# 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)``

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.

## Examples

### Using `Math.clz32()`

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

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

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

## 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;```

## 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);
```

## Browser compatibility

Update compatibility data on GitHub
Desktop Mobile Server Chrome Edge Firefox Internet Explorer Opera Safari Android webview Chrome for Android Firefox for Android Opera for Android Chrome Full support 38 Edge Full support 12 Firefox Full support 31 IE No support No Opera Full support 25 Safari Full support 7 WebView Android Full support Yes Chrome Android Full support 38 Firefox Android Full support 31 Opera Android Full support Yes Safari iOS Full support 7 Samsung Internet Android Full support Yes nodejs Full support 0.12

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