invctrig_test.c revision 251119
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: head/tools/regression/lib/msun/test-invctrig.c 251119 2013-05-30 04:46:36Z das $"); 33 34#include <assert.h> 35#include <complex.h> 36#include <fenv.h> 37#include <float.h> 38#include <math.h> 39#include <stdio.h> 40 41#define ALL_STD_EXCEPT (FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \ 42 FE_OVERFLOW | FE_UNDERFLOW) 43#define OPT_INVALID (ALL_STD_EXCEPT & ~FE_INVALID) 44#define OPT_INEXACT (ALL_STD_EXCEPT & ~FE_INEXACT) 45#define FLT_ULP() ldexpl(1.0, 1 - FLT_MANT_DIG) 46#define DBL_ULP() ldexpl(1.0, 1 - DBL_MANT_DIG) 47#define LDBL_ULP() ldexpl(1.0, 1 - LDBL_MANT_DIG) 48 49#pragma STDC FENV_ACCESS ON 50#pragma STDC CX_LIMITED_RANGE OFF 51 52/* Flags that determine whether to check the signs of the result. */ 53#define CS_REAL 1 54#define CS_IMAG 2 55#define CS_BOTH (CS_REAL | CS_IMAG) 56 57#ifdef DEBUG 58#define debug(...) printf(__VA_ARGS__) 59#else 60#define debug(...) (void)0 61#endif 62 63/* 64 * Test that a function returns the correct value and sets the 65 * exception flags correctly. The exceptmask specifies which 66 * exceptions we should check. We need to be lenient for several 67 * reasons, but mainly because on some architectures it's impossible 68 * to raise FE_OVERFLOW without raising FE_INEXACT. 69 * 70 * These are macros instead of functions so that assert provides more 71 * meaningful error messages. 72 * 73 * XXX The volatile here is to avoid gcc's bogus constant folding and work 74 * around the lack of support for the FENV_ACCESS pragma. 75 */ 76#define test_p(func, z, result, exceptmask, excepts, checksign) do { \ 77 volatile long double complex _d = z; \ 78 debug(" testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func, \ 79 creall(_d), cimagl(_d), creall(result), cimagl(result)); \ 80 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ 81 assert(cfpequal((func)(_d), (result), (checksign))); \ 82 assert(((func), fetestexcept(exceptmask) == (excepts))); \ 83} while (0) 84 85/* 86 * Test within a given tolerance. The tolerance indicates relative error 87 * in ulps. 88 */ 89#define test_p_tol(func, z, result, tol) do { \ 90 volatile long double complex _d = z; \ 91 debug(" testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func, \ 92 creall(_d), cimagl(_d), creall(result), cimagl(result)); \ 93 assert(cfpequal_tol((func)(_d), (result), (tol))); \ 94} while (0) 95 96/* These wrappers apply the identities f(conj(z)) = conj(f(z)). */ 97#define test(func, z, result, exceptmask, excepts, checksign) do { \ 98 test_p(func, z, result, exceptmask, excepts, checksign); \ 99 test_p(func, conjl(z), conjl(result), exceptmask, excepts, checksign); \ 100} while (0) 101#define test_tol(func, z, result, tol) do { \ 102 test_p_tol(func, z, result, tol); \ 103 test_p_tol(func, conjl(z), conjl(result), tol); \ 104} while (0) 105 106/* Test the given function in all precisions. */ 107#define testall(func, x, result, exceptmask, excepts, checksign) do { \ 108 test(func, x, result, exceptmask, excepts, checksign); \ 109 test(func##f, x, result, exceptmask, excepts, checksign); \ 110} while (0) 111#define testall_odd(func, x, result, exceptmask, excepts, checksign) do { \ 112 testall(func, x, result, exceptmask, excepts, checksign); \ 113 testall(func, -(x), -result, exceptmask, excepts, checksign); \ 114} while (0) 115#define testall_even(func, x, result, exceptmask, excepts, checksign) do { \ 116 testall(func, x, result, exceptmask, excepts, checksign); \ 117 testall(func, -(x), result, exceptmask, excepts, checksign); \ 118} while (0) 119 120/* 121 * Test the given function in all precisions, within a given tolerance. 