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/param.h> 32 #include <complex.h> 33 #include <fenv.h> 34 #include <float.h> 35 #include <math.h> 36 #include <stdio.h> 37 38 #include "test-utils.h" 39 40 #pragma STDC FENV_ACCESS ON 41 #pragma STDC CX_LIMITED_RANGE OFF 42 43 /* 44 * Test that a function returns the correct value and sets the 45 * exception flags correctly. The exceptmask specifies which 46 * exceptions we should check. We need to be lenient for several 47 * reasons, but mainly because on some architectures it's impossible 48 * to raise FE_OVERFLOW without raising FE_INEXACT. 49 * 50 * These are macros instead of functions so that assert provides more 51 * meaningful error messages. 52 * 53 * XXX The volatile here is to avoid gcc's bogus constant folding and work 54 * around the lack of support for the FENV_ACCESS pragma. 55 */ 56 #define test_p(func, z, result, exceptmask, excepts, checksign) do { \ 57 volatile long double complex _d = z; \ 58 debug(" testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func, \ 59 creall(_d), cimagl(_d), creall(result), cimagl(result)); \ 60 ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \ 61 CHECK_CFPEQUAL_CS((func)(_d), (result), (checksign)); \ 62 CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \ 63 #func, #z); \ 64 } while (0) 65 66 /* 67 * Test within a given tolerance. The tolerance indicates relative error 68 * in ulps. 69 */ 70 #define test_p_tol(func, z, result, tol) do { \ 71 debug(" testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func, \ 72 creall(z), cimagl(z), creall(result), cimagl(result)); \ 73 CHECK_CFPEQUAL_TOL((func)(z), (result), (tol), CS_BOTH); \ 74 } while (0) 75 76 /* These wrappers apply the identities f(conj(z)) = conj(f(z)). */ 77 #define test(func, z, result, exceptmask, excepts, checksign) do { \ 78 test_p(func, z, result, exceptmask, excepts, checksign); \ 79 test_p(func, conjl(z), conjl(result), exceptmask, excepts, checksign); \ 80 } while (0) 81 #define test_tol(func, z, result, tol) do { \ 82 test_p_tol(func, z, result, tol); \ 83 test_p_tol(func, conjl(z), conjl(result), tol); \ 84 } while (0) 85 86 /* Test the given function in all precisions. */ 87 #define testall(func, x, result, exceptmask, excepts, checksign) do { \ 88 test(func, x, result, exceptmask, excepts, checksign); \ 89 test(func##f, x, result, exceptmask, excepts, checksign); \ 90 } while (0) 91 #define testall_odd(func, x, result, exceptmask, excepts, checksign) do { \ 92 testall(func, x, result, exceptmask, excepts, checksign); \ 93 testall(func, -(x), -result, exceptmask, excepts, checksign); \ 94 } while (0) 95 #define testall_even(func, x, result, exceptmask, excepts, checksign) do { \ 96 testall(func, x, result, exceptmask, excepts, checksign); \ 97 testall(func, -(x), result, exceptmask, excepts, checksign); \ 98 } while (0) 99 100 /* 101 * Test the given function in all precisions, within a given tolerance. 102 * The tolerance is specified in ulps. 103 */ 104 #define testall_tol(func, x, result, tol) do { \ 105 test_tol(func, x, result, (tol) * DBL_ULP()); \ 106 test_tol(func##f, x, result, (tol) * FLT_ULP()); \ 107 } while (0) 108 #define testall_odd_tol(func, x, result, tol) do { \ 109 testall_tol(func, x, result, tol); \ 110 testall_tol(func, -(x), -result, tol); \ 111 } while (0) 112 #define testall_even_tol(func, x, result, tol) do { \ 113 testall_tol(func, x, result, tol); \ 114 testall_tol(func, -(x), result, tol); \ 115 } while (0) 116 117 static const long double 118 pi = 3.14159265358979323846264338327950280L, 119 c3pi = 9.42477796076937971538793014983850839L; 120 121 122 /* Tests for 0 */ 123 ATF_TC_WITHOUT_HEAD(zero); 124 ATF_TC_BODY(zero, tc) 125 { 126 #if defined(__riscv) 127 atf_tc_expect_death("https://bugs.freebsd.org/290099"); 128 #endif 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 #if defined(__riscv) 150 atf_tc_expect_death("https://bugs.freebsd.org/290099"); 151 #endif 152 long double complex nan_nan = CMPLXL(NAN, NAN); 153 long double complex z; 154 155 /* 156 * IN CACOSH CACOS CASINH CATANH 157 * NaN,NaN NaN,NaN