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 * $FreeBSD: src/tools/regression/lib/msun/test-cexp.c,v 1.3 2013/05/29 00:27:12 svnexp Exp $ 27 */ 28 29 /* 30 * Tests for corner cases in cexp*(). 31 */ 32 33 #include <assert.h> 34 #include <complex.h> 35 #include <fenv.h> 36 #include <float.h> 37 #include <math.h> 38 #include <stdio.h> 39 40 #define ALL_STD_EXCEPT (FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \ 41 FE_OVERFLOW | FE_UNDERFLOW) 42 #define FLT_ULP() ldexpl(1.0, 1 - FLT_MANT_DIG) 43 #define DBL_ULP() ldexpl(1.0, 1 - DBL_MANT_DIG) 44 #define LDBL_ULP() ldexpl(1.0, 1 - LDBL_MANT_DIG) 45 46 #define N(i) (sizeof(i) / sizeof((i)[0])) 47 48 #pragma STDC FENV_ACCESS ON 49 #pragma STDC CX_LIMITED_RANGE OFF 50 51 /* 52 * XXX gcc implements complex multiplication incorrectly. In 53 * particular, it implements it as if the CX_LIMITED_RANGE pragma 54 * were ON. Consequently, we need this function to form numbers 55 * such as x + INFINITY * I, since gcc evalutes INFINITY * I as 56 * NaN + INFINITY * I. 57 */ 58 static inline long double complex 59 cpackl(long double x, long double y) 60 { 61 long double complex z; 62 63 __real__ z = x; 64 __imag__ z = y; 65 return (z); 66 } 67 68 /* 69 * Test that a function returns the correct value and sets the 70 * exception flags correctly. The exceptmask specifies which 71 * exceptions we should check. We need to be lenient for several 72 * reasons, but mainly because on some architectures it's impossible 73 * to raise FE_OVERFLOW without raising FE_INEXACT. In some cases, 74 * whether cexp() raises an invalid exception is unspecified. 75 * 76 * These are macros instead of functions so that assert provides more 77 * meaningful error messages. 78 * 79 * XXX The volatile here is to avoid gcc's bogus constant folding and work 80 * around the lack of support for the FENV_ACCESS pragma. 81 */ 82 #define test(func, z, result, exceptmask, excepts, checksign) do { \ 83 volatile long double complex _d = z; \ 84 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ 85 assert(cfpequal((func)(_d), (result), (checksign))); \ 86 assert(((func), fetestexcept(exceptmask) == (excepts))); \ 87 } while (0) 88 89 /* Test within a given tolerance. */ 90 #define test_tol(func, z, result, tol) do { \ 91 volatile long double complex _d = z; \ 92 assert(cfpequal_tol((func)(_d), (result), (tol))); \ 93 } while (0) 94 95 /* Test all the functions that compute cexp(x). */ 96 #define testall(x, result, exceptmask, excepts, checksign) do { \ 97 test(cexp, x, result, exceptmask, excepts, checksign); \ 98 test(cexpf, x, result, exceptmask, excepts, checksign); \ 99 } while (0) 100 101 /* 102 * Test all the functions that compute cexp(x), within a given tolerance. 103 * The tolerance is specified in ulps. 104 */ 105 #define testall_tol(x, result, tol) do { \ 106 test_tol(cexp, x, result, tol * DBL_ULP()); \ 107 test_tol(cexpf, x, result, tol * FLT_ULP()); \ 108 } while (0) 109 110 /* Various finite non-zero numbers to test. */ 111 static const float finites[] = 112 { -42.0e20, -1.0, -1.0e-10, -0.0, 0.0, 1.0e-10, 1.0, 42.0e20 }; 113 114 /* 115 * Determine whether x and y are equal, with two special rules: 116 * +0.0 != -0.0 117 * NaN == NaN 118 * If checksign is 0, we compare the absolute values instead. 119 */ 120 static int 121 fpequal(long double x, long double y, int checksign) 122 { 123 if (isnan(x) || isnan(y)) 124 return (1); 125 if (checksign) 126 return (x == y && !signbit(x) == !signbit(y)); 127 else 128 return (fabsl(x) == fabsl(y)); 129 } 130 131 static int 132 fpequal_tol(long double x, long double y, long double tol) 133 { 134 fenv_t env; 135 int ret; 136 137 if (isnan(x) && isnan(y)) 138 return (1); 139 if (!signbit(x) != !signbit(y)) 140 return (0); 141 if (x == y) 142 return (1); 143 if (tol == 0) 144 return (0); 145 146 /* Hard case: need to check the tolerance. */ 147 feholdexcept(&env); 148 /* 149 * For our purposes here, if y=0, we interpret tol as an absolute 150 * tolerance. This is to account for roundoff in the input, e.g., 151 * cos(Pi/2) ~= 0. 