test-fma.c revision 216222
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: head/tools/regression/lib/msun/test-fma.c 216222 2010-12-06 00:02:49Z das $");
33
34#include <assert.h>
35#include <fenv.h>
36#include <float.h>
37#include <math.h>
38#include <stdio.h>
39
40#define	ALL_STD_EXCEPT	(FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \
41			 FE_OVERFLOW | FE_UNDERFLOW)
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	assert(feclearexcept(FE_ALL_EXCEPT) == 0);			\
57	assert(fpequal((func)((x), (y), (z)), (result)));		\
58	assert(((func), fetestexcept(exceptmask) == (excepts)));	\
59} while (0)
60
61#define	testall(x, y, z, result, exceptmask, excepts)	do {		\
62	test(fma, (x), (y), (z), (double)(result), (exceptmask), (excepts)); \
63	test(fmaf, (x), (y), (z), (float)(result), (exceptmask), (excepts)); \
64	test(fmal, (x), (y), (z), (result), (exceptmask), (excepts));	\
65} while (0)
66
67/* Test in all rounding modes. */
68#define	testrnd(func, x, y, z, rn, ru, rd, rz, exceptmask, excepts)	do { \
69	fesetround(FE_TONEAREST);					\
70	test((func), (x), (y), (z), (rn), (exceptmask), (excepts));	\
71	fesetround(FE_UPWARD);						\
72	test((func), (x), (y), (z), (ru), (exceptmask), (excepts));	\
73	fesetround(FE_DOWNWARD);					\
74	test((func), (x), (y), (z), (rd), (exceptmask), (excepts));	\
75	fesetround(FE_TOWARDZERO);					\
76	test((func), (x), (y), (z), (rz), (exceptmask), (excepts));	\
77} while (0)
78
79/*
80 * Determine whether x and y are equal, with two special rules:
81 *	+0.0 != -0.0
82 *	 NaN == NaN
83 */
84int
85fpequal(long double x, long double y)
86{
87
88	return ((x == y && !signbit(x) == !signbit(y))
89		|| (isnan(x) && isnan(y)));
90}
91
92static void
93test_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(-1.0, 1.0, 1.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
112	testall(1.0, -1.0, 1.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
113	testall(-1.0, -1.0, -1.0, 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
127static void
128test_infinities(void)
129{
130
131	testall(INFINITY, 1.0, -1.0, INFINITY, ALL_STD_EXCEPT, 0);
132	testall(-1.0, INFINITY, 0.0, -INFINITY, ALL_STD_EXCEPT, 0);
133	testall(0.0, 0.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
134	testall(1.0, 1.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
135	testall(1.0, 1.0, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
136
137	testall(INFINITY, -INFINITY, 1.0, -INFINITY, ALL_STD_EXCEPT, 0);
138	testall(INFINITY, INFINITY, 1.0, INFINITY, ALL_STD_EXCEPT, 0);
139	testall(-INFINITY, -INFINITY, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
140
141	testall(0.0, INFINITY, 1.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
142	testall(INFINITY, 0.0, -0.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
143
144	/* The invalid exception is optional in this case. */
145	testall(INFINITY, 0.0, NAN, NAN, ALL_STD_EXCEPT & ~FE_INVALID, 0);
146
147	testall(INFINITY, INFINITY, -INFINITY, NAN,
148		ALL_STD_EXCEPT, FE_INVALID);
149	testall(-INFINITY, INFINITY, INFINITY, NAN,
150		ALL_STD_EXCEPT, FE_INVALID);
151	testall(INFINITY, -1.0, INFINITY, NAN,
152		ALL_STD_EXCEPT, FE_INVALID);
153
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	test(fmaf, FLT_MAX, -FLT_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
159	test(fma, DBL_MAX, -DBL_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
160	test(fmal, LDBL_MAX, -LDBL_MAX, INFINITY, INFINITY,
161	     ALL_STD_EXCEPT, 0);
162}
163
164static void
165test_nans(void)
166{
167
168	testall(NAN, 0.0, 0.0, NAN, ALL_STD_EXCEPT, 0);
169	testall(1.0, NAN, 1.0, NAN, ALL_STD_EXCEPT, 0);
170	testall(1.0, -1.0, NAN, NAN, ALL_STD_EXCEPT, 0);
171	testall(0.0, 0.0, NAN, NAN, ALL_STD_EXCEPT, 0);
172	testall(NAN, NAN, NAN, NAN, ALL_STD_EXCEPT, 0);
173
174	/* x*y should not raise an inexact/overflow/underflow if z is NaN. */
175	testall(M_PI, M_PI, NAN, NAN, ALL_STD_EXCEPT, 0);
176	test(fmaf, FLT_MIN, FLT_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
177	test(fma, DBL_MIN, DBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
178	test(fmal, LDBL_MIN, LDBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
179	test(fmaf, FLT_MAX, FLT_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
180	test(fma, DBL_MAX, DBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
181	test(fmal, LDBL_MAX, LDBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
182}
183
184/*
185 * Tests for cases where z is very small compared to x*y.
