1 /*-
2 * Copyright (c) 2008-2013 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 casin[h](), cacos[h](), and catan[h]().
29 */
30
31 #include <sys/cdefs.h>
32 #include <sys/param.h>
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.
50 *
51 * These are macros instead of functions so that assert provides more
52 * meaningful error messages.
53 *
54 * XXX The volatile here is to avoid gcc's bogus constant folding and work
55 * around the lack of support for the FENV_ACCESS pragma.
56 */
57 #define test_p(func, z, result, exceptmask, excepts, checksign) do { \
58 volatile long double complex _d = z; \
59 debug(" testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func, \
60 creall(_d), cimagl(_d), creall(result), cimagl(result)); \
61 ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \
62 CHECK_CFPEQUAL_CS((func)(_d), (result), (checksign)); \
63 CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \
64 #func, #z); \
65 } while (0)
66
67 /*
68 * Test within a given tolerance. The tolerance indicates relative error
69 * in ulps.
70 */
71 #define test_p_tol(func, z, result, tol) do { \
72 debug(" testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func, \
73 creall(z), cimagl(z), creall(result), cimagl(result)); \
74 CHECK_CFPEQUAL_TOL((func)(z), (result), (tol), CS_BOTH); \
75 } while (0)
76
77 /* These wrappers apply the identities f(conj(z)) = conj(f(z)). */
78 #define test(func, z, result, exceptmask, excepts, checksign) do { \
79 test_p(func, z, result, exceptmask, excepts, checksign); \
80 test_p(func, conjl(z), conjl(result), exceptmask, excepts, checksign); \
81 } while (0)
82 #define test_tol(func, z, result, tol) do { \
83 test_p_tol(func, z, result, tol); \
84 test_p_tol(func, conjl(z), conjl(result), tol); \
85 } while (0)
86
87 /* Test the given function in all precisions. */
88 #define testall(func, x, result, exceptmask, excepts, checksign) do { \
89 test(func, x, result, exceptmask, excepts, checksign); \
90 test(func##f, x, result, exceptmask, excepts, checksign); \
91 } while (0)
92 #define testall_odd(func, x, result, exceptmask, excepts, checksign) do { \
93 testall(func, x, result, exceptmask, excepts, checksign); \
94 testall(func, -(x), -result, exceptmask, excepts, checksign); \
95 } while (0)
96 #define testall_even(func, x, result, exceptmask, excepts, checksign) do { \
97 testall(func, x, result, exceptmask, excepts, checksign); \
98 testall(func, -(x), result, exceptmask, excepts, checksign); \
99 } while (0)
100
101 /*
102 * Test the given function in all precisions, within a given tolerance.
103 * The tolerance is specified in ulps.
104 */
105 #define testall_tol(func, x, result, tol) do { \
106 test_tol(func, x, result, (tol) * DBL_ULP()); \
107 test_tol(func##f, x, result, (tol) * FLT_ULP()); \
108 } while (0)
109 #define testall_odd_tol(func, x, result, tol) do { \
110 testall_tol(func, x, result, tol); \
111 testall_tol(func, -(x), -result, tol); \
112 } while (0)
113 #define testall_even_tol(func, x, result, tol) do { \
114 testall_tol(func, x, result, tol); \
115 testall_tol(func, -(x), result, tol); \
116 } while (0)
117
118 static const long double
119 pi = 3.14159265358979323846264338327950280L,
120 c3pi = 9.42477796076937971538793014983850839L;
121
122
123 /* Tests for 0 */
124 ATF_TC_WITHOUT_HEAD(zero);
ATF_TC_BODY(zero,tc)125 ATF_TC_BODY(zero, tc)
126 {
127 long double complex zero = CMPLXL(0.0, 0.0);
128
129 testall_tol(cacosh, zero, CMPLXL(0.0, pi / 2), 1);
130 testall_tol(cacosh, -zero, CMPLXL(0.0, -pi / 2), 1);
131 testall_tol(cacos, zero, CMPLXL(pi / 2, -0.0), 1);
132 testall_tol(cacos, -zero, CMPLXL(pi / 2, 0.0), 1);
133
134 testall_odd(casinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
135 testall_odd(casin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
136
137 testall_odd(catanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
138 testall_odd(catan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
139 }
140
141 /*
142 * Tests for NaN inputs.
