1 /*-
2 * Copyright (c) 2008 David Schultz <[email protected]>
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 trigonometric functions. Some accuracy tests
29 * are included as well, but these are very basic sanity checks, not
30 * intended to be comprehensive.
31 *
32 * The program for generating representable numbers near multiples of pi is
33 * available at http://www.cs.berkeley.edu/~wkahan/testpi/ .
34 */
35
36 #include <sys/cdefs.h>
37 #include <sys/param.h>
38
39 #include <fenv.h>
40 #include <float.h>
41 #include <math.h>
42 #include <stdio.h>
43
44 #include "test-utils.h"
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. The exceptmask specifies which
51 * exceptions we should check. We need to be lenient for several
52 * reasons, but mainly because on some architectures it's impossible
53 * to raise FE_OVERFLOW without raising FE_INEXACT.
54 *
55 * These are macros instead of functions so that assert provides more
56 * meaningful error messages.
57 *
58 * XXX The volatile here is to avoid gcc's bogus constant folding and work
59 * around the lack of support for the FENV_ACCESS pragma.
60 */
61 #define test(func, x, result, exceptmask, excepts) do { \
62 volatile long double _d = x; \
63 ATF_CHECK(feclearexcept(FE_ALL_EXCEPT) == 0); \
64 CHECK_FPEQUAL((func)(_d), (result)); \
65 CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \
66 #func, #x); \
67 } while (0)
68
69 #define testall(prefix, x, result, exceptmask, excepts) do { \
70 test(prefix, x, (double)result, exceptmask, excepts); \
71 test(prefix##f, x, (float)result, exceptmask, excepts); \
72 test(prefix##l, x, result, exceptmask, excepts); \
73 } while (0)
74
75 #define testdf(prefix, x, result, exceptmask, excepts) do { \
76 test(prefix, x, (double)result, exceptmask, excepts); \
77 test(prefix##f, x, (float)result, exceptmask, excepts); \
78 } while (0)
79
80 ATF_TC(special);
ATF_TC_HEAD(special,tc)81 ATF_TC_HEAD(special, tc)
82 {
83
84 atf_tc_set_md_var(tc, "descr",
85 "test special cases in sin(), cos(), and tan()");
86 }
ATF_TC_BODY(special,tc)87 ATF_TC_BODY(special, tc)
88 {
89
90 /* Values at 0 should be exact. */
91 testall(tan, 0.0, 0.0, ALL_STD_EXCEPT, 0);
92 testall(tan, -0.0, -0.0, ALL_STD_EXCEPT, 0);
93 testall(cos, 0.0, 1.0, ALL_STD_EXCEPT, 0);
94 testall(cos, -0.0, 1.0, ALL_STD_EXCEPT, 0);
95 testall(sin, 0.0, 0.0, ALL_STD_EXCEPT, 0);
96 testall(sin, -0.0, -0.0, ALL_STD_EXCEPT, 0);
97
98 /* func(+-Inf) == NaN */
99 testall(tan, INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
100 testall(sin, INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
101 testall(cos, INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
102 testall(tan, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
103 testall(sin, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
104 testall(cos, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
105
106 /* func(NaN) == NaN */
