The GNU MP Bignum 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.

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

Since version 6, GMP is distributed under the dual licenses,
GNU LGPL v3
and GNU GPL v2.
These licenses make the library free to use, share, and improve, and allow you
to pass on the result. The GNU licenses give freedoms, but also set 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 150
   arithmetic and logic functions in this category.
2. High-level rational arithmetic functions (mpq). This category consists of
   about 35 functions, but all mpz 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 70 functions in this
   category. New projects should strongly consider using the much more
   complete GMP extension library mpfr
   instead of mpf.
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. Of these
   functions about 60 are public.

---

Download the latest release of GMP

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. Starting from the repackaging of gmp-5.1.0 as
gmp-5.1.0a.tar.* the following key is used to sign GMP releases:


Key ID: 0x28C67298
Key type: 2560 bit RSA
Fingerprint: 343C 2FF0 FBEE 5EC2 EDBE F399 F359 9FF8 28C6 7298


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 GMP these days are due to problems not in GMP, but with
the compiler used for compiling the GMP sources. This is a major concern to
the GMP project, since an incorrect computation is an incorrect computation,
whether caused by a GMP bug or a compiler bug. We fight this by making the GMP
testsuite have great coverage, so that it should catch every possible
miscompilation.

---

GMP mailing lists

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

We’re blocking all mail from PR China, since 99% of
the spam arriving to the GMP moderators emanates from PR 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; we will open access for you.

---

Status of the current release

The current stable release is 6.2.1, released 2020-11-14.

Issues with GMP 6.2.1:

• While we added support for Apple’s new Arm based computers, our support
  has a problem. The problem is that Apple reserves CPU register x18, but
  GMP’s mpn/arm64 assembly code uses that register. While GMP runs fine in our
  tests, we expect things to go awry in some execution situation. (Apple has
  not been kind enough to specify how they use x18. Therefore, we don’t know
  what the consequences of using x18 might be.)

Issues with GMP 6.2.0:

• MacOS Xcode 11 prior to 11.3 miscompiles GMP, leading to crashes and
  miscomputation.

Issues with GMP 6.1.2:

• MacOS Xcode 11 prior to 11.3 miscompiles GMP, leading to crashes and
  miscomputation.

Issues with GMP 6.1.1:

• There are several issues with mini-gmp. Please see the special
  mini-gmp-status page.

Issues with GMP 6.1.0:

• An assembly file which is used for Intel Broadwell and Intel Skylake
  (except crippled Pentiums and Celerons without BMI2) will not work
  correctly for Windoze.
  Patch.
• See also issues for subsequent releases above.

Issues with GMP 6.0.0:

• [No issues found yet.]
• See also issues for subsequent releases above.

Issues with GMP 5.1.3:

• The documentation of mpn_set_str is incorrect and
  incomplete wrt allocation requirements.
  Patch.
• See also issues for subsequent releases above.

Issues with GMP 5.1.2:

• The functions mpn_sbpi1_div_qr_sec and
  mpn_sbpi1_div_r_sec compute incorrect results for some
  operands. With uniformly distributed random operands, the error is very
  hard to trigger, and for the intended use of these functions, operands can
  be expected to appear as such random operands from these functions’
  perspective. Patch.
• The internal function mpn_divrem_2 on Itanium clobbers two callee-saves
  registers. This can lead to miscomputations or crashes in the callers.
  Patch.
• See also issues for subsequent releases above.

Issues with GMP 5.1.1:

• Windows only: A 64-bit build for AMD Bulldozer and Piledriver chips, or
  a fat 64-bit build running on these chips, will not work correctly.
  Patch.
• The function mpz_powm_ui computes garbage if the base
  argument is over 15000 decimal or the mod argument is at least 7500 decimal
  digits. No other GMP powm function is affected.
  Patch.
• See also issues for subsequent releases above.

Issues with GMP 5.1.0:

• The mini-gmp.c file, which implements a subset of mpn and mpz, was not
  properly tested and contained a number of bugs. Please do not use the
  5.1.0 version of mini-gmp.c. Note that these bugs do not affect GMP
  itself.
• The included top-level Makefile.in has an automake-generated
  distcheck target which creates a world-writable directory.
  This target is not used in the GMP release process, but it is a potential
  security problem affecting users who invoke this make target. This
  problem (and no other) is corrected in the gmp-5.1.0a.tar.* set of
  files.
• See also issues for subsequent releases above.

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

---

Future releases

Please see the GMPng page for information on
what we’re working on.