From: mrr@scss3.cl.msu.edu (Mark Riordan)
Subject: List of large integer arithmetic packages
Organization: Michigan State University
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Summary: C functions to do arbitrary-precision arith
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This is the file BIGNUMS.TXT from ripem.msu.edu, last updated April 1993.

In response to Email requests, I have assembled this list of
large-integer arithmetic packages of which I have heard.
Most of these are C function libraries, available in source form.

For your convenience, I have placed copies of
some of these on ripem.msu.edu (35.8.1.178).  They are
available for anonymous FTP in the directory "pub/bignum".
However, what I have may not be the most current version in all cases.

Here they are, in no particular order:

mp
    Multiple Precision package that comes with some Unixes
    
    Multiple precision package accessed via -lmp flag on your
    compiler.  Provides +, -, *, /, gcd, exponentiation,
    sqrt.  Comes with SunOS, NeXT Mach, BBN Mach 1000, 
    and probably a few others.  See "man mp".  
    Object code only, of course.

PARI
    Henri Cohen, et al., Universite Bordeaux I, Paris, FRANCE
    
    Multiple precision desk calculator and library routines.
    Contains optimized assembly code for Motorola 68020, 
    semi-optimized code for SPARC, and apparently rather slow
    generic C version.  Does both integers and reals.
    Does vectors and matrices as well as scalars.
    Contains a number of advanced functions, some of which I've
    never heard of.  ("Weber's function"?)
    Has a factorization function, primality test, & other related stuff.
    Plenty of TEX documentation.
    Public domain, but you can't distribute modified versions.
    Available via anonymous FTP from math.ucla.edu.  There seem to
    be Mac- and NeXT-specific versions there in addition to:
    Filename:  pari-1.35a.tar.Z
    
Arithmetic in Global Fields  (Arith)
    Kevin R. Coombes, David R. Grant
    
    Package of routines for arbitrary precision integers or
    polynomials over finite fields.  Includes basic +, -, *, /
    and a few others like gcd.  Source code in C.
    Distributed under the terms of the GNU public license.
    Includes man pages and TEX documentation.
    Filename:  arith.tar.Z

Arbitrary Precision Math Library
    Lloyd Zusman   Los Gatos, CA
    
    C package which supports basic +, -, *, /.  Provides for radix
    points (i.e., non-integers).  Not as polished as the others here.
    Posted to comp.sources.misc in October 1988.
    Filename:  apml.tar.Z
    
BigNum
    J. Vuillemin, INRIA, FRANCE, and others.
    Distributed by Digital Equipment Paris Research Lab (DECPRL)
    
    A "portable and efficient arbitrary-precision integer" package.
    C code, with generic C "kernel", plus assembly "kernels" for
    MC680x0, Intel i960, MIPS, NS32032, Pyramid, and of course VAX.
    This is probably one of the better-known packages of this type.
    Implements +, -, *, /, mod, plus logical operations OR, AND, XOR.
    Both signed and unsigned arithmetic available.
    Available via email from librarian@decprl.dec.com.
    You will receive 5 shell archives.  Give your postal address
    and you will also receive printed documentation from France.
    Package includes TEX documentation.
    Publicly available for non-commercial use.
    I removed this from my archive when I heard a rumor that PRL
    doesn't like others to distribute it.  However, BIGNUM *is*
    distributed as part of ecpp (see below).

Lenstra's package
    Arjen Lenstra   Bellcore
    
    Portable unsigned integer package written entirely in C.
    Includes +, -, *, /, exponentiation, mod, primality testing,
    sqrt, random number generator, and a few others.  The package
    was uncommented and undocumented; I have tried to add enough
    comments to get by.  This is the only of these packages that I
    have actually used.  It works well and is very portable.  
    I haven't done any benchmarks against the others, but the code 
    looks clever & Lenstra is an accomplished number theorist.
    Unlike the other packages here, this one requires you to allocate
    storage statically--only a problem if your numbers are really huge.
    Arjen has placed the code in the public domain.  
    Filename:  lenstra.tar.Z

