invtrig_test.c revision 315121
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 the inverse trigonometric functions. Some 29 * accuracy tests are included as well, but these are very basic 30 * sanity checks, not intended to be comprehensive. 31 */ 32 33#include <sys/cdefs.h> 34__FBSDID("$FreeBSD: stable/11/lib/msun/tests/invtrig_test.c 315121 2017-03-12 04:52:09Z ngie $"); 35 36#include <assert.h> 37#include <fenv.h> 38#include <float.h> 39#include <math.h> 40#include <stdio.h> 41 42#include "test-utils.h" 43 44#pragma STDC FENV_ACCESS ON 45 46/* 47 * Test that a function returns the correct value and sets the 48 * exception flags correctly. A tolerance specifying the maximum 49 * relative error allowed may be specified. For the 'testall' 50 * functions, the tolerance is specified in ulps. 51 * 52 * These are macros instead of functions so that assert provides more 53 * meaningful error messages. 54 */ 55#define test_tol(func, x, result, tol, excepts) do { \ 56 volatile long double _in = (x), _out = (result); \ 57 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ 58 assert(fpequal_tol(func(_in), _out, (tol), CS_BOTH)); \ 59 assert(((void)func, fetestexcept(ALL_STD_EXCEPT) == (excepts))); \ 60} while (0) 61#define test(func, x, result, excepts) \ 62 test_tol(func, (x), (result), 0, (excepts)) 63 64#define _testall_tol(prefix, x, result, tol, excepts) do { \ 65 test_tol(prefix, (double)(x), (double)(result), \ 66 (tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts)); \ 67 test_tol(prefix##f, (float)(x), (float)(result), \ 68 (tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts)); \ 69} while (0) 70 71#if LDBL_PREC == 53 72#define testall_tol _testall_tol 73#else 74#define testall_tol(prefix, x, result, tol, excepts) do { \ 75 _testall_tol(prefix, x, result, tol, excepts); \ 76 test_tol(prefix##l, (x), (result), \ 77 (tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts)); \ 78} while (0) 79#endif 80 81#define testall(prefix, x, result, excepts) \ 82 testall_tol(prefix, (x), (result), 0, (excepts)) 83 84#define test2_tol(func, y, x, result, tol, excepts) do { \ 85 volatile long double _iny = (y), _inx = (x), _out = (result); \ 86 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ 87 assert(fpequal_tol(func(_iny, _inx), _out, (tol), CS_BOTH)); \ 88 assert(((void)func, fetestexcept(ALL_STD_EXCEPT) == (excepts))); \ 89} while (0) 90#define test2(func, y, x, result, excepts) \ 91 test2_tol(func, (y), (x), (result), 0, (excepts)) 92 93#define _testall2_tol(prefix, y, x, result, tol, excepts) do { \ 94 test2_tol(prefix, (double)(y), (double)(x), (double)(result), \ 95 (tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts)); \ 96 test2_tol(prefix##f, (float)(y), (float)(x), (float)(result), \ 97 (tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts)); \ 98} while (0) 99 100#if LDBL_PREC == 53 101#define testall2_tol _testall2_tol 102#else 103#define testall2_tol(prefix, y, x, result, tol, excepts) do { \ 104 _testall2_tol(prefix, y, x, result, tol, excepts); \ 105 test2_tol(prefix##l, (y), (x), (result), \ 106 (tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts)); \ 107} while (0) 