added tests based on dfp library (now a package in commons-math)
git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@992871 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Luc Maisonobe
parent
c2134b3a90
commit
05aebba620
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@ -0,0 +1,915 @@
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/*
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* Licensed to the Apache Software Foundation (ASF) under one or more
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* contributor license agreements. See the NOTICE file distributed with
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* this work for additional information regarding copyright ownership.
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* The ASF licenses this file to You under the Apache License, Version 2.0
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* (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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package org.apache.commons.math.util;
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import org.apache.commons.math.dfp.Dfp;
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import org.apache.commons.math.dfp.DfpField;
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import org.apache.commons.math.dfp.DfpMath;
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import org.apache.commons.math.random.MersenneTwister;
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import org.apache.commons.math.random.RandomGenerator;
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import org.junit.Assert;
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import org.junit.Before;
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import org.junit.Ignore;
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import org.junit.Test;
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public class FastMathTest {
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private final double MAX_ERROR_ULP = 0.51;
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private final int NUMBER_OF_TRIALS = 1000;
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private DfpField field;
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private RandomGenerator generator;
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@Before
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public void setUp() {
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field = new DfpField(40);
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generator = new MersenneTwister(6176597458463500194l);
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}
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@Test
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public void testMinMaxDouble() {
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double[][] pairs = {
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{ -50.0, 50.0 },
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{ Double.POSITIVE_INFINITY, 1.0 },
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{ Double.NEGATIVE_INFINITY, 1.0 },
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{ Double.NaN, 1.0 },
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{ Double.POSITIVE_INFINITY, 0.0 },
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{ Double.NEGATIVE_INFINITY, 0.0 },
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{ Double.NaN, 0.0 },
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{ Double.NaN, Double.NEGATIVE_INFINITY },
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{ Double.NaN, Double.POSITIVE_INFINITY },
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{ MathUtils.SAFE_MIN, MathUtils.EPSILON }
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};
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for (double[] pair : pairs) {
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Assert.assertEquals("min(" + pair[0] + ", " + pair[1] + ")",
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Math.min(pair[0], pair[1]),
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FastMath.min(pair[0], pair[1]),
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MathUtils.EPSILON);
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Assert.assertEquals("min(" + pair[1] + ", " + pair[0] + ")",
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Math.min(pair[1], pair[0]),
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FastMath.min(pair[1], pair[0]),
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MathUtils.EPSILON);
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Assert.assertEquals("max(" + pair[0] + ", " + pair[1] + ")",
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Math.max(pair[0], pair[1]),
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FastMath.max(pair[0], pair[1]),
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MathUtils.EPSILON);
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Assert.assertEquals("max(" + pair[1] + ", " + pair[0] + ")",
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Math.max(pair[1], pair[0]),
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FastMath.max(pair[1], pair[0]),
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MathUtils.EPSILON);
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}
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}
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@Test
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public void testMinMaxFloat() {
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double[][] pairs = {
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{ -50.0, 50.0 },
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{ Float.POSITIVE_INFINITY, 1.0 },
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{ Float.NEGATIVE_INFINITY, 1.0 },
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{ Float.NaN, 1.0 },
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{ Float.POSITIVE_INFINITY, 0.0 },
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{ Float.NEGATIVE_INFINITY, 0.0 },
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{ Float.NaN, 0.0 },
