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 __FBSDID("$FreeBSD$"); 33 34 #include <sys/param.h> 35 #include <complex.h> 36 #include <fenv.h> 37 #include <float.h> 38 #include <math.h> 39 #include <stdio.h> 40 41 #include "test-utils.h" 42 43 #pragma STDC FENV_ACCESS ON 44 #pragma STDC CX_LIMITED_RANGE OFF 45 46 /* 47 * Test that a function returns the correct value and sets the 48 * exception flags correctly. The exceptmask specifies which 49 * exceptions we should check. We need to be lenient for several 50 * reasons, but mainly because on some architectures it's impossible 51 * to raise FE_OVERFLOW without raising FE_INEXACT. 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_p(func, z, result, exceptmask, excepts, checksign) do { \ 60 volatile long double complex _d = z; \ 61 debug(" testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func, \ 62 creall(_d), cimagl(_d), creall(result), cimagl(result)); \ 63 ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \ 64 CHECK_CFPEQUAL_CS((func)(_d), (result), (checksign)); \ 65 CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \ 66 #func, #z); \ 67 } while (0) 68 69 /* 70 * Test within a given tolerance. The tolerance indicates relative error 71 * in ulps. 72 */ 73 #define test_p_tol(func, z, result, tol) do { \ 74 debug(" testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func, \ 75 creall(z), cimagl(z), creall(result), cimagl(result)); \ 76 CHECK_CFPEQUAL_TOL((func)(z), (result), (tol), CS_BOTH); \ 77 } while (0) 78 79 /* These wrappers apply the identities f(conj(z)) = conj(f(z)). */ 80 #define test(func, z, result, exceptmask, excepts, checksign) do { \ 81 test_p(func, z, result, exceptmask, excepts, checksign); \ 82 test_p(func, conjl(z), conjl(result), exceptmask, excepts, checksign); \ 83 } while (0) 84 #define test_tol(func, z, result, tol) do { \ 85 test_p_tol(func, z, result, tol); \ 86 test_p_tol(func, conjl(z), conjl(result), tol); \ 87 } while (0) 88 89 /* Test the given function in all precisions. */ 90 #define testall(func, x, result, exceptmask, excepts, checksign) do { \ 91 test(func, x, result, exceptmask, excepts, checksign); \ 92 test(func##f, x, result, exceptmask, excepts, checksign); \ 93 } while (0) 94 #define testall_odd(func, x, result, exceptmask, excepts, checksign) do { \ 95 testall(func, x, result, exceptmask, excepts, checksign); \ 96 testall(func, -(x), -result, exceptmask, excepts, checksign); \ 97 } while (0) 98 #define testall_even(func, x, result, exceptmask, excepts, checksign) do { \ 99 testall(func, x, result, exceptmask, excepts, checksign); \ 100 testall(func, -(x), result, exceptmask, excepts, checksign); \ 101 } while (0) 102 103 /* 104 * Test the given function in all precisions, within a given tolerance. 105 * The tolerance is specified in ulps. 106 */ 107 #define testall_tol(func, x, result, tol) do { \ 108 test_tol(func, x, result, (tol) * DBL_ULP()); \ 109 test_tol(func##f, x, result, (tol) * FLT_ULP()); \ 110 } while (0) 111 #define testall_odd_tol(func, x, result, tol) do { \ 112 testall_tol(func, x, result, tol); \ 113 testall_tol(func, -(x), -result, tol); \ 114 } while (0) 115 #define testall_even_tol(func, x, result, tol) do { \ 116 testall_tol(func, x, result, tol); \ 117 testall_tol(func, -(x), result, tol); \ 118 } while (0) 119 120 static const long double 121 pi = 3.14159265358979323846264338327950280L, 122 c3pi = 9.42477796076937971538793014983850839L; 123 124 125 /* Tests for 0 */ 126 ATF_TC_WITHOUT_HEAD(zero); 127 ATF_TC_BODY(zero, tc) 128 { 129 long double complex zero = CMPLXL(0.0, 0.0); 130 131 testall_tol(cacosh, zero, CMPLXL(0.0, pi / 2), 1); 132 testall_tol(cacosh, -zero, CMPLXL(0.0, -pi / 2), 1); 133 testall_tol(cacos, zero, CMPLXL(pi / 2, -0.0), 1); 134 testall_tol(cacos, -zero, CMPLXL(pi / 2, 0.0), 1); 135 136 testall_odd(casinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 137 testall_odd(casin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 138 139 testall_odd(catanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 140 testall_odd(catan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 141 } 142 143 /* 144 * Tests for NaN inputs. 