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 * $FreeBSD: src/tools/regression/lib/msun/test-cexp.c,v 1.3 2013/05/29 00:27:12 svnexp Exp $
27 */
28
29 /*
30 * Tests for corner cases in cexp*().
31 */
32
33 #include <assert.h>
34 #include <complex.h>
35 #include <fenv.h>
36 #include <float.h>
37 #include <math.h>
38 #include <stdio.h>
39
40 #define ALL_STD_EXCEPT (FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \
41 FE_OVERFLOW | FE_UNDERFLOW)
42 #define FLT_ULP() ldexpl(1.0, 1 - FLT_MANT_DIG)
43 #define DBL_ULP() ldexpl(1.0, 1 - DBL_MANT_DIG)
44 #define LDBL_ULP() ldexpl(1.0, 1 - LDBL_MANT_DIG)
45
46 #define N(i) (sizeof(i) / sizeof((i)[0]))
47
48 #pragma STDC FENV_ACCESS ON
49 #pragma STDC CX_LIMITED_RANGE OFF
50
51 /*
52 * XXX gcc implements complex multiplication incorrectly. In
53 * particular, it implements it as if the CX_LIMITED_RANGE pragma
54 * were ON. Consequently, we need this function to form numbers
55 * such as x + INFINITY * I, since gcc evalutes INFINITY * I as
56 * NaN + INFINITY * I.
57 */
58 static inline long double complex
cpackl(long double x,long double y)59 cpackl(long double x, long double y)
60 {
61 long double complex z;
62
63 __real__ z = x;
64 __imag__ z = y;
65 return (z);
66 }
67
68 /*
69 * Test that a function returns the correct value and sets the
70 * exception flags correctly. The exceptmask specifies which
71 * exceptions we should check. We need to be lenient for several
72 * reasons, but mainly because on some architectures it's impossible
73 * to raise FE_OVERFLOW without raising FE_INEXACT. In some cases,
74 * whether cexp() raises an invalid exception is unspecified.
75 *
76 * These are macros instead of functions so that assert provides more
77 * meaningful error messages.
78 *
79 * XXX The volatile here is to avoid gcc's bogus constant folding and work
80 * around the lack of support for the FENV_ACCESS pragma.
81 */
82 #define test(func, z, result, exceptmask, excepts, checksign) do { \
83 volatile long double complex _d = z; \
84 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
85 assert(cfpequal((func)(_d), (result), (checksign))); \
86 assert(((func), fetestexcept(exceptmask) == (excepts))); \
87 } while (0)
88
89 /* Test within a given tolerance. */
90 #define test_tol(func, z, result, tol) do { \
91 volatile long double complex _d = z; \
92 assert(cfpequal_tol((func)(_d), (result), (tol))); \
93 } while (0)
94
95 /* Test all the functions that compute cexp(x). */
96 #define testall(x, result, exceptmask, excepts, checksign) do { \
97 test(cexp, x, result, exceptmask, excepts, checksign); \
98 test(cexpf, x, result, exceptmask, excepts, checksign); \
99 } while (0)
100
101 /*
102 * Test all the functions that compute cexp(x), within a given tolerance.
103 * The tolerance is specified in ulps.
104 */
105 #define testall_tol(x, result, tol) do { \
106 test_tol(cexp, x, result, tol * DBL_ULP()); \
107 test_tol(cexpf, x, result, tol * FLT_ULP()); \
108 } while (0)
109
110 /* Various finite non-zero numbers to test. */
111 static const float finites[] =
112 { -42.0e20, -1.0, -1.0e-10, -0.0, 0.0, 1.0e-10, 1.0, 42.0e20 };
113
114 /*
115 * Determine whether x and y are equal, with two special rules:
116 * +0.0 != -0.0
117 * NaN == NaN
118 * If checksign is 0, we compare the absolute values instead.
119 */
120 static int
fpequal(long double x,long double y,int checksign)121 fpequal(long double x, long double y, int checksign)
122 {
123 if (isnan(x) || isnan(y))
124 return (1);
125 if (checksign)
126 return (x == y && !signbit(x) == !signbit(y));
127 else
128 return (fabsl(x) == fabsl(y));
129 }
130
131 static int
fpequal_tol(long double x,long double y,long double tol)132 fpequal_tol(long double x, long double y, long double tol)
133 {
134 fenv_t env;
135 int ret;
136
137 if (isnan(x) && isnan(y))
138 return (1);
139 if (!signbit(x) != !signbit(y))
140 return (0);
141 if (x == y)
142 return (1);
143 if (tol == 0)
144 return (0);
145
146 /* Hard case: need to check the tolerance. */
147 feholdexcept(&env);
148 /*
149 * For our purposes here, if y=0, we interpret tol as an absolute
150 * tolerance. This is to account for roundoff in the input, e.g.,
151 * cos(Pi/2) ~= 0.
