1 /*-
2 * Copyright (c) 2008 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 corner cases in the inverse trigonometric functions. Some
29 * accuracy tests are included as well, but these are very basic
30 * sanity checks, not intended to be comprehensive.
31 */
32
33 #include <sys/cdefs.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
43 /*
44 * Test that a function returns the correct value and sets the
45 * exception flags correctly. A tolerance specifying the maximum
46 * relative error allowed may be specified. For the 'testall'
47 * functions, the tolerance is specified in ulps.
48 *
49 * These are macros instead of functions so that assert provides more
50 * meaningful error messages.
51 */
52 #define test_tol(func, x, result, tol, excepts) do { \
53 volatile long double _in = (x), _out = (result); \
54 ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \
55 REQUIRE_FPEQUAL_TOL(func(_in), _out, (tol), CS_BOTH); \
56 REQUIRE_FP_EXCEPTIONS_MSG(excepts, ALL_STD_EXCEPT, "for %s(%s)", \
57 #func, #x); \
58 } while (0)
59 #define test(func, x, result, excepts) \
60 test_tol(func, (x), (result), 0, (excepts))
61
62 #define _testall_tol(prefix, x, result, tol, excepts) do { \
63 test_tol(prefix, (double)(x), (double)(result), \
64 (tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts)); \
65 test_tol(prefix##f, (float)(x), (float)(result), \
66 (tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts)); \
67 } while (0)
68
69 #ifdef __i386__
70 #define testall_tol _testall_tol
71 #else
72 #define testall_tol(prefix, x, result, tol, excepts) do { \
73 _testall_tol(prefix, x, result, tol, excepts); \
74 test_tol(prefix##l, (x), (result), \
75 (tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts)); \
76 } while (0)
77 #endif
78
79 #define testall(prefix, x, result, excepts) \
80 testall_tol(prefix, (x), (result), 0, (excepts))
81
82 #define test2_tol(func, y, x, result, tol, excepts) do { \
83 volatile long double _iny = (y), _inx = (x), _out = (result); \
84 ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \
85 REQUIRE_FPEQUAL_TOL(func(_iny, _inx), _out, (tol), CS_BOTH); \
86 REQUIRE_FP_EXCEPTIONS_MSG(excepts, ALL_STD_EXCEPT, "for %s(%s)", \
87 #func, #x); \
88 } while (0)
89 #define test2(func, y, x, result, excepts) \
90 test2_tol(func, (y), (x), (result), 0, (excepts))
91
92 #define _testall2_tol(prefix, y, x, result, tol, excepts) do { \
93 test2_tol(prefix, (double)(y), (double)(x), (double)(result), \
94 (tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts)); \
95 test2_tol(prefix##f, (float)(y), (float)(x), (float)(result), \
96 (tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts)); \
97 } while (0)
98
99 #ifdef __i386__
100 #define testall2_tol _testall2_tol
101 #else
102 #define testall2_tol(prefix, y, x, result, tol, excepts) do { \
103 _testall2_tol(prefix, y, x, result, tol, excepts); \
104 test2_tol(prefix##l, (y), (x), (result), \
105 (tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts)); \
106 } while (0)
107 #endif
108
109 #define testall2(prefix, y, x, result, excepts) \
110 testall2_tol(prefix, (y), (x), (result), 0, (excepts))
111
112 static long double
113 pi = 3.14159265358979323846264338327950280e+00L,
114 pio3 = 1.04719755119659774615421446109316766e+00L,
115 c3pi = 9.42477796076937971538793014983850839e+00L,
116 c7pi = 2.19911485751285526692385036829565196e+01L,
117 c5pio3 = 5.23598775598298873077107230546583851e+00L,
118 sqrt2m1 = 4.14213562373095048801688724209698081e-01L;
119
120
121 /*
122 * Test special case inputs in asin(), acos() and atan(): signed
123 * zeroes, infinities, and NaNs.
