Modulus to limit latitude and longitude values

Question

I have doubles that represent latitudes and longitudes.
I can easily limit longitudes to (-180.0, 180.0] with the following function.

double limitLon(double lon)
{
  return fmod(lon - 180.0, 360.0) + 180.0;
}

This works because one end is exclusive and the other is inclusive. fmod includes 0 but not -360.0.

Can anyone think of an elegant method for latitude?
The required interval is [-90.0, 90.0]. A closed form solution would be best, i.e. no loop. I think fmod() is probably a non-starter because both ends are inclusive now.

Edit: As was pointed out, one can't go to 91 degrees latitude anyway. Technically 91 should map to 89.0. Oh boy, that changes things.

Answer 1

There is a much, much more efficient way to do this than using sin and arcsin. The most expensive operation is a single division. The observation that the required interval is closed is key.

• Divide by 360 and take the remainder. This yields a number in the interval [0, 360), which is half-open, as observed.

• Fold the interval in half. If the remainder is >=180, subtract it from 360. This maps the interval [180, 360) to the interval (0, 180]. The union of this interval with the bottom half is the closed interval [0, 180].

• Subtract 90 from the result. This interval is [-90, 90], as desired.

This is, indeed, the exact same function as arcsin(sin(x)), but without the expense or any issue with numeric stability.