author | mchung |
Fri, 22 Aug 2014 14:56:09 -0700 | |
changeset 26197 | 1bb6b68b87cd |
parent 23010 | 6dadb192ad81 |
child 30046 | cf2c86e1819e |
permissions | -rw-r--r-- |
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/* |
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* Copyright (c) 2003, 2012, Oracle and/or its affiliates. All rights reserved. |
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
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* |
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* This code is free software; you can redistribute it and/or modify it |
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* under the terms of the GNU General Public License version 2 only, as |
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* published by the Free Software Foundation. |
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* |
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* This code is distributed in the hope that it will be useful, but WITHOUT |
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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* version 2 for more details (a copy is included in the LICENSE file that |
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* accompanied this code). |
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* |
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* You should have received a copy of the GNU General Public License version |
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* 2 along with this work; if not, write to the Free Software Foundation, |
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
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* |
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
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* or visit www.oracle.com if you need additional information or have any |
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* questions. |
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*/ |
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/* |
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* @test |
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* @bug 4347132 4939441 |
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* @summary Tests for {Math, StrictMath}.cbrt |
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* @author Joseph D. Darcy |
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*/ |
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public class CubeRootTests { |
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private CubeRootTests(){} |
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static final double infinityD = Double.POSITIVE_INFINITY; |
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static final double NaNd = Double.NaN; |
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// Initialize shared random number generator |
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static java.util.Random rand = new java.util.Random(); |
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static int testCubeRootCase(double input, double expected) { |
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int failures=0; |
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double minus_input = -input; |
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double minus_expected = -expected; |
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46 |
failures+=Tests.test("Math.cbrt(double)", input, |
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Math.cbrt(input), expected); |
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failures+=Tests.test("Math.cbrt(double)", minus_input, |
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Math.cbrt(minus_input), minus_expected); |
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failures+=Tests.test("StrictMath.cbrt(double)", input, |
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StrictMath.cbrt(input), expected); |
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failures+=Tests.test("StrictMath.cbrt(double)", minus_input, |
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StrictMath.cbrt(minus_input), minus_expected); |
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return failures; |
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56 |
} |
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58 |
static int testCubeRoot() { |
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59 |
int failures = 0; |
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60 |
double [][] testCases = { |
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{NaNd, NaNd}, |
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{Double.longBitsToDouble(0x7FF0000000000001L), NaNd}, |
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{Double.longBitsToDouble(0xFFF0000000000001L), NaNd}, |
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{Double.longBitsToDouble(0x7FF8555555555555L), NaNd}, |
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{Double.longBitsToDouble(0xFFF8555555555555L), NaNd}, |
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{Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd}, |
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{Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd}, |
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{Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd}, |
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{Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd}, |
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{Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd}, |
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{Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd}, |
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{Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY}, |
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{Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY}, |
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{+0.0, +0.0}, |
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{-0.0, -0.0}, |
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{+1.0, +1.0}, |
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{-1.0, -1.0}, |
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{+8.0, +2.0}, |
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{-8.0, -2.0} |
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}; |
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for(int i = 0; i < testCases.length; i++) { |
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failures += testCubeRootCase(testCases[i][0], |
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testCases[i][1]); |
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} |
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// Test integer perfect cubes less than 2^53. |
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for(int i = 0; i <= 208063; i++) { |
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double d = i; |
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failures += testCubeRootCase(d*d*d, (double)i); |
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} |
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// Test cbrt(2^(3n)) = 2^n. |
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for(int i = 18; i <= Double.MAX_EXPONENT/3; i++) { |
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failures += testCubeRootCase(Math.scalb(1.0, 3*i), |
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Math.scalb(1.0, i) ); |
