glibc/sysdeps/x86/fpu/bits/mathinline.h

/* Inline math functions for i387 and SSE.
   Copyright (C) 1995-2014 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__
__extension__
__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;
}
__extension__
__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_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 __SSE2_MATH__
# 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.  */

#  ifdef __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))


#  ifdef __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;							      \
  }


#  ifdef __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))
#   ifdef __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.  */
#  ifdef __USE_ISOC99

#   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
__extension__
__MATH_INLINE long long int
__NTH (llrintf (float __x))
{
  __llrint_code;
}
__extension__
__MATH_INLINE long long int
__NTH (llrint (double __x))
{
  __llrint_code;
}
__extension__
__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 /* !__SSE2_MATH__ */