124 */
125 ATF_TC_WITHOUT_HEAD(special);
ATF_TC_BODY(special,tc)126 ATF_TC_BODY(special, tc)
127 {
128 #if defined(__aarch64__) || defined(__riscv)
129 atf_tc_expect_fail("https://bugs.freebsd.org/283017");
130 #endif
131 testall(asin, 0.0, 0.0, 0);
132 testall(acos, 0.0, pi / 2, FE_INEXACT);
133 testall(atan, 0.0, 0.0, 0);
134 testall(asin, -0.0, -0.0, 0);
135 testall(acos, -0.0, pi / 2, FE_INEXACT);
136 testall(atan, -0.0, -0.0, 0);
137
138 testall(asin, INFINITY, NAN, FE_INVALID);
139 testall(acos, INFINITY, NAN, FE_INVALID);
140 testall(atan, INFINITY, pi / 2, FE_INEXACT);
141 testall(asin, -INFINITY, NAN, FE_INVALID);
142 testall(acos, -INFINITY, NAN, FE_INVALID);
143 testall(atan, -INFINITY, -pi / 2, FE_INEXACT);
144
145 testall(asin, NAN, NAN, 0);
146 testall(acos, NAN, NAN, 0);
147 testall(atan, NAN, NAN, 0);
148 }
149
150 /*
151 * Test special case inputs in atan2(), where the exact value of y/x is
152 * zero or non-finite.
153 */
154 ATF_TC_WITHOUT_HEAD(special_atan2);
ATF_TC_BODY(special_atan2,tc)155 ATF_TC_BODY(special_atan2, tc)
156 {
157 long double z;
158 int e;
159
160 testall2(atan2, 0.0, -0.0, pi, FE_INEXACT);
161 testall2(atan2, -0.0, -0.0, -pi, FE_INEXACT);
162 testall2(atan2, 0.0, 0.0, 0.0, 0);
163 testall2(atan2, -0.0, 0.0, -0.0, 0);
164
165 testall2(atan2, INFINITY, -INFINITY, c3pi / 4, FE_INEXACT);
166 testall2(atan2, -INFINITY, -INFINITY, -c3pi / 4, FE_INEXACT);
167 testall2(atan2, INFINITY, INFINITY, pi / 4, FE_INEXACT);
168 testall2(atan2, -INFINITY, INFINITY, -pi / 4, FE_INEXACT);
169
170 /* Tests with one input in the range (0, Inf]. */
171 z = 1.23456789L;
172 for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP; e++) {
173 test2(atan2f, 0.0, ldexpf(z, e), 0.0, 0);
174 test2(atan2f, -0.0, ldexpf(z, e), -0.0, 0);
175 test2(atan2f, 0.0, ldexpf(-z, e), (float)pi, FE_INEXACT);
176 test2(atan2f, -0.0, ldexpf(-z, e), (float)-pi, FE_INEXACT);
177 test2(atan2f, ldexpf(z, e), 0.0, (float)pi / 2, FE_INEXACT);
178 test2(atan2f, ldexpf(z, e), -0.0, (float)pi / 2, FE_INEXACT);
179 test2(atan2f, ldexpf(-z, e), 0.0, (float)-pi / 2, FE_INEXACT);
180 test2(atan2f, ldexpf(-z, e), -0.0, (float)-pi / 2, FE_INEXACT);
181 }
182 for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP; e++) {
183 test2(atan2, 0.0, ldexp(z, e), 0.0, 0);
184 test2(atan2, -0.0, ldexp(z, e), -0.0, 0);
185 test2(atan2, 0.0, ldexp(-z, e), (double)pi, FE_INEXACT);
186 test2(atan2, -0.0, ldexp(-z, e), (double)-pi, FE_INEXACT);
187 test2(atan2, ldexp(z, e), 0.0, (double)pi / 2, FE_INEXACT);
188 test2(atan2, ldexp(z, e), -0.0, (double)pi / 2, FE_INEXACT);
