1/* 2 * Copyright (c) 2003, 2017, Oracle and/or its affiliates. All rights reserved. 3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. 4 * 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 16 * 2 along with this work; if not, write to the Free Software Foundation, 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 * @library /test/lib 27 * @build jdk.test.lib.RandomFactory 28 * @run main CubeRootTests 29 * @bug 4347132 4939441 8078672 30 * @summary Tests for {Math, StrictMath}.cbrt (use -Dseed=X to set PRNG seed) 31 * @author Joseph D. Darcy 32 * @key randomness 33 */ 34 35import jdk.test.lib.RandomFactory; 36 37public class CubeRootTests { 38 private CubeRootTests(){} 39 40 static final double infinityD = Double.POSITIVE_INFINITY; 41 static final double NaNd = Double.NaN; 42 43 // Initialize shared random number generator 44 static java.util.Random rand = RandomFactory.getRandom(); 45 46 static int testCubeRootCase(double input, double expected) { 47 int failures=0; 48 49 double minus_input = -input; 50 double minus_expected = -expected; 51 52 failures+=Tests.test("Math.cbrt(double)", input, 53 Math.cbrt(input), expected); 54 failures+=Tests.test("Math.cbrt(double)", minus_input, 55 Math.cbrt(minus_input), minus_expected); 56 failures+=Tests.test("StrictMath.cbrt(double)", input, 57 StrictMath.cbrt(input), expected); 58 failures+=Tests.test("StrictMath.cbrt(double)", minus_input, 59 StrictMath.cbrt(minus_input), minus_expected); 60 61 return failures; 62 } 63 64 static int testCubeRoot() { 65 int failures = 0; 66 double [][] testCases = { 67 {NaNd, NaNd}, 68 {Double.longBitsToDouble(0x7FF0000000000001L), NaNd}, 69 {Double.longBitsToDouble(0xFFF0000000000001L), NaNd}, 70 {Double.longBitsToDouble(0x7FF8555555555555L), NaNd}, 71 {Double.longBitsToDouble(0xFFF8555555555555L), NaNd}, 72 {Double.longBitsToDouble(0x7FFFFFFFFFFFFFFFL), NaNd}, 73 {Double.longBitsToDouble(0xFFFFFFFFFFFFFFFFL), NaNd}, 74 {Double.longBitsToDouble(0x7FFDeadBeef00000L), NaNd}, 75 {Double.longBitsToDouble(0xFFFDeadBeef00000L), NaNd}, 76 {Double.longBitsToDouble(0x7FFCafeBabe00000L), NaNd}, 77 {Double.longBitsToDouble(0xFFFCafeBabe00000L), NaNd}, 78 {Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY}, 79 {Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY}, 80 {+0.0, +0.0}, 81 {-0.0, -0.0}, 82 {+1.0, +1.0}, 83 {-1.0, -1.0}, 84 {+8.0, +2.0}, 85 {-8.0, -2.0} 86 }; 87 88 for(int i = 0; i < testCases.length; i++) { 89 failures += testCubeRootCase(testCases[i][0], 90 testCases[i][1]); 91 } 92 93 // Test integer perfect cubes less than 2^53. 94 for(int i = 0; i <= 208063; i++) { 95 double d = i; 96 failures += testCubeRootCase(d*d*d, (double)i); 97 } 98 99 // Test cbrt(2^(3n)) = 2^n. 100 for(int i = 18; i <= Double.MAX_EXPONENT/3; i++) { 101 failures += testCubeRootCase(Math.scalb(1.0, 3*i), 102 Math.scalb(1.0, i) ); 103 } 104 105 // Test cbrt(2^(-3n)) = 2^-n. 106 for(int i = -1; i >= DoubleConsts.MIN_SUB_EXPONENT/3; i--) { 107 failures += testCubeRootCase(Math.scalb(1.0, 3*i), 108 Math.scalb(1.0, i) ); 109 } 110 111 // Test random perfect cubes. Create double values with 112 // modest exponents but only have at most the 17 most 113 // significant bits in the significand set; 17*3 = 51, which 114 // is less than the number of bits in a double's significand. 