1 /* $OpenBSD: trig_test.c,v 1.1 2021/10/22 18:00:23 mbuhl Exp $ */ 2 /*- 3 * Copyright (c) 2008 David Schultz <das@FreeBSD.org> 4 * All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 18 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 25 * SUCH DAMAGE. 26 */ 27 28 #include "macros.h" 29 30 /* 31 * Tests for corner cases in trigonometric functions. Some accuracy tests 32 * are included as well, but these are very basic sanity checks, not 33 * intended to be comprehensive. 34 * 35 * The program for generating representable numbers near multiples of pi is 36 * available at http://www.cs.berkeley.edu/~wkahan/testpi/ . 37 */ 38 39 #include <sys/cdefs.h> 40 __FBSDID("$FreeBSD$"); 41 42 #include <sys/param.h> 43 44 #include <fenv.h> 45 #include <float.h> 46 #include <math.h> 47 #include <stdio.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 CHECK_FPEQUAL((func)(_d), (result)); \ 70 CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \ 71 #func, #x); \ 72 } while (0) 73 74 #define testall(prefix, x, result, exceptmask, excepts) do { \ 75 test(prefix, x, (double)result, exceptmask, excepts); \ 76 test(prefix##f, x, (float)result, exceptmask, excepts); \ 77 test(prefix##l, x, result, exceptmask, excepts); \ 78 } while (0) 79 80 #define testdf(prefix, x, result, exceptmask, excepts) do { \ 81 test(prefix, x, (double)result, exceptmask, excepts); \ 82 test(prefix##f, x, (float)result, exceptmask, excepts); \ 83 } while (0) 84 85 ATF_TC(special); 86 ATF_TC_HEAD(special, tc) 87 { 88 89 atf_tc_set_md_var(tc, "descr", 90 "test special cases in sin(), cos(), and tan()"); 91 } 92 ATF_TC_BODY(special, tc) 93 { 94 95 /* Values at 0 should be exact. */ 96 testall(tan, 0.0, 0.0, ALL_STD_EXCEPT, 0); 97 testall(tan, -0.0, -0.0, ALL_STD_EXCEPT, 0); 98 testall(cos, 0.0, 1.0, ALL_STD_EXCEPT, 0); 99 testall(cos, -0.0, 1.0, ALL_STD_EXCEPT, 0); 100 testall(sin, 0.0, 0.0, ALL_STD_EXCEPT, 0); 101 testall(sin, -0.0, -0.0, ALL_STD_EXCEPT, 0); 102 103 /* func(+-Inf) == NaN */ 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 testall(tan, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID); 108 testall(sin, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID); 109 testall(cos, -INFINITY, NAN, ALL_STD_EXCEPT, FE_INVALID); 110 111 /* func(NaN) == NaN */ 112 testall(tan, NAN, NAN, ALL_STD_EXCEPT, 0); 113 testall(sin, NAN, NAN, ALL_STD_EXCEPT, 0); 114 testall(cos, NAN, NAN, ALL_STD_EXCEPT, 0); 115 } 116 117 #ifndef __i386__ 118 ATF_TC(reduction); 119 ATF_TC_HEAD(reduction, tc) 120 { 121 122 atf_tc_set_md_var(tc, "descr", 123 "tests to ensure argument reduction for large arguments is accurate"); 124 } 125 ATF_TC_BODY(reduction, tc) 