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("$FreeBSD$"); 33 34#include <sys/param.h> 35 36#include <assert.h> 37#include <complex.h> 38#include <fenv.h> 39#include <float.h> 40#include <math.h> 41#include <stdio.h> 42 43#include "test-utils.h" 44 45#pragma STDC FENV_ACCESS ON 46#pragma STDC CX_LIMITED_RANGE OFF 47 48/* 49 * Test that a function returns the correct value and sets the 50 * exception flags correctly. The exceptmask specifies which 51 * exceptions we should check. We need to be lenient for several 52 * reasons, but mainly because on some architectures it's impossible 53 * to raise FE_OVERFLOW without raising FE_INEXACT. In some cases, 54 * whether cexp() raises an invalid exception is unspecified. 55 * 56 * These are macros instead of functions so that assert provides more 57 * meaningful error messages. 58 * 59 * XXX The volatile here is to avoid gcc's bogus constant folding and work 60 * around the lack of support for the FENV_ACCESS pragma. 61 */ 62#define test_t(type, func, z, result, exceptmask, excepts, checksign) \ 63do { \ 64 volatile long double complex _d = z; \ 65 volatile type complex _r = result; \ 66 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ 67 assert(cfpequal_cs((func)(_d), (_r), (checksign))); \ 68 assert(((void)(func), fetestexcept(exceptmask) == (excepts))); \ 69} while (0) 70 71#define test(func, z, result, exceptmask, excepts, checksign) \ 72 test_t(double, func, z, result, exceptmask, excepts, checksign) 73 74#define test_f(func, z, result, exceptmask, excepts, checksign) \ 75 test_t(float, func, z, result, exceptmask, excepts, checksign) 76 77/* Test within a given tolerance. */ 78#define test_tol(func, z, result, tol) do { \ 79 volatile long double complex _d = z; \ 80 assert(cfpequal_tol((func)(_d), (result), (tol), \ 81 FPE_ABS_ZERO | CS_BOTH)); \ 82} while (0) 83 84/* Test all the functions that compute cexp(x). */ 85#define testall(x, result, exceptmask, excepts, checksign) do { \ 86 test(cexp, x, result, exceptmask, excepts, checksign); \ 87 test_f(cexpf, x, result, exceptmask, excepts, checksign); \ 88} while (0) 89 90/* 91 * Test all the functions that compute cexp(x), within a given tolerance. 92 * The tolerance is specified in ulps. 93 */ 94#define testall_tol(x, result, tol) do { \ 95 test_tol(cexp, x, result, tol * DBL_ULP()); \ 96 test_tol(cexpf, x, result, tol * FLT_ULP()); \ 97} while (0) 98 99/* Various finite non-zero numbers to test. */ 100static const float finites[] = 101{ -42.0e20, -1.0, -1.0e-10, -0.0, 0.0, 1.0e-10, 1.0, 42.0e20 }; 102 103 104/* Tests for 0 */ 105static void 106test_zero(void) 107{ 108 109 /* cexp(0) = 1, no exceptions raised */ 110 testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1); 111 testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1); 112 testall(CMPLXL(0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1); 113 testall(CMPLXL(-0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1); 114} 115 116/* 117 * Tests for NaN. The signs of the results are indeterminate unless the 118 * imaginary part is 0. 119 */ 120static void 121test_nan(void) 122{ 123 unsigned i; 124 125 /* cexp(x + NaNi) = NaN + NaNi and optionally raises invalid */ 126 /* cexp(NaN + yi) = NaN + NaNi and optionally raises invalid (|y|>0) */ 127 for (i = 0; i < nitems(finites); i++) { 128 printf("# Run %d..