Integer division with remainder in JavaScript

Question

In JavaScript  how do I get    The whole number of times a given integer goes into another  The remainder

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JavaScript calculates right the floor of negative numbers and the remainder of non-integer numbers, following the mathematical definitions for them.

FLOOR is defined as "the largest integer number smaller than the parameter", thus:

positive numbers: FLOOR(X)=integer part of X;
negative numbers: FLOOR(X)=integer part of X minus 1 (because it must be SMALLER than the parameter, i.e., more negative!)

REMAINDER is defined as the "left over" of a division (Euclidean arithmetic). When the dividend is not an integer, the quotient is usually also not an integer, i.e., there is no remainder, but if the quotient is forced to be an integer (and that's what happens when someone tries to get the remainder or modulus of a floating-point number), there will be a non-integer "left over", obviously.

JavaScript does calculate everything as expected, so the programmer must be careful to ask the proper questions (and people should be careful to answer what is asked!) Yarin's first question was NOT "what is the integer division of X by Y", but, instead, "the WHOLE number of times a given integer GOES INTO another". For positive numbers, the answer is the same for both, but not for negative numbers, because the integer division (dividend by divisor) will be -1 smaller than the times a number (divisor) "goes into" another (dividend). In other words, FLOOR will return the correct answer for an integer division of a negative number, but Yarin didn't ask that!

gammax answered correctly, that code works as asked by Yarin. On the other hand, Samuel is wrong, he didn't do the maths, I guess, or he would have seen that it does work (also, he didn't say what was the divisor of his example, but I hope it was 3):

Remainder = X % Y = -100 % 3 = -1

GoesInto = (X - Remainder) / Y = (-100 - -1) / 3 = -99 / 3 = -33

By the way, I tested the code on Firefox 27.0.1, it worked as expected, with positive and negative numbers and also with non-integer values, both for dividend and divisor. Example:

-100.34 / 3.57: GoesInto = -28, Remainder = -0.3800000000000079

Yes, I noticed, there is a precision problem there, but I didn't had time to check it (I don't know if it's a problem with Firefox, Windows 7 or with my CPU's FPU). For Yarin's question, though, which only involves integers, the gammax's code works perfectly.

User · Answer

const idivmod    a  b    gt   a b  0  a b    there is also a proposal working on it Modulus and Additional Integer Math

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function integerDivison dividend  divisor                this Division    dividend divisor          this Quotient   Math floor dividend divisor            this Remainder   dividend divisor          this calculate       gt               return  Value this Division Quotient this Quotient Remainder this Remainder                                var divide   new integerDivison 5 2     console log divide Quotient         to get Quotient of two value    console log divide division        to get Floating division of two value    console log divide Remainder        to get Remainder of two value    console log divide calculate        to get object containing all the values

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Math floor operation  returns the rounded down value of the operation   Example of 1st question   var x   5  var y   10 4  var z   Math floor x   y    console log z     Console      15   Example of 2nd question   var x   14  var y   5  var z   Math floor x y    console log x     Console      4

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Alex Moore-Niemi s comment as an answer   For Rubyists here from Google in search of divmod  you can implement it as such    function divmod x  y      var div   Math trunc x y     var rem   x   y    return  div  rem       Result       2  33

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This will always truncate towards zero  Not sure if it is too late  but here it goes   function intdiv dividend  divisor         divisor   divisor - divisor   1      if  divisor    0  throw new Error  division by zero        dividend   dividend - dividend   1      var rem   dividend   divisor      return            remainder  rem           quotient   dividend - rem    divisor

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If you are just dividing with powers of two  you can use bitwise operators   export function divideBy2 num      return  num  gt  gt  1  num  amp  1      export function divideBy4 num      return  num  gt  gt  2  num  amp  3      export function divideBy8 num      return  num  gt  gt  3  num  amp  7        The first is the quotient  the second the remainder

