Use i386 bits/mathinline.h for i386 and x86_64

1 files changed, 968 insertions, 0 deletions

diff --git a/sysdeps/x86/fpu/bits/mathinline.h b/sysdeps/x86/fpu/bits/mathinline.h
new file mode 100644
index 0000000000..6446b1d875
--- /dev/null
+++ b/sysdeps/x86/fpu/bits/mathinline.h
@@ -0,0 +1,968 @@
+/* Inline math functions for i387 and SSE.
+   Copyright (C) 1995-2012 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/mathinline.h> directly; include <math.h> instead."
+#endif
+
+#ifndef __extern_always_inline
+# define __MATH_INLINE __inline
+#else
+# define __MATH_INLINE __extern_always_inline
+#endif
+
+
+#if defined __USE_ISOC99 && defined __GNUC__ && __GNUC__ >= 2
+/* GCC 2.97 and up have builtins that actually can be used.  */
+# if !__GNUC_PREREQ (2,97)
+/* ISO C99 defines some macros to perform unordered comparisons.  The
+   ix87 FPU supports this with special opcodes and we should use them.
+   These must not be inline functions since we have to be able to handle
+   all floating-point types.  */
+#  undef isgreater
+#  undef isgreaterequal
+#  undef isless
+#  undef islessequal
+#  undef islessgreater
+#  undef isunordered
+#  ifdef __i686__
+/* For the PentiumPro and more recent processors we can provide
+   better code.  */
+#   define isgreater(x, y) \
+     ({ register char __result;						      \
+	__asm__ ("fucomip %%st(1), %%st; seta %%al"			      \
+		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st");	      \
+	__result; })
+#   define isgreaterequal(x, y) \
+     ({ register char __result;						      \
+	__asm__ ("fucomip %%st(1), %%st; setae %%al"			      \
+		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st");	      \
+	__result; })
+
+#   define isless(x, y) \
+     ({ register char __result;						      \
+	__asm__ ("fucomip %%st(1), %%st; seta %%al"			      \
+		 : "=a" (__result) : "u" (x), "t" (y) : "cc", "st");	      \
+	__result; })
+
+#   define islessequal(x, y) \
+     ({ register char __result;						      \
+	__asm__ ("fucomip %%st(1), %%st; setae %%al"			      \
+		 : "=a" (__result) : "u" (x), "t" (y) : "cc", "st");	      \
+	__result; })
+
+#   define islessgreater(x, y) \
+     ({ register char __result;						      \
+	__asm__ ("fucomip %%st(1), %%st; setne %%al"			      \
+		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st");	      \
+	__result; })
+
+#   define isunordered(x, y) \
+     ({ register char __result;						      \
+	__asm__ ("fucomip %%st(1), %%st; setp %%al"			      \
+		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st");	      \
+	__result; })
+#  else
+/* This is the dumb, portable code for i386 and above.  */
+#   define isgreater(x, y) \
+     ({ register char __result;						      \
+	__asm__ ("fucompp; fnstsw; testb $0x45, %%ah; setz %%al"	      \
+		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
+	__result; })
+
+#   define isgreaterequal(x, y) \
+     ({ register char __result;						      \
+	__asm__ ("fucompp; fnstsw; testb $0x05, %%ah; setz %%al"	      \
+		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
+	__result; })
+
+#   define isless(x, y) \
+     ({ register char __result;						      \
+	__asm__ ("fucompp; fnstsw; testb $0x45, %%ah; setz %%al"	      \
+		 : "=a" (__result) : "u" (x), "t" (y) : "cc", "st", "st(1)"); \
+	__result; })
+
+#   define islessequal(x, y) \
+     ({ register char __result;						      \
+	__asm__ ("fucompp; fnstsw; testb $0x05, %%ah; setz %%al"	      \
+		 : "=a" (__result) : "u" (x), "t" (y) : "cc", "st", "st(1)"); \
+	__result; })
+
+#   define islessgreater(x, y) \
+     ({ register char __result;						      \
+	__asm__ ("fucompp; fnstsw; testb $0x44, %%ah; setz %%al"	      \
+		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
+	__result; })
+
+#   define isunordered(x, y) \
+     ({ register char __result;						      \
+	__asm__ ("fucompp; fnstsw; sahf; setp %%al"			      \
+		 : "=a" (__result) : "u" (y), "t" (x) : "cc", "st", "st(1)"); \
+	__result; })
+#  endif /* __i686__ */
+# endif	/* GCC 2.97 */
+
+/* The gcc, version 2.7 or below, has problems with all this inlining