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{ Float.NaN, Float.NEGATIVE_INFINITY },
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{ Float.NaN, Float.POSITIVE_INFINITY }
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};
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for (double[] pair : pairs) {
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Assert.assertEquals("min(" + pair[0] + ", " + pair[1] + ")",
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Math.min(pair[0], pair[1]),
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FastMath.min(pair[0], pair[1]),
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MathUtils.EPSILON);
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Assert.assertEquals("min(" + pair[1] + ", " + pair[0] + ")",
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Math.min(pair[1], pair[0]),
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FastMath.min(pair[1], pair[0]),
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MathUtils.EPSILON);
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Assert.assertEquals("max(" + pair[0] + ", " + pair[1] + ")",
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Math.max(pair[0], pair[1]),
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FastMath.max(pair[0], pair[1]),
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MathUtils.EPSILON);
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Assert.assertEquals("max(" + pair[1] + ", " + pair[0] + ")",
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Math.max(pair[1], pair[0]),
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FastMath.max(pair[1], pair[0]),
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MathUtils.EPSILON);
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}
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}
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@Test
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public void testConstants() {
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Assert.assertEquals(Math.PI, FastMath.PI, 1.0e-20);
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Assert.assertEquals(Math.E, FastMath.E, 1.0e-20);
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}
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@Test
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public void testAtan2() {
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double y1 = 1.2713504628280707e10;
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double x1 = -5.674940885228782e-10;
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Assert.assertEquals(Math.atan2(y1, x1), FastMath.atan2(y1, x1), 2 * MathUtils.EPSILON);
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double y2 = 0.0;
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double x2 = Double.POSITIVE_INFINITY;
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Assert.assertEquals(Math.atan2(y2, x2), FastMath.atan2(y2, x2), MathUtils.SAFE_MIN);
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}
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@Test
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public void testHyperbolic() {
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double maxErr = 0;
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for (double x = -30; x < 30; x += 0.001) {
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double tst = FastMath.sinh(x);
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double ref = Math.sinh(x);
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maxErr = FastMath.max(maxErr, FastMath.abs(ref - tst) / FastMath.ulp(ref));
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}
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Assert.assertEquals(0, maxErr, 2);
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maxErr = 0;
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for (double x = -30; x < 30; x += 0.001) {
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double tst = FastMath.cosh(x);
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double ref = Math.cosh(x);
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maxErr = FastMath.max(maxErr, FastMath.abs(ref - tst) / FastMath.ulp(ref));
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}
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Assert.assertEquals(0, maxErr, 2);
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maxErr = 0;
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for (double x = -0.5; x < 0.5; x += 0.001) {
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double tst = FastMath.tanh(x);
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double ref = Math.tanh(x);
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maxErr = FastMath.max(maxErr, FastMath.abs(ref - tst) / FastMath.ulp(ref));
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}
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Assert.assertEquals(0, maxErr, 4);
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}
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@Test
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public void testHyperbolicInverses() {
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double maxErr = 0;
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for (double x = -30; x < 30; x += 0.01) {
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maxErr = FastMath.max(maxErr, FastMath.abs(x - FastMath.sinh(FastMath.asinh(x))) / (2 * FastMath.ulp(x)));
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}
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Assert.assertEquals(0, maxErr, 3);
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maxErr = 0;
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for (double x = 1; x < 30; x += 0.01) {
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maxErr = FastMath.max(maxErr, FastMath.abs(x - FastMath.cosh(FastMath.acosh(x))) / (2 * FastMath.ulp(x)));
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}
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Assert.assertEquals(0, maxErr, 2);
