); }
-
- void vectorFromWorld (dReal px, dReal py, dReal pz, dVector3 result) const
- { dGeomVectorFromWorld (_id, px, py, pz, result); }
- void vectorFromWorld (const dVector3 p, dVector3 result) const
- { vectorFromWorld (p[0], p[1], p[2], result); }
-
- void collide2 (dGeomID g, void *data, dNearCallback *callback)
- { dSpaceCollide2 (_id,g,data,callback); }
-};
-
-
-class dSpace : public dGeom {
- // intentionally undefined, don't use these
- dSpace (dSpace &);
- void operator= (dSpace &);
-
-protected:
- // the default constructor is protected so that you
- // can't instance this class. you must instance one
- // of its subclasses instead.
- dSpace () { _id = 0; }
-
-public:
- dSpaceID id() const
- { return (dSpaceID) _id; }
- operator dSpaceID() const
- { return (dSpaceID) _id; }
-
- void setCleanup (int mode)
- { dSpaceSetCleanup (id(), mode); }
- int getCleanup()
- { return dSpaceGetCleanup (id()); }
-
- void add (dGeomID x)
- { dSpaceAdd (id(), x); }
- void remove (dGeomID x)
- { dSpaceRemove (id(), x); }
- int query (dGeomID x)
- { return dSpaceQuery (id(),x); }
-
- int getNumGeoms()
- { return dSpaceGetNumGeoms (id()); }
- dGeomID getGeom (int i)
- { return dSpaceGetGeom (id(),i); }
-
- void collide (void *data, dNearCallback *callback)
- { dSpaceCollide (id(),data,callback); }
-};
-
-
-class dSimpleSpace : public dSpace {
- // intentionally undefined, don't use these
- dSimpleSpace (dSimpleSpace &);
- void operator= (dSimpleSpace &);
-
-public:
- dSimpleSpace ()
- { _id = (dGeomID) dSimpleSpaceCreate (0); }
- dSimpleSpace (dSpace &space)
- { _id = (dGeomID) dSimpleSpaceCreate (space.id()); }
- dSimpleSpace (dSpaceID space)
- { _id = (dGeomID) dSimpleSpaceCreate (space); }
-};
-
-
-class dHashSpace : public dSpace {
- // intentionally undefined, don't use these
- dHashSpace (dHashSpace &);
- void operator= (dHashSpace &);
-
-public:
- dHashSpace ()
- { _id = (dGeomID) dHashSpaceCreate (0); }
- dHashSpace (dSpace &space)
- { _id = (dGeomID) dHashSpaceCreate (space.id()); }
- dHashSpace (dSpaceID space)
- { _id = (dGeomID) dHashSpaceCreate (space); }
-
- void setLevels (int minlevel, int maxlevel)
- { dHashSpaceSetLevels (id(),minlevel,maxlevel); }
-};
-
-
-class dQuadTreeSpace : public dSpace {
- // intentionally undefined, don't use these
- dQuadTreeSpace (dQuadTreeSpace &);
- void operator= (dQuadTreeSpace &);
-
-public:
- dQuadTreeSpace (const dVector3 center, const dVector3 extents, int depth)
- { _id = (dGeomID) dQuadTreeSpaceCreate (0,center,extents,depth); }
- dQuadTreeSpace (dSpace &space, const dVector3 center, const dVector3 extents, int depth)
- { _id = (dGeomID) dQuadTreeSpaceCreate (space.id(),center,extents,depth); }
- dQuadTreeSpace (dSpaceID space, const dVector3 center, const dVector3 extents, int depth)
- { _id = (dGeomID) dQuadTreeSpaceCreate (space,center,extents,depth); }
-};
-
-
-class dSphere : public dGeom {
- // intentionally undefined, don't use these
- dSphere (dSphere &);
- void operator= (dSphere &);
-
-public:
- dSphere () { }
- dSphere (dReal radius)
- { _id = dCreateSphere (0, radius); }
- dSphere (dSpace &space, dReal radius)
- { _id = dCreateSphere (space.id(), radius); }
- dSphere (dSpaceID space, dReal radius)
- { _id = dCreateSphere (space, radius); }
-
- void create (dSpaceID space, dReal radius) {
- if (_id) dGeomDestroy (_id);
- _id = dCreateSphere (space, radius);
- }
-
- void setRadius (dReal radius)
- { dGeomSphereSetRadius (_id, radius); }
- dReal getRadius() const
- { return dGeomSphereGetRadius (_id); }
-};
-
-
-class dBox : public dGeom {
- // intentionally undefined, don't use these
- dBox (dBox &);
- void operator= (dBox &);
-
-public:
- dBox () { }
- dBox (dReal lx, dReal ly, dReal lz)
- { _id = dCreateBox (0,lx,ly,lz); }
- dBox (dSpace &space, dReal lx, dReal ly, dReal lz)
- { _id = dCreateBox (space,lx,ly,lz); }
- dBox (dSpaceID space, dReal lx, dReal ly, dReal lz)
- { _id = dCreateBox (space,lx,ly,lz); }
-
- void create (dSpaceID space, dReal lx, dReal ly, dReal lz) {
- if (_id) dGeomDestroy (_id);
- _id = dCreateBox (space,lx,ly,lz);
- }
-
- void setLengths (dReal lx, dReal ly, dReal lz)
- { dGeomBoxSetLengths (_id, lx, ly, lz); }
- void getLengths (dVector3 result) const
- { dGeomBoxGetLengths (_id,result); }
-};
-
-
-class dPlane : public dGeom {
- // intentionally undefined, don't use these
- dPlane (dPlane &);
- void operator= (dPlane &);
-
-public:
- dPlane() { }
- dPlane (dReal a, dReal b, dReal c, dReal d)
- { _id = dCreatePlane (0,a,b,c,d); }
- dPlane (dSpace &space, dReal a, dReal b, dReal c, dReal d)
- { _id = dCreatePlane (space.id(),a,b,c,d); }
- dPlane (dSpaceID space, dReal a, dReal b, dReal c, dReal d)
- { _id = dCreatePlane (space,a,b,c,d); }
-
- void create (dSpaceID space, dReal a, dReal b, dReal c, dReal d) {
- if (_id) dGeomDestroy (_id);
- _id = dCreatePlane (space,a,b,c,d);
- }
-
- void setParams (dReal a, dReal b, dReal c, dReal d)
- { dGeomPlaneSetParams (_id, a, b, c, d); }
- void getParams (dVector4 result) const
- { dGeomPlaneGetParams (_id,result); }
-};
-
-
-class dCapsule : public dGeom {
- // intentionally undefined, don't use these
- dCapsule (dCapsule &);
- void operator= (dCapsule &);
-
-public:
- dCapsule() { }
- dCapsule (dReal radius, dReal length)
- { _id = dCreateCapsule (0,radius,length); }
- dCapsule (dSpace &space, dReal radius, dReal length)
- { _id = dCreateCapsule (space.id(),radius,length); }
- dCapsule (dSpaceID space, dReal radius, dReal length)
- { _id = dCreateCapsule (space,radius,length); }
-
- void create (dSpaceID space, dReal radius, dReal length) {
- if (_id) dGeomDestroy (_id);
- _id = dCreateCapsule (space,radius,length);
- }
-
- void setParams (dReal radius, dReal length)
- { dGeomCapsuleSetParams (_id, radius, length); }
- void getParams (dReal *radius, dReal *length) const
- { dGeomCapsuleGetParams (_id,radius,length); }
-};
-
-
-class dCylinder : public dGeom {
- // intentionally undefined, don't use these
- dCylinder (dCylinder &);
- void operator= (dCylinder &);
-
-public:
- dCylinder() { }
- dCylinder (dReal radius, dReal length)
- { _id = dCreateCylinder (0,radius,length); }
- dCylinder (dSpace &space, dReal radius, dReal length)
- { _id = dCreateCylinder (space.id(),radius,length); }
- dCylinder (dSpaceID space, dReal radius, dReal length)
- { _id = dCreateCylinder (space,radius,length); }
-
- void create (dSpaceID space, dReal radius, dReal length) {
- if (_id) dGeomDestroy (_id);
- _id = dCreateCylinder (space,radius,length);
- }
-
- void setParams (dReal radius, dReal length)
- { dGeomCylinderSetParams (_id, radius, length); }
- void getParams (dReal *radius, dReal *length) const
- { dGeomCylinderGetParams (_id,radius,length); }
-};
-
-
-class dRay : public dGeom {
- // intentionally undefined, don't use these
- dRay (dRay &);
- void operator= (dRay &);
-
-public:
- dRay() { }
- dRay (dReal length)
- { _id = dCreateRay (0,length); }
- dRay (dSpace &space, dReal length)
- { _id = dCreateRay (space.id(),length); }
- dRay (dSpaceID space, dReal length)
- { _id = dCreateRay (space,length); }
-
- void create (dSpaceID space, dReal length) {
- if (_id) dGeomDestroy (_id);
- _id = dCreateRay (space,length);
- }
-
- void setLength (dReal length)
- { dGeomRaySetLength (_id, length); }
- dReal getLength()
- { return dGeomRayGetLength (_id); }
-
- void set (dReal px, dReal py, dReal pz, dReal dx, dReal dy, dReal dz)
- { dGeomRaySet (_id, px, py, pz, dx, dy, dz); }
- void get (dVector3 start, dVector3 dir)
- { dGeomRayGet (_id, start, dir); }
-
-#ifdef WIN32
-#pragma warning( push )
-#pragma warning( disable : 4996 )
-#else
-#pragma GCC diagnostic push
-#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
-#endif
- ODE_API_DEPRECATED
- void setParams (int firstContact, int backfaceCull)
- { dGeomRaySetParams (_id, firstContact, backfaceCull); }
-
- ODE_API_DEPRECATED
- void getParams (int *firstContact, int *backfaceCull)
- { dGeomRayGetParams (_id, firstContact, backfaceCull); }
-#ifdef WIN32
-#pragma warning( pop )
-#else
-#pragma GCC diagnostic pop
-#endif
- void setBackfaceCull (int backfaceCull)
- { dGeomRaySetBackfaceCull (_id, backfaceCull); }
- int getBackfaceCull()
- { return dGeomRayGetBackfaceCull (_id); }
-
- void setFirstContact (int firstContact)
- { dGeomRaySetFirstContact (_id, firstContact); }
- int getFirstContact()
- { return dGeomRayGetFirstContact (_id); }
-
- void setClosestHit (int closestHit)
- { dGeomRaySetClosestHit (_id, closestHit); }
- int getClosestHit()
- { return dGeomRayGetClosestHit (_id); }
-};
-
-#ifdef WIN32
-#pragma warning( push )
-#pragma warning( disable : 4996 )
-#else
-#pragma GCC diagnostic push
-#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
-#endif
-
-class ODE_API_DEPRECATED dGeomTransform : public dGeom {
- // intentionally undefined, don't use these
- dGeomTransform (dGeomTransform &);
- void operator= (dGeomTransform &);
-
-public:
- dGeomTransform() { }
- dGeomTransform (dSpace &space)
- { _id = dCreateGeomTransform (space.id()); }
- dGeomTransform (dSpaceID space)
- { _id = dCreateGeomTransform (space); }
-
- void create (dSpaceID space=0) {
- if (_id) dGeomDestroy (_id);
- _id = dCreateGeomTransform (space);
- }
-
- void setGeom (dGeomID geom)
- { dGeomTransformSetGeom (_id, geom); }
- dGeomID getGeom() const
- { return dGeomTransformGetGeom (_id); }
-
- void setCleanup (int mode)
- { dGeomTransformSetCleanup (_id,mode); }
- int getCleanup ()
- { return dGeomTransformGetCleanup (_id); }
-
- void setInfo (int mode)
- { dGeomTransformSetInfo (_id,mode); }
- int getInfo()
- { return dGeomTransformGetInfo (_id); }
-};
-
-#ifdef WIN32
-#pragma warning( pop )
-#else
-#pragma GCC diagnostic pop
-#endif
-
-//}
-
-#endif
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-/* Library initialization/finalization functions. */
-
-#ifndef _ODE_ODEINIT_H_
-#define _ODE_ODEINIT_H_
-
-#include <ode/common.h>
-
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-
-/* ************************************************************************ */
-/* Library initialization */
-
-/**
- * @defgroup init Library Initialization
- *
- * Library initialization functions prepare ODE internal data structures for use
- * and release allocated resources after ODE is not needed any more.
