xref: /dflybsd-src/tools/regression/lib/libm/test-ctrig.c (revision 7f8c68295613ce24cc71827cf210cb3d1e3bc69b) 
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-ctrig.c,v 1.1 2011/10/21 06:34:38 das Exp $
27  */
28 
29 /*
30  * Tests for csin[h](), ccos[h](), and ctan[h]().
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	OPT_INVALID	(ALL_STD_EXCEPT & ~FE_INVALID)
43 #define	OPT_INEXACT	(ALL_STD_EXCEPT & ~FE_INEXACT)
44 #define	FLT_ULP()	ldexpl(1.0, 1 - FLT_MANT_DIG)
45 #define	DBL_ULP()	ldexpl(1.0, 1 - DBL_MANT_DIG)
46 #define	LDBL_ULP()	ldexpl(1.0, 1 - LDBL_MANT_DIG)
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 /* Flags that determine whether to check the signs of the result. */
69 #define	CS_REAL	1
70 #define	CS_IMAG	2
71 #define	CS_BOTH	(CS_REAL | CS_IMAG)
72 
73 #ifdef	DEBUG
74 #define	debug(...)	printf(__VA_ARGS__)
75 #else
76 #define	debug(...)	(void)0
77 #endif
78 
79 /*
80  * Test that a function returns the correct value and sets the
81  * exception flags correctly. The exceptmask specifies which
82  * exceptions we should check. We need to be lenient for several
83  * reasons, but mainly because on some architectures it's impossible
84  * to raise FE_OVERFLOW without raising FE_INEXACT.
85  *
86  * These are macros instead of functions so that assert provides more
87  * meaningful error messages.
88  *
89  * XXX The volatile here is to avoid gcc's bogus constant folding and work
90  *     around the lack of support for the FENV_ACCESS pragma.
91  */
92 #define	test_p(func, z, result, exceptmask, excepts, checksign)	do {	\
93 	volatile long double complex _d = z;				\
94 	debug("  testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func,	\
95 	    creall(_d), cimagl(_d), creall(result), cimagl(result));	\
96 	assert(feclearexcept(FE_ALL_EXCEPT) == 0);			\
97 	assert(cfpequal((func)(_d), (result), (checksign)));		\
98 	assert(((func), fetestexcept(exceptmask) == (excepts)));	\
99 } while (0)
100 
101 /*
102  * Test within a given tolerance.  The tolerance indicates relative error
103  * in ulps.  If result is 0, however, it measures absolute error in units
104  * of <format>_EPSILON.
105  */
106 #define	test_p_tol(func, z, result, tol)			do {	\
107 	volatile long double complex _d = z;				\
108 	debug("  testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func,	\
109 	    creall(_d), cimagl(_d), creall(result), cimagl(result));	\
110 	assert(cfpequal_tol((func)(_d), (result), (tol)));		\
111 } while (0)
112 
113 /* These wrappers apply the identities f(conj(z)) = conj(f(z)). */
114 #define	test(func, z, result, exceptmask, excepts, checksign)	do {	\
115 	test_p(func, z, result, exceptmask, excepts, checksign);	\
116 	test_p(func, conjl(z), conjl(result), exceptmask, excepts, checksign); \
117 } while (0)
118 #define	test_tol(func, z, result, tol)				do {	\
119 	test_p_tol(func, z, result, tol);				\
120 	test_p_tol(func, conjl(z), conjl(result), tol);			\
121 } while (0)
122 
123 /* Test the given function in all precisions. */
124 #define	testall(func, x, result, exceptmask, excepts, checksign) do {	\
125 	test(func, x, result, exceptmask, excepts, checksign);		\
126 	test(func##f, x, result, exceptmask, excepts, checksign);	\
127 } while (0)
128 #define	testall_odd(func, x, result, exceptmask, excepts, checksign) do { \
129 	testall(func, x, result, exceptmask, excepts, checksign);	\
130 	testall(func, -x, -result, exceptmask, excepts, checksign);	\
131 } while (0)
132 #define	testall_even(func, x, result, exceptmask, excepts, checksign) do { \
133 	testall(func, x, result, exceptmask, excepts, checksign);	\
134 	testall(func, -x, result, exceptmask, excepts, checksign);	\
135 } while (0)
136 
137 /*
138  * Test the given function in all precisions, within a given tolerance.