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maxErr = 0;
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for (double x = -1 + MathUtils.EPSILON; x < 1 - MathUtils.EPSILON; x += 0.0001) {
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maxErr = FastMath.max(maxErr, FastMath.abs(x - FastMath.tanh(FastMath.atanh(x))) / (2 * FastMath.ulp(x)));
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}
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Assert.assertEquals(0, maxErr, 2);
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}
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@Test
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public void testLogAccuracy() {
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double maxerrulp = 0.0;
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for (int i = 0; i < NUMBER_OF_TRIALS; i++) {
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double x = Math.exp(generator.nextDouble() * 1416.0 - 708.0) * generator.nextDouble();
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// double x = generator.nextDouble()*2.0;
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double tst = FastMath.log(x);
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double ref = DfpMath.log(field.newDfp(x)).toDouble();
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double err = (tst - ref) / ref;
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if (err != 0.0) {
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double ulp = Math.abs(ref -
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Double.longBitsToDouble((Double
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.doubleToLongBits(ref) ^ 1)));
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double errulp = field.newDfp(tst).subtract(DfpMath.log(field.newDfp(x))).divide(field.newDfp(ulp)).toDouble();
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// System.out.println(x + "\t" + tst + "\t" + ref + "\t" + err + "\t" + errulp);
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maxerrulp = Math.max(maxerrulp, Math.abs(errulp));
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}
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}
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Assert.assertTrue("log() had errors in excess of " + MAX_ERROR_ULP + " ULP", maxerrulp < MAX_ERROR_ULP);
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}
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@Test
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public void testLog10Accuracy() {
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double maxerrulp = 0.0;
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for (int i = 0; i < NUMBER_OF_TRIALS; i++) {
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double x = Math.exp(generator.nextDouble() * 1416.0 - 708.0) * generator.nextDouble();
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// double x = generator.nextDouble()*2.0;
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double tst = FastMath.log10(x);
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double ref = DfpMath.log(field.newDfp(x)).divide(DfpMath.log(field.newDfp("10"))).toDouble();
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double err = (tst - ref) / ref;
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if (err != 0.0) {
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double ulp = Math.abs(ref -
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Double.longBitsToDouble((Double.doubleToLongBits(ref) ^ 1)));
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double errulp = field.newDfp(tst).subtract(DfpMath.log(field.newDfp(x)).divide(DfpMath.log(field.newDfp("10")))).divide(field.newDfp(ulp)).toDouble();
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// System.out.println(x + "\t" + tst + "\t" + ref + "\t" + err + "\t" + errulp);
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maxerrulp = Math.max(maxerrulp, Math.abs(errulp));
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}
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}
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Assert.assertTrue("log10() had errors in excess of " + MAX_ERROR_ULP + " ULP", maxerrulp < MAX_ERROR_ULP);
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}
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@Test
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public void testLog1pAccuracy() {
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double maxerrulp = 0.0;
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for (int i = 0; i < NUMBER_OF_TRIALS; i++) {
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double x = Math.exp(generator.nextDouble() * 10.0 - 5.0) * generator.nextDouble();
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// double x = generator.nextDouble()*2.0;
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double tst = FastMath.log1p(x);
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double ref = DfpMath.log(field.newDfp(x).add(field.getOne())).toDouble();
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double err = (tst - ref) / ref;
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if (err != 0.0) {
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double ulp = Math.abs(ref -
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Double.longBitsToDouble((Double.doubleToLongBits(ref) ^ 1)));
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double errulp = field.newDfp(tst).subtract(DfpMath.log(field.newDfp(x).add(field.getOne()))).divide(field.newDfp(ulp)).toDouble();
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// System.out.println(x + "\t" + tst + "\t" + ref + "\t" + err + "\t" + errulp);
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maxerrulp = Math.max(maxerrulp, Math.abs(errulp));
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}
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}
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Assert.assertTrue("log1p() had errors in excess of " + MAX_ERROR_ULP + " ULP", maxerrulp < MAX_ERROR_ULP);
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}
