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 * $FreeBSD: src/tools/regression/lib/msun/test-invctrig.c,v 1.1 2013/05/31 00:27:55 svnexp Exp $ 27 */ 28 29 /* 30 * Tests for casin[h](), cacos[h](), and catan[h](). 31 */ 32 33 #include <assert.h> 34 #include <complex.h> 35 #include <fenv.h> 36 #include <float.h> 37 #include <math.h> 38 #include <stdio.h> 39 40 #define ALL_STD_EXCEPT (FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \ 41 FE_OVERFLOW | FE_UNDERFLOW) 42 #define OPT_INVALID (ALL_STD_EXCEPT & ~FE_INVALID) 43 #define OPT_INEXACT (ALL_STD_EXCEPT & ~FE_INEXACT) 44 #define FLT_ULP() ldexpl(1.0, 1 - FLT_MANT_DIG) 45 #define DBL_ULP() ldexpl(1.0, 1 - DBL_MANT_DIG) 46 #define LDBL_ULP() ldexpl(1.0, 1 - LDBL_MANT_DIG) 47 48 #pragma STDC FENV_ACCESS ON 49 #pragma STDC CX_LIMITED_RANGE OFF 50 51 /* Flags that determine whether to check the signs of the result. */ 52 #define CS_REAL 1 53 #define CS_IMAG 2 54 #define CS_BOTH (CS_REAL | CS_IMAG) 55 56 #ifdef DEBUG 57 #define debug(...) printf(__VA_ARGS__) 58 #else 59 #define debug(...) (void)0 60 #endif 61 62 /* 63 * Test that a function returns the correct value and sets the 64 * exception flags correctly. The exceptmask specifies which 65 * exceptions we should check. We need to be lenient for several 66 * reasons, but mainly because on some architectures it's impossible 67 * to raise FE_OVERFLOW without raising FE_INEXACT. 68 * 69 * These are macros instead of functions so that assert provides more 70 * meaningful error messages. 71 * 72 * XXX The volatile here is to avoid gcc's bogus constant folding and work 73 * around the lack of support for the FENV_ACCESS pragma. 74 */ 75 #define test_p(func, z, result, exceptmask, excepts, checksign) do { \ 76 volatile long double complex _d = z; \ 77 debug(" testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func, \ 78 creall(_d), cimagl(_d), creall(result), cimagl(result)); \ 79 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ 80 assert(cfpequal((func)(_d), (result), (checksign))); \ 81 assert(((func), fetestexcept(exceptmask) == (excepts))); \ 82 } while (0) 83 84 /* 85 * Test within a given tolerance. The tolerance indicates relative error 86 * in ulps. 87 */ 88 #define test_p_tol(func, z, result, tol) do { \ 89 volatile long double complex _d = z; \ 90 debug(" testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func, \ 91 creall(_d), cimagl(_d), creall(result), cimagl(result)); \ 92 assert(cfpequal_tol((func)(_d), (result), (tol))); \ 93 } while (0) 94 95 /* These wrappers apply the identities f(conj(z)) = conj(f(z)). */ 96 #define test(func, z, result, exceptmask, excepts, checksign) do { \ 97 test_p(func, z, result, exceptmask, excepts, checksign); \ 98 test_p(func, conjl(z), conjl(result), exceptmask, excepts, checksign); \ 99 } while (0) 100 #define test_tol(func, z, result, tol) do { \ 101 test_p_tol(func, z, result, tol); \ 102 test_p_tol(func, conjl(z), conjl(result), tol); \ 103 } while (0) 104 105 /* Test the given function in all precisions. */ 106 #define testall(func, x, result, exceptmask, excepts, checksign) do { \ 107 test(func, x, result, exceptmask, excepts, checksign); \ 108 test(func##f, x, result, exceptmask, excepts, checksign); \ 109 } while (0) 110 #define testall_odd(func, x, result, exceptmask, excepts, checksign) do { \ 111 testall(func, x, result, exceptmask, excepts, checksign); \ 112 testall(func, -(x), -result, exceptmask, excepts, checksign); \ 113 } while (0) 114 #define testall_even(func, x, result, exceptmask, excepts, checksign) do { \ 115 testall(func, x, result, exceptmask, excepts, checksign); \ 116 testall(func, -(x), result, exceptmask, excepts, checksign); \ 117 } while (0) 118 119 /* 120 * Test the given function in all precisions, within a given tolerance. 