152 */
153 if (y == 0.0)
154 ret = fabsl(x - y) <= fabsl(tol);
155 else
156 ret = fabsl(x - y) <= fabsl(y * tol);
157 fesetenv(&env);
158 return (ret);
159 }
160
161 static int
cfpequal(long double complex x,long double complex y,int checksign)162 cfpequal(long double complex x, long double complex y, int checksign)
163 {
164 return (fpequal(creal(x), creal(y), checksign)
165 && fpequal(cimag(x), cimag(y), checksign));
166 }
167
168 static int
cfpequal_tol(long double complex x,long double complex y,long double tol)169 cfpequal_tol(long double complex x, long double complex y, long double tol)
170 {
171 return (fpequal_tol(creal(x), creal(y), tol)
172 && fpequal_tol(cimag(x), cimag(y), tol));
173 }
174
175
176 /* Tests for 0 */
177 void
test_zero(void)178 test_zero(void)
179 {
180
181 /* cexp(0) = 1, no exceptions raised */
182 testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
183 testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1);
184 testall(cpackl(0.0, -0.0), cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
185 testall(cpackl(-0.0, -0.0), cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, 1);
186 }
187
188 /*
189 * Tests for NaN. The signs of the results are indeterminate unless the
190 * imaginary part is 0.
191 */
192 void
test_nan()193 test_nan()
194 {
195 int i;
196
197 /* cexp(x + NaNi) = NaN + NaNi and optionally raises invalid */
198 /* cexp(NaN + yi) = NaN + NaNi and optionally raises invalid (|y|>0) */
199 for (i = 0; i < N(finites); i++) {
200 testall(cpackl(finites[i], NAN), cpackl(NAN, NAN),
201 ALL_STD_EXCEPT & ~FE_INVALID, 0, 0);
202 if (finites[i] == 0.0)
203 continue;
204 /* XXX FE_INEXACT shouldn't be raised here */
205 testall(cpackl(NAN, finites[i]), cpackl(NAN, NAN),
206 ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0);
207 }
208
209 /* cexp(NaN +- 0i) = NaN +- 0i */
210 testall(cpackl(NAN, 0.0), cpackl(NAN, 0.0), ALL_STD_EXCEPT, 0, 1);
211 testall(cpackl(NAN, -0.0), cpackl(NAN, -0.0), ALL_STD_EXCEPT, 0, 1);
212
213 /* cexp(inf + NaN i) = inf + nan i */
214 testall(cpackl(INFINITY, NAN), cpackl(INFINITY, NAN),
215 ALL_STD_EXCEPT, 0, 0);
216 /* cexp(-inf + NaN i) = 0 */
217 testall(cpackl(-INFINITY, NAN), cpackl(0.0, 0.0),
218 ALL_STD_EXCEPT, 0, 0);
219 /* cexp(NaN + NaN i) = NaN + NaN i */
220 testall(cpackl(NAN, NAN), cpackl(NAN, NAN),
221 ALL_STD_EXCEPT, 0, 0);
222 }
223
224 void
test_inf(void)225 test_inf(void)
226 {
227 int i;
228
229 /* cexp(x + inf i) = NaN + NaNi and raises invalid */
230 for (i = 0; i < N(finites); i++) {
231 testall(cpackl(finites[i], INFINITY), cpackl(NAN, NAN),
232 ALL_STD_EXCEPT, FE_INVALID, 1);
233 }
234 /* cexp(-inf + yi) = 0 * (cos(y) + sin(y)i) */
235 /* XXX shouldn't raise an inexact exception */
236 testall(cpackl(-INFINITY, M_PI_4), cpackl(0.0, 0.0),
237 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
238 testall(cpackl(-INFINITY, 3 * M_PI_4), cpackl(-0.0, 0.0),
239 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
240 testall(cpackl(-INFINITY, 5 * M_PI_4), cpackl(-0.0, -0.0),
241 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
242 testall(cpackl(-INFINITY, 7 * M_PI_4), cpackl(0.0, -0.0),
243 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
244 testall(cpackl(-INFINITY, 0.0), cpackl(0.0, 0.0),
245 ALL_STD_EXCEPT, 0, 1);
246 testall(cpackl(-INFINITY, -0.0), cpackl(0.0, -0.0),
247 ALL_STD_EXCEPT, 0, 1);
248 /* cexp(inf + yi) = inf * (cos(y) + sin(y)i) (except y=0) */
249 /* XXX shouldn't raise an inexact exception */
250 testall(cpackl(INFINITY, M_PI_4), cpackl(INFINITY, INFINITY),
251 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
252 testall(cpackl(INFINITY, 3 * M_PI_4), cpackl(-INFINITY, INFINITY),
253 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
254 testall(cpackl(INFINITY, 5 * M_PI_4), cpackl(-INFINITY, -INFINITY),
255 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
256 testall(cpackl(INFINITY, 7 * M_PI_4), cpackl(INFINITY, -INFINITY),
257 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
258 /* cexp(inf + 0i) = inf + 0i */