189 test2(atan2, ldexp(-z, e), 0.0, (double)-pi / 2, FE_INEXACT);
190 test2(atan2, ldexp(-z, e), -0.0, (double)-pi / 2, FE_INEXACT);
191 }
192 for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP; e++) {
193 test2(atan2l, 0.0, ldexpl(z, e), 0.0, 0);
194 test2(atan2l, -0.0, ldexpl(z, e), -0.0, 0);
195 test2(atan2l, 0.0, ldexpl(-z, e), pi, FE_INEXACT);
196 test2(atan2l, -0.0, ldexpl(-z, e), -pi, FE_INEXACT);
197 test2(atan2l, ldexpl(z, e), 0.0, pi / 2, FE_INEXACT);
198 test2(atan2l, ldexpl(z, e), -0.0, pi / 2, FE_INEXACT);
199 test2(atan2l, ldexpl(-z, e), 0.0, -pi / 2, FE_INEXACT);
200 test2(atan2l, ldexpl(-z, e), -0.0, -pi / 2, FE_INEXACT);
201 }
202
203 /* Tests with one input in the range (0, Inf). */
204 for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP - 1; e++) {
205 test2(atan2f, ldexpf(z, e), INFINITY, 0.0, 0);
206 test2(atan2f, ldexpf(-z,e), INFINITY, -0.0, 0);
207 test2(atan2f, ldexpf(z, e), -INFINITY, (float)pi, FE_INEXACT);
208 test2(atan2f, ldexpf(-z,e), -INFINITY, (float)-pi, FE_INEXACT);
209 test2(atan2f, INFINITY, ldexpf(z,e), (float)pi/2, FE_INEXACT);
210 test2(atan2f, INFINITY, ldexpf(-z,e), (float)pi/2, FE_INEXACT);
211 test2(atan2f, -INFINITY, ldexpf(z,e), (float)-pi/2,FE_INEXACT);
212 test2(atan2f, -INFINITY, ldexpf(-z,e),(float)-pi/2,FE_INEXACT);
213 }
214 for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP - 1; e++) {
215 test2(atan2, ldexp(z, e), INFINITY, 0.0, 0);
216 test2(atan2, ldexp(-z,e), INFINITY, -0.0, 0);
217 test2(atan2, ldexp(z, e), -INFINITY, (double)pi, FE_INEXACT);
218 test2(atan2, ldexp(-z,e), -INFINITY, (double)-pi, FE_INEXACT);
219 test2(atan2, INFINITY, ldexp(z,e), (double)pi/2, FE_INEXACT);
220 test2(atan2, INFINITY, ldexp(-z,e), (double)pi/2, FE_INEXACT);
221 test2(atan2, -INFINITY, ldexp(z,e), (double)-pi/2,FE_INEXACT);
222 test2(atan2, -INFINITY, ldexp(-z,e),(double)-pi/2,FE_INEXACT);
223 }
224 for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP - 1; e++) {
225 test2(atan2l, ldexpl(z, e), INFINITY, 0.0, 0);
226 test2(atan2l, ldexpl(-z,e), INFINITY, -0.0, 0);
227 test2(atan2l, ldexpl(z, e), -INFINITY, pi, FE_INEXACT);
228 test2(atan2l, ldexpl(-z,e), -INFINITY, -pi, FE_INEXACT);
229 test2(atan2l, INFINITY, ldexpl(z, e), pi / 2, FE_INEXACT);
230 test2(atan2l, INFINITY, ldexpl(-z, e), pi / 2, FE_INEXACT);
231 test2(atan2l, -INFINITY, ldexpl(z, e), -pi / 2, FE_INEXACT);
232 test2(atan2l, -INFINITY, ldexpl(-z, e), -pi / 2, FE_INEXACT);
233 }
234 }
235
236 /*
237 * Test various inputs to asin(), acos() and atan() and verify that the
238 * results are accurate to within 1 ulp.
