2 * Copyright (c) 2008-2013 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 casin[h](), cacos[h](), and catan[h]().
31 #include <sys/cdefs.h>
32 __FBSDID("$FreeBSD$");
34 #include <sys/param.h>
42 #include "test-utils.h"
44 #pragma STDC FENV_ACCESS ON
45 #pragma STDC CX_LIMITED_RANGE OFF
48 * Test that a function returns the correct value and sets the
49 * exception flags correctly. The exceptmask specifies which
50 * exceptions we should check. We need to be lenient for several
51 * reasons, but mainly because on some architectures it's impossible
52 * to raise FE_OVERFLOW without raising FE_INEXACT.
54 * These are macros instead of functions so that assert provides more
55 * meaningful error messages.
57 * XXX The volatile here is to avoid gcc's bogus constant folding and work
58 * around the lack of support for the FENV_ACCESS pragma.
60 #define test_p(func, z, result, exceptmask, excepts, checksign) do { \
61 volatile long double complex _d = z; \
62 debug(" testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func, \
63 creall(_d), cimagl(_d), creall(result), cimagl(result)); \
64 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
65 assert(cfpequal_cs((func)(_d), (result), (checksign))); \
66 assert(((void)(func), fetestexcept(exceptmask) == (excepts))); \
70 * Test within a given tolerance. The tolerance indicates relative error
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), CS_BOTH)); \
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); \
90 /* Test the given function in all precisions. */
91 #define testall(func, x, result, exceptmask, excepts, checksign) do { \
92 test(func, x, result, exceptmask, excepts, checksign); \
93 test(func##f, x, result, exceptmask, excepts, checksign); \
95 #define testall_odd(func, x, result, exceptmask, excepts, checksign) do { \
96 testall(func, x, result, exceptmask, excepts, checksign); \
97 testall(func, -(x), -result, exceptmask, excepts, checksign); \
99 #define testall_even(func, x, result, exceptmask, excepts, checksign) do { \
100 testall(func, x, result, exceptmask, excepts, checksign); \
101 testall(func, -(x), result, exceptmask, excepts, checksign); \
105 * Test the given function in all precisions, within a given tolerance.
106 * The tolerance is specified in ulps.
108 #define testall_tol(func, x, result, tol) do { \
109 test_tol(func, x, result, (tol) * DBL_ULP()); \
110 test_tol(func##f, x, result, (tol) * FLT_ULP()); \
112 #define testall_odd_tol(func, x, result, tol) do { \
113 testall_tol(func, x, result, tol); \
114 testall_tol(func, -(x), -result, tol); \
116 #define testall_even_tol(func, x, result, tol) do { \
117 testall_tol(func, x, result, tol); \
118 testall_tol(func, -(x), result, tol); \
121 static const long double
122 pi = 3.14159265358979323846264338327950280L,
123 c3pi = 9.42477796076937971538793014983850839L;
130 long double complex zero = CMPLXL(0.0, 0.0);
132 testall_tol(cacosh, zero, CMPLXL(0.0, pi / 2), 1);
133 testall_tol(cacosh, -zero, CMPLXL(0.0, -pi / 2), 1);
134 testall_tol(cacos, zero, CMPLXL(pi / 2, -0.0), 1);
135 testall_tol(cacos, -zero, CMPLXL(pi / 2, 0.0), 1);
137 testall_odd(casinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
138 testall_odd(casin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
140 testall_odd(catanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
141 testall_odd(catan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
145 * Tests for NaN inputs.
150 long double complex nan_nan = CMPLXL(NAN, NAN);
151 long double complex z;
154 * IN CACOSH CACOS CASINH CATANH
155 * NaN,NaN NaN,NaN NaN,NaN NaN,NaN NaN,NaN
156 * finite,NaN NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN*
157 * NaN,finite NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN*
158 * NaN,Inf Inf,NaN NaN,-Inf ?Inf,NaN ?0,pi/2
159 * +-Inf,NaN Inf,NaN NaN,?Inf +-Inf,NaN +-0,NaN
160 * +-0,NaN NaN,NaN* pi/2,NaN NaN,NaN* +-0,NaN
161 * NaN,0 NaN,NaN* NaN,NaN* NaN,0 NaN,NaN*
166 testall(cacosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
167 testall(cacos, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
168 testall(casinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
169 testall(casin, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
170 testall(catanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
171 testall(catan, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
173 z = CMPLXL(0.5, NAN);
174 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
175 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
176 testall(casinh, z, nan_nan, OPT_INVALID, 0, 0);
177 testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
178 testall(catanh, z, nan_nan, OPT_INVALID, 0, 0);
179 testall(catan, z, nan_nan, OPT_INVALID, 0, 0);
181 z = CMPLXL(NAN, 0.5);
182 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
183 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
184 testall(casinh, z, nan_nan, OPT_INVALID, 0, 0);
185 testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
186 testall(catanh, z, nan_nan, OPT_INVALID, 0, 0);
187 testall(catan, z, nan_nan, OPT_INVALID, 0, 0);
189 z = CMPLXL(NAN, INFINITY);
190 testall(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
191 testall(cacosh, -z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
192 testall(cacos, z, CMPLXL(NAN, -INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG);
193 testall(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0);
194 testall(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG);
