Count bits set in parallel

Thu, 07 Jan 2010 00:00:00 +0000

This time it’s not something I make myself. Indeed, I still can’t “see” it 100%: I got it, but it’s a bit complex.

A cute little lady counting (bits? ;-) )

It’s a method to count the number of bits in a number in O(1), in just 5 lines of code. INHUMAN.

The “human” solutions

Of course, there are methods that look way more easy and, given that the size of a number in memory is “fixed”, the O(1) still stands. For example: 0. Based on the “evenness/oddness” of the number

unsigned int bits_counter_v0(unsigned int x) {
    unsigned int count = 0;
    while ( x != 0 ) {
        // If odd, add 1
        count += (x % 2 == 0) ? 0 : 1;
        x >>= 1;
    }
    
    return count;
}

1. Counting one bit at a time (always the least significant one)

unsigned int bits_counter_v1(unsigned int x) {
    unsigned int count = 0;
    while ( x != 0 ) {
        // If least-significant bit is 1, add 1
        count += (x & 1) ? 1 : 0;
        x >>= 1;
    }
    
    return count;
}

2. Counting 4 bit at a time with max 8 shifts, using an “hashmap” with precalculated results The fact that it can count the bits in “max 8 shifts” has the trade off of the memory used by the hashmap.

unsigned int bits_counter_v2(unsigned int x) {
    unsigned int count = 0;
    // "Hashmap" of the values for the least significant 4 bits
    unsigned int int_to_bits_count[16] = {
        0, // 0  00
        1, // 1  01
        1, // 2  10
        2, // 3  11
        1, // 4  100
        2, // 5  101
        2, // 6  110
        3, // 7  111
        1, // 8  1000
        2, // 9  1001
        2, // 10 1010
        3, // 11 1011
        2, // 12 1100
        3, // 13 1101
        3, // 14 1110
        4  // 15 1111
    };
    
    while ( x != 0 ) {
        // Add the bits count of the least significant 4 bits
        count += int_to_bits_count[ x & 15 ];
        x >>= 4;
    }
    
    return count;
}

Let’s see what some insane people made.

Count on Zio Ivan

Count bits set in parallel

The “human” solutions