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Posted to commits@commons.apache.org by er...@apache.org on 2021/06/01 05:06:49 UTC
[commons-math] 01/02: Delete files that were added to the
repository by mistake.
This is an automated email from the ASF dual-hosted git repository.
erans pushed a commit to branch master
in repository https://gitbox.apache.org/repos/asf/commons-math.git
commit 44d1f03669f15776fdc5b0f88bdf0c6b6b165eb6
Author: Gilles Sadowski <gi...@gmail.com>
AuthorDate: Tue Jun 1 07:02:05 2021 +0200
Delete files that were added to the repository by mistake.
---
.../legacy/core/jdkmath/AccurateMath.java.bak | 4351 --------------
.../legacy/core/jdkmath/AccurateMathCalc.java.bak | 658 ---
.../jdkmath/AccurateMathLiteralArrays.java.bak | 6175 --------------------
.../commons/math4/legacy/core/dfp/DfpTest.java.bak | 1674 ------
.../AccurateMathStrictComparisonTest.java.bak | 262 -
.../legacy/core/jdkmath/AccurateMathTest.java.bak | 1965 -------
6 files changed, 15085 deletions(-)
diff --git a/commons-math-legacy-core/src/main/java/org/apache/commons/math4/legacy/core/jdkmath/AccurateMath.java.bak b/commons-math-legacy-core/src/main/java/org/apache/commons/math4/legacy/core/jdkmath/AccurateMath.java.bak
deleted file mode 100644
index 7a39abc..0000000
--- a/commons-math-legacy-core/src/main/java/org/apache/commons/math4/legacy/core/jdkmath/AccurateMath.java.bak
+++ /dev/null
@@ -1,4351 +0,0 @@
-/*
- * 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
- *
- * 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.apache.commons.math4.legacy.util;
-
-import java.io.PrintStream;
-
-import org.apache.commons.numbers.core.Precision;
-import org.apache.commons.math4.legacy.exception.MathArithmeticException;
-import org.apache.commons.math4.legacy.exception.util.LocalizedFormats;
-
-/**
- * Portable alternative to {@link Math} and {@link StrictMath}.
- * <p>
- * Caveat: At the time of implementation, the {@code AccurateMath} functions
- * were often faster and/or more accurate than their JDK equivalent.
- * Nowadays, it would not be surprising that they are always slower (due
- * to the various JVM optimizations that have appeared since Java 5).
- * However, any change to this class should ensure that the current
- * accuracy is not lost.
- * <p>
- * AccurateMath is a drop-in replacement for both Math and StrictMath. This
- * means that for any method in Math (say {@code Math.sin(x)} or
- * {@code Math.cbrt(y)}), user can directly change the class and use the
- * methods as is (using {@code AccurateMath.sin(x)} or {@code AccurateMath.cbrt(y)}
- * in the previous example).
- * </p>
- * <p>
- * AccurateMath speed is achieved by relying heavily on optimizing compilers
- * to native code present in many JVMs today and use of large tables.
- * The larger tables are lazily initialized on first use, so that the setup
- * time does not penalize methods that don't need them.
- * </p>
- * <p>
- * Note that AccurateMath is
- * extensively used inside Apache Commons Math, so by calling some algorithms,
- * the overhead when the tables need to be initialized will occur
- * regardless of the end-user calling AccurateMath methods directly or not.
- * Performance figures for a specific JVM and hardware can be evaluated by
- * running the AccurateMathTestPerformance tests in the test directory of the source
- * distribution.
- * </p>
- * <p>
- * AccurateMath accuracy should be mostly independent of the JVM as it relies only
- * on IEEE-754 basic operations and on embedded tables. Almost all operations
- * are accurate to about 0.5 ulp throughout the domain range. This statement,
- * of course is only a rough global observed behavior, it is <em>not</em> a
- * guarantee for <em>every</em> double numbers input (see William Kahan's <a
- * href="http://en.wikipedia.org/wiki/Rounding#The_table-maker.27s_dilemma">Table
- * Maker's Dilemma</a>).
- * </p>
- * <p>
- * AccurateMath additionally implements the following methods not found in Math/StrictMath:
- * <ul>
- * <li>{@link #asinh(double)}</li>
- * <li>{@link #acosh(double)}</li>
- * <li>{@link #atanh(double)}</li>
- * </ul>
- * The following methods are found in Math/StrictMath since 1.6 only, they are provided
- * by AccurateMath even in 1.5 Java virtual machines
- * <ul>
- * <li>{@link #copySign(double, double)}</li>
- * <li>{@link #getExponent(double)}</li>
- * <li>{@link #nextAfter(double,double)}</li>
- * <li>{@link #nextUp(double)}</li>
- * <li>{@link #scalb(double, int)}</li>
- * <li>{@link #copySign(float, float)}</li>
- * <li>{@link #getExponent(float)}</li>
- * <li>{@link #nextAfter(float,double)}</li>
- * <li>{@link #nextUp(float)}</li>
- * <li>{@link #scalb(float, int)}</li>
- * </ul>
- * @since 2.2
- */
-public class AccurateMath {
- /** Archimede's constant PI, ratio of circle circumference to diameter. */
- public static final double PI = 105414357.0 / 33554432.0 + 1.984187159361080883e-9;
-
- /** Napier's constant e, base of the natural logarithm. */
- public static final double E = 2850325.0 / 1048576.0 + 8.254840070411028747e-8;
-
- /** Index of exp(0) in the array of integer exponentials. */
- static final int EXP_INT_TABLE_MAX_INDEX = 750;
- /** Length of the array of integer exponentials. */
- static final int EXP_INT_TABLE_LEN = EXP_INT_TABLE_MAX_INDEX * 2;
- /** Logarithm table length. */
- static final int LN_MANT_LEN = 1024;
- /** Exponential fractions table length. */
- static final int EXP_FRAC_TABLE_LEN = 1025; // 0, 1/1024, ... 1024/1024
-
- /** StrictMath.log(Double.MAX_VALUE): {@value} */
- private static final double LOG_MAX_VALUE = StrictMath.log(Double.MAX_VALUE);
-
- /** Indicator for tables initialization.
- * <p>
- * This compile-time constant should be set to true only if one explicitly
- * wants to compute the tables at class loading time instead of using the
- * already computed ones provided as literal arrays below.
- * </p>
- */
- private static final boolean RECOMPUTE_TABLES_AT_RUNTIME = false;
-
- /** log(2) (high bits). */
- private static final double LN_2_A = 0.693147063255310059;
-
- /** log(2) (low bits). */
- private static final double LN_2_B = 1.17304635250823482e-7;
-
- /** Coefficients for log, when input 0.99 < x < 1.01. */
- private static final double LN_QUICK_COEF[][] = {
- {1.0, 5.669184079525E-24},
- {-0.25, -0.25},
- {0.3333333134651184, 1.986821492305628E-8},
- {-0.25, -6.663542893624021E-14},
- {0.19999998807907104, 1.1921056801463227E-8},
- {-0.1666666567325592, -7.800414592973399E-9},
- {0.1428571343421936, 5.650007086920087E-9},
- {-0.12502530217170715, -7.44321345601866E-11},
- {0.11113807559013367, 9.219544613762692E-9},
- };
-
- /** Coefficients for log in the range of 1.0 < x < 1.0 + 2^-10. */
- private static final double LN_HI_PREC_COEF[][] = {
- {1.0, -6.032174644509064E-23},
- {-0.25, -0.25},
- {0.3333333134651184, 1.9868161777724352E-8},
- {-0.2499999701976776, -2.957007209750105E-8},
- {0.19999954104423523, 1.5830993332061267E-10},
- {-0.16624879837036133, -2.6033824355191673E-8}
- };
-
- /** Sine, Cosine, Tangent tables are for 0, 1/8, 2/8, ... 13/8 = PI/2 approx. */
- private static final int SINE_TABLE_LEN = 14;
-
- /** Sine table (high bits). */
- private static final double SINE_TABLE_A[] =
- {
- +0.0d,
- +0.1246747374534607d,
- +0.24740394949913025d,
- +0.366272509098053d,
- +0.4794255495071411d,
- +0.5850973129272461d,
- +0.6816387176513672d,
- +0.7675435543060303d,
- +0.8414709568023682d,
- +0.902267575263977d,
- +0.9489846229553223d,
- +0.9808930158615112d,
- +0.9974949359893799d,
- +0.9985313415527344d,
- };
-
- /** Sine table (low bits). */
- private static final double SINE_TABLE_B[] =
- {
- +0.0d,
- -4.068233003401932E-9d,
- +9.755392680573412E-9d,
- +1.9987994582857286E-8d,
- -1.0902938113007961E-8d,
- -3.9986783938944604E-8d,
- +4.23719669792332E-8d,
- -5.207000323380292E-8d,
- +2.800552834259E-8d,
- +1.883511811213715E-8d,
- -3.5997360512765566E-9d,
- +4.116164446561962E-8d,
- +5.0614674548127384E-8d,
- -1.0129027912496858E-9d,
- };
-
- /** Cosine table (high bits). */
- private static final double COSINE_TABLE_A[] =
- {
- +1.0d,
- +0.9921976327896118d,
- +0.9689123630523682d,
- +0.9305076599121094d,
- +0.8775825500488281d,
- +0.8109631538391113d,
- +0.7316888570785522d,
- +0.6409968137741089d,
- +0.5403022766113281d,
- +0.4311765432357788d,
- +0.3153223395347595d,
- +0.19454771280288696d,
- +0.07073719799518585d,
- -0.05417713522911072d,
- };
-
- /** Cosine table (low bits). */
- private static final double COSINE_TABLE_B[] =
- {
- +0.0d,
- +3.4439717236742845E-8d,
- +5.865827662008209E-8d,
- -3.7999795083850525E-8d,
- +1.184154459111628E-8d,
- -3.43338934259355E-8d,
- +1.1795268640216787E-8d,
- +4.438921624363781E-8d,
- +2.925681159240093E-8d,
- -2.6437112632041807E-8d,
- +2.2860509143963117E-8d,
- -4.813899778443457E-9d,
- +3.6725170580355583E-9d,
- +2.0217439756338078E-10d,
- };
-
-
- /** Tangent table, used by atan() (high bits). */
- private static final double TANGENT_TABLE_A[] =
- {
- +0.0d,
- +0.1256551444530487d,
- +0.25534194707870483d,
- +0.3936265707015991d,
- +0.5463024377822876d,
- +0.7214844226837158d,
- +0.9315965175628662d,
- +1.1974215507507324d,
- +1.5574076175689697d,
- +2.092571258544922d,
- +3.0095696449279785d,
- +5.041914939880371d,
- +14.101419448852539d,
- -18.430862426757812d,
- };
-
- /** Tangent table, used by atan() (low bits). */
- private static final double TANGENT_TABLE_B[] =
- {
- +0.0d,
- -7.877917738262007E-9d,
- -2.5857668567479893E-8d,
- +5.2240336371356666E-9d,
- +5.206150291559893E-8d,
- +1.8307188599677033E-8d,
- -5.7618793749770706E-8d,
- +7.848361555046424E-8d,
- +1.0708593250394448E-7d,
- +1.7827257129423813E-8d,
- +2.893485277253286E-8d,
- +3.1660099222737955E-7d,
- +4.983191803254889E-7d,
- -3.356118100840571E-7d,
- };
-
- /** Bits of 1/(2*pi), need for reducePayneHanek(). */
- private static final long RECIP_2PI[] = new long[] {
- (0x28be60dbL << 32) | 0x9391054aL,
- (0x7f09d5f4L << 32) | 0x7d4d3770L,
- (0x36d8a566L << 32) | 0x4f10e410L,
- (0x7f9458eaL << 32) | 0xf7aef158L,
- (0x6dc91b8eL << 32) | 0x909374b8L,
- (0x01924bbaL << 32) | 0x82746487L,
- (0x3f877ac7L << 32) | 0x2c4a69cfL,
- (0xba208d7dL << 32) | 0x4baed121L,
- (0x3a671c09L << 32) | 0xad17df90L,
- (0x4e64758eL << 32) | 0x60d4ce7dL,
- (0x272117e2L << 32) | 0xef7e4a0eL,
- (0xc7fe25ffL << 32) | 0xf7816603L,
- (0xfbcbc462L << 32) | 0xd6829b47L,
- (0xdb4d9fb3L << 32) | 0xc9f2c26dL,
- (0xd3d18fd9L << 32) | 0xa797fa8bL,
- (0x5d49eeb1L << 32) | 0xfaf97c5eL,
- (0xcf41ce7dL << 32) | 0xe294a4baL,
- 0x9afed7ecL << 32 };
-
- /** Bits of pi/4, need for reducePayneHanek(). */
- private static final long PI_O_4_BITS[] = new long[] {
- (0xc90fdaa2L << 32) | 0x2168c234L,
- (0xc4c6628bL << 32) | 0x80dc1cd1L };
-
- /** Eighths.
- * This is used by sinQ, because its faster to do a table lookup than
- * a multiply in this time-critical routine
- */
- private static final double EIGHTHS[] = {0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1.0, 1.125, 1.25, 1.375, 1.5, 1.625};
-
- /** Table of 2^((n+2)/3) */
- private static final double CBRTTWO[] = { 0.6299605249474366,
- 0.7937005259840998,
- 1.0,
- 1.2599210498948732,
- 1.5874010519681994 };
-
- /*
- * There are 52 bits in the mantissa of a double.
- * For additional precision, the code splits double numbers into two parts,
- * by clearing the low order 30 bits if possible, and then performs the arithmetic
- * on each half separately.
- */
-
- /**
- * 0x40000000 - used to split a double into two parts, both with the low order bits cleared.
- * Equivalent to 2^30.
- */
- private static final long HEX_40000000 = 0x40000000L; // 1073741824L
-
- /** Mask used to clear low order 30 bits */
- private static final long MASK_30BITS = -1L - (HEX_40000000 -1); // 0xFFFFFFFFC0000000L;
-
- /** Mask used to clear the non-sign part of an int. */
- private static final int MASK_NON_SIGN_INT = 0x7fffffff;
-
- /** Mask used to clear the non-sign part of a long. */
- private static final long MASK_NON_SIGN_LONG = 0x7fffffffffffffffl;
-
- /** Mask used to extract exponent from double bits. */
- private static final long MASK_DOUBLE_EXPONENT = 0x7ff0000000000000L;
-
- /** Mask used to extract mantissa from double bits. */
- private static final long MASK_DOUBLE_MANTISSA = 0x000fffffffffffffL;
-
- /** Mask used to add implicit high order bit for normalized double. */
- private static final long IMPLICIT_HIGH_BIT = 0x0010000000000000L;
-
- /** 2^52 - double numbers this large must be integral (no fraction) or NaN or Infinite */
- private static final double TWO_POWER_52 = 4503599627370496.0;
-
- /** Constant: {@value}. */
- private static final double F_1_3 = 1d / 3d;
- /** Constant: {@value}. */
- private static final double F_1_5 = 1d / 5d;
- /** Constant: {@value}. */
- private static final double F_1_7 = 1d / 7d;
- /** Constant: {@value}. */
- private static final double F_1_9 = 1d / 9d;
- /** Constant: {@value}. */
- private static final double F_1_11 = 1d / 11d;
- /** Constant: {@value}. */
- private static final double F_1_13 = 1d / 13d;
- /** Constant: {@value}. */
- private static final double F_1_15 = 1d / 15d;
- /** Constant: {@value}. */
- private static final double F_1_17 = 1d / 17d;
- /** Constant: {@value}. */
- private static final double F_3_4 = 3d / 4d;
- /** Constant: {@value}. */
- private static final double F_15_16 = 15d / 16d;
- /** Constant: {@value}. */
- private static final double F_13_14 = 13d / 14d;
- /** Constant: {@value}. */
- private static final double F_11_12 = 11d / 12d;
- /** Constant: {@value}. */
- private static final double F_9_10 = 9d / 10d;
- /** Constant: {@value}. */
- private static final double F_7_8 = 7d / 8d;
- /** Constant: {@value}. */
- private static final double F_5_6 = 5d / 6d;
- /** Constant: {@value}. */
- private static final double F_1_2 = 1d / 2d;
- /** Constant: {@value}. */
- private static final double F_1_4 = 1d / 4d;
-
- /**
- * Private Constructor
- */
- private AccurateMath() {}
-
- // Generic helper methods
-
- /**
- * Get the high order bits from the mantissa.
- * Equivalent to adding and subtracting HEX_40000 but also works for very large numbers
- *
- * @param d the value to split
- * @return the high order part of the mantissa
- */
- private static double doubleHighPart(double d) {
- if (d > -Precision.SAFE_MIN && d < Precision.SAFE_MIN){
- return d; // These are un-normalised - don't try to convert
- }
- long xl = Double.doubleToRawLongBits(d); // can take raw bits because just gonna convert it back
- xl &= MASK_30BITS; // Drop low order bits
- return Double.longBitsToDouble(xl);
- }
-
- /** Compute the square root of a number.
- * <p><b>Note:</b> this implementation currently delegates to {@link Math#sqrt}
- * @param a number on which evaluation is done
- * @return square root of a
- */
- public static double sqrt(final double a) {
- return Math.sqrt(a);
- }
-
- /** Compute the hyperbolic cosine of a number.
- * @param x number on which evaluation is done
- * @return hyperbolic cosine of x
- */
- public static double cosh(double x) {
- if (Double.isNaN(x)) {
- return x;
- }
-
- // cosh[z] = (exp(z) + exp(-z))/2
-
- // for numbers with magnitude 20 or so,
- // exp(-z) can be ignored in comparison with exp(z)
-
- if (x > 20) {
- if (x >= LOG_MAX_VALUE) {
- // Avoid overflow (MATH-905).
- final double t = exp(0.5 * x);
- return (0.5 * t) * t;
- } else {
- return 0.5 * exp(x);
- }
- } else if (x < -20) {
- if (x <= -LOG_MAX_VALUE) {
- // Avoid overflow (MATH-905).
- final double t = exp(-0.5 * x);
- return (0.5 * t) * t;
- } else {
- return 0.5 * exp(-x);
- }
- }
-
- final double hiPrec[] = new double[2];
- if (x < 0.0) {
- x = -x;
- }
- exp(x, 0.0, hiPrec);
-
- double ya = hiPrec[0] + hiPrec[1];
- double yb = -(ya - hiPrec[0] - hiPrec[1]);
-
- double temp = ya * HEX_40000000;
- double yaa = ya + temp - temp;
- double yab = ya - yaa;
-
- // recip = 1/y
- double recip = 1.0/ya;
- temp = recip * HEX_40000000;
- double recipa = recip + temp - temp;
- double recipb = recip - recipa;
-
- // Correct for rounding in division
- recipb += (1.0 - yaa*recipa - yaa*recipb - yab*recipa - yab*recipb) * recip;
- // Account for yb
- recipb += -yb * recip * recip;
-
- // y = y + 1/y
- temp = ya + recipa;
- yb += -(temp - ya - recipa);
- ya = temp;
- temp = ya + recipb;
- yb += -(temp - ya - recipb);
- ya = temp;
-
- double result = ya + yb;
- result *= 0.5;
- return result;
- }
-
- /** Compute the hyperbolic sine of a number.
- * @param x number on which evaluation is done
- * @return hyperbolic sine of x
- */
- public static double sinh(double x) {
- boolean negate = false;
- if (Double.isNaN(x)) {
- return x;
- }
-
- // sinh[z] = (exp(z) - exp(-z) / 2
-
- // for values of z larger than about 20,
- // exp(-z) can be ignored in comparison with exp(z)
-
- if (x > 20) {
- if (x >= LOG_MAX_VALUE) {
- // Avoid overflow (MATH-905).
- final double t = exp(0.5 * x);
- return (0.5 * t) * t;
- } else {
- return 0.5 * exp(x);
- }
- } else if (x < -20) {
- if (x <= -LOG_MAX_VALUE) {
- // Avoid overflow (MATH-905).