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@Test
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public void testLogSpecialCases() {
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double x;
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x = FastMath.log(0.0);
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if (x != Double.NEGATIVE_INFINITY)
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throw new RuntimeException("Log of zero should be -Inf");
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x = FastMath.log(-0.0);
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if (x != Double.NEGATIVE_INFINITY)
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throw new RuntimeException("Log of zero should be -Inf");
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x = FastMath.log(Double.NaN);
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if (x == x)
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throw new RuntimeException("Log of NaN should be NaN");
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x = FastMath.log(-1.0);
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if (x == x)
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throw new RuntimeException("Log of negative number should be NaN");
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x = FastMath.log(Double.MIN_VALUE);
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if (x != -744.4400719213812)
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throw new RuntimeException(
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"Log of Double.MIN_VALUE should be -744.4400719213812");
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x = FastMath.log(-1.0);
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if (x == x)
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throw new RuntimeException("Log of negative number should be NaN");
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x = FastMath.log(Double.POSITIVE_INFINITY);
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if (x != Double.POSITIVE_INFINITY)
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throw new RuntimeException("Log of infinity should be infinity");
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}
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@Test
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public void testExpSpecialCases() {
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double x;
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/* Smallest value that will round up to Double.MIN_VALUE */
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x = FastMath.exp(-745.1332191019411);
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if (x != Double.MIN_VALUE)
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throw new RuntimeException(
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"exp(-745.1332191019411) should be Double.MIN_VALUE");
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x = FastMath.exp(-745.1332191019412);
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if (x != 0.0)
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throw new RuntimeException("exp(-745.1332191019412) should be 0.0");
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x = FastMath.exp(Double.NaN);
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if (x == x)
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throw new RuntimeException("exp of NaN should be NaN");
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x = FastMath.exp(Double.POSITIVE_INFINITY);
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if (x != Double.POSITIVE_INFINITY)
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throw new RuntimeException("exp of infinity should be infinity");
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x = FastMath.exp(Double.NEGATIVE_INFINITY);
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if (x != 0.0)
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throw new RuntimeException("exp of -infinity should be 0.0");
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x = FastMath.exp(1.0);
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if (x != Math.E)
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throw new RuntimeException("exp(1) should be Math.E");
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}
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@Test
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public void testPowSpecialCases() {
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double x;
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x = FastMath.pow(-1.0, 0.0);
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if (x != 1.0)
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throw new RuntimeException("pow(x, 0) should be 1.0");
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x = FastMath.pow(-1.0, -0.0);
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if (x != 1.0)
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throw new RuntimeException("pow(x, -0) should be 1.0");
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x = FastMath.pow(Math.PI, 1.0);
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if (x != Math.PI)
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throw new RuntimeException("pow(PI, 1.0) should be PI");
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x = FastMath.pow(-Math.PI, 1.0);
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if (x != -Math.PI)
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throw new RuntimeException("pow(-PI, 1.0) should be PI");
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x = FastMath.pow(Math.PI, Double.NaN);
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if (x == x)
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throw new RuntimeException("pow(PI, NaN) should be NaN");
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x = FastMath.pow(Double.NaN, Math.PI);
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if (x == x)
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throw new RuntimeException("pow(NaN, PI) should be NaN");
