[thirdparty/gcc.git] / libstdc++-v3 / include / std / ratio

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

// Copyright (C) 2008, 2009, 2010 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 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
{
  /**
   * @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 const intmax_t __gcd =
        __static_gcd<_R1::den, _R2::den>::value;
      
    public:
      typedef ratio<
        __safe_add<
          __safe_multiply<_R1::num, (_R2::den / __gcd)>::value,
          __safe_multiply<_R2::num, (_R1::den / __gcd)>::value>::value,
        __safe_multiply<_R1::den, (_R2::den / __gcd)>::value> type;

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

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

  template<typename _R1, typename _R2>
    const 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 const intmax_t num = type::num;
      static const intmax_t den = type::den;
    };

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

  template<typename _R1, typename _R2>
    const 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 const intmax_t num = type::num;
      static const intmax_t den = type::den;
    };

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

  template<typename _R1, typename _R2>
    const 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 const intmax_t num = type::num;
      static const intmax_t den = type::den;
    };

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

  template<typename _R1, typename _R2>
    const 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>
    { };

  template<typename _R1>
    struct __ratio_less_impl_1
    : integral_constant<bool, _R1::num < _R1::den>
    { }; 

  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<typename ratio_divide<_R1, _R2>::type>::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<typename ratio_divide<_R2, _R1>::type>::type
    { };

