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//usr/local/ssl/include/c++/4.4.4/cmath

// -*- C++ -*- C forwarding header.

// Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005,
// 2006, 2007, 2008, 2009
// Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library.  This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.

// This 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 General Public License for more details.

// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.

// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively.  If not, see
// <http://www.gnu.org/licenses/>.

/** @file include/cmath
 *  This is a Standard C++ Library file.  You should @c #include this file
 *  in your programs, rather than any of the "*.h" implementation files.
 *
 *  This is the C++ version of the Standard C Library header @c math.h,
 *  and its contents are (mostly) the same as that header, but are all
 *  contained in the namespace @c std (except for names which are defined
 *  as macros in C).
 */

//
// ISO C++ 14882: 26.5  C library
//

#pragma GCC system_header

#include <bits/c++config.h>
#include <bits/cpp_type_traits.h>
#include <ext/type_traits.h>
#include <math.h>

#ifndef _GLIBCXX_CMATH
#define _GLIBCXX_CMATH 1

// Get rid of those macros defined in <math.h> in lieu of real functions.
#undef abs
#undef div
#undef acos
#undef asin
#undef atan
#undef atan2
#undef ceil
#undef cos
#undef cosh
#undef exp
#undef fabs
#undef floor
#undef fmod
#undef frexp
#undef ldexp
#undef log
#undef log10
#undef modf
#undef pow
#undef sin
#undef sinh
#undef sqrt
#undef tan
#undef tanh

_GLIBCXX_BEGIN_NAMESPACE(std)

// Forward declaration of a helper function.  This really should be
  // an `exported' forward declaration.
  template<typename _Tp>
    _Tp __cmath_power(_Tp, unsigned int);

template<typename _Tp>
    inline _Tp
    __pow_helper(_Tp __x, int __n)
    {
      return __n < 0
        ? _Tp(1)/__cmath_power(__x, -__n)
        : __cmath_power(__x, __n);
    }

inline double
  abs(double __x)
  { return __builtin_fabs(__x); }

inline float
  abs(float __x)
  { return __builtin_fabsf(__x); }

inline long double
  abs(long double __x)
  { return __builtin_fabsl(__x); }

using ::acos;

inline float
  acos(float __x)
  { return __builtin_acosf(__x); }

inline long double
  acos(long double __x)
  { return __builtin_acosl(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    acos(_Tp __x)
    { return __builtin_acos(__x); }

using ::asin;

inline float
  asin(float __x)
  { return __builtin_asinf(__x); }

inline long double
  asin(long double __x)
  { return __builtin_asinl(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
					   double>::__type
    asin(_Tp __x)
    { return __builtin_asin(__x); }

using ::atan;

inline float
  atan(float __x)
  { return __builtin_atanf(__x); }

inline long double
  atan(long double __x)
  { return __builtin_atanl(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    atan(_Tp __x)
    { return __builtin_atan(__x); }

using ::atan2;

inline float
  atan2(float __y, float __x)
  { return __builtin_atan2f(__y, __x); }

inline long double
  atan2(long double __y, long double __x)
  { return __builtin_atan2l(__y, __x); }

template<typename _Tp, typename _Up>
    inline
    typename __gnu_cxx::__promote_2<
    typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value
				    && __is_arithmetic<_Up>::__value,
				    _Tp>::__type, _Up>::__type
    atan2(_Tp __y, _Up __x)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return atan2(__type(__y), __type(__x));
    }

using ::ceil;

inline float
  ceil(float __x)
  { return __builtin_ceilf(__x); }

inline long double
  ceil(long double __x)
  { return __builtin_ceill(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    ceil(_Tp __x)
    { return __builtin_ceil(__x); }

using ::cos;

inline float
  cos(float __x)
  { return __builtin_cosf(__x); }

inline long double
  cos(long double __x)
  { return __builtin_cosl(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    cos(_Tp __x)
    { return __builtin_cos(__x); }

using ::cosh;

inline float
  cosh(float __x)
  { return __builtin_coshf(__x); }

inline long double
  cosh(long double __x)
  { return __builtin_coshl(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    cosh(_Tp __x)
    { return __builtin_cosh(__x); }

using ::exp;

inline float
  exp(float __x)
  { return __builtin_expf(__x); }

inline long double
  exp(long double __x)
  { return __builtin_expl(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    exp(_Tp __x)
    { return __builtin_exp(__x); }

using ::fabs;

inline float
  fabs(float __x)
  { return __builtin_fabsf(__x); }

inline long double
  fabs(long double __x)
  { return __builtin_fabsl(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    fabs(_Tp __x)
    { return __builtin_fabs(__x); }

using ::floor;

inline float
  floor(float __x)
  { return __builtin_floorf(__x); }

inline long double
  floor(long double __x)
  { return __builtin_floorl(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    floor(_Tp __x)
    { return __builtin_floor(__x); }

using ::fmod;

inline float
  fmod(float __x, float __y)
  { return __builtin_fmodf(__x, __y); }

inline long double
  fmod(long double __x, long double __y)
  { return __builtin_fmodl(__x, __y); }

using ::frexp;

inline float
  frexp(float __x, int* __exp)
  { return __builtin_frexpf(__x, __exp); }

inline long double
  frexp(long double __x, int* __exp)
  { return __builtin_frexpl(__x, __exp); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    frexp(_Tp __x, int* __exp)
    { return __builtin_frexp(__x, __exp); }

using ::ldexp;

inline float
  ldexp(float __x, int __exp)
  { return __builtin_ldexpf(__x, __exp); }

