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
|
# fma.m4 serial 4
dnl Copyright (C) 2011-2023 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_FMA],
[
AC_REQUIRE([gl_MATH_H_DEFAULTS])
dnl Determine FMA_LIBM.
gl_MATHFUNC([fma], [double], [(double, double, double)],
[extern
#ifdef __cplusplus
"C"
#endif
double fma (double, double, double);
])
if test $gl_cv_func_fma_no_libm = yes \
|| test $gl_cv_func_fma_in_libm = yes; then
dnl Also check whether it's declared.
dnl IRIX 6.5 has fma() in libm but doesn't declare it in <math.h>,
dnl and the function is buggy.
AC_CHECK_DECL([fma], , [REPLACE_FMA=1], [[#include <math.h>]])
if test $REPLACE_FMA = 0; then
gl_FUNC_FMA_WORKS
case "$gl_cv_func_fma_works" in
*no) REPLACE_FMA=1 ;;
esac
fi
else
HAVE_FMA=0
fi
if test $HAVE_FMA = 0 || test $REPLACE_FMA = 1; then
dnl Find libraries needed to link lib/fmal.c.
AC_REQUIRE([gl_FUNC_FREXP])
AC_REQUIRE([gl_FUNC_LDEXP])
AC_REQUIRE([gl_FUNC_FEGETROUND])
FMA_LIBM=
dnl Append $FREXP_LIBM to FMA_LIBM, avoiding gratuitous duplicates.
case " $FMA_LIBM " in
*" $FREXP_LIBM "*) ;;
*) FMA_LIBM="$FMA_LIBM $FREXP_LIBM" ;;
esac
dnl Append $LDEXP_LIBM to FMA_LIBM, avoiding gratuitous duplicates.
case " $FMA_LIBM " in
*" $LDEXP_LIBM "*) ;;
*) FMA_LIBM="$FMA_LIBM $LDEXP_LIBM" ;;
esac
dnl Append $FEGETROUND_LIBM to FMA_LIBM, avoiding gratuitous duplicates.
case " $FMA_LIBM " in
*" $FEGETROUND_LIBM "*) ;;
*) FMA_LIBM="$FMA_LIBM $FEGETROUND_LIBM" ;;
esac
fi
AC_SUBST([FMA_LIBM])
])
dnl Test whether fma() has any of the 7 known bugs of glibc 2.11.3 on x86_64.
AC_DEFUN([gl_FUNC_FMA_WORKS],
[
AC_REQUIRE([AC_PROG_CC])
AC_REQUIRE([AC_CANONICAL_HOST]) dnl for cross-compiles
AC_REQUIRE([gl_FUNC_LDEXP])
save_LIBS="$LIBS"
LIBS="$LIBS $FMA_LIBM $LDEXP_LIBM"
AC_CACHE_CHECK([whether fma works], [gl_cv_func_fma_works],
[
AC_RUN_IFELSE(
[AC_LANG_SOURCE([[
#include <float.h>
#include <math.h>
double p0 = 0.0;
int main()
{
int failed_tests = 0;
/* These tests fail with glibc 2.11.3 on x86_64. */
{
volatile double x = 1.5; /* 3 * 2^-1 */
volatile double y = x;
volatile double z = ldexp (1.0, DBL_MANT_DIG + 1); /* 2^54 */
/* x * y + z with infinite precision: 2^54 + 9 * 2^-2.
Lies between (2^52 + 0) * 2^2 and (2^52 + 1) * 2^2
and is closer to (2^52 + 1) * 2^2, therefore the rounding
must round up and produce (2^52 + 1) * 2^2. */
volatile double expected = z + 4.0;
volatile double result = fma (x, y, z);
if (result != expected)
failed_tests |= 1;
}
{
volatile double x = 1.25; /* 2^0 + 2^-2 */
volatile double y = - x;
volatile double z = ldexp (1.0, DBL_MANT_DIG + 1); /* 2^54 */
/* x * y + z with infinite precision: 2^54 - 2^0 - 2^-1 - 2^-4.
