1 /* $OpenBSD: fma_test.c,v 1.3 2021/12/13 18:04:28 deraadt Exp $ */
2 /*-
3 * Copyright (c) 2008 David Schultz <das@FreeBSD.org>
4 * All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 * notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 * notice, this list of conditions and the following disclaimer in the
13 * documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
25 * SUCH DAMAGE.
26 */
27
28 #include "macros.h"
29
30 /*
31 * Tests for fma{,f,l}().
32 */
33
34 #include <sys/types.h>
35 #include <fenv.h>
36 #include <float.h>
37 #include <math.h>
38 #include <stdio.h>
39 #include <stdlib.h>
40
41 #include "test-utils.h"
42
43 #pragma STDC FENV_ACCESS ON
44
45 /*
46 * Test that a function returns the correct value and sets the
47 * exception flags correctly. The exceptmask specifies which
48 * exceptions we should check. We need to be lenient for several
49 * reasons, but mainly because on some architectures it's impossible
50 * to raise FE_OVERFLOW without raising FE_INEXACT.
51 *
52 * These are macros instead of functions so that assert provides more
53 * meaningful error messages.
54 */
55 #define test(func, x, y, z, result, exceptmask, excepts) do { \
56 volatile long double _vx = (x), _vy = (y), _vz = (z); \
57 ATF_CHECK(feclearexcept(FE_ALL_EXCEPT) == 0); \
58 CHECK_FPEQUAL((func)(_vx, _vy, _vz), (result)); \
59 CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \
60 #func, #x); \
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 static volatile double one = 1.0;
88
89 static void
test_zeroes(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
test_infinities(void)125 test_infinities(void)
126 {
127 testall(INFINITY, 1.0, -1.0, INFINITY, ALL_STD_EXCEPT, 0);
128 testall(-1.0, INFINITY, 0.0, -INFINITY, ALL_STD_EXCEPT, 0);
129 testall(0.0, 0.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
130 testall(1.0, 1.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
131 testall(1.0, 1.0, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
132
133 testall(INFINITY, -INFINITY, 1.0, -INFINITY, ALL_STD_EXCEPT, 0);
134 testall(INFINITY, INFINITY, 1.0, INFINITY, ALL_STD_EXCEPT, 0);
135 testall(-INFINITY, -INFINITY, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
136
137 testall(0.0, INFINITY, 1.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
138 testall(INFINITY, 0.0, -0.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
139
140 /* The invalid exception is optional in this case. */
141 testall(INFINITY, 0.0, NAN, NAN, ALL_STD_EXCEPT & ~FE_INVALID, 0);
142
143 testall(INFINITY, INFINITY, -INFINITY, NAN,
144 ALL_STD_EXCEPT, FE_INVALID);
145 testall(-INFINITY, INFINITY, INFINITY, NAN,
146 ALL_STD_EXCEPT, FE_INVALID);
147 testall(INFINITY, -1.0, INFINITY, NAN,
148 ALL_STD_EXCEPT, FE_INVALID);
149
150 test(fmaf, FLT_MAX, FLT_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
151 test(fma, DBL_MAX, DBL_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
152 test(fmal, LDBL_MAX, LDBL_MAX, -INFINITY, -INFINITY,
153 ALL_STD_EXCEPT, 0);
154 test(fmaf, FLT_MAX, -FLT_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
155 test(fma, DBL_MAX, -DBL_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
156 test(fmal, LDBL_MAX, -LDBL_MAX, INFINITY, INFINITY,
157 ALL_STD_EXCEPT, 0);
158 }
159
160 static void
test_nans(void)161 test_nans(void)
162 {
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);
168
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);
177 }
178
179 /*
180 * Tests for cases where z is very small compared to x*y.
