xref: /freebsd/lib/msun/tests/fma_test.c (revision 783d3ff6d7fae619db8a7990b8a6387de0c677b5)
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/param.h>
32 #include <fenv.h>
33 #include <float.h>
34 #include <math.h>
35 #include <stdio.h>
36 #include <stdlib.h>
37 
38 #include "test-utils.h"
39 
40 #pragma STDC FENV_ACCESS ON
41 
42 /*
43  * Test that a function returns the correct value and sets the
44  * exception flags correctly. The exceptmask specifies which
45  * exceptions we should check. We need to be lenient for several
46  * reasons, but mainly because on some architectures it's impossible
47  * to raise FE_OVERFLOW without raising FE_INEXACT.
48  *
49  * These are macros instead of functions so that assert provides more
50  * meaningful error messages.
51  */
52 #define	test(func, x, y, z, result, exceptmask, excepts) do {		\
53 	volatile long double _vx = (x), _vy = (y), _vz = (z);		\
54 	ATF_CHECK(feclearexcept(FE_ALL_EXCEPT) == 0);			\
55 	CHECK_FPEQUAL((func)(_vx, _vy, _vz), (result));		\
56 	CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)",	\
57 	    #func, #x);							\
58 } while (0)
59 
60 #define	testall(x, y, z, result, exceptmask, excepts)	do {		\
61 	test(fma, (double)(x), (double)(y), (double)(z),		\
62 		(double)(result), (exceptmask), (excepts));		\
63 	test(fmaf, (float)(x), (float)(y), (float)(z),			\
64 		(float)(result), (exceptmask), (excepts));		\
65 	test(fmal, (x), (y), (z), (result), (exceptmask), (excepts));	\
66 } while (0)
67 
68 /* Test in all rounding modes. */
69 #define	testrnd(func, x, y, z, rn, ru, rd, rz, exceptmask, excepts)	do { \
70 	fesetround(FE_TONEAREST);					\
71 	test((func), (x), (y), (z), (rn), (exceptmask), (excepts));	\
72 	fesetround(FE_UPWARD);						\
73 	test((func), (x), (y), (z), (ru), (exceptmask), (excepts));	\
74 	fesetround(FE_DOWNWARD);					\
75 	test((func), (x), (y), (z), (rd), (exceptmask), (excepts));	\
76 	fesetround(FE_TOWARDZERO);					\
77 	test((func), (x), (y), (z), (rz), (exceptmask), (excepts));	\
78 } while (0)
79 
80 /*
81  * This is needed because clang constant-folds fma in ways that are incorrect
82  * in rounding modes other than FE_TONEAREST.
83  */
84 static volatile double one = 1.0;
85 
86 static void
87 test_zeroes(void)
88 {
89 	const int rd = (fegetround() == FE_DOWNWARD);
90 
91 	testall(0.0, 0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
92 	testall(1.0, 0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
93 	testall(0.0, 1.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
94 	testall(0.0, 0.0, 1.0, 1.0, ALL_STD_EXCEPT, 0);
95 
96 	testall(-0.0, 0.0, 0.0, rd ? -0.0 : 0.0, 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, 0.0, ALL_STD_EXCEPT, 0);
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 
102 	testall(-0.0, 0.0, -0.0, -0.0, ALL_STD_EXCEPT, 0);
103 	testall(0.0, -0.0, -0.0, -0.0, ALL_STD_EXCEPT, 0);
104 
105 	testall(-one, one, one, rd ? -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 
109 	switch (fegetround()) {
110 	case FE_TONEAREST:
111 	case FE_TOWARDZERO:
112 		test(fmaf, -FLT_MIN, FLT_MIN, 0.0, -0.0,
113 		     ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW);
114 		test(fma, -DBL_MIN, DBL_MIN, 0.0, -0.0,
115 		     ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW);
116 		test(fmal, -LDBL_MIN, LDBL_MIN, 0.0, -0.0,
117 		     ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW);
118 	}
119 }
120 
121 static void
122 test_infinities(void)
123 {
124 	testall(INFINITY, 1.0, -1.0, INFINITY, ALL_STD_EXCEPT, 0);
125 	testall(-1.0, INFINITY, 0.0, -INFINITY, ALL_STD_EXCEPT, 0);
126 	testall(0.0, 0.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
127 	testall(1.0, 1.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
128 	testall(1.0, 1.0, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
129 
130 	testall(INFINITY, -INFINITY, 1.0, -INFINITY, ALL_STD_EXCEPT, 0);
131 	testall(INFINITY, INFINITY, 1.0, INFINITY, ALL_STD_EXCEPT, 0);
132 	testall(-INFINITY, -INFINITY, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
133 
134 	testall(0.0, INFINITY, 1.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
135 	testall(INFINITY, 0.0, -0.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
136 
137 	/* The invalid exception is optional in this case. */
138 	testall(INFINITY, 0.0, NAN, NAN, ALL_STD_EXCEPT & ~FE_INVALID, 0);
139 
140 	testall(INFINITY, INFINITY, -INFINITY, NAN,
141 		ALL_STD_EXCEPT, FE_INVALID);
142 	testall(-INFINITY, INFINITY, INFINITY, NAN,
143 		ALL_STD_EXCEPT, FE_INVALID);
144 	testall(INFINITY, -1.0, INFINITY, NAN,
145 		ALL_STD_EXCEPT, FE_INVALID);
146 
147 	test(fmaf, FLT_MAX, FLT_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
148 	test(fma, DBL_MAX, DBL_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
149 	test(fmal, LDBL_MAX, LDBL_MAX, -INFINITY, -INFINITY,
150 	     ALL_STD_EXCEPT, 0);
151 	test(fmaf, FLT_MAX, -FLT_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
152 	test(fma, DBL_MAX, -DBL_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
153 	test(fmal, LDBL_MAX, -LDBL_MAX, INFINITY, INFINITY,
154 	     ALL_STD_EXCEPT, 0);
155 }
156 
157 static void
158 test_nans(void)
159 {
160 	testall(NAN, 0.0, 0.0, NAN, ALL_STD_EXCEPT, 0);
161 	testall(1.0, NAN, 1.0, NAN, ALL_STD_EXCEPT, 0);
162 	testall(1.0, -1.0, NAN, NAN, ALL_STD_EXCEPT, 0);
163 	testall(0.0, 0.0, NAN, NAN, ALL_STD_EXCEPT, 0);
164 	testall(NAN, NAN, NAN, NAN, ALL_STD_EXCEPT, 0);
165 
166 	/* x*y should not raise an inexact/overflow/underflow if z is NaN. */
167 	testall(M_PI, M_PI, NAN, NAN, ALL_STD_EXCEPT, 0);
168 	test(fmaf, FLT_MIN, FLT_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
169 	test(fma, DBL_MIN, DBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
170 	test(fmal, LDBL_MIN, LDBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
171 	test(fmaf, FLT_MAX, FLT_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
172 	test(fma, DBL_MAX, DBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
173 	test(fmal, LDBL_MAX, LDBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
174 }
175 
176 /*
177  * Tests for cases where z is very small compared to x*y.
