Reciprocal Approximation with 1 Subtraction
7 by mbitsnbites | 3 comments on Hacker News.
Today's find: You can get a floating-point approximation of 1/x that's accurate to 3 bits with a single integer subtraction instruction. float fast_reciprocal(float x) { unsigned i = *(unsigned *) &x; i = 0x7effffffU - i; return *(float *) &i; } The magic number 0x7effffff accomplishes two things: 1) The exponent is calculated as 253-e, which effectively negates the exponent and subtracts 1. 2) The mantissa is approximated as a 1st order polynomial in the interval [1, 2). Interesting, but perhaps not very useful (as most CPU:s have more accurate reciprocal approximations these days).
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