- */
-
-
-/**
- * @brief Library initialization flags.
- *
- * These flags define ODE library initialization options.
- *
- * @c dInitFlagManualThreadCleanup indicates that resources allocated in TLS for threads
- * using ODE are to be cleared by library client with explicit call to @c dCleanupODEAllDataForThread.
- * If this flag is not specified the automatic resource tracking algorithm is used.
- *
- * With automatic resource tracking, On Windows, memory allocated for a thread may
- * remain not freed for some time after the thread exits. The resources may be
- * released when one of other threads calls @c dAllocateODEDataForThread. Ultimately,
- * the resources are released when library is closed with @c dCloseODE. On other
- * operating systems resources are always released by the thread itself on its exit
- * or on library closure with @c dCloseODE.
- *
- * With manual thread data cleanup mode every collision space object must be
- * explicitly switched to manual cleanup mode with @c dSpaceSetManualCleanup
- * after creation. See description of the function for more details.
- *
- * If @c dInitFlagManualThreadCleanup was not specified during initialization,
- * calls to @c dCleanupODEAllDataForThread are not allowed.
- *
- * @see dInitODE2
- * @see dAllocateODEDataForThread
- * @see dSpaceSetManualCleanup
- * @see dCloseODE
- * @ingroup init
- */
-enum dInitODEFlags {
- dInitFlagManualThreadCleanup = 0x00000001 /*@< Thread local data is to be cleared explicitly on @c dCleanupODEAllDataForThread function call*/
-};
-
-/**
- * @brief Initializes ODE library.
- *
- * @c dInitODE is obsolete. @c dInitODE2 is to be used for library initialization.
- *
- * A call to @c dInitODE is equal to the following initialization sequence
- * @code
- * dInitODE2(0);
- * dAllocateODEDataForThread(dAllocateMaskAll);
- * @endcode
- *
- * @see dInitODE2
- * @see dAllocateODEDataForThread
- * @ingroup init
- */
-ODE_API void dInitODE(void);
-
-/**
- * @brief Initializes ODE library.
- * @param uiInitFlags Initialization options bitmask
- * @return A nonzero if initialization succeeded and zero otherwise.
- *
- * This function must be called to initialize ODE library before first use. If
- * initialization succeeds the function may not be called again until library is
- * closed with a call to @c dCloseODE.
- *
- * The @a uiInitFlags parameter specifies initialization options to be used. These
- * can be combination of zero or more @c dInitODEFlags flags.
- *
- * @note
- * If @c dInitFlagManualThreadCleanup flag is used for initialization,
- * @c dSpaceSetManualCleanup must be called to set manual cleanup mode for every
- * space object right after creation. Failure to do so may lead to resource leaks.
- *
- * @see dInitODEFlags
- * @see dCloseODE
- * @see dSpaceSetManualCleanup
- * @ingroup init
- */
-ODE_API int dInitODE2(unsigned int uiInitFlags/*=0*/);
-
-
-/**
- * @brief ODE data allocation flags.
- *
- * These flags are used to indicate which data is to be pre-allocated in call to
- * @c dAllocateODEDataForThread.
- *
- * @c dAllocateFlagBasicData tells to allocate the basic data set required for
- * normal library operation. This flag is equal to zero and is always implicitly
- * included.
- *
- * @c dAllocateFlagCollisionData tells that collision detection data is to be allocated.
- * Collision detection functions may not be called if the data has not be allocated
- * in advance. If collision detection is not going to be used, it is not necessary
- * to specify this flag.
- *
- * @c dAllocateMaskAll is a mask that can be used for for allocating all possible
- * data in cases when it is not known what exactly features of ODE will be used.
- * The mask may not be used in combination with other flags. It is guaranteed to
- * include all the current and future legal allocation flags. However, mature
- * applications should use explicit flags they need rather than allocating everything.
- *
- * @see dAllocateODEDataForThread
- * @ingroup init
- */
-enum dAllocateODEDataFlags {
- dAllocateFlagBasicData = 0, /*@< Allocate basic data required for library to operate*/
-
- dAllocateFlagCollisionData = 0x00000001, /*@< Allocate data for collision detection*/
-
- dAllocateMaskAll = ~0 /*@< Allocate all the possible data that is currently defined or will be defined in the future.*/
-};
-
-/**
- * @brief Allocate thread local data to allow the thread calling ODE.
- * @param uiAllocateFlags Allocation options bitmask.
- * @return A nonzero if allocation succeeded and zero otherwise.
- *
- * The function is required to be called for every thread that is going to use
- * ODE. This function allocates the data that is required for accessing ODE from
- * current thread along with optional data required for particular ODE subsystems.
- *
- * @a uiAllocateFlags parameter can contain zero or more flags from @c dAllocateODEDataFlags
- * enumerated type. Multiple calls with different allocation flags are allowed.
- * The flags that are already allocated are ignored in subsequent calls. If zero
- * is passed as the parameter, it means to only allocate the set of most important
- * data the library can not operate without.
- *
- * If the function returns failure status it means that none of the requested
- * data has been allocated. The client may retry allocation attempt with the same
- * flags when more system resources are available.
- *
- * @see dAllocateODEDataFlags
- * @see dCleanupODEAllDataForThread
- * @ingroup init
- */
-ODE_API int dAllocateODEDataForThread(unsigned int uiAllocateFlags);
-
-/**
- * @brief Free thread local data that was allocated for current thread.
- *
- * If library was initialized with @c dInitFlagManualThreadCleanup flag the function
- * is required to be called on exit of every thread that was calling @c dAllocateODEDataForThread.
- * Failure to call @c dCleanupODEAllDataForThread may result in some resources remaining
- * not freed until program exit. The function may also be called when ODE is still
- * being used to release resources allocated for all the current subsystems and
- * possibly proceed with data pre-allocation for other subsystems.
- *
- * The function can safely be called several times in a row. The function can be
- * called without prior invocation of @c dAllocateODEDataForThread. The function
- * may not be called before ODE is initialized with @c dInitODE2 or after library
- * has been closed with @c dCloseODE. A call to @c dCloseODE implicitly releases
- * all the thread local resources that might be allocated for all the threads that
- * were using ODE.
- *
- * If library was initialized without @c dInitFlagManualThreadCleanup flag
- * @c dCleanupODEAllDataForThread must not be called.
- *
- * @see dAllocateODEDataForThread
- * @see dInitODE2
- * @see dCloseODE
- * @ingroup init
- */
-ODE_API void dCleanupODEAllDataForThread();
-
-
-/**
- * @brief Close ODE after it is not needed any more.
- *
- * The function is required to be called when program does not need ODE features any more.
- * The call to @c dCloseODE releases all the resources allocated for library
- * including all the thread local data that might be allocated for all the threads
- * that were using ODE.
- *
- * @c dCloseODE is a paired function for @c dInitODE2 and must only be called
- * after successful library initialization.
- *
- * @note Important!
- * Make sure that all the threads that were using ODE have already terminated
- * before calling @c dCloseODE. In particular it is not allowed to call
- * @c dCleanupODEAllDataForThread after @c dCloseODE.
- *
- * @see dInitODE2
- * @see dCleanupODEAllDataForThread
- * @ingroup init
- */
-ODE_API void dCloseODE(void);
-
-
-
-#ifdef __cplusplus
-} /* extern "C" */
-#endif
-
-
-#endif /* _ODE_ODEINIT_H_ */
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_ODEMATH_H_
-#define _ODE_ODEMATH_H_
-
-#include <ode/common.h>
-
-/*
- * macro to access elements i,j in an NxM matrix A, independent of the
- * matrix storage convention.
