Import stripped Arm GNU Toolchain 13.2.Rel1HEADumineko

https://developer.arm.com/downloads/-/arm-gnu-toolchain-downloads

Change-Id: I7303388733328cd98ab9aa3c30236db67f2e9e9c

1 files changed, 1475 insertions, 0 deletions

diff --git a/aarch64-none-linux-gnu/libc/usr/include/math.h b/aarch64-none-linux-gnu/libc/usr/include/math.h
new file mode 100644
index 0000000..f136399
--- /dev/null
+++ b/aarch64-none-linux-gnu/libc/usr/include/math.h
@@ -0,0 +1,1475 @@
+/* Declarations for math functions.
+   Copyright (C) 1991-2023 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+/*
+ *	ISO C99 Standard: 7.12 Mathematics	<math.h>
+ */
+
+#ifndef	_MATH_H
+#define	_MATH_H	1
+
+#define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
+#include <bits/libc-header-start.h>
+
+#if defined log && defined __GNUC__
+# warning A macro called log was already defined when <math.h> was included.
+# warning This will cause compilation problems.
+#endif
+
+__BEGIN_DECLS
+
+/* Get definitions of __intmax_t and __uintmax_t.  */
+#include <bits/types.h>
+
+/* Get machine-dependent vector math functions declarations.  */
+#include <bits/math-vector.h>
+
+/* Gather machine dependent type support.  */
+#include <bits/floatn.h>
+
+/* Value returned on overflow.  With IEEE 754 floating point, this is
+   +Infinity, otherwise the largest representable positive value.  */
+#if __GNUC_PREREQ (3, 3)
+# define HUGE_VAL (__builtin_huge_val ())
+#else
+/* This may provoke compiler warnings, and may not be rounded to
+   +Infinity in all IEEE 754 rounding modes, but is the best that can
+   be done in ISO C while remaining a constant expression.  10,000 is
+   greater than the maximum (decimal) exponent for all supported
+   floating-point formats and widths.  */
+# define HUGE_VAL 1e10000
+#endif
+#ifdef __USE_ISOC99
+# if __GNUC_PREREQ (3, 3)
+#  define HUGE_VALF (__builtin_huge_valf ())
+#  define HUGE_VALL (__builtin_huge_vall ())
+# else
+#  define HUGE_VALF 1e10000f
+#  define HUGE_VALL 1e10000L
+# endif
+#endif
+#if __HAVE_FLOAT16 && __GLIBC_USE (IEC_60559_TYPES_EXT)
+# define HUGE_VAL_F16 (__builtin_huge_valf16 ())
+#endif
+#if __HAVE_FLOAT32 && __GLIBC_USE (IEC_60559_TYPES_EXT)
+# define HUGE_VAL_F32 (__builtin_huge_valf32 ())
+#endif
+#if __HAVE_FLOAT64 && __GLIBC_USE (IEC_60559_TYPES_EXT)
+# define HUGE_VAL_F64 (__builtin_huge_valf64 ())
+#endif
+#if __HAVE_FLOAT128 && __GLIBC_USE (IEC_60559_TYPES_EXT)
+# define HUGE_VAL_F128 (__builtin_huge_valf128 ())
+#endif
+#if __HAVE_FLOAT32X && __GLIBC_USE (IEC_60559_TYPES_EXT)
+# define HUGE_VAL_F32X (__builtin_huge_valf32x ())
+#endif
+#if __HAVE_FLOAT64X && __GLIBC_USE (IEC_60559_TYPES_EXT)
+# define HUGE_VAL_F64X (__builtin_huge_valf64x ())
+#endif
+#if __HAVE_FLOAT128X && __GLIBC_USE (IEC_60559_TYPES_EXT)
+# define HUGE_VAL_F128X (__builtin_huge_valf128x ())
+#endif
+
+#ifdef __USE_ISOC99
+/* IEEE positive infinity.  */
+# if __GNUC_PREREQ (3, 3)
+#  define INFINITY (__builtin_inff ())
+# else
+#  define INFINITY HUGE_VALF
+# endif
+
+/* IEEE Not A Number.  */
+# if __GNUC_PREREQ (3, 3)
+#  define NAN (__builtin_nanf (""))
+# else
+/* This will raise an "invalid" exception outside static initializers,
+   but is the best that can be done in ISO C while remaining a
+   constant expression.  */
+#  define NAN (0.0f / 0.0f)
+# endif
+#endif /* __USE_ISOC99 */
+
+#if __GLIBC_USE (IEC_60559_BFP_EXT)
+/* Signaling NaN macros, if supported.  */
+# if __GNUC_PREREQ (3, 3)
+#  define SNANF (__builtin_nansf (""))
+#  define SNAN (__builtin_nans (""))
+#  define SNANL (__builtin_nansl (""))
+# endif
+#endif
+#if (__HAVE_FLOAT16					\
+     && __GLIBC_USE (IEC_60559_TYPES_EXT)		\
+     && (defined __USE_GNU || !__GLIBC_USE (ISOC2X)))
+# define SNANF16 (__builtin_nansf16 (""))
+#endif
+#if (__HAVE_FLOAT32					\
+     && __GLIBC_USE (IEC_60559_TYPES_EXT)		\
+     && (defined __USE_GNU || !__GLIBC_USE (ISOC2X)))
+# define SNANF32 (__builtin_nansf32 (""))
+#endif
+#if (__HAVE_FLOAT64					\
+     && __GLIBC_USE (IEC_60559_TYPES_EXT)		\
+     && (defined __USE_GNU || !__GLIBC_USE (ISOC2X)))
+# define SNANF64 (__builtin_nansf64 (""))
+#endif
+#if (__HAVE_FLOAT128					\
+     && __GLIBC_USE (IEC_60559_TYPES_EXT)		\
+     && (defined __USE_GNU || !__GLIBC_USE (ISOC2X)))
+# define SNANF128 (__builtin_nansf128 (""))
+#endif
+#if (__HAVE_FLOAT32X					\
+     && __GLIBC_USE (IEC_60559_TYPES_EXT)		\
+     && (defined __USE_GNU || !__GLIBC_USE (ISOC2X)))
+# define SNANF32X (__builtin_nansf32x (""))
+#endif
+#if (__HAVE_FLOAT64X					\
+     && __GLIBC_USE (IEC_60559_TYPES_EXT)		\
+     && (defined __USE_GNU || !__GLIBC_USE (ISOC2X)))
+# define SNANF64X (__builtin_nansf64x (""))
+#endif
+#if (__HAVE_FLOAT128X					\
+     && __GLIBC_USE (IEC_60559_TYPES_EXT)		\
+     && (defined __USE_GNU || !__GLIBC_USE (ISOC2X)))
+# define SNANF128X (__builtin_nansf128x (""))
+#endif
+
+/* Get __GLIBC_FLT_EVAL_METHOD.  */
+#include <bits/flt-eval-method.h>
+
+#ifdef __USE_ISOC99
+/* Define the following typedefs.
+
+    float_t	floating-point type at least as wide as `float' used
+		to evaluate `float' expressions
+    double_t	floating-point type at least as wide as `double' used
+		to evaluate `double' expressions
+*/
+# if __GLIBC_FLT_EVAL_METHOD == 0 || __GLIBC_FLT_EVAL_METHOD == 16
+typedef float float_t;
+typedef double double_t;
+# elif __GLIBC_FLT_EVAL_METHOD == 1
+typedef double float_t;
+typedef double double_t;
+# elif __GLIBC_FLT_EVAL_METHOD == 2
+typedef long double float_t;
+typedef long double double_t;
+# elif __GLIBC_FLT_EVAL_METHOD == 32
+typedef _Float32 float_t;
+typedef double double_t;
+# elif __GLIBC_FLT_EVAL_METHOD == 33
+typedef _Float32x float_t;
+typedef _Float32x double_t;
+# elif __GLIBC_FLT_EVAL_METHOD == 64
+typedef _Float64 float_t;
+typedef _Float64 double_t;
+# elif __GLIBC_FLT_EVAL_METHOD == 65
+typedef _Float64x float_t;
+typedef _Float64x double_t;
+# elif __GLIBC_FLT_EVAL_METHOD == 128
+typedef _Float128 float_t;
+typedef _Float128 double_t;
+# elif __GLIBC_FLT_EVAL_METHOD == 129
+typedef _Float128x float_t;
+typedef _Float128x double_t;
+# else
+#  error "Unknown __GLIBC_FLT_EVAL_METHOD"
+# endif
+#endif
+
+/* Define macros for the return values of ilogb and llogb, based on
+   __FP_LOGB0_IS_MIN and __FP_LOGBNAN_IS_MIN.
