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 <fenv.h> 42 #include <float.h> 43 #include <math.h> 44 #include <stdio.h> 45 46 #include "test-utils.h" 47 48 #pragma STDC FENV_ACCESS ON 49 50 /* 51 * Test that a function returns the correct value and sets the 52 * exception flags correctly. The exceptmask specifies which 53 * exceptions we should check. We need to be lenient for several 54 * reasons, but mainly because on some architectures it's impossible 55 * to raise FE_OVERFLOW without raising FE_INEXACT. 56 * 57 * These are macros instead of functions so that assert provides more 58 * meaningful error messages. 59 * 60 * XXX The volatile here is to avoid gcc's bogus constant folding and work 61 * around the lack of support for the FENV_ACCESS pragma. 62 */ 63 #define test(func, x, result, exceptmask, excepts) do { \ 64 volatile long double _d = x; \ 65 ATF_CHECK(feclearexcept(FE_ALL_EXCEPT) == 0); \ 66 CHECK_FPEQUAL((func)(_d), (result)); \ 67 CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \ 68 #func, #x); \ 69 } while (0) 70 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); \ 75 } while (0) 76 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); \ 80 } while (0) 81 82 ATF_TC(special); 83 ATF_TC_HEAD(special, tc) 84 { 85 86 atf_tc_set_md_var(tc, "descr", 87 "test special cases in sin(), cos(), and tan()"); 88 } 89 ATF_TC_BODY(special, tc) 90 { 91 92 /* Values at 0 should be exact. */ 93 testall(tan, 0.0, 0.0, ALL_STD_EXCEPT, 0); 94 testall(tan, -0.0, -0.0, ALL_STD_EXCEPT, 0); 95 testall(cos, 0.0, 1.0, ALL_STD_EXCEPT, 0); 96 testall(cos, -0.0, 1.0, ALL_STD_EXCEPT, 0); 97 testall(sin, 0.0, 0.0, ALL_STD_EXCEPT, 0); 98 testall(sin, -0.0, -0.0, ALL_STD_EXCEPT, 0); 99 100 /* func(+-Inf) == NaN */ 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); 104 testall(tan, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID); 105 testall(sin, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID); 106 testall(cos, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID); 107 108 /* func(NaN) == NaN */ 109 testall(tan, NAN, NAN, ALL_STD_EXCEPT, 0); 110 testall(sin, NAN, NAN, ALL_STD_EXCEPT, 0); 111 testall(cos, NAN, NAN, ALL_STD_EXCEPT, 0); 112 } 113 114 #ifndef __i386__ 115 ATF_TC(reduction); 116 ATF_TC_HEAD(reduction, tc) 117 { 118 119 atf_tc_set_md_var(tc, "descr", 120 "tests to ensure argument reduction for large arguments is accurate"); 121 } 122 ATF_TC_BODY(reduction, tc) 123 { 124 /* floats very close to odd multiples of pi */ 125 static const float f_pi_odd[] = { 126 85563208.0f, 127 43998769152.0f, 128 9.2763667655669323e+25f, 129 1.5458357838905804e+29f, 130 }; 131 /* doubles very close to odd multiples of pi */ 132 static const double d_pi_odd[] = { 133 3.1415926535897931, 134 91.106186954104004, 135 642615.9188844458, 136 3397346.5699258847, 137 6134899525417045.0, 138 3.0213551960457761e+43, 139 1.2646209897993783e+295, 140 6.2083625380677099e+307, 141 }; 142 /* long doubles very close to odd multiples of pi */ 143 #if LDBL_MANT_DIG == 64 144 static const long double ld_pi_odd[] = { 145 1.1891886960373841596e+101L, 146 1.07999475322710967206e+2087L, 147 6.522151627890431836e+2147L, 148 8.9368974898260328229e+2484L, 149 9.2961044110572205863e+2555L, 150 4.90208421886578286e+3189L, 151 1.5275546401232615884e+3317L, 152 1.7227465626338900093e+3565L, 153 2.4160090594000745334e+3808L, 154 9.8477555741888350649e+4314L, 155 1.6061597222105160737e+4326L, 156 }; 157 #endif 158 159 unsigned i; 160 161 #if defined(__amd64__) && defined(__clang__) && __clang_major__ >= 7 && \ 162 __clang_major__ < 10 && __FreeBSD_cc_version < 1300002 163 atf_tc_expect_fail("test fails with clang 7-9 - bug 234040"); 164 #endif 165 166 for (i = 0; i < nitems(f_pi_odd); i++) { 167 ATF_CHECK(fabs(sinf(f_pi_odd[i])) < FLT_EPSILON); 168 ATF_CHECK(cosf(f_pi_odd[i]) == -1.0); 169 ATF_CHECK(fabs(tan(f_pi_odd[i])) < FLT_EPSILON); 