International Business Machines Corporation

Didier Pinchon

Andre R Steimle

Bernard Desrosiers

Didier R Louis

Louis Didier

An apparatus for executing argument reduction in the computation of F(x)=2**x-1 (with .vertline.x.vertline.&lt;1), determining the value of xi and computing (x-xi) according to the IEEE 754 standard floating-point format having a first circuit arrangement operative to perform pipeline operations on a N bit mantissa; the output of the first circuit arrangement being connected to a normalizer circuit of N+4 bits whose three left-most inputs are tied to 'zero' and whose three left-most out bits J(0:2) are output on a three-bits bus (J-BUS). Also incorporated is a leading zero detector/encoder circuit and a second circuit arrangement operative to perform pipeline operations on exponents connected to an encoder circuit whose output controls the aligner circuit and a selector circuit driven by the outputs of the detector/encoder circuit and encoder circuit whose output controls the normalizer circuit; a xi determining circuit that generates the xi mantissa on a xi-BUS connected to the first circuit arrangement such that: mantissa xi=0=K(1) K(2) 1 0 . . . , 0, and a read-only memory to store the F(xi) values whose output is connected to inputs of the first and second circuits for the respective mantissa and exponent parts of F(xi).

Apparatus for argument reduction in exponential computations of IEEE

A method for approximating mathematical functions using polynomial expansions is implemented in a numeric processing system. A partial remainder operation is set forth for high accuracy reduction of polynomials whose arguments are greater than pi/4. The method may be practiced in a processor having a bus of approximately half the width of the precision of the desired result. Temporary registers are utilized for the storage of intermediate results. Full bus width accuracy is obtained through successive half bus width operations.

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Les Ulis, France

Didier Pinchon