178  */
179 static void
180 test_small_z(void)
181 {
182 	/* x*y positive, z positive */
183 	if (fegetround() == FE_UPWARD) {
184 		test(fmaf, one, one, 0x1.0p-100, 1.0 + FLT_EPSILON,
185 		     ALL_STD_EXCEPT, FE_INEXACT);
186 		test(fma, one, one, 0x1.0p-200, 1.0 + DBL_EPSILON,
187 		     ALL_STD_EXCEPT, FE_INEXACT);
188 		test(fmal, one, one, 0x1.0p-200, 1.0 + LDBL_EPSILON,
189 		     ALL_STD_EXCEPT, FE_INEXACT);
190 	} else {
191 		testall(0x1.0p100, one, 0x1.0p-100, 0x1.0p100,
192 			ALL_STD_EXCEPT, FE_INEXACT);
193 	}
194 
195 	/* x*y negative, z negative */
196 	if (fegetround() == FE_DOWNWARD) {
197 		test(fmaf, -one, one, -0x1.0p-100, -(1.0 + FLT_EPSILON),
198 		     ALL_STD_EXCEPT, FE_INEXACT);
199 		test(fma, -one, one, -0x1.0p-200, -(1.0 + DBL_EPSILON),
200 		     ALL_STD_EXCEPT, FE_INEXACT);
201 		test(fmal, -one, one, -0x1.0p-200, -(1.0 + LDBL_EPSILON),
202 		     ALL_STD_EXCEPT, FE_INEXACT);
203 	} else {
204 		testall(0x1.0p100, -one, -0x1.0p-100, -0x1.0p100,
205 			ALL_STD_EXCEPT, FE_INEXACT);
206 	}
207 
208 	/* x*y positive, z negative */
209 	if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
210 		test(fmaf, one, one, -0x1.0p-100, 1.0 - FLT_EPSILON / 2,
211 		     ALL_STD_EXCEPT, FE_INEXACT);
212 		test(fma, one, one, -0x1.0p-200, 1.0 - DBL_EPSILON / 2,
213 		     ALL_STD_EXCEPT, FE_INEXACT);
214 		test(fmal, one, one, -0x1.0p-200, 1.0 - LDBL_EPSILON / 2,
215 		     ALL_STD_EXCEPT, FE_INEXACT);
216 	} else {
217 		testall(0x1.0p100, one, -0x1.0p-100, 0x1.0p100,
218 			ALL_STD_EXCEPT, FE_INEXACT);
219 	}
220 
221 	/* x*y negative, z positive */
222 	if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
223 		test(fmaf, -one, one, 0x1.0p-100, -1.0 + FLT_EPSILON / 2,
224 		     ALL_STD_EXCEPT, FE_INEXACT);
225 		test(fma, -one, one, 0x1.0p-200, -1.0 + DBL_EPSILON / 2,
226 		     ALL_STD_EXCEPT, FE_INEXACT);
227 		test(fmal, -one, one, 0x1.0p-200, -1.0 + LDBL_EPSILON / 2,
228 		     ALL_STD_EXCEPT, FE_INEXACT);
229 	} else {
230 		testall(-0x1.0p100, one, 0x1.0p-100, -0x1.0p100,
231 			ALL_STD_EXCEPT, FE_INEXACT);
232 	}
233 }
234 
235 /*
236  * Tests for cases where z is very large compared to x*y.
237  */
238 static void
239 test_big_z(void)
240 {
241 	/* z positive, x*y positive */
242 	if (fegetround() == FE_UPWARD) {
243 		test(fmaf, 0x1.0p-50, 0x1.0p-50, 1.0, 1.0 + FLT_EPSILON,
244 		     ALL_STD_EXCEPT, FE_INEXACT);
245 		test(fma, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + DBL_EPSILON,
246 		     ALL_STD_EXCEPT, FE_INEXACT);
247 		test(fmal, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + LDBL_EPSILON,
248 		     ALL_STD_EXCEPT, FE_INEXACT);
249 	} else {
250 		testall(-0x1.0p-50, -0x1.0p-50, 0x1.0p100, 0x1.0p100,
