Simplify NAN definitions.

Similar to my patches for HUGE_VAL and INFINITY. this patch eliminates
the bits/nan.h headers.  __builtin_nanf ("") is used to define NAN for
GCC 3.3 and later; the fallback is (0.0f / 0.0f), which is a constant
expression for a quiet NaN of type float, but raises a spurious
"invalid" exception outside static initializers, which seems the best
that can be done purely in standard C.  Again, if anyone actually uses
a compiler with its own incompatible extension for producing a
constant quiet NaN, we can add compiler conditionals.

Tested for x86_64.

	*  math/math.h [__USE_ISOC99] (NAN): Define directly here.  Do not
	include <bits/nan.h>.
	* math/Makefile (headers): Remove bits/nan.h.
	* bits/nan.h: Remove.
	* sysdeps/ieee754/bits/nan.h: Likewise.
	* sysdeps/mips/bits/nan.h: Likewise.

ChangeLog

@@ -1,5 +1,12 @@
 2017-08-31  Joseph Myers  <joseph@codesourcery.com>
 
+	*  math/math.h [__USE_ISOC99] (NAN): Define directly here.  Do not
+	include <bits/nan.h>.
+	* math/Makefile (headers): Remove bits/nan.h.
+	* bits/nan.h: Remove.
+	* sysdeps/ieee754/bits/nan.h: Likewise.
+	* sysdeps/mips/bits/nan.h: Likewise.
+
 	* math/math.h [__USE_ISOC99] (INFINITY): Define directly here.  Do
 	not include <bits/inf.h>.
 	* math/Makefile (headers): Remove bits/inf.h.

bits/nan.h

@@ -1,5 +0,0 @@
-#ifndef _MATH_H
-#error "Never use <bits/nan.h> directly; include <math.h> instead."
-#endif
-
-/* This file should define `NAN' on machines that have such things.  */

math/Makefile

@@ -23,7 +23,6 @@ include ../Makeconfig
 
 # Installed header files.
 headers		:= math.h bits/mathcalls.h bits/mathinline.h \
-		   bits/nan.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 \

math/math.h

@@ -65,8 +65,15 @@ __BEGIN_DECLS
 #  define INFINITY HUGE_VALF
 # endif
 
-/* Get machine-dependent NAN value (returned for some domain errors).  */
+/* IEEE Not A Number.  */
-# include <bits/nan.h>
+# 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)

sysdeps/ieee754/bits/nan.h

@@ -1,52 +0,0 @@
-/* `NAN' constant for IEEE 754 machines.
-   Copyright (C) 1992-2017 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/nan.h> directly; include <math.h> instead."
-#endif
-
-
-/* IEEE Not A Number.  */
-
-#if __GNUC_PREREQ(3,3)
-
-# define NAN	(__builtin_nanf (""))
-
-#elif defined __GNUC__
-
-# define NAN \
-  (__extension__							      \
-   ((union { unsigned __l __attribute__ ((__mode__ (__SI__))); float __d; })  \
-    { __l: 0x7fc00000UL }).__d)
-
-#else
-
-# include <endian.h>
-
-# if __BYTE_ORDER == __BIG_ENDIAN
-#  define __qnan_bytes		{ 0x7f, 0xc0, 0, 0 }
-# endif
-# if __BYTE_ORDER == __LITTLE_ENDIAN
-#  define __qnan_bytes		{ 0, 0, 0xc0, 0x7f }
-# endif
-
-static union { unsigned char __c[4]; float __d; } __qnan_union
-  __attribute__ ((__unused__)) = { __qnan_bytes };
-# define NAN	(__qnan_union.__d)
-
-#endif	/* GCC.  */

sysdeps/mips/bits/nan.h

@@ -1,67 +0,0 @@
-/* `NAN' constant for IEEE 754 machines.  MIPS version.
-   Copyright (C) 1992-2017 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/nan.h> directly; include <math.h> instead."
-#endif
-
-
-/* IEEE Not A Number.  */
-/* In legacy-NaN mode MIPS has the qNaN and sNaN patterns reversed
-   compared to most other architectures.  IEEE 754-1985 left the
-   definition of this open to implementations, and for MIPS the top bit
-   of the mantissa must be SET to indicate a sNaN.  In 2008-NaN mode
-   MIPS aligned to IEEE 754-2008.  */
-
-#if __GNUC_PREREQ(3,3)
-
-# define NAN	(__builtin_nanf (""))
-
-#elif defined __GNUC__
-
-/* No 2008-NaN mode support in any GCC version before 4.9.  */
-
-# define NAN \
-  (__extension__							      \
-   ((union { unsigned __l __attribute__ ((__mode__ (__SI__))); float __d; })  \
-    { __l: 0x7fbfffffUL }).__d)
-
-#else
-
-# include <endian.h>
-
-# if __BYTE_ORDER == __BIG_ENDIAN
-#  ifdef __mips_nan2008
-#   define __qnan_bytes		{ 0x7f, 0xc0, 0, 0 }
-#  else
-#   define __qnan_bytes		{ 0x7f, 0xbf, 0xff, 0xff }
-#  endif
-# endif
-# if __BYTE_ORDER == __LITTLE_ENDIAN
-#  ifdef __mips_nan2008
-#   define __qnan_bytes		{ 0, 0, 0xc0, 0x7f }
-#  else
-#   define __qnan_bytes		{ 0xff, 0xff, 0xbf, 0x7f }
-#  endif
-# endif
-
-static union { unsigned char __c[4]; float __d; } __qnan_union
-  __attribute__ ((__unused__)) = { __qnan_bytes };
-# define NAN	(__qnan_union.__d)
-
-#endif	/* GCC.  */