arm-marvell-linux-uclibcgnueabi/include/c++/4.6.3/ratio - toolchains/prism - Git at Google

 // ratio -*- C++ -*-

 // Copyright (C) 2008, 2009, 2010, 2011 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/ratio
  *  This is a Standard C++ Library header.
  */

 #ifndef _GLIBCXX_RATIO
 #define _GLIBCXX_RATIO 1

 #pragma GCC system_header

 #ifndef __GXX_EXPERIMENTAL_CXX0X__
 # include <bits/c++0x_warning.h>
 #else

 #include <type_traits>
 #include <cstdint>

 #ifdef _GLIBCXX_USE_C99_STDINT_TR1

 namespace std _GLIBCXX_VISIBILITY(default)
 {
 _GLIBCXX_BEGIN_NAMESPACE_VERSION

   /**
    * @defgroup ratio Rational Arithmetic
    * @ingroup utilities
    *
    * Compile time representation of finite rational numbers.
    * @{
    */

   template<intmax_t _Pn>
     struct __static_sign
     : integral_constant<intmax_t, (_Pn < 0) ? -1 : 1>
     { };

   template<intmax_t _Pn>
     struct __static_abs
     : integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value>
     { };

   template<intmax_t _Pn, intmax_t _Qn>
     struct __static_gcd;

   template<intmax_t _Pn, intmax_t _Qn>
     struct __static_gcd
     : __static_gcd<_Qn, (_Pn % _Qn)>
     { };

   template<intmax_t _Pn>
     struct __static_gcd<_Pn, 0>
     : integral_constant<intmax_t, __static_abs<_Pn>::value>
     { };

   template<intmax_t _Qn>
     struct __static_gcd<0, _Qn>
     : integral_constant<intmax_t, __static_abs<_Qn>::value>
     { };

   // Let c = 2^(half # of bits in an intmax_t)
   // then we find a1, a0, b1, b0 s.t. N = a1*c + a0, M = b1*c + b0
   // The multiplication of N and M becomes,
   // N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0
   // Multiplication is safe if each term and the sum of the terms
   // is representable by intmax_t.
   template<intmax_t _Pn, intmax_t _Qn>
     struct __safe_multiply
     {
     private:
       static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4);

       static const uintmax_t __a0 = __static_abs<_Pn>::value % __c;
       static const uintmax_t __a1 = __static_abs<_Pn>::value / __c;
       static const uintmax_t __b0 = __static_abs<_Qn>::value % __c;
       static const uintmax_t __b1 = __static_abs<_Qn>::value / __c;

       static_assert(__a1 == 0 || __b1 == 0,
         "overflow in multiplication");
       static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1),
         "overflow in multiplication");
       static_assert(__b0 * __a0 <= __INTMAX_MAX__,
         "overflow in multiplication");
       static_assert((__a0 * __b1 + __b0 * __a1) * __c <=
         __INTMAX_MAX__ -  __b0 * __a0, "overflow in multiplication");

     public:
       static const intmax_t value = _Pn * _Qn;
     };

   // Helpers for __safe_add
   template<intmax_t _Pn, intmax_t _Qn, bool>
     struct __add_overflow_check_impl
     : integral_constant<bool, (_Pn <= __INTMAX_MAX__ - _Qn)>
     { };

   template<intmax_t _Pn, intmax_t _Qn>
     struct __add_overflow_check_impl<_Pn, _Qn, false>
     : integral_constant<bool, (_Pn >= -__INTMAX_MAX__ - _Qn)>
     { };

   template<intmax_t _Pn, intmax_t _Qn>
     struct __add_overflow_check
     : __add_overflow_check_impl<_Pn, _Qn, (_Qn >= 0)>
     { };

   template<intmax_t _Pn, intmax_t _Qn>
     struct __safe_add
     {
       static_assert(__add_overflow_check<_Pn, _Qn>::value != 0,
         "overflow in addition");

       static const intmax_t value = _Pn + _Qn;
     };

   /**
    *  @brief Provides compile-time rational arithmetic.
    *
    *  This class template represents any finite rational number with a
    *  numerator and denominator representable by compile-time constants of
    *  type intmax_t. The ratio is simplified when instantiated.
    *
    *  For example:
    *  @code
    *    std::ratio<7,-21>::num == -1;
    *    std::ratio<7,-21>::den == 3;
    *  @endcode
    *
   */
   template<intmax_t _Num, intmax_t _Den = 1>
     struct ratio
     {
       static_assert(_Den != 0, "denominator cannot be zero");
       static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__,
 		    "out of range");