- final double t = exp(-0.5 * x);
- return (-0.5 * t) * t;
- } else {
- return -0.5 * exp(-x);
- }
- }
-
- if (x == 0) {
- return x;
- }
-
- if (x < 0.0) {
- x = -x;
- negate = true;
- }
-
- double result;
-
- if (x > 0.25) {
- double hiPrec[] = new double[2];
- exp(x, 0.0, hiPrec);
-
- double ya = hiPrec[0] + hiPrec[1];
- double yb = -(ya - hiPrec[0] - hiPrec[1]);
-
- double temp = ya * HEX_40000000;
- double yaa = ya + temp - temp;
- double yab = ya - yaa;
-
- // recip = 1/y
- double recip = 1.0/ya;
- temp = recip * HEX_40000000;
- double recipa = recip + temp - temp;
- double recipb = recip - recipa;
-
- // Correct for rounding in division
- recipb += (1.0 - yaa*recipa - yaa*recipb - yab*recipa - yab*recipb) * recip;
- // Account for yb
- recipb += -yb * recip * recip;
-
- recipa = -recipa;
- recipb = -recipb;
-
- // y = y + 1/y
- temp = ya + recipa;
- yb += -(temp - ya - recipa);
- ya = temp;
- temp = ya + recipb;
- yb += -(temp - ya - recipb);
- ya = temp;
-
- result = ya + yb;
- result *= 0.5;
- }
- else {
- double hiPrec[] = new double[2];
- expm1(x, hiPrec);
-
- double ya = hiPrec[0] + hiPrec[1];
- double yb = -(ya - hiPrec[0] - hiPrec[1]);
-
- /* Compute expm1(-x) = -expm1(x) / (expm1(x) + 1) */
- double denom = 1.0 + ya;
- double denomr = 1.0 / denom;
- double denomb = -(denom - 1.0 - ya) + yb;
- double ratio = ya * denomr;
- double temp = ratio * HEX_40000000;
- double ra = ratio + temp - temp;
- double rb = ratio - ra;
-
- temp = denom * HEX_40000000;
- double za = denom + temp - temp;
- double zb = denom - za;
-
- rb += (ya - za*ra - za*rb - zb*ra - zb*rb) * denomr;
-
- // Adjust for yb
- rb += yb*denomr; // numerator
- rb += -ya * denomb * denomr * denomr; // denominator
-
- // y = y - 1/y
- temp = ya + ra;
- yb += -(temp - ya - ra);
- ya = temp;
- temp = ya + rb;
- yb += -(temp - ya - rb);
- ya = temp;
-
- result = ya + yb;
- result *= 0.5;
- }
-
- if (negate) {
- result = -result;
- }
-
- return result;
- }
-
- /** Compute the hyperbolic tangent of a number.
- * @param x number on which evaluation is done
- * @return hyperbolic tangent of x
- */
- public static double tanh(double x) {
- boolean negate = false;
-
- if (Double.isNaN(x)) {
- return x;
- }
-
- // tanh[z] = sinh[z] / cosh[z]
- // = (exp(z) - exp(-z)) / (exp(z) + exp(-z))
- // = (exp(2x) - 1) / (exp(2x) + 1)
-
- // for magnitude > 20, sinh[z] == cosh[z] in double precision
-
- if (x > 20.0) {
- return 1.0;
- }
-
- if (x < -20) {
- return -1.0;
- }
-
- if (x == 0) {
- return x;
- }
-
- if (x < 0.0) {
- x = -x;
- negate = true;
- }
-
- double result;
- if (x >= 0.5) {
- double hiPrec[] = new double[2];
- // tanh(x) = (exp(2x) - 1) / (exp(2x) + 1)
- exp(x*2.0, 0.0, hiPrec);
-
- double ya = hiPrec[0] + hiPrec[1];
- double yb = -(ya - hiPrec[0] - hiPrec[1]);
-
- /* Numerator */
- double na = -1.0 + ya;
- double nb = -(na + 1.0 - ya);
- double temp = na + yb;
- nb += -(temp - na - yb);
- na = temp;
-
- /* Denominator */
- double da = 1.0 + ya;
- double db = -(da - 1.0 - ya);
- temp = da + yb;
- db += -(temp - da - yb);
- da = temp;
-
- temp = da * HEX_40000000;
- double daa = da + temp - temp;
- double dab = da - daa;
-
- // ratio = na/da
- double ratio = na/da;
- temp = ratio * HEX_40000000;
- double ratioa = ratio + temp - temp;
- double ratiob = ratio - ratioa;
-
- // Correct for rounding in division
- ratiob += (na - daa*ratioa - daa*ratiob - dab*ratioa - dab*ratiob) / da;
-
- // Account for nb
- ratiob += nb / da;
- // Account for db
- ratiob += -db * na / da / da;
-
- result = ratioa + ratiob;
- }
- else {
- double hiPrec[] = new double[2];
- // tanh(x) = expm1(2x) / (expm1(2x) + 2)
- expm1(x*2.0, hiPrec);
-
- double ya = hiPrec[0] + hiPrec[1];
- double yb = -(ya - hiPrec[0] - hiPrec[1]);
-
- /* Numerator */
- double na = ya;
- double nb = yb;
-
- /* Denominator */
- double da = 2.0 + ya;
- double db = -(da - 2.0 - ya);
- double temp = da + yb;
- db += -(temp - da - yb);
- da = temp;
-
- temp = da * HEX_40000000;
- double daa = da + temp - temp;
- double dab = da - daa;
-
- // ratio = na/da
- double ratio = na/da;
- temp = ratio * HEX_40000000;
- double ratioa = ratio + temp - temp;
- double ratiob = ratio - ratioa;
-
- // Correct for rounding in division
- ratiob += (na - daa*ratioa - daa*ratiob - dab*ratioa - dab*ratiob) / da;
-
- // Account for nb
- ratiob += nb / da;
- // Account for db
- ratiob += -db * na / da / da;
-
- result = ratioa + ratiob;
- }
-
- if (negate) {
- result = -result;
- }
-
- return result;
- }
-
- /** Compute the inverse hyperbolic cosine of a number.
- * @param a number on which evaluation is done
- * @return inverse hyperbolic cosine of a
- */
- public static double acosh(final double a) {
- return AccurateMath.log(a + AccurateMath.sqrt(a * a - 1));
- }
-
- /** Compute the inverse hyperbolic sine of a number.
- * @param a number on which evaluation is done
- * @return inverse hyperbolic sine of a
- */
- public static double asinh(double a) {
- boolean negative = false;
- if (a < 0) {
- negative = true;
- a = -a;
- }
-
- double absAsinh;
- if (a > 0.167) {
- absAsinh = AccurateMath.log(AccurateMath.sqrt(a * a + 1) + a);
- } else {
- final double a2 = a * a;
- if (a > 0.097) {
- absAsinh = a * (1 - a2 * (F_1_3 - a2 * (F_1_5 - a2 * (F_1_7 - a2 * (F_1_9 - a2 * (F_1_11 - a2 * (F_1_13 - a2 * (F_1_15 - a2 * F_1_17 * F_15_16) * F_13_14) * F_11_12) * F_9_10) * F_7_8) * F_5_6) * F_3_4) * F_1_2);
- } else if (a > 0.036) {
- absAsinh = a * (1 - a2 * (F_1_3 - a2 * (F_1_5 - a2 * (F_1_7 - a2 * (F_1_9 - a2 * (F_1_11 - a2 * F_1_13 * F_11_12) * F_9_10) * F_7_8) * F_5_6) * F_3_4) * F_1_2);
- } else if (a > 0.0036) {
- absAsinh = a * (1 - a2 * (F_1_3 - a2 * (F_1_5 - a2 * (F_1_7 - a2 * F_1_9 * F_7_8) * F_5_6) * F_3_4) * F_1_2);
- } else {
- absAsinh = a * (1 - a2 * (F_1_3 - a2 * F_1_5 * F_3_4) * F_1_2);
- }
- }
-
- return negative ? -absAsinh : absAsinh;
- }
-
- /** Compute the inverse hyperbolic tangent of a number.
- * @param a number on which evaluation is done
- * @return inverse hyperbolic tangent of a
- */
- public static double atanh(double a) {
- boolean negative = false;
- if (a < 0) {
- negative = true;
- a = -a;
- }
-
- double absAtanh;
- if (a > 0.15) {
- absAtanh = 0.5 * AccurateMath.log((1 + a) / (1 - a));
- } else {
- final double a2 = a * a;
- if (a > 0.087) {
- absAtanh = a * (1 + a2 * (F_1_3 + a2 * (F_1_5 + a2 * (F_1_7 + a2 * (F_1_9 + a2 * (F_1_11 + a2 * (F_1_13 + a2 * (F_1_15 + a2 * F_1_17))))))));
- } else if (a > 0.031) {
- absAtanh = a * (1 + a2 * (F_1_3 + a2 * (F_1_5 + a2 * (F_1_7 + a2 * (F_1_9 + a2 * (F_1_11 + a2 * F_1_13))))));
- } else if (a > 0.003) {
- absAtanh = a * (1 + a2 * (F_1_3 + a2 * (F_1_5 + a2 * (F_1_7 + a2 * F_1_9))));
- } else {
- absAtanh = a * (1 + a2 * (F_1_3 + a2 * F_1_5));
- }
- }
-
- return negative ? -absAtanh : absAtanh;
- }
-
- /** Compute the signum of a number.
- * The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise
- * @param a number on which evaluation is done
- * @return -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
- */
- public static double signum(final double a) {
- return (a < 0.0) ? -1.0 : ((a > 0.0) ? 1.0 : a); // return +0.0/-0.0/NaN depending on a
- }
-
- /** Compute the signum of a number.
- * The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise
- * @param a number on which evaluation is done
- * @return -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
- */
- public static float signum(final float a) {
- return (a < 0.0f) ? -1.0f : ((a > 0.0f) ? 1.0f : a); // return +0.0/-0.0/NaN depending on a
- }
-
- /** Compute next number towards positive infinity.
- * @param a number to which neighbor should be computed
- * @return neighbor of a towards positive infinity
- */
- public static double nextUp(final double a) {
- return nextAfter(a, Double.POSITIVE_INFINITY);
- }
-
- /** Compute next number towards positive infinity.
- * @param a number to which neighbor should be computed
- * @return neighbor of a towards positive infinity
- */
- public static float nextUp(final float a) {
- return nextAfter(a, Float.POSITIVE_INFINITY);
- }
-
- /** Compute next number towards negative infinity.
- * @param a number to which neighbor should be computed
- * @return neighbor of a towards negative infinity
- * @since 3.4
- */
- public static double nextDown(final double a) {
- return nextAfter(a, Double.NEGATIVE_INFINITY);
- }
-
- /** Compute next number towards negative infinity.
- * @param a number to which neighbor should be computed
- * @return neighbor of a towards negative infinity
- * @since 3.4
- */
- public static float nextDown(final float a) {
- return nextAfter(a, Float.NEGATIVE_INFINITY);
- }
-
- /** Returns a pseudo-random number between 0.0 and 1.0.
- * <p><b>Note:</b> this implementation currently delegates to {@link Math#random}
- * @return a random number between 0.0 and 1.0
- */
- public static double random() {
- return Math.random();
- }
-
- /**
- * Exponential function.
- *
- * Computes exp(x), function result is nearly rounded. It will be correctly
- * rounded to the theoretical value for 99.9% of input values, otherwise it will
- * have a 1 ULP error.
- *
- * Method:
- * Lookup intVal = exp(int(x))
- * Lookup fracVal = exp(int(x-int(x) / 1024.0) * 1024.0 );
- * Compute z as the exponential of the remaining bits by a polynomial minus one
- * exp(x) = intVal * fracVal * (1 + z)
- *
- * Accuracy:
- * Calculation is done with 63 bits of precision, so result should be correctly
- * rounded for 99.9% of input values, with less than 1 ULP error otherwise.
- *
- * @param x a double
- * @return double e<sup>x</sup>
- */
- public static double exp(double x) {
- return exp(x, 0.0, null);
- }
-
- /**
- * Internal helper method for exponential function.
- * @param x original argument of the exponential function
- * @param extra extra bits of precision on input (To Be Confirmed)
- * @param hiPrec extra bits of precision on output (To Be Confirmed)
- * @return exp(x)
- */
- private static double exp(double x, double extra, double[] hiPrec) {
- double intPartA;
- double intPartB;
- int intVal = (int) x;
-
- /* Lookup exp(floor(x)).
- * intPartA will have the upper 22 bits, intPartB will have the lower
- * 52 bits.
- */
- if (x < 0.0) {
-
- // We don't check against intVal here as conversion of large negative double values
- // may be affected by a JIT bug. Subsequent comparisons can safely use intVal
- if (x < -746d) {
- if (hiPrec != null) {
- hiPrec[0] = 0.0;
- hiPrec[1] = 0.0;
- }
- return 0.0;
- }
-
- if (intVal < -709) {
- /* This will produce a subnormal output */
- final double result = exp(x+40.19140625, extra, hiPrec) / 285040095144011776.0;
- if (hiPrec != null) {
- hiPrec[0] /= 285040095144011776.0;
- hiPrec[1] /= 285040095144011776.0;
- }
- return result;
- }
-
- if (intVal == -709) {
- /* exp(1.494140625) is nearly a machine number... */
- final double result = exp(x+1.494140625, extra, hiPrec) / 4.455505956692756620;
- if (hiPrec != null) {
- hiPrec[0] /= 4.455505956692756620;
- hiPrec[1] /= 4.455505956692756620;
- }
- return result;
- }
-
- intVal--;
-
- } else {
- if (intVal > 709) {
- if (hiPrec != null) {
- hiPrec[0] = Double.POSITIVE_INFINITY;
- hiPrec[1] = 0.0;
- }
- return Double.POSITIVE_INFINITY;
- }
-
- }
-
- intPartA = ExpIntTable.EXP_INT_TABLE_A[EXP_INT_TABLE_MAX_INDEX+intVal];
- intPartB = ExpIntTable.EXP_INT_TABLE_B[EXP_INT_TABLE_MAX_INDEX+intVal];
-
- /* Get the fractional part of x, find the greatest multiple of 2^-10 less than
- * x and look up the exp function of it.
- * fracPartA will have the upper 22 bits, fracPartB the lower 52 bits.
- */
- final int intFrac = (int) ((x - intVal) * 1024.0);
- final double fracPartA = ExpFracTable.EXP_FRAC_TABLE_A[intFrac];
- final double fracPartB = ExpFracTable.EXP_FRAC_TABLE_B[intFrac];
-
- /* epsilon is the difference in x from the nearest multiple of 2^-10. It
- * has a value in the range 0 <= epsilon < 2^-10.
- * Do the subtraction from x as the last step to avoid possible loss of precision.
- */
- final double epsilon = x - (intVal + intFrac / 1024.0);
-
- /* Compute z = exp(epsilon) - 1.0 via a minimax polynomial. z has
- full double precision (52 bits). Since z < 2^-10, we will have
- 62 bits of precision when combined with the constant 1. This will be
- used in the last addition below to get proper rounding. */
-
- /* Remez generated polynomial. Converges on the interval [0, 2^-10], error
- is less than 0.5 ULP */
- double z = 0.04168701738764507;
- z = z * epsilon + 0.1666666505023083;
- z = z * epsilon + 0.5000000000042687;
- z = z * epsilon + 1.0;
- z = z * epsilon + -3.940510424527919E-20;
-
- /* Compute (intPartA+intPartB) * (fracPartA+fracPartB) by binomial
- expansion.
- tempA is exact since intPartA and intPartB only have 22 bits each.
- tempB will have 52 bits of precision.
- */
- double tempA = intPartA * fracPartA;
- double tempB = intPartA * fracPartB + intPartB * fracPartA + intPartB * fracPartB;
-
- /* Compute the result. (1+z)(tempA+tempB). Order of operations is
- important. For accuracy add by increasing size. tempA is exact and
- much larger than the others. If there are extra bits specified from the
- pow() function, use them. */
- final double tempC = tempB + tempA;
-
- // If tempC is positive infinite, the evaluation below could result in NaN,
- // because z could be negative at the same time.
- if (tempC == Double.POSITIVE_INFINITY) {
- return Double.POSITIVE_INFINITY;
- }
-
- final double result;
- if (extra != 0.0) {
- result = tempC*extra*z + tempC*extra + tempC*z + tempB + tempA;
- } else {
- result = tempC*z + tempB + tempA;
- }
-
- if (hiPrec != null) {
- // If requesting high precision
- hiPrec[0] = tempA;
- hiPrec[1] = tempC*extra*z + tempC*extra + tempC*z + tempB;
- }
-
- return result;
- }
-
- /** Compute exp(x) - 1
- * @param x number to compute shifted exponential
- * @return exp(x) - 1
- */
- public static double expm1(double x) {
- return expm1(x, null);
- }
-
- /** Internal helper method for expm1
- * @param x number to compute shifted exponential
- * @param hiPrecOut receive high precision result for -1.0 < x < 1.0
- * @return exp(x) - 1
- */
- private static double expm1(double x, double hiPrecOut[]) {
- if (Double.isNaN(x) || x == 0.0) { // NaN or zero
- return x;
- }
-
- if (x <= -1.0 || x >= 1.0) {
- // If not between +/- 1.0
- //return exp(x) - 1.0;
- double hiPrec[] = new double[2];
- exp(x, 0.0, hiPrec);
- if (x > 0.0) {
- return -1.0 + hiPrec[0] + hiPrec[1];
- } else {
- final double ra = -1.0 + hiPrec[0];
- double rb = -(ra + 1.0 - hiPrec[0]);
- rb += hiPrec[1];
- return ra + rb;
- }
- }
-
- double baseA;
- double baseB;
- double epsilon;
- boolean negative = false;
-
- if (x < 0.0) {
- x = -x;
- negative = true;
- }
-
- {
- int intFrac = (int) (x * 1024.0);
- double tempA = ExpFracTable.EXP_FRAC_TABLE_A[intFrac] - 1.0;
- double tempB = ExpFracTable.EXP_FRAC_TABLE_B[intFrac];
-
- double temp = tempA + tempB;
- tempB = -(temp - tempA - tempB);
- tempA = temp;
-
- temp = tempA * HEX_40000000;
- baseA = tempA + temp - temp;
- baseB = tempB + (tempA - baseA);
-
- epsilon = x - intFrac/1024.0;
- }
-
-
- /* Compute expm1(epsilon) */
- double zb = 0.008336750013465571;
- zb = zb * epsilon + 0.041666663879186654;
- zb = zb * epsilon + 0.16666666666745392;
- zb = zb * epsilon + 0.49999999999999994;
- zb *= epsilon;
- zb *= epsilon;
-
- double za = epsilon;
- double temp = za + zb;
- zb = -(temp - za - zb);
- za = temp;
-
- temp = za * HEX_40000000;
- temp = za + temp - temp;
- zb += za - temp;
- za = temp;
-
- /* Combine the parts. expm1(a+b) = expm1(a) + expm1(b) + expm1(a)*expm1(b) */
- double ya = za * baseA;
- //double yb = za*baseB + zb*baseA + zb*baseB;
- temp = ya + za * baseB;
- double yb = -(temp - ya - za * baseB);
- ya = temp;
-
- temp = ya + zb * baseA;
- yb += -(temp - ya - zb * baseA);
- ya = temp;
-
- temp = ya + zb * baseB;
- yb += -(temp - ya - zb*baseB);
- ya = temp;
-
- //ya = ya + za + baseA;
- //yb = yb + zb + baseB;
- temp = ya + baseA;
- yb += -(temp - baseA - ya);
- ya = temp;
-
- temp = ya + za;
- //yb += (ya > za) ? -(temp - ya - za) : -(temp - za - ya);
- yb += -(temp - ya - za);
- ya = temp;
-
- temp = ya + baseB;
- //yb += (ya > baseB) ? -(temp - ya - baseB) : -(temp - baseB - ya);
- yb += -(temp - ya - baseB);
- ya = temp;
-
- temp = ya + zb;
- //yb += (ya > zb) ? -(temp - ya - zb) : -(temp - zb - ya);
- yb += -(temp - ya - zb);
- ya = temp;
-
- if (negative) {
- /* Compute expm1(-x) = -expm1(x) / (expm1(x) + 1) */
- double denom = 1.0 + ya;
- double denomr = 1.0 / denom;
- double denomb = -(denom - 1.0 - ya) + yb;
- double ratio = ya * denomr;
- temp = ratio * HEX_40000000;
- final double ra = ratio + temp - temp;
- double rb = ratio - ra;
-
- temp = denom * HEX_40000000;
- za = denom + temp - temp;
- zb = denom - za;
-
- rb += (ya - za * ra - za * rb - zb * ra - zb * rb) * denomr;
-
- // f(x) = x/1+x
- // Compute f'(x)
- // Product rule: d(uv) = du*v + u*dv
- // Chain rule: d(f(g(x)) = f'(g(x))*f(g'(x))
- // d(1/x) = -1/(x*x)
- // d(1/1+x) = -1/( (1+x)^2) * 1 = -1/((1+x)*(1+x))
- // d(x/1+x) = -x/((1+x)(1+x)) + 1/1+x = 1 / ((1+x)(1+x))
-
- // Adjust for yb
- rb += yb * denomr; // numerator
- rb += -ya * denomb * denomr * denomr; // denominator
-
- // negate
- ya = -ra;
- yb = -rb;
- }
-
- if (hiPrecOut != null) {
- hiPrecOut[0] = ya;
- hiPrecOut[1] = yb;
- }
-
- return ya + yb;
- }
-
- /**
- * Natural logarithm.