139  * The tolerance is specified in ulps.
140  */
141 #define	testall_tol(func, x, result, tol)	       		   do { \
142 	test_tol(func, x, result, tol * DBL_ULP());			\
143 	test_tol(func##f, x, result, tol * FLT_ULP());			\
144 } while (0)
145 #define	testall_odd_tol(func, x, result, tol)	       		   do { \
146 	test_tol(func, x, result, tol * DBL_ULP());			\
147 	test_tol(func, -x, -result, tol * DBL_ULP());			\
148 } while (0)
149 #define	testall_even_tol(func, x, result, tol)	       		   do { \
150 	test_tol(func, x, result, tol * DBL_ULP());			\
151 	test_tol(func, -x, result, tol * DBL_ULP());			\
152 } while (0)
153 
154 /*
155  * Determine whether x and y are equal, with two special rules:
156  *	+0.0 != -0.0
157  *	 NaN == NaN
158  * If checksign is 0, we compare the absolute values instead.
159  */
160 static int
fpequal(long double x,long double y,int checksign)161 fpequal(long double x, long double y, int checksign)
162 {
163 	if (isnan(x) && isnan(y))
164 		return (1);
165 	if (checksign)
166 		return (x == y && !signbit(x) == !signbit(y));
167 	else
168 		return (fabsl(x) == fabsl(y));
169 }
170 
171 static int
fpequal_tol(long double x,long double y,long double tol)172 fpequal_tol(long double x, long double y, long double tol)
173 {
174 	fenv_t env;
175 	int ret;
176 
177 	if (isnan(x) && isnan(y))
178 		return (1);
179 	if (!signbit(x) != !signbit(y) && tol == 0)
180 		return (0);
181 	if (x == y)
182 		return (1);
183 	if (tol == 0)
184 		return (0);
185 
186 	/* Hard case: need to check the tolerance. */
187 	feholdexcept(&env);
188 	/*
189 	 * For our purposes here, if y=0, we interpret tol as an absolute
190 	 * tolerance. This is to account for roundoff in the input, e.g.,
191 	 * cos(Pi/2) ~= 0.
192 	 */
193 	if (y == 0.0)
194 		ret = fabsl(x - y) <= fabsl(tol);
195 	else
196 		ret = fabsl(x - y) <= fabsl(y * tol);
197 	fesetenv(&env);
198 	return (ret);
199 }
200 
201 static int
cfpequal(long double complex x,long double complex y,int checksign)202 cfpequal(long double complex x, long double complex y, int checksign)
203 {
204 	return (fpequal(creal(x), creal(y), checksign & CS_REAL)
205 		&& fpequal(cimag(x), cimag(y), checksign & CS_IMAG));
206 }
207 
208 static int
cfpequal_tol(long double complex x,long double complex y,long double tol)209 cfpequal_tol(long double complex x, long double complex y, long double tol)
210 {
211 	return (fpequal_tol(creal(x), creal(y), tol)
212 		&& fpequal_tol(cimag(x), cimag(y), tol));
213 }
214 
215 
216 /* Tests for 0 */
217 void
test_zero(void)218 test_zero(void)
219 {
220 	long double complex zero = cpackl(0.0, 0.0);
221 
222 	/* csinh(0) = ctanh(0) = 0; ccosh(0) = 1 (no exceptions raised) */
223 	testall_odd(csinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
224 	testall_odd(csin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
225 	testall_even(ccosh, zero, 1.0, ALL_STD_EXCEPT, 0, CS_BOTH);
226 	testall_even(ccos, zero, cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, CS_BOTH);
227 	testall_odd(ctanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
228 	testall_odd(ctan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
229 }
230 
231 /*
232  * Tests for NaN inputs.
