ContFrac arithmetics
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247
contfrac.cc
247
contfrac.cc
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@ -135,68 +135,206 @@ for(int i=1; i<=n; ++i) //truncate if possible
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}
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template <typename T>
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Homographic<T> Homographic<T>::input(const T &z, const bool inf) const
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{
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Homographic<T> hnew;
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if(inf) //effective infinity, end of input
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{
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hnew.v[0][0]=hnew.v[0][1]=v[0][1];
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hnew.v[1][0]=hnew.v[1][1]=v[1][1];
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}
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else
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{
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hnew.v[0][0]=v[0][1];
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hnew.v[1][0]=v[1][1];
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hnew.v[0][1]=v[0][0]+v[0][1]* z;
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hnew.v[1][1]=v[1][0]+v[1][1]* z;
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}
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return hnew;
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}
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template <typename T>
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Homographic<T> Homographic<T>::output(const T &z) const
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{
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Homographic<T> hnew;
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hnew.v[0][0]=v[1][0];
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hnew.v[0][1]=v[1][1];
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hnew.v[1][0]=v[0][0]-v[1][0]*z;
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hnew.v[1][1]=v[0][1]-v[1][1]*z;
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return hnew;
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}
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template <typename T>
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bool Homographic<T>::outputready(T &z) const
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{
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bool inf=0;
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T q0,q1;
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if(v[1][0]==0) inf=1; else q0=v[0][0]/v[1][0];
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if(v[1][1]==0) inf=1; else q1=v[0][1]/v[1][1];
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if(!inf && q0==q1) {z=q0; return true;}
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return false;
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}
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template <typename T>
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bool Homographic<T>::terminate() const
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{
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return v[1][0]==0&&v[1][1]==0;
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}
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template <typename T>
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ContFrac<T> Homographic<T>::value(const ContFrac<T>&x) const
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{
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Homographic<T> h(*this);
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std::list<T> l;
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typename ContFrac<T>::iterator px=x.begin();
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do //scan all input
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for(typename ContFrac<T>::iterator px=x.begin(); px!=x.beyondend(); ++px)
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{
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//digest next input term
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Homographic<T> hnew;
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if(px==x.end()|| px!=x.begin()&& *px==0) //input is infinity
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h=h.input(*px,px==x.end()|| px!=x.begin()&& *px==0);
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//output as much as possible
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T out;
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while(h.outputready(out))
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{
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hnew.x[0][0]=hnew.x[0][1]=h.x[0][1];
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hnew.x[1][0]=hnew.x[1][1]=h.x[1][1];
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}
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else
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{
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hnew.x[0][0]=h.x[0][1];
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hnew.x[1][0]=h.x[1][1];
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hnew.x[0][1]=h.x[0][0]+h.x[0][1]* *px;
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hnew.x[1][1]=h.x[1][0]+h.x[1][1]* *px;
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l.push_back(out);
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h=h.output(out);
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}
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//std::cout<<"hnew\n"<< hnew.x[0][0]<<" "<< hnew.x[0][1]<<"\n"<< hnew.x[1][0]<<" "<< hnew.x[1][1]<<"\n";
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//check if we are ready to output
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bool inf=0;
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T q0,q1;
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if(hnew.x[1][0]==0) inf=1; else q0=hnew.x[0][0]/hnew.x[1][0];
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if(hnew.x[1][1]==0) inf=1; else q1=hnew.x[0][1]/hnew.x[1][1];
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while(!inf && q0==q1) //ready to output
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//terminate if exhausted
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if(h.terminate())
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{
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l.push_back(q0);
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//std::cout <<"out "<<q0<<std::endl;
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Homographic<T> hnew2;
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hnew2.x[0][0]=hnew.x[1][0];
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hnew2.x[0][1]=hnew.x[1][1];
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hnew2.x[1][0]=hnew.x[0][0]-hnew.x[1][0]*q0;
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hnew2.x[1][1]=hnew.x[0][1]-hnew.x[1][1]*q0;
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//std::cout<<"hnew2\n"<< hnew2.x[0][0]<<" "<< hnew2.x[0][1]<<"\n"<< hnew2.x[1][0]<<" "<< hnew2.x[1][1]<<"\n";
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hnew=hnew2;
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inf=0;
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if(hnew.x[1][0]==0) inf=1; else q0=hnew.x[0][0]/hnew.x[1][0];
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if(hnew.x[1][1]==0) inf=1; else q1=hnew.x[0][1]/hnew.x[1][1];
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}
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//termination
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if(hnew.x[1][0]==0&&hnew.x[1][1]==0) //terminate
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{
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//std::cout<<"terminate at "<<i<<"\n";
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if(px!=x.end()) laerror("unexpected termination in Homographic::value");
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break;
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}
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h=hnew;
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++px;
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} while(px!=x.beyondend());
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//std::cout <<"size= "<<l.size()<<std::endl;
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}
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return ContFrac<T>(l);
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}
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template <typename T>
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BiHomographic<T> BiHomographic<T>::inputx(const T &x, const bool inf) const
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{
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BiHomographic<T> hnew;
