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 <assert.h> 36 #include <fenv.h> 37 #include <float.h> 38 #include <math.h> 39 #include <stdio.h> 40 #include <stdlib.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. The exceptmask specifies which 49 * exceptions we should check. We need to be lenient for several 50 * reasons, but mainly because on some architectures it's impossible 51 * to raise FE_OVERFLOW without raising FE_INEXACT. 52 * 53 * These are macros instead of functions so that assert provides more 54 * meaningful error messages. 55 */ 56 #define test(func, x, y, z, result, exceptmask, excepts) do { \ 57 volatile long double _vx = (x), _vy = (y), _vz = (z); \ 58 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ 59 assert(fpequal((func)(_vx, _vy, _vz), (result))); \ 60 assert(((void)(func), fetestexcept(exceptmask) == (excepts))); \ 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 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 { 127 128 testall(INFINITY, 1.0, -1.0, INFINITY, ALL_STD_EXCEPT, 0); 129 testall(-1.0, INFINITY, 0.0, -INFINITY, ALL_STD_EXCEPT, 0); 130 testall(0.0, 0.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0); 131 testall(1.0, 1.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0); 132 testall(1.0, 1.0, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0); 133 134 testall(INFINITY, -INFINITY, 1.0, -INFINITY, ALL_STD_EXCEPT, 0); 135 testall(INFINITY, INFINITY, 1.0, INFINITY, ALL_STD_EXCEPT, 0); 136 testall(-INFINITY, -INFINITY, INFINITY, INFINITY, ALL_STD_EXCEPT, 0); 137 138 testall(0.0, INFINITY, 1.0, NAN, ALL_STD_EXCEPT, FE_INVALID); 139 testall(INFINITY, 0.0, -0.0, NAN, ALL_STD_EXCEPT, FE_INVALID); 140 141 /* The invalid exception is optional in this case. */ 142 testall(INFINITY, 0.0, NAN, NAN, ALL_STD_EXCEPT & ~FE_INVALID, 0); 143 144 testall(INFINITY, INFINITY, -INFINITY, NAN, 145 ALL_STD_EXCEPT, FE_INVALID); 146 testall(-INFINITY, INFINITY, INFINITY, NAN, 147 ALL_STD_EXCEPT, FE_INVALID); 148 testall(INFINITY, -1.0, INFINITY, NAN, 149 ALL_STD_EXCEPT, FE_INVALID); 150 151 test(fmaf, FLT_MAX, FLT_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0); 152 test(fma, DBL_MAX, DBL_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0); 153 test(fmal, LDBL_MAX, LDBL_MAX, -INFINITY, -INFINITY, 154 ALL_STD_EXCEPT, 0); 155 test(fmaf, FLT_MAX, -FLT_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0); 156 test(fma, DBL_MAX, -DBL_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0); 157 test(fmal, LDBL_MAX, -LDBL_MAX, INFINITY, INFINITY, 158 ALL_STD_EXCEPT, 0); 159 } 160 161 static void 162 test_nans(void) 163 { 164 165 testall(NAN, 0.0, 0.0, NAN, ALL_STD_EXCEPT, 0); 166 testall(1.0, NAN, 1.0, NAN, ALL_STD_EXCEPT, 0); 167 testall(1.0, -1.0, NAN, NAN, ALL_STD_EXCEPT, 0); 168 testall(0.0, 