233  */
234 void
test_nan()235 test_nan()
236 {
237 	long double complex nan_nan = cpackl(NAN, NAN);
238 	long double complex z;
239 
240 	/*
241 	 * IN		CSINH		CCOSH		CTANH
242 	 * NaN,NaN	NaN,NaN		NaN,NaN		NaN,NaN
243 	 * finite,NaN	NaN,NaN [inval]	NaN,NaN [inval]	NaN,NaN [inval]
244 	 * NaN,finite	NaN,NaN [inval]	NaN,NaN [inval]	NaN,NaN [inval]
245 	 * NaN,Inf	NaN,NaN [inval]	NaN,NaN	[inval]	NaN,NaN [inval]
246 	 * Inf,NaN	+-Inf,NaN	Inf,NaN		1,+-0
247 	 * 0,NaN	+-0,NaN		NaN,+-0		NaN,NaN	[inval]
248 	 * NaN,0	NaN,0		NaN,+-0		NaN,0
249 	 */
250 	z = nan_nan;
251 	testall_odd(csinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
252 	testall_even(ccosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
253 	testall_odd(ctanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
254 	testall_odd(csin, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
255 	testall_even(ccos, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
256 	testall_odd(ctan, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
257 
258 	z = cpackl(42, NAN);
259 	testall_odd(csinh, z, nan_nan, OPT_INVALID, 0, 0);
260 	testall_even(ccosh, z, nan_nan, OPT_INVALID, 0, 0);
261 	/* XXX We allow a spurious inexact exception here. */
262 	testall_odd(ctanh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0);
263 	testall_odd(csin, z, nan_nan, OPT_INVALID, 0, 0);
264 	testall_even(ccos, z, nan_nan, OPT_INVALID, 0, 0);
265 	testall_odd(ctan, z, nan_nan, OPT_INVALID, 0, 0);
266 
267 	z = cpackl(NAN, 42);
268 	testall_odd(csinh, z, nan_nan, OPT_INVALID, 0, 0);
269 	testall_even(ccosh, z, nan_nan, OPT_INVALID, 0, 0);
270 	testall_odd(ctanh, z, nan_nan, OPT_INVALID, 0, 0);
271 	testall_odd(csin, z, nan_nan, OPT_INVALID, 0, 0);
272 	testall_even(ccos, z, nan_nan, OPT_INVALID, 0, 0);
273 	/* XXX We allow a spurious inexact exception here. */
274 	testall_odd(ctan, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0);
275 
276 	z = cpackl(NAN, INFINITY);
277 	testall_odd(csinh, z, nan_nan, OPT_INVALID, 0, 0);
278 	testall_even(ccosh, z, nan_nan, OPT_INVALID, 0, 0);
279 	testall_odd(ctanh, z, nan_nan, OPT_INVALID, 0, 0);
280 	testall_odd(csin, z, cpackl(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
281 	testall_even(ccos, z, cpackl(INFINITY, NAN), ALL_STD_EXCEPT, 0,
282 	    CS_IMAG);
283 	testall_odd(ctan, z, cpackl(0, 1), ALL_STD_EXCEPT, 0, CS_IMAG);
284 
285 	z = cpackl(INFINITY, NAN);
286 	testall_odd(csinh, z, cpackl(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0);
287 	testall_even(ccosh, z, cpackl(INFINITY, NAN), ALL_STD_EXCEPT, 0,
288 		     CS_REAL);
289 	testall_odd(ctanh, z, cpackl(1, 0), ALL_STD_EXCEPT, 0, CS_REAL);
290 	testall_odd(csin, z, nan_nan, OPT_INVALID, 0, 0);
291 	testall_even(ccos, z, nan_nan, OPT_INVALID, 0, 0);
292 	testall_odd(ctan, z, nan_nan, OPT_INVALID, 0, 0);
293 
294 	z = cpackl(0, NAN);
295 	testall_odd(csinh, z, cpackl(0, NAN), ALL_STD_EXCEPT, 0, 0);
296 	testall_even(ccosh, z, cpackl(NAN, 0), ALL_STD_EXCEPT, 0, 0);
297 	testall_odd(ctanh, z, nan_nan, OPT_INVALID, 0, 0);
298 	testall_odd(csin, z, cpackl(0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
