A FORTRAN MULTIPLE-PRECISION ARITHMETIC PACKAGE

RICHARD P. BRENT

Abstract

A collection of ANSI Standard Fortran subroutines for performing multiple-precision floatingpoint arithmetic and evaluating elementary and special functions is described. The subroutines are machine independent and the precision is arbitrary, subject to storage limitations. The design of the package is discussed, some of the algorithms are described, and test results are given.

Comments

Only the Abstract is given here. The full paper appeared as [1] and the algorithm appeared as [2]. For related work see [3, 4, 5].

References

1. R. P. Brent, “A Fortran multiple-precision arithmetic package”, ACM Transactions on Mathematical Software 4 (1978), 57–70. CR 20#34962. Also appeared as a Technical Report, Department of Computer Science, Carnegie-Mellon University (May 1976), 29 pp. rpb042.

2. R. P. Brent, “Algorithm 524: MP, a Fortran multiple-precision arithmetic package”, ACM Transactions on Mathematical Software 4 (1978), 71–81. rpb043.

3. R. P. Brent, “Remark on Algorithm 524”, ACM Transactions on Mathematical Software 5 (1979), 518–519. rpb043r.

4. R. P. Brent, “Unrestricted algorithms for elementary and special functions”, in Information Processing 80 (edited by S. H. Lavington), North-Holland, Amsterdam, 1980, 613–619. CR 22#38728, MR 81i:68009. rpb052.

5. R. P. Brent, J. A. Hooper and J. M. Yohe, “An Augment interface for Brent’s multiple-precision arithmetic package” ACM Transactions on Mathematical Software 6 (1980), 146–149. CR 21#36520, Zbl 433.68028. A longer version appeared as Technical Summary Report #1868, Mathematics Research Center, University of Wisconsin, Madison (August 1978), 26 pp. rpb054.

Computer Centre, Australian National University, Canberra, Australia

1991 Mathematics Subject Classification. Primary 65-04; Secondary 33-04, 33B10, 33B15, 33B99, 33E05, 33E20, 41A25, 41A60, 65D20, 65G05, 68-04.

Key words and phrases. Arithmetic, multiple-precision, extended precision, floating point, elementary function evaluation, Euler’s constant, gamma function, polyalgorithm, software package, Fortran, machine-independent software, special function evaluation, Bessel functions, exponential integral, logarithmic integral, Bernoulli numbers, zeta function, portable software.

CR Categories. 3.15, 4.49, 5.11, 5.12, 5.15, 5.19, 5.25.

Copyright \begin{matrix}c \\ ◯ \end{matrix} 1978, Association for Computing Machinery, Inc. General permission to make fair use in teaching or research of all or part of this material is granted to individual readers and to nonprofit libraries acting for them provided that ACM’s copyright notice is given and that reference is made to the publication, to its date of issue, and to the fact that reprinting privileges were granted by permission of the Association for Computing Machinery.

Comments \begin{matrix}c \\ ◯ \end{matrix} 1993, R. P. Brent.

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