107 testall(tan, NAN, NAN, ALL_STD_EXCEPT, 0);
108 testall(sin, NAN, NAN, ALL_STD_EXCEPT, 0);
109 testall(cos, NAN, NAN, ALL_STD_EXCEPT, 0);
110 }
111
112 #ifndef __i386__
113 ATF_TC(reduction);
ATF_TC_HEAD(reduction,tc)114 ATF_TC_HEAD(reduction, tc)
115 {
116
117 atf_tc_set_md_var(tc, "descr",
118 "tests to ensure argument reduction for large arguments is accurate");
119 }
ATF_TC_BODY(reduction,tc)120 ATF_TC_BODY(reduction, tc)
121 {
122 /* floats very close to odd multiples of pi */
123 static const float f_pi_odd[] = {
124 85563208.0f,
125 43998769152.0f,
126 9.2763667655669323e+25f,
127 1.5458357838905804e+29f,
128 };
129 /* doubles very close to odd multiples of pi */
130 static const double d_pi_odd[] = {
131 3.1415926535897931,
132 91.106186954104004,
133 642615.9188844458,
134 3397346.5699258847,
135 6134899525417045.0,
136 3.0213551960457761e+43,
137 1.2646209897993783e+295,
138 6.2083625380677099e+307,
139 };
140 /* long doubles very close to odd multiples of pi */
141 #if LDBL_MANT_DIG == 64
142 static const long double ld_pi_odd[] = {
143 1.1891886960373841596e+101L,
144 1.07999475322710967206e+2087L,
145 6.522151627890431836e+2147L,
146 8.9368974898260328229e+2484L,
147 9.2961044110572205863e+2555L,
148 4.90208421886578286e+3189L,
149 1.5275546401232615884e+3317L,
150 1.7227465626338900093e+3565L,
151 2.4160090594000745334e+3808L,
152 9.8477555741888350649e+4314L,
153 1.6061597222105160737e+4326L,
154 };
155 #endif
156
157 unsigned i;
158
159 #if defined(__amd64__) && defined(__clang__) && __clang_major__ >= 7 && \
160 __clang_major__ < 10 && __FreeBSD_cc_version < 1300002
161 atf_tc_expect_fail("test fails with clang 7-9 - bug 234040");
162 #endif
163
164 for (i = 0; i < nitems(f_pi_odd); i++) {
165 ATF_CHECK(fabs(sinf(f_pi_odd[i])) < FLT_EPSILON);
166 ATF_CHECK(cosf(f_pi_odd[i]) == -1.0);
167 ATF_CHECK(fabs(tan(f_pi_odd[i])) < FLT_EPSILON);
168
169 ATF_CHECK(fabs(sinf(-f_pi_odd[i])) < FLT_EPSILON);
170 ATF_CHECK(cosf(-f_pi_odd[i]) == -1.0);
171 ATF_CHECK(fabs(tanf(-f_pi_odd[i])) < FLT_EPSILON);
172
173 ATF_CHECK(fabs(sinf(f_pi_odd[i] * 2)) < FLT_EPSILON);
174 ATF_CHECK(cosf(f_pi_odd[i] * 2) == 1.0);
175 ATF_CHECK(fabs(tanf(f_pi_odd[i] * 2)) < FLT_EPSILON);
176
177 ATF_CHECK(fabs(sinf(-f_pi_odd[i] * 2)) < FLT_EPSILON);
178 ATF_CHECK(cosf(-f_pi_odd[i] * 2) == 1.0);
179 ATF_CHECK(fabs(tanf(-f_pi_odd[i] * 2)) < FLT_EPSILON);
180 }
181
182 for (i = 0; i < nitems(d_pi_odd); i++) {
183 ATF_CHECK(fabs(sin(d_pi_odd[i])) < 2 * DBL_EPSILON);
184 ATF_CHECK(cos(d_pi_odd[i]) == -1.0);
185 ATF_CHECK(fabs(tan(d_pi_odd[i])) < 2 * DBL_EPSILON);
186
187 ATF_CHECK(fabs(sin(-d_pi_odd[i])) < 2 * DBL_EPSILON);
188 ATF_CHECK(cos(-d_pi_odd[i]) == -1.0);
189 ATF_CHECK(fabs(tan(-d_pi_odd[i])) < 2 * DBL_EPSILON);
190
191 ATF_CHECK(fabs(sin(d_pi_odd[i] * 2)) < 2 * DBL_EPSILON);
192 ATF_CHECK(cos(d_pi_odd[i] * 2) == 1.0);
193 ATF_CHECK(fabs(tan(d_pi_odd[i] * 2)) < 2 * DBL_EPSILON);
