xref: /openbsd-src/regress/lib/libm/msun/fma_test.c (revision 4e1ee0786f11cc571bd0be17d38e46f635c719fc)
1 /*	$OpenBSD: fma_test.c,v 1.1 2021/10/22 18:00:22 mbuhl 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/cdefs.h>
35 __FBSDID("$FreeBSD$");
36 
37 #include <sys/param.h>
38 #include <fenv.h>
39 #include <float.h>
40 #include <math.h>
41 #include <stdio.h>
42 #include <stdlib.h>
43 
44 #include "test-utils.h"
45 
46 #pragma STDC FENV_ACCESS ON
47 
48 /*
49  * Test that a function returns the correct value and sets the
50  * exception flags correctly. The exceptmask specifies which
51  * exceptions we should check. We need to be lenient for several
52  * reasons, but mainly because on some architectures it's impossible
53  * to raise FE_OVERFLOW without raising FE_INEXACT.
54  *
55  * These are macros instead of functions so that assert provides more
56  * meaningful error messages.
57  */
58 #define	test(func, x, y, z, result, exceptmask, excepts) do {		\
59 	volatile long double _vx = (x), _vy = (y), _vz = (z);		\
60 	ATF_CHECK(feclearexcept(FE_ALL_EXCEPT) == 0);			\
61 	CHECK_FPEQUAL((func)(_vx, _vy, _vz), (result));		\
62 	CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)",	\
63 	    #func, #x);							\
64 } while (0)
65 
66 #define	testall(x, y, z, result, exceptmask, excepts)	do {		\
67 	test(fma, (double)(x), (double)(y), (double)(z),		\
68 		(double)(result), (exceptmask), (excepts));		\
69 	test(fmaf, (float)(x), (float)(y), (float)(z),			\
70 		(float)(result), (exceptmask), (excepts));		\
71 	test(fmal, (x), (y), (z), (result), (exceptmask), (excepts));	\
72 } while (0)
73 
74 /* Test in all rounding modes. */
75 #define	testrnd(func, x, y, z, rn, ru, rd, rz, exceptmask, excepts)	do { \
76 	fesetround(FE_TONEAREST);					\
77 	test((func), (x), (y), (z), (rn), (exceptmask), (excepts));	\
78 	fesetround(FE_UPWARD);						\
79 	test((func), (x), (y), (z), (ru), (exceptmask), (excepts));	\
80 	fesetround(FE_DOWNWARD);					\
81 	test((func), (x), (y), (z), (rd), (exceptmask), (excepts));	\
82 	fesetround(FE_TOWARDZERO);					\
83 	test((func), (x), (y), (z), (rz), (exceptmask), (excepts));	\
84 } while (0)
85 
86 /*
87  * This is needed because clang constant-folds fma in ways that are incorrect
88  * in rounding modes other than FE_TONEAREST.
89  */
90 static volatile double one = 1.0;
91 
92 static void
93 test_zeroes(void)
94 {
95 	const int rd = (fegetround() == FE_DOWNWARD);
96 
97 	testall(0.0, 0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
98 	testall(1.0, 0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
99 	testall(0.0, 1.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
100 	testall(0.0, 0.0, 1.0, 1.0, ALL_STD_EXCEPT, 0);
101 
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 	testall(-0.0, -0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
105 	testall(0.0, 0.0, -0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
106 	testall(-0.0, -0.0, -0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
107 
108 	testall(-0.0, 0.0, -0.0, -0.0, ALL_STD_EXCEPT, 0);
109 	testall(0.0, -0.0, -0.0, -0.0, ALL_STD_EXCEPT, 0);
110 
111 	testall(-one, one, one, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