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} |
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// Test cbrt(2^(-3n)) = 2^-n. |
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for(int i = -1; i >= DoubleConsts.MIN_SUB_EXPONENT/3; i--) { |
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failures += testCubeRootCase(Math.scalb(1.0, 3*i), |
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Math.scalb(1.0, i) ); |
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} |
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// Test random perfect cubes. Create double values with |
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// modest exponents but only have at most the 17 most |
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// significant bits in the significand set; 17*3 = 51, which |
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// is less than the number of bits in a double's significand. |
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long exponentBits1 = |
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Double.doubleToLongBits(Math.scalb(1.0, 55)) & |
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DoubleConsts.EXP_BIT_MASK; |
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long exponentBits2= |
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Double.doubleToLongBits(Math.scalb(1.0, -55)) & |
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DoubleConsts.EXP_BIT_MASK; |
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for(int i = 0; i < 100; i++) { |
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// Take 16 bits since the 17th bit is implicit in the |
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// exponent |
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double input1 = |
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Double.longBitsToDouble(exponentBits1 | |
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// Significand bits |
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((long) (rand.nextInt() & 0xFFFF))<< |
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(DoubleConsts.SIGNIFICAND_WIDTH-1-16)); |
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failures += testCubeRootCase(input1*input1*input1, input1); |
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double input2 = |
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Double.longBitsToDouble(exponentBits2 | |
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// Significand bits |
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((long) (rand.nextInt() & 0xFFFF))<< |
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(DoubleConsts.SIGNIFICAND_WIDTH-1-16)); |
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failures += testCubeRootCase(input2*input2*input2, input2); |
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} |
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// Directly test quality of implementation properties of cbrt |
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// for values that aren't perfect cubes. Verify returned |
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// result meets the 1 ulp test. That is, we want to verify |
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// that for positive x > 1, |
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// y = cbrt(x), |
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// |
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// if (err1=x - y^3 ) < 0, abs((y_pp^3 -x )) < err1 |
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// if (err1=x - y^3 ) > 0, abs((y_mm^3 -x )) < err1 |
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// |
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// where y_mm and y_pp are the next smaller and next larger |
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// floating-point value to y. In other words, if y^3 is too |
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// big, making y larger does not improve the result; likewise, |
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// if y^3 is too small, making y smaller does not improve the |
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// result. |
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// |
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// ...-----|--?--|--?--|-----... Where is the true result? |
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// y_mm y y_pp |
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// |
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// The returned value y should be one of the floating-point |
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// values braketing the true result. However, given y, a |
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// priori we don't know if the true result falls in [y_mm, y] |
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// or [y, y_pp]. The above test looks at the error in x-y^3 |
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// to determine which region the true result is in; e.g. if |
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// y^3 is smaller than x, the true result should be in [y, |
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// y_pp]. Therefore, it would be an error for y_mm to be a |
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// closer approximation to x^(1/3). In this case, it is |
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// permissible, although not ideal, for y_pp^3 to be a closer |
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// approximation to x^(1/3) than y^3. |
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// |
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// We will use pow(y,3) to compute y^3. Although pow is not |
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// correctly rounded, StrictMath.pow should have at most 1 ulp |
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// error. For y > 1, pow(y_mm,3) and pow(y_pp,3) will differ |
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// from pow(y,3) by more than one ulp so the comparision of |
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// errors should still be valid. |
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for(int i = 0; i < 1000; i++) { |
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double d = 1.0 + rand.nextDouble(); |
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double err, err_adjacent; |
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double y1 = Math.cbrt(d); |
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double y2 = StrictMath.cbrt(d); |
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err = d - StrictMath.pow(y1, 3); |
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if (err != 0.0) { |
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if(Double.isNaN(err)) { |
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failures++; |
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System.err.println("Encountered unexpected NaN value: d = " + d + |
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"\tcbrt(d) = " + y1); |
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} else { |
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if (err < 0.0) { |
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err_adjacent = StrictMath.pow(Math.nextUp(y1), 3) - d; |
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} |
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else { // (err > 0.0) |
