Fastest way to scan for bit pattern in a stream of bits

Question

I need to scan for a 16 bit word in a bit stream. It is not guaranteed to be aligned on byte or word boundaries.

What is the fastest way of achieving this

Answer 1

What I would do is create 16 prefixes and 16 suffixes. Then for each 16 bit input chunk determine the longest suffix match. You've got a match if the next chunk has a prefix match of length (16-N)

A suffix match doesn't actually 16 comparisons. However, this takes pre-calculation based upon the pattern word. For example, if the patternword is 101010101010101010, you can first test the last bit of your 16 bit input chunk. If that bit is 0, you only need to test the ...10101010 suffices. If the last bit is 1, you need to test the ...1010101 suffices. You've got 8 of each, for a total of 1+8 comparisons. If the patternword is 1111111111110000, you'd still test the last bit of your input for a suffix match. If that bit is 1, you have to do 12 suffix matches (regex: 1{1,12}) but if it's 0 you have only 4 possible matches (regex 1111 1111 1111 0{1,4}), again for an average of 9 tests. Add the 16-N prefix match, and you see that you only need 10 checks per 16 bit chunk.