Why Doesn't Modulus Work with Non-Integers in C?

Why Modulus Division Fails for Non-Integers

In mathematics, modulus division, denoted by the modulo operator %, finds the remainder of the division of one integer by another, effectively "wrapping around" the result to the designated range. However, in programming languages like C, this operation does not work for non-integer operands, resulting in an error.

Understanding Remainder for Integers

For integers, the remainder operation makes intuitive sense. For instance, when dividing 13 by 5, we get a quotient of 2 and a remainder of 3. This is because 5 fits into 13 exactly two times, leaving an excess of 3.

Extension to Real Numbers

Extending the concept of remainder to floating-point numbers, or more generally real numbers, introduces complications. Consider the division of 5.2 by 2.3. Mathematically, the result is approximately 2.2609. However, if we apply the modulus operator to the operands directly, we get a different result.

In C, 5.2 % 2.3 results in a compiler error because the operands are not integers. This is because the C standard does not define a hybrid operation that computes the integer quotient of real numbers.

Standard Library Functions

To address this issue, the C standard library provides two functions: fmod and remainder.

• fmod: Computes the remainder of the floating-point division, but it does not follow the rounding rules of integer division.
• remainder: Introduced in C99, it computes the remainder while following the integer division rounding rule.

To resolve the problem in the given code sample, we can use the fmod function:

#include <math.h>

float sin(float x){
    return limited_sin(fmod((x + M_PI), (2 *M_PI)) - M_PI);
}</math.h>

Note that the fmod function expects its operands to be of the same type, so we need to cast them to double if necessary.

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