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Shorter table ATA evaluation of elementary functions in single precision
Keywords:
Computer Arithmetic, Single Precision Elementary Functions, Table-Based Methods, ATA MethodAbstract
In this paper a slightly modification is proposed to the original Wong and Gotos ATA method for the computation of elementary functions in IEEE 754 single precision. The identification of a trade-off leads to the proposition of a different chunk of the mantissa that in turn brings a reduction in the length of the tables. Results are reported for usual elementary functions based on exhaustive simulations. A mixed framework including VHDL and Matlab R is used for those simulations.
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References
[1] J. Bhasker, A Guide to VHDL Syntax, Prentice Hall, 1995.
[2] O. N. Bria and J. O. Giacomantone, “Descripciones VHDL para Calcular la Función Recíproca en Presición Simple,” Annals VIII Congreso Argentino de Ciencias de la Computación, Buenos Aires, Argentina, 2002.
[3] C. Hansen, O. Bringmann. W. Rosenstiel, “A VHDL reusable component model for fixed abstraction level simulation and behavioral synthesis,” Virtual Components Design and Reuse, edited by R. Seepold, N. Martnez, Kluwer, 2001.
[4] W. Kahan, ”Lecture notes on the status of standard IEEE-754, from the website http.cs.berkeley.edu/~wkahan/, 1996.
[5] J.-M. Muller, Elementary Functions - Algorithms and Implementation, Birkhauser, 1997.
[6] B. Parhami, Computer Arithmetic. Algorithms and Hardware Designs, Oxford University Press, 2000.
[7] W. F. Wong, E. Goto, “Hardware for the Fast Computation of the Elementary Functions.” Dr. Eng. Sc. Thesis, University of Tsukuba, Tsukuba, Japan,1995.
[8] W. F. Wong, E. Goto, “Fast hardware-based algorithms for elementary function computations using rectangular multipliers,” IEEE Transactions on Computer, 1994.
[9] W. F. Wong, E. Goto, “Fast evaluation of the elmentary function in single precision,” IEEE Transactions on Computer, 1995.
[2] O. N. Bria and J. O. Giacomantone, “Descripciones VHDL para Calcular la Función Recíproca en Presición Simple,” Annals VIII Congreso Argentino de Ciencias de la Computación, Buenos Aires, Argentina, 2002.
[3] C. Hansen, O. Bringmann. W. Rosenstiel, “A VHDL reusable component model for fixed abstraction level simulation and behavioral synthesis,” Virtual Components Design and Reuse, edited by R. Seepold, N. Martnez, Kluwer, 2001.
[4] W. Kahan, ”Lecture notes on the status of standard IEEE-754, from the website http.cs.berkeley.edu/~wkahan/, 1996.
[5] J.-M. Muller, Elementary Functions - Algorithms and Implementation, Birkhauser, 1997.
[6] B. Parhami, Computer Arithmetic. Algorithms and Hardware Designs, Oxford University Press, 2000.
[7] W. F. Wong, E. Goto, “Hardware for the Fast Computation of the Elementary Functions.” Dr. Eng. Sc. Thesis, University of Tsukuba, Tsukuba, Japan,1995.
[8] W. F. Wong, E. Goto, “Fast hardware-based algorithms for elementary function computations using rectangular multipliers,” IEEE Transactions on Computer, 1994.
[9] W. F. Wong, E. Goto, “Fast evaluation of the elmentary function in single precision,” IEEE Transactions on Computer, 1995.
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Published
2003-10-01
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Original Articles
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[1]
“Shorter table ATA evaluation of elementary functions in single precision”, JCS&T, vol. 3, no. 02, pp. p. 56–61, Oct. 2003, Accessed: Mar. 12, 2026. [Online]. Available: https://journal.info.unlp.edu.ar/JCST/article/view/940
