xref: /freebsd/lib/msun/tests/ctrig_test.c (revision 5819c3eb8a1e2ac0a4f96a3aff5fefac276ae581)
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 csin[h](), ccos[h](), and ctan[h]().
29  */
30 
31 #include <sys/cdefs.h>
32 __FBSDID("$FreeBSD$");
33 
34 #include <sys/param.h>
35 #include <complex.h>
36 #include <fenv.h>
37 #include <float.h>
38 #include <math.h>
39 #include <stdio.h>
40 
41 #include <atf-c.h>
42 
43 #include "test-utils.h"
44 
45 #pragma STDC FENV_ACCESS	ON
46 #pragma	STDC CX_LIMITED_RANGE	OFF
47 
48 /*
49  * Test that a function returns the correct value and sets the
50  * exception flags correctly. The exceptmask specifies which
51  * exceptions we should check. We need to be lenient for several
52  * reasons, but mainly because on some architectures it's impossible
53  * to raise FE_OVERFLOW without raising FE_INEXACT.
54  *
55  * These are macros instead of functions so that assert provides more
56  * meaningful error messages.
57  *
58  * XXX The volatile here is to avoid gcc's bogus constant folding and work
59  *     around the lack of support for the FENV_ACCESS pragma.
60  */
61 #define	test_p(func, z, result, exceptmask, excepts, checksign)	do {	\
62 	volatile long double complex _d = z;				\
63 	debug("  testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func,	\
64 	    creall(_d), cimagl(_d), creall(result), cimagl(result));	\
65 	ATF_CHECK(feclearexcept(FE_ALL_EXCEPT) == 0);			\
66 	ATF_CHECK(cfpequal_cs((func)(_d), (result), (checksign)));		\
67 	ATF_CHECK(((void)(func), fetestexcept(exceptmask) == (excepts)));	\
68 } while (0)
69 
70 /*
71  * Test within a given tolerance.  The tolerance indicates relative error
72  * in ulps.  If result is 0, however, it measures absolute error in units
73  * of <format>_EPSILON.
74  */
75 #define	test_p_tol(func, z, result, tol)			do {	\
76 	volatile long double complex _d = z;				\
77 	debug("  testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func,	\
78 	    creall(_d), cimagl(_d), creall(result), cimagl(result));	\
79 	ATF_CHECK(cfpequal_tol((func)(_d), (result), (tol), FPE_ABS_ZERO)); \
80 } while (0)
81 
82 /* These wrappers apply the identities f(conj(z)) = conj(f(z)). */
83 #define	test(func, z, result, exceptmask, excepts, checksign)	do {	\
84 	test_p(func, z, result, exceptmask, excepts, checksign);	\
85 	test_p(func, conjl(z), conjl(result), exceptmask, excepts, checksign); \
86 } while (0)
87 #define	test_tol(func, z, result, tol)				do {	\
88 	test_p_tol(func, z, result, tol);				\
89 	test_p_tol(func, conjl(z), conjl(result), tol);			\
90 } while (0)
91 #define	test_odd_tol(func, z, result, tol)			do {	\
92 	test_tol(func, z, result, tol);					\
93 	test_tol(func, -(z), -(result), tol);				\
94 } while (0)
95 #define	test_even_tol(func, z, result, tol)			do {	\
96 	test_tol(func, z, result, tol);					\
97 	test_tol(func, -(z), result, tol);				\
98 } while (0)
99 
100 /* Test the given function in all precisions. */
101 #define	testall(func, x, result, exceptmask, excepts, checksign) do {	\
102 	test(func, x, result, exceptmask, excepts, checksign);		\
103 	test(func##f, x, result, exceptmask, excepts, checksign);	\
104 } while (0)
105 #define	testall_odd(func, x, result, exceptmask, excepts, checksign) do { \
106 	testall(func, x, result, exceptmask, excepts, checksign);	\
107 	testall(func, -x, -result, exceptmask, excepts, checksign);	\
108 } while (0)
109 #define	testall_even(func, x, result, exceptmask, excepts, checksign) do { \
110 	testall(func, x, result, exceptmask, excepts, checksign);	\
111 	testall(func, -x, result, exceptmask, excepts, checksign);	\
112 } while (0)
113 
114 /*
115  * Test the given function in all precisions, within a given tolerance.
116  * The tolerance is specified in ulps.
