Math.clz32()

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

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:

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

var b = ~32776;  // 11111111111111110111111111110111 (32776 inversed, 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:

var clz = Math.clz32;
function clon(integer){
    return clz(~integer);
}

Further, this technique could be extended to create jumpless "Count Trailing Zeros" and "Count Trailing Ones" functions 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.

var clz = Math.clz32;
function ctrz(integer){ // count trailing zeros
    // 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) |0; // `|0` ensures integer coercion
}
function ctron(integer){ // count trailing ones
    // 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) |0;
    */
}

Make these helper functions into ASM.JS module; then, you have a true performance masterpiece. Situations like these are exactly what ASM.JS was designed for.

var countTrailsMethods = (function(stdlib, foreign, heap) {
    "use asm";
    var clz = stdlib.Math.clz32;
    function ctrz(integer) { // count trailing zeros
        integer = integer | 0; // coerce to an integer
        // 1. fill in all the higher bits after the first one
        // ASMjs for some reason does not allow ^=,&=, or |=
        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;
    }
    function ctron(integer) { // count trailing ones
        integer = integer | 0; // coerce to an integer
        return ctrz(~integer) |0;
    }
    // unfourtunately, ASM.JS demands slow crummy objects:
    return {a: ctrz, b: ctron};
})(window, null, null);
var ctrz = countTrailsMethods.a;
var ctron = countTrailsMethods.b;

Examples

Using Math.clz32()

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

var 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

Polyfill

The following polyfill is the most efficient.

if (!Math.clz32) Math.clz32 = (function(log, LN2){
  return function(x) {
    // Let n be ToUint32(x).
    // Let p be the number of leading zero bits in 
    // the 32-bit binary representation of n.
    // Return p.
    var asUint = x >>> 0;
    if (asUint === 0) {
      return 32;
    }
    return 31 - (log(asUint) / LN2 | 0) |0; // the "| 0" acts like math.floor
  };
})(Math.log, Math.LN2);

Specifications

Browser compatibility

See also

• Math
• Math.imul