inline long double
  ldexp(long double __x, int __exp)
  { return __builtin_ldexpl(__x, __exp); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
  ldexp(_Tp __x, int __exp)
  { return __builtin_ldexp(__x, __exp); }

using ::log;

inline float
  log(float __x)
  { return __builtin_logf(__x); }

inline long double
  log(long double __x)
  { return __builtin_logl(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    log(_Tp __x)
    { return __builtin_log(__x); }

using ::log10;

inline float
  log10(float __x)
  { return __builtin_log10f(__x); }

inline long double
  log10(long double __x)
  { return __builtin_log10l(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    log10(_Tp __x)
    { return __builtin_log10(__x); }

using ::modf;

inline float
  modf(float __x, float* __iptr)
  { return __builtin_modff(__x, __iptr); }

inline long double
  modf(long double __x, long double* __iptr)
  { return __builtin_modfl(__x, __iptr); }

using ::pow;

inline float
  pow(float __x, float __y)
  { return __builtin_powf(__x, __y); }

inline long double
  pow(long double __x, long double __y)
  { return __builtin_powl(__x, __y); }

#ifndef __GXX_EXPERIMENTAL_CXX0X__
  // _GLIBCXX_RESOLVE_LIB_DEFECTS
  // DR 550. What should the return type of pow(float,int) be?
  inline double
  pow(double __x, int __i)
  { return __builtin_powi(__x, __i); }

inline float
  pow(float __x, int __n)
  { return __builtin_powif(__x, __n); }

inline long double
  pow(long double __x, int __n)
  { return __builtin_powil(__x, __n); }
#endif

template<typename _Tp, typename _Up>
    inline
    typename __gnu_cxx::__promote_2<
    typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value
				    && __is_arithmetic<_Up>::__value,
				    _Tp>::__type, _Up>::__type
    pow(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return pow(__type(__x), __type(__y));
    }

using ::sin;

inline float
  sin(float __x)
  { return __builtin_sinf(__x); }

inline long double
  sin(long double __x)
  { return __builtin_sinl(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    sin(_Tp __x)
    { return __builtin_sin(__x); }

using ::sinh;

inline float
  sinh(float __x)
  { return __builtin_sinhf(__x); }

inline long double
  sinh(long double __x)
  { return __builtin_sinhl(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    sinh(_Tp __x)
    { return __builtin_sinh(__x); }

using ::sqrt;

inline float
  sqrt(float __x)
  { return __builtin_sqrtf(__x); }

inline long double
  sqrt(long double __x)
  { return __builtin_sqrtl(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    sqrt(_Tp __x)
    { return __builtin_sqrt(__x); }

using ::tan;

inline float
  tan(float __x)
  { return __builtin_tanf(__x); }

inline long double
  tan(long double __x)
  { return __builtin_tanl(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    tan(_Tp __x)
    { return __builtin_tan(__x); }

using ::tanh;

inline float
  tanh(float __x)
  { return __builtin_tanhf(__x); }

inline long double
  tanh(long double __x)
  { return __builtin_tanhl(__x); }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value, 
					   double>::__type
    tanh(_Tp __x)
    { return __builtin_tanh(__x); }

_GLIBCXX_END_NAMESPACE

#if _GLIBCXX_USE_C99_MATH
#if !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC

// These are possible macros imported from C99-land.
#undef fpclassify
#undef isfinite
#undef isinf
#undef isnan
#undef isnormal
#undef signbit
#undef isgreater
#undef isgreaterequal
#undef isless
#undef islessequal
#undef islessgreater
#undef isunordered

_GLIBCXX_BEGIN_NAMESPACE(std)

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    fpclassify(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
				  FP_SUBNORMAL, FP_ZERO, __type(__f));
    }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isfinite(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isfinite(__type(__f));
    }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isinf(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isinf(__type(__f));
    }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isnan(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isnan(__type(__f));
    }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isnormal(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isnormal(__type(__f));
    }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    signbit(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_signbit(__type(__f));
    }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isgreater(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isgreater(__type(__f1), __type(__f2));
    }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isgreaterequal(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isgreaterequal(__type(__f1), __type(__f2));
    }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isless(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isless(__type(__f1), __type(__f2));
    }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    islessequal(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_islessequal(__type(__f1), __type(__f2));
    }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    islessgreater(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_islessgreater(__type(__f1), __type(__f2));
    }

template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
					   int>::__type
    isunordered(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isunordered(__type(__f1), __type(__f2));
    }

_GLIBCXX_END_NAMESPACE

#endif /* _GLIBCXX_USE_C99_FP_MACROS_DYNAMIC */
#endif

#ifndef _GLIBCXX_EXPORT_TEMPLATE
# include <bits/cmath.tcc>
#endif

#ifdef __GXX_EXPERIMENTAL_CXX0X__
#  if defined(_GLIBCXX_INCLUDE_AS_TR1)
#    error C++0x header cannot be included from TR1 header
#  endif
#  if defined(_GLIBCXX_INCLUDE_AS_CXX0X)
#    include <tr1_impl/cmath>
#  else
#    define _GLIBCXX_INCLUDE_AS_CXX0X
#    define _GLIBCXX_BEGIN_NAMESPACE_TR1
#    define _GLIBCXX_END_NAMESPACE_TR1
#    define _GLIBCXX_TR1
#    include <tr1_impl/cmath>
#    undef _GLIBCXX_TR1
#    undef _GLIBCXX_END_NAMESPACE_TR1
#    undef _GLIBCXX_BEGIN_NAMESPACE_TR1
#    undef _GLIBCXX_INCLUDE_AS_CXX0X
#  endif
#endif

#endif