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add sprout/rational.hpp

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add sprout/math/common_factor.hpp
This commit is contained in:
bolero-MURAKAMI 2012-05-25 22:21:16 +09:00
parent dc8cb3d14e
commit 5a9b2e4f7d
8 changed files with 1153 additions and 119 deletions
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88
libs/string/example/c_str_to_sprout_string.cpp
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@ -1,44 +1,44 @@
//
// Sprout C++ Library
//
// Copyright (c) 2012
// bolero-MURAKAMI : http://d.hatena.ne.jp/boleros/
// osyo-manga : http://d.hatena.ne.jp/osyo-manga/
//
// Readme:
// https://github.com/bolero-MURAKAMI/Sprout/blob/master/README
//
// License:
// Boost Software License - Version 1.0
// <http://www.boost.org/LICENSE_1_0.txt>
//
#include <sprout/string.hpp>
//
// C style string to Sprout.String
//
int
main(){
constexpr char const* c_str = "homu";
//
// String length is required
//
constexpr auto length = sprout::char_traits<char>::length(c_str);
static_assert(length == 4, "");
//
// To Sprout.String
//
constexpr auto str = sprout::string_from_c_str<length>( c_str );
static_assert(std::is_same<sprout::string<4> const, decltype(str)>{}, "");
static_assert(str == "homu", "");
constexpr auto str2 = sprout::string_from_c_str<length>( c_str, 2 );
static_assert(std::is_same<sprout::string<4> const, decltype(str2)>{}, "");
static_assert(str2 == "ho", "");
return 0;
}
//
// Sprout C++ Library
//
// Copyright (c) 2012
// bolero-MURAKAMI : http://d.hatena.ne.jp/boleros/
// osyo-manga : http://d.hatena.ne.jp/osyo-manga/
//
// Readme:
// https://github.com/bolero-MURAKAMI/Sprout/blob/master/README
//
// License:
// Boost Software License - Version 1.0
// <http://www.boost.org/LICENSE_1_0.txt>
//
#include <sprout/string.hpp>
//
// C style string to Sprout.String
//
int
main(){
constexpr char const* c_str = "homu";
//
// String length is required
//
constexpr auto length = sprout::char_traits<char>::length(c_str);
static_assert(length == 4, "");
//
// To Sprout.String
//
constexpr auto str = sprout::string_from_c_str<length>( c_str );
static_assert(std::is_same<sprout::string<4> const, decltype(str)>{}, "");
static_assert(str == "homu", "");
constexpr auto str2 = sprout::string_from_c_str<length>( c_str, 2 );
static_assert(std::is_same<sprout::string<4> const, decltype(str2)>{}, "");
static_assert(str2 == "ho", "");
return 0;
}

134
libs/weed/example/as_tuple.cpp
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@ -1,67 +1,67 @@
//
// Sprout C++ Library
//
// Copyright (c) 2012
// bolero-MURAKAMI : http://d.hatena.ne.jp/boleros/
// osyo-manga : http://d.hatena.ne.jp/osyo-manga/
//
// Readme:
// https://github.com/bolero-MURAKAMI/Sprout/blob/master/README
//
// License:
// Boost Software License - Version 1.0
// <http://www.boost.org/LICENSE_1_0.txt>
//
#include <sprout/weed.hpp>
int
main(){
namespace w = sprout::weed;
static constexpr auto source = sprout::to_string("homu:mado");
// String parser
static constexpr auto item = *w::lim<4>(w::char_ - ':');
//
// If you do not want to use the as_tuple
//
{
static constexpr auto parser = item >> ':' >> item;
static constexpr auto result = w::parse(
sprout::begin(source), sprout::end(source), parser
);
static_assert(result.success(), "");
// !!!!