Lies between (2^53 - 1) * 2^1 and 2^53 * 2^1
and is closer to (2^53 - 1) * 2^1, therefore the rounding
must round down and produce (2^53 - 1) * 2^1. */
volatile double expected = (ldexp (1.0, DBL_MANT_DIG) - 1.0) * 2.0;
volatile double result = fma (x, y, z);
if (result != expected)
failed_tests |= 2;
}
{
volatile double x = 1.0 + ldexp (1.0, 1 - DBL_MANT_DIG); /* 2^0 + 2^-52 */
volatile double y = x;
volatile double z = 4.0; /* 2^2 */
/* x * y + z with infinite precision: 2^2 + 2^0 + 2^-51 + 2^-104.
Lies between (2^52 + 2^50) * 2^-50 and (2^52 + 2^50 + 1) * 2^-50
and is closer to (2^52 + 2^50 + 1) * 2^-50, therefore the rounding
must round up and produce (2^52 + 2^50 + 1) * 2^-50. */
volatile double expected = 4.0 + 1.0 + ldexp (1.0, 3 - DBL_MANT_DIG);
volatile double result = fma (x, y, z);
if (result != expected)
failed_tests |= 4;
}
{
volatile double x = 1.0 + ldexp (1.0, 1 - DBL_MANT_DIG); /* 2^0 + 2^-52 */
volatile double y = - x;
volatile double z = 8.0; /* 2^3 */
/* x * y + z with infinite precision: 2^2 + 2^1 + 2^0 - 2^-51 - 2^-104.
Lies between (2^52 + 2^51 + 2^50 - 1) * 2^-50 and
(2^52 + 2^51 + 2^50) * 2^-50 and is closer to
(2^52 + 2^51 + 2^50 - 1) * 2^-50, therefore the rounding
must round down and produce (2^52 + 2^51 + 2^50 - 1) * 2^-50. */
volatile double expected = 7.0 - ldexp (1.0, 3 - DBL_MANT_DIG);
volatile double result = fma (x, y, z);
if (result != expected)
failed_tests |= 8;
}
{
volatile double x = 1.25; /* 2^0 + 2^-2 */
volatile double y = - 0.75; /* - 2^0 + 2^-2 */
volatile double z = ldexp (1.0, DBL_MANT_DIG); /* 2^53 */
/* x * y + z with infinite precision: 2^53 - 2^0 + 2^-4.
Lies between (2^53 - 2^0) and 2^53 and is closer to (2^53 - 2^0),
therefore the rounding must round down and produce (2^53 - 2^0). */
volatile double expected = ldexp (1.0, DBL_MANT_DIG) - 1.0;
volatile double result = fma (x, y, z);
if (result != expected)
failed_tests |= 16;
}
if ((DBL_MANT_DIG % 2) == 1)
{
volatile double x = 1.0 + ldexp (1.0, - (DBL_MANT_DIG + 1) / 2); /* 2^0 + 2^-27 */
volatile double y = 1.0 - ldexp (1.0, - (DBL_MANT_DIG + 1) / 2); /* 2^0 - 2^-27 */
volatile double z = - ldexp (1.0, DBL_MIN_EXP - DBL_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 double expected = 1.0 - ldexp (1.0, - DBL_MANT_DIG);
volatile double result = fma (x, y, z);
if (result != expected)
failed_tests |= 32;
}
{
double minus_inf = -1.0 / p0;
volatile double x = ldexp (1.0, DBL_MAX_EXP - 1);
volatile double y = ldexp (1.0, DBL_MAX_EXP - 1);
volatile double z = minus_inf;
volatile double result = fma (x, y, z);
if (!(result == minus_inf))
failed_tests |= 64;
}
return failed_tests;
}]])],
[gl_cv_func_fma_works=yes],
[gl_cv_func_fma_works=no],
[dnl Guess yes on native Windows with MSVC.
dnl Otherwise guess no, even on glibc systems.
gl_cv_func_fma_works="$gl_cross_guess_normal"
case "$host_os" in
mingw*)
AC_EGREP_CPP([Known], [
#ifdef _MSC_VER
Known
#endif
], [gl_cv_func_fma_works="guessing yes"])
;;
esac
])
])
LIBS="$save_LIBS"
])
# Prerequisites of lib/fma.c.
AC_DEFUN([gl_PREREQ_FMA], [:])
|