+
+    FP_ILOGB0	Expands to a value returned by `ilogb (0.0)'.
+    FP_ILOGBNAN	Expands to a value returned by `ilogb (NAN)'.
+    FP_LLOGB0	Expands to a value returned by `llogb (0.0)'.
+    FP_LLOGBNAN	Expands to a value returned by `llogb (NAN)'.
+
+*/
+
+#include <bits/fp-logb.h>
+#ifdef __USE_ISOC99
+# if __FP_LOGB0_IS_MIN
+#  define FP_ILOGB0	(-2147483647 - 1)
+# else
+#  define FP_ILOGB0	(-2147483647)
+# endif
+# if __FP_LOGBNAN_IS_MIN
+#  define FP_ILOGBNAN	(-2147483647 - 1)
+# else
+#  define FP_ILOGBNAN	2147483647
+# endif
+#endif
+#if __GLIBC_USE (IEC_60559_BFP_EXT_C2X)
+# if __WORDSIZE == 32
+#  define __FP_LONG_MAX 0x7fffffffL
+# else
+#  define __FP_LONG_MAX 0x7fffffffffffffffL
+# endif
+# if __FP_LOGB0_IS_MIN
+#  define FP_LLOGB0	(-__FP_LONG_MAX - 1)
+# else
+#  define FP_LLOGB0	(-__FP_LONG_MAX)
+# endif
+# if __FP_LOGBNAN_IS_MIN
+#  define FP_LLOGBNAN	(-__FP_LONG_MAX - 1)
+# else
+#  define FP_LLOGBNAN	__FP_LONG_MAX
+# endif
+#endif
+
+/* Get the architecture specific values describing the floating-point
+   evaluation.  The following symbols will get defined:
+
+    FP_FAST_FMA
+    FP_FAST_FMAF
+    FP_FAST_FMAL
+		If defined it indicates that the `fma' function
+		generally executes about as fast as a multiply and an add.
+		This macro is defined only iff the `fma' function is
+		implemented directly with a hardware multiply-add instructions.
+*/
+
+#include <bits/fp-fast.h>
+
+#if __GLIBC_USE (IEC_60559_BFP_EXT_C2X)
+/* Rounding direction macros for fromfp functions.  */
+enum
+  {
+    FP_INT_UPWARD =
+# define FP_INT_UPWARD 0
+      FP_INT_UPWARD,
+    FP_INT_DOWNWARD =
+# define FP_INT_DOWNWARD 1
+      FP_INT_DOWNWARD,
+    FP_INT_TOWARDZERO =
+# define FP_INT_TOWARDZERO 2
+      FP_INT_TOWARDZERO,
+    FP_INT_TONEARESTFROMZERO =
+# define FP_INT_TONEARESTFROMZERO 3
+      FP_INT_TONEARESTFROMZERO,
+    FP_INT_TONEAREST =
+# define FP_INT_TONEAREST 4
+      FP_INT_TONEAREST,
+  };
+#endif
+
+/* The file <bits/mathcalls.h> contains the prototypes for all the
+   actual math functions.  These macros are used for those prototypes,
+   so we can easily declare each function as both `name' and `__name',
+   and can declare the float versions `namef' and `__namef'.  */
+
+#define __SIMD_DECL(function) __CONCAT (__DECL_SIMD_, function)
+
+#define __MATHCALL_VEC(function, suffix, args) 	\
+  __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
+  __MATHCALL (function, suffix, args)
+
+#define __MATHDECL_VEC(type, function,suffix, args) \
+  __SIMD_DECL (__MATH_PRECNAME (function, suffix)) \
+  __MATHDECL(type, function,suffix, args)
+
+#define __MATHCALL(function,suffix, args)	\
+  __MATHDECL (_Mdouble_,function,suffix, args)
+#define __MATHDECL(type, function,suffix, args) \
+  __MATHDECL_1(type, function,suffix, args); \
+  __MATHDECL_1(type, __CONCAT(__,function),suffix, args)
+#define __MATHCALLX(function,suffix, args, attrib)	\
+  __MATHDECLX (_Mdouble_,function,suffix, args, attrib)
+#define __MATHDECLX(type, function,suffix, args, attrib) \
+  __MATHDECL_1(type, function,suffix, args) __attribute__ (attrib); \
+  __MATHDECL_1(type, __CONCAT(__,function),suffix, args) __attribute__ (attrib)
+#define __MATHDECL_1_IMPL(type, function, suffix, args) \
+  extern type __MATH_PRECNAME(function,suffix) args __THROW
+#define __MATHDECL_1(type, function, suffix, args) \
+  __MATHDECL_1_IMPL(type, function, suffix, args)
+/* Ignore the alias by default.  The alias is only useful with
+   redirections.  */
+#define __MATHDECL_ALIAS(type, function, suffix, args, alias) \
+  __MATHDECL_1(type, function, suffix, args)
+
+#define __MATHREDIR(type, function, suffix, args, to) \
+  extern type __REDIRECT_NTH (__MATH_PRECNAME (function, suffix), args, to)
+
+#define _Mdouble_		double
+#define __MATH_PRECNAME(name,r)	__CONCAT(name,r)
+#define __MATH_DECLARING_DOUBLE  1
+#define __MATH_DECLARING_FLOATN  0
+#include <bits/mathcalls-helper-functions.h>
+#include <bits/mathcalls.h>
+#undef	_Mdouble_
+#undef	__MATH_PRECNAME
+#undef __MATH_DECLARING_DOUBLE
+#undef __MATH_DECLARING_FLOATN
+
+#ifdef __USE_ISOC99
+
+
+/* Include the file of declarations again, this time using `float'
+   instead of `double' and appending f to each function name.  */
+
+# define _Mdouble_		float
+# define __MATH_PRECNAME(name,r) name##f##r
+# define __MATH_DECLARING_DOUBLE  0
+# define __MATH_DECLARING_FLOATN  0
+# include <bits/mathcalls-helper-functions.h>
+# include <bits/mathcalls.h>
+# undef	_Mdouble_
+# undef	__MATH_PRECNAME
+# undef __MATH_DECLARING_DOUBLE
+# undef __MATH_DECLARING_FLOATN
+
+# if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC) \
+     || defined __LDBL_COMPAT \
+     || defined _LIBC_TEST
+#  ifdef __LDBL_COMPAT
+
+#   ifdef __USE_ISOC99
+extern float __nldbl_nexttowardf (float __x, long double __y)
+				  __THROW __attribute__ ((__const__));
+#    ifdef __REDIRECT_NTH
+extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
+			     __nldbl_nexttowardf)
+     __attribute__ ((__const__));
+extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
+			      nextafter) __attribute__ ((__const__));
+extern long double __REDIRECT_NTH (nexttowardl,
+				   (long double __x, long double __y),
+				   nextafter) __attribute__ ((__const__));
+#    endif
+#   endif
+
+#   undef __MATHDECL_1
+#   define __MATHDECL_1(type, function,suffix, args) \
+  __MATHREDIR(type, function, suffix, args, __CONCAT(function,suffix))
+
+#  elif __LDOUBLE_REDIRECTS_TO_FLOAT128_ABI == 1
+#   ifdef __REDIRECT_NTH
+#    ifdef __USE_ISOC99
+extern float __REDIRECT_NTH (nexttowardf, (float __x, long double __y),
+			    __nexttowardf_to_ieee128)
+  __attribute__ ((__const__));
+extern double __REDIRECT_NTH (nexttoward, (double __x, long double __y),
+			     __nexttoward_to_ieee128)
+  __attribute__ ((__const__));
+
+#define __dremieee128 __remainderieee128
+#define __gammaieee128 __lgammaieee128
+
+#    endif
+#   endif
+
+#   undef __MATHDECL_1
+#   undef __MATHDECL_ALIAS
+
+#   define __REDIRTO(function, suffix) \
+  __ ## function ## ieee128 ## suffix
+#   define __REDIRTO_ALT(function, suffix) \
+  __ ## function ## f128 ## suffix
+
+#   define __MATHDECL_1(type, function, suffix, args) \
+  __MATHREDIR (type, function, suffix, args, __REDIRTO (function, suffix))
+#   define __MATHDECL_ALIAS(type, function, suffix, args, alias) \
+  __MATHREDIR (type, function, suffix, args, __REDIRTO_ALT (alias, suffix))
+#  endif
+
