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working on contfrac

This commit is contained in:
Jiri Pittner 2022-02-19 19:10:24 +01:00
parent e67e6a5797
commit b4aaa77da4
4 changed files with 186 additions and 14 deletions
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114
contfrac.cc
View File

@ -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>;

72
contfrac.h
View File

@ -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

2
permutation.h
View File

@ -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;
}

12
t.cc
View File

@ -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);