1 /* $OpenBSD: invctrig_test.c,v 1.1 2021/10/22 18:00:22 mbuhl Exp $ */ 2 /*- 3 * Copyright (c) 2008-2013 David Schultz <das@FreeBSD.org> 4 * All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 18 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 25 * SUCH DAMAGE. 26 */ 27 28 #include "macros.h" 29 30 /* 31 * Tests for casin[h](), cacos[h](), and catan[h](). 32 */ 33 34 #include <sys/cdefs.h> 35 __FBSDID("$FreeBSD$"); 36 37 #include <sys/param.h> 38 #include <complex.h> 39 #include <fenv.h> 40 #include <float.h> 41 #include <math.h> 42 #include <stdio.h> 43 44 #include "test-utils.h" 45 46 #pragma STDC FENV_ACCESS ON 47 #pragma STDC CX_LIMITED_RANGE OFF 48 49 /* 50 * Test that a function returns the correct value and sets the 51 * exception flags correctly. The exceptmask specifies which 52 * exceptions we should check. We need to be lenient for several 53 * reasons, but mainly because on some architectures it's impossible 54 * to raise FE_OVERFLOW without raising FE_INEXACT. 55 * 56 * These are macros instead of functions so that assert provides more 57 * meaningful error messages. 58 * 59 * XXX The volatile here is to avoid gcc's bogus constant folding and work 60 * around the lack of support for the FENV_ACCESS pragma. 61 */ 62 #define test_p(func, z, result, exceptmask, excepts, checksign) do { \ 63 volatile long double complex _d = z; \ 64 debug(" testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func, \ 65 creall(_d), cimagl(_d), creall(result), cimagl(result)); \ 66 ATF_REQUIRE_EQ(0, feclearexcept(FE_ALL_EXCEPT)); \ 67 CHECK_CFPEQUAL_CS((func)(_d), (result), (checksign)); \ 68 CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \ 69 #func, #z); \ 70 } while (0) 71 72 /* 73 * Test within a given tolerance. The tolerance indicates relative error 74 * in ulps. 75 */ 76 #define test_p_tol(func, z, result, tol) do { \ 77 debug(" testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func, \ 78 creall(z), cimagl(z), creall(result), cimagl(result)); \ 79 CHECK_CFPEQUAL_TOL((func)(z), (result), (tol), CS_BOTH); \ 80 } while (0) 81 82 /* These wrappers apply the identities f(conj(z)) = conj(f(z)). */ 83 #define test(func, z, result, exceptmask, excepts, checksign) do { \ 84 test_p(func, z, result, exceptmask, excepts, checksign); \ 85 test_p(func, conjl(z), conjl(result), exceptmask, excepts, checksign); \ 86 } while (0) 87 #define test_tol(func, z, result, tol) do { \ 88 test_p_tol(func, z, result, tol); \ 89 test_p_tol(func, conjl(z), conjl(result), tol); \ 90 } while (0) 91 92 /* Test the given function in all precisions. */ 93 #define testall(func, x, result, exceptmask, excepts, checksign) do { \ 94 test(func, x, result, exceptmask, excepts, checksign); \ 95 test(func##f, x, result, exceptmask, excepts, checksign); \ 96 } while (0) 97 #define testall_odd(func, x, result, exceptmask, excepts, checksign) do { \ 98 testall(func, x, result, exceptmask, excepts, checksign); \ 99 testall(func, -(x), -result, exceptmask, excepts, checksign); \ 100 } while (0) 101 #define testall_even(func, x, result, exceptmask, excepts, checksign) do { \ 102 testall(func, x, result, exceptmask, excepts, checksign); \ 103 testall(func, -(x), result, exceptmask, excepts, checksign); \ 104 } while (0) 105 106 /* 107 * Test the given function in all precisions, within a given tolerance. 108 * The tolerance is specified in ulps. 109 */ 110 #define testall_tol(func, x, result, tol) do { \ 111 test_tol(func, x, result, (tol) * DBL_ULP()); \ 112 test_tol(func##f, x, result, (tol) * FLT_ULP()); \ 113 } while (0) 114 #define testall_odd_tol(func, x, result, tol) do { \ 115 testall_tol(func, x, result, tol); \ 116 testall_tol(func, -(x), -result, tol); \ 117 } while (0) 118 #define testall_even_tol(func, x, result, tol) do { \ 119 testall_tol(func, x, result, tol); \ 120 testall_tol(func, -(x), result, tol); \ 121 } while (0) 122 123 static const long double 124 pi = 3.14159265358979323846264338327950280L, 125 c3pi = 9.42477796076937971538793014983850839L; 126 127 128 /* Tests for 0 */ 129 ATF_TC_WITHOUT_HEAD(zero); 130 ATF_TC_BODY(zero, tc) 131 { 132 long double complex zero = CMPLXL(0.0, 0.0); 133 134 testall_tol(cacosh, zero, CMPLXL(0.0, pi / 2), 1); 135 testall_tol(cacosh, -zero, CMPLXL(0.0, -pi / 2), 1); 136 testall_tol(cacos, zero, CMPLXL(pi / 2, -0.0), 1); 137 testall_tol(cacos, -zero, CMPLXL(pi / 2, 0.0), 1); 138 139 testall_odd(casinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 140 testall_odd(casin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 141 142 testall_odd(catanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 143 testall_odd(catan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 144 } 145 146 /* 147 * Tests for NaN inputs. 