Publication 1998 Issue No. 11 - November Abstract - Powering by a Table Look-Up and a Multiplication with Operand Modification
Powering by a Table Look-Up and a Multiplication with Operand Modification
November 1998 (vol. 47 no. 11)
pp. 1216-1222
 ASCII Text x 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, November, 1998.
 BibTex x @article{ 10.1109/12.736432,author = {Naofumi Takagi},title = {Powering by a Table Look-Up and a Multiplication with Operand Modification},journal ={IEEE Transactions on Computers},volume = {47},number = {11},issn = {0018-9340},year = {1998},pages = {1216-1222},doi = {http://doi.ieeecomputersociety.org/10.1109/12.736432},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Powering by a Table Look-Up and a Multiplication with Operand ModificationIS - 11SN - 0018-9340SP1216EP1222EPD - 1216-1222A1 - Naofumi Takagi, PY - 1998KW - Computer arithmeticKW - poweringKW - divisionKW - square rootingKW - multiplier.VL - 47JA - IEEE Transactions on ComputersER -

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.

[1] N. Takagi, "Generating a Power of an Operand by a Table Look-Up and a Multiplication," Proc. 13th Symp. Computer Arithmetic, pp. 126-131, July 1997.
[2] Numerical Methods, G. Dahlquist, A. Bjorck, and N. Anderson, eds. Prentice Hall, 1974.
[3] A.S. Noetzel, "An Interpolating Memory Unit for Function Evaluation: Analysis and Design," IEEE Trans. Computers, vol. 38, no. 3, pp. 377-384, Mar. 1997.
[4] T. Nishimoto, "Multiple/Divide Unit," U.S. Patent 4337519, June 1982.
[5] N. Takagi, "Studies on Hardware Algorithms for Arithmetic Operations with a Redundant Binary Representation," Doctoral dissertation, Dept. of Information Science, Kyoto Univ., Aug. 1987.
[6] N. Takagi, "Arithmetic Unit Based on a High Speed Multiplier with a Redundant Binary Addition Tree," Proc. SPIE, vol. 1,566, pp. 244-251, July 1991.
[7] C.N. Lyu and D.W. Matula, “Redundant Binary Booth Recoding,” Proc. 12th Symp. Computer Arithmetic, pp. 50-57, 1995.
[8] M. Ito, N. Takagi, and S. Yajima, "Efficient Initial Approximation for Multiplicative Division and Square Root by a Multiplication with Operand Modification," IEEE Trans. Computers, vol. 46, no. 4, pp. 495-498, Apr. 1997.
[9] D. DasSarma and D.W. Matula, "Faithful Interpolation in Reciprocal Tables," Proc. 13th Symp. Computer Arithmetic, pp. 82-91, July 1997.
[10] D. DasSarma and D.W. Matula, “Faithful Bipartite ROM Reciprocal Tables,” Proc. 12th Symp. Computer Arithmetic, pp. 17-28, 1995.

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