Algorithm for finding reference angle

Question

Definition of "reference angle":

An angle ϑ_r in the interval [0, 2π) corresponding to an angle ϑ outside of this interval, satisfying the conditions
sin(ϑ) = sin(ϑ_r) and cos(ϑ) = cos(ϑ_r).

For example (thinking in degrees for simplicity):

ref(390^o) = 30^o
ref(360^o) = 0^o
ref(-40^o) = 320^o
ref(540^o) = 180^o

An example code for finding reference angle is:

double FindReferenceAngle(double Angle)
{
    const double TWOPI = 2.0 * 3.1415926535897932384626433832795;
    while(true)
    {
        if (Angle >= TWOPI)
        {
            Angle -= TWOPI;
        }
        else if (Angle < 0)
        {
            Angle += TWOPI;
        }
        else
        {
            return Angle;
        }
    }
}

However, I don't think that this code is optimal. For instance, if the user calls it with a very large angle value (e.g.; FindReferenceAngle(1e10)) it will take quite a time in the while loop.

Is there any other more efficient algorithm to find reference angle, like a built in standard C++ library routine?

Answer 1

This should do it.

double FindReferenceAngle(double Angle)
{
    const double TWOPI = 2.0 * 3.1415926535897932384626433832795;
    return fmod(Angle, TWOPI);
}

Though it would probably be a good idea to globalize the definition of pi and put it in a header somewhere, or perhaps this:

#define _USE_MATH_DEFINES
#ifdef M_PI
#define TWOPI 2*M_PI
#else
#define TWOPI 2.0*3.1415926535897932384626433832795
#endif