2 * Copyright (c) 2008 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 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.
32 * The program for generating representable numbers near multiples of pi is
33 * available at http://www.cs.berkeley.edu/~wkahan/testpi/ .
36 #include <sys/cdefs.h>
37 __FBSDID("$FreeBSD$");
39 #include <sys/param.h>
47 #include "test-utils.h"
49 #pragma STDC FENV_ACCESS ON
52 * Test that a function returns the correct value and sets the
53 * exception flags correctly. The exceptmask specifies which
54 * exceptions we should check. We need to be lenient for several
55 * reasons, but mainly because on some architectures it's impossible
56 * to raise FE_OVERFLOW without raising FE_INEXACT.
58 * These are macros instead of functions so that assert provides more
59 * meaningful error messages.
61 * XXX The volatile here is to avoid gcc's bogus constant folding and work
62 * around the lack of support for the FENV_ACCESS pragma.
64 #define test(func, x, result, exceptmask, excepts) do { \
65 volatile long double _d = x; \
66 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
67 assert(fpequal((func)(_d), (result))); \
68 assert(((void)(func), fetestexcept(exceptmask) == (excepts))); \
71 #define testall(prefix, x, result, exceptmask, excepts) do { \
72 test(prefix, x, (double)result, exceptmask, excepts); \
73 test(prefix##f, x, (float)result, exceptmask, excepts); \
74 test(prefix##l, x, result, exceptmask, excepts); \
77 #define testdf(prefix, x, result, exceptmask, excepts) do { \
78 test(prefix, x, (double)result, exceptmask, excepts); \
79 test(prefix##f, x, (float)result, exceptmask, excepts); \
83 * Test special cases in sin(), cos(), and tan().
86 run_special_tests(void)
89 /* Values at 0 should be exact. */
90 testall(tan, 0.0, 0.0, ALL_STD_EXCEPT, 0);
91 testall(tan, -0.0, -0.0, ALL_STD_EXCEPT, 0);
92 testall(cos, 0.0, 1.0, ALL_STD_EXCEPT, 0);
93 testall(cos, -0.0, 1.0, ALL_STD_EXCEPT, 0);
94 testall(sin, 0.0, 0.0, ALL_STD_EXCEPT, 0);
95 testall(sin, -0.0, -0.0, ALL_STD_EXCEPT, 0);
97 /* func(+-Inf) == NaN */
98 testall(tan, INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
99 testall(sin, INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
100 testall(cos, INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
101 testall(tan, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
102 testall(sin, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
103 testall(cos, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID);
105 /* func(NaN) == NaN */
106 testall(tan, NAN, NAN, ALL_STD_EXCEPT, 0);
107 testall(sin, NAN, NAN, ALL_STD_EXCEPT, 0);
108 testall(cos, NAN, NAN, ALL_STD_EXCEPT, 0);
112 * Tests to ensure argument reduction for large arguments is accurate.
115 run_reduction_tests(void)
117 /* floats very close to odd multiples of pi */
118 static const float f_pi_odd[] = {
121 9.2763667655669323e+25f,
122 1.5458357838905804e+29f,
124 /* doubles very close to odd multiples of pi */
125 static const double d_pi_odd[] = {
131 3.0213551960457761e+43,
132 1.2646209897993783e+295,
133 6.2083625380677099e+307,
135 /* long doubles very close to odd multiples of pi */
136 #if LDBL_MANT_DIG == 64
137 static const long double ld_pi_odd[] = {
138 1.1891886960373841596e+101L,
139 1.07999475322710967206e+2087L,
140 6.522151627890431836e+2147L,
141 8.9368974898260328229e+2484L,
142 9.2961044110572205863e+2555L,
143 4.90208421886578286e+3189L,
144 1.5275546401232615884e+3317L,
145 1.7227465626338900093e+3565L,
146 2.4160090594000745334e+3808L,
147 9.8477555741888350649e+4314L,
148 1.6061597222105160737e+4326L,