       // Note: sign(N) * abs(N) == N
       static constexpr intmax_t num =
         _Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value;

       static constexpr intmax_t den =
         __static_abs<_Den>::value / __static_gcd<_Num, _Den>::value;

       typedef ratio<num, den> type;
     };

   template<intmax_t _Num, intmax_t _Den>
     constexpr intmax_t ratio<_Num, _Den>::num;

   template<intmax_t _Num, intmax_t _Den>
     constexpr intmax_t ratio<_Num, _Den>::den;

   /// ratio_add
   template<typename _R1, typename _R2>
     struct ratio_add
     {
     private:
       static constexpr intmax_t __gcd =
         __static_gcd<_R1::den, _R2::den>::value;
       static constexpr intmax_t __n = __safe_add<
         __safe_multiply<_R1::num, (_R2::den / __gcd)>::value,
         __safe_multiply<_R2::num, (_R1::den / __gcd)>::value>::value;

       // The new numerator may have common factors with the denominator,
       // but they have to also be factors of __gcd.
       static constexpr intmax_t __gcd2 = __static_gcd<__n, __gcd>::value;

     public:
       typedef ratio<__n / __gcd2,
         __safe_multiply<_R1::den / __gcd2, _R2::den / __gcd>::value> type;

       static constexpr intmax_t num = type::num;
       static constexpr intmax_t den = type::den;
     };

   template<typename _R1, typename _R2>
     constexpr intmax_t ratio_add<_R1, _R2>::num;

   template<typename _R1, typename _R2>
     constexpr intmax_t ratio_add<_R1, _R2>::den;

   /// ratio_subtract
   template<typename _R1, typename _R2>
     struct ratio_subtract
     {
       typedef typename ratio_add<
         _R1,
         ratio<-_R2::num, _R2::den>>::type type;

       static constexpr intmax_t num = type::num;
       static constexpr intmax_t den = type::den;
     };

   template<typename _R1, typename _R2>
     constexpr intmax_t ratio_subtract<_R1, _R2>::num;

   template<typename _R1, typename _R2>
     constexpr intmax_t ratio_subtract<_R1, _R2>::den;

   /// ratio_multiply
   template<typename _R1, typename _R2>
     struct ratio_multiply
     {
     private:
       static const intmax_t __gcd1 =
         __static_gcd<_R1::num, _R2::den>::value;
       static const intmax_t __gcd2 =
         __static_gcd<_R2::num, _R1::den>::value;

     public:
       typedef ratio<
         __safe_multiply<(_R1::num / __gcd1),
                         (_R2::num / __gcd2)>::value,
         __safe_multiply<(_R1::den / __gcd2),
                         (_R2::den / __gcd1)>::value> type;

       static constexpr intmax_t num = type::num;
       static constexpr intmax_t den = type::den;
     };

   template<typename _R1, typename _R2>
     constexpr intmax_t ratio_multiply<_R1, _R2>::num;

   template<typename _R1, typename _R2>
     constexpr intmax_t ratio_multiply<_R1, _R2>::den;

   /// ratio_divide
   template<typename _R1, typename _R2>
     struct ratio_divide
     {
       static_assert(_R2::num != 0, "division by 0");

       typedef typename ratio_multiply<
         _R1,
         ratio<_R2::den, _R2::num>>::type type;

       static constexpr intmax_t num = type::num;
       static constexpr intmax_t den = type::den;
     };

   template<typename _R1, typename _R2>
     constexpr intmax_t ratio_divide<_R1, _R2>::num;

   template<typename _R1, typename _R2>
     constexpr intmax_t ratio_divide<_R1, _R2>::den;

   /// ratio_equal
   template<typename _R1, typename _R2>
     struct ratio_equal
     : integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den>
     { };

   /// ratio_not_equal
   template<typename _R1, typename _R2>
     struct ratio_not_equal
     : integral_constant<bool, !ratio_equal<_R1, _R2>::value>
     { };