- *
- * @param x a double
- * @return log(x)
- */
- public static double log(final double x) {
- return log(x, null);
- }
-
- /**
- * Internal helper method for natural logarithm function.
- * @param x original argument of the natural logarithm function
- * @param hiPrec extra bits of precision on output (To Be Confirmed)
- * @return log(x)
- */
- private static double log(final double x, final double[] hiPrec) {
- if (x==0) { // Handle special case of +0/-0
- return Double.NEGATIVE_INFINITY;
- }
- long bits = Double.doubleToRawLongBits(x);
-
- /* Handle special cases of negative input, and NaN */
- if (((bits & 0x8000000000000000L) != 0 || Double.isNaN(x)) && x != 0.0) {
- if (hiPrec != null) {
- hiPrec[0] = Double.NaN;
- }
-
- return Double.NaN;
- }
-
- /* Handle special cases of Positive infinity. */
- if (x == Double.POSITIVE_INFINITY) {
- if (hiPrec != null) {
- hiPrec[0] = Double.POSITIVE_INFINITY;
- }
-
- return Double.POSITIVE_INFINITY;
- }
-
- /* Extract the exponent */
- int exp = (int)(bits >> 52)-1023;
-
- if ((bits & 0x7ff0000000000000L) == 0) {
- // Subnormal!
- if (x == 0) {
- // Zero
- if (hiPrec != null) {
- hiPrec[0] = Double.NEGATIVE_INFINITY;
- }
-
- return Double.NEGATIVE_INFINITY;
- }
-
- /* Normalize the subnormal number. */
- bits <<= 1;
- while ( (bits & 0x0010000000000000L) == 0) {
- --exp;
- bits <<= 1;
- }
- }
-
-
- if ((exp == -1 || exp == 0) && x < 1.01 && x > 0.99 && hiPrec == null) {
- /* The normal method doesn't work well in the range [0.99, 1.01], so call do a straight
- polynomial expansion in higer precision. */
-
- /* Compute x - 1.0 and split it */
- double xa = x - 1.0;
- double xb = xa - x + 1.0;
- double tmp = xa * HEX_40000000;
- double aa = xa + tmp - tmp;
- double ab = xa - aa;
- xa = aa;
- xb = ab;
-
- final double[] lnCoef_last = LN_QUICK_COEF[LN_QUICK_COEF.length - 1];
- double ya = lnCoef_last[0];
- double yb = lnCoef_last[1];
-
- for (int i = LN_QUICK_COEF.length - 2; i >= 0; i--) {
- /* Multiply a = y * x */
- aa = ya * xa;
- ab = ya * xb + yb * xa + yb * xb;
- /* split, so now y = a */
- tmp = aa * HEX_40000000;
- ya = aa + tmp - tmp;
- yb = aa - ya + ab;
-
- /* Add a = y + lnQuickCoef */
- final double[] lnCoef_i = LN_QUICK_COEF[i];
- aa = ya + lnCoef_i[0];
- ab = yb + lnCoef_i[1];
- /* Split y = a */
- tmp = aa * HEX_40000000;
- ya = aa + tmp - tmp;
- yb = aa - ya + ab;
- }
-
- /* Multiply a = y * x */
- aa = ya * xa;
- ab = ya * xb + yb * xa + yb * xb;
- /* split, so now y = a */
- tmp = aa * HEX_40000000;
- ya = aa + tmp - tmp;
- yb = aa - ya + ab;
-
- return ya + yb;
- }
-
- // lnm is a log of a number in the range of 1.0 - 2.0, so 0 <= lnm < ln(2)
- final double[] lnm = lnMant.LN_MANT[(int)((bits & 0x000ffc0000000000L) >> 42)];
-
- /*
- double epsilon = x / Double.longBitsToDouble(bits & 0xfffffc0000000000L);
-
- epsilon -= 1.0;
- */
-
- // y is the most significant 10 bits of the mantissa
- //double y = Double.longBitsToDouble(bits & 0xfffffc0000000000L);
- //double epsilon = (x - y) / y;
- final double epsilon = (bits & 0x3ffffffffffL) / (TWO_POWER_52 + (bits & 0x000ffc0000000000L));
-
- double lnza = 0.0;
- double lnzb = 0.0;
-
- if (hiPrec != null) {
- /* split epsilon -> x */
- double tmp = epsilon * HEX_40000000;
- double aa = epsilon + tmp - tmp;
- double ab = epsilon - aa;
- double xa = aa;
- double xb = ab;
-
- /* Need a more accurate epsilon, so adjust the division. */
- final double numer = bits & 0x3ffffffffffL;
- final double denom = TWO_POWER_52 + (bits & 0x000ffc0000000000L);
- aa = numer - xa*denom - xb * denom;
- xb += aa / denom;
-
- /* Remez polynomial evaluation */
- final double[] lnCoef_last = LN_HI_PREC_COEF[LN_HI_PREC_COEF.length-1];
- double ya = lnCoef_last[0];
- double yb = lnCoef_last[1];
-
- for (int i = LN_HI_PREC_COEF.length - 2; i >= 0; i--) {
- /* Multiply a = y * x */
- aa = ya * xa;
- ab = ya * xb + yb * xa + yb * xb;
- /* split, so now y = a */
- tmp = aa * HEX_40000000;
- ya = aa + tmp - tmp;
- yb = aa - ya + ab;
-
- /* Add a = y + lnHiPrecCoef */
- final double[] lnCoef_i = LN_HI_PREC_COEF[i];
- aa = ya + lnCoef_i[0];
- ab = yb + lnCoef_i[1];
- /* Split y = a */
- tmp = aa * HEX_40000000;
- ya = aa + tmp - tmp;
- yb = aa - ya + ab;
- }
-
- /* Multiply a = y * x */
- aa = ya * xa;
- ab = ya * xb + yb * xa + yb * xb;
-
- /* split, so now lnz = a */
- /*
- tmp = aa * 1073741824.0;
- lnza = aa + tmp - tmp;
- lnzb = aa - lnza + ab;
- */
- lnza = aa + ab;
- lnzb = -(lnza - aa - ab);
- } else {
- /* High precision not required. Eval Remez polynomial
- using standard double precision */
- lnza = -0.16624882440418567;
- lnza = lnza * epsilon + 0.19999954120254515;
- lnza = lnza * epsilon + -0.2499999997677497;
- lnza = lnza * epsilon + 0.3333333333332802;
- lnza = lnza * epsilon + -0.5;
- lnza = lnza * epsilon + 1.0;
- lnza *= epsilon;
- }
-
- /* Relative sizes:
- * lnzb [0, 2.33E-10]
- * lnm[1] [0, 1.17E-7]
- * ln2B*exp [0, 1.12E-4]
- * lnza [0, 9.7E-4]
- * lnm[0] [0, 0.692]
- * ln2A*exp [0, 709]
- */
-
- /* Compute the following sum:
- * lnzb + lnm[1] + ln2B*exp + lnza + lnm[0] + ln2A*exp;
- */
-
- //return lnzb + lnm[1] + ln2B*exp + lnza + lnm[0] + ln2A*exp;
- double a = LN_2_A*exp;
- double b = 0.0;
- double c = a+lnm[0];
- double d = -(c-a-lnm[0]);
- a = c;
- b += d;
-
- c = a + lnza;
- d = -(c - a - lnza);
- a = c;
- b += d;
-
- c = a + LN_2_B*exp;
- d = -(c - a - LN_2_B*exp);
- a = c;
- b += d;
-
- c = a + lnm[1];
- d = -(c - a - lnm[1]);
- a = c;
- b += d;
-
- c = a + lnzb;
- d = -(c - a - lnzb);
- a = c;
- b += d;
-
- if (hiPrec != null) {
- hiPrec[0] = a;
- hiPrec[1] = b;
- }
-
- return a + b;
- }
-
- /**
- * Computes log(1 + x).
- *
- * @param x Number.
- * @return {@code log(1 + x)}.
- */
- public static double log1p(final double x) {
- if (x == -1) {
- return Double.NEGATIVE_INFINITY;
- }
-
- if (x == Double.POSITIVE_INFINITY) {
- return Double.POSITIVE_INFINITY;
- }
-
- if (x > 1e-6 ||
- x < -1e-6) {
- final double xpa = 1 + x;
- final double xpb = -(xpa - 1 - x);
-
- final double[] hiPrec = new double[2];
- final double lores = log(xpa, hiPrec);
- if (Double.isInfinite(lores)) { // Don't allow this to be converted to NaN
- return lores;
- }
-
- // Do a taylor series expansion around xpa:
- // f(x+y) = f(x) + f'(x) y + f''(x)/2 y^2
- final double fx1 = xpb / xpa;
- final double epsilon = 0.5 * fx1 + 1;
- return epsilon * fx1 + hiPrec[1] + hiPrec[0];
- } else {
- // Value is small |x| < 1e6, do a Taylor series centered on 1.
- final double y = (x * F_1_3 - F_1_2) * x + 1;
- return y * x;
- }
- }
-
- /** Compute the base 10 logarithm.
- * @param x a number
- * @return log10(x)
- */
- public static double log10(final double x) {
- final double hiPrec[] = new double[2];
-
- final double lores = log(x, hiPrec);
- if (Double.isInfinite(lores)){ // don't allow this to be converted to NaN
- return lores;
- }
-
- final double tmp = hiPrec[0] * HEX_40000000;
- final double lna = hiPrec[0] + tmp - tmp;
- final double lnb = hiPrec[0] - lna + hiPrec[1];
-
- final double rln10a = 0.4342944622039795;
- final double rln10b = 1.9699272335463627E-8;
-
- return rln10b * lnb + rln10b * lna + rln10a * lnb + rln10a * lna;
- }
-
- /**
- * Computes the <a href="http://mathworld.wolfram.com/Logarithm.html">
- * logarithm</a> in a given base.
- *
- * Returns {@code NaN} if either argument is negative.
- * If {@code base} is 0 and {@code x} is positive, 0 is returned.
- * If {@code base} is positive and {@code x} is 0,
- * {@code Double.NEGATIVE_INFINITY} is returned.
- * If both arguments are 0, the result is {@code NaN}.
- *
- * @param base Base of the logarithm, must be greater than 0.
- * @param x Argument, must be greater than 0.
- * @return the value of the logarithm, i.e. the number {@code y} such that
- * <code>base<sup>y</sup> = x</code>.
- * @since 3.0
- */
- public static double log(double base, double x) {
- return log(x) / log(base);
- }
-
- /**
- * Power function. Compute x^y.
- *
- * @param x a double
- * @param y a double
- * @return double
- */
- public static double pow(final double x, final double y) {
-
- if (y == 0) {
- // y = -0 or y = +0
- return 1.0;
- } else {
-
- final long yBits = Double.doubleToRawLongBits(y);
- final int yRawExp = (int) ((yBits & MASK_DOUBLE_EXPONENT) >> 52);
- final long yRawMantissa = yBits & MASK_DOUBLE_MANTISSA;
- final long xBits = Double.doubleToRawLongBits(x);
- final int xRawExp = (int) ((xBits & MASK_DOUBLE_EXPONENT) >> 52);
- final long xRawMantissa = xBits & MASK_DOUBLE_MANTISSA;
-
- if (yRawExp > 1085) {
- // y is either a very large integral value that does not fit in a long or it is a special number
-
- if ((yRawExp == 2047 && yRawMantissa != 0) ||
- (xRawExp == 2047 && xRawMantissa != 0)) {
- // NaN
- return Double.NaN;
- } else if (xRawExp == 1023 && xRawMantissa == 0) {
- // x = -1.0 or x = +1.0
- if (yRawExp == 2047) {
- // y is infinite
- return Double.NaN;
- } else {
- // y is a large even integer
- return 1.0;
- }
- } else {
- // the absolute value of x is either greater or smaller than 1.0
-
- // if yRawExp == 2047 and mantissa is 0, y = -infinity or y = +infinity
- // if 1085 < yRawExp < 2047, y is simply a large number, however, due to limited
- // accuracy, at this magnitude it behaves just like infinity with regards to x
- if ((y > 0) ^ (xRawExp < 1023)) {
- // either y = +infinity (or large engouh) and abs(x) > 1.0
- // or y = -infinity (or large engouh) and abs(x) < 1.0
- return Double.POSITIVE_INFINITY;
- } else {
- // either y = +infinity (or large engouh) and abs(x) < 1.0
- // or y = -infinity (or large engouh) and abs(x) > 1.0
- return +0.0;
- }
- }
-
- } else {
- // y is a regular non-zero number
-
- if (yRawExp >= 1023) {
- // y may be an integral value, which should be handled specifically
- final long yFullMantissa = IMPLICIT_HIGH_BIT | yRawMantissa;
- if (yRawExp < 1075) {
- // normal number with negative shift that may have a fractional part
- final long integralMask = (-1L) << (1075 - yRawExp);
- if ((yFullMantissa & integralMask) == yFullMantissa) {
- // all fractional bits are 0, the number is really integral
- final long l = yFullMantissa >> (1075 - yRawExp);
- return AccurateMath.pow(x, (y < 0) ? -l : l);
- }
- } else {
- // normal number with positive shift, always an integral value
- // we know it fits in a primitive long because yRawExp > 1085 has been handled above
- final long l = yFullMantissa << (yRawExp - 1075);
- return AccurateMath.pow(x, (y < 0) ? -l : l);
- }
- }
-
- // y is a non-integral value
-
- if (x == 0) {
- // x = -0 or x = +0
- // the integer powers have already been handled above
- return y < 0 ? Double.POSITIVE_INFINITY : +0.0;
- } else if (xRawExp == 2047) {
- if (xRawMantissa == 0) {
- // x = -infinity or x = +infinity
- return (y < 0) ? +0.0 : Double.POSITIVE_INFINITY;
- } else {
- // NaN
- return Double.NaN;
- }
- } else if (x < 0) {
- // the integer powers have already been handled above
- return Double.NaN;
- } else {
-
- // this is the general case, for regular fractional numbers x and y
-
- // Split y into ya and yb such that y = ya+yb
- final double tmp = y * HEX_40000000;
- final double ya = (y + tmp) - tmp;
- final double yb = y - ya;
-
- /* Compute ln(x) */
- final double lns[] = new double[2];
- final double lores = log(x, lns);
- if (Double.isInfinite(lores)) { // don't allow this to be converted to NaN
- return lores;
- }
-
- double lna = lns[0];
- double lnb = lns[1];
-
- /* resplit lns */
- final double tmp1 = lna * HEX_40000000;
- final double tmp2 = (lna + tmp1) - tmp1;
- lnb += lna - tmp2;
- lna = tmp2;
-
- // y*ln(x) = (aa+ab)
- final double aa = lna * ya;
- final double ab = lna * yb + lnb * ya + lnb * yb;
-
- lna = aa+ab;
- lnb = -(lna - aa - ab);
-
- double z = 1.0 / 120.0;
- z = z * lnb + (1.0 / 24.0);
- z = z * lnb + (1.0 / 6.0);
- z = z * lnb + 0.5;
- z = z * lnb + 1.0;
- z *= lnb;
-
- final double result = exp(lna, z, null);
- //result = result + result * z;
- return result;
-
- }
- }
-
- }
-
- }
-
- /**
- * Raise a double to an int power.
- *
- * @param d Number to raise.
- * @param e Exponent.
- * @return d<sup>e</sup>
- * @since 3.1
- */
- public static double pow(double d, int e) {
- return pow(d, (long) e);
- }
-
-
- /**
- * Raise a double to a long power.
- *
- * @param d Number to raise.
- * @param e Exponent.
- * @return d<sup>e</sup>
- * @since 3.6
- */
- public static double pow(double d, long e) {
- if (e == 0) {
- return 1.0;
- } else if (e > 0) {
- return new Split(d).pow(e).full;
- } else {
- return new Split(d).reciprocal().pow(-e).full;
- }
- }
-
- /** Class operator on double numbers split into one 26 bits number and one 27 bits number. */
- private static class Split {
-
- /** Split version of NaN. */
- public static final Split NAN = new Split(Double.NaN, 0);
-
- /** Split version of positive infinity. */
- public static final Split POSITIVE_INFINITY = new Split(Double.POSITIVE_INFINITY, 0);
-
- /** Split version of negative infinity. */
- public static final Split NEGATIVE_INFINITY = new Split(Double.NEGATIVE_INFINITY, 0);
-
- /** Full number. */
- private final double full;
-
- /** High order bits. */
- private final double high;
-
- /** Low order bits. */
- private final double low;
-
- /** Simple constructor.
- * @param x number to split
- */
- Split(final double x) {
- full = x;
- high = Double.longBitsToDouble(Double.doubleToRawLongBits(x) & ((-1L) << 27));
- low = x - high;
- }
-
- /** Simple constructor.
- * @param high high order bits
- * @param low low order bits
- */
- Split(final double high, final double low) {
- this(high == 0.0 ? (low == 0.0 && Double.doubleToRawLongBits(high) == Long.MIN_VALUE /* negative zero */ ? -0.0 : low) : high + low, high, low);
- }
-
- /** Simple constructor.
- * @param full full number
- * @param high high order bits
- * @param low low order bits
- */
- Split(final double full, final double high, final double low) {
- this.full = full;
- this.high = high;
- this.low = low;
- }
-
- /** Multiply the instance by another one.
- * @param b other instance to multiply by
- * @return product
- */
- public Split multiply(final Split b) {
- // beware the following expressions must NOT be simplified, they rely on floating point arithmetic properties
- final Split mulBasic = new Split(full * b.full);
- final double mulError = low * b.low - (((mulBasic.full - high * b.high) - low * b.high) - high * b.low);
- return new Split(mulBasic.high, mulBasic.low + mulError);
- }
-
- /** Compute the reciprocal of the instance.
- * @return reciprocal of the instance
- */
- public Split reciprocal() {
-
- final double approximateInv = 1.0 / full;
- final Split splitInv = new Split(approximateInv);
-
- // if 1.0/d were computed perfectly, remultiplying it by d should give 1.0
- // we want to estimate the error so we can fix the low order bits of approximateInvLow
- // beware the following expressions must NOT be simplified, they rely on floating point arithmetic properties
- final Split product = multiply(splitInv);
- final double error = (product.high - 1) + product.low;
-
- // better accuracy estimate of reciprocal
- return Double.isNaN(error) ? splitInv : new Split(splitInv.high, splitInv.low - error / full);
-
- }
-
- /** Computes this^e.
- * @param e exponent (beware, here it MUST be > 0; the only exclusion is Long.MIN_VALUE)
- * @return d^e, split in high and low bits
- * @since 3.6
- */
- private Split pow(final long e) {
-
- // prepare result
- Split result = new Split(1);
-
- // d^(2p)
- Split d2p = new Split(full, high, low);
-
- for (long p = e; p != 0; p >>>= 1) {
-
- if ((p & 0x1) != 0) {
- // accurate multiplication result = result * d^(2p) using Veltkamp TwoProduct algorithm
- result = result.multiply(d2p);
- }
-
- // accurate squaring d^(2(p+1)) = d^(2p) * d^(2p) using Veltkamp TwoProduct algorithm
- d2p = d2p.multiply(d2p);
-
- }
-
- if (Double.isNaN(result.full)) {
- if (Double.isNaN(full)) {
- return Split.NAN;
- } else {
- // some intermediate numbers exceeded capacity,
- // and the low order bits became NaN (because infinity - infinity = NaN)
- if (AccurateMath.abs(full) < 1) {
- return new Split(AccurateMath.copySign(0.0, full), 0.0);
- } else if (full < 0 && (e & 0x1) == 1) {
- return Split.NEGATIVE_INFINITY;
- } else {
- return Split.POSITIVE_INFINITY;
- }
- }
- } else {
- return result;
- }
-
- }
-
- }
-
- /**
- * Computes sin(x) - x, where |x| < 1/16.
- * Use a Remez polynomial approximation.
- * @param x a number smaller than 1/16
- * @return sin(x) - x
- */
- private static double polySine(final double x)
- {
- double x2 = x*x;
-
- double p = 2.7553817452272217E-6;
- p = p * x2 + -1.9841269659586505E-4;
- p = p * x2 + 0.008333333333329196;
- p = p * x2 + -0.16666666666666666;
- //p *= x2;
- //p *= x;
- p = p * x2 * x;
-
- return p;
- }
-
- /**
- * Computes cos(x) - 1, where |x| < 1/16.
- * Use a Remez polynomial approximation.
