An accurate linear approximation method utilizing a bipartite reciprocal table for a floating point divider

With the advent of fast multipliers, the latency of a floating point division is greatly reduced using a multiplicative method rather than a subtractive one. For most multiplicative division algorithms, an initial reciprocal approximation of the divisor is largely obtained by a look-up table method. Once the initial approximation is made, it is refined by the use of a functional iteration method until the accuracy of the reciprocal approximation of the divisor is accurate enough to produce the final quotient. This paper introduces a look-up table construction method using the concept of a bipartite reciprocal table that is applied to a piecewise linear approximation. The error of the linear approximation proposed in this paper is less than a quarter of an ulp (unit in the last place). The latency of this reciprocal unit is 3 cycles for the IEEE-754 double precision operation.