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
|
# fmaf.m4 serial 1
dnl Copyright (C) 2011 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_FMAF],
[
AC_REQUIRE([gl_MATH_H_DEFAULTS])
dnl Determine FMAF_LIBM.
gl_MATHFUNC([fmaf], [float], [(float, float, float)])
if test $gl_cv_func_fmaf_no_libm = yes \
|| test $gl_cv_func_fmaf_in_libm = yes; then
gl_FUNC_FMAF_WORKS
case "$gl_cv_func_fmaf_works" in
*no) REPLACE_FMAF=1 ;;
esac
else
HAVE_FMAF=0
fi
if test $HAVE_FMAF = 0 || test $REPLACE_FMAF = 1; then
dnl Find libraries needed to link lib/fmaf.c.
AC_REQUIRE([gl_FUNC_FREXPF])
AC_REQUIRE([gl_FUNC_LDEXPF])
AC_REQUIRE([gl_FUNC_FEGETROUND])
FMAF_LIBM=
dnl Append $FREXPF_LIBM to FMAF_LIBM, avoiding gratuitous duplicates.
case " $FMAF_LIBM " in
*" $FREXPF_LIBM "*) ;;
*) FMAF_LIBM="$FMAF_LIBM $FREXPF_LIBM" ;;
esac
dnl Append $LDEXPF_LIBM to FMAF_LIBM, avoiding gratuitous duplicates.
case " $FMAF_LIBM " in
*" $LDEXPF_LIBM "*) ;;
*) FMAF_LIBM="$FMAF_LIBM $LDEXPF_LIBM" ;;
esac
dnl Append $FEGETROUND_LIBM to FMAF_LIBM, avoiding gratuitous duplicates.
case " $FMAF_LIBM " in
*" $FEGETROUND_LIBM "*) ;;
*) FMAF_LIBM="$FMAF_LIBM $FEGETROUND_LIBM" ;;
esac
fi
AC_SUBST([FMAF_LIBM])
])
dnl Test whether fmaf() has any of the 7 known bugs of glibc 2.11.3 on x86_64.
AC_DEFUN([gl_FUNC_FMAF_WORKS],
[
AC_REQUIRE([AC_PROG_CC])
AC_REQUIRE([AC_CANONICAL_HOST]) dnl for cross-compiles
AC_REQUIRE([gl_FUNC_LDEXPF])
save_LIBS="$LIBS"
LIBS="$LIBS $FMAF_LIBM $LDEXPF_LIBM"
AC_CACHE_CHECK([whether fmaf works], [gl_cv_func_fmaf_works],
[
AC_RUN_IFELSE(
[AC_LANG_SOURCE([[
#include <float.h>
#include <math.h>
float p0 = 0.0f;
int main()
{
int failed_tests = 0;
/* These tests fail with glibc 2.11.3 on x86_64. */
{
volatile float x = 1.5f; /* 3 * 2^-1 */
volatile float y = x;
volatile float z = ldexpf (1.0f, FLT_MANT_DIG + 1); /* 2^25 */
/* x * y + z with infinite precision: 2^25 + 9 * 2^-2.
Lies between (2^23 + 0) * 2^2 and (2^23 + 1) * 2^2
and is closer to (2^23 + 1) * 2^2, therefore the rounding
must round up and produce (2^23 + 1) * 2^2. */
volatile float expected = z + 4.0f;
volatile float result = fmaf (x, y, z);
if (result != expected)
failed_tests |= 1;
}
{
volatile float x = 1.25f; /* 2^0 + 2^-2 */
volatile float y = - x;
volatile float z = ldexpf (1.0f, FLT_MANT_DIG + 1); /* 2^25 */
/* x * y + z with infinite precision: 2^25 - 2^0 - 2^-1 - 2^-4.
Lies between (2^24 - 1) * 2^1 and 2^24 * 2^1
and is closer to (2^24 - 1) * 2^1, therefore the rounding
must round down and produce (2^24 - 1) * 2^1. */
volatile float expected = (ldexpf (1.0f, FLT_MANT_DIG) - 1.0f) * 2.0f;
volatile float result = fmaf (x, y, z);
if (result != expected)
failed_tests |= 2;
}
{
volatile float x = 1.0f + ldexpf (1.0f, 1 - FLT_MANT_DIG); /* 2^0 + 2^-23 */
volatile float y = x;
volatile float z = 4.0f; /* 2^2 */
/* x * y + z with infinite precision: 2^2 + 2^0 + 2^-22 + 2^-46.
