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 fma{,f,l}(). 29 */ 30 31 #include <sys/cdefs.h> 32 __FBSDID("$FreeBSD$"); 33 34 #include <sys/param.h> 35 #include <fenv.h> 36 #include <float.h> 37 #include <math.h> 38 #include <stdio.h> 39 #include <stdlib.h> 40 41 #include "test-utils.h" 42 43 #pragma STDC FENV_ACCESS ON 44 45 /* 46 * Test that a function returns the correct value and sets the 47 * exception flags correctly. The exceptmask specifies which 48 * exceptions we should check. We need to be lenient for several 49 * reasons, but mainly because on some architectures it's impossible 50 * to raise FE_OVERFLOW without raising FE_INEXACT. 51 * 52 * These are macros instead of functions so that assert provides more 53 * meaningful error messages. 54 */ 55 #define test(func, x, y, z, result, exceptmask, excepts) do { \ 56 volatile long double _vx = (x), _vy = (y), _vz = (z); \ 57 ATF_CHECK(feclearexcept(FE_ALL_EXCEPT) == 0); \ 58 CHECK_FPEQUAL((func)(_vx, _vy, _vz), (result)); \ 59 CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \ 60 #func, #x); \ 61 } while (0) 62 63 #define testall(x, y, z, result, exceptmask, excepts) do { \ 64 test(fma, (double)(x), (double)(y), (double)(z), \ 65 (double)(result), (exceptmask), (excepts)); \ 66 test(fmaf, (float)(x), (float)(y), (float)(z), \ 67 (float)(result), (exceptmask), (excepts)); \ 68 test(fmal, (x), (y), (z), (result), (exceptmask), (excepts)); \ 69 } while (0) 70 71 /* Test in all rounding modes. */ 72 #define testrnd(func, x, y, z, rn, ru, rd, rz, exceptmask, excepts) do { \ 73 fesetround(FE_TONEAREST); \ 74 test((func), (x), (y), (z), (rn), (exceptmask), (excepts)); \ 75 fesetround(FE_UPWARD); \ 76 test((func), (x), (y), (z), (ru), (exceptmask), (excepts)); \ 77 fesetround(FE_DOWNWARD); \ 78 test((func), (x), (y), (z), (rd), (exceptmask), (excepts)); \ 79 fesetround(FE_TOWARDZERO); \ 80 test((func), (x), (y), (z), (rz), (exceptmask), (excepts)); \ 81 } while (0) 82 83 /* 84 * This is needed because clang constant-folds fma in ways that are incorrect 85 * in rounding modes other than FE_TONEAREST. 86 */ 87 static volatile double one = 1.0; 88 89 static void 90 test_zeroes(void) 91 { 92 const int rd = (fegetround() == FE_DOWNWARD); 93 94 testall(0.0, 0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0); 95 testall(1.0, 0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0); 96 testall(0.0, 1.0, 0.0, 0.0, ALL_STD_EXCEPT, 0); 97 testall(0.0, 0.0, 1.0, 1.0, ALL_STD_EXCEPT, 0); 98 99 testall(-0.0, 0.0, 0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0); 100 testall(0.0, -0.0, 0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0); 101 testall(-0.0, -0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0); 102 testall(0.0, 0.0, -0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0); 103 