System and method for improving the accuracy of reciprocal square root operations performed by a floating-point unit

摘要

The accuracy of approximating the reciprocal and the reciprocal square root of a number (N) is improved. Approximating the reciprocal of N includes: (a) estimating the reciprocal of N to produce an estimate (X_i); (b) determining a first intermediate result (IR1) according to the equation: IR1=1-N*X_i; (c) multiplying IR1 by X_i to produce a second intermediate result (IR2); and (d) adding X_i to IR2 to produce an approximation of the reciprocal of N. Approximating the reciprocal square root includes: (a) estimating the reciprocal square root of N to produce X_i; (b) multiplying X_i by N to produce IR1; (c) determining IR2 according to the equation: IR2=(1-X_i*IR1)/2; (d) multiplying IR2 by X_i to produce a third intermediate result (IR3); and (e) adding IR3 to X_i to produce an approximation of the reciprocal square root of the number.