1 /*-
2 * Copyright (c) 2008-2011 David Schultz <[email protected]>
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 corner cases in cexp*().
29 */
30
31 #include <sys/cdefs.h>
32 #include <sys/param.h>
33
34 #include <complex.h>
35 #include <fenv.h>
36 #include <float.h>
37 #include <math.h>
38 #include <stdio.h>
39
40 #include "test-utils.h"
41
42 #pragma STDC FENV_ACCESS ON
43 #pragma STDC CX_LIMITED_RANGE OFF
44
45 /*
46 * Test that a function returns the correct value and sets the
47 * exception flags correctly. The exceptmask specifies which
48 * exceptions we should check. We need to be lenient for several
49 * reasons, but mainly because on some architectures it's impossible
50 * to raise FE_OVERFLOW without raising FE_INEXACT. In some cases,
51 * whether cexp() raises an invalid exception is unspecified.
52 *
53 * These are macros instead of functions so that assert provides more
54 * meaningful error messages.
55 *
56 * XXX The volatile here is to avoid gcc's bogus constant folding and work
57 * around the lack of support for the FENV_ACCESS pragma.
58 */
59 #define test_t(type, func, z, result, exceptmask, excepts, checksign) \
60 do { \
61 volatile long double complex _d = z; \
62 volatile type complex _r = result; \
63 ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \
64 CHECK_CFPEQUAL_CS((func)(_d), (_r), (checksign)); \
65 CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \
66 #func, #z); \
67 } while (0)
68
69 #define test(func, z, result, exceptmask, excepts, checksign) \
70 test_t(double, func, z, result, exceptmask, excepts, checksign)
71
72 #define test_f(func, z, result, exceptmask, excepts, checksign) \
73 test_t(float, func, z, result, exceptmask, excepts, checksign)
74
75 /* Test within a given tolerance. */
76 #define test_tol(func, z, result, tol) do { \
77 CHECK_CFPEQUAL_TOL((func)(z), (result), (tol), \
78 FPE_ABS_ZERO | CS_BOTH); \
79 } while (0)
80
81 /* Test all the functions that compute cexp(x). */
82 #define testall(x, result, exceptmask, excepts, checksign) do { \
83 test(cexp, x, result, exceptmask, excepts, checksign); \
84 test_f(cexpf, x, result, exceptmask, excepts, checksign); \
85 } while (0)
86
87 /*
88 * Test all the functions that compute cexp(x), within a given tolerance.
89 * The tolerance is specified in ulps.
90 */
91 #define testall_tol(x, result, tol) do { \
92 test_tol(cexp, x, result, tol * DBL_ULP()); \
93 test_tol(cexpf, x, result, tol * FLT_ULP()); \
94 } while (0)
95
96 /* Various finite non-zero numbers to test. */
97 static const float finites[] =
98 { -42.0e20, -1.0, -1.0e-10, -0.0, 0.0, 1.0e-10, 1.0, 42.0e20 };
99
100
101 /* Tests for 0 */
102 ATF_TC_WITHOUT_HEAD(zero);
ATF_TC_BODY(zero,tc)103 ATF_TC_BODY(zero, tc)
104 {
105
106 /* cexp(0) = 1, no exceptions raised */
107 testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
108 testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
109 testall(CMPLXL(0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
110 testall(CMPLXL(-0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
111 }
112
113 /*
114 * Tests for NaN. The signs of the results are indeterminate unless the
115 * imaginary part is 0.