testall(-0.0, -0.0, -0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0); 104 105 testall(-0.0, 0.0, -0.0, -0.0, ALL_STD_EXCEPT, 0); 106 testall(0.0, -0.0, -0.0, -0.0, ALL_STD_EXCEPT, 0); 107 108 testall(-one, one, one, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0); 109 testall(one, -one, one, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0); 110 testall(-one, -one, -one, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0); 111 112 switch (fegetround()) { 113 case FE_TONEAREST: 114 case FE_TOWARDZERO: 115 test(fmaf, -FLT_MIN, FLT_MIN, 0.0, -0.0, 116 ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW); 117 test(fma, -DBL_MIN, DBL_MIN, 0.0, -0.0, 118 ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW); 119 test(fmal, -LDBL_MIN, LDBL_MIN, 0.0, -0.0, 120 ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW); 121 } 122 } 123 124 static void 125 test_infinities(void) 126 { 127 testall(INFINITY, 1.0, -1.0, INFINITY, ALL_STD_EXCEPT, 0); 128 testall(-1.0, INFINITY, 0.0, -INFINITY, ALL_STD_EXCEPT, 0); 129 testall(0.0, 0.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0); 130 testall(1.0, 1.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0); 131 testall(1.0, 1.0, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0); 132 133 testall(INFINITY, -INFINITY, 1.0, -INFINITY, ALL_STD_EXCEPT, 0); 134 testall(INFINITY, INFINITY, 1.0, INFINITY, ALL_STD_EXCEPT, 0); 135 testall(-INFINITY, -INFINITY, INFINITY, INFINITY, ALL_STD_EXCEPT, 0); 136 137 testall(0.0, INFINITY, 1.0, NAN, ALL_STD_EXCEPT, FE_INVALID); 138 testall(INFINITY, 0.0, -0.0, NAN, ALL_STD_EXCEPT, FE_INVALID); 139 140 /* The invalid exception is optional in this case. */ 141 testall(INFINITY, 0.0, NAN, NAN, ALL_STD_EXCEPT & ~FE_INVALID, 0); 142 143 testall(INFINITY, INFINITY, -INFINITY, NAN, 144 ALL_STD_EXCEPT, FE_INVALID); 145 testall(-INFINITY, INFINITY, INFINITY, NAN, 146 ALL_STD_EXCEPT, FE_INVALID); 147 testall(INFINITY, -1.0, INFINITY, NAN, 148 ALL_STD_EXCEPT, FE_INVALID); 149 150 test(fmaf, FLT_MAX, FLT_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0); 151 test(fma, DBL_MAX, DBL_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0); 152 test(fmal, LDBL_MAX, LDBL_MAX, -INFINITY, -INFINITY, 153 ALL_STD_EXCEPT, 0); 154 test(fmaf, FLT_MAX, -FLT_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0); 155 test(fma, DBL_MAX, -DBL_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0); 156 test(fmal, LDBL_MAX, -LDBL_MAX, INFINITY, INFINITY, 157 ALL_STD_EXCEPT, 0); 158 } 159 160 static void 161 test_nans(void) 162 { 163 testall(NAN, 0.0, 0.0, NAN, ALL_STD_EXCEPT, 0); 164 testall(1.0, NAN, 1.0, NAN, ALL_STD_EXCEPT, 0); 165 testall(1.0, -1.0, NAN, NAN, ALL_STD_EXCEPT, 0); 166 testall(0.0, 0.0, NAN, NAN, ALL_STD_EXCEPT, 0); 167 testall(NAN, NAN, NAN, NAN, ALL_STD_EXCEPT, 0); 168 