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;
}
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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