package com.srbenoit.math;

import java.util.logging.Level;
import com.srbenoit.log.LoggedObject;

/**
 * A library with fast approximations to transcendental functions.
 */
public final class FastMath extends LoggedObject {

    /** a lookup tables used to speed up square computations */
    private final static int[] TABLE = {
            0, 16, 22, 27, 32, 35, 39, 42, 45, 48, 50, 53, 55, 57, 59, 61, 64, 65, 67, 69, 71, 73,
            75, 76, 78, 80, 81, 83, 84, 86, 87, 89, 90, 91, 93, 94, 96, 97, 98, 99, 101, 102, 103,
            104, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122,
            123, 124, 125, 126, 128, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,
            140, 141, 142, 143, 144, 144, 145, 146, 147, 148, 149, 150, 150, 151, 152, 153, 154,
            155, 155, 156, 157, 158, 159, 160, 160, 161, 162, 163, 163, 164, 165, 166, 167, 167,
            168, 169, 170, 170, 171, 172, 173, 173, 174, 175, 176, 176, 177, 178, 178, 179, 180,
            181, 181, 182, 183, 183, 184, 185, 185, 186, 187, 187, 188, 189, 189, 190, 191, 192,
            192, 193, 193, 194, 195, 195, 196, 197, 197, 198, 199, 199, 200, 201, 201, 202, 203,
            203, 204, 204, 205, 206, 206, 207, 208, 208, 209, 209, 210, 211, 211, 212, 212, 213,
            214, 214, 215, 215, 216, 217, 217, 218, 218, 219, 219, 220, 221, 221, 222, 222, 223,
            224, 224, 225, 225, 226, 226, 227, 227, 228, 229, 229, 230, 230, 231, 231, 232, 232,
            233, 234, 234, 235, 235, 236, 236, 237, 237, 238, 238, 239, 240, 240, 241, 241, 242,
            242, 243, 243, 244, 244, 245, 245, 246, 246, 247, 247, 248, 248, 249, 249, 250, 250,
            251, 251, 252, 252, 253, 253, 254, 254, 255
        };

    /**
     * Private constructor to prevent instantiation.
     */
    private FastMath() {

        super();
    }

    /**
     * A faster replacement for (int)(java.lang.Math.sqrt(x)). Completely accurate for x < 289...
     *
     * @param   val  the value whose square root is to be taken
     * @return  the approximate square root
     */
    public static int fastSqrt(final long val) {

        int root;
        int intVal;

        if (val > Integer.MAX_VALUE) {
            root = (int) (Math.sqrt(val));
        } else {
            intVal = (int) val;

            if (intVal >= 0x10000) {

                if (intVal >= 0x1000000) {

                    if (intVal >= 0x10000000) {

                        if (intVal >= 0x40000000) {
                            root = (TABLE[intVal >> 24] << 8);
                        } else {
                            root = (TABLE[intVal >> 22] << 7);
                        }
                    } else if (intVal >= 0x4000000) {
                        root = (TABLE[intVal >> 20] << 6);
                    } else {
                        root = (TABLE[intVal >> 18] << 5);
                    }
                } else if (intVal >= 0x100000) {

                    if (intVal >= 0x400000) {
                        root = (TABLE[intVal >> 16] << 4);
                    } else {
                        root = (TABLE[intVal >> 14] << 3);
                    }
                } else if (intVal >= 0x40000) {
                    root = (TABLE[intVal >> 12] << 2);
                } else {
                    root = (TABLE[intVal >> 10] << 1);
                }
            } else if (intVal >= 0x100) {

                if (intVal >= 0x1000) {

                    if (intVal >= 0x4000) {
                        root = TABLE[intVal >> 8];
                    } else {
                        root = (TABLE[intVal >> 6] >> 1);
                    }
                } else if (intVal >= 0x400) {
                    root = (TABLE[intVal >> 4] >> 2);
                } else {
                    root = (TABLE[intVal >> 2] >> 3);
                }
            } else if (intVal >= 0) {
                root = TABLE[intVal] >> 4;
            } else {
                throw new IllegalArgumentException("Attemt to take the square root of " + intVal);
            }
        }

        return root;
    }

    /**
     * Main method to exercise methods in this class.
     *
     * @param  args  command-line arguments
     */
    public static void main(final String... args) {

        long start;
        long end;
        int total1;
        int total2;
        int root;
        int est;
        float err;
        float maxerr = 0;

        // Compare values
        for (int i = 0; i < 2000000000; i += 20) {
            root = (int) Math.sqrt(i);
            est = FastMath.fastSqrt(i);
            err = (float) Math.abs((root - est) / (double) root);

            if (err > maxerr) {
                maxerr = err;
            }
        }

        LOG.log(Level.INFO, "Maximum error over 0-2000000000 is {0}%", (maxerr * 100));

        // Compare speeds
        total1 = 0;
        start = System.currentTimeMillis();

        for (int i = 0; i < 2000000000; i += 20) {
            total1 += (int) Math.sqrt(i);
        }

        end = System.currentTimeMillis();
        LOG.log(Level.INFO, "Math.sqrt: {0}", (end - start));

        total2 = 0;
        start = System.currentTimeMillis();

        for (int i = 0; i < 2000000000; i += 20) {
            total2 += FastMath.fastSqrt(i);
        }

        end = System.currentTimeMillis();
        LOG.log(Level.INFO, "FastMath.fastSqrt: {0}", (end - start));

        LOG.log(Level.INFO, "Outcomes: {0}, {1}", new Object[] { total1, total2 });
    }
}