Compute fast log base 2 ceiling

Question

What is a fast way to compute the (long int) ceiling(log_2(i)), where the input and output are 64-bit integers? Solutions for signed or unsigned integers are ac

Answer 1

If you're compiling for 64-bit processors on Windows, I think this should work. _BitScanReverse64 is an intrinsic function.

#include 
__int64 log2ceil( __int64 x )
{
  unsigned long index;
  if ( !_BitScanReverse64( &index, x ) )
     return -1LL; //dummy return value for x==0

  // add 1 if x is NOT a power of 2 (to do the ceil)
  return index + (x&(x-1)?1:0);
}

For 32-bit, you can emulate _BitScanReverse64, with 1 or 2 calls to _BitScanReverse. Check the upper 32-bits of x, ((long*)&x)[1], then the lower 32-bits if needed, ((long*)&x)[0].