c - Modulo operation with negative numbers

Question

In a C program I was trying the below operations (Just to check the behavior)

 x = 5 % (-3);
 y = (-5) % (3);
 z = (-5) % (-3); 

printf("%d ,%d ,%d", x, y, z); 

It gave me output as (2, -2 , -2) in gcc. I was expecting a positive result every time. Can a modulus be negative? Can anybody explain this behavior?

Answer 1

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:

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

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

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

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

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

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