High-speed redundant reciprocal approximation

作者: Peter-Michael Seidel

DOI: 10.1016/S0167-9260(99)00008-5

关键词: Double-precision floating-point formatBooth's multiplication algorithmAlgorithmSingle-precision floating-point formatNormalized numberRoundingMathematicsApproximation errorFloating pointReciprocal

摘要: Abstract This paper presents a fast implementation for reciprocal approximation, that can compute redundant of normalized number with precision 2 −28 in roughly 16–17 logic levels. Moreover, less accurate, but much cheaper is proposed. The representation the directly be fed into common Booth multiplier. allows to implement IEEE floating-point division correct rounding all modes latency 7 clock cycles double and 4 single precision. We also consider compressions from carry–save representations Booth-digit representations.

参考文章(22)
M. J. Schulte, J. Omar, E. E. Swartzlander, Optimal initial approximations for the Newton-Raphson division algorithm Computing. ,vol. 53, pp. 233- 242 ,(1994) , 10.1007/BF02307376
Stuart F. Oberman, Michael J. Flynn, Fast IEEE Rounding for Division by Functional Iteration Stanford University. ,(1996)
Stuart Franklin Oberman, Design issues in high performance floating point arithmetic units Stanford University. ,(1996)
M.D. Ercegovac, T. Lang, P. Montuschi, Very high radix division with selection by rounding and prescaling Proceedings of IEEE 11th Symposium on Computer Arithmetic. pp. 112- 119 ,(1993) , 10.1109/ARITH.1993.378102
Peter Soderquist, Miriam Leeser, Area and performance tradeoffs in floating-point divide and square-root implementations ACM Computing Surveys. ,vol. 28, pp. 518- 564 ,(1996) , 10.1145/243439.243481
Domenico Ferrari, A Division Method Using a Parallel Multiplier IEEE Transactions on Electronic Computers. ,vol. EC-16, pp. 224- 226 ,(1967) , 10.1109/PGEC.1967.264580
ANDREW D. BOOTH, A SIGNED BINARY MULTIPLICATION TECHNIQUE Quarterly Journal of Mechanics and Applied Mathematics. ,vol. 4, pp. 236- 240 ,(1951) , 10.1093/QJMAM/4.2.236
P.E. Madrid, B. Millar, E.E. Swartzlander, Modified Booth algorithm for high radix multiplication international conference on computer design. pp. 118- 121 ,(1992) , 10.1109/ICCD.1992.276194
S. F. Anderson, J. G. Earle, R. E. Goldschmidt, D. M. Powers, The IBM system/360 model 91: floating-point execution unit Ibm Journal of Research and Development. ,vol. 11, pp. 34- 53 ,(1967) , 10.1147/RD.111.0034
M. Ito, N. Takagi, S. Yajima, Efficient initial approximation and fast converging methods for division and square root symposium on computer arithmetic. pp. 2- 9 ,(1995) , 10.1109/ARITH.1995.465383