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 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 __FBSDID("$FreeBSD$"); 38 39 #include <sys/param.h> 40 41 #include <assert.h> 42 #include <fenv.h> 43 #include <float.h> 44 #include <math.h> 45 #include <stdio.h> 46 47 #include <atf-c.h> 48 49 #include "test-utils.h" 50 51 #pragma STDC FENV_ACCESS ON 52 53 /* 54 * Test that a function returns the correct value and sets the 55 * exception flags correctly. The exceptmask specifies which 56 * exceptions we should check. We need to be lenient for several 57 * reasons, but mainly because on some architectures it's impossible 58 * to raise FE_OVERFLOW without raising FE_INEXACT. 59 * 60 * These are macros instead of functions so that assert provides more 61 * meaningful error messages. 62 * 63 * XXX The volatile here is to avoid gcc's bogus constant folding and work 64 * around the lack of support for the FENV_ACCESS pragma. 65 */ 66 #define test(func, x, result, exceptmask, excepts) do { \ 67 volatile long double _d = x; \ 68 ATF_CHECK(feclearexcept(FE_ALL_EXCEPT) == 0); \ 69 ATF_CHECK(fpequal((func)(_d), (result))); \ 70 ATF_CHECK(((void)(func), fetestexcept(exceptmask) == (excepts))); \ 71 } while (0) 72 73 #define testall(prefix, x, result, exceptmask, excepts) do { \ 74 test(prefix, x, (double)result, exceptmask, excepts); \ 75 test(prefix##f, x, (float)result, exceptmask, excepts); \ 76 test(prefix##l, x, result, exceptmask, excepts); \ 77 } while (0) 78 79 #define testdf(prefix, x, result, exceptmask, excepts) do { \ 80 test(prefix, x, (double)result, exceptmask, excepts); \ 81 test(prefix##f, x, (float)result, exceptmask, excepts); \ 82 } while (0) 83 84 ATF_TC(special); 85 ATF_TC_HEAD(special, tc) 86 { 87 88 atf_tc_set_md_var(tc, "descr", 89 "test special cases in sin(), cos(), and tan()"); 90 } 91 ATF_TC_BODY(special, tc) 92 { 93 94 /* Values at 0 should be exact. */ 95 testall(tan, 0.0, 0.0, ALL_STD_EXCEPT, 0); 96 testall(tan, -0.0, -0.0, ALL_STD_EXCEPT, 0); 97 testall(cos, 0.0, 1.0, ALL_STD_EXCEPT, 0); 98 testall(cos, -0.0, 1.0, ALL_STD_EXCEPT, 0); 99 testall(sin, 0.0, 0.0, ALL_STD_EXCEPT, 0); 100 testall(sin, -0.0, -0.0, ALL_STD_EXCEPT, 0); 101 102 /* func(+-Inf) == NaN */ 103 testall(tan, INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID); 104 testall(sin, INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID); 105 testall(cos, INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID); 106 testall(tan, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID); 107 testall(sin, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID); 108 testall(cos, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID); 109 110 /* func(NaN) == NaN */ 111 testall(tan, NAN, NAN, ALL_STD_EXCEPT, 0); 112 testall(sin, NAN, NAN, ALL_STD_EXCEPT, 0); 113 testall(cos, NAN, NAN, ALL_STD_EXCEPT, 0); 114 } 115 116 #ifndef __i386__ 117 ATF_TC(reduction); 118 ATF_TC_HEAD(reduction, tc) 119 { 120 121 atf_tc_set_md_var(tc, "descr", 122 "tests to ensure argument reduction for large arguments is accurate"); 123 } 124 ATF_TC_BODY(reduction, tc) 125 { 126 /* floats very close to odd multiples of pi */ 127 static const float f_pi_odd[] = { 128 85563208.0f, 129 43998769152.0f, 130 9.2763667655669323e+25f, 131 1.5458357838905804e+29f, 132 }; 133 /* doubles very close to odd multiples of pi */ 134 static const double d_pi_odd[] = { 135 3.1415926535897931, 136 91.106186954104004, 137 642615.9188844458, 138 3397346.5699258847, 139 6134899525417045.0, 140 3.0213551960457761e+43, 141 1.2646209897993783e+295, 142 6.2083625380677099e+307, 143 }; 144 /* long doubles very close to odd multiples of pi */ 145 #if LDBL_MANT_DIG == 64 146 static const long double ld_pi_odd[] = { 147 1.1891886960373841596e+101L, 148 1.07999475322710967206e+2087L, 149 