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 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:
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;
}
// unfortunately, 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
Specification |
---|
ECMAScript Language Specification # sec-math.clz32 |
Browser compatibility
BCD tables only load in the browser