  /// ratio_less
  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
}

#endif //_GLIBCXX_USE_C99_STDINT_TR1

#endif //__GXX_EXPERIMENTAL_CXX0X__

#endif //_GLIBCXX_RATIO
Commit	Line	Data
5b9daa7e	1	// ratio -- C++ --
4acedca1	2
ab65a4c7	3	// Copyright (C) 2008, 2009, 2010 Free Software Foundation, Inc.
4acedca1 CF	4	//
	5	// This file is part of the GNU ISO C++ Library. This library is free
	6	// software; you can redistribute it and/or modify it under the
	7	// terms of the GNU General Public License as published by the
748086b7	8	// Free Software Foundation; either version 3, or (at your option)
4acedca1 CF	9	// any later version.
	10
	11	// This library is distributed in the hope that it will be useful,
	12	// but WITHOUT ANY WARRANTY; without even the implied warranty of
	13	// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
	14	// GNU General Public License for more details.
	15
748086b7 JJ	16	// Under Section 7 of GPL version 3, you are granted additional
	17	// permissions described in the GCC Runtime Library Exception, version
	18	// 3.1, as published by the Free Software Foundation.
4acedca1	19
748086b7 JJ	20	// You should have received a copy of the GNU General Public License and
	21	// a copy of the GCC Runtime Library Exception along with this program;
	22	// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
	23	// <http://www.gnu.org/licenses/>.
4acedca1 CF	24
	25	/** @file ratio
	26	* This is a Standard C++ Library header.
	27	*/
	28
	29	#ifndef _GLIBCXX_RATIO
	30	#define _GLIBCXX_RATIO 1
	31
	32	#pragma GCC system_header
	33
	34	#ifndef __GXX_EXPERIMENTAL_CXX0X__
ab65a4c7	35	# include <bits/c++0x_warning.h>
4acedca1 CF	36	#else
	37
	38	#include <type_traits>
	39	#include <cstdint>
	40
	41	#ifdef _GLIBCXX_USE_C99_STDINT_TR1
	42
	43	namespace std
	44	{
5b9daa7e BK	45	/**
	46	* @defgroup ratio Rational Arithmetic
	47	* @ingroup utilities
	48	*
79e2c7b0	49	* Compile time representation of finite rational numbers.
5b9daa7e BK	50	* @{
	51	*/
	52
4acedca1 CF	53	template<intmax_t _Pn>
	54	struct __static_sign
	55	: integral_constant<intmax_t, (_Pn < 0) ? -1 : 1>
	56	{ };
	57
	58	template<intmax_t _Pn>
	59	struct __static_abs
	60	: integral_constant<intmax_t, _Pn * __static_sign<_Pn>::value>
	61	{ };
	62
	63	template<intmax_t _Pn, intmax_t _Qn>
	64	struct __static_gcd;
	65
	66	template<intmax_t _Pn, intmax_t _Qn>
	67	struct __static_gcd
	68	: __static_gcd<_Qn, (_Pn % _Qn)>
	69	{ };
	70
	71	template<intmax_t _Pn>
	72	struct __static_gcd<_Pn, 0>
	73	: integral_constant<intmax_t, __static_abs<_Pn>::value>
	74	{ };
	75
	76	template<intmax_t _Qn>
	77	struct __static_gcd<0, _Qn>
	78	: integral_constant<intmax_t, __static_abs<_Qn>::value>
	79	{ };
	80
	81	// Let c = 2^(half # of bits in an intmax_t)
	82	// then we find a1, a0, b1, b0 s.t. N = a1c + a0, M = b1c + b0
	83	// The multiplication of N and M becomes,
	84	// N * M = (a1 * b1)c^2 + (a0 * b1 + b0 * a1)c + a0 * b0
	85	// Multiplication is safe if each term and the sum of the terms
	86	// is representable by intmax_t.
	87	template<intmax_t _Pn, intmax_t _Qn>
	88	struct __safe_multiply
	89	{
	90	private:
	91	static const uintmax_t __c = uintmax_t(1) << (sizeof(intmax_t) * 4);
	92
	93	static const uintmax_t __a0 = __static_abs<_Pn>::value % __c;
	94	static const uintmax_t __a1 = __static_abs<_Pn>::value / __c;
	95	static const uintmax_t __b0 = __static_abs<_Qn>::value % __c;
	96	static const uintmax_t __b1 = __static_abs<_Qn>::value / __c;
	97
	98	static_assert(__a1 == 0 \|\| __b1 == 0,
	99	"overflow in multiplication");
	100	static_assert(__a0 * __b1 + __b0 * __a1 < (__c >> 1),
	101	"overflow in multiplication");
ea31932d	102	static_assert(__b0 * __a0 <= __INTMAX_MAX__,
4acedca1 CF	103	"overflow in multiplication");
4acedca1 CF	104	static_assert((__a0 * __b1 + __b0 * __a1) * __c <=
ea31932d	105	__INTMAX_MAX__ - __b0 * __a0, "overflow in multiplication");
4acedca1 CF	106
	107	public:
	108	static const intmax_t value = _Pn * _Qn;