   // 0 <= _Ri < 1
   // If one is 0, conclude
   // Otherwise, x < y iff 1/y < 1/x
   template<typename _R1, typename _R2>
     struct __ratio_less_impl_2;

   // _Ri > 0
   // Compare the integral parts, and remove them if they are equal
   template<typename _R1, typename _R2, intmax_t __q1 = _R1::num / _R1::den,
            intmax_t __q2 = _R2::num / _R2::den, bool __eq = (__q1 == __q2)>
     struct __ratio_less_impl_1
     : __ratio_less_impl_2<ratio<_R1::num % _R1::den, _R1::den>,
            ratio<_R2::num % _R2::den, _R2::den> >::type
     { };

   template<typename _R1, typename _R2, intmax_t __q1, intmax_t __q2>
     struct __ratio_less_impl_1<_R1, _R2, __q1, __q2, false>
     : integral_constant<bool, (__q1 < __q2) >
     { };

   template<typename _R1, typename _R2>
     struct __ratio_less_impl_2
     : __ratio_less_impl_1<ratio<_R2::den, _R2::num>,
            ratio<_R1::den, _R1::num> >::type
     { };

   template<intmax_t __d1, typename _R2>
     struct __ratio_less_impl_2<ratio<0, __d1>, _R2>
     : integral_constant<bool, true>
     { };

   template<typename _R1, intmax_t __d2>
     struct __ratio_less_impl_2<_R1, ratio<0, __d2> >
     : integral_constant<bool, false>
     { };

   template<intmax_t __d1, intmax_t __d2>
     struct __ratio_less_impl_2<ratio<0, __d1>, ratio<0, __d2> >
     : integral_constant<bool, false>
     { };

   template<typename _R1, typename _R2,
 	   bool = (_R1::num == 0 || _R2::num == 0
 		   || (__static_sign<_R1::num>::value
 		       != __static_sign<_R2::num>::value)),
 	   bool = (__static_sign<_R1::num>::value == -1
 		   && __static_sign<_R2::num>::value == -1)>
     struct __ratio_less_impl
     : __ratio_less_impl_1<_R1, _R2>::type
     { };

   template<typename _R1, typename _R2>
     struct __ratio_less_impl<_R1, _R2, true, false>
     : integral_constant<bool, _R1::num < _R2::num>
     { };

   template<typename _R1, typename _R2>
     struct __ratio_less_impl<_R1, _R2, false, true>
     : __ratio_less_impl_1<ratio<-_R2::num, _R2::den>,
            ratio<-_R1::num, _R1::den> >::type
     { };

   /// ratio_less
   // using a continued fraction expansion
   template<typename _R1, typename _R2>
     struct ratio_less
     : __ratio_less_impl<_R1, _R2>::type
     { };

   /// ratio_less_equal
   template<typename _R1, typename _R2>
     struct ratio_less_equal
     : integral_constant<bool, !ratio_less<_R2, _R1>::value>
     { };

   /// ratio_greater
   template<typename _R1, typename _R2>
     struct ratio_greater
     : integral_constant<bool, ratio_less<_R2, _R1>::value>
     { };

   /// ratio_greater_equal
   template<typename _R1, typename _R2>
     struct ratio_greater_equal
     : integral_constant<bool, !ratio_less<_R1, _R2>::value>
     { };

   typedef ratio<1,       1000000000000000000> atto;
   typedef ratio<1,          1000000000000000> femto;
   typedef ratio<1,             1000000000000> pico;
   typedef ratio<1,                1000000000> nano;
   typedef ratio<1,                   1000000> micro;
   typedef ratio<1,                      1000> milli;
   typedef ratio<1,                       100> centi;
   typedef ratio<1,                        10> deci;
   typedef ratio<                       10, 1> deca;
   typedef ratio<                      100, 1> hecto;
   typedef ratio<                     1000, 1> kilo;
   typedef ratio<                  1000000, 1> mega;
   typedef ratio<               1000000000, 1> giga;
   typedef ratio<            1000000000000, 1> tera;
   typedef ratio<         1000000000000000, 1> peta;
   typedef ratio<      1000000000000000000, 1> exa;

   // @} group ratio
 _GLIBCXX_END_NAMESPACE_VERSION
 } // namespace

 #endif //_GLIBCXX_USE_C99_STDINT_TR1

 #endif //__GXX_EXPERIMENTAL_CXX0X__

 #endif //_GLIBCXX_RATIO
	// ratio -- C++ --

	// Copyright (C) 2008, 2009, 2010, 2011 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/ratio
	* This is a Standard C++ Library header.
	*/

