Returns a fast sine approximation of a value. - Java java.lang

Java examples for java.lang:Math Trigonometric Function

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Description

Returns a fast sine approximation of a value.

Demo Code

/*/*from w  w  w .  j  a va  2 s. c  om*/
 * Copyright (c) 2006-2011 Karsten Schmidt
 * 
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 * 
 * http://creativecommons.org/licenses/LGPL/2.1/
 * 
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA
 */
//package com.java2s;

public class Main {
    /**
     * PI
     */
    public static final float PI = 3.14159265358979323846f;
    /**
     * PI/2
     */
    public static final float HALF_PI = PI / 2;
    /**
     * PI/4
     */
    public static final float QUARTER_PI = PI / 4f;
    /**
     * PI*2
     */
    public static final float TWO_PI = PI * 2f;
    /**
     * PI*1.5
     */
    public static final float THREE_HALVES_PI = TWO_PI - HALF_PI;
    private final static double SIN_A = -4d / (PI * PI);
    private final static double SIN_B = 4d / PI;
    private final static double SIN_P = 9d / 40;

    /**
     * Returns a fast sine approximation of a value. Note: code from <a
     * href="http://wiki.java.net/bin/view/Games/JeffGems">wiki posting on
     * java.net by jeffpk</a>
     * 
     * @param theta
     *            angle in radians.
     * @return sine of theta.
     */
    public static final float sin2(float theta) {
        theta = reduceAngle(theta);
        if (abs(theta) <= QUARTER_PI) {
            return (float) fastSin(theta);
        }
        return (float) fastCos(HALF_PI - theta);
    }

    public static final double reduceAngle(double theta) {
        theta %= TWO_PI;
        if (abs(theta) > PI) {
            theta = theta - TWO_PI;
        }
        if (abs(theta) > HALF_PI) {
            theta = PI - theta;
        }
        return theta;
    }

    /**
     * Reduces the given angle into the -PI/4 ... PI/4 interval for faster
     * computation of sin/cos. This method is used by {@link #sin(float)} &
     * {@link #cos(float)}.
     * 
     * @param theta
     *            angle in radians
     * @return reduced angle
     * @see #sin(float)
     * @see #cos(float)
     */
    public static final float reduceAngle(float theta) {
        theta %= TWO_PI;
        if (abs(theta) > PI) {
            theta = theta - TWO_PI;
        }
        if (abs(theta) > HALF_PI) {
            theta = PI - theta;
        }
        return theta;
    }

    /**
     * @param x
     * @return absolute value of x
     */
    public static final double abs(double x) {
        return x < 0 ? -x : x;
    }

    /**
     * @param x
     * @return absolute value of x
     */
    public static final float abs(float x) {
        return x < 0 ? -x : x;
    }

    /**
     * @param x
     * @return absolute value of x
     */
    public static final int abs(int x) {
        int y = x >> 31;
        return (x ^ y) - y;
    }

    /**
     * Fast sine approximation.
     * 
     * @param x
     *            angle in -PI/2 .. +PI/2 interval
     * @return sine
     */
    public static final double fastSin(double x) {
        // float B = 4/pi;
        // float C = -4/(pi*pi);
        //
        // float y = B * x + C * x * abs(x);
        // y = P * (y * abs(y) - y) + y;

        x = SIN_B * x + SIN_A * x * abs(x);
        return SIN_P * (x * abs(x) - x) + x;
    }

    /**
     * Fast cosine approximation.
     * 
     * @param x
     *            angle in -PI/2 .. +PI/2 interval
     * @return cosine
     */
    public static final double fastCos(final double x) {
        return fastSin(x + ((x > HALF_PI) ? -THREE_HALVES_PI : HALF_PI));
    }
}

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