251 			ALL_STD_EXCEPT, FE_INEXACT);
252 	}
253 
254 	/* z negative, x*y negative */
255 	if (fegetround() == FE_DOWNWARD) {
256 		test(fmaf, -0x1.0p-50, 0x1.0p-50, -1.0, -(1.0 + FLT_EPSILON),
257 		     ALL_STD_EXCEPT, FE_INEXACT);
258 		test(fma, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + DBL_EPSILON),
259 		     ALL_STD_EXCEPT, FE_INEXACT);
260 		test(fmal, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + LDBL_EPSILON),
261 		     ALL_STD_EXCEPT, FE_INEXACT);
262 	} else {
263 		testall(0x1.0p-50, -0x1.0p-50, -0x1.0p100, -0x1.0p100,
264 			ALL_STD_EXCEPT, FE_INEXACT);
265 	}
266 
267 	/* z negative, x*y positive */
268 	if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
269 		test(fmaf, -0x1.0p-50, -0x1.0p-50, -1.0,
270 		     -1.0 + FLT_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
271 		test(fma, -0x1.0p-100, -0x1.0p-100, -1.0,
272 		     -1.0 + DBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
273 		test(fmal, -0x1.0p-100, -0x1.0p-100, -1.0,
274 		     -1.0 + LDBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
275 	} else {
276 		testall(0x1.0p-50, 0x1.0p-50, -0x1.0p100, -0x1.0p100,
277 			ALL_STD_EXCEPT, FE_INEXACT);
278 	}
279 
280 	/* z positive, x*y negative */
281 	if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
282 		test(fmaf, 0x1.0p-50, -0x1.0p-50, 1.0, 1.0 - FLT_EPSILON / 2,
283 		     ALL_STD_EXCEPT, FE_INEXACT);
284 		test(fma, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - DBL_EPSILON / 2,
285 		     ALL_STD_EXCEPT, FE_INEXACT);
286 		test(fmal, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - LDBL_EPSILON / 2,
287 		     ALL_STD_EXCEPT, FE_INEXACT);
288 	} else {
289 		testall(-0x1.0p-50, 0x1.0p-50, 0x1.0p100, 0x1.0p100,
290 			ALL_STD_EXCEPT, FE_INEXACT);
291 	}
292 }
293 
294 static void
295 test_accuracy(void)
296 {
297 
298 	/* ilogb(x*y) - ilogb(z) = 20 */
299 	testrnd(fmaf, -0x1.c139d8p-51, -0x1.600e7ap32, 0x1.26558cp-38,
300 		0x1.34e48ap-18, 0x1.34e48cp-18, 0x1.34e48ap-18, 0x1.34e48ap-18,
301 		ALL_STD_EXCEPT, FE_INEXACT);
302 	testrnd(fma, -0x1.c139d7b84f1a3p-51, -0x1.600e7a2a16484p32,
303 		0x1.26558cac31580p-38, 0x1.34e48a78aae97p-18,
304 		0x1.34e48a78aae97p-18, 0x1.34e48a78aae96p-18,
305 		0x1.34e48a78aae96p-18, ALL_STD_EXCEPT, FE_INEXACT);
306 #if LDBL_MANT_DIG == 113
307 	testrnd(fmal, -0x1.c139d7b84f1a3079263afcc5bae3p-51L,
308 		-0x1.600e7a2a164840edbe2e7d301a72p32L,
309 		0x1.26558cac315807eb07e448042101p-38L,
310 		0x1.34e48a78aae96c76ed36077dd387p-18L,
311 		0x1.34e48a78aae96c76ed36077dd388p-18L,
312 		0x1.34e48a78aae96c76ed36077dd387p-18L,
313 		0x1.34e48a78aae96c76ed36077dd387p-18L,
314 		ALL_STD_EXCEPT, FE_INEXACT);
315 #elif LDBL_MANT_DIG == 64
