232 lines
9.3 KiB
C++
232 lines
9.3 KiB
C++
/*
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LA: linear algebra C++ interface library
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Copyright (C) 2022 Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef _CONTFRAC_H
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#define _CONTFRAC_H
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#include "la_traits.h"
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#include "vec.h"
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namespace LA {
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//Support for rationals and a simple finite continued fraction class
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//NOTE: 0 on any position >0 means actually infinity; simplify() shortens the vector
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//includes Gosper's arithmetics - cf. https://perl.plover.com/classes/cftalk/TALK
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//maybe implement the self-feeding Gosper's algorithm for sqrt(int)
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//maybe do not interpret a_i=0 i>0 as termination???
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template <typename T>
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class ContFrac;
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template <typename T>
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class Rational {
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public:
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T num;
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T den;
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Rational() {};
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Rational(const T p, const T q) : num(p),den(q) {};
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explicit Rational(const T (&a)[2]) :num(a[0]), den(a[1]) {};
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explicit Rational(const ContFrac<T> &cf) {cf.convergent(&num,&den);};
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void simplify();
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//basic rational arithmetics
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Rational operator-() const {return Rational(-num,den);};
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Rational & operator+=(const T &rhs) {num+=den*rhs; return *this;};
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Rational & operator-=(const T &rhs) {num-=den*rhs; return *this;};
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Rational & operator*=(const T &rhs);
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Rational & operator/=(const T &rhs);
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Rational operator+(const T &rhs) const {Rational r(*this); return r+=rhs;};
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Rational operator-(const T &rhs) const {Rational r(*this); return r-=rhs;};
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Rational operator*(const T &rhs) const {Rational r(*this); return r*=rhs;};
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Rational operator/(const T &rhs) const {Rational r(*this); return r/=rhs;};
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Rational & operator*=(const Rational &rhs);
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Rational & operator/=(const Rational &rhs) {return (*this)*=Rational(rhs.den,rhs.num);};
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Rational operator+(const Rational &rhs) const;
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Rational operator-(const Rational &rhs) const;
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Rational operator*(const Rational &rhs) const {Rational r(*this); return r*=rhs;};
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Rational operator/(const Rational &rhs) const {Rational r(*this); return r/=rhs;};
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Rational & operator+=(const Rational &rhs) {*this = *this+rhs; return *this;};
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Rational & operator-=(const Rational &rhs) {*this = *this-rhs; return *this;};
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//combination with continued fractions
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ContFrac<T> operator+(const ContFrac<T> &rhs) const {return rhs + *this;};
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ContFrac<T> operator-(const ContFrac<T> &rhs) const {return -rhs + *this;};
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ContFrac<T> operator*(const ContFrac<T> &rhs) const {return rhs * *this;};
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ContFrac<T> operator/(const ContFrac<T> &rhs) const {return rhs.reciprocal() * *this;};
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//relational operators, relying that operator- yields a form with a positive denominator
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bool operator==(const Rational &rhs) const {Rational t= *this-rhs; return t.num==0;};
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bool operator!=(const Rational &rhs) const {Rational t= *this-rhs; return t.num!=0;};
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bool operator>=(const Rational &rhs) const {Rational t= *this-rhs; return t.num>=0;};
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bool operator<=(const Rational &rhs) const {Rational t= *this-rhs; return t.num<=0;};
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bool operator>(const Rational &rhs) const {Rational t= *this-rhs; return t.num>0;};
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bool operator<(const Rational &rhs) const {Rational t= *this-rhs; return t.num<0;};
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};
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template <typename T>
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std::ostream & operator<<(std::ostream &s, const Rational<T> &x)
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{
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s<<x.num<<"/"<<x.den;
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return s;
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}
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template <typename T>
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std::istream & operator>>(std::istream &s, Rational<T> &x)
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{
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char c;
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s>>x.num>>c>>x.den;
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return s;
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}
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template <typename T>
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class Homographic;
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template <typename T>
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class BiHomographic;
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template <typename T>
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class ContFrac : public NRVec<T> {
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private:
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int size() const; //prevent confusion with vector size
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public:
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ContFrac(): NRVec<T>() {};
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explicit ContFrac(const std::list<T> &x) : NRVec<T>(x) {};
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template<int SIZE> ContFrac(const T (&a)[SIZE]) : NRVec<T>(a) {};
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ContFrac(const NRVec<T> &v) : NRVec<T>(v) {}; //allow implicit conversion from NRVec
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ContFrac(const int n) : NRVec<T>(n+1) {};
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explicit ContFrac(double x, const int n, const T thres=0); //WARNING: it might yield a non-canonical form
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//we could make a template for analogous conversion from an arbitrary-precision type
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ContFrac(T p, T q); //should yield a canonical form
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explicit ContFrac(const Rational<T> &r) : ContFrac(r.num,r.den) {};
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void canonicalize();
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void convergent(T *p, T*q, const int trunc= -1) const;