112 	testall(one, -one, one, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
113 	testall(-one, -one, -one, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
114 
115 	switch (fegetround()) {
116 	case FE_TONEAREST:
117 	case FE_TOWARDZERO:
118 		test(fmaf, -FLT_MIN, FLT_MIN, 0.0, -0.0,
119 		     ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW);
120 		test(fma, -DBL_MIN, DBL_MIN, 0.0, -0.0,
121 		     ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW);
122 		test(fmal, -LDBL_MIN, LDBL_MIN, 0.0, -0.0,
123 		     ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW);
124 	}
125 }
126 
127 static void
128 test_infinities(void)
129 {
130 	testall(INFINITY, 1.0, -1.0, INFINITY, ALL_STD_EXCEPT, 0);
131 	testall(-1.0, INFINITY, 0.0, -INFINITY, ALL_STD_EXCEPT, 0);
132 	testall(0.0, 0.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
133 	testall(1.0, 1.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
134 	testall(1.0, 1.0, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
135 
136 	testall(INFINITY, -INFINITY, 1.0, -INFINITY, ALL_STD_EXCEPT, 0);
137 	testall(INFINITY, INFINITY, 1.0, INFINITY, ALL_STD_EXCEPT, 0);
138 	testall(-INFINITY, -INFINITY, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
139 
140 	testall(0.0, INFINITY, 1.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
141 	testall(INFINITY, 0.0, -0.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
142 
143 	/* The invalid exception is optional in this case. */
144 	testall(INFINITY, 0.0, NAN, NAN, ALL_STD_EXCEPT & ~FE_INVALID, 0);
145 
146 	testall(INFINITY, INFINITY, -INFINITY, NAN,
147 		ALL_STD_EXCEPT, FE_INVALID);
148 	testall(-INFINITY, INFINITY, INFINITY, NAN,
149 		ALL_STD_EXCEPT, FE_INVALID);
150 	testall(INFINITY, -1.0, INFINITY, NAN,
151 		ALL_STD_EXCEPT, FE_INVALID);
152 
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,
156 	     ALL_STD_EXCEPT, 0);
157 	test(fmaf, FLT_MAX, -FLT_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
158 	test(fma, DBL_MAX, -DBL_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
159 	test(fmal, LDBL_MAX, -LDBL_MAX, INFINITY, INFINITY,
160 	     ALL_STD_EXCEPT, 0);
161 }
162 
163 static void
164 test_nans(void)
165 {
166 	testall(NAN, 0.0, 0.0, NAN, ALL_STD_EXCEPT, 0);
167 	testall(1.0, NAN, 1.0, NAN, ALL_STD_EXCEPT, 0);
168 	testall(1.0, -1.0, NAN, NAN, ALL_STD_EXCEPT, 0);
169 	testall(0.0, 0.0, NAN, NAN, ALL_STD_EXCEPT, 0);
170 	testall(NAN, NAN, NAN, NAN, ALL_STD_EXCEPT, 0);
171 
172 	/* x*y should not raise an inexact/overflow/underflow if z is NaN. */
173 	testall(M_PI, M_PI, NAN, NAN, ALL_STD_EXCEPT, 0);
174 	test(fmaf, FLT_MIN, FLT_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
175 	test(fma, DBL_MIN, DBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
176 	test(fmal, LDBL_MIN, LDBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
177 	test(fmaf, FLT_MAX, FLT_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
178 	test(fma, DBL_MAX, DBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
179 	test(fmal, LDBL_MAX, LDBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
180 }
181 
182 /*
183  * Tests for cases where z is very small compared to x*y.
