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.