- * @param x a number smaller than 1/16
- * @return cos(x) - 1
- */
- private static double polyCosine(double x) {
- double x2 = x*x;
-
- double p = 2.479773539153719E-5;
- p = p * x2 + -0.0013888888689039883;
- p = p * x2 + 0.041666666666621166;
- p = p * x2 + -0.49999999999999994;
- p *= x2;
-
- return p;
- }
-
- /**
- * Compute sine over the first quadrant (0 < x < pi/2).
- * Use combination of table lookup and rational polynomial expansion.
- * @param xa number from which sine is requested
- * @param xb extra bits for x (may be 0.0)
- * @return sin(xa + xb)
- */
- private static double sinQ(double xa, double xb) {
- int idx = (int) ((xa * 8.0) + 0.5);
- final double epsilon = xa - EIGHTHS[idx]; //idx*0.125;
-
- // Table lookups
- final double sintA = SINE_TABLE_A[idx];
- final double sintB = SINE_TABLE_B[idx];
- final double costA = COSINE_TABLE_A[idx];
- final double costB = COSINE_TABLE_B[idx];
-
- // Polynomial eval of sin(epsilon), cos(epsilon)
- double sinEpsA = epsilon;
- double sinEpsB = polySine(epsilon);
- final double cosEpsA = 1.0;
- final double cosEpsB = polyCosine(epsilon);
-
- // Split epsilon xa + xb = x
- final double temp = sinEpsA * HEX_40000000;
- double temp2 = (sinEpsA + temp) - temp;
- sinEpsB += sinEpsA - temp2;
- sinEpsA = temp2;
-
- /* Compute sin(x) by angle addition formula */
- double result;
-
- /* Compute the following sum:
- *
- * result = sintA + costA*sinEpsA + sintA*cosEpsB + costA*sinEpsB +
- * sintB + costB*sinEpsA + sintB*cosEpsB + costB*sinEpsB;
- *
- * Ranges of elements
- *
- * xxxtA 0 PI/2
- * xxxtB -1.5e-9 1.5e-9
- * sinEpsA -0.0625 0.0625
- * sinEpsB -6e-11 6e-11
- * cosEpsA 1.0
- * cosEpsB 0 -0.0625
- *
- */
-
- //result = sintA + costA*sinEpsA + sintA*cosEpsB + costA*sinEpsB +
- // sintB + costB*sinEpsA + sintB*cosEpsB + costB*sinEpsB;
-
- //result = sintA + sintA*cosEpsB + sintB + sintB * cosEpsB;
- //result += costA*sinEpsA + costA*sinEpsB + costB*sinEpsA + costB * sinEpsB;
- double a = 0;
- double b = 0;
-
- double t = sintA;
- double c = a + t;
- double d = -(c - a - t);
- a = c;
- b += d;
-
- t = costA * sinEpsA;
- c = a + t;
- d = -(c - a - t);
- a = c;
- b += d;
-
- b = b + sintA * cosEpsB + costA * sinEpsB;
- /*
- t = sintA*cosEpsB;
- c = a + t;
- d = -(c - a - t);
- a = c;
- b = b + d;
-
- t = costA*sinEpsB;
- c = a + t;
- d = -(c - a - t);
- a = c;
- b = b + d;
- */
-
- b = b + sintB + costB * sinEpsA + sintB * cosEpsB + costB * sinEpsB;
- /*
- t = sintB;
- c = a + t;
- d = -(c - a - t);
- a = c;
- b = b + d;
-
- t = costB*sinEpsA;
- c = a + t;
- d = -(c - a - t);
- a = c;
- b = b + d;
-
- t = sintB*cosEpsB;
- c = a + t;
- d = -(c - a - t);
- a = c;
- b = b + d;
-
- t = costB*sinEpsB;
- c = a + t;
- d = -(c - a - t);
- a = c;
- b = b + d;
- */
-
- if (xb != 0.0) {
- t = ((costA + costB) * (cosEpsA + cosEpsB) -
- (sintA + sintB) * (sinEpsA + sinEpsB)) * xb; // approximate cosine*xb
- c = a + t;
- d = -(c - a - t);
- a = c;
- b += d;
- }
-
- result = a + b;
-
- return result;
- }
-
- /**
- * Compute cosine in the first quadrant by subtracting input from PI/2 and
- * then calling sinQ. This is more accurate as the input approaches PI/2.
- * @param xa number from which cosine is requested
- * @param xb extra bits for x (may be 0.0)
- * @return cos(xa + xb)
- */
- private static double cosQ(double xa, double xb) {
- final double pi2a = 1.5707963267948966;
- final double pi2b = 6.123233995736766E-17;
-
- final double a = pi2a - xa;
- double b = -(a - pi2a + xa);
- b += pi2b - xb;
-
- return sinQ(a, b);
- }
-
- /**
- * Compute tangent (or cotangent) over the first quadrant. 0 < x < pi/2
- * Use combination of table lookup and rational polynomial expansion.
- * @param xa number from which sine is requested
- * @param xb extra bits for x (may be 0.0)
- * @param cotanFlag if true, compute the cotangent instead of the tangent
- * @return tan(xa+xb) (or cotangent, depending on cotanFlag)
- */
- private static double tanQ(double xa, double xb, boolean cotanFlag) {
-
- int idx = (int) ((xa * 8.0) + 0.5);
- final double epsilon = xa - EIGHTHS[idx]; //idx*0.125;
-
- // Table lookups
- final double sintA = SINE_TABLE_A[idx];
- final double sintB = SINE_TABLE_B[idx];
- final double costA = COSINE_TABLE_A[idx];
- final double costB = COSINE_TABLE_B[idx];
-
- // Polynomial eval of sin(epsilon), cos(epsilon)
- double sinEpsA = epsilon;
- double sinEpsB = polySine(epsilon);
- final double cosEpsA = 1.0;
- final double cosEpsB = polyCosine(epsilon);
-
- // Split epsilon xa + xb = x
- double temp = sinEpsA * HEX_40000000;
- double temp2 = (sinEpsA + temp) - temp;
- sinEpsB += sinEpsA - temp2;
- sinEpsA = temp2;
-
- /* Compute sin(x) by angle addition formula */
-
- /* Compute the following sum:
- *
- * result = sintA + costA*sinEpsA + sintA*cosEpsB + costA*sinEpsB +
- * sintB + costB*sinEpsA + sintB*cosEpsB + costB*sinEpsB;
- *
- * Ranges of elements
- *
- * xxxtA 0 PI/2
- * xxxtB -1.5e-9 1.5e-9
- * sinEpsA -0.0625 0.0625
- * sinEpsB -6e-11 6e-11
- * cosEpsA 1.0
- * cosEpsB 0 -0.0625
- *
- */
-
- //result = sintA + costA*sinEpsA + sintA*cosEpsB + costA*sinEpsB +
- // sintB + costB*sinEpsA + sintB*cosEpsB + costB*sinEpsB;
-
- //result = sintA + sintA*cosEpsB + sintB + sintB * cosEpsB;
- //result += costA*sinEpsA + costA*sinEpsB + costB*sinEpsA + costB * sinEpsB;
- double a = 0;
- double b = 0;
-
- // Compute sine
- double t = sintA;
- double c = a + t;
- double d = -(c - a - t);
- a = c;
- b += d;
-
- t = costA*sinEpsA;
- c = a + t;
- d = -(c - a - t);
- a = c;
- b += d;
-
- b += sintA*cosEpsB + costA*sinEpsB;
- b += sintB + costB*sinEpsA + sintB*cosEpsB + costB*sinEpsB;
-
- double sina = a + b;
- double sinb = -(sina - a - b);
-
- // Compute cosine
-
- a = b = c = d = 0.0;
-
- t = costA*cosEpsA;
- c = a + t;
- d = -(c - a - t);
- a = c;
- b += d;
-
- t = -sintA*sinEpsA;
- c = a + t;
- d = -(c - a - t);
- a = c;
- b += d;
-
- b += costB*cosEpsA + costA*cosEpsB + costB*cosEpsB;
- b -= sintB*sinEpsA + sintA*sinEpsB + sintB*sinEpsB;
-
- double cosa = a + b;
- double cosb = -(cosa - a - b);
-
- if (cotanFlag) {
- double tmp;
- tmp = cosa; cosa = sina; sina = tmp;
- tmp = cosb; cosb = sinb; sinb = tmp;
- }
-
-
- /* estimate and correct, compute 1.0/(cosa+cosb) */
- /*
- double est = (sina+sinb)/(cosa+cosb);
- double err = (sina - cosa*est) + (sinb - cosb*est);
- est += err/(cosa+cosb);
- err = (sina - cosa*est) + (sinb - cosb*est);
- */
-
- // f(x) = 1/x, f'(x) = -1/x^2
-
- double est = sina/cosa;
-
- /* Split the estimate to get more accurate read on division rounding */
- temp = est * HEX_40000000;
- double esta = (est + temp) - temp;
- double estb = est - esta;
-
- temp = cosa * HEX_40000000;
- double cosaa = (cosa + temp) - temp;
- double cosab = cosa - cosaa;
-
- //double err = (sina - est*cosa)/cosa; // Correction for division rounding
- double err = (sina - esta*cosaa - esta*cosab - estb*cosaa - estb*cosab)/cosa; // Correction for division rounding
- err += sinb/cosa; // Change in est due to sinb
- err += -sina * cosb / cosa / cosa; // Change in est due to cosb
-
- if (xb != 0.0) {
- // tan' = 1 + tan^2 cot' = -(1 + cot^2)
- // Approximate impact of xb
- double xbadj = xb + est*est*xb;
- if (cotanFlag) {
- xbadj = -xbadj;
- }
-
- err += xbadj;
- }
-
- return est+err;
- }
-
- /** Reduce the input argument using the Payne and Hanek method.
- * This is good for all inputs 0.0 < x < inf
- * Output is remainder after dividing by PI/2
- * The result array should contain 3 numbers.
- * result[0] is the integer portion, so mod 4 this gives the quadrant.
- * result[1] is the upper bits of the remainder
- * result[2] is the lower bits of the remainder
- *
- * @param x number to reduce
- * @param result placeholder where to put the result
- */
- private static void reducePayneHanek(double x, double result[])
- {
- /* Convert input double to bits */
- long inbits = Double.doubleToRawLongBits(x);
- int exponent = (int) ((inbits >> 52) & 0x7ff) - 1023;
-
- /* Convert to fixed point representation */
- inbits &= 0x000fffffffffffffL;
- inbits |= 0x0010000000000000L;
-
- /* Normalize input to be between 0.5 and 1.0 */
- exponent++;
- inbits <<= 11;
-
- /* Based on the exponent, get a shifted copy of recip2pi */
- long shpi0;
- long shpiA;
- long shpiB;
- int idx = exponent >> 6;
- int shift = exponent - (idx << 6);
-
- if (shift != 0) {
- shpi0 = (idx == 0) ? 0 : (RECIP_2PI[idx-1] << shift);
- shpi0 |= RECIP_2PI[idx] >>> (64-shift);
- shpiA = (RECIP_2PI[idx] << shift) | (RECIP_2PI[idx+1] >>> (64-shift));
- shpiB = (RECIP_2PI[idx+1] << shift) | (RECIP_2PI[idx+2] >>> (64-shift));
- } else {
- shpi0 = (idx == 0) ? 0 : RECIP_2PI[idx-1];
- shpiA = RECIP_2PI[idx];
- shpiB = RECIP_2PI[idx+1];
- }
-
- /* Multiply input by shpiA */
- long a = inbits >>> 32;
- long b = inbits & 0xffffffffL;
-
- long c = shpiA >>> 32;
- long d = shpiA & 0xffffffffL;
-
- long ac = a * c;
- long bd = b * d;
- long bc = b * c;
- long ad = a * d;
-
- long prodB = bd + (ad << 32);
- long prodA = ac + (ad >>> 32);
-
- boolean bita = (bd & 0x8000000000000000L) != 0;
- boolean bitb = (ad & 0x80000000L ) != 0;
- boolean bitsum = (prodB & 0x8000000000000000L) != 0;
-
- /* Carry */
- if ( (bita && bitb) ||
- ((bita || bitb) && !bitsum) ) {
- prodA++;
- }
-
- bita = (prodB & 0x8000000000000000L) != 0;
- bitb = (bc & 0x80000000L ) != 0;
-
- prodB += bc << 32;
- prodA += bc >>> 32;
-
- bitsum = (prodB & 0x8000000000000000L) != 0;
-
- /* Carry */
- if ( (bita && bitb) ||
- ((bita || bitb) && !bitsum) ) {
- prodA++;
- }
-
- /* Multiply input by shpiB */
- c = shpiB >>> 32;
- d = shpiB & 0xffffffffL;
- ac = a * c;
- bc = b * c;
- ad = a * d;
-
- /* Collect terms */
- ac += (bc + ad) >>> 32;
-
- bita = (prodB & 0x8000000000000000L) != 0;
- bitb = (ac & 0x8000000000000000L ) != 0;
- prodB += ac;
- bitsum = (prodB & 0x8000000000000000L) != 0;
- /* Carry */
- if ( (bita && bitb) ||
- ((bita || bitb) && !bitsum) ) {
- prodA++;
- }
-
- /* Multiply by shpi0 */
- c = shpi0 >>> 32;
- d = shpi0 & 0xffffffffL;
-
- bd = b * d;
- bc = b * c;
- ad = a * d;
-
- prodA += bd + ((bc + ad) << 32);
-
- /*
- * prodA, prodB now contain the remainder as a fraction of PI. We want this as a fraction of
- * PI/2, so use the following steps:
- * 1.) multiply by 4.
- * 2.) do a fixed point muliply by PI/4.
- * 3.) Convert to floating point.
- * 4.) Multiply by 2
- */
-
- /* This identifies the quadrant */
- int intPart = (int)(prodA >>> 62);
-
- /* Multiply by 4 */
- prodA <<= 2;
- prodA |= prodB >>> 62;
- prodB <<= 2;
-
- /* Multiply by PI/4 */
- a = prodA >>> 32;
- b = prodA & 0xffffffffL;
-
- c = PI_O_4_BITS[0] >>> 32;
- d = PI_O_4_BITS[0] & 0xffffffffL;
-
- ac = a * c;
- bd = b * d;
- bc = b * c;
- ad = a * d;
-
- long prod2B = bd + (ad << 32);
- long prod2A = ac + (ad >>> 32);
-
- bita = (bd & 0x8000000000000000L) != 0;
- bitb = (ad & 0x80000000L ) != 0;
- bitsum = (prod2B & 0x8000000000000000L) != 0;
-
- /* Carry */
- if ( (bita && bitb) ||
- ((bita || bitb) && !bitsum) ) {
- prod2A++;
- }
-
- bita = (prod2B & 0x8000000000000000L) != 0;
- bitb = (bc & 0x80000000L ) != 0;
-
- prod2B += bc << 32;
- prod2A += bc >>> 32;
-
- bitsum = (prod2B & 0x8000000000000000L) != 0;
-
- /* Carry */
- if ( (bita && bitb) ||
- ((bita || bitb) && !bitsum) ) {
- prod2A++;
- }
-
- /* Multiply input by pio4bits[1] */
- c = PI_O_4_BITS[1] >>> 32;
- d = PI_O_4_BITS[1] & 0xffffffffL;
- ac = a * c;
- bc = b * c;
- ad = a * d;
-
- /* Collect terms */
- ac += (bc + ad) >>> 32;
-
- bita = (prod2B & 0x8000000000000000L) != 0;
- bitb = (ac & 0x8000000000000000L ) != 0;
- prod2B += ac;
- bitsum = (prod2B & 0x8000000000000000L) != 0;
- /* Carry */
- if ( (bita && bitb) ||
- ((bita || bitb) && !bitsum) ) {
- prod2A++;
- }
-
- /* Multiply inputB by pio4bits[0] */
- a = prodB >>> 32;
- b = prodB & 0xffffffffL;
- c = PI_O_4_BITS[0] >>> 32;
- d = PI_O_4_BITS[0] & 0xffffffffL;
- ac = a * c;
- bc = b * c;
- ad = a * d;
-
- /* Collect terms */
- ac += (bc + ad) >>> 32;
-
- bita = (prod2B & 0x8000000000000000L) != 0;
- bitb = (ac & 0x8000000000000000L ) != 0;
- prod2B += ac;
- bitsum = (prod2B & 0x8000000000000000L) != 0;
- /* Carry */
- if ( (bita && bitb) ||
- ((bita || bitb) && !bitsum) ) {
- prod2A++;
- }
-
- /* Convert to double */
- double tmpA = (prod2A >>> 12) / TWO_POWER_52; // High order 52 bits
- double tmpB = (((prod2A & 0xfffL) << 40) + (prod2B >>> 24)) / TWO_POWER_52 / TWO_POWER_52; // Low bits
-
- double sumA = tmpA + tmpB;
- double sumB = -(sumA - tmpA - tmpB);
-
- /* Multiply by PI/2 and return */
- result[0] = intPart;
- result[1] = sumA * 2.0;
- result[2] = sumB * 2.0;
- }
-
- /**
- * Sine function.
- *
- * @param x Argument.
- * @return sin(x)
- */
- public static double sin(double x) {
- boolean negative = false;
- int quadrant = 0;
- double xa;
- double xb = 0.0;
-
- /* Take absolute value of the input */
- xa = x;
- if (x < 0) {
- negative = true;
- xa = -xa;
- }
-
- /* Check for zero and negative zero */
- if (xa == 0.0) {
- long bits = Double.doubleToRawLongBits(x);
- if (bits < 0) {
- return -0.0;
- }
- return 0.0;
- }
-
- if (xa != xa || xa == Double.POSITIVE_INFINITY) {
- return Double.NaN;
- }
-
- /* Perform any argument reduction */
- if (xa > 3294198.0) {
- // PI * (2**20)
- // Argument too big for CodyWaite reduction. Must use
- // PayneHanek.
- double reduceResults[] = new double[3];
- reducePayneHanek(xa, reduceResults);
- quadrant = ((int) reduceResults[0]) & 3;
- xa = reduceResults[1];
- xb = reduceResults[2];
- } else if (xa > 1.5707963267948966) {
- final CodyWaite cw = new CodyWaite(xa);
- quadrant = cw.getK() & 3;
- xa = cw.getRemA();
- xb = cw.getRemB();
- }
-
- if (negative) {
- quadrant ^= 2; // Flip bit 1
- }
-
- switch (quadrant) {
- case 0:
- return sinQ(xa, xb);
- case 1:
- return cosQ(xa, xb);
- case 2:
- return -sinQ(xa, xb);
- case 3:
- return -cosQ(xa, xb);
- default:
- return Double.NaN;
- }
- }
-
- /**
- * Cosine function.
- *
- * @param x Argument.
- * @return cos(x)
- */
- public static double cos(double x) {
- int quadrant = 0;
-
- /* Take absolute value of the input */
- double xa = x;
- if (x < 0) {
- xa = -xa;
- }
-
- if (xa != xa || xa == Double.POSITIVE_INFINITY) {
- return Double.NaN;
- }
-
- /* Perform any argument reduction */
- double xb = 0;
- if (xa > 3294198.0) {
- // PI * (2**20)
- // Argument too big for CodyWaite reduction. Must use
- // PayneHanek.
- double reduceResults[] = new double[3];
- reducePayneHanek(xa, reduceResults);
- quadrant = ((int) reduceResults[0]) & 3;
- xa = reduceResults[1];
- xb = reduceResults[2];
- } else if (xa > 1.5707963267948966) {
- final CodyWaite cw = new CodyWaite(xa);
- quadrant = cw.getK() & 3;
- xa = cw.getRemA();
- xb = cw.getRemB();
- }
-
- //if (negative)
- // quadrant = (quadrant + 2) % 4;
-
- switch (quadrant) {
- case 0:
- return cosQ(xa, xb);
- case 1:
- return -sinQ(xa, xb);
- case 2:
- return -cosQ(xa, xb);
- case 3:
- return sinQ(xa, xb);
- default:
- return Double.NaN;
- }
- }
-
- /**
- * Tangent function.
- *
- * @param x Argument.
- * @return tan(x)
- */
- public static double tan(double x) {
- boolean negative = false;
- int quadrant = 0;
-
- /* Take absolute value of the input */
- double xa = x;
- if (x < 0) {
- negative = true;
- xa = -xa;
- }
-
- /* Check for zero and negative zero */
- if (xa == 0.0) {
- long bits = Double.doubleToRawLongBits(x);
- if (bits < 0) {
- return -0.0;
- }
- return 0.0;
- }
-
- if (xa != xa || xa == Double.POSITIVE_INFINITY) {
- return Double.NaN;
- }
-
- /* Perform any argument reduction */
- double xb = 0;
- if (xa > 3294198.0) {
- // PI * (2**20)
- // Argument too big for CodyWaite reduction. Must use
- // PayneHanek.