108#endif 109 110#define testall2(prefix, y, x, result, excepts) \ 111 testall2_tol(prefix, (y), (x), (result), 0, (excepts)) 112 113static long double 114pi = 3.14159265358979323846264338327950280e+00L, 115pio3 = 1.04719755119659774615421446109316766e+00L, 116c3pi = 9.42477796076937971538793014983850839e+00L, 117c7pi = 2.19911485751285526692385036829565196e+01L, 118c5pio3 = 5.23598775598298873077107230546583851e+00L, 119sqrt2m1 = 4.14213562373095048801688724209698081e-01L; 120 121 122/* 123 * Test special case inputs in asin(), acos() and atan(): signed 124 * zeroes, infinities, and NaNs. 125 */ 126static void 127test_special(void) 128{ 129 130 testall(asin, 0.0, 0.0, 0); 131 testall(acos, 0.0, pi / 2, FE_INEXACT); 132 testall(atan, 0.0, 0.0, 0); 133 testall(asin, -0.0, -0.0, 0); 134 testall(acos, -0.0, pi / 2, FE_INEXACT); 135 testall(atan, -0.0, -0.0, 0); 136 137 testall(asin, INFINITY, NAN, FE_INVALID); 138 testall(acos, INFINITY, NAN, FE_INVALID); 139 testall(atan, INFINITY, pi / 2, FE_INEXACT); 140 testall(asin, -INFINITY, NAN, FE_INVALID); 141 testall(acos, -INFINITY, NAN, FE_INVALID); 142 testall(atan, -INFINITY, -pi / 2, FE_INEXACT); 143 144 testall(asin, NAN, NAN, 0); 145 testall(acos, NAN, NAN, 0); 146 testall(atan, NAN, NAN, 0); 147} 148 149/* 150 * Test special case inputs in atan2(), where the exact value of y/x is 151 * zero or non-finite. 152 */ 153static void 154test_special_atan2(void) 155{ 156 long double z; 157 int e; 158 159 testall2(atan2, 0.0, -0.0, pi, FE_INEXACT); 160 testall2(atan2, -0.0, -0.0, -pi, FE_INEXACT); 161 testall2(atan2, 0.0, 0.0, 0.0, 0); 162 testall2(atan2, -0.0, 0.0, -0.0, 0); 163 164 testall2(atan2, INFINITY, -INFINITY, c3pi / 4, FE_INEXACT); 165 testall2(atan2, -INFINITY, -INFINITY, -c3pi / 4, FE_INEXACT); 166 testall2(atan2, INFINITY, INFINITY, pi / 4, FE_INEXACT); 167 testall2(atan2, -INFINITY, INFINITY, -pi / 4, FE_INEXACT); 168 169 /* Tests with one input in the range (0, Inf]. */ 170 z = 1.23456789L; 171 for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP; e++) { 172 test2(atan2f, 0.0, ldexpf(z, e), 0.0, 0); 173 test2(atan2f, -0.0, ldexpf(z, e), -0.0, 0); 174 test2(atan2f, 0.0, ldexpf(-z, e), (float)pi, FE_INEXACT); 175 test2(atan2f, -0.0, ldexpf(-z, e), (float)-pi, FE_INEXACT); 176 test2(atan2f, ldexpf(z, e), 0.0, (float)pi / 2, FE_INEXACT); 177 test2(atan2f, ldexpf(z, e), -0.0, (float)pi / 2, FE_INEXACT); 178 test2(atan2f, ldexpf(-z, e), 0.0, (float)-pi / 2, FE_INEXACT); 179 test2(atan2f, ldexpf(-z, e), -0.0, (float)-pi / 2, FE_INEXACT); 180 } 181 for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP; e++) { 182 test2(atan2, 0.0, ldexp(z, e), 0.0, 0); 183 test2(atan2, -0.0, ldexp(z, e), -0.0, 0); 184 test2(atan2, 0.0, ldexp(-z, e), (double)pi, FE_INEXACT); 185 test2(atan2, -0.0, ldexp(-z, e), (double)-pi, FE_INEXACT); 186 test2(atan2, ldexp(z, e), 0.0, (double)pi / 2, FE_INEXACT); 187 test2(atan2, ldexp(z, e), -0.0, (double)pi / 2, FE_INEXACT); 188 test2(atan2, ldexp(-z, e), 0.0, (double)-pi / 2, FE_INEXACT); 189 test2(atan2, ldexp(-z, e), -0.0, (double)-pi / 2, FE_INEXACT); 190 } 191 for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP; e++) { 192 test2(atan2l, 