195 testall_tol(catanh, z, CMPLXL(0.0, pi / 2), 1);
196 testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, CS_IMAG);
198 z = CMPLXL(INFINITY, NAN);
199 testall_even(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
201 testall_even(cacos, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
202 testall_odd(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
204 testall_odd(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
205 testall_odd(catanh, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
206 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0.0), 1);
208 z = CMPLXL(0.0, NAN);
209 /* XXX We allow a spurious inexact exception here. */
210 testall_even(cacosh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0);
211 testall_even_tol(cacos, z, CMPLXL(pi / 2, NAN), 1);
212 testall_odd(casinh, z, nan_nan, OPT_INVALID, 0, 0);
213 testall_odd(casin, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
214 testall_odd(catanh, z, CMPLXL(0.0, NAN), OPT_INVALID, 0, CS_REAL);
215 testall_odd(catan, z, nan_nan, OPT_INVALID, 0, 0);
217 z = CMPLXL(NAN, 0.0);
218 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
219 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
220 testall(casinh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG);
221 testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
222 testall(catanh, z, nan_nan, OPT_INVALID, 0, CS_IMAG);
223 testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 0);
229 long double complex z;
232 * IN CACOSH CACOS CASINH CATANH
233 * Inf,Inf Inf,pi/4 pi/4,-Inf Inf,pi/4 0,pi/2
234 * -Inf,Inf Inf,3pi/4 3pi/4,-Inf --- ---
235 * Inf,finite Inf,0 0,-Inf Inf,0 0,pi/2
236 * -Inf,finite Inf,pi pi,-Inf --- ---
237 * finite,Inf Inf,pi/2 pi/2,-Inf Inf,pi/2 0,pi/2
239 z = CMPLXL(INFINITY, INFINITY);
240 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 4), 1);
241 testall_tol(cacosh, -z, CMPLXL(INFINITY, -c3pi / 4), 1);
242 testall_tol(cacos, z, CMPLXL(pi / 4, -INFINITY), 1);
243 testall_tol(cacos, -z, CMPLXL(c3pi / 4, INFINITY), 1);
244 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 4), 1);
245 testall_odd_tol(casin, z, CMPLXL(pi / 4, INFINITY), 1);
246 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
247 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
249 z = CMPLXL(INFINITY, 0.5);
250 /* XXX We allow a spurious inexact exception here. */
251 testall(cacosh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH);
252 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi), 1);
253 testall(cacos, z, CMPLXL(0, -INFINITY), OPT_INEXACT, 0, CS_BOTH);
254 testall_tol(cacos, -z, CMPLXL(pi, INFINITY), 1);
255 testall_odd(casinh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH);
256 testall_odd_tol(casin, z, CMPLXL(pi / 2, INFINITY), 1);
257 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
258 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
260 z = CMPLXL(0.5, INFINITY);
261 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 2), 1);
262 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi / 2), 1);
263 testall_tol(cacos, z, CMPLXL(pi / 2, -INFINITY), 1);
264 testall_tol(cacos, -z, CMPLXL(pi / 2, INFINITY), 1);
265 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 2), 1);
266 /* XXX We allow a spurious inexact exception here. */
267 testall_odd(casin, z, CMPLXL(0.0, INFINITY), OPT_INEXACT, 0, CS_BOTH);
268 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
269 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
272 /* Tests along the real and imaginary axes. */
276 static const long double nums[] = {
277 -2, -1, -0.5, 0.5, 1, 2
279 long double complex z;
282 for (i = 0; i < nitems(nums); i++) {
284 z = CMPLXL(nums[i], 0.0);
285 if (fabsl(nums[i]) <= 1) {
286 testall_tol(cacosh, z, CMPLXL(0.0, acos(nums[i])), 1);
287 testall_tol(cacos, z, CMPLXL(acosl(nums[i]), -0.0), 1);
288 testall_tol(casin, z, CMPLXL(asinl(nums[i]), 0.0), 1);
289 testall_tol(catanh, z, CMPLXL(atanh(nums[i]), 0.0), 1);
291 testall_tol(cacosh, z,
292 CMPLXL(acosh(fabsl(nums[i])),
293 (nums[i] < 0) ? pi : 0), 1);
294 testall_tol(cacos, z,
295 CMPLXL((nums[i] < 0) ? pi : 0,
296 -acosh(fabsl(nums[i]))), 1);
297 testall_tol(casin, z,
298 CMPLXL(copysign(pi / 2, nums[i]),
299 acosh(fabsl(nums[i]))), 1);
300 testall_tol(catanh, z,
301 CMPLXL(atanh(1 / nums[i]), pi / 2), 1);
303 testall_tol(casinh, z, CMPLXL(asinh(nums[i]), 0.0), 1);
304 testall_tol(catan, z, CMPLXL(atan(nums[i]), 0), 1);
306 /* TODO: Test the imaginary axis. */
315 * acos(z) = Pi/4 - i ln(2)/2
316 * asin(z) = Pi/4 + i ln(2)/2
317 * atan(z) = atan(4)/2 + i ln(17/9)/4
319 complex long double z;
320 complex long double acos_z;
321 complex long double asin_z;
322 complex long double atan_z;
324 z = CMPLXL(0.75L, 0.25L);
325 acos_z = CMPLXL(pi / 4, -0.34657359027997265470861606072908828L);
326 asin_z = CMPLXL(pi / 4, 0.34657359027997265470861606072908828L);
327 atan_z = CMPLXL(0.66290883183401623252961960521423782L,
328 0.15899719167999917436476103600701878L);
330 testall_tol(cacos, z, acos_z, 2);
331 testall_odd_tol(casin, z, asin_z, 2);
332 testall_odd_tol(catan, z, atan_z, 2);
335 /* Test inputs that might cause overflow in a sloppy implementation. */
340 /* TODO: Write these tests */
350 printf("ok 1 - invctrig zero\n");
353 printf("ok 2 - invctrig nan\n");
356 printf("ok 3 - invctrig inf\n");
359 printf("ok 4 - invctrig axes\n");
362 printf("ok 5 - invctrig small\n");
365 printf("ok 6 - invctrig large\n");