316 	testrnd(fmal, -0x1.c139d7b84f1a307ap-51L, -0x1.600e7a2a164840eep32L,
317 		0x1.26558cac315807ecp-38L, 0x1.34e48a78aae96c78p-18L,
318 		0x1.34e48a78aae96c78p-18L, 0x1.34e48a78aae96c76p-18L,
319 		0x1.34e48a78aae96c76p-18L, ALL_STD_EXCEPT, FE_INEXACT);
320 #elif LDBL_MANT_DIG == 53
321 	testrnd(fmal, -0x1.c139d7b84f1a3p-51L, -0x1.600e7a2a16484p32L,
322 		0x1.26558cac31580p-38L, 0x1.34e48a78aae97p-18L,
323 		0x1.34e48a78aae97p-18L, 0x1.34e48a78aae96p-18L,
324 		0x1.34e48a78aae96p-18L, ALL_STD_EXCEPT, FE_INEXACT);
325 #endif
326 
327 	/* ilogb(x*y) - ilogb(z) = -40 */
328 	testrnd(fmaf, 0x1.98210ap53, 0x1.9556acp-24, 0x1.d87da4p70,
329 		0x1.d87da4p70, 0x1.d87da6p70, 0x1.d87da4p70, 0x1.d87da4p70,
330 		ALL_STD_EXCEPT, FE_INEXACT);
331 	testrnd(fma, 0x1.98210ac83fe2bp53, 0x1.9556ac1475f0fp-24,
332 		0x1.d87da3aafc60ep70, 0x1.d87da3aafda40p70,
333 		0x1.d87da3aafda40p70, 0x1.d87da3aafda3fp70,
334 		0x1.d87da3aafda3fp70, ALL_STD_EXCEPT, FE_INEXACT);
335 #if LDBL_MANT_DIG == 113
336 	testrnd(fmal, 0x1.98210ac83fe2a8f65b6278b74cebp53L,
337 		0x1.9556ac1475f0f28968b61d0de65ap-24L,
338 		0x1.d87da3aafc60d830aa4c6d73b749p70L,
339 		0x1.d87da3aafda3f36a69eb86488224p70L,
340 		0x1.d87da3aafda3f36a69eb86488225p70L,
341 		0x1.d87da3aafda3f36a69eb86488224p70L,
342 		0x1.d87da3aafda3f36a69eb86488224p70L,
343 		ALL_STD_EXCEPT, FE_INEXACT);
344 #elif LDBL_MANT_DIG == 64
345 	testrnd(fmal, 0x1.98210ac83fe2a8f6p53L, 0x1.9556ac1475f0f28ap-24L,
346 		0x1.d87da3aafc60d83p70L, 0x1.d87da3aafda3f36ap70L,
347 		0x1.d87da3aafda3f36ap70L, 0x1.d87da3aafda3f368p70L,
348 		0x1.d87da3aafda3f368p70L, ALL_STD_EXCEPT, FE_INEXACT);
349 #elif LDBL_MANT_DIG == 53
350 	testrnd(fmal, 0x1.98210ac83fe2bp53L, 0x1.9556ac1475f0fp-24L,
351 		0x1.d87da3aafc60ep70L, 0x1.d87da3aafda40p70L,
352 		0x1.d87da3aafda40p70L, 0x1.d87da3aafda3fp70L,
353 		0x1.d87da3aafda3fp70L, ALL_STD_EXCEPT, FE_INEXACT);
354 #endif
355 
356 	/* ilogb(x*y) - ilogb(z) = 0 */
357 	testrnd(fmaf, 0x1.31ad02p+100, 0x1.2fbf7ap-42, -0x1.c3e106p+58,
358 		-0x1.64c27cp+56, -0x1.64c27ap+56, -0x1.64c27cp+56,
359 		-0x1.64c27ap+56, ALL_STD_EXCEPT, FE_INEXACT);
360 	testrnd(fma, 0x1.31ad012ede8aap+100, 0x1.2fbf79c839067p-42,
361 		-0x1.c3e106929056ep+58, -0x1.64c282b970a5fp+56,
362 		-0x1.64c282b970a5ep+56, -0x1.64c282b970a5fp+56,
363 		-0x1.64c282b970a5ep+56, ALL_STD_EXCEPT, FE_INEXACT);
364 #if LDBL_MANT_DIG == 113
365 	testrnd(fmal, 0x1.31ad012ede8aa282fa1c19376d16p+100L,
366 		 0x1.2fbf79c839066f0f5c68f6d2e814p-42L,
367 		-0x1.c3e106929056ec19de72bfe64215p+58L,
368 		-0x1.64c282b970a612598fc025ca8cddp+56L,
369 		-0x1.64c282b970a612598fc025ca8cddp+56L,
370 		-0x1.64c282b970a612598fc025ca8cdep+56L,
371 		-0x1.64c282b970a612598fc025ca8cddp+56L,
