Approximation of Elementary Functions by Polynomials and Rational Functions - Some Results for FPGA Based Implementations

  • António J. Araújo Universidade do Porto
  • José S. Matos Universidade do Porto

Resumo


The hardware evaluation of elementary functions such as exp(x) and sin(x) is advantageous due to the performance that can be reached when compared with software solutions. Such evaluations can be done by computing simple functions thal approximate the targeted elementary functions. Actual microprocessors and specific processors like the digital signal processors include computing capabilities for some elementary functions but they could be inappropriate for some situations. Due to the great impact that Field Programmable Gate Arrays (FPGA) have in a wide range of hardware applications, specially in areas where hardware customization can improve the overall performance, the implementation of these functions in FPGA devices is worth considering. The reconfigurabllity they offer increases the flexibility and the power of such custom computing machines. Implementations of common elementary functions using single precision floating point arithmetic are described and the correspondent results are presented.

Palavras-chave: Elementary functions, floating point arithmetic, FPGA, polynomial approximations

Referências

G. A Baker. Essentials of Padé approximants. Academic Press. New York. 1975.

I. S. Board. IEEE Standard for Binary Floating Point Arithmetic. The Institute of Electrical and Electronics Engineers, New York. 1985. ANSI/IEEE Std. 754-1985.

B. W. Char, K. O. Geddes, G. H. Gonnet, B. L. Leong, M. B. Monagan, and S. M. Watt. Maple V Library Reference Manual. Springer Verlag, Berlin. Germany, 1991.

J. F. Han, E. W. Cheney, C. L. Lawson, H. J. Maehly, C. K. Mesztenyi, J. R. Rice, H. G. Thacher, and C. Witzgall. Computer Approximations. Wiley, New York, 1968.

Donald Knuth. The Art of Computer Programming - Seminumerical Algorithms. volume 2. Addison-Wesley. Reading. MA, 1981.

Israel Koren. Computer Arithmetic Algorithms. Brookside Court, Amherst. MA. 1998.

Jean-Michel Muller. Elementary Functions - Algorithms and Implementation. Birkhäuser. Boston. 1997.

Bernie New. Using the dedicated carry logic in XC4000E. Application Note XAPP 013, Xilinx, 1996.

J. R. Rice. The Approximation of Functions. Addison-Wesley. Reading. MA. 1964.

Xilinx. The Programmable Logic Data Book. 1996.
Publicado
29/09/1999
ARAÚJO, António J.; MATOS, José S.. Approximation of Elementary Functions by Polynomials and Rational Functions - Some Results for FPGA Based Implementations. In: INTERNATIONAL SYMPOSIUM ON COMPUTER ARCHITECTURE AND HIGH PERFORMANCE COMPUTING (SBAC-PAD), 11. , 1999, Natal. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 1999 . p. 257-264. DOI: https://doi.org/10.5753/sbac-pad.1999.19798.