2 * Copyright (c) 2008 David Schultz <das@FreeBSD.org>
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
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.
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
28 * Tests for fma{,f,l}().
31 #include <sys/cdefs.h>
32 __FBSDID("$FreeBSD$");
40 #include "test-utils.h"
42 #pragma STDC FENV_ACCESS ON
45 * Test that a function returns the correct value and sets the
46 * exception flags correctly. The exceptmask specifies which
47 * exceptions we should check. We need to be lenient for several
48 * reasons, but mainly because on some architectures it's impossible
49 * to raise FE_OVERFLOW without raising FE_INEXACT.
51 * These are macros instead of functions so that assert provides more
52 * meaningful error messages.
54 #define test(func, x, y, z, result, exceptmask, excepts) do { \
55 volatile long double _vx = (x), _vy = (y), _vz = (z); \
56 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
57 assert(fpequal((func)(_vx, _vy, _vz), (result))); \
58 assert(((void)(func), fetestexcept(exceptmask) == (excepts))); \
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)); \
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)); \
82 * This is needed because clang constant-folds fma in ways that are incorrect
83 * in rounding modes other than FE_TONEAREST.
85 volatile double one = 1.0;
90 const int rd = (fegetround() == FE_DOWNWARD);
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);
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);
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);
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);
110 switch (fegetround()) {
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);
123 test_infinities(void)
126 testall(INFINITY, 1.0, -1.0, INFINITY, ALL_STD_EXCEPT, 0);
127 testall(-1.0, INFINITY, 0.0, -INFINITY, ALL_STD_EXCEPT, 0);
128 testall(0.0, 0.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
129 testall(1.0, 1.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
130 testall(1.0, 1.0, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
132 testall(INFINITY, -INFINITY, 1.0, -INFINITY, ALL_STD_EXCEPT, 0);
133 testall(INFINITY, INFINITY, 1.0, INFINITY, ALL_STD_EXCEPT, 0);
134 testall(-INFINITY, -INFINITY, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
136 testall(0.0, INFINITY, 1.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
137 testall(INFINITY, 0.0, -0.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
139 /* The invalid exception is optional in this case. */
140 testall(INFINITY, 0.0, NAN, NAN, ALL_STD_EXCEPT & ~FE_INVALID, 0);
142 testall(INFINITY, INFINITY, -INFINITY, NAN,
143 ALL_STD_EXCEPT, FE_INVALID);
144 testall(-INFINITY, INFINITY, INFINITY, NAN,
145 ALL_STD_EXCEPT, FE_INVALID);
146 testall(INFINITY, -1.0, INFINITY, NAN,
147 ALL_STD_EXCEPT, FE_INVALID);
149 test(fmaf, FLT_MAX, FLT_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
150 test(fma, DBL_MAX, DBL_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
151 test(fmal, LDBL_MAX, LDBL_MAX, -INFINITY, -INFINITY,
153 test(fmaf, FLT_MAX, -FLT_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
154 test(fma, DBL_MAX, -DBL_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
155 test(fmal, LDBL_MAX, -LDBL_MAX, INFINITY, INFINITY,
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);
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);
180 * Tests for cases where z is very small compared to x*y.
186 /* x*y positive, z positive */
187 if (fegetround() == FE_UPWARD) {
188 test(fmaf, one, one, 0x1.0p-100, 1.0 + FLT_EPSILON,
189 ALL_STD_EXCEPT, FE_INEXACT);
190 test(fma, one, one, 0x1.0p-200, 1.0 + DBL_EPSILON,
191 ALL_STD_EXCEPT, FE_INEXACT);
192 test(fmal, one, one, 0x1.0p-200, 1.0 + LDBL_EPSILON,
193 ALL_STD_EXCEPT, FE_INEXACT);
195 testall(0x1.0p100, one, 0x1.0p-100, 0x1.0p100,
196 ALL_STD_EXCEPT, FE_INEXACT);
199 /* x*y negative, z negative */
200 if (fegetround() == FE_DOWNWARD) {
201 test(fmaf, -one, one, -0x1.0p-100, -(1.0 + FLT_EPSILON),
202 ALL_STD_EXCEPT, FE_INEXACT);
203 test(fma, -one, one, -0x1.0p-200, -(1.0 + DBL_EPSILON),
204 ALL_STD_EXCEPT, FE_INEXACT);
205 test(fmal, -one, one, -0x1.0p-200, -(1.0 + LDBL_EPSILON),
206 ALL_STD_EXCEPT, FE_INEXACT);
208 testall(0x1.0p100, -one, -0x1.0p-100, -0x1.0p100,
209 ALL_STD_EXCEPT, FE_INEXACT);
212 /* x*y positive, z negative */
213 if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
214 test(fmaf, one, one, -0x1.0p-100, 1.0 - FLT_EPSILON / 2,
215 ALL_STD_EXCEPT, FE_INEXACT);
216 test(fma, one, one, -0x1.0p-200, 1.0 - DBL_EPSILON / 2,
217 ALL_STD_EXCEPT, FE_INEXACT);
218 test(fmal, one, one, -0x1.0p-200, 1.0 - LDBL_EPSILON / 2,
219 ALL_STD_EXCEPT, FE_INEXACT);
221 testall(0x1.0p100, one, -0x1.0p-100, 0x1.0p100,
222 ALL_STD_EXCEPT, FE_INEXACT);
225 /* x*y negative, z positive */
226 if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
227 test(fmaf, -one, one, 0x1.0p-100, -1.0 + FLT_EPSILON / 2,
228 ALL_STD_EXCEPT, FE_INEXACT);
229 test(fma, -one, one, 0x1.0p-200, -1.0 + DBL_EPSILON / 2,
230 ALL_STD_EXCEPT, FE_INEXACT);
231 test(fmal, -one, one, 0x1.0p-200, -1.0 + LDBL_EPSILON / 2,
232 ALL_STD_EXCEPT, FE_INEXACT);
234 testall(-0x1.0p100, one, 0x1.0p-100, -0x1.0p100,
235 ALL_STD_EXCEPT, FE_INEXACT);
240 * Tests for cases where z is very large compared to x*y.
246 /* z positive, x*y positive */
247 if (fegetround() == FE_UPWARD) {
248 test(fmaf, 0x1.0p-50, 0x1.0p-50, 1.0, 1.0 + FLT_EPSILON,
249 ALL_STD_EXCEPT, FE_INEXACT);
250 test(fma, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + DBL_EPSILON,
251 ALL_STD_EXCEPT, FE_INEXACT);
252 test(fmal, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + LDBL_EPSILON,
253 ALL_STD_EXCEPT, FE_INEXACT);
255 testall(-0x1.0p-50, -0x1.0p-50, 0x1.0p100, 0x1.0p100,
256 ALL_STD_EXCEPT, FE_INEXACT);
259 /* z negative, x*y negative */
260 if (fegetround() == FE_DOWNWARD) {
261 test(fmaf, -0x1.0p-50, 0x1.0p-50, -1.0, -(1.0 + FLT_EPSILON),
262 ALL_STD_EXCEPT, FE_INEXACT);
263 test(fma, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + DBL_EPSILON),
264 ALL_STD_EXCEPT, FE_INEXACT);
265 test(fmal, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + LDBL_EPSILON),
266 ALL_STD_EXCEPT, FE_INEXACT);
268 testall(0x1.0p-50, -0x1.0p-50, -0x1.0p100, -0x1.0p100,
269 ALL_STD_EXCEPT, FE_INEXACT);
272 /* z negative, x*y positive */
273 if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
274 test(fmaf, -0x1.0p-50, -0x1.0p-50, -1.0,