117  */
118 #define	testall_tol(func, x, result, tol)	       		   do { \
119 	test_tol(func, x, result, tol * DBL_ULP());			\
120 	test_tol(func##f, x, result, tol * FLT_ULP());			\
121 } while (0)
122 #define	testall_odd_tol(func, x, result, tol)	       		   do { \
123 	test_odd_tol(func, x, result, tol * DBL_ULP());			\
124 	test_odd_tol(func##f, x, result, tol * FLT_ULP());		\
125 } while (0)
126 #define	testall_even_tol(func, x, result, tol)	       		   do { \
127 	test_even_tol(func, x, result, tol * DBL_ULP());		\
128 	test_even_tol(func##f, x, result, tol * FLT_ULP());		\
129 } while (0)
130 
131 
132 ATF_TC(test_zero_input);
133 ATF_TC_HEAD(test_zero_input, tc)
134 {
135 	atf_tc_set_md_var(tc, "descr", "test 0 input");
136 }
137 ATF_TC_BODY(test_zero_input, tc)
138 {
139 	long double complex zero = CMPLXL(0.0, 0.0);
140 
141 #if defined(__amd64__)
142 #if defined(__clang__) && \
143 	((__clang_major__ >= 4))
144 	atf_tc_expect_fail("test fails with clang 4.x+ - bug 217528");
145 #endif
146 #endif
147 
148 	/* csinh(0) = ctanh(0) = 0; ccosh(0) = 1 (no exceptions raised) */
149 	testall_odd(csinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
150 	testall_odd(csin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
151 	testall_even(ccosh, zero, 1.0, ALL_STD_EXCEPT, 0, CS_BOTH);
152 	testall_even(ccos, zero, CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, CS_BOTH);
153 	testall_odd(ctanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
154 	testall_odd(ctan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
155 }
156 
157 ATF_TC(test_nan_inputs);
158 ATF_TC_HEAD(test_nan_inputs, tc)
159 {
160 	atf_tc_set_md_var(tc, "descr", "test NaN inputs");
161 }
162 ATF_TC_BODY(test_nan_inputs, tc)
163 {
164 	long double complex nan_nan = CMPLXL(NAN, NAN);
165 	long double complex z;
166 
167 	/*
168 	 * IN		CSINH		CCOSH		CTANH
169 	 * NaN,NaN	NaN,NaN		NaN,NaN		NaN,NaN
170 	 * finite,NaN	NaN,NaN [inval]	NaN,NaN [inval]	NaN,NaN [inval]
171 	 * NaN,finite	NaN,NaN [inval]	NaN,NaN [inval]	NaN,NaN [inval]
172 	 * NaN,Inf	NaN,NaN [inval]	NaN,NaN	[inval]	NaN,NaN [inval]
173 	 * Inf,NaN	+-Inf,NaN	Inf,NaN		1,+-0
174 	 * 0,NaN	+-0,NaN		NaN,+-0		NaN,NaN	[inval]
175 	 * NaN,0	NaN,0		NaN,+-0		NaN,0
176 	 */
177 	z = nan_nan;
178 	testall_odd(csinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
179 	testall_even(ccosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
180 	testall_odd(ctanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
181 	testall_odd(csin, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
182 	testall_even(ccos, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
183 	testall_odd(ctan, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
184 
185 	z = CMPLXL(42, NAN);
186 	testall_odd(csinh, z, nan_nan, OPT_INVALID, 0, 0);
187 	testall_even(ccosh, z, nan_nan, OPT_INVALID, 0, 0);
188 	/* XXX We allow a spurious inexact exception here. */
189 	testall_odd(ctanh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0);
190 	testall_odd(csin, z, nan_nan, OPT_INVALID, 0, 0);
191 	testall_even(ccos, z, nan_nan, OPT_INVALID, 0, 0);
192 	testall_odd(ctan, z, nan_nan, OPT_INVALID, 0, 0);
193 
194 	z = CMPLXL(NAN, 42);