+   code.  So disable it for this version of the compiler.  */
+# if __GNUC_PREREQ (2, 8)
+__BEGIN_NAMESPACE_C99
+
+/* Test for negative number.  Used in the signbit() macro.  */
+__MATH_INLINE int
+__NTH (__signbitf (float __x))
+{
+#  ifdef __SSE2_MATH__
+  int __m;
+  __asm ("pmovmskb %1, %0" : "=r" (__m) : "x" (__x));
+  return (__m & 0x8) != 0;
+#  else
+  __extension__ union { float __f; int __i; } __u = { __f: __x };
+  return __u.__i < 0;
+#  endif
+}
+__MATH_INLINE int
+__NTH (__signbit (double __x))
+{
+#  ifdef __SSE2_MATH__
+  int __m;
+  __asm ("pmovmskb %1, %0" : "=r" (__m) : "x" (__x));
+  return (__m & 0x80) != 0;
+#  else
+  __extension__ union { double __d; int __i[2]; } __u = { __d: __x };
+  return __u.__i[1] < 0;
+#  endif
+}
+__MATH_INLINE int
+__NTH (__signbitl (long double __x))
+{
+  __extension__ union { long double __l; int __i[3]; } __u = { __l: __x };
+  return (__u.__i[2] & 0x8000) != 0;
+}
+
+__END_NAMESPACE_C99
+# endif
+#endif
+
+
+/* The gcc, version 2.7 or below, has problems with all this inlining
+   code.  So disable it for this version of the compiler.  */
+#if __GNUC_PREREQ (2, 8)
+# if !__GNUC_PREREQ (3, 4) && !defined __NO_MATH_INLINES \
+     && defined __OPTIMIZE__
+/* GCC 3.4 introduced builtins for all functions below, so
+   there's no need to define any of these inline functions.  */
+
+#  ifdef __USE_ISOC99
+__BEGIN_NAMESPACE_C99
+
+/* Round to nearest integer.  */
+#   ifdef __SSE_MATH__
+__MATH_INLINE long int
+__NTH (lrintf (float __x))
+{
+  long int __res;
+  /* Mark as volatile since the result is dependent on the state of
+     the SSE control register (the rounding mode).  Otherwise GCC might
+     remove these assembler instructions since it does not know about
+     the rounding mode change and cannot currently be told.  */
+  __asm __volatile__ ("cvtss2si %1, %0" : "=r" (__res) : "xm" (__x));
+  return __res;
+}
+#   endif
+#   ifdef __SSE2_MATH__
+__MATH_INLINE long int
+__NTH (lrint (double __x))
+{
+  long int __res;
+  /* Mark as volatile since the result is dependent on the state of
+     the SSE control register (the rounding mode).  Otherwise GCC might
+     remove these assembler instructions since it does not know about
+     the rounding mode change and cannot currently be told.  */
+  __asm __volatile__ ("cvtsd2si %1, %0" : "=r" (__res) : "xm" (__x));
+  return __res;
+}
+#   endif
+#   ifdef __x86_64__
+__MATH_INLINE long long int
+__NTH (llrintf (float __x))
+{
+  long long int __res;
+  /* Mark as volatile since the result is dependent on the state of
+     the SSE control register (the rounding mode).  Otherwise GCC might
+     remove these assembler instructions since it does not know about
+     the rounding mode change and cannot currently be told.  */
+  __asm __volatile__ ("cvtss2si %1, %0" : "=r" (__res) : "xm" (__x));
+  return __res;
+}
+__MATH_INLINE long long int
+__NTH (llrint (double __x))
+{
+  long long int __res;
+  /* Mark as volatile since the result is dependent on the state of
+     the SSE control register (the rounding mode).  Otherwise GCC might
+     remove these assembler instructions since it does not know about
+     the rounding mode change and cannot currently be told.  */
+  __asm __volatile__ ("cvtsd2si %1, %0" : "=r" (__res) : "xm" (__x));
+  return __res;
+}
+#   endif
+
+#   if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__ > 0 \
+       && defined __SSE2_MATH__
+/* Determine maximum of two values.  */
+__MATH_INLINE float
+__NTH (fmaxf (float __x, float __y))
+{
+#    ifdef __AVX__
+  float __res;
+  __asm ("vmaxss %2, %1, %0" : "=x" (__res) : "x" (x), "xm" (__y));
+  return __res;
+#    else
+  __asm ("maxss %1, %0" : "+x" (__x) : "xm" (__y));
+  return __x;
+#    endif
+}
+__MATH_INLINE double
+__NTH (fmax (double __x, double __y))
+{
+#    ifdef __AVX__
+  float __res;
+  __asm ("vmaxsd %2, %1, %0" : "=x" (__res) : "x" (x), "xm" (__y));
+  return __res;
+#    else
+  __asm ("maxsd %1, %0" : "+x" (__x) : "xm" (__y));
+  return __x;
+#    endif
+}
+
+/* Determine minimum of two values.  */
+__MATH_INLINE float
