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  * $FreeBSD: src/tools/regression/lib/msun/test-invtrig.c,v 1.3 2010/12/06 00:02:49 das Exp $
27  */
28 
29 /*
30  * Tests for corner cases in the inverse trigonometric functions. Some
31  * accuracy tests are included as well, but these are very basic
32  * sanity checks, not intended to be comprehensive.
33  */
34 
35 #include <assert.h>
36 #include <fenv.h>
37 #include <float.h>
38 #include <math.h>
39 #include <stdio.h>
40 
41 #define	ALL_STD_EXCEPT	(FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \
42 			 FE_OVERFLOW | FE_UNDERFLOW)
43 
44 #define	LEN(a)		(sizeof(a) / sizeof((a)[0]))
45 
46 #pragma STDC FENV_ACCESS ON
47 
48 /*
49  * Test that a function returns the correct value and sets the
50  * exception flags correctly. A tolerance specifying the maximum
51  * relative error allowed may be specified. For the 'testall'
52  * functions, the tolerance is specified in ulps.
53  *
54  * These are macros instead of functions so that assert provides more
55  * meaningful error messages.
56  */
57 #define	test_tol(func, x, result, tol, excepts) do {			\
58 	volatile long double _in = (x), _out = (result);		\
59 	assert(feclearexcept(FE_ALL_EXCEPT) == 0);			\
60 	assert(fpequal(func(_in), _out, (tol)));			\
61 	assert((func, fetestexcept(ALL_STD_EXCEPT) == (excepts)));	\
62 } while (0)
63 #define test(func, x, result, excepts)					\
64 	test_tol(func, (x), (result), 0, (excepts))
65 
66 #define	testall_tol(prefix, x, result, tol, excepts) do {		\
67 	test_tol(prefix, (double)(x), (double)(result),			\
68 		 (tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts));	\
69 	test_tol(prefix##f, (float)(x), (float)(result),		\
70 		 (tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts));	\
71 	test_tol(prefix##l, (x), (result),				\
72 		 (tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts));	\
73 } while (0)
74 #define testall(prefix, x, result, excepts)				\
75 	testall_tol(prefix, (x), (result), 0, (excepts))
76 
77 #define	test2_tol(func, y, x, result, tol, excepts) do {		\
78 	volatile long double _iny = (y), _inx = (x), _out = (result);	\
79 	assert(feclearexcept(FE_ALL_EXCEPT) == 0);			\
80 	assert(fpequal(func(_iny, _inx), _out, (tol)));			\
81 	assert((func, fetestexcept(ALL_STD_EXCEPT) == (excepts)));	\
82 } while (0)
83 #define test2(func, y, x, result, excepts)				\
84 	test2_tol(func, (y), (x), (result), 0, (excepts))
85 
86 #define	testall2_tol(prefix, y, x, result, tol, excepts) do {		\
87 	test2_tol(prefix, (double)(y), (double)(x), (double)(result),	\
88 		  (tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts));	\
89 	test2_tol(prefix##f, (float)(y), (float)(x), (float)(result),	\
90 		  (tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts));	\
91 	test2_tol(prefix##l, (y), (x), (result),			\
92 		  (tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts));	\
93 } while (0)
94 #define testall2(prefix, y, x, result, excepts)				\
95 	testall2_tol(prefix, (y), (x), (result), 0, (excepts))
96 
97 long double
98 pi =   3.14159265358979323846264338327950280e+00L,
99 pio3 = 1.04719755119659774615421446109316766e+00L,
100 c3pi = 9.42477796076937971538793014983850839e+00L,
101 c5pi = 1.57079632679489661923132169163975140e+01L,
102 c7pi = 2.19911485751285526692385036829565196e+01L,
103 c5pio3 = 5.23598775598298873077107230546583851e+00L,
104 sqrt2m1 = 4.14213562373095048801688724209698081e-01L;
105 
106 /*
107  * Determine whether x and y are equal to within a relative error of tol,
108  * with two special rules:
109  *	+0.0 != -0.0
110  *	 NaN == NaN
111  */
112 int
113 fpequal(long double x, long double y, long double tol)
114 {
115 	fenv_t env;
116 	int ret;
117 
118 	if (isnan(x) && isnan(y))
119 		return (1);
120 	if (!signbit(x) != !signbit(y))
121 		return (0);
122 	if (x == y)
123 		return (1);
124 	if (tol == 0)
125 		return (0);
126 
127 	/* Hard case: need to check the tolerance. */
128 	feholdexcept(&env);
129 	ret = fabsl(x - y) <= fabsl(y * tol);
130 	fesetenv(&env);
131 	return (ret);
132 }
133 
134 /*
135  * Test special case inputs in asin(), acos() and atan(): signed
136  * zeroes, infinities, and NaNs.
