class FastMath
{
    public static final double PI = Math.PI;
    public static final double TWOPI = PI * 2;
    public static final double HalfPI = PI / 2;
    public static final double OneFourthPI = PI / 4;

    /**
    * This forces the trig functiosn to stay
    * within the safe area on the x86 processor
    *(-45 degrees to +45 degrees)
    * The results may be very slightly off from
     * what the Math and StrictMath trig functions
     * give due to rounding in the angle reduction
     * but it will be very very close.
     */
    public static double reduceSinAngle(double radians) {
        radians %= TWOPI; // put us in -2PI to +2PI space
        if (Math.abs(radians)>PI) { // put us in -PI to +PI space
            radians = radians-(TWOPI);
        }
        if (Math.abs(radians)>HalfPI) {// put us in -PI/2 to +PI/2 space
            radians = PI - radians;
        }

        return radians;
    }

    public static double sin (double radians) {

        radians = reduceSinAngle(radians); // limits angle to between -PI/2 and +PI/2
        if (Math.abs(radians)<=OneFourthPI) {
            return Math.sin(radians);
        } else {
            return Math.cos(HalfPI-radians);
        }
    }

    public static double cos (double radians) {

        return sin (radians+HalfPI);
    }
}