1 /*-
2 * Copyright (c) 2007 David Schultz <das@FreeBSD.org>
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
24 * SUCH DAMAGE.
25 */
26
27 /*
28 * Tests for csqrt{,f}()
29 */
30
31 #include <sys/cdefs.h>
32 __FBSDID("$FreeBSD$");
33
34 #include <sys/param.h>
35
36 #include <assert.h>
37 #include <complex.h>
38 #include <float.h>
39 #include <math.h>
40 #include <stdio.h>
41
42 #include "test-utils.h"
43
44 /*
45 * This is a test hook that can point to csqrtl(), _csqrt(), or to _csqrtf().
46 * The latter two convert to float or double, respectively, and test csqrtf()
47 * and csqrt() with the same arguments.
48 */
49 long double complex (*t_csqrt)(long double complex);
50
51 static long double complex
_csqrtf(long double complex d)52 _csqrtf(long double complex d)
53 {
54
55 return (csqrtf((float complex)d));
56 }
57
58 static long double complex
_csqrt(long double complex d)59 _csqrt(long double complex d)
60 {
61
62 return (csqrt((double complex)d));
63 }
64
65 #pragma STDC CX_LIMITED_RANGE OFF
66
67 /*
68 * Compare d1 and d2 using special rules: NaN == NaN and +0 != -0.
69 * Fail an assertion if they differ.
70 */
71 static void
assert_equal(long double complex d1,long double complex d2)72 assert_equal(long double complex d1, long double complex d2)
73 {
74
75 assert(cfpequal(d1, d2));
76 }
77
78 /*
79 * Test csqrt for some finite arguments where the answer is exact.
80 * (We do not test if it produces correctly rounded answers when the
81 * result is inexact, nor do we check whether it throws spurious
82 * exceptions.)
83 */
84 static void
test_finite()85 test_finite()
86 {
87 static const double tests[] = {
88 /* csqrt(a + bI) = x + yI */
89 /* a b x y */
90 0, 8, 2, 2,
91 0, -8, 2, -2,
92 4, 0, 2, 0,
93 -4, 0, 0, 2,
94 3, 4, 2, 1,
95 3, -4, 2, -1,
96 -3, 4, 1, 2,
97 -3, -4, 1, -2,
98 5, 12, 3, 2,
99 7, 24, 4, 3,
100 9, 40, 5, 4,
101 11, 60, 6, 5,
102 13, 84, 7, 6,
103 33, 56, 7, 4,
104 39, 80, 8, 5,
105 65, 72, 9, 4,
106 987, 9916, 74, 67,
107 5289, 6640, 83, 40,
108 460766389075.0, 16762287900.0, 678910, 12345
109 };
110 /*
111 * We also test some multiples of the above arguments. This
112 * array defines which multiples we use. Note that these have
113 * to be small enough to not cause overflow for float precision
114 * with all of the constants in the above table.
115 */
116 static const double mults[] = {
117 1,
118 2,
119 3,
120 13,
121 16,
122 0x1.p30,
123 0x1.p-30,
124 };
125
126 double a, b;
127 double x, y;
128 int i, j;
129
130 for (i = 0; i < nitems(tests); i += 4) {
131 for (j = 0; j < nitems(mults); j++) {
132 a = tests[i] * mults[j] * mults[j];
133 b = tests[i + 1] * mults[j] * mults[j];
134 x = tests[i + 2] * mults[j];
135 y = tests[i + 3] * mults[j];
136 assert(t_csqrt(CMPLXL(a, b)) == CMPLXL(x, y));
137 }
138 }
139
140 }
141
142 /*
143 * Test the handling of +/- 0.
144 */
145 static void
test_zeros()146 test_zeros()
147 {
148
149 assert_equal(t_csqrt(CMPLXL(0.0, 0.0)), CMPLXL(0.0, 0.0));
150 assert_equal(t_csqrt(CMPLXL(-0.0, 0.0)), CMPLXL(0.0, 0.0));
151 assert_equal(t_csqrt(CMPLXL(0.0, -0.0)), CMPLXL(0.0, -0.0));
152 assert_equal(t_csqrt(CMPLXL(-0.0, -0.0)), CMPLXL(0.0, -0.0));
153 }
154
155 /*
156 * Test the handling of infinities when the other argument is not NaN.
157 */
158 static void
test_infinities()159 test_infinities()
160 {
161 static const double vals[] = {
162 0.0,
163 -0.0,
164 42.0,
165 -42.0,
166 INFINITY,
167 -INFINITY,
168 };
169
170 int i;
171
172 for (i = 0; i < nitems(vals); i++) {
173 if (isfinite(vals[i])) {
174 assert_equal(t_csqrt(CMPLXL(-INFINITY, vals[i])),
175 CMPLXL(0.0, copysignl(INFINITY, vals[i])));
176 assert_equal(t_csqrt(CMPLXL(INFINITY, vals[i])),
177 CMPLXL(INFINITY, copysignl(0.0, vals[i])));
178 }
179 assert_equal(t_csqrt(CMPLXL(vals[i], INFINITY)),
180 CMPLXL(INFINITY, INFINITY));
181 assert_equal(t_csqrt(CMPLXL(vals[i], -INFINITY)),
182 CMPLXL(INFINITY, -INFINITY));
183 }
184 }
185
186 /*
187 * Test the handling of NaNs.