122 * The tolerance is specified in ulps. 123 */ 124#define testall_tol(func, x, result, tol) do { \ 125 test_tol(func, x, result, (tol) * DBL_ULP()); \ 126 test_tol(func##f, x, result, (tol) * FLT_ULP()); \ 127} while (0) 128#define testall_odd_tol(func, x, result, tol) do { \ 129 testall_tol(func, x, result, tol); \ 130 testall_tol(func, -(x), -result, tol); \ 131} while (0) 132#define testall_even_tol(func, x, result, tol) do { \ 133 testall_tol(func, x, result, tol); \ 134 testall_tol(func, -(x), result, tol); \ 135} while (0) 136 137static const long double 138pi = 3.14159265358979323846264338327950280L, 139c3pi = 9.42477796076937971538793014983850839L; 140 141/* 142 * Determine whether x and y are equal, with two special rules: 143 * +0.0 != -0.0 144 * NaN == NaN 145 * If checksign is 0, we compare the absolute values instead. 146 */ 147static int 148fpequal(long double x, long double y, int checksign) 149{ 150 if (isnan(x) && isnan(y)) 151 return (1); 152 if (checksign) 153 return (x == y && !signbit(x) == !signbit(y)); 154 else 155 return (fabsl(x) == fabsl(y)); 156} 157 158static int 159fpequal_tol(long double x, long double y, long double tol) 160{ 161 fenv_t env; 162 int ret; 163 164 if (isnan(x) && isnan(y)) 165 return (1); 166 if (!signbit(x) != !signbit(y)) 167 return (0); 168 if (x == y) 169 return (1); 170 if (tol == 0 || y == 0.0) 171 return (0); 172 173 /* Hard case: need to check the tolerance. */ 174 feholdexcept(&env); 175 ret = fabsl(x - y) <= fabsl(y * tol); 176 fesetenv(&env); 177 return (ret); 178} 179 180static int 181cfpequal(long double complex x, long double complex y, int checksign) 182{ 183 return (fpequal(creal(x), creal(y), checksign & CS_REAL) 184 && fpequal(cimag(x), cimag(y), checksign & CS_IMAG)); 185} 186 187static int 188cfpequal_tol(long double complex x, long double complex y, long double tol) 189{ 190 return (fpequal_tol(creal(x), creal(y), tol) 191 && fpequal_tol(cimag(x), cimag(y), tol)); 192} 193 194 195/* Tests for 0 */ 196void 197test_zero(void) 198{ 199 long double complex zero = CMPLXL(0.0, 0.0); 200 201 testall_tol(cacosh, zero, CMPLXL(0.0, pi / 2), 1); 202 testall_tol(cacosh, -zero, CMPLXL(0.0, -pi / 2), 1); 203 testall_tol(cacos, zero, CMPLXL(pi / 2, -0.0), 1); 204 testall_tol(cacos, -zero, CMPLXL(pi / 2, 0.0), 1); 205 206 testall_odd(casinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 207 testall_odd(casin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 208 209 testall_odd(catanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 210 testall_odd(catan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH); 211} 212 213/* 214 * Tests for NaN inputs. 215 */ 216void 217test_nan() 218{ 219 long double complex nan_nan = CMPLXL(NAN, NAN); 220 long double complex z; 221 222 /* 223 * IN CACOSH CACOS CASINH CATANH 224 * NaN,NaN NaN,NaN NaN,NaN NaN,NaN NaN,NaN 225 * finite,NaN NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN* 226 * NaN,finite NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN* 227 * NaN,Inf Inf,NaN NaN,-Inf ?Inf,NaN ?0,pi/2 228 * +-Inf,NaN Inf,NaN NaN,?Inf +-Inf,NaN +-0,NaN 229 * +-0,NaN NaN,NaN* pi/2,NaN NaN,NaN* +-0,NaN 230 * NaN,0 NaN,NaN* NaN,NaN* NaN,0 NaN,NaN* 231 * 232 * * = raise invalid 233 */ 234 z = nan_nan; 235 testall(cacosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 236 testall(cacos, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 237 testall(casinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 238 testall(casin, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 239 testall(catanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 240 testall(catan, z, nan_nan, ALL_STD_EXCEPT, 