static_assert(result.attr() == "homumado", "");
}
//
// You need to use the as_tuple
//
{
static constexpr auto parser = w::as_tuple[item] >> ':' >> w::as_tuple[item];
static constexpr auto result = w::parse(
sprout::begin(source), sprout::end(source), parser
);
static_assert(result.success(), "");
static constexpr auto attr = result.attr();
// OK
static_assert(std::is_same<
sprout::tuple<sprout::string<4>, sprout::string<4>> const,
decltype(attr)
>::value, "");
static_assert(sprout::get<0>(attr) == "homu", "");
static_assert(sprout::get<1>(attr) == "mado", "");
}
return 0;
}
//
// Sprout C++ Library
//
// Copyright (c) 2012
// bolero-MURAKAMI : http://d.hatena.ne.jp/boleros/
// osyo-manga : http://d.hatena.ne.jp/osyo-manga/
//
// Readme:
// https://github.com/bolero-MURAKAMI/Sprout/blob/master/README
//
// License:
// Boost Software License - Version 1.0
// <http://www.boost.org/LICENSE_1_0.txt>
//
#include <sprout/weed.hpp>
int
main(){
namespace w = sprout::weed;
static constexpr auto source = sprout::to_string("homu:mado");
// String parser
static constexpr auto item = *w::lim<4>(w::char_ - ':');
//
// If you do not want to use the as_tuple
//
{
static constexpr auto parser = item >> ':' >> item;
static constexpr auto result = w::parse(
sprout::begin(source), sprout::end(source), parser
);
static_assert(result.success(), "");
// !!!!
static_assert(result.attr() == "homumado", "");
}
//
// You need to use the as_tuple
//
{
static constexpr auto parser = w::as_tuple[item] >> ':' >> w::as_tuple[item];
static constexpr auto result = w::parse(
sprout::begin(source), sprout::end(source), parser
);
static_assert(result.success(), "");
static constexpr auto attr = result.attr();
// OK
static_assert(std::is_same<
sprout::tuple<sprout::string<4>, sprout::string<4>> const,
decltype(attr)
>::value, "");
static_assert(sprout::get<0>(attr) == "homu", "");
static_assert(sprout::get<1>(attr) == "mado", "");
}
return 0;
}

8
sprout/cinttypes/abs.hpp
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@ -10,14 +10,6 @@ namespace sprout {
SPROUT_CONSTEXPR std::intmax_t imaxabs(std::intmax_t j) {
return j < 0 ? -j : j;
}
template<
typename T,
typename sprout::enabler_if<std::is_same<T, std::intmax_t>::value>::type = sprout::enabler
>
SPROUT_CONSTEXPR T abs(T j) {
return sprout::imaxabs(j);
}
} // namespace sprout
#endif // #ifndef SPROUT_CINTTYPES_ABS_HPP

21
sprout/cstdlib/abs.hpp
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@ -1,7 +1,9 @@
#ifndef SPROUT_CSTDLIB_ABS_HPP
#define SPROUT_CSTDLIB_ABS_HPP
#include <type_traits>
#include <sprout/config.hpp>
#include <sprout/utility/enabler_if.hpp>
namespace sprout {
// Copyright (C) 2011 RiSK (sscrisk)
@ -26,6 +28,25 @@ namespace sprout {
SPROUT_CONSTEXPR long long abs(long long j) {
return sprout::llabs(j);
}
template<
typename IntType,
typename sprout::enabler_if<
std::is_integral<IntType>::value && std::is_signed<IntType>::value
>::type = sprout::enabler
>
SPROUT_CONSTEXPR IntType abs(IntType j) {
return j < 0 ? -j : j;
}
template<
typename IntType,
typename sprout::enabler_if<
std::is_integral<IntType>::value && std::is_unsigned<IntType>::value
>::type = sprout::enabler
>
SPROUT_CONSTEXPR IntType abs(IntType j) {
return j;
}
} // namespace sprout
#endif // #ifndef SPROUT_CSTDLIB_ABS_HPP

7
sprout/math/common_factor.hpp Normal file
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@ -0,0 +1,7 @@
#ifndef SPROUT_MATH_COMMON_FACTOR_HPP
#define SPROUT_MATH_COMMON_FACTOR_HPP
#include <sprout/math/gcd.hpp>
#include <sprout/math/lcm.hpp>
#endif // SPROUT_MATH_COMMON_FACTOR_HPP

188
sprout/math/gcd.hpp Normal file
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@ -0,0 +1,188 @@
#ifndef SPROUT_MATH_GCD_HPP
#define SPROUT_MATH_GCD_HPP
#include <climits>
#include <limits>
#include <sprout/config.hpp>
#include <sprout/array.hpp>
#include <sprout/cstdlib/abs.hpp>
namespace sprout {
namespace math {
namespace detail {
template<typename RingType>
inline SPROUT_CONSTEXPR RingType
gcd_euclidean(RingType a, RingType b) {
return a == static_cast<RingType>(0) ? b
: b % a == static_cast<RingType>(0) ? a
: sprout::math::detail::gcd_euclidean(a % (b % a), b % a)
