The GNU Multiple Precision Arithmetic Library

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 optimised 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's main target platforms are Unix-type systems, such as GNU/Linux, Solaris, HP-UX, Mac OS X/Darwin, BSD, AIX, etc. It also is known to work on Windows in both 32-bit and 64-bit mode.

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

GMP is carefully developed and maintained, both technically and legally. We of course inspect and test contributed code carefully, but equally importantly we make sure we have the legal right to distribute the contributions, meaning users can safely use GMP. To achieve this, we will ask contributors to sign paperwork where they allow us to distribute their work.

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 always 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. 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 separately from GMP. (New projects should consider using mpfr instead of GMP's own mpf.)

Download the latest release of GMP

GMP 5.0.3	xz, 1685288 bytes	bz2, 2010173 bytes
Sweden, gmplib.org	gmp-5.0.3.tar.xz	gmp-5.0.3.tar.bz2
USA, ftp.gnu.org	gmp-5.0.3.tar.xz	gmp-5.0.3.tar.bz2

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:

Key ID: 0xDB899F46
Key type: 1024 bit DSA
Fingerprint: 73D4 6C36 6746 1E4B D939 7249 5D6D 47DF DB89 9F46


GnuPG signatures: gmp-5.0.3.tar.xz.sig gmp-5.0.3.tar.bz2.sig

Alternatively, you could check a cryptographic checksum:

SHA1	gmp-5.0.3.tar	bc0f6722eb48b637707b09b423497a9369f1b973
SHA256	gmp-5.0.3.tar	016c31cc924d65cb185e2ff9e32fecbaf8f34ff05ffdf48582f9fd160d50bee8

Instead of using a release, you may also get the latest code from the GMP repositories. This will require some more work compared to using a release.

Reporting bugs in GMP

Please first see the manual on how to report bugs. The proper address for bug reports is gmp-bugs at gmplib.org.

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. On these pages 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 it 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	gmplib.org/mailman/listinfo/gmp-bugs	gmplib.org/list-archives/gmp-bugs/
gmp-announce	gmplib.org/mailman/listinfo/gmp-announce	gmplib.org/list-archives/gmp-announce/
gmp-discuss	gmplib.org/mailman/listinfo/gmp-discuss	gmplib.org/list-archives/gmp-discuss/
gmp-devel	gmplib.org/mailman/listinfo/gmp-devel	gmplib.org/list-archives/gmp-devel/
gmp-commit	gmplib.org/mailman/listinfo/gmp-commit	gmplib.org/list-archives/gmp-commit/

The gmp-bugs 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. The now obsolete bug report mailing list bug-gmp at gnu.org is archived at the main GNU site.

The gmp-announce 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 5 messages per year).

The gmp-discuss 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 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.

You cannot send mail to any GMP mailing list from Google, since we cannot cope with the spam flood originating from the Google servers. While Google protects their accounts against spam, they are happy to damage the wider mailing infrastructure by being very lenient against spam originating from their systems.

You cannot subscribe an AOL address to any GMP mailing list, since AOL blocks our mail server until we register with them as a "bulk mailer", something we will certainly never do.

We're blocking most Chinese IP addresses since summer 2011, since 99% if the spam arriving to the GMP moderators emanates from China. If you are affected but have a legitimate reason to send mail to the GMP project, e.g., if you work at a university or corporation with an interest in GMP, please let us know.

Status of the current release

The current stable release is 5.0.3, released 2012-01-27.

Issues with GMP 5.0.3:

• There is a one-word buffer overrun bug affecting mpz_powm_sec and mpn_powm_sec, i.e. GMP's modexp functions specifically recommended for cryptographic applications. This bug affects all configurations, but has only been observed when GMP has been configured with --enable-assert --enable-alloca=debug. We have not been able to trigger misbehaviour in a normal build, but this buffer overrun can potentially be exploited by an attacker. It can onoly be triggered for mod argument sizes that match the KARATSUBA squaring threshold (the latter typically being so large that normal cryptographic applications will never strike this bug).
• The above buffer overrun bug might affect fat builds also in previous releases, except that here it might be several words ov overrun. We have not completely analysed this problem. We have not been able to trigger misbehaviour in a normal build.
• There are several problems in the multiply code that can be seen as ASSERTions being triggerered when GMP is configured with --enable-assert. We have not been able to trigger miscomputation in a normal build, meaning that our ASSERTions might simply be too strict.
• Gcc 4.3.2 miscompiles GMP on 64-bit machines; please use a different gcc version (e.g., gcc 4.3.1 and gcc 4.3.3 both work properly). We have not been able to find any workaround for this gcc bug. Unfortunately, Debian 5.0 has decided to stay with this trouble gcc version, resulting in that many users strike this bug.

Issues with GMP 5.0.2:

• Gcc 4.3.2 miscompiles GMP on 64-bit machines; please use a different gcc version (e.g., gcc 4.3.1 and gcc 4.3.3 both work properly). We have not been able to find any workaround for this gcc bug. Unfortunately, Debian 5.0 has decided to stay with this trouble gcc version, resulting in that many users strike this bug.
• There is a GMP bug in mpn/generic/dcpi1_bdiv_q.c that causes incorrect computation with extremely low probability, for unnormalised dividends. The bug might also result in a decrement of memory above dividends, with some potential security impact. The bug might affect several user-level routines, e.g., mpz_invert, but only for operands of at least 3000 bits (for smaller operands, a simpler algorithm is used). Patch.

Issues with GMP 5.0.1:

• Gcc 4.3.2 miscompiles GMP on 64-bit machines; please use a different gcc version (e.g., gcc 4.3.1 and gcc 4.3.3 both work properly). We have not been able to find any workaround for this gcc bug. Unfortunately, Debian 5.0 has decided to stay with this trouble gcc version, resulting in that many users strike this bug.)
• There are problems building GMP using some Apple "Xcode" versions. The symptom is typically about __gmpz_abs being multiply defined. The remedy for now is that you install a different Xcode.
• Under HP's HP-UX operating system running on an HPPA processor, the ABI 2.0N is not correctly supported by GMP 5.0.1 or 5.0.0. This results in many make check failures. The problem is in mpn/pa64/aors_n.asm. Please download a new version of the file from the GMP repository.
• There are spurious test failures with mpz/t-perfpow.c when using an ABI where GMP uses "long long" for internal computations. Examples of such ABIs are MIPS n32, HPUX 2.0n, and PowerPC mode32. Patch.

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

Future releases

A new major release, version 5.1.0, is planned for 2012. Here are some examples of planned improvements:

• Further improved multiplication, for both same-size and different-size operands, in particular for huge operands.
• Further improvements of division where the divisor is small (up to a few dozen words).
• Improved gcd, gcdext, and modular inversion code.
• New Legrende and Jacobi symbol code that run just as fast as the gcd code, O(n log²n log log n). The present GMP code is O(n²).
• Fast and simple n-factorial and binomial computation code will replace the current slow and complex code.
• And as for all GMP releases: improved assembly code for many operations and many processors.