137  */
138 static void
139 test_special(void)
140 {
141 
142 	testall(asin, 0.0, 0.0, 0);
143 	testall(acos, 0.0, pi / 2, FE_INEXACT);
144 	testall(atan, 0.0, 0.0, 0);
145 	testall(asin, -0.0, -0.0, 0);
146 	testall(acos, -0.0, pi / 2, FE_INEXACT);
147 	testall(atan, -0.0, -0.0, 0);
148 
149 	testall(asin, INFINITY, NAN, FE_INVALID);
150 	testall(acos, INFINITY, NAN, FE_INVALID);
151 	testall(atan, INFINITY, pi / 2, FE_INEXACT);
152 	testall(asin, -INFINITY, NAN, FE_INVALID);
153 	testall(acos, -INFINITY, NAN, FE_INVALID);
154 	testall(atan, -INFINITY, -pi / 2, FE_INEXACT);
155 
156 	testall(asin, NAN, NAN, 0);
157 	testall(acos, NAN, NAN, 0);
158 	testall(atan, NAN, NAN, 0);
159 }
160 
161 /*
162  * Test special case inputs in atan2(), where the exact value of y/x is
163  * zero or non-finite.
164  */
165 static void
166 test_special_atan2(void)
167 {
168 	long double z;
169 	int e;
170 
171 	testall2(atan2, 0.0, -0.0, pi, FE_INEXACT);
172 	testall2(atan2, -0.0, -0.0, -pi, FE_INEXACT);
173 	testall2(atan2, 0.0, 0.0, 0.0, 0);
174 	testall2(atan2, -0.0, 0.0, -0.0, 0);
175 
176 	testall2(atan2, INFINITY, -INFINITY, c3pi / 4, FE_INEXACT);
177 	testall2(atan2, -INFINITY, -INFINITY, -c3pi / 4, FE_INEXACT);
178 	testall2(atan2, INFINITY, INFINITY, pi / 4, FE_INEXACT);
179 	testall2(atan2, -INFINITY, INFINITY, -pi / 4, FE_INEXACT);
180 
181 	/* Tests with one input in the range (0, Inf]. */
182 	z = 1.23456789L;
183 	for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP; e++) {
184 		test2(atan2f, 0.0, ldexpf(z, e), 0.0, 0);
185 		test2(atan2f, -0.0, ldexpf(z, e), -0.0, 0);
186 		test2(atan2f, 0.0, ldexpf(-z, e), (float)pi, FE_INEXACT);
187 		test2(atan2f, -0.0, ldexpf(-z, e), (float)-pi, FE_INEXACT);
188 		test2(atan2f, ldexpf(z, e), 0.0, (float)pi / 2, FE_INEXACT);
189 		test2(atan2f, ldexpf(z, e), -0.0, (float)pi / 2, FE_INEXACT);
190 		test2(atan2f, ldexpf(-z, e), 0.0, (float)-pi / 2, FE_INEXACT);
191 		test2(atan2f, ldexpf(-z, e), -0.0, (float)-pi / 2, FE_INEXACT);
192 	}
193 	for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP; e++) {
194 		test2(atan2, 0.0, ldexp(z, e), 0.0, 0);
195 		test2(atan2, -0.0, ldexp(z, e), -0.0, 0);
196 		test2(atan2, 0.0, ldexp(-z, e), (double)pi, FE_INEXACT);
197 		test2(atan2, -0.0, ldexp(-z, e), (double)-pi, FE_INEXACT);
198 		test2(atan2, ldexp(z, e), 0.0, (double)pi / 2, FE_INEXACT);
199 		test2(atan2, ldexp(z, e), -0.0, (double)pi / 2, FE_INEXACT);
200 		test2(atan2, ldexp(-z, e), 0.0, (double)-pi / 2, FE_INEXACT);
201 		test2(atan2, ldexp(-z, e), -0.0, (double)-pi / 2, FE_INEXACT);