184  */
185 static void
186 test_small_z(void)
187 {
188 	/* x*y positive, z positive */
189 	if (fegetround() == FE_UPWARD) {
190 		test(fmaf, one, one, 0x1.0p-100, 1.0 + FLT_EPSILON,
191 		     ALL_STD_EXCEPT, FE_INEXACT);
192 		test(fma, one, one, 0x1.0p-200, 1.0 + DBL_EPSILON,
193 		     ALL_STD_EXCEPT, FE_INEXACT);
194 		test(fmal, one, one, 0x1.0p-200, 1.0 + LDBL_EPSILON,
195 		     ALL_STD_EXCEPT, FE_INEXACT);
196 	} else {
197 		testall(0x1.0p100, one, 0x1.0p-100, 0x1.0p100,
198 			ALL_STD_EXCEPT, FE_INEXACT);
199 	}
200 
201 	/* x*y negative, z negative */
202 	if (fegetround() == FE_DOWNWARD) {
203 		test(fmaf, -one, one, -0x1.0p-100, -(1.0 + FLT_EPSILON),
204 		     ALL_STD_EXCEPT, FE_INEXACT);
205 		test(fma, -one, one, -0x1.0p-200, -(1.0 + DBL_EPSILON),
206 		     ALL_STD_EXCEPT, FE_INEXACT);
207 		test(fmal, -one, one, -0x1.0p-200, -(1.0 + LDBL_EPSILON),
208 		     ALL_STD_EXCEPT, FE_INEXACT);
209 	} else {
210 		testall(0x1.0p100, -one, -0x1.0p-100, -0x1.0p100,
211 			ALL_STD_EXCEPT, FE_INEXACT);
212 	}
213 
214 	/* x*y positive, z negative */
215 	if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
216 		test(fmaf, one, one, -0x1.0p-100, 1.0 - FLT_EPSILON / 2,
217 		     ALL_STD_EXCEPT, FE_INEXACT);
218 		test(fma, one, one, -0x1.0p-200, 1.0 - DBL_EPSILON / 2,
219 		     ALL_STD_EXCEPT, FE_INEXACT);
220 		test(fmal, one, one, -0x1.0p-200, 1.0 - LDBL_EPSILON / 2,
221 		     ALL_STD_EXCEPT, FE_INEXACT);
222 	} else {
223 		testall(0x1.0p100, one, -0x1.0p-100, 0x1.0p100,
224 			ALL_STD_EXCEPT, FE_INEXACT);
225 	}
226 
227 	/* x*y negative, z positive */
228 	if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
229 		test(fmaf, -one, one, 0x1.0p-100, -1.0 + FLT_EPSILON / 2,
230 		     ALL_STD_EXCEPT, FE_INEXACT);
231 		test(fma, -one, one, 0x1.0p-200, -1.0 + DBL_EPSILON / 2,
232 		     ALL_STD_EXCEPT, FE_INEXACT);
233 		test(fmal, -one, one, 0x1.0p-200, -1.0 + LDBL_EPSILON / 2,
234 		     ALL_STD_EXCEPT, FE_INEXACT);
235 	} else {
236 		testall(-0x1.0p100, one, 0x1.0p-100, -0x1.0p100,
237 			ALL_STD_EXCEPT, FE_INEXACT);
238 	}
239 }
240 
241 /*
242  * Tests for cases where z is very large compared to x*y.
243  */
244 static void
245 test_big_z(void)
246 {
247 	/* z positive, x*y positive */
248 	if (fegetround() == FE_UPWARD) {
249 		test(fmaf, 0x1.0p-50, 0x1.0p-50, 1.0, 1.0 + FLT_EPSILON,
250 		     ALL_STD_EXCEPT, FE_INEXACT);
251 		test(fma, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + DBL_EPSILON,
252 		     ALL_STD_EXCEPT, FE_INEXACT);
253 		test(fmal, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + LDBL_EPSILON,
254 		     ALL_STD_EXCEPT, FE_INEXACT);
255 	} else {
256 		testall(-0x1.0p-50, -0x1.0p-50, 0x1.0p100, 0x1.0p100,
