Bit-twiddling optimizations in Zed's Rope

  >  // Parallel bit count intermediates
  >  let a = v - ((v >> 1) & (u64::MAX / 3));
  >  let b = (a & (u64::MAX / 5)) + ((a >> 2) & (u64::MAX / 5));
  >  let c = (b + (b >> 4)) & (u64::MAX / 0x11);
  >  let d = (c + (c >> 8)) & (u64::MAX / 0x101);

That "parallel bit count" is almost certainly slower than using two POPCNT instructions on a modern cpu. Should just call __builtin_popcount() and let the compiler do it the most optimal way. Luckily, people do this sort of thing so often that many modern compilers will try (and often succeed) to detect you trying this insanity and convert it to a POPCOUNT (or a pair of POPCOUNTs as the case may be here)

Which compilers support __builtin_popcount()? From memory, it's a gcc extension. If the compiler selects a CPU POPCOUNT instruction for it, are you sure it will work on all machines that you want to run it on?

The above code is completely source- and binary-portable and reasonably fast -- certainly faster than naively looping through the bits, and within a small constant factor of a CPU POPCOUNT instruction.

Your compiler will know the best way to popcount, that is the point of that builtin. It'll use the best method - sometimes this one. GCC does this, MSVC does this, clang does this, i think even rust has some way to do it (EDIT: it does: count_ones()). On archs which lack POPCNT, it will use this method or another, based on knowing the target. On x86 this approach is OK as is. On arm64, for example, it will be suboptimal due to all the literals needed. On armv6m, this method is bad and table lookups are faster.

I once wrote that algorithm, divided into single lines, intending each line to be a single 64-bit ARM instruction. The compiler did idiom detection, transforming it to "builtin popcnt" and (because 64-bit ARMv8.0 lacks a POPCNT instruction) back to the same algorithm. Only that the emitted code was one instruction larger than my code.

64-bit ARM's actually has a very peculiar encoding of immediates to arithmetic instructions. It supports only recurring bit patterns such as used by this algorithm. For example "add x2, x3, #3333333333333333" is encoded as one four-byte instruction.