- double reduceResults[] = new double[3];
- reducePayneHanek(xa, reduceResults);
- quadrant = ((int) reduceResults[0]) & 3;
- xa = reduceResults[1];
- xb = reduceResults[2];
- } else if (xa > 1.5707963267948966) {
- final CodyWaite cw = new CodyWaite(xa);
- quadrant = cw.getK() & 3;
- xa = cw.getRemA();
- xb = cw.getRemB();
- }
-
- if (xa > 1.5) {
- // Accuracy suffers between 1.5 and PI/2
- final double pi2a = 1.5707963267948966;
- final double pi2b = 6.123233995736766E-17;
-
- final double a = pi2a - xa;
- double b = -(a - pi2a + xa);
- b += pi2b - xb;
-
- xa = a + b;
- xb = -(xa - a - b);
- quadrant ^= 1;
- negative ^= true;
- }
-
- double result;
- if ((quadrant & 1) == 0) {
- result = tanQ(xa, xb, false);
- } else {
- result = -tanQ(xa, xb, true);
- }
-
- if (negative) {
- result = -result;
- }
-
- return result;
- }
-
- /**
- * Arctangent function
- * @param x a number
- * @return atan(x)
- */
- public static double atan(double x) {
- return atan(x, 0.0, false);
- }
-
- /** Internal helper function to compute arctangent.
- * @param xa number from which arctangent is requested
- * @param xb extra bits for x (may be 0.0)
- * @param leftPlane if true, result angle must be put in the left half plane
- * @return atan(xa + xb) (or angle shifted by {@code PI} if leftPlane is true)
- */
- private static double atan(double xa, double xb, boolean leftPlane) {
- if (xa == 0.0) { // Matches +/- 0.0; return correct sign
- return leftPlane ? copySign(Math.PI, xa) : xa;
- }
-
- final boolean negate;
- if (xa < 0) {
- // negative
- xa = -xa;
- xb = -xb;
- negate = true;
- } else {
- negate = false;
- }
-
- if (xa > 1.633123935319537E16) { // Very large input
- return (negate ^ leftPlane) ? (-Math.PI * F_1_2) : (Math.PI * F_1_2);
- }
-
- /* Estimate the closest tabulated arctan value, compute eps = xa-tangentTable */
- final int idx;
- if (xa < 1) {
- idx = (int) (((-1.7168146928204136 * xa * xa + 8.0) * xa) + 0.5);
- } else {
- final double oneOverXa = 1 / xa;
- idx = (int) (-((-1.7168146928204136 * oneOverXa * oneOverXa + 8.0) * oneOverXa) + 13.07);
- }
-
- final double ttA = TANGENT_TABLE_A[idx];
- final double ttB = TANGENT_TABLE_B[idx];
-
- double epsA = xa - ttA;
- double epsB = -(epsA - xa + ttA);
- epsB += xb - ttB;
-
- double temp = epsA + epsB;
- epsB = -(temp - epsA - epsB);
- epsA = temp;
-
- /* Compute eps = eps / (1.0 + xa*tangent) */
- temp = xa * HEX_40000000;
- double ya = xa + temp - temp;
- double yb = xb + xa - ya;
- xa = ya;
- xb += yb;
-
- //if (idx > 8 || idx == 0)
- if (idx == 0) {
- /* If the slope of the arctan is gentle enough (< 0.45), this approximation will suffice */
- //double denom = 1.0 / (1.0 + xa*tangentTableA[idx] + xb*tangentTableA[idx] + xa*tangentTableB[idx] + xb*tangentTableB[idx]);
- final double denom = 1d / (1d + (xa + xb) * (ttA + ttB));
- //double denom = 1.0 / (1.0 + xa*tangentTableA[idx]);
- ya = epsA * denom;
- yb = epsB * denom;
- } else {
- double temp2 = xa * ttA;
- double za = 1d + temp2;
- double zb = -(za - 1d - temp2);
- temp2 = xb * ttA + xa * ttB;
- temp = za + temp2;
- zb += -(temp - za - temp2);
- za = temp;
-
- zb += xb * ttB;
- ya = epsA / za;
-
- temp = ya * HEX_40000000;
- final double yaa = (ya + temp) - temp;
- final double yab = ya - yaa;
-
- temp = za * HEX_40000000;
- final double zaa = (za + temp) - temp;
- final double zab = za - zaa;
-
- /* Correct for rounding in division */
- yb = (epsA - yaa * zaa - yaa * zab - yab * zaa - yab * zab) / za;
-
- yb += -epsA * zb / za / za;
- yb += epsB / za;
- }
-
-
- epsA = ya;
- epsB = yb;
-
- /* Evaluate polynomial */
- final double epsA2 = epsA * epsA;
-
- /*
- yb = -0.09001346640161823;
- yb = yb * epsA2 + 0.11110718400605211;
- yb = yb * epsA2 + -0.1428571349122913;
- yb = yb * epsA2 + 0.19999999999273194;
- yb = yb * epsA2 + -0.33333333333333093;
- yb = yb * epsA2 * epsA;
- */
-
- yb = 0.07490822288864472;
- yb = yb * epsA2 - 0.09088450866185192;
- yb = yb * epsA2 + 0.11111095942313305;
- yb = yb * epsA2 - 0.1428571423679182;
- yb = yb * epsA2 + 0.19999999999923582;
- yb = yb * epsA2 - 0.33333333333333287;
- yb = yb * epsA2 * epsA;
-
-
- ya = epsA;
-
- temp = ya + yb;
- yb = -(temp - ya - yb);
- ya = temp;
-
- /* Add in effect of epsB. atan'(x) = 1/(1+x^2) */
- yb += epsB / (1d + epsA * epsA);
-
- final double eighths = EIGHTHS[idx];
-
- //result = yb + eighths[idx] + ya;
- double za = eighths + ya;
- double zb = -(za - eighths - ya);
- temp = za + yb;
- zb += -(temp - za - yb);
- za = temp;
-
- double result = za + zb;
-
- if (leftPlane) {
- // Result is in the left plane
- final double resultb = -(result - za - zb);
- final double pia = 1.5707963267948966 * 2;
- final double pib = 6.123233995736766E-17 * 2;
-
- za = pia - result;
- zb = -(za - pia + result);
- zb += pib - resultb;
-
- result = za + zb;
- }
-
-
- if (negate ^ leftPlane) {
- result = -result;
- }
-
- return result;
- }
-
- /**
- * Two arguments arctangent function
- * @param y ordinate
- * @param x abscissa
- * @return phase angle of point (x,y) between {@code -PI} and {@code PI}
- */
- public static double atan2(double y, double x) {
- if (Double.isNaN(x) || Double.isNaN(y)) {
- return Double.NaN;
- }
-
- if (y == 0) {
- final double result = x * y;
- final double invx = 1d / x;
- final double invy = 1d / y;
-
- if (invx == 0) { // X is infinite
- if (x > 0) {
- return y; // return +/- 0.0
- } else {
- return copySign(Math.PI, y);
- }
- }
-
- if (x < 0 || invx < 0) {
- if (y < 0 || invy < 0) {
- return -Math.PI;
- } else {
- return Math.PI;
- }
- } else {
- return result;
- }
- }
-
- // y cannot now be zero
-
- if (y == Double.POSITIVE_INFINITY) {
- if (x == Double.POSITIVE_INFINITY) {
- return Math.PI * F_1_4;
- }
-
- if (x == Double.NEGATIVE_INFINITY) {
- return Math.PI * F_3_4;
- }
-
- return Math.PI * F_1_2;
- }
-
- if (y == Double.NEGATIVE_INFINITY) {
- if (x == Double.POSITIVE_INFINITY) {
- return -Math.PI * F_1_4;
- }
-
- if (x == Double.NEGATIVE_INFINITY) {
- return -Math.PI * F_3_4;
- }
-
- return -Math.PI * F_1_2;
- }
-
- if (x == Double.POSITIVE_INFINITY) {
- if (y > 0 || 1 / y > 0) {
- return 0d;
- }
-
- if (y < 0 || 1 / y < 0) {
- return -0d;
- }
- }
-
- if (x == Double.NEGATIVE_INFINITY)
- {
- if (y > 0.0 || 1 / y > 0.0) {
- return Math.PI;
- }
-
- if (y < 0 || 1 / y < 0) {
- return -Math.PI;
- }
- }
-
- // Neither y nor x can be infinite or NAN here
-
- if (x == 0) {
- if (y > 0 || 1 / y > 0) {
- return Math.PI * F_1_2;
- }
-
- if (y < 0 || 1 / y < 0) {
- return -Math.PI * F_1_2;
- }
- }
-
- // Compute ratio r = y/x
- final double r = y / x;
- if (Double.isInfinite(r)) { // bypass calculations that can create NaN
- return atan(r, 0, x < 0);
- }
-
- double ra = doubleHighPart(r);
- double rb = r - ra;
-
- // Split x
- final double xa = doubleHighPart(x);
- final double xb = x - xa;
-
- rb += (y - ra * xa - ra * xb - rb * xa - rb * xb) / x;
-
- final double temp = ra + rb;
- rb = -(temp - ra - rb);
- ra = temp;
-
- if (ra == 0) { // Fix up the sign so atan works correctly
- ra = copySign(0d, y);
- }
-
- // Call atan
- final double result = atan(ra, rb, x < 0);
-
- return result;
- }
-
- /** Compute the arc sine of a number.
- * @param x number on which evaluation is done
- * @return arc sine of x
- */
- public static double asin(double x) {
- if (Double.isNaN(x)) {
- return Double.NaN;
- }
-
- if (x > 1.0 || x < -1.0) {
- return Double.NaN;
- }
-
- if (x == 1.0) {
- return Math.PI/2.0;
- }
-
- if (x == -1.0) {
- return -Math.PI/2.0;
- }
-
- if (x == 0.0) { // Matches +/- 0.0; return correct sign
- return x;
- }
-
- /* Compute asin(x) = atan(x/sqrt(1-x*x)) */
-
- /* Split x */
- double temp = x * HEX_40000000;
- final double xa = x + temp - temp;
- final double xb = x - xa;
-
- /* Square it */
- double ya = xa*xa;
- double yb = xa*xb*2.0 + xb*xb;
-
- /* Subtract from 1 */
- ya = -ya;
- yb = -yb;
-
- double za = 1.0 + ya;
- double zb = -(za - 1.0 - ya);
-
- temp = za + yb;
- zb += -(temp - za - yb);
- za = temp;
-
- /* Square root */
- double y;
- y = sqrt(za);
- temp = y * HEX_40000000;
- ya = y + temp - temp;
- yb = y - ya;
-
- /* Extend precision of sqrt */
- yb += (za - ya*ya - 2*ya*yb - yb*yb) / (2.0*y);
-
- /* Contribution of zb to sqrt */
- double dx = zb / (2.0*y);
-
- // Compute ratio r = x/y
- double r = x/y;
- temp = r * HEX_40000000;
- double ra = r + temp - temp;
- double rb = r - ra;
-
- rb += (x - ra*ya - ra*yb - rb*ya - rb*yb) / y; // Correct for rounding in division
- rb += -x * dx / y / y; // Add in effect additional bits of sqrt.
-
- temp = ra + rb;
- rb = -(temp - ra - rb);
- ra = temp;
-
- return atan(ra, rb, false);
- }
-
- /** Compute the arc cosine of a number.
- * @param x number on which evaluation is done
- * @return arc cosine of x
- */
- public static double acos(double x) {
- if (Double.isNaN(x)) {
- return Double.NaN;
- }
-
- if (x > 1.0 || x < -1.0) {
- return Double.NaN;
- }
-
- if (x == -1.0) {
- return Math.PI;
- }
-
- if (x == 1.0) {
- return 0.0;
- }
-
- if (x == 0) {
- return Math.PI/2.0;
- }
-
- /* Compute acos(x) = atan(sqrt(1-x*x)/x) */
-
- /* Split x */
- double temp = x * HEX_40000000;
- final double xa = x + temp - temp;
- final double xb = x - xa;
-
- /* Square it */
- double ya = xa*xa;
- double yb = xa*xb*2.0 + xb*xb;
-
- /* Subtract from 1 */
- ya = -ya;
- yb = -yb;
-
- double za = 1.0 + ya;
- double zb = -(za - 1.0 - ya);
-
- temp = za + yb;
- zb += -(temp - za - yb);
- za = temp;
-
- /* Square root */
- double y = sqrt(za);
- temp = y * HEX_40000000;
- ya = y + temp - temp;
- yb = y - ya;
-
- /* Extend precision of sqrt */
- yb += (za - ya*ya - 2*ya*yb - yb*yb) / (2.0*y);
-
- /* Contribution of zb to sqrt */
- yb += zb / (2.0*y);
- y = ya+yb;
- yb = -(y - ya - yb);
-
- // Compute ratio r = y/x
- double r = y/x;
-
- // Did r overflow?
- if (Double.isInfinite(r)) { // x is effectively zero
- return Math.PI/2; // so return the appropriate value
- }
-
- double ra = doubleHighPart(r);
- double rb = r - ra;
-
- rb += (y - ra*xa - ra*xb - rb*xa - rb*xb) / x; // Correct for rounding in division
- rb += yb / x; // Add in effect additional bits of sqrt.
-
- temp = ra + rb;
- rb = -(temp - ra - rb);
- ra = temp;
-
- return atan(ra, rb, x<0);
- }
-
- /** Compute the cubic root of a number.
- * @param x number on which evaluation is done
- * @return cubic root of x
- */
- public static double cbrt(double x) {
- /* Convert input double to bits */
- long inbits = Double.doubleToRawLongBits(x);
- int exponent = (int) ((inbits >> 52) & 0x7ff) - 1023;
- boolean subnormal = false;
-
- if (exponent == -1023) {
- if (x == 0) {
- return x;
- }
-
- /* Subnormal, so normalize */
- subnormal = true;
- x *= 1.8014398509481984E16; // 2^54
- inbits = Double.doubleToRawLongBits(x);
- exponent = (int) ((inbits >> 52) & 0x7ff) - 1023;
- }
-
- if (exponent == 1024) {
- // Nan or infinity. Don't care which.
- return x;
- }
-
- /* Divide the exponent by 3 */
- int exp3 = exponent / 3;
-
- /* p2 will be the nearest power of 2 to x with its exponent divided by 3 */
- double p2 = Double.longBitsToDouble((inbits & 0x8000000000000000L) |
- (long)(((exp3 + 1023) & 0x7ff)) << 52);
-
- /* This will be a number between 1 and 2 */
- final double mant = Double.longBitsToDouble((inbits & 0x000fffffffffffffL) | 0x3ff0000000000000L);
-
- /* Estimate the cube root of mant by polynomial */
- double est = -0.010714690733195933;
- est = est * mant + 0.0875862700108075;
- est = est * mant + -0.3058015757857271;
- est = est * mant + 0.7249995199969751;
- est = est * mant + 0.5039018405998233;
-
- est *= CBRTTWO[exponent % 3 + 2];
-
- // est should now be good to about 15 bits of precision. Do 2 rounds of
- // Newton's method to get closer, this should get us full double precision
- // Scale down x for the purpose of doing newtons method. This avoids over/under flows.
- final double xs = x / (p2*p2*p2);
- est += (xs - est*est*est) / (3*est*est);
- est += (xs - est*est*est) / (3*est*est);
-
- // Do one round of Newton's method in extended precision to get the last bit right.
- double temp = est * HEX_40000000;
- double ya = est + temp - temp;
- double yb = est - ya;
-
- double za = ya * ya;
- double zb = ya * yb * 2.0 + yb * yb;
- temp = za * HEX_40000000;
- double temp2 = za + temp - temp;
- zb += za - temp2;
- za = temp2;
-
- zb = za * yb + ya * zb + zb * yb;
- za *= ya;
-
- double na = xs - za;
- double nb = -(na - xs + za);
- nb -= zb;
-
- est += (na+nb)/(3*est*est);
-
- /* Scale by a power of two, so this is exact. */
- est *= p2;
-
- if (subnormal) {
- est *= 3.814697265625E-6; // 2^-18
- }
-
- return est;
- }
-
- /**
- * Convert degrees to radians, with error of less than 0.5 ULP
- * @param x angle in degrees
- * @return x converted into radians
- */
- public static double toRadians(double x)
- {
- if (Double.isInfinite(x) || x == 0.0) { // Matches +/- 0.0; return correct sign
- return x;
- }
-
- // These are PI/180 split into high and low order bits
- final double facta = 0.01745329052209854;
- final double factb = 1.997844754509471E-9;
-
- double xa = doubleHighPart(x);
- double xb = x - xa;
-
- double result = xb * factb + xb * facta + xa * factb + xa * facta;
- if (result == 0) {
- result *= x; // ensure correct sign if calculation underflows
- }
- return result;
- }
-
- /**
- * Convert radians to degrees, with error of less than 0.5 ULP
- * @param x angle in radians
- * @return x converted into degrees
- */
- public static double toDegrees(double x)
- {
- if (Double.isInfinite(x) || x == 0.0) { // Matches +/- 0.0; return correct sign
- return x;
- }
-
- // These are 180/PI split into high and low order bits
- final double facta = 57.2957763671875;
- final double factb = 3.145894820876798E-6;
-
- double xa = doubleHighPart(x);
- double xb = x - xa;
-
- return xb * factb + xb * facta + xa * factb + xa * facta;
- }
-
- /**
- * Absolute value.
- * @param x number from which absolute value is requested
- * @return abs(x)
- */
- public static int abs(final int x) {
- final int i = x >>> 31;
- return (x ^ (~i + 1)) + i;
- }
-
- /**
- * Absolute value.
- * @param x number from which absolute value is requested
- * @return abs(x)
- */
- public static long abs(final long x) {
- final long l = x >>> 63;
- // l is one if x negative zero else
- // ~l+1 is zero if x is positive, -1 if x is negative
- // x^(~l+1) is x is x is positive, ~x if x is negative
- // add around
- return (x ^ (~l + 1)) + l;
- }
-
- /**
- * Absolute value.
- * @param x number from which absolute value is requested
- * @return abs(x)
- */
- public static float abs(final float x) {
- return Float.intBitsToFloat(MASK_NON_SIGN_INT & Float.floatToRawIntBits(x));
- }
-
- /**
- * Absolute value.
- * @param x number from which absolute value is requested
- * @return abs(x)
- */
- public static double abs(double x) {
- return Double.longBitsToDouble(MASK_NON_SIGN_LONG & Double.doubleToRawLongBits(x));
- }
-
- /**
- * Compute least significant bit (Unit in Last Position) for a number.
- * @param x number from which ulp is requested
- * @return ulp(x)
- */
- public static double ulp(double x) {
- if (Double.isInfinite(x)) {
- return Double.POSITIVE_INFINITY;
- }
- return abs(x - Double.longBitsToDouble(Double.doubleToRawLongBits(x) ^ 1));
- }
-
- /**
- * Compute least significant bit (Unit in Last Position) for a number.
- * @param x number from which ulp is requested
- * @return ulp(x)
- */
- public static float ulp(float x) {
- if (Float.isInfinite(x)) {
- return Float.POSITIVE_INFINITY;
- }
- return abs(x - Float.intBitsToFloat(Float.floatToIntBits(x) ^ 1));
- }
-
- /**
- * Multiply a double number by a power of 2.
- * @param d number to multiply
- * @param n power of 2
- * @return d × 2<sup>n</sup>
- */
- public static double scalb(final double d, final int n) {
-
- // first simple and fast handling when 2^n can be represented using normal numbers
- if ((n > -1023) && (n < 1024)) {
- return d * Double.longBitsToDouble(((long) (n + 1023)) << 52);
- }
-
- // handle special cases
- if (Double.isNaN(d) || Double.isInfinite(d) || (d == 0)) {
- return d;
- }
- if (n < -2098) {
- return (d > 0) ? 0.0 : -0.0;
- }
- if (n > 2097) {
- return (d > 0) ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY;
- }
-
- // decompose d
- final long bits = Double.doubleToRawLongBits(d);
- final long sign = bits & 0x8000000000000000L;
- int exponent = ((int) (bits >>> 52)) & 0x7ff;
- long mantissa = bits & 0x000fffffffffffffL;
-
- // compute scaled exponent
- int scaledExponent = exponent + n;
-
- if (n < 0) {
- // we are really in the case n <= -1023
- if (scaledExponent > 0) {
- // both the input and the result are normal numbers, we only adjust the exponent
- return Double.longBitsToDouble(sign | (((long) scaledExponent) << 52) | mantissa);
- } else if (scaledExponent > -53) {
- // the input is a normal number and the result is a subnormal number
-
- // recover the hidden mantissa bit
- mantissa |= 1L << 52;
-
- // scales down complete mantissa, hence losing least significant bits
- final long mostSignificantLostBit = mantissa & (1L << (-scaledExponent));
- mantissa >>>= 1 - scaledExponent;
- if (mostSignificantLostBit != 0) {
- // we need to add 1 bit to round up the result
- mantissa++;
- }
- return Double.longBitsToDouble(sign | mantissa);
-
- } else {
- // no need to compute the mantissa, the number scales down to 0
- return (sign == 0L) ? 0.0 : -0.0;
- }
- } else {
- // we are really in the case n >= 1024
- if (exponent == 0) {
-
- // the input number is subnormal, normalize it
- while ((mantissa >>> 52) != 1) {
- mantissa <<= 1;
- --scaledExponent;
- }
- ++scaledExponent;
- mantissa &= 0x000fffffffffffffL;
-
- if (scaledExponent < 2047) {
- return Double.longBitsToDouble(sign | (((long) scaledExponent) << 52) | mantissa);
- } else {
- return (sign == 0L) ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY;
- }
-
- } else if (scaledExponent < 2047) {
- return Double.longBitsToDouble(sign | (((long) scaledExponent) << 52) | mantissa);
- } else {
- return (sign == 0L) ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY;
- }
- }
-
- }
-
- /**
- * Multiply a float number by a power of 2.
