=================================================================== RCS file: /home/cvs/OpenXM_contrib/gmp/Attic/gmp.info-1,v retrieving revision 1.1 retrieving revision 1.1.1.4 diff -u -p -r1.1 -r1.1.1.4 --- OpenXM_contrib/gmp/Attic/gmp.info-1 2000/01/10 15:35:21 1.1 +++ OpenXM_contrib/gmp/Attic/gmp.info-1 2003/08/25 16:06:02 1.1.1.4 @@ -1,60 +1,72 @@ -This is Info file gmp.info, produced by Makeinfo-1.64 from the input -file gmp.texi. +This is gmp.info, produced by makeinfo version 4.2 from gmp.texi. +This manual describes how to install and use the GNU multiple precision +arithmetic library, version 4.1.2. + + Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, +2001, 2002 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 +1.1 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.info). GNU Multiple Precision Arithmetic Library. +* gmp: (gmp). GNU Multiple Precision Arithmetic Library. END-INFO-DIR-ENTRY - This file documents GNU MP, a library for arbitrary-precision -arithmetic. - - Copyright (C) 1991, 1993, 1994, 1995, 1996 Free Software Foundation, -Inc. - - Permission is granted to make and distribute verbatim copies of this -manual provided the copyright notice and this permission notice are -preserved on all copies. - - Permission is granted to copy and distribute modified versions of -this manual under the conditions for verbatim copying, provided that -the entire resulting derived work is distributed under the terms of a -permission notice identical to this one. - - Permission is granted to copy and distribute translations of this -manual into another language, under the above conditions for modified -versions, except that this permission notice may be stated in a -translation approved by the Foundation. -  File: gmp.info, Node: Top, Next: Copying, Prev: (dir), Up: (dir) GNU MP ****** - This manual documents how to install and use the GNU multiple -precision arithmetic library, version 2.0.2. +This manual describes how to install and use the GNU multiple precision +arithmetic library, version 4.1.2. + Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, +2001, 2002 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 +1.1 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 MP:: Brief introduction to GNU MP. -* Installing MP:: How to configure and compile the MP library. -* MP Basics:: What every MP user should now. -* 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. -* BSD Compatible Functions:: All functions found in BSD MP. -* Custom Allocation:: How to customize the internal allocation. +* Copying:: GMP Copying Conditions (LGPL). +* Introduction to GMP:: Brief introduction to GNU MP. +* Installing GMP:: How to configure and compile the GMP library. +* GMP Basics:: What every GMP user should know. +* Reporting Bugs:: How to usefully report bugs. +* Integer Functions:: Functions for arithmetic on signed integers. +* Rational Number Functions:: Functions for arithmetic on rational numbers. +* Floating-point Functions:: Functions for arithmetic on floats. +* Low-level Functions:: Fast functions for natural numbers. +* Random Number Functions:: Functions for generating random numbers. +* Formatted Output:: `printf' style output. +* Formatted Input:: `scanf' style input. +* C++ Class Interface:: Class wrappers around GMP types. +* BSD Compatible Functions:: All functions found in BSD MP. +* Custom Allocation:: How to customize the internal allocation. +* Language Bindings:: Using GMP from other languages. +* Algorithms:: What happens behind the scenes. +* Internals:: How values are represented behind the scenes. -* Contributors:: -* References:: +* Contributors:: Who brings your this library? +* References:: Some useful papers and books to read. +* GNU Free Documentation License:: * Concept Index:: * Function Index::  -File: gmp.info, Node: Copying, Next: Introduction to MP, Prev: Top, Up: Top +File: gmp.info, Node: Copying, Next: Introduction to GMP, Prev: Top, Up: Top GNU MP Copying Conditions ************************* @@ -85,11 +97,13 @@ know that what they have is not what we distributed, s problems introduced by others will not reflect on our reputation. The precise conditions of the license for the GNU MP library are -found in the Library General Public License that accompany the source -code. +found in the Lesser General Public License version 2.1 that accompanies +the source code, see `COPYING.LIB'. Certain demonstration programs are +provided under the terms of the plain General Public License version 2, +see `COPYING'.  -File: gmp.info, Node: Introduction to MP, Next: Installing MP, Prev: Copying, Up: Top +File: gmp.info, Node: Introduction to GMP, Next: Installing GMP, Prev: Copying, Up: Top Introduction to GNU MP ********************** @@ -101,1183 +115,1057 @@ that need higher precision than is directly supported types. Many applications use just a few hundred bits of precision; but some -applications may need thousands or even millions of bits. MP is +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 MP is achieved by using fullwords as the basic + 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 carefully optimized assembly code for these CPUs: DEC -Alpha, Amd 29000, HPPA 1.0 and 1.1, Intel Pentium and generic x86, -Intel i960, Motorola MC68000, MC68020, MC88100, and MC88110, -Motorola/IBM PowerPC, National NS32000, IBM POWER, MIPS R3000, R4000, -SPARCv7, SuperSPARC, generic SPARCv8, and DEC VAX. Some optimizations -also for ARM, Clipper, IBM ROMP (RT), and Pyramid AP/XP. + There is carefully optimized assembly code for these CPUs: ARM, DEC +Alpha 21064, 21164, and 21264, AMD 29000, AMD K6, K6-2 and Athlon, +Hitachi SuperH and SH-2, HPPA 1.0, 1.1 and 2.0, Intel Pentium, Pentium +Pro/II/III, Pentium 4, generic x86, Intel IA-64, i960, Motorola +MC68000, MC68020, MC88100, and MC88110, Motorola/IBM PowerPC 32 and 64, +National NS32000, IBM POWER, MIPS R3000, R4000, SPARCv7, SuperSPARC, +generic SPARCv8, UltraSPARC, DEC VAX, and Zilog Z8000. Some +optimizations also for Cray vector systems, Clipper, IBM ROMP (RT), and +Pyramid AP/XP. - This version of MP is released under a more liberal license than -previous versions. It is now permitted to link MP to non-free -programs, as long as MP source code is provided when distributing the -non-free program. + There are two public mailing lists of interest. One for general +questions and discussions about usage of the GMP library and one for +discussions about development of GMP. There's more information about +the mailing lists at `http://swox.com/mailman/listinfo/'. These lists +are *not* for bug reports. + The proper place for bug reports is . See *Note +Reporting Bugs:: for info about reporting bugs. + + For up-to-date information on GMP, please see the GMP web pages at + + `http://swox.com/gmp/' + + The latest version of the library is available at + + `ftp://ftp.gnu.org/gnu/gmp' + + Many sites around the world mirror `ftp.gnu.org', please use a mirror +near you, see `http://www.gnu.org/order/ftp.html' for a full list. + How to use this Manual ====================== - Everyone should read *Note MP Basics::. If you need to install the -library yourself, you need to read *Note Installing MP::, too. + Everyone should read *Note GMP Basics::. If you need to install the +library yourself, then read *Note Installing GMP::. If you have a +system with multiple ABIs, then read *Note ABI and ISA::, for the +compiler options that must be used on applications. The rest of the manual can be used for later reference, although it is probably a good idea to glance through it.  -File: gmp.info, Node: Installing MP, Next: MP Basics, Prev: Introduction to MP, Up: Top +File: gmp.info, Node: Installing GMP, Next: GMP Basics, Prev: Introduction to GMP, Up: Top -Installing MP -************* +Installing GMP +************** - To build MP, you first have to configure it for your CPU and -operating system. You need a C compiler, preferably GCC, but any -reasonable compiler should work. And you need a standard Unix `make' -program, plus some other standard Unix utility programs. + GMP has an autoconf/automake/libtool based configuration system. On +a Unix-like system a basic build can be done with - (If you're on an MS-DOS machine, your can build MP using `make.bat'. -It requires that djgpp is installed. It does not require -configuration, nor is `make' needed; `make.bat' both configures and -builds the library.) + ./configure + make - Here are the steps needed to install the library on Unix systems: +Some self-tests can be run with - 1. In most cases, `./configure --target=cpu-vendor-os', should work - both for native and cross-compilation. If you get error messages, - your machine might not be supported. + make check - If you want to compile in a separate object directory, cd to that - directory, and prefix the configure command with the path to the - MP source directory. Not all `make' programs have the necessary - features to support this. In particular, SunOS and Slowaris - `make' have bugs that makes them unable to build from a separate - object directory. Use GNU `make' instead. +And you can install (under `/usr/local' by default) with - In addition to the standard cpu-vendor-os tuples, MP recognizes - sparc8 and supersparc as valid CPU names. Specifying these CPU - names for relevant systems will improve performance significantly. + make install - In general, if you want a library that runs as fast as possible, - you should make sure you configure MP for the exact CPU type your - system uses. + If you experience problems, please report them to . +See *Note Reporting Bugs::, for information on what to include in +useful bug reports. - If you have `gcc' in your `PATH', it will be used by default. To - override this, pass `-with-gcc=no' to `configure'. +* Menu: - 2. `make' +* Build Options:: +* ABI and ISA:: +* Notes for Package Builds:: +* Notes for Particular Systems:: +* Known Build Problems:: - This will compile MP, and create a library archive file `libgmp.a' - in the working directory. + +File: gmp.info, Node: Build Options, Next: ABI and ISA, Prev: Installing GMP, Up: Installing GMP - 3. `make check' +Build Options +============= - This will make sure MP was built correctly. If you get error - messages, please report this to `bug-gmp@prep.ai.mit.edu'. (*Note - Reporting Bugs::, for information on what to include in useful bug - reports.) + All the usual autoconf configure options are available, run +`./configure --help' for a summary. The file `INSTALL.autoconf' has +some generic installation information too. - 4. `make install' +Non-Unix Systems + `configure' requires various Unix-like tools. On an MS-DOS system + DJGPP can be used, and on MS Windows Cygwin or MINGW can be used, - This will copy the file `gmp.h' and `libgmp.a', as well as the info - files, to `/usr/local' (or if you passed the `--prefix' option to - `configure', to the directory given as argument to `--prefix'). + `http://www.cygnus.com/cygwin' + `http://www.delorie.com/djgpp' + `http://www.mingw.org' -If you wish to build and install the BSD MP compatible functions, use -`make libmp.a' and `make install-bsdmp'. + 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. - There are some other useful make targets: + The `macos' directory contains an unsupported port to MacOS 9 on + Power Macintosh, see `macos/README'. Note that MacOS X "Darwin" + should use the normal Unix-style `./configure'. - * `doc' + 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. - Create a DVI version of the manual, in `gmp.dvi' and a set of info - files, in `gmp.info', `gmp.info-1', `gmp.info-2', etc. +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 - * `ps' + cd /my/build/dir + /my/sources/gmp-4.1.2/configure - Create a Postscript version of the manual, in `gmp.ps'. + 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. - * `html' +`--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. - Create a HTML version of the manual, in `gmp.html'. +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, - * `clean' + ./configure --build=ultrasparc-sun-solaris2.7 - Delete all object files and archive files, but not the - configuration files. + 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. - * `distclean' +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, - Delete all files not included in the distribution. + ./configure --build=athlon-pc-freebsd3.5 --host=m68k-mac-linux-gnu - * `uninstall' + 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. - Delete all files copied by `make install'. + 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. -Known Build Problems -==================== + 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. - GCC 2.7.2 (as well as 2.6.3) for the RS/6000 and PowerPC can not be -used to compile MP, due to a bug in GCC. If you want to use GCC for -these machines, you need to apply the patch below to GCC, or use a -later version of the compiler. + 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'. - If you are on a Sequent Symmetry, use the GNU assembler instead of -the system's assembler, since the latter has serious bugs. + 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.) - The system compiler on NeXT is a massacred and old gcc, even if the -compiler calls itself `cc'. This compiler cannot be used to build MP. -You need to get a real gcc, and install that before you compile MP. -(NeXT might have fixed this in newer releases of their system.) +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 system C compiler under SunOS 4 has a bug that makes it -miscompile mpq/get_d.c. This will make `make check' fail. + The following CPUs have specific support. See `configure.in' for + details of what code and compiler options they select. - Please report other problems to `bug-gmp@prep.ai.mit.edu'. *Note -Reporting Bugs::. + * Alpha: alpha, alphaev5, alphaev56, alphapca56, alphapca57, + alphaev6, alphaev67, alphaev68 - Patch to apply to GCC 2.6.3 and 2.7.2: + * Cray: c90, j90, t90, sv1 - *** config/rs6000/rs6000.md Sun Feb 11 08:22:11 1996 - --- config/rs6000/rs6000.md.new Sun Feb 18 03:33:37 1996 - *************** - *** 920,926 **** - (set (match_operand:SI 0 "gpc_reg_operand" "=r") - (not:SI (match_dup 1)))] - "" - ! "nor. %0,%2,%1" - [(set_attr "type" "compare")]) - - (define_insn "" - --- 920,926 ---- - (set (match_operand:SI 0 "gpc_reg_operand" "=r") - (not:SI (match_dup 1)))] - "" - ! "nor. %0,%1,%1" - [(set_attr "type" "compare")]) - - (define_insn "" + * HPPA: hppa1.0, hppa1.1, hppa2.0, hppa2.0n, hppa2.0w - -File: gmp.info, Node: MP Basics, Next: Reporting Bugs, Prev: Installing MP, Up: Top + * MIPS: mips, mips3, mips64 -MP Basics -********* + * Motorola: m68k, m68000, m68010, m68020, m68030, m68040, + m68060, m68302, m68360, m88k, m88110 - All declarations needed to use MP are collected in the include file -`gmp.h'. It is designed to work with both C and C++ compilers. + * POWER: power, power1, power2, power2sc -Nomenclature and Types -====================== + * PowerPC: powerpc, powerpc64, powerpc401, powerpc403, + powerpc405, powerpc505, powerpc601, powerpc602, powerpc603, + powerpc603e, powerpc604, powerpc604e, powerpc620, powerpc630, + powerpc740, powerpc7400, powerpc7450, powerpc750, powerpc801, + powerpc821, powerpc823, powerpc860, -In this manual, "integer" usually means a multiple precision integer, as -defined by the MP library. The C data type for such integers is -`mpz_t'. Here are some examples of how to declare such integers: + * SPARC: sparc, sparcv8, microsparc, supersparc, sparcv9, + ultrasparc, ultrasparc2, ultrasparc2i, ultrasparc3, sparc64 - mpz_t sum; - - struct foo { mpz_t x, y; }; - - mpz_t vec[20]; + * 80x86 family: i386, i486, i586, pentium, pentiummmx, + pentiumpro, pentium2, pentium3, pentium4, k6, k62, k63, athlon -"Rational number" means a multiple precision fraction. The C data type -for these fractions is `mpq_t'. For example: + * Other: a29k, arm, clipper, i960, ns32k, pyramid, sh, sh2, vax, + z8k - mpq_t quotient; + CPUs not listed will use generic C code. -"Floating point number" or "Float" for short, is an arbitrary precision -mantissa with an limited precision exponent. The C data type for such -objects is `mpf_t'. +Generic C Build + If some of the assembly code causes problems, or if otherwise + desired, the generic C code can be selected with CPU `none'. For + example, -A "limb" means the part of a multi-precision number that fits in a -single 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 contains 32 or 64 bits. The C data type for a limb is -`mp_limb_t'. + ./configure --host=none-unknown-freebsd3.5 -Function Classes -================ + 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. - There are six classes of functions in the MP library: +`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 - 1. Functions for signed integer arithmetic, with names beginning with - `mpz_'. The associated type is `mpz_t'. There are about 100 - functions in this class. + ./configure --host=mips64-sgi-irix6 ABI=n32 - 2. Functions for rational number arithmetic, with names beginning with - `mpq_'. The associated type is `mpq_t'. There are about 20 - functions in this class, but the functions in the previous class - can be used for performing arithmetic on the numerator and - denominator separately. + See *Note ABI and ISA::, for the available choices on relevant + CPUs, and what applications need to do. - 3. Functions for floating-point arithmetic, with names beginning with - `mpf_'. The associated type is `mpf_t'. There are about 50 - functions is this class. +`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. - 4. Functions compatible with Berkeley MP, such as `itom', `madd', and - `mult'. The associated type is `MINT'. + For some 