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/param.h> 32 33 #include <complex.h> 34 #include <fenv.h> 35 #include <float.h> 36 #include <math.h> 37 #include <stdio.h> 38 39 #include "test-utils.h" 40 41 #pragma STDC FENV_ACCESS ON 42 #pragma STDC CX_LIMITED_RANGE OFF 43 44 /* 45 * Test that a function returns the correct value and sets the 46 * exception flags correctly. The exceptmask specifies which 47 * exceptions we should check. We need to be lenient for several 48 * reasons, but mainly because on some architectures it's impossible 49 * to raise FE_OVERFLOW without raising FE_INEXACT. In some cases, 50 * whether cexp() raises an invalid exception is unspecified. 51 * 52 * These are macros instead of functions so that assert provides more 53 * meaningful error messages. 54 * 55 * XXX The volatile here is to avoid gcc's bogus constant folding and work 56 * around the lack of support for the FENV_ACCESS pragma. 57 */ 58 #define test_t(type, func, z, result, exceptmask, excepts, checksign) \ 59 do { \ 60 volatile long double complex _d = z; \ 61 volatile type complex _r = result; \ 62 ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \ 63 CHECK_CFPEQUAL_CS((func)(_d), (_r), (checksign)); \ 64 CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \ 65 #func, #z); \ 66 } while (0) 67 68 #define test(func, z, result, exceptmask, excepts, checksign) \ 69 test_t(double, func, z, result, exceptmask, excepts, checksign) 70 71 #define test_f(func, z, result, exceptmask, excepts, checksign) \ 72 test_t(float, func, z, result, exceptmask, excepts, checksign) 73 74 /* Test within a given tolerance. */ 75 #define test_tol(func, z, result, tol) do { \ 76 CHECK_CFPEQUAL_TOL((func)(z), (result), (tol), \ 77 FPE_ABS_ZERO | CS_BOTH); \ 78 } while (0) 79 80 /* Test all the functions that compute cexp(x). */ 81 #define testall(x, result, exceptmask, excepts, checksign) do { \ 82 test(cexp, x, result, exceptmask, excepts, checksign); \ 83 test_f(cexpf, x, result, exceptmask, excepts, checksign); \ 84 } while (0) 85 86 /* 87 * Test all the functions that compute cexp(x), within a given tolerance. 88 * The tolerance is specified in ulps. 89 */ 90 #define testall_tol(x, result, tol) do { \ 91 test_tol(cexp, x, result, tol * DBL_ULP()); \ 92 test_tol(cexpf, x, result, tol * FLT_ULP()); \ 93 } while (0) 94 95 /* Various finite non-zero numbers to test. */ 96 static const float finites[] = 97 { -42.0e20, -1.0, -1.0e-10, -0.0, 0.0, 1.0e-10, 1.0, 42.0e20 }; 98 99 100 /* Tests for 0 */ 101 ATF_TC_WITHOUT_HEAD(zero); 102 ATF_TC_BODY(zero, tc) 103 { 104 105 /* cexp(0) = 1, no exceptions raised */ 106 testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1); 107 testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1); 108 testall(CMPLXL(0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1); 109 testall(CMPLXL(-0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1); 110 } 111 112 /* 113 * Tests for NaN. The signs of the results are indeterminate unless the 114 * imaginary part is 0. 