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
test_zeroes(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
test_infinities(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
test_nans(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
test_small_z(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
test_big_z(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
test_accuracy(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
test_double_rounding(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);
ATF_TC_BODY(zeroes,tc)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);
ATF_TC_BODY(infinities,tc)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);
ATF_TC_BODY(nans,tc)493 ATF_TC_BODY(nans, tc)
494 {
495 fesetround(FE_TONEAREST);
496 test_nans();
497 }
498
499
500 ATF_TC_WITHOUT_HEAD(small_z);
ATF_TC_BODY(small_z,tc)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);
ATF_TC_BODY(big_z,tc)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);
ATF_TC_BODY(accuracy,tc)522 ATF_TC_BODY(accuracy, tc)
523 {
524 fesetround(FE_TONEAREST);
525 test_accuracy();
526 }
527
528 ATF_TC_WITHOUT_HEAD(double_rounding);
ATF_TC_BODY(double_rounding,tc)529 ATF_TC_BODY(double_rounding, tc) {
530 test_double_rounding();
531 }
532
ATF_TP_ADD_TCS(tp)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