181 */
182 static void
test_small_z(void)183 test_small_z(void)
184 {
185 /* x*y positive, z positive */
186 if (fegetround() == FE_UPWARD) {
187 test(fmaf, one, one, 0x1.0p-100, 1.0 + FLT_EPSILON,
188 ALL_STD_EXCEPT, FE_INEXACT);
189 test(fma, one, one, 0x1.0p-200, 1.0 + DBL_EPSILON,
190 ALL_STD_EXCEPT, FE_INEXACT);
191 test(fmal, one, one, 0x1.0p-200, 1.0 + LDBL_EPSILON,
192 ALL_STD_EXCEPT, FE_INEXACT);
193 } else {
194 testall(0x1.0p100, one, 0x1.0p-100, 0x1.0p100,
195 ALL_STD_EXCEPT, FE_INEXACT);
196 }
197
198 /* x*y negative, z negative */
199 if (fegetround() == FE_DOWNWARD) {
200 test(fmaf, -one, one, -0x1.0p-100, -(1.0 + FLT_EPSILON),
201 ALL_STD_EXCEPT, FE_INEXACT);
202 test(fma, -one, one, -0x1.0p-200, -(1.0 + DBL_EPSILON),
203 ALL_STD_EXCEPT, FE_INEXACT);
204 test(fmal, -one, one, -0x1.0p-200, -(1.0 + LDBL_EPSILON),
205 ALL_STD_EXCEPT, FE_INEXACT);
206 } else {
207 testall(0x1.0p100, -one, -0x1.0p-100, -0x1.0p100,
208 ALL_STD_EXCEPT, FE_INEXACT);
209 }
210
211 /* x*y positive, z negative */
212 if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
213 test(fmaf, one, one, -0x1.0p-100, 1.0 - FLT_EPSILON / 2,
214 ALL_STD_EXCEPT, FE_INEXACT);
215 test(fma, one, one, -0x1.0p-200, 1.0 - DBL_EPSILON / 2,
216 ALL_STD_EXCEPT, FE_INEXACT);
217 test(fmal, one, one, -0x1.0p-200, 1.0 - LDBL_EPSILON / 2,
218 ALL_STD_EXCEPT, FE_INEXACT);
219 } else {
220 testall(0x1.0p100, one, -0x1.0p-100, 0x1.0p100,
221 ALL_STD_EXCEPT, FE_INEXACT);
222 }
223
224 /* x*y negative, z positive */
225 if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
226 test(fmaf, -one, one, 0x1.0p-100, -1.0 + FLT_EPSILON / 2,
227 ALL_STD_EXCEPT, FE_INEXACT);
228 test(fma, -one, one, 0x1.0p-200, -1.0 + DBL_EPSILON / 2,
229 ALL_STD_EXCEPT, FE_INEXACT);
230 test(fmal, -one, one, 0x1.0p-200, -1.0 + LDBL_EPSILON / 2,
231 ALL_STD_EXCEPT, FE_INEXACT);
232 } else {
233 testall(-0x1.0p100, one, 0x1.0p-100, -0x1.0p100,
234 ALL_STD_EXCEPT, FE_INEXACT);
235 }
236 }
237
238 /*
239 * Tests for cases where z is very large compared to x*y.
240 */
241 static void
test_big_z(void)242 test_big_z(void)
243 {
244 /* z positive, x*y positive */
245 if (fegetround() == FE_UPWARD) {
246 test(fmaf, 0x1.0p-50, 0x1.0p-50, 1.0, 1.0 + FLT_EPSILON,
247 ALL_STD_EXCEPT, FE_INEXACT);
248 test(fma, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + DBL_EPSILON,
249 ALL_STD_EXCEPT, FE_INEXACT);
250 test(fmal, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + LDBL_EPSILON,
251 ALL_STD_EXCEPT, FE_INEXACT);
252 } else {
253 testall(-0x1.0p-50, -0x1.0p-50, 0x1.0p100, 0x1.0p100,
254 ALL_STD_EXCEPT, FE_INEXACT);