;
}
template<typename IntType>
inline SPROUT_CONSTEXPR IntType
gcd_integer_impl(IntType result) {
return result < static_cast<IntType>(0) ? -result : result;
}
template<typename IntType>
inline SPROUT_CONSTEXPR IntType
gcd_integer(IntType const& a, IntType const& b) {
return sprout::math::detail::gcd_integer_impl(
sprout::math::detail::gcd_euclidean(a, b)
);
}
template<typename BuiltInUnsigned>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary_2_1(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which);
template<typename BuiltInUnsigned>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary_2_2(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which) {
return !(r[ which ] & 1u) ? sprout::math::detail::gcd_binary_2_2(
shifts,
which ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] >> 1)}}
: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] >> 1), r[1]}}
,
which
)
: r[!which] > r[which] ? sprout::math::detail::gcd_binary_2_1(
shifts,
which ^ 1u ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] - r[0])}}
: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] - r[1]), r[1]}}
,
which ^ 1u
)
: sprout::math::detail::gcd_binary_2_1(
shifts,
which ? sprout::array<BuiltInUnsigned, 2>{{r[0], BuiltInUnsigned(r[1] - r[0])}}
: sprout::array<BuiltInUnsigned, 2>{{BuiltInUnsigned(r[0] - r[1]), r[1]}}
,
which
)
;
}
template<typename BuiltInUnsigned>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary_2_1(unsigned shifts, sprout::array<BuiltInUnsigned, 2> const& r, unsigned which) {
return r[which] ? sprout::math::detail::gcd_binary_2_2(shifts, r, which)
: r[!which] << shifts
;
}
template<typename BuiltInUnsigned>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary_1(BuiltInUnsigned u, BuiltInUnsigned v, unsigned shifts = 0) {
return (!(u & 1u) && !(v & 1u)) ? sprout::math::detail::gcd_binary_1(u >> 1, v >> 1, shifts + 1)
: sprout::math::detail::gcd_binary_2_2(
shifts, sprout::array<BuiltInUnsigned, 2>{{u, v}}, static_cast<bool>(u & 1u)
)
;
}
template<typename BuiltInUnsigned>
inline SPROUT_CONSTEXPR BuiltInUnsigned
gcd_binary(BuiltInUnsigned u, BuiltInUnsigned v) {
return u && v ? sprout::math::detail::gcd_binary_1(u, v)
: u + v
;
}
template<typename T, bool IsSpecialized, bool IsSigned>
struct gcd_optimal_evaluator_helper_t {
public:
SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
return sprout::math::detail::gcd_euclidean(a, b);
}
};
template<typename T>
struct gcd_optimal_evaluator_helper_t<T, true, true> {
public:
SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
return sprout::math::detail::gcd_integer(a, b);
}
};
template<typename T>
struct gcd_optimal_evaluator {
public:
SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
typedef std::numeric_limits<T> limits_type;
typedef sprout::math::detail::gcd_optimal_evaluator_helper_t<
T, limits_type::is_specialized, limits_type::is_signed
> helper_type;
return helper_type().operator()(a, b);
}
};
# define SPROUT_PRIVATE_GCD_UF(Ut) \
template<> \
struct gcd_optimal_evaluator<Ut> { \
public: \
SPROUT_CONSTEXPR Ut operator()(Ut a, Ut b) const { \
return sprout::math::detail::gcd_binary(a, b); \
} \
}
SPROUT_PRIVATE_GCD_UF(unsigned char);
SPROUT_PRIVATE_GCD_UF(unsigned short);
SPROUT_PRIVATE_GCD_UF(unsigned);
SPROUT_PRIVATE_GCD_UF(unsigned long);
SPROUT_PRIVATE_GCD_UF(unsigned long long);
# if CHAR_MIN == 0
SPROUT_PRIVATE_GCD_UF(char);
# endif
#undef SPROUT_PRIVATE_GCD_UF
# define SPROUT_PRIVATE_GCD_SF(St, Ut) \
template<> \
struct gcd_optimal_evaluator<St> { \
public: \
SPROUT_CONSTEXPR St operator()(St a, St b) const { \
using sprout::abs; \
return static_cast<St>(sprout::math::detail::gcd_optimal_evaluator<Ut>().operator()( \
static_cast<Ut>(abs(a)), static_cast<Ut>(abs(b)) \
)); \
} \
}
SPROUT_PRIVATE_GCD_SF(signed char, unsigned char);
SPROUT_PRIVATE_GCD_SF(short, unsigned short);
SPROUT_PRIVATE_GCD_SF(int, unsigned);
SPROUT_PRIVATE_GCD_SF(long, unsigned long);
# if CHAR_MIN < 0
SPROUT_PRIVATE_GCD_SF(char, unsigned char);
# endif
SPROUT_PRIVATE_GCD_SF(long long, unsigned long long);
#undef SPROUT_PRIVATE_GCD_SF
template<typename T>
inline SPROUT_CONSTEXPR T
gcd_optimal(T const& a, T const& b) {
