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Rational
(src/algebra/rational.hpp)
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- Last update: 2022-04-06 15:29:33+09:00
- Include:
#include "src/algebra/rational.hpp"
Depends on
Operation Traits
(src/algebra/system/operation.hpp)
Code
#pragma once
/**
* @file rational.hpp
* @brief Rational
*/
#include <cassert>
#include "lib/cxx17"
#include "system/operation.hpp"
namespace workspace {
/**
* @brief Rational.
* @tparam _Tp Ring structure
*/
template <class _Tp> class rational {
_Tp __num, __den;
public:
_CXX14_CONSTEXPR rational(const _Tp &__x, const _Tp &__y) noexcept
: __num(__x), __den(__y) {}
_CXX14_CONSTEXPR rational(const _Tp &__x, _Tp &&__y) noexcept
: __num(__x), __den(std::move(__y)) {}
_CXX14_CONSTEXPR rational(_Tp &&__x, const _Tp &__y) noexcept
: __num(std::move(__x)), __den(__y) {}
_CXX14_CONSTEXPR rational(_Tp &&__x = 0, _Tp &&__y = 1) noexcept
: __num(std::move(__x)), __den(std::move(__y)) {}
_CXX14_CONSTEXPR rational(std::initializer_list<_Tp> __x) noexcept
: __num(__x.size() > 0 ? *__x.begin() : _Tp(0)),
__den(__x.size() > 1 ? *std::next(__x.begin()) : _Tp(1)) {}
_CXX14_CONSTEXPR rational operator+() const noexcept { return *this; }
_CXX14_CONSTEXPR rational operator-() const noexcept {
return {-__num, __den};
}
_CXX14_CONSTEXPR rational operator+(const rational &__x) const noexcept {
return {__num * __x.__den + __x.__num * __den, __den * __x.__den};
}
_CXX14_CONSTEXPR rational operator-(const rational &__x) const noexcept {
return {__num * __x.__den - __x.__num * __den, __den * __x.__den};
}
_CXX14_CONSTEXPR rational operator*(const rational &__x) const noexcept {
return {__num * __x.__num, __den * __x.__den};
}
_CXX14_CONSTEXPR rational operator/(const rational &__x) const noexcept {
assert(__x.__num != _Tp(0));
return {__num * __x.__den, __den * __x.__num};
}
_CXX14_CONSTEXPR rational &operator+=(const rational &__x) noexcept {
(__num *= __x.__den) += __den * __x.__num, __den *= __x.__den;
return *this;
}
_CXX14_CONSTEXPR rational &operator-=(const rational &__x) noexcept {
(__num *= __x.__den) -= __den * __x.__num, __den *= __x.__den;
return *this;
}
_CXX14_CONSTEXPR rational &operator*=(const rational &__x) noexcept {
__num *= __x.__num, __den *= __x.__den;
return *this;
}
_CXX14_CONSTEXPR rational &operator/=(const rational &__x) noexcept {
__num *= __x.__den, __den *= __x.__num;
return *this;
}
_CXX14_CONSTEXPR bool operator==(const rational &__x) const noexcept {
return __num * __x.__den == __den * __x.__num;
}
_CXX14_CONSTEXPR bool operator!=(const rational &__x) const noexcept {
return __num * __x.__den != __den * __x.__num;
}
_CXX14_CONSTEXPR bool operator<(const rational &__x) const noexcept {
return (__den > 0) ^ (__x.__den > 0)
? __num * __x.__den > __den * __x.__num
: __num * __x.__den < __den * __x.__num;
}
_CXX14_CONSTEXPR bool operator>(const rational &__x) const noexcept {
return (__den > 0) ^ (__x.__den > 0)
? __num * __x.__den < __den * __x.__num
: __num * __x.__den > __den * __x.__num;
}
_CXX14_CONSTEXPR bool operator<=(const rational &__x) const noexcept {
return !operator>(__x);
}
_CXX14_CONSTEXPR bool operator>=(const rational &__x) const noexcept {
return !operator<(__x);
}
_CXX14_CONSTEXPR
std::enable_if_t<std::is_swappable<_Tp>::value> swap(rational &__x) noexcept {
std::swap(__num, __x.__num), std::swap(__den, __x.__den);