257 			ALL_STD_EXCEPT, FE_INEXACT);
258 	}
259 
260 	/* z negative, x*y negative */
261 	if (fegetround() == FE_DOWNWARD) {
262 		test(fmaf, -0x1.0p-50, 0x1.0p-50, -1.0, -(1.0 + FLT_EPSILON),
263 		     ALL_STD_EXCEPT, FE_INEXACT);
264 		test(fma, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + DBL_EPSILON),
265 		     ALL_STD_EXCEPT, FE_INEXACT);
266 		test(fmal, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + LDBL_EPSILON),
267 		     ALL_STD_EXCEPT, FE_INEXACT);
268 	} else {
269 		testall(0x1.0p-50, -0x1.0p-50, -0x1.0p100, -0x1.0p100,
270 			ALL_STD_EXCEPT, FE_INEXACT);
271 	}
272 
273 	/* z negative, x*y positive */
274 	if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
275 		test(fmaf, -0x1.0p-50, -0x1.0p-50, -1.0,
276 		     -1.0 + FLT_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
277 		test(fma, -0x1.0p-100, -0x1.0p-100, -1.0,
278 		     -1.0 + DBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
279 		test(fmal, -0x1.0p-100, -0x1.0p-100, -1.0,
280 		     -1.0 + LDBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
281 	} else {
282 		testall(0x1.0p-50, 0x1.0p-50, -0x1.0p100, -0x1.0p100,
283 			ALL_STD_EXCEPT, FE_INEXACT);
284 	}
285 
286 	/* z positive, x*y negative */
287 	if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
288 		test(fmaf, 0x1.0p-50, -0x1.0p-50, 1.0, 1.0 - FLT_EPSILON / 2,
289 		     ALL_STD_EXCEPT, FE_INEXACT);
290 		test(fma, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - DBL_EPSILON / 2,
291 		     ALL_STD_EXCEPT, FE_INEXACT);
292 		test(fmal, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - LDBL_EPSILON / 2,
293 		     ALL_STD_EXCEPT, FE_INEXACT);
294 	} else {
295 		testall(-0x1.0p-50, 0x1.0p-50, 0x1.0p100, 0x1.0p100,
296 			ALL_STD_EXCEPT, FE_INEXACT);
297 	}
298 }
299 
300 static void
301 test_accuracy(void)
302 {
303 
304 	/* ilogb(x*y) - ilogb(z) = 20 */
305 	testrnd(fmaf, -0x1.c139d8p-51, -0x1.600e7ap32, 0x1.26558cp-38,
306 		0x1.34e48ap-18, 0x1.34e48cp-18, 0x1.34e48ap-18, 0x1.34e48ap-18,
307 		ALL_STD_EXCEPT, FE_INEXACT);
308 	testrnd(fma, -0x1.c139d7b84f1a3p-51, -0x1.600e7a2a16484p32,
309 		0x1.26558cac31580p-38, 0x1.34e48a78aae97p-18,
310 		0x1.34e48a78aae97p-18, 0x1.34e48a78aae96p-18,
311 		0x1.34e48a78aae96p-18, ALL_STD_EXCEPT, FE_INEXACT);
312 #if LDBL_MANT_DIG == 113
313 	testrnd(fmal, -0x1.c139d7b84f1a3079263afcc5bae3p-51L,
314 		-0x1.600e7a2a164840edbe2e7d301a72p32L,
315 		0x1.26558cac315807eb07e448042101p-38L,
316 		0x1.34e48a78aae96c76ed36077dd387p-18L,
317 		0x1.34e48a78aae96c76ed36077dd388p-18L,
318 		0x1.34e48a78aae96c76ed36077dd387p-18L,
319 		0x1.34e48a78aae96c76ed36077dd387p-18L,
320 		ALL_STD_EXCEPT, FE_INEXACT);
321 #elif LDBL_MANT_DIG == 64
