diff --git a/bits/floatn.h b/bits/floatn.h
new file mode 100644
index 0000000..57db3a6
--- /dev/null
+++ b/bits/floatn.h
@@ -0,0 +1,27 @@
+/* Macros to control TS 18661-3 glibc features.
+   Copyright (C) 2016 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
+   <http://www.gnu.org/licenses/>.  */
+
+/* Defined if the compiler supports the _Float128 (and __float128) type.  */
+#define __USE_FLOAT128 0
+
+/* Defined if the runtime supports _Float128.  */
+#define __HAVE_FLOAT128 0
+
+/* Defined for GCC versions which support the __float128 type, but not
+   _Complex __float128.  This resolves to a complex binary128 type.  */
+#undef __CFLOAT128
diff --git a/bits/huge_val_flt128.h b/bits/huge_val_flt128.h
new file mode 100644
index 0000000..562d026
--- /dev/null
+++ b/bits/huge_val_flt128.h
@@ -0,0 +1,29 @@
+/* Default `HUGE_VAL_F128' constant.
+   Copyright (C) 2016 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
+   <http://www.gnu.org/licenses/>.  */
+
+#ifndef _MATH_H
+# error "Never use <bits/huge_val_flt128.h> directly; include <math.h> instead."
+#endif
+
+#if __GNUC_PREREQ (7, 0)
+# define HUGE_VAL_F128	(__builtin_huge_valf128 ())
+#elif __GNUC_PREREQ (6,2)
+# define HUGE_VAL_F128	(__builtin_huge_valq ())
+#else
+# define HUGE_VAL_F128	((_Float128) HUGE_VAL)
+#endif
diff --git a/math/Makefile b/math/Makefile
index 37e7ea0..f6adf09 100644
--- a/math/Makefile
+++ b/math/Makefile
@@ -27,7 +27,9 @@ headers		:= math.h bits/mathcalls.h bits/mathinline.h bits/huge_val.h \
 		   fpu_control.h complex.h bits/cmathcalls.h fenv.h \
 		   bits/fenv.h bits/fenvinline.h bits/mathdef.h tgmath.h \
 		   bits/math-finite.h bits/math-vector.h \
-		   bits/libm-simd-decl-stubs.h bits/iscanonical.h
+		   bits/libm-simd-decl-stubs.h bits/iscanonical.h \
+		   bits/huge_val_flt128.h \
+		   bits/floatn.h
 
 # FPU support code.
 aux		:= setfpucw fpu_control
diff --git a/math/bits/cmathcalls.h b/math/bits/cmathcalls.h
index e02707e..c94976b 100644
--- a/math/bits/cmathcalls.h
+++ b/math/bits/cmathcalls.h
@@ -44,7 +44,9 @@
 #error "Never use <bits/cmathcalls.h> directly; include <complex.h> instead."
 #endif
 
-#define _Mdouble_complex_ _Mdouble_ _Complex
+#ifndef _Mdouble_complex_
+# define _Mdouble_complex_ _Mdouble_ _Complex
+#endif
 
 
 /* Trigonometric functions.  */
diff --git a/math/bits/mathcalls.h b/math/bits/mathcalls.h
index 2fd1d28..8a31aea 100644
--- a/math/bits/mathcalls.h
+++ b/math/bits/mathcalls.h
@@ -121,7 +121,9 @@ __MATHCALL (exp10,, (_Mdouble_ __x));
 #endif
 #ifdef __USE_GNU
 /* Another name occasionally used.  */
+# ifndef __FLOATN_TYPE
 __MATHCALL (pow10,, (_Mdouble_ __x));
+# endif
 #endif
 
 #if defined __USE_XOPEN_EXTENDED || defined __USE_ISOC99
@@ -198,14 +200,16 @@ __MATHDECL_1 (int,__finite,, (_Mdouble_ __value)) __attribute__ ((__const__));
 _Mdouble_END_NAMESPACE
 
 #ifdef __USE_MISC
-# if (!defined __cplusplus \
-      || __cplusplus < 201103L /* isinf conflicts with C++11.  */ \
-      || __MATH_DECLARING_DOUBLE == 0) /* isinff or isinfl don't.  */
+# if ((!defined __cplusplus \
+       || __cplusplus < 201103L /* isinf conflicts with C++11.  */ \
+       || __MATH_DECLARING_DOUBLE == 0)) /* isinff or isinfl don't.  */ \
+      && !defined __FLOATN_TYPE
 /* Return 0 if VALUE is finite or NaN, +1 if it
    is +Infinity, -1 if it is -Infinity.  */
 __MATHDECL_1 (int,isinf,, (_Mdouble_ __value)) __attribute__ ((__const__));
 # endif
 
