1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
|
# fmal.m4 serial 4
dnl Copyright (C) 2011-2012 Free Software Foundation, Inc.
dnl This file is free software; the Free Software Foundation
dnl gives unlimited permission to copy and/or distribute it,
dnl with or without modifications, as long as this notice is preserved.
AC_DEFUN([gl_FUNC_FMAL],
[
AC_REQUIRE([gl_MATH_H_DEFAULTS])
AC_REQUIRE([gl_LONG_DOUBLE_VS_DOUBLE])
dnl Persuade glibc <math.h> to declare fmal().
AC_REQUIRE([gl_USE_SYSTEM_EXTENSIONS])
dnl Determine FMAL_LIBM.
gl_MATHFUNC([fmal], [long double], [(long double, long double, long double)],
[extern
#ifdef __cplusplus
"C"
#endif
long double fmal (long double, long double, long double);
])
if test $gl_cv_func_fmal_no_libm = yes \
|| test $gl_cv_func_fmal_in_libm = yes; then
dnl Also check whether it's declared.
dnl IRIX 6.5 has fmal() in libm but doesn't declare it in <math.h>,
dnl and the function is buggy.
AC_CHECK_DECL([fmal], , [REPLACE_FMAL=1], [[#include <math.h>]])
if test $REPLACE_FMAL = 0; then
gl_FUNC_FMAL_WORKS
case "$gl_cv_func_fmal_works" in
*no) REPLACE_FMAL=1 ;;
esac
fi
else
HAVE_FMAL=0
fi
if test $HAVE_FMAL = 0 || test $REPLACE_FMAL = 1; then
dnl Find libraries needed to link lib/fmal.c.
if test $HAVE_SAME_LONG_DOUBLE_AS_DOUBLE = 1; then
AC_REQUIRE([gl_FUNC_FMA])
FMAL_LIBM="$FMA_LIBM"
else
AC_REQUIRE([gl_FUNC_FREXPL])
AC_REQUIRE([gl_FUNC_LDEXPL])
AC_REQUIRE([gl_FUNC_FEGETROUND])
FMAL_LIBM=
dnl Append $FREXPL_LIBM to FMAL_LIBM, avoiding gratuitous duplicates.
case " $FMAL_LIBM " in
*" $FREXPL_LIBM "*) ;;
*) FMAL_LIBM="$FMAL_LIBM $FREXPL_LIBM" ;;
esac
dnl Append $LDEXPL_LIBM to FMAL_LIBM, avoiding gratuitous duplicates.
case " $FMAL_LIBM " in
*" $LDEXPL_LIBM "*) ;;
*) FMAL_LIBM="$FMAL_LIBM $LDEXPL_LIBM" ;;
esac
dnl Append $FEGETROUND_LIBM to FMAL_LIBM, avoiding gratuitous duplicates.
case " $FMAL_LIBM " in
*" $FEGETROUND_LIBM "*) ;;
*) FMAL_LIBM="$FMAL_LIBM $FEGETROUND_LIBM" ;;
esac
fi
fi
AC_SUBST([FMAL_LIBM])
])
dnl Test whether fmal() has any of the 15 known bugs of glibc 2.11.3 on x86_64.
AC_DEFUN([gl_FUNC_FMAL_WORKS],
[
AC_REQUIRE([AC_PROG_CC])
AC_REQUIRE([AC_CANONICAL_HOST]) dnl for cross-compiles
AC_REQUIRE([gl_FUNC_LDEXPL])
save_LIBS="$LIBS"
LIBS="$LIBS $FMAL_LIBM $LDEXPL_LIBM"
AC_CACHE_CHECK([whether fmal works], [gl_cv_func_fmal_works],
[
AC_RUN_IFELSE(
[AC_LANG_SOURCE([[
#include <float.h>
#include <math.h>
/* Override the values of <float.h>, like done in float.in.h. */
#if defined __i386__ && (defined __BEOS__ || defined __OpenBSD__)
# undef LDBL_MANT_DIG
# define LDBL_MANT_DIG 64
# undef LDBL_MIN_EXP
# define LDBL_MIN_EXP (-16381)
# undef LDBL_MAX_EXP
# define LDBL_MAX_EXP 16384
#endif
#if defined __i386__ && defined __FreeBSD__
# undef LDBL_MANT_DIG
# define LDBL_MANT_DIG 64
# undef LDBL_MIN_EXP
# define LDBL_MIN_EXP (-16381)
# undef LDBL_MAX_EXP
# define LDBL_MAX_EXP 16384
#endif
#if (defined _ARCH_PPC || defined _POWER) && defined _AIX && (LDBL_MANT_DIG == 106) && defined __GNUC__
# undef LDBL_MIN_EXP
# define LDBL_MIN_EXP DBL_MIN_EXP
#endif
#if defined __sgi && (LDBL_MANT_DIG >= 106)
# undef LDBL_MANT_DIG
# define LDBL_MANT_DIG 106
# if defined __GNUC__
# undef LDBL_MIN_EXP
# define LDBL_MIN_EXP DBL_MIN_EXP
# endif
#endif
long double p0 = 0.0L;
int main()
{
int failed_tests = 0;
/* This test fails on glibc 2.11 powerpc. */
{
volatile long double x = 1.5L; /* 3 * 2^-1 */
volatile long double y = x;
volatile long double z = ldexpl (1.0L, LDBL_MANT_DIG + 1); /* 2^65 */
/* x * y + z with infinite precision: 2^65 + 9 * 2^-2.
