Fast hamming distance between 2 bitset

Question

I'm writing a software that heavily relies on (1) accessing single bit and (2) Hamming distance computations between 2 bitset A and B (ie. the numbers of bits that differ between A and B). The bitsets are quite big, between 10K and 1M bits and i have a bunch of them. Since it is impossible to know the bitset sizes at compilation time, i'm using vector < bool > , but i plan to migrate to boost::dynamic_bitset soon.

Hereafter are my questions:

(1) Any ideas about which implementations have the fastest single bit access time?

(2) To compute Hamming distance, the naive approach is to loop over the single bits and to count differences between the 2 bitsets. But, my feeling is that it might be much faster to loop over bytes instead of bits, perform R = byteA XOR byteB, and look in a table with 255 entries what "local" distance is associated with R. Another solutions would be store a 255 x 255 matrix and access directly without operation to the distance between byteA and byteB. So my question: Any idea how to implement that from std::vector < bool > or boost::dynamic_bitset? In other words, do you know if there is a way to get access to the bytes array or i have to recode everything from scratch?

Answer 1

(1) Probably vector<char> (or even vector<int>), but that wastes at least 7/8 space on typical hardware. You don't need to unpack the bits if you use a byte or more to store them. Which of vector<bool> or dynamic_bitset is faster, I don't know. That might depend on the C++ implementation.

(2) boost::dynamic_bitset has operator^ and a count member, which together can be used to compute the Hamming distance in a probably fast, though memory-wasting way. You can also get to the underlying buffer with to_block_range; to use that, you need to implement a Hamming distance calculator as an OutputIterator.