return sprout::math::detail::gcd_optimal_evaluator<T>().operator()(a, b);
}
} // namespace detail
//
// gcd_evaluator
//
template<typename IntType>
class gcd_evaluator {
public:
typedef IntType result_type;
typedef IntType first_argument_type;
typedef IntType second_argument_type;
public:
SPROUT_CONSTEXPR result_type
operator()(first_argument_type const& a, second_argument_type const& b) const {
return sprout::math::detail::gcd_optimal(a, b);
}
};
//
// gcd
//
template<typename IntType>
inline SPROUT_CONSTEXPR IntType
gcd(IntType const& a, IntType const& b) {
return sprout::math::gcd_evaluator<IntType>().operator()(a, b);
}
} // namespace math
} // namespace boost
#endif // SPROUT_MATH_GCD_HPP

101
sprout/math/lcm.hpp Normal file
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@ -0,0 +1,101 @@
#ifndef SPROUT_MATH_LCM_HPP
#define SPROUT_MATH_LCM_HPP
#include <climits>
#include <limits>
#include <sprout/config.hpp>
#include <sprout/math/gcd.hpp>
namespace sprout {
namespace math {
namespace detail {
template<typename RingType>
inline SPROUT_CONSTEXPR RingType
lcm_euclidean_impl(RingType a, RingType b, RingType temp) {
return temp != static_cast<RingType>(0) ? (a / temp * b)
: static_cast<RingType>(0)
;
}
template<typename RingType>
inline SPROUT_CONSTEXPR RingType
lcm_euclidean(RingType a, RingType b) {
return sprout::math::detail::lcm_euclidean_impl(
a, b, sprout::math::detail::gcd_euclidean(a, b)
);
}
template<typename IntType>
inline SPROUT_CONSTEXPR IntType
lcm_integer_impl(IntType result) {
return result < static_cast<IntType>(0) ? -result : result;
}
template<typename IntType>
inline SPROUT_CONSTEXPR IntType
lcm_integer(IntType const& a, IntType const& b) {
return sprout::math::detail::lcm_integer_impl(
sprout::math::detail::lcm_euclidean(a, b)
);
}
template<typename T, bool IsSpecialized, bool IsSigned>
struct lcm_optimal_evaluator_helper_t {
public:
SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
return sprout::math::detail::lcm_euclidean(a, b);
}
};
template<typename T>
struct lcm_optimal_evaluator_helper_t<T, true, true> {
public:
SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
return sprout::math::detail::lcm_integer(a, b);
}
};
template<typename T>
struct lcm_optimal_evaluator {
public:
SPROUT_CONSTEXPR T operator()(T const& a, T const& b) const {
typedef std::numeric_limits<T> limits_type;
typedef sprout::math::detail::lcm_optimal_evaluator_helper_t<
T, limits_type::is_specialized, limits_type::is_signed
> helper_type;
return helper_type().operator()(a, b);
}
};
template<typename T>
inline SPROUT_CONSTEXPR T
lcm_optimal(T const& a, T const& b) {
return sprout::math::detail::lcm_optimal_evaluator<T>().operator()(a, b);
}
} // namespace detail
//
// lcm_evaluator
//
template<typename IntType>
class lcm_evaluator {
public:
typedef IntType result_type;
typedef IntType first_argument_type;
typedef IntType second_argument_type;
public:
SPROUT_CONSTEXPR result_type
operator()(first_argument_type const& a, second_argument_type const& b) const {
return sprout::math::detail::lcm_optimal(a, b);
}
};
//
// lcm
//
template<typename IntType>
inline SPROUT_CONSTEXPR IntType
lcm(IntType const& a, IntType const& b) {
return sprout::math::lcm_evaluator<IntType>().operator()(a, b);
}
} // namespace math
} // namespace boost
#endif // SPROUT_MATH_LCM_HPP

725
sprout/rational.hpp Normal file
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@ -0,0 +1,725 @@
#ifndef SPROUT_RATIONAL_HPP
#define SPROUT_RATIONAL_HPP
#include <limits>
#include <utility>
#include <stdexcept>
#include <ios>
#include <iostream>
#include <sprout/config.hpp>
#include <sprout/cstdlib/abs.hpp>
#include <sprout/math/gcd.hpp>
#include <sprout/detail/call_traits.hpp>
#include <sprout/detail/io/ios_state.hpp>
namespace sprout {
//
// bad_rational
//
class bad_rational
: public std::domain_error
{
public:
explicit bad_rational()
: std::domain_error("bad rational: zero denominator")
{}
};
template<typename IntType>
class rational;
namespace detail {
struct rational_private_constructor_tag {};
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType> make_rational(
typename sprout::detail::call_traits<IntType>::param_type n,