}
template <size_t _Nm> friend constexpr auto &get(rational &__x) noexcept {
static_assert(_Nm < 2);
if _CXX17_CONSTEXPR (_Nm) return __x.__den;
return __x.__num;
}
template <size_t _Nm>
friend constexpr const auto &get(const rational &__x) noexcept {
static_assert(_Nm < 2);
if _CXX17_CONSTEXPR (_Nm) return __x.__den;
return __x.__num;
}
template <size_t _Nm> friend constexpr auto &&get(rational &&__x) noexcept {
static_assert(_Nm < 2);
if _CXX17_CONSTEXPR (_Nm) return std::move(__x.__den);
return std::move(__x.__num);
}
};
} // namespace workspace
namespace std {
template <class _Tp>
struct tuple_size<workspace::rational<_Tp>> : integral_constant<size_t, 2> {};
template <class _Tp, size_t _Nm>
struct tuple_element<_Nm, workspace::rational<_Tp>> {
using type = _Tp;
};
} // namespace std#line 2 "src/algebra/rational.hpp"
/**
* @file rational.hpp
* @brief Rational
*/
#include <cassert>
#line 2 "lib/cxx17"
#line 2 "lib/cxx14"
#ifndef _CXX14_CONSTEXPR
#if __cplusplus >= 201402L
#define _CXX14_CONSTEXPR constexpr
#else
#define _CXX14_CONSTEXPR
#endif
#endif
#line 4 "lib/cxx17"
#ifndef _CXX17_CONSTEXPR
#if __cplusplus >= 201703L
#define _CXX17_CONSTEXPR constexpr
#else
#define _CXX17_CONSTEXPR
#endif
#endif
#ifndef _CXX17_STATIC_ASSERT
#if __cplusplus >= 201703L
#define _CXX17_STATIC_ASSERT static_assert
#else
#define _CXX17_STATIC_ASSERT assert
#endif
#endif
#include <iterator>
#if __cplusplus < 201703L
namespace std {
/**
* @brief Return the size of a container.
* @param __cont Container.
*/
template <typename _Container>
constexpr auto size(const _Container& __cont) noexcept(noexcept(__cont.size()))
-> decltype(__cont.size()) {
return __cont.size();
}
/**
* @brief Return the size of an array.
*/
template <typename _Tp, size_t _Nm>
constexpr size_t size(const _Tp (&)[_Nm]) noexcept {
return _Nm;
}
/**
* @brief Return whether a container is empty.
* @param __cont Container.
*/
template <typename _Container>
[[nodiscard]] constexpr auto empty(const _Container& __cont) noexcept(
noexcept(__cont.empty())) -> decltype(__cont.empty()) {
return __cont.empty();
}
/**
* @brief Return whether an array is empty (always false).
*/
template <typename _Tp, size_t _Nm>
[[nodiscard]] constexpr bool empty(const _Tp (&)[_Nm]) noexcept {
return false;
}
/**
* @brief Return whether an initializer_list is empty.
* @param __il Initializer list.
*/
template <typename _Tp>
[[nodiscard]] constexpr bool empty(initializer_list<_Tp> __il) noexcept {
return __il.size() == 0;
}
struct monostate {};
} // namespace std
#else
#include <variant>
#endif
#line 2 "src/algebra/system/operation.hpp"
/**
* @file operation.hpp
* @brief Operation Traits
*/
#include <functional>
#include <type_traits>
#line 12 "src/algebra/system/operation.hpp"
namespace workspace {
// Unary `+`
template <class _Tp>
using require_unary_plus = std::enable_if_t<
std::is_convertible<decltype(+std::declval<const _Tp &>()), _Tp>::value>;
template <class _Tp, class = void> struct has_unary_plus : std::false_type {};
template <class _Tp>
struct has_unary_plus<_Tp, require_unary_plus<_Tp>> : std::true_type {};
// Unary `-`
template <class _Tp>
using require_unary_minus = std::enable_if_t<
std::is_convertible<decltype(-std::declval<const _Tp &>()), _Tp>::value>;
template <class _Tp, class = void> struct has_unary_minus : std::false_type {};