Lies between (2^63 + 0) * 2^2 and (2^63 + 1) * 2^2
and is closer to (2^63 + 1) * 2^2, therefore the rounding
must round up and produce (2^63 + 1) * 2^2. */
volatile long double expected = z + 4.0L;
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 1;
}
/* This test fails on glibc 2.11 powerpc. */
{
volatile long double x = 1.25L; /* 2^0 + 2^-2 */
volatile long double y = - x;
volatile long double z = ldexpl (1.0L, LDBL_MANT_DIG + 1); /* 2^65 */
/* x * y + z with infinite precision: 2^65 - 2^0 - 2^-1 - 2^-4.
Lies between (2^64 - 1) * 2^1 and 2^64 * 2^1
and is closer to (2^64 - 1) * 2^1, therefore the rounding
must round down and produce (2^64 - 1) * 2^1. */
volatile long double expected = (ldexpl (1.0L, LDBL_MANT_DIG) - 1.0L) * 2.0L;
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 1;
}
/* This test fails on glibc 2.11 x86,x86_64,powerpc, glibc 2.7 hppa,sparc,
OSF/1 5.1, mingw. */
{
volatile long double x = 1.0L + ldexpl (1.0L, 1 - LDBL_MANT_DIG); /* 2^0 + 2^-63 */
volatile long double y = x;
volatile long double z = 4.0L; /* 2^2 */
/* x * y + z with infinite precision: 2^2 + 2^0 + 2^-62 + 2^-126.
Lies between (2^63 + 2^61) * 2^-61 and (2^63 + 2^61 + 1) * 2^-61
and is closer to (2^63 + 2^61 + 1) * 2^-61, therefore the rounding
must round up and produce (2^63 + 2^61 + 1) * 2^-61. */
volatile long double expected = 4.0L + 1.0L + ldexpl (1.0L, 3 - LDBL_MANT_DIG);
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 2;
}
/* This test fails on glibc 2.11 x86,x86_64,powerpc glibc 2.7 hppa,sparc,
OSF/1 5.1, mingw. */
{
volatile long double x = 1.0L + ldexpl (1.0L, 1 - LDBL_MANT_DIG); /* 2^0 + 2^-63 */
volatile long double y = - x;
volatile long double z = 8.0L; /* 2^3 */
/* x * y + z with infinite precision: 2^2 + 2^1 + 2^0 - 2^-62 - 2^-126.
Lies between (2^63 + 2^62 + 2^61 - 1) * 2^-61 and
(2^63 + 2^62 + 2^61) * 2^-61 and is closer to
(2^63 + 2^62 + 2^61 - 1) * 2^-61, therefore the rounding
must round down and produce (2^63 + 2^62 + 2^61 - 1) * 2^-61. */
volatile long double expected = 7.0L - ldexpl (1.0L, 3 - LDBL_MANT_DIG);
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 2;
}
/* This test fails on glibc 2.11 powerpc. */
{
volatile long double x = 1.25L; /* 2^0 + 2^-2 */
volatile long double y = - 0.75L; /* - 2^0 + 2^-2 */
volatile long double z = ldexpl (1.0L, LDBL_MANT_DIG); /* 2^64 */
/* x * y + z with infinite precision: 2^64 - 2^0 + 2^-4.
Lies between (2^64 - 2^0) and 2^64 and is closer to (2^64 - 2^0),
therefore the rounding must round down and produce (2^64 - 2^0). */
volatile long double expected = ldexpl (1.0L, LDBL_MANT_DIG) - 1.0L;
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 1;
}
if ((LDBL_MANT_DIG % 2) == 1)
{
/* These tests fail on glibc 2.7 hppa,sparc, OSF/1 5.1. */
{
volatile long double x = 1.0L + ldexpl (1.0L, - (LDBL_MANT_DIG + 1) / 2); /* 2^0 + 2^-27 */
volatile long double y = 1.0L - ldexpl (1.0L, - (LDBL_MANT_DIG + 1) / 2); /* 2^0 - 2^-27 */
volatile long double z = - ldexpl (1.0L, LDBL_MIN_EXP - LDBL_MANT_DIG); /* - 2^-1074 */
/* x * y + z with infinite precision: 2^0 - 2^-54 - 2^-1074.
