1 /*
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   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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   5  * This code is free software; you can redistribute it and/or modify it
   6  * under the terms of the GNU General Public License version 2 only, as
   7  * published by the Free Software Foundation.
   8  *
   9  * This code is distributed in the hope that it will be useful, but WITHOUT
  10  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  11  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  12  * version 2 for more details (a copy is included in the LICENSE file that
  13  * accompanied this code).
  14  *
  15  * You should have received a copy of the GNU General Public License version
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  17  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
  18  *
  19  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
  20  * or visit www.oracle.com if you need additional information or have any
  21  * questions.
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  23 
  24 /*
  25  * @test
  26  * @bug 4851638 4939441
  27  * @summary Tests for {Math, StrictMath}.log1p
  28  * @author Joseph D. Darcy
  29  */
  30 
  31 import sun.misc.DoubleConsts;
  32 
  33 public class Log1pTests {
  34     private Log1pTests(){}
  35 
  36     static final double infinityD = Double.POSITIVE_INFINITY;
  37     static final double NaNd = Double.NaN;
  38 
  39     /**
  40      * Formulation taken from HP-15C Advanced Functions Handbook, part
  41      * number HP 0015-90011, p 181.  This is accurate to a few ulps.
  42      */
  43     static double hp15cLogp(double x) {
  44         double u = 1.0 + x;
  45         return (u==1.0? x : StrictMath.log(u)*x/(u-1) );
  46     }
  47 
  48     /*
  49      * The Taylor expansion of ln(1 + x) for -1 < x <= 1 is:
  50      *
  51      * x - x^2/2 + x^3/3 - ... -(-x^j)/j
  52      *
  53      * Therefore, for small values of x, log1p(x) ~= x.  For large
  54      * values of x, log1p(x) ~= log(x).
  55      *
  56      * Also x/(x+1) < ln(1+x) < x
  57      */
  58 
  59     static int testLog1p() {
  60         int failures = 0;
  61 
  62         double [][] testCases = {
  63             {Double.NaN,                NaNd},
  64             {Double.longBitsToDouble(0x7FF0000000000001L),      NaNd},
  65             {Double.longBitsToDouble(0xFFF0000000000001L),      NaNd},
  66             {Double.longBitsToDouble(0x7FF8555555555555L),      NaNd},
  67             {Double.longBitsToDouble(0xFFF8555555555555L),      NaNd},
  68             {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL),      NaNd},
  69             {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL),      NaNd},
  70             {Double.longBitsToDouble(0x7FFDeadBeef00000L),      NaNd},
  71             {Double.longBitsToDouble(0xFFFDeadBeef00000L),      NaNd},
  72             {Double.longBitsToDouble(0x7FFCafeBabe00000L),      NaNd},
  73             {Double.longBitsToDouble(0xFFFCafeBabe00000L),      NaNd},
  74             {Double.NEGATIVE_INFINITY,  NaNd},
  75             {-8.0,                      NaNd},
  76             {-1.0,                      -infinityD},
  77             {-0.0,                      -0.0},
  78             {+0.0,                      +0.0},
  79             {infinityD,                 infinityD},
  80         };
  81 
  82         // Test special cases
  83         for(int i = 0; i < testCases.length; i++) {
  84             failures += testLog1pCaseWithUlpDiff(testCases[i][0],
  85                                                  testCases[i][1], 0);
  86         }
  87 
  88         // For |x| < 2^-54 log1p(x) ~= x
  89         for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) {
  90             double d = Math.scalb(2, i);
  91             failures += testLog1pCase(d, d);
  92             failures += testLog1pCase(-d, -d);
  93         }
  94 
  95         // For x > 2^53 log1p(x) ~= log(x)
  96         for(int i = 53; i <= DoubleConsts.MAX_EXPONENT; i++) {
  97             double d = Math.scalb(2, i);
  98             failures += testLog1pCaseWithUlpDiff(d, StrictMath.log(d), 2.001);
  99         }
 100 
 101         // Construct random values with exponents ranging from -53 to
 102         // 52 and compare against HP-15C formula.