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for(int i=0; i<2; ++i)
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{
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hnew.v[i][0][0]= v[i][0][1];
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hnew.v[i][0][1]= inf?v[i][0][1] : v[i][0][0]+v[i][0][1]*x;
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hnew.v[i][1][0]= v[i][1][1];
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hnew.v[i][1][1]= inf?v[i][1][1] : v[i][1][0]+v[i][1][1]*x;
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}
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return hnew;
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}
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template <typename T>
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BiHomographic<T> BiHomographic<T>::inputy(const T &y, const bool inf) const
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{
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BiHomographic<T> hnew;
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for(int i=0; i<2; ++i)
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{
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hnew.v[i][0][0]= v[i][1][0];
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hnew.v[i][0][1]= v[i][1][1];
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hnew.v[i][1][0]= inf?v[i][1][0] : v[i][0][0]+v[i][1][0]*y;
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hnew.v[i][1][1]= inf?v[i][1][1] : v[i][0][1]+v[i][1][1]*y;
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}
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return hnew;
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}
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template <typename T>
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BiHomographic<T> BiHomographic<T>::output(const T &z) const
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{
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BiHomographic<T> hnew;
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for(int i=0; i<2; ++i) for(int j=0; j<2; ++j)
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{
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hnew.v[0][i][j]= v[1][i][j];
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hnew.v[1][i][j]= v[0][i][j] - v[1][i][j]*z;
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}
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return hnew;
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}
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template <typename T>
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int BiHomographic<T>::inputselect() const
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{
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if(v[1][0][0]==0)
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{
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if(v[1][0][1]==0) return 1;
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else return 0;
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}
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if(v[1][0][1]==0) return 0;
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if(v[1][1][0]==0) return 1;
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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;
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return 1;
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}
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template <typename T>
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bool BiHomographic<T>::outputready(T &z) const
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{
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T q[2][2];
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for(int i=0; i<2; ++i) for(int j=0; j<2; ++j)
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{
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if(v[1][i][j]==0) return false;
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else q[i][j]=v[0][i][j]/v[1][i][j];
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if(q[i][j]!=q[0][0]) return false;
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}
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z=q[0][0];
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return true;
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}
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template <typename T>
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bool BiHomographic<T>::terminate() const
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{
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return v[1][0][0]==0&&v[1][0][1]==0&&v[1][1][0]==0&&v[1][1][1]==0;
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}
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template <typename T>
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ContFrac<T> BiHomographic<T>::value(const ContFrac<T>&x, const ContFrac<T>&y) const
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{
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BiHomographic<T> h(*this);
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std::list<T> l;
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typename ContFrac<T>::iterator px=x.begin();
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typename ContFrac<T>::iterator py=y.begin();
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do
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{
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//select next input term
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int which;
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if(px==x.beyondend()) which=1;
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else if(py==y.beyondend()) which=0;
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else which = h.inputselect();
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if(which) {h=h.inputy(*py,py==y.end()|| py!=y.begin()&& *py==0); ++py;}
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else {h=h.inputx(*px,px==x.end()|| px!=x.begin()&& *px==0); ++px;}
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//output as much as possible
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T out;
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while(h.outputready(out))
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{
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l.push_back(out);
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h=h.output(out);
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}
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//terminate if exhausted
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if(h.terminate())
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{
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if(px!=x.end()&&px!=x.beyondend() || py!=y.end()&&py!=y.beyondend()) laerror("unexpected termination in Homographic::value");
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break;
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}
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}
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while(px!=x.beyondend() || py!=y.beyondend());
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return ContFrac<T>(l);
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}
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template <typename T>
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void Rational<T>::simplify()
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{
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@ -206,7 +344,7 @@ if(den<0)
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den= -den;
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}
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T g=gcd(num,den);
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if(g>1)
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if(MYABS(g)>1)
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{
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num/=g;
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den/=g;
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@ -218,7 +356,7 @@ Rational<T> & Rational<T>::operator*=(const T &rhs)
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{
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T r=rhs;
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T g=gcd(r,den);
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if(g>1)
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if(MYABS(g)>1)
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{
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r/=g;
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den/=g;
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@ -233,7 +371,7 @@ Rational<T> & Rational<T>::operator/=(const T &rhs)
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{
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T r=rhs;
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T g=gcd(r,num);
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if(g>1)