202 	}
203 	for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP; e++) {
204 		test2(atan2l, 0.0, ldexpl(z, e), 0.0, 0);
205 		test2(atan2l, -0.0, ldexpl(z, e), -0.0, 0);
206 		test2(atan2l, 0.0, ldexpl(-z, e), pi, FE_INEXACT);
207 		test2(atan2l, -0.0, ldexpl(-z, e), -pi, FE_INEXACT);
208 		test2(atan2l, ldexpl(z, e), 0.0, pi / 2, FE_INEXACT);
209 		test2(atan2l, ldexpl(z, e), -0.0, pi / 2, FE_INEXACT);
210 		test2(atan2l, ldexpl(-z, e), 0.0, -pi / 2, FE_INEXACT);
211 		test2(atan2l, ldexpl(-z, e), -0.0, -pi / 2, FE_INEXACT);
212 	}
213 
214 	/* Tests with one input in the range (0, Inf). */
215 	for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP - 1; e++) {
216 		test2(atan2f, ldexpf(z, e), INFINITY, 0.0, 0);
217 		test2(atan2f, ldexpf(-z,e), INFINITY, -0.0, 0);
218 		test2(atan2f, ldexpf(z, e), -INFINITY, (float)pi, FE_INEXACT);
219 		test2(atan2f, ldexpf(-z,e), -INFINITY, (float)-pi, FE_INEXACT);
220 		test2(atan2f, INFINITY, ldexpf(z,e), (float)pi/2, FE_INEXACT);
221 		test2(atan2f, INFINITY, ldexpf(-z,e), (float)pi/2, FE_INEXACT);
222 		test2(atan2f, -INFINITY, ldexpf(z,e), (float)-pi/2,FE_INEXACT);
223 		test2(atan2f, -INFINITY, ldexpf(-z,e),(float)-pi/2,FE_INEXACT);
224 	}
225 	for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP - 1; e++) {
226 		test2(atan2, ldexp(z, e), INFINITY, 0.0, 0);
227 		test2(atan2, ldexp(-z,e), INFINITY, -0.0, 0);
228 		test2(atan2, ldexp(z, e), -INFINITY, (double)pi, FE_INEXACT);
229 		test2(atan2, ldexp(-z,e), -INFINITY, (double)-pi, FE_INEXACT);
230 		test2(atan2, INFINITY, ldexp(z,e), (double)pi/2, FE_INEXACT);
231 		test2(atan2, INFINITY, ldexp(-z,e), (double)pi/2, FE_INEXACT);
232 		test2(atan2, -INFINITY, ldexp(z,e), (double)-pi/2,FE_INEXACT);
233 		test2(atan2, -INFINITY, ldexp(-z,e),(double)-pi/2,FE_INEXACT);
234 	}
235 	for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP - 1; e++) {
236 		test2(atan2l, ldexpl(z, e), INFINITY, 0.0, 0);
237 		test2(atan2l, ldexpl(-z,e), INFINITY, -0.0, 0);
238 		test2(atan2l, ldexpl(z, e), -INFINITY, pi, FE_INEXACT);
239 		test2(atan2l, ldexpl(-z,e), -INFINITY, -pi, FE_INEXACT);
240 		test2(atan2l, INFINITY, ldexpl(z, e), pi / 2, FE_INEXACT);
241 		test2(atan2l, INFINITY, ldexpl(-z, e), pi / 2, FE_INEXACT);
242 		test2(atan2l, -INFINITY, ldexpl(z, e), -pi / 2, FE_INEXACT);
243 		test2(atan2l, -INFINITY, ldexpl(-z, e), -pi / 2, FE_INEXACT);
244 	}
245 }
246 
247 /*
248  * Test various inputs to asin(), acos() and atan() and verify that the
249  * results are accurate to within 1 ulp.