- */
-#define dACCESS33(A,i,j) ((A)[(i)*4+(j)])
-
-/*
- * Macro to test for valid floating point values
- */
-#define dVALIDVEC3(v) (!(dIsNan(v[0]) || dIsNan(v[1]) || dIsNan(v[2])))
-#define dVALIDVEC4(v) (!(dIsNan(v[0]) || dIsNan(v[1]) || dIsNan(v[2]) || dIsNan(v[3])))
-#define dVALIDMAT3(m) (!(dIsNan(m[0]) || dIsNan(m[1]) || dIsNan(m[2]) || dIsNan(m[3]) || dIsNan(m[4]) || dIsNan(m[5]) || dIsNan(m[6]) || dIsNan(m[7]) || dIsNan(m[8]) || dIsNan(m[9]) || dIsNan(m[10]) || dIsNan(m[11])))
-#define dVALIDMAT4(m) (!(dIsNan(m[0]) || dIsNan(m[1]) || dIsNan(m[2]) || dIsNan(m[3]) || dIsNan(m[4]) || dIsNan(m[5]) || dIsNan(m[6]) || dIsNan(m[7]) || dIsNan(m[8]) || dIsNan(m[9]) || dIsNan(m[10]) || dIsNan(m[11]) || dIsNan(m[12]) || dIsNan(m[13]) || dIsNan(m[14]) || dIsNan(m[15]) ))
-
-
-ODE_PURE_INLINE void dZeroVector3(dVector3 res)
-{
- res[dV3E_X] = REAL(0.0);
- res[dV3E_Y] = REAL(0.0);
- res[dV3E_Z] = REAL(0.0);
-}
-
-ODE_PURE_INLINE void dAssignVector3(dVector3 res, dReal x, dReal y, dReal z)
-{
- res[dV3E_X] = x;
- res[dV3E_Y] = y;
- res[dV3E_Z] = z;
-}
-
-ODE_PURE_INLINE void dZeroMatrix3(dMatrix3 res)
-{
- res[dM3E_XX] = REAL(0.0); res[dM3E_XY] = REAL(0.0); res[dM3E_XZ] = REAL(0.0);
- res[dM3E_YX] = REAL(0.0); res[dM3E_YY] = REAL(0.0); res[dM3E_YZ] = REAL(0.0);
- res[dM3E_ZX] = REAL(0.0); res[dM3E_ZY] = REAL(0.0); res[dM3E_ZZ] = REAL(0.0);
-}
-
-ODE_PURE_INLINE void dZeroMatrix4(dMatrix4 res)
-{
- res[dM4E_XX] = REAL(0.0); res[dM4E_XY] = REAL(0.0); res[dM4E_XZ] = REAL(0.0); res[dM4E_XO] = REAL(0.0);
- res[dM4E_YX] = REAL(0.0); res[dM4E_YY] = REAL(0.0); res[dM4E_YZ] = REAL(0.0); res[dM4E_YO] = REAL(0.0);
- res[dM4E_ZX] = REAL(0.0); res[dM4E_ZY] = REAL(0.0); res[dM4E_ZZ] = REAL(0.0); res[dM4E_ZO] = REAL(0.0);
- res[dM4E_OX] = REAL(0.0); res[dM4E_OY] = REAL(0.0); res[dM4E_OZ] = REAL(0.0); res[dM4E_OO] = REAL(0.0);
-}
-
-/* Some vector math */
-ODE_PURE_INLINE void dAddVectors3(dReal *res, const dReal *a, const dReal *b)
-{
- const dReal res_0 = a[0] + b[0];
- const dReal res_1 = a[1] + b[1];
- const dReal res_2 = a[2] + b[2];
- /* Only assign after all the calculations are over to avoid incurring memory aliasing*/
- res[0] = res_0; res[1] = res_1; res[2] = res_2;
-}
-
-ODE_PURE_INLINE void dSubtractVectors3(dReal *res, const dReal *a, const dReal *b)
-{
- const dReal res_0 = a[0] - b[0];
- const dReal res_1 = a[1] - b[1];
- const dReal res_2 = a[2] - b[2];
- /* Only assign after all the calculations are over to avoid incurring memory aliasing*/
- res[0] = res_0; res[1] = res_1; res[2] = res_2;
-}
-
-ODE_PURE_INLINE void dAddVectorScaledVector3(dReal *res, const dReal *a, const dReal *b, dReal b_scale)
-{
- const dReal res_0 = a[0] + b_scale * b[0];
- const dReal res_1 = a[1] + b_scale * b[1];
- const dReal res_2 = a[2] + b_scale * b[2];
- /* Only assign after all the calculations are over to avoid incurring memory aliasing*/
- res[0] = res_0; res[1] = res_1; res[2] = res_2;
-}
-
-ODE_PURE_INLINE void dAddScaledVectors3(dReal *res, const dReal *a, const dReal *b, dReal a_scale, dReal b_scale)
-{
- const dReal res_0 = a_scale * a[0] + b_scale * b[0];
- const dReal res_1 = a_scale * a[1] + b_scale * b[1];
- const dReal res_2 = a_scale * a[2] + b_scale * b[2];
- /* Only assign after all the calculations are over to avoid incurring memory aliasing*/
- res[0] = res_0; res[1] = res_1; res[2] = res_2;
-}
-
-ODE_PURE_INLINE void dAddThreeScaledVectors3(dReal *res, const dReal *a, const dReal *b, const dReal *c, dReal a_scale, dReal b_scale, dReal c_scale)
-{
- const dReal res_0 = a_scale * a[0] + b_scale * b[0] + c_scale * c[0];
- const dReal res_1 = a_scale * a[1] + b_scale * b[1] + c_scale * c[1];
- const dReal res_2 = a_scale * a[2] + b_scale * b[2] + c_scale * c[2];
- /* Only assign after all the calculations are over to avoid incurring memory aliasing*/
- res[0] = res_0; res[1] = res_1; res[2] = res_2;
-}
-
-ODE_PURE_INLINE void dScaleVector3(dReal *res, dReal nScale)
-{
- res[0] *= nScale ;
- res[1] *= nScale ;
- res[2] *= nScale ;
-}
-
-ODE_PURE_INLINE void dNegateVector3(dReal *res)
-{
- res[0] = -res[0];
- res[1] = -res[1];
- res[2] = -res[2];
-}
-
-ODE_PURE_INLINE void dCopyVector3(dReal *res, const dReal *a)
-{
- const dReal res_0 = a[0];
- const dReal res_1 = a[1];
- const dReal res_2 = a[2];
- /* Only assign after all the calculations are over to avoid incurring memory aliasing*/
- res[0] = res_0; res[1] = res_1; res[2] = res_2;
-}
-
-ODE_PURE_INLINE void dCopyScaledVector3(dReal *res, const dReal *a, dReal nScale)
-{
- const dReal res_0 = a[0] * nScale;
- const dReal res_1 = a[1] * nScale;
- const dReal res_2 = a[2] * nScale;
- /* Only assign after all the calculations are over to avoid incurring memory aliasing*/
- res[0] = res_0; res[1] = res_1; res[2] = res_2;
-}
-
-ODE_PURE_INLINE void dCopyNegatedVector3(dReal *res, const dReal *a)
-{
- const dReal res_0 = -a[0];
- const dReal res_1 = -a[1];
- const dReal res_2 = -a[2];
- /* Only assign after all the calculations are over to avoid incurring memory aliasing*/
- res[0] = res_0; res[1] = res_1; res[2] = res_2;
-}
-
-ODE_PURE_INLINE void dCopyVector4(dReal *res, const dReal *a)
-{
- const dReal res_0 = a[0];
- const dReal res_1 = a[1];
- const dReal res_2 = a[2];
- const dReal res_3 = a[3];
- /* Only assign after all the calculations are over to avoid incurring memory aliasing*/
- res[0] = res_0; res[1] = res_1; res[2] = res_2; res[3] = res_3;
-}
-
-ODE_PURE_INLINE void dCopyMatrix4x4(dReal *res, const dReal *a)
-{
- dCopyVector4(res + 0, a + 0);
- dCopyVector4(res + 4, a + 4);
- dCopyVector4(res + 8, a + 8);
-}
-
-ODE_PURE_INLINE void dCopyMatrix4x3(dReal *res, const dReal *a)
-{
- dCopyVector3(res + 0, a + 0);
- dCopyVector3(res + 4, a + 4);
- dCopyVector3(res + 8, a + 8);
-}
-
-ODE_PURE_INLINE void dGetMatrixColumn3(dReal *res, const dReal *a, unsigned n)
-{
- const dReal res_0 = a[n + 0];
- const dReal res_1 = a[n + 4];
- const dReal res_2 = a[n + 8];
- /* Only assign after all the calculations are over to avoid incurring memory aliasing*/
- res[0] = res_0; res[1] = res_1; res[2] = res_2;
-}
-
-ODE_PURE_INLINE dReal dCalcVectorLength3(const dReal *a)
-{
- return dSqrt(a[0] * a[0] + a[1] * a[1] + a[2] * a[2]);
-}
-
-ODE_PURE_INLINE dReal dCalcVectorLengthSquare3(const dReal *a)
-{
- return (a[0] * a[0] + a[1] * a[1] + a[2] * a[2]);
-}
-
-ODE_PURE_INLINE dReal dCalcPointDepth3(const dReal *test_p, const dReal *plane_p, const dReal *plane_n)
-{
- return (plane_p[0] - test_p[0]) * plane_n[0] + (plane_p[1] - test_p[1]) * plane_n[1] + (plane_p[2] - test_p[2]) * plane_n[2];
-}
-
-
-/*
-* 3-way dot product. _dCalcVectorDot3 means that elements of `a' and `b' are spaced
-* step_a and step_b indexes apart respectively. dCalcVectorDot3() means dDot311.
-*/
-
-ODE_PURE_INLINE dReal _dCalcVectorDot3(const dReal *a, const dReal *b, unsigned step_a, unsigned step_b)
-{
- return a[0] * b[0] + a[step_a] * b[step_b] + a[2 * step_a] * b[2 * step_b];
-}
-
-
-ODE_PURE_INLINE dReal dCalcVectorDot3 (const dReal *a, const dReal *b) { return _dCalcVectorDot3(a,b,1,1); }
-ODE_PURE_INLINE dReal dCalcVectorDot3_13 (const dReal *a, const dReal *b) { return _dCalcVectorDot3(a,b,1,3); }
-ODE_PURE_INLINE dReal dCalcVectorDot3_31 (const dReal *a, const dReal *b) { return _dCalcVectorDot3(a,b,3,1); }
-ODE_PURE_INLINE dReal dCalcVectorDot3_33 (const dReal *a, const dReal *b) { return _dCalcVectorDot3(a,b,3,3); }
-ODE_PURE_INLINE dReal dCalcVectorDot3_14 (const dReal *a, const dReal *b) { return _dCalcVectorDot3(a,b,1,4); }
-ODE_PURE_INLINE dReal dCalcVectorDot3_41 (const dReal *a, const dReal *b) { return _dCalcVectorDot3(a,b,4,1); }
-ODE_PURE_INLINE dReal dCalcVectorDot3_44 (const dReal *a, const dReal *b) { return _dCalcVectorDot3(a,b,4,4); }
-
-
-/*
- * cross product, set res = a x b. _dCalcVectorCross3 means that elements of `res', `a'
- * and `b' are spaced step_res, step_a and step_b indexes apart respectively.