186 */
187static void
188test_small_z(void)
189{
190
191	/* x*y positive, z positive */
192	if (fegetround() == FE_UPWARD) {
193		test(fmaf, 1.0, 1.0, 0x1.0p-100, 1.0 + FLT_EPSILON,
194		     ALL_STD_EXCEPT, FE_INEXACT);
195		test(fma, 1.0, 1.0, 0x1.0p-200, 1.0 + DBL_EPSILON,
196		     ALL_STD_EXCEPT, FE_INEXACT);
197		test(fmal, 1.0, 1.0, 0x1.0p-200, 1.0 + LDBL_EPSILON,
198		     ALL_STD_EXCEPT, FE_INEXACT);
199	} else {
200		testall(0x1.0p100, 1.0, 0x1.0p-100, 0x1.0p100,
201			ALL_STD_EXCEPT, FE_INEXACT);
202	}
203
204	/* x*y negative, z negative */
205	if (fegetround() == FE_DOWNWARD) {
206		test(fmaf, -1.0, 1.0, -0x1.0p-100, -(1.0 + FLT_EPSILON),
207		     ALL_STD_EXCEPT, FE_INEXACT);
208		test(fma, -1.0, 1.0, -0x1.0p-200, -(1.0 + DBL_EPSILON),
209		     ALL_STD_EXCEPT, FE_INEXACT);
210		test(fmal, -1.0, 1.0, -0x1.0p-200, -(1.0 + LDBL_EPSILON),
211		     ALL_STD_EXCEPT, FE_INEXACT);
212	} else {
213		testall(0x1.0p100, -1.0, -0x1.0p-100, -0x1.0p100,
214			ALL_STD_EXCEPT, FE_INEXACT);
215	}
216
217	/* x*y positive, z negative */
218	if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
219		test(fmaf, 1.0, 1.0, -0x1.0p-100, 1.0 - FLT_EPSILON / 2,
220		     ALL_STD_EXCEPT, FE_INEXACT);
221		test(fma, 1.0, 1.0, -0x1.0p-200, 1.0 - DBL_EPSILON / 2,
222		     ALL_STD_EXCEPT, FE_INEXACT);
223		test(fmal, 1.0, 1.0, -0x1.0p-200, 1.0 - LDBL_EPSILON / 2,
224		     ALL_STD_EXCEPT, FE_INEXACT);
225	} else {
226		testall(0x1.0p100, 1.0, -0x1.0p-100, 0x1.0p100,
227			ALL_STD_EXCEPT, FE_INEXACT);
228	}
229
230	/* x*y negative, z positive */
231	if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
232		test(fmaf, -1.0, 1.0, 0x1.0p-100, -1.0 + FLT_EPSILON / 2,
233		     ALL_STD_EXCEPT, FE_INEXACT);
234		test(fma, -1.0, 1.0, 0x1.0p-200, -1.0 + DBL_EPSILON / 2,
235		     ALL_STD_EXCEPT, FE_INEXACT);
236		test(fmal, -1.0, 1.0, 0x1.0p-200, -1.0 + LDBL_EPSILON / 2,
237		     ALL_STD_EXCEPT, FE_INEXACT);
238	} else {
239		testall(-0x1.0p100, 1.0, 0x1.0p-100, -0x1.0p100,
240			ALL_STD_EXCEPT, FE_INEXACT);
241	}
242}
243
244/*
245 * Tests for cases where z is very large compared to x*y.