121 * The tolerance is specified in ulps. 122 */ 123 #define testall_tol(func, x, result, tol) do { \ 124 test_tol(func, x, result, (tol) * DBL_ULP()); \ 125 test_tol(func##f, x, result, (tol) * FLT_ULP()); \ 126 } while (0) 127 #define testall_odd_tol(func, x, result, tol) do { \ 128 testall_tol(func, x, result, tol); \ 129 testall_tol(func, -(x), -result, tol); \ 130 } while (0) 131 #define testall_even_tol(func, x, result, tol) do { \ 132 testall_tol(func, x, result, tol); \ 133 testall_tol(func, -(x), result, tol); \ 134 } while (0) 135 136 /* XXX static const long double */ 137 #define pi 3.14159265358979323846264338327950280L 138 #define c3pi 9.42477796076937971538793014983850839L 139 140 /* 141 * Determine whether x and y are equal, with two special rules: 142 * +0.0 != -0.0 143 * NaN == NaN 144 * If checksign is 0, we compare the absolute values instead. 145 */ 146 static int 147 fpequal(long double x, long double y, int checksign) 148 { 149 if (isnan(x) && isnan(y)) 150 return (1); 151 if (checksign) 152 return (x == y && !signbit(x) == !signbit(y)); 153 else 154 return (fabsl(x) == fabsl(y)); 155 } 156 157 static int 158 fpequal_tol(long double x, long double y, long double tol) 159 { 160 fenv_t env; 161 int ret; 162 163 if (isnan(x) && isnan(y)) 164 return (1); 165 if (!signbit(x) != !signbit(y)) 166 return (0); 167 if (x == y) 168 return (1); 169 if (tol == 0 || y == 0.0) 170 return (0); 171 172 /* Hard case: need to check the tolerance. */ 173 feholdexcept(&env); 174 ret = fabsl(x - y) <= fabsl(y * tol); 175 fesetenv(&env); 176 return (ret); 177 } 178 179 static int 180 cfpequal(long double complex x, long double complex y, int checksign) 181 { 182 return (fpequal(creal(x), creal(y), checksign & CS_REAL) 183 && fpequal(cimag(x), cimag(y), checksign & CS_IMAG)); 184 } 185 186 static int 187 cfpequal_tol(long double complex x, long double complex y, long double tol) 188 { 189 return (fpequal_tol(creal(x), creal(y), tol) 190 && fpequal_tol(cimag(x), cimag(y), tol)); 191 } 192 193 194 /* Tests for 0 */ 195 void 196 test_zero(void) 197 { 198 long double complex zero = CMPLXL(0.0, 0.0); 199 200 testall_tol(cacosh, zero, CMPLXL(0.0, pi / 2), 1); 201 testall_tol(cacosh, -zero, CMPLXL(0.0, -pi / 2), 1); 202 testall_tol(cacos, zero, CMPLXL(pi / 2, -0.0), 1); 203 testall_tol(cacos, -zero, CMPLXL(pi / 2, 0.0), 1); 204 205 testall_odd(casinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 206 testall_odd(casin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 207 208 testall_odd(catanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 209 testall_odd(catan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 210 } 211 212 /* 213 * Tests for NaN inputs. 214 */ 215 void 216 test_nan() 217 { 218 long double complex nan_nan = CMPLXL(NAN, NAN); 219 long double complex z; 220 221 /* 222 * IN CACOSH CACOS CASINH CATANH 223 * NaN,NaN NaN,NaN NaN,NaN NaN,NaN NaN,NaN 224 * finite,NaN NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN* 225 * NaN,finite NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN* 226 * NaN,Inf Inf,NaN NaN,-Inf ?Inf,NaN ?0,pi/2 227 * +-Inf,NaN Inf,NaN NaN,?Inf +-Inf,NaN +-0,NaN 228 * +-0,NaN NaN,NaN* pi/2,NaN NaN,NaN* +-0,NaN 229 * NaN,0 NaN,NaN* NaN,NaN* NaN,0 NaN,NaN* 230 * 231 * * = raise invalid 232 */ 233 z = nan_nan; 234 testall(cacosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 235 testall(cacos, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 236 testall(casinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 237 testall(casin, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 238 testall(catanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 