- * dCalcVectorCross3() means dCross3111.
- */
-
-ODE_PURE_INLINE void _dCalcVectorCross3(dReal *res, const dReal *a, const dReal *b, unsigned step_res, unsigned step_a, unsigned step_b)
-{
- const dReal res_0 = a[ step_a]*b[2*step_b] - a[2*step_a]*b[ step_b];
- const dReal res_1 = a[2*step_a]*b[ 0] - a[ 0]*b[2*step_b];
- const dReal res_2 = a[ 0]*b[ step_b] - a[ step_a]*b[ 0];
- /* Only assign after all the calculations are over to avoid incurring memory aliasing*/
- res[ 0] = res_0;
- res[ step_res] = res_1;
- res[2*step_res] = res_2;
-}
-
-ODE_PURE_INLINE void dCalcVectorCross3 (dReal *res, const dReal *a, const dReal *b) { _dCalcVectorCross3(res, a, b, 1, 1, 1); }
-ODE_PURE_INLINE void dCalcVectorCross3_114(dReal *res, const dReal *a, const dReal *b) { _dCalcVectorCross3(res, a, b, 1, 1, 4); }
-ODE_PURE_INLINE void dCalcVectorCross3_141(dReal *res, const dReal *a, const dReal *b) { _dCalcVectorCross3(res, a, b, 1, 4, 1); }
-ODE_PURE_INLINE void dCalcVectorCross3_144(dReal *res, const dReal *a, const dReal *b) { _dCalcVectorCross3(res, a, b, 1, 4, 4); }
-ODE_PURE_INLINE void dCalcVectorCross3_411(dReal *res, const dReal *a, const dReal *b) { _dCalcVectorCross3(res, a, b, 4, 1, 1); }
-ODE_PURE_INLINE void dCalcVectorCross3_414(dReal *res, const dReal *a, const dReal *b) { _dCalcVectorCross3(res, a, b, 4, 1, 4); }
-ODE_PURE_INLINE void dCalcVectorCross3_441(dReal *res, const dReal *a, const dReal *b) { _dCalcVectorCross3(res, a, b, 4, 4, 1); }
-ODE_PURE_INLINE void dCalcVectorCross3_444(dReal *res, const dReal *a, const dReal *b) { _dCalcVectorCross3(res, a, b, 4, 4, 4); }
-
-ODE_PURE_INLINE void dAddVectorCross3(dReal *res, const dReal *a, const dReal *b)
-{
- dReal tmp[3];
- dCalcVectorCross3(tmp, a, b);
- dAddVectors3(res, res, tmp);
-}
-
-ODE_PURE_INLINE void dSubtractVectorCross3(dReal *res, const dReal *a, const dReal *b)
-{
- dReal tmp[3];
- dCalcVectorCross3(tmp, a, b);
- dSubtractVectors3(res, res, tmp);
-}
-
-
-/*
- * set a 3x3 submatrix of A to a matrix such that submatrix(A)*b = a x b.
- * A is stored by rows, and has `skip' elements per row. the matrix is
- * assumed to be already zero, so this does not write zero elements!
- * if (plus,minus) is (+,-) then a positive version will be written.
- * if (plus,minus) is (-,+) then a negative version will be written.
- */
-
-ODE_PURE_INLINE void dSetCrossMatrixPlus(dReal *res, const dReal *a, unsigned skip)
-{
- const dReal a_0 = a[0], a_1 = a[1], a_2 = a[2];
- res[1] = -a_2;
- res[2] = +a_1;
- res[skip+0] = +a_2;
- res[skip+2] = -a_0;
- res[2*skip+0] = -a_1;
- res[2*skip+1] = +a_0;
-}
-
-ODE_PURE_INLINE void dSetCrossMatrixMinus(dReal *res, const dReal *a, unsigned skip)
-{
- const dReal a_0 = a[0], a_1 = a[1], a_2 = a[2];
- res[1] = +a_2;
- res[2] = -a_1;
- res[skip+0] = -a_2;
- res[skip+2] = +a_0;
- res[2*skip+0] = +a_1;
- res[2*skip+1] = -a_0;
-}
-
-
-/*
- * compute the distance between two 3D-vectors
- */
-
-ODE_PURE_INLINE dReal dCalcPointsDistance3(const dReal *a, const dReal *b)
-{
- dReal res;
- dReal tmp[3];
- dSubtractVectors3(tmp, a, b);
- res = dCalcVectorLength3(tmp);
- return res;
-}
-
-/*
- * special case matrix multiplication, with operator selection
- */
-
-ODE_PURE_INLINE void dMultiplyHelper0_331(dReal *res, const dReal *a, const dReal *b)
-{
- const dReal res_0 = dCalcVectorDot3(a, b);
- const dReal res_1 = dCalcVectorDot3(a + 4, b);
- const dReal res_2 = dCalcVectorDot3(a + 8, b);
- /* Only assign after all the calculations are over to avoid incurring memory aliasing*/
- res[0] = res_0; res[1] = res_1; res[2] = res_2;
-}
-
-ODE_PURE_INLINE void dMultiplyHelper1_331(dReal *res, const dReal *a, const dReal *b)
-{
- const dReal res_0 = dCalcVectorDot3_41(a, b);
- const dReal res_1 = dCalcVectorDot3_41(a + 1, b);
- const dReal res_2 = dCalcVectorDot3_41(a + 2, b);
- /* Only assign after all the calculations are over to avoid incurring memory aliasing*/
- res[0] = res_0; res[1] = res_1; res[2] = res_2;
-}
-
-ODE_PURE_INLINE void dMultiplyHelper0_133(dReal *res, const dReal *a, const dReal *b)
-{
- dMultiplyHelper1_331(res, b, a);
-}
-
-ODE_PURE_INLINE void dMultiplyHelper1_133(dReal *res, const dReal *a, const dReal *b)
-{
- const dReal res_0 = dCalcVectorDot3_44(a, b);
- const dReal res_1 = dCalcVectorDot3_44(a + 1, b);
- const dReal res_2 = dCalcVectorDot3_44(a + 2, b);
- /* Only assign after all the calculations are over to avoid incurring memory aliasing*/
- res[0] = res_0; res[1] = res_1; res[2] = res_2;
-}
-
-/*
-Note: NEVER call any of these functions/macros with the same variable for A and C,
-it is not equivalent to A*=B.
-*/
-
-ODE_PURE_INLINE void dMultiply0_331(dReal *res, const dReal *a, const dReal *b)
-{
- dMultiplyHelper0_331(res, a, b);
-}
-
-ODE_PURE_INLINE void dMultiply1_331(dReal *res, const dReal *a, const dReal *b)
-{
- dMultiplyHelper1_331(res, a, b);
-}
-
-ODE_PURE_INLINE void dMultiply0_133(dReal *res, const dReal *a, const dReal *b)
-{
- dMultiplyHelper0_133(res, a, b);
-}
-
-ODE_PURE_INLINE void dMultiply0_333(dReal *res, const dReal *a, const dReal *b)
-{
- dMultiplyHelper0_133(res + 0, a + 0, b);
- dMultiplyHelper0_133(res + 4, a + 4, b);
- dMultiplyHelper0_133(res + 8, a + 8, b);
-}
-
-ODE_PURE_INLINE void dMultiply1_333(dReal *res, const dReal *a, const dReal *b)
-{
- dMultiplyHelper1_133(res + 0, b, a + 0);
- dMultiplyHelper1_133(res + 4, b, a + 1);
- dMultiplyHelper1_133(res + 8, b, a + 2);
-}
-
-ODE_PURE_INLINE void dMultiply2_333(dReal *res, const dReal *a, const dReal *b)
-{
- dMultiplyHelper0_331(res + 0, b, a + 0);
- dMultiplyHelper0_331(res + 4, b, a + 4);
- dMultiplyHelper0_331(res + 8, b, a + 8);
-}
-
-ODE_PURE_INLINE void dMultiplyAdd0_331(dReal *res, const dReal *a, const dReal *b)
-{
- dReal tmp[3];
- dMultiplyHelper0_331(tmp, a, b);
- dAddVectors3(res, res, tmp);
-}
-
-ODE_PURE_INLINE void dMultiplyAdd1_331(dReal *res, const dReal *a, const dReal *b)
-{
- dReal tmp[3];
- dMultiplyHelper1_331(tmp, a, b);
- dAddVectors3(res, res, tmp);
-}
-
-ODE_PURE_INLINE void dMultiplyAdd0_133(dReal *res, const dReal *a, const dReal *b)
-{
- dReal tmp[3];
- dMultiplyHelper0_133(tmp, a, b);
- dAddVectors3(res, res, tmp);
-}
-
-ODE_PURE_INLINE void dMultiplyAdd0_333(dReal *res, const dReal *a, const dReal *b)
-{
- dReal tmp[3];
- dMultiplyHelper0_133(tmp, a + 0, b);
- dAddVectors3(res+ 0, res + 0, tmp);
- dMultiplyHelper0_133(tmp, a + 4, b);
- dAddVectors3(res + 4, res + 4, tmp);
- dMultiplyHelper0_133(tmp, a + 8, b);
- dAddVectors3(res + 8, res + 8, tmp);
-}
-
-ODE_PURE_INLINE void dMultiplyAdd1_333(dReal *res, const dReal *a, const dReal *b)
-{
- dReal tmp[3];
- dMultiplyHelper1_133(tmp, b, a + 0);
- dAddVectors3(res + 0, res + 0, tmp);
- dMultiplyHelper1_133(tmp, b, a + 1);
- dAddVectors3(res + 4, res + 4, tmp);
- dMultiplyHelper1_133(tmp, b, a + 2);
- dAddVectors3(res + 8, res + 8, tmp);
-}
-
-ODE_PURE_INLINE void dMultiplyAdd2_333(dReal *res, const dReal *a, const dReal *b)
-{
- dReal tmp[3];
- dMultiplyHelper0_331(tmp, b, a + 0);
- dAddVectors3(res + 0, res + 0, tmp);
- dMultiplyHelper0_331(tmp, b, a + 4);
- dAddVectors3(res + 4, res + 4, tmp);
- dMultiplyHelper0_331(tmp, b, a + 8);
- dAddVectors3(res + 8, res + 8, tmp);
-}
-
-ODE_PURE_INLINE dReal dCalcMatrix3Det( const dReal* mat )
-{
- dReal det;
-
- det = mat[0] * ( mat[5]*mat[10] - mat[9]*mat[6] )
- - mat[1] * ( mat[4]*mat[10] - mat[8]*mat[6] )
- + mat[2] * ( mat[4]*mat[9] - mat[8]*mat[5] );
-
- return( det );
-}
-
-/**
- Closed form matrix inversion, copied from
- collision_util.h for use in the stepper.