+/* Include the file of declarations again, this time using `long double'
+   instead of `double' and appending l to each function name.  */
+
+#  define _Mdouble_		long double
+#  define __MATH_PRECNAME(name,r) name##l##r
+#  define __MATH_DECLARING_DOUBLE  0
+#  define __MATH_DECLARING_FLOATN  0
+#  define __MATH_DECLARE_LDOUBLE   1
+#  include <bits/mathcalls-helper-functions.h>
+#  include <bits/mathcalls.h>
+
+#  undef _Mdouble_
+#  undef __MATH_PRECNAME
+#  undef __MATH_DECLARING_DOUBLE
+#  undef __MATH_DECLARING_FLOATN
+
+#  if defined __LDBL_COMPAT \
+      || __LDOUBLE_REDIRECTS_TO_FLOAT128_ABI == 1
+#   undef __REDIRTO
+#   undef __REDIRTO_ALT
+#   undef __MATHDECL_1
+#   undef __MATHDECL_ALIAS
+#   define __MATHDECL_1(type, function, suffix, args) \
+  __MATHDECL_1_IMPL(type, function, suffix, args)
+#   define __MATHDECL_ALIAS(type, function, suffix, args, alias) \
+  __MATHDECL_1(type, function, suffix, args)
+#  endif
+# endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
+
+#endif	/* Use ISO C99.  */
+
+/* Include the file of declarations for _FloatN and _FloatNx
+   types.  */
+
+#if __HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !defined _LIBC)
+# define _Mdouble_		_Float16
+# define __MATH_PRECNAME(name,r) name##f16##r
+# define __MATH_DECLARING_DOUBLE  0
+# define __MATH_DECLARING_FLOATN  1
+# if __HAVE_DISTINCT_FLOAT16
+#  include <bits/mathcalls-helper-functions.h>
+# endif
+# if __GLIBC_USE (IEC_60559_TYPES_EXT)
+#  include <bits/mathcalls.h>
+# endif
+# undef _Mdouble_
+# undef __MATH_PRECNAME
+# undef __MATH_DECLARING_DOUBLE
+# undef __MATH_DECLARING_FLOATN
+#endif /* __HAVE_DISTINCT_FLOAT16 || (__HAVE_FLOAT16 && !_LIBC).  */
+
+#if __HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !defined _LIBC)
+# define _Mdouble_		_Float32
+# define __MATH_PRECNAME(name,r) name##f32##r
+# define __MATH_DECLARING_DOUBLE  0
+# define __MATH_DECLARING_FLOATN  1
+# if __HAVE_DISTINCT_FLOAT32
+#  include <bits/mathcalls-helper-functions.h>
+# endif
+# if __GLIBC_USE (IEC_60559_TYPES_EXT)
+#  include <bits/mathcalls.h>
+# endif
+# undef _Mdouble_
+# undef __MATH_PRECNAME
+# undef __MATH_DECLARING_DOUBLE
+# undef __MATH_DECLARING_FLOATN
+#endif /* __HAVE_DISTINCT_FLOAT32 || (__HAVE_FLOAT32 && !_LIBC).  */
+
+#if __HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !defined _LIBC)
+# define _Mdouble_		_Float64
+# define __MATH_PRECNAME(name,r) name##f64##r
+# define __MATH_DECLARING_DOUBLE  0
+# define __MATH_DECLARING_FLOATN  1
+# if __HAVE_DISTINCT_FLOAT64
+#  include <bits/mathcalls-helper-functions.h>
+# endif
+# if __GLIBC_USE (IEC_60559_TYPES_EXT)
+#  include <bits/mathcalls.h>
+# endif
+# undef _Mdouble_
+# undef __MATH_PRECNAME
+# undef __MATH_DECLARING_DOUBLE
+# undef __MATH_DECLARING_FLOATN
+#endif /* __HAVE_DISTINCT_FLOAT64 || (__HAVE_FLOAT64 && !_LIBC).  */
+
+#if __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !defined _LIBC)
+# define _Mdouble_		_Float128
+# define __MATH_PRECNAME(name,r) name##f128##r
+# define __MATH_DECLARING_DOUBLE  0
+# define __MATH_DECLARING_FLOATN  1
+# if __HAVE_DISTINCT_FLOAT128
+#  include <bits/mathcalls-helper-functions.h>
+# endif
+# if __GLIBC_USE (IEC_60559_TYPES_EXT)
+#  include <bits/mathcalls.h>
+# endif
+# undef _Mdouble_
+# undef __MATH_PRECNAME
+# undef __MATH_DECLARING_DOUBLE
+# undef __MATH_DECLARING_FLOATN
+#endif /* __HAVE_DISTINCT_FLOAT128 || (__HAVE_FLOAT128 && !_LIBC).  */
+
+#if __HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !defined _LIBC)
+# define _Mdouble_		_Float32x
+# define __MATH_PRECNAME(name,r) name##f32x##r
+# define __MATH_DECLARING_DOUBLE  0
+# define __MATH_DECLARING_FLOATN  1
+# if __HAVE_DISTINCT_FLOAT32X
+#  include <bits/mathcalls-helper-functions.h>
+# endif
+# if __GLIBC_USE (IEC_60559_TYPES_EXT)
+#  include <bits/mathcalls.h>
+# endif
+# undef _Mdouble_
+# undef __MATH_PRECNAME
+# undef __MATH_DECLARING_DOUBLE
+# undef __MATH_DECLARING_FLOATN
+#endif /* __HAVE_DISTINCT_FLOAT32X || (__HAVE_FLOAT32X && !_LIBC).  */
+
+#if __HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !defined _LIBC)
+# define _Mdouble_		_Float64x
+# define __MATH_PRECNAME(name,r) name##f64x##r
+# define __MATH_DECLARING_DOUBLE  0
+# define __MATH_DECLARING_FLOATN  1
+# if __HAVE_DISTINCT_FLOAT64X
+#  include <bits/mathcalls-helper-functions.h>
+# endif
+# if __GLIBC_USE (IEC_60559_TYPES_EXT)
+#  include <bits/mathcalls.h>
+# endif
+# undef _Mdouble_
+# undef __MATH_PRECNAME
+# undef __MATH_DECLARING_DOUBLE
+# undef __MATH_DECLARING_FLOATN
+#endif /* __HAVE_DISTINCT_FLOAT64X || (__HAVE_FLOAT64X && !_LIBC).  */
+
+#if __HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !defined _LIBC)
+# define _Mdouble_		_Float128x
+# define __MATH_PRECNAME(name,r) name##f128x##r
+# define __MATH_DECLARING_DOUBLE  0
+# define __MATH_DECLARING_FLOATN  1
+# if __HAVE_DISTINCT_FLOAT128X
+#  include <bits/mathcalls-helper-functions.h>
+# endif
+# if __GLIBC_USE (IEC_60559_TYPES_EXT)
+#  include <bits/mathcalls.h>
+# endif
+# undef _Mdouble_
+# undef __MATH_PRECNAME
+# undef __MATH_DECLARING_DOUBLE
+# undef __MATH_DECLARING_FLOATN
+#endif /* __HAVE_DISTINCT_FLOAT128X || (__HAVE_FLOAT128X && !_LIBC).  */
+
+#undef	__MATHDECL_1_IMPL
+#undef	__MATHDECL_1
+#undef	__MATHDECL_ALIAS
+#undef	__MATHDECL
+#undef	__MATHCALL
+
+/* Declare functions returning a narrower type.  */
+#define __MATHCALL_NARROW_ARGS_1 (_Marg_ __x)
+#define __MATHCALL_NARROW_ARGS_2 (_Marg_ __x, _Marg_ __y)
+#define __MATHCALL_NARROW_ARGS_3 (_Marg_ __x, _Marg_ __y, _Marg_ __z)
+#define __MATHCALL_NARROW_NORMAL(func, nargs)			\
+  extern _Mret_ func __MATHCALL_NARROW_ARGS_ ## nargs __THROW
+#define __MATHCALL_NARROW_REDIR(func, redir, nargs)			\
+  extern _Mret_ __REDIRECT_NTH (func, __MATHCALL_NARROW_ARGS_ ## nargs, \
+				redir)
+#define __MATHCALL_NARROW(func, redir, nargs)	\
+  __MATHCALL_NARROW_NORMAL (func, nargs)
+
+#if __GLIBC_USE (IEC_60559_BFP_EXT_C2X)
+
+# define _Mret_ float
+# define _Marg_ double
+# define __MATHCALL_NAME(name) f ## name
+# include <bits/mathcalls-narrow.h>
+# undef _Mret_
+# undef _Marg_
+# undef __MATHCALL_NAME
+
+# define _Mret_ float
+# define _Marg_ long double
+# define __MATHCALL_NAME(name) f ## name ## l
+# ifdef __LDBL_COMPAT
+#  define __MATHCALL_REDIR_NAME(name) f ## name
+#  define __MATHCALL_REDIR_NAME2(name) f ## name
+#  undef __MATHCALL_NARROW
+#  define __MATHCALL_NARROW(func, redir, nargs) \