255 }
256
257 /* z negative, x*y negative */
258 if (fegetround() == FE_DOWNWARD) {
259 test(fmaf, -0x1.0p-50, 0x1.0p-50, -1.0, -(1.0 + FLT_EPSILON),
260 ALL_STD_EXCEPT, FE_INEXACT);
261 test(fma, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + DBL_EPSILON),
262 ALL_STD_EXCEPT, FE_INEXACT);
263 test(fmal, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + LDBL_EPSILON),
264 ALL_STD_EXCEPT, FE_INEXACT);
265 } else {
266 testall(0x1.0p-50, -0x1.0p-50, -0x1.0p100, -0x1.0p100,
267 ALL_STD_EXCEPT, FE_INEXACT);
268 }
269
270 /* z negative, x*y positive */
271 if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
272 test(fmaf, -0x1.0p-50, -0x1.0p-50, -1.0,
273 -1.0 + FLT_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
274 test(fma, -0x1.0p-100, -0x1.0p-100, -1.0,
275 -1.0 + DBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
276 test(fmal, -0x1.0p-100, -0x1.0p-100, -1.0,
277 -1.0 + LDBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
278 } else {
279 testall(0x1.0p-50, 0x1.0p-50, -0x1.0p100, -0x1.0p100,
280 ALL_STD_EXCEPT, FE_INEXACT);
281 }
282
283 /* z positive, x*y negative */
284 if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
285 test(fmaf, 0x1.0p-50, -0x1.0p-50, 1.0, 1.0 - FLT_EPSILON / 2,
286 ALL_STD_EXCEPT, FE_INEXACT);
287 test(fma, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - DBL_EPSILON / 2,
288 ALL_STD_EXCEPT, FE_INEXACT);
289 test(fmal, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - LDBL_EPSILON / 2,
290 ALL_STD_EXCEPT, FE_INEXACT);
291 } else {
292 testall(-0x1.0p-50, 0x1.0p-50, 0x1.0p100, 0x1.0p100,
293 ALL_STD_EXCEPT, FE_INEXACT);
294 }
295 }
296
297 static void
test_accuracy(void)298 test_accuracy(void)
299 {
300
301 /* ilogb(x*y) - ilogb(z) = 20 */
302 testrnd(fmaf, -0x1.c139d8p-51, -0x1.600e7ap32, 0x1.26558cp-38,
303 0x1.34e48ap-18, 0x1.34e48cp-18, 0x1.34e48ap-18, 0x1.34e48ap-18,
304 ALL_STD_EXCEPT, FE_INEXACT);
305 testrnd(fma, -0x1.c139d7b84f1a3p-51, -0x1.600e7a2a16484p32,
306 0x1.26558cac31580p-38, 0x1.34e48a78aae97p-18,
307 0x1.34e48a78aae97p-18, 0x1.34e48a78aae96p-18,
308 0x1.34e48a78aae96p-18, ALL_STD_EXCEPT, FE_INEXACT);
309 #if LDBL_MANT_DIG == 113
310 testrnd(fmal, -0x1.c139d7b84f1a3079263afcc5bae3p-51L,
311 -0x1.600e7a2a164840edbe2e7d301a72p32L,
312 0x1.26558cac315807eb07e448042101p-38L,
313 0x1.34e48a78aae96c76ed36077dd387p-18L,
314 0x1.34e48a78aae96c76ed36077dd388p-18L,
315 0x1.34e48a78aae96c76ed36077dd387p-18L,
316 0x1.34e48a78aae96c76ed36077dd387p-18L,
317 ALL_STD_EXCEPT, FE_INEXACT);
318 #elif LDBL_MANT_DIG == 64
319 testrnd(fmal, -0x1.c139d7b84f1a307ap-51L, -0x1.600e7a2a164840eep32L,
