Table-driven implementation of the exponential function in IEEE floating-point arithmetic

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Table-driven implementation of the exponential function in IEEE floating-point arithmetic

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 15 , Issue 2 (June 1989) table of contents

Pages: 144 - 157

Year of Publication: 1989

ISSN:0098-3500

Author

Ping-Tak Peter Tang

Mathematics and Computer Science Division, Argonne National Laboratory, 9700, South Cass Avenue, Argonne, IL

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 13, Downloads (12 Months): 93, Citation Count: 11

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ABSTRACT

Algorithms and implementation details for the exponential function in both single- and double-precision of IEEE 754 arithmetic are presented here. With a table of moderate size, the implementations need only working-precision arithmetic and are provably accurate to within 0.54 ulp as long as the final result does not underflow. When the final result suffers gradual underflow, the error is still no worse than 0.77 ulp.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	Ramesh C Agarwal , James W Cooley , Fred G Gustavson , James B Shearer , Gordon Slishman , Bryant Tuckerman, New scalar and vector elementary functions for the IBM system/370, IBM Journal of Research and Development, v.30 n.2, p.123-144, March 1986
	2	William James Cody, Software Manual for the Elementary Functions (Prentice-Hall series in computational mathematics), Prentice-Hall, Inc., Upper Saddle River, NJ, 1980
	3	Shmuel Gal, Computing Elementary Functions: A New Approach for Achieving High Accuracy and Good Performance, Proceedings of the Symposium on Accurate Scientific Computations, p.1-16, March 12-14, 1985
	4	John F. Hart, Computer Approximations, Krieger Publishing Co., Inc., Melbourne, FL, 1978
	5	HOUGH, D. Elementary functions based upon IEEE arithmetic. Mini/Micro West Conference Record, Electronic Conventions Inc., Los Angeles, 1983.
	6	IBM Elementary Math Library. Programming RPQ P81005, Program 5799-BTB, Program Reference and Operations Manual. SH20-2230-1, Aug. 1984.
	7	IEEE Standard for Binary Floating-Point Arithmetic, ANSI/IEEE Standard 754-1985. Institute of Electrical and Electronic Engineers, New York, 1985.

CITED BY 11

	Ren-Cang Li, Near Optimality of Chebyshev Interpolation for Elementary Function Computations, IEEE Transactions on Computers, v.53 n.6, p.678-687, June 2004
	David Harris, An Exponentiation Unit for an OpenGL Lighting Engine, IEEE Transactions on Computers, v.53 n.3, p.251-258, March 2004
	Ping-Tak Peter Tang, Table-driven implementation of the logarithm function in IEEE floating-point arithmetic, ACM Transactions on Mathematical Software (TOMS), v.16 n.4, p.378-400, Dec. 1990
	Ping Tak Peter Tang, Table-driven implementation of the Expm1 function in IEEE floating-point arithmetic, ACM Transactions on Mathematical Software (TOMS), v.18 n.2, p.211-222, June 1992
	Walter Krämer, A Priori Worst Case Error Bounds for Floating-Point Computations, IEEE Transactions on Computers, v.47 n.7, p.750-756, July 1998
	David Goldberg, The design of floating-point data types, ACM Letters on Programming Languages and Systems (LOPLAS), v.1 n.2, p.138-151, June 1992
	Ping-Tak Peter Tang, Accurate and efficient testing of the exponential and logarithm functions, ACM Transactions on Mathematical Software (TOMS), v.16 n.3, p.185-200, Sept. 1990
	Nicolas Brisebarre , Jean-Michel Muller , Arnaud Tisserand, Computing machine-efficient polynomial approximations, ACM Transactions on Mathematical Software (TOMS), v.32 n.2, p.236-256, June 2006
	Ping Tak Peter Tang, A portable generic elementary function package in Ada and an accurate test suite, ACM SIGAda Ada Letters, v.XI n.7, p.180-216, Fall 1991
	Ping Tak Peter Tang, A portable generic elementary function package in Ada and an accurate test suite, ACM SIGAda Ada Letters, v.XI n.7, p.180-216, Fall 1991
	John Harrison, Floating Point Verification in HOL Light: The Exponential Function, Formal Methods in System Design, v.16 n.3, p.271-305, June 2000