+__NTH (fminf (float __x, float __y))
+{
+#    ifdef __AVX__
+  float __res;
+  __asm ("vminss %2, %1, %0" : "=x" (__res) : "x" (x), "xm" (__y));
+  return __res;
+#    else
+  __asm ("minss %1, %0" : "+x" (__x) : "xm" (__y));
+  return __x;
+#    endif
+}
+__MATH_INLINE double
+__NTH (fmin (double __x, double __y))
+{
+#    ifdef __AVX__
+  float __res;
+  __asm ("vminsd %2, %1, %0" : "=x" (__res) : "x" (x), "xm" (__y));
+  return __res;
+#    else
+  __asm ("minsd %1, %0" : "+x" (__x) : "xm" (__y));
+  return __x;
+#    endif
+}
+#   endif
+
+__END_NAMESPACE_C99
+#  endif
+
+#  if defined __SSE4_1__ && defined __SSE2_MATH__
+#   if defined __USE_MISC || defined __USE_XOPEN_EXTENDED || defined __USE_ISOC99
+__BEGIN_NAMESPACE_C99
+
+/* Round to nearest integer.  */
+__MATH_INLINE double
+__NTH (rint (double __x))
+{
+  double __res;
+  /* Mark as volatile since the result is dependent on the state of
+     the SSE control register (the rounding mode).  Otherwise GCC might
+     remove these assembler instructions since it does not know about
+     the rounding mode change and cannot currently be told.  */
+  __asm __volatile__ ("roundsd $4, %1, %0" : "=x" (__res) : "xm" (__x));
+  return __res;
+}
+__MATH_INLINE float
+__NTH (rintf (float __x))
+{
+  float __res;
+  /* Mark as volatile since the result is dependent on the state of
+     the SSE control register (the rounding mode).  Otherwise GCC might
+     remove these assembler instructions since it does not know about
+     the rounding mode change and cannot currently be told.  */
+  __asm __volatile__ ("roundss $4, %1, %0" : "=x" (__res) : "xm" (__x));
+  return __res;
+}
+
+#    ifdef __USE_ISOC99
+/* Round to nearest integer without raising inexact exception.  */
+__MATH_INLINE double
+__NTH (nearbyint (double __x))
+{
+  double __res;
+  /* Mark as volatile since the result is dependent on the state of
+     the SSE control register (the rounding mode).  Otherwise GCC might
+     remove these assembler instructions since it does not know about
+     the rounding mode change and cannot currently be told.  */
+  __asm __volatile__ ("roundsd $0xc, %1, %0" : "=x" (__res) : "xm" (__x));
+  return __res;
+}
+__MATH_INLINE float
+__NTH (nearbyintf (float __x))
+{
+  float __res;
+  /* Mark as volatile since the result is dependent on the state of
+     the SSE control register (the rounding mode).  Otherwise GCC might
+     remove these assembler instructions since it does not know about
+     the rounding mode change and cannot currently be told.  */
+  __asm __volatile__ ("roundss $0xc, %1, %0" : "=x" (__res) : "xm" (__x));
+  return __res;
+}
+#    endif
+
+__END_NAMESPACE_C99
+#   endif
+
+__BEGIN_NAMESPACE_STD
+/* Smallest integral value not less than X.  */
+__MATH_INLINE double
+__NTH (ceil (double __x))
+{
+  double __res;
+  __asm ("roundsd $2, %1, %0" : "=x" (__res) : "xm" (__x));
+  return __res;
+}
+__END_NAMESPACE_STD
+
+__BEGIN_NAMESPACE_C99
+__MATH_INLINE float
+__NTH (ceilf (float __x))
+{
+  float __res;
+  __asm ("roundss $2, %1, %0" : "=x" (__res) : "xm" (__x));
+  return __res;
+}
+__END_NAMESPACE_C99
+
+__BEGIN_NAMESPACE_STD
+/* Largest integer not greater than X.  */
+__MATH_INLINE double
+__NTH (floor (double __x))
+{
+  double __res;
+  __asm ("roundsd $1, %1, %0" : "=x" (__res) : "xm" (__x));
+  return __res;
+}
+__END_NAMESPACE_STD
+
+__BEGIN_NAMESPACE_C99
+__MATH_INLINE float
+__NTH (floorf (float __x))
+{
+  float __res;
+  __asm ("roundss $1, %1, %0" : "=x" (__res) : "xm" (__x));
+  return __res;
+}
+__END_NAMESPACE_C99
+#  endif
+# endif
+#endif
+
+#ifndef __x86_64__
+# if ((!defined __NO_MATH_INLINES || defined __LIBC_INTERNAL_MATH_INLINES) \
+     && defined __OPTIMIZE__)
+
+/* The inline functions do not set errno or raise necessarily the
+   correct exceptions.  */
+#  undef math_errhandling
+
+/* A macro to define float, double, and long double versions of various
+   math functions for the ix87 FPU.  FUNC is the function name (which will
+   be suffixed with f and l for the float and long double version,
+   respectively).  OP is the name of the FPU operation.
