1 /*- 2 * Copyright (c) 2007 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 csqrt{,f}() 29 */ 30 31 #include <sys/cdefs.h> 32 __FBSDID("$FreeBSD$"); 33 34 #include <sys/param.h> 35 36 #include <assert.h> 37 #include <complex.h> 38 #include <float.h> 39 #include <math.h> 40 #include <stdio.h> 41 42 #include "test-utils.h" 43 44 /* 45 * This is a test hook that can point to csqrtl(), _csqrt(), or to _csqrtf(). 46 * The latter two convert to float or double, respectively, and test csqrtf() 47 * and csqrt() with the same arguments. 48 */ 49 static long double complex (*t_csqrt)(long double complex); 50 51 static long double complex 52 _csqrtf(long double complex d) 53 { 54 55 return (csqrtf((float complex)d)); 56 } 57 58 static long double complex 59 _csqrt(long double complex d) 60 { 61 62 return (csqrt((double complex)d)); 63 } 64 65 #pragma STDC CX_LIMITED_RANGE OFF 66 67 /* 68 * Compare d1 and d2 using special rules: NaN == NaN and +0 != -0. 69 * Fail an assertion if they differ. 70 */ 71 static void 72 assert_equal(long double complex d1, long double complex d2) 73 { 74 75 assert(cfpequal(d1, d2)); 76 } 77 78 /* 79 * Test csqrt for some finite arguments where the answer is exact. 80 * (We do not test if it produces correctly rounded answers when the 81 * result is inexact, nor do we check whether it throws spurious 82 * exceptions.) 83 */ 84 static void 85 test_finite(void) 86 { 87 static const double tests[] = { 88 /* csqrt(a + bI) = x + yI */ 89 /* a b x y */ 90 0, 8, 2, 2, 91 0, -8, 2, -2, 92 4, 0, 2, 0, 93 -4, 0, 0, 2, 94 3, 4, 2, 1, 95 3, -4, 2, -1, 96 -3, 4, 1, 2, 97 -3, -4, 1, -2, 98 5, 12, 3, 2, 99 7, 24, 4, 3, 100 9, 40, 5, 4, 101 11, 60, 6, 5, 102 13, 84, 7, 6, 103 33, 56, 7, 4, 104 39, 80, 8, 5, 105 65, 72, 9, 4, 106 987, 9916, 74, 67, 107 5289, 6640, 83, 40, 108 460766389075.0, 16762287900.0, 678910, 12345 109 }; 110 /* 111 * We also test some multiples of the above arguments. This 112 * array defines which multiples we use. Note that these have 113 * to be small enough to not cause overflow for float precision 114 * with all of the constants in the above table. 115 */ 116 static const double mults[] = { 117 1, 118 2, 119 3, 120 13, 121 16, 122 0x1.p30, 123 0x1.p-30, 124 }; 125 126 double a, b; 127 double x, y; 128 unsigned i, j; 129 130 for (i = 0; i < nitems(tests); i += 4) { 131 for (j = 0; j < nitems(mults); j++) { 132 a = tests[i] * mults[j] * mults[j]; 133 b = tests[i + 1] * mults[j] * mults[j]; 134 x = tests[i + 2] * mults[j]; 135 y = tests[i + 3] * mults[j]; 136 assert(t_csqrt(CMPLXL(a, b)) == CMPLXL(x, y)); 137 } 138 } 139 140 } 141 142 /* 143 * Test the handling of +/- 0. 