cexp_test.c revision 293267
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: stable/10/lib/msun/tests/cexp_test.c 293267 2016-01-06 20:21:40Z ngie $"); 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(func, z, result, exceptmask, excepts, checksign) do { \ 63 volatile long double complex _d = z; \ 64 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ 65 assert(cfpequal_cs((func)(_d), (result), (checksign))); \ 66 assert(((void)(func), fetestexcept(exceptmask) == (excepts))); \ 67} while (0) 68 69/* Test within a given tolerance. */ 70#define test_tol(func, z, result, tol) do { \ 71 volatile long double complex _d = z; \ 72 assert(cfpequal_tol((func)(_d), (result), (tol), \ 73 FPE_ABS_ZERO | CS_BOTH)); \ 74} while (0) 75 76/* Test all the functions that compute cexp(x). */ 77#define testall(x, result, exceptmask, excepts, checksign) do { \ 78 test(cexp, x, result, exceptmask, excepts, checksign); \ 79 test(cexpf, x, result, exceptmask, excepts, checksign); \ 80} while (0) 81 82/* 83 * Test all the functions that compute cexp(x), within a given tolerance. 84 * The tolerance is specified in ulps. 85 */ 86#define testall_tol(x, result, tol) do { \ 87 test_tol(cexp, x, result, tol * DBL_ULP()); \ 88 test_tol(cexpf, x, result, tol * FLT_ULP()); \ 89} while (0) 90 91/* Various finite non-zero numbers to test. */ 92static const float finites[] = 93{ -42.0e20, -1.0, -1.0e-10, -0.0, 0.0, 1.0e-10, 1.0, 42.0e20 }; 94 95 96/* Tests for 0 */ 97void 98test_zero(void) 99{ 100 101 /* cexp(0) = 1, no exceptions raised */ 102 testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1); 103 testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1); 104 testall(CMPLXL(0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1); 105 testall(CMPLXL(-0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1); 106} 107 108/* 109 * Tests for NaN. The signs of the results are indeterminate unless the 110 * imaginary part is 0. 111 */ 112void 113test_nan() 114{ 115 int i; 116 117 /* cexp(x + NaNi) = NaN + NaNi and optionally raises invalid */ 118 /* cexp(NaN + yi) = NaN + NaNi and optionally raises invalid (|y|>0) */ 119 for (i = 0; i < nitems(finites); i++) { 120 printf("# Run %d..\n", i); 121 testall(CMPLXL(finites[i], NAN), CMPLXL(NAN, NAN), 122 ALL_STD_EXCEPT & ~FE_INVALID, 0, 0); 123 if (finites[i] == 0.0) 124 continue; 125 /* XXX FE_INEXACT shouldn't be raised here */ 126 testall(CMPLXL(NAN, finites[i]), CMPLXL(NAN, NAN), 127 ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0); 128 } 129 130 /* cexp(NaN +- 0i) = NaN +- 0i */ 131 testall(CMPLXL(NAN, 0.0), CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 1); 132 testall(CMPLXL(NAN, -0.0), CMPLXL(NAN, -0.0), ALL_STD_EXCEPT, 0, 1); 133 134 /* cexp(inf + NaN i) = inf + nan i */ 135 testall(CMPLXL(INFINITY, NAN), CMPLXL(INFINITY, NAN), 136 ALL_STD_EXCEPT, 0, 0); 137 /* cexp(-inf + NaN i) = 0 */ 138 testall(CMPLXL(-INFINITY, NAN), CMPLXL(0.0, 0.0), 139 ALL_STD_EXCEPT, 0, 0); 140 /* cexp(NaN + NaN i) = NaN + NaN i */ 141 testall(CMPLXL(NAN, NAN), CMPLXL(NAN, NAN), 142 ALL_STD_EXCEPT, 0, 0); 143} 144 145void 146test_inf(void) 147{ 148 int i; 149 150 /* cexp(x + inf i) = NaN + NaNi and raises invalid */ 151 for (i = 0; i < nitems(finites); i++) { 152 printf("# Run %d..