A precision- and range-independent tool for testing floating-point arithmetic I: Basic operations, square root, and remainder

ACM Transactions on Mathematical Software

Volumn 27, Issue 1, 2001, Pages 92-118

  Verdonk, Brigitte ^a   Cuyt, Annie ^a   Verschaeren, Dennis ^a  

^a UNIVERSITY OF ANTWERP   (Belgium)

Author keywords

Arithmetic; D.3.0 programming languages : General Standards; Floating point; G.1.0 numerical analysis : General Computer arithmetic; IEEE floating point standard; Multiprecision; Validation; Verification

Indexed keywords

EID: 0012096424     PISSN: 00983500     EISSN: None     Source Type: Journal    
DOI: 10.1145/382043.382404     Document Type: Article

References (29)

1. BAILEY, D. H. 1995. A Fortran 90-based multiprecision system. ACM Trans. Math. Softw. 21, 4 (Dec.), 379-387.
2. BAILEY, D., SIMON, H., BARTON, J., AND FOUTS, M. 1989. Floating-point arithmetic in future supercomputers. Int. J. Supercomput. Appl. High Perform. Eng. 3, 3, 86-90.
3. BATUT, C., BERNARDI, D., COHEN, H., AND OLIVIER, M. 2000. User's guide to PARI-GP. Laboratoire A2X, Université Bordeaux I, Bordeaux, France. http://www.parigp-home.de/.
4. BRENT, R. P. 1978. A Fortran multiple precision arithmetic package. ACM Trans. Math. Softw. 4, 1 (Mar.), 57-70.
5. COONEN, J. 1984. Contributions to a proposed standard for binary floating-point arithmetic. Ph.D. Dissertation. University of California at Berkeley, Berkeley, CA.
6. CORNEA-HASEGAN, M. 1998. Proving the IEEE correctness of iterative floating-point square root, divide and remainder algorithms. Intel Tech. J. Quarter 2.
7. CUYT, A., KUTERNA, P., VERDONK, B., AND VERSCHAEREN, D. 2000a. Underflow revisited. Tech. Rep. Univ. of Antwerp, Antwerp, Belgium. Available via http://win-www.uia.ac.be/u/cant/ publications.html. Submitted for publication.
8. CUYT, A. ET AL. 2000b. The Arithmos project. Univ. of Antwerp, Antwerp, Belgium. http://win-www.uia.ac.be/u/cant/arithmos.
9. DU CROZ, J., ERL, M., GARDNER, P., HODGSON, G., AND PONT, M. 1989. Validation of numerical computations in Ada. Tech. Rep. TR2/89. Numerical Algorithms Group Ltd., Oxford, UK.
10. GERMAN, S. 1999. Introductions to the special issue on verification of arithmetic hardware. Formal Methods Syst. Des. 14, 1, 5-6.
11. GHANLUND, T. 2000. The GNU multiple precision arithmetic library. Swox AB, Stcokholm, Sweden. http://www.swox.com/gmp.
12. HAIBLE, B. 2000. CLN, a class library for numbers. http://ma2s2.mathematik.uni-karlsruhe.de/pub/gnu/cln.tar.z.
13. HARRISON, J. 2000. Floating-point verification in HOL Light: The exponential function. Formal Methods Syst. Des. 16, 3, 271-305.
14. HIGHAM, N. J. 1996. Accuracy and Stability of Numerical Algorithms. SIAM, Philadelphia, PA.
15. HOUGH, D. 1988. UCBTEST, a suite of programs for testing certain difficult cases of IEEE 754 floating-point arithmetic. Restricted public domain software from http://netlib.bell-labs.com/netlib/fp/index.html.
16. IEEE. 1985. ANSI/IEEE standard for binary floating point arithmetic: Standard 754-1985. IEEE Press, Piscataway, NJ. Reprinted in ACM SIGPLAN Not. 22, 2 (1987), pp. 9-25.
17. IEEE. 1985. ANSI/IEEE standard for binary floating point arithmetic: Standard 754-1985. IEEE Press, Piscataway, NJ. Reprinted in ACM SIGPLAN Not. 22, 2 (1987), pp. 9-25.
18. IEEE. 1987. ANSI/IEEE standard for radix-independent floating-point arithmetic: Standard 854-1987. IEEE Press, Piscataway, NJ.
19. KAHAN, W. 1994. Computer benchmarks versus accuracy. Draft manuscript.
20. KAHAN, W. 1996. A test for correctly rounded SQRT. http://www.es.berkeley.edu/~wkahan/ SQRTest.ps.
21. KARPINSKI, R. 1985. Paranoia: A floating-point benchmark. BYTE 10, 223-235.
22. MOSHIER, S. L. 1989. Methods and Programs for Mathematical Functions. Ellis Horwood, Upper Saddle River, NJ.
23. RUSSINOFF, D. 1998. A mechanically checked proof of IEEE compliance of the AMD-K7 floating point multiplication, division, and square root instructions. London Math. Soc. J. Comput. Math. 1, 148-200.
24. SCHRYER, N. 1981. A test of a computer's floating-point unit. Computer Science Tech. Rep. 89. AT&T Bell Laboratories, Inc., Murray Hill, NJ.
25. SMITH, D. M. 1991. Algorithm 693: A FORTRAN package for floating-point multiple-precision arithmetic. ACM Trans. Math. Softw. 17, 2 (June), 273-283.
26. SUN MICROSYSTEMS. 1997. The UltraSparc processor. Technology White Paper. Sun Microsystems, Inc., Mountain View, CA. http://www.sun.com.
27. TOMMILA, M. 2000. APFLOAT, A C++ high performance arbitrary precision arithmetic package. Computing Centre, Helsinki Univ. Tech., Helsinki, Finland. http://www.jjj.de/ mtommila/apfloat.
28. VERDONK, B., CUYT, A., AND VERSCHAEREN, D. 2001. A precision- and range-independent tool for testing floating-point arithmetic II: Conversions. ACM Trans. Math. Softw. 27, 1 (Mar.). This issue.
29. ZIMMERMANN, P. AND HANROT, G. 2000. MPFR: A library for multiprecision floating-point arithmetic with exact rounding. http://www.loria.fr/projets/mpfr/.