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
Nativeint modules from the OCaml standard
library, with some additional functions. See the file
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 (coded in assembly for some platforms and functions) 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 (
This requires OCaml version 3.12.1 or later, though.
Additional features include:
- a module
Qfor rationals, built on top of
- a compatibility layer
Big_int_Zthat implements the same API as Big_int from the legacy
Numlibrary, but uses
- OCaml, preferably version 3.12.1 or later. (Earlier versions are usable but generic comparisons will misbehave.)
- 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 Perl programming language.
- The Findlib package manager (optional, recommended).
- First, run the "configure" script by typing:
configure script has a few options. Use the
-help option to get a
list and short description of each option.
- It creates a Makefile, which can be invoked by:
This builds native and bytecode versions of the library.
- The libraries are installed by typing:
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
The libraries are named
zarith.cma, and the Findlib module
Compiling and linking with the library requires passing the
ocamlopt, or the
-package zarith option to
- (optional, recommended) Test programs are built and run by the additional command
(but these are not installed).
- (optional) HTML API documentation is built (using
ocamldoc) by the additional command
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, Université Pierre et Marie Curie, formerly ENS Paris.
- Xavier Leroy, INRIA Paris-Rocquencourt.
- Pascal Cuoq, CEA LIST.
- 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).
|caml_z.c||C implementation of all functions|
|caml_z_*.S||asm implementation for a few functions|
|z_pp.pl||script to generate z.ml[i] from z.ml[i]p|
|z.ml[i]p||templates used to generate z.ml[i]p|
|big_int_z.ml[i]||wrapper to provide a Big_int compatible API to Z|
|q.ml[i]||rational library, pure OCaml on top of Z|
|zarith_top.ml||toplevel module to provide pretty-printing|
|projet.mak||builds Z, Q and the tests|
|tests/||simple regression tests and benchmarks|
z_pp.pl simply scans the asm file (if any) to see which functions have
an asm implementation. It then fixes the external statements in .mlp and
The argument to
z_pp.pl is the suffix
* of the
caml_z_*.S to use (guessed by configure).