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. - 5. Fast low-level functions that operate on natural numbers. These - are used by the functions in the preceding groups, and you can - also call them directly from very time-critical user programs. - These functions' names begin with `mpn_'. There are about 30 - (hard-to-use) functions in this class. + 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. - The associated type is array of `mp_limb_t'. + 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 assembler code. - 6. Miscellaneous functions. Functions for setting up custom - allocation. + 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). -MP Variable Conventions -======================= +`CPPFLAGS' + Any flags like `-D' defines or `-I' includes required by the + preprocessor should be set in `CPPFLAGS' rather than `CFLAGS'. + Compiling is done with both `CPPFLAGS' and `CFLAGS', but + preprocessing uses just `CPPFLAGS'. This distinction is because + most preprocessors won't accept all the flags the compiler does. + Preprocessing is done separately in some configure tests, and in + the `ansi2knr' support for K&R compilers. - As a general rule, all MP functions expect output arguments before -input arguments. This notation is based on an analogy with the -assignment operator. (The BSD MP compatibility functions disobey this -rule, having the output argument(s) last.) +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'. - MP allows you to use the same variable for both input and output in -the same expression. For example, the main function for integer -multiplication, `mpz_mul', can be used like this: `mpz_mul (x, x, x)'. -This computes the square of X and puts the result back in X. + 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. - Before you can assign to an MP 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. + `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. - A variable should only be initialized once, or at least cleared out -between each initialization. After a variable has been initialized, it -may be assigned to any number of times. + 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. - For efficiency reasons, avoid to initialize and clear out a variable -in loops. Instead, initialize it before entering the loop, and clear -it out after the loop has exited. +`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++'. - You don't need to be concerned about allocating additional space for -MP variables. All functions in MP automatically allocate additional -space when a variable does not already have enough space. They do not, -however, reduce the space when a smaller number is stored in the -object. Most of the time, this policy is best, since it avoids -frequent re-allocation. + 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. -Useful Macros and Constants -=========================== + 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 object files. - - Global Constant: const int mp_bits_per_limb - The number of bits per limb. +Temporary Memory, `--enable-alloca=' + GMP allocates temporary workspace using one of the following three + methods, which can be selected with for instance + `--enable-alloca=malloc-reentrant'. - - Macro: __GNU_MP_VERSION - - Macro: __GNU_MP_VERSION_MINOR - The major and minor MP version, respectively, as integers. + * `alloca' - C library or compiler builtin. -Compatibility with Version 1.x -============================== + * `malloc-reentrant' - the heap, in a re-entrant fashion. - This version of MP is upward compatible with previous versions of -MP, with a few exceptions. + * `malloc-notreentrant' - the heap, with global variables. - 1. Integer division functions round the result differently. The old - functions (`mpz_div', `mpz_divmod', `mpz_mdiv', `mpz_mdivmod', - etc) now all use floor rounding (i.e., they round the quotient to - -infinity). There are a lot of new functions for integer - division, giving the user better control over the rounding. + For convenience, the following choices are also available. + `--disable-alloca' is the same as `--enable-alloca=no'. - 2. The function `mpz_mod' now compute the true *mod* function. + * `yes' - a synonym for `alloca'. - 3. The functions `mpz_powm' and `mpz_powm_ui' now use *mod* for - reduction. + * `no' - a synonym for `malloc-reentrant'. - 4. The assignment functions for rational numbers do no longer - canonicalize their results. In the case a non-canonical result - could arise from an assignment, the user need to insert an - explicit call to `mpq_canonicalize'. This change was made for - efficiency. + * `reentrant' - `alloca' if available, otherwise + `malloc-reentrant'. This is the default. - 5. Output generated by `mpz_out_raw' in this release cannot be read - by `mpz_inp_raw' in previous releases. This change was made for - making the file format truly portable between machines with - different word sizes. + * `notreentrant' - `alloca' if available, otherwise + `malloc-notreentrant'. - 6. Several `mpn' functions have changed. But they were intentionally - undocumented in previous releases. + `alloca' is reentrant and fast, and is recommended, but when + working with large numbers it can overflow the available stack + space, in which case one of the two malloc methods will need to be + used. Alternately it might be possible to increase available + stack with `limit', `ulimit' or `setrlimit', or under DJGPP with + `stubedit' or `_stklen'. Note that depending on the system the + only indication of stack overflow might be a segmentation + violation. - 7. The functions `mpz_cmp_ui', `mpz_cmp_si', and `mpq_cmp_ui' are now - implementated as macros, and thereby sometimes evaluate their - arguments multiple times. + `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. - 8. The functions `mpz_pow_ui' and `mpz_ui_pow_ui' now yield 1 for - 0^0. (In version 1, they yielded 0.) + 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::). -Getting the Latest Version of MP -================================ +FFT Multiplication, `--disable-fft' + By default multiplications are done using Karatsuba, 3-way + Toom-Cook, and Fermat FFT. The FFT is only used on large to very + large operands and can be disabled to save code size if desired. - The latest version of the MP library is available by anonymous ftp -from from `prep.ai.mit.edu'. The file name is -`/pub/gnu/gmp-M.N.tar.gz'. Many sites around the world mirror `prep'; -please use a mirror site near you. +Berkeley MP, `--enable-mpbsd' + The Berkeley MP compatibility library (`libmp') and header file + (`mp.h') are built and installed only if `--enable-mpbsd' is used. + *Note BSD Compatible Functions::. - -File: gmp.info, Node: Reporting Bugs, Next: Integer Functions, Prev: MP Basics, Up: Top +MPFR, `--enable-mpfr' + The optional MPFR functions are built and installed only if + `--enable-mpfr' is used. These are in a separate library + `libmpfr.a' and are documented separately too (*note Introduction + to MPFR: (mpfr)Introduction to MPFR.). -Reporting Bugs -************** +Assertion Checking, `--enable-assert' + This option enables some consistency checking within the library. + This can be of use while debugging, *note Debugging::. - If you think you have found a bug in the MP library, please -investigate it and report it. We have made this library available to -you, and it is not to ask too much from you, to ask you to report the -bugs that you find. +Execution Profiling, `--enable-profiling=prof/gprof' + Profiling support can be enabled either for `prof' or `gprof'. + This adds `-p' or `-pg' respectively to `CFLAGS', and for some + systems adds corresponding `mcount' calls to the assembler code. + *Note Profiling::. - There are a few things you should think about when you put your bug -report together. +`MPN_PATH' + Various assembler 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 - You have to send us a test case that makes it possible for us to -reproduce the bug. Include instructions on how to run the test case. + MPN_PATH="sparc32/v8 sparc32 generic" - You also have to explain what is wrong; if you get a crash, or if -the results printed are incorrect and in that case, in what way. + 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. - It is not uncommon that an observed problem is actually due to a bug -in the compiler used when building MP; the MP code tends to explore -interesting corners in compilers. Therefore, please include compiler -version information in your bug report. This can be extracted using -`what `which cc`', or, if you're using gcc, `gcc -v'. Also, include -the output from `uname -a'. +Documentation + The document you're now reading is `gmp.texi'. The usual automake + targets are available to make PostScript `gmp.ps' and/or DVI + `gmp.dvi'. - If your bug report is good, we will do our best to help you to get a -corrected version of the library; if the bug report is poor, we won't -do anything about it (aside of chiding you to send better bug reports). + HTML can be produced with `makeinfo --html', see *Note Generating + HTML: (texinfo)makeinfo html. Or alternately `texi2html', see + *Note Texinfo to HTML: (texi2html)Top. - Send your bug report to: `bug-gmp@prep.ai.mit.edu'. + PDF can be produced with `texi2dvi --pdf' (*note PDF: (texinfo)PDF + Output.) or with `pdftex'. - 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. + Some supplementary notes can be found in the `doc' subdirectory.  -File: gmp.info, Node: Integer Functions, Next: Rational Number Functions, Prev: Reporting Bugs, Up: Top +File: gmp.info, Node: ABI and ISA, Next: Notes for Package Builds, Prev: Build Options, Up: Installing GMP -Integer Functions -***************** +ABI and ISA +=========== - This chapter describes the MP functions for performing integer -arithmetic. These functions start with the prefix `mpz_'. + 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. - Arbitrary precision integers are stored in objects of type `mpz_t'. + 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'. -* Menu: + 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, -* Initializing Integers:: -* Assigning Integers:: -* Simultaneous Integer Init & Assign:: -* Converting Integers:: -* Integer Arithmetic:: -* Comparison Functions:: -* Integer Logic and Bit Fiddling:: -* I/O of Integers:: -* Miscellaneous Integer Functions:: + ./configure ABI=32 - -File: gmp.info, Node: Initializing Integers, Next: Assigning Integers, Up: Integer Functions + In all cases it's vital that all object code used in a given program +is compiled for the same ABI. -Initialization and Assignment Functions -======================================= + 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. - The functions for integer arithmetic assume that all integer objects -are initialized. You do that by calling the function `mpz_init'. + 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. - - Function: void mpz_init (mpz_t INTEGER) - Initialize INTEGER with limb space and set the initial numeric - value to 0. Each variable should normally only be initialized - once, or at least cleared out (using `mpz_clear') between each - initialization. - Here is an example of using `mpz_init': +HPPA 2.0 (`hppa2.0*') - { - mpz_t integ; - mpz_init (integ); - ... - mpz_add (integ, ...); - ... - mpz_sub (integ, ...); - - /* Unless the program is about to exit, do ... */ - mpz_clear (integ); - } + `ABI=2.0w' + The 2.0w ABI uses 64-bit limbs and pointers and is available + on HP-UX 11 or up when using `cc'. `gcc' support for this is + in progress. Applications must be compiled with -As you can see, you can store new values any number of times, once an -object is initialized. + cc +DD64 - - Function: void mpz_clear (mpz_t INTEGER) - Free the limb space occupied by INTEGER. Make sure to call this - function for all `mpz_t' variables when you are done with them. + `ABI=2.0n' + The 2.0n ABI means the 32-bit HPPA 1.0 ABI but with a 64-bit + limb using `long long'. This is available on HP-UX 10 or up + when using `cc'. No `gcc' support is planned for this. + Applications must be compiled with - - Function: void * _mpz_realloc (mpz_t INTEGER, mp_size_t NEW_ALLOC) - Change the limb space allocation to NEW_ALLOC limbs. This - function is not normally called from user code, but it can be used - to give memory back to the heap, or to increase the space of a - variable to avoid repeated automatic re-allocation. + cc +DA2.0 +e - - Function: void mpz_array_init (mpz_t INTEGER_ARRAY[], size_t - ARRAY_SIZE, mp_size_t FIXED_NUM_BITS) - Allocate *fixed* limb space for all ARRAY_SIZE integers in - INTEGER_ARRAY. The fixed allocation for each integer in the array - is enough to store FIXED_NUM_BITS. If the fixed space will be - insufficient for storing the result of a subsequent calculation, - the result is unpredictable. + `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. - This function is useful for decreasing the working set for some - algorithms that use large integer arrays. + All three ABIs are available for CPUs `hppa2.0w' and `hppa2.0', but + for CPU `hppa2.0n' only 2.0n or 1.0 are allowed. - There is no way to de-allocate the storage allocated by this - function. Don't call `mpz_clear'! - -File: gmp.info, Node: Assigning Integers, Next: Simultaneous Integer Init & Assign, Prev: Initializing Integers, Up: Integer Functions +MIPS under IRIX 6 (`mips*-*-irix[6789]') + IRIX 6 supports the n32 and 64 ABIs and always has a 64-bit MIPS 3 + or better CPU. In both these ABIs GMP uses a 64-bit limb. A new + enough `gcc' is required (2.95 for instance). -Assignment Functions --------------------- + `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 - These functions assign new values to already initialized integers -(*note Initializing Integers::.). + gcc -mabi=n32 + cc -n32 - - Function: void mpz_set (mpz_t ROP, mpz_t OP) - - Function: void mpz_set_ui (mpz_t ROP, unsigned long int OP) - - Function: void mpz_set_si (mpz_t ROP, signed long int OP) - - Function: void mpz_set_d (mpz_t ROP, double OP) - - Function: void mpz_set_q (mpz_t ROP, mpq_t OP) - - Function: void mpz_set_f (mpz_t ROP, mpf_t OP) - Set the value of ROP from OP. + `ABI=64' + The 64-bit ABI is 64-bit pointers and integers. Applications + must be compiled with - - Function: int mpz_set_str (mpz_t ROP, char *STR, int BASE) - Set the value of ROP from STR, a '\0'-terminated C string in base - BASE. White space is allowed in the string, and is simply - ignored. The base may vary from 2 to 36. If BASE is 0, the - actual base is determined from the leading characters: if the - first two characters are `0x' or `0X', hexadecimal is assumed, - otherwise if the first character is `0', octal is assumed, - otherwise decimal is assumed. + gcc -mabi=64 + cc -64 - This function returns 0 if the entire string up to the '\0' is a - valid number in base BASE. Otherwise it returns -1. + 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. - -File: gmp.info, Node: Simultaneous Integer Init & Assign, Next: Converting Integers, Prev: Assigning Integers, Up: Integer Functions -Combined Initialization and Assignment Functions ------------------------------------------------- +PowerPC 64 (`powerpc64', `powerpc620', `powerpc630') - For convenience, MP 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...' + `ABI=aix64' + The AIX 64 ABI uses 64-bit limbs and pointers and is + available on systems `*-*-aix*'. Applications must be + compiled (and linked) with - Here is an example of using one: + gcc -maix64 + xlc -q64 - { - mpz_t pie; - mpz_init_set_str (pie, "3141592653589793238462643383279502884", 10); - ... - mpz_sub (pie, ...); - ... - mpz_clear (pie); - } + `ABI=32' + This is the basic 32-bit PowerPC ABI. No special compiler + options are needed for applications. -Once the integer has been initialized by any of the `mpz_init_set...' -functions, it can be used as the source or destination operand for the -ordinary integer functions. Don't use an initialize-and-set function -on a variable already initialized! - - Function: void mpz_init_set (mpz_t ROP, mpz_t OP) - - Function: void mpz_init_set_ui (mpz_t ROP, unsigned long int OP) - - Function: void mpz_init_set_si (mpz_t ROP, signed long int OP) - - Function: void mpz_init_set_d (mpz_t ROP, double OP) - Initialize ROP with limb space and set the initial numeric value - from OP. +Sparc V9 (`sparcv9' and `ultrasparc*') - - Function: int mpz_init_set_str (mpz_t ROP, char *STR, int BASE) - Initialize ROP and set its value like `mpz_set_str' (see its - documentation above for details). + `ABI=64' + The 64-bit V9 ABI is available on Solaris 2.7 and up and + GNU/Linux. GCC 2.95 or up, or Sun `cc' is required. + Applications must be compiled with - 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.) + gcc -m64 -mptr64 -Wa,-xarch=v9 -mcpu=v9 + cc -xarch=v9 - -File: gmp.info, Node: Converting Integers, Next: Integer Arithmetic, Prev: Simultaneous Integer Init & Assign, Up: Integer Functions + `ABI=32' + On Solaris 2.6 and earlier, and on Solaris 2.7 with the + kernel in 32-bit mode, only the plain V8 32-bit ABI can be + used, since the kernel doesn't save all registers. GMP still + uses as much of the V9 ISA as it can in these circumstances. + No special compiler options are required for applications, + though using something like the following requesting V9 code + within the V8 ABI is recommended. -Conversion Functions -==================== + gcc -mv8plus + cc -xarch=v8plus - This section describes functions for converting arbitrary precision -integers to standard C types. Functions for converting *to* arbitrary -precision integers are described in *Note Assigning Integers:: and -*Note I/O of Integers::. + `gcc' 2.8 and earlier only supports `-mv8' though. - - Function: unsigned long int