116 */
117 ATF_TC_WITHOUT_HEAD(nan);
ATF_TC_BODY(nan,tc)118 ATF_TC_BODY(nan, tc)
119 {
120 unsigned i;
121
122 /* cexp(x + NaNi) = NaN + NaNi and optionally raises invalid */
123 /* cexp(NaN + yi) = NaN + NaNi and optionally raises invalid (|y|>0) */
124 for (i = 0; i < nitems(finites); i++) {
125 testall(CMPLXL(finites[i], NAN), CMPLXL(NAN, NAN),
126 ALL_STD_EXCEPT & ~FE_INVALID, 0, 0);
127 if (finites[i] == 0.0)
128 continue;
129 /* XXX FE_INEXACT shouldn't be raised here */
130 testall(CMPLXL(NAN, finites[i]), CMPLXL(NAN, NAN),
131 ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0);
132 }
133
134 /* cexp(NaN +- 0i) = NaN +- 0i */
135 testall(CMPLXL(NAN, 0.0), CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 1);
136 testall(CMPLXL(NAN, -0.0), CMPLXL(NAN, -0.0), ALL_STD_EXCEPT, 0, 1);
137
138 /* cexp(inf + NaN i) = inf + nan i */
139 testall(CMPLXL(INFINITY, NAN), CMPLXL(INFINITY, NAN),
140 ALL_STD_EXCEPT, 0, 0);
141 /* cexp(-inf + NaN i) = 0 */
142 testall(CMPLXL(-INFINITY, NAN), CMPLXL(0.0, 0.0),
143 ALL_STD_EXCEPT, 0, 0);
144 /* cexp(NaN + NaN i) = NaN + NaN i */
145 testall(CMPLXL(NAN, NAN), CMPLXL(NAN, NAN),
146 ALL_STD_EXCEPT, 0, 0);
147 }
148
149 ATF_TC_WITHOUT_HEAD(inf);
ATF_TC_BODY(inf,tc)150 ATF_TC_BODY(inf, tc)
151 {
152 unsigned i;
153
154 /* cexp(x + inf i) = NaN + NaNi and raises invalid */
155 for (i = 0; i < nitems(finites); i++) {
156 testall(CMPLXL(finites[i], INFINITY), CMPLXL(NAN, NAN),
157 ALL_STD_EXCEPT, FE_INVALID, 1);
158 }
159 /* cexp(-inf + yi) = 0 * (cos(y) + sin(y)i) */
160 /* XXX shouldn't raise an inexact exception */
161 testall(CMPLXL(-INFINITY, M_PI_4), CMPLXL(0.0, 0.0),
162 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
163 testall(CMPLXL(-INFINITY, 3 * M_PI_4), CMPLXL(-0.0, 0.0),
164 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
165 testall(CMPLXL(-INFINITY, 5 * M_PI_4), CMPLXL(-0.0, -0.0),
166 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
167 testall(CMPLXL(-INFINITY, 7 * M_PI_4), CMPLXL(0.0, -0.0),
168 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
169 testall(CMPLXL(-INFINITY, 0.0), CMPLXL(0.0, 0.0),
170 ALL_STD_EXCEPT, 0, 1);
171 testall(CMPLXL(-INFINITY, -0.0), CMPLXL(0.0, -0.0),
172 ALL_STD_EXCEPT, 0, 1);
173 /* cexp(inf + yi) = inf * (cos(y) + sin(y)i) (except y=0) */
174 /* XXX shouldn't raise an inexact exception */
175 testall(CMPLXL(INFINITY, M_PI_4), CMPLXL(INFINITY, INFINITY),
176 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
177 testall(CMPLXL(INFINITY, 3 * M_PI_4), CMPLXL(-INFINITY, INFINITY),
178 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
179 testall(CMPLXL(INFINITY, 5 * M_PI_4), CMPLXL(-INFINITY, -INFINITY),
180 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
181 testall(CMPLXL(INFINITY, 7 * M_PI_4), CMPLXL(INFINITY, -INFINITY),
182 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
183 /* cexp(inf + 0i) = inf + 0i */
184 testall(CMPLXL(INFINITY, 0.0), CMPLXL(INFINITY, 0.0),
185 ALL_STD_EXCEPT, 0, 1);
186 testall(CMPLXL(INFINITY, -0.0), CMPLXL(INFINITY, -0.0),
187 ALL_STD_EXCEPT, 0, 1);
188 }
189
190 ATF_TC_WITHOUT_HEAD(reals);
ATF_TC_BODY(reals,tc)191 ATF_TC_BODY(reals, tc)
192 {
193 unsigned i;
194
195 for (i = 0; i < nitems(finites); i++) {
196 /* XXX could check exceptions more meticulously */
197 test(cexp, CMPLXL(finites[i], 0.0),
198 CMPLXL(exp(finites[i]), 0.0),
199 FE_INVALID | FE_DIVBYZERO, 0, 1);
200 test(cexp, CMPLXL(finites[i], -0.0),
201 CMPLXL(exp(finites[i]), -0.0),
