How does java do modulus calculations with negative numbers

Question

Am I doing modulus wrong  Because in Java -13   64 is supposed to evaluate to -13 but I get 51

User · Answer

Your result is wrong for Java  Please provide some context how you arrived at it  your program  implementation and version of Java    From the Java Language Specification   15 17 3 Remainder Operator           The remainder operation for operands that are integers after binary numeric promotion    5 6 2  produces a result value such that  a b  b  a b  is equal to a     15 17 2 Division Operator         Integer division rounds toward 0    Since   is rounded towards zero  resulting in zero   the result of   should be negative in this case

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To overcome this  you could add 64  or whatever your modulus base is  to the negative value until it is positive  int k   -13  int modbase   64   while  k  lt  0        k    modbase     int result   k   modbase    The result will still be in the same equivalence class

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In my version of Java  JDK 1 8 0 05  -13 64 -13  you could try  -13- int -13 64   in other words  do division cast to an integer to get rid of the fraction part then subtract from numerator So numerator- int numerator denominator     should give the correct remainder  amp  sign

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Since  mathematically  both are correct       -13   64   -13  on modulus 64    -13   64   51  on modulus 64    One of the options had to be chosen by Java language developers and they chose      the sign of the result equals the sign of the dividend    Says it in Java specs   https   docs oracle com javase specs jls se7 html jls-15 html jls-15 17 3

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Both definitions of modulus of negative numbers are in use - some languages use one definition and some the other   If you want to get a negative number for negative inputs then you can use this   int r   x   n  if  r  gt  0  amp  amp  x  lt  0        r -  n      Likewise if you were using a language that returns a negative number on a negative input and you would prefer positive   int r   x   n  if  r  lt  0        r    n

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you can use    x   n  -  x  lt  0   n   0

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Are you sure you are working in Java   cause Java gives -13   64   -13 as expected  The sign of dividend

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x   x   m   x - m in modulus m  so -13   -13   64 in modulus 64  and -13   51 in modulus 64  assume Z   X   d   r  if 0  lt  r  lt  X then in division Z X we call r the remainder  Z   X returns the remainder of Z X

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According to section 15 17 3 of the JLS   The remainder operation for operands that are integers after binary numeric promotion produces a result value such that  a b  b  a b  is equal to a  This identity holds even in the special case that the dividend is the negative integer of largest possible magnitude for its type and the divisor is -1  the remainder is 0     Hope that helps

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Your answer is in wikipedia  modulo operation  It says  that in Java the sign on modulo operation is the same as that of dividend  and since we re talking about the rest of the division operation is just fine  that it returns -13 in your case  since -13 64   0  -13-0   -13    EDIT  Sorry  misunderstood your question   You re right  java should give -13  Can you provide more surrounding code

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Modulo arithmetic with negative operands is defined by the language designer  who might leave it to the language implementation  who might defer the definition to the CPU architecture   I wasn t able to find a Java language definition   Thanks Ishtar  Java Language Specification for the Remainder Operator   says that the sign of the result is the same as the sign of the numerator

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The mod function is defined as the amount by which a number exceeds the largest integer multiple of the divisor that is not greater than that number  So in your case of   -13   64   the largest integer multiple of 64 that does not exceed -13 is -64  Now  when you subtract -13 from -64 it equals 51 -13 -  -64    -13   64   51

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I don t think Java returns 51 in this case  I am running Java 8 on a Mac and I get   -13   64   -13   Program   public class Test       public static void main String   args            int i   -13          int j   64          System out println i   j

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In Java latest versions you get -13 64   -13  The answer will always have sign of numerator

[java] How does java do modulus calculations with negative numbers?

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