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x = FastMath.pow(2.0, Double.POSITIVE_INFINITY);
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if (x != Double.POSITIVE_INFINITY)
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throw new RuntimeException("pow(2.0, Infinity) should be Infinity");
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x = FastMath.pow(0.5, Double.NEGATIVE_INFINITY);
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if (x != Double.POSITIVE_INFINITY)
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throw new RuntimeException("pow(0.5, -Infinity) should be Infinity");
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x = FastMath.pow(0.5, Double.POSITIVE_INFINITY);
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if (x != 0.0)
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throw new RuntimeException("pow(0.5, Infinity) should be 0.0");
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x = FastMath.pow(2.0, Double.NEGATIVE_INFINITY);
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if (x != 0.0)
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throw new RuntimeException("pow(2.0, -Infinity) should be 0.0");
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x = FastMath.pow(0.0, 0.5);
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if (x != 0.0)
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throw new RuntimeException("pow(0.0, 0.5) should be 0.0");
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x = FastMath.pow(Double.POSITIVE_INFINITY, -0.5);
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if (x != 0.0)
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throw new RuntimeException("pow(Inf, -0.5) should be 0.0");
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x = FastMath.pow(0.0, -0.5);
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if (x != Double.POSITIVE_INFINITY)
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throw new RuntimeException("pow(0.0, -0.5) should be Inf");
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x = FastMath.pow(Double.POSITIVE_INFINITY, 0.5);
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if (x != Double.POSITIVE_INFINITY)
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throw new RuntimeException("pow(Inf, 0.5) should be Inf");
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x = FastMath.pow(-0.0, -3.0);
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if (x != Double.NEGATIVE_INFINITY)
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throw new RuntimeException("pow(-0.0, -3.0) should be -Inf");
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x = FastMath.pow(Double.NEGATIVE_INFINITY, 3.0);
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if (x != Double.NEGATIVE_INFINITY)
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throw new RuntimeException("pow(-Inf, -3.0) should be -Inf");
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x = FastMath.pow(-0.0, -3.5);
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if (x != Double.POSITIVE_INFINITY)
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throw new RuntimeException("pow(-0.0, -3.5) should be Inf");
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x = FastMath.pow(Double.POSITIVE_INFINITY, 3.5);
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if (x != Double.POSITIVE_INFINITY)
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throw new RuntimeException("pow(Inf, 3.5) should be Inf");
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x = FastMath.pow(-2.0, 3.0);
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if (x != -8.0)
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throw new RuntimeException("pow(-2.0, 3.0) should be -8.0");
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x = FastMath.pow(-2.0, 3.5);
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if (x == x)
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throw new RuntimeException("pow(-2.0, 3.5) should be NaN");
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}
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@Test
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public void testAtan2SpecialCases() {
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double x;
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x = FastMath.atan2(Double.NaN, 0.0);
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if (x == x)
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throw new RuntimeException("atan2(NaN, 0.0) should be NaN");
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x = FastMath.atan2(0.0, Double.NaN);
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if (x == x)
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throw new RuntimeException("atan2(0.0, NaN) should be NaN");
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x = FastMath.atan2(0.0, 0.0);
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if (x != 0.0 || 1 / x != Double.POSITIVE_INFINITY)
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throw new RuntimeException("atan2(0.0, 0.0) should be 0.0");
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x = FastMath.atan2(0.0, 0.001);
|
||||
if (x != 0.0 || 1 / x != Double.POSITIVE_INFINITY)
|
||||
throw new RuntimeException("atan2(0.0, 0.001) should be 0.0");
|
||||
|
||||
x = FastMath.atan2(0.1, Double.POSITIVE_INFINITY);
|
||||
if (x != 0.0 || 1 / x != Double.POSITIVE_INFINITY)
|
||||
throw new RuntimeException("atan2(0.1, +Inf) should be 0.0");
|
||||
|
||||
x = FastMath.atan2(-0.0, 0.0);
|
||||
if (x != 0.0 || 1 / x != Double.NEGATIVE_INFINITY)
|
||||
throw new RuntimeException("atan2(-0.0, 0.0) should be -0.0");
|
||||
|
||||
x = FastMath.atan2(-0.0, 0.001);
|
||||
if (x != 0.0 || 1 / x != Double.NEGATIVE_INFINITY)
|
||||
throw new RuntimeException("atan2(-0.0, 0.001) should be -0.0");
|
||||
|
||||
x = FastMath.atan2(-0.1, Double.POSITIVE_INFINITY);
|
||||
if (x != 0.0 || 1 / x != Double.NEGATIVE_INFINITY)
|
||||
throw new RuntimeException("atan2(-0.0, +Inf) should be -0.0");
|
||||
|
||||
x = FastMath.atan2(0.0, -0.0);
|
||||
if (x != Math.PI)
