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this resolves incorrectly licensed code in #49009. ESSloppyMath is made as a wrapper around FastMath.java which is not meant to be modified with code beyond the original source
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libs/core/src/main/java/org/elasticsearch/common/util/FastMath.java
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| /* | ||
| * 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. | ||
| */ | ||
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| /* | ||
| * ============================================================================= | ||
| * 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. | ||
| * ============================================================================= | ||
| */ | ||
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| /* | ||
| * This code sourced from: | ||
| * https://github.com/yannrichet/jmathplot/blob/f25426e0ab0e68647ad2b75f577c7be050ecac86/src/main/java/org/math/plot/utils/FastMath.java | ||
| */ | ||
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| package org.elasticsearch.common.util; | ||
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| /** | ||
| * Additions or modifications to this class should only come from the original org.math.plot.utils.FastMath source | ||
| */ | ||
| final class FastMath { | ||
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| private FastMath() { } | ||
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| //-------------------------------------------------------------------------- | ||
| // RE-USABLE CONSTANTS | ||
| //-------------------------------------------------------------------------- | ||
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| 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); | ||
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| //-------------------------------------------------------------------------- | ||
| // CONSTANTS AND TABLES FOR ATAN | ||
| //-------------------------------------------------------------------------- | ||
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| // 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. | ||
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| // 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)); | ||
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| 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]; | ||
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| 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 | ||
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| 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; | ||
| } | ||
| } | ||
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| /** | ||
| * 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; | ||
| } | ||
| } | ||
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| /** | ||
| * 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; | ||
| } | ||
| } | ||
| } | ||
| } | ||
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| } |
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