	109	};
	110
	111	// Helpers for __safe_add
	112	template<intmax_t _Pn, intmax_t _Qn, bool>
	113	struct __add_overflow_check_impl
ea31932d	114	: integral_constant<bool, (_Pn <= __INTMAX_MAX__ - _Qn)>
4acedca1 CF	115	{ };
	116
	117	template<intmax_t _Pn, intmax_t _Qn>
	118	struct __add_overflow_check_impl<_Pn, _Qn, false>
ea31932d	119	: integral_constant<bool, (_Pn >= -__INTMAX_MAX__ - _Qn)>
4acedca1 CF	120	{ };
	121
	122	template<intmax_t _Pn, intmax_t _Qn>
	123	struct __add_overflow_check
	124	: __add_overflow_check_impl<_Pn, _Qn, (_Qn >= 0)>
	125	{ };
	126
	127	template<intmax_t _Pn, intmax_t _Qn>
	128	struct __safe_add
	129	{
	130	static_assert(__add_overflow_check<_Pn, _Qn>::value != 0,
	131	"overflow in addition");
	132
	133	static const intmax_t value = _Pn + _Qn;
	134	};
	135
ea31932d PC	136	/**
ea31932d PC	137	* @brief Provides compile-time rational arithmetic.
5b9daa7e	138	*
ea31932d PC	139	* This class template represents any finite rational number with a
	140	* numerator and denominator representable by compile-time constants of
	141	* type intmax_t. The ratio is simplified when instantiated.
	142	*
	143	* For example:
	144	* @code
	145	* std::ratio<7,-21>::num == -1;
	146	* std::ratio<7,-21>::den == 3;
	147	* @endcode
	148	*
	149	*/
4acedca1 CF	150	template<intmax_t _Num, intmax_t _Den = 1>
	151	struct ratio
	152	{
	153	static_assert(_Den != 0, "denominator cannot be zero");
ea31932d PC	154	static_assert(_Num >= -__INTMAX_MAX__ && _Den >= -__INTMAX_MAX__,
	155	"out of range");
	156
4acedca1	157	// Note: sign(N) * abs(N) == N
94a86be0	158	static constexpr intmax_t num =
4acedca1 CF	159	_Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value;
4acedca1 CF	160
94a86be0	161	static constexpr intmax_t den =
4acedca1	162	__static_abs<_Den>::value / __static_gcd<_Num, _Den>::value;
e1d4e035 PC	163
e1d4e035 PC	164	typedef ratio<num, den> type;
4acedca1 CF	165	};
	166
	167	template<intmax_t _Num, intmax_t _Den>
94a86be0	168	constexpr intmax_t ratio<_Num, _Den>::num;
4acedca1 CF	169
4acedca1 CF	170	template<intmax_t _Num, intmax_t _Den>
94a86be0	171	constexpr intmax_t ratio<_Num, _Den>::den;
4acedca1	172
ad68e9fc	173	/// ratio_add
4acedca1 CF	174	template<typename _R1, typename _R2>
	175	struct ratio_add
	176	{
	177	private:
	178	static const intmax_t __gcd =
	179	__static_gcd<_R1::den, _R2::den>::value;
	180
	181	public:
	182	typedef ratio<
	183	__safe_add<
	184	__safe_multiply<_R1::num, (_R2::den / __gcd)>::value,
	185	__safe_multiply<_R2::num, (_R1::den / __gcd)>::value>::value,
	186	__safe_multiply<_R1::den, (_R2::den / __gcd)>::value> type;
e1d4e035 PC	187
	188	static const intmax_t num = type::num;
	189	static const intmax_t den = type::den;
4acedca1 CF	190	};
4acedca1 CF	191
e1d4e035 PC	192	template<typename _R1, typename _R2>
	193	const intmax_t ratio_add<_R1, _R2>::num;
	194
	195	template<typename _R1, typename _R2>
	196	const intmax_t ratio_add<_R1, _R2>::den;
	197
ad68e9fc	198	/// ratio_subtract
4acedca1 CF	199	template<typename _R1, typename _R2>
	200	struct ratio_subtract
	201	{
	202	typedef typename ratio_add<
	203	_R1,
	204	ratio<-_R2::num, _R2::den>>::type type;
e1d4e035 PC	205
	206	static const intmax_t num = type::num;
	207	static const intmax_t den = type::den;
4acedca1 CF	208	};
4acedca1 CF	209
e1d4e035 PC	210	template<typename _R1, typename _R2>
	211	const intmax_t ratio_subtract<_R1, _R2>::num;
	212
	213	template<typename _R1, typename _R2>
	214	const intmax_t ratio_subtract<_R1, _R2>::den;
	215
ad68e9fc	216	/// ratio_multiply
4acedca1 CF	217	template<typename _R1, typename _R2>
	218	struct ratio_multiply
	219	{
	220	private:
	221	static const intmax_t __gcd1 =
	222	__static_gcd<_R1::num, _R2::den>::value;
	223	static const intmax_t __gcd2 =
	224	__static_gcd<_R2::num, _R1::den>::value;
	225
	226	public:
	227	typedef ratio<
	228	__safe_multiply<(_R1::num / __gcd1),
	229	(_R2::num / __gcd2)>::value,
	230	__safe_multiply<(_R1::den / __gcd2),
