LA_library/contfrac.h

187 lines
6.5 KiB
C++

/*
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;
template <typename T>
class Rational {
public:
T num;
T den;
Rational() {};
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);};
void simplify();
//basic rational arithmetics
Rational operator-() const {return Rational(-num,den);};
Rational & operator+=(const T &rhs) {num+=den*rhs; return *this;};
Rational & operator-=(const T &rhs) {num-=den*rhs; return *this;};
Rational & operator*=(const T &rhs);
Rational & operator/=(const T &rhs);
Rational operator+(const T &rhs) const {Rational r(*this); return r+=rhs;};
Rational operator-(const T &rhs) const {Rational r(*this); return r-=rhs;};
Rational operator*(const T &rhs) const {Rational r(*this); return r*=rhs;};
Rational operator/(const T &rhs) const {Rational r(*this); return r/=rhs;};
Rational & operator*=(const Rational &rhs);
Rational & operator/=(const Rational &rhs) {return (*this)*=Rational(rhs.den,rhs.num);};
Rational operator+(const Rational &rhs) const;
Rational operator-(const Rational &rhs) const;
Rational operator*(const Rational &rhs) const {Rational r(*this); return r*=rhs;};
Rational operator/(const Rational &rhs) const {Rational r(*this); return r/=rhs;};
Rational & operator+=(const Rational &rhs) {*this = *this+rhs; return *this;};
Rational & operator-=(const Rational &rhs) {*this = *this-rhs; return *this;};
};
template <typename T>
std::ostream & operator<<(std::ostream &s, const Rational<T> &x)
{
s<<x.num<<"/"<<x.den;
return s;
}
template <typename T>
std::istream & operator>>(std::istream &s, Rational<T> &x)
{
char c;
s>>x.num>>c>>x.den;
return s;
}
template <typename T>
class Homographic;
template <typename T>
class BiHomographic;
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
//we could make a template for analogous conversion from an arbitrary-precision type
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; //we could make also a template usable with an arbitrary-precision type
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;
}
//arithmetics with a single ContFrac operand
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);};
ContFrac & operator+=(const T &rhs) {this->copyonwrite(); (*this)[0]+=rhs; return *this;};
ContFrac & operator-=(const T &rhs) {this->copyonwrite(); (*this)[0]-=rhs; return *this;};
ContFrac operator+(const T &rhs) const {ContFrac r(*this); r+=rhs; return r;};
ContFrac operator-(const T &rhs) const {ContFrac r(*this); r-=rhs; return r;};
ContFrac operator*(const T &rhs) const {Homographic<T> h({{0,rhs},{1,0}}); return h.value(*this);};
ContFrac operator/(const T &rhs) const {Homographic<T> h({{0,1},{rhs,0}}); return h.value(*this);};
//arithmetics with two ContFrac operands
//@@@
//iterator
class iterator {
private:
T *p;
public:
iterator() {};
~iterator() {};
iterator(T *v): p(v) {};
bool operator==(const iterator rhs) const {return p==rhs.p;}
bool operator!=(const iterator rhs) const {return p!=rhs.p;}
iterator operator++() {return ++p;}
iterator operator++(int) {return p++;}
T& operator*() const {return *p;}
T *operator->() const {return p;}
};
iterator begin() const {return NRVec<T>::v;}
iterator end() const {return NRVec<T>::v+NRVec<T>::nn;}
iterator beyondend() const {return NRVec<T>::v+NRVec<T>::nn+1;}
};
//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