2 * Copyright (c) 2008-2011 David Schultz <das@FreeBSD.org>
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
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.
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
28 * Tests for csin[h](), ccos[h](), and ctan[h]().
31 #include <sys/cdefs.h>
32 __FBSDID("$FreeBSD$");
41 #include "test-utils.h"
43 #pragma STDC FENV_ACCESS ON
44 #pragma STDC CX_LIMITED_RANGE OFF
47 * Test that a function returns the correct value and sets the
48 * exception flags correctly. The exceptmask specifies which
49 * exceptions we should check. We need to be lenient for several
50 * reasons, but mainly because on some architectures it's impossible
51 * to raise FE_OVERFLOW without raising FE_INEXACT.
53 * These are macros instead of functions so that assert provides more
54 * meaningful error messages.
56 * XXX The volatile here is to avoid gcc's bogus constant folding and work
57 * around the lack of support for the FENV_ACCESS pragma.
59 #define test_p(func, z, result, exceptmask, excepts, checksign) do { \
60 volatile long double complex _d = z; \
61 debug(" testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func, \
62 creall(_d), cimagl(_d), creall(result), cimagl(result)); \
63 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
64 assert(cfpequal_cs((func)(_d), (result), (checksign))); \
65 assert(((void)(func), fetestexcept(exceptmask) == (excepts))); \
69 * Test within a given tolerance. The tolerance indicates relative error
70 * in ulps. If result is 0, however, it measures absolute error in units
71 * of <format>_EPSILON.
73 #define test_p_tol(func, z, result, tol) do { \
74 volatile long double complex _d = z; \
75 debug(" testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func, \
76 creall(_d), cimagl(_d), creall(result), cimagl(result)); \
77 assert(cfpequal_tol((func)(_d), (result), (tol), FPE_ABS_ZERO)); \
80 /* These wrappers apply the identities f(conj(z)) = conj(f(z)). */
81 #define test(func, z, result, exceptmask, excepts, checksign) do { \
82 test_p(func, z, result, exceptmask, excepts, checksign); \
83 test_p(func, conjl(z), conjl(result), exceptmask, excepts, checksign); \
85 #define test_tol(func, z, result, tol) do { \
86 test_p_tol(func, z, result, tol); \
87 test_p_tol(func, conjl(z), conjl(result), tol); \
89 #define test_odd_tol(func, z, result, tol) do { \
90 test_tol(func, z, result, tol); \
91 test_tol(func, -(z), -(result), tol); \
93 #define test_even_tol(func, z, result, tol) do { \
94 test_tol(func, z, result, tol); \
95 test_tol(func, -(z), result, tol); \
98 /* Test the given function in all precisions. */
99 #define testall(func, x, result, exceptmask, excepts, checksign) do { \
100 test(func, x, result, exceptmask, excepts, checksign); \
101 test(func##f, x, result, exceptmask, excepts, checksign); \
103 #define testall_odd(func, x, result, exceptmask, excepts, checksign) do { \
104 testall(func, x, result, exceptmask, excepts, checksign); \
105 testall(func, -x, -result, exceptmask, excepts, checksign); \
107 #define testall_even(func, x, result, exceptmask, excepts, checksign) do { \
108 testall(func, x, result, exceptmask, excepts, checksign); \
109 testall(func, -x, result, exceptmask, excepts, checksign); \
113 * Test the given function in all precisions, within a given tolerance.
114 * The tolerance is specified in ulps.
116 #define testall_tol(func, x, result, tol) do { \
117 test_tol(func, x, result, tol * DBL_ULP()); \
118 test_tol(func##f, x, result, tol * FLT_ULP()); \
120 #define testall_odd_tol(func, x, result, tol) do { \
121 test_odd_tol(func, x, result, tol * DBL_ULP()); \
122 test_odd_tol(func##f, x, result, tol * FLT_ULP()); \
124 #define testall_even_tol(func, x, result, tol) do { \
125 test_even_tol(func, x, result, tol * DBL_ULP()); \
126 test_even_tol(func##f, x, result, tol * FLT_ULP()); \
134 long double complex zero = CMPLXL(0.0, 0.0);
136 /* csinh(0) = ctanh(0) = 0; ccosh(0) = 1 (no exceptions raised) */
137 testall_odd(csinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
138 testall_odd(csin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
139 testall_even(ccosh, zero, 1.0, ALL_STD_EXCEPT, 0, CS_BOTH);
140 testall_even(ccos, zero, CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, CS_BOTH);
141 testall_odd(ctanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
142 testall_odd(ctan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
146 * Tests for NaN inputs.