	#ifndef _GLIBCXX_RATIO
	#define _GLIBCXX_RATIO 1

	#pragma GCC system_header

	#ifndef __GXX_EXPERIMENTAL_CXX0X__
	# include <bits/c++0x_warning.h>
	#else

	#include <type_traits>
	#include <cstdint>

	#ifdef _GLIBCXX_USE_C99_STDINT_TR1

	namespace std _GLIBCXX_VISIBILITY(default)
	{
	_GLIBCXX_BEGIN_NAMESPACE_VERSION

	/**
	* @defgroup ratio Rational Arithmetic
	* @ingroup utilities
	*
	* Compile time representation of finite rational numbers.
	* @{
	*/

	template<intmax_t _Pn>
	struct __static_sign
	: integral_constant<intmax_t, (_Pn < 0) ? -1 : 1>
	{ };

	template<intmax_t _Pn>
	struct __static_abs
	: integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value>
	{ };

	template<intmax_t _Pn, intmax_t _Qn>
	struct __static_gcd;

	template<intmax_t _Pn, intmax_t _Qn>
	struct __static_gcd
	: __static_gcd<_Qn, (_Pn % _Qn)>
	{ };

	template<intmax_t _Pn>
	struct __static_gcd<_Pn, 0>
	: integral_constant<intmax_t, __static_abs<_Pn>::value>
	{ };

	template<intmax_t _Qn>
	struct __static_gcd<0, _Qn>
	: integral_constant<intmax_t, __static_abs<_Qn>::value>
	{ };

	// Let c = 2^(half # of bits in an intmax_t)
	// then we find a1, a0, b1, b0 s.t. N = a1c + a0, M = b1c + b0
	// The multiplication of N and M becomes,
	// N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0
	// Multiplication is safe if each term and the sum of the terms
	// is representable by intmax_t.
	template<intmax_t _Pn, intmax_t _Qn>
	struct __safe_multiply
	{
	private:
	static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4);

	static const uintmax_t __a0 = __static_abs<_Pn>::value % __c;
	static const uintmax_t __a1 = __static_abs<_Pn>::value / __c;
	static const uintmax_t __b0 = __static_abs<_Qn>::value % __c;
	static const uintmax_t __b1 = __static_abs<_Qn>::value / __c;

	static_assert(__a1 == 0 \|\| __b1 == 0,
	"overflow in multiplication");
	static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1),
	"overflow in multiplication");
	static_assert(__b0 * __a0 <= __INTMAX_MAX__,
	"overflow in multiplication");
	static_assert((__a0 * __b1 + __b0 * __a1) * __c <=
	__INTMAX_MAX__ - __b0 * __a0, "overflow in multiplication");

	public:
	static const intmax_t value = _Pn * _Qn;
	};

	// Helpers for __safe_add
	template<intmax_t _Pn, intmax_t _Qn, bool>
	struct __add_overflow_check_impl
	: integral_constant<bool, (_Pn <= __INTMAX_MAX__ - _Qn)>
	{ };

	template<intmax_t _Pn, intmax_t _Qn>
	struct __add_overflow_check_impl<_Pn, _Qn, false>
	: integral_constant<bool, (_Pn >= -__INTMAX_MAX__ - _Qn)>
	{ };

	template<intmax_t _Pn, intmax_t _Qn>
	struct __add_overflow_check
	: __add_overflow_check_impl<_Pn, _Qn, (_Qn >= 0)>
	{ };

	template<intmax_t _Pn, intmax_t _Qn>
	struct __safe_add
	{
	static_assert(__add_overflow_check<_Pn, _Qn>::value != 0,
	"overflow in addition");

	static const intmax_t value = _Pn + _Qn;
	};

	/**
	* @brief Provides compile-time rational arithmetic.
	*
	* This class template represents any finite rational number with a
	* numerator and denominator representable by compile-time constants of
	* type intmax_t. The ratio is simplified when instantiated.
	*
	* For example:
	* @code
	* std::ratio<7,-21>::num == -1;
	* std::ratio<7,-21>::den == 3;
	* @endcode
	*
	*/
	template<intmax_t _Num, intmax_t _Den = 1>
	struct ratio
	{
	static_assert(_Den != 0, "denominator cannot be zero");
	static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__,
	"out of range");