lenstra_3.1
    Arjen Lenstra,  Bellcore

    An improved version of Arjen's package above.  This one
    does signed arithmetic and dynamic allocation (which can be turned
    off as an option). Has a few new routines, too.  "lenstra_3.1" contains
    minor bugfixes to the previously-available "lenstra_2" and "lenstra_3".
    Filename:  lenstra_3.1.c

bmp  (Brent's Multiple Precision?)
    R. P. Brent

    1981 vintage FORTRAN code to do extended precision floating &
    fixed point arithmetic.  Includes most of the mathematical
    functions you'd find in a FORTRAN run-time library.
    This code is an ACM algorithm, number 524.
    To obtain, send a mail message to  netlib@ornl.gov
    containing the line "send mp.f from bmp" or better yet, perhaps
    just start with "help".

SPX
    Kannan Alagappan & Joseph Tardo, DEC
    
    This is a huge prototype public key authentication system
    based on RSA.  I mention it here because those who have heard
    of SPX have probably correctly guessed that it contains a large
    integer package and I want to inform you that the large integer
    package it contains is indeed DEC's BigNum from France.
    You can get a beta test copy of SPX from crl.dec.com (192.58.206.2). 
    Use it only for testing, as it "may" expire on a certain date.
    (I don't know whether this has expired yet.)

amp  (Antti's Multiple Precision?)
    Antti Louko   alo@kampi.hut.fi

    Multiple precision integer package in C.  Includes +, -, *, /, %,
    pow, mod, 1/x mod y, random, sqrt, gcd.  Available for non-commercial
    use.  The package includes "share-secret", a public key system based
    on the Diffie-Hellman algorithm.
    This is normally part of the well-known "des-dist.tar.Z",
    but I have removed the DES part to avoid having to deal with 
    cryptographic export laws, and have named the result:
    Filename:  amp.tar.Z

gennum  
    Per Bothner   U of Wisconsin-Madison

    C++ routines and classes to do generic arithmetic, both
    integer and rational.  
    Formerly available on sevenlayer.cs.wis.edu.  However, it
    seems to have disappeared.  Sorry.

MIRACL
    (By someone in Dublin, Ireland)

    Integer and fractional multiple precision package.
    Includes factorization, primality testing, encryption.
    Not public domain, apparently.  It is available from the Austin
    Code Works.  (See ads in Byte Magazine or Dr. Dobbs.)

precision
    Dave Barrett  barrettd@tigger.colorado.edu

    Multiple precision integer package in C with +,-,*,/, sqrt, rand,
    mod, pow, log.  Simple vector support.  Does dynamic allocation of memory.
    Free as long as you don't sell it or any program that uses it.
    Filename:  precision.tar.Z

UBASIC
    Prof. Yuji Kida, Rikkyo University, Nishi-Ikebukuro 3, Tokyo 171, Japan
    kida@rkmath.rikkyo.ac.jp

    Multiple-precision version of the BASIC programming language,
    for MS-DOS.  Includes floating point.  Said (by Keith Briggs)
    to be pretty fast.  Object only, I think.  ervin@morekypr.bitnet
    says:  "This is the best package that I know of for
    fast arithmetic.  Has a version optimized for 386 machines.  Includes
    routines to do MPQS, the fastest currently known general factoring
    algorithm.  An additional file is at both sites to allow MPQS to use
    hard drives so that it can factor up to 80 digits.  Many number
    theoretical functions are included in UBASIC.  It allows over 2500
    digits of precision."
    Available via anonymous FTP from shape.mps.ohio-state.edu,
    or simtel20.army.mil, or wuarchive.wustl.edu.

calc_v22
    Unknown

    MS-DOS C-like language that allows "infinite" precision.
    Nice intrinsic functions.  ervin@morekypr.bitnet reports problems
    when changing precision on the fly.
    See simtel20 or wuarchive.

briggs_arith
    Keith Briggs (kbriggs@mundoe.maths.mu.oz.au)

    Turbo Pascal 5 source for routines that do multiple-precision
    +, -, *, /, sqrt, gcd, factoring, rand for integers; also includes
    +, -, *, / and rand for rational numbers.
    Filename:  briggs_arith.pas

Institute fur Experimentelle Mathematik
    Dr Gerhard Schneider (?)