152 */ 153 if (y == 0.0) 154 ret = fabsl(x - y) <= fabsl(tol); 155 else 156 ret = fabsl(x - y) <= fabsl(y * tol); 157 fesetenv(&env); 158 return (ret); 159 } 160 161 static int 162 cfpequal(long double complex x, long double complex y, int checksign) 163 { 164 return (fpequal(creal(x), creal(y), checksign) 165 && fpequal(cimag(x), cimag(y), checksign)); 166 } 167 168 static int 169 cfpequal_tol(long double complex x, long double complex y, long double tol) 170 { 171 return (fpequal_tol(creal(x), creal(y), tol) 172 && fpequal_tol(cimag(x), cimag(y), tol)); 173 } 174 175 176 /* Tests for 0 */ 177 void 178 test_zero(void) 179 { 180 181 /* cexp(0) = 1, no exceptions raised */ 182 testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1); 183 testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1); 184 testall(cpackl(0.0, -0.0), cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, 1); 185 testall(cpackl(-0.0, -0.0), cpackl(1.0, -0.0), ALL_STD_EXCEPT, 0, 1); 186 } 187 188 /* 189 * Tests for NaN. The signs of the results are indeterminate unless the 190 * imaginary part is 0. 191 */ 192 void 193 test_nan() 194 { 195 int i; 196 197 /* cexp(x + NaNi) = NaN + NaNi and optionally raises invalid */ 198 /* cexp(NaN + yi) = NaN + NaNi and optionally raises invalid (|y|>0) */ 199 for (i = 0; i < N(finites); i++) { 200 testall(cpackl(finites[i], NAN), cpackl(NAN, NAN), 201 ALL_STD_EXCEPT & ~FE_INVALID, 0, 0); 202 if (finites[i] == 0.0) 203 continue; 204 /* XXX FE_INEXACT shouldn't be raised here */ 205 testall(cpackl(NAN, finites[i]), cpackl(NAN, NAN), 206 ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0); 207 } 208 209 /* cexp(NaN +- 0i) = NaN +- 0i */ 210 testall(cpackl(NAN, 0.0), cpackl(NAN, 0.0), ALL_STD_EXCEPT, 0, 1); 211 testall(cpackl(NAN, -0.0), cpackl(NAN, -0.0), ALL_STD_EXCEPT, 0, 1); 212 213 /* cexp(inf + NaN i) = inf + nan i */ 214 testall(cpackl(INFINITY, NAN), cpackl(INFINITY, NAN), 215 ALL_STD_EXCEPT, 0, 0); 216 /* cexp(-inf + NaN i) = 0 */ 217 testall(cpackl(-INFINITY, NAN), cpackl(0.0, 0.0), 218 ALL_STD_EXCEPT, 0, 0); 219 /* cexp(NaN + NaN i) = NaN + NaN i */ 220 testall(cpackl(NAN, NAN), cpackl(NAN, NAN), 221 ALL_STD_EXCEPT, 0, 0); 222 } 223 224 void 225 test_inf(void) 226 { 227 int i; 228 229 /* cexp(x + inf i) = NaN + NaNi and raises invalid */ 230 for (i = 0; i < N(finites); i++) { 231 testall(cpackl(finites[i], INFINITY), cpackl(NAN, NAN), 232 ALL_STD_EXCEPT, FE_INVALID, 1); 233 } 234 /* cexp(-inf + yi) = 0 * (cos(y) + sin(y)i) */ 235 /* XXX shouldn't raise an inexact exception */ 236 testall(cpackl(-INFINITY, M_PI_4), cpackl(0.0, 0.0), 237 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 238 testall(cpackl(-INFINITY, 3 * M_PI_4), cpackl(-0.0, 0.0), 239 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 240 testall(cpackl(-INFINITY, 5 * M_PI_4), cpackl(-0.0, -0.0), 241 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 242 testall(cpackl(-INFINITY, 7 * M_PI_4), cpackl(0.0, -0.0), 243 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 244 testall(cpackl(-INFINITY, 0.0), cpackl(0.0, 0.0), 245 ALL_STD_EXCEPT, 0, 1); 246 testall(cpackl(-INFINITY, -0.0), cpackl(0.0, -0.0), 247 ALL_STD_EXCEPT, 0, 1); 248 /* cexp(inf + yi) = inf * (cos(y) + sin(y)i) (except y=0) */ 249 /* XXX shouldn't raise an inexact exception */ 250 testall(cpackl(INFINITY, M_PI_4), cpackl(INFINITY, INFINITY), 251 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 252 testall(cpackl(INFINITY, 3 * M_PI_4), cpackl(-INFINITY, INFINITY), 253 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 254 testall(cpackl(INFINITY, 5 * M_PI_4), cpackl(-INFINITY, -INFINITY), 255 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 256 testall(cpackl(INFINITY, 7 * M_PI_4), cpackl(INFINITY, -INFINITY), 257 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 258 /* cexp(inf + 0i) = inf + 0i */ 259 