143 */
144 ATF_TC_WITHOUT_HEAD(nan);
ATF_TC_BODY(nan,tc)145 ATF_TC_BODY(nan, tc)
146 {
147 long double complex nan_nan = CMPLXL(NAN, NAN);
148 long double complex z;
149
150 /*
151 * IN CACOSH CACOS CASINH CATANH
152 * NaN,NaN NaN,NaN NaN,NaN NaN,NaN NaN,NaN
153 * finite,NaN NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN*
154 * NaN,finite NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN*
155 * NaN,Inf Inf,NaN NaN,-Inf ?Inf,NaN ?0,pi/2
156 * +-Inf,NaN Inf,NaN NaN,?Inf +-Inf,NaN +-0,NaN
157 * +-0,NaN NaN,NaN* pi/2,NaN NaN,NaN* +-0,NaN
158 * NaN,0 NaN,NaN* NaN,NaN* NaN,0 NaN,NaN*
159 *
160 * * = raise invalid
161 */
162 z = nan_nan;
163 testall(cacosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
164 testall(cacos, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
165 testall(casinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
166 testall(casin, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
167 testall(catanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
168 testall(catan, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
169
170 z = CMPLXL(0.5, NAN);
171 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
172 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
173 testall(casinh, z, nan_nan, OPT_INVALID, 0, 0);
174 testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
175 testall(catanh, z, nan_nan, OPT_INVALID, 0, 0);
176 testall(catan, z, nan_nan, OPT_INVALID, 0, 0);
177
178 z = CMPLXL(NAN, 0.5);
179 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
180 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
181 testall(casinh, z, nan_nan, OPT_INVALID, 0, 0);
182 testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
183 testall(catanh, z, nan_nan, OPT_INVALID, 0, 0);
184 testall(catan, z, nan_nan, OPT_INVALID, 0, 0);
185
186 z = CMPLXL(NAN, INFINITY);
187 testall(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
188 testall(cacosh, -z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
189 testall(cacos, z, CMPLXL(NAN, -INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG);
190 testall(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0);
191 testall(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG);
192 testall_tol(catanh, z, CMPLXL(0.0, pi / 2), 1);
193 testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, CS_IMAG);
194
195 z = CMPLXL(INFINITY, NAN);
196 testall_even(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
197 CS_REAL);
198 testall_even(cacos, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
199 testall_odd(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
200 CS_REAL);
201 testall_odd(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
202 testall_odd(catanh, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
203 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0.0), 1);
204
205 z = CMPLXL(0.0, NAN);
206 /* XXX We allow a spurious inexact exception here. */
207 testall_even(cacosh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0);
208 testall_even_tol(cacos, z, CMPLXL(pi / 2, NAN), 1);
209 testall_odd(casinh, z, nan_nan, OPT_INVALID, 0, 0);
210 testall_odd(casin, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
211 testall_odd(catanh, z, CMPLXL(0.0, NAN), OPT_INVALID, 0, CS_REAL);
212 testall_odd(catan, z, nan_nan, OPT_INVALID, 0, 0);
213
214 z = CMPLXL(NAN, 0.0);
215 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
216 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
217 testall(casinh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG);
218 testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
219 testall(catanh, z, nan_nan, OPT_INVALID, 0, CS_IMAG);
220 testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 0);
221 }
222
223 ATF_TC_WITHOUT_HEAD(inf);
ATF_TC_BODY(inf,tc)224 ATF_TC_BODY(inf, tc)
225 {
226 long double complex z;
227
228 /*
229 * IN CACOSH CACOS CASINH CATANH
230 * Inf,Inf Inf,pi/4 pi/4,-Inf Inf,pi/4 0,pi/2
231 * -Inf,Inf Inf,3pi/4 3pi/4,-Inf --- ---
232 * Inf,finite Inf,0 0,-Inf Inf,0 0,pi/2
233 * -Inf,finite Inf,pi pi,-Inf --- ---
234 * finite,Inf Inf,pi/2 pi/2,-Inf Inf,pi/2 0,pi/2
235 */