320 0x1.26558cac315807ecp-38L, 0x1.34e48a78aae96c78p-18L,
321 0x1.34e48a78aae96c78p-18L, 0x1.34e48a78aae96c76p-18L,
322 0x1.34e48a78aae96c76p-18L, ALL_STD_EXCEPT, FE_INEXACT);
323 #elif LDBL_MANT_DIG == 53
324 testrnd(fmal, -0x1.c139d7b84f1a3p-51L, -0x1.600e7a2a16484p32L,
325 0x1.26558cac31580p-38L, 0x1.34e48a78aae97p-18L,
326 0x1.34e48a78aae97p-18L, 0x1.34e48a78aae96p-18L,
327 0x1.34e48a78aae96p-18L, ALL_STD_EXCEPT, FE_INEXACT);
328 #endif
329
330 /* ilogb(x*y) - ilogb(z) = -40 */
331 testrnd(fmaf, 0x1.98210ap53, 0x1.9556acp-24, 0x1.d87da4p70,
332 0x1.d87da4p70, 0x1.d87da6p70, 0x1.d87da4p70, 0x1.d87da4p70,
333 ALL_STD_EXCEPT, FE_INEXACT);
334 testrnd(fma, 0x1.98210ac83fe2bp53, 0x1.9556ac1475f0fp-24,
335 0x1.d87da3aafc60ep70, 0x1.d87da3aafda40p70,
336 0x1.d87da3aafda40p70, 0x1.d87da3aafda3fp70,
337 0x1.d87da3aafda3fp70, ALL_STD_EXCEPT, FE_INEXACT);
338 #if LDBL_MANT_DIG == 113
339 testrnd(fmal, 0x1.98210ac83fe2a8f65b6278b74cebp53L,
340 0x1.9556ac1475f0f28968b61d0de65ap-24L,
341 0x1.d87da3aafc60d830aa4c6d73b749p70L,
342 0x1.d87da3aafda3f36a69eb86488224p70L,
343 0x1.d87da3aafda3f36a69eb86488225p70L,
344 0x1.d87da3aafda3f36a69eb86488224p70L,
345 0x1.d87da3aafda3f36a69eb86488224p70L,
346 ALL_STD_EXCEPT, FE_INEXACT);
347 #elif LDBL_MANT_DIG == 64
348 testrnd(fmal, 0x1.98210ac83fe2a8f6p53L, 0x1.9556ac1475f0f28ap-24L,
349 0x1.d87da3aafc60d83p70L, 0x1.d87da3aafda3f36ap70L,
350 0x1.d87da3aafda3f36ap70L, 0x1.d87da3aafda3f368p70L,
351 0x1.d87da3aafda3f368p70L, ALL_STD_EXCEPT, FE_INEXACT);
352 #elif LDBL_MANT_DIG == 53
353 testrnd(fmal, 0x1.98210ac83fe2bp53L, 0x1.9556ac1475f0fp-24L,
354 0x1.d87da3aafc60ep70L, 0x1.d87da3aafda40p70L,
355 0x1.d87da3aafda40p70L, 0x1.d87da3aafda3fp70L,
356 0x1.d87da3aafda3fp70L, ALL_STD_EXCEPT, FE_INEXACT);
357 #endif
358
359 /* ilogb(x*y) - ilogb(z) = 0 */
360 testrnd(fmaf, 0x1.31ad02p+100, 0x1.2fbf7ap-42, -0x1.c3e106p+58,
361 -0x1.64c27cp+56, -0x1.64c27ap+56, -0x1.64c27cp+56,
362 -0x1.64c27ap+56, ALL_STD_EXCEPT, FE_INEXACT);
363 testrnd(fma, 0x1.31ad012ede8aap+100, 0x1.2fbf79c839067p-42,
364 -0x1.c3e106929056ep+58, -0x1.64c282b970a5fp+56,
365 -0x1.64c282b970a5ep+56, -0x1.64c282b970a5fp+56,
366 -0x1.64c282b970a5ep+56, ALL_STD_EXCEPT, FE_INEXACT);
367 #if LDBL_MANT_DIG == 113
368 testrnd(fmal, 0x1.31ad012ede8aa282fa1c19376d16p+100L,
369 0x1.2fbf79c839066f0f5c68f6d2e814p-42L,
370 -0x1.c3e106929056ec19de72bfe64215p+58L,
371 -0x1.64c282b970a612598fc025ca8cddp+56L,
372 -0x1.64c282b970a612598fc025ca8cddp+56L,
373 -0x1.64c282b970a612598fc025ca8cdep+56L,
374 -0x1.64c282b970a612598fc025ca8cddp+56L,
375 ALL_STD_EXCEPT, FE_INEXACT);