typename sprout::detail::call_traits<IntType>::param_type d,
sprout::detail::rational_private_constructor_tag
);
} // namespace detail
namespace detail {
template<typename IntType>
class rational_impl {
protected:
typedef IntType int_type;
typedef typename sprout::detail::call_traits<IntType>::param_type param_type;
protected:
IntType num_;
IntType den_;
protected:
SPROUT_CONSTEXPR rational_impl()
: num_(0)
, den_(1)
{}
rational_impl(rational_impl const&) = default;
SPROUT_CONSTEXPR rational_impl(param_type n)
: num_(n)
, den_(1)
{}
SPROUT_CONSTEXPR rational_impl(param_type n, param_type d)
: num_(n)
, den_(d)
{}
SPROUT_CONSTEXPR rational_impl(param_type n, param_type d, param_type g)
: num_(n / g)
, den_(d / g)
{}
};
} // namespace detail
//
// rational
//
template<typename IntType>
class rational
: private sprout::detail::rational_impl<IntType>
{
static_assert(std::numeric_limits<IntType>::is_specialized, "std::numeric_limits<IntType>::is_specialized");
public:
typedef IntType int_type;
typedef typename sprout::detail::call_traits<IntType>::param_type param_type;
private:
struct private_constructor_tag {};
typedef sprout::detail::rational_impl<IntType> base_type;
private:
static SPROUT_CONSTEXPR IntType normalize_g_1(IntType den, IntType g) {
return den / g < 0 ? -g : g;
}
static SPROUT_CONSTEXPR IntType normalize_g(IntType num, IntType den) {
return den == 0 ? throw sprout::bad_rational()
: num == 0 ? den
: normalize_g_1(den, sprout::math::gcd(num, den))
;
}
private:
using base_type::num_;
using base_type::den_;
private:
SPROUT_CONSTEXPR rational(param_type n, param_type d, private_constructor_tag)
: base_type(n, d)
{}
public:
SPROUT_CONSTEXPR rational()
: base_type()
{}
rational(rational const&) = default;
SPROUT_CONSTEXPR rational(param_type n)
: base_type(n)
{}
SPROUT_CONSTEXPR rational(param_type n, param_type d)
: base_type(n, d, normalize_g(n, d))
{}
rational& operator=(rational const&) = default;
rational& operator=(param_type n) {
return assign(n, 1);
}
rational& assign(param_type n, param_type d) {
using std::swap;
rational temp(n, d);
swap(temp, *this);
return *this;
}
SPROUT_CONSTEXPR IntType numerator() const {
return num_;
}
SPROUT_CONSTEXPR IntType denominator() const {
return den_;
}
rational& operator+=(rational const& rhs) {
IntType g = sprout::math::gcd(den_, rhs.den_);
den_ /= g;
num_ = num_ * (rhs.den_ / g) + rhs.num_ * den_;
g = sprout::math::gcd(num_, g);
num_ /= g;
den_ *= rhs.den_ / g;
return *this;
}
rational& operator-=(rational const& rhs) {
IntType g = sprout::math::gcd(den_, rhs.den_);
den_ /= g;
num_ = num_ * (rhs.den_ / g) - rhs.num_ * den_;
g = sprout::math::gcd(num_, g);
num_ /= g;
den_ *= rhs.den_ / g;
return *this;
}
rational& operator*=(rational const& rhs) {
IntType gcd1 = sprout::math::gcd(num_, rhs.den_);
IntType gcd2 = sprout::math::gcd(rhs.num_, den_);
num_ =(num_ / gcd1) * (rhs.num_ / gcd2);
den_ =(den_ / gcd2) * (rhs.den_ / gcd1);
return *this;
}
rational& operator/=(rational const& rhs) {
if (rhs.num_ == IntType(0)) {
throw bad_rational();
}
if (num_ == IntType(0)) {
return *this;
}
IntType gcd1 = sprout::math::gcd(num_, rhs.num_);
IntType gcd2 = sprout::math::gcd(rhs.den_, den_);
num_ =(num_ / gcd1) * (rhs.den_ / gcd2);
den_ =(den_ / gcd2) * (rhs.num_ / gcd1);
if (den_ < IntType(0)) {
num_ = -num_;
den_ = -den_;
}
return *this;
}
rational& operator+=(param_type rhs) {
return *this += rational(rhs);
}
rational& operator-=(param_type rhs) {
return *this -= rational(rhs);
}
rational& operator*=(param_type rhs) {
return *this *= rational(rhs);
}
rational& operator/=(param_type rhs) {
return *this /= rational(rhs);
}
rational& operator++() {
num_ += den_;
return *this;
}
rational& operator--() {
num_ -= den_;
return *this;
}
rational operator++(int) {
rational result(*this);
++*this;
return result;
}
rational operator--(int) {
rational result(*this);
--*this;
return result;
}
SPROUT_CONSTEXPR bool operator!() const {
return !num_;
}
SPROUT_CONSTEXPR operator bool() const {
return num_ != 0;
}
public:
friend sprout::rational<IntType> sprout::detail::make_rational<IntType>(
typename sprout::detail::call_traits<IntType>::param_type n,
