CosineIntegral.java

package com.bringholm.javatest;

public class Main {

    private static double EULER_MASCHERONI_CONSTANT = 0.577215664901532860606512090082;

    public static void main(String[] args) {
        System.out.println(cosineIntegral(1));
    }

    static double cosineIntegral(double arg) {
        double result = naturalLog(arg);
        for (int n = 1; n <= 15; n++) {
            double term = intPower(arg, 2 * n) / (factorial(2 * n) * 2 * n);
            if (n % 2 == 0) {
                result += term;
            } else {
                result -= term;
            }
        }
        return result + EULER_MASCHERONI_CONSTANT;
    }

    static double naturalLog(double arg) {
        if (arg > 1) {
            double inverse = 1.0 / arg;
            return -computeNaturalLogMaclaurin(inverse);
        } else {
            return computeNaturalLogMaclaurin(arg);
        }
    }

    static double computeNaturalLogMaclaurin(double arg) {
        double result = 0;
        for (int n = 1; n <= 50; n++) {
            double term = 1.0 / n * intPower(arg - 1, n);
            if (n % 2 == 0) {
                result -= term;
            } else {
                result += term;
            }
        }
        return result;
    }

    /*
     * If this were to be done properly, one should build in a way to use Stirling's approximation for large values.
     * This implementations only handles values up to 15.
     */
    static int factorial(int arg) {
        int result = 1;
        for (int i = arg; i > 1; i--) {
            result *= i;
        }
        return result;
    }

    static double intPower(double arg, int power) {
        double result = arg;
        for (int i = 1; i < power; i++) {
            result *= arg;
        }
        return result;
    }
}