0.0, ldexpl(z, e), 0.0, 0); 193 test2(atan2l, -0.0, ldexpl(z, e), -0.0, 0); 194 test2(atan2l, 0.0, ldexpl(-z, e), pi, FE_INEXACT); 195 test2(atan2l, -0.0, ldexpl(-z, e), -pi, FE_INEXACT); 196 test2(atan2l, ldexpl(z, e), 0.0, pi / 2, FE_INEXACT); 197 test2(atan2l, ldexpl(z, e), -0.0, pi / 2, FE_INEXACT); 198 test2(atan2l, ldexpl(-z, e), 0.0, -pi / 2, FE_INEXACT); 199 test2(atan2l, ldexpl(-z, e), -0.0, -pi / 2, FE_INEXACT); 200 } 201 202 /* Tests with one input in the range (0, Inf). */ 203 for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP - 1; e++) { 204 test2(atan2f, ldexpf(z, e), INFINITY, 0.0, 0); 205 test2(atan2f, ldexpf(-z,e), INFINITY, -0.0, 0); 206 test2(atan2f, ldexpf(z, e), -INFINITY, (float)pi, FE_INEXACT); 207 test2(atan2f, ldexpf(-z,e), -INFINITY, (float)-pi, FE_INEXACT); 208 test2(atan2f, INFINITY, ldexpf(z,e), (float)pi/2, FE_INEXACT); 209 test2(atan2f, INFINITY, ldexpf(-z,e), (float)pi/2, FE_INEXACT); 210 test2(atan2f, -INFINITY, ldexpf(z,e), (float)-pi/2,FE_INEXACT); 211 test2(atan2f, -INFINITY, ldexpf(-z,e),(float)-pi/2,FE_INEXACT); 212 } 213 for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP - 1; e++) { 214 test2(atan2, ldexp(z, e), INFINITY, 0.0, 0); 215 test2(atan2, ldexp(-z,e), INFINITY, -0.0, 0); 216 test2(atan2, ldexp(z, e), -INFINITY, (double)pi, FE_INEXACT); 217 test2(atan2, ldexp(-z,e), -INFINITY, (double)-pi, FE_INEXACT); 218 test2(atan2, INFINITY, ldexp(z,e), (double)pi/2, FE_INEXACT); 219 test2(atan2, INFINITY, ldexp(-z,e), (double)pi/2, FE_INEXACT); 220 test2(atan2, -INFINITY, ldexp(z,e), (double)-pi/2,FE_INEXACT); 221 test2(atan2, -INFINITY, ldexp(-z,e),(double)-pi/2,FE_INEXACT); 222 } 223 for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP - 1; e++) { 224 test2(atan2l, ldexpl(z, e), INFINITY, 0.0, 0); 225 test2(atan2l, ldexpl(-z,e), INFINITY, -0.0, 0); 226 test2(atan2l, ldexpl(z, e), -INFINITY, pi, FE_INEXACT); 227 test2(atan2l, ldexpl(-z,e), -INFINITY, -pi, FE_INEXACT); 228 test2(atan2l, INFINITY, ldexpl(z, e), pi / 2, FE_INEXACT); 229 test2(atan2l, INFINITY, ldexpl(-z, e), pi / 2, FE_INEXACT); 230 test2(atan2l, -INFINITY, ldexpl(z, e), -pi / 2, FE_INEXACT); 231 test2(atan2l, -INFINITY, ldexpl(-z, e), -pi / 2, FE_INEXACT); 232 } 233} 234 235/* 236 * Test various inputs to asin(), acos() and atan() and verify that the 237 * results are accurate to within 1 ulp. 238 */ 239static void 240test_accuracy(void) 241{ 242 243 /* We expect correctly rounded results for these basic cases. */ 244 testall(asin, 1.0, pi / 2, FE_INEXACT); 245 testall(acos, 1.0, 0, 0); 246 testall(atan, 1.0, pi / 4, FE_INEXACT); 247 testall(asin, -1.0, -pi / 2, FE_INEXACT); 248 testall(acos, -1.0, pi, FE_INEXACT); 249 testall(atan, -1.0, -pi / 4, FE_INEXACT); 250 251 /* 252 * Here we expect answers to be within 1 ulp, although inexactness 253 * in the input, combined with double rounding, could cause larger 254 * errors. 