169 /* x*y should not raise an inexact/overflow/underflow if z is NaN. */ 170 testall(M_PI, M_PI, NAN, NAN, ALL_STD_EXCEPT, 0); 171 test(fmaf, FLT_MIN, FLT_MIN, NAN, NAN, ALL_STD_EXCEPT, 0); 172 test(fma, DBL_MIN, DBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0); 173 test(fmal, LDBL_MIN, LDBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0); 174 test(fmaf, FLT_MAX, FLT_MAX, NAN, NAN, ALL_STD_EXCEPT, 0); 175 test(fma, DBL_MAX, DBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0); 176 test(fmal, LDBL_MAX, LDBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0); 177 } 178 179 /* 180 * Tests for cases where z is very small compared to x*y. 181 */ 182 static void 183 test_small_z(void) 184 { 185 /* x*y positive, z positive */ 186 if (fegetround() == FE_UPWARD) { 187 test(fmaf, one, one, 0x1.0p-100, 1.0 + FLT_EPSILON, 188 ALL_STD_EXCEPT, FE_INEXACT); 189 test(fma, one, one, 0x1.0p-200, 1.0 + DBL_EPSILON, 190 ALL_STD_EXCEPT, FE_INEXACT); 191 test(fmal, one, one, 0x1.0p-200, 1.0 + LDBL_EPSILON, 192 ALL_STD_EXCEPT, FE_INEXACT); 193 } else { 194 testall(0x1.0p100, one, 0x1.0p-100, 0x1.0p100, 195 ALL_STD_EXCEPT, FE_INEXACT); 196 } 197 198 /* x*y negative, z negative */ 199 if (fegetround() == FE_DOWNWARD) { 200 test(fmaf, -one, one, -0x1.0p-100, -(1.0 + FLT_EPSILON), 201 ALL_STD_EXCEPT, FE_INEXACT); 202 test(fma, -one, one, -0x1.0p-200, -(1.0 + DBL_EPSILON), 203 ALL_STD_EXCEPT, FE_INEXACT); 204 test(fmal, -one, one, -0x1.0p-200, -(1.0 + LDBL_EPSILON), 205 ALL_STD_EXCEPT, FE_INEXACT); 206 } else { 207 testall(0x1.0p100, -one, -0x1.0p-100, -0x1.0p100, 208 ALL_STD_EXCEPT, FE_INEXACT); 209 } 210 211 /* x*y positive, z negative */ 212 if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) { 213 test(fmaf, one, one, -0x1.0p-100, 1.0 - FLT_EPSILON / 2, 214 ALL_STD_EXCEPT, FE_INEXACT); 215 test(fma, one, one, -0x1.0p-200, 1.0 - DBL_EPSILON / 2, 216 ALL_STD_EXCEPT, FE_INEXACT); 217 test(fmal, one, one, -0x1.0p-200, 1.0 - LDBL_EPSILON / 2, 218 ALL_STD_EXCEPT, FE_INEXACT); 219 } else { 220 testall(0x1.0p100, one, -0x1.0p-100, 0x1.0p100, 221 ALL_STD_EXCEPT, FE_INEXACT); 222 } 223 224 /* x*y negative, z positive */ 225 if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) { 226 test(fmaf, -one, one, 0x1.0p-100, -1.0 + FLT_EPSILON / 2, 227 ALL_STD_EXCEPT, FE_INEXACT); 228 test(fma, -one, one, 0x1.0p-200, -1.0 + DBL_EPSILON / 2, 229 ALL_STD_EXCEPT, FE_INEXACT); 230 test(fmal, -one, one, 0x1.0p-200, -1.0 + LDBL_EPSILON / 2, 231 ALL_STD_EXCEPT, FE_INEXACT); 232 } else { 233 testall(-0x1.0p100, one, 0x1.0p-100, -0x1.0p100, 234 ALL_STD_EXCEPT, FE_INEXACT); 235 } 236 } 237 238 /* 239 * Tests for cases where z is very large compared to x*y. 240 */ 241 static void 242 test_big_z(void) 243 { 244 /* z positive, x*y positive */ 245 if (fegetround() == FE_UPWARD) { 246 test(fmaf, 