\n", i); 129 testall(CMPLXL(finites[i], NAN), CMPLXL(NAN, NAN), 130 ALL_STD_EXCEPT & ~FE_INVALID, 0, 0); 131 if (finites[i] == 0.0) 132 continue; 133 /* XXX FE_INEXACT shouldn't be raised here */ 134 testall(CMPLXL(NAN, finites[i]), CMPLXL(NAN, NAN), 135 ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0); 136 } 137 138 /* cexp(NaN +- 0i) = NaN +- 0i */ 139 testall(CMPLXL(NAN, 0.0), CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 1); 140 testall(CMPLXL(NAN, -0.0), CMPLXL(NAN, -0.0), ALL_STD_EXCEPT, 0, 1); 141 142 /* cexp(inf + NaN i) = inf + nan i */ 143 testall(CMPLXL(INFINITY, NAN), CMPLXL(INFINITY, NAN), 144 ALL_STD_EXCEPT, 0, 0); 145 /* cexp(-inf + NaN i) = 0 */ 146 testall(CMPLXL(-INFINITY, NAN), CMPLXL(0.0, 0.0), 147 ALL_STD_EXCEPT, 0, 0); 148 /* cexp(NaN + NaN i) = NaN + NaN i */ 149 testall(CMPLXL(NAN, NAN), CMPLXL(NAN, NAN), 150 ALL_STD_EXCEPT, 0, 0); 151} 152 153static void 154test_inf(void) 155{ 156 unsigned i; 157 158 /* cexp(x + inf i) = NaN + NaNi and raises invalid */ 159 for (i = 0; i < nitems(finites); i++) { 160 printf("# Run %d..\n", i); 161 testall(CMPLXL(finites[i], INFINITY), CMPLXL(NAN, NAN), 162 ALL_STD_EXCEPT, FE_INVALID, 1); 163 } 164 /* cexp(-inf + yi) = 0 * (cos(y) + sin(y)i) */ 165 /* XXX shouldn't raise an inexact exception */ 166 testall(CMPLXL(-INFINITY, M_PI_4), CMPLXL(0.0, 0.0), 167 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 168 testall(CMPLXL(-INFINITY, 3 * M_PI_4), CMPLXL(-0.0, 0.0), 169 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 170 testall(CMPLXL(-INFINITY, 5 * M_PI_4), CMPLXL(-0.0, -0.0), 171 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 172 testall(CMPLXL(-INFINITY, 7 * M_PI_4), CMPLXL(0.0, -0.0), 173 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 174 testall(CMPLXL(-INFINITY, 0.0), CMPLXL(0.0, 0.0), 175 ALL_STD_EXCEPT, 0, 1); 176 testall(CMPLXL(-INFINITY, -0.0), CMPLXL(0.0, -0.0), 177 ALL_STD_EXCEPT, 0, 1); 178 /* cexp(inf + yi) = inf * (cos(y) + sin(y)i) (except y=0) */ 179 /* XXX shouldn't raise an inexact exception */ 180 testall(CMPLXL(INFINITY, M_PI_4), CMPLXL(INFINITY, INFINITY), 181 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 182 testall(CMPLXL(INFINITY, 3 * M_PI_4), CMPLXL(-INFINITY, INFINITY), 183 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 184 testall(CMPLXL(INFINITY, 5 * M_PI_4), CMPLXL(-INFINITY, -INFINITY), 185 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 186 testall(CMPLXL(INFINITY, 7 * M_PI_4), CMPLXL(INFINITY, -INFINITY), 187 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 188 /* cexp(inf + 0i) = inf + 0i */ 189 testall(CMPLXL(INFINITY, 0.0), CMPLXL(INFINITY, 0.0), 190 ALL_STD_EXCEPT, 0, 1); 191 testall(CMPLXL(INFINITY, -0.0), CMPLXL(INFINITY, -0.0), 192 ALL_STD_EXCEPT, 0, 1); 193} 194 195static void 196test_reals(void) 197{ 198 unsigned i; 199 200 for (i = 0; i < nitems(finites); i++) { 201 /* XXX could check exceptions more meticulously */ 202 printf("# Run %d..\n", i); 203 test(cexp, CMPLXL(finites[i], 0.0), 204 CMPLXL(exp(finites[i]), 0.0), 205 FE_INVALID | FE_DIVBYZERO, 0, 1); 206 test(cexp, CMPLXL(finites[i], -0.0), 207 CMPLXL(exp(finites[i]), -0.0), 208 FE_INVALID | FE_DIVBYZERO, 0, 1); 209 test_f(cexpf, CMPLXL(finites[i], 0.0), 210 CMPLXL(expf(finites[i]), 0.0), 211 FE_INVALID | FE_DIVBYZERO, 0, 1); 212 test_f(cexpf, CMPLXL(finites[i], -0.0), 213 CMPLXL(expf(finites[i]), -0.0), 214 FE_INVALID | FE_DIVBYZERO, 0, 1); 215 } 216} 217 218static void 219test_imaginaries(void) 220{ 221 unsigned i; 222 223 for (i = 0; i < nitems(finites); i++) { 224 printf("# Run %d..