+# ifndef __FLOATN_TYPE
 /* Return nonzero if VALUE is finite and not NaN.  */
 __MATHDECL_1 (int,finite,, (_Mdouble_ __value)) __attribute__ ((__const__));
 
@@ -215,6 +219,8 @@ __MATHCALL (drem,, (_Mdouble_ __x, _Mdouble_ __y));
 
 /* Return the fractional part of X after dividing out `ilogb (X)'.  */
 __MATHCALL (significand,, (_Mdouble_ __x));
+# endif
+
 #endif /* Use misc.  */
 
 #ifdef __USE_ISOC99
@@ -236,9 +242,10 @@ __END_NAMESPACE_C99
 __MATHDECL_1 (int,__isnan,, (_Mdouble_ __value)) __attribute__ ((__const__));
 
 #if defined __USE_MISC || (defined __USE_XOPEN && !defined __USE_XOPEN2K)
-# if (!defined __cplusplus \
-      || __cplusplus < 201103L /* isnan conflicts with C++11.  */ \
-      || __MATH_DECLARING_DOUBLE == 0) /* isnanf or isnanl don't.  */
+# if ((!defined __cplusplus \
+       || __cplusplus < 201103L /* isnan conflicts with C++11.  */ \
+       || __MATH_DECLARING_DOUBLE == 0)) /* isnanf or isnanl don't.  */ \
+      && !defined __FLOATN_TYPE
 /* Return nonzero if VALUE is not a number.  */
 __MATHDECL_1 (int,isnan,, (_Mdouble_ __value)) __attribute__ ((__const__));
 # endif
@@ -272,8 +279,10 @@ __END_NAMESPACE_C99
 #endif
 
 #if defined __USE_MISC || (defined __USE_XOPEN && !defined __USE_XOPEN2K)
+# ifndef __FLOATN_TYPE
 /* Obsolete alias for `lgamma'.  */
 __MATHCALL (gamma,, (_Mdouble_));
+# endif
 #endif
 
 #ifdef __USE_MISC
@@ -292,7 +301,7 @@ __MATHCALL (rint,, (_Mdouble_ __x));
 
 /* Return X + epsilon if X < Y, X - epsilon if X > Y.  */
 __MATHCALLX (nextafter,, (_Mdouble_ __x, _Mdouble_ __y), (__const__));
-# if defined __USE_ISOC99 && !defined __LDBL_COMPAT
+# if defined __USE_ISOC99 && !defined __LDBL_COMPAT && !defined __FLOATN_TYPE
 __MATHCALLX (nexttoward,, (_Mdouble_ __x, long double __y), (__const__));
 # endif
 
@@ -402,9 +411,10 @@ __MATHDECL_1 (int, canonicalize,, (_Mdouble_ *__cx, const _Mdouble_ *__x));
 __MATHCALL (getpayload,, (const _Mdouble_ *__x));
 #endif
 
-#if defined __USE_MISC || (defined __USE_XOPEN_EXTENDED \
-			   && __MATH_DECLARING_DOUBLE	\
-			   && !defined __USE_XOPEN2K8)
+#if (defined __USE_MISC || (defined __USE_XOPEN_EXTENDED \
+			    && __MATH_DECLARING_DOUBLE	  \
+			    && !defined __USE_XOPEN2K8))  \
+     && !defined __FLOATN_TYPE
 /* Return X times (2 to the Nth power).  */
 __MATHCALL (scalb,, (_Mdouble_ __x, _Mdouble_ __n));
 #endif
diff --git a/math/complex.h b/math/complex.h
index 331975e..4adc742 100644
--- a/math/complex.h
+++ b/math/complex.h
@@ -22,11 +22,15 @@
 #ifndef _COMPLEX_H
 #define _COMPLEX_H	1
 
-#include <features.h>
+#define __GLIBC_INTERNAL_STARTING_HEADER_IMPLEMENTATION
+#include <bits/libc-header-start.h>
 
 /* Get general and ISO C99 specific information.  */
 #include <bits/mathdef.h>
 
+/* Gather machine-dependent _FloatN type support.  */
+#include <bits/floatn.h>
+
 __BEGIN_DECLS
 
 /* We might need to add support for more compilers here.  But since ISO
@@ -55,6 +59,10 @@ __BEGIN_DECLS
 # define CMPLXL(x, y) __builtin_complex ((long double) (x), (long double) (y))
 #endif
 
+#if __USE_FLOAT128
+# define CMPLXF128(x, y) __builtin_complex ((__float128) (x), (__float128) (y))
+#endif
+
 /* The file <bits/cmathcalls.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',
@@ -84,6 +92,23 @@ __BEGIN_DECLS
 #undef	_Mdouble_
 #undef	__MATH_PRECNAME
 