Lies between (2^53 - 1) * 2^-53 and 2^53 * 2^-53 and is closer to
(2^53 - 1) * 2^-53, therefore the rounding must round down and
produce (2^53 - 1) * 2^-53. */
volatile long double expected = 1.0L - ldexpl (1.0L, - LDBL_MANT_DIG);
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 4;
}
{
volatile long double x = 1.0L + ldexpl (1.0L, - (LDBL_MANT_DIG + 1) / 2); /* 2^0 + 2^-57 */
volatile long double y = x;
volatile long double z = ldexpl (1.0L, - LDBL_MANT_DIG); /* 2^-113 */
/* x * y + z with infinite precision: 2^0 + 2^-56 + 2^-113 + 2^-114.
Lies between (2^112 + 2^56) * 2^-112 and (2^112 + 2^56 + 1) * 2^-112
and is closer to (2^112 + 2^56 + 1) * 2^-112, therefore the rounding
must round up and produce (2^112 + 2^56 + 1) * 2^-112. */
volatile long double expected =
1.0L + ldexpl (1.0L, - (LDBL_MANT_DIG - 1) / 2) + ldexpl (1.0L, 1 - LDBL_MANT_DIG);
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 4;
}
}
else
{
/* These tests fail on glibc 2.11 x86,x86_64,powerpc, mingw. */
{
volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */
volatile long double y = x;
volatile long double z = ldexpl (1.0L, LDBL_MIN_EXP - LDBL_MANT_DIG); /* 2^-16445 */
/* x * y + z with infinite precision: 2^0 + 2^-31 + 2^-64 + 2^-16445.
Lies between (2^63 + 2^32 + 0) * 2^-63 and (2^63 + 2^32 + 1) * 2^-63
and is closer to (2^63 + 2^32 + 1) * 2^-63, therefore the rounding
must round up and produce (2^63 + 2^32 + 1) * 2^-63. */
volatile long double expected =
1.0L + ldexpl (1.0L, 1 - LDBL_MANT_DIG / 2) + ldexpl (1.0L, 1 - LDBL_MANT_DIG);
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 8;
}
{
volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */
volatile long double y = x;
volatile long double z = ldexpl (1.0L, - LDBL_MANT_DIG); /* 2^-64 */
/* x * y + z with infinite precision: 2^0 + 2^-31 + 2^-63.
Rounding must return this value unchanged. */
volatile long double expected = 1.0L + ldexpl (1.0L, 1 - LDBL_MANT_DIG / 2) + ldexpl (1.0L, 1 - LDBL_MANT_DIG);
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 8;
}
{
volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */
volatile long double y = x;
volatile long double z = ldexpl (1.0L, 1 - LDBL_MANT_DIG); /* 2^-63 */
/* x * y + z with infinite precision: 2^0 + 2^-31 + 2^-63 + 2^-64.
Lies between (2^63 + 2^32 + 1) * 2^-63 and (2^63 + 2^32 + 2) * 2^-63
and is at the same distance from each. According to the round-to-even
rule, the rounding must round up and produce (2^63 + 2^32 + 2) * 2^-63. */
volatile long double expected = 1.0L + ldexpl (1.0L, -31) + ldexpl (1.0L, -62);
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 8;
}
{
volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */
volatile long double y = x;
volatile long double z = ldexpl (1.0L, LDBL_MANT_DIG / 2 + 1); /* 2^33 */
/* x * y + z with infinite precision: 2^33 + 2^0 + 2^-31 + 2^-64.
Lies between (2^63 + 2^30) * 2^-30 and (2^63 + 2^30 + 1) * 2^-30
and is closer to (2^63 + 2^30 + 1) * 2^-30, therefore the rounding
must round up and produce (2^63 + 2^30 + 1) * 2^-30. */
volatile long double expected = z + 1.0L + ldexp (1.0L, 2 - LDBL_MANT_DIG / 2);
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 8;
}
{
volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */
volatile long double y = x;
volatile long double z = - ldexpl (1.0, 1 - LDBL_MANT_DIG); /* - 2^-63 */
/* x * y + z with infinite precision: 2^0 + 2^-31 - 2^-64.