376 #elif LDBL_MANT_DIG == 64
377 testrnd(fmal, 0x1.31ad012ede8aa4eap+100L, 0x1.2fbf79c839066aeap-42L,
378 -0x1.c3e106929056e61p+58L, -0x1.64c282b970a60298p+56L,
379 -0x1.64c282b970a60298p+56L, -0x1.64c282b970a6029ap+56L,
380 -0x1.64c282b970a60298p+56L, ALL_STD_EXCEPT, FE_INEXACT);
381 #elif LDBL_MANT_DIG == 53
382 testrnd(fmal, 0x1.31ad012ede8aap+100L, 0x1.2fbf79c839067p-42L,
383 -0x1.c3e106929056ep+58L, -0x1.64c282b970a5fp+56L,
384 -0x1.64c282b970a5ep+56L, -0x1.64c282b970a5fp+56L,
385 -0x1.64c282b970a5ep+56L, ALL_STD_EXCEPT, FE_INEXACT);
386 #endif
387
388 /* x*y (rounded) ~= -z */
389 /* XXX spurious inexact exceptions */
390 testrnd(fmaf, 0x1.bbffeep-30, -0x1.1d164cp-74, 0x1.ee7296p-104,
391 -0x1.c46ea8p-128, -0x1.c46ea8p-128, -0x1.c46ea8p-128,
392 -0x1.c46ea8p-128, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
393 testrnd(fma, 0x1.bbffeea6fc7d6p-30, 0x1.1d164c6cbf078p-74,
394 -0x1.ee72993aff948p-104, -0x1.71f72ac7d9d8p-159,
395 -0x1.71f72ac7d9d8p-159, -0x1.71f72ac7d9d8p-159,
396 -0x1.71f72ac7d9d8p-159, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
397 #if LDBL_MANT_DIG == 113
398 testrnd(fmal, 0x1.bbffeea6fc7d65927d147f437675p-30L,
399 0x1.1d164c6cbf078b7a22607d1cd6a2p-74L,
400 -0x1.ee72993aff94973876031bec0944p-104L,
401 0x1.64e086175b3a2adc36e607058814p-217L,
402 0x1.64e086175b3a2adc36e607058814p-217L,
403 0x1.64e086175b3a2adc36e607058814p-217L,
404 0x1.64e086175b3a2adc36e607058814p-217L,
405 ALL_STD_EXCEPT & ~FE_INEXACT, 0);
406 #elif LDBL_MANT_DIG == 64
407 testrnd(fmal, 0x1.bbffeea6fc7d6592p-30L, 0x1.1d164c6cbf078b7ap-74L,
408 -0x1.ee72993aff949736p-104L, 0x1.af190e7a1ee6ad94p-168L,
409 0x1.af190e7a1ee6ad94p-168L, 0x1.af190e7a1ee6ad94p-168L,
410 0x1.af190e7a1ee6ad94p-168L, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
411 #elif LDBL_MANT_DIG == 53
412 testrnd(fmal, 0x1.bbffeea6fc7d6p-30L, 0x1.1d164c6cbf078p-74L,
413 -0x1.ee72993aff948p-104L, -0x1.71f72ac7d9d8p-159L,
414 -0x1.71f72ac7d9d8p-159L, -0x1.71f72ac7d9d8p-159L,
415 -0x1.71f72ac7d9d8p-159L, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
416 #endif
417 }
418
419 static void
test_double_rounding(void)420 test_double_rounding(void)
421 {
422
423 /*
424 * a = 0x1.8000000000001p0
425 * b = 0x1.8000000000001p0
426 * c = -0x0.0000000000000000000000000080...1p+1
427 * a * b = 0x1.2000000000001800000000000080p+1
428 *
429 * The correct behavior is to round DOWN to 0x1.2000000000001p+1 in
430 * round-to-nearest mode. An implementation that computes a*b+c in
431 * double+double precision, however, will get 0x1.20000000000018p+1,
432 * and then round UP.
