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correct licensing and incorporation of FastMath #49122

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Nov 21, 2019
Merged

correct licensing and incorporation of FastMath #49122

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8bc6297
correct licensing and incorporation of FastMath
talevy Nov 14, 2019
ff43fd9
wrap FastMath with ESSloppyMath
talevy Nov 20, 2019
c02a27e
package private FastMath
talevy Nov 20, 2019
f02e266
Merge branch 'master' into asf-49009
elasticmachine Nov 20, 2019
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178 changes: 17 additions & 161 deletions libs/core/src/main/java/org/elasticsearch/common/util/ESSloppyMath.java
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Original file line number Diff line number Diff line change
@@ -1,38 +1,23 @@
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You 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
* Licensed to Elasticsearch under one or more contributor
* license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright
* ownership. Elasticsearch licenses this file to you 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
* 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.
*/
package org.elasticsearch.common.util;

/*
* =============================================================================
*
* sinh and atan ported from
* https://github.com/yannrichet/jmathplot/blob/f25426e0ab0e68647ad2b75f577c7be050ecac86/src/main/java/org/math/plot/utils/FastMath.java
* (Apache 2.0) Copyright 2012 Jeff Hain, which is partially derived from fdlibm package
*
* =============================================================================
* 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.
* =============================================================================
* 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.
*/

package org.elasticsearch.common.util;

/**
* Similar to Lucene's SloppyMath, but for additional math functions.
Expand All @@ -41,140 +26,11 @@ public class ESSloppyMath {

private ESSloppyMath() {}

//--------------------------------------------------------------------------
// 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;
}
return FastMath.sinh(value);
}

/**
* 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;
}
}
}
return FastMath.atan(value);
}
}
181 changes: 181 additions & 0 deletions libs/core/src/main/java/org/elasticsearch/common/util/FastMath.java
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Original file line number Diff line number Diff line change
@@ -0,0 +1,181 @@
/*
* 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;
}
}
}
}

}
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