151 long double complex nan_nan = CMPLXL(NAN, NAN);
152 long double complex z;
155 * IN CSINH CCOSH CTANH
156 * NaN,NaN NaN,NaN NaN,NaN NaN,NaN
157 * finite,NaN NaN,NaN [inval] NaN,NaN [inval] NaN,NaN [inval]
158 * NaN,finite NaN,NaN [inval] NaN,NaN [inval] NaN,NaN [inval]
159 * NaN,Inf NaN,NaN [inval] NaN,NaN [inval] NaN,NaN [inval]
160 * Inf,NaN +-Inf,NaN Inf,NaN 1,+-0
161 * 0,NaN +-0,NaN NaN,+-0 NaN,NaN [inval]
162 * NaN,0 NaN,0 NaN,+-0 NaN,0
165 testall_odd(csinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
166 testall_even(ccosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
167 testall_odd(ctanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
168 testall_odd(csin, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
169 testall_even(ccos, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
170 testall_odd(ctan, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
173 testall_odd(csinh, z, nan_nan, OPT_INVALID, 0, 0);
174 testall_even(ccosh, z, nan_nan, OPT_INVALID, 0, 0);
175 /* XXX We allow a spurious inexact exception here. */
176 testall_odd(ctanh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0);
177 testall_odd(csin, z, nan_nan, OPT_INVALID, 0, 0);
178 testall_even(ccos, z, nan_nan, OPT_INVALID, 0, 0);
179 testall_odd(ctan, z, nan_nan, OPT_INVALID, 0, 0);
182 testall_odd(csinh, z, nan_nan, OPT_INVALID, 0, 0);
183 testall_even(ccosh, z, nan_nan, OPT_INVALID, 0, 0);
184 testall_odd(ctanh, z, nan_nan, OPT_INVALID, 0, 0);
185 testall_odd(csin, z, nan_nan, OPT_INVALID, 0, 0);
186 testall_even(ccos, z, nan_nan, OPT_INVALID, 0, 0);
187 /* XXX We allow a spurious inexact exception here. */
188 testall_odd(ctan, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0);
190 z = CMPLXL(NAN, INFINITY);
191 testall_odd(csinh, z, nan_nan, OPT_INVALID, 0, 0);
192 testall_even(ccosh, z, nan_nan, OPT_INVALID, 0, 0);
193 testall_odd(ctanh, z, nan_nan, OPT_INVALID, 0, 0);
194 testall_odd(csin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
195 testall_even(ccos, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
197 testall_odd(ctan, z, CMPLXL(0, 1), ALL_STD_EXCEPT, 0, CS_IMAG);
199 z = CMPLXL(INFINITY, NAN);
200 testall_odd(csinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0);
201 testall_even(ccosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
203 testall_odd(ctanh, z, CMPLXL(1, 0), ALL_STD_EXCEPT, 0, CS_REAL);
204 testall_odd(csin, z, nan_nan, OPT_INVALID, 0, 0);
205 testall_even(ccos, z, nan_nan, OPT_INVALID, 0, 0);
206 testall_odd(ctan, z, nan_nan, OPT_INVALID, 0, 0);
209 testall_odd(csinh, z, CMPLXL(0, NAN), ALL_STD_EXCEPT, 0, 0);
210 testall_even(ccosh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, 0);
211 testall_odd(ctanh, z, nan_nan, OPT_INVALID, 0, 0);
212 testall_odd(csin, z, CMPLXL(0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
213 testall_even(ccos, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, 0);
214 testall_odd(ctan, z, CMPLXL(0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