- * @param f number to multiply
- * @param n power of 2
- * @return f × 2<sup>n</sup>
- */
- public static float scalb(final float f, final int n) {
-
- // first simple and fast handling when 2^n can be represented using normal numbers
- if ((n > -127) && (n < 128)) {
- return f * Float.intBitsToFloat((n + 127) << 23);
- }
-
- // handle special cases
- if (Float.isNaN(f) || Float.isInfinite(f) || (f == 0f)) {
- return f;
- }
- if (n < -277) {
- return (f > 0) ? 0.0f : -0.0f;
- }
- if (n > 276) {
- return (f > 0) ? Float.POSITIVE_INFINITY : Float.NEGATIVE_INFINITY;
- }
-
- // decompose f
- final int bits = Float.floatToIntBits(f);
- final int sign = bits & 0x80000000;
- int exponent = (bits >>> 23) & 0xff;
- int mantissa = bits & 0x007fffff;
-
- // compute scaled exponent
- int scaledExponent = exponent + n;
-
- if (n < 0) {
- // we are really in the case n <= -127
- if (scaledExponent > 0) {
- // both the input and the result are normal numbers, we only adjust the exponent
- return Float.intBitsToFloat(sign | (scaledExponent << 23) | mantissa);
- } else if (scaledExponent > -24) {
- // the input is a normal number and the result is a subnormal number
-
- // recover the hidden mantissa bit
- mantissa |= 1 << 23;
-
- // scales down complete mantissa, hence losing least significant bits
- final int mostSignificantLostBit = mantissa & (1 << (-scaledExponent));
- mantissa >>>= 1 - scaledExponent;
- if (mostSignificantLostBit != 0) {
- // we need to add 1 bit to round up the result
- mantissa++;
- }
- return Float.intBitsToFloat(sign | mantissa);
-
- } else {
- // no need to compute the mantissa, the number scales down to 0
- return (sign == 0) ? 0.0f : -0.0f;
- }
- } else {
- // we are really in the case n >= 128
- if (exponent == 0) {
-
- // the input number is subnormal, normalize it
- while ((mantissa >>> 23) != 1) {
- mantissa <<= 1;
- --scaledExponent;
- }
- ++scaledExponent;
- mantissa &= 0x007fffff;
-
- if (scaledExponent < 255) {
- return Float.intBitsToFloat(sign | (scaledExponent << 23) | mantissa);
- } else {
- return (sign == 0) ? Float.POSITIVE_INFINITY : Float.NEGATIVE_INFINITY;
- }
-
- } else if (scaledExponent < 255) {
- return Float.intBitsToFloat(sign | (scaledExponent << 23) | mantissa);
- } else {
- return (sign == 0) ? Float.POSITIVE_INFINITY : Float.NEGATIVE_INFINITY;
- }
- }
-
- }
-
- /**
- * Get the next machine representable number after a number, moving
- * in the direction of another number.
- * <p>
- * The ordering is as follows (increasing):
- * <ul>
- * <li>-INFINITY</li>
- * <li>-MAX_VALUE</li>
- * <li>-MIN_VALUE</li>
- * <li>-0.0</li>
- * <li>+0.0</li>
- * <li>+MIN_VALUE</li>
- * <li>+MAX_VALUE</li>
- * <li>+INFINITY</li>
- * <li></li>
- * </ul>
- * <p>
- * If arguments compare equal, then the second argument is returned.
- * <p>
- * If {@code direction} is greater than {@code d},
- * the smallest machine representable number strictly greater than
- * {@code d} is returned; if less, then the largest representable number
- * strictly less than {@code d} is returned.</p>
- * <p>
- * If {@code d} is infinite and direction does not
- * bring it back to finite numbers, it is returned unchanged.</p>
- *
- * @param d base number
- * @param direction (the only important thing is whether
- * {@code direction} is greater or smaller than {@code d})
- * @return the next machine representable number in the specified direction
- */
- public static double nextAfter(double d, double direction) {
-
- // handling of some important special cases
- if (Double.isNaN(d) || Double.isNaN(direction)) {
- return Double.NaN;
- } else if (d == direction) {
- return direction;
- } else if (Double.isInfinite(d)) {
- return (d < 0) ? -Double.MAX_VALUE : Double.MAX_VALUE;
- } else if (d == 0) {
- return (direction < 0) ? -Double.MIN_VALUE : Double.MIN_VALUE;
- }
- // special cases MAX_VALUE to infinity and MIN_VALUE to 0
- // are handled just as normal numbers
- // can use raw bits since already dealt with infinity and NaN
- final long bits = Double.doubleToRawLongBits(d);
- final long sign = bits & 0x8000000000000000L;
- if ((direction < d) ^ (sign == 0L)) {
- return Double.longBitsToDouble(sign | ((bits & 0x7fffffffffffffffL) + 1));
- } else {
- return Double.longBitsToDouble(sign | ((bits & 0x7fffffffffffffffL) - 1));
- }
-
- }
-
- /**
- * Get the next machine representable number after a number, moving
- * in the direction of another number.
- * <p>
- * The ordering is as follows (increasing):
- * <ul>
- * <li>-INFINITY</li>
- * <li>-MAX_VALUE</li>
- * <li>-MIN_VALUE</li>
- * <li>-0.0</li>
- * <li>+0.0</li>
- * <li>+MIN_VALUE</li>
- * <li>+MAX_VALUE</li>
- * <li>+INFINITY</li>
- * <li></li>
- * </ul>
- * <p>
- * If arguments compare equal, then the second argument is returned.
- * <p>
- * If {@code direction} is greater than {@code f},
- * the smallest machine representable number strictly greater than
- * {@code f} is returned; if less, then the largest representable number
- * strictly less than {@code f} is returned.</p>
- * <p>
- * If {@code f} is infinite and direction does not
- * bring it back to finite numbers, it is returned unchanged.</p>
- *
- * @param f base number
- * @param direction (the only important thing is whether
- * {@code direction} is greater or smaller than {@code f})
- * @return the next machine representable number in the specified direction
- */
- public static float nextAfter(final float f, final double direction) {
-
- // handling of some important special cases
- if (Double.isNaN(f) || Double.isNaN(direction)) {
- return Float.NaN;
- } else if (f == direction) {
- return (float) direction;
- } else if (Float.isInfinite(f)) {
- return (f < 0f) ? -Float.MAX_VALUE : Float.MAX_VALUE;
- } else if (f == 0f) {
- return (direction < 0) ? -Float.MIN_VALUE : Float.MIN_VALUE;
- }
- // special cases MAX_VALUE to infinity and MIN_VALUE to 0
- // are handled just as normal numbers
-
- final int bits = Float.floatToIntBits(f);
- final int sign = bits & 0x80000000;
- if ((direction < f) ^ (sign == 0)) {
- return Float.intBitsToFloat(sign | ((bits & 0x7fffffff) + 1));
- } else {
- return Float.intBitsToFloat(sign | ((bits & 0x7fffffff) - 1));
- }
-
- }
-
- /** Get the largest whole number smaller than x.
- * @param x number from which floor is requested
- * @return a double number f such that f is an integer f <= x < f + 1.0
- */
- public static double floor(double x) {
- long y;
-
- if (Double.isNaN(x)) {
- return x;
- }
-
- if (x >= TWO_POWER_52 || x <= -TWO_POWER_52) {
- return x;
- }
-
- y = (long) x;
- if (x < 0 && y != x) {
- y--;
- }
-
- if (y == 0) {
- return x*y;
- }
-
- return y;
- }
-
- /** Get the smallest whole number larger than x.
- * @param x number from which ceil is requested
- * @return a double number c such that c is an integer c - 1.0 < x <= c
- */
- public static double ceil(double x) {
- double y;
-
- if (Double.isNaN(x)) {
- return x;
- }
-
- y = floor(x);
- if (y == x) {
- return y;
- }
-
- y += 1.0;
-
- if (y == 0) {
- return x*y;
- }
-
- return y;
- }
-
- /** Get the whole number that is the nearest to x, or the even one if x is exactly half way between two integers.
- * @param x number from which nearest whole number is requested
- * @return a double number r such that r is an integer r - 0.5 <= x <= r + 0.5
- */
- public static double rint(double x) {
- double y = floor(x);
- double d = x - y;
-
- if (d > 0.5) {
- if (y == -1.0) {
- return -0.0; // Preserve sign of operand
- }
- return y+1.0;
- }
- if (d < 0.5) {
- return y;
- }
-
- /* half way, round to even */
- long z = (long) y;
- return (z & 1) == 0 ? y : y + 1.0;
- }
-
- /** Get the closest long to x.
- * @param x number from which closest long is requested
- * @return closest long to x
- */
- public static long round(double x) {
- final long bits = Double.doubleToRawLongBits(x);
- final int biasedExp = ((int)(bits>>52)) & 0x7ff;
- // Shift to get rid of bits past comma except first one: will need to
- // 1-shift to the right to end up with correct magnitude.
- final int shift = (52 - 1 + Double.MAX_EXPONENT) - biasedExp;
- if ((shift & -64) == 0) {
- // shift in [0,63], so unbiased exp in [-12,51].
- long extendedMantissa = 0x0010000000000000L | (bits & 0x000fffffffffffffL);
- if (bits < 0) {
- extendedMantissa = -extendedMantissa;
- }
- // If value is positive and first bit past comma is 0, rounding
- // to lower integer, else to upper one, which is what "+1" and
- // then ">>1" do.
- return ((extendedMantissa >> shift) + 1L) >> 1;
- } else {
- // +-Infinity, NaN, or a mathematical integer.
- return (long) x;
- }
- }
-
- /** Get the closest int to x.
- * @param x number from which closest int is requested
- * @return closest int to x
- */
- public static int round(final float x) {
- final int bits = Float.floatToRawIntBits(x);
- final int biasedExp = (bits>>23) & 0xff;
- // Shift to get rid of bits past comma except first one: will need to
- // 1-shift to the right to end up with correct magnitude.
- final int shift = (23 - 1 + Float.MAX_EXPONENT) - biasedExp;
- if ((shift & -32) == 0) {
- // shift in [0,31], so unbiased exp in [-9,22].
- int extendedMantissa = 0x00800000 | (bits & 0x007fffff);
- if (bits < 0) {
- extendedMantissa = -extendedMantissa;
- }
- // If value is positive and first bit past comma is 0, rounding
- // to lower integer, else to upper one, which is what "+1" and
- // then ">>1" do.
- return ((extendedMantissa >> shift) + 1) >> 1;
- } else {
- // +-Infinity, NaN, or a mathematical integer.
- return (int) x;
- }
- }
-
- /** Compute the minimum of two values
- * @param a first value
- * @param b second value
- * @return a if a is lesser or equal to b, b otherwise
- */
- public static int min(final int a, final int b) {
- return (a <= b) ? a : b;
- }
-
- /** Compute the minimum of two values
- * @param a first value
- * @param b second value
- * @return a if a is lesser or equal to b, b otherwise
- */
- public static long min(final long a, final long b) {
- return (a <= b) ? a : b;
- }
-
- /** Compute the minimum of two values
- * @param a first value
- * @param b second value
- * @return a if a is lesser or equal to b, b otherwise
- */
- public static float min(final float a, final float b) {
- if (a > b) {
- return b;
- }
- if (a < b) {
- return a;
- }
- /* if either arg is NaN, return NaN */
- if (a != b) {
- return Float.NaN;
- }
- /* min(+0.0,-0.0) == -0.0 */
- /* 0x80000000 == Float.floatToRawIntBits(-0.0d) */
- int bits = Float.floatToRawIntBits(a);
- if (bits == 0x80000000) {
- return a;
- }
- return b;
- }
-
- /** Compute the minimum of two values
- * @param a first value
- * @param b second value
- * @return a if a is lesser or equal to b, b otherwise
- */
- public static double min(final double a, final double b) {
- if (a > b) {
- return b;
- }
- if (a < b) {
- return a;
- }
- /* if either arg is NaN, return NaN */
- if (a != b) {
- return Double.NaN;
- }
- /* min(+0.0,-0.0) == -0.0 */
- /* 0x8000000000000000L == Double.doubleToRawLongBits(-0.0d) */
- long bits = Double.doubleToRawLongBits(a);
- if (bits == 0x8000000000000000L) {
- return a;
- }
- return b;
- }
-
- /** Compute the maximum of two values
- * @param a first value
- * @param b second value
- * @return b if a is lesser or equal to b, a otherwise
- */
- public static int max(final int a, final int b) {
- return (a <= b) ? b : a;
- }
-
- /** Compute the maximum of two values
- * @param a first value
- * @param b second value
- * @return b if a is lesser or equal to b, a otherwise
- */
- public static long max(final long a, final long b) {
- return (a <= b) ? b : a;
- }
-
- /** Compute the maximum of two values
- * @param a first value
- * @param b second value
- * @return b if a is lesser or equal to b, a otherwise
- */
- public static float max(final float a, final float b) {
- if (a > b) {
- return a;
- }
- if (a < b) {
- return b;
- }
- /* if either arg is NaN, return NaN */
- if (a != b) {
- return Float.NaN;
- }
- /* min(+0.0,-0.0) == -0.0 */
- /* 0x80000000 == Float.floatToRawIntBits(-0.0d) */
- int bits = Float.floatToRawIntBits(a);
- if (bits == 0x80000000) {
- return b;
- }
- return a;
- }
-
- /** Compute the maximum of two values
- * @param a first value
- * @param b second value
- * @return b if a is lesser or equal to b, a otherwise
- */
- public static double max(final double a, final double b) {
- if (a > b) {
- return a;
- }
- if (a < b) {
- return b;
- }
- /* if either arg is NaN, return NaN */
- if (a != b) {
- return Double.NaN;
- }
- /* min(+0.0,-0.0) == -0.0 */
- /* 0x8000000000000000L == Double.doubleToRawLongBits(-0.0d) */
- long bits = Double.doubleToRawLongBits(a);
- if (bits == 0x8000000000000000L) {
- return b;
- }
- return a;
- }
-
- /**
- * Returns the hypotenuse of a triangle with sides {@code x} and {@code y}
- * - sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)<br>
- * avoiding intermediate overflow or underflow.
- *
- * <ul>
- * <li> If either argument is infinite, then the result is positive infinity.</li>
- * <li> else, if either argument is NaN then the result is NaN.</li>
- * </ul>
- *
- * @param x a value
- * @param y a value
- * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
- */
- public static double hypot(final double x, final double y) {
- if (Double.isInfinite(x) || Double.isInfinite(y)) {
- return Double.POSITIVE_INFINITY;
- } else if (Double.isNaN(x) || Double.isNaN(y)) {
- return Double.NaN;
- } else {
-
- final int expX = getExponent(x);
- final int expY = getExponent(y);
- if (expX > expY + 27) {
- // y is neglectible with respect to x
- return abs(x);
- } else if (expY > expX + 27) {
- // x is neglectible with respect to y
- return abs(y);
- } else {
-
- // find an intermediate scale to avoid both overflow and underflow
- final int middleExp = (expX + expY) / 2;
-
- // scale parameters without losing precision
- final double scaledX = scalb(x, -middleExp);
- final double scaledY = scalb(y, -middleExp);
-
- // compute scaled hypotenuse
- final double scaledH = sqrt(scaledX * scaledX + scaledY * scaledY);
-
- // remove scaling
- return scalb(scaledH, middleExp);
-
- }
-
- }
- }
-
- /**
- * Computes the remainder as prescribed by the IEEE 754 standard.
- * The remainder value is mathematically equal to {@code x - y*n}
- * where {@code n} is the mathematical integer closest to the exact mathematical value
- * of the quotient {@code x/y}.
- * If two mathematical integers are equally close to {@code x/y} then
- * {@code n} is the integer that is even.
- * <ul>
- * <li>If either operand is NaN, the result is NaN.</li>
- * <li>If the result is not NaN, the sign of the result equals the sign of the dividend.</li>
- * <li>If the dividend is an infinity, or the divisor is a zero, or both, the result is NaN.</li>
- * <li>If the dividend is finite and the divisor is an infinity, the result equals the dividend.</li>
- * <li>If the dividend is a zero and the divisor is finite, the result equals the dividend.</li>
- * </ul>
- * @param dividend the number to be divided
- * @param divisor the number by which to divide
- * @return the remainder, rounded
- */
- public static double IEEEremainder(final double dividend, final double divisor) {
- if (getExponent(dividend) == 1024 || getExponent(divisor) == 1024 || divisor == 0.0) {
- // we are in one of the special cases
- if (Double.isInfinite(divisor) && !Double.isInfinite(dividend)) {
- return dividend;
- } else {
- return Double.NaN;
- }
- } else {
- // we are in the general case
- final double n = AccurateMath.rint(dividend / divisor);
- final double remainder = Double.isInfinite(n) ? 0.0 : dividend - divisor * n;
- return (remainder == 0) ? AccurateMath.copySign(remainder, dividend) : remainder;
- }
- }
-
- /** Convert a long to integer, detecting overflows
- * @param n number to convert to int
- * @return integer with same value as n if no overflows occur
- * @exception MathArithmeticException if n cannot fit into an int
- * @since 3.4
- */
- public static int toIntExact(final long n) throws MathArithmeticException {
- if (n < Integer.MIN_VALUE || n > Integer.MAX_VALUE) {
- throw new MathArithmeticException(LocalizedFormats.OVERFLOW);
- }
- return (int) n;
- }
-
- /** Increment a number, detecting overflows.
- * @param n number to increment
- * @return n+1 if no overflows occur
- * @exception MathArithmeticException if an overflow occurs
- * @since 3.4
- */
- public static int incrementExact(final int n) throws MathArithmeticException {
-
- if (n == Integer.MAX_VALUE) {
- throw new MathArithmeticException(LocalizedFormats.OVERFLOW_IN_ADDITION, n, 1);
- }
-
- return n + 1;
-
- }
-
- /** Increment a number, detecting overflows.
- * @param n number to increment
- * @return n+1 if no overflows occur
- * @exception MathArithmeticException if an overflow occurs
- * @since 3.4
- */
- public static long incrementExact(final long n) throws MathArithmeticException {
-
- if (n == Long.MAX_VALUE) {
- throw new MathArithmeticException(LocalizedFormats.OVERFLOW_IN_ADDITION, n, 1);
- }
-
- return n + 1;
-
- }
-
- /** Decrement a number, detecting overflows.
- * @param n number to decrement
- * @return n-1 if no overflows occur
- * @exception MathArithmeticException if an overflow occurs
- * @since 3.4
- */
- public static int decrementExact(final int n) throws MathArithmeticException {
-
- if (n == Integer.MIN_VALUE) {
- throw new MathArithmeticException(LocalizedFormats.OVERFLOW_IN_SUBTRACTION, n, 1);
- }
-
- return n - 1;
-
- }
-
- /** Decrement a number, detecting overflows.
- * @param n number to decrement
- * @return n-1 if no overflows occur
- * @exception MathArithmeticException if an overflow occurs
- * @since 3.4
- */
- public static long decrementExact(final long n) throws MathArithmeticException {
-
- if (n == Long.MIN_VALUE) {
- throw new MathArithmeticException(LocalizedFormats.OVERFLOW_IN_SUBTRACTION, n, 1);
- }
-
- return n - 1;
-
- }
-
- /** Add two numbers, detecting overflows.