0, 0); 241 242 z = CMPLXL(0.5, NAN); 243 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0); 244 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0); 245 testall(casinh, z, nan_nan, OPT_INVALID, 0, 0); 246 testall(casin, z, nan_nan, OPT_INVALID, 0, 0); 247 testall(catanh, z, nan_nan, OPT_INVALID, 0, 0); 248 testall(catan, z, nan_nan, OPT_INVALID, 0, 0); 249 250 z = CMPLXL(NAN, 0.5); 251 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0); 252 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0); 253 testall(casinh, z, nan_nan, OPT_INVALID, 0, 0); 254 testall(casin, z, nan_nan, OPT_INVALID, 0, 0); 255 testall(catanh, z, nan_nan, OPT_INVALID, 0, 0); 256 testall(catan, z, nan_nan, OPT_INVALID, 0, 0); 257 258 z = CMPLXL(NAN, INFINITY); 259 testall(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 260 testall(cacosh, -z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 261 testall(cacos, z, CMPLXL(NAN, -INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG); 262 testall(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0); 263 testall(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG); 264 testall_tol(catanh, z, CMPLXL(0.0, pi / 2), 1); 265 testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, CS_IMAG); 266 267 z = CMPLXL(INFINITY, NAN); 268 testall_even(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 269 CS_REAL); 270 testall_even(cacos, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0); 271 testall_odd(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 272 CS_REAL); 273 testall_odd(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0); 274 testall_odd(catanh, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 275 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0.0), 1); 276 277 z = CMPLXL(0.0, NAN); 278 /* XXX We allow a spurious inexact exception here. */ 279 testall_even(cacosh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0); 280 testall_even_tol(cacos, z, CMPLXL(pi / 2, NAN), 1); 281 testall_odd(casinh, z, nan_nan, OPT_INVALID, 0, 0); 282 testall_odd(casin, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL); 283 testall_odd(catanh, z, CMPLXL(0.0, NAN), OPT_INVALID, 0, CS_REAL); 284 testall_odd(catan, z, nan_nan, OPT_INVALID, 0, 0); 285 286 z = CMPLXL(NAN, 0.0); 287 testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0); 288 testall(cacos, z, nan_nan, OPT_INVALID, 0, 0); 289 testall(casinh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG); 290 testall(casin, z, nan_nan, OPT_INVALID, 0, 0); 291 testall(catanh, z, nan_nan, OPT_INVALID, 0, CS_IMAG); 292 testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 0); 293} 294 295void 296test_inf(void) 297{ 298 long double complex z; 299 300 /* 301 * IN CACOSH CACOS CASINH CATANH 302 * Inf,Inf Inf,pi/4 pi/4,-Inf Inf,pi/4 0,pi/2 303 * -Inf,Inf Inf,3pi/4 3pi/4,-Inf --- --- 304 * Inf,finite Inf,0 0,-Inf Inf,0 0,pi/2 305 * -Inf,finite Inf,pi pi,-Inf --- --- 306 * finite,Inf Inf,pi/2 pi/2,-Inf Inf,pi/2 0,pi/2 307 */ 308 z = CMPLXL(INFINITY, INFINITY); 309 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 4), 1); 310 testall_tol(cacosh, -z, CMPLXL(INFINITY, -c3pi / 4), 1); 311 testall_tol(cacos, z, CMPLXL(pi / 4, -INFINITY), 1); 312 testall_tol(cacos, -z, CMPLXL(c3pi / 4, INFINITY), 1); 313 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 4), 1); 314 testall_odd_tol(casin, z, CMPLXL(pi / 4, INFINITY), 1); 315 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 316 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 317 318 z = CMPLXL(INFINITY, 0.5); 319 /* XXX We allow a spurious inexact exception here. */ 320 testall(cacosh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH); 