246 */
247static void
248test_big_z(void)
249{
250
251	/* z positive, x*y positive */
252	if (fegetround() == FE_UPWARD) {
253		test(fmaf, 0x1.0p-50, 0x1.0p-50, 1.0, 1.0 + FLT_EPSILON,
254		     ALL_STD_EXCEPT, FE_INEXACT);
255		test(fma, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + DBL_EPSILON,
256		     ALL_STD_EXCEPT, FE_INEXACT);
257		test(fmal, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + LDBL_EPSILON,
258		     ALL_STD_EXCEPT, FE_INEXACT);
259	} else {
260		testall(-0x1.0p-50, -0x1.0p-50, 0x1.0p100, 0x1.0p100,
261			ALL_STD_EXCEPT, FE_INEXACT);
262	}
263
264	/* z negative, x*y negative */
265	if (fegetround() == FE_DOWNWARD) {
266		test(fmaf, -0x1.0p-50, 0x1.0p-50, -1.0, -(1.0 + FLT_EPSILON),
267		     ALL_STD_EXCEPT, FE_INEXACT);
268		test(fma, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + DBL_EPSILON),
269		     ALL_STD_EXCEPT, FE_INEXACT);
270		test(fmal, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + LDBL_EPSILON),
271		     ALL_STD_EXCEPT, FE_INEXACT);
272	} else {
273		testall(0x1.0p-50, -0x1.0p-50, -0x1.0p100, -0x1.0p100,
274			ALL_STD_EXCEPT, FE_INEXACT);
275	}
276
277	/* z negative, x*y positive */
278	if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
279		test(fmaf, -0x1.0p-50, -0x1.0p-50, -1.0,
280		     -1.0 + FLT_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
281		test(fma, -0x1.0p-100, -0x1.0p-100, -1.0,
282		     -1.0 + DBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
283		test(fmal, -0x1.0p-100, -0x1.0p-100, -1.0,
284		     -1.0 + LDBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
285	} else {
286		testall(0x1.0p-50, 0x1.0p-50, -0x1.0p100, -0x1.0p100,
287			ALL_STD_EXCEPT, FE_INEXACT);
288	}
289
290	/* z positive, x*y negative */
291	if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
292		test(fmaf, 0x1.0p-50, -0x1.0p-50, 1.0, 1.0 - FLT_EPSILON / 2,
293		     ALL_STD_EXCEPT, FE_INEXACT);
294		test(fma, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - DBL_EPSILON / 2,
295		     ALL_STD_EXCEPT, FE_INEXACT);
296		test(fmal, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - LDBL_EPSILON / 2,
297		     ALL_STD_EXCEPT, FE_INEXACT);
298	} else {
299		testall(-0x1.0p-50, 0x1.0p-50, 0x1.0p100, 0x1.0p100,
300			ALL_STD_EXCEPT, FE_INEXACT);
301	}
302}
303
304static void
305test_accuracy(void)
306{
307
308	/* ilogb(x*y) - ilogb(z) = 20 */
309	testrnd(fmaf, -0x1.c139d8p-51, -0x1.600e7ap32, 0x1.26558cp-38,
310		0x1.34e48ap-18, 0x1.34e48cp-18, 0x1.34e48ap-18, 0x1.34e48ap-18,
311		ALL_STD_EXCEPT, FE_INEXACT);
312	testrnd(fma, -0x1.c139d7b84f1a3p-51, -0x1.600e7a2a16484p32,
313		0x1.26558cac31580p-38, 0x1.34e48a78aae97p-18,
314		0x1.34e48a78aae97p-18, 0x1.34e48a78aae96p-18,
315		0x1.34e48a78aae96p-18, ALL_STD_EXCEPT, FE_INEXACT);
316#if LDBL_MANT_DIG == 113
317	testrnd(fmal, -0x1.c139d7b84f1a3079263afcc5bae3p-51L,
318		-0x1.600e7a2a164840edbe2e7d301a72p32L,
319		0x1.26558cac315807eb07e448042101p-38L,
320		0x1.34e48a78aae96c76ed36077dd387p-18L,
321		0x1.34e48a78aae96c76ed36077dd388p-18L,