+  __MATHCALL_NARROW_REDIR (func, redir, nargs)
+# elif __LDOUBLE_REDIRECTS_TO_FLOAT128_ABI == 1
+#  define __MATHCALL_REDIR_NAME(name) __ ## f32 ## name ## ieee128
+#  define __MATHCALL_REDIR_NAME2(name) __ ## f32 ## name ## ieee128
+#  undef __MATHCALL_NARROW
+#  define __MATHCALL_NARROW(func, redir, nargs) \
+  __MATHCALL_NARROW_REDIR (func, redir, nargs)
+# endif
+# include <bits/mathcalls-narrow.h>
+# undef _Mret_
+# undef _Marg_
+# undef __MATHCALL_NAME
+# if defined __LDBL_COMPAT \
+     || __LDOUBLE_REDIRECTS_TO_FLOAT128_ABI == 1
+#  undef __MATHCALL_REDIR_NAME
+#  undef __MATHCALL_REDIR_NAME2
+#  undef __MATHCALL_NARROW
+#  define __MATHCALL_NARROW(func, redir, nargs) \
+  __MATHCALL_NARROW_NORMAL (func, nargs)
+# endif
+
+# define _Mret_ double
+# define _Marg_ long double
+# define __MATHCALL_NAME(name) d ## name ## l
+# ifdef __LDBL_COMPAT
+#  define __MATHCALL_REDIR_NAME(name) __nldbl_d ## name ## l
+#  define __MATHCALL_REDIR_NAME2(name) name
+#  undef __MATHCALL_NARROW
+#  define __MATHCALL_NARROW(func, redir, nargs) \
+  __MATHCALL_NARROW_REDIR (func, redir, nargs)
+# elif __LDOUBLE_REDIRECTS_TO_FLOAT128_ABI == 1
+#  define __MATHCALL_REDIR_NAME(name) __ ## f64 ## name ## ieee128
+#  define __MATHCALL_REDIR_NAME2(name) __ ## f64 ## name ## ieee128
+#  undef __MATHCALL_NARROW
+#  define __MATHCALL_NARROW(func, redir, nargs) \
+  __MATHCALL_NARROW_REDIR (func, redir, nargs)
+# endif
+# include <bits/mathcalls-narrow.h>
+# undef _Mret_
+# undef _Marg_
+# undef __MATHCALL_NAME
+# if defined __LDBL_COMPAT \
+     || __LDOUBLE_REDIRECTS_TO_FLOAT128_ABI == 1
+#  undef __MATHCALL_REDIR_NAME
+#  undef __MATHCALL_REDIR_NAME2
+#  undef __MATHCALL_NARROW
+#  define __MATHCALL_NARROW(func, redir, nargs) \
+  __MATHCALL_NARROW_NORMAL (func, nargs)
+# endif
+
+#endif
+
+#if __GLIBC_USE (IEC_60559_TYPES_EXT)
+
+# if __HAVE_FLOAT16 && __HAVE_FLOAT32
+#  define _Mret_ _Float16
+#  define _Marg_ _Float32
+#  define __MATHCALL_NAME(name) f16 ## name ## f32
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT16 && __HAVE_FLOAT32X
+#  define _Mret_ _Float16
+#  define _Marg_ _Float32x
+#  define __MATHCALL_NAME(name) f16 ## name ## f32x
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT16 && __HAVE_FLOAT64
+#  define _Mret_ _Float16
+#  define _Marg_ _Float64
+#  define __MATHCALL_NAME(name) f16 ## name ## f64
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT16 && __HAVE_FLOAT64X
+#  define _Mret_ _Float16
+#  define _Marg_ _Float64x
+#  define __MATHCALL_NAME(name) f16 ## name ## f64x
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT16 && __HAVE_FLOAT128
+#  define _Mret_ _Float16
+#  define _Marg_ _Float128
+#  define __MATHCALL_NAME(name) f16 ## name ## f128
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT16 && __HAVE_FLOAT128X
+#  define _Mret_ _Float16
+#  define _Marg_ _Float128x
+#  define __MATHCALL_NAME(name) f16 ## name ## f128x
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT32 && __HAVE_FLOAT32X
+#  define _Mret_ _Float32
+#  define _Marg_ _Float32x
+#  define __MATHCALL_NAME(name) f32 ## name ## f32x
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT32 && __HAVE_FLOAT64
+#  define _Mret_ _Float32
+#  define _Marg_ _Float64
+#  define __MATHCALL_NAME(name) f32 ## name ## f64
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT32 && __HAVE_FLOAT64X
+#  define _Mret_ _Float32
+#  define _Marg_ _Float64x
+#  define __MATHCALL_NAME(name) f32 ## name ## f64x
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT32 && __HAVE_FLOAT128
+#  define _Mret_ _Float32
+#  define _Marg_ _Float128
+#  define __MATHCALL_NAME(name) f32 ## name ## f128
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT32 && __HAVE_FLOAT128X
+#  define _Mret_ _Float32
+#  define _Marg_ _Float128x
+#  define __MATHCALL_NAME(name) f32 ## name ## f128x
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT32X && __HAVE_FLOAT64
+#  define _Mret_ _Float32x
+#  define _Marg_ _Float64
+#  define __MATHCALL_NAME(name) f32x ## name ## f64
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT32X && __HAVE_FLOAT64X
+#  define _Mret_ _Float32x
+#  define _Marg_ _Float64x
+#  define __MATHCALL_NAME(name) f32x ## name ## f64x
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT32X && __HAVE_FLOAT128
+#  define _Mret_ _Float32x
+#  define _Marg_ _Float128
+#  define __MATHCALL_NAME(name) f32x ## name ## f128
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT32X && __HAVE_FLOAT128X
+#  define _Mret_ _Float32x
+#  define _Marg_ _Float128x
+#  define __MATHCALL_NAME(name) f32x ## name ## f128x
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT64 && __HAVE_FLOAT64X
+#  define _Mret_ _Float64
+#  define _Marg_ _Float64x
+#  define __MATHCALL_NAME(name) f64 ## name ## f64x
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT64 && __HAVE_FLOAT128
+#  define _Mret_ _Float64
+#  define _Marg_ _Float128
+#  define __MATHCALL_NAME(name) f64 ## name ## f128
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT64 && __HAVE_FLOAT128X
+#  define _Mret_ _Float64
+#  define _Marg_ _Float128x
+#  define __MATHCALL_NAME(name) f64 ## name ## f128x
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT64X && __HAVE_FLOAT128
+#  define _Mret_ _Float64x
+#  define _Marg_ _Float128
+#  define __MATHCALL_NAME(name) f64x ## name ## f128
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT64X && __HAVE_FLOAT128X
+#  define _Mret_ _Float64x
+#  define _Marg_ _Float128x
+#  define __MATHCALL_NAME(name) f64x ## name ## f128x
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+# if __HAVE_FLOAT128 && __HAVE_FLOAT128X
+#  define _Mret_ _Float128
+#  define _Marg_ _Float128x
+#  define __MATHCALL_NAME(name) f128 ## name ## f128x
+#  include <bits/mathcalls-narrow.h>
+#  undef _Mret_
+#  undef _Marg_
+#  undef __MATHCALL_NAME
+# endif
+
+#endif
+
+#undef __MATHCALL_NARROW_ARGS_1
+#undef __MATHCALL_NARROW_ARGS_2
+#undef __MATHCALL_NARROW_ARGS_3
+#undef __MATHCALL_NARROW_NORMAL
+#undef __MATHCALL_NARROW_REDIR
+#undef __MATHCALL_NARROW
+
+#if defined __USE_MISC || defined __USE_XOPEN
+/* This variable is used by `gamma' and `lgamma'.  */
+extern int signgam;
+#endif
+
+#if (__HAVE_DISTINCT_FLOAT16			\
+     || __HAVE_DISTINCT_FLOAT32			\
+     || __HAVE_DISTINCT_FLOAT64			\
+     || __HAVE_DISTINCT_FLOAT32X		\
+     || __HAVE_DISTINCT_FLOAT64X		\
+     || __HAVE_DISTINCT_FLOAT128X)
+# error "Unsupported _FloatN or _FloatNx types for <math.h>."