145 */ 146 ATF_TC_WITHOUT_HEAD(nan); 147 ATF_TC_BODY(nan, tc) 148 { 149 long double complex nan_nan = CMPLXL(NAN, NAN); 150 long double complex z; 151 152 /* 153 * IN CACOSH CACOS CASINH CATANH 154 * NaN,NaN NaN,NaN NaN,NaN NaN,NaN NaN,NaN 155 * finite,NaN NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN* 156 * NaN,finite NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN* 157 * NaN,Inf Inf,NaN NaN,-Inf ?Inf,NaN ?0,pi/2 158 * +-Inf,NaN Inf,NaN NaN,?Inf +-Inf,NaN +-0,NaN 159 * +-0,NaN NaN,NaN* pi/2,NaN NaN,NaN* +-0,NaN 160 * NaN,0 NaN,NaN* NaN,NaN* NaN,0 NaN,NaN* 161 * 162 * * = raise invalid 163 */ 164 z = nan_nan; 165 testall(cacosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 166 testall(cacos, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 167 testall(casinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 168 testall(casin, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 169 testall(catanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 170 testall(catan, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 171 172 z = CMPLXL(0.5, NAN); 173 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0); 174 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0); 175 testall(casinh, z, nan_nan, OPT_INVALID, 0, 0); 176 testall(casin, z, nan_nan, OPT_INVALID, 0, 0); 177 testall(catanh, z, nan_nan, OPT_INVALID, 0, 0); 178 testall(catan, z, nan_nan, OPT_INVALID, 0, 0); 179 180 z = CMPLXL(NAN, 0.5); 181 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0); 182 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0); 183 testall(casinh, z, nan_nan, OPT_INVALID, 0, 0); 184 testall(casin, z, nan_nan, OPT_INVALID, 0, 0); 185 testall(catanh, z, nan_nan, OPT_INVALID, 0, 0); 186 testall(catan, z, nan_nan, OPT_INVALID, 0, 0); 187 188 z = CMPLXL(NAN, INFINITY); 189 testall(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 190 testall(cacosh, -z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 191 testall(cacos, z, CMPLXL(NAN, -INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG); 192 testall(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0); 193 testall(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG); 194 testall_tol(catanh, z, CMPLXL(0.0, pi / 2), 1); 195 testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, CS_IMAG); 196 197 z = CMPLXL(INFINITY, NAN); 198 testall_even(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 199 CS_REAL); 200 testall_even(cacos, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0); 201 testall_odd(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 202 CS_REAL); 203 testall_odd(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0); 204 testall_odd(catanh, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 205 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0.0), 1); 206 207 z = CMPLXL(0.0, NAN); 208 /* XXX We allow a spurious inexact exception here. */ 209 testall_even(cacosh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0); 210 testall_even_tol(cacos, z, CMPLXL(pi / 2, NAN), 1); 211 testall_odd(casinh, z, nan_nan, OPT_INVALID, 0, 0); 212 testall_odd(casin, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 213 testall_odd(catanh, z, CMPLXL(0.0, NAN), OPT_INVALID, 0, CS_REAL); 214 testall_odd(catan, z, nan_nan, OPT_INVALID, 0, 0); 215 216 z = CMPLXL(NAN, 0.0); 217 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0); 218 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0); 219 testall(casinh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG); 220 testall(casin, z, nan_nan, OPT_INVALID, 0, 0); 221 testall(catanh, z, nan_nan, OPT_INVALID, 0, CS_IMAG); 222 testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 0); 223 } 224 225 ATF_TC_WITHOUT_HEAD(inf); 226 ATF_TC_BODY(inf, tc) 227 { 228 long double complex z; 229 230 /* 231 * IN CACOSH CACOS CASINH CATANH 232 * Inf,Inf Inf,pi/4 pi/4,-Inf Inf,pi/4 0,pi/2 233 * -Inf,Inf Inf,3pi/4 3pi/4,-Inf --- --- 234 * Inf,finite Inf,0 0,-Inf Inf,0 0,pi/2 235 * -Inf,finite Inf,pi pi,-Inf --- --- 236 * finite,Inf