170 171 ATF_CHECK(fabs(sinf(-f_pi_odd[i])) < FLT_EPSILON); 172 ATF_CHECK(cosf(-f_pi_odd[i]) == -1.0); 173 ATF_CHECK(fabs(tanf(-f_pi_odd[i])) < FLT_EPSILON); 174 175 ATF_CHECK(fabs(sinf(f_pi_odd[i] * 2)) < FLT_EPSILON); 176 ATF_CHECK(cosf(f_pi_odd[i] * 2) == 1.0); 177 ATF_CHECK(fabs(tanf(f_pi_odd[i] * 2)) < FLT_EPSILON); 178 179 ATF_CHECK(fabs(sinf(-f_pi_odd[i] * 2)) < FLT_EPSILON); 180 ATF_CHECK(cosf(-f_pi_odd[i] * 2) == 1.0); 181 ATF_CHECK(fabs(tanf(-f_pi_odd[i] * 2)) < FLT_EPSILON); 182 } 183 184 for (i = 0; i < nitems(d_pi_odd); i++) { 185 ATF_CHECK(fabs(sin(d_pi_odd[i])) < 2 * DBL_EPSILON); 186 ATF_CHECK(cos(d_pi_odd[i]) == -1.0); 187 ATF_CHECK(fabs(tan(d_pi_odd[i])) < 2 * DBL_EPSILON); 188 189 ATF_CHECK(fabs(sin(-d_pi_odd[i])) < 2 * DBL_EPSILON); 190 ATF_CHECK(cos(-d_pi_odd[i]) == -1.0); 191 ATF_CHECK(fabs(tan(-d_pi_odd[i])) < 2 * DBL_EPSILON); 192 193 ATF_CHECK(fabs(sin(d_pi_odd[i] * 2)) < 2 * DBL_EPSILON); 194 ATF_CHECK(cos(d_pi_odd[i] * 2) == 1.0); 195 ATF_CHECK(fabs(tan(d_pi_odd[i] * 2)) < 2 * DBL_EPSILON); 196 197 ATF_CHECK(fabs(sin(-d_pi_odd[i] * 2)) < 2 * DBL_EPSILON); 198 ATF_CHECK(cos(-d_pi_odd[i] * 2) == 1.0); 199 ATF_CHECK(fabs(tan(-d_pi_odd[i] * 2)) < 2 * DBL_EPSILON); 200 } 201 202 #if LDBL_MANT_DIG == 64 /* XXX: || LDBL_MANT_DIG == 113 */ 203 for (i = 0; i < nitems(ld_pi_odd); i++) { 204 ATF_CHECK(fabsl(sinl(ld_pi_odd[i])) < LDBL_EPSILON); 205 ATF_CHECK(cosl(ld_pi_odd[i]) == -1.0); 206 ATF_CHECK(fabsl(tanl(ld_pi_odd[i])) < LDBL_EPSILON); 207 208 ATF_CHECK(fabsl(sinl(-ld_pi_odd[i])) < LDBL_EPSILON); 209 ATF_CHECK(cosl(-ld_pi_odd[i]) == -1.0); 210 ATF_CHECK(fabsl(tanl(-ld_pi_odd[i])) < LDBL_EPSILON); 211 212 ATF_CHECK(fabsl(sinl(ld_pi_odd[i] * 2)) < LDBL_EPSILON); 213 ATF_CHECK(cosl(ld_pi_odd[i] * 2) == 1.0); 214 ATF_CHECK(fabsl(tanl(ld_pi_odd[i] * 2)) < LDBL_EPSILON); 215 216 ATF_CHECK(fabsl(sinl(-ld_pi_odd[i] * 2)) < LDBL_EPSILON); 217 ATF_CHECK(cosl(-ld_pi_odd[i] * 2) == 1.0); 218 ATF_CHECK(fabsl(tanl(-ld_pi_odd[i] * 2)) < LDBL_EPSILON); 219 } 220 #endif 221 } 222 223 ATF_TC(accuracy); 224 ATF_TC_HEAD(accuracy, tc) 225 { 226 227 atf_tc_set_md_var(tc, "descr", 228 "tests the accuracy of these functions over the primary range"); 229 } 230 ATF_TC_BODY(accuracy, tc) 231 { 232 233 /* For small args, sin(x) = tan(x) = x, and cos(x) = 1. */ 234 testall(sin, 0xd.50ee515fe4aea16p-114L, 0xd.50ee515fe4aea16p-114L, 235 ALL_STD_EXCEPT, FE_INEXACT); 236 testall(tan, 0xd.50ee515fe4aea16p-114L, 0xd.50ee515fe4aea16p-114L, 237 ALL_STD_EXCEPT, FE_INEXACT); 238 testall(cos, 0xd.50ee515fe4aea16p-114L, 1.0, 239 ALL_STD_EXCEPT, FE_INEXACT); 240 241 /* 242 * These tests should pass for f32, d64, and ld80 as long as 243 * the error is <= 0.75 ulp (round to nearest) 244 */ 245 #if LDBL_MANT_DIG <= 64 246 #define testacc testall 247 #else 248 #define testacc testdf 249 #endif 250 testacc(sin, 0.17255452780841205174L, 0.17169949801444412683L, 251 ALL_STD_EXCEPT, FE_INEXACT); 252 testacc(sin, -0.75431944555904520893L, -0.68479288156557286353L, 253 ALL_STD_EXCEPT, FE_INEXACT); 254 testacc(cos, 0.70556358769838947292L, 0.76124620693117771850L, 255 ALL_STD_EXCEPT, FE_INEXACT); 256 testacc(cos, -0.34061437849088045332L, 0.94254960031831729956L, 257 ALL_STD_EXCEPT, FE_INEXACT); 258 testacc(tan, -0.15862817413325692897L, -0.15997221861309522115L, 259 ALL_STD_EXCEPT, FE_INEXACT); 260 testacc(tan, 0.38374784931303813530L, 0.40376500259976759951L, 261 ALL_STD_EXCEPT, FE_INEXACT); 262 263 /* 264 * XXX missing: 265 * - tests for ld128 266 * - tests for other rounding modes (probably won't pass for now) 267 * - tests for large numbers that get reduced to hi+lo with lo!=0 268 */ 269 } 270 #endif 271 272 ATF_TP_ADD_TCS(tp) 273 { 274 275 ATF_TP_ADD_TC(tp, special); 276 277 #ifndef __i386__ 278 ATF_TP_ADD_TC(tp, accuracy); 279 ATF_TP_ADD_TC(tp, reduction); 280 #endif 281 282 return (atf_no_error()); 283 } 284