126 { 127 /* floats very close to odd multiples of pi */ 128 static const float f_pi_odd[] = { 129 85563208.0f, 130 43998769152.0f, 131 9.2763667655669323e+25f, 132 1.5458357838905804e+29f, 133 }; 134 /* doubles very close to odd multiples of pi */ 135 static const double d_pi_odd[] = { 136 3.1415926535897931, 137 91.106186954104004, 138 642615.9188844458, 139 3397346.5699258847, 140 6134899525417045.0, 141 3.0213551960457761e+43, 142 1.2646209897993783e+295, 143 6.2083625380677099e+307, 144 }; 145 /* long doubles very close to odd multiples of pi */ 146 #if LDBL_MANT_DIG == 64 147 static const long double ld_pi_odd[] = { 148 1.1891886960373841596e+101L, 149 1.07999475322710967206e+2087L, 150 6.522151627890431836e+2147L, 151 8.9368974898260328229e+2484L, 152 9.2961044110572205863e+2555L, 153 4.90208421886578286e+3189L, 154 1.5275546401232615884e+3317L, 155 1.7227465626338900093e+3565L, 156 2.4160090594000745334e+3808L, 157 9.8477555741888350649e+4314L, 158 1.6061597222105160737e+4326L, 159 }; 160 #endif 161 162 unsigned i; 163 164 #if defined(__amd64__) && defined(__clang__) && __clang_major__ >= 7 && \ 165 __clang_major__ < 10 && __FreeBSD_cc_version < 1300002 166 atf_tc_expect_fail("test fails with clang 7-9 - bug 234040"); 167 #endif 168 169 for (i = 0; i < nitems(f_pi_odd); i++) { 170 ATF_CHECK(fabs(sinf(f_pi_odd[i])) < FLT_EPSILON); 171 ATF_CHECK(cosf(f_pi_odd[i]) == -1.0); 172 ATF_CHECK(fabs(tan(f_pi_odd[i])) < FLT_EPSILON); 173 174 ATF_CHECK(fabs(sinf(-f_pi_odd[i])) < FLT_EPSILON); 175 ATF_CHECK(cosf(-f_pi_odd[i]) == -1.0); 176 ATF_CHECK(fabs(tanf(-f_pi_odd[i])) < FLT_EPSILON); 177 178 ATF_CHECK(fabs(sinf(f_pi_odd[i] * 2)) < FLT_EPSILON); 179 ATF_CHECK(cosf(f_pi_odd[i] * 2) == 1.0); 180 ATF_CHECK(fabs(tanf(f_pi_odd[i] * 2)) < FLT_EPSILON); 181 182 ATF_CHECK(fabs(sinf(-f_pi_odd[i] * 2)) < FLT_EPSILON); 183 ATF_CHECK(cosf(-f_pi_odd[i] * 2) == 1.0); 184 ATF_CHECK(fabs(tanf(-f_pi_odd[i] * 2)) < FLT_EPSILON); 185 } 186 187 for (i = 0; i < nitems(d_pi_odd); i++) { 188 ATF_CHECK(fabs(sin(d_pi_odd[i])) < 2 * DBL_EPSILON); 189 ATF_CHECK(cos(d_pi_odd[i]) == -1.0); 190 ATF_CHECK(fabs(tan(d_pi_odd[i])) < 2 * DBL_EPSILON); 191 192 ATF_CHECK(fabs(sin(-d_pi_odd[i])) < 2 * DBL_EPSILON); 193 ATF_CHECK(cos(-d_pi_odd[i]) == -1.0); 194 ATF_CHECK(fabs(tan(-d_pi_odd[i])) < 2 * DBL_EPSILON); 195 196 ATF_CHECK(fabs(sin(d_pi_odd[i] * 2)) < 2 * DBL_EPSILON); 197 ATF_CHECK(cos(d_pi_odd[i] * 2) == 1.0); 198 ATF_CHECK(fabs(tan(d_pi_odd[i] * 2)) < 2 * DBL_EPSILON); 199 200 ATF_CHECK(fabs(sin(-d_pi_odd[i] * 2)) < 2 * DBL_EPSILON); 201 ATF_CHECK(cos(-d_pi_odd[i] * 2) == 1.0); 202 ATF_CHECK(fabs(tan(-d_pi_odd[i] * 2)) < 2 * DBL_EPSILON); 203 } 204 205 #if LDBL_MANT_DIG == 64 /* XXX: || LDBL_MANT_DIG == 113 */ 206 for (i = 0; i < nitems(ld_pi_odd); i++) { 207 ATF_CHECK(fabsl(sinl(ld_pi_odd[i])) < LDBL_EPSILON); 208 ATF_CHECK(cosl(ld_pi_odd[i]) == -1.0); 209 ATF_CHECK(fabsl(tanl(ld_pi_odd[i])) < LDBL_EPSILON); 210 211 ATF_CHECK(fabsl(sinl(-ld_pi_odd[i])) < LDBL_EPSILON); 212 ATF_CHECK(cosl(-ld_pi_odd[i]) == -1.0); 213 ATF_CHECK(fabsl(tanl(-ld_pi_odd[i])) < LDBL_EPSILON); 214 215 ATF_CHECK(fabsl(sinl(ld_pi_odd[i] * 2)) < LDBL_EPSILON); 216 ATF_CHECK(cosl(ld_pi_odd[i] * 2) == 1.0); 217 ATF_CHECK(fabsl(tanl(ld_pi_odd[i] * 2)) < LDBL_EPSILON); 218 219 ATF_CHECK(fabsl(sinl(-ld_pi_odd[i] * 2)) < LDBL_EPSILON); 220 ATF_CHECK(cosl(-ld_pi_odd[i] * 2) == 1.0); 221 ATF_CHECK(fabsl(tanl(-ld_pi_odd[i] * 2)) < LDBL_EPSILON); 222 } 223 #endif 224 } 225 226 ATF_TC(accuracy); 227 ATF_TC_HEAD(accuracy, tc) 228 { 229 230 atf_tc_set_md_var(tc, "descr", 231 "tests the accuracy of these functions over the primary range"); 232 } 233 ATF_TC_BODY(accuracy, tc) 234 { 235 236 /* For small args, sin(x) = tan(x) = x, and cos(x) = 1. */ 237 testall(sin, 0xd.50ee515fe4aea16p-114L, 0xd.50ee515fe4aea16p-114L, 238 ALL_STD_EXCEPT, FE_INEXACT); 239 testall(tan, 0xd.50ee515fe4aea16p-114L, 0xd.50ee515fe4aea16p-114L, 240 ALL_STD_EXCEPT, FE_INEXACT); 241 testall(cos, 0xd.50ee515fe4aea16p-114L, 1.0, 242 ALL_STD_EXCEPT, FE_INEXACT); 243 244 /* 245 * These tests should pass for f32, d64, and ld80 as long as 246 * the error is <= 0.75 ulp (round to nearest) 247 */ 248 #if LDBL_MANT_DIG <= 64 249 #define testacc testall 250 #else 251 #define testacc testdf 252 #endif 253 testacc(sin, 0.17255452780841205174L, 0.17169949801444412683L, 254 ALL_STD_EXCEPT, FE_INEXACT); 255 testacc(sin, -0.75431944555904520893L, -0.68479288156557286353L, 256 ALL_STD_EXCEPT, FE_INEXACT); 257 testacc(cos, 0.70556358769838947292L, 0.76124620693117771850L, 258 ALL_STD_EXCEPT, FE_INEXACT); 259 testacc(cos, -0.34061437849088045332L, 0.94254960031831729956L, 260 ALL_STD_EXCEPT, FE_INEXACT); 261 testacc(tan, -0.15862817413325692897L, -0.15997221861309522115L, 262 ALL_STD_EXCEPT, FE_INEXACT); 263 testacc(tan, 0.38374784931303813530L, 0.40376500259976759951L, 264 ALL_STD_EXCEPT, FE_INEXACT); 265 266 /* 267 * XXX missing: 268 * - tests for ld128 269 * - tests for other rounding modes (probably won't pass for now) 270 * - tests for large numbers that get reduced to hi+lo with lo!=0 271 */ 272 } 273 #endif 274 275 ATF_TP_ADD_TCS(tp) 276 { 277 278 ATF_TP_ADD_TC(tp, special); 279 280 #ifndef __i386__ 281 ATF_TP_ADD_TC(tp, accuracy); 282 ATF_TP_ADD_TC(tp, reduction); 283 #endif 284 285 return (atf_no_error()); 286 } 287