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

The naive linear search may be an option for evenly distributed integers, since it needs slightly less than 2 comparisons on average (for any integer size).

/* between 1 and 64 comparisons, ~2 on average */
#define u64_size(c) (              \
    0x8000000000000000 < (c) ? 64  \
  : 0x4000000000000000 < (c) ? 63  \
  : 0x2000000000000000 < (c) ? 62  \
  : 0x1000000000000000 < (c) ? 61  \
...
  : 0x0000000000000002 < (c) ?  2  \
  : 0x0000000000000001 < (c) ?  1  \
  :                             0  \
)