JavaScript % (modulo) gives a negative result for negative numbers

Question

According to Google Calculator (-13) % 64 is 51.

According to Javascript (see this JSBin) it is -13.

How do I fix this?

Answer 1

Number.prototype.mod = function (n) {
  "use strict";
  return ((this % n) + n) % n;
};

Taken from this article: The JavaScript Modulo Bug

Answer 2

Using Number.prototype is SLOW, because each time you use the prototype method your number is wrapped in an Object. Instead of this:

Number.prototype.mod = function(n) {
  return ((this % n) + n) % n;
}

Use:

function mod(n, m) {
  return ((n % m) + m) % m;
}

See: https://jsperf.app/negative-modulo/2

~97% faster than using prototype. If performance is of importance to you of course..

Answer 3

The % operator in JavaScript is the remainder operator, not the modulo operator (the main difference being in how negative numbers are treated):

-1 % 8 // -1, not 7

Answer 4

A "mod" function to return a positive result.

var mod = function (n, m) {
    var remain = n % m;
    return Math.floor(remain >= 0 ? remain : remain + m);
};
mod(5,22)   // 5
mod(25,22)  // 3
mod(-1,22)  // 21
mod(-2,22)  // 20
mod(0,22)   // 0
mod(-1,22)  // 21
mod(-21,22) // 1

And of course

mod(-13,64) // 51

Answer 5

The accepted answer makes me a little nervous because it re-uses the % operator. What if Javascript changes the behavior in the future?

Here is a workaround that does not re-use %:

function mod(a, n) {
    return a - (n * Math.floor(a/n));
}

mod(1,64); // 1
mod(63,64); // 63
mod(64,64); // 0
mod(65,64); // 1
mod(0,64); // 0
mod(-1,64); // 63
mod(-13,64); // 51
mod(-63,64); // 1
mod(-64,64); // 0
mod(-65,64); // 63

Answer 6

If x is an integer and n is a power of 2, you can use x & (n - 1) instead of x % n.

> -13 & (64 - 1)
51 

Answer 7

Fix negative modulo (reminder operator %)

Simplified using ES6 Arrow function, and without dangerously extending the Number prototype

const mod = (n, m) => (n % m + m) % m;

console.log(mod(-90, 360));    //  270  (Instead of -90)

Answer 8

Though it isn't behaving as you expected, it doesn't mean that JavaScript is not 'behaving'. It is a choice JavaScript made for its modulo calculation. Because, by definition either answer makes sense.

See this from Wikipedia. You can see on the right how different languages chose the result's sign.

Answer 9

This is not a bug, there's 3 functions to calculate modulo, you can use the one which fit your needs (I would recommend to use Euclidean function)

Truncating the decimal part function

console.log(  41 %  7 ); //  6
console.log( -41 %  7 ); // -6
console.log( -41 % -7 ); // -6
console.log(  41 % -7 ); //  6

Integer part function

Number.prototype.mod = function(n) {
    return ((this%n)+n)%n;
};

console.log( parseInt( 41).mod( 7) ); //  6
console.log( parseInt(-41).mod( 7) ); //  1
console.log( parseInt(-41).mod(-7) ); // -6
console.log( parseInt( 41).mod(-7) ); // -1

Euclidean function

Number.prototype.mod = function(n) {
    var m = ((this%n)+n)%n;
    return m < 0 ? m + Math.abs(n) : m;
};

console.log( parseInt( 41).mod( 7) ); // 6
console.log( parseInt(-41).mod( 7) ); // 1
console.log( parseInt(-41).mod(-7) ); // 1
console.log( parseInt( 41).mod(-7) ); // 6

Answer 10

So it seems that if you're trying to mod around degrees (so that if you have -50 degrees - 200 degrees), you'd want to use something like:

function modrad(m) {
    return ((((180+m) % 360) + 360) % 360)-180;
}

Answer 11

I deal with négative a and negative n too

 //best perf, hard to read
   function modul3(a,n){
        r = a/n | 0 ;
        if(a < 0){ 
            r += n < 0 ? 1 : -1
        }
        return a - n * r 
    }
    // shorter code
    function modul(a,n){
        return  a%n + (a < 0 && Math.abs(n)); 
    }

    //beetween perf and small code
    function modul(a,n){
        return a - n * Math[n > 0 ? 'floor' : 'ceil'](a/n); 
    }

Answer 12

There is a NPM package that will do the work for you. You can install it with the following command.

npm install just-modulo --save

Usage copied from the README

import modulo from 'just-modulo';

modulo(7, 5); // 2
modulo(17, 23); // 17
modulo(16.2, 3.8); // 17
modulo(5.8, 3.4); //2.4
modulo(4, 0); // 4
modulo(-7, 5); // 3
modulo(-2, 15); // 13
modulo(-5.8, 3.4); // 1
modulo(12, -1); // NaN
modulo(-3, -8); // NaN
modulo(12, 'apple'); // NaN
modulo('bee', 9); // NaN
modulo(null, undefined); // NaN

GitHub repository can be found via the following link:

https://github.com/angus-c/just/tree/master/packages/number-modulo

Answer 13

For fun, here's a "wrap" function that works sorta like a modulo, except you can also specify the minimum value of the range (instead of it being 0):

const wrap = (value = 0, min = 0, max = 10) =>
  ((((value - min) % (max - min)) + (max - min)) % (max - min)) + min;

Basically just takes the true modulo formula, offsets it such that min ends up at 0, then adds min back in after.

Useful if you have a value that you want to keep between two values.