+   We define two sets of macros.  The set with the additional NP
+   doesn't add a prototype declaration.  */
+
+#  if defined __USE_MISC || defined __USE_ISOC99
+#   define __inline_mathop(func, op) \
+  __inline_mathop_ (double, func, op)					      \
+  __inline_mathop_ (float, __CONCAT(func,f), op)			      \
+  __inline_mathop_ (long double, __CONCAT(func,l), op)
+#   define __inline_mathopNP(func, op) \
+  __inline_mathopNP_ (double, func, op)					      \
+  __inline_mathopNP_ (float, __CONCAT(func,f), op)			      \
+  __inline_mathopNP_ (long double, __CONCAT(func,l), op)
+#  else
+#   define __inline_mathop(func, op) \
+  __inline_mathop_ (double, func, op)
+#   define __inline_mathopNP(func, op) \
+  __inline_mathopNP_ (double, func, op)
+#  endif
+
+#  define __inline_mathop_(float_type, func, op) \
+  __inline_mathop_decl_ (float_type, func, op, "0" (__x))
+#  define __inline_mathopNP_(float_type, func, op) \
+  __inline_mathop_declNP_ (float_type, func, op, "0" (__x))
+
+
+#  if defined __USE_MISC || defined __USE_ISOC99
+#   define __inline_mathop_decl(func, op, params...) \
+  __inline_mathop_decl_ (double, func, op, params)			      \
+  __inline_mathop_decl_ (float, __CONCAT(func,f), op, params)		      \
+  __inline_mathop_decl_ (long double, __CONCAT(func,l), op, params)
+#   define __inline_mathop_declNP(func, op, params...) \
+  __inline_mathop_declNP_ (double, func, op, params)			      \
+  __inline_mathop_declNP_ (float, __CONCAT(func,f), op, params)		      \
+  __inline_mathop_declNP_ (long double, __CONCAT(func,l), op, params)
+#  else
+#   define __inline_mathop_decl(func, op, params...) \
+  __inline_mathop_decl_ (double, func, op, params)
+#   define __inline_mathop_declNP(func, op, params...) \
+  __inline_mathop_declNP_ (double, func, op, params)
+#  endif
+
+#  define __inline_mathop_decl_(float_type, func, op, params...) \
+  __MATH_INLINE float_type func (float_type) __THROW;			      \
+  __inline_mathop_declNP_ (float_type, func, op, params)
+
+#  define __inline_mathop_declNP_(float_type, func, op, params...) \
+  __MATH_INLINE float_type __NTH (func (float_type __x))		      \
+  {									      \
+    register float_type __result;					      \
+    __asm __volatile__ (op : "=t" (__result) : params);			      \
+    return __result;							      \
+  }
+
+
+#  if defined __USE_MISC || defined __USE_ISOC99
+#   define __inline_mathcode(func, arg, code) \
+  __inline_mathcode_ (double, func, arg, code)				      \
+  __inline_mathcode_ (float, __CONCAT(func,f), arg, code)		      \
+  __inline_mathcode_ (long double, __CONCAT(func,l), arg, code)
+#   define __inline_mathcodeNP(func, arg, code) \
+  __inline_mathcodeNP_ (double, func, arg, code)			      \
+  __inline_mathcodeNP_ (float, __CONCAT(func,f), arg, code)		      \
+  __inline_mathcodeNP_ (long double, __CONCAT(func,l), arg, code)
+#   define __inline_mathcode2(func, arg1, arg2, code) \
+  __inline_mathcode2_ (double, func, arg1, arg2, code)			      \
+  __inline_mathcode2_ (float, __CONCAT(func,f), arg1, arg2, code)	      \
+  __inline_mathcode2_ (long double, __CONCAT(func,l), arg1, arg2, code)
+#   define __inline_mathcodeNP2(func, arg1, arg2, code) \
+  __inline_mathcodeNP2_ (double, func, arg1, arg2, code)		      \
+  __inline_mathcodeNP2_ (float, __CONCAT(func,f), arg1, arg2, code)	      \
+  __inline_mathcodeNP2_ (long double, __CONCAT(func,l), arg1, arg2, code)
+#   define __inline_mathcode3(func, arg1, arg2, arg3, code) \
+  __inline_mathcode3_ (double, func, arg1, arg2, arg3, code)		      \
+  __inline_mathcode3_ (float, __CONCAT(func,f), arg1, arg2, arg3, code)	      \
+  __inline_mathcode3_ (long double, __CONCAT(func,l), arg1, arg2, arg3, code)
+#   define __inline_mathcodeNP3(func, arg1, arg2, arg3, code) \
+  __inline_mathcodeNP3_ (double, func, arg1, arg2, arg3, code)		      \
+  __inline_mathcodeNP3_ (float, __CONCAT(func,f), arg1, arg2, arg3, code)     \
