I think most CRC libraries should have a rolling implemenation built in (i.e. as you read bit by bit, or word by word, it calculates the crc for the last N bits (i.e. a rolling crc32 would allow you to read bit by bit and get the crc for the last 32 bits read). Its actually relatively straight forward to do, and surprisingly useful, but post libraries don't implement it.

my practice code at implementing it for fun: https://github.com/sjpotter/window-crc32