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Fast Division Using Accurate Quotient Approximations to Reduce the Number of Iterations
August 1992 (vol. 41 no. 8)
pp. 981-995

A class of iterative integer division algorithms is presented based on look-up table and Taylor-series approximations to the reciprocal. The algorithm iterates by using the reciprocal to find an approximate quotient and then subtracting the quotient multiplied by the divisor from the dividend to find a remaining dividend. Fast implementations can produce an average of either 14 or 27 b per iteration, depending on whether the basic or advanced version of this method is implemented. Detailed analyses are presented to support the claimed accuracy per iteration. Speed estimates using state-of-the-art ECL components show that this method is faster than the Newton-Raphson technique and can produce 53-b quotients of 53-b numbers in about 25 ns using the basic method and 21 ns using the advanced method. In addition, these methods naturally produce an exact remainder, which is very useful for implementing precise rounding specifications.

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Index Terms:
quotient approximations; iterative integer division algorithms; look-up table; Taylor-series; reciprocal; ECL components; exact remainder; precise rounding specifications; algorithm theory; approximation theory; digital arithmetic; dividing circuits; iterative methods; number theory.
Citation:
D. Wong, M. Flynn, "Fast Division Using Accurate Quotient Approximations to Reduce the Number of Iterations," IEEE Transactions on Computers, vol. 41, no. 8, pp. 981-995, Aug. 1992, doi:10.1109/12.156541
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