+  __inline_mathcodeNP3_ (long double, __CONCAT(func,l), arg1, arg2, arg3, code)
+#  else
+#   define __inline_mathcode(func, arg, code) \
+  __inline_mathcode_ (double, func, (arg), code)
+#   define __inline_mathcodeNP(func, arg, code) \
+  __inline_mathcodeNP_ (double, func, (arg), code)
+#   define __inline_mathcode2(func, arg1, arg2, code) \
+  __inline_mathcode2_ (double, func, arg1, arg2, code)
+#   define __inline_mathcodeNP2(func, arg1, arg2, code) \
+  __inline_mathcodeNP2_ (double, func, arg1, arg2, code)
+#   define __inline_mathcode3(func, arg1, arg2, arg3, code) \
+  __inline_mathcode3_ (double, func, arg1, arg2, arg3, code)
+#   define __inline_mathcodeNP3(func, arg1, arg2, arg3, code) \
+  __inline_mathcodeNP3_ (double, func, arg1, arg2, arg3, code)
+#  endif
+
+#  define __inline_mathcode_(float_type, func, arg, code) \
+  __MATH_INLINE float_type func (float_type) __THROW;			      \
+  __inline_mathcodeNP_(float_type, func, arg, code)
+
+#  define __inline_mathcodeNP_(float_type, func, arg, code) \
+  __MATH_INLINE float_type __NTH (func (float_type arg))		      \
+  {									      \
+    code;								      \
+  }
+
+
+#  define __inline_mathcode2_(float_type, func, arg1, arg2, code) \
+  __MATH_INLINE float_type func (float_type, float_type) __THROW;	      \
+  __inline_mathcodeNP2_ (float_type, func, arg1, arg2, code)
+
+#  define __inline_mathcodeNP2_(float_type, func, arg1, arg2, code) \
+  __MATH_INLINE float_type __NTH (func (float_type arg1, float_type arg2))    \
+  {									      \
+    code;								      \
+  }
+
+#  define __inline_mathcode3_(float_type, func, arg1, arg2, arg3, code) \
+  __MATH_INLINE float_type func (float_type, float_type, float_type) __THROW; \
+  __inline_mathcodeNP3_(float_type, func, arg1, arg2, arg3, code)
+
+#  define __inline_mathcodeNP3_(float_type, func, arg1, arg2, arg3, code) \
+  __MATH_INLINE float_type __NTH (func (float_type arg1, float_type arg2,     \
+					float_type arg3))		      \
+  {									      \
+    code;								      \
+  }
+# endif
+
+
+# if !defined __NO_MATH_INLINES && defined __OPTIMIZE__
+/* Miscellaneous functions  */
+
+/* __FAST_MATH__ is defined by gcc -ffast-math.  */
+#  ifdef __FAST_MATH__
+#   ifdef __USE_GNU
+#    define __sincos_code \
+  register long double __cosr;						      \
+  register long double __sinr;						      \
+  register unsigned int __swtmp;					      \
+  __asm __volatile__							      \
+    ("fsincos\n\t"							      \
+     "fnstsw	%w2\n\t"						      \
+     "testl	$0x400, %2\n\t"						      \
+     "jz	1f\n\t"							      \
+     "fldpi\n\t"							      \
+     "fadd	%%st(0)\n\t"						      \
+     "fxch	%%st(1)\n\t"						      \
+     "2: fprem1\n\t"							      \
+     "fnstsw	%w2\n\t"						      \
+     "testl	$0x400, %2\n\t"						      \
+     "jnz	2b\n\t"							      \
+     "fstp	%%st(1)\n\t"						      \
+     "fsincos\n\t"							      \
+     "1:"								      \
+     : "=t" (__cosr), "=u" (__sinr), "=a" (__swtmp) : "0" (__x));	      \
+  *__sinx = __sinr;							      \
+  *__cosx = __cosr
+
+__MATH_INLINE void
+__NTH (__sincos (double __x, double *__sinx, double *__cosx))
+{
+  __sincos_code;
+}
+
+__MATH_INLINE void
+__NTH (__sincosf (float __x, float *__sinx, float *__cosx))
+{
+  __sincos_code;
+}
+
+__MATH_INLINE void
+__NTH (__sincosl (long double __x, long double *__sinx, long double *__cosx))
+{
+  __sincos_code;
+}
+#   endif
+
+
+/* Optimized inline implementation, sometimes with reduced precision
+   and/or argument range.  */
+
+#   if __GNUC_PREREQ (3, 5)
+#    define __expm1_code \
+  register long double __temp;						      \
+  __temp = __builtin_expm1l (__x);					      \
+  return __temp ? __temp : __x
+#   else
+#    define __expm1_code \
+  register long double __value;						      \
+  register long double __exponent;					      \
+  register long double __temp;						      \
+  __asm __volatile__							      \
+    ("fldl2e			# e^x - 1 = 2^(x * log2(e)) - 1\n\t"	      \