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err_adjacent = StrictMath.pow(Math.nextAfter(y1,0.0), 3) - d; |
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} |
188 |
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189 |
if (Math.abs(err) > Math.abs(err_adjacent)) { |
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failures++; |
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191 |
System.err.println("For Math.cbrt(" + d + "), returned result " + |
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y1 + "is not as good as adjacent value."); |
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} |
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} |
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} |
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err = d - StrictMath.pow(y2, 3); |
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if (err != 0.0) { |
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if(Double.isNaN(err)) { |
1826 | 201 |
failures++; |
202 |
System.err.println("Encountered unexpected NaN value: d = " + d + |
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"\tcbrt(d) = " + y2); |
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} else { |
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if (err < 0.0) { |
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err_adjacent = StrictMath.pow(Math.nextUp(y2), 3) - d; |
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} |
208 |
else { // (err > 0.0) |
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err_adjacent = StrictMath.pow(Math.nextAfter(y2,0.0), 3) - d; |
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} |
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212 |
if (Math.abs(err) > Math.abs(err_adjacent)) { |
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failures++; |
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System.err.println("For StrictMath.cbrt(" + d + "), returned result " + |
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215 |
y2 + "is not as good as adjacent value."); |
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} |
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} |
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} |
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220 |
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} |
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222 |
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223 |
// Test monotonicity properites near perfect cubes; test two |
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224 |
// numbers before and two numbers after; i.e. for |
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225 |
// |
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226 |
// pcNeighbors[] = |
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227 |
// {nextDown(nextDown(pc)), |
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228 |
// nextDown(pc), |
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229 |
// pc, |
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230 |
// nextUp(pc), |
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231 |
// nextUp(nextUp(pc))} |
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232 |
// |
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233 |
// test that cbrt(pcNeighbors[i]) <= cbrt(pcNeighbors[i+1]) |
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234 |
{ |
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235 |
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236 |
double pcNeighbors[] = new double[5]; |
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237 |
double pcNeighborsCbrt[] = new double[5]; |
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238 |
double pcNeighborsStrictCbrt[] = new double[5]; |
|
239 |
||
240 |
// Test near cbrt(2^(3n)) = 2^n. |
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26197
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mchung
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23010
diff
changeset
|
241 |
for(int i = 18; i <= Double.MAX_EXPONENT/3; i++) { |
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242 |
double pc = Math.scalb(1.0, 3*i); |
1826 | 243 |
|
244 |
pcNeighbors[2] = pc; |
|
10608 | 245 |
pcNeighbors[1] = Math.nextDown(pc); |
246 |
pcNeighbors[0] = Math.nextDown(pcNeighbors[1]); |
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247 |
pcNeighbors[3] = Math.nextUp(pc); |
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248 |
pcNeighbors[4] = Math.nextUp(pcNeighbors[3]); |
1826 | 249 |
|
250 |
for(int j = 0; j < pcNeighbors.length; j++) { |
|
251 |
pcNeighborsCbrt[j] = Math.cbrt(pcNeighbors[j]); |
|
252 |
pcNeighborsStrictCbrt[j] = StrictMath.cbrt(pcNeighbors[j]); |
|
253 |
} |
|
254 |
||
255 |
for(int j = 0; j < pcNeighborsCbrt.length-1; j++) { |
|
256 |
if(pcNeighborsCbrt[j] > pcNeighborsCbrt[j+1] ) { |
|
257 |
failures++; |
|
258 |
System.err.println("Monotonicity failure for Math.cbrt on " + |
|
259 |
pcNeighbors[j] + " and " + |
|
260 |
pcNeighbors[j+1] + "\n\treturned " + |
|
261 |
pcNeighborsCbrt[j] + " and " + |
|
262 |
pcNeighborsCbrt[j+1] ); |
|
263 |
} |
|
264 |
||
265 |
if(pcNeighborsStrictCbrt[j] > pcNeighborsStrictCbrt[j+1] ) { |
|
266 |
failures++; |
|
267 |
System.err.println("Monotonicity failure for StrictMath.cbrt on " + |
|
268 |
pcNeighbors[j] + " and " + |
|
269 |
pcNeighbors[j+1] + "\n\treturned " + |
|
270 |
pcNeighborsStrictCbrt[j] + " and " + |
|
271 |
pcNeighborsStrictCbrt[j+1] ); |
|
272 |
} |
|
273 |
||
274 |
||
275 |
} |
|
276 |
||
277 |
} |
|
278 |
||
279 |
// Test near cbrt(2^(-3n)) = 2^-n. |
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280 |
for(int i = -1; i >= DoubleConsts.MIN_SUB_EXPONENT/3; i--) { |
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281 |
double pc = Math.scalb(1.0, 3*i); |
1826 | 282 |
|
283 |
pcNeighbors[2] = pc; |
|
10608 | 284 |
pcNeighbors[1] = Math.nextDown(pc); |
285 |
pcNeighbors[0] = Math.nextDown(pcNeighbors[1]); |
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286 |
pcNeighbors[3] = Math.nextUp(pc); |
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287 |
pcNeighbors[4] = Math.nextUp(pcNeighbors[3]); |
1826 | 288 |
|
289 |
for(int j = 0; j < pcNeighbors.length; j++) { |
|
290 |
pcNeighborsCbrt[j] = Math.cbrt(pcNeighbors[j]); |
|
291 |
pcNeighborsStrictCbrt[j] = StrictMath.cbrt(pcNeighbors[j]); |
|
292 |
} |
|
293 |
||
294 |
for(int j = 0; j < pcNeighborsCbrt.length-1; j++) { |
|
295 |
if(pcNeighborsCbrt[j] > pcNeighborsCbrt[j+1] ) { |
|
296 |
failures++; |
|
297 |
System.err.println("Monotonicity failure for Math.cbrt on " + |
|
298 |
pcNeighbors[j] + " and " + |
|
299 |
pcNeighbors[j+1] + "\n\treturned " + |
|
300 |
pcNeighborsCbrt[j] + " and " + |
|
301 |
pcNeighborsCbrt[j+1] ); |
|
302 |
} |
|
303 |
||
304 |
if(pcNeighborsStrictCbrt[j] > pcNeighborsStrictCbrt[j+1] ) { |
|
305 |
failures++; |
|
306 |
System.err.println("Monotonicity failure for StrictMath.cbrt on " + |
|
307 |
pcNeighbors[j] + " and " + |
|
308 |
pcNeighbors[j+1] + "\n\treturned " + |
|
309 |
pcNeighborsStrictCbrt[j] + " and " + |
|
310 |
pcNeighborsStrictCbrt[j+1] ); |
|
311 |
} |
|
312 |
||
313 |
||
314 |
} |
|
315 |
} |
|
316 |
} |
|
317 |
||
318 |
return failures; |
|
319 |
} |
|
320 |
||
321 |
public static void main(String argv[]) { |
|
322 |
int failures = 0; |
|
323 |
||
324 |
failures += testCubeRoot(); |
|
325 |
||
326 |
if (failures > 0) { |
|
327 |
System.err.println("Testing cbrt incurred " |
|
328 |
+ failures + " failures."); |
|
329 |
throw new RuntimeException(); |
|
330 |
} |
|
331 |
} |
|
332 |
||
333 |
} |