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System and method for improving the accuracy of reciprocal square root operations performed by a floating-point unit
System and method for improving the accuracy of reciprocal square root operations performed by a floating-point unit
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机译:用于提高由浮点单元执行的平方根倒数运算的系统和方法
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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 (Xi); (b) determining a first intermediate result (IR1) according to the equation: IR1=1−N*Xi; (c) multiplying IR1 by Xi to produce a second intermediate result (IR2); and (d) adding Xi 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 Xi; (b) multiplying Xi by N to produce IR1; (c) determining IR2 according to the equation: IR2=(1−Xi*IR1)/2; (d) multiplying IR2 by Xi to produce a third intermediate result (IR3); and (e) adding IR3 to Xi to produce an approximation of the reciprocal square root of the number.
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机译:提高了近似数(N)的倒数和倒数平方根的精度。近似N的倒数包括:(a)估计N的倒数以产生估计(X i Sub>); (b)根据以下公式确定第一中间结果(IR1):IR1 = 1-N * X i Sub>; (c)将IR1乘以X i Sub>产生第二个中间结果(IR2); (d)将X i Sub>添加到IR2以产生N的倒数的近似值。近似倒数平方根包括:(a)估计N的倒数平方根以产生X i Sub>; (b)将X i Sub>乘以N以产生IR1; (c)根据以下公式确定IR2:IR2 =(1-X i Sub> * IR1)/ 2; (d)将IR2乘以X i Sub>产生第三中间结果(IR3); (e)将IR3加到X i Sub>上,以得出数字倒数平方根的近似值。
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