-
- Returns the determinant.
- returns 0 and does nothing
- if the matrix is singular.
-*/
-ODE_PURE_INLINE dReal dInvertMatrix3(dReal *dst, const dReal *ma)
-{
- dReal det;
- dReal detRecip;
-
- det = dCalcMatrix3Det( ma );
-
-
- /* Setting an arbitrary non-zero threshold
- for the determinant doesn't do anyone
- any favors. The condition number is the
- important thing. If all the eigen-values
- of the matrix are small, so is the
- determinant, but it can still be well
- conditioned.
- A single extremely large eigen-value could
- push the determinant over threshold, but
- produce a very unstable result if the other
- eigen-values are small. So we just say that
- the determinant must be non-zero and trust the
- caller to provide well-conditioned matrices.
- */
- if ( det == 0 )
- {
- return 0;
- }
-
- detRecip = dRecip(det);
-
- dst[0] = ( ma[5]*ma[10] - ma[6]*ma[9] ) * detRecip;
- dst[1] = ( ma[9]*ma[2] - ma[1]*ma[10] ) * detRecip;
- dst[2] = ( ma[1]*ma[6] - ma[5]*ma[2] ) * detRecip;
-
- dst[4] = ( ma[6]*ma[8] - ma[4]*ma[10] ) * detRecip;
- dst[5] = ( ma[0]*ma[10] - ma[8]*ma[2] ) * detRecip;
- dst[6] = ( ma[4]*ma[2] - ma[0]*ma[6] ) * detRecip;
-
- dst[8] = ( ma[4]*ma[9] - ma[8]*ma[5] ) * detRecip;
- dst[9] = ( ma[8]*ma[1] - ma[0]*ma[9] ) * detRecip;
- dst[10] = ( ma[0]*ma[5] - ma[1]*ma[4] ) * detRecip;
-
- return det;
-}
-
-
-/* Include legacy macros here */
-#include <ode/odemath_legacy.h>
-
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-/*
- * normalize 3x1 and 4x1 vectors (i.e. scale them to unit length)
- */
-
-/* For DLL export*/
-ODE_API int dSafeNormalize3 (dVector3 a);
-ODE_API int dSafeNormalize4 (dVector4 a);
-ODE_API void dNormalize3 (dVector3 a); /* Potentially asserts on zero vec*/
-ODE_API void dNormalize4 (dVector4 a); /* Potentially asserts on zero vec*/
-
-/*
- * given a unit length "normal" vector n, generate vectors p and q vectors
- * that are an orthonormal basis for the plane space perpendicular to n.
- * i.e. this makes p,q such that n,p,q are all perpendicular to each other.
- * q will equal n x p. if n is not unit length then p will be unit length but
- * q wont be.
- */
-
-ODE_API void dPlaneSpace (const dVector3 n, dVector3 p, dVector3 q);
-/* Makes sure the matrix is a proper rotation, returns a boolean status */
-ODE_API int dOrthogonalizeR(dMatrix3 m);
-
-
-
-#ifdef __cplusplus
-}
-#endif
-
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_ODEMATH_LEGACY_H_
-#define _ODE_ODEMATH_LEGACY_H_
-
-
-/*
- * These macros are not used any more inside of ODE
- * They are kept for backward compatibility with external code that
- * might still be using them.
- */
-
-/*
- * General purpose vector operations with other vectors or constants.
- */
-
-#define dOP(a,op,b,c) do { \
- (a)[0] = ((b)[0]) op ((c)[0]); \
- (a)[1] = ((b)[1]) op ((c)[1]); \
- (a)[2] = ((b)[2]) op ((c)[2]); \
-} while (0)
-#define dOPC(a,op,b,c) do { \
- (a)[0] = ((b)[0]) op (c); \
- (a)[1] = ((b)[1]) op (c); \
- (a)[2] = ((b)[2]) op (c); \
-} while (0)
-#define dOPE(a,op,b) do {\
- (a)[0] op ((b)[0]); \
- (a)[1] op ((b)[1]); \
- (a)[2] op ((b)[2]); \
-} while (0)
-#define dOPEC(a,op,c) do { \
- (a)[0] op (c); \
- (a)[1] op (c); \
- (a)[2] op (c); \
-} while (0)
-
-/* Define an equation with operators
- * For example this function can be used to replace
- * <PRE>
- * for (int i=0; i<3; ++i)
- * a[i] += b[i] + c[i];
- * </PRE>
- */
-#define dOPE2(a,op1,b,op2,c) do { \
- (a)[0] op1 ((b)[0]) op2 ((c)[0]); \
- (a)[1] op1 ((b)[1]) op2 ((c)[1]); \
- (a)[2] op1 ((b)[2]) op2 ((c)[2]); \
-} while (0)
-
-
-#define dLENGTHSQUARED(a) dCalcVectorLengthSquare3(a)
-#define dLENGTH(a) dCalcVectorLength3(a)
-#define dDISTANCE(a, b) dCalcPointsDistance3(a, b)
-
-
-#define dDOT(a, b) dCalcVectorDot3(a, b)
-#define dDOT13(a, b) dCalcVectorDot3_13(a, b)
-#define dDOT31(a, b) dCalcVectorDot3_31(a, b)
-#define dDOT33(a, b) dCalcVectorDot3_33(a, b)
-#define dDOT14(a, b) dCalcVectorDot3_14(a, b)
-#define dDOT41(a, b) dCalcVectorDot3_41(a, b)
-#define dDOT44(a, b) dCalcVectorDot3_44(a, b)
-
-
-/*
- * cross product, set a = b x c. dCROSSpqr means that elements of `a', `b'
- * and `c' are spaced p, q and r indexes apart respectively.
- * dCROSS() means dCROSS111. `op' is normally `=', but you can set it to
- * +=, -= etc to get other effects.
- */
-
-#define dCROSS(a,op,b,c) \
- do { \
- (a)[0] op ((b)[1]*(c)[2] - (b)[2]*(c)[1]); \
- (a)[1] op ((b)[2]*(c)[0] - (b)[0]*(c)[2]); \
- (a)[2] op ((b)[0]*(c)[1] - (b)[1]*(c)[0]); \
- } while(0)
-#define dCROSSpqr(a,op,b,c,p,q,r) \
- do { \
- (a)[ 0] op ((b)[ q]*(c)[2*r] - (b)[2*q]*(c)[ r]); \
- (a)[ p] op ((b)[2*q]*(c)[ 0] - (b)[ 0]*(c)[2*r]); \
- (a)[2*p] op ((b)[ 0]*(c)[ r] - (b)[ q]*(c)[ 0]); \
- } while(0)
-#define dCROSS114(a,op,b,c) dCROSSpqr(a,op,b,c,1,1,4)
-#define dCROSS141(a,op,b,c) dCROSSpqr(a,op,b,c,1,4,1)
-#define dCROSS144(a,op,b,c) dCROSSpqr(a,op,b,c,1,4,4)
-#define dCROSS411(a,op,b,c) dCROSSpqr(a,op,b,c,4,1,1)
-#define dCROSS414(a,op,b,c) dCROSSpqr(a,op,b,c,4,1,4)
-#define dCROSS441(a,op,b,c) dCROSSpqr(a,op,b,c,4,4,1)
-#define dCROSS444(a,op,b,c) dCROSSpqr(a,op,b,c,4,4,4)
-
-
-/*
-* set a 3x3 submatrix of A to a matrix such that submatrix(A)*b = a x b.
-* A is stored by rows, and has `skip' elements per row. the matrix is
-* assumed to be already zero, so this does not write zero elements!
-* if (plus,minus) is (+,-) then a positive version will be written.
-* if (plus,minus) is (-,+) then a negative version will be written.
-*/
-
-#define dCROSSMAT(A,a,skip,plus,minus) \
- do { \
- (A)[1] = minus (a)[2]; \
- (A)[2] = plus (a)[1]; \
- (A)[(skip)+0] = plus (a)[2]; \
- (A)[(skip)+2] = minus (a)[0]; \
- (A)[2*(skip)+0] = minus (a)[1]; \
- (A)[2*(skip)+1] = plus (a)[0]; \
- } while(0)
-
-
-
-
-/*
-Note: NEVER call any of these functions/macros with the same variable for A and C,
-it is not equivalent to A*=B.
-*/
-
-#define dMULTIPLY0_331(A, B, C) dMultiply0_331(A, B, C)
-#define dMULTIPLY1_331(A, B, C) dMultiply1_331(A, B, C)
-#define dMULTIPLY0_133(A, B, C) dMultiply0_133(A, B, C)
-#define dMULTIPLY0_333(A, B, C) dMultiply0_333(A, B, C)
-#define dMULTIPLY1_333(A, B, C) dMultiply1_333(A, B, C)
-#define dMULTIPLY2_333(A, B, C) dMultiply2_333(A, B, C)
-
-#define dMULTIPLYADD0_331(A, B, C) dMultiplyAdd0_331(A, B, C)
-#define dMULTIPLYADD1_331(A, B, C) dMultiplyAdd1_331(A, B, C)
-#define dMULTIPLYADD0_133(A, B, C) dMultiplyAdd0_133(A, B, C)
-#define dMULTIPLYADD0_333(A, B, C) dMultiplyAdd0_333(A, B, C)
-#define dMULTIPLYADD1_333(A, B, C) dMultiplyAdd1_333(A, B, C)
-#define dMULTIPLYADD2_333(A, B, C) dMultiplyAdd2_333(A, B, C)
-
-
-/*
- * These macros are not used any more inside of ODE
- * They are kept for backward compatibility with external code that
- * might still be using them.
- */
-
-
-#endif /* #ifndef _ODE_ODEMATH_LEGACY_H_ */
+++ /dev/null
-#ifndef _ODE_PRECISION_H_
-#define _ODE_PRECISION_H_
-
-/* Define dSINGLE for single precision, dDOUBLE for double precision,
- * but never both!
