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 #include <sys/param.h> 33 34 #include <complex.h> 35 #include <fenv.h> 36 #include <float.h> 37 #include <math.h> 38 #include <stdio.h> 39 40 #include "test-utils.h" 41 42 #pragma STDC FENV_ACCESS ON 43 #pragma STDC CX_LIMITED_RANGE OFF 44 45 /* 46 * Test that a function returns the correct value and sets the 47 * exception flags correctly. The exceptmask specifies which 48 * exceptions we should check. We need to be lenient for several 49 * reasons, but mainly because on some architectures it's impossible 50 * to raise FE_OVERFLOW without raising FE_INEXACT. In some cases, 51 * whether cexp() raises an invalid exception is unspecified. 52 * 53 * These are macros instead of functions so that assert provides more 54 * meaningful error messages. 55 * 56 * XXX The volatile here is to avoid gcc's bogus constant folding and work 57 * around the lack of support for the FENV_ACCESS pragma. 58 */ 59 #define test_t(type, func, z, result, exceptmask, excepts, checksign) \ 60 do { \ 61 volatile long double complex _d = z; \ 62 volatile type complex _r = result; \ 63 ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \ 64 CHECK_CFPEQUAL_CS((func)(_d), (_r), (checksign)); \ 65 CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \ 66 #func, #z); \ 67 } while (0) 68 69 #define test(func, z, result, exceptmask, excepts, checksign) \ 70 test_t(double, func, z, result, exceptmask, excepts, checksign) 71 72 #define test_f(func, z, result, exceptmask, excepts, checksign) \ 73 test_t(float, func, z, result, exceptmask, excepts, checksign) 74 75 /* Test within a given tolerance. */ 76 #define test_tol(func, z, result, tol) do { \ 77 CHECK_CFPEQUAL_TOL((func)(z), (result), (tol), \ 78 FPE_ABS_ZERO | CS_BOTH); \ 79 } while (0) 80 81 /* Test all the functions that compute cexp(x). */ 82 #define testall(x, result, exceptmask, excepts, checksign) do { \ 83 test(cexp, x, result, exceptmask, excepts, checksign); \ 84 test_f(cexpf, x, result, exceptmask, excepts, checksign); \ 85 } while (0) 86 87 /* 88 * Test all the functions that compute cexp(x), within a given tolerance. 89 * The tolerance is specified in ulps. 90 */ 91 #define testall_tol(x, result, tol) do { \ 92 test_tol(cexp, x, result, tol * DBL_ULP()); \ 93 test_tol(cexpf, x, result, tol * FLT_ULP()); \ 94 } while (0) 95 96 /* Various finite non-zero numbers to test. */ 97 static const float finites[] = 98 { -42.0e20, -1.0, -1.0e-10, -0.0, 0.0, 1.0e-10, 1.0, 42.0e20 }; 99 100 101 /* Tests for 0 */ 102 ATF_TC_WITHOUT_HEAD(zero); 103 ATF_TC_BODY(zero, tc) 104 { 105 106 /* cexp(0) = 1, no exceptions raised */ 107 testall(0.0, 1.0, ALL_STD_EXCEPT, 0, 1); 108 testall(-0.0, 1.0, ALL_STD_EXCEPT, 0, 1); 109 testall(CMPLXL(0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1); 110 testall(CMPLXL(-0.0, -0.0), CMPLXL(1.0, -0.0), ALL_STD_EXCEPT, 0, 1); 111 } 112 113 /* 114 * Tests for NaN. The signs of the results are indeterminate unless the 115 * imaginary part is 0. 116 */ 117 ATF_TC_WITHOUT_HEAD(nan); 118 ATF_TC_BODY(nan, tc) 119 { 120 unsigned i; 121 122 /* cexp(x + NaNi) = NaN + NaNi and optionally raises invalid */ 123 /* cexp(NaN + yi) = NaN + NaNi and optionally raises invalid (|y|>0) */ 124 for (i = 0; i < nitems(finites); i++) { 125 testall(CMPLXL(finites[i], NAN), CMPLXL(NAN, NAN), 126 ALL_STD_EXCEPT & ~FE_INVALID, 0, 0); 127 if (finites[i] == 0.0) 128 continue; 129 /* XXX FE_INEXACT shouldn't be raised here */ 130 testall(CMPLXL(NAN, finites[i]), CMPLXL(NAN, NAN), 131 ALL_STD_EXCEPT & ~(FE_INVALID | FE_INEXACT), 0, 0); 132 } 133 134 /* cexp(NaN +- 0i) = NaN +- 0i */ 135 testall(CMPLXL(NAN, 0.0), CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 1); 136 testall(CMPLXL(NAN, -0.0), CMPLXL(NAN, -0.0), ALL_STD_EXCEPT, 0, 1); 137 138 /* cexp(inf + NaN i) = inf + nan i */ 139 testall(CMPLXL(INFINITY, NAN), CMPLXL(INFINITY, NAN), 140 ALL_STD_EXCEPT, 0, 0); 141 /* cexp(-inf + NaN i) = 0 */ 142 testall(CMPLXL(-INFINITY, NAN), CMPLXL(0.0, 0.0), 143 ALL_STD_EXCEPT, 0, 0); 144 /* cexp(NaN + NaN i) = NaN + NaN i */ 145 testall(CMPLXL(NAN, NAN), CMPLXL(NAN, NAN), 146 ALL_STD_EXCEPT, 0, 0); 147 } 148 