239 */
240 ATF_TC_WITHOUT_HEAD(accuracy);
ATF_TC_BODY(accuracy,tc)241 ATF_TC_BODY(accuracy, tc)
242 {
243 #if defined(__riscv)
244 atf_tc_expect_fail("https://bugs.freebsd.org/290099");
245 #endif
246 /* We expect correctly rounded results for these basic cases. */
247 testall(asin, 1.0, pi / 2, FE_INEXACT);
248 testall(acos, 1.0, 0, 0);
249 testall(atan, 1.0, pi / 4, FE_INEXACT);
250 testall(asin, -1.0, -pi / 2, FE_INEXACT);
251 testall(acos, -1.0, pi, FE_INEXACT);
252 testall(atan, -1.0, -pi / 4, FE_INEXACT);
253
254 /*
255 * Here we expect answers to be within 1 ulp, although inexactness
256 * in the input, combined with double rounding, could cause larger
257 * errors.
258 */
259
260 testall_tol(asin, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT);
261 testall_tol(acos, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT);
262 testall_tol(asin, -sqrtl(2) / 2, -pi / 4, 1, FE_INEXACT);
263 testall_tol(acos, -sqrtl(2) / 2, c3pi / 4, 1, FE_INEXACT);
264
265 testall_tol(asin, sqrtl(3) / 2, pio3, 1, FE_INEXACT);
266 testall_tol(acos, sqrtl(3) / 2, pio3 / 2, 1, FE_INEXACT);
267 testall_tol(atan, sqrtl(3), pio3, 1, FE_INEXACT);
268 testall_tol(asin, -sqrtl(3) / 2, -pio3, 1, FE_INEXACT);
269 testall_tol(acos, -sqrtl(3) / 2, c5pio3 / 2, 1, FE_INEXACT);
270 testall_tol(atan, -sqrtl(3), -pio3, 1, FE_INEXACT);
271
272 testall_tol(atan, sqrt2m1, pi / 8, 1, FE_INEXACT);
273 testall_tol(atan, -sqrt2m1, -pi / 8, 1, FE_INEXACT);
274 }
275
276 /*
277 * Test inputs to atan2() where x is a power of 2. These are easy cases
278 * because y/x is exact.
279 */
280 ATF_TC_WITHOUT_HEAD(p2x_atan2);
ATF_TC_BODY(p2x_atan2,tc)281 ATF_TC_BODY(p2x_atan2, tc)
282 {
283 #if defined(__riscv)
284 atf_tc_expect_fail("https://bugs.freebsd.org/290099");
285 #endif
286 testall2(atan2, 1.0, 1.0, pi / 4, FE_INEXACT);
287 testall2(atan2, 1.0, -1.0, c3pi / 4, FE_INEXACT);
288 testall2(atan2, -1.0, 1.0, -pi / 4, FE_INEXACT);
289 testall2(atan2, -1.0, -1.0, -c3pi / 4, FE_INEXACT);
290
291 testall2_tol(atan2, sqrt2m1 * 2, 2.0, pi / 8, 1, FE_INEXACT);
292 testall2_tol(atan2, sqrt2m1 * 2, -2.0, c7pi / 8, 1, FE_INEXACT);
293 testall2_tol(atan2, -sqrt2m1 * 2, 2.0, -pi / 8, 1, FE_INEXACT);
294 testall2_tol(atan2, -sqrt2m1 * 2, -2.0, -c7pi / 8, 1, FE_INEXACT);
295
296 testall2_tol(atan2, sqrtl(3) * 0.5, 0.5, pio3, 1, FE_INEXACT);
297 testall2_tol(atan2, sqrtl(3) * 0.5, -0.5, pio3 * 2, 1, FE_INEXACT);
298 testall2_tol(atan2, -sqrtl(3) * 0.5, 0.5, -pio3, 1, FE_INEXACT);
299 testall2_tol(atan2, -sqrtl(3) * 0.5, -0.5, -pio3 * 2, 1, FE_INEXACT);
300 }
301
302 /*
303 * Test inputs very close to 0.
