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 have 80-bit or 128-bit floats available, cast to that type and then read off the exponent bits. This link has details (for integers up to 52 bits) and several other methods:

http://graphics.stanford.edu/~seander/bithacks.html#IntegerLogIEEE64Float

Also, check the ffmpeg source. I know they have a very fast algorithm. Even if it's not directly extensible to larger sizes, you can easily do something like if (x>INT32_MAX) return fastlog2(x>>32)+32; else return fastlog2(x);