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 }