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 #include <sys/param.h> 33 34 #include <complex.h> 35 #include <float.h> 36 #include <math.h> 37 #include <stdio.h> 38 39 #include "test-utils.h" 40 41 /* 42 * This is a test hook that can point to csqrtl(), _csqrt(), or to _csqrtf(). 43 * The latter two convert to float or double, respectively, and test csqrtf() 44 * and csqrt() with the same arguments. 45 */ 46 static long double complex (*t_csqrt)(long double complex); 47 48 static long double complex 49 _csqrtf(long double complex d) 50 { 51 52 return (csqrtf((float complex)d)); 53 } 54 55 static long double complex 56 _csqrt(long double complex d) 57 { 58 59 return (csqrt((double complex)d)); 60 } 61 62 #pragma STDC CX_LIMITED_RANGE OFF 63 64 /* 65 * Compare d1 and d2 using special rules: NaN == NaN and +0 != -0. 66 * Fail an assertion if they differ. 67 */ 68 #define assert_equal(d1, d2) CHECK_CFPEQUAL_CS(d1, d2, CS_BOTH) 69 70 /* 71 * Test csqrt for some finite arguments where the answer is exact. 72 * (We do not test if it produces correctly rounded answers when the 73 * result is inexact, nor do we check whether it throws spurious 74 * exceptions.) 75 */ 76 static void 77 test_finite(void) 78 { 79 static const double tests[] = { 80 /* csqrt(a + bI) = x + yI */ 81 /* a b x y */ 82 0, 8, 2, 2, 83 0, -8, 2, -2, 84 4, 0, 2, 0, 85 -4, 0, 0, 2, 86 3, 4, 2, 1, 87 3, -4, 2, -1, 88 -3, 4, 1, 2, 89 -3, -4, 1, -2, 90 5, 12, 3, 2, 91 7, 24, 4, 3, 92 9, 40, 5, 4, 93 11, 60, 6, 5, 94 13, 84, 7, 6, 95 33, 56, 7, 4, 96 39, 80, 8, 5, 97 65, 72, 9, 4, 98 987, 9916, 74, 67, 99 5289, 6640, 83, 40, 100 460766389075.0, 16762287900.0, 678910, 12345 101 }; 102 /* 103 * We also test some multiples of the above arguments. This 104 * array defines which multiples we use. Note that these have 105 * to be small enough to not cause overflow for float precision 106 * with all of the constants in the above table. 107 */ 108 static const double mults[] = { 109 1, 110 2, 111 3, 112 13, 113 16, 114 0x1.p30, 115 0x1.p-30, 116 }; 117 118 double a, b; 119 double x, y; 120 unsigned i, j; 121 122 for (i = 0; i < nitems(tests); i += 4) { 123 for (j = 0; j < nitems(mults); j++) { 124 a = tests[i] * mults[j] * mults[j]; 125 b = tests[i + 1] * mults[j] * mults[j]; 126 x = tests[i + 2] * mults[j]; 127 y = tests[i + 3] * mults[j]; 128 ATF_CHECK(t_csqrt(CMPLXL(a, b)) == CMPLXL(x, y)); 129 } 130 } 131 132 } 133 134 /* 135 * Test the handling of +/- 0. 136 */ 137 static void 138 test_zeros(void) 139 { 140 141 assert_equal(t_csqrt(CMPLXL(0.0, 0.0)), CMPLXL(0.0, 0.0)); 142 assert_equal(t_csqrt(CMPLXL(-0.0, 0.0)), CMPLXL(0.0, 0.0)); 143 assert_equal(t_csqrt(CMPLXL(0.0, -0.0)), CMPLXL(0.0, -0.0)); 144 assert_equal(t_csqrt(CMPLXL(-0.0, -0.0)), CMPLXL(0.0, -0.0)); 145 } 146 147 /* 148 * Test the handling of infinities when the other argument is not NaN. 149 */ 150 static void 151 test_infinities(void) 152 { 