	231	(_R2::den / __gcd1)>::value> type;
e1d4e035 PC	232
	233	static const intmax_t num = type::num;
	234	static const intmax_t den = type::den;
4acedca1 CF	235	};
4acedca1 CF	236
e1d4e035 PC	237	template<typename _R1, typename _R2>
	238	const intmax_t ratio_multiply<_R1, _R2>::num;
	239
	240	template<typename _R1, typename _R2>
	241	const intmax_t ratio_multiply<_R1, _R2>::den;
	242
ad68e9fc	243	/// ratio_divide
4acedca1 CF	244	template<typename _R1, typename _R2>
	245	struct ratio_divide
	246	{
	247	static_assert(_R2::num != 0, "division by 0");
	248
	249	typedef typename ratio_multiply<
	250	_R1,
	251	ratio<_R2::den, _R2::num>>::type type;
e1d4e035 PC	252
	253	static const intmax_t num = type::num;
	254	static const intmax_t den = type::den;
4acedca1 CF	255	};
4acedca1 CF	256
e1d4e035 PC	257	template<typename _R1, typename _R2>
	258	const intmax_t ratio_divide<_R1, _R2>::num;
	259
	260	template<typename _R1, typename _R2>
	261	const intmax_t ratio_divide<_R1, _R2>::den;
	262
ad68e9fc	263	/// ratio_equal
4acedca1 CF	264	template<typename _R1, typename _R2>
	265	struct ratio_equal
	266	: integral_constant<bool, _R1::num == _R2::num && _R1::den == _R2::den>
	267	{ };
	268
ad68e9fc	269	/// ratio_not_equal
4acedca1 CF	270	template<typename _R1, typename _R2>
	271	struct ratio_not_equal
	272	: integral_constant<bool, !ratio_equal<_R1, _R2>::value>
	273	{ };
cd6b4a4b PC	274
	275	template<typename _R1>
	276	struct __ratio_less_impl_1
	277	: integral_constant<bool, _R1::num < _R1::den>
	278	{ };
	279
	280	template<typename _R1, typename _R2,
	281	bool = (_R1::num == 0 \|\| _R2::num == 0
	282	\|\| (__static_sign<_R1::num>::value
	283	!= __static_sign<_R2::num>::value)),
	284	bool = (__static_sign<_R1::num>::value == -1
	285	&& __static_sign<_R2::num>::value == -1)>
	286	struct __ratio_less_impl
	287	: __ratio_less_impl_1<typename ratio_divide<_R1, _R2>::type>::type
	288	{ };
	289
4acedca1	290	template<typename _R1, typename _R2>
cd6b4a4b PC	291	struct __ratio_less_impl<_R1, _R2, true, false>
cd6b4a4b PC	292	: integral_constant<bool, _R1::num < _R2::num>
ea31932d PC	293	{ };
ea31932d PC	294
ea31932d	295	template<typename _R1, typename _R2>
cd6b4a4b PC	296	struct __ratio_less_impl<_R1, _R2, false, true>
cd6b4a4b PC	297	: __ratio_less_impl_1<typename ratio_divide<_R2, _R1>::type>::type
ea31932d PC	298	{ };
ea31932d PC	299
ad68e9fc	300	/// ratio_less
ea31932d PC	301	template<typename _R1, typename _R2>
	302	struct ratio_less
	303	: __ratio_less_impl<_R1, _R2>::type
4acedca1 CF	304	{ };
4acedca1 CF	305
ad68e9fc	306	/// ratio_less_equal
4acedca1 CF	307	template<typename _R1, typename _R2>
	308	struct ratio_less_equal
	309	: integral_constant<bool, !ratio_less<_R2, _R1>::value>
	310	{ };
	311
ad68e9fc	312	/// ratio_greater
4acedca1 CF	313	template<typename _R1, typename _R2>
	314	struct ratio_greater
	315	: integral_constant<bool, ratio_less<_R2, _R1>::value>
	316	{ };
	317
ad68e9fc	318	/// ratio_greater_equal
4acedca1 CF	319	template<typename _R1, typename _R2>
	320	struct ratio_greater_equal
	321	: integral_constant<bool, !ratio_less<_R1, _R2>::value>
	322	{ };
	323
	324	typedef ratio<1, 1000000000000000000> atto;
	325	typedef ratio<1, 1000000000000000> femto;
	326	typedef ratio<1, 1000000000000> pico;
	327	typedef ratio<1, 1000000000> nano;
	328	typedef ratio<1, 1000000> micro;
	329	typedef ratio<1, 1000> milli;
	330	typedef ratio<1, 100> centi;
	331	typedef ratio<1, 10> deci;
	332	typedef ratio< 10, 1> deca;
	333	typedef ratio< 100, 1> hecto;
	334	typedef ratio< 1000, 1> kilo;
	335	typedef ratio< 1000000, 1> mega;
	336	typedef ratio< 1000000000, 1> giga;
	337	typedef ratio< 1000000000000, 1> tera;
	338	typedef ratio< 1000000000000000, 1> peta;
	339	typedef ratio< 1000000000000000000, 1> exa;
5b9daa7e BK	340
5b9daa7e BK	341	// @} group ratio
4acedca1 CF	342	}
	343
	344	#endif //_GLIBCXX_USE_C99_STDINT_TR1
	345
	346	#endif //__GXX_EXPERIMENTAL_CXX0X__
	347
	348	#endif //_GLIBCXX_RATIO