6.522151627890431836e+2147L, 150 8.9368974898260328229e+2484L, 151 9.2961044110572205863e+2555L, 152 4.90208421886578286e+3189L, 153 1.5275546401232615884e+3317L, 154 1.7227465626338900093e+3565L, 155 2.4160090594000745334e+3808L, 156 9.8477555741888350649e+4314L, 157 1.6061597222105160737e+4326L, 158 }; 159 #endif 160 161 unsigned i; 162 163 #if defined(__amd64__) && defined(__clang__) && __clang_major__ >= 7 && \ 164 __FreeBSD_cc_version < 1300002 165 atf_tc_expect_fail("test fails with clang 7+ - bug 234040"); 166 #endif 167 168 for (i = 0; i < nitems(f_pi_odd); i++) { 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(tan(f_pi_odd[i])) < FLT_EPSILON); 172 173 ATF_CHECK(fabs(sinf(-f_pi_odd[i])) < FLT_EPSILON); 174 ATF_CHECK(cosf(-f_pi_odd[i]) == -1.0); 175 ATF_CHECK(fabs(tanf(-f_pi_odd[i])) < 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 ATF_CHECK(fabs(sinf(-f_pi_odd[i] * 2)) < FLT_EPSILON); 182 ATF_CHECK(cosf(-f_pi_odd[i] * 2) == 1.0); 183 ATF_CHECK(fabs(tanf(-f_pi_odd[i] * 2)) < FLT_EPSILON); 184 } 185 186 for (i = 0; i < nitems(d_pi_odd); i++) { 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 * DBL_EPSILON); 192 ATF_CHECK(cos(-d_pi_odd[i]) == -1.0); 193 ATF_CHECK(fabs(tan(-d_pi_odd[i])) < 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 ATF_CHECK(fabs(sin(-d_pi_odd[i] * 2)) < 2 * DBL_EPSILON); 200 ATF_CHECK(cos(-d_pi_odd[i] * 2) == 1.0); 201 ATF_CHECK(fabs(tan(-d_pi_odd[i] * 2)) < 2 * DBL_EPSILON); 202 } 203 204 #if LDBL_MANT_DIG == 64 /* XXX: || LDBL_MANT_DIG == 113 */ 205 for (i = 0; i < nitems(ld_pi_odd); i++) { 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])) < LDBL_EPSILON); 211 ATF_CHECK(cosl(-ld_pi_odd[i]) == -1.0); 212 ATF_CHECK(fabsl(tanl(-ld_pi_odd[i])) < 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 ATF_CHECK(fabsl(sinl(-ld_pi_odd[i] * 2)) < LDBL_EPSILON); 219 ATF_CHECK(cosl(-ld_pi_odd[i] * 2) == 1.0); 220 ATF_CHECK(fabsl(tanl(-ld_pi_odd[i] * 2)) < LDBL_EPSILON); 221 } 222 #endif 223 } 224 225 ATF_TC(accuracy); 226 ATF_TC_HEAD(accuracy, tc) 227 { 228 229 atf_tc_set_md_var(tc, "descr", 230 "tests the accuracy of these functions over the primary range"); 231 } 232 ATF_TC_BODY(accuracy, tc) 233 { 234 235 /* For small args, sin(x) = tan(x) = x, and cos(x) = 1. */ 236 testall(sin, 0xd.50ee515fe4aea16p-114L, 0xd.50ee515fe4aea16p-114L, 237 ALL_STD_EXCEPT, FE_INEXACT); 238 testall(tan, 0xd.50ee515fe4aea16p-114L, 0xd.50ee515fe4aea16p-114L, 239 ALL_STD_EXCEPT, FE_INEXACT); 240 testall(cos, 0xd.50ee515fe4aea16p-114L, 1.0, 241 ALL_STD_EXCEPT, FE_INEXACT); 242 243 /* 244 * These tests should pass for f32, d64, and ld80 as long as 245 * the error is <= 0.75 ulp (round to nearest) 246 */ 247 #if LDBL_MANT_DIG <= 64 248 #define testacc testall 249 #else 250 #define testacc testdf 251 #endif 252 testacc(sin, 0.17255452780841205174L, 0.17169949801444412683L, 253 ALL_STD_EXCEPT, FE_INEXACT); 254 testacc(sin, -0.75431944555904520893L, -0.68479288156557286353L, 255 ALL_STD_EXCEPT, FE_INEXACT); 256 testacc(cos, 0.70556358769838947292L, 0.76124620693117771850L, 257 ALL_STD_EXCEPT, FE_INEXACT); 258 testacc(cos, -0.34061437849088045332L, 0.94254960031831729956L, 259 ALL_STD_EXCEPT, FE_INEXACT); 260 testacc(tan, -0.15862817413325692897L, -0.15997221861309522115L, 261 ALL_STD_EXCEPT, FE_INEXACT); 262 testacc(tan, 0.38374784931303813530L, 0.40376500259976759951L, 263 ALL_STD_EXCEPT, FE_INEXACT); 264 265 /* 266 * XXX missing: 267 * - tests for ld128 268 * - tests for other rounding modes (probably won't pass for now) 269 * - tests for large numbers that get reduced to hi+lo with lo!=0 270 */ 271 } 272 #endif 273 274 ATF_TP_ADD_TCS(tp) 275 { 276 277 ATF_TP_ADD_TC(tp, special); 278 279 #ifndef __i386__ 280 ATF_TP_ADD_TC(tp, accuracy); 281 ATF_TP_ADD_TC(tp, reduction); 282 #endif 283 284 return (atf_no_error()); 285 } 286