invtrig_test.c revision 294243
1/*- 2 * Copyright (c) 2008 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 corner cases in the inverse trigonometric functions. Some 29 * accuracy tests are included as well, but these are very basic 30 * sanity checks, not intended to be comprehensive. 31 */ 32 33#include <sys/cdefs.h> 34__FBSDID("$FreeBSD: stable/10/lib/msun/tests/invtrig_test.c 294243 2016-01-18 03:55:40Z ngie $"); 35 36#include <assert.h> 37#include <fenv.h> 38#include <float.h> 39#include <math.h> 40#include <stdio.h> 41 42#include "test-utils.h" 43 44#pragma STDC FENV_ACCESS ON 45 46/* 47 * Test that a function returns the correct value and sets the 48 * exception flags correctly. A tolerance specifying the maximum 49 * relative error allowed may be specified. For the 'testall' 50 * functions, the tolerance is specified in ulps. 51 * 52 * These are macros instead of functions so that assert provides more 53 * meaningful error messages. 54 */ 55#define test_tol(func, x, result, tol, excepts) do { \ 56 volatile long double _in = (x), _out = (result); \ 57 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ 58 assert(fpequal_tol(func(_in), _out, (tol), CS_BOTH)); \ 59 assert(((void)func, fetestexcept(ALL_STD_EXCEPT) == (excepts))); \ 60} while (0) 61#define test(func, x, result, excepts) \ 62 test_tol(func, (x), (result), 0, (excepts)) 63 64#define _testall_tol(prefix, x, result, tol, excepts) do { \ 65 test_tol(prefix, (double)(x), (double)(result), \ 66 (tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts)); \ 67 test_tol(prefix##f, (float)(x), (float)(result), \ 68 (tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts)); \ 69} while (0) 70 71#if LDBL_PREC == 53 72#define testall_tol _testall_tol 73#else 74#define testall_tol(prefix, x, result, tol, excepts) do { \ 75 _testall_tol(prefix, x, result, tol, excepts); \ 76 test_tol(prefix##l, (x), (result), \ 77 (tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts)); \ 78} while (0) 79#endif 80 81#define testall(prefix, x, result, excepts) \ 82 testall_tol(prefix, (x), (result), 0, (excepts)) 83 84#define test2_tol(func, y, x, result, tol, excepts) do { \ 85 volatile long double _iny = (y), _inx = (x), _out = (result); \ 86 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ 87 assert(fpequal_tol(func(_iny, _inx), _out, (tol), CS_BOTH)); \ 88 assert(((void)func, fetestexcept(ALL_STD_EXCEPT) == (excepts))); \ 89} while (0) 90#define test2(func, y, x, result, excepts) \ 91 test2_tol(func, (y), (x), (result), 0, (excepts)) 92 93#define _testall2_tol(prefix, y, x, result, tol, excepts) do { \ 94 test2_tol(prefix, (double)(y), (double)(x), (double)(result), \ 95 (tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts)); \ 96 test2_tol(prefix##f, (float)(y), (float)(x), (float)(result), \ 97 (tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts)); \ 98} while (0) 99 100#if LDBL_PREC == 53 101#define testall2_tol _testall2_tol 102#else 103#define testall2_tol(prefix, y, x, result, tol, excepts) do { \ 104 _testall2_tol(prefix, y, x, result, tol, excepts); \ 105 test2_tol(prefix##l, (y), (x), (result), \ 106 (tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts)); \ 