/*
 * Copyright 2012 Jeff Hain
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

/*
 * =============================================================================
 * Notice of fdlibm package this program is partially derived from:
 *
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * =============================================================================
 */

/*
 * This code sourced from:
 * https://github.com/yannrichet/jmathplot/blob/f25426e0ab0e68647ad2b75f577c7be050ecac86/src/main/java/org/math/plot/utils/FastMath.java
 */

package org.elasticsearch.common.util;

/**
 * Additions or modifications to this class should only come from the original org.math.plot.utils.FastMath source
 */
final class FastMath {

    private FastMath() { }

    //--------------------------------------------------------------------------
    // RE-USABLE CONSTANTS
    //--------------------------------------------------------------------------

    private static final double ONE_DIV_F2 = 1/2.0;
    private static final double ONE_DIV_F3 = 1/6.0;
    private static final double ONE_DIV_F4 = 1/24.0;
    private static final double TWO_POW_N28 = Double.longBitsToDouble(0x3E30000000000000L);
    private static final double TWO_POW_66 = Double.longBitsToDouble(0x4410000000000000L);
    private static final double LOG_DOUBLE_MAX_VALUE = StrictMath.log(Double.MAX_VALUE);

    //--------------------------------------------------------------------------
    // CONSTANTS AND TABLES FOR ATAN
    //--------------------------------------------------------------------------

    // We use the formula atan(-x) = -atan(x)
    // ---> we only have to compute atan(x) on [0,+infinity[.
    // For values corresponding to angles not close to +-PI/2, we use look-up tables;
    // for values corresponding to angles near +-PI/2, we use code derived from fdlibm.

    // Supposed to be >= tan(67.7deg), as fdlibm code is supposed to work with values > 2.4375.
    private static final double ATAN_MAX_VALUE_FOR_TABS = StrictMath.tan(Math.toRadians(74.0));

    private static final int ATAN_TABS_SIZE = 1<<12 + 1;
    private static final double ATAN_DELTA = ATAN_MAX_VALUE_FOR_TABS/(ATAN_TABS_SIZE - 1);
    private static final double ATAN_INDEXER = 1/ATAN_DELTA;
    private static final double[] atanTab = new double[ATAN_TABS_SIZE];
    private static final double[] atanDer1DivF1Tab = new double[ATAN_TABS_SIZE];
    private static final double[] atanDer2DivF2Tab = new double[ATAN_TABS_SIZE];
    private static final double[] atanDer3DivF3Tab = new double[ATAN_TABS_SIZE];
    private static final double[] atanDer4DivF4Tab = new double[ATAN_TABS_SIZE];

    private static final double ATAN_HI3 = Double.longBitsToDouble(0x3ff921fb54442d18L); // 1.57079632679489655800e+00 atan(inf)hi
    private static final double ATAN_LO3 = Double.longBitsToDouble(0x3c91a62633145c07L); // 6.12323399573676603587e-17 atan(inf)lo
    private static final double ATAN_AT0 = Double.longBitsToDouble(0x3fd555555555550dL); //  3.33333333333329318027e-01
    private static final double ATAN_AT1 = Double.longBitsToDouble(0xbfc999999998ebc4L); // -1.99999999998764832476e-01
    private static final double ATAN_AT2 = Double.longBitsToDouble(0x3fc24924920083ffL); //  1.42857142725034663711e-01
    private static final double ATAN_AT3 = Double.longBitsToDouble(0xbfbc71c6fe231671L); // -1.11111104054623557880e-01
    private static final double ATAN_AT4 = Double.longBitsToDouble(0x3fb745cdc54c206eL); //  9.09088713343650656196e-02
    private static final double ATAN_AT5 = Double.longBitsToDouble(0xbfb3b0f2af749a6dL); // -7.69187620504482999495e-02
    private static final double ATAN_AT6 = Double.longBitsToDouble(0x3fb10d66a0d03d51L); //  6.66107313738753120669e-02
    private static final double ATAN_AT7 = Double.longBitsToDouble(0xbfadde2d52defd9aL); // -5.83357013379057348645e-02
    private static final double ATAN_AT8 = Double.longBitsToDouble(0x3fa97b4b24760debL); //  4.97687799461593236017e-02
    private static final double ATAN_AT9 = Double.longBitsToDouble(0xbfa2b4442c6a6c2fL); // -3.65315727442169155270e-02
    private static final double ATAN_AT10 = Double.longBitsToDouble(0x3f90ad3ae322da11L); // 1.62858201153657823623e-02