115 */ 116 ATF_TC_WITHOUT_HEAD(nan); 117 ATF_TC_BODY(nan, tc) 118 { 119 unsigned i; 120 121 /* cexp(x + NaNi) = NaN + NaNi and optionally raises invalid */ 122 /* cexp(NaN + yi) = NaN + NaNi and optionally raises invalid (|y|>0) */ 123 for (i = 0; i < nitems(finites); i++) { 124 testall(CMPLXL(finites[i], NAN), CMPLXL(NAN, NAN), 125 ALL_STD_EXCEPT & ~FE_INVALID, 0, 0); 126 if (finites[i] == 0.0) 127 continue; 128 /* XXX FE_INEXACT shouldn't be raised here */ 129 testall(CMPLXL(NAN, finites[i]), CMPLXL(NAN, NAN), 130 ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0); 131 } 132 133 /* cexp(NaN +- 0i) = NaN +- 0i */ 134 testall(CMPLXL(NAN, 0.0), CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 1); 135 testall(CMPLXL(NAN, -0.0), CMPLXL(NAN, -0.0), ALL_STD_EXCEPT, 0, 1); 136 137 /* cexp(inf + NaN i) = inf + nan i */ 138 testall(CMPLXL(INFINITY, NAN), CMPLXL(INFINITY, NAN), 139 ALL_STD_EXCEPT, 0, 0); 140 /* cexp(-inf + NaN i) = 0 */ 141 testall(CMPLXL(-INFINITY, NAN), CMPLXL(0.0, 0.0), 142 ALL_STD_EXCEPT, 0, 0); 143 /* cexp(NaN + NaN i) = NaN + NaN i */ 144 testall(CMPLXL(NAN, NAN), CMPLXL(NAN, NAN), 145 ALL_STD_EXCEPT, 0, 0); 146 } 147 148 ATF_TC_WITHOUT_HEAD(inf); 149 ATF_TC_BODY(inf, tc) 150 { 151 unsigned i; 152 153 /* cexp(x + inf i) = NaN + NaNi and raises invalid */ 154 for (i = 0; i < nitems(finites); i++) { 155 testall(CMPLXL(finites[i], INFINITY), CMPLXL(NAN, NAN), 156 ALL_STD_EXCEPT, FE_INVALID, 1); 157 } 158 /* cexp(-inf + yi) = 0 * (cos(y) + sin(y)i) */ 159 /* XXX shouldn't raise an inexact exception */ 160 testall(CMPLXL(-INFINITY, M_PI_4), CMPLXL(0.0, 0.0), 161 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 162 testall(CMPLXL(-INFINITY, 3 * M_PI_4), CMPLXL(-0.0, 0.0), 163 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 164 testall(CMPLXL(-INFINITY, 5 * M_PI_4), CMPLXL(-0.0, -0.0), 165 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 166 testall(CMPLXL(-INFINITY, 7 * M_PI_4), CMPLXL(0.0, -0.0), 167 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 168 testall(CMPLXL(-INFINITY, 0.0), CMPLXL(0.0, 0.0), 169 ALL_STD_EXCEPT, 0, 1); 170 testall(CMPLXL(-INFINITY, -0.0), CMPLXL(0.0, -0.0), 171 ALL_STD_EXCEPT, 0, 1); 172 /* cexp(inf + yi) = inf * (cos(y) + sin(y)i) (except y=0) */ 173 /* XXX shouldn't raise an inexact exception */ 174 testall(CMPLXL(INFINITY, M_PI_4), CMPLXL(INFINITY, INFINITY), 175 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 176 testall(CMPLXL(INFINITY, 3 * M_PI_4), CMPLXL(-INFINITY, INFINITY), 177 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 178 testall(CMPLXL(INFINITY, 5 * M_PI_4), CMPLXL(-INFINITY, -INFINITY), 179 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 180 testall(CMPLXL(INFINITY, 7 * M_PI_4), CMPLXL(INFINITY, -INFINITY), 181 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 182 /* cexp(inf + 0i) = inf + 0i */ 183 testall(CMPLXL(INFINITY, 0.0), CMPLXL(INFINITY, 0.0), 184 ALL_STD_EXCEPT, 