148 */ 149 ATF_TC_WITHOUT_HEAD(nan); 150 ATF_TC_BODY(nan, tc) 151 { 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 long double complex z; 232 233 /* 234 * IN CACOSH CACOS CASINH CATANH 235 * Inf,Inf Inf,pi/4 pi/4,-Inf Inf,pi/4 0,pi/2 236 * -Inf,Inf Inf,3pi/4 3pi/4,-Inf --- --- 237 * Inf,finite Inf,0 0,-Inf Inf,0 0,pi/2 238 * -Inf,finite Inf,pi pi,-Inf --- --- 239 * finite,Inf Inf,pi/2 pi/2,-Inf Inf,pi/2 0,pi/2 240 */ 241 z = CMPLXL(INFINITY, INFINITY); 242 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 4), 1); 243 testall_tol(cacosh, -z, CMPLXL(INFINITY, -c3pi / 4), 1); 244 testall_tol(cacos, z, CMPLXL(pi / 4, -INFINITY), 1); 245 testall_tol(cacos, -z, CMPLXL(c3pi / 4, INFINITY), 1); 246 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 4), 1); 247 testall_odd_tol(casin, z, CMPLXL(pi / 4, INFINITY), 1); 248 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 249 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 250 251 z = CMPLXL(INFINITY, 0.5); 252 /* XXX We allow a spurious inexact exception here. */ 253 testall(cacosh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH); 254 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi), 1); 255 testall(cacos, z, CMPLXL(0, -INFINITY), OPT_INEXACT, 0, CS_BOTH); 256 testall_tol(cacos, -z, CMPLXL(pi, INFINITY), 1); 257 testall_odd(casinh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH); 258 testall_odd_tol(casin, z, CMPLXL(pi / 2, INFINITY), 1); 259 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 260 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 261 262 z = CMPLXL(0.5, INFINITY); 263 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 2), 1); 264 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi / 2), 1); 265 testall_tol(cacos, z, CMPLXL(pi / 2, -INFINITY), 1); 266 testall_tol(cacos, -z, CMPLXL(pi / 2, INFINITY), 1); 267 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 2), 1); 268 /* XXX We allow a spurious inexact exception here. */ 269 testall_odd(casin, z, CMPLXL(0.0, INFINITY), OPT_INEXACT, 0, CS_BOTH); 270 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 271 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 272 } 273 274 /* Tests along the real and imaginary axes. */ 275 ATF_TC_WITHOUT_HEAD(axes); 276 ATF_TC_BODY(axes, tc) 277 { 278 static const long double nums[] = { 279 -2, -1, -0.5, 0.5, 1, 2 280 }; 281 long double complex z; 282 unsigned i; 283 284 for (i = 0; i < nitems(nums); i++) { 285 /* Real axis */ 286 z = CMPLXL(nums[i], 0.0); 287 if (fabsl(nums[i]) <= 1) { 288 testall_tol(cacosh, z, CMPLXL(0.0, acos(nums[i])), 1); 289 testall_tol(cacos, z, CMPLXL(acosl(nums[i]), -0.0), 1); 290 testall_tol(casin, z, CMPLXL(asinl(nums[i]), 0.0), 1); 291 testall_tol(catanh, z, CMPLXL(atanh(nums[i]), 0.0), 1); 292 } else { 293 testall_tol(cacosh, z, 294 CMPLXL(acosh(fabsl(nums[i])), 295 (nums[i] < 0) ? pi : 0), 1); 296 testall_tol(cacos, z, 297 CMPLXL((nums[i] < 0) ? pi : 0, 298 -acosh(fabsl(nums[i]))), 1); 299 testall_tol(casin, z, 300 CMPLXL(copysign(pi / 2, nums[i]), 301 acosh(fabsl(nums[i]))), 1); 302 testall_tol(catanh, z, 303 CMPLXL(atanh(1 / nums[i]), pi / 2), 1); 304 } 305 testall_tol(casinh, z, CMPLXL(asinh(nums[i]), 0.0), 1); 306 testall_tol(catan, z, CMPLXL(atan(nums[i]), 0), 1); 307 308 /* TODO: Test the imaginary axis. */ 309 } 310 } 311 312 ATF_TC_WITHOUT_HEAD(small); 313 ATF_TC_BODY(small, tc) 314 { 315 /* 316 * z = 0.75 + i 0.25 317 * acos(z) = Pi/4 - i ln(2)/2 318 * asin(z) = Pi/4 + i ln(2)/2 319 * atan(z) = atan(4)/2 + i ln(17/9)/4 320 */ 321 complex long double z; 322 complex long double acos_z; 323 complex long double asin_z; 324 complex long double atan_z; 325 326 z = CMPLXL(0.75L, 0.25L); 327 acos_z = CMPLXL(pi / 4, -0.34657359027997265470861606072908828L); 328 asin_z = CMPLXL(pi / 4, 0.34657359027997265470861606072908828L); 329 atan_z = CMPLXL(0.66290883183401623252961960521423782L, 330 0.15899719167999917436476103600701878L); 331 332 testall_tol(cacos, z, acos_z, 2); 333 testall_odd_tol(casin, z, asin_z, 2); 334 testall_odd_tol(catan, z, atan_z, 2); 335 } 336 337 /* Test inputs that might cause overflow in a sloppy implementation. */ 338 ATF_TC_WITHOUT_HEAD(large); 339 ATF_TC_BODY(large, tc) 340 { 341 /* TODO: Write these tests */ 342 } 343 344 ATF_TP_ADD_TCS(tp) 345 { 346 ATF_TP_ADD_TC(tp, zero); 347 ATF_TP_ADD_TC(tp, nan); 348 ATF_TP_ADD_TC(tp, inf); 349 ATF_TP_ADD_TC(tp, axes); 350 ATF_TP_ADD_TC(tp, small); 351 ATF_TP_ADD_TC(tp, large); 352 353 return (atf_no_error()); 354 } 355