- */
-
-#if defined(dIDESINGLE)
-#define dSINGLE
-#elif defined(dIDEDOUBLE)
-#define dDOUBLE
-#else
-#define dDOUBLE
-#endif
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_ROTATION_H_
-#define _ODE_ROTATION_H_
-
-#include <ode/common.h>
-#include <ode/compatibility.h>
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-
-ODE_API void dRSetIdentity (dMatrix3 R);
-
-ODE_API void dRFromAxisAndAngle (dMatrix3 R, dReal ax, dReal ay, dReal az,
- dReal angle);
-
-ODE_API void dRFromEulerAngles (dMatrix3 R, dReal phi, dReal theta, dReal psi);
-
-ODE_API void dRFrom2Axes (dMatrix3 R, dReal ax, dReal ay, dReal az,
- dReal bx, dReal by, dReal bz);
-
-ODE_API void dRFromZAxis (dMatrix3 R, dReal ax, dReal ay, dReal az);
-
-ODE_API void dQSetIdentity (dQuaternion q);
-
-ODE_API void dQFromAxisAndAngle (dQuaternion q, dReal ax, dReal ay, dReal az,
- dReal angle);
-
-/* Quaternion multiplication, analogous to the matrix multiplication routines. */
-/* qa = rotate by qc, then qb */
-ODE_API void dQMultiply0 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc);
-/* qa = rotate by qc, then by inverse of qb */
-ODE_API void dQMultiply1 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc);
-/* qa = rotate by inverse of qc, then by qb */
-ODE_API void dQMultiply2 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc);
-/* qa = rotate by inverse of qc, then by inverse of qb */
-ODE_API void dQMultiply3 (dQuaternion qa, const dQuaternion qb, const dQuaternion qc);
-
-ODE_API void dRfromQ (dMatrix3 R, const dQuaternion q);
-ODE_API void dQfromR (dQuaternion q, const dMatrix3 R);
-ODE_API void dDQfromW (dReal dq[4], const dVector3 w, const dQuaternion q);
-
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * Threading support header file. *
- * Copyright (C) 2011-2019 Oleh Derevenko. All rights reserved. *
- * e-mail: odar@eleks.com (change all "a" to "e") *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-/*
- * ODE threading support interfaces
- */
-
-
-#ifndef _ODE_THREADING_H_
-#define _ODE_THREADING_H_
-
-#include <ode/odeconfig.h>
-// Include <time.h> since time_t is used and it is not available by default in some OSes
-#include <time.h>
-
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-
-struct dxThreadingImplementation;
-typedef struct dxThreadingImplementation *dThreadingImplementationID;
-
-typedef unsigned dmutexindex_t;
-struct dxMutexGroup;
-typedef struct dxMutexGroup *dMutexGroupID;
-
-
-#define dTHREADING_THREAD_COUNT_UNLIMITED 0U
-
-
-
-/**
- * @brief Allocates a group of muteces.
- *
- * The Mutex allocated do not need to support recursive locking.
- *
- * The Mutex names are provided to aid in debugging and thread state tracking.
- *
- * @param impl Threading implementation ID
- * @param Mutex_count Number of Mutex to create
- * @Mutex_names_ptr Pointer to optional Mutex names array to be associated with individual Mutex
- * @returns MutexGroup ID or NULL if error occurred.
- *
- * @ingroup threading
- * @see dMutexGroupFreeFunction
- * @see dMutexGroupMutexLockFunction
- * @see dMutexGroupMutexUnlockFunction
- */
-typedef dMutexGroupID dMutexGroupAllocFunction (dThreadingImplementationID impl, dmutexindex_t Mutex_count, const char *const *Mutex_names_ptr/*=NULL*/);
-
-/**
- * @brief Deletes a group of muteces.
- *
- * @param impl Threading implementation ID
- * @param mutex_group Mutex group to deallocate
- *
- * @ingroup threading
- * @see dMutexGroupAllocFunction
- * @see dMutexGroupMutexLockFunction
- * @see dMutexGroupMutexUnlockFunction
- */
-typedef void dMutexGroupFreeFunction (dThreadingImplementationID impl, dMutexGroupID mutex_group);
-
-/**
- * @brief Locks a mutex in a group of muteces.
- *
- * The function is to block execution until requested mutex can be locked.
- *
- * Note: Mutex provided may not support recursive locking. Calling this function
- * while mutex is already locked by current thread will result in unpredictable behavior.
- *
- * @param impl Threading implementation ID
- * @param mutex_group Mutex group to use for locking
- * @param mutex_index The index of mutex to be locked (0..Mutex_count - 1)
- *
- * @ingroup threading
- * @see dMutexGroupAllocFunction
- * @see dMutexGroupFreeFunction
- * @see dMutexGroupMutexUnlockFunction
- */
-typedef void dMutexGroupMutexLockFunction (dThreadingImplementationID impl, dMutexGroupID mutex_group, dmutexindex_t mutex_index);
-
-/**
- * @brief Attempts to lock a mutex in a group of muteces.
- *
- * The function is to lock the requested mutex if it is unoccupied or
- * immediately return failure if mutex is already locked by other thread.
- *
- * Note: Mutex provided may not support recursive locking. Calling this function
- * while mutex is already locked by current thread will result in unpredictable behavior.
- *
- * @param impl Threading implementation ID
- * @param mutex_group Mutex group to use for locking
- * @param mutex_index The index of mutex to be locked (0..Mutex_count - 1)
- * @returns 1 for success (mutex is locked) and 0 for failure (mutex is not locked)
- *
- * @ingroup threading
- * @see dMutexGroupAllocFunction
- * @see dMutexGroupFreeFunction
- * @see dMutexGroupMutexLockFunction
- * @see dMutexGroupMutexUnlockFunction
- */
-/* typedef int dMutexGroupMutexTryLockFunction (dThreadingImplementationID impl, dMutexGroupID mutex_group, dmutexindex_t mutex_index);*/
-
-/**
- * @brief Unlocks a mutex in a group of muteces.
- *
- * The function is to unlock the given mutex provided it had been locked before.
- *
- * @param impl Threading implementation ID
- * @param mutex_group Mutex group to use for unlocking
- * @param mutex_index The index of mutex to be unlocked (0..Mutex_count - 1)
- *
- * @ingroup threading
- * @see dMutexGroupAllocFunction
- * @see dMutexGroupFreeFunction
- * @see dMutexGroupMutexLockFunction
- */
-typedef void dMutexGroupMutexUnlockFunction (dThreadingImplementationID impl, dMutexGroupID mutex_group, dmutexindex_t mutex_index);
-
-
-struct dxCallReleasee;
-typedef struct dxCallReleasee *dCallReleaseeID;
-
-struct dxCallWait;
-typedef struct dxCallWait *dCallWaitID;
-
-typedef dsizeint ddependencycount_t;
-typedef ddiffint ddependencychange_t;
-typedef dsizeint dcallindex_t;
-typedef int dThreadedCallFunction(void *call_context, dcallindex_t instance_index,
- dCallReleaseeID this_releasee);
-
-typedef struct dxThreadedWaitTime
-{
- time_t wait_sec;
- unsigned long wait_nsec;
-
-} dThreadedWaitTime;
-
-
-/**
- * @brief Allocates a Wait ID that can be used to wait for a call.
- *
- * @param impl Threading implementation ID
- * @returns Wait ID or NULL if error occurred
- *
- * @ingroup threading
- * @see dThreadedCallWaitResetFunction
- * @see dThreadedCallWaitFreeFunction
- * @see dThreadedCallPostFunction
- * @see dThreadedCallWaitFunction
- */
-typedef dCallWaitID dThreadedCallWaitAllocFunction(dThreadingImplementationID impl);
-
-/**
- * @brief Resets a Wait ID so that it could be used to wait for another call.
- *
- * @param impl Threading implementation ID
- * @param call_wait Wait ID to reset
- *
- * @ingroup threading
- * @see dThreadedCallWaitAllocFunction
- * @see dThreadedCallWaitFreeFunction
- * @see dThreadedCallPostFunction
- * @see dThreadedCallWaitFunction
- */
-typedef void dThreadedCallWaitResetFunction(dThreadingImplementationID impl, dCallWaitID call_wait);
-
-/**
- * @brief Frees a Wait ID.
- *
- * @param impl Threading implementation ID
- * @param call_wait Wait ID to delete
- *
- * @ingroup threading
- * @see dThreadedCallWaitAllocFunction
- * @see dThreadedCallPostFunction
- * @see dThreadedCallWaitFunction
- */
-typedef void dThreadedCallWaitFreeFunction(dThreadingImplementationID impl, dCallWaitID call_wait);
-
-
-/**
- * @brief Post a function to be called in another thread.
- *
- * A call is scheduled to be executed asynchronously.
- *
- * A @a out_summary_fault variable can be provided for call to accumulate any
- * possible faults from its execution and execution of any possible sub-calls.
- * This variable gets result that @a call_func returns. Also, if dependent calls
- * are executed after the call already exits, the variable is also going to be
- * updated with results of all those calls before control is released to master.
- *
- * @a out_post_releasee parameter receives a value of @c dCallReleaseeID that can
- * later be used for @a dependent_releasee while scheduling sub-calls to make
- * current call depend on them. The value is only returned if @a dependencies_count
- * is not zero (i.e. if any dependencies are expected at all). The call is not going
- * to start until all its dependencies complete.
- *
- * In case if number of dependencies is unknown in advance 1 can be passed on call
- * scheduling. Then @c dThreadedCallDependenciesCountAlterFunction can be used to
- * add one more extra dependencies before scheduling each subcall. And then, after
- * all sub-calls had been scheduled, @c dThreadedCallDependenciesCountAlterFunction
- * can be used again to subtract initial extra dependency from total number.
- * Adding one dependency in advance is necessary to obtain releasee ID and to make
- * sure the call will not start and will not terminate before all sub-calls are scheduled.
- *
- * Extra dependencies can also be added from the call itself after it has already
- * been started (with parameter received in @c dThreadedCallFunction).
- * In that case those dependencies will start immediately or after call returns
- * but the call's master will not be released/notified until all additional
- * dependencies complete. This can be used to schedule sub-calls from a call and
- * then pass own job to another sub-call dependent on those initial sub-calls.
- *
- * By using @ call_wait it is possible to assign a Wait ID that can later
- * be passed into @c dThreadedCallWaitFunction to wait for call completion.
- *
- * If @a call_name is available (and it should!) the string must remain valid until
- * after call completion. In most cases this should be a static string literal.
