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Powering by a Table Look-Up and a Multiplication with Operand Modification
November 1998 (vol. 47 no. 11)
pp. 1216-1222

Abstract—An efficient method for generating a power of an operand, i.e., Xp for an operand X and a given p, is proposed. It is applicable to ps in the form of ±2k, where k is any integer and of $\pm 2^{k_1}\ \pm 2^{-k_2},$ where k1 is any integer and k2 is any nonnegative integer. The reciprocal, the square root, the reciprocal square root, the reciprocal square, the reciprocal cube, and so forth are included. The method is a modification of the piecewise linear approximation. A power of an operand is generated through a table look-up and a multiplication with operand modification. The same accuracy is achieved as the piecewise linear approximation. The multiplication and an addition required for the piecewise linear approximation are replaced by only one double-sized multiplication with a slight modification of the operand and, hence, one clock cycle may be reduced. The required table size is reduced because only one coefficient instead of two has to be stored.

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Index Terms:
Computer arithmetic, powering, division, square rooting, multiplier.
Citation:
Naofumi Takagi, "Powering by a Table Look-Up and a Multiplication with Operand Modification," IEEE Transactions on Computers, vol. 47, no. 11, pp. 1216-1222, Nov. 1998, doi:10.1109/12.736432
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