107} while (0) 108#endif 109 110#define testall2(prefix, y, x, result, excepts) \ 111 testall2_tol(prefix, (y), (x), (result), 0, (excepts)) 112 113long double 114pi = 3.14159265358979323846264338327950280e+00L, 115pio3 = 1.04719755119659774615421446109316766e+00L, 116c3pi = 9.42477796076937971538793014983850839e+00L, 117c5pi = 1.57079632679489661923132169163975140e+01L, 118c7pi = 2.19911485751285526692385036829565196e+01L, 119c5pio3 = 5.23598775598298873077107230546583851e+00L, 120sqrt2m1 = 4.14213562373095048801688724209698081e-01L; 121 122 123/* 124 * Test special case inputs in asin(), acos() and atan(): signed 125 * zeroes, infinities, and NaNs. 126 */ 127static void 128test_special(void) 129{ 130 131 testall(asin, 0.0, 0.0, 0); 132 testall(acos, 0.0, pi / 2, FE_INEXACT); 133 testall(atan, 0.0, 0.0, 0); 134 testall(asin, -0.0, -0.0, 0); 135 testall(acos, -0.0, pi / 2, FE_INEXACT); 136 testall(atan, -0.0, -0.0, 0); 137 138 testall(asin, INFINITY, NAN, FE_INVALID); 139 testall(acos, INFINITY, NAN, FE_INVALID); 140 testall(atan, INFINITY, pi / 2, FE_INEXACT); 141 testall(asin, -INFINITY, NAN, FE_INVALID); 142 testall(acos, -INFINITY, NAN, FE_INVALID); 143 testall(atan, -INFINITY, -pi / 2, FE_INEXACT); 144 145 testall(asin, NAN, NAN, 0); 146 testall(acos, NAN, NAN, 0); 147 testall(atan, NAN, NAN, 0); 148} 149 150/* 151 * Test special case inputs in atan2(), where the exact value of y/x is 152 * zero or non-finite. 153 */ 154static void 155test_special_atan2(void) 156{ 157 long double z; 158 int e; 159 160 testall2(atan2, 0.0, -0.0, pi, FE_INEXACT); 161 testall2(atan2, -0.0, -0.0, -pi, FE_INEXACT); 162 testall2(atan2, 0.0, 0.0, 0.0, 0); 163 testall2(atan2, -0.0, 0.0, -0.0, 0); 164 165 testall2(atan2, INFINITY, -INFINITY, c3pi / 4, FE_INEXACT); 166 testall2(atan2, -INFINITY, -INFINITY, -c3pi / 4, FE_INEXACT); 167 testall2(atan2, INFINITY, INFINITY, pi / 4, FE_INEXACT); 168 testall2(atan2, -INFINITY, INFINITY, -pi / 4, FE_INEXACT); 169 170 /* Tests with one input in the range (0, Inf]. */ 171 z = 1.23456789L; 172 for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP; e++) { 173 test2(atan2f, 0.0, ldexpf(z, e), 0.0, 0); 174 test2(atan2f, -0.0, ldexpf(z, e), -0.0, 0); 175 test2(atan2f, 0.0, ldexpf(-z, e), (float)pi, FE_INEXACT); 176 test2(atan2f, -0.0, ldexpf(-z, e), (float)-pi, FE_INEXACT); 177 test2(atan2f, ldexpf(z, e), 0.0, (float)pi / 2, FE_INEXACT); 178 test2(atan2f, ldexpf(z, e), -0.0, (float)pi / 2, FE_INEXACT); 179 test2(atan2f, ldexpf(-z, e), 0.0, (float)-pi / 2, FE_INEXACT); 180 test2(atan2f, ldexpf(-z, e), -0.0, (float)-pi / 2, FE_INEXACT); 181 } 182 for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP; e++) { 183 test2(atan2, 0.0, ldexp(z, e), 0.0, 0); 184 test2(atan2, -0.0, ldexp(z, e), -0.0, 0); 185 test2(atan2, 0.0, ldexp(-z, e), (double)pi, FE_INEXACT); 186 test2(atan2, -0.0, ldexp(-z, e), (double)-pi, FE_INEXACT); 187 test2(atan2, ldexp(z, e), 0.0, (double)pi / 2, FE_INEXACT); 188 test2(atan2, ldexp(z, e), -0.0, (double)pi / 2, FE_INEXACT); 189 test2(atan2, ldexp(-z, e), 0.0, (double)-pi / 2, FE_INEXACT); 190 test2(atan2, ldexp(-z, e), -0.0, (double)-pi / 2, FE_INEXACT); 191 } 192 for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP; e++) { 