Reciprocal Approximation with 1 Subtraction

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).