typename sprout::detail::call_traits<IntType>::param_type d,
sprout::detail::rational_private_constructor_tag
);
};
namespace detail {
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType> make_rational(
typename sprout::detail::call_traits<IntType>::param_type n,
typename sprout::detail::call_traits<IntType>::param_type d,
sprout::detail::rational_private_constructor_tag
)
{
return sprout::rational<IntType>(
n, d,
typename sprout::rational<IntType>::private_constructor_tag()
);
}
} // namespace detail
//
// operator+
// operator-
//
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
operator+(rational<IntType> const& r) {
return r;
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
operator-(rational<IntType> const& r) {
return sprout::detail::make_rational<IntType>(
-r.numerator(), r.denominator(),
sprout::detail::rational_private_constructor_tag()
);
}
//
// operator+
// operator-
// operator*
// operator/
//
namespace detail {
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
rational_add_impl_3(
sprout::rational<IntType> const& rhs,
IntType g, IntType den, IntType num
)
{
return sprout::detail::make_rational<IntType>(
num / g, den * (rhs.denominator() / g),
sprout::detail::rational_private_constructor_tag()
);
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
rational_add_impl_2(
sprout::rational<IntType> const& rhs,
IntType g, IntType den, IntType num
)
{
return rational_add_impl_3(
rhs,
sprout::math::gcd(num, g), den, num
);
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
rational_add_impl_1(
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
IntType g, IntType den
)
{
return rational_add_impl_2(
rhs,
g, den, lhs.numerator() * (rhs.denominator() / g) + rhs.numerator() * den
);
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
rational_add_impl(
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
IntType g
)
{
return rational_add_impl_1(
lhs, rhs,
g, lhs.denominator() / g
);
}
} // namespace detail
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
operator+(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
return sprout::detail::rational_add_impl(
lhs, rhs,
sprout::math::gcd(lhs.denominator(), rhs.denominator())
);
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
operator+(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
return lhs + sprout::rational<IntType>(rhs);
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
operator+(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
return sprout::rational<IntType>(lhs) + rhs;
}
namespace detail {
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
rational_sub_impl_3(
sprout::rational<IntType> const& rhs,
IntType g, IntType den, IntType num
)
{
return sprout::detail::make_rational<IntType>(
num / g, den * (rhs.denominator() / g),
sprout::detail::rational_private_constructor_tag()
);
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
rational_sub_impl_2(
sprout::rational<IntType> const& rhs,
IntType g, IntType den, IntType num
)
{
return rational_sub_impl_3(
rhs,
sprout::math::gcd(num, g), den, num
);
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
rational_sub_impl_1(
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
IntType g, IntType den
)
{
return rational_sub_impl_2(
rhs,
g, den, lhs.numerator() * (rhs.denominator() / g) - rhs.numerator() * den
);
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
rational_sub_impl(
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
IntType g
)
{
return rational_sub_impl_1(
lhs, rhs,
g, lhs.denominator() / g
);
}
} // namespace detail
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
operator-(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
return sprout::detail::rational_sub_impl(
lhs, rhs,
sprout::math::gcd(lhs.denominator(), rhs.denominator())
);
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
operator-(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
return lhs - sprout::rational<IntType>(rhs);
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
operator-(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
return sprout::rational<IntType>(lhs) - rhs;
}
namespace detail {