|
||||
throw new RuntimeException("atan2(0.0, -0.0) should be PI");
|
||||
|
||||
x = FastMath.atan2(0.1, Double.NEGATIVE_INFINITY);
|
||||
if (x != Math.PI)
|
||||
throw new RuntimeException("atan2(0.1, -Inf) should be PI");
|
||||
|
||||
x = FastMath.atan2(-0.0, -0.0);
|
||||
if (x != -Math.PI)
|
||||
throw new RuntimeException("atan2(-0.0, -0.0) should be -PI");
|
||||
|
||||
x = FastMath.atan2(-0.1, Double.NEGATIVE_INFINITY);
|
||||
if (x != -Math.PI)
|
||||
throw new RuntimeException("atan2(0.1, -Inf) should be -PI");
|
||||
|
||||
x = FastMath.atan2(0.1, 0.0);
|
||||
if (x != Math.PI / 2)
|
||||
throw new RuntimeException("atan2(0.1, 0.0) should be PI/2");
|
||||
|
||||
x = FastMath.atan2(0.1, -0.0);
|
||||
if (x != Math.PI / 2)
|
||||
throw new RuntimeException("atan2(0.1, -0.0) should be PI/2");
|
||||
|
||||
x = FastMath.atan2(Double.POSITIVE_INFINITY, 0.1);
|
||||
if (x != Math.PI / 2)
|
||||
throw new RuntimeException("atan2(Inf, 0.1) should be PI/2");
|
||||
|
||||
x = FastMath.atan2(Double.POSITIVE_INFINITY, -0.1);
|
||||
if (x != Math.PI / 2)
|
||||
throw new RuntimeException("atan2(Inf, -0.1) should be PI/2");
|
||||
|
||||
x = FastMath.atan2(-0.1, 0.0);
|
||||
if (x != -Math.PI / 2)
|
||||
throw new RuntimeException("atan2(-0.1, 0.0) should be -PI/2");
|
||||
|
||||
x = FastMath.atan2(-0.1, -0.0);
|
||||
if (x != -Math.PI / 2)
|
||||
throw new RuntimeException("atan2(-0.1, -0.0) should be -PI/2");
|
||||
|
||||
x = FastMath.atan2(Double.NEGATIVE_INFINITY, 0.1);
|
||||
if (x != -Math.PI / 2)
|
||||
throw new RuntimeException("atan2(-Inf, 0.1) should be -PI/2");
|
||||
|
||||
x = FastMath.atan2(Double.NEGATIVE_INFINITY, -0.1);
|
||||
if (x != -Math.PI / 2)
|
||||
throw new RuntimeException("atan2(-Inf, -0.1) should be -PI/2");
|
||||
|
||||
x = FastMath.atan2(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);
|
||||
if (x != Math.PI / 4)
|
||||
throw new RuntimeException("atan2(Inf, Inf) should be PI/4");
|
||||
|
||||
x = FastMath.atan2(Double.POSITIVE_INFINITY, Double.NEGATIVE_INFINITY);
|
||||
if (x != Math.PI * 3.0 / 4.0)
|
||||
throw new RuntimeException("atan2(Inf, -Inf) should be PI * 3/4");
|
||||
|
||||
x = FastMath.atan2(Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);
|
||||
if (x != -Math.PI / 4)
|
||||
throw new RuntimeException("atan2(-Inf, Inf) should be -PI/4");
|
||||
|
||||
x = FastMath.atan2(Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY);
|
||||
if (x != -Math.PI * 3.0 / 4.0)
|
||||
throw new RuntimeException("atan2(-Inf, -Inf) should be -PI * 3/4");
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testPowAccuracy() {
|
||||
double maxerrulp = 0.0;
|
||||
|
||||
for (int i = 0; i < NUMBER_OF_TRIALS; i++) {
|
||||
double x = (generator.nextDouble() * 2.0 + 0.25);
|
||||
double y = (generator.nextDouble() * 1200.0 - 600.0) * generator.nextDouble();
|
||||
/*
|
||||
* double x = FastMath.floor(generator.nextDouble()*1024.0 - 512.0); double
|
||||
* y; if (x != 0) y = FastMath.floor(512.0 / FastMath.abs(x)); else
|
||||
* y = generator.nextDouble()*1200.0; y = y - y/2; x = FastMath.pow(2.0, x) *
|
||||
* generator.nextDouble(); y = y * generator.nextDouble();
|
||||
*/
|
||||
|
||||
// double x = generator.nextDouble()*2.0;
|
||||
double tst = FastMath.pow(x, y);
|
||||
double ref = DfpMath.pow(field.newDfp(x), field.newDfp(y)).toDouble();
|
||||
double err = (tst - ref) / ref;
|
||||
|
||||
if (err != 0) {
|
||||
double ulp = Math.abs(ref -
|
||||
Double.longBitsToDouble((Double
|
||||
.doubleToLongBits(ref) ^ 1)));
|
||||
double errulp = field.newDfp(tst).subtract(DfpMath.pow(field.newDfp(x), field.newDfp(y))).divide(field.newDfp(ulp)).toDouble();
|
||||
// System.out.println(x + "\t" + y + "\t" + tst + "\t" + ref + "\t" + err + "\t" + errulp);
|
||||
|
||||
maxerrulp = Math.max(maxerrulp, Math.abs(errulp));
|
||||
}
|
||||
}
|
||||
|
||||
Assert.assertTrue("pow() had errors in excess of " + MAX_ERROR_ULP + " ULP", maxerrulp < MAX_ERROR_ULP);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testExpAccuracy() {
|
||||
double maxerrulp = 0.0;
|
||||
|
||||
for (int i = 0; i < NUMBER_OF_TRIALS; i++) {
|
||||
/* double x = 1.0 + i/1024.0/2.0; */
|
||||
double x = ((generator.nextDouble() * 1416.0) - 708.0) * generator.nextDouble();
|
||||
// double x = (generator.nextDouble() * 20.0) - 10.0;
|
||||
// double x = ((generator.nextDouble() * 2.0) - 1.0) * generator.nextDouble();
|
||||
/* double x = 3.0 / 512.0 * i - 3.0; */
|
||||
double tst = FastMath.exp(x);
|
||||
double ref = DfpMath.exp(field.newDfp(x)).toDouble();
|
||||
double err = (tst - ref) / ref;
|
||||
|
||||
if (err != 0) {
|
||||
double ulp = Math.abs(ref -
|
||||
Double.longBitsToDouble((Double.doubleToLongBits(ref) ^ 1)));
|
||||
double errulp = field.newDfp(tst).subtract(DfpMath.exp(field.newDfp(x))).divide(field.newDfp(ulp)).toDouble();
|
||||
// System.out.println(x + "\t" + tst + "\t" + ref + "\t" + err + "\t" + errulp);
|
||||
|
||||
maxerrulp = Math.max(maxerrulp, Math.abs(errulp));
|
||||
}
|
||||
}
|
||||
|
||||
Assert.assertTrue("exp() had errors in excess of " + MAX_ERROR_ULP + " ULP", maxerrulp < MAX_ERROR_ULP);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testSinAccuracy() {
|
||||
double maxerrulp = 0.0;
|
||||
|
||||
for (int i = 0; i < NUMBER_OF_TRIALS; i++) {
|
||||
/* double x = 1.0 + i/1024.0/2.0; */
|
||||
// double x = ((generator.nextDouble() * 1416.0) - 708.0) * generator.nextDouble();
|
||||
double x = ((generator.nextDouble() * Math.PI) - Math.PI / 2.0) *
|
||||
Math.pow(2, 21) * generator.nextDouble();
|
||||
// double x = (generator.nextDouble() * 20.0) - 10.0;
|
||||
// double x = ((generator.nextDouble() * 2.0) - 1.0) * generator.nextDouble();
|
||||
/* double x = 3.0 / 512.0 * i - 3.0; */
|
||||
double tst = FastMath.sin(x);
|
||||
double ref = DfpMath.sin(field.newDfp(x)).toDouble();
|
||||
double err = (tst - ref) / ref;
|
||||
|
||||
if (err != 0) {
|
||||
double ulp = Math.abs(ref -
|
||||
Double.longBitsToDouble((Double.doubleToLongBits(ref) ^ 1)));
|
||||
double errulp = field.newDfp(tst).subtract(DfpMath.sin(field.newDfp(x))).divide(field.newDfp(ulp)).toDouble();
|
||||
