Web/JavaScript/Reference/Global objects/Math/imul

The Math.imul() function returns the result of the C-like 32-bit multiplication of the two parameters.

Syntax

var product = Math.imul(a, b);

Parameters

a: First number.
b: Second number.

Return value

The result of the C-like 32-bit multiplication of the given arguments.

Description

Math.imul() allows for 32-bit integer multiplication with C-like semantics. This feature is useful for projects like Emscripten.

Because imul() is a static method of Math, you always use it as Math.imul(), rather than as a method of a Math object you created (Math is not a constructor).

If you use normal JavaScript floating point numbers in imul, you will experience a degrade in performance. This is because of the costly conversion from a floating point to an integer for multiplication, and then converting the multiplied integer back into a floating point. The reason imul exists is because it is faster in only one (so far) circumstance: AsmJS. AsmJS allows for JIST-optimizers to more easily implement internal integers in JavaScript. Multiplying two numbers stored internally as integers (which is only possible with AsmJS) with imul is the only potential circumstance where Math.imul may prove performant in current browsers.

Examples

Using Math.imul()

Math.imul(2, 4);          // 8
Math.imul(-1, 8);         // -8
Math.imul(-2, -2);        // 4
Math.imul(0xffffffff, 5); // -5
Math.imul(0xfffffffe, 5); // -10

Polyfill

This can be emulated with the following function:

if (!Math.imul) Math.imul = function(a, b) {
  var aHi = (a >>> 16) & 0xffff;
  var aLo = a & 0xffff;
  var bHi = (b >>> 16) & 0xffff;
  var bLo = b & 0xffff;
  // the shift by 0 fixes the sign on the high part
  // the final |0 converts the unsigned value into a signed value
  return ((aLo * bLo) + (((aHi * bLo + aLo * bHi) << 16) >>> 0) | 0);
};

However, the following function is more performant because it is likely that browsers in which this polyfill would be used do not optimize with an internal integer type in JavaScript, instead using floating points for all numbers.

if (!Math.imul) Math.imul = function(opA, opB) {
  opB |= 0; // ensure that opB is an integer. opA will automatically be coerced.
  // floating points give us 53 bits of precision to work with plus 1 sign bit
  // automatically handled for our convienence:
  // 1. 0x003fffff /*opA & 0x000fffff*/ * 0x7fffffff /*opB*/ = 0x1fffff7fc00001
  //    0x1fffff7fc00001 < Number.MAX_SAFE_INTEGER /*0x1fffffffffffff*/
  var result = (opA & 0x003fffff) * opB;
  // 2. We can remove an integer coersion from the statement above because:
  //    0x1fffff7fc00001 + 0xffc00000 = 0x1fffffff800001
  //    0x1fffffff800001 < Number.MAX_SAFE_INTEGER /*0x1fffffffffffff*/
  if (opA & 0xffc00000 /*!== 0*/) result += (opA & 0xffc00000) * opB |0;
  return result |0;
};

Specifications

Specification
ECMAScript (ECMA-262)The definition of 'Math.imul' in that specification.

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	Safari on iOS	Samsung Internet	Node.js
`imul`	Chrome Full support 28	Edge Full support 12	Firefox Full support 20	IE No support No	Opera Full support 16	Safari Full support 7	WebView Android Full support ≤37	Chrome Android Full support 28	Firefox Android Full support 20	Opera Android Full support 15	Safari iOS Full support 7	Samsung Internet Android Full support 1.5	nodejs Full support 0.12

Legend

Full support: Full support
No support: No support