259 testall(cpackl(INFINITY, 0.0), cpackl(INFINITY, 0.0),
260 ALL_STD_EXCEPT, 0, 1);
261 testall(cpackl(INFINITY, -0.0), cpackl(INFINITY, -0.0),
262 ALL_STD_EXCEPT, 0, 1);
263 }
264
265 void
test_reals(void)266 test_reals(void)
267 {
268 int i;
269
270 for (i = 0; i < N(finites); i++) {
271 /* XXX could check exceptions more meticulously */
272 test(cexp, cpackl(finites[i], 0.0),
273 cpackl(exp(finites[i]), 0.0),
274 FE_INVALID | FE_DIVBYZERO, 0, 1);
275 test(cexp, cpackl(finites[i], -0.0),
276 cpackl(exp(finites[i]), -0.0),
277 FE_INVALID | FE_DIVBYZERO, 0, 1);
278 test(cexpf, cpackl(finites[i], 0.0),
279 cpackl(expf(finites[i]), 0.0),
280 FE_INVALID | FE_DIVBYZERO, 0, 1);
281 test(cexpf, cpackl(finites[i], -0.0),
282 cpackl(expf(finites[i]), -0.0),
283 FE_INVALID | FE_DIVBYZERO, 0, 1);
284 }
285 }
286
287 void
test_imaginaries(void)288 test_imaginaries(void)
289 {
290 int i;
291
292 for (i = 0; i < N(finites); i++) {
293 test(cexp, cpackl(0.0, finites[i]),
294 cpackl(cos(finites[i]), sin(finites[i])),
295 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
296 test(cexp, cpackl(-0.0, finites[i]),
297 cpackl(cos(finites[i]), sin(finites[i])),
298 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
299 test(cexpf, cpackl(0.0, finites[i]),
300 cpackl(cosf(finites[i]), sinf(finites[i])),
301 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
302 test(cexpf, cpackl(-0.0, finites[i]),
303 cpackl(cosf(finites[i]), sinf(finites[i])),
304 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1);
305 }
306 }
307
308 void
test_small(void)309 test_small(void)
310 {
311 static const double tests[] = {
312 /* csqrt(a + bI) = x + yI */
313 /* a b x y */
314 1.0, M_PI_4, M_SQRT2 * 0.5 * M_E, M_SQRT2 * 0.5 * M_E,
315 -1.0, M_PI_4, M_SQRT2 * 0.5 / M_E, M_SQRT2 * 0.5 / M_E,
316 2.0, M_PI_2, 0.0, M_E * M_E,
317 M_LN2, M_PI, -2.0, 0.0,
318 };
319 double a, b;
320 double x, y;
321 int i;
322
323 for (i = 0; i < N(tests); i += 4) {
324 a = tests[i];
325 b = tests[i + 1];
326 x = tests[i + 2];
327 y = tests[i + 3];
328 test_tol(cexp, cpackl(a, b), cpackl(x, y), 3 * DBL_ULP());
329
330 /* float doesn't have enough precision to pass these tests */
331 if (x == 0 || y == 0)
332 continue;
333 test_tol(cexpf, cpackl(a, b), cpackl(x, y), 1 * FLT_ULP());
334 }
335 }
336
337 /* Test inputs with a real part r that would overflow exp(r). */
338 void
test_large(void)339 test_large(void)
340 {
341
342 test_tol(cexp, cpackl(709.79, 0x1p-1074),
343 cpackl(INFINITY, 8.94674309915433533273e-16), DBL_ULP());
344 test_tol(cexp, cpackl(1000, 0x1p-1074),
345 cpackl(INFINITY, 9.73344457300016401328e+110), DBL_ULP());
346 test_tol(cexp, cpackl(1400, 0x1p-1074),
347 cpackl(INFINITY, 5.08228858149196559681e+284), DBL_ULP());
348 test_tol(cexp, cpackl(900, 0x1.23456789abcdep-1020),
349 cpackl(INFINITY, 7.42156649354218408074e+83), DBL_ULP());
350 test_tol(cexp, cpackl(1300, 0x1.23456789abcdep-1020),
351 cpackl(INFINITY, 3.87514844965996756704e+257), DBL_ULP());
352
353 test_tol(cexpf, cpackl(88.73, 0x1p-149),
354 cpackl(INFINITY, 4.80265603e-07), 2 * FLT_ULP());
355 test_tol(cexpf, cpackl(90, 0x1p-149),
356 cpackl(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP());
357 test_tol(cexpf, cpackl(192, 0x1p-149),
358 cpackl(INFINITY, 3.396809344e+38f), 2 * FLT_ULP());
359 test_tol(cexpf, cpackl(120, 0x1.234568p-120),
360 cpackl(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP());
361 test_tol(cexpf, cpackl(170, 0x1.234568p-120),
362 cpackl(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP());
363 }
364
365 int
main(int argc,char * argv[])366 main(int argc, char *argv[])
367 {
368
369 printf("1..7\n");
370
371 test_zero();
372 printf("ok 1 - cexp zero\n");
373
374 test_nan();
375 printf("ok 2 - cexp nan\n");
376
377 test_inf();
378 printf("ok 3 - cexp inf\n");
379
380 test_reals();
381 printf("ok 4 - cexp reals\n");
382
383 test_imaginaries();
384 printf("ok 5 - cexp imaginaries\n");
385
386 test_small();
387 printf("ok 6 - cexp small\n");
388
389 test_large();
390 printf("ok 7 - cexp large\n");
391
392 return (0);
393 }
394