250  */
251 static void
252 test_accuracy(void)
253 {
254 
255 	/* We expect correctly rounded results for these basic cases. */
256 	testall(asin, 1.0, pi / 2, FE_INEXACT);
257 	testall(acos, 1.0, 0, 0);
258 	testall(atan, 1.0, pi / 4, FE_INEXACT);
259 	testall(asin, -1.0, -pi / 2, FE_INEXACT);
260 	testall(acos, -1.0, pi, FE_INEXACT);
261 	testall(atan, -1.0, -pi / 4, FE_INEXACT);
262 
263 	/*
264 	 * Here we expect answers to be within 1 ulp, although inexactness
265 	 * in the input, combined with double rounding, could cause larger
266 	 * errors.
267 	 */
268 
269 	testall_tol(asin, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT);
270 	testall_tol(acos, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT);
271 	testall_tol(asin, -sqrtl(2) / 2, -pi / 4, 1, FE_INEXACT);
272 	testall_tol(acos, -sqrtl(2) / 2, c3pi / 4, 1, FE_INEXACT);
273 
274 	testall_tol(asin, sqrtl(3) / 2, pio3, 1, FE_INEXACT);
275 	testall_tol(acos, sqrtl(3) / 2, pio3 / 2, 1, FE_INEXACT);
276 	testall_tol(atan, sqrtl(3), pio3, 1, FE_INEXACT);
277 	testall_tol(asin, -sqrtl(3) / 2, -pio3, 1, FE_INEXACT);
278 	testall_tol(acos, -sqrtl(3) / 2, c5pio3 / 2, 1, FE_INEXACT);
279 	testall_tol(atan, -sqrtl(3), -pio3, 1, FE_INEXACT);
280 
281 	testall_tol(atan, sqrt2m1, pi / 8, 1, FE_INEXACT);
282 	testall_tol(atan, -sqrt2m1, -pi / 8, 1, FE_INEXACT);
283 }
284 
285 /*
286  * Test inputs to atan2() where x is a power of 2. These are easy cases
287  * because y/x is exact.
288  */
289 static void
290 test_p2x_atan2(void)
291 {
292 
293 	testall2(atan2, 1.0, 1.0, pi / 4, FE_INEXACT);
294 	testall2(atan2, 1.0, -1.0, c3pi / 4, FE_INEXACT);
295 	testall2(atan2, -1.0, 1.0, -pi / 4, FE_INEXACT);
296 	testall2(atan2, -1.0, -1.0, -c3pi / 4, FE_INEXACT);
297 
298 	testall2_tol(atan2, sqrt2m1 * 2, 2.0, pi / 8, 1, FE_INEXACT);
299 	testall2_tol(atan2, sqrt2m1 * 2, -2.0, c7pi / 8, 1, FE_INEXACT);
300 	testall2_tol(atan2, -sqrt2m1 * 2, 2.0, -pi / 8, 1, FE_INEXACT);
301 	testall2_tol(atan2, -sqrt2m1 * 2, -2.0, -c7pi / 8, 1, FE_INEXACT);
302 
303 	testall2_tol(atan2, sqrtl(3) * 0.5, 0.5, pio3, 1, FE_INEXACT);
304 	testall2_tol(atan2, sqrtl(3) * 0.5, -0.5, pio3 * 2, 1, FE_INEXACT);
305 	testall2_tol(atan2, -sqrtl(3) * 0.5, 0.5, -pio3, 1, FE_INEXACT);
306 	testall2_tol(atan2, -sqrtl(3) * 0.5, -0.5, -pio3 * 2, 1, FE_INEXACT);
307 }
308 
309 /*
310  * Test inputs very close to 0.
311  */
312 static void
313 test_tiny(void)
314 {
315 	float tiny = 0x1.23456p-120f;
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 	testall(asin, -tiny, -tiny, FE_INEXACT);
322 	testall(acos, -tiny, pi / 2, FE_INEXACT);
323 	testall(atan, -tiny, -tiny, FE_INEXACT);
324 
325 	/* Test inputs to atan2() that would cause y/x to 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, -0.0, FE_INEXACT | FE_UNDERFLOW);
331 	test2(atan2, -0x1.0p-1000, 0x1.0p1000, -0.0, FE_INEXACT | FE_UNDERFLOW);
332 	test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP),
333 	      ldexpl(1.0, LDBL_MAX_EXP - 100), -0.0, FE_INEXACT | FE_UNDERFLOW);
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 	test2(atan2f, -0x1.0p-100, -0x1.0p100, (float)-pi, FE_INEXACT);
339 	test2(atan2, -0x1.0p-1000, -0x1.0p1000, (double)-pi, FE_INEXACT);
340 	test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP),
341 	      -ldexpl(1.0, LDBL_MAX_EXP - 100), -pi, FE_INEXACT);
342 }
343 
344 /*
345  * Test very large inputs to atan().
