riordanmr@clvax1.cl.msu.edu (Mark Riordan) (04/20/91)
Archive-name: math/bignum/msu-bignum-archive/1991-04-19
Archive-directory: cl-next1.cl.msu.edu:/math/ [35.8.4.21]
Original-posting-by: riordanmr@clvax1.cl.msu.edu (Mark Riordan)
Original-subject: Large Integer Arithmetic Packages, v. 2
Reposted-by: emv@msen.com (Edward Vielmetti, MSEN)
Thanks to Email messages from numerous correspondents, I now have an updated
version of the list I posted two days ago:
------------------------------------------------------------------
In response to recent Email requests, I have assembled this list of
large-integer packages of which I have heard.
For your convenience, I have placed compressed tar files of
some of these on cl-next1.cl.msu.edu (35.8.4.21). They are
available for anonymous FTP in the directory "math".
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.
Filename: bignum.tar.Z
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_2
Arjen Lenstra, Bellcore
This just in--an improved version of Arjen's package. This one
does signed arithmetic and can do dynamic memory management as
an option. Has a few new routines, too. May not be as fully
debugged as the earlier package, though.
Filename: lenstra_2.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.
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.
Obtain from sevenlayer.cs.wis.edu.
MIRACL
(By someone in Dublin, Ireland)
Integer and fractional multiple precision package.
Includes factorization, primality testing, encryption.
ath@linkoping.telesoft.se says there's a version from the
C User's Group and a more recent version available via ads
in Byte magazine. Not clear on whether this is commercial
software.
Perl
Larry Wall
This well-known programming language--kind of an alternative to
AWK--includes built-in multiple precision integer and floating point.
Because the source code to this package is available (under the
terms of the GNU public license), I include it in this list.
Available via anonymous FTP from devvax.jpl.nasa.gov.
Other languages
Various
Multiple precision arithmetic is available in a number of
programming languages, such as Lisp and ABC (cf. mcsun.eu.net).
For some of these, source code may be available. This list is
long enough already, so I'm not going to pursue it aggressively.
Thanks to Ed Vielmetti and several others who contributed to this list.
Mark Riordan riordanmr@clvax1.cl.msu.edu
Michigan State University 19 April 1991
-- comp.archives file verification
cl-next1.cl.msu.edu
total 913
-rw-r--r-- 1 ftp other 6956 Apr 19 19:42 BIGNUMS.TXT
-rw-r--r-- 1 ftp other 40541 Apr 19 19:28 amp.tar.Z
-rw-r--r-- 1 ftp other 74733 Apr 17 22:07 apml.tar.Z
-rw-r--r-- 1 ftp other 72153 Apr 17 21:41 arith.tar.Z
-rw-r--r-- 1 ftp other 25345 Apr 17 22:05 lenstra.tar.Z
-rw-r--r-- 1 ftp other 82761 Apr 19 03:08 lenstra_2.c
-rw-r--r-- 1 ftp other 620209 Apr 19 18:45 pari-1.35a.tar.Z
found msu-bignum-archive ok
cl-next1.cl.msu.edu:/math/