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 "test-utils.h" 48 49 #pragma STDC FENV_ACCESS ON 50 51 /* 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. 57 * 58 * These are macros instead of functions so that assert provides more 59 * meaningful error messages. 60 * 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. 63 */ 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))); \ 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 /* 83 * Test special cases in sin(), cos(), and tan(). 84 */ 85 static void 86 run_special_tests(void) 87 { 88 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); 96 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); 104 105 /* 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); 109 } 110 111 /* 112 * Tests to ensure argument reduction for large arguments is accurate. 113 */ 114 static void 115 run_reduction_tests(void) 116 { 117 /* floats very close to odd multiples of pi */ 118 static const float f_pi_odd[] = { 119 85563208.0f, 120 43998769152.0f, 121 9.2763667655669323e+25f, 122 1.5458357838905804e+29f, 123 }; 124 /* doubles very close to odd multiples of pi */ 125 static const double d_pi_odd[] = { 126 3.1415926535897931, 127 91.106186954104004, 128 642615.9188844458, 129 3397346.5699258847, 130 6134899525417045.0, 131 3.0213551960457761e+43, 132 1.2646209897993783e+295, 133 6.2083625380677099e+307, 134 }; 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, 149 }; 150 #elif LDBL_MANT_DIG == 113 151 static const long double ld_pi_odd[] = { 152 /* XXX */ 153 }; 154 #endif 155 156 int i; 157 158 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); 162 163 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); 166 167 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); 170 171 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); 174 } 175 176 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); 180 181 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); 184 185 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); 188 189 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); 192 } 193 194 #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); 199 200 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); 203 204 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); 207 208 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); 211 } 212 #endif 213 } 214 215 /* 216 * Tests the accuracy of these functions over the primary range. 217 */ 218 static void 219 run_accuracy_tests(void) 220 { 221 222 /* 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); 229 230 /* 231 * These tests should pass for f32, d64, and ld80 as long as 232 * the error is <= 0.75 ulp (round to nearest) 233 */ 234 #if LDBL_MANT_DIG <= 64 235 #define testacc testall 236 #else 237 #define testacc testdf 238 #endif 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); 251 252 /* 253 * XXX missing: 254 * - tests for ld128 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!=0 257 */ 258 } 259 260 int 261 main(int argc, char *argv[]) 262 { 263 264 printf("1..3\n"); 265 266 run_special_tests(); 267 printf("ok 1 - trig\n"); 268 269 #ifndef __i386__ 270 run_reduction_tests(); 271 #endif 272 printf("ok 2 - trig\n"); 273 274 #ifndef __i386__ 275 run_accuracy_tests(); 276 #endif 277 printf("ok 3 - trig\n"); 278 279 return (0); 280 } 281