195 	testall_odd(csinh, z, nan_nan, OPT_INVALID, 0, 0);
196 	testall_even(ccosh, z, nan_nan, OPT_INVALID, 0, 0);
197 	testall_odd(ctanh, z, nan_nan, OPT_INVALID, 0, 0);
198 	testall_odd(csin, z, nan_nan, OPT_INVALID, 0, 0);
199 	testall_even(ccos, z, nan_nan, OPT_INVALID, 0, 0);
200 	/* XXX We allow a spurious inexact exception here. */
201 	testall_odd(ctan, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0);
202 
203 	z = CMPLXL(NAN, INFINITY);
204 	testall_odd(csinh, z, nan_nan, OPT_INVALID, 0, 0);
205 	testall_even(ccosh, z, nan_nan, OPT_INVALID, 0, 0);
206 	testall_odd(ctanh, z, nan_nan, OPT_INVALID, 0, 0);
207 	testall_odd(csin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
208 	testall_even(ccos, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
209 	    CS_IMAG);
210 	testall_odd(ctan, z, CMPLXL(0, 1), ALL_STD_EXCEPT, 0, CS_IMAG);
211 
212 	z = CMPLXL(INFINITY, NAN);
213 	testall_odd(csinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0);
214 	testall_even(ccosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
215 		     CS_REAL);
216 	testall_odd(ctanh, z, CMPLXL(1, 0), ALL_STD_EXCEPT, 0, CS_REAL);
217 	testall_odd(csin, z, nan_nan, OPT_INVALID, 0, 0);
218 	testall_even(ccos, z, nan_nan, OPT_INVALID, 0, 0);
219 	testall_odd(ctan, z, nan_nan, OPT_INVALID, 0, 0);
220 
221 	z = CMPLXL(0, NAN);
222 	testall_odd(csinh, z, CMPLXL(0, NAN), ALL_STD_EXCEPT, 0, 0);
223 	testall_even(ccosh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, 0);
224 	testall_odd(ctanh, z, nan_nan, OPT_INVALID, 0, 0);
225 	testall_odd(csin, z, CMPLXL(0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
226 	testall_even(ccos, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, 0);
227 	testall_odd(ctan, z, CMPLXL(0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
228 
229 	z = CMPLXL(NAN, 0);
230 	testall_odd(csinh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG);
231 	testall_even(ccosh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, 0);
232 	testall_odd(ctanh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG);
233 	testall_odd(csin, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, 0);
234 	testall_even(ccos, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, 0);
235 	testall_odd(ctan, z, nan_nan, OPT_INVALID, 0, 0);
236 }
237 
238 ATF_TC(test_inf_inputs);
239 ATF_TC_HEAD(test_inf_inputs, tc)
240 {
241 	atf_tc_set_md_var(tc, "descr", "test infinity inputs");
242 }
243 ATF_TC_BODY(test_inf_inputs, tc)
244 {
245 	static const long double finites[] = {
246 	    0, M_PI / 4, 3 * M_PI / 4, 5 * M_PI / 4,
247 	};
248 	long double complex z, c, s;
249 	unsigned i;
250 
251 	/*
252 	 * IN		CSINH		CCOSH		CTANH
253 	 * Inf,Inf	+-Inf,NaN inval	+-Inf,NaN inval	1,+-0
254 	 * Inf,finite	Inf cis(finite)	Inf cis(finite)	1,0 sin(2 finite)
255 	 * 0,Inf	+-0,NaN	inval	NaN,+-0 inval	NaN,NaN	inval
256 	 * finite,Inf	NaN,NaN inval	NaN,NaN inval	NaN,NaN inval
257 	 */
258 	z = CMPLXL(INFINITY, INFINITY);
259 	testall_odd(csinh, z, CMPLXL(INFINITY, NAN),
260 		    ALL_STD_EXCEPT, FE_INVALID, 0);
261 	testall_even(ccosh, z, CMPLXL(INFINITY, NAN),
262 		     ALL_STD_EXCEPT, FE_INVALID, 0);
