cexp_test.c revision 219362
1/*- 2 * Copyright (c) 2008-2011 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 cexp*(). 29 */ 30 31#include <sys/cdefs.h> 32__FBSDID("$FreeBSD: head/tools/regression/lib/msun/test-cexp.c 219362 2011-03-07 03:15:49Z das $"); 33 34#include <assert.h> 35#include <complex.h> 36#include <fenv.h> 37#include <float.h> 38#include <math.h> 39#include <stdio.h> 40 41#define ALL_STD_EXCEPT (FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \ 42 FE_OVERFLOW | FE_UNDERFLOW) 43#define FLT_ULP() ldexpl(1.0, 1 - FLT_MANT_DIG) 44#define DBL_ULP() ldexpl(1.0, 1 - DBL_MANT_DIG) 45#define LDBL_ULP() ldexpl(1.0, 1 - LDBL_MANT_DIG) 46 47#define N(i) (sizeof(i) / sizeof((i)[0])) 48 49#pragma STDC FENV_ACCESS ON 50#pragma STDC CX_LIMITED_RANGE OFF 51 52/* 53 * XXX gcc implements complex multiplication incorrectly. In 54 * particular, it implements it as if the CX_LIMITED_RANGE pragma 55 * were ON. Consequently, we need this function to form numbers 56 * such as x + INFINITY * I, since gcc evalutes INFINITY * I as 57 * NaN + INFINITY * I. 58 */ 59static inline long double complex 60cpackl(long double x, long double y) 61{ 62 long double complex z; 63 64 __real__ z = x; 65 __imag__ z = y; 66 return (z); 67} 68 69/* 70 * Test that a function returns the correct value and sets the 71 * exception flags correctly. The exceptmask specifies which 72 * exceptions we should check. We need to be lenient for several 73 * reasons, but mainly because on some architectures it's impossible 74 * to raise FE_OVERFLOW without raising FE_INEXACT. In some cases, 75 * whether cexp() raises an invalid exception is unspecified. 76 * 77 * These are macros instead of functions so that assert provides more 78 * meaningful error messages. 79 * 80 * XXX The volatile here is to avoid gcc's bogus constant folding and work 81 * around the lack of support for the FENV_ACCESS pragma. 82 */ 83#define test(func, z, result, exceptmask, excepts, checksign) do { \ 84 volatile long double complex _d = z; \ 85 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ 86 assert(cfpequal((func)(_d), (result), (checksign))); \ 87 assert(((func), fetestexcept(exceptmask) == (excepts))); \ 88} while (0) 89 90/* Test within a given tolerance. */ 91#define test_tol(func, z, result, tol) do { \ 92 volatile long double complex _d = z; \ 93 assert(cfpequal_tol((func)(_d), (result), (tol))); \ 94} while (0) 95 96/* Test all the functions that compute cexp(x). */ 97#define testall(x, result, exceptmask, excepts, checksign) do { \ 98 test(cexp, x, result, exceptmask, excepts, checksign); \ 99 test(cexpf, x, result, exceptmask, excepts, checksign); \ 100} while (0) 101 102/* 103 * Test all the functions that compute cexp(x), within a given tolerance. 104 * The tolerance is specified in ulps. 105 */ 106#define testall_tol(x, result, tol) do { \ 107 test_tol(cexp, x, result, tol * DBL_ULP()); \ 108 test_tol(cexpf, x, result, tol * FLT_ULP()); \ 109} while (0) 110 111/* Various finite non-zero numbers to test. */ 112static const float finites[] = 113{ -42.0e20, -1.0 -1.0e-10, -0.0, 0.0, 1.0e-10, 1.0, 42.0e20 }; 114 115/* 116 * Determine whether x and y are equal, with two special rules: 117 * +0.0 != -0.0 118 * NaN == NaN 119 * If checksign is 0, we compare the absolute values instead. 