    static {
        // atan
        for (int i=0;i<ATAN_TABS_SIZE;i++) {
            // x: in [0,ATAN_MAX_VALUE_FOR_TABS].
            double x = i * ATAN_DELTA;
            double onePlusXSqInv = 1.0/(1+x*x);
            double onePlusXSqInv2 = onePlusXSqInv*onePlusXSqInv;
            double onePlusXSqInv3 = onePlusXSqInv2*onePlusXSqInv;
            double onePlusXSqInv4 = onePlusXSqInv2*onePlusXSqInv2;
            atanTab[i] = StrictMath.atan(x);
            atanDer1DivF1Tab[i] = onePlusXSqInv;
            atanDer2DivF2Tab[i] = (-2*x*onePlusXSqInv2) * ONE_DIV_F2;
            atanDer3DivF3Tab[i] = ((-2+6*x*x)*onePlusXSqInv3) * ONE_DIV_F3;
            atanDer4DivF4Tab[i] = ((24*x*(1-x*x))*onePlusXSqInv4) * ONE_DIV_F4;
        }
    }

    /**
     * A faster and less accurate {@link Math#sinh}
     *
     * @param value A double value.
     * @return Value hyperbolic sine.
     */
    public static double sinh(double value) {
        // sinh(x) = (exp(x)-exp(-x))/2
        double h;
        if (value < 0.0) {
            value = -value;
            h = -0.5;
        } else {
            h = 0.5;
        }
        if (value < 22.0) {
            if (value < TWO_POW_N28) {
                return (h < 0.0) ? -value : value;
            } else {
                double t = Math.expm1(value);
                // Might be more accurate, if value < 1: return h*((t+t)-t*t/(t+1.0)).
                return h * (t + t/(t+1.0));
            }
        } else if (value < LOG_DOUBLE_MAX_VALUE) {
            return h * Math.exp(value);
        } else {
            double t = Math.exp(value*0.5);
            return (h*t)*t;
        }
    }

    /**
     * A faster and less accurate {@link Math#atan}
     *
     * @param value A double value.
     * @return Value arctangent, in radians, in [-PI/2,PI/2].
     */
    public static double atan(double value) {
        boolean negateResult;
        if (value < 0.0) {
            value = -value;
            negateResult = true;
        } else {
            negateResult = false;
        }
        if (value == 1.0) {
            // We want "exact" result for 1.0.
            return negateResult ? -Math.PI/4 : Math.PI/4;
        } else if (value <= ATAN_MAX_VALUE_FOR_TABS) {
            int index = (int)(value * ATAN_INDEXER + 0.5);
            double delta = value - index * ATAN_DELTA;
            double result = atanTab[index] + delta * (atanDer1DivF1Tab[index] + delta * (atanDer2DivF2Tab[index]
                + delta * (atanDer3DivF3Tab[index] + delta * atanDer4DivF4Tab[index])));
            return negateResult ? -result : result;
        } else { // value > ATAN_MAX_VALUE_FOR_TABS, or value is NaN
            // This part is derived from fdlibm.
            if (value < TWO_POW_66) {
                double x = -1/value;
                double x2 = x*x;
                double x4 = x2*x2;
                double s1 = x2*(ATAN_AT0+x4*(ATAN_AT2+x4*(ATAN_AT4+x4*(ATAN_AT6+x4*(ATAN_AT8+x4*ATAN_AT10)))));
                double s2 = x4*(ATAN_AT1+x4*(ATAN_AT3+x4*(ATAN_AT5+x4*(ATAN_AT7+x4*ATAN_AT9))));
                double result = ATAN_HI3-((x*(s1+s2)-ATAN_LO3)-x);
                return negateResult ? -result : result;
            } else { // value >= 2^66, or value is NaN
                if (Double.isNaN(value)) {
                    return Double.NaN;
                } else {
                    return negateResult ? -Math.PI/2 : Math.PI/2;
                }
            }
        }
    }

}