	// Note: sign(N) * abs(N) == N
	static constexpr intmax_t num =
	_Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value;

	static constexpr intmax_t den =
	__static_abs<_Den>::value / __static_gcd<_Num, _Den>::value;

	typedef ratio<num, den> type;
	};

	template<intmax_t _Num, intmax_t _Den>
	constexpr intmax_t ratio<_Num, _Den>::num;

	template<intmax_t _Num, intmax_t _Den>
	constexpr intmax_t ratio<_Num, _Den>::den;

	/// ratio_add
	template<typename _R1, typename _R2>
	struct ratio_add
	{
	private:
	static constexpr intmax_t __gcd =
	__static_gcd<_R1::den, _R2::den>::value;
	static constexpr intmax_t __n = __safe_add<
	__safe_multiply<_R1::num, (_R2::den / __gcd)>::value,
	__safe_multiply<_R2::num, (_R1::den / __gcd)>::value>::value;

	// The new numerator may have common factors with the denominator,
	// but they have to also be factors of __gcd.
	static constexpr intmax_t __gcd2 = __static_gcd<__n, __gcd>::value;

	public:
	typedef ratio<__n / __gcd2,
	__safe_multiply<_R1::den / __gcd2, _R2::den / __gcd>::value> type;

	static constexpr intmax_t num = type::num;
	static constexpr intmax_t den = type::den;
	};

	template<typename _R1, typename _R2>
	constexpr intmax_t ratio_add<_R1, _R2>::num;

	template<typename _R1, typename _R2>
	constexpr intmax_t ratio_add<_R1, _R2>::den;

	/// ratio_subtract
	template<typename _R1, typename _R2>
	struct ratio_subtract
	{
	typedef typename ratio_add<
	_R1,
	ratio<-_R2::num, _R2::den>>::type type;

	static constexpr intmax_t num = type::num;
	static constexpr intmax_t den = type::den;
	};

	template<typename _R1, typename _R2>
	constexpr intmax_t ratio_subtract<_R1, _R2>::num;

	template<typename _R1, typename _R2>
	constexpr intmax_t ratio_subtract<_R1, _R2>::den;

	/// ratio_multiply
	template<typename _R1, typename _R2>
	struct ratio_multiply
	{
	private:
	static const intmax_t __gcd1 =
	__static_gcd<_R1::num, _R2::den>::value;
	static const intmax_t __gcd2 =
	__static_gcd<_R2::num, _R1::den>::value;

	public:
	typedef ratio<
	__safe_multiply<(_R1::num / __gcd1),
	(_R2::num / __gcd2)>::value,
	__safe_multiply<(_R1::den / __gcd2),
	(_R2::den / __gcd1)>::value> type;

	static constexpr intmax_t num = type::num;
	static constexpr intmax_t den = type::den;
	};

	template<typename _R1, typename _R2>
	constexpr intmax_t ratio_multiply<_R1, _R2>::num;

	template<typename _R1, typename _R2>
	constexpr intmax_t ratio_multiply<_R1, _R2>::den;

	/// ratio_divide
	template<typename _R1, typename _R2>
	struct ratio_divide
	{
	static_assert(_R2::num != 0, "division by 0");

	typedef typename ratio_multiply<
	_R1,
	ratio<_R2::den, _R2::num>>::type type;

	static constexpr intmax_t num = type::num;
	static constexpr intmax_t den = type::den;
	};

	template<typename _R1, typename _R2>
	constexpr intmax_t ratio_divide<_R1, _R2>::num;

	template<typename _R1, typename _R2>
	constexpr intmax_t ratio_divide<_R1, _R2>::den;

	/// ratio_equal
	template<typename _R1, typename _R2>
	struct ratio_equal
	: integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den>
	{ };

	/// ratio_not_equal
	template<typename _R1, typename _R2>
	struct ratio_not_equal
	: integral_constant<bool, !ratio_equal<_R1, _R2>::value>
	{ };

	// 0 <= _Ri < 1
	// If one is 0, conclude
	// Otherwise, x < y iff 1/y < 1/x
	template<typename _R1, typename _R2>
	struct __ratio_less_impl_2;