433 */
434 fesetround(FE_TONEAREST);
435 test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0,
436 -0x1.0000000000001p-104, 0x1.2000000000001p+1,
437 ALL_STD_EXCEPT, FE_INEXACT);
438 fesetround(FE_DOWNWARD);
439 test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0,
440 -0x1.0000000000001p-104, 0x1.2000000000001p+1,
441 ALL_STD_EXCEPT, FE_INEXACT);
442 fesetround(FE_UPWARD);
443 test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0,
444 -0x1.0000000000001p-104, 0x1.2000000000002p+1,
445 ALL_STD_EXCEPT, FE_INEXACT);
446
447 fesetround(FE_TONEAREST);
448 test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200002p+1,
449 ALL_STD_EXCEPT, FE_INEXACT);
450 fesetround(FE_DOWNWARD);
451 test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200002p+1,
452 ALL_STD_EXCEPT, FE_INEXACT);
453 fesetround(FE_UPWARD);
454 test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200004p+1,
455 ALL_STD_EXCEPT, FE_INEXACT);
456
457 fesetround(FE_TONEAREST);
458 #if LDBL_MANT_DIG == 64
459 test(fmal, 0x1.4p+0L, 0x1.0000000000000004p+0L, 0x1p-128L,
460 0x1.4000000000000006p+0L, ALL_STD_EXCEPT, FE_INEXACT);
461 #elif LDBL_MANT_DIG == 113
462 test(fmal, 0x1.8000000000000000000000000001p+0L,
463 0x1.8000000000000000000000000001p+0L,
464 -0x1.0000000000000000000000000001p-224L,
465 0x1.2000000000000000000000000001p+1L, ALL_STD_EXCEPT, FE_INEXACT);
466 #endif
467
468 }
469
470 static const int rmodes[] = {
471 FE_TONEAREST, FE_UPWARD, FE_DOWNWARD, FE_TOWARDZERO
472 };
473
474 ATF_TC_WITHOUT_HEAD(zeroes);
ATF_TC_BODY(zeroes,tc)475 ATF_TC_BODY(zeroes, tc)
476 {
477 size_t i;
478 for (i = 0; i < nitems(rmodes); i++) {
479 printf("rmode = %d\n", rmodes[i]);
480 fesetround(rmodes[i]);
481 test_zeroes();
482 }
483 }
484
485 ATF_TC_WITHOUT_HEAD(infinities);
ATF_TC_BODY(infinities,tc)486 ATF_TC_BODY(infinities, tc)
487 {
488 size_t i;
489 for (i = 0; i < nitems(rmodes); i++) {
490 printf("rmode = %d\n", rmodes[i]);
491 fesetround(rmodes[i]);
492 test_infinities();
493 }
494 }
495
496 ATF_TC_WITHOUT_HEAD(nans);
ATF_TC_BODY(nans,tc)497 ATF_TC_BODY(nans, tc)
498 {
499 fesetround(FE_TONEAREST);
500 test_nans();
501 }
502
503
504 ATF_TC_WITHOUT_HEAD(small_z);
ATF_TC_BODY(small_z,tc)505 ATF_TC_BODY(small_z, tc)
506 {
507 size_t i;
508 for (i = 0; i < nitems(rmodes); i++) {
509 printf("rmode = %d\n", rmodes[i]);
510 fesetround(rmodes[i]);
511 test_small_z();
512 }
513 }
514
515
516 ATF_TC_WITHOUT_HEAD(big_z);
ATF_TC_BODY(big_z,tc)517 ATF_TC_BODY(big_z, tc)
518 {
519 size_t i;
520 for (i = 0; i < nitems(rmodes); i++) {
521 printf("rmode = %d\n", rmodes[i]);
522 fesetround(rmodes[i]);
523 test_big_z();
524 }
525 }
526
527 ATF_TC_WITHOUT_HEAD(accuracy);
ATF_TC_BODY(accuracy,tc)528 ATF_TC_BODY(accuracy, tc)
529 {
530 fesetround(FE_TONEAREST);
531 test_accuracy();
532 }
533
534 ATF_TC_WITHOUT_HEAD(double_rounding);
ATF_TC_BODY(double_rounding,tc)535 ATF_TC_BODY(double_rounding, tc) {
536 test_double_rounding();
537 }
538
ATF_TP_ADD_TCS(tp)539 ATF_TP_ADD_TCS(tp)
540 {
541 ATF_TP_ADD_TC(tp, zeroes);
542 ATF_TP_ADD_TC(tp, infinities);
543 ATF_TP_ADD_TC(tp, nans);
544 ATF_TP_ADD_TC(tp, small_z);
545 ATF_TP_ADD_TC(tp, big_z);
546 ATF_TP_ADD_TC(tp, accuracy);
547 ATF_TP_ADD_TC(tp, double_rounding);
548 /*
549 * TODO:
550 * - Tests for subnormals
551 * - Cancellation tests (e.g., z = (double)x*y, but x*y is inexact)
552 */
553 return (atf_no_error());
554 }
555