org.elasticsearch.core.FastMath Maven / Gradle / Ivy
/*
* Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
* or more contributor license agreements. Licensed under the Elastic License
* 2.0 and the Server Side Public License, v 1; you may not use this file except
* in compliance with, at your election, the Elastic License 2.0 or the Server
* Side Public License, v 1.
*/
/* @notice
* 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.core;
/**
* 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;
}
}
}
}
}
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