1 /*
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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.
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  19  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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  23 
  24 /*
  25  * @test
  26  * @bug 4347132 4939441
  27  * @summary Tests for {Math, StrictMath}.cbrt
  28  * @library /lib/testlibrary
  29  * @build jdk.testlibrary.DoubleUtils jdk.testlibrary.FloatUtils
  30  * @run main CubeRootTests
  31  * @author Joseph D. Darcy
  32  */
  33 
  34 import static jdk.testlibrary.DoubleUtils.*;
  35 
  36 public class CubeRootTests {
  37     private CubeRootTests(){}
  38 
  39     static final double infinityD = Double.POSITIVE_INFINITY;
  40     static final double NaNd = Double.NaN;
  41 
  42     // Initialize shared random number generator
  43     static java.util.Random rand = new java.util.Random();
  44 
  45     static int testCubeRootCase(double input, double expected) {
  46         int failures=0;
  47 
  48         double minus_input = -input;
  49         double minus_expected = -expected;
  50 
  51         failures+=Tests.test("Math.cbrt(double)", input,
  52                              Math.cbrt(input), expected);
  53         failures+=Tests.test("Math.cbrt(double)", minus_input,
  54                              Math.cbrt(minus_input), minus_expected);
  55         failures+=Tests.test("StrictMath.cbrt(double)", input,
  56                              StrictMath.cbrt(input), expected);
  57         failures+=Tests.test("StrictMath.cbrt(double)", minus_input,
  58                              StrictMath.cbrt(minus_input), minus_expected);
  59 
  60         return failures;
  61     }
  62 
  63     static int testCubeRoot() {
  64         int failures = 0;
  65         double [][] testCases = {
  66             {NaNd,                      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.POSITIVE_INFINITY,  Double.POSITIVE_INFINITY},
  78             {Double.NEGATIVE_INFINITY,  Double.NEGATIVE_INFINITY},
  79             {+0.0,                      +0.0},
  80             {-0.0,                      -0.0},
  81             {+1.0,                      +1.0},
  82             {-1.0,                      -1.0},
  83             {+8.0,                      +2.0},
  84             {-8.0,                      -2.0}
  85         };
  86 
  87         for(int i = 0; i < testCases.length; i++) {
  88             failures += testCubeRootCase(testCases[i][0],
  89                                          testCases[i][1]);
  90         }
  91 
  92         // Test integer perfect cubes less than 2^53.
  93         for(int i = 0; i <= 208063; i++) {
  94             double d = i;
  95             failures += testCubeRootCase(d*d*d, (double)i);
  96         }
  97 
  98         // Test cbrt(2^(3n)) = 2^n.
  99         for(int i = 18; i <= Double.MAX_EXPONENT/3; i++) {
 100             failures += testCubeRootCase(Math.scalb(1.0, 3*i),
 101                                          Math.scalb(1.0, i) );
 102         }
 103 
 104         // Test cbrt(2^(-3n)) = 2^-n.
 105         for(int i = -1; i >= MIN_SUB_EXPONENT/3; i--) {
 106             failures += testCubeRootCase(Math.scalb(1.0, 3*i),
 107                                          Math.scalb(1.0, i) );
 108         }
 109 
 110         // Test random perfect cubes.  Create double values with
 111         // modest exponents but only have at most the 17 most
 112         // significant bits in the significand set; 17*3 = 51, which
 113         // is less than the number of bits in a double's significand.
 114         long exponentBits1 =
 115             Double.doubleToLongBits(Math.scalb(1.0, 55)) &
 116             EXP_BIT_MASK;
 117         long exponentBits2=
 118             Double.doubleToLongBits(Math.scalb(1.0, -55)) &
 119             EXP_BIT_MASK;
 120         for(int i = 0; i < 100; i++) {
 121             // Take 16 bits since the 17th bit is implicit in the
 122             // exponent
 123            double input1 =
 124                Double.longBitsToDouble(exponentBits1 |
 125                                        // Significand bits
 126                                        ((long) (rand.nextInt() & 0xFFFF))<<
 127                                        (SIGNIFICAND_WIDTH-1-16));
 128            failures += testCubeRootCase(input1*input1*input1, input1);
 129 
 130            double input2 =
 131                Double.longBitsToDouble(exponentBits2 |
 132                                        // Significand bits
 133                                        ((long) (rand.nextInt() & 0xFFFF))<<
 134                                        (SIGNIFICAND_WIDTH-1-16));
 135            failures += testCubeRootCase(input2*input2*input2, input2);
 136         }
 137 
 138         // Directly test quality of implementation properties of cbrt
 139         // for values that aren't perfect cubes.  Verify returned
 140         // result meets the 1 ulp test.  That is, we want to verify
 141         // that for positive x > 1,
 142         // y = cbrt(x),
 143         //
 144         // if (err1=x - y^3 ) < 0, abs((y_pp^3 -x )) < err1
 145         // if (err1=x - y^3 ) > 0, abs((y_mm^3 -x )) < err1
 146         //
 147         // where y_mm and y_pp are the next smaller and next larger
 148         // floating-point value to y.  In other words, if y^3 is too
 149         // big, making y larger does not improve the result; likewise,
 150         // if y^3 is too small, making y smaller does not improve the
 151         // result.
