xref: /freebsd/lib/msun/tests/fma_test.c (revision 79ac3c12a714bcd3f2354c52d948aed9575c46d6)
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 __FBSDID("$FreeBSD$");
33 
34 #include <sys/param.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
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
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
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
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
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
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
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);
475 ATF_TC_BODY(zeroes, tc)
476 {
477 	for (size_t i = 0; i < nitems(rmodes); i++) {
478 		printf("rmode = %d\n", rmodes[i]);
479 		fesetround(rmodes[i]);
480 		test_zeroes();
481 	}
482 }
483 
484 ATF_TC_WITHOUT_HEAD(infinities);
485 ATF_TC_BODY(infinities, tc)
486 {
487 	for (size_t i = 0; i < nitems(rmodes); i++) {
488 		printf("rmode = %d\n", rmodes[i]);
489 		fesetround(rmodes[i]);
490 		test_infinities();
491 	}
492 }
493 
494 ATF_TC_WITHOUT_HEAD(nans);
495 ATF_TC_BODY(nans, tc)
496 {
497 	fesetround(FE_TONEAREST);
498 	test_nans();
499 }
500 
501 
502 ATF_TC_WITHOUT_HEAD(small_z);
503 ATF_TC_BODY(small_z, tc)
504 {
505 	for (size_t i = 0; i < nitems(rmodes); i++) {
506 		printf("rmode = %d\n", rmodes[i]);
507 		fesetround(rmodes[i]);
508 		test_small_z();
509 	}
510 }
511 
512 
513 ATF_TC_WITHOUT_HEAD(big_z);
514 ATF_TC_BODY(big_z, tc)
515 {
516 	for (size_t i = 0; i < nitems(rmodes); i++) {
517 		printf("rmode = %d\n", rmodes[i]);
518 		fesetround(rmodes[i]);
519 		test_big_z();
520 	}
521 }
522 
523 ATF_TC_WITHOUT_HEAD(accuracy);
524 ATF_TC_BODY(accuracy, tc)
525 {
526 	fesetround(FE_TONEAREST);
527 	test_accuracy();
528 }
529 
530 ATF_TC_WITHOUT_HEAD(double_rounding);
531 ATF_TC_BODY(double_rounding, tc) {
532 	test_double_rounding();
533 }
534 
535 ATF_TP_ADD_TCS(tp)
536 {
537 	ATF_TP_ADD_TC(tp, zeroes);
538 	ATF_TP_ADD_TC(tp, infinities);
539 	ATF_TP_ADD_TC(tp, nans);
540 	ATF_TP_ADD_TC(tp, small_z);
541 	ATF_TP_ADD_TC(tp, big_z);
542 	ATF_TP_ADD_TC(tp, accuracy);
543 	ATF_TP_ADD_TC(tp, double_rounding);
544 	/*
545 	 * TODO:
546 	 * - Tests for subnormals
547 	 * - Cancellation tests (e.g., z = (double)x*y, but x*y is inexact)
548 	 */
549 	return (atf_no_error());
550 }
551