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Reciprocal Approximation with 1 Subtraction

  • Thread starter Thread starter mbitsnbites
  • Start date Start date
M

mbitsnbites

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.

Code: 
  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).


Comments URL: Reciprocal Approximation with 1 Subtraction | Hacker News

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