255 */ 256 257 testall_tol(asin, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT); 258 testall_tol(acos, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT); 259 testall_tol(asin, -sqrtl(2) / 2, -pi / 4, 1, FE_INEXACT); 260 testall_tol(acos, -sqrtl(2) / 2, c3pi / 4, 1, FE_INEXACT); 261 262 testall_tol(asin, sqrtl(3) / 2, pio3, 1, FE_INEXACT); 263 testall_tol(acos, sqrtl(3) / 2, pio3 / 2, 1, FE_INEXACT); 264 testall_tol(atan, sqrtl(3), pio3, 1, FE_INEXACT); 265 testall_tol(asin, -sqrtl(3) / 2, -pio3, 1, FE_INEXACT); 266 testall_tol(acos, -sqrtl(3) / 2, c5pio3 / 2, 1, FE_INEXACT); 267 testall_tol(atan, -sqrtl(3), -pio3, 1, FE_INEXACT); 268 269 testall_tol(atan, sqrt2m1, pi / 8, 1, FE_INEXACT); 270 testall_tol(atan, -sqrt2m1, -pi / 8, 1, FE_INEXACT); 271} 272 273/* 274 * Test inputs to atan2() where x is a power of 2. These are easy cases 275 * because y/x is exact. 276 */ 277static void 278test_p2x_atan2(void) 279{ 280 281 testall2(atan2, 1.0, 1.0, pi / 4, FE_INEXACT); 282 testall2(atan2, 1.0, -1.0, c3pi / 4, FE_INEXACT); 283 testall2(atan2, -1.0, 1.0, -pi / 4, FE_INEXACT); 284 testall2(atan2, -1.0, -1.0, -c3pi / 4, FE_INEXACT); 285 286 testall2_tol(atan2, sqrt2m1 * 2, 2.0, pi / 8, 1, FE_INEXACT); 287 testall2_tol(atan2, sqrt2m1 * 2, -2.0, c7pi / 8, 1, FE_INEXACT); 288 testall2_tol(atan2, -sqrt2m1 * 2, 2.0, -pi / 8, 1, FE_INEXACT); 289 testall2_tol(atan2, -sqrt2m1 * 2, -2.0, -c7pi / 8, 1, FE_INEXACT); 290 291 testall2_tol(atan2, sqrtl(3) * 0.5, 0.5, pio3, 1, FE_INEXACT); 292 testall2_tol(atan2, sqrtl(3) * 0.5, -0.5, pio3 * 2, 1, FE_INEXACT); 293 testall2_tol(atan2, -sqrtl(3) * 0.5, 0.5, -pio3, 1, FE_INEXACT); 294 testall2_tol(atan2, -sqrtl(3) * 0.5, -0.5, -pio3 * 2, 1, FE_INEXACT); 295} 296 297/* 298 * Test inputs very close to 0. 299 */ 300static void 301test_tiny(void) 302{ 303 float tiny = 0x1.23456p-120f; 304 305 testall(asin, tiny, tiny, FE_INEXACT); 306 testall(acos, tiny, pi / 2, FE_INEXACT); 307 testall(atan, tiny, tiny, FE_INEXACT); 308 309 testall(asin, -tiny, -tiny, FE_INEXACT); 310 testall(acos, -tiny, pi / 2, FE_INEXACT); 311 testall(atan, -tiny, -tiny, FE_INEXACT); 312 313 /* Test inputs to atan2() that would cause y/x to underflow. */ 314 test2(atan2f, 0x1.0p-100, 0x1.0p100, 0.0, FE_INEXACT | FE_UNDERFLOW); 315 test2(atan2, 0x1.0p-1000, 0x1.0p1000, 0.0, FE_INEXACT | FE_UNDERFLOW); 316 test2(atan2l, ldexpl(1.0, 100 - LDBL_MAX_EXP), 317 ldexpl(1.0, LDBL_MAX_EXP - 100), 0.0, FE_INEXACT | FE_UNDERFLOW); 318 test2(atan2f, -0x1.0p-100, 0x1.0p100, -0.0, FE_INEXACT | FE_UNDERFLOW); 319 test2(atan2, -0x1.0p-1000, 0x1.0p1000, -0.0, FE_INEXACT | FE_UNDERFLOW); 320 test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP), 321 ldexpl(1.0, LDBL_MAX_EXP - 100), -0.0, FE_INEXACT | FE_UNDERFLOW); 322 test2(atan2f, 0x1.0p-100, -0x1.0p100, (float)pi, FE_INEXACT); 323 test2(atan2, 0x1.0p-1000, -0x1.0p1000, (double)pi, FE_INEXACT); 324 test2(atan2l, ldexpl(1.0, 100 - LDBL_MAX_EXP), 325 -ldexpl(1.0, LDBL_MAX_EXP - 100), pi, FE_INEXACT); 326 test2(atan2f, -0x1.0p-100, -0x1.0p100, (float)-pi, FE_INEXACT); 327 test2(atan2, -0x1.0p-1000, -0x1.0p1000, (double)-pi, FE_INEXACT); 328 test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP), 329 -ldexpl(1.0, LDBL_MAX_EXP - 100), -pi, FE_INEXACT); 330} 331 332/* 333 * Test very large inputs to atan(). 