Algorithm 719: Multiprecision Translation and Execution of FORTRAN Programs

ACM Transactions on Mathematical Software (TOMS)

Volumn 19, Issue 3, 1993, Pages 288-319

  Bailey, David H ^a  

^a NASA AMES RESEARCH CENTER   (United States)

Author keywords

multiple precision computation; multiprecision arithmetic

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; COMPUTER SOFTWARE; DATA STRUCTURES; DIGITAL ARITHMETIC; FORTRAN (PROGRAMMING LANGUAGE); NUMERICAL ANALYSIS; PROGRAM TRANSLATORS; STORAGE ALLOCATION (COMPUTER); SUBROUTINES; UTILITY PROGRAMS;

ALGORITHM 719; FORTRAN PROGRAMS; MULTIPRECISION ARITHMETIC; MULTIPRECISION COMPUTATION;

ALGORITHMS;

EID: 0027668405     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/155743.155767     Document Type: Article

References (32)

1. BAILEY, D. H. The computation of p to 29,360,000 decimal digits using Borweins' quartically convergent algorithm. Math. Comput. 50 (Jan. 1988), 283-296.
2. BAILEY, D. H. A high performance FFT algorithm for vector supercomputers. Int. J. Supercomput. Appl. 2 (Spring 1988), 82-87.
3. BAILEY, D. H. Numerical results on the transcendence of constants involving p, e, and Euler's constant. Math. Comput. 50 (Jan. 1988), 275-281.
4. BAILEY, D. H. A portable high performance multiprecision package. Tech. Rep. RNR-90-022, NASA Ames Research Center, 1990.
5. BAILEY, D. H., AND FERGUSON, H. R. P. Numerical results on relations between numerical constants using a new algorithm. Math. Comput. 53 (Oct. 1989), 649-656.
6. BECKMANN, P. A History of Pi. Golem Press, Boulder, Colo., 1977
7. BORWEIN, J. M., AND BORWEIN, P. B. The arithmetic-geometric mean and fast computation of elementary functions. SIAM Rev. 26 (1984), 351-365.
8. BORWEIN, J. M., AND BORWEIN, P. B. Pi and the AGM. Wiley, New York, 1987.
9. BORWEIN, J. M., BORWEIN, P. B., AND BAILEY, D. H. Ramanujan, modular equations, and approximations to Pi. Am. Math. Monthly 96 (1989), 201-219.
10. BRENT, R. P. Fast multiple-precision evaluation of elementary functions. J. ACM 23 (1976), 242-251.
11. BRENT, R. P. A Fortran multiple precision arithmetic package. ACM Trans. Math. Softw. 4 (1978), 57-70.
12. BRENT, R. P. Multiple-precision zero-finding methods and the complexity of elementary function evaluation. In Analytic Computational Complexity, Academic Press, New York, 1976, 151-176.
13. BRIGGS, K. A precise calculation of the Feigenbaum constants. Math. Comput. 57 (1991), 435-439.
14. BUELL, D., AND WARD, R. A multiprecise integer arithmetic package. J. Supercomput. 3 (1989), 89-107.
15. CHUDNOVSKY, D. V., AND CHUDNOVSKY, G. V. Computation and arithmetic nature of classical constants IBM Res. Rep. IBM T. J. Watson Research Center, RC14950 (66818), 1989.
16. CHUDNOVSKY, D. V., AND CHUDNOVSKY, G. V. Personal communication, 1991.
17. COMBA, P. G. Exponentiation cryptosystems on the IBM PC. IBM Syst. J. 29 (1990), 526-538.
18. DONGARRA, J. J. The Linpack benchmark: An explanation. In SuperComputing 96, 3 (Spring 1988), 10-14.
19. FEINGENBAUM, M. J. Quantitative universality for a class of nonlinear transformations. J. Stat. Phys. 19 (1978), 25-52.
20. FERGUSON, H. R. P., AND BAILEY, D. H. A polynomial time, numerically stable integer relation algorithm. Tech. Rep. RNR-91-032, NAS Applied Research Branch, NASA Ames Research Center, Moffett Field, Calif., Mar. 1992.
21. HASTAD, J., JUST, B., LAGARIAS, J. C., AND SCHNORR, C. Polynomial time algorithms for finding integer relations among real numbers. SIAM J. Comput. 18, (1988), 859-881.
22. KANADA, Y. Personal communication, 1989.
23. KNUTH, D. E. The Art of Computer Programming. Addison Wesley, Reading, Mass., 1981.
24. KRASNY, R. Desingularization of periodic vortex sheet roll-up. J. Comput. Phys. 65, 2 (Aug. 1986), 292-313.
25. LENSTRA, A. K., LENSTRA, H. W., MANASSE, M. S., AND POLLARD, J. M. The number field sieve. In 1990 ACM Symposium on the Theory of Computing. ACM, New York, 1990, 564-572.
26. ODLYZKO, A. M., AND TE RIELE, H. J. J. Disproof of the Mertens conjecture. J. Reine Angew. Math. 357 (1985), 138-160.
27. RIVEST, R. L., SHAMIR, A., AND ADLEMAN, L. A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21 (1978), 120-126.
28. SALAMIN, E. Computation of p using arithmetic-geometric mean. Math. Comput. 30 (1976), 565-570.
29. SLOWINSKI, D. Personal communication, 1991.
30. SMITH, D. M. A FORTRAN package for floating-point multiple-precision arithmetic. ACM Trans. Math. Softw. 17, 2 (June 1991), 273-283.
31. VARGA, R. S. Scientific Computation on Mathematical Problems and Conjectures. SIAM, Philadelphia, 1990.
32. WOLFRAM, S. Mathematica: A System for Doing Mathematics by Computer. Addison-Wesley, Reading, Mass., 1988.