From: SINCLAIR DOUGLAS N <sinclai@ecf.toronto.edu> The only sane way to count the number of 1 bits in a byte is to use a lookup table: return table[result]; On an intel chip this produces ONE opcode: XLAT Do you think we'd all be spending weeks on it if it were that easy? Or are you suggesting that 32-bits of address space of RAM is reasonable for this problem? Even if it's a 16-bit table you still have to do the add; worse, the non-local access shits all over the bus timings and the cache. Much better to avoid going off-chip and keep the CPU running at full speed (which might be 100 times faster than memory). Again, remember we're nottalking about PCs here but real computers. G PS I dunno what superoptimisizer Perry is talking about but I've never heard of a real one that works. You have to feed in a complete machine description at register transfer level and i don't know if those exist for real machines; also the problem is almost certainly exponential time for a *guaranteed* solution as Perry claims is possible.