SYMPOSIUM MINISYMPOSIA

ABSTRACT

When solving numerically algebraic equations of high degree polynomial (e.g. 2048 degrees), quadruple precision complex number of usual Fortran does not have enough precision, and multiple-precision number operations are necessary in that kind of programs. Multiple-precision number operations are usually processed by software and they need large CPU costs. If the operations are parallelized, it is possible to speed up them. Usual methods to use multiple-precision number operations are; bare library call method[2], using translator method[1], and using C++ class library method[3]. But the codes by these methods are not proper for automatic parallelizing compilers.

We are developing a parallelizing compiler that supports parallelization of multiple-precision number operations in language level. It parallelizes between operations and inside each operation. The CPU costs of multipleprecision number operations are more than the costs of communication between processors. Therefore the operation costs hide the communication costs, and parallelizing multiple-precision number operations is effective. We verified that acceleration of longer multiple operations are larger through the preparatory experiments on a parallel machine, IBM SP2.

References:

[1] Watt,W.T., Lozier,P.W. and Orser, P.J.: "A Portable Extended Precision Arithmetic Package and Library with Fortran Precompiler", ACM Trans. Math. Soft. 2 pp.209-231 (1976)

[2] Brent,R.P.: "A Fortran Multiple-Precision Arithmetic Package", ACM Trans. Math. Soft. Vol.4 No.1 pp.57-70 (Mar. 1978)

[3] Hiroshi Hirayama: "Speed-up of Multiple precision package MPPACK", IPSJ SIG Notes 98-ARC-128 Vol.98 No.18 pp.1-6 (Mar. 1998) (in Japanese)

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