322 	testrnd(fmal, -0x1.c139d7b84f1a307ap-51L, -0x1.600e7a2a164840eep32L,
323 		0x1.26558cac315807ecp-38L, 0x1.34e48a78aae96c78p-18L,
324 		0x1.34e48a78aae96c78p-18L, 0x1.34e48a78aae96c76p-18L,
325 		0x1.34e48a78aae96c76p-18L, ALL_STD_EXCEPT, FE_INEXACT);
326 #elif LDBL_MANT_DIG == 53
327 	testrnd(fmal, -0x1.c139d7b84f1a3p-51L, -0x1.600e7a2a16484p32L,
328 		0x1.26558cac31580p-38L, 0x1.34e48a78aae97p-18L,
329 		0x1.34e48a78aae97p-18L, 0x1.34e48a78aae96p-18L,
330 		0x1.34e48a78aae96p-18L, ALL_STD_EXCEPT, FE_INEXACT);
331 #endif
332 
333 	/* ilogb(x*y) - ilogb(z) = -40 */
334 	testrnd(fmaf, 0x1.98210ap53, 0x1.9556acp-24, 0x1.d87da4p70,
335 		0x1.d87da4p70, 0x1.d87da6p70, 0x1.d87da4p70, 0x1.d87da4p70,
336 		ALL_STD_EXCEPT, FE_INEXACT);
337 	testrnd(fma, 0x1.98210ac83fe2bp53, 0x1.9556ac1475f0fp-24,
338 		0x1.d87da3aafc60ep70, 0x1.d87da3aafda40p70,
339 		0x1.d87da3aafda40p70, 0x1.d87da3aafda3fp70,
340 		0x1.d87da3aafda3fp70, ALL_STD_EXCEPT, FE_INEXACT);
341 #if LDBL_MANT_DIG == 113
342 	testrnd(fmal, 0x1.98210ac83fe2a8f65b6278b74cebp53L,
343 		0x1.9556ac1475f0f28968b61d0de65ap-24L,
344 		0x1.d87da3aafc60d830aa4c6d73b749p70L,
345 		0x1.d87da3aafda3f36a69eb86488224p70L,
346 		0x1.d87da3aafda3f36a69eb86488225p70L,
347 		0x1.d87da3aafda3f36a69eb86488224p70L,
348 		0x1.d87da3aafda3f36a69eb86488224p70L,
349 		ALL_STD_EXCEPT, FE_INEXACT);
350 #elif LDBL_MANT_DIG == 64
351 	testrnd(fmal, 0x1.98210ac83fe2a8f6p53L, 0x1.9556ac1475f0f28ap-24L,
352 		0x1.d87da3aafc60d83p70L, 0x1.d87da3aafda3f36ap70L,
353 		0x1.d87da3aafda3f36ap70L, 0x1.d87da3aafda3f368p70L,
354 		0x1.d87da3aafda3f368p70L, ALL_STD_EXCEPT, FE_INEXACT);
355 #elif LDBL_MANT_DIG == 53
356 	testrnd(fmal, 0x1.98210ac83fe2bp53L, 0x1.9556ac1475f0fp-24L,
357 		0x1.d87da3aafc60ep70L, 0x1.d87da3aafda40p70L,
358 		0x1.d87da3aafda40p70L, 0x1.d87da3aafda3fp70L,
359 		0x1.d87da3aafda3fp70L, ALL_STD_EXCEPT, FE_INEXACT);
360 #endif
361 
362 	/* ilogb(x*y) - ilogb(z) = 0 */
363 	testrnd(fmaf, 0x1.31ad02p+100, 0x1.2fbf7ap-42, -0x1.c3e106p+58,
364 		-0x1.64c27cp+56, -0x1.64c27ap+56, -0x1.64c27cp+56,
365 		-0x1.64c27ap+56, ALL_STD_EXCEPT, FE_INEXACT);
366 	testrnd(fma, 0x1.31ad012ede8aap+100, 0x1.2fbf79c839067p-42,
367 		-0x1.c3e106929056ep+58, -0x1.64c282b970a5fp+56,
368 		-0x1.64c282b970a5ep+56, -0x1.64c282b970a5fp+56,
369 		-0x1.64c282b970a5ep+56, ALL_STD_EXCEPT, FE_INEXACT);
370 #if LDBL_MANT_DIG == 113
371 	testrnd(fmal, 0x1.31ad012ede8aa282fa1c19376d16p+100L,
372 		 0x1.2fbf79c839066f0f5c68f6d2e814p-42L,
373 		-0x1.c3e106929056ec19de72bfe64215p+58L,
374 		-0x1.64c282b970a612598fc025ca8cddp+56L,
375 		-0x1.64c282b970a612598fc025ca8cddp+56L,
376 		-0x1.64c282b970a612598fc025ca8cdep+56L,
377 		-0x1.64c282b970a612598fc025ca8cddp+56L,