// System.out.println(x + "\t" + tst + "\t" + ref + "\t" + err + "\t" + errulp);
|
||||
|
||||
maxerrulp = Math.max(maxerrulp, Math.abs(errulp));
|
||||
}
|
||||
}
|
||||
|
||||
Assert.assertTrue("sin() had errors in excess of " + MAX_ERROR_ULP + " ULP", maxerrulp < MAX_ERROR_ULP);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testCosAccuracy() {
|
||||
double maxerrulp = 0.0;
|
||||
|
||||
for (int i = 0; i < NUMBER_OF_TRIALS; i++) {
|
||||
/* double x = 1.0 + i/1024.0/2.0; */
|
||||
// double x = ((generator.nextDouble() * 1416.0) - 708.0) * generator.nextDouble();
|
||||
double x = ((generator.nextDouble() * Math.PI) - Math.PI / 2.0) *
|
||||
Math.pow(2, 21) * generator.nextDouble();
|
||||
// double x = (generator.nextDouble() * 20.0) - 10.0;
|
||||
// double x = ((generator.nextDouble() * 2.0) - 1.0) * generator.nextDouble();
|
||||
/* double x = 3.0 / 512.0 * i - 3.0; */
|
||||
double tst = FastMath.cos(x);
|
||||
double ref = DfpMath.cos(field.newDfp(x)).toDouble();
|
||||
double err = (tst - ref) / ref;
|
||||
|
||||
if (err != 0) {
|
||||
double ulp = Math.abs(ref -
|
||||
Double.longBitsToDouble((Double.doubleToLongBits(ref) ^ 1)));
|
||||
double errulp = field.newDfp(tst).subtract(DfpMath.cos(field.newDfp(x))).divide(field.newDfp(ulp)).toDouble();
|
||||
// System.out.println(x + "\t" + tst + "\t" + ref + "\t" + err + "\t" + errulp);
|
||||
|
||||
maxerrulp = Math.max(maxerrulp, Math.abs(errulp));
|
||||
}
|
||||
}
|
||||
|
||||
Assert.assertTrue("cos() had errors in excess of " + MAX_ERROR_ULP + " ULP", maxerrulp < MAX_ERROR_ULP);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testTanAccuracy() {
|
||||
double maxerrulp = 0.0;
|
||||
|
||||
for (int i = 0; i < NUMBER_OF_TRIALS; i++) {
|
||||
/* double x = 1.0 + i/1024.0/2.0; */
|
||||
// double x = ((generator.nextDouble() * 1416.0) - 708.0) * generator.nextDouble();
|
||||
double x = ((generator.nextDouble() * Math.PI) - Math.PI / 2.0) *
|
||||
Math.pow(2, 12) * generator.nextDouble();
|
||||
// double x = (generator.nextDouble() * 20.0) - 10.0;
|
||||
// double x = ((generator.nextDouble() * 2.0) - 1.0) * generator.nextDouble();
|
||||
/* double x = 3.0 / 512.0 * i - 3.0; */
|
||||
double tst = FastMath.tan(x);
|
||||
double ref = DfpMath.tan(field.newDfp(x)).toDouble();
|
||||
double err = (tst - ref) / ref;
|
||||
|
||||
if (err != 0) {
|
||||
double ulp = Math.abs(ref -
|
||||
Double.longBitsToDouble((Double.doubleToLongBits(ref) ^ 1)));
|
||||
double errulp = field.newDfp(tst).subtract(DfpMath.tan(field.newDfp(x))).divide(field.newDfp(ulp)).toDouble();
|
||||
// System.out.println(x + "\t" + tst + "\t" + ref + "\t" + err + "\t" + errulp);
|
||||
|
||||
maxerrulp = Math.max(maxerrulp, Math.abs(errulp));
|
||||
}
|
||||
}
|
||||
|
||||
Assert.assertTrue("tan() had errors in excess of " + MAX_ERROR_ULP + " ULP", maxerrulp < MAX_ERROR_ULP);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testAtanAccuracy() {
|
||||
double maxerrulp = 0.0;
|
||||
|
||||
for (int i = 0; i < NUMBER_OF_TRIALS; i++) {
|
||||
/* double x = 1.0 + i/1024.0/2.0; */
|
||||
// double x = ((generator.nextDouble() * 1416.0) - 708.0) * generator.nextDouble();
|
||||
// double x = ((generator.nextDouble() * Math.PI) - Math.PI/2.0) *
|
||||
// generator.nextDouble();
|
||||
double x = ((generator.nextDouble() * 16.0) - 8.0) * generator.nextDouble();
|
||||
|
||||
// double x = (generator.nextDouble() * 20.0) - 10.0;
|
||||
// double x = ((generator.nextDouble() * 2.0) - 1.0) * generator.nextDouble();
|
||||
/* double x = 3.0 / 512.0 * i - 3.0; */
|
||||
double tst = FastMath.atan(x);
|
||||
double ref = DfpMath.atan(field.newDfp(x)).toDouble();
|
||||
double err = (tst - ref) / ref;
|
||||
|
||||
if (err != 0) {
|
||||
double ulp = Math.abs(ref -
|
||||
Double.longBitsToDouble((Double.doubleToLongBits(ref) ^ 1)));
|
||||
double errulp = field.newDfp(tst).subtract(DfpMath.atan(field.newDfp(x))).divide(field.newDfp(ulp)).toDouble();
|
||||
// System.out.println(x + "\t" + tst + "\t" + ref + "\t" + err + "\t" + errulp);
|
||||
|
||||
maxerrulp = Math.max(maxerrulp, Math.abs(errulp));
|
||||
}
|
||||
}
|
||||
|
||||
Assert.assertTrue("atan() had errors in excess of " + MAX_ERROR_ULP + " ULP", maxerrulp < MAX_ERROR_ULP);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testAtan2Accuracy() {
|
||||
double maxerrulp = 0.0;
|
||||
|
||||
for (int i = 0; i < NUMBER_OF_TRIALS; i++) {
|
||||
/* double x = 1.0 + i/1024.0/2.0; */
|
||||
// double x = ((generator.nextDouble() * 1416.0) - 708.0) * generator.nextDouble();
|
||||
double x = generator.nextDouble() - 0.5;
|
||||
double y = generator.nextDouble() - 0.5;
|
||||
// double x = (generator.nextDouble() * 20.0) - 10.0;
|
||||
// double x = ((generator.nextDouble() * 2.0) - 1.0) * generator.nextDouble();
|
||||
/* double x = 3.0 / 512.0 * i - 3.0; */
|
||||
double tst = FastMath.atan2(y, x);
|
||||
Dfp refdfp = DfpMath.atan(field.newDfp(y)
|
||||
.divide(field.newDfp(x)));
|
||||
/* Make adjustments for sign */
|
||||
if (x < 0.0) {
|
||||
if (y > 0.0)
|
||||
refdfp = field.getPi().add(refdfp);
|
||||
else
|
||||
refdfp = refdfp.subtract(field.getPi());
|
||||
}
|
||||
|
||||
double ref = refdfp.toDouble();
|
||||
double err = (tst - ref) / ref;
|
||||
|
||||
if (err != 0) {
|
||||
double ulp = Math.abs(ref -
|
||||
Double.longBitsToDouble((Double
|
||||
.doubleToLongBits(ref) ^ 1)));
|
||||
double errulp = field.newDfp(tst).subtract(refdfp).divide(field.newDfp(ulp)).toDouble();
|
||||
// System.out.println(x + "\t" + y + "\t" + tst + "\t" + ref + "\t" + errulp);
|
||||
|
||||
maxerrulp = Math.max(maxerrulp, Math.abs(errulp));
|
||||
}
|
||||
}
|
||||
|
||||
Assert.assertTrue("atan2() had errors in excess of " + MAX_ERROR_ULP + " ULP", maxerrulp < MAX_ERROR_ULP);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testExpm1Accuracy() {
|
||||
double maxerrulp = 0.0;
|
||||
|
||||
for (int i = 0; i < NUMBER_OF_TRIALS; i++) {
|
||||
/* double x = 1.0 + i/1024.0/2.0; */
|
||||
// double x = (generator.nextDouble() * 20.0) - 10.0;
|
||||
double x = ((generator.nextDouble() * 16.0) - 8.0) * generator.nextDouble();
|
||||
/* double x = 3.0 / 512.0 * i - 3.0; */
|
||||
double tst = FastMath.expm1(x);
|
