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Quellcode-Bibliothek© Kompilation durch diese Firma[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]Datei: Sprache: JAVA |
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/*
* Copyright (c) 2003, 2022, Oracle and/or its affiliates. All rights reserved. * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. * * This code is free software; you can redistribute it and/or modify it * under the terms of the GNU General Public License version 2 only, as * published by the Free Software Foundation. * * This code is distributed in the hope that it will be useful, but WITHOUT * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License * version 2 for more details (a copy is included in the LICENSE file that * accompanied this code). * * You should have received a copy of the GNU General Public License version * 2 along with this work; if not, write to the Free Software Foundation, * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. * * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA * or visit www.oracle.com if you need additional information or have any * questions. */ /* * @test * @bug 4851638 4900189 4939441 * @summary Tests for {Math, StrictMath}.expm1 */ /* * The Taylor expansion of expxm1(x) = exp(x) -1 is * * 1 + x/1! + x^2/2! + x^3/3| + ... -1 = * * x + x^2/2! + x^3/3 + ... * * Therefore, for small values of x, expxm1 ~= x. * * For large values of x, expxm1(x) ~= exp(x) * * For large negative x, expxm1(x) ~= -1. */ public class Expm1Tests { private Expm1Tests(){} static final double infinityD = Double.POSITIVE_INFINITY; static final double NaNd = Double.NaN; static int testExpm1() { int failures = 0; double [][] testCases = { {Double.NaN, NaNd}, {Double.longBitsToDouble(0x7FF0000000000001L), NaNd}, {Double.longBitsToDouble(0xFFF0000000000001L), NaNd}, {Double.longBitsToDouble(0x7FF8555555555555L), NaNd}, {Double.longBitsToDouble(0xFFF8555555555555L), NaNd}, {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd}, {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd}, {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd}, {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd}, {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd}, {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd}, {infinityD, infinityD}, {-infinityD, -1.0}, {-0.0, -0.0}, {+0.0, +0.0}, }; // Test special cases for(int i = 0; i < testCases.length; i++) { failures += testExpm1CaseWithUlpDiff(testCases[i][0], testCases[i][1], 0, null); } // For |x| < 2^-54 expm1(x) ~= x for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) { double d = Math.scalb(2, i); failures += testExpm1Case(d, d); failures += testExpm1Case(-d, -d); } // For values of y where exp(y) > 2^54, expm1(x) ~= exp(x). // The least such y is ln(2^54) ~= 37.42994775023705; exp(x) // overflows for x > ~= 709.8 // Use a 2-ulp error threshold to account for errors in the // exp implementation; the increments of d in the loop will be // exact. for(double d = 37.5; d <= 709.5; d += 1.0) { failures += testExpm1CaseWithUlpDiff(d, StrictMath.exp(d), 2, null); } // For x > 710, expm1(x) should be infinity for(int i = 10; i <= Double.MAX_EXPONENT; i++) { double d = Math.scalb(2, i); failures += testExpm1Case(d, infinityD); } // By monotonicity, once the limit is reached, the // implemenation should return the limit for all smaller // values. boolean reachedLimit [] = {false, false}; // Once exp(y) < 0.5 * ulp(1), expm1(y) ~= -1.0; // The greatest such y is ln(2^-53) ~= -36.7368005696771. for(double d = -36.75; d >= -127.75; d -= 1.0) { failures += testExpm1CaseWithUlpDiff(d, -1.0, 1, reachedLimit); } for(int i = 7; i <= Double.MAX_EXPONENT; i++) { double d = -Math.scalb(2, i); failures += testExpm1CaseWithUlpDiff(d, -1.0, 1, reachedLimit); } // Test for monotonicity failures near multiples of log(2). // Test two numbers before and two numbers after each chosen // value; i.e. // // pcNeighbors[] = // {nextDown(nextDown(pc)), // nextDown(pc), // pc, // nextUp(pc), // nextUp(nextUp(pc))} // // and we test that expm1(pcNeighbors[i]) <= expm1(pcNeighbors[i+1]) { double pcNeighbors[] = new double[5]; double pcNeighborsExpm1[] = new double[5]; double pcNeighborsStrictExpm1[] = new double[5]; for(int i = -50; i <= 50; i++) { double pc = StrictMath.log(2)*i; pcNeighbors[2] = pc; pcNeighbors[1] = Math.nextDown(pc); pcNeighbors[0] = Math.nextDown(pcNeighbors[1]); pcNeighbors[3] = Math.nextUp(pc); pcNeighbors[4] = Math.nextUp(pcNeighbors[3]); for(int j = 0; j < pcNeighbors.length; j++) { pcNeighborsExpm1[j] = Math.expm1(pcNeighbors[j]); pcNeighborsStrictExpm1[j] = StrictMath.expm1(pcNeighbors[j]); } for(int j = 0; j < pcNeighborsExpm1.length-1; j++) { if(pcNeighborsExpm1[j] > pcNeighborsExpm1[j+1] ) { failures++; System.err.println("Monotonicity failure for Math.expm1 on " + pcNeighbors[j] + " and " + pcNeighbors[j+1] + "\n\treturned " + pcNeighborsExpm1[j] + " and " + pcNeighborsExpm1[j+1] ); } if(pcNeighborsStrictExpm1[j] > pcNeighborsStrictExpm1[j+1] ) { failures++; System.err.println("Monotonicity failure for StrictMath.expm1 on " + pcNeighbors[j] + " and " + pcNeighbors[j+1] + "\n\treturned " + pcNeighborsStrictExpm1[j] + " and " + pcNeighborsStrictExpm1[j+1] ); } } } } return failures; } public static int testExpm1Case(double input, double expected) { return testExpm1CaseWithUlpDiff(input, expected, 1, null); } public static int testExpm1CaseWithUlpDiff(double input, double expected, double ulps, boolean [] reachedLimit) { int failures = 0; double mathUlps = ulps, strictUlps = ulps; double mathOutput; double strictOutput; if (reachedLimit != null) { if (reachedLimit[0]) mathUlps = 0; if (reachedLimit[1]) strictUlps = 0; } failures += Tests.testUlpDiffWithLowerBound("Math.expm1(double)", input, mathOutput=Math.expm1(input), expected, mathUlps, -1.0); failures += Tests.testUlpDiffWithLowerBound("StrictMath.expm1(double)", input, strictOutput=StrictMath.expm1(input), expected, strictUlps, -1.0); if (reachedLimit != null) { reachedLimit[0] |= (mathOutput == -1.0); reachedLimit[1] |= (strictOutput == -1.0); } return failures; } public static void main(String... argv) { int failures = 0; failures += testExpm1(); if (failures > 0) { System.err.println("Testing expm1 incurred " + failures + " failures."); throw new RuntimeException(); } } } ¤ Dauer der Verarbeitung: 0.2 Sekunden (vorverarbeitet) ¤ |
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