Question

I recently ran into an issue that could easily be solved using modulus division, but the input was a float:

Given a periodic function (e.g. sin) and a computer function that can only compute it within the period range (e.g. [-π, π]), make a function that can handle any input.

The “obvious” solution is something like:

#include <cmath>

float sin(float x){
    return limited_sin((x + M_PI) % (2 *M_PI) - M_PI);
}

Why doesn’t this work? I get this error:

error: invalid operands of types double and double to binary operator %

Interestingly, it does work in Python:

def sin(x):
    return limited_sin((x + math.pi) % (2 * math.pi) - math.pi)

Answer 1

Because the normal mathematical notion of “remainder” is only applicable to integer division. i.e. division that is required to generate integer quotient.

In order to extend the concept of “remainder” to real numbers you have to introduce a new kind of “hybrid” operation that would generate integer quotient for real operands. Core C language does not support such operation, but it is provided as a standard library fmod function, as well as remainder function in C99. (Note that these functions are not the same and have some peculiarities. In particular, they do not follow the rounding rules of integer division.)