188 */
189 static void
test_nans()190 test_nans()
191 {
192
193 assert(creall(t_csqrt(CMPLXL(INFINITY, NAN))) == INFINITY);
194 assert(isnan(cimagl(t_csqrt(CMPLXL(INFINITY, NAN)))));
195
196 assert(isnan(creall(t_csqrt(CMPLXL(-INFINITY, NAN)))));
197 assert(isinf(cimagl(t_csqrt(CMPLXL(-INFINITY, NAN)))));
198
199 assert_equal(t_csqrt(CMPLXL(NAN, INFINITY)),
200 CMPLXL(INFINITY, INFINITY));
201 assert_equal(t_csqrt(CMPLXL(NAN, -INFINITY)),
202 CMPLXL(INFINITY, -INFINITY));
203
204 assert_equal(t_csqrt(CMPLXL(0.0, NAN)), CMPLXL(NAN, NAN));
205 assert_equal(t_csqrt(CMPLXL(-0.0, NAN)), CMPLXL(NAN, NAN));
206 assert_equal(t_csqrt(CMPLXL(42.0, NAN)), CMPLXL(NAN, NAN));
207 assert_equal(t_csqrt(CMPLXL(-42.0, NAN)), CMPLXL(NAN, NAN));
208 assert_equal(t_csqrt(CMPLXL(NAN, 0.0)), CMPLXL(NAN, NAN));
209 assert_equal(t_csqrt(CMPLXL(NAN, -0.0)), CMPLXL(NAN, NAN));
210 assert_equal(t_csqrt(CMPLXL(NAN, 42.0)), CMPLXL(NAN, NAN));
211 assert_equal(t_csqrt(CMPLXL(NAN, -42.0)), CMPLXL(NAN, NAN));
212 assert_equal(t_csqrt(CMPLXL(NAN, NAN)), CMPLXL(NAN, NAN));
213 }
214
215 /*
216 * Test whether csqrt(a + bi) works for inputs that are large enough to
217 * cause overflow in hypot(a, b) + a. In this case we are using
218 * csqrt(115 + 252*I) == 14 + 9*I
219 * scaled up to near MAX_EXP.
220 */
221 static void
test_overflow(int maxexp)222 test_overflow(int maxexp)
223 {
224 long double a, b;
225 long double complex result;
226
227 a = ldexpl(115 * 0x1p-8, maxexp);
228 b = ldexpl(252 * 0x1p-8, maxexp);
229 result = t_csqrt(CMPLXL(a, b));
230 assert(creall(result) == ldexpl(14 * 0x1p-4, maxexp / 2));
231 assert(cimagl(result) == ldexpl(9 * 0x1p-4, maxexp / 2));
232 }
233
234 int
main(int argc,char * argv[])235 main(int argc, char *argv[])
236 {
237
238 printf("1..15\n");
239
240 /* Test csqrt() */
241 t_csqrt = _csqrt;
242
243 test_finite();
244 printf("ok 1 - csqrt\n");
245
246 test_zeros();
247 printf("ok 2 - csqrt\n");
248
249 test_infinities();
250 printf("ok 3 - csqrt\n");
251
252 test_nans();
253 printf("ok 4 - csqrt\n");
254
255 test_overflow(DBL_MAX_EXP);
256 printf("ok 5 - csqrt\n");
257
258 /* Now test csqrtf() */
259 t_csqrt = _csqrtf;
260
261 test_finite();
262 printf("ok 6 - csqrt\n");
263
264 test_zeros();
265 printf("ok 7 - csqrt\n");
266
267 test_infinities();
268 printf("ok 8 - csqrt\n");
269
270 test_nans();
271 printf("ok 9 - csqrt\n");
272
273 test_overflow(FLT_MAX_EXP);
274 printf("ok 10 - csqrt\n");
275
276 /* Now test csqrtl() */
277 t_csqrt = csqrtl;
278
279 test_finite();
280 printf("ok 11 - csqrt\n");
281
282 test_zeros();
283 printf("ok 12 - csqrt\n");
284
285 test_infinities();
286 printf("ok 13 - csqrt\n");
287
288 test_nans();
289 printf("ok 14 - csqrt\n");
290
291 test_overflow(LDBL_MAX_EXP);
292 printf("ok 15 - csqrt\n");
293
294 return (0);
295 }
296