mpz_get_ui (mpz_t OP) - Return the least significant part from OP. This function combined - with - `mpz_tdiv_q_2exp(..., OP, CHAR_BIT*sizeof(unsigned long int))' can - be used to extract the limbs of an integer. + Don't be confused by the names of these sparc `-m' and `-x' + options, they're called `arch' but they effectively control the + ABI. - - Function: signed long int mpz_get_si (mpz_t OP) - If OP fits into a `signed long int' return the value of OP. - Otherwise return the least significant part of OP, with the same - sign as OP. + 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 - If OP is too large to fit in a `signed long int', the returned - result is probably not very useful. + ./configure --build=none --host=sparcv9-sun-solaris2.7 ABI=64 - - Function: double mpz_get_d (mpz_t OP) - Convert OP to a double. - - - Function: char * mpz_get_str (char *STR, int BASE, mpz_t OP) - Convert OP to a string of digits in base BASE. The base may vary - from 2 to 36. - - If STR is NULL, space for the result string is allocated using the - default allocation function, and a pointer to the string is - returned. - - If STR is not NULL, it should point to a block of storage enough - large for the result. To find out the right amount of space to - provide for STR, use `mpz_sizeinbase (OP, BASE) + 2'. The two - extra bytes are for a possible minus sign, and for the terminating - null character. -  -File: gmp.info, Node: Integer Arithmetic, Next: Comparison Functions, Prev: Converting Integers, Up: Integer Functions +File: gmp.info, Node: Notes for Package Builds, Next: Notes for Particular Systems, Prev: ABI and ISA, Up: Installing GMP -Arithmetic Functions -==================== +Notes for Package Builds +======================== - - Function: void mpz_add (mpz_t ROP, mpz_t OP1, mpz_t OP2) - - Function: void mpz_add_ui (mpz_t ROP, mpz_t OP1, unsigned long int - OP2) - Set ROP to OP1 + OP2. + GMP should present no great difficulties for packaging in a binary +distribution. - - Function: void mpz_sub (mpz_t ROP, mpz_t OP1, mpz_t OP2) - - Function: void mpz_sub_ui (mpz_t ROP, mpz_t OP1, unsigned long int - OP2) - Set ROP to OP1 - OP2. + Libtool is used to build the library and `-version-info' is set +appropriately, having started from `3:0:0' in GMP 3.0. 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. - - Function: void mpz_mul (mpz_t ROP, mpz_t OP1, mpz_t OP2) - - Function: void mpz_mul_ui (mpz_t ROP, mpz_t OP1, unsigned long int - OP2) - Set ROP to OP1 times OP2. + 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. - - Function: void mpz_mul_2exp (mpz_t ROP, mpz_t OP1, unsigned long int - OP2) - Set ROP to OP1 times 2 raised to OP2. This operation can also be - defined as a left shift, OP2 steps. + Using `DESTDIR' or a `prefix' override with `make install' and a +shared `libgmpxx' may run into a libtool relinking problem, see *Note +Known Build Problems::. - - Function: void mpz_neg (mpz_t ROP, mpz_t OP) - Set ROP to -OP. + 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 +necessitate `i386' for x86s, or plain `sparc' (meaning V7) for SPARCs. - - Function: void mpz_abs (mpz_t ROP, mpz_t OP) - Set ROP to the absolute value of OP. + Users who care about speed will want GMP built for their exact CPU +type, to make 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. - - Function: void mpz_fac_ui (mpz_t ROP, unsigned long int OP) - Set ROP to OP!, the factorial of OP. + Note that `gmp.h' is a generated file, and will be architecture and +ABI dependent. -Division functions ------------------- + +File: gmp.info, Node: Notes for Particular Systems, Next: Known Build Problems, Prev: Notes for Package Builds, Up: Installing GMP - Division is undefined if the divisor is zero, and passing a zero -divisor to the divide or modulo functions, as well passing a zero mod -argument to the `mpz_powm' and `mpz_powm_ui' functions, will make these -functions intentionally divide by zero. This gives the user the -possibility to handle arithmetic exceptions in these functions in the -same manner as other arithmetic exceptions. +Notes for Particular Systems +============================ - There are three main groups of division functions: - * Functions that truncate the quotient towards 0. The names of these - functions start with `mpz_tdiv'. The `t' in the name is short for - `truncate'. +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 - * Functions that round the quotient towards -infinity. The names of - these routines start with `mpz_fdiv'. The `f' in the name is - short for `floor'. + ./configure --enable-shared --disable-static - * Functions that round the quotient towards +infinity. The names of - these routines start with `mpz_cdiv'. The `c' in the name is - short for `ceil'. + 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. - For each rounding mode, there are a couple of variants. Here `q' -means that the quotient is computed, while `r' means that the remainder -is computed. Functions that compute both the quotient and remainder -have `qr' in the name. +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. - - Function: void mpz_tdiv_q (mpz_t ROP, mpz_t OP1, mpz_t OP2) - - Function: void mpz_tdiv_q_ui (mpz_t ROP, mpz_t OP1, unsigned long - int OP2) - Set ROP to [OP1/OP2]. The quotient is truncated towards 0. +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 - - Function: void mpz_tdiv_r (mpz_t ROP, mpz_t OP1, mpz_t OP2) - - Function: void mpz_tdiv_r_ui (mpz_t ROP, mpz_t OP1, unsigned long - int OP2) - Set ROP to (OP1 - [OP1/OP2] * OP2). Unless the remainder is zero, - it has the same sign as the dividend. + ./configure --enable-cxx CPPFLAGS=-D__USE_STD_IOSTREAM - - Function: void mpz_tdiv_qr (mpz_t ROP1, mpz_t ROP2, mpz_t OP1, mpz_t - OP2) - - Function: void mpz_tdiv_qr_ui (mpz_t ROP1, mpz_t ROP2, mpz_t OP1, - unsigned long int OP2) - Divide OP1 by OP2 and put the quotient in ROP1 and the remainder - in ROP2. The quotient is rounded towards 0. Unless the remainder - is zero, it has the same sign as the dividend. +Microsoft Windows + On systems `*-*-cygwin*', `*-*-mingw*' and `*-*-pw32*' by default + GMP builds only a static library, but a DLL can be built instead + using - If ROP1 and ROP2 are the same variable, the results are undefined. + ./configure --disable-static --enable-shared - - Function: void mpz_fdiv_q (mpz_t ROP1, mpz_t OP1, mpz_t OP2) - - Function: void mpz_fdiv_q_ui (mpz_t ROP, mpz_t OP1, unsigned long - int OP2) - Set ROP to OP1/OP2. The quotient is rounded towards -infinity. + Static and DLL libraries can't both be built, since certain export + directives in `gmp.h' must be different. `--enable-cxx' cannot be + used when building a DLL, since libtool doesn't currently support + C++ DLLs. This might change in the future. - - Function: void mpz_fdiv_r (mpz_t ROP, mpz_t OP1, mpz_t OP2) - - Function: unsigned long int mpz_fdiv_r_ui (mpz_t ROP, mpz_t OP1, - unsigned long int OP2) - Divide OP1 by OP2 and put the remainder in ROP. Unless the - remainder is zero, it has the same sign as the divisor. +Microsoft C + A MINGW DLL build of GMP can be used with Microsoft C. Libtool + doesn't install `.lib' and `.exp' files, but they can be created + with the following commands, where `/my/inst/dir' is the install + directory (with a `lib' subdirectory). - For `mpz_fdiv_r_ui' the remainder is small enough to fit in an - `unsigned long int', and is therefore returned. + lib /machine:IX86 /def:_libs/libgmp-3.dll-def + cp libgmp-3.lib /my/inst/dir/lib + cp _libs/libgmp-3.dll-exp /my/inst/dir/lib/libgmp-3.exp - - Function: void mpz_fdiv_qr (mpz_t ROP1, mpz_t ROP2, mpz_t OP1, mpz_t - OP2) - - Function: unsigned long int mpz_fdiv_qr_ui (mpz_t ROP1, mpz_t ROP2, - mpz_t OP1, unsigned long int OP2) - Divide OP1 by OP2 and put the quotient in ROP1 and the remainder - in ROP2. The quotient is rounded towards -infinity. Unless the - remainder is zero, it has the same sign as the divisor. + MINGW uses `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 I/O choices provided by MS C is desired + then the suggestion is to use the GMP string functions and confine + I/O to the application. - For `mpz_fdiv_qr_ui' the remainder is small enough to fit in an - `unsigned long int', and is therefore returned. +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'. - If ROP1 and ROP2 are the same variable, the results are undefined. +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. - - Function: unsigned long int mpz_fdiv_ui (mpz_t OP1, unsigned long - int OP2) - This function is similar to `mpz_fdiv_r_ui', but the remainder is - only returned; it is not stored anywhere. +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 assembler code support for using just the common + instruction subset. To get executables that run on both, the + current suggestion is to use the generic C code (CPU `none'), + possibly with appropriate compiler options (like `-mcpu=common' for + `gcc'). CPU `rs6000' (which is not a CPU but a family of + workstations) is accepted by `config.sub', but is currently + equivalent to `none'. - - Function: void mpz_cdiv_q (mpz_t ROP1, mpz_t OP1, mpz_t OP2) - - Function: void mpz_cdiv_q_ui (mpz_t ROP, mpz_t OP1, unsigned long - int OP2) - Set ROP to OP1/OP2. The quotient is rounded towards +infinity. +Sparc CPU Types + `sparcv8' or `supersparc' on relevant systems will give a + significant performance increase over the V7 code. - - Function: void mpz_cdiv_r (mpz_t ROP, mpz_t OP1, mpz_t OP2) - - Function: unsigned long int mpz_cdiv_r_ui (mpz_t ROP, mpz_t OP1, - unsigned long int OP2) - Divide OP1 by OP2 and put the remainder in ROP. Unless the - remainder is zero, it has the opposite sign as the divisor. +Sparc App Regs + The GMP assembler 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.). - For `mpz_cdiv_r_ui' the negated remainder is small enough to fit - in an `unsigned long int', and it is therefore returned. + This makes that code unsuitable for use with the special V9 + `-mcmodel=embmedany' (which uses `g4' as a data segment pointer), + and for applications wanting to use those registers for special + purposes. In these cases the only suggestion currently is to + build GMP with CPU `none' to avoid the assembler code. - - Function: void mpz_cdiv_qr (mpz_t ROP1, mpz_t ROP2, mpz_t OP1, mpz_t - OP2) - - Function: unsigned long int mpz_cdiv_qr_ui (mpz_t ROP1, mpz_t ROP2, - mpz_t OP1, unsigned long int OP2) - Divide OP1 by OP2 and put the quotient in ROP1 and the remainder - in ROP2. The quotient is rounded towards +infinity. Unless the - remainder is zero, it has the opposite sign as the divisor. +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). - For `mpz_cdiv_qr_ui' the negated remainder is small enough to fit - in an `unsigned long int', and it is therefore returned. +x86 CPU Types + `i386' selects generic code which will run reasonably well on all + x86 chips. - If ROP1 and ROP2 are the same variable, the results are undefined. + `i586', `pentium' or `pentiummmx' code is good for the 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. - - Function: unsigned long int mpz_cdiv_ui (mpz_t OP1, unsigned long - int OP2) - Return the negated remainder, similar to `mpz_cdiv_r_ui'. (The - difference is that this function doesn't store the remainder - anywhere.) + `pentium4' and an SSE2 capable assembler are important for best + results on Pentium 4. The specific code is for instance roughly a + 2x to 3x speedup over the generic `i386' code. - - Function: void mpz_mod (mpz_t ROP, mpz_t OP1, mpz_t OP2) - - Function: unsigned long int mpz_mod_ui (mpz_t ROP, mpz_t OP1, - unsigned long int OP2) - Set ROP to OP1 `mod' OP2. The sign of the divisor is ignored, and - the result is always non-negative. +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. - For `mpz_mod_ui' the remainder is small enough to fit in an - `unsigned long int', and is therefore returned. + Old versions of `gas' don't support MMX instructions, in particular + version 1.92.3 that comes with FreeBSD 2.2.8 doesn't (and + unfortunately there's no newer assembler for that system). - - Function: void mpz_divexact (mpz_t ROP, mpz_t OP1, mpz_t OP2) - Set ROP to OP1/OP2. This function produces correct results only - when it is known in advance that OP2 divides OP1. + 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. - Since mpz_divexact is much faster than any of the other routines - that produce the quotient (*note References::. Jebelean), it is - the best choice for instances in which exact division is known to - occur, such as reducing a rational to lowest terms. - - - Function: void mpz_tdiv_q_2exp (mpz_t ROP, mpz_t OP1, unsigned long - int OP2) - Set ROP to OP1 divided by 2 raised to OP2. The quotient is - rounded towards 0. - - - Function: void mpz_tdiv_r_2exp (mpz_t ROP, mpz_t OP1, unsigned long - int OP2) - Divide OP1 by (2 raised to OP2) and put the remainder in ROP. - Unless it is zero, ROP will have the same sign as OP1. - - - Function: void mpz_fdiv_q_2exp (mpz_t ROP, mpz_t OP1, unsigned long - int OP2) - Set ROP to OP1 divided by 2 raised to OP2. The quotient is - rounded towards -infinity. - - - Function: void mpz_fdiv_r_2exp (mpz_t ROP, mpz_t OP1, unsigned long - int OP2) - Divide OP1 by (2 raised to OP2) and put the remainder in ROP. The - sign of ROP will always be positive. - - This operation can also be defined as masking of the OP2 least - significant bits. - -Exponentialization Functions ----------------------------- - - - Function: void mpz_powm (mpz_t ROP, mpz_t BASE, mpz_t EXP, mpz_t MOD) - - Function: void mpz_powm_ui (mpz_t ROP, mpz_t BASE, unsigned long int - EXP, mpz_t MOD) - Set ROP to (BASE raised to EXP) `mod' MOD. If EXP is negative, - the result is undefined. - - - Function: void mpz_pow_ui (mpz_t ROP, mpz_t BASE, unsigned long int - EXP) - - Function: void mpz_ui_pow_ui (mpz_t ROP, unsigned long int BASE, - unsigned long int EXP) - Set ROP to BASE raised to EXP. The case of 0^0 yields 1. - -Square Root Functions ---------------------- - - - Function: void mpz_sqrt (mpz_t ROP, mpz_t OP) - Set ROP to the truncated integer part of the square root of OP. - - - Function: void mpz_sqrtrem (mpz_t ROP1, mpz_t ROP2, mpz_t OP) - Set ROP1 to the truncated integer part of the square root of OP, - like `mpz_sqrt'. Set ROP2 to OP-ROP1*ROP1, (i.e., zero if OP is a - perfect square). - - If ROP1 and ROP2 are the same variable, the results are undefined. - - - Function: int mpz_perfect_square_p (mpz_t OP) - Return non-zero if OP is a perfect square, i.e., if the square - root of OP is an integer. Return zero otherwise. - -Number Theoretic Functions --------------------------- - - - Function: int mpz_probab_prime_p (mpz_t OP, int REPS) - If this function returns 0, OP is definitely not prime. If it - returns 1, then OP is `probably' prime. The probability of a - false positive is (1/4)**REPS. A reasonable value of reps is 25. - - An implementation of the probabilistic primality test found in - Seminumerical Algorithms (*note References::. Knuth). - - - Function: void mpz_gcd (mpz_t ROP, mpz_t OP1, mpz_t OP2) - Set ROP to the greatest common divisor of OP1 and OP2. - - - Function: unsigned long int mpz_gcd_ui (mpz_t ROP, mpz_t OP1, - unsigned long int OP2) - Compute the greatest common divisor of OP1 and OP2. If ROP is not - NULL, store the result there. - - If the result is small enough to fit in an `unsigned long int', it - is returned. If the result does not fit, 0 is returned, and the - result is equal to the argument OP1. Note that the result will - always fit if OP2 is non-zero. - - - Function: void mpz_gcdext (mpz_t G, mpz_t S, mpz_t T, mpz_t A, mpz_t - B) - Compute G, S, and T, such that AS + BT = G = `gcd' (A, B). If T is - NULL, that argument is not computed. - - - Function: int mpz_invert (mpz_t ROP, mpz_t OP1, mpz_t OP2) - Compute the inverse of OP1 modulo OP2 and put the result in ROP. - Return non-zero if an inverse exist, zero otherwise. When the - function returns zero, do not assume anything about the value in - ROP. - - - Function: int mpz_jacobi (mpz_t OP1, mpz_t OP2) - - Function: int mpz_legendre (mpz_t OP1, mpz_t OP2) - Compute the Jacobi and Legendre symbols, respectively. -  -File: gmp.info, Node: Comparison Functions, Next: Integer Logic and Bit Fiddling, Prev: Integer Arithmetic, Up: Integer Functions +File: gmp.info, Node: Known Build Problems, Prev: Notes for Particular Systems, Up: Installing GMP -Comparison Functions +Known Build Problems ==================== - - Function: int mpz_cmp (mpz_t OP1, 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. + You might find more up-to-date information at `http://swox.com/gmp/'. - - Macro: int mpz_cmp_ui (mpz_t OP1, unsigned long int OP2) - - Macro: int mpz_cmp_si (mpz_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. +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 - These functions are actually implemented as macros. They evaluate - their arguments multiple times. + ./configure CC=gcc-with-my-options - - Macro: int mpz_sgn (mpz_t OP) - Return +1 if OP > 0, 0 if OP = 0, and -1 if OP < 0. +DJGPP + 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. - This function is actually implemented as a macro. It evaluates its - arguments multiple times. + `make all' was found to run out of memory during the final + `libgmp.la' link on one system tested, despite having 64Mb + available. A separate `make libgmp.la' helped, perhaps recursing + into the various subdirectories uses up memory. - -File: gmp.info, Node: Integer Logic and Bit Fiddling, Next: I/O of Integers, Prev: Comparison Functions, Up: Integer Functions +`DESTDIR' and shared `libgmpxx' + `make install DESTDIR=/my/staging/area', or the same with a + `prefix' override, to install to a temporary directory is not + fully supported by