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ContFrac arithmetics

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Jiri Pittner
2022-02-21 16:45:44 +01:00
parent b4aaa77da4
commit a032344c66
3 changed files with 229 additions and 67 deletions
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247
contfrac.cc
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@@ -135,68 +135,206 @@ for(int i=1; i<=n; ++i) //truncate if possible
}
template <typename T>
Homographic<T> Homographic<T>::input(const T &z, const bool inf) const
{
Homographic<T> hnew;
if(inf) //effective infinity, end of input
{
hnew.v[0][0]=hnew.v[0][1]=v[0][1];
hnew.v[1][0]=hnew.v[1][1]=v[1][1];
}
else
{
hnew.v[0][0]=v[0][1];
hnew.v[1][0]=v[1][1];
hnew.v[0][1]=v[0][0]+v[0][1]* z;
hnew.v[1][1]=v[1][0]+v[1][1]* z;
}
return hnew;
}
template <typename T>
Homographic<T> Homographic<T>::output(const T &z) const
{
Homographic<T> hnew;
hnew.v[0][0]=v[1][0];
hnew.v[0][1]=v[1][1];
hnew.v[1][0]=v[0][0]-v[1][0]*z;
hnew.v[1][1]=v[0][1]-v[1][1]*z;
return hnew;
}
template <typename T>
bool Homographic<T>::outputready(T &z) const
{
bool inf=0;
T q0,q1;
if(v[1][0]==0) inf=1; else q0=v[0][0]/v[1][0];
if(v[1][1]==0) inf=1; else q1=v[0][1]/v[1][1];
if(!inf && q0==q1) {z=q0; return true;}
return false;
}
template <typename T>
bool Homographic<T>::terminate() const
{
return v[1][0]==0&&v[1][1]==0;
}
template <typename T>
ContFrac<T> Homographic<T>::value(const ContFrac<T>&x) const
{
Homographic<T> h(*this);
std::list<T> l;
typename ContFrac<T>::iterator px=x.begin();
do //scan all input
for(typename ContFrac<T>::iterator px=x.begin(); px!=x.beyondend(); ++px)
{
//digest next input term
Homographic<T> hnew;
if(px==x.end()|| px!=x.begin()&& *px==0) //input is infinity
h=h.input(*px,px==x.end()|| px!=x.begin()&& *px==0);
//output as much as possible
T out;
while(h.outputready(out))
{
hnew.x[0][0]=hnew.x[0][1]=h.x[0][1];
hnew.x[1][0]=hnew.x[1][1]=h.x[1][1];
}
else
{
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]* *px;
hnew.x[1][1]=h.x[1][0]+h.x[1][1]* *px;
l.push_back(out);
h=h.output(out);
}
//std::cout<<"hnew\n"<< hnew.x[0][0]<<" "<< hnew.x[0][1]<<"\n"<< hnew.x[1][0]<<" "<< hnew.x[1][1]<<"\n";
//check if we are ready to output
bool inf=0;
T q0,q1;
if(hnew.x[1][0]==0) inf=1; else q0=hnew.x[0][0]/hnew.x[1][0];
if(hnew.x[1][1]==0) inf=1; else q1=hnew.x[0][1]/hnew.x[1][1];
while(!inf && q0==q1) //ready to output
//terminate if exhausted
if(h.terminate())
{
l.push_back(q0);
//std::cout <<"out "<<q0<<std::endl;
Homographic<T> hnew2;
hnew2.x[0][0]=hnew.x[1][0];
hnew2.x[0][1]=hnew.x[1][1];
hnew2.x[1][0]=hnew.x[0][0]-hnew.x[1][0]*q0;
hnew2.x[1][1]=hnew.x[0][1]-hnew.x[1][1]*q0;
//std::cout<<"hnew2\n"<< hnew2.x[0][0]<<" "<< hnew2.x[0][1]<<"\n"<< hnew2.x[1][0]<<" "<< hnew2.x[1][1]<<"\n";
hnew=hnew2;
inf=0;
if(hnew.x[1][0]==0) inf=1; else q0=hnew.x[0][0]/hnew.x[1][0];
if(hnew.x[1][1]==0) inf=1; else q1=hnew.x[0][1]/hnew.x[1][1];
}
//termination
if(hnew.x[1][0]==0&&hnew.x[1][1]==0) //terminate
{
//std::cout<<"terminate at "<<i<<"\n";
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>
BiHomographic<T> BiHomographic<T>::inputx(const T &x, const bool inf) const
{
BiHomographic<T> hnew;
for(int i=0; i<2; ++i)
{
hnew.v[i][0][0]= v[i][0][1];
hnew.v[i][0][1]= inf?v[i][0][1] : v[i][0][0]+v[i][0][1]*x;
hnew.v[i][1][0]= v[i][1][1];
hnew.v[i][1][1]= inf?v[i][1][1] : v[i][1][0]+v[i][1][1]*x;
}
return hnew;
}
template <typename T>
BiHomographic<T> BiHomographic<T>::inputy(const T &y, const bool inf) const
