Welcome to the GMP web pages! Here you can find information about the GNU Multiple Precision Arithmetic Library, the fastest bignum library on the planet!

IMPORTANT INFORMATION FOR ALL GMP USERS:

GMP is very often miscompiled! Please never use your newly compiled libgmp.a or libgmp.so without first running make check. If it doesn't complete without errors, don't trust the library. Please try another compiler release, or change optimization flags until it works. If you don't have the skill to isolate the problem, please report it to us if it was a GMP bug; else to the compiler vendor. (The compilers that cause most problems are HP's unbundled compilers and GCC, in particular Apple's GCC releases.)

What is GMP?

GMP is a free library for arbitrary precision arithmetic, operating on signed integers, rational numbers, and floating point numbers. There is no practical limit to the precision except the ones implied by the available memory in the machine GMP runs on. GMP has a rich set of functions, and the functions have a regular interface.

The main target applications for GMP are cryptography applications and research, Internet security applications, algebra systems, computational algebra research, etc.

GMP is carefully designed to be as fast as possible, both for small operands and for huge operands. The speed is achieved by using fullwords as the basic arithmetic type, by using fast algorithms, with highly optimized assembly code for the most common inner loops for a lot of CPUs, and by a general emphasis on speed.

GMP is faster than any other bignum library. The advantage for GMP increases with the operand sizes for many operations, since GMP uses asymptotically faster algorithms.

The first GMP release was made in 1991. It is continually developed and maintained, with a new release about once a year.

GMP is distributed under the GNU LGPL. This license makes the library free to use, share, and improve, and allows you to pass on the result. The license gives freedoms, but also sets firm restrictions on the use with non-free programs.

GMP is part of the GNU project. For more information about the GNU project, please see the official GNU web site.

GMP is brought to you by a team listed in the manual.

GMP function categories

There are several categories of functions in GMP:

1. High-level signed integer arithmetic functions (mpz). There are about 140 arithmetic and logic functions in this category.
2. High-level rational arithmetic functions (mpq). This category consists of about 35 functions, but all signed integer arithmetic functions can be used too, by applying them to the numerator and denominator separately.
3. High-level floating-point arithmetic functions (mpf). This is the GMP function category to use if the C type `double' doesn't give enough precision for an application. There are about 65 functions in this category.
4. C++ class based interface to all of the above. (The C functions and types can of course be used directly from C++ too.)
5. Low-level positive-integer, hard-to-use, very low overhead functions are found in the mpn category. No memory management is performed; the caller must ensure enough space is available for the results. The set of functions is not regular, nor is the calling interface. These functions accept input arguments in the form of pairs consisting of a pointer to the least significant word, and an integral size telling how many limbs (= words) there are in that argument. The functions in the other categories call mpn for almost all their calculations.
6. Berkeley MP compatible functions.
7. Externally supported: High-level floating-point accurately rounding arithmetic functions (mpfr). See the mpfr site for more information. Starting with GMP 4.2, mpfr is released only separately from the project site.

GMP documentation (online and offline)

Complete documentation for GMP is available in the online GMP Manual. It is also available for download in a number of formats:

DVI format	170078 bytes bzip2'ed
PostScript format	320601 bytes bzip2'ed
PDF format	1002466 bytes

These manual files are compressed using bzip2.

The speed of GMP varies a lot on different CPUs. See the GMPbench 0.1 results, or the really obsolete GMP speed chart for details.

Download the latest release of GMP

Location
Sweden, gmplib.org	gmp-4.2.4.tar.bz2	gmp-4.2.4.tar.gz
USA, East, ftp.gnu.org	gmp-4.2.4.tar.bz2	gmp-4.2.4.tar.gz

To try to verify that the file you have downloaded has not been tampered with, you can check that the GnuPG signature matches the contents of the file. Use your GnuPG software or a key server directly to get the key that was used for creating the signature. These are the properties of the signing key:

Name: Swox AB (Software signing key 2004) <info@swox.com>
Key ID: 0xDB899F46
Key type: 1024 bit DSA
Fingerprint: 73D4 6C36 6746 1E4B D939 7249 5D6D 47DF DB89 9F46


The GnuPG signature of gmp-4.2.4.tar.bz2 is here: ftp://ftp.gmplib.org/pub/gmp-4.2.4.tar.bz2.sig

The GnuPG signature of gmp-4.2.4.tar.gz is here: ftp://ftp.gmplib.org/pub/gmp-4.2.4.tar.gz.sig

Alternatively, you could check the MD5 checksum:

MD5 (gmp-4.2.4.tar.bz2) = fc1e3b3a2a5038d4d74138d0b9cf8dbe
MD5 (gmp-4.2.4.tar.gz) = 430f966bf8fe28d45ad8670a52b40e8c
SHA1 (gmp-4.2.4.tar.bz2) = bb721f94fbeeb8c609104540b408da6707c370ec
SHA1 (gmp-4.2.4.tar.gz) = a92b7a67543010ed917c054c01de67732b8d91a9


Improving GMP

Since GMP is free software, anybody can improve it and pass on the result, as permitted by the GNU LGPL. If you need an enhancement, but don't want to do the work yourself, you can pay somebody to do it for you. Try asking gmp-discuss@swox.com! For example, clever computer manufacturers should have somebody tune GMP for their processors!