+#endif
+
+/* Depending on the type of TG_ARG, call an appropriately suffixed
+   version of FUNC with arguments (including parentheses) ARGS.
+   Suffixed functions may not exist for long double if it has the same
+   format as double, or for other types with the same format as float,
+   double or long double.  The behavior is undefined if the argument
+   does not have a real floating type.  The definition may use a
+   conditional expression, so all suffixed versions of FUNC must
+   return the same type (FUNC may include a cast if necessary rather
+   than being a single identifier).  */
+#ifdef __NO_LONG_DOUBLE_MATH
+# if __HAVE_DISTINCT_FLOAT128
+#  error "Distinct _Float128 without distinct long double not supported."
+# endif
+# define __MATH_TG(TG_ARG, FUNC, ARGS)					\
+  (sizeof (TG_ARG) == sizeof (float) ? FUNC ## f ARGS : FUNC ARGS)
+#elif __HAVE_DISTINCT_FLOAT128
+# if __HAVE_GENERIC_SELECTION
+#  if __HAVE_FLOATN_NOT_TYPEDEF && __HAVE_FLOAT32
+#   define __MATH_TG_F32(FUNC, ARGS) _Float32: FUNC ## f ARGS,
+#  else
+#   define __MATH_TG_F32(FUNC, ARGS)
+#  endif
+#  if __HAVE_FLOATN_NOT_TYPEDEF && __HAVE_FLOAT64X
+#   if __HAVE_FLOAT64X_LONG_DOUBLE
+#    define __MATH_TG_F64X(FUNC, ARGS) _Float64x: FUNC ## l ARGS,
+#   else
+#    define __MATH_TG_F64X(FUNC, ARGS) _Float64x: FUNC ## f128 ARGS,
+#   endif
+#  else
+#   define __MATH_TG_F64X(FUNC, ARGS)
+#  endif
+#  define __MATH_TG(TG_ARG, FUNC, ARGS)	\
+     _Generic ((TG_ARG),			\
+	       float: FUNC ## f ARGS,		\
+	       __MATH_TG_F32 (FUNC, ARGS)	\
+	       default: FUNC ARGS,		\
+	       long double: FUNC ## l ARGS,	\
+	       __MATH_TG_F64X (FUNC, ARGS)	\
+	       _Float128: FUNC ## f128 ARGS)
+# else
+#  if __HAVE_FLOATN_NOT_TYPEDEF
+#   error "Non-typedef _FloatN but no _Generic."
+#  endif
+#  define __MATH_TG(TG_ARG, FUNC, ARGS)					\
+     __builtin_choose_expr						\
+     (__builtin_types_compatible_p (__typeof (TG_ARG), float),		\
+      FUNC ## f ARGS,							\
+      __builtin_choose_expr						\
+      (__builtin_types_compatible_p (__typeof (TG_ARG), double),	\
+       FUNC ARGS,							\
+       __builtin_choose_expr						\
+       (__builtin_types_compatible_p (__typeof (TG_ARG), long double),	\
+	FUNC ## l ARGS,							\
+	FUNC ## f128 ARGS)))
+# endif
+#else
+# define __MATH_TG(TG_ARG, FUNC, ARGS)		\
+  (sizeof (TG_ARG) == sizeof (float)		\
+   ? FUNC ## f ARGS				\
+   : sizeof (TG_ARG) == sizeof (double)		\
+   ? FUNC ARGS					\
+   : FUNC ## l ARGS)
+#endif
+
+/* ISO C99 defines some generic macros which work on any data type.  */
+#ifdef __USE_ISOC99
+
+/* All floating-point numbers can be put in one of these categories.  */
+enum
+  {
+    FP_NAN =
+# define FP_NAN 0
+      FP_NAN,
+    FP_INFINITE =
+# define FP_INFINITE 1
+      FP_INFINITE,
+    FP_ZERO =
+# define FP_ZERO 2
+      FP_ZERO,
+    FP_SUBNORMAL =
+# define FP_SUBNORMAL 3
+      FP_SUBNORMAL,
+    FP_NORMAL =
+# define FP_NORMAL 4
+      FP_NORMAL
+  };
+
+/* GCC bug 66462 means we cannot use the math builtins with -fsignaling-nan,
+   so disable builtins if this is enabled.  When fixed in a newer GCC,
+   the __SUPPORT_SNAN__ check may be skipped for those versions.  */
+
+/* Return number of classification appropriate for X.  */
+# if ((__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__)		      \
+      || __glibc_clang_prereq (2,8))					      \
+     && (!defined __OPTIMIZE_SIZE__ || defined __cplusplus)
+     /* The check for __cplusplus allows the use of the builtin, even
+	when optimization for size is on.  This is provided for
+	libstdc++, only to let its configure test work when it is built
+	with -Os.  No further use of this definition of fpclassify is
+	expected in C++ mode, since libstdc++ provides its own version
+	of fpclassify in cmath (which undefines fpclassify).  */
+#  define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE,	      \
+     FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
+# else
+#  define fpclassify(x) __MATH_TG ((x), __fpclassify, (x))
+# endif
+
+/* Return nonzero value if sign of X is negative.  */
+# if __GNUC_PREREQ (6,0) || __glibc_clang_prereq (3,3)
+#  define signbit(x) __builtin_signbit (x)
+# elif defined __cplusplus
+  /* In C++ mode, __MATH_TG cannot be used, because it relies on
+     __builtin_types_compatible_p, which is a C-only builtin.