0x1.0p-50, 0x1.0p-50, 1.0, 1.0 + FLT_EPSILON, 247 ALL_STD_EXCEPT, FE_INEXACT); 248 test(fma, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + DBL_EPSILON, 249 ALL_STD_EXCEPT, FE_INEXACT); 250 test(fmal, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + LDBL_EPSILON, 251 ALL_STD_EXCEPT, FE_INEXACT); 252 } else { 253 testall(-0x1.0p-50, -0x1.0p-50, 0x1.0p100, 0x1.0p100, 254 ALL_STD_EXCEPT, FE_INEXACT); 255 } 256 257 /* z negative, x*y negative */ 258 if (fegetround() == FE_DOWNWARD) { 259 test(fmaf, -0x1.0p-50, 0x1.0p-50, -1.0, -(1.0 + FLT_EPSILON), 260 ALL_STD_EXCEPT, FE_INEXACT); 261 test(fma, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + DBL_EPSILON), 262 ALL_STD_EXCEPT, FE_INEXACT); 263 test(fmal, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + LDBL_EPSILON), 264 ALL_STD_EXCEPT, FE_INEXACT); 265 } else { 266 testall(0x1.0p-50, -0x1.0p-50, -0x1.0p100, -0x1.0p100, 267 ALL_STD_EXCEPT, FE_INEXACT); 268 } 269 270 /* z negative, x*y positive */ 271 if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) { 272 test(fmaf, -0x1.0p-50, -0x1.0p-50, -1.0, 273 -1.0 + FLT_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT); 274 test(fma, -0x1.0p-100, -0x1.0p-100, -1.0, 275 -1.0 + DBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT); 276 test(fmal, -0x1.0p-100, -0x1.0p-100, -1.0, 277 -1.0 + LDBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT); 278 } else { 279 testall(0x1.0p-50, 0x1.0p-50, -0x1.0p100, -0x1.0p100, 280 ALL_STD_EXCEPT, FE_INEXACT); 281 } 282 283 /* z positive, x*y negative */ 284 if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) { 285 test(fmaf, 0x1.0p-50, -0x1.0p-50, 1.0, 1.0 - FLT_EPSILON / 2, 286 ALL_STD_EXCEPT, FE_INEXACT); 287 test(fma, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - DBL_EPSILON / 2, 288 ALL_STD_EXCEPT, FE_INEXACT); 289 test(fmal, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - LDBL_EPSILON / 2, 290 ALL_STD_EXCEPT, FE_INEXACT); 291 } else { 292 testall(-0x1.0p-50, 0x1.0p-50, 0x1.0p100, 0x1.0p100, 293 ALL_STD_EXCEPT, FE_INEXACT); 294 } 295 } 296 297 static void 298 test_accuracy(void) 299 { 300 301 /* ilogb(x*y) - ilogb(z) = 20 */ 302 testrnd(fmaf, -0x1.c139d8p-51, -0x1.600e7ap32, 0x1.26558cp-38, 303 0x1.34e48ap-18, 0x1.34e48cp-18, 0x1.34e48ap-18, 0x1.34e48ap-18, 304 ALL_STD_EXCEPT, FE_INEXACT); 305 testrnd(fma, -0x1.c139d7b84f1a3p-51, -0x1.600e7a2a16484p32, 306 0x1.26558cac31580p-38, 0x1.34e48a78aae97p-18, 307 0x1.34e48a78aae97p-18, 0x1.34e48a78aae96p-18, 308 0x1.34e48a78aae96p-18, ALL_STD_EXCEPT, FE_INEXACT); 309 #if LDBL_MANT_DIG == 113 310 testrnd(fmal, -0x1.c139d7b84f1a3079263afcc5bae3p-51L, 311 -0x1.600e7a2a164840edbe2e7d301a72p32L, 312 0x1.26558cac315807eb07e448042101p-38L, 313 0x1.34e48a78aae96c76ed36077dd387p-18L, 314 0x1.34e48a78aae96c76ed36077dd388p-18L, 315 