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FloatingPoint Divide Operation without Special Hardware Supports
Takashi AMISAKI Umpei NAGASHIMA Kazutoshi TANABE
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E82A
No.1
pp.173177 Publication Date: 1999/01/25 Online ISSN:
DOI: Print ISSN: 09168508 Type of Manuscript: LETTER Category: Numerical Analysis and Optimization Keyword: computer arithmetic, division, FPU, error analysis, specialpurpose,
Full Text: PDF>>
Summary:
Three multiplicative algorithms for the floatingpoint divide operation are compared: the NewtonRaphson method, Goldschmidt's algorithm, and a naive method that simply calculates a form of the Taylor series expansion of a reciprocal. The series also provides a theoretical basis for Goldschmidt's algorithm. It is well known that, of the NewtonRaphson method and Goldschmidt's algorithm, the former is the more accurate while the latter is the faster on a pipelined unit. However, little is reported about the naive method. In this report, we analyze the speed and accuracy of each method and present the results of numerical tests, which we conducted to confirm the validity of the accuracy analysis. Basically, the comparison are made in the context of software implementation (e. g. , a macro library) and compliance with the IEEE Standard 754 rounding is not considered. It is shown that the naive method is useful in a realistic setting where the number of iterations is small and the method is implemented on a pipelined floatingpoint unit with a multiplyaccumulate configuration. In such a situation, the naive method gives a more accurate result with a slightly lower latency, as compared with Goldschmidt's algorithm, and is much faster than but slightly inferior in accuracy to the NewtonRaphson method.

