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