- * @param a first number to add
- * @param b second number to add
- * @return a+b if no overflows occur
- * @exception MathArithmeticException if an overflow occurs
- * @since 3.4
- */
- public static int addExact(final int a, final int b) throws MathArithmeticException {
-
- // compute sum
- final int sum = a + b;
-
- // check for overflow
- if ((a ^ b) >= 0 && (sum ^ b) < 0) {
- throw new MathArithmeticException(LocalizedFormats.OVERFLOW_IN_ADDITION, a, b);
- }
-
- return sum;
-
- }
-
- /** Add two numbers, detecting overflows.
- * @param a first number to add
- * @param b second number to add
- * @return a+b if no overflows occur
- * @exception MathArithmeticException if an overflow occurs
- * @since 3.4
- */
- public static long addExact(final long a, final long b) throws MathArithmeticException {
-
- // compute sum
- final long sum = a + b;
-
- // check for overflow
- if ((a ^ b) >= 0 && (sum ^ b) < 0) {
- throw new MathArithmeticException(LocalizedFormats.OVERFLOW_IN_ADDITION, a, b);
- }
-
- return sum;
-
- }
-
- /** Subtract two numbers, detecting overflows.
- * @param a first number
- * @param b second number to subtract from a
- * @return a-b if no overflows occur
- * @exception MathArithmeticException if an overflow occurs
- * @since 3.4
- */
- public static int subtractExact(final int a, final int b) {
-
- // compute subtraction
- final int sub = a - b;
-
- // check for overflow
- if ((a ^ b) < 0 && (sub ^ b) >= 0) {
- throw new MathArithmeticException(LocalizedFormats.OVERFLOW_IN_SUBTRACTION, a, b);
- }
-
- return sub;
-
- }
-
- /** Subtract two numbers, detecting overflows.
- * @param a first number
- * @param b second number to subtract from a
- * @return a-b if no overflows occur
- * @exception MathArithmeticException if an overflow occurs
- * @since 3.4
- */
- public static long subtractExact(final long a, final long b) {
-
- // compute subtraction
- final long sub = a - b;
-
- // check for overflow
- if ((a ^ b) < 0 && (sub ^ b) >= 0) {
- throw new MathArithmeticException(LocalizedFormats.OVERFLOW_IN_SUBTRACTION, a, b);
- }
-
- return sub;
-
- }
-
- /** Multiply two numbers, detecting overflows.
- * @param a first number to multiply
- * @param b second number to multiply
- * @return a*b if no overflows occur
- * @exception MathArithmeticException if an overflow occurs
- * @since 3.4
- */
- public static int multiplyExact(final int a, final int b) {
- if (((b > 0) && (a > Integer.MAX_VALUE / b || a < Integer.MIN_VALUE / b)) ||
- ((b < -1) && (a > Integer.MIN_VALUE / b || a < Integer.MAX_VALUE / b)) ||
- ((b == -1) && (a == Integer.MIN_VALUE))) {
- throw new MathArithmeticException(LocalizedFormats.OVERFLOW_IN_MULTIPLICATION, a, b);
- }
- return a * b;
- }
-
- /** Multiply two numbers, detecting overflows.
- * @param a first number to multiply
- * @param b second number to multiply
- * @return a*b if no overflows occur
- * @exception MathArithmeticException if an overflow occurs
- * @since 3.4
- */
- public static long multiplyExact(final long a, final long b) {
- if (((b > 0l) && (a > Long.MAX_VALUE / b || a < Long.MIN_VALUE / b)) ||
- ((b < -1l) && (a > Long.MIN_VALUE / b || a < Long.MAX_VALUE / b)) ||
- ((b == -1l) && (a == Long.MIN_VALUE))) {
- throw new MathArithmeticException(LocalizedFormats.OVERFLOW_IN_MULTIPLICATION, a, b);
- }
- return a * b;
- }
-
- /** Finds q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.
- * <p>
- * This methods returns the same value as integer division when
- * a and b are same signs, but returns a different value when
- * they are opposite (i.e. q is negative).
- * </p>
- * @param a dividend
- * @param b divisor
- * @return q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0
- * @exception MathArithmeticException if b == 0
- * @see #floorMod(int, int)
- * @since 3.4
- */
- public static int floorDiv(final int a, final int b) throws MathArithmeticException {
-
- if (b == 0) {
- throw new MathArithmeticException(LocalizedFormats.ZERO_DENOMINATOR);
- }
-
- final int m = a % b;
- if ((a ^ b) >= 0 || m == 0) {
- // a an b have same sign, or division is exact
- return a / b;
- } else {
- // a and b have opposite signs and division is not exact
- return (a / b) - 1;
- }
-
- }
-
- /** Finds q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.
- * <p>
- * This methods returns the same value as integer division when
- * a and b are same signs, but returns a different value when
- * they are opposite (i.e. q is negative).
- * </p>
- * @param a dividend
- * @param b divisor
- * @return q such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0
- * @exception MathArithmeticException if b == 0
- * @see #floorMod(long, long)
- * @since 3.4
- */
- public static long floorDiv(final long a, final long b) throws MathArithmeticException {
-
- if (b == 0l) {
- throw new MathArithmeticException(LocalizedFormats.ZERO_DENOMINATOR);
- }
-
- final long m = a % b;
- if ((a ^ b) >= 0l || m == 0l) {
- // a an b have same sign, or division is exact
- return a / b;
- } else {
- // a and b have opposite signs and division is not exact
- return (a / b) - 1l;
- }
-
- }
-
- /** Finds r such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.
- * <p>
- * This methods returns the same value as integer modulo when
- * a and b are same signs, but returns a different value when
- * they are opposite (i.e. q is negative).
- * </p>
- * @param a dividend
- * @param b divisor
- * @return r such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0
- * @exception MathArithmeticException if b == 0
- * @see #floorDiv(int, int)
- * @since 3.4
- */
- public static int floorMod(final int a, final int b) throws MathArithmeticException {
-
- if (b == 0) {
- throw new MathArithmeticException(LocalizedFormats.ZERO_DENOMINATOR);
- }
-
- final int m = a % b;
- if ((a ^ b) >= 0 || m == 0) {
- // a an b have same sign, or division is exact
- return m;
- } else {
- // a and b have opposite signs and division is not exact
- return b + m;
- }
-
- }
-
- /** Finds r such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0.
- * <p>
- * This methods returns the same value as integer modulo when
- * a and b are same signs, but returns a different value when
- * they are opposite (i.e. q is negative).
- * </p>
- * @param a dividend
- * @param b divisor
- * @return r such that a = q b + r with 0 <= r < b if b > 0 and b < r <= 0 if b < 0
- * @exception MathArithmeticException if b == 0
- * @see #floorDiv(long, long)
- * @since 3.4
- */
- public static long floorMod(final long a, final long b) {
-
- if (b == 0l) {
- throw new MathArithmeticException(LocalizedFormats.ZERO_DENOMINATOR);
- }
-
- final long m = a % b;
- if ((a ^ b) >= 0l || m == 0l) {
- // a an b have same sign, or division is exact
- return m;
- } else {
- // a and b have opposite signs and division is not exact
- return b + m;
- }
-
- }
-
- /**
- * Returns the first argument with the sign of the second argument.
- * A NaN {@code sign} argument is treated as positive.
- *
- * @param magnitude the value to return
- * @param sign the sign for the returned value
- * @return the magnitude with the same sign as the {@code sign} argument
- */
- public static double copySign(double magnitude, double sign){
- // The highest order bit is going to be zero if the
- // highest order bit of m and s is the same and one otherwise.
- // So (m^s) will be positive if both m and s have the same sign
- // and negative otherwise.
- final long m = Double.doubleToRawLongBits(magnitude); // don't care about NaN
- final long s = Double.doubleToRawLongBits(sign);
- if ((m^s) >= 0) {
- return magnitude;
- }
- return -magnitude; // flip sign
- }
-
- /**
- * Returns the first argument with the sign of the second argument.
- * A NaN {@code sign} argument is treated as positive.
- *
- * @param magnitude the value to return
- * @param sign the sign for the returned value
- * @return the magnitude with the same sign as the {@code sign} argument
- */
- public static float copySign(float magnitude, float sign){
- // The highest order bit is going to be zero if the
- // highest order bit of m and s is the same and one otherwise.
- // So (m^s) will be positive if both m and s have the same sign
- // and negative otherwise.
- final int m = Float.floatToRawIntBits(magnitude);
- final int s = Float.floatToRawIntBits(sign);
- if ((m^s) >= 0) {
- return magnitude;
- }
- return -magnitude; // flip sign
- }
-
- /**
- * Return the exponent of a double number, removing the bias.
- * <p>
- * For double numbers of the form 2<sup>x</sup>, the unbiased
- * exponent is exactly x.
- * </p>
- * @param d number from which exponent is requested
- * @return exponent for d in IEEE754 representation, without bias
- */
- public static int getExponent(final double d) {
- // NaN and Infinite will return 1024 anywho so can use raw bits
- return (int) ((Double.doubleToRawLongBits(d) >>> 52) & 0x7ff) - 1023;
- }
-
- /**
- * Return the exponent of a float number, removing the bias.
- * <p>
- * For float numbers of the form 2<sup>x</sup>, the unbiased
- * exponent is exactly x.
- * </p>
- * @param f number from which exponent is requested
- * @return exponent for d in IEEE754 representation, without bias
- */
- public static int getExponent(final float f) {
- // NaN and Infinite will return the same exponent anywho so can use raw bits
- return ((Float.floatToRawIntBits(f) >>> 23) & 0xff) - 127;
- }
-
- /**
- * Print out contents of arrays, and check the length.
- * <p>used to generate the preset arrays originally.</p>
- * @param a unused
- */
- public static void main(String[] a) {
- PrintStream out = System.out;
- AccurateMathCalc.printarray(out, "EXP_INT_TABLE_A", EXP_INT_TABLE_LEN, ExpIntTable.EXP_INT_TABLE_A);
- AccurateMathCalc.printarray(out, "EXP_INT_TABLE_B", EXP_INT_TABLE_LEN, ExpIntTable.EXP_INT_TABLE_B);
- AccurateMathCalc.printarray(out, "EXP_FRAC_TABLE_A", EXP_FRAC_TABLE_LEN, ExpFracTable.EXP_FRAC_TABLE_A);
- AccurateMathCalc.printarray(out, "EXP_FRAC_TABLE_B", EXP_FRAC_TABLE_LEN, ExpFracTable.EXP_FRAC_TABLE_B);
- AccurateMathCalc.printarray(out, "LN_MANT",LN_MANT_LEN, lnMant.LN_MANT);
- AccurateMathCalc.printarray(out, "SINE_TABLE_A", SINE_TABLE_LEN, SINE_TABLE_A);
- AccurateMathCalc.printarray(out, "SINE_TABLE_B", SINE_TABLE_LEN, SINE_TABLE_B);
- AccurateMathCalc.printarray(out, "COSINE_TABLE_A", SINE_TABLE_LEN, COSINE_TABLE_A);
- AccurateMathCalc.printarray(out, "COSINE_TABLE_B", SINE_TABLE_LEN, COSINE_TABLE_B);
- AccurateMathCalc.printarray(out, "TANGENT_TABLE_A", SINE_TABLE_LEN, TANGENT_TABLE_A);
- AccurateMathCalc.printarray(out, "TANGENT_TABLE_B", SINE_TABLE_LEN, TANGENT_TABLE_B);
- }
-
- /** Enclose large data table in nested static class so it's only loaded on first access. */
- private static class ExpIntTable {
- /** Exponential evaluated at integer values,
- * exp(x) = expIntTableA[x + EXP_INT_TABLE_MAX_INDEX] + expIntTableB[x+EXP_INT_TABLE_MAX_INDEX].
- */
- private static final double[] EXP_INT_TABLE_A;
- /** Exponential evaluated at integer values,
- * exp(x) = expIntTableA[x + EXP_INT_TABLE_MAX_INDEX] + expIntTableB[x+EXP_INT_TABLE_MAX_INDEX]
- */
- private static final double[] EXP_INT_TABLE_B;
-
- static {
- if (RECOMPUTE_TABLES_AT_RUNTIME) {
- EXP_INT_TABLE_A = new double[AccurateMath.EXP_INT_TABLE_LEN];
- EXP_INT_TABLE_B = new double[AccurateMath.EXP_INT_TABLE_LEN];
-
- final double tmp[] = new double[2];
- final double recip[] = new double[2];
-
- // Populate expIntTable
- for (int i = 0; i < AccurateMath.EXP_INT_TABLE_MAX_INDEX; i++) {
- AccurateMathCalc.expint(i, tmp);
- EXP_INT_TABLE_A[i + AccurateMath.EXP_INT_TABLE_MAX_INDEX] = tmp[0];
- EXP_INT_TABLE_B[i + AccurateMath.EXP_INT_TABLE_MAX_INDEX] = tmp[1];
-
- if (i != 0) {
- // Negative integer powers
- AccurateMathCalc.splitReciprocal(tmp, recip);
- EXP_INT_TABLE_A[AccurateMath.EXP_INT_TABLE_MAX_INDEX - i] = recip[0];
- EXP_INT_TABLE_B[AccurateMath.EXP_INT_TABLE_MAX_INDEX - i] = recip[1];
- }
- }
- } else {
- EXP_INT_TABLE_A = AccurateMathLiteralArrays.loadExpIntA();
- EXP_INT_TABLE_B = AccurateMathLiteralArrays.loadExpIntB();
- }
- }
- }
-
- /** Enclose large data table in nested static class so it's only loaded on first access. */
- private static class ExpFracTable {
- /** Exponential over the range of 0 - 1 in increments of 2^-10
- * exp(x/1024) = expFracTableA[x] + expFracTableB[x].
- * 1024 = 2^10
- */
- private static final double[] EXP_FRAC_TABLE_A;
- /** Exponential over the range of 0 - 1 in increments of 2^-10
- * exp(x/1024) = expFracTableA[x] + expFracTableB[x].
- */
- private static final double[] EXP_FRAC_TABLE_B;
-
- static {
- if (RECOMPUTE_TABLES_AT_RUNTIME) {
- EXP_FRAC_TABLE_A = new double[AccurateMath.EXP_FRAC_TABLE_LEN];
- EXP_FRAC_TABLE_B = new double[AccurateMath.EXP_FRAC_TABLE_LEN];
-
- final double tmp[] = new double[2];
-
- // Populate expFracTable
- final double factor = 1d / (EXP_FRAC_TABLE_LEN - 1);
- for (int i = 0; i < EXP_FRAC_TABLE_A.length; i++) {
- AccurateMathCalc.slowexp(i * factor, tmp);
- EXP_FRAC_TABLE_A[i] = tmp[0];
- EXP_FRAC_TABLE_B[i] = tmp[1];
- }
- } else {
- EXP_FRAC_TABLE_A = AccurateMathLiteralArrays.loadExpFracA();
- EXP_FRAC_TABLE_B = AccurateMathLiteralArrays.loadExpFracB();
- }
- }
- }
-
- /** Enclose large data table in nested static class so it's only loaded on first access. */
- private static class lnMant {
- /** Extended precision logarithm table over the range 1 - 2 in increments of 2^-10. */
- private static final double[][] LN_MANT;
-
- static {
- if (RECOMPUTE_TABLES_AT_RUNTIME) {
- LN_MANT = new double[AccurateMath.LN_MANT_LEN][];
-
- // Populate lnMant table
- for (int i = 0; i < LN_MANT.length; i++) {
- final double d = Double.longBitsToDouble( (((long) i) << 42) | 0x3ff0000000000000L );
- LN_MANT[i] = AccurateMathCalc.slowLog(d);
- }
- } else {
- LN_MANT = AccurateMathLiteralArrays.loadLnMant();
- }
- }
- }
-
- /** Enclose the Cody/Waite reduction (used in "sin", "cos" and "tan"). */
- private static class CodyWaite {
- /** k */
- private final int finalK;
- /** remA */
- private final double finalRemA;
- /** remB */
- private final double finalRemB;
-
- /**
- * @param xa Argument.
- */
- CodyWaite(double xa) {
- // Estimate k.
- //k = (int)(xa / 1.5707963267948966);
- int k = (int)(xa * 0.6366197723675814);
-
- // Compute remainder.
- double remA;
- double remB;
- while (true) {
- double a = -k * 1.570796251296997;
- remA = xa + a;
- remB = -(remA - xa - a);
-
- a = -k * 7.549789948768648E-8;
- double b = remA;
- remA = a + b;
- remB += -(remA - b - a);
-
- a = -k * 6.123233995736766E-17;
- b = remA;
- remA = a + b;
- remB += -(remA - b - a);
-
- if (remA > 0) {
- break;
- }
-
- // Remainder is negative, so decrement k and try again.
- // This should only happen if the input is very close
- // to an even multiple of pi/2.
- --k;
- }
-
- this.finalK = k;
- this.finalRemA = remA;
- this.finalRemB = remB;
- }
-
- /**
- * @return k
- */
- int getK() {
- return finalK;
- }
- /**
- * @return remA
- */
- double getRemA() {
- return finalRemA;
- }
- /**
- * @return remB
- */
- double getRemB() {
- return finalRemB;
- }
- }
-}
diff --git a/commons-math-legacy-core/src/main/java/org/apache/commons/math4/legacy/core/jdkmath/AccurateMathCalc.java.bak b/commons-math-legacy-core/src/main/java/org/apache/commons/math4/legacy/core/jdkmath/AccurateMathCalc.java.bak
deleted file mode 100644
index 13ff2f1..0000000
--- a/commons-math-legacy-core/src/main/java/org/apache/commons/math4/legacy/core/jdkmath/AccurateMathCalc.java.bak
+++ /dev/null
@@ -1,658 +0,0 @@
-/*
- * 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
- *
- * 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.apache.commons.math4.legacy.util;
-
-import java.io.PrintStream;
-
-import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
-
-/** Class used to compute the classical functions tables.
- * @since 3.0
- */
-class AccurateMathCalc {
-
- /**
- * 0x40000000 - used to split a double into two parts, both with the low order bits cleared.
- * Equivalent to 2^30.
- */
- private static final long HEX_40000000 = 0x40000000L; // 1073741824L
-
- /** Factorial table, for Taylor series expansions. 0!, 1!, 2!, ... 19! */
- private static final double FACT[] = new double[]
- {
- +1.0d, // 0
- +1.0d, // 1
- +2.0d, // 2
- +6.0d, // 3
- +24.0d, // 4
- +120.0d, // 5
- +720.0d, // 6
- +5040.0d, // 7
- +40320.0d, // 8
- +362880.0d, // 9
- +3628800.0d, // 10
- +39916800.0d, // 11
- +479001600.0d, // 12
- +6227020800.0d, // 13
- +87178291200.0d, // 14
- +1307674368000.0d, // 15
- +20922789888000.0d, // 16
- +355687428096000.0d, // 17
- +6402373705728000.0d, // 18
- +121645100408832000.0d, // 19
- };
-
- /** Coefficients for slowLog. */
- private static final double LN_SPLIT_COEF[][] = {
- {2.0, 0.0},
- {0.6666666269302368, 3.9736429850260626E-8},
- {0.3999999761581421, 2.3841857910019882E-8},
- {0.2857142686843872, 1.7029898543501842E-8},
- {0.2222222089767456, 1.3245471311735498E-8},
- {0.1818181574344635, 2.4384203044354907E-8},
- {0.1538461446762085, 9.140260083262505E-9},
- {0.13333332538604736, 9.220590270857665E-9},
- {0.11764700710773468, 1.2393345855018391E-8},
- {0.10526403784751892, 8.251545029714408E-9},
- {0.0952233225107193, 1.2675934823758863E-8},
- {0.08713622391223907, 1.1430250008909141E-8},
- {0.07842259109020233, 2.404307984052299E-9},
- {0.08371849358081818, 1.176342548272881E-8},
- {0.030589580535888672, 1.2958646899018938E-9},
- {0.14982303977012634, 1.225743062930824E-8},
- };
-
- /** Table start declaration. */
- private static final String TABLE_START_DECL = " {";
-
- /** Table end declaration. */
- private static final String TABLE_END_DECL = " };";
-
- /**
- * Private Constructor.
- */
- private AccurateMathCalc() {
- }
-
- /** Build the sine and cosine tables.
