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Best algorithm to count the number of set bits in a 32-bit integer?

Given a 32bit unsigned integer, we want to count the number of non-zero bits in its binary representation. What is the fastest way to do that ?

We want to do this N~10^10 times.

note: using a large look up table is usually not a good idea because of the architecture of current cpu’s . it is much faster to calculate it locally than to use a huge array that needs looking at the external memory

Answer 1

There are actually several options, I presume the native way is way too slow for this.

You can go with lookup table for 8-bit value and do it in parallel for all four bytes from unsigned int value, then sum the result. This one could be also quite well-paralelizable (be it multi-core, or maybe even some SSE3/4 could help).

You can also go with Brian Kernighan’s solution:

unsigned int v;              // count the number of bits set in v
unsigned int c;              // c accumulates the total bits set in v
for (c = 0; v; c++)
{
  v &= v - 1;                // clear the least significant bit set
}

And the last possible way I found somewhere some time ago is (on 64-bit machines, as the modulo operation would be really fast there):

unsigned int v;      // count the number of bits set in v
unsigned int c;      // c accumulates the total bits set in v

c =  ((v & 0xfff) * 0x1001001001001ULL & 0x84210842108421ULL) % 0x1f;
c += (((v & 0xfff000) >> 12) * 0x1001001001001ULL & 0x84210842108421ULL) % 0x1f;
c += ((v >> 24) * 0x1001001001001ULL & 0x84210842108421ULL) % 0x1f;