On-line high-radix exponential with selection by rounding

Author

Piñeiro, J.A. ; Bruguera, J.D. ; Ercegovac, M.D.

Author_Institution

Dept. of Electron. & Comput. Eng, Santiago de Compostela Univ., Spain

Volume

4

fYear

2003

fDate

25-28 May 2003

Abstract

An on-line high-radix algorithm for computing the exponential function (e^x) with arbitrary precision n is presented. Selection by rounding and a redundant digit-set for the digits e_j are used, with selection by table in the first iteration to guarantee the convergence of the algorithm, and the on-line delay is δ = 2 cycles. A sequential architecture implementing the algorithm is proposed, and the execution times and hardware requirements are estimated for 32-bit and 64-bit computations for several radix values. An analysis of the tradeoff between area and speed shows that the most efficient implementations are obtained for radix values from r = 32 to 256, depending on the precision.

Keywords

digital arithmetic; iterative methods; normalising; 32 bit; 64 bit; arbitrary precision; area; convergence; execution times; hardware requirements; iteration; on-line delay; on-line high-radix exponential; redundant digit-set; rounding; sequential architecture; speed; Arithmetic; Bandwidth; Computer architecture; Computer science; Contracts; Convergence; Delay; Hardware; Signal processing algorithms; System-on-a-chip;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 2003. ISCAS '03. Proceedings of the 2003 International Symposium on

Print_ISBN

0-7803-7761-3

Type

conf

DOI

10.1109/ISCAS.2003.1205788

Filename

1205788