239 testall(catan, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 240 241 z = CMPLXL(0.5, NAN); 242 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0); 243 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0); 244 testall(casinh, z, nan_nan, OPT_INVALID, 0, 0); 245 testall(casin, z, nan_nan, OPT_INVALID, 0, 0); 246 testall(catanh, z, nan_nan, OPT_INVALID, 0, 0); 247 testall(catan, z, nan_nan, OPT_INVALID, 0, 0); 248 249 z = CMPLXL(NAN, 0.5); 250 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0); 251 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0); 252 testall(casinh, z, nan_nan, OPT_INVALID, 0, 0); 253 testall(casin, z, nan_nan, OPT_INVALID, 0, 0); 254 testall(catanh, z, nan_nan, OPT_INVALID, 0, 0); 255 testall(catan, z, nan_nan, OPT_INVALID, 0, 0); 256 257 z = CMPLXL(NAN, INFINITY); 258 testall(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 259 testall(cacosh, -z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 260 testall(cacos, z, CMPLXL(NAN, -INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG); 261 testall(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0); 262 testall(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG); 263 testall_tol(catanh, z, CMPLXL(0.0, pi / 2), 1); 264 testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, CS_IMAG); 265 266 z = CMPLXL(INFINITY, NAN); 267 testall_even(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 268 CS_REAL); 269 testall_even(cacos, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0); 270 testall_odd(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 271 CS_REAL); 272 testall_odd(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0); 273 testall_odd(catanh, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 274 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0.0), 1); 275 276 z = CMPLXL(0.0, NAN); 277 /* XXX We allow a spurious inexact exception here. */ 278 testall_even(cacosh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0); 279 testall_even_tol(cacos, z, CMPLXL(pi / 2, NAN), 1); 280 testall_odd(casinh, z, nan_nan, OPT_INVALID, 0, 0); 281 testall_odd(casin, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 282 testall_odd(catanh, z, CMPLXL(0.0, NAN), OPT_INVALID, 0, CS_REAL); 283 testall_odd(catan, z, nan_nan, OPT_INVALID, 0, 0); 284 285 z = CMPLXL(NAN, 0.0); 286 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0); 287 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0); 288 testall(casinh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG); 289 testall(casin, z, nan_nan, OPT_INVALID, 0, 0); 290 testall(catanh, z, nan_nan, OPT_INVALID, 0, CS_IMAG); 291 testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 0); 292 } 293 294 void 295 test_inf(void) 296 { 297 long double complex z; 298 299 /* 300 * IN CACOSH CACOS CASINH CATANH 301 * Inf,Inf Inf,pi/4 pi/4,-Inf Inf,pi/4 0,pi/2 302 * -Inf,Inf Inf,3pi/4 3pi/4,-Inf --- --- 303 * Inf,finite Inf,0 0,-Inf Inf,0 0,pi/2 304 * -Inf,finite Inf,pi pi,-Inf --- --- 305 * finite,Inf Inf,pi/2 pi/2,-Inf Inf,pi/2 0,pi/2 306 */ 307 z = CMPLXL(INFINITY, INFINITY); 308 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 4), 1); 309 testall_tol(cacosh, -z, CMPLXL(INFINITY, -c3pi / 4), 1); 310 testall_tol(cacos, z, CMPLXL(pi / 4, -INFINITY), 1); 311 testall_tol(cacos, -z, CMPLXL(c3pi / 4, INFINITY), 1); 312 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 4), 1); 313 testall_odd_tol(casin, z, CMPLXL(pi / 4, INFINITY), 1); 314 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 315 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 316 317 z = CMPLXL(INFINITY, 0.5); 318 /* XXX We allow a spurious inexact exception here. */ 319 