How to find the position of the only-set-bit in a 64-bit value using bit manipulation efficiently?

Question

Just say I have a value of type uint64_t seen as sequence of octets (1 octet = 8-bit). The uint64_t value is known containing only one set bit<

Answer 1

The value mod 0x8C yields a unique value for each of the cases.

This value mod 0x11 is still unique.

The second value in the table is the resulting mod 0x11.

128 9
32768   5
8388608 10
2147483648  0
549755813888    14
140737488355328 2
36028797018963968   4
9223372036854775808     15

So a simple lookup table will suffice.

int find_bit(uint64_t bit){ 
  int lookup[] = { the seventeen values };
  return lookup[ (bit % 0x8C) % 0x11];
}

No branching, no compiler tricks.

For completeness, the array is

{ 31, 0, 47, 15, 55, 0, 0, 7, 23, 0, 0, 0, 39, 63, 0, 0}