+     The check for __cplusplus allows the use of the builtin instead of
+     __MATH_TG. This is provided for libstdc++, only to let its configure
+     test work. No further use of this definition of signbit is expected
+     in C++ mode, since libstdc++ provides its own version of signbit
+     in cmath (which undefines signbit). */
+#  define signbit(x) __builtin_signbitl (x)
+# elif __GNUC_PREREQ (4,0)
+#  define signbit(x) __MATH_TG ((x), __builtin_signbit, (x))
+# else
+#  define signbit(x) __MATH_TG ((x), __signbit, (x))
+# endif
+
+/* Return nonzero value if X is not +-Inf or NaN.  */
+# if (__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \
+     || __glibc_clang_prereq (2,8)
+#  define isfinite(x) __builtin_isfinite (x)
+# else
+#  define isfinite(x) __MATH_TG ((x), __finite, (x))
+# endif
+
+/* Return nonzero value if X is neither zero, subnormal, Inf, nor NaN.  */
+# if (__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \
+     || __glibc_clang_prereq (2,8)
+#  define isnormal(x) __builtin_isnormal (x)
+# else
+#  define isnormal(x) (fpclassify (x) == FP_NORMAL)
+# endif
+
+/* Return nonzero value if X is a NaN.  We could use `fpclassify' but
+   we already have this functions `__isnan' and it is faster.  */
+# if (__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \
+     || __glibc_clang_prereq (2,8)
+#  define isnan(x) __builtin_isnan (x)
+# else
+#  define isnan(x) __MATH_TG ((x), __isnan, (x))
+# endif
+
+/* Return nonzero value if X is positive or negative infinity.  */
+# if __HAVE_DISTINCT_FLOAT128 && !__GNUC_PREREQ (7,0) \
+     && !defined __SUPPORT_SNAN__ && !defined __cplusplus \
+     && !defined __clang__
+   /* Since __builtin_isinf_sign is broken for float128 before GCC 7.0,
+      use the helper function, __isinff128, with older compilers.  This is
+      only provided for C mode, because in C++ mode, GCC has no support
+      for __builtin_types_compatible_p (and when in C++ mode, this macro is
+      not used anyway, because libstdc++ headers undefine it).  */
+#  define isinf(x) \
+    (__builtin_types_compatible_p (__typeof (x), _Float128) \
+     ? __isinff128 (x) : __builtin_isinf_sign (x))
+# elif (__GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__) \
+       || __glibc_clang_prereq (3,7)
+#  define isinf(x) __builtin_isinf_sign (x)
+# else
+#  define isinf(x) __MATH_TG ((x), __isinf, (x))
+# endif
+
+/* Bitmasks for the math_errhandling macro.  */
+# define MATH_ERRNO	1	/* errno set by math functions.  */
+# define MATH_ERREXCEPT	2	/* Exceptions raised by math functions.  */
+
+/* By default all math functions support both errno and exception handling
+   (except for soft floating point implementations which may only support
+   errno handling).  If errno handling is disabled, exceptions are still
+   supported by GLIBC.  Set math_errhandling to 0 with -ffast-math (this is
+   nonconforming but it is more useful than leaving it undefined).  */
+# ifdef __FAST_MATH__
+#  define math_errhandling	0
+# elif defined __NO_MATH_ERRNO__
+#  define math_errhandling	(MATH_ERREXCEPT)
+# else
+#  define math_errhandling	(MATH_ERRNO | MATH_ERREXCEPT)
+# endif
+
+#endif /* Use ISO C99.  */
+
+#if __GLIBC_USE (IEC_60559_BFP_EXT_C2X)
+# include <bits/iscanonical.h>
+
+/* Return nonzero value if X is a signaling NaN.  */
+# ifndef __cplusplus
+#  define issignaling(x) __MATH_TG ((x), __issignaling, (x))
+# else
+   /* In C++ mode, __MATH_TG cannot be used, because it relies on
+      __builtin_types_compatible_p, which is a C-only builtin.  On the
+      other hand, overloading provides the means to distinguish between
+      the floating-point types.  The overloading resolution will match
+      the correct parameter (regardless of type qualifiers (i.e.: const
+      and volatile)).  */
+extern "C++" {
+inline int issignaling (float __val) { return __issignalingf (__val); }
+inline int issignaling (double __val) { return __issignaling (__val); }
+inline int
+issignaling (long double __val)
+{
+#  ifdef __NO_LONG_DOUBLE_MATH
+  return __issignaling (__val);
+#  else
+  return __issignalingl (__val);
+#  endif
+}
+#  if __HAVE_FLOAT128_UNLIKE_LDBL
+/* When using an IEEE 128-bit long double, _Float128 is defined as long double
+   in C++.  */
+inline int issignaling (_Float128 __val) { return __issignalingf128 (__val); }
+#  endif
+} /* extern C++ */
+# endif
+
+/* Return nonzero value if X is subnormal.  */
+# define issubnormal(x) (fpclassify (x) == FP_SUBNORMAL)
+
+/* Return nonzero value if X is zero.  */
+# ifndef __cplusplus
+#  ifdef __SUPPORT_SNAN__
+#   define iszero(x) (fpclassify (x) == FP_ZERO)
+#  else
+#   define iszero(x) (((__typeof (x)) (x)) == 0)
+#  endif
+# else	/* __cplusplus */
+extern "C++" {
+#  ifdef __SUPPORT_SNAN__
+inline int
+iszero (float __val)
+{
+  return __fpclassifyf (__val) == FP_ZERO;
+}
+inline int
+iszero (double __val)
+{
+  return __fpclassify (__val) == FP_ZERO;
+}
+inline int
+iszero (long double __val)
+{
+#   ifdef __NO_LONG_DOUBLE_MATH
+  return __fpclassify (__val) == FP_ZERO;
+#   else
+  return __fpclassifyl (__val) == FP_ZERO;
+#   endif
+}
+#   if __HAVE_FLOAT128_UNLIKE_LDBL
+  /* When using an IEEE 128-bit long double, _Float128 is defined as long double
+     in C++.  */
+inline int
+iszero (_Float128 __val)
+{
+  return __fpclassifyf128 (__val) == FP_ZERO;
+}
+#   endif
+#  else
+template <class __T> inline bool
+iszero (__T __val)
+{
+  return __val == 0;
+}
+#  endif
+} /* extern C++ */
+# endif	/* __cplusplus */
+#endif /* Use IEC_60559_BFP_EXT.  */
+
+#ifdef __USE_XOPEN
+/* X/Open wants another strange constant.  */
+# define MAXFLOAT	3.40282347e+38F
+#endif
+
+
+/* Some useful constants.  */
+#if defined __USE_MISC || defined __USE_XOPEN
+# define M_E		2.7182818284590452354	/* e */
+# define M_LOG2E	1.4426950408889634074	/* log_2 e */
+# define M_LOG10E	0.43429448190325182765	/* log_10 e */
+# define M_LN2		0.69314718055994530942	/* log_e 2 */
+# define M_LN10		2.30258509299404568402	/* log_e 10 */
+# define M_PI		3.14159265358979323846	/* pi */
+# define M_PI_2		1.57079632679489661923	/* pi/2 */
+# define M_PI_4		0.78539816339744830962	/* pi/4 */
+# define M_1_PI		0.31830988618379067154	/* 1/pi */
+# define M_2_PI		0.63661977236758134308	/* 2/pi */
+# define M_2_SQRTPI	1.12837916709551257390	/* 2/sqrt(pi) */
+# define M_SQRT2	1.41421356237309504880	/* sqrt(2) */
+# define M_SQRT1_2	0.70710678118654752440	/* 1/sqrt(2) */
+#endif
+
+/* GNU extension to provide float constants with similar names.  */
+#ifdef __USE_GNU
+# define M_Ef		2.7182818284590452354f	/* e */
+# define M_LOG2Ef	1.4426950408889634074f	/* log_2 e */
+# define M_LOG10Ef	0.43429448190325182765f	/* log_10 e */
+# define M_LN2f		0.69314718055994530942f	/* log_e 2 */
+# define M_LN10f	2.30258509299404568402f	/* log_e 10 */
+# define M_PIf		3.14159265358979323846f	/* pi */
+# define M_PI_2f	1.57079632679489661923f	/* pi/2 */
+# define M_PI_4f	0.78539816339744830962f	/* pi/4 */
+# define M_1_PIf	0.31830988618379067154f	/* 1/pi */
+# define M_2_PIf	0.63661977236758134308f	/* 2/pi */
+# define M_2_SQRTPIf	1.12837916709551257390f	/* 2/sqrt(pi) */
+# define M_SQRT2f	1.41421356237309504880f	/* sqrt(2) */
+# define M_SQRT1_2f	0.70710678118654752440f	/* 1/sqrt(2) */
+#endif
+
+/* The above constants are not adequate for computation using `long double's.