149 ATF_TC_WITHOUT_HEAD(inf); 150 ATF_TC_BODY(inf, tc) 151 { 152 unsigned i; 153 154 /* cexp(x + inf i) = NaN + NaNi and raises invalid */ 155 for (i = 0; i < nitems(finites); i++) { 156 testall(CMPLXL(finites[i], INFINITY), CMPLXL(NAN, NAN), 157 ALL_STD_EXCEPT, FE_INVALID, 1); 158 } 159 /* cexp(-inf + yi) = 0 * (cos(y) + sin(y)i) */ 160 /* XXX shouldn't raise an inexact exception */ 161 testall(CMPLXL(-INFINITY, M_PI_4), CMPLXL(0.0, 0.0), 162 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 163 testall(CMPLXL(-INFINITY, 3 * M_PI_4), CMPLXL(-0.0, 0.0), 164 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 165 testall(CMPLXL(-INFINITY, 5 * M_PI_4), CMPLXL(-0.0, -0.0), 166 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 167 testall(CMPLXL(-INFINITY, 7 * M_PI_4), CMPLXL(0.0, -0.0), 168 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 169 testall(CMPLXL(-INFINITY, 0.0), CMPLXL(0.0, 0.0), 170 ALL_STD_EXCEPT, 0, 1); 171 testall(CMPLXL(-INFINITY, -0.0), CMPLXL(0.0, -0.0), 172 ALL_STD_EXCEPT, 0, 1); 173 /* cexp(inf + yi) = inf * (cos(y) + sin(y)i) (except y=0) */ 174 /* XXX shouldn't raise an inexact exception */ 175 testall(CMPLXL(INFINITY, M_PI_4), CMPLXL(INFINITY, INFINITY), 176 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 177 testall(CMPLXL(INFINITY, 3 * M_PI_4), CMPLXL(-INFINITY, INFINITY), 178 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 179 testall(CMPLXL(INFINITY, 5 * M_PI_4), CMPLXL(-INFINITY, -INFINITY), 180 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 181 testall(CMPLXL(INFINITY, 7 * M_PI_4), CMPLXL(INFINITY, -INFINITY), 182 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 183 /* cexp(inf + 0i) = inf + 0i */ 184 testall(CMPLXL(INFINITY, 0.0), CMPLXL(INFINITY, 0.0), 185 ALL_STD_EXCEPT, 0, 1); 186 testall(CMPLXL(INFINITY, -0.0), CMPLXL(INFINITY, -0.0), 187 ALL_STD_EXCEPT, 0, 1); 188 } 189 190 ATF_TC_WITHOUT_HEAD(reals); 191 ATF_TC_BODY(reals, tc) 192 { 193 unsigned i; 194 195 for (i = 0; i < nitems(finites); i++) { 196 /* XXX could check exceptions more meticulously */ 197 test(cexp, CMPLXL(finites[i], 0.0), 198 CMPLXL(exp(finites[i]), 0.0), 199 FE_INVALID | FE_DIVBYZERO, 0, 1); 200 test(cexp, CMPLXL(finites[i], -0.0), 201 CMPLXL(exp(finites[i]), -0.0), 202 FE_INVALID | FE_DIVBYZERO, 0, 1); 203 test_f(cexpf, CMPLXL(finites[i], 0.0), 204 CMPLXL(expf(finites[i]), 0.0), 205 FE_INVALID | FE_DIVBYZERO, 0, 1); 206 test_f(cexpf, CMPLXL(finites[i], -0.0), 207 CMPLXL(expf(finites[i]), -0.0), 208 FE_INVALID | FE_DIVBYZERO, 0, 1); 209 } 210 } 211 212 ATF_TC_WITHOUT_HEAD(imaginaries); 213 ATF_TC_BODY(imaginaries, tc) 214 { 215 unsigned i; 216 217 for (i = 0; i < nitems(finites); i++) { 218 test(cexp, CMPLXL(0.0, finites[i]), 219 CMPLXL(cos(finites[i]), sin(finites[i])), 220 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 221 test(cexp, CMPLXL(-0.0, finites[i]), 222 CMPLXL(cos(finites[i]), sin(finites[i])), 223 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 224 test_f(cexpf, CMPLXL(0.0, finites[i]), 225 CMPLXL(cosf(finites[i]), sinf(finites[i])), 226 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 227 test_f(cexpf, CMPLXL(-0.0, finites[i]), 228 CMPLXL(cosf(finites[i]), sinf(finites[i])), 229 ALL_STD_EXCEPT & ~FE_INEXACT, 0, 1); 230 } 231 } 232 233 ATF_TC_WITHOUT_HEAD(small); 234 ATF_TC_BODY(small, tc) 235 { 236 static const double tests[] = { 237 /* csqrt(a + bI) = x + yI */ 238 /* a b x y */ 239 1.0, M_PI_4, M_SQRT2 * 0.5 * M_E, M_SQRT2 * 0.5 * M_E, 240 -1.0, M_PI_4, M_SQRT2 * 0.5 / M_E, M_SQRT2 * 0.5 / M_E, 241 2.0, M_PI_2, 0.0, M_E * M_E, 242 M_LN2, M_PI, -2.0, 0.0, 243 }; 244 double a, b; 245 double x, y; 246 unsigned i; 247 248 for (i = 0; i < nitems(tests); i += 4) { 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). */ 263 ATF_TC_WITHOUT_HEAD(large); 264 ATF_TC_BODY(large, tc) 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 } 289 290 ATF_TP_ADD_TCS(tp) 291 { 292 ATF_TP_ADD_TC(tp, zero); 293 ATF_TP_ADD_TC(tp, nan); 294 ATF_TP_ADD_TC(tp, inf); 295 ATF_TP_ADD_TC(tp, reals); 296 ATF_TP_ADD_TC(tp, imaginaries); 297 ATF_TP_ADD_TC(tp, small); 298 ATF_TP_ADD_TC(tp, large); 299 300 return (atf_no_error()); 301 } 302