299 	testall_even(ccos, z, cpackl(NAN, 0), ALL_STD_EXCEPT, 0, 0);
300 	testall_odd(ctan, z, cpackl(0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
301 
302 	z = cpackl(NAN, 0);
303 	testall_odd(csinh, z, cpackl(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG);
304 	testall_even(ccosh, z, cpackl(NAN, 0), ALL_STD_EXCEPT, 0, 0);
305 	testall_odd(ctanh, z, cpackl(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG);
306 	testall_odd(csin, z, cpackl(NAN, 0), ALL_STD_EXCEPT, 0, 0);
307 	testall_even(ccos, z, cpackl(NAN, 0), ALL_STD_EXCEPT, 0, 0);
308 	testall_odd(ctan, z, nan_nan, OPT_INVALID, 0, 0);
309 }
310 
311 void
test_inf(void)312 test_inf(void)
313 {
314 	static const long double finites[] = {
315 	    0, M_PI / 4, 3 * M_PI / 4, 5 * M_PI / 4,
316 	};
317 	long double complex z, c, s;
318 	int i;
319 
320 	/*
321 	 * IN		CSINH		CCOSH		CTANH
322 	 * Inf,Inf	+-Inf,NaN inval	+-Inf,NaN inval	1,+-0
323 	 * Inf,finite	Inf cis(finite)	Inf cis(finite)	1,0 sin(2 finite)
324 	 * 0,Inf	+-0,NaN	inval	NaN,+-0 inval	NaN,NaN	inval
325 	 * finite,Inf	NaN,NaN inval	NaN,NaN inval	NaN,NaN inval
326 	 */
327 	z = cpackl(INFINITY, INFINITY);
328 	testall_odd(csinh, z, cpackl(INFINITY, NAN),
329 		    ALL_STD_EXCEPT, FE_INVALID, 0);
330 	testall_even(ccosh, z, cpackl(INFINITY, NAN),
331 		     ALL_STD_EXCEPT, FE_INVALID, 0);
332 	testall_odd(ctanh, z, cpackl(1, 0), ALL_STD_EXCEPT, 0, CS_REAL);
333 	testall_odd(csin, z, cpackl(NAN, INFINITY),
334 		    ALL_STD_EXCEPT, FE_INVALID, 0);
335 	testall_even(ccos, z, cpackl(INFINITY, NAN),
336 		     ALL_STD_EXCEPT, FE_INVALID, 0);
337 	testall_odd(ctan, z, cpackl(0, 1), ALL_STD_EXCEPT, 0, CS_REAL);
338 
339 	/* XXX We allow spurious inexact exceptions here (hard to avoid). */
340 	for (i = 0; i < sizeof(finites) / sizeof(finites[0]); i++) {
341 		z = cpackl(INFINITY, finites[i]);
342 		c = INFINITY * cosl(finites[i]);
343 		s = finites[i] == 0 ? finites[i] : INFINITY * sinl(finites[i]);
344 		testall_odd(csinh, z, cpackl(c, s), OPT_INEXACT, 0, CS_BOTH);
345 		testall_even(ccosh, z, cpackl(c, s), OPT_INEXACT, 0, CS_BOTH);
346 		testall_odd(ctanh, z, cpackl(1, 0 * sin(finites[i] * 2)),
347 			    OPT_INEXACT, 0, CS_BOTH);
348 		z = cpackl(finites[i], INFINITY);
349 		testall_odd(csin, z, cpackl(s, c), OPT_INEXACT, 0, CS_BOTH);
350 		testall_even(ccos, z, cpackl(c, -s), OPT_INEXACT, 0, CS_BOTH);
351 		testall_odd(ctan, z, cpackl(0 * sin(finites[i] * 2), 1),
352 			    OPT_INEXACT, 0, CS_BOTH);
353 	}
354 
355 	z = cpackl(0, INFINITY);
356 	testall_odd(csinh, z, cpackl(0, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
357 	testall_even(ccosh, z, cpackl(NAN, 0), ALL_STD_EXCEPT, FE_INVALID, 0);
358 	testall_odd(ctanh, z, cpackl(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
359 	z = cpackl(INFINITY, 0);
360 	testall_odd(csin, z, cpackl(NAN, 0), ALL_STD_EXCEPT, FE_INVALID, 0);
361 	testall_even(ccos, z, cpackl(NAN, 0), ALL_STD_EXCEPT, FE_INVALID, 0);
362 	testall_odd(ctan, z, cpackl(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
363 
364 	z = cpackl(42, INFINITY);
365 	testall_odd(csinh, z, cpackl(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
