5 * A really shoddy implementation of Rational numbers
17 template <class T> T Tabs(const T & a)
21 template <> Arbint Tabs(const Arbint & a);
22 template <> Gmpint Tabs(const Gmpint & a);
24 /* Recursive version of GCD
26 T gcd(const T & a, const T & b)
28 Debug("Called on %li/%li", int64_t(a), int64_t(b));
29 if (a == T(1) || a == T(0)) return T(1);
30 if (b == T(0)) return a;
38 if (a > b) return gcd(a-b,b);
43 /** Greatest Common Divisor of p and q **/
45 T gcd(const T & p, const T & q)
59 while ((g = big % small) > T(0))
61 //Debug("big = %li, small = %li", int64_t(big), int64_t(small));
64 //Debug("Loop %u", ++count);
70 template <class T = int64_t>
73 /** Construct from a double.**/
74 Rational(double d=0) : P(d*1e6), Q(1e6) // Possibly the worst thing ever...
79 Rational(const T & _P, const T & _Q) : P(_P), Q(_Q)
84 Rational(const Rational & cpy) : P(cpy.P), Q(cpy.Q)
106 T g = gcd(Tabs(P), Tabs(Q));
112 bool operator==(const Rational & r) const
114 if (P == r.P && Q == r.Q) return true;
115 return ToDouble() == r.ToDouble();
119 bool operator<(const Rational & r) const {return (P*r.Q < r.P * Q);}
120 bool operator>(const Rational & r) const {return !(*this < r);}
121 bool operator<=(const Rational & r) const {return *this == r || *this < r;}
122 bool operator>=(const Rational & r) const {return *this == r || *this > r;}
123 bool operator!=(const Rational & r) const {return !(*this == r);}
125 Rational operator+(const Rational & r) const
127 Rational result = (r.P == T(0)) ? Rational(P,Q) : Rational(P*r.Q + r.P*Q, Q*r.Q);
128 //if (!result.CheckAccuracy(ToDouble() * r.ToDouble(),"+"))
130 // Debug("This is %s (%f) and r is %s (%f)", Str().c_str(), ToDouble(), r.Str().c_str(), r.ToDouble());
134 Rational operator-(const Rational & r) const
136 Rational result = (r.P == T(0)) ? Rational(P,Q) : Rational(P*r.Q - r.P*Q, Q*r.Q);
137 //result.CheckAccuracy(ToDouble() - r.ToDouble(),"-");
140 Rational operator*(const Rational & r) const
142 Rational result(P * r.P, Q * r.Q);
143 //if (!result.CheckAccuracy(ToDouble() * r.ToDouble(),"*"))
145 // Debug("This is %s (%f) and r is %s (%f)", Str().c_str(), ToDouble(), r.Str().c_str(), r.ToDouble());
149 Rational operator/(const Rational & r) const
151 Rational result(P * r.Q, Q*r.P);
152 //if (!result.CheckAccuracy(ToDouble() / r.ToDouble(),"/"))
154 // Debug("This is %s (%f) and r is %s (%f)", Str().c_str(), ToDouble(), r.Str().c_str(), r.ToDouble());
159 /** To cheat, use these **/
160 //Rational operator+(const Rational & r) const {return Rational(ToDouble()+r.ToDouble());}
161 //Rational operator-(const Rational & r) const {return Rational(ToDouble()-r.ToDouble());}
162 //Rational operator*(const Rational & r) const {return Rational(ToDouble()*r.ToDouble());}
163 //Rational operator/(const Rational & r) const {return Rational(ToDouble()/r.ToDouble());}
165 Rational operator-() const {Rational r(*this); r.P = -r.P;}
166 Rational & operator=(const Rational & r) {P = r.P; Q = r.Q; Simplify(); return *this;}
167 Rational & operator+=(const Rational & r) {this->operator=(*this+r); return *this;}
168 Rational & operator-=(const Rational & r) {this->operator=(*this-r); return *this;}
169 Rational & operator*=(const Rational & r) {this->operator=(*this*r); return *this;}
170 Rational & operator/=(const Rational & r) {this->operator=(*this/r); return *this;}
172 double ToDouble() const
174 return (double)P/(double)Q;
176 bool CheckAccuracy(double d, const char * msg, double threshold = 1e-3) const
178 double result = fabs(ToDouble() - d);
179 if (d != 0e0) result /= d;
180 if (result > threshold)
182 Warn("(%s) : Rational %s (%f) is not close enough at representing %f (%f vs %f)", msg, Str().c_str(), ToDouble(), d, result, threshold);
188 std::string Str() const
191 s << int64_t(P) << "/" << int64_t(Q);