SignalCorrelation.java

class SignalCorrelation {
 
    /** Approximate {@code sin(i / 1000)}. */
    public static double sin(int i) {
        double x = i / 1000.0;
        double term3 = (x*x*x) / (3 * 2 * 1);
        double term5 = (x*x*x*x*x) / (5 * 4 * 3 * 2 * 1);
        return x - term3 + term5;
    }
 
    public static double[] sinTable(int n) {
        double[] table = new double[n];
        for (int i = 0; i < n; i++) {
            table[i] = sin(i);
        }
        return table;
    }
 
    /** Approximate {@code cos(i / 1000)}. */
    public static double cos(int i) {
        double x = i / 1000.0;
        double term2 = (x*x) / (2 * 1);
        double term4 = (x*x*x*x) / (4 * 3 * 2 * 1);
        return 1 - term2 + term4;
    }
 
    public static double[] cosTable(int n) {
        double[] table = new double[n];
        for (int i = 0; i < n; i++) {
            table[i] = cos(i);
        }
        return table;
    }
 
    public static double correlate(double[] a, double[] b) {
        double correlation = 0.0;
        for (int i = 0; i < a.length; i++) {
            correlation += a[i] * b[i];
        }
        return correlation;
    }
 
    public static double computeCorrelation(double[] a, double[] b) {
        return correlate(a, b);
    }
 
    public static void main(String[] args) {
        int n = args.length > 0 ? Integer.valueOf(args[0]) : 100_000_000;
 
        for (int j = 0; j < 10; j++) {
            long tablesStart = System.nanoTime();
            double[] sin = sinTable(n);
            double[] cos = cosTable(n);
            long tablesEnd = System.nanoTime();
            System.out.println("table computation: " + (tablesEnd - tablesStart) / 1_000_000 + " ms");
 
            long correlationStart = System.nanoTime();
            double sinSin = computeCorrelation(sin, sin);
            double sinCos = computeCorrelation(sin, cos);
            double cosSin = computeCorrelation(cos, sin);
            double cosCos = computeCorrelation(cos, cos);
 
            double sinSinNormalized = sinSin / sinSin;
            double sinCosNormalized = sinCos / Math.sqrt(sinSin * cosCos);
            double cosSinNormalized = cosSin / Math.sqrt(cosCos * sinSin);
            double cosCosNormalized = cosCos / cosCos;
            long correlationEnd = System.nanoTime();
 
            System.out.println("sin/sin correlation: " + sinSinNormalized);
            System.out.println("sin/cos correlation: " + sinCosNormalized);
            System.out.println("cos/sin correlation: " + cosSinNormalized);
            System.out.println("cos/cos correlation: " + cosCosNormalized);
            System.out.println("correlation: " + (correlationEnd - correlationStart) / 1_000_000 + " ms");
        }
    }
}