Reciprocation, Square Root, Inverse Square Root, and Some Elementary Functions Using Small Multipliers

Authors:
Milos D. Ercegovac;Tomás Lang;Jean-Michel Muller;Arnaud Tisserand
Affiliations:
Univ. of California at Los Angeles, Los Angeles;Univ. of California at Irvine, Irvine;Ecole Normale Supérieure de Lyon, Lyon, France;Ecole Normale Supérieure de Lyon, Lyon, France
Venue:
IEEE Transactions on Computers - Special issue on computer arithmetic
Year:
2000

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Abstract

This paper deals with the computation of reciprocals, square roots, inverse square roots, and some elementary functions using small tables, small multipliers, and, for some functions, a final 驴large驴 (almost full-length) multiplication. We propose a method, based on argument reduction and series expansion, that allows fast evaluation of these functions in high precision. The strength of this method is that the same scheme allows the computation of all these functions. We estimate the delay, the size/number of tables, and the size/number of multipliers and compare with other related methods.