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