321 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi), 1); 322 testall(cacos, z, CMPLXL(0, -INFINITY), OPT_INEXACT, 0, CS_BOTH); 323 testall_tol(cacos, -z, CMPLXL(pi, INFINITY), 1); 324 testall_odd(casinh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH); 325 testall_odd_tol(casin, z, CMPLXL(pi / 2, INFINITY), 1); 326 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 327 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 328 329 z = CMPLXL(0.5, INFINITY); 330 testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 2), 1); 331 testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi / 2), 1); 332 testall_tol(cacos, z, CMPLXL(pi / 2, -INFINITY), 1); 333 testall_tol(cacos, -z, CMPLXL(pi / 2, INFINITY), 1); 334 testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 2), 1); 335 /* XXX We allow a spurious inexact exception here. */ 336 testall_odd(casin, z, CMPLXL(0.0, INFINITY), OPT_INEXACT, 0, CS_BOTH); 337 testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1); 338 testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1); 339} 340 341/* Tests along the real and imaginary axes. */ 342void 343test_axes(void) 344{ 345 static const long double nums[] = { 346 -2, -1, -0.5, 0.5, 1, 2 347 }; 348 long double complex z; 349 int i; 350 351 for (i = 0; i < sizeof(nums) / sizeof(nums[0]); i++) { 352 /* Real axis */ 353 z = CMPLXL(nums[i], 0.0); 354 if (fabs(nums[i]) <= 1) { 355 testall_tol(cacosh, z, CMPLXL(0.0, acos(nums[i])), 1); 356 testall_tol(cacos, z, CMPLXL(acosl(nums[i]), -0.0), 1); 357 testall_tol(casin, z, CMPLXL(asinl(nums[i]), 0.0), 1); 358 testall_tol(catanh, z, CMPLXL(atanh(nums[i]), 0.0), 1); 359 } else { 360 testall_tol(cacosh, z, 361 CMPLXL(acosh(fabs(nums[i])), 362 (nums[i] < 0) ? pi : 0), 1); 363 testall_tol(cacos, z, 364 CMPLXL((nums[i] < 0) ? pi : 0, 365 -acosh(fabs(nums[i]))), 1); 366 testall_tol(casin, z, 367 CMPLXL(copysign(pi / 2, nums[i]), 368 acosh(fabs(nums[i]))), 1); 369 testall_tol(catanh, z, 370 CMPLXL(atanh(1 / nums[i]), pi / 2), 1); 371 } 372 testall_tol(casinh, z, CMPLXL(asinh(nums[i]), 0.0), 1); 373 testall_tol(catan, z, CMPLXL(atan(nums[i]), 0), 1); 374 375 /* TODO: Test the imaginary axis. */ 376 } 377} 378 379void 380test_small(void) 381{ 382 /* 383 * z = 0.75 + i 0.25 384 * acos(z) = Pi/4 - i ln(2)/2 385 * asin(z) = Pi/4 + i ln(2)/2 386 * atan(z) = atan(4)/2 + i ln(17/9)/4 387 */ 388 static const struct { 389 complex long double z; 390 complex long double acos_z; 391 complex long double asin_z; 392 complex long double atan_z; 393 } tests[] = { 394 { CMPLXL(0.75L, 0.25L), 395 CMPLXL(pi / 4, -0.34657359027997265470861606072908828L), 396 CMPLXL(pi / 4, 0.34657359027997265470861606072908828L), 397 CMPLXL(0.66290883183401623252961960521423782L, 398 0.15899719167999917436476103600701878L) }, 399 }; 400 int i; 401 402 for (i = 0; i < sizeof(tests) / sizeof(tests[0]); i++) { 403 testall_tol(cacos, tests[i].z, tests[i].acos_z, 2); 404 testall_odd_tol(casin, tests[i].z, tests[i].asin_z, 2); 405 testall_odd_tol(catan, tests[i].z, tests[i].atan_z, 2); 406 } 407} 408 409/* Test inputs that might cause overflow in a sloppy implementation. */ 410void 411test_large(void) 412{ 413 414 /* TODO: Write these tests */ 415} 416 417int 418main(int argc, char *argv[]) 419{ 420 421 printf("1..6\n"); 422 423 test_zero(); 424 printf("ok 1 - invctrig zero\n"); 425 426 test_nan(); 427 printf("ok 2 - invctrig nan\n"); 428 429 test_inf(); 430 printf("ok 3 - invctrig inf\n"); 431 432 test_axes(); 433 printf("ok 4 - invctrig axes\n"); 434 435 test_small(); 436 printf("ok 5 - invctrig small\n"); 437 438 test_large(); 439 printf("ok 6 - invctrig large\n"); 440 441 return (0); 442} 443