193 test2(atan2l, 0.0, ldexpl(z, e), 0.0, 0); 194 test2(atan2l, -0.0, ldexpl(z, e), -0.0, 0); 195 test2(atan2l, 0.0, ldexpl(-z, e), pi, FE_INEXACT); 196 test2(atan2l, -0.0, ldexpl(-z, e), -pi, FE_INEXACT); 197 test2(atan2l, ldexpl(z, e), 0.0, pi / 2, FE_INEXACT); 198 test2(atan2l, ldexpl(z, e), -0.0, pi / 2, FE_INEXACT); 199 test2(atan2l, ldexpl(-z, e), 0.0, -pi / 2, FE_INEXACT); 200 test2(atan2l, ldexpl(-z, e), -0.0, -pi / 2, FE_INEXACT); 201 } 202 203 /* Tests with one input in the range (0, Inf). */ 204 for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP - 1; e++) { 205 test2(atan2f, ldexpf(z, e), INFINITY, 0.0, 0); 206 test2(atan2f, ldexpf(-z,e), INFINITY, -0.0, 0); 207 test2(atan2f, ldexpf(z, e), -INFINITY, (float)pi, FE_INEXACT); 208 test2(atan2f, ldexpf(-z,e), -INFINITY, (float)-pi, FE_INEXACT); 209 test2(atan2f, INFINITY, ldexpf(z,e), (float)pi/2, FE_INEXACT); 210 test2(atan2f, INFINITY, ldexpf(-z,e), (float)pi/2, FE_INEXACT); 211 test2(atan2f, -INFINITY, ldexpf(z,e), (float)-pi/2,FE_INEXACT); 212 test2(atan2f, -INFINITY, ldexpf(-z,e),(float)-pi/2,FE_INEXACT); 213 } 214 for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP - 1; e++) { 215 test2(atan2, ldexp(z, e), INFINITY, 0.0, 0); 216 test2(atan2, ldexp(-z,e), INFINITY, -0.0, 0); 217 test2(atan2, ldexp(z, e), -INFINITY, (double)pi, FE_INEXACT); 218 test2(atan2, ldexp(-z,e), -INFINITY, (double)-pi, FE_INEXACT); 219 test2(atan2, INFINITY, ldexp(z,e), (double)pi/2, FE_INEXACT); 220 test2(atan2, INFINITY, ldexp(-z,e), (double)pi/2, FE_INEXACT); 221 test2(atan2, -INFINITY, ldexp(z,e), (double)-pi/2,FE_INEXACT); 222 test2(atan2, -INFINITY, ldexp(-z,e),(double)-pi/2,FE_INEXACT); 223 } 224 for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP - 1; e++) { 225 test2(atan2l, ldexpl(z, e), INFINITY, 0.0, 0); 226 test2(atan2l, ldexpl(-z,e), INFINITY, -0.0, 0); 227 test2(atan2l, ldexpl(z, e), -INFINITY, pi, FE_INEXACT); 228 test2(atan2l, ldexpl(-z,e), -INFINITY, -pi, FE_INEXACT); 229 test2(atan2l, INFINITY, ldexpl(z, e), pi / 2, FE_INEXACT); 230 test2(atan2l, INFINITY, ldexpl(-z, e), pi / 2, FE_INEXACT); 231 test2(atan2l, -INFINITY, ldexpl(z, e), -pi / 2, FE_INEXACT); 232 test2(atan2l, -INFINITY, ldexpl(-z, e), -pi / 2, FE_INEXACT); 233 } 234} 235 236/* 237 * Test various inputs to asin(), acos() and atan() and verify that the 238 * results are accurate to within 1 ulp. 239 */ 240static void 241test_accuracy(void) 242{ 243 244 /* We expect correctly rounded results for these basic cases. */ 245 testall(asin, 1.0, pi / 2, FE_INEXACT); 246 testall(acos, 1.0, 0, 0); 247 testall(atan, 1.0, pi / 4, FE_INEXACT); 248 testall(asin, -1.0, -pi / 2, FE_INEXACT); 249 testall(acos, -1.0, pi, FE_INEXACT); 250 testall(atan, -1.0, -pi / 4, FE_INEXACT); 251 252 /* 253 * Here we expect answers to be within 1 ulp, although inexactness 254 * in the input, combined with double rounding, could cause larger 255 * errors. 