Modulo Of Negative Numbers In C

Users can determine the modulus of a negative number by omitting the minus (-) symbol. The modulus of a number is obtained by enclosing it within vertical lines. It is important to note that the modulus of a negative number is calculated by multiplying it by negative one, such as in the instance where (-9) equals 9.

"Modulus":

The modulo operation, also referred to as "mod," represents the remainder of a division. In 1801, Gauss released a thesis on modular arithmetic. A formal mathematical explanation later presented by Donald Knuth is universally acknowledged today.

The modulo operator computes the result of a division operation. However, the behavior becomes more complex when negative values are involved. Let's explore some instances of calculating the modulus with negative numbers. Take note of the outputs produced by the code snippets.

Example:

C program:

#include <stdio.h>



int main() {

    int x = -7, y = 11, z = 2;



    int result = x % y;

    printf("C Program Output: %d %% %d = %d\n", x, y, result);



    return 0;

}

Output:

C Program Output: -7 % 11 = -7

C++ program:

#include <iostream>

int main() {

    int x = -7, y = 11, z = 2;



    int result = x % y;

    std::cout << "C++ Program Output: " << x << " % " << y << " = " << result << std::endl;



    return 0;

}

Output:

C++ Program Output: -7 % 11 = -7

Example:2

In certain situations, irrespective of the sign of the dividend, it may be necessary to ensure that the result of the modulo operation is positive. One common technique to achieve this is by repeatedly adding the divisor to the result until it becomes non-negative. This strategy for obtaining a positive remainder when the dividend is negative is commonly employed in C programming.

C program:

#include <stdio.h>



int main() {

    int x = 4, y = -9;



    int result = x % y;

    printf("C Program Output: %d %% %d = %d\n", x, y, result);



    return 0;

}

Output:

C Program Output: 4 % -9 = 4

For Reference:

C++ program:

#include <iostream>



int main() {

    int x = 4, y = -9;



    int result = x % y;

    std::cout << "C++ Program Output: " << x << " % " << y << " = " << result << std::endl;



    return 0;

}

Output:

C Program Output: 4 % -9 = 4

Example:3

C program:

#include <stdio.h>

int main() {

    int x = -4, y = 9;



    int result = x % y;

    printf("C Program Output: %d %% %d = %d\n", x, y, result);



    return 0;

}

Output:

C Program Output: -4 % 9 = -4

For Reference:

C++ program:

#include <iostream>



int main() {

    int x = -4, y = 9;



    int result = x % y;

    std::cout << "C++ Program Output: " << x << " % " << y << " = " << result << std::endl;



    return 0;

}

Output:

C++ Program Output: -4 % 9 = -4

Chart:

Conclusion:

When negative values are employed, the modulo operation in C retains the sign of the dividend. Despite seeming counterintuitive at first, this follows a consistent principle. To ensure a positive result for negative dividends, you can repeatedly add the divisor to the quotient until it becomes non-negative.

When engaging in diverse programming tasks like circular buffers, date calculations, and managing negative offsets, it is crucial to understand how the modulo operation behaves with negative values. This understanding empowers you to develop reliable and accurate code, preventing unexpected errors and ensuring the precision of your algorithms.