372 		ALL_STD_EXCEPT, FE_INEXACT);
373 #elif LDBL_MANT_DIG == 64
374 	testrnd(fmal, 0x1.31ad012ede8aa4eap+100L, 0x1.2fbf79c839066aeap-42L,
375 		-0x1.c3e106929056e61p+58L, -0x1.64c282b970a60298p+56L,
376 		-0x1.64c282b970a60298p+56L, -0x1.64c282b970a6029ap+56L,
377 		-0x1.64c282b970a60298p+56L, ALL_STD_EXCEPT, FE_INEXACT);
378 #elif LDBL_MANT_DIG == 53
379 	testrnd(fmal, 0x1.31ad012ede8aap+100L, 0x1.2fbf79c839067p-42L,
380 		-0x1.c3e106929056ep+58L, -0x1.64c282b970a5fp+56L,
381 		-0x1.64c282b970a5ep+56L, -0x1.64c282b970a5fp+56L,
382 		-0x1.64c282b970a5ep+56L, ALL_STD_EXCEPT, FE_INEXACT);
383 #endif
384 
385 	/* x*y (rounded) ~= -z */
386 	/* XXX spurious inexact exceptions */
387 	testrnd(fmaf, 0x1.bbffeep-30, -0x1.1d164cp-74, 0x1.ee7296p-104,
388 		-0x1.c46ea8p-128, -0x1.c46ea8p-128, -0x1.c46ea8p-128,
389 		-0x1.c46ea8p-128, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
390 	testrnd(fma, 0x1.bbffeea6fc7d6p-30, 0x1.1d164c6cbf078p-74,
391 		-0x1.ee72993aff948p-104, -0x1.71f72ac7d9d8p-159,
392 		-0x1.71f72ac7d9d8p-159, -0x1.71f72ac7d9d8p-159,
393 		-0x1.71f72ac7d9d8p-159, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
394 #if LDBL_MANT_DIG == 113
395 	testrnd(fmal, 0x1.bbffeea6fc7d65927d147f437675p-30L,
396 		0x1.1d164c6cbf078b7a22607d1cd6a2p-74L,
397 		-0x1.ee72993aff94973876031bec0944p-104L,
398 		0x1.64e086175b3a2adc36e607058814p-217L,
399 		0x1.64e086175b3a2adc36e607058814p-217L,
400 		0x1.64e086175b3a2adc36e607058814p-217L,
401 		0x1.64e086175b3a2adc36e607058814p-217L,
402 		ALL_STD_EXCEPT & ~FE_INEXACT, 0);
403 #elif LDBL_MANT_DIG == 64
404 	testrnd(fmal, 0x1.bbffeea6fc7d6592p-30L, 0x1.1d164c6cbf078b7ap-74L,
405 		-0x1.ee72993aff949736p-104L, 0x1.af190e7a1ee6ad94p-168L,
406 		0x1.af190e7a1ee6ad94p-168L, 0x1.af190e7a1ee6ad94p-168L,
407 		0x1.af190e7a1ee6ad94p-168L, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
408 #elif LDBL_MANT_DIG == 53
409 	testrnd(fmal, 0x1.bbffeea6fc7d6p-30L, 0x1.1d164c6cbf078p-74L,
410 		-0x1.ee72993aff948p-104L, -0x1.71f72ac7d9d8p-159L,
411 		-0x1.71f72ac7d9d8p-159L, -0x1.71f72ac7d9d8p-159L,
412 		-0x1.71f72ac7d9d8p-159L, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
413 #endif
414 }
415 
416 static void
417 test_double_rounding(void)
418 {
419 
420 	/*
421 	 *     a =  0x1.8000000000001p0
422 	 *     b =  0x1.8000000000001p0
423 	 *     c = -0x0.0000000000000000000000000080...1p+1
424 	 * a * b =  0x1.2000000000001800000000000080p+1
425 	 *
426 	 * The correct behavior is to round DOWN to 0x1.2000000000001p+1 in
427 	 * round-to-nearest mode.  An implementation that computes a*b+c in
428 	 * double+double precision, however, will get 0x1.20000000000018p+1,
429 	 * and then round UP.
