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).
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  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.
  22  */
  23 
  24 /*
  25  * @test
  26  * @bug 4851638 4939441
  27  * @summary Tests for {Math, StrictMath}.log1p
  28  * @library /lib/testlibrary
  29  * @build jdk.testlibrary.DoubleUtils jdk.testlibrary.FloatUtils
  30  * @run main Log1pTests
  31  * @author Joseph D. Darcy
  32  */
  33 
  34 import static jdk.testlibrary.DoubleUtils.*;
  35 
  36 public class Log1pTests {
  37     private Log1pTests(){}
  38 
  39     static final double infinityD = Double.POSITIVE_INFINITY;
  40     static final double NaNd = Double.NaN;
  41 
  42     /**
  43      * Formulation taken from HP-15C Advanced Functions Handbook, part
  44      * number HP 0015-90011, p 181.  This is accurate to a few ulps.
  45      */
  46     static double hp15cLogp(double x) {
  47         double u = 1.0 + x;
  48         return (u==1.0? x : StrictMath.log(u)*x/(u-1) );
  49     }
  50 
  51     /*
  52      * The Taylor expansion of ln(1 + x) for -1 < x <= 1 is:
  53      *
  54      * x - x^2/2 + x^3/3 - ... -(-x^j)/j
  55      *
  56      * Therefore, for small values of x, log1p(x) ~= x.  For large
  57      * values of x, log1p(x) ~= log(x).
  58      *
  59      * Also x/(x+1) < ln(1+x) < x
  60      */
  61 
  62     static int testLog1p() {
  63         int failures = 0;
  64 
  65         double [][] testCases = {
  66             {Double.NaN,                NaNd},
  67             {Double.longBitsToDouble(0x7FF0000000000001L),      NaNd},
  68             {Double.longBitsToDouble(0xFFF0000000000001L),      NaNd},
  69             {Double.longBitsToDouble(0x7FF8555555555555L),      NaNd},
  70             {Double.longBitsToDouble(0xFFF8555555555555L),      NaNd},
  71             {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL),      NaNd},
  72             {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL),      NaNd},
  73             {Double.longBitsToDouble(0x7FFDeadBeef00000L),      NaNd},
  74             {Double.longBitsToDouble(0xFFFDeadBeef00000L),      NaNd},
  75             {Double.longBitsToDouble(0x7FFCafeBabe00000L),      NaNd},
  76             {Double.longBitsToDouble(0xFFFCafeBabe00000L),      NaNd},
  77             {Double.NEGATIVE_INFINITY,  NaNd},
  78             {-8.0,                      NaNd},
  79             {-1.0,                      -infinityD},
  80             {-0.0,                      -0.0},
  81             {+0.0,                      +0.0},
  82             {infinityD,                 infinityD},
  83         };
  84 
  85         // Test special cases
  86         for(int i = 0; i < testCases.length; i++) {
  87             failures += testLog1pCaseWithUlpDiff(testCases[i][0],
  88                                                  testCases[i][1], 0);
  89         }
  90 
  91         // For |x| < 2^-54 log1p(x) ~= x
  92         for(int i = MIN_SUB_EXPONENT; i <= -54; i++) {
  93             double d = Math.scalb(2, i);
  94             failures += testLog1pCase(d, d);
  95             failures += testLog1pCase(-d, -d);
  96         }
  97 
  98         // For x > 2^53 log1p(x) ~= log(x)
  99         for(int i = 53; i <= Double.MAX_EXPONENT; i++) {
 100             double d = Math.scalb(2, i);
 101             failures += testLog1pCaseWithUlpDiff(d, StrictMath.log(d), 2.001);
 102         }
 103 
 104         // Construct random values with exponents ranging from -53 to
 105         // 52 and compare against HP-15C formula.
