1 /*- 2 * Copyright (c) 2008-2013 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 casin[h](), cacos[h](), and catan[h](). 29 */ 30 31 #include <sys/cdefs.h> 32 #include <sys/param.h> 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. 50 * 51 * These are macros instead of functions so that assert provides more 52 * meaningful error messages. 53 * 54 * XXX The volatile here is to avoid gcc's bogus constant folding and work 55 * around the lack of support for the FENV_ACCESS pragma. 56 */ 57 #define test_p(func, z, result, exceptmask, excepts, checksign) do { \ 58 volatile long double complex _d = z; \ 59 debug(" testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func, \ 60 creall(_d), cimagl(_d), creall(result), cimagl(result)); \ 61 ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \ 62 CHECK_CFPEQUAL_CS((func)(_d), (result), (checksign)); \ 63 CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \ 64 #func, #z); \ 65 } while (0) 66 67 /* 68 * Test within a given tolerance. The tolerance indicates relative error 69 * in ulps. 70 */ 71 #define test_p_tol(func, z, result, tol) do { \ 72 debug(" testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func, \ 73 creall(z), cimagl(z), creall(result), cimagl(result)); \ 74 CHECK_CFPEQUAL_TOL((func)(z), (result), (tol), CS_BOTH); \ 75 } while (0) 76 77 /* These wrappers apply the identities f(conj(z)) = conj(f(z)). */ 78 #define test(func, z, result, exceptmask, excepts, checksign) do { \ 79 test_p(func, z, result, exceptmask, excepts, checksign); \ 80 test_p(func, conjl(z), conjl(result), exceptmask, excepts, checksign); \ 81 } while (0) 82 #define test_tol(func, z, result, tol) do { \ 83 test_p_tol(func, z, result, tol); \ 84 test_p_tol(func, conjl(z), conjl(result), tol); \ 85 } while (0) 86 87 /* Test the given function in all precisions. */ 88 #define testall(func, x, result, exceptmask, excepts, checksign) do { \ 89 test(func, x, result, exceptmask, excepts, checksign); \ 90 test(func##f, x, result, exceptmask, excepts, checksign); \ 91 } while (0) 92 #define testall_odd(func, x, result, exceptmask, excepts, checksign) do { \ 93 testall(func, x, result, exceptmask, excepts, checksign); \ 94 testall(func, -(x), -result, exceptmask, excepts, checksign); \ 95 } while (0) 96 #define testall_even(func, x, result, exceptmask, excepts, checksign) do { \ 97 testall(func, x, result, exceptmask, excepts, checksign); \ 98 testall(func, -(x), result, exceptmask, excepts, checksign); \ 99 } while (0) 100 101 /* 102 * Test the given function in all precisions, within a given tolerance. 103 * The tolerance is specified in ulps. 104 */ 105 #define testall_tol(func, x, result, tol) do { \ 106 test_tol(func, x, result, (tol) * DBL_ULP()); \ 107 test_tol(func##f, x, result, (tol) * FLT_ULP()); \ 108 } while (0) 109 #define testall_odd_tol(func, x, result, tol) do { \ 110 testall_tol(func, x, result, tol); \ 111 testall_tol(func, -(x), -result, tol); \ 112 } while (0) 113 #define testall_even_tol(func, x, result, tol) do { \ 114 testall_tol(func, x, result, tol); \ 115 testall_tol(func, -(x), result, tol); \ 116 } while (0) 117 118 static const long double 119 pi = 3.14159265358979323846264338327950280L, 120 c3pi = 9.42477796076937971538793014983850839L; 121 122 123 /* Tests for 0 */ 124 ATF_TC_WITHOUT_HEAD(zero); 125 ATF_TC_BODY(zero, tc) 126 { 127 long double complex zero = CMPLXL(0.0, 0.0); 128 129 testall_tol(cacosh, zero, CMPLXL(0.0, pi / 2), 1); 130 testall_tol(cacosh, -zero, CMPLXL(0.0, -pi / 2), 1); 131 testall_tol(cacos, zero, CMPLXL(pi / 2, -0.0), 1); 132 testall_tol(cacos, -zero, CMPLXL(pi / 2, 0.0), 1); 133 134 testall_odd(casinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 135 testall_odd(casin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 136 137 testall_odd(catanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 138 testall_odd(catan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 139 } 140 141 /* 142 * Tests for NaN inputs. 