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