0.0, NAN, NAN, ALL_STD_EXCEPT, 0); 169 testall(NAN, NAN, NAN, NAN, ALL_STD_EXCEPT, 0); 170 171 /* x*y should not raise an inexact/overflow/underflow if z is NaN. */ 172 testall(M_PI, M_PI, NAN, NAN, ALL_STD_EXCEPT, 0); 173 test(fmaf, FLT_MIN, FLT_MIN, NAN, NAN, ALL_STD_EXCEPT, 0); 174 test(fma, DBL_MIN, DBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0); 175 test(fmal, LDBL_MIN, LDBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0); 176 test(fmaf, FLT_MAX, FLT_MAX, NAN, NAN, ALL_STD_EXCEPT, 0); 177 test(fma, DBL_MAX, DBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0); 178 test(fmal, LDBL_MAX, LDBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0); 179 } 180 181 /* 182 * Tests for cases where z is very small compared to x*y. 183 */ 184 static void 185 test_small_z(void) 186 { 187 188 /* x*y positive, z positive */ 189 if (fegetround() == FE_UPWARD) { 190 test(fmaf, one, one, 0x1.0p-100, 1.0 + FLT_EPSILON, 191 ALL_STD_EXCEPT, FE_INEXACT); 192 test(fma, one, one, 0x1.0p-200, 1.0 + DBL_EPSILON, 193 ALL_STD_EXCEPT, FE_INEXACT); 194 test(fmal, one, one, 0x1.0p-200, 1.0 + LDBL_EPSILON, 195 ALL_STD_EXCEPT, FE_INEXACT); 196 } else { 197 testall(0x1.0p100, one, 0x1.0p-100, 0x1.0p100, 198 ALL_STD_EXCEPT, FE_INEXACT); 199 } 200 201 /* x*y negative, z negative */ 202 if (fegetround() == FE_DOWNWARD) { 203 test(fmaf, -one, one, -0x1.0p-100, -(1.0 + FLT_EPSILON), 204 ALL_STD_EXCEPT, FE_INEXACT); 205 test(fma, -one, one, -0x1.0p-200, -(1.0 + DBL_EPSILON), 206 ALL_STD_EXCEPT, FE_INEXACT); 207 test(fmal, -one, one, -0x1.0p-200, -(1.0 + LDBL_EPSILON), 208 ALL_STD_EXCEPT, FE_INEXACT); 209 } else { 210 testall(0x1.0p100, -one, -0x1.0p-100, -0x1.0p100, 211 ALL_STD_EXCEPT, FE_INEXACT); 212 } 213 214 /* x*y positive, z negative */ 215 if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) { 216 test(fmaf, one, one, -0x1.0p-100, 1.0 - FLT_EPSILON / 2, 217 ALL_STD_EXCEPT, FE_INEXACT); 218 test(fma, one, one, -0x1.0p-200, 1.0 - DBL_EPSILON / 2, 219 ALL_STD_EXCEPT, FE_INEXACT); 220 test(fmal, one, one, -0x1.0p-200, 1.0 - LDBL_EPSILON / 2, 221 ALL_STD_EXCEPT, FE_INEXACT); 222 } else { 223 testall(0x1.0p100, one, -0x1.0p-100, 0x1.0p100, 224 ALL_STD_EXCEPT, FE_INEXACT); 225 } 226 227 /* x*y negative, z positive */ 228 if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) { 229 test(fmaf, -one, one, 0x1.0p-100, -1.0 + FLT_EPSILON / 2, 230 ALL_STD_EXCEPT, FE_INEXACT); 231 test(fma, -one, one, 0x1.0p-200, -1.0 + DBL_EPSILON / 2, 232 ALL_STD_EXCEPT, FE_INEXACT); 233 test(fmal, -one, one, 0x1.0p-200, -1.0 + LDBL_EPSILON / 2, 234 ALL_STD_EXCEPT, FE_INEXACT); 235 } else { 236 testall(-0x1.0p100, one, 0x1.0p-100, -0x1.0p100, 237 ALL_STD_EXCEPT, FE_INEXACT); 238 } 239 } 240 241 /* 242 * Tests for cases where z is very large compared to x*y. 243 */ 244 