template <class _Tp>
struct has_unary_minus<_Tp, require_unary_minus<_Tp>> : std::true_type {};
// Binary `+`
template <class _Tp1, class _Tp2 = _Tp1>
using require_binary_plus =
std::enable_if_t<std::is_convertible<decltype(std::declval<const _Tp1 &>() +
std::declval<const _Tp2 &>()),
_Tp1>::value>;
template <class _Tp1, class _Tp2 = _Tp1, class = void>
struct has_binary_plus : std::false_type {};
template <class _Tp1, class _Tp2>
struct has_binary_plus<_Tp1, _Tp2, require_binary_plus<_Tp1, _Tp2>>
: std::true_type {};
// Binary `-`
template <class _Tp1, class _Tp2 = _Tp1>
using require_binary_minus =
std::__void_t<decltype(std::declval<const _Tp1 &>() -
std::declval<const _Tp2 &>())>;
template <class _Tp1, class _Tp2 = _Tp1, class = void>
struct has_binary_minus : std::false_type {};
template <class _Tp1, class _Tp2>
struct has_binary_minus<_Tp1, _Tp2, require_binary_minus<_Tp1, _Tp2>>
: std::true_type {};
// Binary `*`
template <class _Tp1, class _Tp2 = _Tp1>
using require_binary_multiplies =
std::enable_if_t<std::is_convertible<decltype(std::declval<const _Tp1 &>() *
std::declval<const _Tp2 &>()),
_Tp1>::value>;
template <class _Tp1, class _Tp2 = _Tp1, class = void>
struct has_binary_multiplies : std::false_type {};
template <class _Tp1, class _Tp2>
struct has_binary_multiplies<_Tp1, _Tp2, require_binary_multiplies<_Tp1, _Tp2>>
: std::true_type {};
// Binary `/`
template <class _Tp1, class _Tp2 = _Tp1>
using require_binary_divides =
std::enable_if_t<std::is_convertible<decltype(std::declval<const _Tp1 &>() /
std::declval<const _Tp2 &>()),
_Tp1>::value>;
template <class _Tp1, class _Tp2 = _Tp1, class = void>
struct has_binary_divides : std::false_type {};
template <class _Tp1, class _Tp2>
struct has_binary_divides<_Tp1, _Tp2, require_binary_divides<_Tp1, _Tp2>>
: std::true_type {};
// Binary `%`
template <class _Tp1, class _Tp2 = _Tp1>
using require_binary_modulus =
std::enable_if_t<std::is_convertible<decltype(std::declval<const _Tp1 &>() %
std::declval<const _Tp2 &>()),
_Tp1>::value>;
template <class _Tp1, class _Tp2 = _Tp1, class = void>
struct has_binary_modulus : std::false_type {};
template <class _Tp1, class _Tp2>
struct has_binary_modulus<_Tp1, _Tp2, require_binary_modulus<_Tp1, _Tp2>>
: std::true_type {};
template <class _Tp1, class _Tp2 = _Tp1, class = void, class = void,
class = void, class = void>
struct has_arithmetic : std::false_type {};
template <class _Tp1, class _Tp2>
struct has_arithmetic<_Tp1, _Tp2, require_binary_plus<_Tp1, _Tp2>,
require_binary_minus<_Tp1, _Tp2>,
require_binary_multiplies<_Tp1, _Tp2>,
require_binary_divides<_Tp1, _Tp2>> : std::true_type {};
template <class _Tp1, class _Tp2 = _Tp1>
using require_arithmetic = std::enable_if_t<has_arithmetic<_Tp1, _Tp2>::value>;
// Binary `<`
template <class _Tp, class = void> struct is_comparable : std::false_type {};
template <class _Tp>
struct is_comparable<_Tp, std::__void_t<decltype(std::declval<const _Tp &>() <
std::declval<const _Tp &>())>>
: std::true_type {};
template <class _Tp, bool _Default = false> struct try_less : std::less<_Tp> {
constexpr bool operator()(const _Tp &__x, const _Tp &__y) noexcept {
if _CXX17_CONSTEXPR (is_comparable<_Tp>::value)
return std::less<_Tp>::operator()(__x, __y);
else
return _Default;
}
};
} // namespace workspace
#line 12 "src/algebra/rational.hpp"
namespace workspace {
/**
* @brief Rational.
* @tparam _Tp Ring structure
*/
template <class _Tp> class rational {
_Tp __num, __den;
public:
_CXX14_CONSTEXPR rational(const _Tp &__x, const _Tp &__y) noexcept
: __num(__x), __den(__y) {}
_CXX14_CONSTEXPR rational(const _Tp &__x, _Tp &&__y) noexcept
: __num(__x), __den(std::move(__y)) {}
_CXX14_CONSTEXPR rational(_Tp &&__x, const _Tp &__y) noexcept
: __num(std::move(__x)), __den(__y) {}
_CXX14_CONSTEXPR rational(_Tp &&__x = 0, _Tp &&__y = 1) noexcept
: __num(std::move(__x)), __den(std::move(__y)) {}
_CXX14_CONSTEXPR rational(std::initializer_list<_Tp> __x) noexcept
: __num(__x.size() > 0 ? *__x.begin() : _Tp(0)),
__den(__x.size() > 1 ? *std::next(__x.begin()) : _Tp(1)) {}
_CXX14_CONSTEXPR rational operator+() const noexcept { return *this; }
_CXX14_CONSTEXPR rational operator-() const noexcept {
return {-__num, __den};
}
_CXX14_CONSTEXPR rational operator+(const rational &__x) const noexcept {
return {__num * __x.__den + __x.__num * __den, __den * __x.__den};
}
_CXX14_CONSTEXPR rational operator-(const rational &__x) const noexcept {
return {__num * __x.__den - __x.__num * __den, __den * __x.__den};
}
_CXX14_CONSTEXPR rational operator*(const rational &__x) const noexcept {
return {__num * __x.__num, __den * __x.__den};
}
_CXX14_CONSTEXPR rational operator/(const rational &__x) const noexcept {
assert(__x.__num != _Tp(0));
return {__num * __x.__den, __den * __x.__num};
}
_CXX14_CONSTEXPR rational &operator+=(const rational &__x) noexcept {
(__num *= __x.__den) += __den * __x.__num, __den *= __x.__den;
return *this;
}
_CXX14_CONSTEXPR rational &operator-=(const rational &__x) noexcept {
(__num *= __x.__den) -= __den * __x.__num, __den *= __x.__den;
return *this;
}
_CXX14_CONSTEXPR rational &operator*=(const rational &__x) noexcept {
__num *= __x.__num, __den *= __x.__den;
return *this;
}
_CXX14_CONSTEXPR rational &operator/=(const rational &__x) noexcept {
__num *= __x.__den, __den *= __x.__num;
return *this;
}
_CXX14_CONSTEXPR bool operator==(const rational &__x) const noexcept {
return __num * __x.__den == __den * __x.__num;
}
_CXX14_CONSTEXPR bool operator!=(const rational &__x) const noexcept {
return __num * __x.__den != __den * __x.__num;
}
_CXX14_CONSTEXPR bool operator<(const rational &__x) const noexcept {
return (__den > 0) ^ (__x.__den > 0)
? __num * __x.__den > __den * __x.__num
: __num * __x.__den < __den * __x.__num;
}
_CXX14_CONSTEXPR bool operator>(const rational &__x) const noexcept {
return (__den > 0) ^ (__x.__den > 0)
? __num * __x.__den < __den * __x.__num
: __num * __x.__den > __den * __x.__num;
}
_CXX14_CONSTEXPR bool operator<=(const rational &__x) const noexcept {
return !operator>(__x);
}
_CXX14_CONSTEXPR bool operator>=(const rational &__x) const noexcept {
return !operator<(__x);
}
_CXX14_CONSTEXPR
std::enable_if_t<std::is_swappable<_Tp>::value> swap(rational &__x) noexcept {
std::swap(__num, __x.__num), std::swap(__den, __x.__den);
}
template <size_t _Nm> friend constexpr auto &get(rational &__x) noexcept {
static_assert(_Nm < 2);
if _CXX17_CONSTEXPR (_Nm) return __x.__den;
return __x.__num;
}
template <size_t _Nm>
friend constexpr const auto &get(const rational &__x) noexcept {
static_assert(_Nm < 2);
if _CXX17_CONSTEXPR (_Nm) return __x.__den;
return __x.__num;
}
template <size_t _Nm> friend constexpr auto &&get(rational &&__x) noexcept {
static_assert(_Nm < 2);
if _CXX17_CONSTEXPR (_Nm) return std::move(__x.__den);
return std::move(__x.__num);
}
};
} // namespace workspace
namespace std {
template <class _Tp>
struct tuple_size<workspace::rational<_Tp>> : integral_constant<size_t, 2> {};
template <class _Tp, size_t _Nm>
struct tuple_element<_Nm, workspace::rational<_Tp>> {
using type = _Tp;
};
} // namespace std