378 		ALL_STD_EXCEPT, FE_INEXACT);
379 #elif LDBL_MANT_DIG == 64
380 	testrnd(fmal, 0x1.31ad012ede8aa4eap+100L, 0x1.2fbf79c839066aeap-42L,
381 		-0x1.c3e106929056e61p+58L, -0x1.64c282b970a60298p+56L,
382 		-0x1.64c282b970a60298p+56L, -0x1.64c282b970a6029ap+56L,
383 		-0x1.64c282b970a60298p+56L, ALL_STD_EXCEPT, FE_INEXACT);
384 #elif LDBL_MANT_DIG == 53
385 	testrnd(fmal, 0x1.31ad012ede8aap+100L, 0x1.2fbf79c839067p-42L,
386 		-0x1.c3e106929056ep+58L, -0x1.64c282b970a5fp+56L,
387 		-0x1.64c282b970a5ep+56L, -0x1.64c282b970a5fp+56L,
388 		-0x1.64c282b970a5ep+56L, ALL_STD_EXCEPT, FE_INEXACT);
389 #endif
390 
391 	/* x*y (rounded) ~= -z */
392 	/* XXX spurious inexact exceptions */
393 	testrnd(fmaf, 0x1.bbffeep-30, -0x1.1d164cp-74, 0x1.ee7296p-104,
394 		-0x1.c46ea8p-128, -0x1.c46ea8p-128, -0x1.c46ea8p-128,
395 		-0x1.c46ea8p-128, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
396 	testrnd(fma, 0x1.bbffeea6fc7d6p-30, 0x1.1d164c6cbf078p-74,
397 		-0x1.ee72993aff948p-104, -0x1.71f72ac7d9d8p-159,
398 		-0x1.71f72ac7d9d8p-159, -0x1.71f72ac7d9d8p-159,
399 		-0x1.71f72ac7d9d8p-159, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
400 #if LDBL_MANT_DIG == 113
401 	testrnd(fmal, 0x1.bbffeea6fc7d65927d147f437675p-30L,
402 		0x1.1d164c6cbf078b7a22607d1cd6a2p-74L,
403 		-0x1.ee72993aff94973876031bec0944p-104L,
404 		0x1.64e086175b3a2adc36e607058814p-217L,
405 		0x1.64e086175b3a2adc36e607058814p-217L,
406 		0x1.64e086175b3a2adc36e607058814p-217L,
407 		0x1.64e086175b3a2adc36e607058814p-217L,
408 		ALL_STD_EXCEPT & ~FE_INEXACT, 0);
409 #elif LDBL_MANT_DIG == 64
410 	testrnd(fmal, 0x1.bbffeea6fc7d6592p-30L, 0x1.1d164c6cbf078b7ap-74L,
411 		-0x1.ee72993aff949736p-104L, 0x1.af190e7a1ee6ad94p-168L,
412 		0x1.af190e7a1ee6ad94p-168L, 0x1.af190e7a1ee6ad94p-168L,
413 		0x1.af190e7a1ee6ad94p-168L, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
414 #elif LDBL_MANT_DIG == 53
415 	testrnd(fmal, 0x1.bbffeea6fc7d6p-30L, 0x1.1d164c6cbf078p-74L,
416 		-0x1.ee72993aff948p-104L, -0x1.71f72ac7d9d8p-159L,
417 		-0x1.71f72ac7d9d8p-159L, -0x1.71f72ac7d9d8p-159L,
418 		-0x1.71f72ac7d9d8p-159L, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
419 #endif
420 }
421 
422 static void
423 test_double_rounding(void)
424 {
425 
426 	/*
427 	 *     a =  0x1.8000000000001p0
428 	 *     b =  0x1.8000000000001p0
429 	 *     c = -0x0.0000000000000000000000000080...1p+1
430 	 * a * b =  0x1.2000000000001800000000000080p+1
431 	 *
432 	 * The correct behavior is to round DOWN to 0x1.2000000000001p+1 in
433 	 * round-to-nearest mode.  An implementation that computes a*b+c in
434 	 * double+double precision, however, will get 0x1.20000000000018p+1,
435 	 * and then round UP.