304 */
305 ATF_TC_WITHOUT_HEAD(tiny);
ATF_TC_BODY(tiny,tc)306 ATF_TC_BODY(tiny, tc)
307 {
308 #if defined(__aarch64__) || defined(__riscv)
309 atf_tc_expect_fail("https://bugs.freebsd.org/283017");
310 #endif
311 float tiny = 0x1.23456p-120f;
312
313 testall(asin, tiny, tiny, FE_INEXACT);
314 testall(acos, tiny, pi / 2, FE_INEXACT);
315 testall(atan, tiny, tiny, FE_INEXACT);
316
317 testall(asin, -tiny, -tiny, FE_INEXACT);
318 testall(acos, -tiny, pi / 2, FE_INEXACT);
319 testall(atan, -tiny, -tiny, FE_INEXACT);
320
321 /* Test inputs to atan2() that would cause y/x to underflow. */
322 test2(atan2f, 0x1.0p-100, 0x1.0p100, 0.0, FE_INEXACT | FE_UNDERFLOW);
323 test2(atan2, 0x1.0p-1000, 0x1.0p1000, 0.0, FE_INEXACT | FE_UNDERFLOW);
324 test2(atan2l, ldexpl(1.0, 100 - LDBL_MAX_EXP),
325 ldexpl(1.0, LDBL_MAX_EXP - 100), 0.0, FE_INEXACT | FE_UNDERFLOW);
326 test2(atan2f, -0x1.0p-100, 0x1.0p100, -0.0, FE_INEXACT | FE_UNDERFLOW);
327 test2(atan2, -0x1.0p-1000, 0x1.0p1000, -0.0, FE_INEXACT | FE_UNDERFLOW);
328 test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP),
329 ldexpl(1.0, LDBL_MAX_EXP - 100), -0.0, FE_INEXACT | FE_UNDERFLOW);
330 test2(atan2f, 0x1.0p-100, -0x1.0p100, (float)pi, FE_INEXACT);
331 test2(atan2, 0x1.0p-1000, -0x1.0p1000, (double)pi, FE_INEXACT);
332 test2(atan2l, ldexpl(1.0, 100 - LDBL_MAX_EXP),
333 -ldexpl(1.0, LDBL_MAX_EXP - 100), pi, FE_INEXACT);
334 test2(atan2f, -0x1.0p-100, -0x1.0p100, (float)-pi, FE_INEXACT);
335 test2(atan2, -0x1.0p-1000, -0x1.0p1000, (double)-pi, FE_INEXACT);
336 test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP),
337 -ldexpl(1.0, LDBL_MAX_EXP - 100), -pi, FE_INEXACT);
338 }
339
340 /*
341 * Test very large inputs to atan().
342 */
343 ATF_TC_WITHOUT_HEAD(atan_huge);
ATF_TC_BODY(atan_huge,tc)344 ATF_TC_BODY(atan_huge, tc)
345 {
346 float huge = 0x1.23456p120;
347
348 testall(atan, huge, pi / 2, FE_INEXACT);
349 testall(atan, -huge, -pi / 2, FE_INEXACT);
350
351 /* Test inputs to atan2() that would cause y/x to overflow. */
352 test2(atan2f, 0x1.0p100, 0x1.0p-100, (float)pi / 2, FE_INEXACT);
353 test2(atan2, 0x1.0p1000, 0x1.0p-1000, (double)pi / 2, FE_INEXACT);
354 test2(atan2l, ldexpl(1.0, LDBL_MAX_EXP - 100),
355 ldexpl(1.0, 100 - LDBL_MAX_EXP), pi / 2, FE_INEXACT);
356 test2(atan2f, -0x1.0p100, 0x1.0p-100, (float)-pi / 2, FE_INEXACT);
357 test2(atan2, -0x1.0p1000, 0x1.0p-1000, (double)-pi / 2, FE_INEXACT);
358 test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100),
359 ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT);
360
361 test2(atan2f, 0x1.0p100, -0x1.0p-100, (float)pi / 2, FE_INEXACT);
362 test2(atan2, 0x1.0p1000, -0x1.0p-1000, (double)pi / 2, FE_INEXACT);
363 test2(atan2l, ldexpl(1.0, LDBL_MAX_EXP - 100),
364 -ldexpl(1.0, 100 - LDBL_MAX_EXP), pi / 2, FE_INEXACT);
365 test2(atan2f, -0x1.0p100, -0x1.0p-100, (float)-pi / 2, FE_INEXACT);
366 test2(atan2, -0x1.0p1000, -0x1.0p-1000, (double)-pi / 2, FE_INEXACT);
367 test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100),
368 -ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT);
369 }
370
371 /*
372 * Test that sin(asin(x)) == x, and similarly for acos() and atan().
