modulo function

[Louis-Aime]

I'd like to add a modulo function, different from standard %.
Let's call it Math.mod (x, d).

• if either x or d is not a number, return NaN.;
• if (d= 0) return NaN;
• if (x = 0) return 0;
• if (d > 0) then
  • if (x > 0) {return x % d }
  • else /* that is, if (x < 0) */ return (x % d) + d;
• else /* that is, if d < 0 */ return Math.mod (- x, -d);

Motivation: operator % produces the remainder of x diveded by Math.abs(d). There is no function that yields the algebraic modulo of x by d, which is of the same sign as d.
Not having this function handy causes frequent bugs in calendrical computations, including ICUs.

[Andrew-Cottrell]

The following implementation, of the suggested function, appears to satisfy the criteria described above.

/**
 * A modulo operation that finds the remainder after division of a dividend
 * by divisor, using Donald E. Knuth's floored division.
 * 
 * The remainder will have an absolute value less than the absolute
 * value of the divisor. Unlike the ECMAScript remainder (%)
 * operator, the remainder will have the same sign as the divisor.
 * 
 * @param {number|BigInt} dividend - A finite number.
 * @param {number|BigInt} divisor - A non-zero number.
 * @return {number|BigInt} The remainder.
 * @throws {TypeError} If exactly one of the parameters is a BigInt.
 * @throws {RangeError} If the divisor is 0n.
 */
Math.mod = function ( dividend, divisor ) {
    /* based on https://github.com/google/closure-library/blob/v20210106/closure/goog/math/math.js#L68 */
    var remainder = dividend % divisor;
    if ( remainder * divisor < 0 ) {
        remainder += divisor;
    }
    return remainder;
};

/* if either dividend or divisor is not a number, return NaN */
Math.mod( "a", 1 );        // NaN
Math.mod( 1, "a" );        // NaN
Math.mod( NaN, 1 );        // NaN
Math.mod( 1, NaN );        // NaN

/* if divisor is a zero, return NaN or throw RangeError */
Math.mod( 1, 0 );          // NaN
Math.mod( 1, -0 );         // NaN
Math.mod( 1n, 0n );        // RangeError: Division by zero

/* if dividend is a zero, return the dividend */
Math.mod( 0, 1 );          // 0
Math.mod( -0, 1 );         // -0
Math.mod( 0, Infinity );   // 0
Math.mod( 0, -Infinity );  // 0
Math.mod( -0, Infinity );  // -0
Math.mod( -0, -Infinity ); // -0
Math.mod( 0n, 1n );        // 0n

/* if the dividend is an infinity, return NaN */
Math.mod( Infinity, 1 );   // NaN
Math.mod( -Infinity, 1 );  // NaN

/* if the divisor is an infinity with the same sign as the dividend, return the dividend */
Math.mod( 1, Infinity );   // 1
Math.mod( -1, -Infinity ); // -1

/* if the divisor is an infinity with the opposite sign as the dividend, return the divisor */
Math.mod( -1, Infinity );  // Infinity
Math.mod( 1, -Infinity );  // -Infinity

/* integers */
Math.mod( 4, 3 );          // 1
Math.mod( 4n, 3n );        // 1n
Math.mod( 4, -3 );         // -2
Math.mod( 4n, -3n );       // -2n
Math.mod( -4, 3 );         // 2
Math.mod( -4n, 3n );       // 2n
Math.mod( -4, -3 );        // -1
Math.mod( -4n, -3n );      // -1n

/* non-integers */
Math.mod( 5.5, 2 );        // 1.5
Math.mod( 5.5, -2 );       // -0.5
Math.mod( -5.5, 2 );       // 0.5
Math.mod( -5.5, -2 );      // -1.5

Except corner cases, this is the same as

• java.lang.Math.floorMod (integers only)
• Python's % (modulo) operator
• Microsoft Excel's and LibreOffice Calc's MOD function
• https://google.github.io/closure-library/api/goog.math.html#modulo
• https://mathjs.org/docs/reference/functions/mod.html
• and other modulo operations that use floored division

[Rudxain]

My concern is that Math.mod may be an ambiguous name, and there's multiple valid definitions of mod, and there's even another definition not mentioned there which makes use of roundInf expand (rounding away from zero, and towards unsigned Infinity).

Even if none of those definitions are ever added (specially modCeil which is useless compared to modFloor), we should be aware of them, because maybe someday modEuclid gets added.

And we have another problem (only if more than 2 definitions are added): Should all be merged into 1 mod method with a 3rd string argument to specify the variant? Or should they all be splitted into standalone methods?

Yet another problem is modPow: should modPow only use 1 variant? Should it have a 4th arg to specify the variant? Or should it be split in multiple methods?

[Andrew-Cottrell]

My concern is that Math.mod may be an ambiguous name...

In my own library, I named it floorMod (following Java's java.lang.Math.floorMod) to avoid ambiguity by clarifying the rounding mode. However, given Microsoft Excel and LibreOffice Calc use MOD, it is reasonable to use mod to mean the floored modulo. Something like modEuclid could be added, concurrently or later, with a longer name for — what I assume would be — less common use cases.

[Rudxain]

I agree, seems reasonable considering the "most" standard mod definition (in mathematics) is defined using floor division

[Rudxain]

Today I learned that what I call "roundInf" is actually named expand in the official and standard Intl.NumberFormat API. Here (at the roundingMode option). In Java, that same rounding mode is named UP.

I'll open a new Issue about rounding modes.
Update: #28

[ghost]

I'd like to add a modulo function, different from standard %. Let's call it Math.mod (x, d).

* if either x or d is not a number, return NaN.;

...

Note that these functions would just coerce their arguments to numbers instead.

[Crissov]

I’ve frequently had the need for a non-zero modulo function, where zmod(a*b, b) returns b instead of 0, e.g. when calculating ordinal indices starting with 1 as in dates. This is easily done with mod(a*b - 1, b) + 1, except I’m not sure this always behaves as expected for parameters being negative or zero.

PS: Apparently, Mathematica has a generalized modulo function with variable offset d for this: Mod[a, n, d].

Math.mod = function ( dividend, divisor, offset = 0 ) {
    var remainder = (dividend - offset) % divisor + offset;
    if ( remainder * divisor < 0 ) {
        remainder += divisor;/*?*/
    }
    return remainder;
};

(Naively adapted from the code @Andrew-Cottrell had posted.)

[ljharb]

can't you maybeZero || b in that case?