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if(MYABS(g)>1)
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{
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r/=g;
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num/=g;
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@ -270,19 +408,20 @@ Rational<T> & Rational<T>::operator*=(const Rational &rhs)
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Rational r(rhs);
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T g;
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g=gcd(num,r.den);
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if(g>1)
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if(MYABS(g)>1)
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{
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num/=g;
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r.den/=g;
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}
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g=gcd(den,r.num);
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if(g>1)
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if(MYABS(g)>1)
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{
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den/=g;
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r.num/=g;
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}
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num*=r.num;
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den*=r.den;
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if(den<0) {den= -den; num= -num;}
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return *this;
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}
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@ -293,32 +432,20 @@ return *this;
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* forced instantization in the corresponding object file
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******************************************************************************/
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template class Rational<int>;
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template class Rational<unsigned int>;
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template class Rational<long>;
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template class Rational<unsigned long>;
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template class Rational<long long>;
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template class Rational<unsigned long long>;
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template class ContFrac<int>;
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template class ContFrac<unsigned int>;
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template class ContFrac<long>;
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template class ContFrac<unsigned long>;
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template class ContFrac<long long>;
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template class ContFrac<unsigned long long>;
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template class Homographic<int>;
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template class Homographic<unsigned int>;
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template class Homographic<long>;
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template class Homographic<unsigned long>;
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template class Homographic<long long>;
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template class Homographic<unsigned long long>;
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template class BiHomographic<int>;
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template class BiHomographic<unsigned int>;
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template class BiHomographic<long>;
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template class BiHomographic<unsigned long>;
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template class BiHomographic<long long>;
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template class BiHomographic<unsigned long long>;
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32
contfrac.h
32
contfrac.h
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@ -34,6 +34,8 @@ namespace LA {
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template <typename T>
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class ContFrac;
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//@@@operator== > >= etc.
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template <typename T>
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class Rational {
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public:
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@ -93,6 +95,8 @@ class BiHomographic;
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//@@@operator== > >= etc.
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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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@ -133,7 +137,10 @@ public:
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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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//@@@
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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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//iterator
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class iterator {
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@ -161,11 +168,16 @@ public:
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template <typename T>
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class Homographic {
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public:
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T x[2][2]; //{{a,b},{c,d}} for (a+b.z)/(c+d.z)
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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(x,a,2*2*sizeof(T));};
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ContFrac<T> value(const ContFrac<T>&x) const;
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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) const;
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bool terminate() const;
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};
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@ -173,11 +185,19 @@ T x[2][2]; //{{a,b},{c,d}} for (a+b.z)/(c+d.z)
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template <typename T>
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class BiHomographic {
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public:
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T x[2][2][2];
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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(x,a,2*2*2*sizeof(T));};
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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) const;
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bool terminate() const;
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};
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17
t.cc
17
t.cc
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@ -2431,7 +2431,7 @@ NRMat<double> mm=m.permuted_rows(p);
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cout <<mm;
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}
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if(1)
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if(0)
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{
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Rational<int> p,q;
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cin>>p>>q;
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@ -2483,5 +2483,20 @@ ContFrac<int> z= x*Rational<int>({2,3});
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cout<<Rational<int>(z)<<endl;
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}
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if(1)
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{
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ContFrac<int> x(11,101);
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ContFrac<int> v(3,7);
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ContFrac<int> y= x+v;
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cout<<Rational<int>(y)<<endl;
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ContFrac<int> z= x*v;
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cout<<Rational<int>(z)<<endl;
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BiHomographic<int> h({{{12,4},{3,1}},{{0,1},{-1,0}}});
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ContFrac<int> zz=h.value(x,v);
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cout<<Rational<int>(zz)<<endl;
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cout<<(Rational<int>(x)+3)*(Rational<int>(v)+4)/(Rational<int>(x)-Rational<int>(v))<<endl;
|
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}
|
||||
|
||||
|
||||
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue