-// <ratio> -*- C++ -*-
+// ratio -*- C++ -*-
-// Copyright (C) 2008 Free Software Foundation, Inc.
+// 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 2, or (at your option)
+// 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,
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
-// You should have received a copy of the GNU General Public License
-// along with this library; see the file COPYING. If not, write to
-// the Free Software Foundation, 51 Franklin Street, Fifth Floor,
-// Boston, MA 02110-1301, USA.
-
-// As a special exception, you may use this file as part of a free software
-// library without restriction. Specifically, if other files instantiate
-// templates or use macros or inline functions from this file, or you compile
-// this file and link it with other files to produce an executable, this
-// file does not by itself cause the resulting executable to be covered by
-// the GNU General Public License. This exception does not however
-// invalidate any other reasons why the executable file might be covered by
-// the GNU General Public License.
-
-/** @file ratio
+// 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.
*/
#pragma GCC system_header
#ifndef __GXX_EXPERIMENTAL_CXX0X__
-# include <c++0x_warning.h>
+# include <bits/c++0x_warning.h>
#else
#include <type_traits>
#ifdef _GLIBCXX_USE_C99_STDINT_TR1
-namespace std
+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>
/**
* @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.
"out of range");
// Note: sign(N) * abs(N) == N
- static const intmax_t num =
+ static constexpr intmax_t num =
_Num * __static_sign<_Den>::value / __static_gcd<_Num, _Den>::value;
- static const intmax_t den =
+ 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>
- const intmax_t ratio<_Num, _Den>::num;
+ constexpr intmax_t ratio<_Num, _Den>::num;
template<intmax_t _Num, intmax_t _Den>
- const intmax_t ratio<_Num, _Den>::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 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<
- __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;
+ 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
(_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
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
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_simple_impl
- : integral_constant<bool,
- (__safe_multiply<_R1::num, _R2::den>::value
- < __safe_multiply<_R2::num, _R1::den>::value)>
+ 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) >
{ };
- // If the denominators are equal or the signs differ, we can just compare
- // numerators, otherwise fallback to the simple cross-multiply method.
template<typename _R1, typename _R2>
- struct __ratio_less_impl
- : conditional<(_R1::den == _R2::den
+ 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)),
- integral_constant<bool, (_R1::num < _R2::num)>,
- __ratio_less_simple_impl<_R1, _R2>>::type
+ 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
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
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