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Math.clz32()

The Math.clz32() function returns the number of leading zero bits in the 32-bit binary representation of a number.

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Syntax

Math.clz32(x)

Parameters

x: A number.

Return value

The number of leading zero bits in the 32-bit binary representation of the given number.

Description

clz32 is short for CountLeadingZeroes32.

If x is not a number, then it will be converted to a number first, then converted to a 32-bit unsigned integer.

If the converted 32-bit unsigned integer is 0, then return 32, because all bits are 0.

This function is particularly useful for systems that compile to JS, like Emscripten.

Count Leading Ones and beyond

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 inversing 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, inversing 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:

const a = 32776;   // 00000000000000001000000000001000 (16 leading zeros)
Math.clz32(a);   // 16

const b = ~32776;  // 11111111111111110111111111110111 (32776 inverted, 0 leading zeros)
Math.clz32(b);   // 0 (this is equal to how many leading one's there are in a)

Using this logic, a clon function can be created as follows:

const clz = Math.clz32;

function clon(integer) {
  return clz(~integer);
}

Further, this technique could be extended to create a jumpless "Count Trailing Zeros" function, as seen below. The ctrz function below fills in all the high bits with the lowest filled bit, then negates the bits to erase all higher set bits so that clz can then be used.

const clz = Math.clz32;

// count trailing zeros
function ctrz(integer) {
  // 1. fill in all the higher bits after the first one
  integer |= integer << 16;
  integer |= integer << 8;
  integer |= integer << 4;
  integer |= integer << 2;
  integer |= integer << 1;
  // 2. Now, inversing the bits reveals the lowest bits
  return 32 - clz(~integer);
}

However, a simpler and possibly more efficient algorithm is the following:

function ctrz(integer) {
  integer >>>= 0; // ensures coercion to Uint32
  if (integer === 0) {
    // skipping this step would make it return -1
    return 32;
  }
  integer &= -integer; // equivalent to `int = int & (~int + 1)`
  return 31 - clz(integer);
}

Then we can define a "Count Trailing Ones" function like so:

// count trailing ones
function ctron(integer) {
  // No shift-filling-in-with-ones operator is available in
  // JavaScript, so the below code is the fastest
  return ctrz(~integer);

  /* Alternate implementation for demonstrational purposes:
      // 1. erase all the higher bits after the first zero
      integer &= (integer << 16) | 0xffff;
      integer &= (integer << 8 ) | 0x00ff;
      integer &= (integer << 4 ) | 0x000f;
      integer &= (integer << 2 ) | 0x0003;
      integer &= (integer << 1 ) | 0x0001;
      // 2. Now, inversing the bits reveals the lowest zeros
      return 32 - clon(~integer);
  */
}

These helper functions can be made into an asm.js module for a potential performance improvement.

const countTrailsMethods = (function (stdlib, foreign, heap) {
  "use asm";
  const clz = stdlib.Math.clz32;

  // count trailing zeros
  function ctrz(integer) {
    integer = integer | 0; // coerce to an integer
    // 1. fill in all the higher bits after the first one
    // Note: asm.js doesn't have compound assignment operators such as |=
    integer = integer | (integer << 16);
    integer = integer | (integer << 8);
    integer = integer | (integer << 4);
    integer = integer | (integer << 2);
    integer = integer | (integer << 1);
    // 2. Now, inversing the bits reveals the lowest bits
    return 32 - clz(~integer) | 0;
  }

  // count trailing ones
  function ctron(integer) {
    integer = integer | 0; // coerce to an integer
    return ctrz(~integer) | 0;
  }

  // asm.js demands plain objects:
  return { ctrz: ctrz, ctron: ctron };
})(window, null, null);

const { ctrz, ctron } = countTrailsMethods;

Examples

Using Math.clz32()

Math.clz32(1);           // 31
Math.clz32(1000);        // 22
Math.clz32();            // 32

const stuff = [NaN, Infinity, -Infinity, 0, -0, false, null, undefined, 'foo', {}, []];
stuff.every((n) => Math.clz32(n) === 32);  // true

Math.clz32(true);        // 31
Math.clz32(3.5);         // 30

Specifications

Specification
ECMAScript Language Specification # sec-math.clz32

Browser compatibility

	Desktop						Mobile						Server
	Chrome	Edge	Firefox	Internet Explorer	Opera	Safari	WebView Android	Chrome Android	Firefox for Android	Opera Android	Safari on IOS	Samsung Internet	Deno	Node.js
`clz32`	38	12	31	No	25	7	38	38	31	25	7	3.0	1.0	0.12.0