115 long exponentBits1 = 116 Double.doubleToLongBits(Math.scalb(1.0, 55)) & 117 DoubleConsts.EXP_BIT_MASK; 118 long exponentBits2= 119 Double.doubleToLongBits(Math.scalb(1.0, -55)) & 120 DoubleConsts.EXP_BIT_MASK; 121 for(int i = 0; i < 100; i++) { 122 // Take 16 bits since the 17th bit is implicit in the 123 // exponent 124 double input1 = 125 Double.longBitsToDouble(exponentBits1 | 126 // Significand bits 127 ((long) (rand.nextInt() & 0xFFFF))<< 128 (DoubleConsts.SIGNIFICAND_WIDTH-1-16)); 129 failures += testCubeRootCase(input1*input1*input1, input1); 130 131 double input2 = 132 Double.longBitsToDouble(exponentBits2 | 133 // Significand bits 134 ((long) (rand.nextInt() & 0xFFFF))<< 135 (DoubleConsts.SIGNIFICAND_WIDTH-1-16)); 136 failures += testCubeRootCase(input2*input2*input2, input2); 137 } 138 139 // Directly test quality of implementation properties of cbrt 140 // for values that aren't perfect cubes. Verify returned 141 // result meets the 1 ulp test. That is, we want to verify 142 // that for positive x > 1, 143 // y = cbrt(x), 144 // 145 // if (err1=x - y^3 ) < 0, abs((y_pp^3 -x )) < err1 146 // if (err1=x - y^3 ) > 0, abs((y_mm^3 -x )) < err1 147 // 148 // where y_mm and y_pp are the next smaller and next larger 149 // floating-point value to y. In other words, if y^3 is too 150 // big, making y larger does not improve the result; likewise, 151 // if y^3 is too small, making y smaller does not improve the 152 // result. 153 // 154 // ...-----|--?--|--?--|-----... Where is the true result? 155 // y_mm y y_pp 156 // 157 // The returned value y should be one of the floating-point 158 // values braketing the true result. However, given y, a 159 // priori we don't know if the true result falls in [y_mm, y] 160 // or [y, y_pp]. The above test looks at the error in x-y^3 161 // to determine which region the true result is in; e.g. if 162 // y^3 is smaller than x, the true result should be in [y, 163 // y_pp]. Therefore, it would be an error for y_mm to be a 164 // closer approximation to x^(1/3). In this case, it is 165 // permissible, although not ideal, for y_pp^3 to be a closer 166 // approximation to x^(1/3) than y^3. 167 // 168 // We will use pow(y,3) to compute y^3. Although pow is not 169 // correctly rounded, StrictMath.pow should have at most 1 ulp 170 // error. For y > 1, pow(y_mm,3) and pow(y_pp,3) will differ 171 // from pow(y,3) by more than one ulp so the comparision of 172 // errors should still be valid. 173 174 for(int i = 0; i < 1000; i++) { 175 double d = 1.0 + rand.nextDouble(); 176 double err, err_adjacent; 177 178 double y1 = Math.cbrt(d); 179 double y2 = StrictMath.cbrt(d); 180 181 err = d - StrictMath.pow(y1, 3); 182 if (err != 0.0) { 183 if(Double.isNaN(err)) { 184 failures++; 185 System.err.println("Encountered unexpected NaN value: d = " + d + 186 "\tcbrt(d) = " + y1); 187 } else { 188 if (err < 0.0) { 189 err_adjacent = StrictMath.pow(Math.nextUp(y1), 3) - d; 190 } 191 else { // (err > 0.0) 192 err_adjacent = StrictMath.pow(Math.nextAfter(y1,0.0), 3) - d; 193 } 194 195 if (Math.abs(err) > Math.abs(err_adjacent)) { 196 failures++; 197 System.err.println("For Math.cbrt(" + d + "), returned result " + 198 y1 + "is not as good as adjacent value."); 199 } 200 } 201 } 202 203 204 err = d - StrictMath.pow(y2, 3); 205 if (err != 0.0) { 206 if(Double.isNaN(err)) { 207 failures++; 208 System.err.println("Encountered unexpected NaN value: d = " + d + 209 "\tcbrt(d) = " + y2); 210 } else { 211 if (err < 0.0) { 212 err_adjacent = StrictMath.pow(Math.nextUp(y2), 3) - d; 213 } 214 else { // (err > 0.0) 215 err_adjacent = StrictMath.pow(Math.nextAfter(y2,0.0), 