Why does the % operator sometimes output positive and sometimes negative?

Question

I was working on a script in unity when i realized something odd and after I finished the script I tested my realization in a visual studio console project.

class Program
{
    static void Main(string[] args)
    {
        Console.WriteLine(-3.5 % 1);
        Console.WriteLine(3.5 % (-1));
    }
}

The output was:

-0.5

0.5

Shouldn't the modulus operator give me -0.5 in both cases?

It returns the remainder. Eric Lippert has a good blog post on it somewhere — pinkfloydx33, Mar 08 '17 at 02:48
FYI, this is not unique to C#. SQL Server behaves identically. — Tim, Mar 08 '17 at 02:53
That blog post btw: https://blogs.msdn.microsoft.com/ericlippert/2011/12/05/whats-the-difference-remainder-vs-modulus/ — pinkfloydx33, Mar 08 '17 at 10:16

Rob Wilkins · Answer 1 · 2017-03-08T07:25:36.377

4

C#'s % operator is actually a remainder -- so it simply returns what's left over from the division. The most important part of that is that the remainder is only affected by the sign of the numerator, and not the divisor.

In the case of 3.5 positive, the 3 will divide perfectly, with 0.5 left over -- with -3.5, -3 will divide perfectly, with -0.5 left over. Whether you divide by -1 or 1 doesn't affect the outcome in either case, the remainder will be the same, and is only affected by the sign of the number itself.

edited Mar 08 '17 at 07:25

answered Mar 08 '17 at 02:52

Rob Wilkins

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Not really. Modulo is mainly a computing thing, and there are differences in how it's implemented between coding languages. It's just good to know which approach your current language takes when applying it. – Rob Wilkins Mar 08 '17 at 18:35

Ripple · Accepted Answer · 2017-03-08T04:59:27.517

Shouldn't the modulus operator give me -0.5 in both cases?

Why should it? Mathematically, both 0.5 and -0.5 are correct for the both cases.

-3.5 = -3 * 1 + (-0.5)
-3.5 = -4 * 1 + 0.5
3.5 = -3 * (-1) + 0.5
3.5 = -4 * (-1) + (-0.5)

Programmatically, it's defined by the C# language specification.

7.8.3 Remainder operator

Floating-point remainder:
float operator %(float x, float y);
double operator %(double x, double y); 
The following table lists the results of all possible combinations of nonzero finite values, zeros, infinities, and NaN’s. In the table, x and y are positive finite values. z is the result of x % y and is computed as x – n * y, where n is the largest possible integer that is less than or equal to x / y. This method of computing the remainder is analogous to that used for integer operands, but differs from the IEEE 754 definition (in which n is the integer closest to x / y).

The table says that the sign of the remainder is the same as the sign of the first operand x.

In the case of -3.5 % 1:

x = 3.5
y = 1
n = 3
z = 3.5 - 3 * 1 = 0.5

According to the table, the result is -z, that is -0.5.

In the case of 3.5 % -1, x, y, n, z are the same as above. According to the table, the result is +z, that is 0.5.

Thank you, I'll keep the table as reference. – Bilal Shafi Mar 08 '17 at 22:57 — Bilal Shafi, Mar 08 '17 at 22:57

Why does the % operator sometimes output positive and sometimes negative?

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