 106         java.util.Random rand = new java.util.Random();
 107         for(int i = 0; i < 1000; i++) {
 108             double d = rand.nextDouble();
 109 
 110             d = Math.scalb(d, -53 - Tests.ilogb(d));
 111 
 112             for(int j = -53; j <= 52; j++) {
 113                 failures += testLog1pCaseWithUlpDiff(d, hp15cLogp(d), 5);
 114 
 115                 d *= 2.0; // increase exponent by 1
 116             }
 117         }
 118 
 119         // Test for monotonicity failures near values y-1 where y ~=
 120         // e^x.  Test two numbers before and two numbers after each
 121         // chosen value; i.e.
 122         //
 123         // pcNeighbors[] =
 124         // {nextDown(nextDown(pc)),
 125         // nextDown(pc),
 126         // pc,
 127         // nextUp(pc),
 128         // nextUp(nextUp(pc))}
 129         //
 130         // and we test that log1p(pcNeighbors[i]) <= log1p(pcNeighbors[i+1])
 131         {
 132             double pcNeighbors[] = new double[5];
 133             double pcNeighborsLog1p[] = new double[5];
 134             double pcNeighborsStrictLog1p[] = new double[5];
 135 
 136             for(int i = -36; i <= 36; i++) {
 137                 double pc = StrictMath.pow(Math.E, i) - 1;
 138 
 139                 pcNeighbors[2] = pc;
 140                 pcNeighbors[1] = Math.nextDown(pc);
 141                 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]);
 142                 pcNeighbors[3] = Math.nextUp(pc);
 143                 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);
 144 
 145                 for(int j = 0; j < pcNeighbors.length; j++) {
 146                     pcNeighborsLog1p[j]       =       Math.log1p(pcNeighbors[j]);
 147                     pcNeighborsStrictLog1p[j] = StrictMath.log1p(pcNeighbors[j]);
 148                 }
 149 
 150                 for(int j = 0; j < pcNeighborsLog1p.length-1; j++) {
 151                     if(pcNeighborsLog1p[j] >  pcNeighborsLog1p[j+1] ) {
 152                         failures++;
 153                         System.err.println("Monotonicity failure for Math.log1p on " +
 154                                           pcNeighbors[j] + " and "  +
 155                                           pcNeighbors[j+1] + "\n\treturned " +
 156                                           pcNeighborsLog1p[j] + " and " +
 157                                           pcNeighborsLog1p[j+1] );
 158                     }
 159 
 160                     if(pcNeighborsStrictLog1p[j] >  pcNeighborsStrictLog1p[j+1] ) {
 161                         failures++;
 162                         System.err.println("Monotonicity failure for StrictMath.log1p on " +
 163                                           pcNeighbors[j] + " and "  +
 164                                           pcNeighbors[j+1] + "\n\treturned " +
 165                                           pcNeighborsStrictLog1p[j] + " and " +
 166                                           pcNeighborsStrictLog1p[j+1] );
 167                     }
 168 
 169 
 170                 }
 171 
 172             }
 173         }
 174 
 175         return failures;
 176     }
 177 
 178     public static int testLog1pCase(double input,
 179                                     double expected) {
 180         return testLog1pCaseWithUlpDiff(input, expected, 1);
 181     }
 182 
 183     public static int testLog1pCaseWithUlpDiff(double input,
 184                                                double expected,
 185                                                double ulps) {
 186         int failures = 0;
 187         failures += Tests.testUlpDiff("Math.lop1p(double",
 188                                       input, Math.log1p(input),
 189                                       expected, ulps);
 190         failures += Tests.testUlpDiff("StrictMath.log1p(double",
 191                                       input, StrictMath.log1p(input),
 192                                       expected, ulps);
 193         return failures;
 194     }
 195 
 196     public static void main(String argv[]) {
 197         int failures = 0;
 198 
 199         failures += testLog1p();
 200 
 201         if (failures > 0) {
 202             System.err.println("Testing log1p incurred "
 203                                + failures + " failures.");
 204             throw new RuntimeException();
 205         }
 206     }
 207 }