3) - d; 216 } 217 218 if (Math.abs(err) > Math.abs(err_adjacent)) { 219 failures++; 220 System.err.println("For StrictMath.cbrt(" + d + "), returned result " + 221 y2 + "is not as good as adjacent value."); 222 } 223 } 224 } 225 226 227 } 228 229 // Test monotonicity properites near perfect cubes; test two 230 // numbers before and two numbers after; i.e. for 231 // 232 // pcNeighbors[] = 233 // {nextDown(nextDown(pc)), 234 // nextDown(pc), 235 // pc, 236 // nextUp(pc), 237 // nextUp(nextUp(pc))} 238 // 239 // test that cbrt(pcNeighbors[i]) <= cbrt(pcNeighbors[i+1]) 240 { 241 242 double pcNeighbors[] = new double[5]; 243 double pcNeighborsCbrt[] = new double[5]; 244 double pcNeighborsStrictCbrt[] = new double[5]; 245 246 // Test near cbrt(2^(3n)) = 2^n. 247 for(int i = 18; i <= Double.MAX_EXPONENT/3; i++) { 248 double pc = Math.scalb(1.0, 3*i); 249 250 pcNeighbors[2] = pc; 251 pcNeighbors[1] = Math.nextDown(pc); 252 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]); 253 pcNeighbors[3] = Math.nextUp(pc); 254 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]); 255 256 for(int j = 0; j < pcNeighbors.length; j++) { 257 pcNeighborsCbrt[j] = Math.cbrt(pcNeighbors[j]); 258 pcNeighborsStrictCbrt[j] = StrictMath.cbrt(pcNeighbors[j]); 259 } 260 261 for(int j = 0; j < pcNeighborsCbrt.length-1; j++) { 262 if(pcNeighborsCbrt[j] > pcNeighborsCbrt[j+1] ) { 263 failures++; 264 System.err.println("Monotonicity failure for Math.cbrt on " + 265 pcNeighbors[j] + " and " + 266 pcNeighbors[j+1] + "\n\treturned " + 267 pcNeighborsCbrt[j] + " and " + 268 pcNeighborsCbrt[j+1] ); 269 } 270 271 if(pcNeighborsStrictCbrt[j] > pcNeighborsStrictCbrt[j+1] ) { 272 failures++; 273 System.err.println("Monotonicity failure for StrictMath.cbrt on " + 274 pcNeighbors[j] + " and " + 275 pcNeighbors[j+1] + "\n\treturned " + 276 pcNeighborsStrictCbrt[j] + " and " + 277 pcNeighborsStrictCbrt[j+1] ); 278 } 279 280 281 } 282 283 } 284 285 // Test near cbrt(2^(-3n)) = 2^-n. 286 for(int i = -1; i >= DoubleConsts.MIN_SUB_EXPONENT/3; i--) { 287 double pc = Math.scalb(1.0, 3*i); 288 289 pcNeighbors[2] = pc; 290 pcNeighbors[1] = Math.nextDown(pc); 291 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]); 292 pcNeighbors[3] = Math.nextUp(pc); 293 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]); 294 295 for(int j = 0; j < pcNeighbors.length; j++) { 296 pcNeighborsCbrt[j] = Math.cbrt(pcNeighbors[j]); 297 pcNeighborsStrictCbrt[j] = StrictMath.cbrt(pcNeighbors[j]); 298 } 299 300 for(int j = 0; j < pcNeighborsCbrt.length-1; j++) { 301 if(pcNeighborsCbrt[j] > pcNeighborsCbrt[j+1] ) { 302 failures++; 303 System.err.println("Monotonicity failure for Math.cbrt on " + 304 pcNeighbors[j] + " and " + 305 pcNeighbors[j+1] + "\n\treturned " + 306 pcNeighborsCbrt[j] + " and " + 307 pcNeighborsCbrt[j+1] ); 308 } 309 310 if(pcNeighborsStrictCbrt[j] > pcNeighborsStrictCbrt[j+1] ) { 311 failures++; 312 System.err.println("Monotonicity failure for StrictMath.cbrt on " + 313 pcNeighbors[j] + " and " + 314 pcNeighbors[j+1] + "\n\treturned " + 315 pcNeighborsStrictCbrt[j] + " and " + 316 pcNeighborsStrictCbrt[j+1] ); 317 } 318 319 320 } 321 } 322 } 323 324 return failures; 325 } 326 327 public static void main(String argv[]) { 328 int failures = 0; 329 330 failures += testCubeRoot(); 331 332 if (failures > 0) { 333 System.err.println("Testing cbrt incurred " 334 + failures + " failures."); 335 throw new RuntimeException(); 336 } 337 } 338 339} 340