NaN,NaN NaN,NaN NaN,NaN 158 * finite,NaN NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN* 159 * NaN,finite NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN* 160 * NaN,Inf Inf,NaN NaN,-Inf ?Inf,NaN ?0,pi/2 161 * +-Inf,NaN Inf,NaN NaN,?Inf +-Inf,NaN +-0,NaN 162 * +-0,NaN NaN,NaN* pi/2,NaN NaN,NaN* +-0,NaN 163 * NaN,0 NaN,NaN* NaN,NaN* NaN,0 NaN,NaN* 164 * 165 * * = raise invalid 166 */ 167 z = nan_nan; 168 testall(cacosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 169 testall(cacos, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 170 testall(casinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 171 testall(casin, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 172 testall(catanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 173 testall(catan, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 174 175 z = CMPLXL(0.5, NAN); 176 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0); 177 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0); 178 testall(casinh, z, nan_nan, OPT_INVALID, 0, 0); 179 testall(casin, z, nan_nan, OPT_INVALID, 0, 0); 180 testall(catanh, z, nan_nan, OPT_INVALID, 0, 0); 181 testall(catan, z, nan_nan, OPT_INVALID, 0, 0); 182 183 z = CMPLXL(NAN, 0.5); 184 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0); 185 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0); 186 testall(casinh, z, nan_nan, OPT_INVALID, 0, 0); 187 testall(casin, z, nan_nan, OPT_INVALID, 0, 0); 188 testall(catanh, z, nan_nan, OPT_INVALID, 0, 0); 189 testall(catan, z, nan_nan, OPT_INVALID, 0, 0); 190 191 z = CMPLXL(NAN, INFINITY); 192 testall(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 193 testall(cacosh, -z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 194 testall(cacos, z, CMPLXL(NAN, -INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG); 195 testall(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0); 196 testall(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG); 197 testall_tol(catanh, z, CMPLXL(0.0, pi / 2), 1); 198 testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, CS_IMAG); 199 200 z = CMPLXL(INFINITY, NAN); 201 testall_even(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 202 CS_REAL); 203 testall_even(cacos, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0); 204 testall_odd(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 205 CS_REAL); 206 testall_odd(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0); 207 testall_odd(catanh, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 208 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0.0), 1); 209 210 z = CMPLXL(0.0, NAN); 211 /* XXX We allow a spurious inexact exception here. */ 212 testall_even(cacosh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0); 213 testall_even_tol(cacos, z, CMPLXL(pi / 2, NAN), 1); 214 testall_odd(casinh, z, nan_nan, OPT_INVALID, 0, 0); 215 testall_odd(casin, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 216 testall_odd(catanh, z, CMPLXL(0.0, NAN), OPT_INVALID, 0, CS_REAL); 217 testall_odd(catan, z, nan_nan, OPT_INVALID, 0, 0); 218 219 z = CMPLXL(NAN, 0.0); 220 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0); 221 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0); 222 testall(casinh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG); 223 testall(casin, z, nan_nan, OPT_INVALID, 0, 0); 224 testall(catanh, z, nan_nan, OPT_INVALID, 0, CS_IMAG); 225 testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 0); 226 } 227 228 ATF_TC_WITHOUT_HEAD(inf); 229 ATF_TC_BODY(inf, tc) 230 { 231 #if defined(__riscv) 232 atf_tc_expect_death("https://bugs.freebsd.org/290099"); 233 #endif 234 long double complex z; 235 236 /* 237 * IN CACOSH CACOS CASINH CATANH 238 * Inf,Inf Inf,pi/4 pi/4,-Inf Inf,pi/4 0,pi/2 239 * -Inf,Inf Inf,3pi/4 3pi/4,-Inf --- --- 240 * Inf,finite Inf,0 0,-Inf Inf,0 0,pi/2 241 * -Inf,finite Inf,pi pi,-Inf --- --- 242 * finite,Inf Inf,pi/2 pi/2,-Inf Inf,pi/2 0,pi/2 243 */ 244 z = CMPLXL(INFINITY, INFINITY); 245 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 4), 1); 246 testall_tol(cacosh, -z, CMPLXL(INFINITY, -c3pi / 4), 1); 247 testall_tol(cacos, z, CMPLXL(pi / 4, -INFINITY), 1); 248 testall_tol(cacos, -z, CMPLXL(c3pi / 4, INFINITY), 1); 249 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 4), 1); 250 testall_odd_tol(casin, z, CMPLXL(pi / 4, INFINITY), 1); 251 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 252 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 253 254 z = CMPLXL(INFINITY, 0.5); 255 /* XXX We allow a spurious inexact exception here. */ 256 testall(cacosh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH); 257 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi), 1); 258 testall(cacos, z, CMPLXL(0, -INFINITY), OPT_INEXACT, 0, CS_BOTH); 259 testall_tol(cacos, -z, CMPLXL(pi, INFINITY), 1); 260 testall_odd(casinh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH); 261 testall_odd_tol(casin, z, CMPLXL(pi / 2, INFINITY), 1); 262 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 263 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 264 265 z = CMPLXL(0.5, INFINITY); 266 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 2), 1); 267 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi / 2), 1); 268 testall_tol(cacos, z, CMPLXL(pi / 2, -INFINITY), 1); 269 testall_tol(cacos, -z, CMPLXL(pi / 2, INFINITY), 1); 270 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 2), 1); 271 /* XXX We allow a spurious inexact exception here. */ 272 testall_odd(casin, z, CMPLXL(0.0, INFINITY), OPT_INEXACT, 0, CS_BOTH); 273 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 274 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 275 } 276 277 /* Tests along the real and imaginary axes. */ 278 ATF_TC_WITHOUT_HEAD(axes); 279 ATF_TC_BODY(axes, tc) 280 { 281 #if defined(__riscv) 282 atf_tc_expect_death("https://bugs.freebsd.org/290099"); 283 #endif 284 static const long double nums[] = { 285 -2, -1, -0.5, 0.5, 1, 2 286 }; 287 long double complex z; 288 unsigned i; 289 290 for (i = 0; i < nitems(nums); i++) { 291 /* Real axis */ 292 z = CMPLXL(nums[i], 0.0); 293 if (fabsl(nums[i]) <= 1) { 294 testall_tol(cacosh, z, CMPLXL(0.0, acos(nums[i])), 1); 295 testall_tol(cacos, z, CMPLXL(acosl(nums[i]), -0.0), 1); 296 testall_tol(casin, z, CMPLXL(asinl(nums[i]), 0.0), 1); 297 testall_tol(catanh, z, CMPLXL(atanh(nums[i]), 0.0), 1); 298 } else { 299 testall_tol(cacosh, z, 300 CMPLXL(acosh(fabsl(nums[i])), 301 (nums[i] < 0) ? pi : 0), 1); 302 testall_tol(cacos, z, 303 CMPLXL((nums[i] < 0) ? pi : 0, 304 -acosh(fabsl(nums[i]))), 1); 305 testall_tol(casin, z, 306 CMPLXL(copysign(pi / 2, nums[i]), 307 acosh(fabsl(nums[i]))), 1); 308 testall_tol(catanh, z, 309 CMPLXL(atanh(1 / nums[i]), pi / 2), 1); 310 } 311 testall_tol(casinh, z, CMPLXL(asinh(nums[i]), 0.0), 1); 312 testall_tol(catan, z, CMPLXL(atan(nums[i]), 0), 1); 313 314 /* TODO: Test the imaginary axis. */ 315 } 316 } 317 318 ATF_TC_WITHOUT_HEAD(small); 319 ATF_TC_BODY(small, tc) 320 { 321 #if defined(__riscv) 322 atf_tc_expect_death("https://bugs.freebsd.org/290099"); 323 #endif 324 /* 325 * z = 0.75 + i 0.25 326 * acos(z) = Pi/4 - i ln(2)/2 327 * asin(z) = Pi/4 + i ln(2)/2 328 * atan(z) = atan(4)/2 + i ln(17/9)/4 329 */ 330 complex long double z; 331 complex long double acos_z; 332 complex long double asin_z; 333 complex long double atan_z; 334 335 z = CMPLXL(0.75L, 0.25L); 336 acos_z = CMPLXL(pi / 4, -0.34657359027997265470861606072908828L); 337 asin_z = CMPLXL(pi / 4, 0.34657359027997265470861606072908828L); 338 atan_z = CMPLXL(0.66290883183401623252961960521423782L, 339 0.15899719167999917436476103600701878L); 340 341 testall_tol(cacos, z, acos_z, 2); 342 testall_odd_tol(casin, z, asin_z, 2); 343 testall_odd_tol(catan, z, atan_z, 2); 344 } 345 346 /* Test inputs that might cause overflow in a sloppy implementation. */ 347 ATF_TC_WITHOUT_HEAD(large); 348 ATF_TC_BODY(large, tc) 349 { 350 /* TODO: Write these tests */ 351 } 352 353 ATF_TP_ADD_TCS(tp) 354 { 355 ATF_TP_ADD_TC(tp, zero); 356 ATF_TP_ADD_TC(tp, nan); 357 ATF_TP_ADD_TC(tp, inf); 358 ATF_TP_ADD_TC(tp, axes); 359 ATF_TP_ADD_TC(tp, small); 360 ATF_TP_ADD_TC(tp, large); 361 362 return (atf_no_error()); 363 } 364