0x1.34e48a78aae96c76ed36077dd387p-18L, 316 0x1.34e48a78aae96c76ed36077dd387p-18L, 317 ALL_STD_EXCEPT, FE_INEXACT); 318 #elif LDBL_MANT_DIG == 64 319 testrnd(fmal, -0x1.c139d7b84f1a307ap-51L, -0x1.600e7a2a164840eep32L, 320 0x1.26558cac315807ecp-38L, 0x1.34e48a78aae96c78p-18L, 321 0x1.34e48a78aae96c78p-18L, 0x1.34e48a78aae96c76p-18L, 322 0x1.34e48a78aae96c76p-18L, ALL_STD_EXCEPT, FE_INEXACT); 323 #elif LDBL_MANT_DIG == 53 324 testrnd(fmal, -0x1.c139d7b84f1a3p-51L, -0x1.600e7a2a16484p32L, 325 0x1.26558cac31580p-38L, 0x1.34e48a78aae97p-18L, 326 0x1.34e48a78aae97p-18L, 0x1.34e48a78aae96p-18L, 327 0x1.34e48a78aae96p-18L, ALL_STD_EXCEPT, FE_INEXACT); 328 #endif 329 330 /* ilogb(x*y) - ilogb(z) = -40 */ 331 testrnd(fmaf, 0x1.98210ap53, 0x1.9556acp-24, 0x1.d87da4p70, 332 0x1.d87da4p70, 0x1.d87da6p70, 0x1.d87da4p70, 0x1.d87da4p70, 333 ALL_STD_EXCEPT, FE_INEXACT); 334 testrnd(fma, 0x1.98210ac83fe2bp53, 0x1.9556ac1475f0fp-24, 335 0x1.d87da3aafc60ep70, 0x1.d87da3aafda40p70, 336 0x1.d87da3aafda40p70, 0x1.d87da3aafda3fp70, 337 0x1.d87da3aafda3fp70, ALL_STD_EXCEPT, FE_INEXACT); 338 #if LDBL_MANT_DIG == 113 339 testrnd(fmal, 0x1.98210ac83fe2a8f65b6278b74cebp53L, 340 0x1.9556ac1475f0f28968b61d0de65ap-24L, 341 0x1.d87da3aafc60d830aa4c6d73b749p70L, 342 0x1.d87da3aafda3f36a69eb86488224p70L, 343 0x1.d87da3aafda3f36a69eb86488225p70L, 344 0x1.d87da3aafda3f36a69eb86488224p70L, 345 0x1.d87da3aafda3f36a69eb86488224p70L, 346 ALL_STD_EXCEPT, FE_INEXACT); 347 #elif LDBL_MANT_DIG == 64 348 testrnd(fmal, 0x1.98210ac83fe2a8f6p53L, 0x1.9556ac1475f0f28ap-24L, 349 0x1.d87da3aafc60d83p70L, 0x1.d87da3aafda3f36ap70L, 350 0x1.d87da3aafda3f36ap70L, 0x1.d87da3aafda3f368p70L, 351 0x1.d87da3aafda3f368p70L, ALL_STD_EXCEPT, FE_INEXACT); 352 #elif LDBL_MANT_DIG == 53 353 testrnd(fmal, 0x1.98210ac83fe2bp53L, 0x1.9556ac1475f0fp-24L, 354 0x1.d87da3aafc60ep70L, 0x1.d87da3aafda40p70L, 355 0x1.d87da3aafda40p70L, 0x1.d87da3aafda3fp70L, 356 0x1.d87da3aafda3fp70L, ALL_STD_EXCEPT, FE_INEXACT); 357 #endif 358 359 /* ilogb(x*y) - ilogb(z) = 0 */ 360 testrnd(fmaf, 0x1.31ad02p+100, 0x1.2fbf7ap-42, -0x1.c3e106p+58, 361 -0x1.64c27cp+56, -0x1.64c27ap+56, -0x1.64c27cp+56, 362 -0x1.64c27ap+56, ALL_STD_EXCEPT, FE_INEXACT); 363 testrnd(fma, 0x1.31ad012ede8aap+100, 0x1.2fbf79c839067p-42, 364 -0x1.c3e106929056ep+58, -0x1.64c282b970a5fp+56, 365 -0x1.64c282b970a5ep+56, -0x1.64c282b970a5fp+56, 366 -0x1.64c282b970a5ep+56, ALL_STD_EXCEPT, FE_INEXACT); 367 #if LDBL_MANT_DIG == 113 368 testrnd(fmal, 0x1.31ad012ede8aa282fa1c19376d16p+100L, 369 0x1.2fbf79c839066f0f5c68f6d2e814p-42L, 370 -0x1.c3e106929056ec19de72bfe64215p+58L, 371 -0x1.64c282b970a612598fc025ca8cddp+56L, 372 -0x1.64c282b970a612598fc025ca8cddp+56L, 373 -0x1.64c282b970a612598fc025ca8cdep+56L, 374 -0x1.64c282b970a612598fc025ca8cddp+56L, 375 ALL_STD_EXCEPT, FE_INEXACT); 376 #elif LDBL_MANT_DIG == 