263 	testall_odd(ctanh, z, CMPLXL(1, 0), ALL_STD_EXCEPT, 0, CS_REAL);
264 	testall_odd(csin, z, CMPLXL(NAN, INFINITY),
265 		    ALL_STD_EXCEPT, FE_INVALID, 0);
266 	testall_even(ccos, z, CMPLXL(INFINITY, NAN),
267 		     ALL_STD_EXCEPT, FE_INVALID, 0);
268 	testall_odd(ctan, z, CMPLXL(0, 1), ALL_STD_EXCEPT, 0, CS_REAL);
269 
270 	/* XXX We allow spurious inexact exceptions here (hard to avoid). */
271 	for (i = 0; i < nitems(finites); i++) {
272 		z = CMPLXL(INFINITY, finites[i]);
273 		c = INFINITY * cosl(finites[i]);
274 		s = finites[i] == 0 ? finites[i] : INFINITY * sinl(finites[i]);
275 		testall_odd(csinh, z, CMPLXL(c, s), OPT_INEXACT, 0, CS_BOTH);
276 		testall_even(ccosh, z, CMPLXL(c, s), OPT_INEXACT, 0, CS_BOTH);
277 		testall_odd(ctanh, z, CMPLXL(1, 0 * sin(finites[i] * 2)),
278 			    OPT_INEXACT, 0, CS_BOTH);
279 		z = CMPLXL(finites[i], INFINITY);
280 		testall_odd(csin, z, CMPLXL(s, c), OPT_INEXACT, 0, CS_BOTH);
281 		testall_even(ccos, z, CMPLXL(c, -s), OPT_INEXACT, 0, CS_BOTH);
282 		testall_odd(ctan, z, CMPLXL(0 * sin(finites[i] * 2), 1),
283 			    OPT_INEXACT, 0, CS_BOTH);
284 	}
285 
286 	z = CMPLXL(0, INFINITY);
287 	testall_odd(csinh, z, CMPLXL(0, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
288 	testall_even(ccosh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, FE_INVALID, 0);
289 	testall_odd(ctanh, z, CMPLXL(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
290 	z = CMPLXL(INFINITY, 0);
291 	testall_odd(csin, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, FE_INVALID, 0);
292 	testall_even(ccos, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, FE_INVALID, 0);
293 	testall_odd(ctan, z, CMPLXL(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
294 
295 	z = CMPLXL(42, INFINITY);
296 	testall_odd(csinh, z, CMPLXL(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
297 	testall_even(ccosh, z, CMPLXL(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
298 	/* XXX We allow a spurious inexact exception here. */
299 	testall_odd(ctanh, z, CMPLXL(NAN, NAN), OPT_INEXACT, FE_INVALID, 0);
300 	z = CMPLXL(INFINITY, 42);
301 	testall_odd(csin, z, CMPLXL(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
302 	testall_even(ccos, z, CMPLXL(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
303 	/* XXX We allow a spurious inexact exception here. */
304 	testall_odd(ctan, z, CMPLXL(NAN, NAN), OPT_INEXACT, FE_INVALID, 0);
305 }
306 
307 ATF_TC(test_axes);
308 ATF_TC_HEAD(test_axes, tc)
309 {
310 	atf_tc_set_md_var(tc, "descr", "test along the real/imaginary axes");
311 }
312 ATF_TC_BODY(test_axes, tc)
313 {
314 	static const long double nums[] = {
315 	    M_PI / 4, M_PI / 2, 3 * M_PI / 4,
316 	    5 * M_PI / 4, 3 * M_PI / 2, 7 * M_PI / 4,
317 	};
318 	long double complex z;
319 	unsigned i;
320 
321 	for (i = 0; i < nitems(nums); i++) {
322 		/* Real axis */
323 		z = CMPLXL(nums[i], 0.0);
324 		test_odd_tol(csinh, z, CMPLXL(sinh(nums[i]), 0), DBL_ULP());
325 		test_even_tol(ccosh, z, CMPLXL(cosh(nums[i]), 0), DBL_ULP());
326 		test_odd_tol(ctanh, z, CMPLXL(tanh(nums[i]), 0), DBL_ULP());
327 		test_odd_tol(csin, z, CMPLXL(sin(nums[i]),
328 		    copysign(0, cos(nums[i]))), DBL_ULP());