static void 245 test_big_z(void) 246 { 247 248 /* z positive, x*y positive */ 249 if (fegetround() == FE_UPWARD) { 250 test(fmaf, 0x1.0p-50, 0x1.0p-50, 1.0, 1.0 + FLT_EPSILON, 251 ALL_STD_EXCEPT, FE_INEXACT); 252 test(fma, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + DBL_EPSILON, 253 ALL_STD_EXCEPT, FE_INEXACT); 254 test(fmal, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + LDBL_EPSILON, 255 ALL_STD_EXCEPT, FE_INEXACT); 256 } else { 257 testall(-0x1.0p-50, -0x1.0p-50, 0x1.0p100, 0x1.0p100, 258 ALL_STD_EXCEPT, FE_INEXACT); 259 } 260 261 /* z negative, x*y negative */ 262 if (fegetround() == FE_DOWNWARD) { 263 test(fmaf, -0x1.0p-50, 0x1.0p-50, -1.0, -(1.0 + FLT_EPSILON), 264 ALL_STD_EXCEPT, FE_INEXACT); 265 test(fma, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + DBL_EPSILON), 266 ALL_STD_EXCEPT, FE_INEXACT); 267 test(fmal, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + LDBL_EPSILON), 268 ALL_STD_EXCEPT, FE_INEXACT); 269 } else { 270 testall(0x1.0p-50, -0x1.0p-50, -0x1.0p100, -0x1.0p100, 271 ALL_STD_EXCEPT, FE_INEXACT); 272 } 273 274 /* z negative, x*y positive */ 275 if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) { 276 test(fmaf, -0x1.0p-50, -0x1.0p-50, -1.0, 277 -1.0 + FLT_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT); 278 test(fma, -0x1.0p-100, -0x1.0p-100, -1.0, 279 -1.0 + DBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT); 280 test(fmal, -0x1.0p-100, -0x1.0p-100, -1.0, 281 -1.0 + LDBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT); 282 } else { 283 testall(0x1.0p-50, 0x1.0p-50, -0x1.0p100, -0x1.0p100, 284 ALL_STD_EXCEPT, FE_INEXACT); 285 } 286 287 /* z positive, x*y negative */ 288 if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) { 289 test(fmaf, 0x1.0p-50, -0x1.0p-50, 1.0, 1.0 - FLT_EPSILON / 2, 290 ALL_STD_EXCEPT, FE_INEXACT); 291 test(fma, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - DBL_EPSILON / 2, 292 ALL_STD_EXCEPT, FE_INEXACT); 293 test(fmal, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - LDBL_EPSILON / 2, 294 ALL_STD_EXCEPT, FE_INEXACT); 295 } else { 296 testall(-0x1.0p-50, 0x1.0p-50, 0x1.0p100, 0x1.0p100, 297 ALL_STD_EXCEPT, FE_INEXACT); 298 } 299 } 300 301 static void 302 test_accuracy(void) 303 { 304 305 /* ilogb(x*y) - ilogb(z) = 20 */ 306 testrnd(fmaf, -0x1.c139d8p-51, -0x1.600e7ap32, 0x1.26558cp-38, 307 0x1.34e48ap-18, 0x1.34e48cp-18, 0x1.34e48ap-18, 0x1.34e48ap-18, 308 ALL_STD_EXCEPT, FE_INEXACT); 309 testrnd(fma, -0x1.c139d7b84f1a3p-51, -0x1.600e7a2a16484p32, 310 0x1.26558cac31580p-38, 0x1.34e48a78aae97p-18, 311 0x1.34e48a78aae97p-18, 0x1.34e48a78aae96p-18, 312 0x1.34e48a78aae96p-18, ALL_STD_EXCEPT, FE_INEXACT); 313 #if LDBL_MANT_DIG == 113 314 testrnd(fmal, -0x1.c139d7b84f1a3079263afcc5bae3p-51L, 315 -0x1.600e7a2a164840edbe2e7d301a72p32L, 316 