366 	testall_even(ccosh, z, cpackl(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
367 	/* XXX We allow a spurious inexact exception here. */
368 	testall_odd(ctanh, z, cpackl(NAN, NAN), OPT_INEXACT, FE_INVALID, 0);
369 	z = cpackl(INFINITY, 42);
370 	testall_odd(csin, z, cpackl(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
371 	testall_even(ccos, z, cpackl(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
372 	/* XXX We allow a spurious inexact exception here. */
373 	testall_odd(ctan, z, cpackl(NAN, NAN), OPT_INEXACT, FE_INVALID, 0);
374 }
375 
376 /* Tests along the real and imaginary axes. */
377 void
test_axes(void)378 test_axes(void)
379 {
380 	static const long double nums[] = {
381 	    M_PI / 4, M_PI / 2, 3 * M_PI / 4,
382 	    5 * M_PI / 4, 3 * M_PI / 2, 7 * M_PI / 4,
383 	};
384 	long double complex z;
385 	int i;
386 
387 	for (i = 0; i < sizeof(nums) / sizeof(nums[0]); i++) {
388 		/* Real axis */
389 		z = cpackl(nums[i], 0.0);
390 		testall_odd_tol(csinh, z, cpackl(sinh(nums[i]), 0), 0);
391 		testall_even_tol(ccosh, z, cpackl(cosh(nums[i]), 0), 0);
392 		testall_odd_tol(ctanh, z, cpackl(tanh(nums[i]), 0), 1);
393 		testall_odd_tol(csin, z, cpackl(sin(nums[i]),
394 					    copysign(0, cos(nums[i]))), 0);
395 		testall_even_tol(ccos, z, cpackl(cos(nums[i]),
396 		    -copysign(0, sin(nums[i]))), 0);
397 		testall_odd_tol(ctan, z, cpackl(tan(nums[i]), 0), 1);
398 
399 		/* Imaginary axis */
400 		z = cpackl(0.0, nums[i]);
401 		testall_odd_tol(csinh, z, cpackl(copysign(0, cos(nums[i])),
402 						 sin(nums[i])), 0);
403 		testall_even_tol(ccosh, z, cpackl(cos(nums[i]),
404 		    copysign(0, sin(nums[i]))), 0);
405 		testall_odd_tol(ctanh, z, cpackl(0, tan(nums[i])), 1);
406 		testall_odd_tol(csin, z, cpackl(0, sinh(nums[i])), 0);
407 		testall_even_tol(ccos, z, cpackl(cosh(nums[i]), -0.0), 0);
408 		testall_odd_tol(ctan, z, cpackl(0, tanh(nums[i])), 1);
409 	}
410 }
411 
412 void
test_small(void)413 test_small(void)
414 {
415 	/*
416 	 * z =  0.5 + i Pi/4
417 	 *     sinh(z) = (sinh(0.5) + i cosh(0.5)) * sqrt(2)/2
418 	 *     cosh(z) = (cosh(0.5) + i sinh(0.5)) * sqrt(2)/2
419 	 *     tanh(z) = (2cosh(0.5)sinh(0.5) + i) / (2 cosh(0.5)**2 - 1)
420 	 * z = -0.5 + i Pi/2
421 	 *     sinh(z) = cosh(0.5)
422 	 *     cosh(z) = -i sinh(0.5)
423 	 *     tanh(z) = -coth(0.5)
424 	 * z =  1.0 + i 3Pi/4
425 	 *     sinh(z) = (-sinh(1) + i cosh(1)) * sqrt(2)/2
426 	 *     cosh(z) = (-cosh(1) + i sinh(1)) * sqrt(2)/2
427 	 *     tanh(z) = (2cosh(1)sinh(1) - i) / (2cosh(1)**2 - 1)
428 	 */
429 	static const struct {
430 		long double a, b;
431 		long double sinh_a, sinh_b;
432 		long double cosh_a, cosh_b;
433 		long double tanh_a, tanh_b;
434 	} tests[] = {
435 		{  0.5L,
436 		   0.78539816339744830961566084581987572L,
437 		   0.36847002415910435172083660522240710L,
438 		   0.79735196663945774996093142586179334L,
439 		   0.79735196663945774996093142586179334L,
440 		   0.36847002415910435172083660522240710L,
441 		   0.76159415595576488811945828260479359L,
442 		   0.64805427366388539957497735322615032L },
443 		{ -0.5L,
444 		   1.57079632679489661923132169163975144L,
