Numerical Computation Guide |

## References

For a list of Sun WorkShop

^{TM}manuals that contain information on Sun compilers, refer to Related Documentation.The following manual provides more information about SPARC floating-point hardware:

SPARC Architecture Manual, Version 9, PTR Prentice Hall, New Jersey, 1994.The remaining references are organized by chapter. Information on obtaining Standards documents and test programs is included at the end.

## Chapter 2: "IEEE Arithmetic"

Cody et al., "A Proposed Radix- and Word-length-independent Standard for Floating-Point Arithmetic,"

IEEE Computer, August 1984.Coonen, J.T., "An Implementation Guide to a Proposed Standard for Floating Point Arithmetic",

Computer, Vol. 13, No. 1, Jan. 1980, pp 68-79.Demmel, J., "Underflow and the Reliability of Numerical Software", SIAM J.

Scientific Statistical Computing, Volume 5 (1984), 887-919.Hough, D., "Applications of the Proposed IEEE 754 Standard for Floating-Point Arithmetic",

Computer, Vol. 13, No. 1, Jan. 1980, pp 70-74.Kahan, W., and Coonen, J.T., "The Near Orthogonality of Syntax, Semantics, and Diagnostics in Numerical Programming Environments", published in

The Relationship between Numerical Computation and Programming Languages, Reid, J.K., (editor), North-Holland Publishing Company, 1982.Kahan, W., "Implementation of Algorithms",

Computer Science Technical Report No. 20, University of California, Berkeley CA, 1973. Available from National Technical Information Service, NTIS Document No. AD-769 124 (339 pages),

1-703-487-4650 (ordinary orders) or 1-800-336-4700 (rush orders.)Karpinski, R., "Paranoia: a Floating-Point Benchmark",

Byte, February 1985.Knuth, D.E.,

The Art of Computer Programming, Vol.2: Semi-Numerical Algorithms, Addison-Wesley, Reading, Mass, 1969, p 195.Linnainmaa, S., "Combatting the effects of Underflow and Overflow in Determining Real Roots of Polynomials", SIGNUM Newsletter 16, (1981),

11-16.Rump, S.M., "How Reliable are Results of Computers?", translation of "Wie zuverlassig sind die Ergebnisse unserer Rechenanlagen?",

Jahrbuch Uberblicke Mathematik 1983, pp 163-168, C Bibliographisches Institut AG 1984.Sterbenz, P,

Floating-Point Computation, Prentice-Hall, Englewood Cliffs, NJ, 1974. (Out of print; most university libraries have copies.)Stevenson, D. et al., Cody, W., Hough, D. Coonen, J., various papers proposing and analyzing a draft standard for binary floating-point arithmetic,

IEEE Computer, March 1981.

The Proposed IEEE Floating-Point Standard, special issue of the ACMSIGNUM Newsletter, October 1979.## Chapter 3: "The Math Libraries"

Cody, William J. and Waite, William,

Software Manual for the Elementary Functions, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 07632, 1980.Coonen, J.T.,

Contributions to a Proposed Standard for Binary Floating-Point Arithmetic, PhD Dissertation, University of California, Berkeley, 1984.Tang, Peter Ping Tak,

Some Software Implementations of the Functions Sin and Cos, Technical Report ANL-90/3, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois, February 1990.Tang, Peter Ping Tak,

Table-driven Implementations of the Exponential Function EXPM1 in IEEE Floating-Point Arithmetic, Preprint MCS-P125-0290, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois, February, 1990.Tang, Peter Ping Tak,

Table-driven Implementation of the Exponential Function in IEEE Floating-Point Arithmetic, ACM Transactions on Mathematical Software, Vol. 15, No. 2, June 1989, pp 144-157 communication, July 18, 1988.Tang, Peter Ping Tak,

Table-driven Implementation of the Logarithm Function in IEEE Floating-Point Arithmetic, preprint MCS-P55-0289, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois, February 1989 (to appear in ACM Trans. on Math. Soft.)Park, Stephen K. and Miller, Keith W., "Random Number Generators: Good Ones Are Hard To Find",

Communications of the ACM, Vol. 31, No. 10, October 1988, pp 1192 - 1201.## Chapter 4: "Exceptions and Signal Handling"

Coonen, J.T, "Underflow and the Denormalized Numbers",

Computer, 14, No. 3, March 1981, pp 75-87.Demmel, J., and X. Li, "Faster Numerical Algorithms via Exception Handling",

IEEE Trans. Comput.Vol. 48, No. 8, August 1994, pp 983-992.Kahan, W., "A Survey of Error Analysis",

Information Processing 71, North-Holland, Amsterdam, 1972, pp 1214-1239.## Appendix B: "SPARC Behavior and Implementation"

The following manufacturer's documentation provides more information about the floating-point hardware and main processor chips. It is organized by system architecture.

Texas Instruments,

SN74ACT8800 Family, 32-Bit CMOS Processor Building Blocks: Date Manual, 1st edition, Texas Instruments Incorporated, 1988.Weitek,

WTL 3170 Floating Point Coprocessor: Preliminary Data, 1988, published by Weitek Corporation, 1060 E. Arques Avenue, Sunnyvale, CA 94086.Weitek,

WTL 1164/WTL 1165 64-bit IEEE Floating Point Multiplier/Divider and ALU: Preliminary Data, 1986, published by Weitek Corporation, 1060 E. Arques Avenue, Sunnyvale, CA 94086.## Standards

American National Standard for Information Systems - Programming Language C(ANSI C), Document no. X3.159-1989, American National Standards Institute, 1430 Broadway, New York, NY 10018.

IEEE Standard for Binary Floating-Point Arithmetic, ANSI/IEEE Std 754-1985(IEEE 754), published by the Institute of Electrical and Electronics Engineers, Inc, 345 East 47th Street, New York, NY 10017, 1985.

IEEE Standard Glossary of Mathematics of Computing Terminology, ANSI/IEEE Std 1084-1986, published by the Institute of Electrical and Electronics Engineers, Inc, 345 East 47th Street, New York, NY 10017, 1986.

IEEE Standard Portable Operating System Interface for Computer Environments(POSIX), IEEE Std 1003.1-1988, The Institute of Electrical and Electronics Engineers, Inc., 345 East 47th Street, New York, NY 10017.

System V Application Binary Interface(ABI), AT&T (1-800-432-6600), 1989.

SPARC System V ABI Supplement(SPARC ABI), AT&T (1-800-432-6600), 1990.

System V Interface Definition, 3rd edition, (SVID89, or SVID Issue 3), Volumes I-IV, Part number 320-135, AT&T (1-800-432-6600), 1989.

X/OPEN Portability Guide, Set of 7 Volumes, Prentice-Hall, Inc., Englewood Cliffs, New Jersey 07632, 1989.## Test Programs

A number of test programs for floating-point arithmetic and math libraries are available from Netlib in the ucbtest package. These programs include versions of Paranoia, Z. Alex Liu's Berkeley Elementary Function test program, the IEEE test vectors, and programs based on number-theoretic methods developed by Prof. W. Kahan that generate hard test cases for correctly rounded multiplication, division, and square root.

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