256 */ 257 258 testall_tol(asin, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT); 259 testall_tol(acos, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT); 260 testall_tol(asin, -sqrtl(2) / 2, -pi / 4, 1, FE_INEXACT); 261 testall_tol(acos, -sqrtl(2) / 2, c3pi / 4, 1, FE_INEXACT); 262 263 testall_tol(asin, sqrtl(3) / 2, pio3, 1, FE_INEXACT); 264 testall_tol(acos, sqrtl(3) / 2, pio3 / 2, 1, FE_INEXACT); 265 testall_tol(atan, sqrtl(3), pio3, 1, FE_INEXACT); 266 testall_tol(asin, -sqrtl(3) / 2, -pio3, 1, FE_INEXACT); 267 testall_tol(acos, -sqrtl(3) / 2, c5pio3 / 2, 1, FE_INEXACT); 268 testall_tol(atan, -sqrtl(3), -pio3, 1, FE_INEXACT); 269 270 testall_tol(atan, sqrt2m1, pi / 8, 1, FE_INEXACT); 271 testall_tol(atan, -sqrt2m1, -pi / 8, 1, FE_INEXACT); 272} 273 274/* 275 * Test inputs to atan2() where x is a power of 2. These are easy cases 276 * because y/x is exact. 277 */ 278static void 279test_p2x_atan2(void) 280{ 281 282 testall2(atan2, 1.0, 1.0, pi / 4, FE_INEXACT); 283 testall2(atan2, 1.0, -1.0, c3pi / 4, FE_INEXACT); 284 testall2(atan2, -1.0, 1.0, -pi / 4, FE_INEXACT); 285 testall2(atan2, -1.0, -1.0, -c3pi / 4, FE_INEXACT); 286 287 testall2_tol(atan2, sqrt2m1 * 2, 2.0, pi / 8, 1, FE_INEXACT); 288 testall2_tol(atan2, sqrt2m1 * 2, -2.0, c7pi / 8, 1, FE_INEXACT); 289 testall2_tol(atan2, -sqrt2m1 * 2, 2.0, -pi / 8, 1, FE_INEXACT); 290 testall2_tol(atan2, -sqrt2m1 * 2, -2.0, -c7pi / 8, 1, FE_INEXACT); 291 292 testall2_tol(atan2, sqrtl(3) * 0.5, 0.5, pio3, 1, FE_INEXACT); 293 testall2_tol(atan2, sqrtl(3) * 0.5, -0.5, pio3 * 2, 1, FE_INEXACT); 294 testall2_tol(atan2, -sqrtl(3) * 0.5, 0.5, -pio3, 1, FE_INEXACT); 295 testall2_tol(atan2, -sqrtl(3) * 0.5, -0.5, -pio3 * 2, 1, FE_INEXACT); 296} 297 298/* 299 * Test inputs very close to 0. 300 */ 301static void 302test_tiny(void) 303{ 304 float tiny = 0x1.23456p-120f; 305 306 testall(asin, tiny, tiny, FE_INEXACT); 307 testall(acos, tiny, pi / 2, FE_INEXACT); 308 testall(atan, tiny, tiny, FE_INEXACT); 309 310 testall(asin, -tiny, -tiny, FE_INEXACT); 311 testall(acos, -tiny, pi / 2, FE_INEXACT); 312 testall(atan, -tiny, -tiny, FE_INEXACT); 313 314 /* Test inputs to atan2() that would cause y/x to underflow. */ 315 test2(atan2f, 0x1.0p-100, 0x1.0p100, 0.0, FE_INEXACT | FE_UNDERFLOW); 316 test2(atan2, 0x1.0p-1000, 0x1.0p1000, 0.0, FE_INEXACT | FE_UNDERFLOW); 317 test2(atan2l, ldexpl(1.0, 100 - LDBL_MAX_EXP), 318 ldexpl(1.0, LDBL_MAX_EXP - 100), 0.0, FE_INEXACT | FE_UNDERFLOW); 319 test2(atan2f, -0x1.0p-100, 0x1.0p100, -0.0, FE_INEXACT | FE_UNDERFLOW); 320 test2(atan2, -0x1.0p-1000, 0x1.0p1000, -0.0, FE_INEXACT | FE_UNDERFLOW); 321 test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP), 322 ldexpl(1.0, LDBL_MAX_EXP - 100), -0.0, FE_INEXACT | FE_UNDERFLOW); 323 test2(atan2f, 0x1.0p-100, -0x1.0p100, (float)pi, FE_INEXACT); 324 test2(atan2, 0x1.0p-1000, -0x1.0p1000, (double)pi, FE_INEXACT); 325 test2(atan2l, ldexpl(1.0, 100 - LDBL_MAX_EXP), 326 -ldexpl(1.0, LDBL_MAX_EXP - 100), pi, FE_INEXACT); 327 test2(atan2f, -0x1.0p-100, -0x1.0p100, (float)-pi, FE_INEXACT); 328 test2(atan2, -0x1.0p-1000, -0x1.0p1000, (double)-pi, FE_INEXACT); 329 test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP), 330 -ldexpl(1.0, LDBL_MAX_EXP - 100), -pi, FE_INEXACT); 331} 332 333/* 334 * Test very large inputs to atan(). 