+     "fmul	%%st(1)		# x * log2(e)\n\t"			      \
+     "fst	%%st(1)\n\t"						      \
+     "frndint			# int(x * log2(e))\n\t"			      \
+     "fxch\n\t"								      \
+     "fsub	%%st(1)		# fract(x * log2(e))\n\t"		      \
+     "f2xm1			# 2^(fract(x * log2(e))) - 1\n\t"	      \
+     "fscale			# 2^(x * log2(e)) - 2^(int(x * log2(e)))\n\t" \
+     : "=t" (__value), "=u" (__exponent) : "0" (__x));			      \
+  __asm __volatile__							      \
+    ("fscale			# 2^int(x * log2(e))\n\t"		      \
+     : "=t" (__temp) : "0" (1.0), "u" (__exponent));			      \
+  __temp -= 1.0;							      \
+  __temp += __value;							      \
+  return __temp ? __temp : __x
+#   endif
+__inline_mathcodeNP_ (long double, __expm1l, __x, __expm1_code)
+
+#   if __GNUC_PREREQ (3, 4)
+__inline_mathcodeNP_ (long double, __expl, __x, return __builtin_expl (__x))
+#   else
+#    define __exp_code \
+  register long double __value;						      \
+  register long double __exponent;					      \
+  __asm __volatile__							      \
+    ("fldl2e			# e^x = 2^(x * log2(e))\n\t"		      \
+     "fmul	%%st(1)		# x * log2(e)\n\t"			      \
+     "fst	%%st(1)\n\t"						      \
+     "frndint			# int(x * log2(e))\n\t"			      \
+     "fxch\n\t"								      \
+     "fsub	%%st(1)		# fract(x * log2(e))\n\t"		      \
+     "f2xm1			# 2^(fract(x * log2(e))) - 1\n\t"	      \
+     : "=t" (__value), "=u" (__exponent) : "0" (__x));			      \
+  __value += 1.0;							      \
+  __asm __volatile__							      \
+    ("fscale"								      \
+     : "=t" (__value) : "0" (__value), "u" (__exponent));		      \
+  return __value
+__inline_mathcodeNP (exp, __x, __exp_code)
+__inline_mathcodeNP_ (long double, __expl, __x, __exp_code)
+#   endif
+
+
+#   if !__GNUC_PREREQ (3, 5)
+__inline_mathcodeNP (tan, __x, \
+  register long double __value;						      \
+  register long double __value2 __attribute__ ((__unused__));		      \
+  __asm __volatile__							      \
+    ("fptan"								      \
+     : "=t" (__value2), "=u" (__value) : "0" (__x));			      \
+  return __value)
+#   endif
+#  endif /* __FAST_MATH__ */
+
+
+#  if __GNUC_PREREQ (3, 4)
+__inline_mathcodeNP2_ (long double, __atan2l, __y, __x,
+		       return __builtin_atan2l (__y, __x))
+#  else
+#   define __atan2_code \
+  register long double __value;						      \
+  __asm __volatile__							      \
+    ("fpatan"								      \
+     : "=t" (__value) : "0" (__x), "u" (__y) : "st(1)");		      \
+  return __value
+#   ifdef __FAST_MATH__
+__inline_mathcodeNP2 (atan2, __y, __x, __atan2_code)
+#   endif
+__inline_mathcodeNP2_ (long double, __atan2l, __y, __x, __atan2_code)
+#  endif
+
+
+#  if defined __FAST_MATH__ && !__GNUC_PREREQ (3, 5)
+__inline_mathcodeNP2 (fmod, __x, __y, \
+  register long double __value;						      \
+  __asm __volatile__							      \
+    ("1:	fprem\n\t"						      \
+     "fnstsw	%%ax\n\t"						      \
+     "sahf\n\t"								      \
+     "jp	1b"							      \
+     : "=t" (__value) : "0" (__x), "u" (__y) : "ax", "cc");		      \
+  return __value)
+#  endif
+
+
+#  ifdef __FAST_MATH__
+#   if !__GNUC_PREREQ (3,3)
+__inline_mathopNP (sqrt, "fsqrt")
+__inline_mathopNP_ (long double, __sqrtl, "fsqrt")
+#    define __libc_sqrtl(n) __sqrtl (n)
+#   else
+#    define __libc_sqrtl(n) __builtin_sqrtl (n)
+#   endif
+#  endif
+
+#  if __GNUC_PREREQ (2, 8)
+__inline_mathcodeNP_ (double, fabs, __x, return __builtin_fabs (__x))
+#   if defined __USE_MISC || defined __USE_ISOC99
+__inline_mathcodeNP_ (float, fabsf, __x, return __builtin_fabsf (__x))
+__inline_mathcodeNP_ (long double, fabsl, __x, return __builtin_fabsl (__x))
+#   endif
+__inline_mathcodeNP_ (long double, __fabsl, __x, return __builtin_fabsl (__x))
+#  else
+__inline_mathop (fabs, "fabs")
+__inline_mathop_ (long double, __fabsl, "fabs")
+# endif
+
+#  ifdef __FAST_MATH__
+#   if !__GNUC_PREREQ (3, 4)
+/* The argument range of this inline version is reduced.  */
+__inline_mathopNP (sin, "fsin")
