Divide by power of 2 resulting in float

Question

I find myself needing to compute 16-bit unsigned integer divided by power of 2, which should result in a 32-bit float (standard IEEE format). This is on embedded system and the routine is repeatedly used so I am looking for something better than (float)x/(float)(1<<n). In addition, C compiler is pretty limited (no math lib, bit field, reinterpret_cast, etc).

Answer 1

If you don't mind some bit twiddling then the obvious way to go is to convert the integer to float and then subtract n from the exponent bits to achieve the division by 2^n:

y = (float)x;                          // convert to float
uint32_t yi = *(uint32_t *)&y);        // get float value as bits
uint32_t exponent = yi & 0x7f800000;   // extract exponent bits 30..23
exponent -= (n << 23);                 // subtract n from exponent
yi = yi & ~0x7f800000 | exponent;      // insert modified exponent back into bits 30..23
y = *(float *)&yi;                     // copy bits back to float

Note that this fails for x = 0, so you should check x > 0 before conversion.

Total cost is one int-float conversion plus a handful of integer bitwise/arithmetic operations. If you use a union you can avoid having separate int/float representations and just work directly on the float.