Importance

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Abstract

A method of computing a square root or a reciprocal square root of a number in a computing device uses a piece-wise quadratic approximation of the number. The square root computation uses the piece-wise quadratic approximation in the form: squareroot(X)=A.sub.i x.sup.2 +B.sub.i x+C.sub.i, in each interval i. The reciprocal square root computation uses the piece-wise quadratic approximation in the form: 1/squareroot(X)=A.sub.i x.sup.2 +B.sub.i x+C.sub.i, in each interval i. The coefficients A.sub.i, B.sub.i, and C.sub.i, and A.sub.i, B.sub.i, and C.sub.i are derived for the square root operation and for the reciprocal square root operation to reduce the least mean square error using a least squares approximation of a plurality of equally-spaced points within an interval. In one embodiment, 256 equally-spaced intervals are defined to represent the 23 bits of the mantissa. The coefficients are stored in a storage and accessed during execution of the square root or reciprocal square root computation instruction.

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First Claim