334 */ 335static void 336test_atan_huge(void) 337{ 338 float huge = 0x1.23456p120; 339 340 testall(atan, huge, pi / 2, FE_INEXACT); 341 testall(atan, -huge, -pi / 2, FE_INEXACT); 342 343 /* Test inputs to atan2() that would cause y/x to overflow. */ 344 test2(atan2f, 0x1.0p100, 0x1.0p-100, (float)pi / 2, FE_INEXACT); 345 test2(atan2, 0x1.0p1000, 0x1.0p-1000, (double)pi / 2, FE_INEXACT); 346 test2(atan2l, ldexpl(1.0, LDBL_MAX_EXP - 100), 347 ldexpl(1.0, 100 - LDBL_MAX_EXP), pi / 2, FE_INEXACT); 348 test2(atan2f, -0x1.0p100, 0x1.0p-100, (float)-pi / 2, FE_INEXACT); 349 test2(atan2, -0x1.0p1000, 0x1.0p-1000, (double)-pi / 2, FE_INEXACT); 350 test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100), 351 ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT); 352 353 test2(atan2f, 0x1.0p100, -0x1.0p-100, (float)pi / 2, FE_INEXACT); 354 test2(atan2, 0x1.0p1000, -0x1.0p-1000, (double)pi / 2, FE_INEXACT); 355 test2(atan2l, ldexpl(1.0, LDBL_MAX_EXP - 100), 356 -ldexpl(1.0, 100 - LDBL_MAX_EXP), pi / 2, FE_INEXACT); 357 test2(atan2f, -0x1.0p100, -0x1.0p-100, (float)-pi / 2, FE_INEXACT); 358 test2(atan2, -0x1.0p1000, -0x1.0p-1000, (double)-pi / 2, FE_INEXACT); 359 test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100), 360 -ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT); 361} 362 363/* 364 * Test that sin(asin(x)) == x, and similarly for acos() and atan(). 365 * You need to have a working sinl(), cosl(), and tanl() for these 366 * tests to pass. 367 */ 368static long double 369sinasinf(float x) 370{ 371 372 return (sinl(asinf(x))); 373} 374 375static long double 376sinasin(double x) 377{ 378 379 return (sinl(asin(x))); 380} 381 382static long double 383sinasinl(long double x) 384{ 385 386 return (sinl(asinl(x))); 387} 388 389static long double 390cosacosf(float x) 391{ 392 393 return (cosl(acosf(x))); 394} 395 396static long double 397cosacos(double x) 398{ 399 400 return (cosl(acos(x))); 401} 402 403static long double 404cosacosl(long double x) 405{ 406 407 return (cosl(acosl(x))); 408} 409 410static long double 411tanatanf(float x) 412{ 413 414 return (tanl(atanf(x))); 415} 416 417static long double 418tanatan(double x) 419{ 420 421 return (tanl(atan(x))); 422} 423 424static long double 425tanatanl(long double x) 426{ 427 428 return (tanl(atanl(x))); 429} 430 431static void 432test_inverse(void) 433{ 434 float i; 435 436 for (i = -1; i <= 1; i += 0x1.0p-12f) { 437 testall_tol(sinasin, i, i, 2, i == 0 ? 0 : FE_INEXACT); 438 /* The relative error for cosacos is very large near x=0. */ 439 if (fabsf(i) > 0x1.0p-4f) 440 testall_tol(cosacos, i, i, 16, i == 1 ? 0 : FE_INEXACT); 441 testall_tol(tanatan, i, i, 2, i == 0 ? 0 : FE_INEXACT); 442 } 443} 444 445int 446main(void) 447{ 448 449#if defined(__i386__) 450 printf("1..0 # SKIP fails all assertions on i386\n"); 451 return (0); 452#endif 453 454 printf("1..7\n"); 455 456 test_special(); 457 printf("ok 1 - special\n"); 458 459 test_special_atan2(); 460 printf("ok 2 - atan2 special\n"); 461 462 test_accuracy(); 463 printf("ok 3 - accuracy\n"); 464 465 test_p2x_atan2(); 466 printf("ok 4 - atan2 p2x\n"); 467 468 test_tiny(); 469 printf("ok 5 - tiny inputs\n"); 470 471 test_atan_huge(); 472 printf("ok 6 - atan huge inputs\n"); 473 474 test_inverse(); 475 printf("ok 7 - inverse\n"); 476 477 return (0); 478} 479