0x1.26558cac315807eb07e448042101p-38L, 317 0x1.34e48a78aae96c76ed36077dd387p-18L, 318 0x1.34e48a78aae96c76ed36077dd388p-18L, 319 0x1.34e48a78aae96c76ed36077dd387p-18L, 320 0x1.34e48a78aae96c76ed36077dd387p-18L, 321 ALL_STD_EXCEPT, FE_INEXACT); 322 #elif LDBL_MANT_DIG == 64 323 testrnd(fmal, -0x1.c139d7b84f1a307ap-51L, -0x1.600e7a2a164840eep32L, 324 0x1.26558cac315807ecp-38L, 0x1.34e48a78aae96c78p-18L, 325 0x1.34e48a78aae96c78p-18L, 0x1.34e48a78aae96c76p-18L, 326 0x1.34e48a78aae96c76p-18L, ALL_STD_EXCEPT, FE_INEXACT); 327 #elif LDBL_MANT_DIG == 53 328 testrnd(fmal, -0x1.c139d7b84f1a3p-51L, -0x1.600e7a2a16484p32L, 329 0x1.26558cac31580p-38L, 0x1.34e48a78aae97p-18L, 330 0x1.34e48a78aae97p-18L, 0x1.34e48a78aae96p-18L, 331 0x1.34e48a78aae96p-18L, ALL_STD_EXCEPT, FE_INEXACT); 332 #endif 333 334 /* ilogb(x*y) - ilogb(z) = -40 */ 335 testrnd(fmaf, 0x1.98210ap53, 0x1.9556acp-24, 0x1.d87da4p70, 336 0x1.d87da4p70, 0x1.d87da6p70, 0x1.d87da4p70, 0x1.d87da4p70, 337 ALL_STD_EXCEPT, FE_INEXACT); 338 testrnd(fma, 0x1.98210ac83fe2bp53, 0x1.9556ac1475f0fp-24, 339 0x1.d87da3aafc60ep70, 0x1.d87da3aafda40p70, 340 0x1.d87da3aafda40p70, 0x1.d87da3aafda3fp70, 341 0x1.d87da3aafda3fp70, ALL_STD_EXCEPT, FE_INEXACT); 342 #if LDBL_MANT_DIG == 113 343 testrnd(fmal, 0x1.98210ac83fe2a8f65b6278b74cebp53L, 344 0x1.9556ac1475f0f28968b61d0de65ap-24L, 345 0x1.d87da3aafc60d830aa4c6d73b749p70L, 346 0x1.d87da3aafda3f36a69eb86488224p70L, 347 0x1.d87da3aafda3f36a69eb86488225p70L, 348 0x1.d87da3aafda3f36a69eb86488224p70L, 349 0x1.d87da3aafda3f36a69eb86488224p70L, 350 ALL_STD_EXCEPT, FE_INEXACT); 351 #elif LDBL_MANT_DIG == 64 352 testrnd(fmal, 0x1.98210ac83fe2a8f6p53L, 0x1.9556ac1475f0f28ap-24L, 353 0x1.d87da3aafc60d83p70L, 0x1.d87da3aafda3f36ap70L, 354 0x1.d87da3aafda3f36ap70L, 0x1.d87da3aafda3f368p70L, 355 0x1.d87da3aafda3f368p70L, ALL_STD_EXCEPT, FE_INEXACT); 356 #elif LDBL_MANT_DIG == 53 357 testrnd(fmal, 0x1.98210ac83fe2bp53L, 0x1.9556ac1475f0fp-24L, 358 0x1.d87da3aafc60ep70L, 0x1.d87da3aafda40p70L, 359 0x1.d87da3aafda40p70L, 0x1.d87da3aafda3fp70L, 360 0x1.d87da3aafda3fp70L, ALL_STD_EXCEPT, FE_INEXACT); 361 #endif 362 363 /* ilogb(x*y) - ilogb(z) = 0 */ 364 testrnd(fmaf, 0x1.31ad02p+100, 0x1.2fbf7ap-42, -0x1.c3e106p+58, 365 -0x1.64c27cp+56, -0x1.64c27ap+56, -0x1.64c27cp+56, 366 -0x1.64c27ap+56, ALL_STD_EXCEPT, FE_INEXACT); 367 testrnd(fma, 0x1.31ad012ede8aap+100, 0x1.2fbf79c839067p-42, 368 -0x1.c3e106929056ep+58, -0x1.64c282b970a5fp+56, 369 -0x1.64c282b970a5ep+56, -0x1.64c282b970a5fp+56, 370 -0x1.64c282b970a5ep+56, ALL_STD_EXCEPT, FE_INEXACT); 371 #if LDBL_MANT_DIG == 113 372 testrnd(fmal, 0x1.31ad012ede8aa282fa1c19376d16p+100L, 373 0x1.2fbf79c839066f0f5c68f6d2e814p-42L, 374 -0x1.c3e106929056ec19de72bfe64215p+58L, 375 -0x1.64c282b970a612598fc025ca8cddp+56L, 376 -0x1.64c282b970a612598fc025ca8cddp+56L, 