275 -1.0 + FLT_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
276 test(fma, -0x1.0p-100, -0x1.0p-100, -1.0,
277 -1.0 + DBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
278 test(fmal, -0x1.0p-100, -0x1.0p-100, -1.0,
279 -1.0 + LDBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
281 testall(0x1.0p-50, 0x1.0p-50, -0x1.0p100, -0x1.0p100,
282 ALL_STD_EXCEPT, FE_INEXACT);
285 /* z positive, x*y negative */
286 if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
287 test(fmaf, 0x1.0p-50, -0x1.0p-50, 1.0, 1.0 - FLT_EPSILON / 2,
288 ALL_STD_EXCEPT, FE_INEXACT);
289 test(fma, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - DBL_EPSILON / 2,
290 ALL_STD_EXCEPT, FE_INEXACT);
291 test(fmal, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - LDBL_EPSILON / 2,
292 ALL_STD_EXCEPT, FE_INEXACT);
294 testall(-0x1.0p-50, 0x1.0p-50, 0x1.0p100, 0x1.0p100,
295 ALL_STD_EXCEPT, FE_INEXACT);
303 /* ilogb(x*y) - ilogb(z) = 20 */
304 testrnd(fmaf, -0x1.c139d8p-51, -0x1.600e7ap32, 0x1.26558cp-38,
305 0x1.34e48ap-18, 0x1.34e48cp-18, 0x1.34e48ap-18, 0x1.34e48ap-18,
306 ALL_STD_EXCEPT, FE_INEXACT);
307 testrnd(fma, -0x1.c139d7b84f1a3p-51, -0x1.600e7a2a16484p32,
308 0x1.26558cac31580p-38, 0x1.34e48a78aae97p-18,
309 0x1.34e48a78aae97p-18, 0x1.34e48a78aae96p-18,
310 0x1.34e48a78aae96p-18, ALL_STD_EXCEPT, FE_INEXACT);
311 #if LDBL_MANT_DIG == 113
312 testrnd(fmal, -0x1.c139d7b84f1a3079263afcc5bae3p-51L,
313 -0x1.600e7a2a164840edbe2e7d301a72p32L,
314 0x1.26558cac315807eb07e448042101p-38L,
315 0x1.34e48a78aae96c76ed36077dd387p-18L,
316 0x1.34e48a78aae96c76ed36077dd388p-18L,
317 0x1.34e48a78aae96c76ed36077dd387p-18L,
318 0x1.34e48a78aae96c76ed36077dd387p-18L,
319 ALL_STD_EXCEPT, FE_INEXACT);
320 #elif LDBL_MANT_DIG == 64
321 testrnd(fmal, -0x1.c139d7b84f1a307ap-51L, -0x1.600e7a2a164840eep32L,
322 0x1.26558cac315807ecp-38L, 0x1.34e48a78aae96c78p-18L,
323 0x1.34e48a78aae96c78p-18L, 0x1.34e48a78aae96c76p-18L,
324 0x1.34e48a78aae96c76p-18L, ALL_STD_EXCEPT, FE_INEXACT);
325 #elif LDBL_MANT_DIG == 53
326 testrnd(fmal, -0x1.c139d7b84f1a3p-51L, -0x1.600e7a2a16484p32L,
327 0x1.26558cac31580p-38L, 0x1.34e48a78aae97p-18L,
328 0x1.34e48a78aae97p-18L, 0x1.34e48a78aae96p-18L,
329 0x1.34e48a78aae96p-18L, ALL_STD_EXCEPT, FE_INEXACT);
332 /* ilogb(x*y) - ilogb(z) = -40 */
333 testrnd(fmaf, 0x1.98210ap53, 0x1.9556acp-24, 0x1.d87da4p70,
334 0x1.d87da4p70, 0x1.d87da6p70, 0x1.d87da4p70, 0x1.d87da4p70,
335 ALL_STD_EXCEPT, FE_INEXACT);
336 testrnd(fma, 0x1.98210ac83fe2bp53, 0x1.9556ac1475f0fp-24,
337 0x1.d87da3aafc60ep70, 0x1.d87da3aafda40p70,
338 0x1.d87da3aafda40p70, 0x1.d87da3aafda3fp70,
339 0x1.d87da3aafda3fp70, ALL_STD_EXCEPT, FE_INEXACT);
340 #if LDBL_MANT_DIG == 113
341 testrnd(fmal, 0x1.98210ac83fe2a8f65b6278b74cebp53L,
342 0x1.9556ac1475f0f28968b61d0de65ap-24L,
343 0x1.d87da3aafc60d830aa4c6d73b749p70L,
344 0x1.d87da3aafda3f36a69eb86488224p70L,
345 0x1.d87da3aafda3f36a69eb86488225p70L,
346 0x1.d87da3aafda3f36a69eb86488224p70L,
347 0x1.d87da3aafda3f36a69eb86488224p70L,