335 */ 336static void 337test_atan_huge(void) 338{ 339 float huge = 0x1.23456p120; 340 341 testall(atan, huge, pi / 2, FE_INEXACT); 342 testall(atan, -huge, -pi / 2, FE_INEXACT); 343 344 /* Test inputs to atan2() that would cause y/x to overflow. */ 345 test2(atan2f, 0x1.0p100, 0x1.0p-100, (float)pi / 2, FE_INEXACT); 346 test2(atan2, 0x1.0p1000, 0x1.0p-1000, (double)pi / 2, FE_INEXACT); 347 test2(atan2l, ldexpl(1.0, LDBL_MAX_EXP - 100), 348 ldexpl(1.0, 100 - LDBL_MAX_EXP), pi / 2, FE_INEXACT); 349 test2(atan2f, -0x1.0p100, 0x1.0p-100, (float)-pi / 2, FE_INEXACT); 350 test2(atan2, -0x1.0p1000, 0x1.0p-1000, (double)-pi / 2, FE_INEXACT); 351 test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100), 352 ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT); 353 354 test2(atan2f, 0x1.0p100, -0x1.0p-100, (float)pi / 2, FE_INEXACT); 355 test2(atan2, 0x1.0p1000, -0x1.0p-1000, (double)pi / 2, FE_INEXACT); 356 test2(atan2l, ldexpl(1.0, LDBL_MAX_EXP - 100), 357 -ldexpl(1.0, 100 - LDBL_MAX_EXP), pi / 2, FE_INEXACT); 358 test2(atan2f, -0x1.0p100, -0x1.0p-100, (float)-pi / 2, FE_INEXACT); 359 test2(atan2, -0x1.0p1000, -0x1.0p-1000, (double)-pi / 2, FE_INEXACT); 360 test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100), 361 -ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT); 362} 363 364/* 365 * Test that sin(asin(x)) == x, and similarly for acos() and atan(). 366 * You need to have a working sinl(), cosl(), and tanl() for these 367 * tests to pass. 368 */ 369static long double 370sinasinf(float x) 371{ 372 373 return (sinl(asinf(x))); 374} 375 376static long double 377sinasin(double x) 378{ 379 380 return (sinl(asin(x))); 381} 382 383static long double 384sinasinl(long double x) 385{ 386 387 return (sinl(asinl(x))); 388} 389 390static long double 391cosacosf(float x) 392{ 393 394 return (cosl(acosf(x))); 395} 396 397static long double 398cosacos(double x) 399{ 400 401 return (cosl(acos(x))); 402} 403 404static long double 405cosacosl(long double x) 406{ 407 408 return (cosl(acosl(x))); 409} 410 411static long double 412tanatanf(float x) 413{ 414 415 return (tanl(atanf(x))); 416} 417 418static long double 419tanatan(double x) 420{ 421 422 return (tanl(atan(x))); 423} 424 425static long double 426tanatanl(long double x) 427{ 428 429 return (tanl(atanl(x))); 430} 431 432static void 433test_inverse(void) 434{ 435 float i; 436 437 for (i = -1; i <= 1; i += 0x1.0p-12f) { 438 testall_tol(sinasin, i, i, 2, i == 0 ? 0 : FE_INEXACT); 439 /* The relative error for cosacos is very large near x=0. */ 440 if (fabsf(i) > 0x1.0p-4f) 441 testall_tol(cosacos, i, i, 16, i == 1 ? 0 : FE_INEXACT); 442 testall_tol(tanatan, i, i, 2, i == 0 ? 0 : FE_INEXACT); 443 } 444} 445 446int 447main(int argc, char *argv[]) 448{ 449 450#if defined(__i386__) 451 printf("1..0 # SKIP fails all assertions on i386\n"); 452 return (0); 453#endif 454 455 printf("1..7\n"); 456 457 test_special(); 458 printf("ok 1 - special\n"); 459 460 test_special_atan2(); 461 printf("ok 2 - atan2 special\n"); 462 463 test_accuracy(); 464 printf("ok 3 - accuracy\n"); 465 466 test_p2x_atan2(); 467 printf("ok 4 - atan2 p2x\n"); 468 469 test_tiny(); 470 printf("ok 5 - tiny inputs\n"); 471 472 test_atan_huge(); 473 printf("ok 6 - atan huge inputs\n"); 474 475 test_inverse(); 476 printf("ok 7 - inverse\n"); 477 478 return (0); 479} 480