217 testall_odd(csinh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG);
218 testall_even(ccosh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, 0);
219 testall_odd(ctanh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG);
220 testall_odd(csin, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, 0);
221 testall_even(ccos, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, 0);
222 testall_odd(ctan, z, nan_nan, OPT_INVALID, 0, 0);
228 static const long double finites[] = {
229 0, M_PI / 4, 3 * M_PI / 4, 5 * M_PI / 4,
231 long double complex z, c, s;
235 * IN CSINH CCOSH CTANH
236 * Inf,Inf +-Inf,NaN inval +-Inf,NaN inval 1,+-0
237 * Inf,finite Inf cis(finite) Inf cis(finite) 1,0 sin(2 finite)
238 * 0,Inf +-0,NaN inval NaN,+-0 inval NaN,NaN inval
239 * finite,Inf NaN,NaN inval NaN,NaN inval NaN,NaN inval
241 z = CMPLXL(INFINITY, INFINITY);
242 testall_odd(csinh, z, CMPLXL(INFINITY, NAN),
243 ALL_STD_EXCEPT, FE_INVALID, 0);
244 testall_even(ccosh, z, CMPLXL(INFINITY, NAN),
245 ALL_STD_EXCEPT, FE_INVALID, 0);
246 testall_odd(ctanh, z, CMPLXL(1, 0), ALL_STD_EXCEPT, 0, CS_REAL);
247 testall_odd(csin, z, CMPLXL(NAN, INFINITY),
248 ALL_STD_EXCEPT, FE_INVALID, 0);
249 testall_even(ccos, z, CMPLXL(INFINITY, NAN),
250 ALL_STD_EXCEPT, FE_INVALID, 0);
251 testall_odd(ctan, z, CMPLXL(0, 1), ALL_STD_EXCEPT, 0, CS_REAL);
253 /* XXX We allow spurious inexact exceptions here (hard to avoid). */
254 for (i = 0; i < sizeof(finites) / sizeof(finites[0]); i++) {
255 z = CMPLXL(INFINITY, finites[i]);
256 c = INFINITY * cosl(finites[i]);
257 s = finites[i] == 0 ? finites[i] : INFINITY * sinl(finites[i]);
258 testall_odd(csinh, z, CMPLXL(c, s), OPT_INEXACT, 0, CS_BOTH);
259 testall_even(ccosh, z, CMPLXL(c, s), OPT_INEXACT, 0, CS_BOTH);
260 testall_odd(ctanh, z, CMPLXL(1, 0 * sin(finites[i] * 2)),
261 OPT_INEXACT, 0, CS_BOTH);
262 z = CMPLXL(finites[i], INFINITY);
263 testall_odd(csin, z, CMPLXL(s, c), OPT_INEXACT, 0, CS_BOTH);
264 testall_even(ccos, z, CMPLXL(c, -s), OPT_INEXACT, 0, CS_BOTH);
265 testall_odd(ctan, z, CMPLXL(0 * sin(finites[i] * 2), 1),
266 OPT_INEXACT, 0, CS_BOTH);
269 z = CMPLXL(0, INFINITY);
270 testall_odd(csinh, z, CMPLXL(0, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
271 testall_even(ccosh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, FE_INVALID, 0);
272 testall_odd(ctanh, z, CMPLXL(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
273 z = CMPLXL(INFINITY, 0);
274 testall_odd(csin, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, FE_INVALID, 0);
275 testall_even(ccos, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, FE_INVALID, 0);
276 testall_odd(ctan, z, CMPLXL(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
278 z = CMPLXL(42, INFINITY);
279 testall_odd(csinh, z, CMPLXL(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
280 testall_even(ccosh, z, CMPLXL(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
281 /* XXX We allow a spurious inexact exception here. */
282 testall_odd(ctanh, z, CMPLXL(NAN, NAN), OPT_INEXACT, FE_INVALID, 0);
