jiri/LA_library
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

finished ContFrac implementation

Browse Source
This commit is contained in:
Jiri Pittner
2022-02-22 15:46:07 +01:00
parent a032344c66
commit 6c5f0eb68e
3 changed files with 178 additions and 22 deletions
Download Patch File Download Diff File Expand all files Collapse all files

50
contfrac.h
View File

@@ -25,17 +25,16 @@
namespace LA {
//simple finite continued fraction class
//Support for rationals and a simple finite continued fraction class
//NOTE: 0 on any position >0 means actually infinity; simplify() shortens the vector
//presently implements just conversion to/from rationals and floats
//maybe implement arithmetic by Gosper's method cf. https://perl.plover.com/classes/cftalk/TALK
//
//includes Gosper's arithmetics - cf. https://perl.plover.com/classes/cftalk/TALK
//maybe implement the self-feeding Gosper's algorithm for sqrt(int)
//maybe do not interpret a_i=0 i>0 as termination???
template <typename T>
class ContFrac;
//@@@operator== > >= etc.
template <typename T>
class Rational {
public:
@@ -45,7 +44,7 @@ public:
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);};
explicit Rational(const ContFrac<T> &cf) {cf.convergent(&num,&den);};
void simplify();
//basic rational arithmetics
@@ -67,7 +66,21 @@ public:
Rational & operator+=(const Rational &rhs) {*this = *this+rhs; return *this;};
Rational & operator-=(const Rational &rhs) {*this = *this-rhs; return *this;};
//combination with continued fractions
ContFrac<T> operator+(const ContFrac<T> &rhs) const {return rhs + *this;};
ContFrac<T> operator-(const ContFrac<T> &rhs) const {return -rhs + *this;};
ContFrac<T> operator*(const ContFrac<T> &rhs) const {return rhs * *this;};
ContFrac<T> operator/(const ContFrac<T> &rhs) const {return rhs.reciprocal() * *this;};
//relational operators, relying that operator- yields a form with a positive denominator
bool operator==(const Rational &rhs) const {Rational t= *this-rhs; return t.num==0;};
bool operator!=(const Rational &rhs) const {Rational t= *this-rhs; return t.num!=0;};
bool operator>=(const Rational &rhs) const {Rational t= *this-rhs; return t.num>=0;};
bool operator<=(const Rational &rhs) const {Rational t= *this-rhs; return t.num<=0;};
bool operator>(const Rational &rhs) const {Rational t= *this-rhs; return t.num>0;};
bool operator<(const Rational &rhs) const {Rational t= *this-rhs; return t.num<0;};
};
template <typename T>
@@ -96,7 +109,6 @@ class BiHomographic;
//@@@operator== > >= etc.
template <typename T>
class ContFrac : public NRVec<T> {
private:
@@ -106,16 +118,17 @@ 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
explicit ContFrac(double x, const int n, const T thres=0); //WARNING: it 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) {};
ContFrac(T p, T q); //should yield a canonical form
explicit 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; //we could make also a template usable with an arbitrary-precision type
ContFrac reciprocal() const;
ContFrac operator-() const; //unary minus
int length() const {return NRVec<T>::size()-1;};
void resize(const int n, const bool preserve=true)
{
@@ -123,6 +136,7 @@ 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);};
@@ -142,6 +156,16 @@ public:
ContFrac operator*(const ContFrac &rhs) const {BiHomographic<T> h({{{0,0},{0,1}},{{1,0},{0,0}}}); return h.value(*this,rhs);};
ContFrac operator/(const ContFrac &rhs) const {BiHomographic<T> h({{{0,1},{0,0}},{{0,0},{1,0}}}); return h.value(*this,rhs);};
//relational operators, guaranteed only to work correctly for canonicalized CF!
T compare(const ContFrac &rhs) const;
bool operator==(const ContFrac &rhs) const {return compare(rhs)==0;};
bool operator>(const ContFrac &rhs) const {return compare(rhs)>0;};
bool operator<(const ContFrac &rhs) const {return rhs.operator>(*this);};
bool operator!=(const ContFrac &rhs) const {return ! this->operator==(rhs) ;}
bool operator<=(const ContFrac &rhs) const {return ! this->operator>(rhs) ;}
bool operator>=(const ContFrac &rhs) const {return ! this->operator<(rhs) ;}
//iterator
class iterator {
private:
@@ -176,7 +200,7 @@ T v[2][2]; //{{a,b},{c,d}} for (a+b.x)/(c+d.x) i.e. [denominator][power_x]
Homographic input(const T &x, const bool inf) const;
Homographic output(const T &x) const;
bool outputready(T &x) const;
bool outputready(T &x, bool first) const;
bool terminate() const;
};
@@ -195,7 +219,7 @@ T v[2][2][2]; //{{{a,b},{c,d}},{{e,f},{g,h}}} i.e.[denominator][power_y][power_
BiHomographic inputy(const T &y, const bool inf) const;
BiHomographic output(const T &z) const;
int inputselect() const;
bool outputready(T &x) const;
bool outputready(T &x,bool first) const;
bool terminate() const;
};