346  */
347 static void
348 test_atan_huge(void)
349 {
350 	float huge = 0x1.23456p120;
351 
352 	testall(atan, huge, pi / 2, FE_INEXACT);
353 	testall(atan, -huge, -pi / 2, FE_INEXACT);
354 
355 	/* Test inputs to atan2() that would cause y/x to overflow. */
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 	test2(atan2f, -0x1.0p100, 0x1.0p-100, (float)-pi / 2, FE_INEXACT);
361 	test2(atan2, -0x1.0p1000, 0x1.0p-1000, (double)-pi / 2, FE_INEXACT);
362 	test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100),
363 	      ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT);
364 
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 	test2(atan2f, -0x1.0p100, -0x1.0p-100, (float)-pi / 2, FE_INEXACT);
370 	test2(atan2, -0x1.0p1000, -0x1.0p-1000, (double)-pi / 2, FE_INEXACT);
371 	test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100),
372 	      -ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT);
373 }
374 
375 /*
376  * Test that sin(asin(x)) == x, and similarly for acos() and atan().
377  * You need to have a working sinl(), cosl(), and tanl() for these
378  * tests to pass.
379  */
380 static long double
381 sinasinf(float x)
382 {
383 
384 	return (sinl(asinf(x)));
385 }
386 
387 static long double
388 sinasin(double x)
389 {
390 
391 	return (sinl(asin(x)));
392 }
393 
394 static long double
395 sinasinl(long double x)
396 {
397 
398 	return (sinl(asinl(x)));
399 }
400 
401 static long double
402 cosacosf(float x)
403 {
404 
405 	return (cosl(acosf(x)));
406 }
407 
408 static long double
409 cosacos(double x)
410 {
411 
412 	return (cosl(acos(x)));
413 }
414 
415 static long double
416 cosacosl(long double x)
417 {
418 
419 	return (cosl(acosl(x)));
420 }
421 
422 static long double
423 tanatanf(float x)
424 {
425 
426 	return (tanl(atanf(x)));
427 }
428 
429 static long double
430 tanatan(double x)
431 {
432 
433 	return (tanl(atan(x)));
434 }
435 
436 static long double
437 tanatanl(long double x)
438 {
439 
440 	return (tanl(atanl(x)));
441 }
442 
443 static void
444 test_inverse(void)
445 {
446 	float i;
447 
448 	for (i = -1; i <= 1; i += 0x1.0p-12f) {
449 		testall_tol(sinasin, i, i, 2, i == 0 ? 0 : FE_INEXACT);
450 		/* The relative error for cosacos is very large near x=0. */
451 		if (fabsf(i) > 0x1.0p-4f)
452 			testall_tol(cosacos, i, i, 16, i == 1 ? 0 : FE_INEXACT);
453 		testall_tol(tanatan, i, i, 2, i == 0 ? 0 : FE_INEXACT);
454 	}
455 }
456 
457 int
458 main(int argc, char *argv[])
459 {
460 
461 	printf("1..7\n");
462 
463 	test_special();
464 	printf("ok 1 - special\n");
465 
466 	test_special_atan2();
467 	printf("ok 2 - atan2 special\n");
468 
469 	test_accuracy();
470 	printf("ok 3 - accuracy\n");
471 
472 	test_p2x_atan2();
473 	printf("ok 4 - atan2 p2x\n");
474 
475 	test_tiny();
476 	printf("ok 5 - tiny inputs\n");
477 
478 	test_atan_huge();
479 	printf("ok 6 - atan huge inputs\n");
480 
481 	test_inverse();
482 	printf("ok 7 - inverse\n");
483 
484 	return (0);
485 }
486