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// Copyright 2022 Junekey Jeon
//
// The contents of this file may be used under the terms of
// the Apache License v2.0 with LLVM Exceptions.
//
// (See accompanying file LICENSE-Apache or copy at
// https://llvm.org/foundation/relicensing/LICENSE.txt)
//
// Alternatively, the contents of this file may be used under the terms of
// the Boost Software License, Version 1.0.
// (See accompanying file LICENSE-Boost or copy at
// https://www.boost.org/LICENSE_1_0.txt)
//
// Unless required by applicable law or agreed to in writing, this software
// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, either express or implied.
#ifndef JKJ_HEADER_CONTINUED_FRACTIONS
#define JKJ_HEADER_CONTINUED_FRACTIONS
namespace jkj {
// Continued fractions calculator for positive numbers.
template <class UInt>
struct unsigned_rational {
UInt numerator = 0;
UInt denominator = 0;
unsigned_rational() = default;
unsigned_rational(UInt const& numerator) : numerator{numerator}, denominator{1} {}
unsigned_rational(UInt&& numerator)
: numerator{static_cast<UInt&&>(numerator)}, denominator{1} {}
unsigned_rational(UInt const& numerator, UInt const& denominator)
: numerator{numerator}, denominator{denominator} {}
unsigned_rational(UInt&& numerator, UInt const& denominator)
: numerator{static_cast<UInt&&>(numerator)}, denominator{denominator} {}
unsigned_rational(UInt const& numerator, UInt&& denominator)
: numerator{numerator}, denominator{static_cast<UInt&&>(denominator)} {}
unsigned_rational(UInt&& numerator, UInt&& denominator)
: numerator{static_cast<UInt&&>(numerator)}, denominator{
static_cast<UInt&&>(denominator)} {}
friend bool operator<(unsigned_rational const& x, unsigned_rational const& y) {
return x.numerator * y.denominator < y.numerator * x.denominator;
}
friend bool operator<=(unsigned_rational const& x, unsigned_rational const& y) {
return x.numerator * y.denominator <= y.numerator * x.denominator;
}
friend bool operator>(unsigned_rational const& x, unsigned_rational const& y) {
return x.numerator * y.denominator > y.numerator * x.denominator;
}
friend bool operator>=(unsigned_rational const& x, unsigned_rational const& y) {
return x.numerator * y.denominator >= y.numerator * x.denominator;
}
friend bool operator==(unsigned_rational const& x, unsigned_rational const& y) {
return x.numerator * y.denominator == y.numerator * x.denominator;
}
friend bool operator!=(unsigned_rational const& x, unsigned_rational const& y) {
return x.numerator * y.denominator != y.numerator * x.denominator;
}
// Performs no reduction.
friend unsigned_rational operator+(unsigned_rational const& x, unsigned_rational const& y) {
return {x.numerator * y.denominator + y.numerator * x.denominator,
x.denominator * y.denominator};
}
// Performs no reduction.
unsigned_rational& operator+=(unsigned_rational const& y) & {
numerator *= y.denominator;
numerator += y.numerator * denominator;
denominator *= y.denominator;
return *this;
}
// Performs no reduction.
friend unsigned_rational operator-(unsigned_rational const& x, unsigned_rational const& y) {
return {x.numerator * y.denominator - y.numerator * x.denominator,
x.denominator * y.denominator};
}
// Performs no reduction.
unsigned_rational& operator-=(unsigned_rational const& y) & {
numerator *= y.denominator;
numerator -= y.numerator * denominator;
denominator *= y.denominator;
return *this;
}
// Performs no reduction.
friend unsigned_rational operator*(unsigned_rational const& x, unsigned_rational const& y) {
return {x.numerator * y.numerator, x.denominator * y.denominator};
}
// Performs no reduction.
unsigned_rational& operator*=(unsigned_rational const& y) & {
numerator *= y.numerator;
denominator *= y.denominator;
return *this;
}
// Performs no reduction.
friend unsigned_rational operator/(unsigned_rational const& x, unsigned_rational const& y) {
return {x.numerator * y.denominator, x.denominator * y.numerator};
}
// Performs no reduction.
unsigned_rational& operator/=(unsigned_rational const& y) & {
numerator *= y.denominator;
denominator *= y.numerator;
return *this;
}
};
template <class Impl, class UInt>
class continued_fractions {
// The (-1)st coefficient is assumed to be 0.
UInt current_coefficient_{0};
unsigned_rational<UInt> current_convergent_{1, 0};
unsigned_rational<UInt> previous_convergent_{0, 1};
int current_index_ = -1;
bool terminated_ = false;
protected:
void set_terminate_flag() noexcept { terminated_ = true; }
public:
using uint_type = UInt;
int current_index() const noexcept { return current_index_; }
UInt const& current_coefficient() const noexcept { return current_coefficient_; }
unsigned_rational<UInt> const& current_convergent() const noexcept {
return current_convergent_;
}
UInt const& current_numerator() const noexcept { return current_convergent().numerator; }
UInt const& current_denominator() const noexcept {
return current_convergent().denominator;
}
unsigned_rational<UInt> const& previous_convergent() const noexcept {
return previous_convergent_;
}
UInt const& previous_numerator() const noexcept { return previous_convergent().numerator; }
UInt const& previous_denominator() const noexcept {
return previous_convergent().denominator;
}
bool is_terminated() const noexcept { return terminated_; }
// Do nothing if the procedure is terminated.
// Returns true if the update is done,
// and returns false if the procedure is already terminated.
bool update() {
if (!is_terminated()) {
unsigned_rational<UInt> new_output;
current_coefficient_ = static_cast<Impl&>(*this).compute_next_coefficient();
unsigned_rational<UInt> new_convergent{
previous_numerator() + current_coefficient_ * current_numerator(),
previous_denominator() + current_coefficient_ * current_denominator()};
previous_convergent_ = static_cast<unsigned_rational<UInt>&&>(current_convergent_);
current_convergent_ = static_cast<unsigned_rational<UInt>&&>(new_convergent);
++current_index_;
return true;
}
else {
return false;
}
}
};
}
#endif
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