153 static const double vals[] = { 154 0.0, 155 -0.0, 156 42.0, 157 -42.0, 158 INFINITY, 159 -INFINITY, 160 }; 161 162 unsigned i; 163 164 for (i = 0; i < nitems(vals); i++) { 165 if (isfinite(vals[i])) { 166 assert_equal(t_csqrt(CMPLXL(-INFINITY, vals[i])), 167 CMPLXL(0.0, copysignl(INFINITY, vals[i]))); 168 assert_equal(t_csqrt(CMPLXL(INFINITY, vals[i])), 169 CMPLXL(INFINITY, copysignl(0.0, vals[i]))); 170 } 171 assert_equal(t_csqrt(CMPLXL(vals[i], INFINITY)), 172 CMPLXL(INFINITY, INFINITY)); 173 assert_equal(t_csqrt(CMPLXL(vals[i], -INFINITY)), 174 CMPLXL(INFINITY, -INFINITY)); 175 } 176 } 177 178 /* 179 * Test the handling of NaNs. 180 */ 181 static void 182 test_nans(void) 183 { 184 185 ATF_CHECK(creall(t_csqrt(CMPLXL(INFINITY, NAN))) == INFINITY); 186 ATF_CHECK(isnan(cimagl(t_csqrt(CMPLXL(INFINITY, NAN))))); 187 188 ATF_CHECK(isnan(creall(t_csqrt(CMPLXL(-INFINITY, NAN))))); 189 ATF_CHECK(isinf(cimagl(t_csqrt(CMPLXL(-INFINITY, NAN))))); 190 191 assert_equal(t_csqrt(CMPLXL(NAN, INFINITY)), 192 CMPLXL(INFINITY, INFINITY)); 193 assert_equal(t_csqrt(CMPLXL(NAN, -INFINITY)), 194 CMPLXL(INFINITY, -INFINITY)); 195 196 assert_equal(t_csqrt(CMPLXL(0.0, NAN)), CMPLXL(NAN, NAN)); 197 assert_equal(t_csqrt(CMPLXL(-0.0, NAN)), CMPLXL(NAN, NAN)); 198 assert_equal(t_csqrt(CMPLXL(42.0, NAN)), CMPLXL(NAN, NAN)); 199 assert_equal(t_csqrt(CMPLXL(-42.0, NAN)), CMPLXL(NAN, NAN)); 200 assert_equal(t_csqrt(CMPLXL(NAN, 0.0)), CMPLXL(NAN, NAN)); 201 assert_equal(t_csqrt(CMPLXL(NAN, -0.0)), CMPLXL(NAN, NAN)); 202 assert_equal(t_csqrt(CMPLXL(NAN, 42.0)), CMPLXL(NAN, NAN)); 203 assert_equal(t_csqrt(CMPLXL(NAN, -42.0)), CMPLXL(NAN, NAN)); 204 assert_equal(t_csqrt(CMPLXL(NAN, NAN)), CMPLXL(NAN, NAN)); 205 } 206 207 /* 208 * Test whether csqrt(a + bi) works for inputs that are large enough to 209 * cause overflow in hypot(a, b) + a. Each of the tests is scaled up to 210 * near MAX_EXP. 211 */ 212 static void 213 test_overflow(int maxexp) 214 { 215 long double a, b; 216 long double complex result; 217 int exp, i; 218 219 ATF_CHECK(maxexp > 0 && maxexp % 2 == 0); 220 221 for (i = 0; i < 4; i++) { 222 exp = maxexp - 2 * i; 223 224 /* csqrt(115 + 252*I) == 14 + 9*I */ 225 a = ldexpl(115 * 0x1p-8, exp); 226 b = ldexpl(252 * 0x1p-8, exp); 227 result = t_csqrt(CMPLXL(a, b)); 228 ATF_CHECK_EQ(creall(result), ldexpl(14 * 0x1p-4, exp / 2)); 229 ATF_CHECK_EQ(cimagl(result), ldexpl(9 * 0x1p-4, exp / 2)); 230 231 /* csqrt(-11 + 60*I) = 5 + 6*I */ 232 a = ldexpl(-11 * 0x1p-6, exp); 233 b = ldexpl(60 * 0x1p-6, exp); 234 result = t_csqrt(CMPLXL(a, b)); 235 ATF_CHECK_EQ(creall(result), ldexpl(5 * 0x1p-3, exp / 2)); 236 ATF_CHECK_EQ(cimagl(result), ldexpl(6 * 0x1p-3, exp / 2)); 237 238 /* csqrt(225 + 0*I) == 15 + 0*I */ 239 a = ldexpl(225 * 0x1p-8, exp); 240 b = 0; 241 result = t_csqrt(CMPLXL(a, b)); 242 ATF_CHECK_EQ(creall(result), ldexpl(15 * 0x1p-4, exp / 2)); 243 ATF_CHECK_EQ(cimagl(result), 0); 244 } 245 } 246 247 /* 248 * Test that precision is maintained for some large squares. Set all or 249 * some bits in the lower mantdig/2 bits, square the number, and try to 250 * recover the sqrt. Note: 251 * (x + xI)**2 = 2xxI 252 */ 253 static void 254 test_precision(int maxexp, int mantdig) 255 { 256 long double b, x; 257 long double complex result; 258 #if LDBL_MANT_DIG <= 64 259 typedef uint64_t ldbl_mant_type; 260 #elif LDBL_MANT_DIG <= 128 261 typedef __uint128_t ldbl_mant_type; 262 #else 263 #error "Unsupported long double format" 264 #endif 265 ldbl_mant_type mantbits, sq_mantbits; 266 int exp, i; 267 268 ATF_REQUIRE(maxexp > 0 && maxexp % 2 == 0); 269 ATF_REQUIRE(mantdig <= LDBL_MANT_DIG); 270 mantdig = rounddown(mantdig, 2); 271 272 for (exp = 0; exp <= maxexp; exp += 2) { 273 mantbits = ((ldbl_mant_type)1 << (mantdig / 2)) - 1; 274 for (i = 0; i < 100 && 275 mantbits > ((ldbl_mant_type)1 << (mantdig / 2 - 1)); 276 i++, mantbits--) { 277 sq_mantbits = mantbits * mantbits; 278 /* 279 * sq_mantibts is a mantdig-bit number. Divide by 280 * 2**mantdig to normalize it to [0.5, 1), where, 281 * note, the binary power will be -1. Raise it by 282 * 2**exp for the test. exp is even. Lower it by 283 * one to reach a final binary power which is also 284 * even. The result should be exactly 285 * representable, given that mantdig is less than or 286 * equal to the available precision. 287 */ 288 b = ldexpl((long double)sq_mantbits, 289 exp - 1 - mantdig); 290 x = ldexpl(mantbits, (exp - 2 - mantdig) / 2); 291 CHECK_FPEQUAL(b, x * x * 2); 292 result = t_csqrt(CMPLXL(0, b)); 293 CHECK_FPEQUAL(x, creall(result)); 294 CHECK_FPEQUAL(x, cimagl(result)); 295 } 296 } 297 } 298 299 ATF_TC_WITHOUT_HEAD(csqrt); 300 ATF_TC_BODY(csqrt, tc) 301 { 302 /* Test csqrt() */ 303 t_csqrt = _csqrt; 304 305 test_finite(); 306 307 test_zeros(); 308 309 test_infinities(); 310 311 test_nans(); 312 313 test_overflow(DBL_MAX_EXP); 314 315 test_precision(DBL_MAX_EXP, DBL_MANT_DIG); 316 } 317 318 ATF_TC_WITHOUT_HEAD(csqrtf); 319 ATF_TC_BODY(csqrtf, tc) 320 { 321 /* Now test csqrtf() */ 322 t_csqrt = _csqrtf; 323 324 test_finite(); 325 326 test_zeros(); 327 328 test_infinities(); 329 330 test_nans(); 331 332 test_overflow(FLT_MAX_EXP); 333 334 test_precision(FLT_MAX_EXP, FLT_MANT_DIG); 335 } 336 337 ATF_TC_WITHOUT_HEAD(csqrtl); 338 ATF_TC_BODY(csqrtl, tc) 339 { 340 /* Now test csqrtl() */ 341 t_csqrt = csqrtl; 342 343 test_finite(); 344 345 test_zeros(); 346 347 test_infinities(); 348 349 test_nans(); 350 351 test_overflow(LDBL_MAX_EXP); 352 353 /* i386 is configured to use 53-bit rounding precision for long double. */ 354 test_precision(LDBL_MAX_EXP, 355 #ifndef __i386__ 356 LDBL_MANT_DIG 357 #else 358 DBL_MANT_DIG 359 #endif 360 ); 361 } 362 363 ATF_TP_ADD_TCS(tp) 364 { 365 ATF_TP_ADD_TC(tp, csqrt); 366 ATF_TP_ADD_TC(tp, csqrtf); 367 ATF_TP_ADD_TC(tp, csqrtl); 368 369 return (atf_no_error()); 370 } 371