current versions of libtool when building a + shared version of a library which depends on another being built + at the same time, like `libgmpxx' and `libgmp'. -Logical and Bit Manipulation Functions -====================================== + The problem is that `libgmpxx' is relinked at the install stage to + ensure that if the system puts a hard-coded path to `libgmp' within + `libgmpxx' then that path will be correct. Naturally the linker is + directed to look only at the final location, not the staging area, + so if `libgmp' is not already in that final location then the link + will fail. - These functions behave as if two's complement arithmetic were used -(although sign-magnitude is used by the actual implementation). + A workaround for this on SVR4 style systems, such as GNU/Linux, + where paths are not hard-coded, is to include the staging area in + the linker's search using `LD_LIBRARY_PATH'. For example with + `--prefix=/usr' but installing under `/my/staging/area', - - Function: void mpz_and (mpz_t ROP, mpz_t OP1, mpz_t OP2) - Set ROP to OP1 logical-and OP2. + LD_LIBRARY_PATH=/my/staging/area/usr/lib \ + make install DESTDIR=/my/staging/area - - Function: void mpz_ior (mpz_t ROP, mpz_t OP1, mpz_t OP2) - Set ROP to OP1 inclusive-or OP2. +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. - - Function: void mpz_com (mpz_t ROP, mpz_t OP) - Set ROP to the one's complement of OP. + The shared libraries `libgmp.so' and `libmp.so' are not affected by + this and any version of `strip' can be used on them. - - Function: unsigned long int mpz_popcount (mpz_t OP) - For non-negative numbers, return the population count of OP. For - negative numbers, return the largest possible value (MAX_ULONG). +`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'. - - Function: unsigned long int mpz_hamdist (mpz_t OP1, mpz_t OP2) - If OP1 and OP2 are both non-negative, return the hamming distance - between the two operands. Otherwise, return the largest possible - value (MAX_ULONG). + libgmp.la: $(libgmp_la_OBJECTS) $(libgmp_la_DEPENDENCIES) - It is possible to extend this function to return a useful value - when the operands are both negative, but the current - implementation returns MAX_ULONG in this case. *Do not depend on - this behavior, since it will change in future versions of the - library.* + Either use GNU Make, or as a workaround remove + `$(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). - - Function: unsigned long int mpz_scan0 (mpz_t OP, unsigned long int - STARTING_BIT) - Scan OP, starting with bit STARTING_BIT, towards more significant - bits, until the first clear bit is found. Return the index of the - found bit. +MacOS X and GCC + 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'). - - Function: unsigned long int mpz_scan1 (mpz_t OP, unsigned long int - STARTING_BIT) - Scan OP, starting with bit STARTING_BIT, towards more significant - bits, until the first set bit is found. Return the index of the - found bit. + Also, libtool currently cannot build C++ shared libraries on MacOS + X, so if `--enable-cxx' is desired then `--disable-shared' must be + used. Hopefully this will be fixed in the future. - - Function: void mpz_setbit (mpz_t ROP, unsigned long int BIT_INDEX) - Set bit BIT_INDEX in OP1. +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.) - - Function: void mpz_clrbit (mpz_t ROP, unsigned long int BIT_INDEX) - Clear bit BIT_INDEX in OP1. +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). - -File: gmp.info, Node: I/O of Integers, Next: Miscellaneous Integer Functions, Prev: Integer Logic and Bit Fiddling, Up: Integer Functions +Sequent Symmetry + Use the GNU assembler instead of the system assembler, since the + latter has serious bugs. -Input and Output Functions -========================== +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. - Functions that perform input from a stdio stream, and functions that -output to a stdio stream. Passing a NULL pointer for a STREAM argument -to any of these functions will make them read from `stdin' and write to -`stdout', respectively. +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. - 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. +Windows DLL test programs + When creating a DLL version of `libgmp', libtool creates wrapper + scripts like `t-mul' for programs that would normally be + `t-mul.exe', in order to setup the right library paths etc. This + works fine, but the absence of `t-mul.exe' etc causes `make' to + think they need recompiling every time, which is an annoyance when + re-running a `make check'. - - Function: size_t mpz_out_str (FILE *STREAM, int BASE, mpz_t OP) - Output OP on stdio stream STREAM, as a string of digits in base - BASE. The base may vary from 2 to 36. - - 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 36. If BASE is 0, the actual base is - determined from the leading characters: if the first two - characters are `0x' or `0X', hexadecimal is assumed, otherwise if - the first character is `0', octal is assumed, otherwise decimal is - assumed. - - Return the number of bytes read, or if an error occurred, return 0. - - - Function: size_t mpz_out_raw (FILE *STREAM, mpz_t OP) - Output OP on stdio stream STREAM, in raw binary format. The - integer is written in a portable format, with 4 bytes of size - information, and that many bytes of limbs. Both the size and the - limbs are written in decreasing significance order (i.e., in - big-endian). - - The output can be read with `mpz_inp_raw'. - - Return the number of bytes written, or if an error occurred, - return 0. - - The output of this can not be read by `mpz_inp_raw' from GMP 1, - because of changes necessary for compatibility between 32-bit and - 64-bit machines. - - - Function: size_t mpz_inp_raw (mpz_t ROP, FILE *STREAM) - Input from stdio stream STREAM in the format written by - `mpz_out_raw', and put the result in ROP. Return the number of - bytes read, or if an error occurred, return 0. - - This routine can read the output from `mpz_out_raw' also from GMP - 1, in spite of changes necessary for compatibility between 32-bit - and 64-bit machines. -  -File: gmp.info, Node: Miscellaneous Integer Functions, Prev: I/O of Integers, Up: Integer Functions +File: gmp.info, Node: GMP Basics, Next: Reporting Bugs, Prev: Installing GMP, Up: Top -Miscellaneous Functions -======================= +GMP Basics +********** - - 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. + *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.* - - 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. +* Menu: - - Function: size_t mpz_size (mpz_t OP) - Return the size of OP measured in number of limbs. If OP is zero, - the returned value will be zero. +* 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:: - *This function is obsolete. It will disappear from future MP - releases.* - - - Function: size_t mpz_sizeinbase (mpz_t OP, int BASE) - Return the size of OP measured in number of digits in base BASE. - The base may vary from 2 to 36. The returned value will be exact - or 1 too big. If BASE is a power of 2, the returned value will - always be exact. - - This function is useful in order to allocate the right amount of - space before 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 - terminating '\0'). -  -File: gmp.info, Node: Rational Number Functions, Next: Floating-point Functions, Prev: Integer Functions, Up: Top +File: gmp.info, Node: Headers and Libraries, Next: Nomenclature and Types, Prev: GMP Basics, Up: GMP Basics -Rational Number Functions -************************* +Headers and Libraries +===================== - This chapter describes the MP functions for performing arithmetic on -rational numbers. These functions start with the prefix `mpq_'. + 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. - Rational numbers are stored in objects of type `mpq_t'. + #include - All rational arithmetic functions assume operands have a canonical -form, and canonicalize their result. The canonical from means that the -denominator and the numerator have no common factors, and that the -denominator is positive. Zero has the unique representation 0/1. + Note however that prototypes for GMP functions with `FILE *' +parameters are only provided if `' is included too. - 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. *Note that this is an incompatible change from version 1 of -the library.