64 377 testrnd(fmal, 0x1.31ad012ede8aa4eap+100L, 0x1.2fbf79c839066aeap-42L, 378 -0x1.c3e106929056e61p+58L, -0x1.64c282b970a60298p+56L, 379 -0x1.64c282b970a60298p+56L, -0x1.64c282b970a6029ap+56L, 380 -0x1.64c282b970a60298p+56L, ALL_STD_EXCEPT, FE_INEXACT); 381 #elif LDBL_MANT_DIG == 53 382 testrnd(fmal, 0x1.31ad012ede8aap+100L, 0x1.2fbf79c839067p-42L, 383 -0x1.c3e106929056ep+58L, -0x1.64c282b970a5fp+56L, 384 -0x1.64c282b970a5ep+56L, -0x1.64c282b970a5fp+56L, 385 -0x1.64c282b970a5ep+56L, ALL_STD_EXCEPT, FE_INEXACT); 386 #endif 387 388 /* x*y (rounded) ~= -z */ 389 /* XXX spurious inexact exceptions */ 390 testrnd(fmaf, 0x1.bbffeep-30, -0x1.1d164cp-74, 0x1.ee7296p-104, 391 -0x1.c46ea8p-128, -0x1.c46ea8p-128, -0x1.c46ea8p-128, 392 -0x1.c46ea8p-128, ALL_STD_EXCEPT & ~FE_INEXACT, 0); 393 testrnd(fma, 0x1.bbffeea6fc7d6p-30, 0x1.1d164c6cbf078p-74, 394 -0x1.ee72993aff948p-104, -0x1.71f72ac7d9d8p-159, 395 -0x1.71f72ac7d9d8p-159, -0x1.71f72ac7d9d8p-159, 396 -0x1.71f72ac7d9d8p-159, ALL_STD_EXCEPT & ~FE_INEXACT, 0); 397 #if LDBL_MANT_DIG == 113 398 testrnd(fmal, 0x1.bbffeea6fc7d65927d147f437675p-30L, 399 0x1.1d164c6cbf078b7a22607d1cd6a2p-74L, 400 -0x1.ee72993aff94973876031bec0944p-104L, 401 0x1.64e086175b3a2adc36e607058814p-217L, 402 0x1.64e086175b3a2adc36e607058814p-217L, 403 0x1.64e086175b3a2adc36e607058814p-217L, 404 0x1.64e086175b3a2adc36e607058814p-217L, 405 ALL_STD_EXCEPT & ~FE_INEXACT, 0); 406 #elif LDBL_MANT_DIG == 64 407 testrnd(fmal, 0x1.bbffeea6fc7d6592p-30L, 0x1.1d164c6cbf078b7ap-74L, 408 -0x1.ee72993aff949736p-104L, 0x1.af190e7a1ee6ad94p-168L, 409 0x1.af190e7a1ee6ad94p-168L, 0x1.af190e7a1ee6ad94p-168L, 410 0x1.af190e7a1ee6ad94p-168L, ALL_STD_EXCEPT & ~FE_INEXACT, 0); 411 #elif LDBL_MANT_DIG == 53 412 testrnd(fmal, 0x1.bbffeea6fc7d6p-30L, 0x1.1d164c6cbf078p-74L, 413 -0x1.ee72993aff948p-104L, -0x1.71f72ac7d9d8p-159L, 414 -0x1.71f72ac7d9d8p-159L, -0x1.71f72ac7d9d8p-159L, 415 -0x1.71f72ac7d9d8p-159L, ALL_STD_EXCEPT & ~FE_INEXACT, 0); 416 #endif 417 } 418 419 static void 420 test_double_rounding(void) 421 { 422 423 /* 424 * a = 0x1.8000000000001p0 425 * b = 0x1.8000000000001p0 426 * c = -0x0.0000000000000000000000000080...1p+1 427 * a * b = 0x1.2000000000001800000000000080p+1 428 * 429 * The correct behavior is to round DOWN to 0x1.2000000000001p+1 in 430 * round-to-nearest mode. An implementation that computes a*b+c in 431 * double+double precision, however, will get 0x1.20000000000018p+1, 432 * and then round UP. 433 */ 434 fesetround(FE_TONEAREST); 435 test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0, 436 -0x1.0000000000001p-104, 0x1.2000000000001p+1, 437 ALL_STD_EXCEPT, FE_INEXACT); 438 fesetround(FE_DOWNWARD); 439 test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0, 440 -0x1.0000000000001p-104, 0x1.2000000000001p+1, 441 ALL_STD_EXCEPT, FE_INEXACT); 