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 * @run main CubeRootTests
28 * @bug 4347132 4939441 8078672
29 * @summary Tests for {Math, StrictMath}.cbrt (use -Dseed=X to set PRNG seed)
30 * @author Joseph D. Darcy
31 * @key randomness
32 */
33
34 import jdk.test.lib.RandomFactory;
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 = RandomFactory.getRandom();
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 >= DoubleConsts.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 DoubleConsts.EXP_BIT_MASK;
117 long exponentBits2=
118 Double.doubleToLongBits(Math.scalb(1.0, -55)) &
119 DoubleConsts.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 (DoubleConsts.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 (DoubleConsts.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 >= DoubleConsts.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 }