329 		test_even_tol(ccos, z, CMPLXL(cos(nums[i]),
330 		    -copysign(0, sin(nums[i]))), DBL_ULP());
331 		test_odd_tol(ctan, z, CMPLXL(tan(nums[i]), 0), DBL_ULP());
332 
333 		test_odd_tol(csinhf, z, CMPLXL(sinhf(nums[i]), 0), FLT_ULP());
334 		test_even_tol(ccoshf, z, CMPLXL(coshf(nums[i]), 0), FLT_ULP());
335 		printf("%a %a\n", creal(z), cimag(z));
336 		printf("%a %a\n", creal(ctanhf(z)), cimag(ctanhf(z)));
337 		printf("%a\n", nextafterf(tanhf(nums[i]), INFINITY));
338 		test_odd_tol(ctanhf, z, CMPLXL(tanhf(nums[i]), 0),
339 			     1.3 * FLT_ULP());
340 		test_odd_tol(csinf, z, CMPLXL(sinf(nums[i]),
341 		    copysign(0, cosf(nums[i]))), FLT_ULP());
342 		test_even_tol(ccosf, z, CMPLXL(cosf(nums[i]),
343 		    -copysign(0, sinf(nums[i]))), 2 * FLT_ULP());
344 		test_odd_tol(ctanf, z, CMPLXL(tanf(nums[i]), 0), FLT_ULP());
345 
346 		/* Imaginary axis */
347 		z = CMPLXL(0.0, nums[i]);
348 		test_odd_tol(csinh, z, CMPLXL(copysign(0, cos(nums[i])),
349 						 sin(nums[i])), DBL_ULP());
350 		test_even_tol(ccosh, z, CMPLXL(cos(nums[i]),
351 		    copysign(0, sin(nums[i]))), DBL_ULP());
352 		test_odd_tol(ctanh, z, CMPLXL(0, tan(nums[i])), DBL_ULP());
353 		test_odd_tol(csin, z, CMPLXL(0, sinh(nums[i])), DBL_ULP());
354 		test_even_tol(ccos, z, CMPLXL(cosh(nums[i]), -0.0), DBL_ULP());
355 		test_odd_tol(ctan, z, CMPLXL(0, tanh(nums[i])), DBL_ULP());
356 
357 		test_odd_tol(csinhf, z, CMPLXL(copysign(0, cosf(nums[i])),
358 						 sinf(nums[i])), FLT_ULP());
359 		test_even_tol(ccoshf, z, CMPLXL(cosf(nums[i]),
360 		    copysign(0, sinf(nums[i]))), FLT_ULP());
361 		test_odd_tol(ctanhf, z, CMPLXL(0, tanf(nums[i])), FLT_ULP());
362 		test_odd_tol(csinf, z, CMPLXL(0, sinhf(nums[i])), FLT_ULP());
363 		test_even_tol(ccosf, z, CMPLXL(coshf(nums[i]), -0.0),
364 			      FLT_ULP());
365 		test_odd_tol(ctanf, z, CMPLXL(0, tanhf(nums[i])),
366 			     1.3 * FLT_ULP());
367 	}
368 }
369 
370 ATF_TC(test_small_inputs);
371 ATF_TC_HEAD(test_small_inputs, tc)
372 {
373 	atf_tc_set_md_var(tc, "descr", "test underflow inputs");
374 }
375 ATF_TC_BODY(test_small_inputs, tc)
376 {
377 	/*
378 	 * z =  0.5 + i Pi/4
379 	 *     sinh(z) = (sinh(0.5) + i cosh(0.5)) * sqrt(2)/2
380 	 *     cosh(z) = (cosh(0.5) + i sinh(0.5)) * sqrt(2)/2
381 	 *     tanh(z) = (2cosh(0.5)sinh(0.5) + i) / (2 cosh(0.5)**2 - 1)
382 	 * z = -0.5 + i Pi/2
383 	 *     sinh(z) = cosh(0.5)
384 	 *     cosh(z) = -i sinh(0.5)
385 	 *     tanh(z) = -coth(0.5)
386 	 * z =  1.0 + i 3Pi/4
387 	 *     sinh(z) = (-sinh(1) + i cosh(1)) * sqrt(2)/2
388 	 *     cosh(z) = (-cosh(1) + i sinh(1)) * sqrt(2)/2
389 	 *     tanh(z) = (2cosh(1)sinh(1) - i) / (2cosh(1)**2 - 1)
390 	 */
391 	static const struct {
392 		long double a, b;
393 		long double sinh_a, sinh_b;
394 		long double cosh_a, cosh_b;
395 		long double tanh_a, tanh_b;
396 	} tests[] = {
397 		{  0.5L,
398 		   0.78539816339744830961566084581987572L,
399 		   0.36847002415910435172083660522240710L,
400 		   0.79735196663945774996093142586179334L,
401 		   0.79735196663945774996093142586179334L,
402 		   0.36847002415910435172083660522240710L,
403 		   0.76159415595576488811945828260479359L,
404 		   0.64805427366388539957497735322615032L },