373 * You need to have a working sinl(), cosl(), and tanl() for these
374 * tests to pass.
375 */
376 static long double
sinasinf(float x)377 sinasinf(float x)
378 {
379
380 return (sinl(asinf(x)));
381 }
382
383 static long double
sinasin(double x)384 sinasin(double x)
385 {
386
387 return (sinl(asin(x)));
388 }
389
390 #ifndef __i386__
391 static long double
sinasinl(long double x)392 sinasinl(long double x)
393 {
394
395 return (sinl(asinl(x)));
396 }
397 #endif
398
399 static long double
cosacosf(float x)400 cosacosf(float x)
401 {
402
403 return (cosl(acosf(x)));
404 }
405
406 static long double
cosacos(double x)407 cosacos(double x)
408 {
409
410 return (cosl(acos(x)));
411 }
412
413 #ifndef __i386__
414 static long double
cosacosl(long double x)415 cosacosl(long double x)
416 {
417
418 return (cosl(acosl(x)));
419 }
420 #endif
421
422 static long double
tanatanf(float x)423 tanatanf(float x)
424 {
425
426 return (tanl(atanf(x)));
427 }
428
429 static long double
tanatan(double x)430 tanatan(double x)
431 {
432
433 return (tanl(atan(x)));
434 }
435
436 #ifndef __i386__
437 static long double
tanatanl(long double x)438 tanatanl(long double x)
439 {
440
441 return (tanl(atanl(x)));
442 }
443 #endif
444
445 ATF_TC_WITHOUT_HEAD(inverse);
ATF_TC_BODY(inverse,tc)446 ATF_TC_BODY(inverse, tc)
447 {
448 #if defined(__riscv)
449 atf_tc_expect_death("https://bugs.freebsd.org/290099");
450 #endif
451 float i;
452
453 for (i = -1; i <= 1; i += 0x1.0p-12f) {
454 testall_tol(sinasin, i, i, 2, i == 0 ? 0 : FE_INEXACT);
455 /* The relative error for cosacos is very large near x=0. */
456 if (fabsf(i) > 0x1.0p-4f)
457 testall_tol(cosacos, i, i, 16, i == 1 ? 0 : FE_INEXACT);
458 testall_tol(tanatan, i, i, 2, i == 0 ? 0 : FE_INEXACT);
459 }
460 }
461
ATF_TP_ADD_TCS(tp)462 ATF_TP_ADD_TCS(tp)
463 {
464 ATF_TP_ADD_TC(tp, special);
465 ATF_TP_ADD_TC(tp, special_atan2);
466 ATF_TP_ADD_TC(tp, accuracy);
467 ATF_TP_ADD_TC(tp, p2x_atan2);
468 ATF_TP_ADD_TC(tp, tiny);
469 ATF_TP_ADD_TC(tp, atan_huge);
470 ATF_TP_ADD_TC(tp, inverse);
471
472 return (atf_no_error());
473 }
474