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
rational_mul_impl(
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
IntType gcd1, IntType gcd2
)
{
return sprout::detail::make_rational<IntType>(
(lhs.numerator() / gcd1) * (rhs.numerator() / gcd2),
(lhs.denominator() / gcd2) * (rhs.denominator() / gcd1),
sprout::detail::rational_private_constructor_tag()
);
}
} // namespace detail
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
operator*(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
return sprout::detail::rational_mul_impl(
lhs, rhs,
sprout::math::gcd(lhs.numerator(), rhs.denominator()),
sprout::math::gcd(rhs.numerator(), lhs.denominator())
);
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
operator*(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
return lhs * sprout::rational<IntType>(rhs);
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
operator*(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
return sprout::rational<IntType>(lhs) * rhs;
}
namespace detail {
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
rational_div_impl_1(IntType num, IntType den) {
return den < IntType(0) ? sprout::detail::make_rational<IntType>(
-num, -den,
sprout::detail::rational_private_constructor_tag()
)
: sprout::detail::make_rational<IntType>(
num, den,
sprout::detail::rational_private_constructor_tag()
)
;
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
rational_div_impl(
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
IntType gcd1, IntType gcd2
)
{
return sprout::detail::rational_div_impl_1(
(lhs.numerator() / gcd1) * (rhs.denominator() / gcd2),
(lhs.denominator() / gcd2) * (rhs.numerator() / gcd1)
);
}
} // namespace detail
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
operator/(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
return rhs.numerator() == IntType(0) ? throw sprout::bad_rational()
: lhs.numerator() == IntType(0) ? lhs
: sprout::detail::rational_div_impl(
lhs, rhs,
sprout::math::gcd(lhs.numerator(), rhs.numerator()),
sprout::math::gcd(rhs.denominator(), lhs.denominator())
)
;
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
operator/(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
return lhs / sprout::rational<IntType>(rhs);
}
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
operator/(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
return sprout::rational<IntType>(lhs) / rhs;
}
//
// operator==
// operator!=
//
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator==(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
return lhs.numerator() == rhs.numerator() && lhs.denominator() == rhs.denominator();
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator==(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
return lhs.denominator() == IntType(1) && lhs.numerator() == rhs;
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator==(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
return rhs == lhs;
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator!=(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
return !(lhs == rhs);
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator!=(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
return !(lhs == rhs);
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator!=(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
return !(lhs == rhs);
}
//
// operator<
// operator>
// operator<=
// operator>=
//
namespace detail {
template<typename IntType>
inline SPROUT_CONSTEXPR bool
rational_less_impl_2(
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
IntType d1, IntType q1, IntType r1,
IntType d2, IntType q2, IntType r2,
unsigned reverse = 0
)
{
return q1 != q2 ? reverse ? q1 > q2 : q1 < q2
: r1 == IntType(0) || r2 == IntType(0)
? r1 == r2 ? false
: (r1 != IntType(0)) != static_cast<bool>(reverse ^ 1)
: sprout::detail::rational_less_impl_2(
lhs, rhs,
r1, d1 / r1, d1 % r1,
r2, d2 / r2, d2 % r2,
reverse ^ 1
)
;
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
rational_less_impl_1(
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
IntType d1, IntType q1, IntType r1,
IntType d2, IntType q2, IntType r2
)
{
