How to wrap around a range

Angles in my program are expressed in 0 to 2pi. I want a way to add two angles and have it wrap around the 2pi to 0 if the result is higher than 2pi. Or if I subtracted an angle from an angle and it was below 0 it would wrap around 2pi.

Is there a way to do this?

Thanks.

Solution

What you are looking for is the modulus. The fmod function will not work because it calculates the remainder and not the arithmetic modulus. Something like this should work:

inline double wrapAngle( double angle )
{
    double twoPi = 2.0 * 3.141592865358979;
    return angle - twoPi * floor( angle / twoPi );
}

Edit:

The remainder is commonly defined as what is left over after long division (eg. the remainder of 18/4 is 2, because 18 = 4 * 4 + 2). This gets hairy when you have negative numbers. The common way to find the remainder of a signed division is for the remainder to have the same sign as the result (eg. the remainder of -18/4 is -2, because -18 = -4 * 4 + -2).

The definition of x modulus y is the smallest positive value of m in the equation x=y*c+m, given c is an integer. So 18 mod 4 would be 2 (where c=4), however -18 mod 4 would also be 2 (where c=-5).

The simplest calculation of x mod y is x-y*floor(x/y), where floor is the largest integer that is less than or equal to the input.