LA_library/contfrac.h

/*
    LA: linear algebra C++ interface library
    Copyright (C) 2022 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>

    This program 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 of the License, or
    (at your option) any later version.

    This program 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.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
*/


#ifndef _CONTFRAC_H
#define _CONTFRAC_H

#include "la_traits.h"
#include "vec.h"

namespace LA {

//simple finite continued fraction class
//NOTE: 0 on any position >0 means actually infinity; simplify()  shortens the vector
//presently implements just conversion to/from rationals and floats
//maybe implement arithmetic by Gosper's method cf. https://perl.plover.com/classes/cftalk/TALK
//

template <typename T>
class ContFrac;

//@@@basic rational arithmetics
template <typename T>
class Rational {
public:
	T num;
	T den;

	Rational(const T p, const T q) : num(p),den(q) {};
	explicit Rational(const T (&a)[2]) :num(a[0]), den(a[1]) {};
	Rational(const ContFrac<T> &cf) {cf.convergent(&num,&den);};
};

template <typename T>
std::ostream & operator<<(std::ostream &s, const Rational<T> &x) 
{
s<<x.num<<"/"<<x.den;
return s;
}

template <typename T>
class Homographic;

template <typename T>
class BiHomographic;


//@@@implement iterator and rewrite  Homographic<T>::value

template <typename T>
class ContFrac : public NRVec<T> {
private:
	int size() const; //prevent confusion with vector size
public:
	ContFrac():  NRVec<T>() {};
	template<int SIZE>  ContFrac(const T (&a)[SIZE]) : NRVec<T>(a) {};
	ContFrac(const NRVec<T> &v) : NRVec<T>(v) {}; //allow implicit conversion from NRVec
	ContFrac(const int n) : NRVec<T>(n+1) {};
	ContFrac(double x, const int n, const T thres=0); //might yield a non-canonical form
	ContFrac(const T p, const T q); //should yield a canonical form
	ContFrac(const Rational<T> &r) : ContFrac(r.num,r.den) {};

	void canonicalize();
	void convergent(T *p, T*q, const int trunc= -1) const;
	Rational<T> rational(const int trunc= -1) const {T p,q; convergent(&p,&q,trunc); return Rational<T>(p,q);};
	double value(const int trunc= -1) const;
	ContFrac reciprocal() const;
	int length() const {return NRVec<T>::size()-1;};
	void resize(const int n, const bool preserve=true) 
		{
		int nold=length();
		NRVec<T>::resize(n+1,preserve);
		if(preserve) for(int i=nold+1; i<=n;++i) (*this)[i]=0;
		} 

	ContFrac operator+(const Rational<T> &rhs) const {Homographic<T> h({{rhs.num,rhs.den},{rhs.den,0}}); return h.value(*this);};
	ContFrac operator-(const Rational<T> &rhs) const {Homographic<T> h({{-rhs.num,rhs.den},{rhs.den,0}}); return h.value(*this);};
	ContFrac operator*(const Rational<T> &rhs) const {Homographic<T> h({{0,rhs.num},{rhs.den,0}}); return h.value(*this);};
	ContFrac operator/(const Rational<T> &rhs) const {Homographic<T> h({{0,rhs.den},{rhs.num,0}}); return h.value(*this);};

	
};

//for Gosper's arithmetic

template <typename T>
class Homographic {
public:
T x[2][2]; //{{a,b},{c,d}} for (a+b.z)/(c+d.z)

	Homographic(){};
	explicit Homographic(const T (&a)[2][2]) {memcpy(x,a,2*2*sizeof(T));};
	ContFrac<T> value(const ContFrac<T>&x) const;
	
};


template <typename T>
class BiHomographic {
public:
T x[2][2][2];
	
	BiHomographic(){};
	explicit BiHomographic(const T (&a)[2][2][2]) {memcpy(x,a,2*2*2*sizeof(T));};
	ContFrac<T> value(const ContFrac<T>&x, const ContFrac<T>&y) const;
};



}//namespace
#endif