1 /*
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   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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   6  * under the terms of the GNU General Public License version 2 only, as
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   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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  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
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  23 
  24 /*
  25  * @test
  26  * @bug 4347132 4939441
  27  * @summary Tests for {Math, StrictMath}.cbrt
  28  * @author Joseph D. Darcy

  29  */
  30 
  31 public class CubeRootTests {
  32     private CubeRootTests(){}
  33 
  34     static final double infinityD = Double.POSITIVE_INFINITY;
  35     static final double NaNd = Double.NaN;
  36 
  37     // Initialize shared random number generator
  38     static java.util.Random rand = new java.util.Random();
  39 
  40     static int testCubeRootCase(double input, double expected) {
  41         int failures=0;
  42 
  43         double minus_input = -input;
  44         double minus_expected = -expected;
  45 
  46         failures+=Tests.test("Math.cbrt(double)", input,
  47                              Math.cbrt(input), expected);
  48         failures+=Tests.test("Math.cbrt(double)", minus_input,
  49                              Math.cbrt(minus_input), minus_expected);
  50         failures+=Tests.test("StrictMath.cbrt(double)", input,
  51                              StrictMath.cbrt(input), expected);
  52         failures+=Tests.test("StrictMath.cbrt(double)", minus_input,
  53                              StrictMath.cbrt(minus_input), minus_expected);
  54 
  55         return failures;
  56     }
  57 
  58     static int testCubeRoot() {
  59         int failures = 0;
  60         double [][] testCases = {
  61             {NaNd,                      NaNd},
  62             {Double.longBitsToDouble(0x7FF0000000000001L),      NaNd},
  63             {Double.longBitsToDouble(0xFFF0000000000001L),      NaNd},
  64             {Double.longBitsToDouble(0x7FF8555555555555L),      NaNd},
  65             {Double.longBitsToDouble(0xFFF8555555555555L),      NaNd},
  66             {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL),      NaNd},
  67             {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL),      NaNd},
  68             {Double.longBitsToDouble(0x7FFDeadBeef00000L),      NaNd},
  69             {Double.longBitsToDouble(0xFFFDeadBeef00000L),      NaNd},
  70             {Double.longBitsToDouble(0x7FFCafeBabe00000L),      NaNd},
  71             {Double.longBitsToDouble(0xFFFCafeBabe00000L),      NaNd},
  72             {Double.POSITIVE_INFINITY,  Double.POSITIVE_INFINITY},
  73             {Double.NEGATIVE_INFINITY,  Double.NEGATIVE_INFINITY},
  74             {+0.0,                      +0.0},
  75             {-0.0,                      -0.0},
  76             {+1.0,                      +1.0},
  77             {-1.0,                      -1.0},
  78             {+8.0,                      +2.0},
  79             {-8.0,                      -2.0}
  80         };
  81 
  82         for(int i = 0; i < testCases.length; i++) {
  83             failures += testCubeRootCase(testCases[i][0],
  84                                          testCases[i][1]);
  85         }
  86 
  87         // Test integer perfect cubes less than 2^53.
  88         for(int i = 0; i <= 208063; i++) {
  89             double d = i;
  90             failures += testCubeRootCase(d*d*d, (double)i);
  91         }
  92 
  93         // Test cbrt(2^(3n)) = 2^n.
  94         for(int i = 18; i <= Double.MAX_EXPONENT/3; i++) {
  95             failures += testCubeRootCase(Math.scalb(1.0, 3*i),
  96                                          Math.scalb(1.0, i) );
  97         }
  98 
  99         // Test cbrt(2^(-3n)) = 2^-n.
 100         for(int i = -1; i >= DoubleConsts.MIN_SUB_EXPONENT/3; i--) {
 101             failures += testCubeRootCase(Math.scalb(1.0, 3*i),
 102                                          Math.scalb(1.0, i) );
 103         }
 104 
 105         // Test random perfect cubes.  Create double values with
 106         // modest exponents but only have at most the 17 most
 107         // significant bits in the significand set; 17*3 = 51, which
 108         // is less than the number of bits in a double's significand.
 109         long exponentBits1 =
 110             Double.doubleToLongBits(Math.scalb(1.0, 55)) &
 111             DoubleConsts.EXP_BIT_MASK;
 112         long exponentBits2=
 113             Double.doubleToLongBits(Math.scalb(1.0, -55)) &
 114             DoubleConsts.EXP_BIT_MASK;
 115         for(int i = 0; i < 100; i++) {
 116             // Take 16 bits since the 17th bit is implicit in the
 117             // exponent
 118            double input1 =
 119                Double.longBitsToDouble(exponentBits1 |
 120                                        // Significand bits
 121                                        ((long) (rand.nextInt() & 0xFFFF))<<
 122                                        (DoubleConsts.SIGNIFICAND_WIDTH-1-16));
 123            failures += testCubeRootCase(input1*input1*input1, input1);
 124 
 125            double input2 =
 126                Double.longBitsToDouble(exponentBits2 |
 127                                        // Significand bits
 128                                        ((long) (rand.nextInt() & 0xFFFF))<<
 129                                        (DoubleConsts.SIGNIFICAND_WIDTH-1-16));
 130            failures += testCubeRootCase(input2*input2*input2, input2);
 131         }
 132 
 133         // Directly test quality of implementation properties of cbrt
 134         // for values that aren't perfect cubes.  Verify returned
 135         // result meets the 1 ulp test.  That is, we want to verify
 136         // that for positive x > 1,
 137         // y = cbrt(x),
 138         //
 139         // if (err1=x - y^3 ) < 0, abs((y_pp^3 -x )) < err1
 140         // if (err1=x - y^3 ) > 0, abs((y_mm^3 -x )) < err1
 141         //
 142         // where y_mm and y_pp are the next smaller and next larger
 143         // floating-point value to y.  In other words, if y^3 is too
 144         // big, making y larger does not improve the result; likewise,
 145         // if y^3 is too small, making y smaller does not improve the
 146         // result.
