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