If you have written an improvement, please send it to gmp-devel@swox.com so that it may be included in the next public release. If you are working on an improvement, please write to the same address, to make sure your effort is not duplicated.

There are up-to-date lists of improvements we think would be useful to many users. There are both smaller tasks and larger projects. Some of these projects have a section at the GMP development tidbits page.

Reporting bugs in GMP

Please first see the manual on how to report bugs. The FAQ below might also be useful reading. The proper address for bug reports is gmp-bugs@swox.com.

Most problems with compiling GMP these days are due to problems not in GMP, but with the compiler. In the past, system compilers caused the most trouble, but in the last years, gcc has gradually caused more and more trouble. Here, we don't list compiler problems, just problems with the GMP code itself. To save you some time, we suggest that you cut any compiler error message and paste them into your favourite web search engine before you report problems to the GMP bug report list.

GMP mailing lists

List	Subscribe URL	Archive URL
gmp-bugs@swox.com	http://swox.com/mailman/listinfo/gmp-bugs	http://swox.com/list-archives/gmp-bugs/
gmp-announce@swox.com	http://swox.com/mailman/listinfo/gmp-announce	http://swox.com/list-archives/gmp-announce/
gmp-discuss@swox.com	http://swox.com/mailman/listinfo/gmp-discuss	http://swox.com/list-archives/gmp-discuss/
gmp-devel@swox.com	http://swox.com/mailman/listinfo/gmp-devel	http://swox.com/list-archives/gmp-devel/

The gmp-bugs@swox.com list is intended for bug reports. Please do not send general questions to that list. Information on how to write useful bug reports is available in the manual. Archives of the now obsolete bug report mailing list bug-gmp@gnu.org are available at the main GNU site http://lists.gnu.org/archive/html/bug-gmp/.

The gmp-announce@swox.com list is where important announcements from the GMP maintainers are made. All GMP users should be on this list. It is really very low volume (around one message per year).

The gmp-discuss@swox.com list is intended for discussing GMP issues with other users and developers. This is NOT for bug reports. This is the right place to ask questions, but please check the manual first.

The gmp-devel@swox.com list is for the technical discussions between GMP developers, and in general, non-developers will not be allowed to post here. Therefore, this list is moderated.

Note that we perform spam and virus filtering of these lists. The lists have been 100% spam-free during the last years.

Frequently asked questions

Q1: Is there a C++ wrapper for GMP?

A1: Yes, beginning with GMP 4.0 one is bundled with the release.

Q2: When will the next release happen?

A2: See Future releases below.

Q3: I get a segfault in a program that uses GMP to calculate numbers with several hundred thousand digits. Why?

A3: Upgrade to GMP 4.2.x. (Previous version of GMP allocated huge blocks of temporary memory on the stack, causing problems for some system.)

Q4: Are there known bugs in GMP?

A4: See under "Status ..." right below.

Q5: When running make check or when trying to link my program to gmp, I get error messages about libgcc_s.so.1. What's the deal?

A5: As the name suggests, libgcc_s.so.1 is a gcc support library. It is not within GMP's power to locate this file. You need to find out why your gcc installation doesn't properly point to its internal files.

Status of the current release

The current release is 4.2.4, released 2008-09-19. It fixes some minor problems found in 4.2.3. Note that we did not to work around all compiler bugs in this release. Never forget to do  make check  after building the library to make likely it was not miscompiled!

Issues with GMP 4.2.4:

• Miscompilation on several platforms using several different compilers. There is nothing the GMP developers can do about this. Remember to run make check!

Additional issues with GMP 4.2.3:

• [2008-08-25] The exponent base fix from 2007-12-10 caused unary plus to become invalid. That was an unintentional change. Patch
• [2008-08-25] When passing mpf_set_str, mpf_init_set_str, or mpf_inp_str a number with a mantissa of larger precision than the destination variable, a buffer overrun may occur. The overrun can be arbitrarily large. The problem is a completely incorrect allocation in mpf_set_str (in the file mpf/set_str), where the destination variable's precision was used for an allocation that needed a size propotional to the string size. Patch

Additional issues with GMP 4.2.2:

• [2007-12-10] When using mpf_set_str, mpf_init_set_str, or mpf_inp_str with a base > 36, the supplied base will actually be ignored, and the exponent 0 will be supplanted. Patch

Additional issues with GMP 4.2.1:

• [2006-11-30] With the C++ wrapper, ternary operations such as a=c+b*a where the destination variable is also used as a source, will compute garbage. Patch
• [2006-09-23] In mpz_set_d, arguments smaller than 1e-19 will trigger undefined behaviour, typically a crash. Note that this is a somewhat degenerate use of mpz_set_d that should not normally happen, since any arguments < 1 will yield 0. Patch
• [2006-05-24] On ia64-*-hpux, using the 32-bit ABI, mpz_popcount, mpz_hamdist, and mpn_popcount will work unreliably when GMP is compiled with certain compilers. The symptom is segmentation fault. This is due to a GMP bug. Patch
• [2006-05-17] On powerpc-ibm-aix, using the system assembler, the assembly code will yield syntax errors. Patch
• [2006-05-17] On VMX/Altivec capable powerpc processors, there are problems using old toolchains resulting in syntax errors. Also, not all such processors are properly recognized, leading to an inferior build. Patch [Updated 2006-06-12 to apply more smoothly]
• [2006-05-17] The --enable-fat feature has two problems. First, some GNU/Linux systems give an undefined symbol for an orphaned object, due to a bug in mpn/generic/addsub_n.c. Second, GMP's build system passes options such as -march=athlon or -march=pentium4, and this can of course result in surprises for older processors. Patch [Updated 2006-06-12 to apply more smoothly]
• [2006-05-04] GMP does not build on MacInteltosh machines. We've been told that the main problem is a serious Apple linker bug that Apple hasn't fixed for several years. There are ugly GMP workarounds floating around the net that we will not apply to GMP.

Additional issues with GMP 4.2:

• The solib numbers for the shared version of libgmp and libgmpxx are very wrong, making them appear older than version 4.1.4.

For patches to older GMP versions, please see the Info on older GMP releases.

Projects using GMP

There are many interesting projects that rely on GMP. Here are a few examples:

• MPFR, an add-on library for floating-point arithmetic. This library's mpfr functions are usually to prefer before GMP's own mpf functions.
• PARI/GP, a software package for computer-aided number theory.
• NTL, a number theory library.
• lsh is a project to develop a free (GPLed) implementation of the Secure Shell protocol V2.
• LiDIA, an object-oriental library for computational number theory.
• ECMNET, a factorization project initiated and coordinated by Paul Zimmermann. Please join it if you have free computer cycles!
• CLN by Bruno Haible, which uses low-level routines from GMP to build a different high-level user interface.
• The Kaffe project . The well-known Java machine.
• Some well-known non-free algebra systems are now using GMP. While this is a recognition of GMP, these programs' non-free nature is unfortunate.

Try GMP!

Demo 1 -- Integer expressions

Enter an integer expression in the field below. The expression may include +, -, *, /, %, ^ (exponentiation), and ! (factorial), the n-ary functions `gcd', `lcm', `and', `ior', `xor', `mul', `plus', the binary functions `minus', `div', `mod', `rem', and the unary function `popc' (population count). Most functions may also be used in infix form. All constants must be integers.

An example of a valid expression is: 1 + gcd(87324,78263148,7896) * (10^1989879887 mod 471!)

This is computed by demos/pexpr.c from the GMP distribution.

Demo 2 -- Find Anagrams

The program generating these anagrams forms special sums representing the characters of a string, adds and compares such sums to figure out what strings can be combined. Since the sums can be several hundred bits large, GMP comes in handy.

Future releases

GMP 4.3.0 will be released during 2008. It will come with speed improvements to various functions, as well as better amd64 code.

GMP 5.0 is planned to come out in a couple of years. This release will make all functions of GMP sub-quadratic, including gcd, gcdext, exact division, modular computation (by means of redc), etc. Truncating division will be improved from O(M(n)log(n)) to O(M(n)). The mpn layer will be extended to be much more complete, and mpz will as a result become simpler. More complete list:

• An extended mpn layer with a^b mod c, redc, and many other functions currently only available in mpz, or not available in GMP at all.
• Much faster multiplication assembly loops for many machines, by means of "overlapped software pipelining". Since these loops are basic GMP building blocks, all higher level operations are affected. Flow chart outlining the principles.
• Faster huge operands multiplication by means of improved FFT code.
• Faster small operands division by means of multi-limb divisor inverse approximations.
• Asymptotically faster division by means of Newton inverses and Barrett's algorithm.
• New user-visible mod and division routines for invariant divisors.
• New user-visible multi-limb routines for invariant multiplicands.
• Sub-quadratic gcd, extended gcd, redc, exact division.
• Improved allocation scheme for library-internal temporaries. This will streamline things, and avoid allocating huge amounts of memory on the stack, but also reduce overall temporary allocation.
• Improvements for better caching effectiveness. (In assembly code, in operands splitting strategies, and in temporary allocation.)
• Support at the mpn and mpz levels for operands of up to 2⁵⁰ bits (on 64-bit machines). Current limits are: on 32-bit machines, 2³¹ bits; on 64-bit machines, 2³⁷ bits.
• Pending vendor sponsorship: improved assembly support for AMD64, POWER4, POWER5, PPC970, Alpha, Itanium.