405 		{ -0.5L,
406 		   1.57079632679489661923132169163975144L,
407 		   0.0L,
408 		   1.12762596520638078522622516140267201L,
409 		   0.0L,
410 		  -0.52109530549374736162242562641149156L,
411 		  -2.16395341373865284877000401021802312L,
412 		   0.0L },
413 		{  1.0L,
414 		   2.35619449019234492884698253745962716L,
415 		  -0.83099273328405698212637979852748608L,
416 		   1.09112278079550143030545602018565236L,
417 		  -1.09112278079550143030545602018565236L,
418 		   0.83099273328405698212637979852748609L,
419 		   0.96402758007581688394641372410092315L,
420 		  -0.26580222883407969212086273981988897L }
421 	};
422 	long double complex z;
423 	unsigned i;
424 
425 	for (i = 0; i < nitems(tests); i++) {
426 		z = CMPLXL(tests[i].a, tests[i].b);
427 		testall_odd_tol(csinh, z,
428 		    CMPLXL(tests[i].sinh_a, tests[i].sinh_b), 1.1);
429 		testall_even_tol(ccosh, z,
430 		    CMPLXL(tests[i].cosh_a, tests[i].cosh_b), 1.1);
431 		testall_odd_tol(ctanh, z,
432 		    CMPLXL(tests[i].tanh_a, tests[i].tanh_b), 1.4);
433         }
434 }
435 
436 ATF_TC(test_large_inputs);
437 ATF_TC_HEAD(test_large_inputs, tc)
438 {
439 	atf_tc_set_md_var(tc, "descr",
440 	    "Test inputs that might cause overflow in a sloppy implementation");
441 }
442 ATF_TC_BODY(test_large_inputs, tc)
443 {
444 	long double complex z;
445 
446 	/* tanh() uses a threshold around x=22, so check both sides. */
447 	z = CMPLXL(21, 0.78539816339744830961566084581987572L);
448 	testall_odd_tol(ctanh, z,
449 	    CMPLXL(1.0, 1.14990445285871196133287617611468468e-18L), 1.2);
450 	z++;
451 	testall_odd_tol(ctanh, z,
452 	    CMPLXL(1.0, 1.55622644822675930314266334585597964e-19L), 1);
453 
454 	z = CMPLXL(355, 0.78539816339744830961566084581987572L);
455 	test_odd_tol(ctanh, z,
456 		     CMPLXL(1.0, 8.95257245135025991216632140458264468e-309L),
457 		     DBL_ULP());
458 	z = CMPLXL(30, 0x1p1023L);
459 	test_odd_tol(ctanh, z,
460 		     CMPLXL(1.0, -1.62994325413993477997492170229268382e-26L),
461 		     DBL_ULP());
462 	z = CMPLXL(1, 0x1p1023L);
463 	test_odd_tol(ctanh, z,
464 		     CMPLXL(0.878606311888306869546254022621986509L,
465 			    -0.225462792499754505792678258169527424L),
466 		     DBL_ULP());
467 
468 	z = CMPLXL(710.6, 0.78539816339744830961566084581987572L);
469 	test_odd_tol(csinh, z,
470 	    CMPLXL(1.43917579766621073533185387499658944e308L,
471 		   1.43917579766621073533185387499658944e308L), DBL_ULP());
472 	test_even_tol(ccosh, z,
473 	    CMPLXL(1.43917579766621073533185387499658944e308L,
474 		   1.43917579766621073533185387499658944e308L), DBL_ULP());
475 
476 	z = CMPLXL(1500, 0.78539816339744830961566084581987572L);
477 	testall_odd(csinh, z, CMPLXL(INFINITY, INFINITY), OPT_INEXACT,
478 	    FE_OVERFLOW, CS_BOTH);
479 	testall_even(ccosh, z, CMPLXL(INFINITY, INFINITY), OPT_INEXACT,
480 	    FE_OVERFLOW, CS_BOTH);
481 }
482 
483 ATF_TP_ADD_TCS(tp)
484 {
485 
486 	ATF_TP_ADD_TC(tp, test_zero_input);
487 	ATF_TP_ADD_TC(tp, test_nan_inputs);
488 	ATF_TP_ADD_TC(tp, test_inf_inputs);
489 	ATF_TP_ADD_TC(tp, test_axes);
490 	ATF_TP_ADD_TC(tp, test_small_inputs);
491 	ATF_TP_ADD_TC(tp, test_large_inputs);
492 
493 	return (atf_no_error());
494 }
495