Intel Corporation

Lntel Corporation

Theodore Kubaska

Ping Tak Peter Tang

John R Harrison

There is disclosed method, software and apparatus for evaluating a function f in a computing device using a reduction, core approximation and final reconstruction stage. According to one embodiment of the invention, an argument reduction stage uses an approximate reciprocal table in the computing device. According to another embodiment, an approximate reciprocal instruction I is operative on the computing device to use the approximate reciprocal table such that the argument reduction stage provides that&#x2014;C:=I(X) and R:=X&#xd7;C&#x2212;1, the core approximation stage provides that p(R) is computed so that it approximates f(1+R), and the final reconstruction stage provides that T=f(1/C) is fetched and calculated if necessary, and f(X) is reconstructed based on f(X)=f([1/C]&#xd7;[X&#xd7;C])=g(f(1/C), f(1+R)).

Methods and apparatus for fast argument reduction in a computing system

A method suitable for calculating an expression having the form (A/B) by a processor that features separate sets of floating point units which can operate in parallel for greater speed of execution. The processor issues instructions to determine an approximate reciprocal R of a first variable B. Further instructions are issued to raise a second variable to the power of a third variable K by a first set of arithmetic units of the processor, where the second variable is a function of the approximate reciprocal R . Still further instructions are issued to calculate a polynomial q at a fourth variable delta by a second set of arithmetic units of the processor. The fourth variable delta is also a function of the approximate reciprocal R . Finally, one or more instructions are issued to multiply the calculated polynomial by the second variable, having been raised to the power of the third variable, to yield (A/B) .

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Portland, OR, United States of America

Theodore Kubaska