377 -0x1.64c282b970a612598fc025ca8cdep+56L, 378 -0x1.64c282b970a612598fc025ca8cddp+56L, 379 ALL_STD_EXCEPT, FE_INEXACT); 380 #elif LDBL_MANT_DIG == 64 381 testrnd(fmal, 0x1.31ad012ede8aa4eap+100L, 0x1.2fbf79c839066aeap-42L, 382 -0x1.c3e106929056e61p+58L, -0x1.64c282b970a60298p+56L, 383 -0x1.64c282b970a60298p+56L, -0x1.64c282b970a6029ap+56L, 384 -0x1.64c282b970a60298p+56L, ALL_STD_EXCEPT, FE_INEXACT); 385 #elif LDBL_MANT_DIG == 53 386 testrnd(fmal, 0x1.31ad012ede8aap+100L, 0x1.2fbf79c839067p-42L, 387 -0x1.c3e106929056ep+58L, -0x1.64c282b970a5fp+56L, 388 -0x1.64c282b970a5ep+56L, -0x1.64c282b970a5fp+56L, 389 -0x1.64c282b970a5ep+56L, ALL_STD_EXCEPT, FE_INEXACT); 390 #endif 391 392 /* x*y (rounded) ~= -z */ 393 /* XXX spurious inexact exceptions */ 394 testrnd(fmaf, 0x1.bbffeep-30, -0x1.1d164cp-74, 0x1.ee7296p-104, 395 -0x1.c46ea8p-128, -0x1.c46ea8p-128, -0x1.c46ea8p-128, 396 -0x1.c46ea8p-128, ALL_STD_EXCEPT & ~FE_INEXACT, 0); 397 testrnd(fma, 0x1.bbffeea6fc7d6p-30, 0x1.1d164c6cbf078p-74, 398 -0x1.ee72993aff948p-104, -0x1.71f72ac7d9d8p-159, 399 -0x1.71f72ac7d9d8p-159, -0x1.71f72ac7d9d8p-159, 400 -0x1.71f72ac7d9d8p-159, ALL_STD_EXCEPT & ~FE_INEXACT, 0); 401 #if LDBL_MANT_DIG == 113 402 testrnd(fmal, 0x1.bbffeea6fc7d65927d147f437675p-30L, 403 0x1.1d164c6cbf078b7a22607d1cd6a2p-74L, 404 -0x1.ee72993aff94973876031bec0944p-104L, 405 0x1.64e086175b3a2adc36e607058814p-217L, 406 0x1.64e086175b3a2adc36e607058814p-217L, 407 0x1.64e086175b3a2adc36e607058814p-217L, 408 0x1.64e086175b3a2adc36e607058814p-217L, 409 ALL_STD_EXCEPT & ~FE_INEXACT, 0); 410 #elif LDBL_MANT_DIG == 64 411 testrnd(fmal, 0x1.bbffeea6fc7d6592p-30L, 0x1.1d164c6cbf078b7ap-74L, 412 -0x1.ee72993aff949736p-104L, 0x1.af190e7a1ee6ad94p-168L, 413 0x1.af190e7a1ee6ad94p-168L, 0x1.af190e7a1ee6ad94p-168L, 414 0x1.af190e7a1ee6ad94p-168L, ALL_STD_EXCEPT & ~FE_INEXACT, 0); 415 #elif LDBL_MANT_DIG == 53 416 testrnd(fmal, 0x1.bbffeea6fc7d6p-30L, 0x1.1d164c6cbf078p-74L, 417 -0x1.ee72993aff948p-104L, -0x1.71f72ac7d9d8p-159L, 418 -0x1.71f72ac7d9d8p-159L, -0x1.71f72ac7d9d8p-159L, 419 -0x1.71f72ac7d9d8p-159L, ALL_STD_EXCEPT & ~FE_INEXACT, 0); 420 #endif 421 } 422 423 static void 424 test_double_rounding(void) 425 { 426 427 /* 428 * a = 0x1.8000000000001p0 429 * b = 0x1.8000000000001p0 430 * c = -0x0.0000000000000000000000000080...1p+1 431 * a * b = 0x1.2000000000001800000000000080p+1 432 * 433 * The correct behavior is to round DOWN to 0x1.2000000000001p+1 in 434 * round-to-nearest mode. An implementation that computes a*b+c in 435 * double+double precision, however, will get 0x1.20000000000018p+1, 436 * and then round UP. 437 */ 438 fesetround(FE_TONEAREST); 439 test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0, 440 -0x1.0000000000001p-104, 0x1.2000000000001p+1, 441 ALL_STD_EXCEPT, FE_INEXACT); 