testall(cacosh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH); 320 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi), 1); 321 testall(cacos, z, CMPLXL(0, -INFINITY), OPT_INEXACT, 0, CS_BOTH); 322 testall_tol(cacos, -z, CMPLXL(pi, INFINITY), 1); 323 testall_odd(casinh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH); 324 testall_odd_tol(casin, z, CMPLXL(pi / 2, INFINITY), 1); 325 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 326 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 327 328 z = CMPLXL(0.5, INFINITY); 329 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 2), 1); 330 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi / 2), 1); 331 testall_tol(cacos, z, CMPLXL(pi / 2, -INFINITY), 1); 332 testall_tol(cacos, -z, CMPLXL(pi / 2, INFINITY), 1); 333 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 2), 1); 334 /* XXX We allow a spurious inexact exception here. */ 335 testall_odd(casin, z, CMPLXL(0.0, INFINITY), OPT_INEXACT, 0, CS_BOTH); 336 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 337 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 338 } 339 340 /* Tests along the real and imaginary axes. */ 341 void 342 test_axes(void) 343 { 344 static const long double nums[] = { 345 -2, -1, -0.5, 0.5, 1, 2 346 }; 347 long double complex z; 348 int i; 349 350 for (i = 0; i < sizeof(nums) / sizeof(nums[0]); i++) { 351 /* Real axis */ 352 z = CMPLXL(nums[i], 0.0); 353 if (fabs(nums[i]) <= 1) { 354 testall_tol(cacosh, z, CMPLXL(0.0, acos(nums[i])), 1); 355 testall_tol(cacos, z, CMPLXL(acosl(nums[i]), -0.0), 1); 356 testall_tol(casin, z, CMPLXL(asinl(nums[i]), 0.0), 1); 357 testall_tol(catanh, z, CMPLXL(atanh(nums[i]), 0.0), 1); 358 } else { 359 testall_tol(cacosh, z, 360 CMPLXL(acosh(fabs(nums[i])), 361 (nums[i] < 0) ? pi : 0), 1); 362 testall_tol(cacos, z, 363 CMPLXL((nums[i] < 0) ? pi : 0, 364 -acosh(fabs(nums[i]))), 1); 365 testall_tol(casin, z, 366 CMPLXL(copysign(pi / 2, nums[i]), 367 acosh(fabs(nums[i]))), 1); 368 testall_tol(catanh, z, 369 CMPLXL(atanh(1 / nums[i]), pi / 2), 1); 370 } 371 testall_tol(casinh, z, CMPLXL(asinh(nums[i]), 0.0), 1); 372 testall_tol(catan, z, CMPLXL(atan(nums[i]), 0), 1); 373 374 /* TODO: Test the imaginary axis. */ 375 } 376 } 377 378 void 379 test_small(void) 380 { 381 /* 382 * z = 0.75 + i 0.25 383 * acos(z) = Pi/4 - i ln(2)/2 384 * asin(z) = Pi/4 + i ln(2)/2 385 * atan(z) = atan(4)/2 + i ln(17/9)/4 386 */ 387 static const struct { 388 complex long double z; 389 complex long double acos_z; 390 complex long double asin_z; 391 complex long double atan_z; 392 } tests[] = { 393 { CMPLXL(0.75L, 0.25L), 394 CMPLXL(pi / 4, -0.34657359027997265470861606072908828L), 395 CMPLXL(pi / 4, 0.34657359027997265470861606072908828L), 396 CMPLXL(0.66290883183401623252961960521423782L, 397 0.15899719167999917436476103600701878L) }, 398 }; 399 int i; 400 401 for (i = 0; i < sizeof(tests) / sizeof(tests[0]); i++) { 402 testall_tol(cacos, tests[i].z, tests[i].acos_z, 2); 403 testall_odd_tol(casin, tests[i].z, tests[i].asin_z, 2); 404 testall_odd_tol(catan, tests[i].z, tests[i].atan_z, 2); 405 } 406 } 407 408 /* Test inputs that might cause overflow in a sloppy implementation. */ 409 void 410 test_large(void) 411 { 412 413 /* TODO: Write these tests */ 414 } 415 416 int 417 main(int argc, char *argv[]) 418 { 419 420 printf("1..6\n"); 421 422 test_zero(); 423 printf("ok 1 - invctrig zero\n"); 424 425 test_nan(); 426 printf("ok 2 - invctrig nan\n"); 427 428 test_inf(); 429 printf("ok 3 - invctrig inf\n"); 430 431 test_axes(); 432 printf("ok 4 - invctrig axes\n"); 433 434 test_small(); 435 printf("ok 5 - invctrig small\n"); 436 437 test_large(); 438 printf("ok 6 - invctrig large\n"); 439 440 return (0); 441 } 442