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  * @key randomness
  30  */
  31 
  32 public class Log1pTests {
  33     private Log1pTests(){}
  34 
  35     static final double infinityD = Double.POSITIVE_INFINITY;
  36     static final double NaNd = Double.NaN;
  37 
  38     /**
  39      * Formulation taken from HP-15C Advanced Functions Handbook, part
  40      * number HP 0015-90011, p 181.  This is accurate to a few ulps.
  41      */
  42     static double hp15cLogp(double x) {
  43         double u = 1.0 + x;
  44         return (u==1.0? x : StrictMath.log(u)*x/(u-1) );
  45     }
  46 
  47     /*
  48      * The Taylor expansion of ln(1 + x) for -1 < x <= 1 is:
  49      *
  50      * x - x^2/2 + x^3/3 - ... -(-x^j)/j
  51      *
  52      * Therefore, for small values of x, log1p(x) ~= x.  For large
  53      * values of x, log1p(x) ~= log(x).
  54      *
  55      * Also x/(x+1) < ln(1+x) < x
  56      */
  57 
  58     static int testLog1p() {
  59         int failures = 0;
  60 
  61         double [][] testCases = {
  62             {Double.NaN,                NaNd},
  63             {Double.longBitsToDouble(0x7FF0000000000001L),      NaNd},
  64             {Double.longBitsToDouble(0xFFF0000000000001L),      NaNd},
  65             {Double.longBitsToDouble(0x7FF8555555555555L),      NaNd},
  66             {Double.longBitsToDouble(0xFFF8555555555555L),      NaNd},
  67             {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL),      NaNd},
  68             {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL),      NaNd},
  69             {Double.longBitsToDouble(0x7FFDeadBeef00000L),      NaNd},
  70             {Double.longBitsToDouble(0xFFFDeadBeef00000L),      NaNd},
  71             {Double.longBitsToDouble(0x7FFCafeBabe00000L),      NaNd},
  72             {Double.longBitsToDouble(0xFFFCafeBabe00000L),      NaNd},
  73             {Double.NEGATIVE_INFINITY,  NaNd},
  74             {-8.0,                      NaNd},
  75             {-1.0,                      -infinityD},
  76             {-0.0,                      -0.0},
  77             {+0.0,                      +0.0},
  78             {infinityD,                 infinityD},
  79         };
  80 
  81         // Test special cases
  82         for(int i = 0; i < testCases.length; i++) {
  83             failures += testLog1pCaseWithUlpDiff(testCases[i][0],
  84                                                  testCases[i][1], 0);
  85         }
  86 
  87         // For |x| < 2^-54 log1p(x) ~= x
  88         for(int i = DoubleConsts.MIN_SUB_EXPONENT; i <= -54; i++) {
  89             double d = Math.scalb(2, i);
  90             failures += testLog1pCase(d, d);
  91             failures += testLog1pCase(-d, -d);
  92         }
  93 
  94         // For x > 2^53 log1p(x) ~= log(x)
  95         for(int i = 53; i <= Double.MAX_EXPONENT; i++) {
  96             double d = Math.scalb(2, i);
  97             failures += testLog1pCaseWithUlpDiff(d, StrictMath.log(d), 2.001);
  98         }
  99 
 100         // Construct random values with exponents ranging from -53 to
 101         // 52 and compare against HP-15C formula.
 102         java.util.Random rand = new java.util.Random();
 103         for(int i = 0; i < 1000; i++) {
 104             double d = rand.nextDouble();
 105 
 106             d = Math.scalb(d, -53 - Tests.ilogb(d));
 107 
 108             for(int j = -53; j <= 52; j++) {
 109                 failures += testLog1pCaseWithUlpDiff(d, hp15cLogp(d), 5);
 110 
 111                 d *= 2.0; // increase exponent by 1
 112             }
 113         }
 114 
 115         // Test for monotonicity failures near values y-1 where y ~=
 116         // e^x.  Test two numbers before and two numbers after each
 117         // chosen value; i.e.
 118         //
 119         // pcNeighbors[] =
 120         // {nextDown(nextDown(pc)),
 121         // nextDown(pc),
 122         // pc,
 123         // nextUp(pc),
 124         // nextUp(nextUp(pc))}
 125         //
 126         // and we test that log1p(pcNeighbors[i]) <= log1p(pcNeighbors[i+1])
 127         {
 128             double pcNeighbors[] = new double[5];
 129             double pcNeighborsLog1p[] = new double[5];
 130             double pcNeighborsStrictLog1p[] = new double[5];
 131 
 132             for(int i = -36; i <= 36; i++) {
 133                 double pc = StrictMath.pow(Math.E, i) - 1;
 134 
 135                 pcNeighbors[2] = pc;
 136                 pcNeighbors[1] = Math.nextDown(pc);
 137                 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]);
 138                 pcNeighbors[3] = Math.nextUp(pc);
 139                 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);
 140 
 141                 for(int j = 0; j < pcNeighbors.length; j++) {
 142                     pcNeighborsLog1p[j]       =       Math.log1p(pcNeighbors[j]);
 143                     pcNeighborsStrictLog1p[j] = StrictMath.log1p(pcNeighbors[j]);
 144                 }
 145 
 146                 for(int j = 0; j < pcNeighborsLog1p.length-1; j++) {
 147                     if(pcNeighborsLog1p[j] >  pcNeighborsLog1p[j+1] ) {
 148                         failures++;
 149                         System.err.println("Monotonicity failure for Math.log1p on " +
 150                                           pcNeighbors[j] + " and "  +
 151                                           pcNeighbors[j+1] + "\n\treturned " +
 152                                           pcNeighborsLog1p[j] + " and " +
 153                                           pcNeighborsLog1p[j+1] );
 154                     }
 155 
 156                     if(pcNeighborsStrictLog1p[j] >  pcNeighborsStrictLog1p[j+1] ) {
 157                         failures++;
 158                         System.err.println("Monotonicity failure for StrictMath.log1p on " +
 159                                           pcNeighbors[j] + " and "  +
 160                                           pcNeighbors[j+1] + "\n\treturned " +
 161                                           pcNeighborsStrictLog1p[j] + " and " +
 162                                           pcNeighborsStrictLog1p[j+1] );
 163                     }
 164 
 165 
 166                 }
 167 
 168             }
 169         }
 170 
 171         return failures;
 172     }
 173 
 174     public static int testLog1pCase(double input,
 175                                     double expected) {
 176         return testLog1pCaseWithUlpDiff(input, expected, 1);
 177     }
 178 
 179     public static int testLog1pCaseWithUlpDiff(double input,
 180                                                double expected,
 181                                                double ulps) {
 182         int failures = 0;
 183         failures += Tests.testUlpDiff("Math.lop1p(double",
 184                                       input, Math.log1p(input),
 185                                       expected, ulps);
 186         failures += Tests.testUlpDiff("StrictMath.log1p(double",
 187                                       input, StrictMath.log1p(input),
 188                                       expected, ulps);
 189         return failures;
 190     }
 191 
 192     public static void main(String argv[]) {
 193         int failures = 0;
 194 
 195         failures += testLog1p();
 196 
 197         if (failures > 0) {
 198             System.err.println("Testing log1p incurred "
 199                                + failures + " failures.");
 200             throw new RuntimeException();
 201         }
 202     }
 203 }