 147         //
 148         // ...-----|--?--|--?--|-----... Where is the true result?
 149         //         y_mm  y     y_pp
 150         //
 151         // The returned value y should be one of the floating-point
 152         // values braketing the true result.  However, given y, a
 153         // priori we don't know if the true result falls in [y_mm, y]
 154         // or [y, y_pp].  The above test looks at the error in x-y^3
 155         // to determine which region the true result is in; e.g. if
 156         // y^3 is smaller than x, the true result should be in [y,
 157         // y_pp].  Therefore, it would be an error for y_mm to be a
 158         // closer approximation to x^(1/3).  In this case, it is
 159         // permissible, although not ideal, for y_pp^3 to be a closer
 160         // approximation to x^(1/3) than y^3.
 161         //
 162         // We will use pow(y,3) to compute y^3.  Although pow is not
 163         // correctly rounded, StrictMath.pow should have at most 1 ulp
 164         // error.  For y > 1, pow(y_mm,3) and pow(y_pp,3) will differ
 165         // from pow(y,3) by more than one ulp so the comparision of
 166         // errors should still be valid.
 167 
 168         for(int i = 0; i < 1000; i++) {
 169             double d = 1.0 + rand.nextDouble();
 170             double err, err_adjacent;
 171 
 172             double y1 = Math.cbrt(d);
 173             double y2 = StrictMath.cbrt(d);
 174 
 175             err = d - StrictMath.pow(y1, 3);
 176             if (err != 0.0) {
 177                 if(Double.isNaN(err)) {
 178                     failures++;
 179                     System.err.println("Encountered unexpected NaN value: d = " + d +
 180                                        "\tcbrt(d) = " + y1);
 181                 } else {
 182                     if (err < 0.0) {
 183                         err_adjacent = StrictMath.pow(Math.nextUp(y1), 3) - d;
 184                     }
 185                     else  { // (err > 0.0)
 186                         err_adjacent = StrictMath.pow(Math.nextAfter(y1,0.0), 3) - d;
 187                     }
 188 
 189                     if (Math.abs(err) > Math.abs(err_adjacent)) {
 190                         failures++;
 191                         System.err.println("For Math.cbrt(" + d + "), returned result " +
 192                                            y1 + "is not as good as adjacent value.");
 193                     }
 194                 }
 195             }
 196 
 197 
 198             err = d - StrictMath.pow(y2, 3);
 199             if (err != 0.0) {
 200                 if(Double.isNaN(err)) {
 201                     failures++;
 202                     System.err.println("Encountered unexpected NaN value: d = " + d +
 203                                        "\tcbrt(d) = " + y2);
 204                 } else {
 205                     if (err < 0.0) {
 206                         err_adjacent = StrictMath.pow(Math.nextUp(y2), 3) - d;
 207                     }
 208                     else  { // (err > 0.0)
 209                         err_adjacent = StrictMath.pow(Math.nextAfter(y2,0.0), 3) - d;
 210                     }
 211 
 212                     if (Math.abs(err) > Math.abs(err_adjacent)) {
 213                         failures++;
 214                         System.err.println("For StrictMath.cbrt(" + d + "), returned result " +
 215                                            y2 + "is not as good as adjacent value.");
 216                     }
 217                 }
 218             }
 219 
 220 
 221         }
 222 
 223         // Test monotonicity properites near perfect cubes; test two
 224         // numbers before and two numbers after; i.e. for
 225         //
 226         // pcNeighbors[] =
 227         // {nextDown(nextDown(pc)),
 228         // nextDown(pc),
 229         // pc,
 230         // nextUp(pc),
 231         // nextUp(nextUp(pc))}
 232         //
 233         // test that cbrt(pcNeighbors[i]) <= cbrt(pcNeighbors[i+1])
 234         {
 235 
 236             double pcNeighbors[] = new double[5];
 237             double pcNeighborsCbrt[] = new double[5];
 238             double pcNeighborsStrictCbrt[] = new double[5];
 239 
 240             // Test near cbrt(2^(3n)) = 2^n.
 241             for(int i = 18; i <= Double.MAX_EXPONENT/3; i++) {
 242                 double pc = Math.scalb(1.0, 3*i);
 243 
 244                 pcNeighbors[2] = pc;
 245                 pcNeighbors[1] = Math.nextDown(pc);
 246                 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]);
 247                 pcNeighbors[3] = Math.nextUp(pc);
 248                 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);
 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.
 280             for(int i = -1; i >= DoubleConsts.MIN_SUB_EXPONENT/3; i--) {
 281                 double pc = Math.scalb(1.0, 3*i);
 282 
 283                 pcNeighbors[2] = pc;
 284                 pcNeighbors[1] = Math.nextDown(pc);
 285                 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]);
 286                 pcNeighbors[3] = Math.nextUp(pc);
 287                 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);
 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 }
--- EOF ---