- *
- * Since the function is an analogue of normal method call it is not supposed to fail.
- * Any complications with resource allocation on call scheduling should be
- * anticipated, avoided and worked around by implementation.
- *
- * @param impl Threading implementation ID
- * @param out_summary_fault Optional pointer to variable to be set to 1 if function
- * call (or any sub-call) fails internally, or 0 if all calls return success
- * @param out_post_releasee Optional pointer to variable to receive releasee ID
- * associated with the call
- * @param dependencies_count Number of dependencies that are going to reference
- * this call as dependent releasee
- * @param dependent_releasee Optional releasee ID to reference with this call
- * @param call_wait Optional Wait ID that can later be used to wait for the call
- * @param call_func Pointer to function to be called
- * @param call_context Context parameter to be passed into the call
- * @param instance_index Index parameter to be passed into the call
- * @param call_name Optional name to be associated with the call (for debugging and state tracking)
- *
- * @ingroup threading
- * @see dThreadedCallWaitFunction
- * @see dThreadedCallDependenciesCountAlterFunction
- * @see dThreadingImplResourcesForCallsPreallocateFunction
- */
-typedef void dThreadedCallPostFunction(dThreadingImplementationID impl, int *out_summary_fault/*=NULL*/,
- dCallReleaseeID *out_post_releasee/*=NULL*/, ddependencycount_t dependencies_count, dCallReleaseeID dependent_releasee/*=NULL*/,
- dCallWaitID call_wait/*=NULL*/,
- dThreadedCallFunction *call_func, void *call_context, dcallindex_t instance_index,
- const char *call_name/*=NULL*/);
-
-/**
- * @brief Add or remove extra dependencies from call that has been scheduled
- * or is in process of execution.
- *
- * Extra dependencies can be added to a call if exact number of sub-calls is
- * not known in advance at the moment the call is scheduled. Also, some dependencies
- * can be removed if sub-calls were planned but then dropped.
- *
- * In case if total dependency count of a call reaches zero by result of invoking
- * this function, the call is free to start executing immediately.
- *
- * After the call execution had been started, any additional dependencies can only
- * be added from the call function itself!
- *
- * @param impl Threading implementation ID
- * @param target_releasee ID of releasee to apply dependencies count change to
- * @param dependencies_count_change Number of dependencies to add or remove
- *
- * @ingroup threading
- * @see dThreadedCallPostFunction
- */
-typedef void dThreadedCallDependenciesCountAlterFunction(dThreadingImplementationID impl, dCallReleaseeID target_releasee,
- ddependencychange_t dependencies_count_change);
-
-/**
- * @brief Wait for a posted call to complete.
- *
- * Function blocks until a call identified by @a call_wait completes or
- * timeout elapses.
- *
- * IT IS ILLEGAL TO INVOKE THIS FUNCTION FROM WITHIN A THREADED CALL!
- * This is because doing so will block a physical thread and will require
- * increasing worker thread count to avoid starvation. Use call dependencies
- * if it is necessary make sure sub-calls have been completed instead!
- *
- * If @a timeout_time_ptr is NULL, the function waits without time limit. If @a timeout_time_ptr
- * points to zero value, the function only checks status and does not block.
- *
- * If @a wait_name is available (and it should!) the string must remain valid for
- * the duration of wait. In most cases this should be a static string literal.
- *
- * Function is not expected to return failures caused by system call faults as
- * those are hardly ever possible to be handled in this case anyway. In event of
- * system call fault the function is supposed to terminate application.
- *
- * @param impl Threading implementation ID
- * @param out_wait_status Optional pointer to variable to receive 1 if waiting succeeded
- * or 0 in case of timeout
- * @param call_wait Wait ID that had been passed to scheduling a call that needs to be waited for
- * @param timeout_time_ptr Optional pointer to time specification the wait must not
- * last longer than (pass NULL for infinite timeout)
- * @param wait_name Optional name to be associated with the wait (for debugging and state tracking)
- *
- * @ingroup threading
- * @see dThreadedCallPostFunction
- */
-typedef void dThreadedCallWaitFunction(dThreadingImplementationID impl, int *out_wait_status/*=NULL*/,
- dCallWaitID call_wait, const dThreadedWaitTime *timeout_time_ptr/*=NULL*/,
- const char *wait_name/*=NULL*/);
-
-/**
- * @brief Retrieve number of active threads that serve the implementation.
- *
- * @param impl Threading implementation ID
- * @returns Number of active threads
- *
- * @ingroup threading
- */
-typedef unsigned dThreadingImplThreadCountRetrieveFunction(dThreadingImplementationID impl);
-
-/**
- * @brief Preallocate resources to handle posted calls.
- *
- * The function is intended to make sure enough resources is preallocated for the
- * implementation to be able to handle posted calls. Then @c max_simultaneous_calls_estimate
- * is an estimate of how many posted calls can potentially be active or scheduled
- * at the same time. The value is usually derived from the way the calls are posted
- * in library code and dependencies between them.
- *
- * @warning While working on an implementation be prepared that the estimate provided
- * yet rarely but theoretically can be exceeded due to unpredictability of thread execution.
- *
- * This function is normally going to be invoked by library each time it is entered
- * from outside to do the job but before any threaded calls are going to be posted.
- *
- * @param impl Threading implementation ID
- * @param max_simultaneous_calls_estimate An estimated number of calls that can be posted simultaneously
- * @returns 1 or 0 to indicate success or failure
- *
- * @ingroup threading
- * @see dThreadedCallPostFunction
- */
-typedef int dThreadingImplResourcesForCallsPreallocateFunction(dThreadingImplementationID impl,
- ddependencycount_t max_simultaneous_calls_estimate);
-
-
-/**
- * @brief An interface structure with function pointers to be provided by threading implementation.
- */
-typedef struct dxThreadingFunctionsInfo
-{
- unsigned struct_size;
-
- dMutexGroupAllocFunction *alloc_mutex_group;
- dMutexGroupFreeFunction *free_mutex_group;
- dMutexGroupMutexLockFunction *lock_group_mutex;
- dMutexGroupMutexUnlockFunction *unlock_group_mutex;
-
- dThreadedCallWaitAllocFunction *alloc_call_wait;
- dThreadedCallWaitResetFunction *reset_call_wait;
- dThreadedCallWaitFreeFunction *free_call_wait;
-
- dThreadedCallPostFunction *post_call;
- dThreadedCallDependenciesCountAlterFunction *alter_call_dependencies_count;
- dThreadedCallWaitFunction *wait_call;
-
- dThreadingImplThreadCountRetrieveFunction *retrieve_thread_count;
- dThreadingImplResourcesForCallsPreallocateFunction *preallocate_resources_for_calls;
-
- /*
- * Beware of Jon Watte's anger if you dare to uncomment this!
- * May cryptic text below be you a warning!
- * Стародавні легенди розказують, що кожного сміливця, хто наважиться порушити табу
- * і відкрити заборонений код, спіткає страшне прокляття і він відразу почне робити
- * одні лиш помилки.
- *
- * dMutexGroupMutexTryLockFunction *trylock_group_mutex;
- */
-
-} dThreadingFunctionsInfo;
-
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif /* #ifndef _ODE_THREADING_H_ */
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * Builtin ODE threading implementation header. *
- * Copyright (C) 2011-2019 Oleh Derevenko. All rights reserved. *
- * e-mail: odar@eleks.com (change all "a" to "e") *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-/*
- * A threading implementation built into ODE for those who does not care to
- * or can't implement an own one.
- */
-
-#ifndef _ODE_THREADING_IMPL_H_
-#define _ODE_THREADING_IMPL_H_
-
-
-#include <ode/odeconfig.h>
-#include <ode/threading.h>
-
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-
-struct dxThreadingThreadPool;
-typedef struct dxThreadingThreadPool *dThreadingThreadPoolID;
-
-
-/**
- * @brief Allocates built-in self-threaded threading implementation object.
- *
- * A self-threaded implementation is a type of implementation that performs
- * processing of posted calls by means of caller thread itself. This type of
- * implementation does not need thread pool to serve it.
- *
- * Note that since May 9th, 2017 (rev. #2066) the Self-Threaded implementation
- * returns 0 rather than 1 as available thread count to distinguish from
- * thread pools with just one thread in them.
- *
- * The processing is arranged in a way to prevent call stack depth growth
- * as more and more nested calls are posted.
- *
- * Note that it is not necessary to create and assign a self-threaded
- * implementation to a world, as there is a global one used by default
- * if no implementation is explicitly assigned. You should only assign
- * each world an individual threading implementation instance if simulations
- * need to be run in parallel in multiple threads for the worlds.
- *
- * @returns ID of object allocated or NULL on failure
- *
- * @ingroup threading
- * @see dThreadingAllocateMultiThreadedImplementation
- * @see dThreadingFreeImplementation
- */
-ODE_API dThreadingImplementationID dThreadingAllocateSelfThreadedImplementation();
-
-/**
- * @brief Allocates built-in multi-threaded threading implementation object.
- *
- * A multi-threaded implementation is a type of implementation that has to be
- * served with a thread pool. The thread pool can be either the built-in ODE object
- * or set of external threads that dedicate themselves to this purpose and stay
- * in ODE until implementation releases them.
- *
- * @returns ID of object allocated or NULL on failure
- *
- * @ingroup threading
- * @see dThreadingThreadPoolServeMultiThreadedImplementation
- * @see dExternalThreadingServeMultiThreadedImplementation
- * @see dThreadingFreeImplementation
- */
-ODE_API dThreadingImplementationID dThreadingAllocateMultiThreadedImplementation();
-
-/**
- * @brief Retrieves the functions record of a built-in threading implementation.
- *
- * The implementation can be the one allocated by ODE (from @c dThreadingAllocateMultiThreadedImplementation).
- * Do not use this function with self-made custom implementations -
- * they should be bundled with their own set of functions.
- *
- * @param impl Threading implementation ID
- * @returns Pointer to associated functions structure
- *
- * @ingroup threading
- * @see dThreadingAllocateMultiThreadedImplementation
- */
-ODE_API const dThreadingFunctionsInfo *dThreadingImplementationGetFunctions(dThreadingImplementationID impl);
-
-/**
- * @brief Requests a built-in implementation to release threads serving it.
- *
- * The function unblocks threads employed in implementation serving and lets them
- * return to from where they originate. It's the responsibility of external code
- * to make sure all the calls to ODE that might be dependent on given threading
- * implementation object had already returned before this call is made. If threading
- * implementation is still processing some posted calls while this function is
- * invoked the behavior is implementation dependent.