150 #elif LDBL_MANT_DIG == 113
151 static const long double ld_pi_odd[] = {
158 for (i = 0; i < nitems(f_pi_odd); i++) {
159 assert(fabs(sinf(f_pi_odd[i])) < FLT_EPSILON);
160 assert(cosf(f_pi_odd[i]) == -1.0);
161 assert(fabs(tan(f_pi_odd[i])) < FLT_EPSILON);
163 assert(fabs(sinf(-f_pi_odd[i])) < FLT_EPSILON);
164 assert(cosf(-f_pi_odd[i]) == -1.0);
165 assert(fabs(tanf(-f_pi_odd[i])) < FLT_EPSILON);
167 assert(fabs(sinf(f_pi_odd[i] * 2)) < FLT_EPSILON);
168 assert(cosf(f_pi_odd[i] * 2) == 1.0);
169 assert(fabs(tanf(f_pi_odd[i] * 2)) < FLT_EPSILON);
171 assert(fabs(sinf(-f_pi_odd[i] * 2)) < FLT_EPSILON);
172 assert(cosf(-f_pi_odd[i] * 2) == 1.0);
173 assert(fabs(tanf(-f_pi_odd[i] * 2)) < FLT_EPSILON);
176 for (i = 0; i < nitems(d_pi_odd); i++) {
177 assert(fabs(sin(d_pi_odd[i])) < 2 * DBL_EPSILON);
178 assert(cos(d_pi_odd[i]) == -1.0);
179 assert(fabs(tan(d_pi_odd[i])) < 2 * DBL_EPSILON);
181 assert(fabs(sin(-d_pi_odd[i])) < 2 * DBL_EPSILON);
182 assert(cos(-d_pi_odd[i]) == -1.0);
183 assert(fabs(tan(-d_pi_odd[i])) < 2 * DBL_EPSILON);
185 assert(fabs(sin(d_pi_odd[i] * 2)) < 2 * DBL_EPSILON);
186 assert(cos(d_pi_odd[i] * 2) == 1.0);
187 assert(fabs(tan(d_pi_odd[i] * 2)) < 2 * DBL_EPSILON);
189 assert(fabs(sin(-d_pi_odd[i] * 2)) < 2 * DBL_EPSILON);
190 assert(cos(-d_pi_odd[i] * 2) == 1.0);
191 assert(fabs(tan(-d_pi_odd[i] * 2)) < 2 * DBL_EPSILON);
194 #if LDBL_MANT_DIG > 53
195 for (i = 0; i < nitems(ld_pi_odd); i++) {
196 assert(fabsl(sinl(ld_pi_odd[i])) < LDBL_EPSILON);
197 assert(cosl(ld_pi_odd[i]) == -1.0);
198 assert(fabsl(tanl(ld_pi_odd[i])) < LDBL_EPSILON);
200 assert(fabsl(sinl(-ld_pi_odd[i])) < LDBL_EPSILON);
201 assert(cosl(-ld_pi_odd[i]) == -1.0);
202 assert(fabsl(tanl(-ld_pi_odd[i])) < LDBL_EPSILON);
204 assert(fabsl(sinl(ld_pi_odd[i] * 2)) < LDBL_EPSILON);
205 assert(cosl(ld_pi_odd[i] * 2) == 1.0);
206 assert(fabsl(tanl(ld_pi_odd[i] * 2)) < LDBL_EPSILON);
208 assert(fabsl(sinl(-ld_pi_odd[i] * 2)) < LDBL_EPSILON);
209 assert(cosl(-ld_pi_odd[i] * 2) == 1.0);
210 assert(fabsl(tanl(-ld_pi_odd[i] * 2)) < LDBL_EPSILON);
216 * Tests the accuracy of these functions over the primary range.
219 run_accuracy_tests(void)
222 /* For small args, sin(x) = tan(x) = x, and cos(x) = 1. */
223 testall(sin, 0xd.50ee515fe4aea16p-114L, 0xd.50ee515fe4aea16p-114L,
224 ALL_STD_EXCEPT, FE_INEXACT);
225 testall(tan, 0xd.50ee515fe4aea16p-114L, 0xd.50ee515fe4aea16p-114L,
226 ALL_STD_EXCEPT, FE_INEXACT);
227 testall(cos, 0xd.50ee515fe4aea16p-114L, 1.0,
228 ALL_STD_EXCEPT, FE_INEXACT);
231 * These tests should pass for f32, d64, and ld80 as long as
232 * the error is <= 0.75 ulp (round to nearest)
234 #if LDBL_MANT_DIG <= 64
235 #define testacc testall
237 #define testacc testdf
239 testacc(sin, 0.17255452780841205174L, 0.17169949801444412683L,
240 ALL_STD_EXCEPT, FE_INEXACT);
241 testacc(sin, -0.75431944555904520893L, -0.68479288156557286353L,
242 ALL_STD_EXCEPT, FE_INEXACT);
243 testacc(cos, 0.70556358769838947292L, 0.76124620693117771850L,
244 ALL_STD_EXCEPT, FE_INEXACT);
245 testacc(cos, -0.34061437849088045332L, 0.94254960031831729956L,
246 ALL_STD_EXCEPT, FE_INEXACT);
247 testacc(tan, -0.15862817413325692897L, -0.15997221861309522115L,
248 ALL_STD_EXCEPT, FE_INEXACT);
249 testacc(tan, 0.38374784931303813530L, 0.40376500259976759951L,
250 ALL_STD_EXCEPT, FE_INEXACT);
255 * - tests for other rounding modes (probably won't pass for now)
256 * - tests for large numbers that get reduced to hi+lo with lo!=0
261 main(int argc, char *argv[])
267 printf("ok 1 - trig\n");
270 run_reduction_tests();
272 printf("ok 2 - trig\n");
275 run_accuracy_tests();
277 printf("ok 3 - trig\n");