+#if __USE_FLOAT128
+# ifndef _Mfloat128_
+#  define _Mfloat128_		_Float128
+# endif
+/* GCC < 7 requires extra convincing to expose a complex float128 type.  */
+# ifdef __CFLOAT128
+#  undef _Mdouble_complex_
+#  define _Mdouble_complex_	__CFLOAT128
+# endif
+# define _Mdouble_ 		_Mfloat128_
+# define __MATH_PRECNAME(name)	name##f128
+# include <bits/cmathcalls.h>
+# undef	_Mdouble_
+# undef	__MATH_PRECNAME
+# undef	_Mdouble_complex_
+#endif
+
 /* And the long double versions.  It is non-critical to define them
    here unconditionally since `long double' is required in ISO C99.  */
 #if !(defined __NO_LONG_DOUBLE_MATH && defined _LIBC)	\
diff --git a/math/math.h b/math/math.h
index 70d9b86..87eb19d 100644
--- a/math/math.h
+++ b/math/math.h
@@ -31,9 +31,17 @@ __BEGIN_DECLS
 /* Get machine-dependent vector math functions declarations.  */
 #include <bits/math-vector.h>
 
+/* Gather machine dependent type support.  */
+#include <bits/floatn.h>
+
 /* Get machine-dependent HUGE_VAL value (returned on overflow).
    On all IEEE754 machines, this is +Infinity.  */
 #include <bits/huge_val.h>
+
+#if __USE_FLOAT128
+# include <bits/huge_val_flt128.h>
+#endif
+
 #ifdef __USE_ISOC99
 # include <bits/huge_valf.h>
 # include <bits/huge_vall.h>
@@ -106,6 +114,7 @@ __BEGIN_DECLS
   extern type __MATH_PRECNAME(function,suffix) args __THROW
 
 #define _Mdouble_		double
+#undef __FLOATN_TYPE
 #define __MATH_PRECNAME(name,r)	__CONCAT(name,r)
 #define __MATH_DECLARING_DOUBLE  1
 #define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_STD
@@ -126,6 +135,7 @@ __BEGIN_DECLS
 # ifndef _Mfloat_
 #  define _Mfloat_		float
 # endif
+# undef __FLOATN_TYPE
 # define _Mdouble_		_Mfloat_
 # define __MATH_PRECNAME(name,r) name##f##r
 # define __MATH_DECLARING_DOUBLE  0
@@ -172,6 +182,7 @@ extern long double __REDIRECT_NTH (nexttowardl,
 #  ifndef _Mlong_double_
 #   define _Mlong_double_	long double
 #  endif
+#  undef __FLOATN_TYPE
 #  define _Mdouble_		_Mlong_double_
 #  define __MATH_PRECNAME(name,r) name##l##r
 #  define __MATH_DECLARING_DOUBLE  0
@@ -188,6 +199,29 @@ extern long double __REDIRECT_NTH (nexttowardl,
 # endif /* !(__NO_LONG_DOUBLE_MATH && _LIBC) || __LDBL_COMPAT */
 
 #endif	/* Use ISO C99.  */
+
+/* Include the file of declarations again, this time using `_Float128'
+   instead of `double' and appending f128 to each function name.  */
+
+#if __USE_FLOAT128
+#ifndef _Mfloat128_
+# define _Mfloat128_		_Float128
+#endif
+#define __FLOATN_TYPE		1
+#define _Mdouble_		_Mfloat128_
+#define __MATH_PRECNAME(name,r) name##f128##r
+#define __MATH_DECLARING_DOUBLE  0
+#define _Mdouble_BEGIN_NAMESPACE __BEGIN_NAMESPACE_C99
+#define _Mdouble_END_NAMESPACE   __END_NAMESPACE_C99
+#include <bits/mathcalls.h>
+#undef __FLOATN_TYPE
+#undef	_Mdouble_
+#undef _Mdouble_BEGIN_NAMESPACE
+#undef _Mdouble_END_NAMESPACE
+#undef	__MATH_PRECNAME
+#undef __MATH_DECLARING_DOUBLE
+#endif /* Use _Float128.  */
+
 #undef	__MATHDECL_1
 #undef	__MATHDECL
 #undef	__MATHCALL
@@ -231,6 +265,13 @@ enum
      && !defined __OPTIMIZE_SIZE__
 #  define fpclassify(x) __builtin_fpclassify (FP_NAN, FP_INFINITE,	      \
      FP_NORMAL, FP_SUBNORMAL, FP_ZERO, x)
+# elif __USE_FLOAT128
+#  define fpclassify(x)		      \
+    _Generic ((x),		      \
+	_Float128: __fpclassifyf128,  \
+	long double: __fpclassifyl,   \
+	float: __fpclassifyf,	      \
+	default: __fpclassify)(x)
 # elif defined __NO_LONG_DOUBLE_MATH
 #  define fpclassify(x) \
      (sizeof (x) == sizeof (float) ? __fpclassifyf (x) : __fpclassify (x))
@@ -243,7 +284,16 @@ enum
 # endif
 