testall(cpackl(INFINITY, 0.0), cpackl(INFINITY, 0.0), 260 ALL_STD_EXCEPT, 0, 1); 261 testall(cpackl(INFINITY, -0.0), cpackl(INFINITY, -0.0), 262 ALL_STD_EXCEPT, 0, 1); 263 } 264 265 void 266 test_reals(void) 267 { 268 int i; 269 270 for (i = 0; i < N(finites); i++) { 271 /* XXX could check exceptions more meticulously */ 272 test(cexp, cpackl(finites[i], 0.0), 273 cpackl(exp(finites[i]), 0.0), 274 FE_INVALID | FE_DIVBYZERO, 0, 1); 275 test(cexp, cpackl(finites[i], -0.0), 276 cpackl(exp(finites[i]), -0.0), 277 FE_INVALID | FE_DIVBYZERO, 0, 1); 278 test(cexpf, cpackl(finites[i], 0.0), 279 cpackl(expf(finites[i]), 0.0), 280 FE_INVALID | FE_DIVBYZERO, 0, 1); 281 test(cexpf, cpackl(finites[i], -0.0), 282 cpackl(expf(finites[i]), -0.0), 283 FE_INVALID | FE_DIVBYZERO, 0, 1); 284 } 285 } 286 287 void 288 test_imaginaries(void) 289 { 290 int i; 291 292 for (i = 0; i < N(finites); i++) { 293 test(cexp, cpackl(0.0, finites[i]), 294 cpackl(cos(finites[i]), sin(finites[i])), 295 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 296 test(cexp, cpackl(-0.0, finites[i]), 297 cpackl(cos(finites[i]), sin(finites[i])), 298 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 299 test(cexpf, cpackl(0.0, finites[i]), 300 cpackl(cosf(finites[i]), sinf(finites[i])), 301 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 302 test(cexpf, cpackl(-0.0, finites[i]), 303 cpackl(cosf(finites[i]), sinf(finites[i])), 304 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 305 } 306 } 307 308 void 309 test_small(void) 310 { 311 static const double tests[] = { 312 /* csqrt(a + bI) = x + yI */ 313 /* a b x y */ 314 1.0, M_PI_4, M_SQRT2 * 0.5 * M_E, M_SQRT2 * 0.5 * M_E, 315 -1.0, M_PI_4, M_SQRT2 * 0.5 / M_E, M_SQRT2 * 0.5 / M_E, 316 2.0, M_PI_2, 0.0, M_E * M_E, 317 M_LN2, M_PI, -2.0, 0.0, 318 }; 319 double a, b; 320 double x, y; 321 int i; 322 323 for (i = 0; i < N(tests); i += 4) { 324 a = tests[i]; 325 b = tests[i + 1]; 326 x = tests[i + 2]; 327 y = tests[i + 3]; 328 test_tol(cexp, cpackl(a, b), cpackl(x, y), 3 * DBL_ULP()); 329 330 /* float doesn't have enough precision to pass these tests */ 331 if (x == 0 || y == 0) 332 continue; 333 test_tol(cexpf, cpackl(a, b), cpackl(x, y), 1 * FLT_ULP()); 334 } 335 } 336 337 /* Test inputs with a real part r that would overflow exp(r). */ 338 void 339 test_large(void) 340 { 341 342 test_tol(cexp, cpackl(709.79, 0x1p-1074), 343 cpackl(INFINITY, 8.94674309915433533273e-16), DBL_ULP()); 344 test_tol(cexp, cpackl(1000, 0x1p-1074), 345 cpackl(INFINITY, 9.73344457300016401328e+110), DBL_ULP()); 346 test_tol(cexp, cpackl(1400, 0x1p-1074), 347 cpackl(INFINITY, 5.08228858149196559681e+284), DBL_ULP()); 348 test_tol(cexp, cpackl(900, 0x1.23456789abcdep-1020), 349 cpackl(INFINITY, 7.42156649354218408074e+83), DBL_ULP()); 350 test_tol(cexp, cpackl(1300, 0x1.23456789abcdep-1020), 351 cpackl(INFINITY, 3.87514844965996756704e+257), DBL_ULP()); 352 353 test_tol(cexpf, cpackl(88.73, 0x1p-149), 354 cpackl(INFINITY, 4.80265603e-07), 2 * FLT_ULP()); 355 test_tol(cexpf, cpackl(90, 0x1p-149), 356 cpackl(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP()); 357 test_tol(cexpf, cpackl(192, 0x1p-149), 358 cpackl(INFINITY, 3.396809344e+38f), 2 * FLT_ULP()); 359 test_tol(cexpf, cpackl(120, 0x1.234568p-120), 360 cpackl(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP()); 361 test_tol(cexpf, cpackl(170, 0x1.234568p-120), 362 cpackl(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP()); 363 } 364 365 int 366 main(int argc, char *argv[]) 367 { 368 369 printf("1..7\n"); 370 371 test_zero(); 372 printf("ok 1 - cexp zero\n"); 373 374 test_nan(); 375 printf("ok 2 - cexp nan\n"); 376 377 test_inf(); 378 printf("ok 3 - cexp inf\n"); 379 380 test_reals(); 381 printf("ok 4 - cexp reals\n"); 382 383 test_imaginaries(); 384 printf("ok 5 - cexp imaginaries\n"); 385 386 test_small(); 387 printf("ok 6 - cexp small\n"); 388 389 test_large(); 390 printf("ok 7 - cexp large\n"); 391 392 return (0); 393 } 394