- *
- * This call is to be used to request the threads to be released before waiting
- * for them in host pool or before waiting for them to exit. Implementation object
- * must not be destroyed before it is known that all the serving threads have already
- * returned from it. If implementation needs to be reused after this function is called
- * and all the threads have exited from it a call to @c dThreadingImplementationCleanupForRestart
- * must be made to restore internal state of the object.
- *
- * If this function is called for self-threaded built-in threading implementation
- * the call has no effect.
- *
- * @param impl Threading implementation ID
- *
- * @ingroup threading
- * @see dThreadingAllocateMultiThreadedImplementation
- * @see dThreadingImplementationCleanupForRestart
- */
-ODE_API void dThreadingImplementationShutdownProcessing(dThreadingImplementationID impl);
-
-/**
- * @brief Restores built-in implementation's state to let it be reused after shutdown.
- *
- * If a multi-threaded built-in implementation needs to be reused after a call
- * to @c dThreadingImplementationShutdownProcessing this call is to be made to
- * restore object's internal state. After that the implementation can be served again.
- *
- * If this function is called for self-threaded built-in threading implementation
- * the call has no effect.
- *
- * @param impl Threading implementation ID
- *
- * @ingroup threading
- * @see dThreadingAllocateMultiThreadedImplementation
- * @see dThreadingImplementationShutdownProcessing
- */
-ODE_API void dThreadingImplementationCleanupForRestart(dThreadingImplementationID impl);
-
-/**
- * @brief Deletes an instance of built-in threading implementation.
- *
- * @warning A care must be taken to make sure the implementation is unassigned
- * from all the objects it was assigned to and that there are no more threads
- * serving it before attempting to call this function.
- *
- * @param impl Threading implementation ID
- *
- * @ingroup threading
- * @see dThreadingAllocateMultiThreadedImplementation
- */
-ODE_API void dThreadingFreeImplementation(dThreadingImplementationID impl);
-
-
-typedef void (dThreadReadyToServeCallback)(void *callback_context);
-
-/**
- * @brief An entry point for external threads that would like to serve a built-in
- * threading implementation object.
- *
- * A thread that calls this function remains blocked in ODE and serves implementation
- * object @p impl until being released with @c dThreadingImplementationShutdownProcessing call.
- * This function can be used to provide external threads instead of ODE's built-in
- * thread pools.
- *
- * The optional callback @readiness_callback is called after the thread has reached
- * and has registered within the implementation. The implementation should not
- * be used until all dedicated threads register within it as otherwise it will not
- * have accurate view of the execution resources available.
- *
- * @param impl Threading implementation ID
- * @param readiness_callback Optional readiness callback to be called after thread enters the implementation
- * @param callback_context A value to be passed as parameter to readiness callback
- *
- * @ingroup threading
- * @see dThreadingAllocateMultiThreadedImplementation
- * @see dThreadingImplementationShutdownProcessing
- */
-ODE_API void dExternalThreadingServeMultiThreadedImplementation(dThreadingImplementationID impl,
- dThreadReadyToServeCallback *readiness_callback/*=NULL*/, void *callback_context/*=NULL*/);
-
-
-/**
- * @brief Creates an instance of built-in thread pool object that can be used to serve
- * multi-threaded threading implementations.
- *
- * The threads allocated inherit priority of caller thread. Their affinity is not
- * explicitly adjusted and gets the value the system assigns by default. Threads
- * have their stack memory fully committed immediately on start. On POSIX platforms
- * threads are started with all the possible signals blocked. Threads execute
- * calls to @c dAllocateODEDataForThread with @p ode_data_allocate_flags
- * on initialization.
- *
- * On POSIX platforms this function must be called with signals masked
- * or other measures must be taken to prevent reception of signals by calling thread
- * for the duration of the call.
- *
- * @param thread_count Number of threads to start in pool
- * @param stack_size Size of stack to be used for every thread or 0 for system default value
- * @param ode_data_allocate_flags Flags to be passed to @c dAllocateODEDataForThread on behalf of each thread
- * @returns ID of object allocated or NULL on failure
- *
- * @ingroup threading
- * @see dThreadingAllocateMultiThreadedImplementation
- * @see dThreadingImplementationShutdownProcessing
- * @see dThreadingFreeThreadPool
- */
-ODE_API dThreadingThreadPoolID dThreadingAllocateThreadPool(unsigned thread_count,
- dsizeint stack_size, unsigned int ode_data_allocate_flags, void *reserved/*=NULL*/);
-
-/**
- * @brief Commands an instance of built-in thread pool to serve a built-in multi-threaded
- * threading implementation.
- *
- * A pool can only serve one threading implementation at a time.
- * Call @c dThreadingImplementationShutdownProcessing to release pool threads
- * from implementation serving and make them idle. Pool threads must be released
- * from any implementations before pool is attempted to be deleted.
- *
- * This function waits for threads to register within implementation before returning.
- * So, after the function call exits the implementation can be used immediately.
- *
- * @param pool Thread pool ID to serve the implementation
- * @param impl Implementation ID of implementation to be served
- *
- * @ingroup threading
- * @see dThreadingAllocateThreadPool
- * @see dThreadingAllocateMultiThreadedImplementation
- * @see dThreadingImplementationShutdownProcessing
- */
-ODE_API void dThreadingThreadPoolServeMultiThreadedImplementation(dThreadingThreadPoolID pool, dThreadingImplementationID impl);
-
-/**
- * @brief Waits until all pool threads are released from threading implementation
- * they might be serving.
- *
- * The function can be used after a call to @c dThreadingImplementationShutdownProcessing
- * to make sure all the threads have already been released by threading implementation
- * and it can be deleted or it can be cleaned up for restart and served by another pool
- * or this pool's threads can be used to serve another threading implementation.
- *
- * Note that is it not necessary to call this function before pool destruction
- * since @c dThreadingFreeThreadPool performs similar wait operation implicitly on its own.
- *
- * It is OK to call this function even if pool was not serving any threading implementation
- * in which case the call exits immediately with minimal delay.
- *
- * @param pool Thread pool ID to wait for
- *
- * @ingroup threading
- * @see dThreadingAllocateThreadPool
- * @see dThreadingImplementationShutdownProcessing
- * @see dThreadingFreeThreadPool
- */
-ODE_API void dThreadingThreadPoolWaitIdleState(dThreadingThreadPoolID pool);
-
-/**
- * @brief Deletes a built-in thread pool instance.
- *
- * The pool threads must be released from any implementations they might be serving
- * before this function is called. Otherwise the call is going to block
- * and wait until pool's threads return.
- *
- * @param pool Thread pool ID to delete
- *
- * @ingroup threading
- * @see dThreadingAllocateThreadPool
- * @see dThreadingImplementationShutdownProcessing
- */
-ODE_API void dThreadingFreeThreadPool(dThreadingThreadPoolID pool);
-
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif /* #ifndef _ODE_THREADING_IMPL_H_ */
+++ /dev/null
-/*************************************************************************
- * *
- * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
- * All rights reserved. Email: russ@q12.org Web: www.q12.org *
- * *
- * This library is free software; you can redistribute it and/or *
- * modify it under the terms of EITHER: *
- * (1) The GNU Lesser General Public License as published by the Free *
- * Software Foundation; either version 2.1 of the License, or (at *
- * your option) any later version. The text of the GNU Lesser *
- * General Public License is included with this library in the *
- * file LICENSE.TXT. *
- * (2) The BSD-style license that is included with this library in *
- * the file LICENSE-BSD.TXT. *
- * *
- * This 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 files *
- * LICENSE.TXT and LICENSE-BSD.TXT for more details. *
- * *
- *************************************************************************/
-
-#ifndef _ODE_TIMER_H_
-#define _ODE_TIMER_H_
-
-#include <ode/odeconfig.h>
-
-#ifdef __cplusplus
-extern "C" {
-#endif
-
-
-/* stop watch objects */
-
-typedef struct dStopwatch {
- double time; /* total clock count */
- unsigned long cc[2]; /* clock count since last `start' */
-} dStopwatch;
-
-ODE_API void dStopwatchReset (dStopwatch *);
-ODE_API void dStopwatchStart (dStopwatch *);
-ODE_API void dStopwatchStop (dStopwatch *);
-ODE_API double dStopwatchTime (dStopwatch *); /* returns total time in secs */
-
-
-/* code timers */
-
-ODE_API void dTimerStart (const char *description); /* pass a static string here */
-ODE_API void dTimerNow (const char *description); /* pass a static string here */
-ODE_API void dTimerEnd(void);
-
-/* print out a timer report. if `average' is nonzero, print out the average
- * time for each slot (this is only meaningful if the same start-now-end
- * calls are being made repeatedly.
- */
-ODE_API void dTimerReport (FILE *fout, int average);
-
-
-/* resolution */
-
-/* returns the timer ticks per second implied by the timing hardware or API.
- * the actual timer resolution may not be this great.
- */
-ODE_API double dTimerTicksPerSecond(void);
-
-/* returns an estimate of the actual timer resolution, in seconds. this may
- * be greater than 1/ticks_per_second.
- */
-ODE_API double dTimerResolution(void);
-
-
-#ifdef __cplusplus
-}
-#endif
-
-#endif
+++ /dev/null
-#ifndef _ODE_VERSION_H_
-#define _ODE_VERSION_H_
-
-#define dODE_VERSION "0.16.2"
-
-#endif
+++ /dev/null
-# libode.la - a libtool library file
-# Generated by libtool (GNU libtool) 2.4.6 Debian-2.4.6-0.1
-#
-# 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='libode.a'
-
-# Linker flags that cannot go in dependency_libs.
-inherited_linker_flags=''
-
-# Libraries that this one depends upon.
-dependency_libs=' -lrt -lpthread'
-
-# Names of additional weak libraries provided by this library
-weak_library_names=''
-
-# Version information for libode.
-current=8
-age=0
-revision=2
-
-# 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/ode/lib'
+++ /dev/null
-prefix=/tmp/ode
-exec_prefix=${prefix}
-libdir=${exec_prefix}/lib
-includedir=${prefix}/include
-precision=dDOUBLE
-
-Name: ode
-Description: Open Dynamics Engine
-Version: 0.16.2
-Libs: -L${libdir} -lode
-Libs.private: -lstdc++ -lm
-Cflags: -I${includedir}
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