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Comparison of three public-domain multiprecision libraries.pdf

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Comparison of three public-domain multiprecision libraries

Comparison of three public-domain multiprecision libraries:BigNum, Gmp and PariPaul ZimmermannPaul.Zimmermann@inria.frFebruary 12, 1998Abstract. We describe the use of three mul-tiprecision libraries on two sample problems:compute digits of and compute a recursive se-quence of integers. Our conclusion is that (i) amultiprecision library is about ten times fasterthan a general computer algebra system on spe-cic problems and that (ii) the smaller programis usually the faster one.A lot of tools are nowadays available for the math-ematician or computer scientist. There are two mainfamilies: general computer algebra systems on theone hand, and other systems, designed for specic ap-plications, on the other hand. The main advantagesof general computer algebra systems like Macsyma,Maple, Mathematica, Scratchpad are: you have all in one, they are interactive, they are easy to program.Besides the fact they are not cheap, general computeralgebra systems are usually not very ecient for largeproblems, rst because they use general data struc-tures that require a lot of memory space, secondlybecause the programs are interpreted and not com-piled.Therefore in the last few years several peoplehave developed special-purpose applications. Mostof these packages are public-domain and thus eas-ily available. But they are not enough widely used,perhaps because the potential users think they are too dicult to program. With the example of mul-tiprecision libraries written in the C language, weprove that using special-purpose systems is not thatdicult, and moreover may be very ecient.For our comparison, we have chosen the followingmultiprecision libraries: the BIGNUM package de-veloped jointly by people at Inria and Dec Prl (ver-sion from July 1991);GMP or gnu mp, version 2.0.2,the package of the Free Software Foundation devel-oped by T. Granlund, TMG Datakonsult; and PARI,version 1.36, the library developed by people at theUniversity of Bordeaux, France, which is the basis ofthe