445 		   0.0L,
446 		   1.12762596520638078522622516140267201L,
447 		   0.0L,
448 		  -0.52109530549374736162242562641149156L,
449 		  -2.16395341373865284877000401021802312L,
450 		   0.0L },
451 		{  1.0L,
452 		   2.35619449019234492884698253745962716L,
453 		  -0.83099273328405698212637979852748608L,
454 		   1.09112278079550143030545602018565236L,
455 		  -1.09112278079550143030545602018565236L,
456 		   0.83099273328405698212637979852748609L,
457 		   0.96402758007581688394641372410092315L,
458 		  -0.26580222883407969212086273981988897L }
459 	};
460 	long double complex z;
461 	int i;
462 
463 	for (i = 0; i < sizeof(tests) / sizeof(tests[0]); i++) {
464 		z = cpackl(tests[i].a, tests[i].b);
465 		testall_odd_tol(csinh, z,
466 		    cpackl(tests[i].sinh_a, tests[i].sinh_b), 1.1);
467 		testall_even_tol(ccosh, z,
468 		    cpackl(tests[i].cosh_a, tests[i].cosh_b), 1.1);
469 		testall_odd_tol(ctanh, z,
470 		    cpackl(tests[i].tanh_a, tests[i].tanh_b), 1.1);
471         }
472 }
473 
474 /* Test inputs that might cause overflow in a sloppy implementation. */
475 void
test_large(void)476 test_large(void)
477 {
478 	long double complex z;
479 
480 	/* tanh() uses a threshold around x=22, so check both sides. */
481 	z = cpackl(21, 0.78539816339744830961566084581987572L);
482 	testall_odd_tol(ctanh, z,
483 	    cpackl(1.0, 1.14990445285871196133287617611468468e-18L), 1);
484 	z++;
485 	testall_odd_tol(ctanh, z,
486 	    cpackl(1.0, 1.55622644822675930314266334585597964e-19L), 1);
487 
488 	z = cpackl(355, 0.78539816339744830961566084581987572L);
489 	testall_odd_tol(ctanh, z,
490 	    cpackl(1.0, 8.95257245135025991216632140458264468e-309L), 1);
491 	z = cpackl(30, 0x1p1023L);
492 	testall_odd_tol(ctanh, z,
493 	    cpackl(1.0, -1.62994325413993477997492170229268382e-26L), 1);
494 	z = cpackl(1, 0x1p1023L);
495 	testall_odd_tol(ctanh, z,
496 	    cpackl(0.878606311888306869546254022621986509L,
497 		   -0.225462792499754505792678258169527424L), 1);
498 
499 	z = cpackl(710.6, 0.78539816339744830961566084581987572L);
500 	testall_odd_tol(csinh, z,
501 	    cpackl(1.43917579766621073533185387499658944e308L,
502 		   1.43917579766621073533185387499658944e308L), 1);
503 	testall_even_tol(ccosh, z,
504 	    cpackl(1.43917579766621073533185387499658944e308L,
505 		   1.43917579766621073533185387499658944e308L), 1);
506 
507 	z = cpackl(1500, 0.78539816339744830961566084581987572L);
508 	testall_odd(csinh, z, cpackl(INFINITY, INFINITY), OPT_INEXACT,
509 	    FE_OVERFLOW, CS_BOTH);
510 	testall_even(ccosh, z, cpackl(INFINITY, INFINITY), OPT_INEXACT,
511 	    FE_OVERFLOW, CS_BOTH);
512 }
513 
514 int
main(int argc,char * argv[])515 main(int argc, char *argv[])
516 {
517 
518 	printf("1..6\n");
519 
520 	test_zero();
521 	printf("ok 1 - ctrig zero\n");
522 
523 	test_nan();
524 	printf("ok 2 - ctrig nan\n");
525 
526 	test_inf();
527 	printf("ok 3 - ctrig inf\n");
528 
529 	test_axes();
530 	printf("ok 4 - ctrig axes\n");
531 
532 	test_small();
533 	printf("ok 5 - ctrig small\n");
534 
535 	test_large();
536 	printf("ok 6 - ctrig large\n");
537 
538 	return (0);
539 }
540