Lies between (2^63 + 2^32 - 1) * 2^-63 and (2^63 + 2^32) * 2^-63
and is at the same distance from each. According to the round-to-even
rule, the rounding must round up and produce (2^63 + 2^32) * 2^-63. */
volatile long double expected = 1.0L + ldexpl (1.0L, 1 - LDBL_MANT_DIG / 2);
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 8;
}
{
volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */
volatile long double y = x;
volatile long double z = - 1.0L; /* - 2^0 */
/* x * y + z with infinite precision: 2^-31 + 2^-64.
Rounding must return this value unchanged. */
volatile long double expected = ldexpl (1.0L, 1 - LDBL_MANT_DIG / 2) + ldexpl (1.0L, - LDBL_MANT_DIG);
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 8;
}
{
volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */
volatile long double y = - x;
volatile long double z = 2.0L; /* 2^1 */
/* x * y + z with infinite precision: 2^0 - 2^31 - 2^-64.
Rounding must return this value unchanged. */
volatile long double expected = 1.0L - ldexpl (1.0L, 1 - LDBL_MANT_DIG / 2) - ldexpl (1.0L, - LDBL_MANT_DIG);
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 8;
}
{
volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2); /* 2^0 + 2^-32 */
volatile long double y = - x;
volatile long double z = ldexpl (1.0L, LDBL_MANT_DIG / 2 + 2); /* 2^34 */
/* x * y + z with infinite precision: 2^34 - (2^0 + 2^-31 + 2^-64).
Lies between (2^64 - 2^30 - 1) * 2^-30 and (2^64 - 2^30) * 2^-30
and is closer to (2^64 - 2^30 - 1) * 2^-30, therefore the rounding
must round down and produce (2^64 - 2^30 - 1) * 2^-30. */
volatile long double expected = z - 1.0L - ldexpl (1.0L, 2 - LDBL_MANT_DIG / 2);
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 8;
}
{
volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2 - 1); /* 2^0 + 2^-33 */
volatile long double y = 1.0L - ldexpl (1.0L, - LDBL_MANT_DIG / 2 - 1); /* 2^0 - 2^-33 */
volatile long double z = - ldexpl (1.0L, - LDBL_MANT_DIG - 1); /* 2^-65 */
/* x * y + z with infinite precision: 2^0 - 2^-65 - 2^-66.
Lies between (2^64 - 1) * 2^-64 and 2^64 * 2^-64 and is closer to
(2^64 - 1) * 2^-64, therefore the rounding must round down and
produce (2^64 - 1) * 2^-64. */
volatile long double expected = 1.0L - ldexpl (1.0L, - LDBL_MANT_DIG);
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 8;
}
{
volatile long double x = 1.0L + ldexpl (1.0L, - LDBL_MANT_DIG / 2 - 1); /* 2^0 + 2^-33 */
volatile long double y = 1.0L - ldexpl (1.0L, - LDBL_MANT_DIG / 2 - 1); /* 2^0 - 2^-33 */
volatile long double z = - 1.0L; /* 2^0 */
/* x * y + z with infinite precision: - 2^-66.
Rounding must return this value unchanged. */
volatile long double expected = - ldexpl (1.0L, - LDBL_MANT_DIG - 2);
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 8;
}
}
/* This test fails on glibc 2.11 x86,x86_64,powerpc, glibc 2.7 hppa,sparc,
FreeBSD 6.4 x86, mingw. */
{
long double minus_inf = -1.0L / p0;
volatile long double x = ldexpl (1.0L, LDBL_MAX_EXP - 1);
volatile long double y = ldexpl (1.0L, LDBL_MAX_EXP - 1);
volatile long double z = minus_inf;
volatile long double result = fmal (x, y, z);
if (!(result == minus_inf))
failed_tests |= 16;
}
/* This test fails on glibc 2.11 x86,x86_64,powerpc glibc 2.7 hppa,sparc,
Mac OS X 10.5, FreeBSD 6.4 x86, OSF/1 5.1, mingw. */
{
volatile long double x = ldexpl (1.0L, LDBL_MAX_EXP - 1);
volatile long double y = 2.0L;
volatile long double z =
- ldexpl (ldexpl (1.0L, LDBL_MAX_EXP - 1) - ldexpl (1.0L, LDBL_MAX_EXP - LDBL_MANT_DIG - 1), 1);
volatile long double expected = ldexpl (1.0L, LDBL_MAX_EXP - LDBL_MANT_DIG);
volatile long double result = fmal (x, y, z);
if (result != expected)
failed_tests |= 32;
}
return failed_tests;
}]])],
[gl_cv_func_fmal_works=yes],
[gl_cv_func_fmal_works=no],
[dnl Guess no, even on glibc systems.
gl_cv_func_fmal_works="guessing no"
])
])
LIBS="$save_LIBS"
])
# Prerequisites of lib/fmal.c.
AC_DEFUN([gl_PREREQ_FMAL], [:])
|
