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# fma.m4 serial 3
dnl Copyright (C) 2011-2018 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="guessing no"
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], [:])
|