{
BiHomographic<T> hnew;
for(int i=0; i<2; ++i)
{
hnew.v[i][0][0]= v[i][1][0];
hnew.v[i][0][1]= v[i][1][1];
hnew.v[i][1][0]= inf?v[i][1][0] : v[i][0][0]+v[i][1][0]*y;
hnew.v[i][1][1]= inf?v[i][1][1] : v[i][0][1]+v[i][1][1]*y;
}
return hnew;
}
template <typename T>
BiHomographic<T> BiHomographic<T>::output(const T &z) const
{
BiHomographic<T> hnew;
for(int i=0; i<2; ++i) for(int j=0; j<2; ++j)
{
hnew.v[0][i][j]= v[1][i][j];
hnew.v[1][i][j]= v[0][i][j] - v[1][i][j]*z;
}
return hnew;
}
template <typename T>
int BiHomographic<T>::inputselect() const
{
if(v[1][0][0]==0)
{
if(v[1][0][1]==0) return 1;
else return 0;
}
if(v[1][0][1]==0) return 0;
if(v[1][1][0]==0) return 1;
if(MYABS(v[0][0][1]/v[1][0][1] - v[0][0][0]/v[1][0][0]) > MYABS(v[0][1][0]/v[1][1][0] - v[0][0][0]/v[1][0][0])) return 0;
return 1;
}
template <typename T>
bool BiHomographic<T>::outputready(T &z) const
{
T q[2][2];
for(int i=0; i<2; ++i) for(int j=0; j<2; ++j)
{
if(v[1][i][j]==0) return false;
else q[i][j]=v[0][i][j]/v[1][i][j];
if(q[i][j]!=q[0][0]) return false;
}
z=q[0][0];
return true;
}
template <typename T>
bool BiHomographic<T>::terminate() const
{
return v[1][0][0]==0&&v[1][0][1]==0&&v[1][1][0]==0&&v[1][1][1]==0;
}
template <typename T>
ContFrac<T> BiHomographic<T>::value(const ContFrac<T>&x, const ContFrac<T>&y) const
{
BiHomographic<T> h(*this);
std::list<T> l;
typename ContFrac<T>::iterator px=x.begin();
typename ContFrac<T>::iterator py=y.begin();
do
{
//select next input term
int which;
if(px==x.beyondend()) which=1;
else if(py==y.beyondend()) which=0;
else which = h.inputselect();
if(which) {h=h.inputy(*py,py==y.end()|| py!=y.begin()&& *py==0); ++py;}
else {h=h.inputx(*px,px==x.end()|| px!=x.begin()&& *px==0); ++px;}
//output as much as possible
T out;
while(h.outputready(out))
{
l.push_back(out);
h=h.output(out);
}
//terminate if exhausted
if(h.terminate())
{
if(px!=x.end()&&px!=x.beyondend() || py!=y.end()&&py!=y.beyondend()) laerror("unexpected termination in Homographic::value");
break;
}
}
while(px!=x.beyondend() || py!=y.beyondend());
return ContFrac<T>(l);
}
template <typename T>
void Rational<T>::simplify()
{
@@ -206,7 +344,7 @@ if(den<0)
den= -den;
}
T g=gcd(num,den);
if(g>1)
if(MYABS(g)>1)
{
num/=g;
den/=g;
@@ -218,7 +356,7 @@ Rational<T> & Rational<T>::operator*=(const T &rhs)
{
T r=rhs;
T g=gcd(r,den);
if(g>1)
if(MYABS(g)>1)
{
r/=g;
den/=g;
@@ -233,7 +371,7 @@ Rational<T> & Rational<T>::operator/=(const T &rhs)
{
T r=rhs;
T g=gcd(r,num);
if(g>1)
if(MYABS(g)>1)
{
r/=g;
num/=g;
@@ -270,19 +408,20 @@ Rational<T> & Rational<T>::operator*=(const Rational &rhs)
Rational r(rhs);
T g;
g=gcd(num,r.den);
if(g>1)
if(MYABS(g)>1)
{
num/=g;
r.den/=g;
}
g=gcd(den,r.num);
if(g>1)
if(MYABS(g)>1)
{
den/=g;
r.num/=g;
}
num*=r.num;
den*=r.den;
if(den<0) {den= -den; num= -num;}
return *this;
}
@@ -293,32 +432,20 @@ 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>;
template class ContFrac<unsigned long>;
template class ContFrac<long long>;
template class ContFrac<unsigned long long>;
template class Homographic<int>;
template class Homographic<unsigned int>;
template class Homographic<long>;
template class Homographic<unsigned long>;
template class Homographic<long long>;
template class Homographic<unsigned long long>;
template class BiHomographic<int>;
template class BiHomographic<unsigned int>;
template class BiHomographic<long>;
template class BiHomographic<unsigned long>;
template class BiHomographic<long long>;
template class BiHomographic<unsigned long long>;