gnulib/m4/fma.m4 - toolchain/make - Git at Google

 # fma.m4 serial 4
 dnl Copyright (C) 2011-2020 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], [:])
	# fma.m4 serial 4
	dnl Copyright (C) 2011-2020 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], [:])