202 FE_INVALID | FE_DIVBYZERO, 0, 1);
203 test_f(cexpf, CMPLXL(finites[i], 0.0),
204 CMPLXL(expf(finites[i]), 0.0),
205 FE_INVALID | FE_DIVBYZERO, 0, 1);
206 test_f(cexpf, CMPLXL(finites[i], -0.0),
207 CMPLXL(expf(finites[i]), -0.0),
208 FE_INVALID | FE_DIVBYZERO, 0, 1);
209 }
210 }
211
212 ATF_TC_WITHOUT_HEAD(imaginaries);
ATF_TC_BODY(imaginaries,tc)213 ATF_TC_BODY(imaginaries, tc)
214 {
215 unsigned i;
216
217 for (i = 0; i < nitems(finites); i++) {
218 test(cexp, CMPLXL(0.0, finites[i]),
219 CMPLXL(cos(finites[i]), sin(finites[i])),
220 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
221 test(cexp, CMPLXL(-0.0, finites[i]),
222 CMPLXL(cos(finites[i]), sin(finites[i])),
223 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
224 test_f(cexpf, CMPLXL(0.0, finites[i]),
225 CMPLXL(cosf(finites[i]), sinf(finites[i])),
226 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
227 test_f(cexpf, CMPLXL(-0.0, finites[i]),
228 CMPLXL(cosf(finites[i]), sinf(finites[i])),
229 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
230 }
231 }
232
233 ATF_TC_WITHOUT_HEAD(small);
ATF_TC_BODY(small,tc)234 ATF_TC_BODY(small, tc)
235 {
236 static const double tests[] = {
237 /* csqrt(a + bI) = x + yI */
238 /* a b x y */
239 1.0, M_PI_4, M_SQRT2 * 0.5 * M_E, M_SQRT2 * 0.5 * M_E,
240 -1.0, M_PI_4, M_SQRT2 * 0.5 / M_E, M_SQRT2 * 0.5 / M_E,
241 2.0, M_PI_2, 0.0, M_E * M_E,
242 M_LN2, M_PI, -2.0, 0.0,
243 };
244 double a, b;
245 double x, y;
246 unsigned i;
247
248 for (i = 0; i < nitems(tests); i += 4) {
249 a = tests[i];
250 b = tests[i + 1];
251 x = tests[i + 2];
252 y = tests[i + 3];
253 test_tol(cexp, CMPLXL(a, b), CMPLXL(x, y), 3 * DBL_ULP());
254
255 /* float doesn't have enough precision to pass these tests */
256 if (x == 0 || y == 0)
257 continue;
258 test_tol(cexpf, CMPLXL(a, b), CMPLXL(x, y), 1 * FLT_ULP());
259 }
260 }
261
262 /* Test inputs with a real part r that would overflow exp(r). */
263 ATF_TC_WITHOUT_HEAD(large);
ATF_TC_BODY(large,tc)264 ATF_TC_BODY(large, tc)
265 {
266
267 test_tol(cexp, CMPLXL(709.79, 0x1p-1074),
268 CMPLXL(INFINITY, 8.94674309915433533273e-16), DBL_ULP());
269 test_tol(cexp, CMPLXL(1000, 0x1p-1074),
270 CMPLXL(INFINITY, 9.73344457300016401328e+110), DBL_ULP());
271 test_tol(cexp, CMPLXL(1400, 0x1p-1074),
272 CMPLXL(INFINITY, 5.08228858149196559681e+284), DBL_ULP());
273 test_tol(cexp, CMPLXL(900, 0x1.23456789abcdep-1020),
274 CMPLXL(INFINITY, 7.42156649354218408074e+83), DBL_ULP());
275 test_tol(cexp, CMPLXL(1300, 0x1.23456789abcdep-1020),
276 CMPLXL(INFINITY, 3.87514844965996756704e+257), DBL_ULP());
277
278 test_tol(cexpf, CMPLXL(88.73, 0x1p-149),
279 CMPLXL(INFINITY, 4.80265603e-07), 2 * FLT_ULP());
280 test_tol(cexpf, CMPLXL(90, 0x1p-149),
281 CMPLXL(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP());
282 test_tol(cexpf, CMPLXL(192, 0x1p-149),
283 CMPLXL(INFINITY, 3.396809344e+38f), 2 * FLT_ULP());
284 test_tol(cexpf, CMPLXL(120, 0x1.234568p-120),
285 CMPLXL(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP());
286 test_tol(cexpf, CMPLXL(170, 0x1.234568p-120),
287 CMPLXL(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP());
288 }
289
ATF_TP_ADD_TCS(tp)290 ATF_TP_ADD_TCS(tp)
291 {
292 ATF_TP_ADD_TC(tp, zero);
293 ATF_TP_ADD_TC(tp, nan);
294 ATF_TP_ADD_TC(tp, inf);
295 ATF_TP_ADD_TC(tp, reals);
296 ATF_TP_ADD_TC(tp, imaginaries);
297 ATF_TP_ADD_TC(tp, small);
298 ATF_TP_ADD_TC(tp, large);
299
300 return (atf_no_error());
301 }
302