Lies between (2^23 + 2^21) * 2^-21 and (2^23 + 2^21 + 1) * 2^-21
and is closer to (2^23 + 2^21 + 1) * 2^-21, therefore the rounding
must round up and produce (2^23 + 2^21 + 1) * 2^-21. */
volatile float expected = 4.0f + 1.0f + ldexpf (1.0f, 3 - FLT_MANT_DIG);
volatile float result = fmaf (x, y, z);
if (result != expected)
failed_tests |= 4;
}
{
volatile float x = 1.0f + ldexpf (1.0f, 1 - FLT_MANT_DIG); /* 2^0 + 2^-23 */
volatile float y = - x;
volatile float z = 8.0f; /* 2^3 */
/* x * y + z with infinite precision: 2^2 + 2^1 + 2^0 - 2^-22 - 2^-46.
Lies between (2^23 + 2^22 + 2^21 - 1) * 2^-21 and
(2^23 + 2^22 + 2^21) * 2^-21 and is closer to
(2^23 + 2^22 + 2^21 - 1) * 2^-21, therefore the rounding
must round down and produce (2^23 + 2^22 + 2^21 - 1) * 2^-21. */
volatile float expected = 7.0f - ldexpf (1.0f, 3 - FLT_MANT_DIG);
volatile float result = fmaf (x, y, z);
if (result != expected)
failed_tests |= 8;
}
{
volatile float x = 1.25f; /* 2^0 + 2^-2 */
volatile float y = - 0.75f; /* - 2^0 + 2^-2 */
volatile float z = ldexpf (1.0f, FLT_MANT_DIG); /* 2^24 */
/* x * y + z with infinite precision: 2^24 - 2^0 + 2^-4.
Lies between (2^24 - 2^0) and 2^24 and is closer to (2^24 - 2^0),
therefore the rounding must round down and produce (2^24 - 2^0). */
volatile float expected = ldexpf (1.0f, FLT_MANT_DIG) - 1.0f;
volatile float result = fmaf (x, y, z);
if (result != expected)
failed_tests |= 16;
}
if ((FLT_MANT_DIG % 2) == 0)
{
volatile float x = 1.0f + ldexpf (1.0f, - FLT_MANT_DIG / 2); /* 2^0 + 2^-12 */
volatile float y = x;
volatile float z = ldexpf (1.0f, FLT_MIN_EXP - FLT_MANT_DIG); /* 2^-149 */
/* x * y + z with infinite precision: 2^0 + 2^-11 + 2^-24 + 2^-149.
Lies between (2^23 + 2^12 + 0) * 2^-23 and (2^23 + 2^12 + 1) * 2^-23
and is closer to (2^23 + 2^12 + 1) * 2^-23, therefore the rounding
must round up and produce (2^23 + 2^12 + 1) * 2^-23. */
volatile float expected =
1.0f + ldexpf (1.0f, 1 - FLT_MANT_DIG / 2) + ldexpf (1.0f, 1 - FLT_MANT_DIG);
volatile float result = fmaf (x, y, z);
if (result != expected)
failed_tests |= 32;
}
{
float minus_inf = -1.0f / p0;
volatile float x = ldexpf (1.0f, FLT_MAX_EXP - 1);
volatile float y = ldexpf (1.0f, FLT_MAX_EXP - 1);
volatile float z = minus_inf;
volatile float result = fmaf (x, y, z);
if (!(result == minus_inf))
failed_tests |= 64;
}
return failed_tests;
}]])],
[gl_cv_func_fmaf_works=yes],
[gl_cv_func_fmaf_works=no],
[dnl Guess no, even on glibc systems.
gl_cv_func_fmaf_works="guessing no"
])
])
LIBS="$save_LIBS"
])
# Prerequisites of lib/fmaf.c.
AC_DEFUN([gl_PREREQ_FMAF], [:])
|