- * @param SINE_TABLE_A table of the most significant part of the sines
- * @param SINE_TABLE_B table of the least significant part of the sines
- * @param COSINE_TABLE_A table of the most significant part of the cosines
- * @param COSINE_TABLE_B table of the most significant part of the cosines
- * @param SINE_TABLE_LEN length of the tables
- * @param TANGENT_TABLE_A table of the most significant part of the tangents
- * @param TANGENT_TABLE_B table of the most significant part of the tangents
- */
- @SuppressWarnings("unused")
- private static void buildSinCosTables(double[] SINE_TABLE_A, double[] SINE_TABLE_B,
- double[] COSINE_TABLE_A, double[] COSINE_TABLE_B,
- int SINE_TABLE_LEN, double[] TANGENT_TABLE_A, double[] TANGENT_TABLE_B) {
- final double result[] = new double[2];
-
- /* Use taylor series for 0 <= x <= 6/8 */
- for (int i = 0; i < 7; i++) {
- double x = i / 8.0;
-
- slowSin(x, result);
- SINE_TABLE_A[i] = result[0];
- SINE_TABLE_B[i] = result[1];
-
- slowCos(x, result);
- COSINE_TABLE_A[i] = result[0];
- COSINE_TABLE_B[i] = result[1];
- }
-
- /* Use angle addition formula to complete table to 13/8, just beyond pi/2 */
- for (int i = 7; i < SINE_TABLE_LEN; i++) {
- double xs[] = new double[2];
- double ys[] = new double[2];
- double as[] = new double[2];
- double bs[] = new double[2];
- double temps[] = new double[2];
-
- if ( (i & 1) == 0) {
- // Even, use double angle
- xs[0] = SINE_TABLE_A[i/2];
- xs[1] = SINE_TABLE_B[i/2];
- ys[0] = COSINE_TABLE_A[i/2];
- ys[1] = COSINE_TABLE_B[i/2];
-
- /* compute sine */
- splitMult(xs, ys, result);
- SINE_TABLE_A[i] = result[0] * 2.0;
- SINE_TABLE_B[i] = result[1] * 2.0;
-
- /* Compute cosine */
- splitMult(ys, ys, as);
- splitMult(xs, xs, temps);
- temps[0] = -temps[0];
- temps[1] = -temps[1];
- splitAdd(as, temps, result);
- COSINE_TABLE_A[i] = result[0];
- COSINE_TABLE_B[i] = result[1];
- } else {
- xs[0] = SINE_TABLE_A[i/2];
- xs[1] = SINE_TABLE_B[i/2];
- ys[0] = COSINE_TABLE_A[i/2];
- ys[1] = COSINE_TABLE_B[i/2];
- as[0] = SINE_TABLE_A[i/2+1];
- as[1] = SINE_TABLE_B[i/2+1];
- bs[0] = COSINE_TABLE_A[i/2+1];
- bs[1] = COSINE_TABLE_B[i/2+1];
-
- /* compute sine */
- splitMult(xs, bs, temps);
- splitMult(ys, as, result);
- splitAdd(result, temps, result);
- SINE_TABLE_A[i] = result[0];
- SINE_TABLE_B[i] = result[1];
-
- /* Compute cosine */
- splitMult(ys, bs, result);
- splitMult(xs, as, temps);
- temps[0] = -temps[0];
- temps[1] = -temps[1];
- splitAdd(result, temps, result);
- COSINE_TABLE_A[i] = result[0];
- COSINE_TABLE_B[i] = result[1];
- }
- }
-
- /* Compute tangent = sine/cosine */
- for (int i = 0; i < SINE_TABLE_LEN; i++) {
- double xs[] = new double[2];
- double ys[] = new double[2];
- double as[] = new double[2];
-
- as[0] = COSINE_TABLE_A[i];
- as[1] = COSINE_TABLE_B[i];
-
- splitReciprocal(as, ys);
-
- xs[0] = SINE_TABLE_A[i];
- xs[1] = SINE_TABLE_B[i];
-
- splitMult(xs, ys, as);
-
- TANGENT_TABLE_A[i] = as[0];
- TANGENT_TABLE_B[i] = as[1];
- }
-
- }
-
- /**
- * For x between 0 and pi/4 compute cosine using Talor series
- * cos(x) = 1 - x^2/2! + x^4/4! ...
- * @param x number from which cosine is requested
- * @param result placeholder where to put the result in extended precision
- * (may be null)
- * @return cos(x)
- */
- static double slowCos(final double x, final double result[]) {
-
- final double xs[] = new double[2];
- final double ys[] = new double[2];
- final double facts[] = new double[2];
- final double as[] = new double[2];
- split(x, xs);
- ys[0] = ys[1] = 0.0;
-
- for (int i = FACT.length-1; i >= 0; i--) {
- splitMult(xs, ys, as);
- ys[0] = as[0]; ys[1] = as[1];
-
- if ( (i & 1) != 0) { // skip odd entries
- continue;
- }
-
- split(FACT[i], as);
- splitReciprocal(as, facts);
-
- if ( (i & 2) != 0 ) { // alternate terms are negative
- facts[0] = -facts[0];
- facts[1] = -facts[1];
- }
-
- splitAdd(ys, facts, as);
- ys[0] = as[0]; ys[1] = as[1];
- }
-
- if (result != null) {
- result[0] = ys[0];
- result[1] = ys[1];
- }
-
- return ys[0] + ys[1];
- }
-
- /**
- * For x between 0 and pi/4 compute sine using Taylor expansion:
- * sin(x) = x - x^3/3! + x^5/5! - x^7/7! ...
- * @param x number from which sine is requested
- * @param result placeholder where to put the result in extended precision
- * (may be null)
- * @return sin(x)
- */
- static double slowSin(final double x, final double result[]) {
- final double xs[] = new double[2];
- final double ys[] = new double[2];
- final double facts[] = new double[2];
- final double as[] = new double[2];
- split(x, xs);
- ys[0] = ys[1] = 0.0;
-
- for (int i = FACT.length-1; i >= 0; i--) {
- splitMult(xs, ys, as);
- ys[0] = as[0]; ys[1] = as[1];
-
- if ( (i & 1) == 0) { // Ignore even numbers
- continue;
- }
-
- split(FACT[i], as);
- splitReciprocal(as, facts);
-
- if ( (i & 2) != 0 ) { // alternate terms are negative
- facts[0] = -facts[0];
- facts[1] = -facts[1];
- }
-
- splitAdd(ys, facts, as);
- ys[0] = as[0]; ys[1] = as[1];
- }
-
- if (result != null) {
- result[0] = ys[0];
- result[1] = ys[1];
- }
-
- return ys[0] + ys[1];
- }
-
-
- /**
- * For x between 0 and 1, returns exp(x), uses extended precision
- * @param x argument of exponential
- * @param result placeholder where to place exp(x) split in two terms
- * for extra precision (i.e. exp(x) = result[0] + result[1]
- * @return exp(x)
- */
- static double slowexp(final double x, final double result[]) {
- final double xs[] = new double[2];
- final double ys[] = new double[2];
- final double facts[] = new double[2];
- final double as[] = new double[2];
- split(x, xs);
- ys[0] = ys[1] = 0.0;
-
- for (int i = FACT.length-1; i >= 0; i--) {
- splitMult(xs, ys, as);
- ys[0] = as[0];
- ys[1] = as[1];
-
- split(FACT[i], as);
- splitReciprocal(as, facts);
-
- splitAdd(ys, facts, as);
- ys[0] = as[0];
- ys[1] = as[1];
- }
-
- if (result != null) {
- result[0] = ys[0];
- result[1] = ys[1];
- }
-
- return ys[0] + ys[1];
- }
-
- /** Compute split[0], split[1] such that their sum is equal to d,
- * and split[0] has its 30 least significant bits as zero.
- * @param d number to split
- * @param split placeholder where to place the result
- */
- private static void split(final double d, final double split[]) {
- if (d < 8e298 && d > -8e298) {
- final double a = d * HEX_40000000;
- split[0] = (d + a) - a;
- split[1] = d - split[0];
- } else {
- final double a = d * 9.31322574615478515625E-10;
- split[0] = (d + a - d) * HEX_40000000;
- split[1] = d - split[0];
- }
- }
-
- /** Recompute a split.
- * @param a input/out array containing the split, changed
- * on output
- */
- private static void resplit(final double a[]) {
- final double c = a[0] + a[1];
- final double d = -(c - a[0] - a[1]);
-
- if (c < 8e298 && c > -8e298) { // MAGIC NUMBER
- double z = c * HEX_40000000;
- a[0] = (c + z) - z;
- a[1] = c - a[0] + d;
- } else {
- double z = c * 9.31322574615478515625E-10;
- a[0] = (c + z - c) * HEX_40000000;
- a[1] = c - a[0] + d;
- }
- }
-
- /** Multiply two numbers in split form.
- * @param a first term of multiplication
- * @param b second term of multiplication
- * @param ans placeholder where to put the result
- */
- private static void splitMult(double a[], double b[], double ans[]) {
- ans[0] = a[0] * b[0];
- ans[1] = a[0] * b[1] + a[1] * b[0] + a[1] * b[1];
-
- /* Resplit */
- resplit(ans);
- }
-
- /** Add two numbers in split form.
- * @param a first term of addition
- * @param b second term of addition
- * @param ans placeholder where to put the result
- */
- private static void splitAdd(final double a[], final double b[], final double ans[]) {
- ans[0] = a[0] + b[0];
- ans[1] = a[1] + b[1];
-
- resplit(ans);
- }
-
- /** Compute the reciprocal of in. Use the following algorithm.
- * in = c + d.
- * want to find x + y such that x+y = 1/(c+d) and x is much
- * larger than y and x has several zero bits on the right.
- *
- * Set b = 1/(2^22), a = 1 - b. Thus (a+b) = 1.
- * Use following identity to compute (a+b)/(c+d)
- *
- * (a+b)/(c+d) = a/c + (bc - ad) / (c^2 + cd)
- * set x = a/c and y = (bc - ad) / (c^2 + cd)
- * This will be close to the right answer, but there will be
- * some rounding in the calculation of X. So by carefully
- * computing 1 - (c+d)(x+y) we can compute an error and
- * add that back in. This is done carefully so that terms
- * of similar size are subtracted first.
- * @param in initial number, in split form
- * @param result placeholder where to put the result
- */
- static void splitReciprocal(final double in[], final double result[]) {
- final double b = 1.0/4194304.0;
- final double a = 1.0 - b;
-
- if (in[0] == 0.0) {
- in[0] = in[1];
- in[1] = 0.0;
- }
-
- result[0] = a / in[0];
- result[1] = (b*in[0]-a*in[1]) / (in[0]*in[0] + in[0]*in[1]);
-
- if (result[1] != result[1]) { // can happen if result[1] is NAN
- result[1] = 0.0;
- }
-
- /* Resplit */
- resplit(result);
-
- for (int i = 0; i < 2; i++) {
- /* this may be overkill, probably once is enough */
- double err = 1.0 - result[0] * in[0] - result[0] * in[1] -
- result[1] * in[0] - result[1] * in[1];
- /*err = 1.0 - err; */
- err *= result[0] + result[1];
- /*printf("err = %16e\n", err); */
- result[1] += err;
- }
- }
-
- /** Compute (a[0] + a[1]) * (b[0] + b[1]) in extended precision.
- * @param a first term of the multiplication
- * @param b second term of the multiplication
- * @param result placeholder where to put the result
- */
- private static void quadMult(final double a[], final double b[], final double result[]) {
- final double xs[] = new double[2];
- final double ys[] = new double[2];
- final double zs[] = new double[2];
-
- /* a[0] * b[0] */
- split(a[0], xs);
- split(b[0], ys);
- splitMult(xs, ys, zs);
-
- result[0] = zs[0];
- result[1] = zs[1];
-
- /* a[0] * b[1] */
- split(b[1], ys);
- splitMult(xs, ys, zs);
-
- double tmp = result[0] + zs[0];
- result[1] -= tmp - result[0] - zs[0];
- result[0] = tmp;
- tmp = result[0] + zs[1];
- result[1] -= tmp - result[0] - zs[1];
- result[0] = tmp;
-
- /* a[1] * b[0] */
- split(a[1], xs);
- split(b[0], ys);
- splitMult(xs, ys, zs);
-
- tmp = result[0] + zs[0];
- result[1] -= tmp - result[0] - zs[0];
- result[0] = tmp;
- tmp = result[0] + zs[1];
- result[1] -= tmp - result[0] - zs[1];
- result[0] = tmp;
-
- /* a[1] * b[0] */
- split(a[1], xs);
- split(b[1], ys);
- splitMult(xs, ys, zs);
-
- tmp = result[0] + zs[0];
- result[1] -= tmp - result[0] - zs[0];
- result[0] = tmp;
- tmp = result[0] + zs[1];
- result[1] -= tmp - result[0] - zs[1];
- result[0] = tmp;
- }
-
- /** Compute exp(p) for a integer p in extended precision.
- * @param p integer whose exponential is requested
- * @param result placeholder where to put the result in extended precision
- * @return exp(p) in standard precision (equal to result[0] + result[1])
- */
- static double expint(int p, final double result[]) {
- //double x = M_E;
- final double xs[] = new double[2];
- final double as[] = new double[2];
- final double ys[] = new double[2];
- //split(x, xs);
- //xs[1] = (double)(2.7182818284590452353602874713526625L - xs[0]);
- //xs[0] = 2.71827697753906250000;
- //xs[1] = 4.85091998273542816811e-06;
- //xs[0] = Double.longBitsToDouble(0x4005bf0800000000L);
- //xs[1] = Double.longBitsToDouble(0x3ed458a2bb4a9b00L);
-
- /* E */
- xs[0] = 2.718281828459045;
- xs[1] = 1.4456468917292502E-16;
-
- split(1.0, ys);
-
- while (p > 0) {
- if ((p & 1) != 0) {
- quadMult(ys, xs, as);
- ys[0] = as[0]; ys[1] = as[1];
- }
-
- quadMult(xs, xs, as);
- xs[0] = as[0]; xs[1] = as[1];
-
- p >>= 1;
- }
-
- if (result != null) {
- result[0] = ys[0];
- result[1] = ys[1];
-
- resplit(result);
- }
-
- return ys[0] + ys[1];
- }
- /** xi in the range of [1, 2].
- * 3 5 7
- * x+1 / x x x \
- * ln ----- = 2 * | x + ---- + ---- + ---- + ... |
- * 1-x \ 3 5 7 /
- *
- * So, compute a Remez approximation of the following function
- *
- * ln ((sqrt(x)+1)/(1-sqrt(x))) / x
- *
- * This will be an even function with only positive coefficents.
- * x is in the range [0 - 1/3].
- *
- * Transform xi for input to the above function by setting
- * x = (xi-1)/(xi+1). Input to the polynomial is x^2, then
- * the result is multiplied by x.
- * @param xi number from which log is requested
- * @return log(xi)
- */
- static double[] slowLog(double xi) {
- double x[] = new double[2];
- double x2[] = new double[2];
- double y[] = new double[2];
- double a[] = new double[2];
-
- split(xi, x);
-
- /* Set X = (x-1)/(x+1) */
- x[0] += 1.0;
- resplit(x);
- splitReciprocal(x, a);
- x[0] -= 2.0;
- resplit(x);
- splitMult(x, a, y);
- x[0] = y[0];
- x[1] = y[1];
-
- /* Square X -> X2*/
- splitMult(x, x, x2);
-
-
- //x[0] -= 1.0;
- //resplit(x);
-
- y[0] = LN_SPLIT_COEF[LN_SPLIT_COEF.length-1][0];
- y[1] = LN_SPLIT_COEF[LN_SPLIT_COEF.length-1][1];
-
- for (int i = LN_SPLIT_COEF.length-2; i >= 0; i--) {
- splitMult(y, x2, a);
- y[0] = a[0];
- y[1] = a[1];
- splitAdd(y, LN_SPLIT_COEF[i], a);
- y[0] = a[0];
- y[1] = a[1];
- }
-
- splitMult(y, x, a);
- y[0] = a[0];
- y[1] = a[1];
-
- return y;
- }
-
-
- /**
- * Print an array.
- * @param out text output stream where output should be printed
- * @param name array name
- * @param expectedLen expected length of the array
- * @param array2d array data
- */
- static void printarray(PrintStream out, String name, int expectedLen, double[][] array2d) {
- out.println(name);
- checkLen(expectedLen, array2d.length);
- out.println(TABLE_START_DECL + " ");
- int i = 0;
- for(double[] array : array2d) { // "double array[]" causes PMD parsing error
- out.print(" {");
- for(double d : array) { // assume inner array has very few entries
- out.printf("%-25.25s", format(d)); // multiple entries per line
- }
- out.println("}, // " + i++);
- }
- out.println(TABLE_END_DECL);
- }
-
- /**
- * Print an array.
- * @param out text output stream where output should be printed
- * @param name array name
- * @param expectedLen expected length of the array
- * @param array array data
- */
- static void printarray(PrintStream out, String name, int expectedLen, double[] array) {
- out.println(name + "=");
- checkLen(expectedLen, array.length);
- out.println(TABLE_START_DECL);
- for(double d : array){
- out.printf(" %s%n", format(d)); // one entry per line
- }
- out.println(TABLE_END_DECL);
- }
-
- /** Format a double.
- * @param d double number to format
- * @return formatted number
- */
- static String format(double d) {
- if (d != d) {
- return "Double.NaN,";
- } else {
- return ((d >= 0) ? "+" : "") + Double.toString(d) + "d,";
- }
- }
-
- /**
- * Check two lengths are equal.
- * @param expectedLen expected length
- * @param actual actual length
- * @exception DimensionMismatchException if the two lengths are not equal
- */
- private static void checkLen(int expectedLen, int actual)
- throws DimensionMismatchException {
- if (expectedLen != actual) {
- throw new DimensionMismatchException(actual, expectedLen);
- }
- }
-
-}
diff --git a/commons-math-legacy-core/src/main/java/org/apache/commons/math4/legacy/core/jdkmath/AccurateMathLiteralArrays.java.bak b/commons-math-legacy-core/src/main/java/org/apache/commons/math4/legacy/core/jdkmath/AccurateMathLiteralArrays.java.bak
deleted file mode 100644
index 1767ddf..0000000
--- a/commons-math-legacy-core/src/main/java/org/apache/commons/math4/legacy/core/jdkmath/AccurateMathLiteralArrays.java.bak
+++ /dev/null
@@ -1,6175 +0,0 @@
-/*
- * 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
- *
- * 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.apache.commons.math4.legacy.util;
-
-/**
- * Utility class for loading tabulated data used by {@link AccurateMath}.
- *
- */
-class AccurateMathLiteralArrays {
- /** Exponential evaluated at integer values,
- * exp(x) = expIntTableA[x + EXP_INT_TABLE_MAX_INDEX] + expIntTableB[x+EXP_INT_TABLE_MAX_INDEX].
- */
- private static final double[] EXP_INT_A = new double[] {
- +0.0d,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- +1.2167807682331913E-308d,
- +3.3075532478807267E-308d,
- +8.990862214387203E-308d,
- +2.4439696075216986E-307d,
- +6.64339758024534E-307d,
- +1.8058628951432254E-306d,
- +4.908843759498681E-306d,
- +1.334362017065677E-305d,
- +3.627172425759641E-305d,
- +9.85967600992008E-305d,
- +2.680137967689915E-304d,
- +7.285370725133842E-304d,
- +1.9803689272433392E-303d,
- +5.3832011494782624E-303d,
- +1.463305638201413E-302d,
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- Double.NaN,
- Double.NaN,
- };
-
- /** Exponential evaluated at integer values,
- * exp(x) = expIntTableA[x + EXP_INT_TABLE_MAX_INDEX] + expIntTableB[x+EXP_INT_TABLE_MAX_INDEX]
- */
- private static final double[] EXP_INT_B = new double[] {
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- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
- Double.NaN,
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- Double.NaN,
- Double.NaN,
- Double.NaN,
- };
-
-
- /** Exponential over the range of 0 - 1 in increments of 2^-10
- * exp(x/1024) = expFracTableA[x] + expFracTableB[x].
- * 1024 = 2^10
- */
- private static final double[] EXP_FRAC_A = new double[] {
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- +2.7182817459106445d,
- };
-
- /** Exponential over the range of 0 - 1 in increments of 2^-10
- * exp(x/1024) = expFracTableA[x] + expFracTableB[x].
- */
- private static final double[] EXP_FRAC_B = new double[] {
- +0.0d,
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- -8.281845251820919E-8d,
- -3.126416414805498E-8d,
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- -4.9452513107409435E-8d,
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- -7.698155155722897E-8d,
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- -4.443661736519001E-8d,
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- -7.227368462584163E-9d,
- -8.129108387083023E-9d,
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- -1.154629885168314E-7d,
- -2.399186832888246E-8d,
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- -2.070841011504222E-9d,
- -6.97066538508643E-8d,
- -1.0898941254272996E-7d,
- -1.1895963756343625E-7d,
- -9.865691193993138E-8d,
- -4.711988033385175E-8d,
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- -8.491135959370133E-8d,
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- -2.462631860370667E-9d,
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