 103         java.util.Random rand = new java.util.Random();
 104         for(int i = 0; i < 1000; i++) {
 105             double d = rand.nextDouble();
 106 
 107             d = Math.scalb(d, -53 - Tests.ilogb(d));
 108 
 109             for(int j = -53; j <= 52; j++) {
 110                 failures += testLog1pCaseWithUlpDiff(d, hp15cLogp(d), 5);
 111 
 112                 d *= 2.0; // increase exponent by 1
 113             }
 114         }
 115 
 116         // Test for monotonicity failures near values y-1 where y ~=
 117         // e^x.  Test two numbers before and two numbers after each
 118         // chosen value; i.e.
 119         //
 120         // pcNeighbors[] =
 121         // {nextDown(nextDown(pc)),
 122         // nextDown(pc),
 123         // pc,
 124         // nextUp(pc),
 125         // nextUp(nextUp(pc))}
 126         //
 127         // and we test that log1p(pcNeighbors[i]) <= log1p(pcNeighbors[i+1])
 128         {
 129             double pcNeighbors[] = new double[5];
 130             double pcNeighborsLog1p[] = new double[5];
 131             double pcNeighborsStrictLog1p[] = new double[5];
 132 
 133             for(int i = -36; i <= 36; i++) {
 134                 double pc = StrictMath.pow(Math.E, i) - 1;
 135 
 136                 pcNeighbors[2] = pc;
 137                 pcNeighbors[1] = Math.nextDown(pc);
 138                 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]);
 139                 pcNeighbors[3] = Math.nextUp(pc);
 140                 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);
 141 
 142                 for(int j = 0; j < pcNeighbors.length; j++) {
 143                     pcNeighborsLog1p[j]       =       Math.log1p(pcNeighbors[j]);
 144                     pcNeighborsStrictLog1p[j] = StrictMath.log1p(pcNeighbors[j]);
 145                 }
 146 
 147                 for(int j = 0; j < pcNeighborsLog1p.length-1; j++) {
 148                     if(pcNeighborsLog1p[j] >  pcNeighborsLog1p[j+1] ) {
 149                         failures++;
 150                         System.err.println("Monotonicity failure for Math.log1p on " +
 151                                           pcNeighbors[j] + " and "  +
 152                                           pcNeighbors[j+1] + "\n\treturned " +
 153                                           pcNeighborsLog1p[j] + " and " +
 154                                           pcNeighborsLog1p[j+1] );
 155                     }
 156 
 157                     if(pcNeighborsStrictLog1p[j] >  pcNeighborsStrictLog1p[j+1] ) {
 158                         failures++;
 159                         System.err.println("Monotonicity failure for StrictMath.log1p on " +
 160                                           pcNeighbors[j] + " and "  +
 161                                           pcNeighbors[j+1] + "\n\treturned " +
 162                                           pcNeighborsStrictLog1p[j] + " and " +
 163                                           pcNeighborsStrictLog1p[j+1] );
 164                     }
 165 
 166 
 167                 }
 168 
 169             }
 170         }
 171 
 172         return failures;
 173     }
 174 
 175     public static int testLog1pCase(double input,
 176                                     double expected) {
 177         return testLog1pCaseWithUlpDiff(input, expected, 1);
 178     }
 179 
 180     public static int testLog1pCaseWithUlpDiff(double input,
 181                                                double expected,
 182                                                double ulps) {
 183         int failures = 0;
 184         failures += Tests.testUlpDiff("Math.lop1p(double",
 185                                       input, Math.log1p(input),
 186                                       expected, ulps);
 187         failures += Tests.testUlpDiff("StrictMath.log1p(double",
 188                                       input, StrictMath.log1p(input),
 189                                       expected, ulps);
 190         return failures;
 191     }
 192 
 193     public static void main(String argv[]) {
 194         int failures = 0;
 195 
 196         failures += testLog1p();
 197 
 198         if (failures > 0) {
 199             System.err.println("Testing log1p incurred "
 200                                + failures + " failures.");
 201             throw new RuntimeException();
 202         }
 203     }
 204 }