0, 1); 185 testall(CMPLXL(INFINITY, -0.0), CMPLXL(INFINITY, -0.0), 186 ALL_STD_EXCEPT, 0, 1); 187 } 188 189 ATF_TC_WITHOUT_HEAD(reals); 190 ATF_TC_BODY(reals, tc) 191 { 192 unsigned i; 193 194 for (i = 0; i < nitems(finites); i++) { 195 /* XXX could check exceptions more meticulously */ 196 test(cexp, CMPLXL(finites[i], 0.0), 197 CMPLXL(exp(finites[i]), 0.0), 198 FE_INVALID | FE_DIVBYZERO, 0, 1); 199 test(cexp, CMPLXL(finites[i], -0.0), 200 CMPLXL(exp(finites[i]), -0.0), 201 FE_INVALID | FE_DIVBYZERO, 0, 1); 202 test_f(cexpf, CMPLXL(finites[i], 0.0), 203 CMPLXL(expf(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 } 209 } 210 211 ATF_TC_WITHOUT_HEAD(imaginaries); 212 ATF_TC_BODY(imaginaries, tc) 213 { 214 unsigned i; 215 216 for (i = 0; i < nitems(finites); 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_f(cexpf, CMPLXL(0.0, finites[i]), 224 CMPLXL(cosf(finites[i]), sinf(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 } 230 } 231 232 ATF_TC_WITHOUT_HEAD(small); 233 ATF_TC_BODY(small, tc) 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 unsigned i; 246 247 for (i = 0; i < nitems(tests); i += 4) { 248 a = tests[i]; 249 b = tests[i + 1]; 250 x = tests[i + 2]; 251 y = tests[i + 3]; 252 test_tol(cexp, CMPLXL(a, b), CMPLXL(x, y), 3 * DBL_ULP()); 253 254 /* float doesn't have enough precision to pass these tests */ 255 if (x == 0 || y == 0) 256 continue; 257 test_tol(cexpf, CMPLXL(a, b), CMPLXL(x, y), 1 * FLT_ULP()); 258 } 259 } 260 261 /* Test inputs with a real part r that would overflow exp(r). */ 262 ATF_TC_WITHOUT_HEAD(large); 263 ATF_TC_BODY(large, tc) 264 { 265 266 test_tol(cexp, CMPLXL(709.79, 0x1p-1074), 267 CMPLXL(INFINITY, 8.94674309915433533273e-16), DBL_ULP()); 268 test_tol(cexp, CMPLXL(1000, 0x1p-1074), 269 CMPLXL(INFINITY, 9.73344457300016401328e+110), DBL_ULP()); 270 test_tol(cexp, CMPLXL(1400, 0x1p-1074), 271 CMPLXL(INFINITY, 5.08228858149196559681e+284), DBL_ULP()); 272 test_tol(cexp, CMPLXL(900, 0x1.23456789abcdep-1020), 273 CMPLXL(INFINITY, 7.42156649354218408074e+83), DBL_ULP()); 274 test_tol(cexp, CMPLXL(1300, 0x1.23456789abcdep-1020), 275 CMPLXL(INFINITY, 3.87514844965996756704e+257), DBL_ULP()); 276 277 test_tol(cexpf, CMPLXL(88.73, 0x1p-149), 278 CMPLXL(INFINITY, 4.80265603e-07), 2 * FLT_ULP()); 279 test_tol(cexpf, CMPLXL(90, 0x1p-149), 280 CMPLXL(INFINITY, 1.7101492622e-06f), 2 * FLT_ULP()); 281 test_tol(cexpf, CMPLXL(192, 0x1p-149), 282 CMPLXL(INFINITY, 3.396809344e+38f), 2 * FLT_ULP()); 283 test_tol(cexpf, CMPLXL(120, 0x1.234568p-120), 284 CMPLXL(INFINITY, 1.1163382522e+16f), 2 * FLT_ULP()); 285 test_tol(cexpf, CMPLXL(170, 0x1.234568p-120), 286 CMPLXL(INFINITY, 5.7878851079e+37f), 2 * FLT_ULP()); 287 } 288 289 ATF_TP_ADD_TCS(tp) 290 { 291 ATF_TP_ADD_TC(tp, zero); 292 ATF_TP_ADD_TC(tp, nan); 293 ATF_TP_ADD_TC(tp, inf); 294 ATF_TP_ADD_TC(tp, reals); 295 ATF_TP_ADD_TC(tp, imaginaries); 296 ATF_TP_ADD_TC(tp, small); 297 ATF_TP_ADD_TC(tp, large); 298 299 return (atf_no_error()); 300 } 301