\n", i); 153 testall(CMPLXL(finites[i], INFINITY), CMPLXL(NAN, NAN), 154 ALL_STD_EXCEPT, FE_INVALID, 1); 155 } 156 /* cexp(-inf + yi) = 0 * (cos(y) + sin(y)i) */ 157 /* XXX shouldn't raise an inexact exception */ 158 testall(CMPLXL(-INFINITY, M_PI_4), CMPLXL(0.0, 0.0), 159 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 160 testall(CMPLXL(-INFINITY, 3 * M_PI_4), CMPLXL(-0.0, 0.0), 161 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 162 testall(CMPLXL(-INFINITY, 5 * M_PI_4), CMPLXL(-0.0, -0.0), 163 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 164 testall(CMPLXL(-INFINITY, 7 * M_PI_4), CMPLXL(0.0, -0.0), 165 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 166 testall(CMPLXL(-INFINITY, 0.0), CMPLXL(0.0, 0.0), 167 ALL_STD_EXCEPT, 0, 1); 168 testall(CMPLXL(-INFINITY, -0.0), CMPLXL(0.0, -0.0), 169 ALL_STD_EXCEPT, 0, 1); 170 /* cexp(inf + yi) = inf * (cos(y) + sin(y)i) (except y=0) */ 171 /* XXX shouldn't raise an inexact exception */ 172 testall(CMPLXL(INFINITY, M_PI_4), CMPLXL(INFINITY, INFINITY), 173 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 174 testall(CMPLXL(INFINITY, 3 * M_PI_4), CMPLXL(-INFINITY, INFINITY), 175 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 176 testall(CMPLXL(INFINITY, 5 * M_PI_4), CMPLXL(-INFINITY, -INFINITY), 177 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 178 testall(CMPLXL(INFINITY, 7 * M_PI_4), CMPLXL(INFINITY, -INFINITY), 179 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 180 /* cexp(inf + 0i) = inf + 0i */ 181 testall(CMPLXL(INFINITY, 0.0), CMPLXL(INFINITY, 0.0), 182 ALL_STD_EXCEPT, 0, 1); 183 testall(CMPLXL(INFINITY, -0.0), CMPLXL(INFINITY, -0.0), 184 ALL_STD_EXCEPT, 0, 1); 185} 186 187void 188test_reals(void) 189{ 190 int i; 191 192 for (i = 0; i < nitems(finites); i++) { 193 /* XXX could check exceptions more meticulously */ 194 printf("# Run %d..\n", i); 195 test(cexp, CMPLXL(finites[i], 0.0), 196 CMPLXL(exp(finites[i]), 0.0), 197 FE_INVALID | FE_DIVBYZERO, 0, 1); 198 test(cexp, CMPLXL(finites[i], -0.0), 199 CMPLXL(exp(finites[i]), -0.0), 200 FE_INVALID | FE_DIVBYZERO, 0, 1); 201 test(cexpf, CMPLXL(finites[i], 0.0), 202 CMPLXL(expf(finites[i]), 0.0), 203 FE_INVALID | FE_DIVBYZERO, 0, 1); 204 test(cexpf, CMPLXL(finites[i], -0.0), 205 CMPLXL(expf(finites[i]), -0.0), 206 FE_INVALID | FE_DIVBYZERO, 0, 1); 207 } 208} 209 210void 211test_imaginaries(void) 212{ 213 int i; 214 215 for (i = 0; i < nitems(finites); i++) { 216 printf("# Run %d..