* + #include + #include - - 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. + Likewise `' (or `') is required for prototypes +with `va_list' parameters, such as `gmp_vprintf'. And `' +for prototypes with `struct obstack' parameters, such as +`gmp_obstack_printf', when available. -* Menu: + All programs using GMP must link against the `libgmp' library. On a +typical Unix-like system this can be done with `-lgmp', for example -* Initializing Rationals:: -* Assigning Rationals:: -* Simultaneous Integer Init & Assign:: -* Comparing Rationals:: -* Applying Integer Functions:: -* Miscellaneous Rational Functions:: + gcc myprogram.c -lgmp - -File: gmp.info, Node: Initializing Rationals, Next: Assigning Rationals, Prev: Rational Number Functions, Up: Rational Number Functions + 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, -Initialization and Assignment Functions -======================================= + g++ mycxxprog.cc -lgmpxx -lgmp - - Function: void mpq_init (mpq_t DEST_RATIONAL) - Initialize DEST_RATIONAL 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. + GMP is built using Libtool and an application can use that to link +if desired, *note Shared library support for GNU: (libtool)Top. - - Function: void mpq_clear (mpq_t RATIONAL_NUMBER) - Free the space occupied by RATIONAL_NUMBER. Make sure to call this - function for all `mpq_t' variables when you are done with them. + 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. +Consult your compiler documentation, for instance *Note Introduction: +(gcc)Top. - - Function: void mpq_set (mpq_t ROP, mpq_t OP) - - Function: void mpq_set_z (mpq_t ROP, mpz_t OP) - Assign ROP from OP. - - - Function: void mpq_set_ui (mpq_t ROP, unsigned long int OP1, - unsigned long int OP2) - - Function: void mpq_set_si (mpq_t ROP, signed long int OP1, unsigned - long int OP2) - Set the value of ROP to OP1/OP2. Note that if OP1 and OP2 have - common factors, ROP has to be passed to `mpq_canonicalize' before - any operations are performed on ROP. -  -File: gmp.info, Node: Assigning Rationals, Next: Comparing Rationals, Prev: Initializing Rationals, Up: Rational Number Functions +File: gmp.info, Node: Nomenclature and Types, Next: Function Classes, Prev: Headers and Libraries, Up: GMP Basics -Arithmetic Functions -==================== +Nomenclature and Types +====================== - - Function: void mpq_add (mpq_t SUM, mpq_t ADDEND1, mpq_t ADDEND2) - Set SUM to ADDEND1 + ADDEND2. +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: - - Function: void mpq_sub (mpq_t DIFFERENCE, mpq_t MINUEND, mpq_t - SUBTRAHEND) - Set DIFFERENCE to MINUEND - SUBTRAHEND. + mpz_t sum; + + struct foo { mpz_t x, y; }; + + mpz_t vec[20]; - - Function: void mpq_mul (mpq_t PRODUCT, mpq_t MULTIPLIER, mpq_t - MULTIPLICAND) - Set PRODUCT to MULTIPLIER times MULTIPLICAND. +"Rational number" means a multiple precision fraction. The C data type +for these fractions is `mpq_t'. For example: - - Function: void mpq_div (mpq_t QUOTIENT, mpq_t DIVIDEND, mpq_t - DIVISOR) - Set QUOTIENT to DIVIDEND/DIVISOR. + mpq_t quotient; - - Function: void mpq_neg (mpq_t NEGATED_OPERAND, mpq_t OPERAND) - Set NEGATED_OPERAND to -OPERAND. +"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'. - - Function: void mpq_inv (mpq_t INVERTED_NUMBER, mpq_t NUMBER) - Set INVERTED_NUMBER to 1/NUMBER. If the new denominator is zero, - this routine will divide by zero. +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'.  -File: gmp.info, Node: Comparing Rationals, Next: Applying Integer Functions, Prev: Assigning Rationals, Up: Rational Number Functions +File: gmp.info, Node: Function Classes, Next: Variable Conventions, Prev: Nomenclature and Types, Up: GMP Basics -Comparison Functions -==================== +Function Classes +================ - - Function: int mpq_cmp (mpq_t OP1, mpq_t OP2) - Compare OP1 and OP2. Return a positive value if OP1 > OP2, zero - if OP1 = OP2, and a negative value if OP1 < OP2. + There are six classes of functions in the GMP library: - To determine if two rationals are equal, `mpq_equal' is faster than - `mpq_cmp'. + 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. - - Macro: int mpq_cmp_ui (mpq_t OP1, unsigned 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. + 2. Functions for rational number arithmetic, with names beginning with + `mpq_'. The associated type is `mpq_t'. There are about 40 + functions in this class, but the integer functions can be used for + arithmetic on the numerator and denominator separately. - This routine allows that NUM2 and DEN2 have common factors. + 3. Functions for floating-point arithmetic, with names beginning with + `mpf_'. The associated type is `mpf_t'. There are about 60 + functions is this class. - This function is actually implemented as a macro. It evaluates its - arguments multiple times. + 4. Functions compatible with Berkeley MP, such as `itom', `madd', and + `mult'. The associated type is `MINT'. - - Macro: int mpq_sgn (mpq_t OP) - Return +1 if OP > 0, 0 if OP = 0, and -1 if OP < 0. + 5. Fast low-level functions that operate on natural numbers. These + are used by the functions in the preceding groups, and you can + also call them directly from very time-critical user programs. + These functions' names begin with `mpn_'. The associated type is + array of `mp_limb_t'. There are about 30 (hard-to-use) functions + in this class. - This function is actually implemented as a macro. It evaluates its - arguments multiple times. + 6. Miscellaneous functions. Functions for setting up custom + allocation and functions for generating random numbers. - - Function: int mpq_equal (mpq_t OP1, mpq_t OP2) - Return non-zero if OP1 and OP2 are equal, zero if they are - non-equal. Although `mpq_cmp' can be used for the same purpose, - this function is much faster. -  -File: gmp.info, Node: Applying Integer Functions, Next: Miscellaneous Rational Functions, Prev: Comparing Rationals, Up: Rational Number Functions +File: gmp.info, Node: Variable Conventions, Next: Parameter Conventions, Prev: Function Classes, Up: GMP Basics -Applying Integer Functions to Rationals -======================================= +Variable Conventions +==================== - The set of `mpq' functions is quite small. In particular, there are -no functions for either input or output. But there are two macros that -allow us to apply any `mpz' function on the numerator or denominator of -a rational number. If these macros are used to assign to the rational -number, `mpq_canonicalize' normally need to be called afterwards. + GMP functions generally have output arguments before input +arguments. This notation is by analogy with the assignment operator. +The BSD MP compatibility functions are exceptions, having the output +arguments last. - - Macro: mpz_t mpq_numref (mpq_t OP) - - Macro: mpz_t mpq_denref (mpq_t OP) - Return a reference to the numerator and denominator of OP, - respectively. The `mpz' functions can be used on the result of - these macros. + 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 - -File: gmp.info, Node: Miscellaneous Rational Functions, Prev: Applying Integer Functions, Up: Rational Number Functions + mpz_mul (x, x, x); -Miscellaneous Functions -======================= + 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. - - Function: double mpq_get_d (mpq_t OP) - Convert OP to a double. + 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. - These functions assign between either the numerator or denominator -of a rational, and an integer. Instead of using these functions, it is -preferable to use the more general mechanisms `mpq_numref' and -`mpq_denref', together with `mpz_set'. + For efficiency reasons, avoid excessive initializing and clearing. +In general, initialize near the start of a function and clear near the +end. For example, - - Function: void mpq_set_num (mpq_t RATIONAL, mpz_t NUMERATOR) - Copy NUMERATOR to the numerator of RATIONAL. When this risks to - make the numerator and denominator of RATIONAL have common - factors, you have to pass RATIONAL to `mpq_canonicalize' before - any operations are performed on RATIONAL. - - This function is equivalent to `mpz_set (mpq_numref (RATIONAL), - NUMERATOR)'. - - - Function: void mpq_set_den (mpq_t RATIONAL, mpz_t DENOMINATOR) - Copy DENOMINATOR to the denominator of RATIONAL. When this risks - to make the numerator and denominator of RATIONAL have common - factors, or if the denominator might be negative, you have to pass - RATIONAL to `mpq_canonicalize' before any operations are performed - on RATIONAL. - - *In version 1 of the library, negative denominators were handled by - copying the sign to the numerator. That is no longer done.* - - This function is equivalent to `mpz_set (mpq_denref (RATIONAL), - DENOMINATORS)'. - - - Function: void mpq_get_num (mpz_t NUMERATOR, mpq_t RATIONAL) - Copy the numerator of RATIONAL to the integer NUMERATOR, to - prepare for integer operations on the numerator. - - This function is equivalent to `mpz_set (NUMERATOR, mpq_numref - (RATIONAL))'. - - - Function: void mpq_get_den (mpz_t DENOMINATOR, mpq_t RATIONAL) - Copy the denominator of RATIONAL to the integer DENOMINATOR, to - prepare for integer operations on the denominator. - - This function is equivalent to `mpz_set (DENOMINATOR, mpq_denref - (RATIONAL))'. + 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); + }