 152         //
 153         // ...-----|--?--|--?--|-----... Where is the true result?
 154         //         y_mm  y     y_pp
 155         //
 156         // The returned value y should be one of the floating-point
 157         // values braketing the true result.  However, given y, a
 158         // priori we don't know if the true result falls in [y_mm, y]
 159         // or [y, y_pp].  The above test looks at the error in x-y^3
 160         // to determine which region the true result is in; e.g. if
 161         // y^3 is smaller than x, the true result should be in [y,
 162         // y_pp].  Therefore, it would be an error for y_mm to be a
 163         // closer approximation to x^(1/3).  In this case, it is
 164         // permissible, although not ideal, for y_pp^3 to be a closer
 165         // approximation to x^(1/3) than y^3.
 166         //
 167         // We will use pow(y,3) to compute y^3.  Although pow is not
 168         // correctly rounded, StrictMath.pow should have at most 1 ulp
 169         // error.  For y > 1, pow(y_mm,3) and pow(y_pp,3) will differ
 170         // from pow(y,3) by more than one ulp so the comparision of
 171         // errors should still be valid.
 172 
 173         for(int i = 0; i < 1000; i++) {
 174             double d = 1.0 + rand.nextDouble();
 175             double err, err_adjacent;
 176 
 177             double y1 = Math.cbrt(d);
 178             double y2 = StrictMath.cbrt(d);
 179 
 180             err = d - StrictMath.pow(y1, 3);
 181             if (err != 0.0) {
 182                 if(Double.isNaN(err)) {
 183                     failures++;
 184                     System.err.println("Encountered unexpected NaN value: d = " + d +
 185                                        "\tcbrt(d) = " + y1);
 186                 } else {
 187                     if (err < 0.0) {
 188                         err_adjacent = StrictMath.pow(Math.nextUp(y1), 3) - d;
 189                     }
 190                     else  { // (err > 0.0)
 191                         err_adjacent = StrictMath.pow(Math.nextAfter(y1,0.0), 3) - d;
 192                     }
 193 
 194                     if (Math.abs(err) > Math.abs(err_adjacent)) {
 195                         failures++;
 196                         System.err.println("For Math.cbrt(" + d + "), returned result " +
 197                                            y1 + "is not as good as adjacent value.");
 198                     }
 199                 }
 200             }
 201 
 202 
 203             err = d - StrictMath.pow(y2, 3);
 204             if (err != 0.0) {
 205                 if(Double.isNaN(err)) {
 206                     failures++;
 207                     System.err.println("Encountered unexpected NaN value: d = " + d +
 208                                        "\tcbrt(d) = " + y2);
 209                 } else {
 210                     if (err < 0.0) {
 211                         err_adjacent = StrictMath.pow(Math.nextUp(y2), 3) - d;
 212                     }
 213                     else  { // (err > 0.0)
 214                         err_adjacent = StrictMath.pow(Math.nextAfter(y2,0.0), 3) - d;
 215                     }
 216 
 217                     if (Math.abs(err) > Math.abs(err_adjacent)) {
 218                         failures++;
 219                         System.err.println("For StrictMath.cbrt(" + d + "), returned result " +
 220                                            y2 + "is not as good as adjacent value.");
 221                     }
 222                 }
 223             }
 224 
 225 
 226         }
 227 
 228         // Test monotonicity properites near perfect cubes; test two
 229         // numbers before and two numbers after; i.e. for
 230         //
 231         // pcNeighbors[] =
 232         // {nextDown(nextDown(pc)),
 233         // nextDown(pc),
 234         // pc,
 235         // nextUp(pc),
 236         // nextUp(nextUp(pc))}
 237         //
 238         // test that cbrt(pcNeighbors[i]) <= cbrt(pcNeighbors[i+1])
 239         {
 240 
 241             double pcNeighbors[] = new double[5];
 242             double pcNeighborsCbrt[] = new double[5];
 243             double pcNeighborsStrictCbrt[] = new double[5];
 244 
 245             // Test near cbrt(2^(3n)) = 2^n.