283 z = CMPLXL(INFINITY, 42);
284 testall_odd(csin, z, CMPLXL(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
285 testall_even(ccos, z, CMPLXL(NAN, NAN), ALL_STD_EXCEPT, FE_INVALID, 0);
286 /* XXX We allow a spurious inexact exception here. */
287 testall_odd(ctan, z, CMPLXL(NAN, NAN), OPT_INEXACT, FE_INVALID, 0);
290 /* Tests along the real and imaginary axes. */
294 static const long double nums[] = {
295 M_PI / 4, M_PI / 2, 3 * M_PI / 4,
296 5 * M_PI / 4, 3 * M_PI / 2, 7 * M_PI / 4,
298 long double complex z;
301 for (i = 0; i < sizeof(nums) / sizeof(nums[0]); i++) {
303 z = CMPLXL(nums[i], 0.0);
304 test_odd_tol(csinh, z, CMPLXL(sinh(nums[i]), 0), DBL_ULP());
305 test_even_tol(ccosh, z, CMPLXL(cosh(nums[i]), 0), DBL_ULP());
306 test_odd_tol(ctanh, z, CMPLXL(tanh(nums[i]), 0), DBL_ULP());
307 test_odd_tol(csin, z, CMPLXL(sin(nums[i]),
308 copysign(0, cos(nums[i]))), DBL_ULP());
309 test_even_tol(ccos, z, CMPLXL(cos(nums[i]),
310 -copysign(0, sin(nums[i]))), DBL_ULP());
311 test_odd_tol(ctan, z, CMPLXL(tan(nums[i]), 0), DBL_ULP());
313 test_odd_tol(csinhf, z, CMPLXL(sinhf(nums[i]), 0), FLT_ULP());
314 test_even_tol(ccoshf, z, CMPLXL(coshf(nums[i]), 0), FLT_ULP());
315 printf("%a %a\n", creal(z), cimag(z));
316 printf("%a %a\n", creal(ctanhf(z)), cimag(ctanhf(z)));
317 printf("%a\n", nextafterf(tanhf(nums[i]), INFINITY));
318 test_odd_tol(ctanhf, z, CMPLXL(tanhf(nums[i]), 0),
320 test_odd_tol(csinf, z, CMPLXL(sinf(nums[i]),
321 copysign(0, cosf(nums[i]))), FLT_ULP());
322 test_even_tol(ccosf, z, CMPLXL(cosf(nums[i]),
323 -copysign(0, sinf(nums[i]))), 2 * FLT_ULP());
324 test_odd_tol(ctanf, z, CMPLXL(tanf(nums[i]), 0), FLT_ULP());
327 z = CMPLXL(0.0, nums[i]);
328 test_odd_tol(csinh, z, CMPLXL(copysign(0, cos(nums[i])),
329 sin(nums[i])), DBL_ULP());
330 test_even_tol(ccosh, z, CMPLXL(cos(nums[i]),
331 copysign(0, sin(nums[i]))), DBL_ULP());
332 test_odd_tol(ctanh, z, CMPLXL(0, tan(nums[i])), DBL_ULP());
333 test_odd_tol(csin, z, CMPLXL(0, sinh(nums[i])), DBL_ULP());
334 test_even_tol(ccos, z, CMPLXL(cosh(nums[i]), -0.0), DBL_ULP());
335 test_odd_tol(ctan, z, CMPLXL(0, tanh(nums[i])), DBL_ULP());
337 test_odd_tol(csinhf, z, CMPLXL(copysign(0, cosf(nums[i])),
338 sinf(nums[i])), FLT_ULP());
339 test_even_tol(ccoshf, z, CMPLXL(cosf(nums[i]),
340 copysign(0, sinf(nums[i]))), FLT_ULP());
341 test_odd_tol(ctanhf, z, CMPLXL(0, tanf(nums[i])), FLT_ULP());
342 test_odd_tol(csinf, z, CMPLXL(0, sinhf(nums[i])), FLT_ULP());
343 test_even_tol(ccosf, z, CMPLXL(coshf(nums[i]), -0.0),
345 test_odd_tol(ctanf, z, CMPLXL(0, tanhf(nums[i])),
355 * sinh(z) = (sinh(0.5) + i cosh(0.5)) * sqrt(2)/2
356 * cosh(z) = (cosh(0.5) + i sinh(0.5)) * sqrt(2)/2
357 * tanh(z) = (2cosh(0.5)sinh(0.5) + i) / (2 cosh(0.5)**2 - 1)
359 * sinh(z) = cosh(0.5)
360 * cosh(z) = -i sinh(0.5)
361 * tanh(z) = -coth(0.5)
363 * sinh(z) = (-sinh(1) + i cosh(1)) * sqrt(2)/2
364 * cosh(z) = (-cosh(1) + i sinh(1)) * sqrt(2)/2
365 * tanh(z) = (2cosh(1)sinh(1) - i) / (2cosh(1)**2 - 1)