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If you need to calculate the remainder for very large integers  which the JS runtime cannot represent as such  any integer greater than 2 32 is represented as a float and so it loses precision   you need to do some trick   This is especially important for checking many case of check digits which are present in many instances of our daily life  bank account numbers  credit cards        First of all you need your number as a string  otherwise you have already lost precision and the remainder does not make sense    str    123456789123456789123456789    You now need to split your string in smaller parts  small enough so the concatenation of any remainder and a piece of string can fit in 9 digits   digits   9 - String divisor  length   Prepare a regular expression to split the string  splitter   new RegExp    1   digits          digits          g     For instance  if digits is 7  the regexp is     1 7       7      g   It matches a nonempty substring of maximum length 7  which is followed          is a positive lookahead  by a number of characters that is multiple of 7  The  g  is to make the expression run through all string  not stopping at first match   Now convert each part to integer  and calculate the remainders by reduce  adding back the previous remainder - or 0 - multiplied by the correct power of 10    reducer    rem  piece    gt   rem   Math pow 10  digits    piece    divisor   This will work because of the  subtraction  remainder algorithm   n mod d    n - kd  mod d   which allows to replace any  initial part  of the decimal representation of a number with its remainder  without affecting the final remainder   The final code would look like   function remainder num  div      const digits   9 - String div  length    const splitter   new RegExp    1   digits          digits          g      const mult   Math pow 10  digits     const reducer    rem  piece    gt   rem   mult   piece    div     return str match splitter  map Number  reduce reducer  0

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You can use the function parseInt to get a truncated result   parseInt a b    To get a remainder  use mod operator   a b   parseInt have some pitfalls with strings  to avoid use radix parameter with base 10  parseInt  09   10    In some cases the string representation of the number can be a scientific notation  in this case  parseInt will produce a wrong result   parseInt 100000000000000000000000000000000  10     1e 32   This call will produce 1 as result

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For some number y and some divisor x compute the quotient  quotient  and remainder  remainder  as   var quotient   Math floor y x   var remainder   y   x

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I m no expert in bitwise operators  but here s another way to get the whole number   var num      a   b     This will work properly for negative numbers as well  while Math floor   will round in the wrong direction   This seems correct as well   var num    a   b   gt  gt  0

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ES6 introduces the new Math trunc method  This allows to fix  MarkElliot s answer to make it work for negative numbers too   var div   Math trunc y x   var rem   y   x    Note that Math methods have the advantage over bitwise operators that they work with numbers over 231

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var remainder   x   y  return  x - remainder    y

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You can use ternary to decide how to handle positive and negative integer values as well   var myInt    y  gt  0    Math floor y x    Math floor y x    1   If the number is a positive  all is fine  If the number is a negative  it will add 1 because of how Math floor handles negatives

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I normally use   const quotient     a - a   b    b  const remainder   a   b    It s probably not the most elegant  but it works

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Here is a way to do this   Personally I would not do it this way  but thought it was a fun way to do it for an example   x000D   x000D  function intDivide numerator  denominator      return parseInt  numerator denominator  toString   split      0       let x   intDivide 4 5   let y   intDivide 5 5   let z   intDivide 6 5   console log x   console log y   console log z   x000D   x000D   x000D

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I did some speed tests on Firefox   -100 3                -33 33     0 3663 millisec Math floor -100 3     -34        0 5016 millisec    -100 3             -33        0 3619 millisec  -100 3 gt  gt 0            -33        0 3632 millisec  -100 3 0             -33        0 3856 millisec  -100- -100 3   3     -33        0 3591 millisec     a -100  b 3    a b                   -33 33     0 4863 millisec Math floor a b        -34        0 6019 millisec    a b                -33        0 5148 millisec  a b gt  gt 0               -33        0 5048 millisec  a b 0                -33        0 5078 millisec  a- a b   b           -33        0 6649 millisec   The above is based on 10 million trials for each   Conclusion  Use  a b gt  gt 0   or     a b   or  a b 0   to achieve about 20  gain in efficiency  Also keep in mind that they are all inconsistent with Math floor  when a b lt 0  amp  amp  a b  0

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Calculating number of pages may be done in one step  Math ceil x y

[javascript] Integer division with remainder in JavaScript?

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