Bit twiddling: which bit is set?

Question

I have a 64-bit unsigned integer with exactly 1 bit set. I’d like to assign a value to each of the possible 64 values (in this case, the odd primes, so 0x1 corresponds to 3, 0x2 corresponds to 5, …, 0x8000000000000000 corresponds to 313).

It seems like the best way would be to convert 1 → 0, 2 → 1, 4 → 2, 8 → 3, …, 2⁶³ → 63 and look up the values in an array. But even if that’s so, I’m not sure what the fastest way to get at the binary exponent is. And there may be more efficient ways, still.

This operation will be used 10¹⁴ to 10¹⁶ times, so performance is a serious issue.

user_1022707 · Answer

This is for 32 bit, java, but it should be possible to adapt it to 64 bit. It assume this will be the fastest cause there is no branching involved.

static public final int msb(int n) {
    n |= n >>> 1;  
    n |= n >>> 2; 
    n |= n >>> 4; 
    n |= n >>> 8; 
    n |= n >>> 16; 
    n >>>= 1;
    n += 1; 
    return n;
}

static public final int msb_index(int n) {

    final int[] multiply_de_bruijn_bit_position = {
        0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8, 
        31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9
    };
    return multiply_de_bruijn_bit_position[(msb(n) * 0x077CB531) >>> 27];
}

Here is more information from: http://graphics.stanford.edu/~seander/bithacks.html#ZerosOnRightMultLookup

// Count the consecutive zero bits (trailing) on the right with multiply and lookup

unsigned int v;  // find the number of trailing zeros in 32-bit v 
int r;           // result goes here
static const int MultiplyDeBruijnBitPosition[32] = 
{
  0, 1, 28, 2, 29, 14, 24, 3, 30, 22, 20, 15, 25, 17, 4, 8, 
  31, 27, 13, 23, 21, 19, 16, 7, 26, 12, 18, 6, 11, 5, 10, 9
};
r = MultiplyDeBruijnBitPosition[((uint32_t)((v & -v) * 0x077CB531U)) >> 27];

// Converting bit vectors to indices of set bits is an example use for this. 
// It requires one more operation than the earlier one involving modulus 
// division, but the multiply may be faster. The expression (v & -v) extracts 
// the least significant 1 bit from v. The constant 0x077CB531UL is a de Bruijn 
// sequence, which produces a unique pattern of bits into the high 5 bits for 
// each possible bit position that it is multiplied against. When there are no 
// bits set, it returns 0. More information can be found by reading the paper 
// Using de Bruijn Sequences to Index 1 in a Computer Word by 
// Charles E. Leiserson, Harald Prokof, and Keith H. Randall.

and as last: http://supertech.csail.mit.edu/papers/debruijn.pdf

Bit twiddling: which bit is set?

15 Answers