144 */ 145 static void 146 test_zeros(void) 147 { 148 149 assert_equal(t_csqrt(CMPLXL(0.0, 0.0)), CMPLXL(0.0, 0.0)); 150 assert_equal(t_csqrt(CMPLXL(-0.0, 0.0)), CMPLXL(0.0, 0.0)); 151 assert_equal(t_csqrt(CMPLXL(0.0, -0.0)), CMPLXL(0.0, -0.0)); 152 assert_equal(t_csqrt(CMPLXL(-0.0, -0.0)), CMPLXL(0.0, -0.0)); 153 } 154 155 /* 156 * Test the handling of infinities when the other argument is not NaN. 157 */ 158 static void 159 test_infinities(void) 160 { 161 static const double vals[] = { 162 0.0, 163 -0.0, 164 42.0, 165 -42.0, 166 INFINITY, 167 -INFINITY, 168 }; 169 170 unsigned i; 171 172 for (i = 0; i < nitems(vals); i++) { 173 if (isfinite(vals[i])) { 174 assert_equal(t_csqrt(CMPLXL(-INFINITY, vals[i])), 175 CMPLXL(0.0, copysignl(INFINITY, vals[i]))); 176 assert_equal(t_csqrt(CMPLXL(INFINITY, vals[i])), 177 CMPLXL(INFINITY, copysignl(0.0, vals[i]))); 178 } 179 assert_equal(t_csqrt(CMPLXL(vals[i], INFINITY)), 180 CMPLXL(INFINITY, INFINITY)); 181 assert_equal(t_csqrt(CMPLXL(vals[i], -INFINITY)), 182 CMPLXL(INFINITY, -INFINITY)); 183 } 184 } 185 186 /* 187 * Test the handling of NaNs. 188 */ 189 static void 190 test_nans(void) 191 { 192 193 assert(creall(t_csqrt(CMPLXL(INFINITY, NAN))) == INFINITY); 194 assert(isnan(cimagl(t_csqrt(CMPLXL(INFINITY, NAN))))); 195 196 assert(isnan(creall(t_csqrt(CMPLXL(-INFINITY, NAN))))); 197 assert(isinf(cimagl(t_csqrt(CMPLXL(-INFINITY, NAN))))); 198 199 assert_equal(t_csqrt(CMPLXL(NAN, INFINITY)), 200 CMPLXL(INFINITY, INFINITY)); 201 assert_equal(t_csqrt(CMPLXL(NAN, -INFINITY)), 202 CMPLXL(INFINITY, -INFINITY)); 203 204 assert_equal(t_csqrt(CMPLXL(0.0, NAN)), CMPLXL(NAN, NAN)); 205 assert_equal(t_csqrt(CMPLXL(-0.0, NAN)), CMPLXL(NAN, NAN)); 206 assert_equal(t_csqrt(CMPLXL(42.0, NAN)), CMPLXL(NAN, NAN)); 207 assert_equal(t_csqrt(CMPLXL(-42.0, NAN)), CMPLXL(NAN, NAN)); 208 assert_equal(t_csqrt(CMPLXL(NAN, 0.0)), CMPLXL(NAN, NAN)); 209 assert_equal(t_csqrt(CMPLXL(NAN, -0.0)), CMPLXL(NAN, NAN)); 210 assert_equal(t_csqrt(CMPLXL(NAN, 42.0)), CMPLXL(NAN, NAN)); 211 assert_equal(t_csqrt(CMPLXL(NAN, -42.0)), CMPLXL(NAN, NAN)); 212 assert_equal(t_csqrt(CMPLXL(NAN, NAN)), CMPLXL(NAN, NAN)); 213 } 214 215 /* 216 * Test whether csqrt(a + bi) works for inputs that are large enough to 217 * cause overflow in hypot(a, b) + a. Each of the tests is scaled up to 218 * near MAX_EXP. 219 */ 220 static void 221 test_overflow(int maxexp) 222 { 223 long double a, b; 224 long double complex result; 225 int exp, i; 226 227 assert(maxexp > 0 && maxexp % 2 == 0); 228 229 for (i = 0; i < 4; i++) { 230 exp = maxexp - 2 * i; 231 232 /* csqrt(115 + 252*I) == 14 + 9*I */ 233 a = ldexpl(115 * 0x1p-8, exp); 234 b = ldexpl(252 * 0x1p-8, exp); 235 result = t_csqrt(CMPLXL(a, b)); 236 assert(creall(result) == ldexpl(14 * 0x1p-4, exp / 2)); 237 assert(cimagl(result) == ldexpl(9 * 0x1p-4, exp / 2)); 238 239 /* csqrt(-11 + 60*I) = 5 + 6*I */ 240 a = ldexpl(-11 * 0x1p-6, exp); 241 b = ldexpl(60 * 0x1p-6, exp); 242 result = t_csqrt(CMPLXL(a, b)); 243 assert(creall(result) == ldexpl(5 * 0x1p-3, exp / 2)); 244 assert(cimagl(result) == ldexpl(6 * 0x1p-3, exp / 2)); 245 246 /* csqrt(225 + 0*I) == 15 + 0*I */ 247 a = ldexpl(225 * 0x1p-8, exp); 248 b = 0; 249 result = t_csqrt(CMPLXL(a, b)); 