 246             for(int i = 18; i <= Double.MAX_EXPONENT/3; i++) {
 247                 double pc = Math.scalb(1.0, 3*i);
 248 
 249                 pcNeighbors[2] = pc;
 250                 pcNeighbors[1] = Math.nextDown(pc);
 251                 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]);
 252                 pcNeighbors[3] = Math.nextUp(pc);
 253                 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);
 254 
 255                 for(int j = 0; j < pcNeighbors.length; j++) {
 256                     pcNeighborsCbrt[j] =           Math.cbrt(pcNeighbors[j]);
 257                     pcNeighborsStrictCbrt[j] = StrictMath.cbrt(pcNeighbors[j]);
 258                 }
 259 
 260                 for(int j = 0; j < pcNeighborsCbrt.length-1; j++) {
 261                     if(pcNeighborsCbrt[j] >  pcNeighborsCbrt[j+1] ) {
 262                         failures++;
 263                         System.err.println("Monotonicity failure for Math.cbrt on " +
 264                                           pcNeighbors[j] + " and "  +
 265                                           pcNeighbors[j+1] + "\n\treturned " +
 266                                           pcNeighborsCbrt[j] + " and " +
 267                                           pcNeighborsCbrt[j+1] );
 268                     }
 269 
 270                     if(pcNeighborsStrictCbrt[j] >  pcNeighborsStrictCbrt[j+1] ) {
 271                         failures++;
 272                         System.err.println("Monotonicity failure for StrictMath.cbrt on " +
 273                                           pcNeighbors[j] + " and "  +
 274                                           pcNeighbors[j+1] + "\n\treturned " +
 275                                           pcNeighborsStrictCbrt[j] + " and " +
 276                                           pcNeighborsStrictCbrt[j+1] );
 277                     }
 278 
 279 
 280                 }
 281 
 282             }
 283 
 284             // Test near cbrt(2^(-3n)) = 2^-n.
 285             for(int i = -1; i >= MIN_SUB_EXPONENT/3; i--) {
 286                 double pc = Math.scalb(1.0, 3*i);
 287 
 288                 pcNeighbors[2] = pc;
 289                 pcNeighbors[1] = Math.nextDown(pc);
 290                 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]);
 291                 pcNeighbors[3] = Math.nextUp(pc);
 292                 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]);
 293 
 294                 for(int j = 0; j < pcNeighbors.length; j++) {
 295                     pcNeighborsCbrt[j] =           Math.cbrt(pcNeighbors[j]);
 296                     pcNeighborsStrictCbrt[j] = StrictMath.cbrt(pcNeighbors[j]);
 297                 }
 298 
 299                 for(int j = 0; j < pcNeighborsCbrt.length-1; j++) {
 300                     if(pcNeighborsCbrt[j] >  pcNeighborsCbrt[j+1] ) {
 301                         failures++;
 302                         System.err.println("Monotonicity failure for Math.cbrt on " +
 303                                           pcNeighbors[j] + " and "  +
 304                                           pcNeighbors[j+1] + "\n\treturned " +
 305                                           pcNeighborsCbrt[j] + " and " +
 306                                           pcNeighborsCbrt[j+1] );
 307                     }
 308 
 309                     if(pcNeighborsStrictCbrt[j] >  pcNeighborsStrictCbrt[j+1] ) {
 310                         failures++;
 311                         System.err.println("Monotonicity failure for StrictMath.cbrt on " +
 312                                           pcNeighbors[j] + " and "  +
 313                                           pcNeighbors[j+1] + "\n\treturned " +
 314                                           pcNeighborsStrictCbrt[j] + " and " +
 315                                           pcNeighborsStrictCbrt[j+1] );
 316                     }
 317 
 318 
 319                 }
 320             }
 321         }
 322 
 323         return failures;
 324     }
 325 
 326     public static void main(String argv[]) {
 327         int failures = 0;
 328 
 329         failures += testCubeRoot();
 330 
 331         if (failures > 0) {
 332             System.err.println("Testing cbrt incurred "
 333                                + failures + " failures.");
 334             throw new RuntimeException();
 335         }
 336     }
 337 
 338 }