430 	 */
431 	fesetround(FE_TONEAREST);
432 	test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0,
433 	     -0x1.0000000000001p-104, 0x1.2000000000001p+1,
434 	     ALL_STD_EXCEPT, FE_INEXACT);
435 	fesetround(FE_DOWNWARD);
436 	test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0,
437 	     -0x1.0000000000001p-104, 0x1.2000000000001p+1,
438 	     ALL_STD_EXCEPT, FE_INEXACT);
439 	fesetround(FE_UPWARD);
440 	test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0,
441 	     -0x1.0000000000001p-104, 0x1.2000000000002p+1,
442 	     ALL_STD_EXCEPT, FE_INEXACT);
443 
444 	fesetround(FE_TONEAREST);
445 	test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200002p+1,
446 	     ALL_STD_EXCEPT, FE_INEXACT);
447 	fesetround(FE_DOWNWARD);
448 	test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200002p+1,
449 	     ALL_STD_EXCEPT, FE_INEXACT);
450 	fesetround(FE_UPWARD);
451 	test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200004p+1,
452 	     ALL_STD_EXCEPT, FE_INEXACT);
453 
454 	fesetround(FE_TONEAREST);
455 #if LDBL_MANT_DIG == 64
456 	test(fmal, 0x1.4p+0L, 0x1.0000000000000004p+0L, 0x1p-128L,
457 	     0x1.4000000000000006p+0L, ALL_STD_EXCEPT, FE_INEXACT);
458 #elif LDBL_MANT_DIG == 113
459 	test(fmal, 0x1.8000000000000000000000000001p+0L,
460 	     0x1.8000000000000000000000000001p+0L,
461 	     -0x1.0000000000000000000000000001p-224L,
462 	     0x1.2000000000000000000000000001p+1L, ALL_STD_EXCEPT, FE_INEXACT);
463 #endif
464 
465 }
466 
467 static const int rmodes[] = {
468 	FE_TONEAREST, FE_UPWARD, FE_DOWNWARD, FE_TOWARDZERO
469 };
470 
471 ATF_TC_WITHOUT_HEAD(zeroes);
472 ATF_TC_BODY(zeroes, tc)
473 {
474 	for (size_t i = 0; i < nitems(rmodes); i++) {
475 		printf("rmode = %d\n", rmodes[i]);
476 		fesetround(rmodes[i]);
477 		test_zeroes();
478 	}
479 }
480 
481 ATF_TC_WITHOUT_HEAD(infinities);
482 ATF_TC_BODY(infinities, tc)
483 {
484 	for (size_t i = 0; i < nitems(rmodes); i++) {
485 		printf("rmode = %d\n", rmodes[i]);
486 		fesetround(rmodes[i]);
487 		test_infinities();
488 	}
489 }
490 
491 ATF_TC_WITHOUT_HEAD(nans);
492 ATF_TC_BODY(nans, tc)
493 {
494 	fesetround(FE_TONEAREST);
495 	test_nans();
496 }
497 
498 
499 ATF_TC_WITHOUT_HEAD(small_z);
500 ATF_TC_BODY(small_z, tc)
501 {
502 	for (size_t i = 0; i < nitems(rmodes); i++) {
503 		printf("rmode = %d\n", rmodes[i]);
504 		fesetround(rmodes[i]);
505 		test_small_z();
506 	}
507 }
508 
509 
510 ATF_TC_WITHOUT_HEAD(big_z);
511 ATF_TC_BODY(big_z, tc)
512 {
513 	for (size_t i = 0; i < nitems(rmodes); i++) {
514 		printf("rmode = %d\n", rmodes[i]);
515 		fesetround(rmodes[i]);
516 		test_big_z();
517 	}
518 }
519 
520 ATF_TC_WITHOUT_HEAD(accuracy);
521 ATF_TC_BODY(accuracy, tc)
522 {
523 	fesetround(FE_TONEAREST);
524 	test_accuracy();
525 }
526 
527 ATF_TC_WITHOUT_HEAD(double_rounding);
528 ATF_TC_BODY(double_rounding, tc) {
529 	test_double_rounding();
530 }
531 
532 ATF_TP_ADD_TCS(tp)
533 {
534 	ATF_TP_ADD_TC(tp, zeroes);
535 	ATF_TP_ADD_TC(tp, infinities);
536 	ATF_TP_ADD_TC(tp, nans);
537 	ATF_TP_ADD_TC(tp, small_z);
538 	ATF_TP_ADD_TC(tp, big_z);
539 	ATF_TP_ADD_TC(tp, accuracy);
540 	ATF_TP_ADD_TC(tp, double_rounding);
541 	/*
542 	 * TODO:
543 	 * - Tests for subnormals
544 	 * - Cancellation tests (e.g., z = (double)x*y, but x*y is inexact)
545 	 */
546 	return (atf_no_error());
547 }
548