+   Therefore we provide as an extension constants with similar names as a
+   GNU extension.  Provide enough digits for the 128-bit IEEE quad.  */
+#ifdef __USE_GNU
+# define M_El		2.718281828459045235360287471352662498L /* e */
+# define M_LOG2El	1.442695040888963407359924681001892137L /* log_2 e */
+# define M_LOG10El	0.434294481903251827651128918916605082L /* log_10 e */
+# define M_LN2l		0.693147180559945309417232121458176568L /* log_e 2 */
+# define M_LN10l	2.302585092994045684017991454684364208L /* log_e 10 */
+# define M_PIl		3.141592653589793238462643383279502884L /* pi */
+# define M_PI_2l	1.570796326794896619231321691639751442L /* pi/2 */
+# define M_PI_4l	0.785398163397448309615660845819875721L /* pi/4 */
+# define M_1_PIl	0.318309886183790671537767526745028724L /* 1/pi */
+# define M_2_PIl	0.636619772367581343075535053490057448L /* 2/pi */
+# define M_2_SQRTPIl	1.128379167095512573896158903121545172L /* 2/sqrt(pi) */
+# define M_SQRT2l	1.414213562373095048801688724209698079L /* sqrt(2) */
+# define M_SQRT1_2l	0.707106781186547524400844362104849039L /* 1/sqrt(2) */
+#endif
+
+#if __HAVE_FLOAT16 && defined __USE_GNU
+# define M_Ef16		__f16 (2.718281828459045235360287471352662498) /* e */
+# define M_LOG2Ef16	__f16 (1.442695040888963407359924681001892137) /* log_2 e */
+# define M_LOG10Ef16	__f16 (0.434294481903251827651128918916605082) /* log_10 e */
+# define M_LN2f16	__f16 (0.693147180559945309417232121458176568) /* log_e 2 */
+# define M_LN10f16	__f16 (2.302585092994045684017991454684364208) /* log_e 10 */
+# define M_PIf16	__f16 (3.141592653589793238462643383279502884) /* pi */
+# define M_PI_2f16	__f16 (1.570796326794896619231321691639751442) /* pi/2 */
+# define M_PI_4f16	__f16 (0.785398163397448309615660845819875721) /* pi/4 */
+# define M_1_PIf16	__f16 (0.318309886183790671537767526745028724) /* 1/pi */
+# define M_2_PIf16	__f16 (0.636619772367581343075535053490057448) /* 2/pi */
+# define M_2_SQRTPIf16	__f16 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
+# define M_SQRT2f16	__f16 (1.414213562373095048801688724209698079) /* sqrt(2) */
+# define M_SQRT1_2f16	__f16 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
+#endif
+
+#if __HAVE_FLOAT32 && defined __USE_GNU
+# define M_Ef32		__f32 (2.718281828459045235360287471352662498) /* e */
+# define M_LOG2Ef32	__f32 (1.442695040888963407359924681001892137) /* log_2 e */
+# define M_LOG10Ef32	__f32 (0.434294481903251827651128918916605082) /* log_10 e */
+# define M_LN2f32	__f32 (0.693147180559945309417232121458176568) /* log_e 2 */
+# define M_LN10f32	__f32 (2.302585092994045684017991454684364208) /* log_e 10 */
+# define M_PIf32	__f32 (3.141592653589793238462643383279502884) /* pi */
+# define M_PI_2f32	__f32 (1.570796326794896619231321691639751442) /* pi/2 */
+# define M_PI_4f32	__f32 (0.785398163397448309615660845819875721) /* pi/4 */
+# define M_1_PIf32	__f32 (0.318309886183790671537767526745028724) /* 1/pi */
+# define M_2_PIf32	__f32 (0.636619772367581343075535053490057448) /* 2/pi */
+# define M_2_SQRTPIf32	__f32 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
+# define M_SQRT2f32	__f32 (1.414213562373095048801688724209698079) /* sqrt(2) */
+# define M_SQRT1_2f32	__f32 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
+#endif
+
+#if __HAVE_FLOAT64 && defined __USE_GNU
+# define M_Ef64		__f64 (2.718281828459045235360287471352662498) /* e */
+# define M_LOG2Ef64	__f64 (1.442695040888963407359924681001892137) /* log_2 e */
+# define M_LOG10Ef64	__f64 (0.434294481903251827651128918916605082) /* log_10 e */
+# define M_LN2f64	__f64 (0.693147180559945309417232121458176568) /* log_e 2 */
+# define M_LN10f64	__f64 (2.302585092994045684017991454684364208) /* log_e 10 */
+# define M_PIf64	__f64 (3.141592653589793238462643383279502884) /* pi */
+# define M_PI_2f64	__f64 (1.570796326794896619231321691639751442) /* pi/2 */
+# define M_PI_4f64	__f64 (0.785398163397448309615660845819875721) /* pi/4 */
+# define M_1_PIf64	__f64 (0.318309886183790671537767526745028724) /* 1/pi */
+# define M_2_PIf64	__f64 (0.636619772367581343075535053490057448) /* 2/pi */
+# define M_2_SQRTPIf64	__f64 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
+# define M_SQRT2f64	__f64 (1.414213562373095048801688724209698079) /* sqrt(2) */
+# define M_SQRT1_2f64	__f64 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
+#endif
+
+#if __HAVE_FLOAT128 && defined __USE_GNU
+# define M_Ef128	__f128 (2.718281828459045235360287471352662498) /* e */
+# define M_LOG2Ef128	__f128 (1.442695040888963407359924681001892137) /* log_2 e */
+# define M_LOG10Ef128	__f128 (0.434294481903251827651128918916605082) /* log_10 e */
+# define M_LN2f128	__f128 (0.693147180559945309417232121458176568) /* log_e 2 */
+# define M_LN10f128	__f128 (2.302585092994045684017991454684364208) /* log_e 10 */
+# define M_PIf128	__f128 (3.141592653589793238462643383279502884) /* pi */
+# define M_PI_2f128	__f128 (1.570796326794896619231321691639751442) /* pi/2 */
+# define M_PI_4f128	__f128 (0.785398163397448309615660845819875721) /* pi/4 */
+# define M_1_PIf128	__f128 (0.318309886183790671537767526745028724) /* 1/pi */
+# define M_2_PIf128	__f128 (0.636619772367581343075535053490057448) /* 2/pi */
+# define M_2_SQRTPIf128	__f128 (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
+# define M_SQRT2f128	__f128 (1.414213562373095048801688724209698079) /* sqrt(2) */
+# define M_SQRT1_2f128	__f128 (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
+#endif
+
+#if __HAVE_FLOAT32X && defined __USE_GNU
+# define M_Ef32x	__f32x (2.718281828459045235360287471352662498) /* e */
+# define M_LOG2Ef32x	__f32x (1.442695040888963407359924681001892137) /* log_2 e */
+# define M_LOG10Ef32x	__f32x (0.434294481903251827651128918916605082) /* log_10 e */
+# define M_LN2f32x	__f32x (0.693147180559945309417232121458176568) /* log_e 2 */
+# define M_LN10f32x	__f32x (2.302585092994045684017991454684364208) /* log_e 10 */
+# define M_PIf32x	__f32x (3.141592653589793238462643383279502884) /* pi */
+# define M_PI_2f32x	__f32x (1.570796326794896619231321691639751442) /* pi/2 */
+# define M_PI_4f32x	__f32x (0.785398163397448309615660845819875721) /* pi/4 */
+# define M_1_PIf32x	__f32x (0.318309886183790671537767526745028724) /* 1/pi */
+# define M_2_PIf32x	__f32x (0.636619772367581343075535053490057448) /* 2/pi */
+# define M_2_SQRTPIf32x	__f32x (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
+# define M_SQRT2f32x	__f32x (1.414213562373095048801688724209698079) /* sqrt(2) */
+# define M_SQRT1_2f32x	__f32x (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
+#endif
+
+#if __HAVE_FLOAT64X && defined __USE_GNU
+# define M_Ef64x	__f64x (2.718281828459045235360287471352662498) /* e */
+# define M_LOG2Ef64x	__f64x (1.442695040888963407359924681001892137) /* log_2 e */
