Logo Questions Linux Laravel Mysql Ubuntu Git Menu
 

Modulo operation with negative numbers

People also ask

Can you do modulus with negative numbers?

The modulus of a negative number is found by ignoring the minus sign. The modulus of a number is denoted by writing vertical lines around the number. Note also that the modulus of a negative number can be found by multiplying it by −1 since, for example, −(−8) = 8.

How does modulo work with negative numbers in C?

Anyone can predict the output of a modulus operator when both operands are positive. But when it comes to the negative numbers, different languages give different outputs. In C language, modulus is calculated as, a % n = a – ( n * trunc( a/n ) ).


C99 requires that when a/b is representable:

(a/b) * b + a%b shall equal a

This makes sense, logically. Right?

Let's see what this leads to:


Example A. 5/(-3) is -1

=> (-1) * (-3) + 5%(-3) = 5

This can only happen if 5%(-3) is 2.


Example B. (-5)/3 is -1

=> (-1) * 3 + (-5)%3 = -5

This can only happen if (-5)%3 is -2


The % operator in C is not the modulo operator but the remainder operator.

Modulo and remainder operators differ with respect to negative values.

With a remainder operator, the sign of the result is the same as the sign of the dividend (numerator) while with a modulo operator the sign of the result is the same as the divisor (denominator).

C defines the % operation for a % b as:

  a == (a / b * b) + a % b

with / the integer division with truncation towards 0. That's the truncation that is done towards 0 (and not towards negative inifinity) that defines the % as a remainder operator rather than a modulo operator.


Based on the C99 Specification: a == (a / b) * b + a % b

We can write a function to calculate (a % b) == a - (a / b) * b!

int remainder(int a, int b)
{
    return a - (a / b) * b;
}

For modulo operation, we can have the following function (assuming b > 0)

int mod(int a, int b)
{
    int r = a % b;
    return r < 0 ? r + b : r;
}

My conclusion is that a % b in C is a remainder operation and NOT a modulo operation.


I don't think there isn't any need to check if the number is negative.

A simple function to find the positive modulo would be this -

Edit: Assuming N > 0 and N + N - 1 <= INT_MAX

int modulo(int x,int N){
    return (x % N + N) %N;
}

This will work for both positive and negative values of x.

Original P.S: also as pointed out by @chux, If your x and N may reach something like INT_MAX-1 and INT_MAX respectively, just replace int with long long int.

And If they are crossing limits of long long as well (i.e. near LLONG_MAX), then you shall handle positive and negative cases separately as described in other answers here.


Donate For Us

If you love us? You can donate to us via Paypal or buy me a coffee so we can maintain and grow! Thank you!