Appeal No. 2004-0115 Page 3
Application No. 09/363,637
intermediate result, the appellants assert that the intermediate result would most likely
be in a "denormalized" form when N was large, which would reduce accuracy. (Id.)
The appellants assert that IR2 "is typically a very small number." (Id.) When IR2
is expressed in a normalized floating-point form, they add, "the precision of the result is
increased, thereby improving the approximation of the reciprocal." (Id at 4-5.)
A further understanding of the invention can be achieved by reading the following
claim.
17. A method for approximating the reciprocal square root of a number,
comprising:
(a) estimating the reciprocal square root of the number to produce
an estimate (Xi);
(b) multiplying said estimate by the number to produce a first
intermediate result (IR1);
(c) determining a second intermediate result (IR2) according to the
equation: IR2=(1-Xi*IR1)/2;
(d) multiplying said second intermediate result by said estimate to
produce a third intermediate result; and
(e) adding said third intermediate result to said estimate to produce
an approximation of the reciprocal square root of the number.
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