120 */ 121static int 122fpequal(long double x, long double y, int checksign) 123{ 124 if (isnan(x) || isnan(y)) 125 return (1); 126 if (checksign) 127 return (x == y && !signbit(x) == !signbit(y)); 128 else 129 return (fabsl(x) == fabsl(y)); 130} 131 132static int 133fpequal_tol(long double x, long double y, long double tol) 134{ 135 fenv_t env; 136 int ret; 137 138 if (isnan(x) && isnan(y)) 139 return (1); 140 if (!signbit(x) != !signbit(y)) 141 return (0); 142 if (x == y) 143 return (1); 144 if (tol == 0) 145 return (0); 146 147 /* Hard case: need to check the tolerance. */ 148 feholdexcept(&env); 149 /* 150 * For our purposes here, if y=0, we interpret tol as an absolute 151 * tolerance. This is to account for roundoff in the input, e.g., 152 * cos(Pi/2) ~= 0. 153 */ 154 if (y == 0.0) 155 ret = fabsl(x - y) <= fabsl(tol); 156 else 157 ret = fabsl(x - y) <= fabsl(y * tol); 158 fesetenv(&env); 159 return (ret); 160} 161 162static int 163cfpequal(long double complex x, long double complex y, int checksign) 164{ 165 return (fpequal(creal(x), creal(y), checksign) 166 && fpequal(cimag(x), cimag(y), checksign)); 167} 168 169static int 170cfpequal_tol(long double complex x, long double complex y, long double tol) 171{ 172 return (fpequal_tol(creal(x), creal(y), tol) 173 && fpequal_tol(cimag(x), cimag(y), tol)); 174} 175 176 177/* Tests for 0 */ 178void 179test_zero(void) 180{ 181 182 /* cexp(0) = 1, no exceptions raised */ 183 testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1); 184 testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1); 185 testall(cpackl(0.0, -0.0), cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, 1); 186 testall(cpackl(-0.0, -0.0), cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, 1); 187} 188 189/* 190 * Tests for NaN. The signs of the results are indeterminate unless the 191 * imaginary part is 0. 192 */ 193void 194test_nan() 195{ 196 int i; 197 198 /* cexp(x + NaNi) = NaN + NaNi and optionally raises invalid */ 199 /* cexp(NaN + yi) = NaN + NaNi and optionally raises invalid (|y|>0) */ 200 for (i = 0; i < N(finites); i++) { 201 testall(cpackl(finites[i], NAN), cpackl(NAN, NAN), 202 ALL_STD_EXCEPT & ~FE_INVALID, 0, 0); 203 if (finites[i] == 0.0) 204 continue; 205 /* XXX FE_INEXACT shouldn't be raised here */ 206 testall(cpackl(NAN, finites[i]), cpackl(NAN, NAN), 207 ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0); 208 } 209 210 /* cexp(NaN +- 0i) = NaN +- 0i */ 211 testall(cpackl(NAN, 0.0), cpackl(NAN, 0.0), ALL_STD_EXCEPT, 0, 1); 212 testall(cpackl(NAN, -0.0), cpackl(NAN, -0.0), ALL_STD_EXCEPT, 0, 1); 213 214 /* cexp(inf + NaN i) = inf + nan i */ 215 testall(cpackl(INFINITY, NAN), cpackl(INFINITY, NAN), 216 ALL_STD_EXCEPT, 0, 0); 217 /* cexp(-inf + NaN i) = 0 */ 218 testall(cpackl(-INFINITY, NAN), cpackl(0.0, 0.0), 219 ALL_STD_EXCEPT, 0, 0); 220 /* cexp(NaN + NaN i) = NaN + NaN i */ 221 testall(cpackl(NAN, NAN), cpackl(NAN, NAN), 222 ALL_STD_EXCEPT, 0, 0); 223} 224 225void 226test_inf(void) 227{ 228 int i; 229 230 /* cexp(x + inf i) = NaN + NaNi and raises invalid */ 231 /* cexp(inf + yi) = 0 + 0yi */ 232 /* cexp(-inf + yi) = inf + inf yi (except y=0) */ 233 for (i = 0; i < N(finites); i++) { 234 testall(cpackl(finites[i], INFINITY), cpackl(NAN, NAN), 235 ALL_STD_EXCEPT, FE_INVALID, 1); 236 /* XXX shouldn't raise an inexact exception */ 237 testall(cpackl(-INFINITY, finites[i]), 238 cpackl(0.0, 0.0 * finites[i]), 239 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 240 if (finites[i] == 0) 241 continue; 242 testall(cpackl(INFINITY, finites[i]), 243 cpackl(INFINITY, INFINITY * finites[i]), 244 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 245 } 246 testall(cpackl(INFINITY, 0.0), cpackl(INFINITY, 0.0), 247 ALL_STD_EXCEPT, 0, 1); 248 testall(cpackl(INFINITY, -0.0), cpackl(INFINITY, -0.0), 249 ALL_STD_EXCEPT, 0, 1); 250} 251 252void 253test_reals(void) 254{ 255 int i; 256 257 for (i = 0; i < N(finites); i++) { 258 /* XXX could check exceptions more