return r2 < IntType(0) ? sprout::detail::rational_less_impl_1(
lhs, rhs,
d1, q1, r1,
d2, q2 - 1, r2 + d2
)
: sprout::detail::rational_less_impl_2(
lhs, rhs,
d1, q1, r1,
d2, q2, r2
)
;
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
rational_less_impl(
sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs,
IntType d1, IntType q1, IntType r1
)
{
return r1 < IntType(0) ? sprout::detail::rational_less_impl(
lhs, rhs,
d1, q1 - 1, r1 + d1
)
: sprout::detail::rational_less_impl_1(
lhs, rhs,
d1, q1, r1,
rhs.denominator(), rhs.numerator() / rhs.denominator(), rhs.numerator() % rhs.denominator()
)
;
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
rational_less_impl(
sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs,
IntType q, IntType r
)
{
return r < IntType(0) ? sprout::detail::rational_less_impl(
lhs, rhs,
r + lhs.denominator(), q - 1
)
: q < rhs
;
}
} // namespace detail
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator<(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
return sprout::detail::rational_less_impl(
lhs, rhs,
lhs.denominator(), lhs.numerator() / lhs.denominator(), lhs.numerator() % lhs.denominator()
);
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator<(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
return sprout::detail::rational_less_impl(
lhs, rhs,
lhs.numerator() / lhs.denominator(), lhs.numerator() % lhs.denominator()
);
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator<(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
return lhs != rhs && !(rhs < lhs);
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator>(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
return rhs < lhs;
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator>(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
return rhs < lhs;
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator>(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
return rhs < lhs;
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator<=(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
return !(rhs < lhs);
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator<=(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
return !(rhs < lhs);
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator<=(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
return !(rhs < lhs);
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator>=(sprout::rational<IntType> const& lhs, sprout::rational<IntType> const& rhs) {
return !(lhs < rhs);
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator>=(sprout::rational<IntType> const& lhs, typename sprout::rational<IntType>::param_type rhs) {
return !(lhs < rhs);
}
template<typename IntType>
inline SPROUT_CONSTEXPR bool
operator>=(typename sprout::rational<IntType>::param_type lhs, sprout::rational<IntType> const& rhs) {
return !(lhs < rhs);
}
//
// operator>>
// operator<<
//
template<typename Elem, typename Traits, typename IntType>
inline std::basic_istream<Elem, Traits>&
operator>>(std::basic_istream<Elem, Traits>& lhs, sprout::rational<IntType>& rhs) {
IntType n = IntType(0);
IntType d = IntType(1);
Elem c = 0;
sprout::detail::io::ios_flags_saver saver(lhs);
lhs >> n;
c = lhs.get();
if (c != Elem('/')) {
lhs.clear(std::istream::badbit);
}
lhs >> std::noskipws;
lhs >> d;
if (lhs) {
rhs.assign(n, d);
}
return lhs;
}
template<typename Elem, typename Traits, typename IntType>
inline std::basic_ostream<Elem, Traits>&
operator<<(std::basic_ostream<Elem, Traits>& lhs, sprout::rational<IntType> const& rhs) {
return lhs << rhs.numerator() << Elem('/') << rhs.denominator();
}
//
// rational_cast
//
template<typename T, typename IntType>
inline SPROUT_CONSTEXPR T
rational_cast(sprout::rational<IntType> const& src) {
return static_cast<T>(src.numerator()) / static_cast<T>(src.denominator());
}
//
// abs
//
template<typename IntType>
inline SPROUT_CONSTEXPR sprout::rational<IntType>
abs(sprout::rational<IntType> const& x) {
return x.numerator() >= IntType(0) ? x
: sprout::detail::make_rational<IntType>(
-x.numerator(), x.denominator(),
sprout::detail::rational_private_constructor_tag()
)
;
}
} // namespace sprout
#endif // SPROUT_RATIONAL_HPP