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gnulib/m4/fmal.m4
Paul Eggert a3fd683de3 version-etc: new year 
* build-aux/gendocs.sh (version):
* doc/gendocs_template:
* doc/gendocs_template_min:
* doc/gnulib.texi:
* lib/version-etc.c (COPYRIGHT_YEAR):
Update copyright dates by hand in templates and the like.
* all files: Run 'make update-copyright'.
2017-01-01 02:59:23 +00:00

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# fmal.m4 serial 4
dnl Copyright (C) 2011-2017 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], [:])
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