436 	 */
437 	fesetround(FE_TONEAREST);
438 	test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0,
439 	     -0x1.0000000000001p-104, 0x1.2000000000001p+1,
440 	     ALL_STD_EXCEPT, FE_INEXACT);
441 	fesetround(FE_DOWNWARD);
442 	test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0,
443 	     -0x1.0000000000001p-104, 0x1.2000000000001p+1,
444 	     ALL_STD_EXCEPT, FE_INEXACT);
445 	fesetround(FE_UPWARD);
446 	test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0,
447 	     -0x1.0000000000001p-104, 0x1.2000000000002p+1,
448 	     ALL_STD_EXCEPT, FE_INEXACT);
449 
450 	fesetround(FE_TONEAREST);
451 	test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200002p+1,
452 	     ALL_STD_EXCEPT, FE_INEXACT);
453 	fesetround(FE_DOWNWARD);
454 	test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200002p+1,
455 	     ALL_STD_EXCEPT, FE_INEXACT);
456 	fesetround(FE_UPWARD);
457 	test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200004p+1,
458 	     ALL_STD_EXCEPT, FE_INEXACT);
459 
460 	fesetround(FE_TONEAREST);
461 #if LDBL_MANT_DIG == 64
462 	test(fmal, 0x1.4p+0L, 0x1.0000000000000004p+0L, 0x1p-128L,
463 	     0x1.4000000000000006p+0L, ALL_STD_EXCEPT, FE_INEXACT);
464 #elif LDBL_MANT_DIG == 113
465 	test(fmal, 0x1.8000000000000000000000000001p+0L,
466 	     0x1.8000000000000000000000000001p+0L,
467 	     -0x1.0000000000000000000000000001p-224L,
468 	     0x1.2000000000000000000000000001p+1L, ALL_STD_EXCEPT, FE_INEXACT);
469 #endif
470 
471 }
472 
473 static const int rmodes[] = {
474 	FE_TONEAREST, FE_UPWARD, FE_DOWNWARD, FE_TOWARDZERO
475 };
476 
477 ATF_TC_WITHOUT_HEAD(zeroes);
478 ATF_TC_BODY(zeroes, tc)
479 {
480 	size_t i;
481 	for (i = 0; i < nitems(rmodes); i++) {
482 		printf("rmode = %d\n", rmodes[i]);
483 		fesetround(rmodes[i]);
484 		test_zeroes();
485 	}
486 }
487 
488 ATF_TC_WITHOUT_HEAD(infinities);
489 ATF_TC_BODY(infinities, tc)
490 {
491 	size_t i;
492 	for (i = 0; i < nitems(rmodes); i++) {
493 		printf("rmode = %d\n", rmodes[i]);
494 		fesetround(rmodes[i]);
495 		test_infinities();
496 	}
497 }
498 
499 ATF_TC_WITHOUT_HEAD(nans);
500 ATF_TC_BODY(nans, tc)
501 {
502 	fesetround(FE_TONEAREST);
503 	test_nans();
504 }
505 
506 
507 ATF_TC_WITHOUT_HEAD(small_z);
508 ATF_TC_BODY(small_z, tc)
509 {
510 	size_t i;
511 	for (i = 0; i < nitems(rmodes); i++) {
512 		printf("rmode = %d\n", rmodes[i]);
513 		fesetround(rmodes[i]);
514 		test_small_z();
515 	}
516 }
517 
518 
519 ATF_TC_WITHOUT_HEAD(big_z);
520 ATF_TC_BODY(big_z, tc)
521 {
522 	size_t i;
523 	for (i = 0; i < nitems(rmodes); i++) {
524 		printf("rmode = %d\n", rmodes[i]);
525 		fesetround(rmodes[i]);
526 		test_big_z();
527 	}
528 }
529 
530 ATF_TC_WITHOUT_HEAD(accuracy);
531 ATF_TC_BODY(accuracy, tc)
532 {
533 	fesetround(FE_TONEAREST);
534 	test_accuracy();
535 }
536 
537 ATF_TC_WITHOUT_HEAD(double_rounding);
538 ATF_TC_BODY(double_rounding, tc) {
539 	test_double_rounding();
540 }
541 
542 ATF_TP_ADD_TCS(tp)
543 {
544 	ATF_TP_ADD_TC(tp, zeroes);
545 	ATF_TP_ADD_TC(tp, infinities);
546 	ATF_TP_ADD_TC(tp, nans);
547 	ATF_TP_ADD_TC(tp, small_z);
548 	ATF_TP_ADD_TC(tp, big_z);
549 	ATF_TP_ADD_TC(tp, accuracy);
550 	ATF_TP_ADD_TC(tp, double_rounding);
551 	/*
552 	 * TODO:
553 	 * - Tests for subnormals
554 	 * - Cancellation tests (e.g., z = (double)x*y, but x*y is inexact)
555 	 */
556 	return (atf_no_error());
557 }
558