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 #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); 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 } 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); 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 } 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); 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 } 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 269 270 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