meticulously */ 259 test(cexp, cpackl(finites[i], 0.0), 260 cpackl(exp(finites[i]), 0.0), 261 FE_INVALID | FE_DIVBYZERO, 0, 1); 262 test(cexp, cpackl(finites[i], -0.0), 263 cpackl(exp(finites[i]), -0.0), 264 FE_INVALID | FE_DIVBYZERO, 0, 1); 265 test(cexpf, cpackl(finites[i], 0.0), 266 cpackl(expf(finites[i]), 0.0), 267 FE_INVALID | FE_DIVBYZERO, 0, 1); 268 test(cexpf, cpackl(finites[i], -0.0), 269 cpackl(expf(finites[i]), -0.0), 270 FE_INVALID | FE_DIVBYZERO, 0, 1); 271 } 272} 273 274void 275test_imaginaries(void) 276{ 277 int i; 278 279 for (i = 0; i < N(finites); i++) { 280 test(cexp, cpackl(0.0, finites[i]), 281 cpackl(cos(finites[i]), sin(finites[i])), 282 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 283 test(cexp, cpackl(-0.0, finites[i]), 284 cpackl(cos(finites[i]), sin(finites[i])), 285 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 286 test(cexpf, cpackl(0.0, finites[i]), 287 cpackl(cosf(finites[i]), sinf(finites[i])), 288 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 289 test(cexpf, cpackl(-0.0, finites[i]), 290 cpackl(cosf(finites[i]), sinf(finites[i])), 291 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 292 } 293} 294 295void 296test_small(void) 297{ 298 static const double tests[] = { 299 /* csqrt(a + bI) = x + yI */ 300 /* a b x y */ 301 1.0, M_PI_4, M_SQRT2 * 0.5 * M_E, M_SQRT2 * 0.5 * M_E, 302 -1.0, M_PI_4, M_SQRT2 * 0.5 / M_E, M_SQRT2 * 0.5 / M_E, 303 2.0, M_PI_2, 0.0, M_E * M_E, 304 M_LN2, M_PI, -2.0, 0.0, 305 }; 306 double a, b; 307 double x, y; 308 int i; 309 310 for (i = 0; i < N(tests); i += 4) { 311 a = tests[i]; 312 b = tests[i + 1]; 313 x = tests[i + 2]; 314 y = tests[i + 3]; 315 test_tol(cexp, cpackl(a, b), cpackl(x, y), 3 * DBL_ULP()); 316 317 /* float doesn't have enough precision to pass these tests */ 318 if (x == 0 || y == 0) 319 continue; 320 test_tol(cexpf, cpackl(a, b), cpackl(x, y), 1 * FLT_ULP()); 321 } 322} 323 324/* Test inputs with a real part r that would overflow exp(r). */ 325void 326test_large(void) 327{ 328 329 test_tol(cexp, cpackl(709.79, 0x1p-1074), 330 cpackl(INFINITY, 8.94674309915433533273e-16), DBL_ULP()); 331 test_tol(cexp, cpackl(1000, 0x1p-1074), 332 cpackl(INFINITY, 9.73344457300016401328e+110), DBL_ULP()); 333 test_tol(cexp, cpackl(1400, 0x1p-1074), 334 cpackl(INFINITY, 5.08228858149196559681e+284), DBL_ULP()); 335 test_tol(cexp, cpackl(900, 0x1.23456789abcdep-1020), 336 cpackl(INFINITY, 7.42156649354218408074e+83), DBL_ULP()); 337 test_tol(cexp, cpackl(1300, 0x1.23456789abcdep-1020), 338 cpackl(INFINITY, 3.87514844965996756704e+257), DBL_ULP()); 339 340 test_tol(cexpf, cpackl(88.73, 0x1p-149), 341 cpackl(INFINITY, 4.80265603e-07), 2 * FLT_ULP()); 342 test_tol(cexpf, cpackl(90, 0x1p-149), 343 cpackl(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP()); 344 test_tol(cexpf, cpackl(192, 0x1p-149), 345 cpackl(INFINITY, 3.396809344e+38f), 2 * FLT_ULP()); 346 test_tol(cexpf, cpackl(120, 0x1.234568p-120), 347 cpackl(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP()); 348 test_tol(cexpf, cpackl(170, 0x1.234568p-120), 349 cpackl(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP()); 350} 351 352int 353main(int argc, char *argv[]) 354{ 355 356 printf("1..7\n"); 357 358 test_zero(); 359 printf("ok 1 - cexp zero\n"); 360 361 test_nan(); 362 printf("ok 2 - cexp nan\n"); 363 364 test_inf(); 365 printf("ok 3 - cexp inf\n"); 366 367 test_reals(); 368 printf("ok 4 - cexp reals\n"); 369 370 test_imaginaries(); 371 printf("ok 5 - cexp imaginaries\n"); 372 373 test_small(); 374 printf("ok 6 - cexp small\n"); 375 376 test_large(); 377 printf("ok 7 - cexp large\n"); 378 379 return (0); 380} 381