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