Inf,pi/2 pi/2,-Inf Inf,pi/2 0,pi/2 237 */ 238 z = CMPLXL(INFINITY, INFINITY); 239 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 4), 1); 240 testall_tol(cacosh, -z, CMPLXL(INFINITY, -c3pi / 4), 1); 241 testall_tol(cacos, z, CMPLXL(pi / 4, -INFINITY), 1); 242 testall_tol(cacos, -z, CMPLXL(c3pi / 4, INFINITY), 1); 243 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 4), 1); 244 testall_odd_tol(casin, z, CMPLXL(pi / 4, INFINITY), 1); 245 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 246 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 247 248 z = CMPLXL(INFINITY, 0.5); 249 /* XXX We allow a spurious inexact exception here. */ 250 testall(cacosh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH); 251 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi), 1); 252 testall(cacos, z, CMPLXL(0, -INFINITY), OPT_INEXACT, 0, CS_BOTH); 253 testall_tol(cacos, -z, CMPLXL(pi, INFINITY), 1); 254 testall_odd(casinh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH); 255 testall_odd_tol(casin, z, CMPLXL(pi / 2, INFINITY), 1); 256 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 257 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 258 259 z = CMPLXL(0.5, INFINITY); 260 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 2), 1); 261 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi / 2), 1); 262 testall_tol(cacos, z, CMPLXL(pi / 2, -INFINITY), 1); 263 testall_tol(cacos, -z, CMPLXL(pi / 2, INFINITY), 1); 264 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 2), 1); 265 /* XXX We allow a spurious inexact exception here. */ 266 testall_odd(casin, z, CMPLXL(0.0, INFINITY), OPT_INEXACT, 0, CS_BOTH); 267 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 268 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 269 } 270 271 /* Tests along the real and imaginary axes. */ 272 ATF_TC_WITHOUT_HEAD(axes); 273 ATF_TC_BODY(axes, tc) 274 { 275 static const long double nums[] = { 276 -2, -1, -0.5, 0.5, 1, 2 277 }; 278 long double complex z; 279 unsigned i; 280 281 for (i = 0; i < nitems(nums); i++) { 282 /* Real axis */ 283 z = CMPLXL(nums[i], 0.0); 284 if (fabsl(nums[i]) <= 1) { 285 testall_tol(cacosh, z, CMPLXL(0.0, acos(nums[i])), 1); 286 testall_tol(cacos, z, CMPLXL(acosl(nums[i]), -0.0), 1); 287 testall_tol(casin, z, CMPLXL(asinl(nums[i]), 0.0), 1); 288 testall_tol(catanh, z, CMPLXL(atanh(nums[i]), 0.0), 1); 289 } else { 290 testall_tol(cacosh, z, 291 CMPLXL(acosh(fabsl(nums[i])), 292 (nums[i] < 0) ? pi : 0), 1); 293 testall_tol(cacos, z, 294 CMPLXL((nums[i] < 0) ? pi : 0, 295 -acosh(fabsl(nums[i]))), 1); 296 testall_tol(casin, z, 297 CMPLXL(copysign(pi / 2, nums[i]), 298 acosh(fabsl(nums[i]))), 1); 299 testall_tol(catanh, z, 300 CMPLXL(atanh(1 / nums[i]), pi / 2), 1); 301 } 302 testall_tol(casinh, z, CMPLXL(asinh(nums[i]), 0.0), 1); 303 testall_tol(catan, z, CMPLXL(atan(nums[i]), 0), 1); 304 305 /* TODO: Test the imaginary axis. */ 306 } 307 } 308 309 ATF_TC_WITHOUT_HEAD(small); 310 ATF_TC_BODY(small, tc) 311 { 312 /* 313 * z = 0.75 + i 0.25 314 * acos(z) = Pi/4 - i ln(2)/2 315 * asin(z) = Pi/4 + i ln(2)/2 316 * atan(z) = atan(4)/2 + i ln(17/9)/4 317 */ 318 complex long double z; 319 complex long double acos_z; 320 complex long double asin_z; 321 complex long double atan_z; 322 323 z = CMPLXL(0.75L, 0.25L); 324 acos_z = CMPLXL(pi / 4, -0.34657359027997265470861606072908828L); 325 asin_z = CMPLXL(pi / 4, 0.34657359027997265470861606072908828L); 326 atan_z = CMPLXL(0.66290883183401623252961960521423782L, 327 0.15899719167999917436476103600701878L); 328 329 testall_tol(cacos, z, acos_z, 2); 330 testall_odd_tol(casin, z, asin_z, 2); 331 testall_odd_tol(catan, z, atan_z, 2); 332 } 333 334 /* Test inputs that might cause overflow in a sloppy implementation. */ 335 ATF_TC_WITHOUT_HEAD(large); 336 ATF_TC_BODY(large, tc) 337 { 338 /* TODO: Write these tests */ 339 } 340 341 ATF_TP_ADD_TCS(tp) 342 { 343 ATF_TP_ADD_TC(tp, zero); 344 ATF_TP_ADD_TC(tp, nan); 345 ATF_TP_ADD_TC(tp, inf); 346 ATF_TP_ADD_TC(tp, axes); 347 ATF_TP_ADD_TC(tp, small); 348 ATF_TP_ADD_TC(tp, large); 349 350 return (atf_no_error()); 351 } 352