367 static const struct {
369 long double sinh_a, sinh_b;
370 long double cosh_a, cosh_b;
371 long double tanh_a, tanh_b;
374 0.78539816339744830961566084581987572L,
375 0.36847002415910435172083660522240710L,
376 0.79735196663945774996093142586179334L,
377 0.79735196663945774996093142586179334L,
378 0.36847002415910435172083660522240710L,
379 0.76159415595576488811945828260479359L,
380 0.64805427366388539957497735322615032L },
382 1.57079632679489661923132169163975144L,
384 1.12762596520638078522622516140267201L,
386 -0.52109530549374736162242562641149156L,
387 -2.16395341373865284877000401021802312L,
390 2.35619449019234492884698253745962716L,
391 -0.83099273328405698212637979852748608L,
392 1.09112278079550143030545602018565236L,
393 -1.09112278079550143030545602018565236L,
394 0.83099273328405698212637979852748609L,
395 0.96402758007581688394641372410092315L,
396 -0.26580222883407969212086273981988897L }
398 long double complex z;
401 for (i = 0; i < sizeof(tests) / sizeof(tests[0]); i++) {
402 z = CMPLXL(tests[i].a, tests[i].b);
403 testall_odd_tol(csinh, z,
404 CMPLXL(tests[i].sinh_a, tests[i].sinh_b), 1.1);
405 testall_even_tol(ccosh, z,
406 CMPLXL(tests[i].cosh_a, tests[i].cosh_b), 1.1);
407 testall_odd_tol(ctanh, z,
408 CMPLXL(tests[i].tanh_a, tests[i].tanh_b), 1.4);
412 /* Test inputs that might cause overflow in a sloppy implementation. */
416 long double complex z;
418 /* tanh() uses a threshold around x=22, so check both sides. */
419 z = CMPLXL(21, 0.78539816339744830961566084581987572L);
420 testall_odd_tol(ctanh, z,
421 CMPLXL(1.0, 1.14990445285871196133287617611468468e-18L), 1.2);
423 testall_odd_tol(ctanh, z,
424 CMPLXL(1.0, 1.55622644822675930314266334585597964e-19L), 1);
426 z = CMPLXL(355, 0.78539816339744830961566084581987572L);
427 test_odd_tol(ctanh, z,
428 CMPLXL(1.0, 8.95257245135025991216632140458264468e-309L),
430 #if !defined(__i386__)
431 z = CMPLXL(30, 0x1p1023L);
432 test_odd_tol(ctanh, z,
433 CMPLXL(1.0, -1.62994325413993477997492170229268382e-26L),
435 z = CMPLXL(1, 0x1p1023L);
436 test_odd_tol(ctanh, z,
437 CMPLXL(0.878606311888306869546254022621986509L,
438 -0.225462792499754505792678258169527424L),
442 z = CMPLXL(710.6, 0.78539816339744830961566084581987572L);
443 test_odd_tol(csinh, z,
444 CMPLXL(1.43917579766621073533185387499658944e308L,
445 1.43917579766621073533185387499658944e308L), DBL_ULP());
446 test_even_tol(ccosh, z,
447 CMPLXL(1.43917579766621073533185387499658944e308L,
448 1.43917579766621073533185387499658944e308L), DBL_ULP());
450 z = CMPLXL(1500, 0.78539816339744830961566084581987572L);
451 testall_odd(csinh, z, CMPLXL(INFINITY, INFINITY), OPT_INEXACT,
452 FE_OVERFLOW, CS_BOTH);
453 testall_even(ccosh, z, CMPLXL(INFINITY, INFINITY), OPT_INEXACT,
454 FE_OVERFLOW, CS_BOTH);
458 main(int argc, char *argv[])
464 printf("ok 1 - ctrig zero\n");
467 printf("ok 2 - ctrig nan\n");
470 printf("ok 3 - ctrig inf\n");
473 printf("ok 4 - ctrig axes\n");
476 printf("ok 5 - ctrig small\n");
479 printf("ok 6 - ctrig large\n");