143 */ 144 ATF_TC_WITHOUT_HEAD(nan); 145 ATF_TC_BODY(nan, tc) 146 { 147 long double complex nan_nan = CMPLXL(NAN, NAN); 148 long double complex z; 149 150 /* 151 * IN CACOSH CACOS CASINH CATANH 152 * NaN,NaN NaN,NaN NaN,NaN NaN,NaN NaN,NaN 153 * finite,NaN NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN* 154 * NaN,finite NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN* 155 * NaN,Inf Inf,NaN NaN,-Inf ?Inf,NaN ?0,pi/2 156 * +-Inf,NaN Inf,NaN NaN,?Inf +-Inf,NaN +-0,NaN 157 * +-0,NaN NaN,NaN* pi/2,NaN NaN,NaN* +-0,NaN 158 * NaN,0 NaN,NaN* NaN,NaN* NaN,0 NaN,NaN* 159 * 160 * * = raise invalid 161 */ 162 z = nan_nan; 163 testall(cacosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 164 testall(cacos, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 165 testall(casinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 166 testall(casin, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 167 testall(catanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 168 testall(catan, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 169 170 z = CMPLXL(0.5, NAN); 171 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0); 172 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0); 173 testall(casinh, z, nan_nan, OPT_INVALID, 0, 0); 174 testall(casin, z, nan_nan, OPT_INVALID, 0, 0); 175 testall(catanh, z, nan_nan, OPT_INVALID, 0, 0); 176 testall(catan, z, nan_nan, OPT_INVALID, 0, 0); 177 178 z = CMPLXL(NAN, 0.5); 179 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0); 180 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0); 181 testall(casinh, z, nan_nan, OPT_INVALID, 0, 0); 182 testall(casin, z, nan_nan, OPT_INVALID, 0, 0); 183 testall(catanh, z, nan_nan, OPT_INVALID, 0, 0); 184 testall(catan, z, nan_nan, OPT_INVALID, 0, 0); 185 186 z = CMPLXL(NAN, INFINITY); 187 testall(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 188 testall(cacosh, -z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 189 testall(cacos, z, CMPLXL(NAN, -INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG); 190 testall(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0); 191 testall(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG); 192 testall_tol(catanh, z, CMPLXL(0.0, pi / 2), 1); 193 testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, CS_IMAG); 194 195 z = CMPLXL(INFINITY, NAN); 196 testall_even(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 197 CS_REAL); 198 testall_even(cacos, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0); 199 testall_odd(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 200 CS_REAL); 201 testall_odd(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0); 202 testall_odd(catanh, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 203 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0.0), 1); 204 205 z = CMPLXL(0.0, NAN); 206 /* XXX We allow a spurious inexact exception here. */ 207 testall_even(cacosh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0); 208 testall_even_tol(cacos, z, CMPLXL(pi / 2, NAN), 1); 209 testall_odd(casinh, z, nan_nan, OPT_INVALID, 0, 0); 210 testall_odd(casin, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 211 testall_odd(catanh, z, CMPLXL(0.0, NAN), OPT_INVALID, 0, CS_REAL); 212 testall_odd(catan, z, nan_nan, OPT_INVALID, 0, 0); 213 214 z = CMPLXL(NAN, 0.0); 215 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0); 216 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0); 217 testall(casinh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG); 218 testall(casin, z, nan_nan, OPT_INVALID, 0, 0); 219 testall(catanh, z, nan_nan, OPT_INVALID, 0, CS_IMAG); 220 testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 0); 221 } 222 223 ATF_TC_WITHOUT_HEAD(inf); 224 ATF_TC_BODY(inf, tc) 225 { 226 long double complex z; 227 228 /* 229 * IN CACOSH CACOS CASINH CATANH 230 * Inf,Inf Inf,pi/4 pi/4,-Inf Inf,pi/4 0,pi/2 231 * -Inf,Inf Inf,3pi/4 3pi/4,-Inf --- --- 232 * Inf,finite Inf,0 0,-Inf Inf,0 0,pi/2 233 * -Inf,finite Inf,pi pi,-Inf --- --- 234 * finite,Inf Inf,pi/2 pi/2,-Inf Inf,pi/2 0,pi/2 235 */ 236 z = CMPLXL(INFINITY, INFINITY); 