// 1-15-Java.java
//
// Java programs are organized into classes, and methods
// such as mySin are members of those classes.
//
// The java.lang package, which contains Math and Double,
// is automatically available and does not need to be
// imported.

public class Main {
    public static void main(String[] args) {
        double x = 3.2;

        System.out.println("Trig.mySin(x): " + Trig.mySin(x));
        System.out.println("Math.sin(x):   " + Math.sin(x));
        System.out.println("reference:     "
            + -0.058374143427579909137);

        System.out.println("Trig.mySin(Double.POSITIVE_INFINITY): "
            + Trig.mySin(Double.POSITIVE_INFINITY));
    }
}

class Trig {
    // mySin(double x)
    //
    // Approximate sin(x) using the Taylor series
    //
    //                 x^3   x^5   x^7
    //     sin(x) = x - --- + --- - --- + ...
    //                  3!    5!    7!
    //
    // Rather than calculating each power and factorial
    // separately, calculate each term from the previous
    // term:
    //
    //                    x^2
    //     next = -term -----------,
    //                  n(n + 1)
    //
    // where n takes the values 2, 4, 6, ...
    public static double mySin(double x) {
        if (!Double.isFinite(x)) {
            return Double.NaN;
        }

        double result = x;
        double term = x;

        for (double n = 2.0; ; n += 2.0) {
            term *= -(x/n)*(x/(n + 1.0));

            if (Math.abs(term) < 1e-16) {
                break;
            }

            result += term;
        }

        return result;
    }
}