Modulus and Additional Integer Math

Updated September 1, 2020


Champion: Peter Hoddie (assisted by Dan Ehrenberg)

Stage: 0


This proposal consists of two related extensions to the Math object: integer math and true modulus.

Integer Math

Integer math operations are often more efficient than floating point math. This tends to be true even in hardware with an FPU.

While ECMA-262 defines mathematical operations in terms of floating point numbers, some engines (XS) and ECMAScript compilers (Emscripten) implement optimizations to use integers where the result is unobservable.

Engines can infer some situations where integer optimizations are possible, but it is not always practical. For this reason, ES6 added Math.imul to allow source text to directly express a 32-bit signed integer multiply operation.

This proposal introduces additional static methods on Math for signed 32-bit integer values.


The % operator is often incorrectly referred to as the "modulo operator" but the actual operation is remainder:

Remainder and modulo operations are equivalent for positive inputs, but not negative values. This article describes the differences.

Brendan Eich recently noted:

...we still need to add mod (as distinct from C-like %) to JS.

This proposal introduces additional static methods on Math for the modulus operation on Number and signed 32-bit integer values.

Use cases

  • Engine optimizations (targets without an FPU, in particular)
  • Compiler optimizations
  • Application optimizations - J5e (embedded robotics)


  • Math.mod(x, y) – IEEE 754 modulus
  • Math.idiv(x, y) – Int32 division
  • Math.imod(x, y) – Int32 modulus
  • Math.idivmod(x, y) – Int32 division with modulus, returns [division result, modulus result]
  • Math.imuldiv(x, y, z) – Int32 multiply and divide with 64-bit intermediate result - (x * y) / z
  • Math.irem(x, y) – Int32 remainder


Most languages provide some subset of these integer and modulo operations. This section contains examples from Python and Ruby.


  • math.remainder and math.fmod

...fmod() is generally preferred when working with floats, while Python’s x % y is preferred when working with integers.

But... % is defined as "remainder"

  • //

floored quotient... Also referred to as integer division

  • divmod(x, y)

[returns] the pair (x // y, x % y)


  • x.divmod(y) – returns [quotient, modulus]
  • x.modulo(y)x - y * (x / y).floor
  • x.remainder(y)x - y * (x / y).truncate.


Polyfill/transpiler implementations

  • (none)

Native implementations

  • XS - initial implementation


Q: Why not use operators instead of static methods?

A: This proposal follows the approach established by Math.imul. If ECMAScript supports operator overloading in the future, developers may apply operators here.

Q: Why does this need to be built-in, instead of being implemented in ECMAScript?

A: These static methods allow engines to optimize in ways that are impractical with equivalent functions implemented in ECMAScript.

Q: Do these static methods accept BigInt arguments?

A: No, to be consistent with the other static methods on Math, including Math.imul. There is no fundamental objection to supporting BigInt where it makes sense should that be the committee's preference.