237 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 4), 1); 238 testall_tol(cacosh, -z, CMPLXL(INFINITY, -c3pi / 4), 1); 239 testall_tol(cacos, z, CMPLXL(pi / 4, -INFINITY), 1); 240 testall_tol(cacos, -z, CMPLXL(c3pi / 4, INFINITY), 1); 241 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 4), 1); 242 testall_odd_tol(casin, z, CMPLXL(pi / 4, INFINITY), 1); 243 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 244 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 245 246 z = CMPLXL(INFINITY, 0.5); 247 /* XXX We allow a spurious inexact exception here. */ 248 testall(cacosh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH); 249 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi), 1); 250 testall(cacos, z, CMPLXL(0, -INFINITY), OPT_INEXACT, 0, CS_BOTH); 251 testall_tol(cacos, -z, CMPLXL(pi, INFINITY), 1); 252 testall_odd(casinh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH); 253 testall_odd_tol(casin, z, CMPLXL(pi / 2, INFINITY), 1); 254 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 255 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 256 257 z = CMPLXL(0.5, INFINITY); 258 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 2), 1); 259 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi / 2), 1); 260 testall_tol(cacos, z, CMPLXL(pi / 2, -INFINITY), 1); 261 testall_tol(cacos, -z, CMPLXL(pi / 2, INFINITY), 1); 262 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 2), 1); 263 /* XXX We allow a spurious inexact exception here. */ 264 testall_odd(casin, z, CMPLXL(0.0, INFINITY), OPT_INEXACT, 0, CS_BOTH); 265 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 266 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 267 } 268 269 /* Tests along the real and imaginary axes. */ 270 ATF_TC_WITHOUT_HEAD(axes); 271 ATF_TC_BODY(axes, tc) 272 { 273 static const long double nums[] = { 274 -2, -1, -0.5, 0.5, 1, 2 275 }; 276 long double complex z; 277 unsigned i; 278 279 for (i = 0; i < nitems(nums); i++) { 280 /* Real axis */ 281 z = CMPLXL(nums[i], 0.0); 282 if (fabsl(nums[i]) <= 1) { 283 testall_tol(cacosh, z, CMPLXL(0.0, acos(nums[i])), 1); 284 testall_tol(cacos, z, CMPLXL(acosl(nums[i]), -0.0), 1); 285 testall_tol(casin, z, CMPLXL(asinl(nums[i]), 0.0), 1); 286 testall_tol(catanh, z, CMPLXL(atanh(nums[i]), 0.0), 1); 287 } else { 288 testall_tol(cacosh, z, 289 CMPLXL(acosh(fabsl(nums[i])), 290 (nums[i] < 0) ? pi : 0), 1); 291 testall_tol(cacos, z, 292 CMPLXL((nums[i] < 0) ? pi : 0, 293 -acosh(fabsl(nums[i]))), 1); 294 testall_tol(casin, z, 295 CMPLXL(copysign(pi / 2, nums[i]), 296 acosh(fabsl(nums[i]))), 1); 297 testall_tol(catanh, z, 298 CMPLXL(atanh(1 / nums[i]), pi / 2), 1); 299 } 300 testall_tol(casinh, z, CMPLXL(asinh(nums[i]), 0.0), 1); 301 testall_tol(catan, z, CMPLXL(atan(nums[i]), 0), 1); 302 303 /* TODO: Test the imaginary axis. */ 304 } 305 } 306 307 ATF_TC_WITHOUT_HEAD(small); 308 ATF_TC_BODY(small, tc) 309 { 310 /* 311 * z = 0.75 + i 0.25 312 * acos(z) = Pi/4 - i ln(2)/2 313 * asin(z) = Pi/4 + i ln(2)/2 314 * atan(z) = atan(4)/2 + i ln(17/9)/4 315 */ 316 complex long double z; 317 complex long double acos_z; 318 complex long double asin_z; 319 complex long double atan_z; 320 321 z = CMPLXL(0.75L, 0.25L); 322 acos_z = CMPLXL(pi / 4, -0.34657359027997265470861606072908828L); 323 asin_z = CMPLXL(pi / 4, 0.34657359027997265470861606072908828L); 324 atan_z = CMPLXL(0.66290883183401623252961960521423782L, 325 0.15899719167999917436476103600701878L); 326 327 testall_tol(cacos, z, acos_z, 2); 328 testall_odd_tol(casin, z, asin_z, 2); 329 testall_odd_tol(catan, z, atan_z, 2); 330 } 331 332 /* Test inputs that might cause overflow in a sloppy implementation. */ 333 ATF_TC_WITHOUT_HEAD(large); 334 ATF_TC_BODY(large, tc) 335 { 336 /* TODO: Write these tests */ 337 } 338 339 ATF_TP_ADD_TCS(tp) 340 { 341 ATF_TP_ADD_TC(tp, zero); 342 ATF_TP_ADD_TC(tp, nan); 343 ATF_TP_ADD_TC(tp, inf); 344 ATF_TP_ADD_TC(tp, axes); 345 ATF_TP_ADD_TC(tp, small); 346 ATF_TP_ADD_TC(tp, large); 347 348 return (atf_no_error()); 349 } 350