+/* The argument range of this inline version is reduced.  */
+__inline_mathopNP (cos, "fcos")
+
+__inline_mathop_declNP (log, "fldln2; fxch; fyl2x", "0" (__x) : "st(1)")
+#   endif
+
+#   if !__GNUC_PREREQ (3, 5)
+__inline_mathop_declNP (log10, "fldlg2; fxch; fyl2x", "0" (__x) : "st(1)")
+
+__inline_mathcodeNP (asin, __x, return __atan2l (__x, __libc_sqrtl (1.0 - __x * __x)))
+__inline_mathcodeNP (acos, __x, return __atan2l (__libc_sqrtl (1.0 - __x * __x), __x))
+#   endif
+
+#   if !__GNUC_PREREQ (3, 4)
+__inline_mathop_declNP (atan, "fld1; fpatan", "0" (__x) : "st(1)")
+#   endif
+#  endif /* __FAST_MATH__ */
+
+__inline_mathcode_ (long double, __sgn1l, __x, \
+  __extension__ union { long double __xld; unsigned int __xi[3]; } __n =      \
+    { __xld: __x };							      \
+  __n.__xi[2] = (__n.__xi[2] & 0x8000) | 0x3fff;			      \
+  __n.__xi[1] = 0x80000000;						      \
+  __n.__xi[0] = 0;							      \
+  return __n.__xld)
+
+
+#  ifdef __FAST_MATH__
+/* The argument range of the inline version of sinhl is slightly reduced.  */
+__inline_mathcodeNP (sinh, __x, \
+  register long double __exm1 = __expm1l (__fabsl (__x));		      \
+  return 0.5 * (__exm1 / (__exm1 + 1.0) + __exm1) * __sgn1l (__x))
+
+__inline_mathcodeNP (cosh, __x, \
+  register long double __ex = __expl (__x);				      \
+  return 0.5 * (__ex + 1.0 / __ex))
+
+__inline_mathcodeNP (tanh, __x, \
+  register long double __exm1 = __expm1l (-__fabsl (__x + __x));	      \
+  return __exm1 / (__exm1 + 2.0) * __sgn1l (-__x))
+#  endif
+
+__inline_mathcodeNP (floor, __x, \
+  register long double __value;						      \
+  register int __ignore;						      \
+  unsigned short int __cw;						      \
+  unsigned short int __cwtmp;						      \
+  __asm __volatile ("fnstcw %3\n\t"					      \
+		    "movzwl %3, %1\n\t"					      \
+		    "andl $0xf3ff, %1\n\t"				      \
+		    "orl $0x0400, %1\n\t"	/* rounding down */	      \
+		    "movw %w1, %2\n\t"					      \
+		    "fldcw %2\n\t"					      \
+		    "frndint\n\t"					      \
+		    "fldcw %3"						      \
+		    : "=t" (__value), "=&q" (__ignore), "=m" (__cwtmp),	      \
+		      "=m" (__cw)					      \
+		    : "0" (__x));					      \
+  return __value)
+
+__inline_mathcodeNP (ceil, __x, \
+  register long double __value;						      \
+  register int __ignore;						      \
+  unsigned short int __cw;						      \
+  unsigned short int __cwtmp;						      \
+  __asm __volatile ("fnstcw %3\n\t"					      \
+		    "movzwl %3, %1\n\t"					      \
+		    "andl $0xf3ff, %1\n\t"				      \
+		    "orl $0x0800, %1\n\t"	/* rounding up */	      \
+		    "movw %w1, %2\n\t"					      \
+		    "fldcw %2\n\t"					      \
+		    "frndint\n\t"					      \
+		    "fldcw %3"						      \
+		    : "=t" (__value), "=&q" (__ignore), "=m" (__cwtmp),	      \
+		      "=m" (__cw)					      \
+		    : "0" (__x));					      \
+  return __value)
+
+#  ifdef __FAST_MATH__
+#   define __ldexp_code \
+  register long double __value;						      \
+  __asm __volatile__							      \
+    ("fscale"								      \
+     : "=t" (__value) : "0" (__x), "u" ((long double) __y));		      \
+  return __value
+
+__MATH_INLINE double
+__NTH (ldexp (double __x, int __y))
+{
+  __ldexp_code;
+}
+#  endif
+
+
+/* Optimized versions for some non-standardized functions.  */
+#  if defined __USE_ISOC99 || defined __USE_MISC
+
+#   ifdef __FAST_MATH__
+__inline_mathcodeNP (expm1, __x, __expm1_code)
+
+/* We cannot rely on M_SQRT being defined.  So we do it for ourself
+   here.  */
+#    define __M_SQRT2	1.41421356237309504880L	/* sqrt(2) */
+
+#    if !__GNUC_PREREQ (3, 5)
+__inline_mathcodeNP (log1p, __x, \
+  register long double __value;						      \
+  if (__fabsl (__x) >= 1.0 - 0.5 * __M_SQRT2)				      \
+    __value = logl (1.0 + __x);						      \
+  else									      \
+    __asm __volatile__							      \
+      ("fldln2\n\t"							      \
+       "fxch\n\t"							      \
+       "fyl2xp1"							      \
