1 /*
2 * Copyright (c) 2003, 2015, 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 /lib/testlibrary/
27 * @build jdk.testlibrary.*
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
35 import jdk.testlibrary.RandomFactory;
36
37 public 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 }