348 ALL_STD_EXCEPT, FE_INEXACT);
349 #elif LDBL_MANT_DIG == 64
350 testrnd(fmal, 0x1.98210ac83fe2a8f6p53L, 0x1.9556ac1475f0f28ap-24L,
351 0x1.d87da3aafc60d83p70L, 0x1.d87da3aafda3f36ap70L,
352 0x1.d87da3aafda3f36ap70L, 0x1.d87da3aafda3f368p70L,
353 0x1.d87da3aafda3f368p70L, ALL_STD_EXCEPT, FE_INEXACT);
354 #elif LDBL_MANT_DIG == 53
355 testrnd(fmal, 0x1.98210ac83fe2bp53L, 0x1.9556ac1475f0fp-24L,
356 0x1.d87da3aafc60ep70L, 0x1.d87da3aafda40p70L,
357 0x1.d87da3aafda40p70L, 0x1.d87da3aafda3fp70L,
358 0x1.d87da3aafda3fp70L, ALL_STD_EXCEPT, FE_INEXACT);
361 /* ilogb(x*y) - ilogb(z) = 0 */
362 testrnd(fmaf, 0x1.31ad02p+100, 0x1.2fbf7ap-42, -0x1.c3e106p+58,
363 -0x1.64c27cp+56, -0x1.64c27ap+56, -0x1.64c27cp+56,
364 -0x1.64c27ap+56, ALL_STD_EXCEPT, FE_INEXACT);
365 testrnd(fma, 0x1.31ad012ede8aap+100, 0x1.2fbf79c839067p-42,
366 -0x1.c3e106929056ep+58, -0x1.64c282b970a5fp+56,
367 -0x1.64c282b970a5ep+56, -0x1.64c282b970a5fp+56,
368 -0x1.64c282b970a5ep+56, ALL_STD_EXCEPT, FE_INEXACT);
369 #if LDBL_MANT_DIG == 113
370 testrnd(fmal, 0x1.31ad012ede8aa282fa1c19376d16p+100L,
371 0x1.2fbf79c839066f0f5c68f6d2e814p-42L,
372 -0x1.c3e106929056ec19de72bfe64215p+58L,
373 -0x1.64c282b970a612598fc025ca8cddp+56L,
374 -0x1.64c282b970a612598fc025ca8cddp+56L,
375 -0x1.64c282b970a612598fc025ca8cdep+56L,
376 -0x1.64c282b970a612598fc025ca8cddp+56L,
377 ALL_STD_EXCEPT, FE_INEXACT);
378 #elif LDBL_MANT_DIG == 64
379 testrnd(fmal, 0x1.31ad012ede8aa4eap+100L, 0x1.2fbf79c839066aeap-42L,
380 -0x1.c3e106929056e61p+58L, -0x1.64c282b970a60298p+56L,
381 -0x1.64c282b970a60298p+56L, -0x1.64c282b970a6029ap+56L,
382 -0x1.64c282b970a60298p+56L, ALL_STD_EXCEPT, FE_INEXACT);
383 #elif LDBL_MANT_DIG == 53
384 testrnd(fmal, 0x1.31ad012ede8aap+100L, 0x1.2fbf79c839067p-42L,
385 -0x1.c3e106929056ep+58L, -0x1.64c282b970a5fp+56L,
386 -0x1.64c282b970a5ep+56L, -0x1.64c282b970a5fp+56L,
387 -0x1.64c282b970a5ep+56L, ALL_STD_EXCEPT, FE_INEXACT);
390 /* x*y (rounded) ~= -z */
391 /* XXX spurious inexact exceptions */
392 testrnd(fmaf, 0x1.bbffeep-30, -0x1.1d164cp-74, 0x1.ee7296p-104,
393 -0x1.c46ea8p-128, -0x1.c46ea8p-128, -0x1.c46ea8p-128,
394 -0x1.c46ea8p-128, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
395 testrnd(fma, 0x1.bbffeea6fc7d6p-30, 0x1.1d164c6cbf078p-74,
396 -0x1.ee72993aff948p-104, -0x1.71f72ac7d9d8p-159,
397 -0x1.71f72ac7d9d8p-159, -0x1.71f72ac7d9d8p-159,
398 -0x1.71f72ac7d9d8p-159, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
399 #if LDBL_MANT_DIG == 113
400 testrnd(fmal, 0x1.bbffeea6fc7d65927d147f437675p-30L,
401 0x1.1d164c6cbf078b7a22607d1cd6a2p-74L,
402 -0x1.ee72993aff94973876031bec0944p-104L,
403 0x1.64e086175b3a2adc36e607058814p-217L,
404 0x1.64e086175b3a2adc36e607058814p-217L,
405 0x1.64e086175b3a2adc36e607058814p-217L,
406 0x1.64e086175b3a2adc36e607058814p-217L,
407 ALL_STD_EXCEPT & ~FE_INEXACT, 0);
408 #elif LDBL_MANT_DIG == 64
409 testrnd(fmal, 0x1.bbffeea6fc7d6592p-30L, 0x1.1d164c6cbf078b7ap-74L,
410 -0x1.ee72993aff949736p-104L, 0x1.af190e7a1ee6ad94p-168L,
