1 /* 2 * Copyright (c) 2003, 2012, 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 * @bug 4347132 4939441 27 * @summary Tests for {Math, StrictMath}.cbrt 28 * @author Joseph D. Darcy 29 * @key randomness 30 */ 31 32 public class CubeRootTests { 33 private CubeRootTests(){} 34 35 static final double infinityD = Double.POSITIVE_INFINITY; 36 static final double NaNd = Double.NaN; 37 38 // Initialize shared random number generator 39 static java.util.Random rand = new java.util.Random(); 40 41 static int testCubeRootCase(double input, double expected) { 42 int failures=0; 43 44 double minus_input = -input; 45 double minus_expected = -expected; 46 47 failures+=Tests.test("Math.cbrt(double)", input, 48 Math.cbrt(input), expected); 49 failures+=Tests.test("Math.cbrt(double)", minus_input, 50 Math.cbrt(minus_input), minus_expected); 51 failures+=Tests.test("StrictMath.cbrt(double)", input, 52 StrictMath.cbrt(input), expected); 53 failures+=Tests.test("StrictMath.cbrt(double)", minus_input, 54 StrictMath.cbrt(minus_input), minus_expected); 55 56 return failures; 57 } 58 59 static int testCubeRoot() { 60 int failures = 0; 61 double [][] testCases = { 62 {NaNd, 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.POSITIVE_INFINITY, Double.POSITIVE_INFINITY}, 74 {Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY}, 75 {+0.0, +0.0}, 76 {-0.0, -0.0}, 77 {+1.0, +1.0}, 78 {-1.0, -1.0}, 79 {+8.0, +2.0}, 80 {-8.0, -2.0} 81 }; 82 83 for(int i = 0; i < testCases.length; i++) { 84 failures += testCubeRootCase(testCases[i][0], 85 testCases[i][1]); 86 } 87 88 // Test integer perfect cubes less than 2^53. 89 for(int i = 0; i <= 208063; i++) { 90 double d = i; 91 failures += testCubeRootCase(d*d*d, (double)i); 92 } 93 94 // Test cbrt(2^(3n)) = 2^n. 95 for(int i = 18; i <= Double.MAX_EXPONENT/3; i++) { 96 failures += testCubeRootCase(Math.scalb(1.0, 3*i), 97 Math.scalb(1.0, i) ); 98 } 99 100 // Test cbrt(2^(-3n)) = 2^-n. 101 for(int i = -1; i >= DoubleConsts.MIN_SUB_EXPONENT/3; i--) { 102 failures += testCubeRootCase(Math.scalb(1.0, 3*i), 103 Math.scalb(1.0, i) ); 104 } 105 106 // Test random perfect cubes. Create double values with 107 // modest exponents but only have at most the 17 most 108 // significant bits in the significand set; 17*3 = 51, which 109 // is less than the number of bits in a double's significand. 110 long exponentBits1 = 111 Double.doubleToLongBits(Math.scalb(1.0, 55)) & 112 DoubleConsts.EXP_BIT_MASK; 113 long exponentBits2= 114 Double.doubleToLongBits(Math.scalb(1.0, -55)) & 115 DoubleConsts.EXP_BIT_MASK; 116 for(int i = 0; i < 100; i++) { 117 // Take 16 bits since the 17th bit is implicit in the 118 // exponent 119 double input1 = 120 Double.longBitsToDouble(exponentBits1 | 121 // Significand bits 122 ((long) (rand.nextInt() & 0xFFFF))<< 123 (DoubleConsts.SIGNIFICAND_WIDTH-1-16)); 124 failures += testCubeRootCase(input1*input1*input1, input1); 125 126 double input2 = 127 Double.longBitsToDouble(exponentBits2 | 128 // Significand bits 129 ((long) (rand.nextInt() & 0xFFFF))<< 130 (DoubleConsts.SIGNIFICAND_WIDTH-1-16)); 131 failures += testCubeRootCase(input2*input2*input2, input2); 