If you are using integers to represent subsets then int.bit_count is the number of elements of the set. There is a machine instruction to count the number of ones in the binary representation, maybe popcnt is the name, I am not sure.

Edited, more info: AMD's Barcelona architecture introduced the advanced bit manipulation (ABM) ISA introducing the POPCNT instruction as part of the SSE4a extensions in 2007. Intel Core processors introduced a POPCNT instruction with the SSE4.2 instruction set extension, first available in a Nehalem-based Core i7 processor, released in November 2008.

https://www.rosettacode.org/wiki/Population_count