250 assert(creall(result) == ldexpl(15 * 0x1p-4, exp / 2)); 251 assert(cimagl(result) == 0); 252 } 253 } 254 255 /* 256 * Test that precision is maintained for some large squares. Set all or 257 * some bits in the lower mantdig/2 bits, square the number, and try to 258 * recover the sqrt. Note: 259 * (x + xI)**2 = 2xxI 260 */ 261 static void 262 test_precision(int maxexp, int mantdig) 263 { 264 long double b, x; 265 long double complex result; 266 uint64_t mantbits, sq_mantbits; 267 int exp, i; 268 269 assert(maxexp > 0 && maxexp % 2 == 0); 270 assert(mantdig <= 64); 271 mantdig = rounddown(mantdig, 2); 272 273 for (exp = 0; exp <= maxexp; exp += 2) { 274 mantbits = ((uint64_t)1 << (mantdig / 2 )) - 1; 275 for (i = 0; 276 i < 100 && mantbits > ((uint64_t)1 << (mantdig / 2 - 1)); 277 i++, mantbits--) { 278 sq_mantbits = mantbits * mantbits; 279 /* 280 * sq_mantibts is a mantdig-bit number. Divide by 281 * 2**mantdig to normalize it to [0.5, 1), where, 282 * note, the binary power will be -1. Raise it by 283 * 2**exp for the test. exp is even. Lower it by 284 * one to reach a final binary power which is also 285 * even. The result should be exactly 286 * representable, given that mantdig is less than or 287 * equal to the available precision. 288 */ 289 b = ldexpl((long double)sq_mantbits, 290 exp - 1 - mantdig); 291 x = ldexpl(mantbits, (exp - 2 - mantdig) / 2); 292 assert(b == x * x * 2); 293 result = t_csqrt(CMPLXL(0, b)); 294 assert(creall(result) == x); 295 assert(cimagl(result) == x); 296 } 297 } 298 } 299 300 int 301 main(void) 302 { 303 304 printf("1..18\n"); 305 306 /* Test csqrt() */ 307 t_csqrt = _csqrt; 308 309 test_finite(); 310 printf("ok 1 - csqrt\n"); 311 312 test_zeros(); 313 printf("ok 2 - csqrt\n"); 314 315 test_infinities(); 316 printf("ok 3 - csqrt\n"); 317 318 test_nans(); 319 printf("ok 4 - csqrt\n"); 320 321 test_overflow(DBL_MAX_EXP); 322 printf("ok 5 - csqrt\n"); 323 324 test_precision(DBL_MAX_EXP, DBL_MANT_DIG); 325 printf("ok 6 - csqrt\n"); 326 327 /* Now test csqrtf() */ 328 t_csqrt = _csqrtf; 329 330 test_finite(); 331 printf("ok 7 - csqrt\n"); 332 333 test_zeros(); 334 printf("ok 8 - csqrt\n"); 335 336 test_infinities(); 337 printf("ok 9 - csqrt\n"); 338 339 test_nans(); 340 printf("ok 10 - csqrt\n"); 341 342 test_overflow(FLT_MAX_EXP); 343 printf("ok 11 - csqrt\n"); 344 345 test_precision(FLT_MAX_EXP, FLT_MANT_DIG); 346 printf("ok 12 - csqrt\n"); 347 348 /* Now test csqrtl() */ 349 t_csqrt = csqrtl; 350 351 test_finite(); 352 printf("ok 13 - csqrt\n"); 353 354 test_zeros(); 355 printf("ok 14 - csqrt\n"); 356 357 test_infinities(); 358 printf("ok 15 - csqrt\n"); 359 360 test_nans(); 361 printf("ok 16 - csqrt\n"); 362 363 test_overflow(LDBL_MAX_EXP); 364 printf("ok 17 - csqrt\n"); 365 366 test_precision(LDBL_MAX_EXP, 367 #ifndef __i386__ 368 LDBL_MANT_DIG 369 #else 370 DBL_MANT_DIG 371 #endif 372 ); 373 printf("ok 18 - csqrt\n"); 374 375 return (0); 376 } 377