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Rational<T> rational(const int trunc= -1) const {T p,q; convergent(&p,&q,trunc); return Rational<T>(p,q);};
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double value(const int trunc= -1) const; //we could make also a template usable with an arbitrary-precision type
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ContFrac reciprocal() const;
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ContFrac operator-() const; //unary minus
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int length() const {return NRVec<T>::size()-1;};
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void resize(const int n, const bool preserve=true)
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{
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int nold=length();
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NRVec<T>::resize(n+1,preserve);
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if(preserve) for(int i=nold+1; i<=n;++i) (*this)[i]=0;
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}
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//arithmetics with a single ContFrac operand
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ContFrac operator+(const Rational<T> &rhs) const {Homographic<T> h({{rhs.num,rhs.den},{rhs.den,0}}); return h.value(*this);};
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ContFrac operator-(const Rational<T> &rhs) const {Homographic<T> h({{-rhs.num,rhs.den},{rhs.den,0}}); return h.value(*this);};
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ContFrac operator*(const Rational<T> &rhs) const {Homographic<T> h({{0,rhs.num},{rhs.den,0}}); return h.value(*this);};
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ContFrac operator/(const Rational<T> &rhs) const {Homographic<T> h({{0,rhs.den},{rhs.num,0}}); return h.value(*this);};
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ContFrac & operator+=(const T &rhs) {this->copyonwrite(); (*this)[0]+=rhs; return *this;};
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ContFrac & operator-=(const T &rhs) {this->copyonwrite(); (*this)[0]-=rhs; return *this;};
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ContFrac operator+(const T &rhs) const {ContFrac r(*this); r+=rhs; return r;};
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ContFrac operator-(const T &rhs) const {ContFrac r(*this); r-=rhs; return r;};
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ContFrac operator*(const T &rhs) const {Homographic<T> h({{0,rhs},{1,0}}); return h.value(*this);};
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ContFrac operator/(const T &rhs) const {Homographic<T> h({{0,1},{rhs,0}}); return h.value(*this);};
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//arithmetics with two ContFrac operands
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ContFrac operator+(const ContFrac &rhs) const {BiHomographic<T> h({{{0,1},{1,0}},{{1,0},{0,0}}}); return h.value(*this,rhs);};
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ContFrac operator-(const ContFrac &rhs) const {BiHomographic<T> h({{{0,1},{-1,0}},{{1,0},{0,0}}}); return h.value(*this,rhs);};
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ContFrac operator*(const ContFrac &rhs) const {BiHomographic<T> h({{{0,0},{0,1}},{{1,0},{0,0}}}); return h.value(*this,rhs);};
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ContFrac operator/(const ContFrac &rhs) const {BiHomographic<T> h({{{0,1},{0,0}},{{0,0},{1,0}}}); return h.value(*this,rhs);};
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//relational operators, guaranteed only to work correctly for canonicalized CF!
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T compare(const ContFrac &rhs) const;
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bool operator==(const ContFrac &rhs) const {return compare(rhs)==0;};
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bool operator>(const ContFrac &rhs) const {return compare(rhs)>0;};
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bool operator<(const ContFrac &rhs) const {return rhs.operator>(*this);};
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bool operator!=(const ContFrac &rhs) const {return ! this->operator==(rhs) ;}
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bool operator<=(const ContFrac &rhs) const {return ! this->operator>(rhs) ;}
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bool operator>=(const ContFrac &rhs) const {return ! this->operator<(rhs) ;}
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//iterator
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class iterator {
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private:
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T *p;
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public:
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iterator() {};
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~iterator() {};
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iterator(T *v): p(v) {};
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bool operator==(const iterator rhs) const {return p==rhs.p;}
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bool operator!=(const iterator rhs) const {return p!=rhs.p;}
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iterator operator++() {return ++p;}
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iterator operator++(int) {return p++;}
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T& operator*() const {return *p;}
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T *operator->() const {return p;}
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};
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iterator begin() const {return NRVec<T>::v;}
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iterator end() const {return NRVec<T>::v+NRVec<T>::nn;}
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iterator beyondend() const {return NRVec<T>::v+NRVec<T>::nn+1;}
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};
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//for Gosper's arithmetic
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template <typename T>
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class Homographic {
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public:
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T v[2][2]; //{{a,b},{c,d}} for (a+b.x)/(c+d.x) i.e. [denominator][power_x]
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Homographic(){};
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explicit Homographic(const T (&a)[2][2]) {memcpy(v,a,2*2*sizeof(T));};
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ContFrac<T> value(const ContFrac<T>&z) const;
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Homographic input(const T &x, const bool inf) const;
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Homographic output(const T &x) const;
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bool outputready(T &x, bool first) const;
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bool terminate() const;
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};
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template <typename T>
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class BiHomographic {
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public:
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T v[2][2][2]; //{{{a,b},{c,d}},{{e,f},{g,h}}} i.e.[denominator][power_y][power_x]
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BiHomographic(){};
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explicit BiHomographic(const T (&a)[2][2][2]) {memcpy(v,a,2*2*2*sizeof(T));};
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ContFrac<T> value(const ContFrac<T>&x, const ContFrac<T>&y) const;
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BiHomographic inputx(const T &x, const bool inf) const;
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BiHomographic inputy(const T &y, const bool inf) const;
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BiHomographic output(const T &z) const;
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int inputselect() const;
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bool outputready(T &x,bool first) const;
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bool terminate() const;
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};
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}//namespace
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#endif
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