411 0x1.af190e7a1ee6ad94p-168L, 0x1.af190e7a1ee6ad94p-168L,
412 0x1.af190e7a1ee6ad94p-168L, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
413 #elif LDBL_MANT_DIG == 53
414 testrnd(fmal, 0x1.bbffeea6fc7d6p-30L, 0x1.1d164c6cbf078p-74L,
415 -0x1.ee72993aff948p-104L, -0x1.71f72ac7d9d8p-159L,
416 -0x1.71f72ac7d9d8p-159L, -0x1.71f72ac7d9d8p-159L,
417 -0x1.71f72ac7d9d8p-159L, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
422 test_double_rounding(void)
426 * a = 0x1.8000000000001p0
427 * b = 0x1.8000000000001p0
428 * c = -0x0.0000000000000000000000000080...1p+1
429 * a * b = 0x1.2000000000001800000000000080p+1
431 * The correct behavior is to round DOWN to 0x1.2000000000001p+1 in
432 * round-to-nearest mode. An implementation that computes a*b+c in
433 * double+double precision, however, will get 0x1.20000000000018p+1,
436 fesetround(FE_TONEAREST);
437 test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0,
438 -0x1.0000000000001p-104, 0x1.2000000000001p+1,
439 ALL_STD_EXCEPT, FE_INEXACT);
440 fesetround(FE_DOWNWARD);
441 test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0,
442 -0x1.0000000000001p-104, 0x1.2000000000001p+1,
443 ALL_STD_EXCEPT, FE_INEXACT);
444 fesetround(FE_UPWARD);
445 test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0,
446 -0x1.0000000000001p-104, 0x1.2000000000002p+1,
447 ALL_STD_EXCEPT, FE_INEXACT);
449 fesetround(FE_TONEAREST);
450 test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200002p+1,
451 ALL_STD_EXCEPT, FE_INEXACT);
452 fesetround(FE_DOWNWARD);
453 test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200002p+1,
454 ALL_STD_EXCEPT, FE_INEXACT);
455 fesetround(FE_UPWARD);
456 test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200004p+1,
457 ALL_STD_EXCEPT, FE_INEXACT);
459 fesetround(FE_TONEAREST);
460 #if LDBL_MANT_DIG == 64
461 test(fmal, 0x1.4p+0L, 0x1.0000000000000004p+0L, 0x1p-128L,
462 0x1.4000000000000006p+0L, ALL_STD_EXCEPT, FE_INEXACT);
463 #elif LDBL_MANT_DIG == 113
464 test(fmal, 0x1.8000000000000000000000000001p+0L,
465 0x1.8000000000000000000000000001p+0L,
466 -0x1.0000000000000000000000000001p-224L,
467 0x1.2000000000000000000000000001p+1L, ALL_STD_EXCEPT, FE_INEXACT);
473 main(int argc, char *argv[])
475 int rmodes[] = { FE_TONEAREST, FE_UPWARD, FE_DOWNWARD, FE_TOWARDZERO };
480 for (i = 0; i < 4; i++) {
481 fesetround(rmodes[i]);
483 printf("ok %d - fma zeroes\n", i + 1);
486 for (i = 0; i < 4; i++) {
487 fesetround(rmodes[i]);
489 printf("ok %d - fma infinities\n", i + 5);
492 fesetround(FE_TONEAREST);
494 printf("ok 9 - fma NaNs\n");
496 for (i = 0; i < 4; i++) {
497 fesetround(rmodes[i]);
499 printf("ok %d - fma small z\n", i + 10);
502 for (i = 0; i < 4; i++) {
503 fesetround(rmodes[i]);
505 printf("ok %d - fma big z\n", i + 14);
508 fesetround(FE_TONEAREST);
510 printf("ok 18 - fma accuracy\n");
512 test_double_rounding();
513 printf("ok 19 - fma double rounding\n");
517 * - Tests for subnormals
518 * - Cancellation tests (e.g., z = (double)x*y, but x*y is inexact)