	// _Ri > 0
	// Compare the integral parts, and remove them if they are equal
	template<typename _R1, typename _R2, intmax_t __q1 = _R1::num / _R1::den,
	intmax_t __q2 = _R2::num / _R2::den, bool __eq = (__q1 == __q2)>
	struct __ratio_less_impl_1
	: __ratio_less_impl_2<ratio<_R1::num % _R1::den, _R1::den>,
	ratio<_R2::num % _R2::den, _R2::den> >::type
	{ };

	template<typename _R1, typename _R2, intmax_t __q1, intmax_t __q2>
	struct __ratio_less_impl_1<_R1, _R2, __q1, __q2, false>
	: integral_constant<bool, (__q1 < __q2) >
	{ };

	template<typename _R1, typename _R2>
	struct __ratio_less_impl_2
	: __ratio_less_impl_1<ratio<_R2::den, _R2::num>,
	ratio<_R1::den, _R1::num> >::type
	{ };

	template<intmax_t __d1, typename _R2>
	struct __ratio_less_impl_2<ratio<0, __d1>, _R2>
	: integral_constant<bool, true>
	{ };

	template<typename _R1, intmax_t __d2>
	struct __ratio_less_impl_2<_R1, ratio<0, __d2> >
	: integral_constant<bool, false>
	{ };

	template<intmax_t __d1, intmax_t __d2>
	struct __ratio_less_impl_2<ratio<0, __d1>, ratio<0, __d2> >
	: integral_constant<bool, false>
	{ };

	template<typename _R1, typename _R2,
	bool = (_R1::num == 0 \|\| _R2::num == 0
	\|\| (__static_sign<_R1::num>::value
	!= __static_sign<_R2::num>::value)),
	bool = (__static_sign<_R1::num>::value == -1
	&& __static_sign<_R2::num>::value == -1)>
	struct __ratio_less_impl
	: __ratio_less_impl_1<_R1, _R2>::type
	{ };

	template<typename _R1, typename _R2>
	struct __ratio_less_impl<_R1, _R2, true, false>
	: integral_constant<bool, _R1::num < _R2::num>
	{ };

	template<typename _R1, typename _R2>
	struct __ratio_less_impl<_R1, _R2, false, true>
	: __ratio_less_impl_1<ratio<-_R2::num, _R2::den>,
	ratio<-_R1::num, _R1::den> >::type
	{ };

	/// ratio_less
	// using a continued fraction expansion
	template<typename _R1, typename _R2>
	struct ratio_less
	: __ratio_less_impl<_R1, _R2>::type
	{ };

	/// ratio_less_equal
	template<typename _R1, typename _R2>
	struct ratio_less_equal
	: integral_constant<bool, !ratio_less<_R2, _R1>::value>
	{ };

	/// ratio_greater
	template<typename _R1, typename _R2>
	struct ratio_greater
	: integral_constant<bool, ratio_less<_R2, _R1>::value>
	{ };

	/// ratio_greater_equal
	template<typename _R1, typename _R2>
	struct ratio_greater_equal
	: integral_constant<bool, !ratio_less<_R1, _R2>::value>
	{ };

	typedef ratio<1, 1000000000000000000> atto;
	typedef ratio<1, 1000000000000000> femto;
	typedef ratio<1, 1000000000000> pico;
	typedef ratio<1, 1000000000> nano;
	typedef ratio<1, 1000000> micro;
	typedef ratio<1, 1000> milli;
	typedef ratio<1, 100> centi;
	typedef ratio<1, 10> deci;
	typedef ratio< 10, 1> deca;
	typedef ratio< 100, 1> hecto;
	typedef ratio< 1000, 1> kilo;
	typedef ratio< 1000000, 1> mega;
	typedef ratio< 1000000000, 1> giga;
	typedef ratio< 1000000000000, 1> tera;
	typedef ratio< 1000000000000000, 1> peta;
	typedef ratio< 1000000000000000000, 1> exa;

	// @} group ratio
	_GLIBCXX_END_NAMESPACE_VERSION
	} // namespace

	#endif //_GLIBCXX_USE_C99_STDINT_TR1

	#endif //__GXX_EXPERIMENTAL_CXX0X__

	#endif //_GLIBCXX_RATIO