Math.imul()

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

a

First number.

b

Second number.

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

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 JIT-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.

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 convenience:
  // 1. 0x003fffff /*opA & 0x000fffff*/ * 0x7fffffff /*opB*/ = 0x1fffff7fc00001
  //    0x1fffff7fc00001 < Number.MAX_SAFE_INTEGER /*0x1fffffffffffff*/
  var result = (opA & 0x003fffff) * opB;
  // 2. We can remove an integer coercion 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;
};

• Polyfill of Math.imul in core-js
• Emscripten