+# define M_LOG10Ef64x	__f64x (0.434294481903251827651128918916605082) /* log_10 e */
+# define M_LN2f64x	__f64x (0.693147180559945309417232121458176568) /* log_e 2 */
+# define M_LN10f64x	__f64x (2.302585092994045684017991454684364208) /* log_e 10 */
+# define M_PIf64x	__f64x (3.141592653589793238462643383279502884) /* pi */
+# define M_PI_2f64x	__f64x (1.570796326794896619231321691639751442) /* pi/2 */
+# define M_PI_4f64x	__f64x (0.785398163397448309615660845819875721) /* pi/4 */
+# define M_1_PIf64x	__f64x (0.318309886183790671537767526745028724) /* 1/pi */
+# define M_2_PIf64x	__f64x (0.636619772367581343075535053490057448) /* 2/pi */
+# define M_2_SQRTPIf64x	__f64x (1.128379167095512573896158903121545172) /* 2/sqrt(pi) */
+# define M_SQRT2f64x	__f64x (1.414213562373095048801688724209698079) /* sqrt(2) */
+# define M_SQRT1_2f64x	__f64x (0.707106781186547524400844362104849039) /* 1/sqrt(2) */
+#endif
+
+#if __HAVE_FLOAT128X && defined __USE_GNU
+# error "M_* values needed for _Float128x"
+#endif
+
+#ifdef __USE_ISOC99
+# if __GNUC_PREREQ (3, 1)
+/* ISO C99 defines some macros to compare number while taking care for
+   unordered numbers.  Many FPUs provide special instructions to support
+   these operations.  Generic support in GCC for these as builtins went
+   in 2.97, but not all cpus added their patterns until 3.1.  Therefore
+   we enable the builtins from 3.1 onwards and use a generic implementation
+   otherwise.  */
+#  define isgreater(x, y)	__builtin_isgreater(x, y)
+#  define isgreaterequal(x, y)	__builtin_isgreaterequal(x, y)
+#  define isless(x, y)		__builtin_isless(x, y)
+#  define islessequal(x, y)	__builtin_islessequal(x, y)
+#  define islessgreater(x, y)	__builtin_islessgreater(x, y)
+#  define isunordered(x, y)	__builtin_isunordered(x, y)
+# else
+#  define isgreater(x, y) \
+  (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
+		    !isunordered (__x, __y) && __x > __y; }))
+#  define isgreaterequal(x, y) \
+  (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
+		    !isunordered (__x, __y) && __x >= __y; }))
+#  define isless(x, y) \
+  (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
+		    !isunordered (__x, __y) && __x < __y; }))
+#  define islessequal(x, y) \
+  (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
+		    !isunordered (__x, __y) && __x <= __y; }))
+#  define islessgreater(x, y) \
+  (__extension__ ({ __typeof__ (x) __x = (x); __typeof__ (y) __y = (y); \
+		    !isunordered (__x, __y) && __x != __y; }))
+/* isunordered must always check both operands first for signaling NaNs.  */
+#  define isunordered(x, y) \
+  (__extension__ ({ __typeof__ (x) __u = (x); __typeof__ (y) __v = (y); \
+		    __u != __v && (__u != __u || __v != __v); }))
+# endif
+#endif
+
+#if __GLIBC_USE (IEC_60559_BFP_EXT_C2X)
+/* An expression whose type has the widest of the evaluation formats
+   of X and Y (which are of floating-point types).  */
+# if __FLT_EVAL_METHOD__ == 2 || __FLT_EVAL_METHOD__ > 64
+#  define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0L)
+# elif __FLT_EVAL_METHOD__ == 1 || __FLT_EVAL_METHOD__ > 32
+#  define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0)
+# elif __FLT_EVAL_METHOD__ == 0 || __FLT_EVAL_METHOD__ == 32
+#  define __MATH_EVAL_FMT2(x, y) ((x) + (y) + 0.0f)
+# else
+#  define __MATH_EVAL_FMT2(x, y) ((x) + (y))
+# endif
+
+/* Return X == Y but raising "invalid" and setting errno if X or Y is
+   a NaN.  */
+# if !defined __cplusplus || (__cplusplus < 201103L && !defined __GNUC__)
+#  define iseqsig(x, y) \
+   __MATH_TG (__MATH_EVAL_FMT2 (x, y), __iseqsig, ((x), (y)))
+# else
+/* In C++ mode, __MATH_TG cannot be used, because it relies on
+   __builtin_types_compatible_p, which is a C-only builtin.  Moreover,
+   the comparison macros from ISO C take two floating-point arguments,
+   which need not have the same type.  Choosing what underlying function
+   to call requires evaluating the formats of the arguments, then
+   selecting which is wider.  The macro __MATH_EVAL_FMT2 provides this
+   information, however, only the type of the macro expansion is
+   relevant (actually evaluating the expression would be incorrect).
+   Thus, the type is used as a template parameter for __iseqsig_type,
+   which calls the appropriate underlying function.  */
+extern "C++" {
+template<typename> struct __iseqsig_type;
+
+template<> struct __iseqsig_type<float>
+{
+  static int __call (float __x, float __y) throw ()
+  {
+    return __iseqsigf (__x, __y);
+  }
+};
+
+template<> struct __iseqsig_type<double>
+{
+  static int __call (double __x, double __y) throw ()
+  {
+    return __iseqsig (__x, __y);
+  }
+};
+
+template<> struct __iseqsig_type<long double>
+{
+  static int __call (long double __x, long double __y) throw ()
+  {
+#  ifndef __NO_LONG_DOUBLE_MATH
+    return __iseqsigl (__x, __y);
+#  else
+    return __iseqsig (__x, __y);
+#  endif
+  }
+};
+
+#  if __HAVE_FLOAT32 && __GNUC_PREREQ (13, 0)
+template<> struct __iseqsig_type<_Float32>
+{
+  static int __call (_Float32 __x, _Float32 __y) throw ()
+  {
+    return __iseqsigf (__x, __y);
+  }
+};
+#  endif
+
+#  if __HAVE_FLOAT64 && __GNUC_PREREQ (13, 0)
+template<> struct __iseqsig_type<_Float64>
+{
+  static int __call (_Float64 __x, _Float64 __y) throw ()
+  {
+    return __iseqsig (__x, __y);
+  }
+};
+#  endif
+
+#  if __HAVE_FLOAT128_UNLIKE_LDBL || (__HAVE_FLOAT128 && __GNUC_PREREQ (13, 0))
+  /* When using an IEEE 128-bit long double, _Float128 is defined as long double
+     in C++.  */
+template<> struct __iseqsig_type<_Float128>
+{
+  static int __call (_Float128 __x, _Float128 __y) throw ()
+  {
+#   if __HAVE_FLOAT128_UNLIKE_LDBL
+    return __iseqsigf128 (__x, __y);
+#   else
+    return __iseqsigl (__x, __y);
+#   endif
+  }
+};
+#  endif
+
+#  if __HAVE_FLOAT32X && __GNUC_PREREQ (13, 0)
+template<> struct __iseqsig_type<_Float32x>
+{
+  static int __call (_Float32x __x, _Float32x __y) throw ()
+  {
+    return __iseqsig (__x, __y);
+  }
+};
+#  endif
+
+#  if __HAVE_FLOAT64X && __GNUC_PREREQ (13, 0)
+template<> struct __iseqsig_type<_Float64x>
+{
+  static int __call (_Float64x __x, _Float64x __y) throw ()
+  {
+#   if __HAVE_FLOAT64X_LONG_DOUBLE
+    return __iseqsigl (__x, __y);
+#   else
+    return __iseqsigf128 (__x, __y);
+#   endif
+  }
+};
+#  endif
+
+template<typename _T1, typename _T2>
+inline int
+iseqsig (_T1 __x, _T2 __y) throw ()
+{
+#  if __cplusplus >= 201103L
+  typedef decltype (__MATH_EVAL_FMT2 (__x, __y)) _T3;
+#  else
+  typedef __typeof (__MATH_EVAL_FMT2 (__x, __y)) _T3;
+#  endif
+  return __iseqsig_type<_T3>::__call (__x, __y);
+}
+
+} /* extern "C++" */
+# endif /* __cplusplus */
+
+#endif
+
+__END_DECLS
+
+
+#endif /* math.h  */