132 } 133 134 // Directly test quality of implementation properties of cbrt 135 // for values that aren't perfect cubes. Verify returned 136 // result meets the 1 ulp test. That is, we want to verify 137 // that for positive x > 1, 138 // y = cbrt(x), 139 // 140 // if (err1=x - y^3 ) < 0, abs((y_pp^3 -x )) < err1 141 // if (err1=x - y^3 ) > 0, abs((y_mm^3 -x )) < err1 142 // 143 // where y_mm and y_pp are the next smaller and next larger 144 // floating-point value to y. In other words, if y^3 is too 145 // big, making y larger does not improve the result; likewise, 146 // if y^3 is too small, making y smaller does not improve the 147 // result. 148 // 149 // ...-----|--?--|--?--|-----... Where is the true result? 150 // y_mm y y_pp 151 // 152 // The returned value y should be one of the floating-point 153 // values braketing the true result. However, given y, a 154 // priori we don't know if the true result falls in [y_mm, y] 155 // or [y, y_pp]. The above test looks at the error in x-y^3 156 // to determine which region the true result is in; e.g. if 157 // y^3 is smaller than x, the true result should be in [y, 158 // y_pp]. Therefore, it would be an error for y_mm to be a 159 // closer approximation to x^(1/3). In this case, it is 160 // permissible, although not ideal, for y_pp^3 to be a closer 161 // approximation to x^(1/3) than y^3. 162 // 163 // We will use pow(y,3) to compute y^3. Although pow is not 164 // correctly rounded, StrictMath.pow should have at most 1 ulp 165 // error. For y > 1, pow(y_mm,3) and pow(y_pp,3) will differ 166 // from pow(y,3) by more than one ulp so the comparision of 167 // errors should still be valid. 168 169 for(int i = 0; i < 1000; i++) { 170 double d = 1.0 + rand.nextDouble(); 171 double err, err_adjacent; 172 173 double y1 = Math.cbrt(d); 174 double y2 = StrictMath.cbrt(d); 175 176 err = d - StrictMath.pow(y1, 3); 177 if (err != 0.0) { 178 if(Double.isNaN(err)) { 179 failures++; 180 System.err.println("Encountered unexpected NaN value: d = " + d + 181 "\tcbrt(d) = " + y1); 182 } else { 183 if (err < 0.0) { 184 err_adjacent = StrictMath.pow(Math.nextUp(y1), 3) - d; 185 } 186 else { // (err > 0.0) 187 err_adjacent = StrictMath.pow(Math.nextAfter(y1,0.0), 3) - d; 188 } 189 190 if (Math.abs(err) > Math.abs(err_adjacent)) { 191 failures++; 192 System.err.println("For Math.cbrt(" + d + "), returned result " + 193 y1 + "is not as good as adjacent value."); 194 } 195 } 196 } 197 198 199 err = d - StrictMath.pow(y2, 3); 200 if (err != 0.0) { 201 if(Double.isNaN(err)) { 202 failures++; 203 System.err.println("Encountered unexpected NaN value: d = " + d + 204 "\tcbrt(d) = " + y2); 205 } else { 206 if (err < 0.0) { 207 err_adjacent = StrictMath.pow(Math.nextUp(y2), 3) - d; 208 } 209 else { // (err > 0.0) 210 err_adjacent = StrictMath.pow(Math.nextAfter(y2,0.0), 3) - d; 211 } 212 213 if (Math.abs(err) > Math.abs(err_adjacent)) { 214 failures++; 215 System.err.println("For StrictMath.cbrt(" + d + "), returned result " + 216 y2 + "is not as good as adjacent value."); 217 } 218 } 219 } 220 221 222 } 223 224 // Test monotonicity properites near perfect