\n", i); 217 test(cexp, CMPLXL(0.0, finites[i]), 218 CMPLXL(cos(finites[i]), sin(finites[i])), 219 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 220 test(cexp, CMPLXL(-0.0, finites[i]), 221 CMPLXL(cos(finites[i]), sin(finites[i])), 222 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 223 test(cexpf, CMPLXL(0.0, finites[i]), 224 CMPLXL(cosf(finites[i]), sinf(finites[i])), 225 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 226 test(cexpf, CMPLXL(-0.0, finites[i]), 227 CMPLXL(cosf(finites[i]), sinf(finites[i])), 228 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 229 } 230} 231 232void 233test_small(void) 234{ 235 static const double tests[] = { 236 /* csqrt(a + bI) = x + yI */ 237 /* a b x y */ 238 1.0, M_PI_4, M_SQRT2 * 0.5 * M_E, M_SQRT2 * 0.5 * M_E, 239 -1.0, M_PI_4, M_SQRT2 * 0.5 / M_E, M_SQRT2 * 0.5 / M_E, 240 2.0, M_PI_2, 0.0, M_E * M_E, 241 M_LN2, M_PI, -2.0, 0.0, 242 }; 243 double a, b; 244 double x, y; 245 int i; 246 247 for (i = 0; i < nitems(tests); i += 4) { 248 printf("# Run %d..\n", i); 249 a = tests[i]; 250 b = tests[i + 1]; 251 x = tests[i + 2]; 252 y = tests[i + 3]; 253 test_tol(cexp, CMPLXL(a, b), CMPLXL(x, y), 3 * DBL_ULP()); 254 255 /* float doesn't have enough precision to pass these tests */ 256 if (x == 0 || y == 0) 257 continue; 258 test_tol(cexpf, CMPLXL(a, b), CMPLXL(x, y), 1 * FLT_ULP()); 259 } 260} 261 262/* Test inputs with a real part r that would overflow exp(r). */ 263void 264test_large(void) 265{ 266 267 test_tol(cexp, CMPLXL(709.79, 0x1p-1074), 268 CMPLXL(INFINITY, 8.94674309915433533273e-16), DBL_ULP()); 269 test_tol(cexp, CMPLXL(1000, 0x1p-1074), 270 CMPLXL(INFINITY, 9.73344457300016401328e+110), DBL_ULP()); 271 test_tol(cexp, CMPLXL(1400, 0x1p-1074), 272 CMPLXL(INFINITY, 5.08228858149196559681e+284), DBL_ULP()); 273 test_tol(cexp, CMPLXL(900, 0x1.23456789abcdep-1020), 274 CMPLXL(INFINITY, 7.42156649354218408074e+83), DBL_ULP()); 275 test_tol(cexp, CMPLXL(1300, 0x1.23456789abcdep-1020), 276 CMPLXL(INFINITY, 3.87514844965996756704e+257), DBL_ULP()); 277 278 test_tol(cexpf, CMPLXL(88.73, 0x1p-149), 279 CMPLXL(INFINITY, 4.80265603e-07), 2 * FLT_ULP()); 280 test_tol(cexpf, CMPLXL(90, 0x1p-149), 281 CMPLXL(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP()); 282 test_tol(cexpf, CMPLXL(192, 0x1p-149), 283 CMPLXL(INFINITY, 3.396809344e+38f), 2 * FLT_ULP()); 284 test_tol(cexpf, CMPLXL(120, 0x1.234568p-120), 285 CMPLXL(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP()); 286 test_tol(cexpf, CMPLXL(170, 0x1.234568p-120), 287 CMPLXL(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP()); 288} 289 290int 291main(int argc, char *argv[]) 292{ 293 294 printf("1..7\n"); 295 296 test_zero(); 297 printf("ok 1 - cexp zero\n"); 298 299 test_nan(); 300 printf("ok 2 - cexp nan\n"); 301 302 test_inf(); 303 printf("ok 3 - cexp inf\n"); 304 305#if defined(__i386__) 306 printf("not ok 4 - cexp reals # TODO: PR # 191676 fails assertion on i386\n"); 307#else 308 test_reals(); 309 printf("ok 4 - cexp reals\n"); 310#endif 311 312 test_imaginaries(); 313 printf("ok 5 - cexp imaginaries\n"); 314 315 test_small(); 316 printf("ok 6 - cexp small\n"); 317 318 test_large(); 319 printf("ok 7 - cexp large\n"); 320 321 return (0); 322} 323