236 z = CMPLXL(INFINITY, INFINITY);
237 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 4), 1);
238 testall_tol(cacosh, -z, CMPLXL(INFINITY, -c3pi / 4), 1);
239 testall_tol(cacos, z, CMPLXL(pi / 4, -INFINITY), 1);
240 testall_tol(cacos, -z, CMPLXL(c3pi / 4, INFINITY), 1);
241 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 4), 1);
242 testall_odd_tol(casin, z, CMPLXL(pi / 4, INFINITY), 1);
243 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
244 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
245
246 z = CMPLXL(INFINITY, 0.5);
247 /* XXX We allow a spurious inexact exception here. */
248 testall(cacosh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH);
249 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi), 1);
250 testall(cacos, z, CMPLXL(0, -INFINITY), OPT_INEXACT, 0, CS_BOTH);
251 testall_tol(cacos, -z, CMPLXL(pi, INFINITY), 1);
252 testall_odd(casinh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH);
253 testall_odd_tol(casin, z, CMPLXL(pi / 2, INFINITY), 1);
254 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
255 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
256
257 z = CMPLXL(0.5, INFINITY);
258 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 2), 1);
259 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi / 2), 1);
260 testall_tol(cacos, z, CMPLXL(pi / 2, -INFINITY), 1);
261 testall_tol(cacos, -z, CMPLXL(pi / 2, INFINITY), 1);
262 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 2), 1);
263 /* XXX We allow a spurious inexact exception here. */
264 testall_odd(casin, z, CMPLXL(0.0, INFINITY), OPT_INEXACT, 0, CS_BOTH);
265 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
266 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
267 }
268
269 /* Tests along the real and imaginary axes. */
270 ATF_TC_WITHOUT_HEAD(axes);
ATF_TC_BODY(axes,tc)271 ATF_TC_BODY(axes, tc)
272 {
273 static const long double nums[] = {
274 -2, -1, -0.5, 0.5, 1, 2
275 };
276 long double complex z;
277 unsigned i;
278
279 for (i = 0; i < nitems(nums); i++) {
280 /* Real axis */
281 z = CMPLXL(nums[i], 0.0);
282 if (fabsl(nums[i]) <= 1) {
283 testall_tol(cacosh, z, CMPLXL(0.0, acos(nums[i])), 1);
284 testall_tol(cacos, z, CMPLXL(acosl(nums[i]), -0.0), 1);
285 testall_tol(casin, z, CMPLXL(asinl(nums[i]), 0.0), 1);
286 testall_tol(catanh, z, CMPLXL(atanh(nums[i]), 0.0), 1);
287 } else {
288 testall_tol(cacosh, z,
289 CMPLXL(acosh(fabsl(nums[i])),
290 (nums[i] < 0) ? pi : 0), 1);
291 testall_tol(cacos, z,
292 CMPLXL((nums[i] < 0) ? pi : 0,
293 -acosh(fabsl(nums[i]))), 1);
294 testall_tol(casin, z,
295 CMPLXL(copysign(pi / 2, nums[i]),
296 acosh(fabsl(nums[i]))), 1);
297 testall_tol(catanh, z,
298 CMPLXL(atanh(1 / nums[i]), pi / 2), 1);
299 }
300 testall_tol(casinh, z, CMPLXL(asinh(nums[i]), 0.0), 1);
301 testall_tol(catan, z, CMPLXL(atan(nums[i]), 0), 1);
302
303 /* TODO: Test the imaginary axis. */
304 }
305 }
306
307 ATF_TC_WITHOUT_HEAD(small);
ATF_TC_BODY(small,tc)308 ATF_TC_BODY(small, tc)
309 {
310 /*
311 * z = 0.75 + i 0.25
312 * acos(z) = Pi/4 - i ln(2)/2
313 * asin(z) = Pi/4 + i ln(2)/2
314 * atan(z) = atan(4)/2 + i ln(17/9)/4
315 */
316 complex long double z;
317 complex long double acos_z;
318 complex long double asin_z;
319 complex long double atan_z;
320
321 z = CMPLXL(0.75L, 0.25L);
322 acos_z = CMPLXL(pi / 4, -0.34657359027997265470861606072908828L);
323 asin_z = CMPLXL(pi / 4, 0.34657359027997265470861606072908828L);
324 atan_z = CMPLXL(0.66290883183401623252961960521423782L,
325 0.15899719167999917436476103600701878L);
326
327 testall_tol(cacos, z, acos_z, 2);
328 testall_odd_tol(casin, z, asin_z, 2);
329 testall_odd_tol(catan, z, atan_z, 2);
330 }
331
332 /* Test inputs that might cause overflow in a sloppy implementation. */
333 ATF_TC_WITHOUT_HEAD(large);
ATF_TC_BODY(large,tc)334 ATF_TC_BODY(large, tc)
335 {
336 /* TODO: Write these tests */
337 }
338
ATF_TP_ADD_TCS(tp)339 ATF_TP_ADD_TCS(tp)
340 {
341 ATF_TP_ADD_TC(tp, zero);
342 ATF_TP_ADD_TC(tp, nan);
343 ATF_TP_ADD_TC(tp, inf);
344 ATF_TP_ADD_TC(tp, axes);
345 ATF_TP_ADD_TC(tp, small);
346 ATF_TP_ADD_TC(tp, large);
347
348 return (atf_no_error());
349 }
350