442 fesetround(FE_UPWARD); 443 test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0, 444 -0x1.0000000000001p-104, 0x1.2000000000002p+1, 445 ALL_STD_EXCEPT, FE_INEXACT); 446 447 fesetround(FE_TONEAREST); 448 test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200002p+1, 449 ALL_STD_EXCEPT, FE_INEXACT); 450 fesetround(FE_DOWNWARD); 451 test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200002p+1, 452 ALL_STD_EXCEPT, FE_INEXACT); 453 fesetround(FE_UPWARD); 454 test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200004p+1, 455 ALL_STD_EXCEPT, FE_INEXACT); 456 457 fesetround(FE_TONEAREST); 458 #if LDBL_MANT_DIG == 64 459 test(fmal, 0x1.4p+0L, 0x1.0000000000000004p+0L, 0x1p-128L, 460 0x1.4000000000000006p+0L, ALL_STD_EXCEPT, FE_INEXACT); 461 #elif LDBL_MANT_DIG == 113 462 test(fmal, 0x1.8000000000000000000000000001p+0L, 463 0x1.8000000000000000000000000001p+0L, 464 -0x1.0000000000000000000000000001p-224L, 465 0x1.2000000000000000000000000001p+1L, ALL_STD_EXCEPT, FE_INEXACT); 466 #endif 467 468 } 469 470 static const int rmodes[] = { 471 FE_TONEAREST, FE_UPWARD, FE_DOWNWARD, FE_TOWARDZERO 472 }; 473 474 ATF_TC_WITHOUT_HEAD(zeroes); 475 ATF_TC_BODY(zeroes, tc) 476 { 477 for (size_t i = 0; i < nitems(rmodes); i++) { 478 printf("rmode = %d\n", rmodes[i]); 479 fesetround(rmodes[i]); 480 test_zeroes(); 481 } 482 } 483 484 ATF_TC_WITHOUT_HEAD(infinities); 485 ATF_TC_BODY(infinities, tc) 486 { 487 for (size_t i = 0; i < nitems(rmodes); i++) { 488 printf("rmode = %d\n", rmodes[i]); 489 fesetround(rmodes[i]); 490 test_infinities(); 491 } 492 } 493 494 ATF_TC_WITHOUT_HEAD(nans); 495 ATF_TC_BODY(nans, tc) 496 { 497 fesetround(FE_TONEAREST); 498 test_nans(); 499 } 500 501 502 ATF_TC_WITHOUT_HEAD(small_z); 503 ATF_TC_BODY(small_z, tc) 504 { 505 for (size_t i = 0; i < nitems(rmodes); i++) { 506 printf("rmode = %d\n", rmodes[i]); 507 fesetround(rmodes[i]); 508 test_small_z(); 509 } 510 } 511 512 513 ATF_TC_WITHOUT_HEAD(big_z); 514 ATF_TC_BODY(big_z, tc) 515 { 516 for (size_t i = 0; i < nitems(rmodes); i++) { 517 printf("rmode = %d\n", rmodes[i]); 518 fesetround(rmodes[i]); 519 test_big_z(); 520 } 521 } 522 523 ATF_TC_WITHOUT_HEAD(accuracy); 524 ATF_TC_BODY(accuracy, tc) 525 { 526 fesetround(FE_TONEAREST); 527 test_accuracy(); 528 } 529 530 ATF_TC_WITHOUT_HEAD(double_rounding); 531 ATF_TC_BODY(double_rounding, tc) { 532 test_double_rounding(); 533 } 534 535 ATF_TP_ADD_TCS(tp) 536 { 537 ATF_TP_ADD_TC(tp, zeroes); 538 ATF_TP_ADD_TC(tp, infinities); 539 ATF_TP_ADD_TC(tp, nans); 540 ATF_TP_ADD_TC(tp, small_z); 541 ATF_TP_ADD_TC(tp, big_z); 542 ATF_TP_ADD_TC(tp, accuracy); 543 ATF_TP_ADD_TC(tp, double_rounding); 544 /* 545 * TODO: 546 * - Tests for subnormals 547 * - Cancellation tests (e.g., z = (double)x*y, but x*y is inexact) 548 */ 549 return (atf_no_error()); 550 } 551