How does this implementation of bitset::count() work?

Question

Here's the implementation of std::bitset::count with MSVC 2010:

size_t count() const
    {   // count number of set bits
    static char _Bitsperhex[] = "\0\1\1\2\1\2\2\3\1\2\2\3\2\3\3\4";
    size_t _Val = 0;
    for (int _Wpos = _Words; 0 <= _Wpos; --_Wpos)
        for (_Ty _Wordval = _Array[_Wpos]; _Wordval != 0; _Wordval >>= 4)
            _Val += _Bitsperhex[_Wordval & 0xF];
    return (_Val);
    }

Can someone explain to me how this is working? what's the trick with _Bitsperhex?

Answer 1

_Bitsperhex contains the number of set bits in a hexadecimal digit, indexed by the digit.

digit: 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111
value: 0    1    1    2    1    2    2    3    1    2    2    3    2    3    3    4
index: 0    1    2    3    4    5    6    7    8    9    A    B    C    D    E    F

The function retrieves one digit at a time from the value it's working with by ANDing with 0xF (binary 1111), looks up the number of set bits in that digit, and sums them.