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// When MPFR is enabled and double is passed to a templated function
// The function should use precise(ttype) to make sure calculations run
// within the more precise type
#define precise(T) typename precise<T>::precise_type
template<class T> struct precise { typedef T precise_type; };
template<> struct precise<double> { typedef Double precise_type; };
template<> struct precise<complex<double> > { typedef Complex precise_type; };
#ifdef USE_MPFR
template<> struct precise<long long> { typedef double precise_type; };
#else
template<> struct precise<long long> { typedef long long precise_type; };
#endif
//typedef precise<long long>::precise_type Long;
typedef long long Long;
// To aid conversion to int value
inline double lcalc_to_double(const Double& x) {
#ifdef USE_MPFR
return x.get_d();
#else
return x;
#endif
}
#ifdef USE_MPFR
inline double lcalc_to_double(const double& x) { return x; }
#endif
//inline double lcalc_to_double(const long double& x) { return x; }
//inline double lcalc_to_double(const int& x) { return x; }
//inline double lcalc_to_double(const long long& x) { return x; }
//inline double lcalc_to_double(const short& x) { return x; }
//inline double lcalc_to_double(const char& x) { return x; }
//inline double lcalc_to_double(const long int& x) { return x; }
//inline double lcalc_to_double(const unsigned int& x) { return x; }
//inline double lcalc_to_double(const long unsigned int& x) { return x; }
#define Int(x) (int)(lcalc_to_double(x))
#define Long(x) (Long)(lcalc_to_double(x))
#define double(x) (double)(lcalc_to_double(x))
template<class T> inline int sn(T x)
{
if (x>=0) return 1;
else return -1;
}
const bool outputSeries=true; // Whether to output the coefficients or just the answer
// Loop i from m to n
// Useful in tidying up most for loops
#define loop(i,m,n) for(auto i=(m); i!=(n); i++)
// A class for calculations involving polynomials of small degree
// Not efficient enough for huge polynomials
//
// Polynomial of fixed degree N-1 with coefficients over T
template<class T=Complex> struct smallPoly {
valarray<T> coeffs;
typedef smallPoly<T> poly;
int N;
T zero;
smallPoly(int N=0) {
this->N=N;
coeffs.resize(N);
zero=0;
}
void resize(int N) {
coeffs.resize(N);
loop(i,this->N,N)
coeffs[i]=zero;
this->N=N;
}
// Access a coefficient as a subscript
T& operator[](int n) {
return (n<0 ? zero : coeffs[n]);
}
const T& operator[](int n) const {
return (n<0 ? zero : coeffs[n]);
}
// Multiply two polys together, truncating the result
friend poly operator*(const poly& f, const poly& g) {
poly result(max(f.N,g.N));
loop(i,0,f.N) result[i]=0;
double test;
loop(i,0,f.N) loop(j,0,result.N-i) {
result[i+j]+=f[i]*g[j];
}
return result;
}
// Divide (in place) by (x-1/a) = (1-ax)/(-a) with a!=0
void divideSpecial(T a) {
loop(i,1,N) coeffs[i]+=coeffs[i-1]*a;
coeffs*= -a;
}
// Evaluate the polynomial at x
template<class U> U operator()(U x) {
U sum=coeffs[0];
U cur=1;
loop(i,1,N) {
cur*=x;
sum+=coeffs[i]*x;
}
return sum;
}
// Output to stdout
friend ostream& operator<<(ostream& s, const poly p) {
loop(i,0,p.N) s << (i ? " + " : "") << p[i] << "x^" << i;
return s;
}
// Arithmetic
template<class U> poly& operator*=(const U& x) {
coeffs*=x;
return *this;
}
template<class U> poly& operator/=(const U& x) {
coeffs/=x;
return *this;
}
};
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