+       : "=t" (__value) : "0" (__x) : "st(1)");				      \
+  return __value)
+#    endif
+
+
+/* The argument range of the inline version of asinhl is slightly reduced.  */
+__inline_mathcodeNP (asinh, __x, \
+  register long double  __y = __fabsl (__x);				      \
+  return (log1pl (__y * __y / (__libc_sqrtl (__y * __y + 1.0) + 1.0) + __y)   \
+	  * __sgn1l (__x)))
+
+__inline_mathcodeNP (acosh, __x, \
+  return logl (__x + __libc_sqrtl (__x - 1.0) * __libc_sqrtl (__x + 1.0)))
+
+__inline_mathcodeNP (atanh, __x, \
+  register long double __y = __fabsl (__x);				      \
+  return -0.5 * log1pl (-(__y + __y) / (1.0 + __y)) * __sgn1l (__x))
+
+/* The argument range of the inline version of hypotl is slightly reduced.  */
+__inline_mathcodeNP2 (hypot, __x, __y,
+		      return __libc_sqrtl (__x * __x + __y * __y))
+
+#    if !__GNUC_PREREQ (3, 5)
+__inline_mathcodeNP(logb, __x, \
+  register long double __value;						      \
+  register long double __junk;						      \
+  __asm __volatile__							      \
+    ("fxtract\n\t"							      \
+     : "=t" (__junk), "=u" (__value) : "0" (__x));			      \
+  return __value)
+#    endif
+
+#   endif
+#  endif
+
+#  ifdef __USE_ISOC99
+#   ifdef __FAST_MATH__
+
+#    if !__GNUC_PREREQ (3, 5)
+__inline_mathop_declNP (log2, "fld1; fxch; fyl2x", "0" (__x) : "st(1)")
+#    endif
+
+__MATH_INLINE float
+__NTH (ldexpf (float __x, int __y))
+{
+  __ldexp_code;
+}
+
+__MATH_INLINE long double
+__NTH (ldexpl (long double __x, int __y))
+{
+  __ldexp_code;
+}
+
+__inline_mathopNP (rint, "frndint")
+#   endif /* __FAST_MATH__ */
+
+#   define __lrint_code \
+  long int __lrintres;							      \
+  __asm__ __volatile__							      \
+    ("fistpl %0"							      \
+     : "=m" (__lrintres) : "t" (__x) : "st");				      \
+  return __lrintres
+__MATH_INLINE long int
+__NTH (lrintf (float __x))
+{
+  __lrint_code;
+}
+__MATH_INLINE long int
+__NTH (lrint (double __x))
+{
+  __lrint_code;
+}
+__MATH_INLINE long int
+__NTH (lrintl (long double __x))
+{
+  __lrint_code;
+}
+#   undef __lrint_code
+
+#   define __llrint_code \
+  long long int __llrintres;						      \
+  __asm__ __volatile__							      \
+    ("fistpll %0"							      \
+     : "=m" (__llrintres) : "t" (__x) : "st");				      \
+  return __llrintres
+__MATH_INLINE long long int
+__NTH (llrintf (float __x))
+{
+  __llrint_code;
+}
+__MATH_INLINE long long int
+__NTH (llrint (double __x))
+{
+  __llrint_code;
+}
+__MATH_INLINE long long int
+__NTH (llrintl (long double __x))
+{
+  __llrint_code;
+}
+#   undef __llrint_code
+
+# endif
+
+
+#  ifdef __USE_MISC
+
+#   if defined __FAST_MATH__ && !__GNUC_PREREQ (3, 5)
+__inline_mathcodeNP2 (drem, __x, __y, \
+  register double __value;						      \
+  register int __clobbered;						      \
+  __asm __volatile__							      \
+    ("1:	fprem1\n\t"						      \
+     "fstsw	%%ax\n\t"						      \
+     "sahf\n\t"								      \
+     "jp	1b"							      \
+     : "=t" (__value), "=&a" (__clobbered) : "0" (__x), "u" (__y) : "cc");    \
+  return __value)
+#  endif
+
+
+/* This function is used in the `isfinite' macro.  */
+__MATH_INLINE int
+__NTH (__finite (double __x))
+{
+  return (__extension__
+	  (((((union { double __d; int __i[2]; }) {__d: __x}).__i[1]
+	     | 0x800fffffu) + 1) >> 31));
+}
+
+#  endif /* __USE_MISC  */
+
+/* Undefine some of the large macros which are not used anymore.  */
+#  undef __atan2_code
+#  ifdef __FAST_MATH__
+#   undef __expm1_code
+#   undef __exp_code
+#   undef __sincos_code
+#  endif /* __FAST_MATH__ */
+
+# endif /* __NO_MATH_INLINES  */
+
+
+/* This code is used internally in the GNU libc.  */
+# ifdef __LIBC_INTERNAL_MATH_INLINES
+__inline_mathop (__ieee754_sqrt, "fsqrt")
+__inline_mathcode2 (__ieee754_atan2, __y, __x,
+		    register long double __value;
+		    __asm __volatile__ ("fpatan\n\t"
+					: "=t" (__value)
+					: "0" (__x), "u" (__y) : "st(1)");
+		    return __value;)
+# endif
+
+#endif /* !__x86_64__ */