cubes; test two 225 // numbers before and two numbers after; i.e. for 226 // 227 // pcNeighbors[] = 228 // {nextDown(nextDown(pc)), 229 // nextDown(pc), 230 // pc, 231 // nextUp(pc), 232 // nextUp(nextUp(pc))} 233 // 234 // test that cbrt(pcNeighbors[i]) <= cbrt(pcNeighbors[i+1]) 235 { 236 237 double pcNeighbors[] = new double[5]; 238 double pcNeighborsCbrt[] = new double[5]; 239 double pcNeighborsStrictCbrt[] = new double[5]; 240 241 // Test near cbrt(2^(3n)) = 2^n. 242 for(int i = 18; i <= Double.MAX_EXPONENT/3; i++) { 243 double pc = Math.scalb(1.0, 3*i); 244 245 pcNeighbors[2] = pc; 246 pcNeighbors[1] = Math.nextDown(pc); 247 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]); 248 pcNeighbors[3] = Math.nextUp(pc); 249 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]); 250 251 for(int j = 0; j < pcNeighbors.length; j++) { 252 pcNeighborsCbrt[j] = Math.cbrt(pcNeighbors[j]); 253 pcNeighborsStrictCbrt[j] = StrictMath.cbrt(pcNeighbors[j]); 254 } 255 256 for(int j = 0; j < pcNeighborsCbrt.length-1; j++) { 257 if(pcNeighborsCbrt[j] > pcNeighborsCbrt[j+1] ) { 258 failures++; 259 System.err.println("Monotonicity failure for Math.cbrt on " + 260 pcNeighbors[j] + " and " + 261 pcNeighbors[j+1] + "\n\treturned " + 262 pcNeighborsCbrt[j] + " and " + 263 pcNeighborsCbrt[j+1] ); 264 } 265 266 if(pcNeighborsStrictCbrt[j] > pcNeighborsStrictCbrt[j+1] ) { 267 failures++; 268 System.err.println("Monotonicity failure for StrictMath.cbrt on " + 269 pcNeighbors[j] + " and " + 270 pcNeighbors[j+1] + "\n\treturned " + 271 pcNeighborsStrictCbrt[j] + " and " + 272 pcNeighborsStrictCbrt[j+1] ); 273 } 274 275 276 } 277 278 } 279 280 // Test near cbrt(2^(-3n)) = 2^-n. 281 for(int i = -1; i >= DoubleConsts.MIN_SUB_EXPONENT/3; i--) { 282 double pc = Math.scalb(1.0, 3*i); 283 284 pcNeighbors[2] = pc; 285 pcNeighbors[1] = Math.nextDown(pc); 286 pcNeighbors[0] = Math.nextDown(pcNeighbors[1]); 287 pcNeighbors[3] = Math.nextUp(pc); 288 pcNeighbors[4] = Math.nextUp(pcNeighbors[3]); 289 290 for(int j = 0; j < pcNeighbors.length; j++) { 291 pcNeighborsCbrt[j] = Math.cbrt(pcNeighbors[j]); 292 pcNeighborsStrictCbrt[j] = StrictMath.cbrt(pcNeighbors[j]); 293 } 294 295 for(int j = 0; j < pcNeighborsCbrt.length-1; j++) { 296 if(pcNeighborsCbrt[j] > pcNeighborsCbrt[j+1] ) { 297 failures++; 298 System.err.println("Monotonicity failure for Math.cbrt on " + 299 pcNeighbors[j] + " and " + 300 pcNeighbors[j+1] + "\n\treturned " + 301 pcNeighborsCbrt[j] + " and " + 302 pcNeighborsCbrt[j+1] ); 303 } 304 305 if(pcNeighborsStrictCbrt[j] > pcNeighborsStrictCbrt[j+1] ) { 306 failures++; 307 System.err.println("Monotonicity failure for StrictMath.cbrt on " + 308 pcNeighbors[j] + " and " + 309 pcNeighbors[j+1] + "\n\treturned " + 310 pcNeighborsStrictCbrt[j] + " and " + 311 pcNeighborsStrictCbrt[j+1] ); 312 } 313 314 315 } 316 } 317 } 318 319 return failures; 320 } 321 322 public static void main(String argv[]) { 323 int failures = 0; 324 325 failures += testCubeRoot(); 326 327 if (failures > 0) { 328 System.err.println("Testing cbrt incurred " 329 + failures + " failures."); 330 throw new RuntimeException(); 331 } 332 } 333 334 }