From b4aaa77da4590feb35157b9db870560843763ee1 Mon Sep 17 00:00:00 2001
From: Jiri Pittner <jiri@pittnerovi.com>
Date: Sat, 19 Feb 2022 19:10:24 +0100
Subject: [PATCH] working on contfrac

---
 contfrac.cc   | 114 +++++++++++++++++++++++++++++++++++++++++++++++---
 contfrac.h    |  72 ++++++++++++++++++++++++++++---
 permutation.h |   2 +-
 t.cc          |  12 +++++-
 4 files changed, 186 insertions(+), 14 deletions(-)

diff --git a/contfrac.cc b/contfrac.cc
index 565820f..94eaa5c 100644
--- a/contfrac.cc
+++ b/contfrac.cc
@@ -17,6 +17,7 @@
 */
 
 #include "contfrac.h"
+#include "permutation.h"
 #include <stdio.h>
 #include <string.h>
 #include <math.h>
@@ -121,6 +122,7 @@ void ContFrac<T>::canonicalize()
 {
 int n=this->length();
 if(n==0) return;
+this->copyonwrite();
 if((*this)[n]==1) {(*this)[n]=0; ++(*this)[n-1];} //avoid deepest 1/1
 for(int i=1; i<=n; ++i) //truncate if possible
 	{
@@ -139,11 +141,13 @@ ContFrac<T> Homographic<T>::value(const ContFrac<T>&x) const
 Homographic<T> h(*this);
 
 std::list<T> l;
-for(int i=0; i<=x.length()+1; ++i) //scan all input
+typename ContFrac<T>::iterator px=x.begin();
+
+do //scan all input
 	{
 	//digest next input term
 	Homographic<T> hnew;
-	if(i>x.length()||i!=0&&x[i]==0) //input is infinity
+	if(px==x.end()|| px!=x.begin()&& *px==0) //input is infinity
 		{
 		hnew.x[0][0]=hnew.x[0][1]=h.x[0][1];
                 hnew.x[1][0]=hnew.x[1][1]=h.x[1][1];
@@ -152,8 +156,8 @@ for(int i=0; i<=x.length()+1; ++i) //scan all input
 		{
 		hnew.x[0][0]=h.x[0][1];
 		hnew.x[1][0]=h.x[1][1];
-		hnew.x[0][1]=h.x[0][0]+h.x[0][1]*x[i];
-        	hnew.x[1][1]=h.x[1][0]+h.x[1][1]*x[i];
+		hnew.x[0][1]=h.x[0][0]+h.x[0][1]* *px;
+        	hnew.x[1][1]=h.x[1][0]+h.x[1][1]* *px;
 		}
 
 	//std::cout<<"hnew\n"<< hnew.x[0][0]<<" "<< hnew.x[0][1]<<"\n"<< hnew.x[1][0]<<" "<< hnew.x[1][1]<<"\n";
@@ -182,21 +186,119 @@ for(int i=0; i<=x.length()+1; ++i) //scan all input
 	if(hnew.x[1][0]==0&&hnew.x[1][1]==0) //terminate
 		{
 		//std::cout<<"terminate at "<<i<<"\n";
-		if(i<=x.length()) laerror("unexpected termination in Homographic::value");
+		if(px!=x.end()) laerror("unexpected termination in Homographic::value");
 		break;
 		}
 	h=hnew;
-	}
+	++px;
+	} while(px!=x.beyondend());
 //std::cout <<"size= "<<l.size()<<std::endl;
 return ContFrac<T>(l);
 }
 
 
+template <typename T>
+void Rational<T>::simplify()
+{
+if(den<0)
+	{
+	num= -num;
+	den= -den;
+	}
+T g=gcd(num,den); 
+if(g>1) 
+	{
+	num/=g; 
+	den/=g;
+	}
+}
+
+template <typename T>
+Rational<T> & Rational<T>::operator*=(const T  &rhs)
+{
+T r=rhs;
+T g=gcd(r,den);
+if(g>1)
+        {
+        r/=g;
+        den/=g;
+        }
+num*=r;
+return *this;
+}
+
+
+template <typename T>
+Rational<T> & Rational<T>::operator/=(const T  &rhs)
+{
+T r=rhs;
+T g=gcd(r,num);
+if(g>1)
+        {
+        r/=g;
+        num/=g;
+        }
+den*=r;
+return *this;
+}
+
+
+template <typename T>
+Rational<T>  Rational<T>::operator+(const Rational &rhs) const
+{
+Rational r;
+r.den = lcm(den,rhs.den);
+r.num = num*(r.den/den) + rhs.num*(r.den/rhs.den);
+r.simplify();
+return r;
+}
+
+template <typename T>
+Rational<T>  Rational<T>::operator-(const Rational &rhs) const
+{
+Rational r;
+r.den = lcm(den,rhs.den);
+r.num = num*(r.den/den) - rhs.num*(r.den/rhs.den);
+r.simplify();
+return r;
+}
+
+
+template <typename T>
+Rational<T> & Rational<T>::operator*=(const Rational &rhs)
+{
+Rational r(rhs);
+T g;
+g=gcd(num,r.den);
+if(g>1)
+	{
+	num/=g;
+	r.den/=g;
+	}
+g=gcd(den,r.num);
+if(g>1)
+        {
+        den/=g;
+        r.num/=g;
+        }
+num*=r.num;
+den*=r.den;
+return *this;
+}
+
+
 
 
 /***************************************************************************//**
  * forced instantization in the corresponding object file
  ******************************************************************************/
+template class Rational<int>;
+template class Rational<unsigned int>;
+template class Rational<long>;
+template class Rational<unsigned long>;
+template class Rational<long long>;
+template class Rational<unsigned long long>;
+
 template class ContFrac<int>;
 template class ContFrac<unsigned int>;
 template class ContFrac<long>;
diff --git a/contfrac.h b/contfrac.h
index cfd038f..4cd2606 100644
--- a/contfrac.h
+++ b/contfrac.h
@@ -34,16 +34,38 @@ namespace LA {
 template <typename T>
 class ContFrac;
 
-//@@@basic rational arithmetics
 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>
@@ -53,6 +75,16 @@ 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;
 
@@ -60,7 +92,6 @@ template <typename T>
 class BiHomographic;
 
 
-//@@@implement iterator and rewrite  Homographic<T>::value
 
 template <typename T>
 class ContFrac : public NRVec<T> {
@@ -71,14 +102,15 @@ public:
 	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(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;
+	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) 
@@ -87,13 +119,41 @@ public:
 		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
diff --git a/permutation.h b/permutation.h
index fb69c5a..52f76ad 100644
--- a/permutation.h
+++ b/permutation.h
@@ -119,7 +119,7 @@ return big;
 template <typename T> 
 inline T lcm(T a, T b)
 {
-return (a*b)/gcd(a,b);
+return (a/gcd(a,b))*b;
 }
 
 
diff --git a/t.cc b/t.cc
index d9d61b0..d8a1df6 100644
--- a/t.cc
+++ b/t.cc
@@ -2431,6 +2431,16 @@ NRMat<double> mm=m.permuted_rows(p);
 cout <<mm;
 }
 
+if(1)
+{
+Rational<int> p,q;
+cin>>p>>q;
+cout <<p+q<<endl;
+cout <<p-q<<endl;
+cout <<p*q<<endl;
+cout <<p/q<<endl;
+}
+
 if(0)
 {
 double x;
@@ -2463,7 +2473,7 @@ double zzz=zz.value();
 cout <<z<<" "<<zzz<<endl;
 }
 
-if(1)
+if(0)
 {
 Rational<int> r({11,101});
 ContFrac<int> x(r);