194
195 ATF_CHECK(fabs(sin(-d_pi_odd[i] * 2)) < 2 * DBL_EPSILON);
196 ATF_CHECK(cos(-d_pi_odd[i] * 2) == 1.0);
197 ATF_CHECK(fabs(tan(-d_pi_odd[i] * 2)) < 2 * DBL_EPSILON);
198 }
199
200 #if LDBL_MANT_DIG == 64 /* XXX: || LDBL_MANT_DIG == 113 */
201 for (i = 0; i < nitems(ld_pi_odd); i++) {
202 ATF_CHECK(fabsl(sinl(ld_pi_odd[i])) < LDBL_EPSILON);
203 ATF_CHECK(cosl(ld_pi_odd[i]) == -1.0);
204 ATF_CHECK(fabsl(tanl(ld_pi_odd[i])) < LDBL_EPSILON);
205
206 ATF_CHECK(fabsl(sinl(-ld_pi_odd[i])) < LDBL_EPSILON);
207 ATF_CHECK(cosl(-ld_pi_odd[i]) == -1.0);
208 ATF_CHECK(fabsl(tanl(-ld_pi_odd[i])) < LDBL_EPSILON);
209
210 ATF_CHECK(fabsl(sinl(ld_pi_odd[i] * 2)) < LDBL_EPSILON);
211 ATF_CHECK(cosl(ld_pi_odd[i] * 2) == 1.0);
212 ATF_CHECK(fabsl(tanl(ld_pi_odd[i] * 2)) < LDBL_EPSILON);
213
214 ATF_CHECK(fabsl(sinl(-ld_pi_odd[i] * 2)) < LDBL_EPSILON);
215 ATF_CHECK(cosl(-ld_pi_odd[i] * 2) == 1.0);
216 ATF_CHECK(fabsl(tanl(-ld_pi_odd[i] * 2)) < LDBL_EPSILON);
217 }
218 #endif
219 }
220
221 ATF_TC(accuracy);
ATF_TC_HEAD(accuracy,tc)222 ATF_TC_HEAD(accuracy, tc)
223 {
224
225 atf_tc_set_md_var(tc, "descr",
226 "tests the accuracy of these functions over the primary range");
227 }
ATF_TC_BODY(accuracy,tc)228 ATF_TC_BODY(accuracy, tc)
229 {
230
231 /* For small args, sin(x) = tan(x) = x, and cos(x) = 1. */
232 testall(sin, 0xd.50ee515fe4aea16p-114L, 0xd.50ee515fe4aea16p-114L,
233 ALL_STD_EXCEPT, FE_INEXACT);
234 testall(tan, 0xd.50ee515fe4aea16p-114L, 0xd.50ee515fe4aea16p-114L,
235 ALL_STD_EXCEPT, FE_INEXACT);
236 testall(cos, 0xd.50ee515fe4aea16p-114L, 1.0,
237 ALL_STD_EXCEPT, FE_INEXACT);
238
239 /*
240 * These tests should pass for f32, d64, and ld80 as long as
241 * the error is <= 0.75 ulp (round to nearest)
242 */
243 #if LDBL_MANT_DIG <= 64
244 #define testacc testall
245 #else
246 #define testacc testdf
247 #endif
248 testacc(sin, 0.17255452780841205174L, 0.17169949801444412683L,
249 ALL_STD_EXCEPT, FE_INEXACT);
250 testacc(sin, -0.75431944555904520893L, -0.68479288156557286353L,
251 ALL_STD_EXCEPT, FE_INEXACT);
252 testacc(cos, 0.70556358769838947292L, 0.76124620693117771850L,
253 ALL_STD_EXCEPT, FE_INEXACT);
254 testacc(cos, -0.34061437849088045332L, 0.94254960031831729956L,
255 ALL_STD_EXCEPT, FE_INEXACT);
256 testacc(tan, -0.15862817413325692897L, -0.15997221861309522115L,
257 ALL_STD_EXCEPT, FE_INEXACT);
258 testacc(tan, 0.38374784931303813530L, 0.40376500259976759951L,
259 ALL_STD_EXCEPT, FE_INEXACT);
260
261 /*
262 * XXX missing:
263 * - tests for ld128
264 * - tests for other rounding modes (probably won't pass for now)
265 * - tests for large numbers that get reduced to hi+lo with lo!=0
266 */
267 }
268 #endif
269
ATF_TP_ADD_TCS(tp)270 ATF_TP_ADD_TCS(tp)
271 {
272
273 ATF_TP_ADD_TC(tp, special);
274
275 #ifndef __i386__
276 ATF_TP_ADD_TC(tp, accuracy);
277 ATF_TP_ADD_TC(tp, reduction);
278 #endif
279
280 return (atf_no_error());
281 }
282