322		0x1.34e48a78aae96c76ed36077dd387p-18L,
323		0x1.34e48a78aae96c76ed36077dd387p-18L,
324		ALL_STD_EXCEPT, FE_INEXACT);
325#elif LDBL_MANT_DIG == 64
326	testrnd(fmal, -0x1.c139d7b84f1a307ap-51L, -0x1.600e7a2a164840eep32L,
327		0x1.26558cac315807ecp-38L, 0x1.34e48a78aae96c78p-18L,
328		0x1.34e48a78aae96c78p-18L, 0x1.34e48a78aae96c76p-18L,
329		0x1.34e48a78aae96c76p-18L, ALL_STD_EXCEPT, FE_INEXACT);
330#elif LDBL_MANT_DIG == 53
331	testrnd(fmal, -0x1.c139d7b84f1a3p-51L, -0x1.600e7a2a16484p32L,
332		0x1.26558cac31580p-38L, 0x1.34e48a78aae97p-18L,
333		0x1.34e48a78aae97p-18L, 0x1.34e48a78aae96p-18L,
334		0x1.34e48a78aae96p-18L, ALL_STD_EXCEPT, FE_INEXACT);
335#endif
336
337	/* ilogb(x*y) - ilogb(z) = -40 */
338	testrnd(fmaf, 0x1.98210ap53, 0x1.9556acp-24, 0x1.d87da4p70,
339		0x1.d87da4p70, 0x1.d87da6p70, 0x1.d87da4p70, 0x1.d87da4p70,
340		ALL_STD_EXCEPT, FE_INEXACT);
341	testrnd(fma, 0x1.98210ac83fe2bp53, 0x1.9556ac1475f0fp-24,
342		0x1.d87da3aafc60ep70, 0x1.d87da3aafda40p70,
343		0x1.d87da3aafda40p70, 0x1.d87da3aafda3fp70,
344		0x1.d87da3aafda3fp70, ALL_STD_EXCEPT, FE_INEXACT);
345#if LDBL_MANT_DIG == 113
346	testrnd(fmal, 0x1.98210ac83fe2a8f65b6278b74cebp53L,
347		0x1.9556ac1475f0f28968b61d0de65ap-24L,
348		0x1.d87da3aafc60d830aa4c6d73b749p70L,
349		0x1.d87da3aafda3f36a69eb86488224p70L,
350		0x1.d87da3aafda3f36a69eb86488225p70L,
351		0x1.d87da3aafda3f36a69eb86488224p70L,
352		0x1.d87da3aafda3f36a69eb86488224p70L,
353		ALL_STD_EXCEPT, FE_INEXACT);
354#elif LDBL_MANT_DIG == 64
355	testrnd(fmal, 0x1.98210ac83fe2a8f6p53L, 0x1.9556ac1475f0f28ap-24L,
356		0x1.d87da3aafc60d83p70L, 0x1.d87da3aafda3f36ap70L,
357		0x1.d87da3aafda3f36ap70L, 0x1.d87da3aafda3f368p70L,
358		0x1.d87da3aafda3f368p70L, ALL_STD_EXCEPT, FE_INEXACT);
359#elif LDBL_MANT_DIG == 53
360	testrnd(fmal, 0x1.98210ac83fe2bp53L, 0x1.9556ac1475f0fp-24L,
361		0x1.d87da3aafc60ep70L, 0x1.d87da3aafda40p70L,
362		0x1.d87da3aafda40p70L, 0x1.d87da3aafda3fp70L,
363		0x1.d87da3aafda3fp70L, ALL_STD_EXCEPT, FE_INEXACT);
364#endif
365}
366
367int
368main(int argc, char *argv[])
369{
370	int rmodes[] = { FE_TONEAREST, FE_UPWARD, FE_DOWNWARD, FE_TOWARDZERO };
371	int i;
372
373	printf("1..18\n");
374
375	for (i = 0; i < 4; i++) {
376		fesetround(rmodes[i]);
377		test_zeroes();
378		printf("ok %d - fma zeroes\n", i + 1);
379	}
380
381	for (i = 0; i < 4; i++) {
382		fesetround(rmodes[i]);
383		test_infinities();
384		printf("ok %d - fma infinities\n", i + 5);
385	}
386
387	fesetround(FE_TONEAREST);
388	test_nans();
389	printf("ok 9 - fma NaNs\n");
390
391	for (i = 0; i < 4; i++) {
392		fesetround(rmodes[i]);
393		test_small_z();
394		printf("ok %d - fma small z\n", i + 10);
395	}
396
397	for (i = 0; i < 4; i++) {
398		fesetround(rmodes[i]);
399		test_big_z();
400		printf("ok %d - fma big z\n", i + 14);
401	}
402
403	fesetround(FE_TONEAREST);
404	test_accuracy();
405	printf("ok 18 - fma accuracy\n");
406
407	/*
408	 * TODO:
409	 * - Tests for subnormals
410	 * - Cancellation tests (e.g., z = (double)x*y, but x*y is inexact)
411	 */
412
413	return (0);
414}
415