\n", i); 225 test(cexp, CMPLXL(0.0, finites[i]), 226 CMPLXL(cos(finites[i]), sin(finites[i])), 227 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 228 test(cexp, CMPLXL(-0.0, finites[i]), 229 CMPLXL(cos(finites[i]), sin(finites[i])), 230 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 231 test_f(cexpf, CMPLXL(0.0, finites[i]), 232 CMPLXL(cosf(finites[i]), sinf(finites[i])), 233 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 234 test_f(cexpf, CMPLXL(-0.0, finites[i]), 235 CMPLXL(cosf(finites[i]), sinf(finites[i])), 236 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 237 } 238} 239 240static void 241test_small(void) 242{ 243 static const double tests[] = { 244 /* csqrt(a + bI) = x + yI */ 245 /* a b x y */ 246 1.0, M_PI_4, M_SQRT2 * 0.5 * M_E, M_SQRT2 * 0.5 * M_E, 247 -1.0, M_PI_4, M_SQRT2 * 0.5 / M_E, M_SQRT2 * 0.5 / M_E, 248 2.0, M_PI_2, 0.0, M_E * M_E, 249 M_LN2, M_PI, -2.0, 0.0, 250 }; 251 double a, b; 252 double x, y; 253 unsigned i; 254 255 for (i = 0; i < nitems(tests); i += 4) { 256 printf("# Run %d..\n", i); 257 a = tests[i]; 258 b = tests[i + 1]; 259 x = tests[i + 2]; 260 y = tests[i + 3]; 261 test_tol(cexp, CMPLXL(a, b), CMPLXL(x, y), 3 * DBL_ULP()); 262 263 /* float doesn't have enough precision to pass these tests */ 264 if (x == 0 || y == 0) 265 continue; 266 test_tol(cexpf, CMPLXL(a, b), CMPLXL(x, y), 1 * FLT_ULP()); 267 } 268} 269 270/* Test inputs with a real part r that would overflow exp(r). */ 271static void 272test_large(void) 273{ 274 275 test_tol(cexp, CMPLXL(709.79, 0x1p-1074), 276 CMPLXL(INFINITY, 8.94674309915433533273e-16), DBL_ULP()); 277 test_tol(cexp, CMPLXL(1000, 0x1p-1074), 278 CMPLXL(INFINITY, 9.73344457300016401328e+110), DBL_ULP()); 279 test_tol(cexp, CMPLXL(1400, 0x1p-1074), 280 CMPLXL(INFINITY, 5.08228858149196559681e+284), DBL_ULP()); 281 test_tol(cexp, CMPLXL(900, 0x1.23456789abcdep-1020), 282 CMPLXL(INFINITY, 7.42156649354218408074e+83), DBL_ULP()); 283 test_tol(cexp, CMPLXL(1300, 0x1.23456789abcdep-1020), 284 CMPLXL(INFINITY, 3.87514844965996756704e+257), DBL_ULP()); 285 286 test_tol(cexpf, CMPLXL(88.73, 0x1p-149), 287 CMPLXL(INFINITY, 4.80265603e-07), 2 * FLT_ULP()); 288 test_tol(cexpf, CMPLXL(90, 0x1p-149), 289 CMPLXL(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP()); 290 test_tol(cexpf, CMPLXL(192, 0x1p-149), 291 CMPLXL(INFINITY, 3.396809344e+38f), 2 * FLT_ULP()); 292 test_tol(cexpf, CMPLXL(120, 0x1.234568p-120), 293 CMPLXL(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP()); 294 test_tol(cexpf, CMPLXL(170, 0x1.234568p-120), 295 CMPLXL(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP()); 296} 297 298int 299main(void) 300{ 301 302 printf("1..7\n"); 303 304 test_zero(); 305 printf("ok 1 - cexp zero\n"); 306 307 test_nan(); 308 printf("ok 2 - cexp nan\n"); 309 310 test_inf(); 311 printf("ok 3 - cexp inf\n"); 312 313 test_reals(); 314 printf("ok 4 - cexp reals\n"); 315 316 test_imaginaries(); 317 printf("ok 5 - cexp imaginaries\n"); 318 319 test_small(); 320 printf("ok 6 - cexp small\n"); 321 322 test_large(); 323 printf("ok 7 - cexp large\n"); 324 325 return (0); 326} 327