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The Zarith library


This library implements arithmetic and logical operations over arbitrary-precision integers.

The module is simply named Z. Its interface is similar to that of the Int32, Int64 and Nativeint modules from the OCaml standard library, with some additional functions. See the file z.mlip for documentation.

The implementation uses GMP (the GNU Multiple Precision arithmetic library) to compute over big integers. However, small integers are represented as unboxed Caml integers, to save space and improve performance. Big integers are allocated in the Caml heap, bypassing GMP's memory management and achieving better GC behavior than e.g. the MLGMP library. Computations on small integers use a special, faster path (in C or OCaml) eschewing calls to GMP, while computations on large intergers use the low-level MPN functions from GMP.

Arbitrary-precision integers can be compared correctly using OCaml's polymorphic comparison operators (=, <, >, etc.).

Additional features include:

  • a module Q for rationals, built on top of Z (see q.mli)
  • a compatibility layer Big_int_Z that implements the same API as Big_int from the legacy Num library, but uses Z internally


  • OCaml, version 4.04.0 or later.
  • Either the GMP library or the MPIR library, including development files.
  • GCC or Clang or a gcc-compatible C compiler and assembler (other compilers may work).
  • The Findlib package manager (optional, recommended).


  1. First, run the "configure" script by typing:

The configure script has a few options. Use the -help option to get a list and short description of each option.

  1. It creates a Makefile, which can be invoked by:

This builds native and bytecode versions of the library.

  1. The libraries are installed by typing:
   make install

or, if you install to a system location but are not an administrator

   sudo make install

If Findlib is detected, it is used to install files. Otherwise, the files are copied to a zarith/ subdirectory of the directory given by ocamlc -where.

The libraries are named zarith.cmxa and zarith.cma, and the Findlib module is named zarith.

Compiling and linking with the library requires passing the -I +zarith option to ocamlc / ocamlopt, or the -package zarith option to ocamlfind.

  1. (optional, recommended) Test programs are built and run by the additional command
  make tests

(but these are not installed).

  1. (optional) HTML API documentation is built (using ocamldoc) by the additional command
  make doc


The documentation for the latest release is hosted on GitHub Pages.


This Library is distributed under the terms of the GNU Library General Public License version 2, with a special exception allowing unconstrained static linking. See LICENSE file for details.


  • Antoine Miné, Sorbonne Université, formerly at ENS Paris.
  • Xavier Leroy, Collège de France, formerly at Inria Paris.
  • Pascal Cuoq, TrustInSoft.
  • Christophe Troestler (toplevel module)


Copyright (c) 2010-2011 Antoine Miné, Abstraction project. Abstraction is part of the LIENS (Laboratoire d'Informatique de l'ENS), a joint laboratory by: CNRS (Centre national de la recherche scientifique, France), ENS (École normale supérieure, Paris, France), INRIA Rocquencourt (Institut national de recherche en informatique, France).


Source files Description
configure configuration script[i] Z module and implementation for small integers
caml_z.c C implementation[i] wrapper to provide a Big_int compatible API to Z[i] rational library, pure OCaml on top of Z toplevel module to provide pretty-printing
projet.mak builds Z, Q and the tests
zarith.opam package description for opam[i] conversion between Zarith and MLGMPIDL
tests/ simple regression tests and benchmarks


The Zarith library implements arithmetic and logical operations over arbitrary-precision integers and rational numbers. The implementation, based on GMP, is very efficient.




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