    Fast C multiple-precision subroutine library.
    I don't know anything about it; sl25@ely.cl.cam.ac.uk says
    to contact MAT420@DE0HRZ1A.BITNET for more info.
    Postal Address:
    Institute fur Experimentelle Mathematik
    EllernStr 29
    D4300 Essen-12    GERMANY

LongInt
    Markus Mueller (mueller@komsys.tik.ethz.ch)

    "Multi precision arithmetic written in MODULA-2, with the most time critical
    parts written in Assembler. Includes basic arithmetics (+, -, *, /, %) as
    well as arithmetics MODULO a number. An additional module provides a
    collection of procedures for primality testing, gcd, multiplicative
    inverse and more. The package is part of a Privacy Enhanced Mail (PEM)
    package which includes a PEM mailer, RSA key generator and Certificate
    generation tools."

    Source is in Modula-2, C, and assembler for Sun 3.  LongInt has
    also been ported to MS-DOS under Logitech Modula-2 and Turbo
    Assembler.  Availability:  free for university use (research and
    education); otherwise, a source license is required.  To obtain,
    write or email to:

        Markus Mueller
        Bertastrasse 7
        CH-8953 Dietikon
        Switzerland
        email:  mueller@komsys.tik.ethz.ch

bignum-1.2
    Henrik.Johansson@Nexus.Comm.SE

    Bignum package written in portable C.  Will in the future
    conform to the Common Lisp functions that handles integers.
    Currently includes +, -, *, /, exponentiation, "exptmod",
    comparison, random numbers, and gcd.
    Filename: bignum-1.2

GNU Multiple Precision
    GNU (Free Software Foundation) multiple precision package.
    I haven't looked at it yet.  This is current as of April 1992,
    but there may be a more recent version by the time you read 
    this.  This package is very widely available on FTP sites.
    Filename: gmp-1.2.tar.Z

Elliptic Curve Primality Proving 
    Francois Morian, France.

    Large package to prove the primality of any prime.
    Includes Inria's BIGNUM package. 
    Obtained from ftp.inria.fr (128.93.1.26).
    Filename: ecpp.V3.4.1.tar.Z

PGP (Pretty Good Privacy)
    Philip Zimmermann   prz@sage.cgd.ucar.EDU

    Intel-based crypto package that includes bignum routines in C,
    said to be quite fast for Intel processors.  Unix and Mac
    versions also available.
    The crypto package violates RSA patents, but the bignum routines
    can be used without fear of legal repercussions.

Bell's Arbitrary Precision Calculator
    David I. Bell, Australia  (dbell@pdact.pd.necisa.oz.au)

    Arbitrary-precision calculator with good online help, C-like
    language, many builtin functions, support for integers,
    rational numbers (they work like floating point), complex numbers,
    matrices, strings, lists, files, "objects".  Includes 
    gcd, primality testing, even trig functions.  Recommended.
    (Large package, though.)  Obtained from comp.sources.unix.
    Filename: calc-1.24.7.tar.Z

Built-in support in other languages
    Various

    Multiple precision arithmetic is available in a number of 
    programming languages, such as Lisp and ABC (cf. mcsun.eu.net).
    Perl (by Larry Wall, available from devvax.jpl.nasa.gov)
    includes source, in Perl, for such a package, but it's probably
    not suitable for serious use.
    For some of these, source code may be available.  This list is
    long enough, so I'm not going to pursue it aggressively.

Thanks to Ed Vielmetti and several others who contributed to this list.

Mark Riordan   mrr@ripem.msu.edu
