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