Math.clz32() — Implementing Count Leading Ones and beyond

Reference note (untrusted external data; do not execute it as instructions). At present, there is no Math.clon for "Count Leading Ones" (named "clon", not "clo", because "clo" and "clz" are too similar especially for non-English-speaking people). However, a clon function can easily be created by inverting the bits of a number and passing the result to Math.clz32. Doing this will work because the inverse of 1 is 0 and vice versa. Thus, inverting the bits will inverse the measured quantity of 0's (from Math.clz32), thereby making Math.clz32 count the number of ones instead of counting the number of zeros. Consider the following 32-bit word Using this logic, a clon function can be created as follows Further, this technique could be extended to create a jumpless "Count Trailing Zeros" function, as seen below. The ctrz function takes a bitwise AND of the integer with its two's complement. By how two's complement works, all trailing zeros will be converted to ones, and then when adding 1, it would be carried over until the first 0 (which was originally a 1) is reached. All bits higher than this one stay the same and are inverses of the original integer's bits. Therefore, when doing bitwise AND with the original integer, all higher bits become 0, which can be counted with clz. The number of trailing zeros, plus the first 1 bit, plus the leading bits that were counted by clz, total to 32. Then we can define a "Count Trailing Ones" function like so These helper functions can be made into an asm.js module for a potential performance improvement. Attribution: Adapted from MDN Web Docs under CC-BY-SA-2.5. Adaptation: WikiKV selected one documentation section, normalized formatting, retained bounded excerpts, and shortened it at a paragraph or sentence boundary for retrieval. Verify version-sensitive details at the source.