||||
double ref = DfpMath.exp(field.newDfp(x)).subtract(field.getOne()).toDouble();
|
||||
double err = (tst - ref) / ref;
|
||||
|
||||
if (err != 0) {
|
||||
double ulp = Math.abs(ref -
|
||||
Double.longBitsToDouble((Double
|
||||
.doubleToLongBits(ref) ^ 1)));
|
||||
double errulp = field.newDfp(tst).subtract(DfpMath.exp(field.newDfp(x)).subtract(field.getOne())).divide(field.newDfp(ulp)).toDouble();
|
||||
// System.out.println(x + "\t" + tst + "\t" + ref + "\t" + err + "\t" + errulp);
|
||||
|
||||
maxerrulp = Math.max(maxerrulp, Math.abs(errulp));
|
||||
}
|
||||
}
|
||||
|
||||
Assert.assertTrue("expm1() had errors in excess of " + MAX_ERROR_ULP + " ULP", maxerrulp < MAX_ERROR_ULP);
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testToDegrees() {
|
||||
double maxerrulp = 0.0;
|
||||
for (int i = 0; i < NUMBER_OF_TRIALS; i++) {
|
||||
double x = generator.nextDouble();
|
||||
double tst = field.newDfp(x).multiply(180).divide(field.getPi()).toDouble();
|
||||
double ref = FastMath.toDegrees(x);
|
||||
double err = (tst - ref) / ref;
|
||||
|
||||
if (err != 0) {
|
||||
double ulp = Math.abs(ref -
|
||||
Double.longBitsToDouble((Double.doubleToLongBits(ref) ^ 1)));
|
||||
double errulp = field.newDfp(tst).subtract(DfpMath.exp(field.newDfp(x)).subtract(field.getOne())).divide(field.newDfp(ulp)).toDouble();
|
||||
// System.out.println(x + "\t" + tst + "\t" + ref + "\t" + err + "\t" + errulp);
|
||||
|
||||
maxerrulp = Math.max(maxerrulp, Math.abs(errulp));
|
||||
}
|
||||
}
|
||||
Assert.assertTrue("toDegrees() had errors in excess of " + MAX_ERROR_ULP + " ULP", maxerrulp < MAX_ERROR_ULP);
|
||||
|
||||
}
|
||||
|
||||
@Test
|
||||
public void testToRadians() {
|
||||
double maxerrulp = 0.0;
|
||||
for (int i = 0; i < NUMBER_OF_TRIALS; i++) {
|
||||
double x = generator.nextDouble();
|
||||
double tst = field.newDfp(x).multiply(field.getPi()).divide(180).toDouble();
|
||||
double ref = FastMath.toRadians(x);
|
||||
double err = (tst - ref) / ref;
|
||||
|
||||
if (err != 0) {
|
||||
double ulp = Math.abs(ref -
|
||||
Double.longBitsToDouble((Double
|
||||
.doubleToLongBits(ref) ^ 1)));
|
||||
double errulp = field.newDfp(tst).subtract(DfpMath.exp(field.newDfp(x)).subtract(field.getOne())).divide(field.newDfp(ulp)).toDouble();
|
||||
// System.out.println(x + "\t" + tst + "\t" + ref + "\t" + err + "\t" + errulp);
|
||||
|
||||
maxerrulp = Math.max(maxerrulp, Math.abs(errulp));
|
||||
}
|
||||
}
|
||||
Assert.assertTrue("toRadians() had errors in excess of " + MAX_ERROR_ULP + " ULP", maxerrulp < MAX_ERROR_ULP);
|
||||
|
||||
}
|
||||
|
||||
@Ignore
|
||||
@Test
|
||||
public void testPerformance() {
|
||||
final int numberOfRuns = 10000000;
|
||||
for (int j = 0; j < 10; j++) {
|
||||
double x = 0;
|
||||
long time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += StrictMath.log(Math.PI + i/* 1.0 + i/1e9 */);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.print("StrictMath.log " + time + "\t" + x + "\t");
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += FastMath.log(Math.PI + i/* 1.0 + i/1e9 */);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.println("FastMath.log " + time + "\t" + x);
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += StrictMath.pow(Math.PI + i / 1e6, i / 1e6);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.print("StrictMath.pow " + time + "\t" + x + "\t");
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += FastMath.pow(Math.PI + i / 1e6, i / 1e6);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.println("FastMath.pow " + time + "\t" + x);
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += StrictMath.exp(i / 1000000.0);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.print("StrictMath.exp " + time + "\t" + x + "\t");
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += FastMath.exp(i / 1000000.0);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.println("FastMath.exp " + time + "\t" + x);
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += StrictMath.sin(i / 1000000.0);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.print("StrictMath.sin " + time + "\t" + x + "\t");
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += FastMath.sin(i / 1000000.0);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.println("FastMath.sin " + time + "\t" + x);
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += StrictMath.cos(i / 1000000.0);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.print("StrictMath.cos " + time + "\t" + x + "\t");
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += FastMath.cos(i / 1000000.0);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.println("FastMath.cos " + time + "\t" + x);
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += StrictMath.tan(i / 1000000.0);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.print("StrictMath.tan " + time + "\t" + x + "\t");
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += FastMath.tan(i / 1000000.0);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.println("FastMath.tan " + time + "\t" + x);
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += StrictMath.atan(i / 1000000.0);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.print("StrictMath.atan " + time + "\t" + x + "\t");
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += FastMath.atan(i / 1000000.0);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.println("FastMath.atan " + time + "\t" + x);
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += StrictMath.expm1(-i / 100000.0);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.print("StrictMath.expm1 " + time + "\t" + x + "\t");
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += FastMath.expm1(-i / 100000.0);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.println("FastMath.expm1 " + time + "\t" + x);
|
||||
|
||||
x = 0;
|
||||
time = System.currentTimeMillis();
|
||||
for (int i = 0; i < numberOfRuns; i++)
|
||||
x += FastMath.expm1(-i / 100000.0);
|
||||
time = System.currentTimeMillis() - time;
|
||||
System.out.println("FastMath.expm1 " + time + "\t" + x);
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
Loading…
Reference in New Issue