 /* Return nonzero value if sign of X is negative.  */
-# if __GNUC_PREREQ (4,0)
+# if __GNUC_PREREQ (6,2)
+#  define signbit(x) __builtin_signbit (x)
+# elif __USE_FLOAT128
+#  define signbit(x)		  \
+    _Generic ((x),		  \
+	_Float128: __signbitf128, \
+	long double: __signbitl,  \
+	float: __signbitf,	  \
+	default: __signbit)(x)
+# elif __GNUC_PREREQ (4,0)
 #  define signbit(x) \
      (sizeof (x) == sizeof (float)                                            \
       ? __builtin_signbitf (x)                                                        \
@@ -265,6 +315,13 @@ enum
 /* Return nonzero value if X is not +-Inf or NaN.  */
 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 #  define isfinite(x) __builtin_isfinite (x)
+# elif __USE_FLOAT128
+#  define isfinite(x)		  \
+    _Generic ((x),		  \
+	_Float128: __finitef128,  \
+	long double: __finitel,	  \
+	float: __finitef,	  \
+	default: __finite) (x)
 # elif defined __NO_LONG_DOUBLE_MATH
 #  define isfinite(x) \
      (sizeof (x) == sizeof (float) ? __finitef (x) : __finite (x))
@@ -287,6 +344,13 @@ enum
    we already have this functions `__isnan' and it is faster.  */
 # if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 #  define isnan(x) __builtin_isnan (x)
+# elif __USE_FLOAT128
+#  define isnan(x)		  \
+    _Generic ((x),		  \
+	_Float128: __isnanf128,	  \
+	long double: __isnanl,	  \
+	float: __isnanf,	  \
+	default: __isnan) (x)
 # elif defined __NO_LONG_DOUBLE_MATH
 #  define isnan(x) \
      (sizeof (x) == sizeof (float) ? __isnanf (x) : __isnan (x))
@@ -299,8 +363,20 @@ enum
 # endif
 
 /* Return nonzero value if X is positive or negative infinity.  */
-# if __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
+# if __USE_FLOAT128 && !defined __SUPPORT_SNAN__ && defined __GNUC__
+/* __builtin_isinf_sign is broken for float128.  */
+#  define isinf(x) \
+     (__builtin_types_compatible_p (typeof (x), _Float128) \
+      ? __isinff128 (x) : __builtin_isinf_sign (x))
+# elif __GNUC_PREREQ (4,4) && !defined __SUPPORT_SNAN__
 #  define isinf(x) __builtin_isinf_sign (x)
+# elif __USE_FLOAT128
+#  define isinf(x)		  \
+    _Generic ((x),		  \
+	_Float128: __isinff128,	  \
+	long double: __isinfl,	  \
+	float: __isinff,	  \
+	default: __isinf) (x)
 # elif defined __NO_LONG_DOUBLE_MATH
 #  define isinf(x) \
      (sizeof (x) == sizeof (float) ? __isinff (x) : __isinf (x))
@@ -332,6 +408,13 @@ enum
 # ifdef __NO_LONG_DOUBLE_MATH
 #  define issignaling(x) \
      (sizeof (x) == sizeof (float) ? __issignalingf (x) : __issignaling (x))
+# elif __USE_FLOAT128
+#  define issignaling(x) \
+    _Generic((x),			\
+	_Float128: __issignalingf128,	\
+	long double: __issignalingl,	\
+	float: __issignalingf,		\
+	default: __issignaling)(x)
 # else
 #  define issignaling(x) \
      (sizeof (x) == sizeof (float)					      \
@@ -467,6 +550,26 @@ extern int matherr (struct exception *__exc);
 # define M_SQRT1_2l	0.707106781186547524400844362104849039L /* 1/sqrt(2) */
 #endif
 
+#if __USE_FLOAT128
+# if defined __GNUC__ && !__GNUC_PREREQ (7,0)
+#  define __f128(x) x ## q
+# else
+#  define __f128(x) x ## f128
+# endif
+# 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
 
 /* When compiling in strict ISO C compatible mode we must not use the
    inline functions since they, among other things, do not set the