442 fesetround(FE_DOWNWARD); 443 test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0, 444 -0x1.0000000000001p-104, 0x1.2000000000001p+1, 445 ALL_STD_EXCEPT, FE_INEXACT); 446 fesetround(FE_UPWARD); 447 test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0, 448 -0x1.0000000000001p-104, 0x1.2000000000002p+1, 449 ALL_STD_EXCEPT, FE_INEXACT); 450 451 fesetround(FE_TONEAREST); 452 test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200002p+1, 453 ALL_STD_EXCEPT, FE_INEXACT); 454 fesetround(FE_DOWNWARD); 455 test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200002p+1, 456 ALL_STD_EXCEPT, FE_INEXACT); 457 fesetround(FE_UPWARD); 458 test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200004p+1, 459 ALL_STD_EXCEPT, FE_INEXACT); 460 461 fesetround(FE_TONEAREST); 462 #if LDBL_MANT_DIG == 64 463 test(fmal, 0x1.4p+0L, 0x1.0000000000000004p+0L, 0x1p-128L, 464 0x1.4000000000000006p+0L, ALL_STD_EXCEPT, FE_INEXACT); 465 #elif LDBL_MANT_DIG == 113 466 test(fmal, 0x1.8000000000000000000000000001p+0L, 467 0x1.8000000000000000000000000001p+0L, 468 -0x1.0000000000000000000000000001p-224L, 469 0x1.2000000000000000000000000001p+1L, ALL_STD_EXCEPT, FE_INEXACT); 470 #endif 471 472 } 473 474 int 475 main(int argc, char *argv[]) 476 { 477 int rmodes[] = { FE_TONEAREST, FE_UPWARD, FE_DOWNWARD, FE_TOWARDZERO }; 478 int i, j; 479 480 #if defined(__i386__) 481 printf("1..0 # SKIP all testcases fail on i386\n"); 482 exit(0); 483 #endif 484 485 j = 1; 486 487 printf("1..19\n"); 488 489 for (i = 0; i < nitems(rmodes); i++, j++) { 490 printf("rmode = %d\n", rmodes[i]); 491 fesetround(rmodes[i]); 492 test_zeroes(); 493 printf("ok %d - fma zeroes\n", j); 494 } 495 496 for (i = 0; i < nitems(rmodes); i++, j++) { 497 #if defined(__amd64__) 498 printf("ok %d # SKIP testcase fails assertion on " 499 "amd64\n", j); 500 continue; 501 #endif 502 printf("rmode = %d\n", rmodes[i]); 503 fesetround(rmodes[i]); 504 test_infinities(); 505 printf("ok %d - fma infinities\n", j); 506 } 507 508 fesetround(FE_TONEAREST); 509 test_nans(); 510 printf("ok 9 - fma NaNs\n"); 511 512 for (i = 0; i < nitems(rmodes); i++, j++) { 513 printf("rmode = %d\n", rmodes[i]); 514 fesetround(rmodes[i]); 515 test_small_z(); 516 printf("ok %d - fma small z\n", j); 517 } 518 519 for (i = 0; i < nitems(rmodes); i++, j++) { 520 printf("rmode = %d\n", rmodes[i]); 521 fesetround(rmodes[i]); 522 test_big_z(); 523 printf("ok %d - fma big z\n", j); 524 } 525 526 fesetround(FE_TONEAREST); 527 test_accuracy(); 528 printf("ok %d - fma accuracy\n", j); 529 j++; 530 531 test_double_rounding(); 532 printf("ok %d - fma double rounding\n", j); 533 j++; 534 535 /* 536 * TODO: 537 * - Tests for subnormals 538 * - Cancellation tests (e.g., z = (double)x*y, but x*y is inexact) 539 */ 540 541 return (0); 542 } 543