lzz_pex.h

数值算法库for Windows

inline zz_pEX operator+(long a, const zz_pEX& b)
   { zz_pEX x; add(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }


inline zz_pEX operator-(const zz_pEX& a, const zz_pEX& b)
   { zz_pEX x; sub(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX operator-(const zz_pEX& a, const zz_pE& b)
   { zz_pEX x; sub(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX operator-(const zz_pEX& a, const zz_p& b)
   { zz_pEX x; sub(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX operator-(const zz_pEX& a, long b)
   { zz_pEX x; sub(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX operator-(const zz_pE& a, const zz_pEX& b)
   { zz_pEX x; sub(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX operator-(const zz_p& a, const zz_pEX& b)
   { zz_pEX x; sub(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX operator-(long a, const zz_pEX& b)
   { zz_pEX x; sub(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }


inline zz_pEX& operator+=(zz_pEX& x, const zz_pEX& b)
   { add(x, x, b); return x; }

inline zz_pEX& operator+=(zz_pEX& x, const zz_pE& b)
   { add(x, x, b); return x; }

inline zz_pEX& operator+=(zz_pEX& x, const zz_p& b)
   { add(x, x, b); return x; }

inline zz_pEX& operator+=(zz_pEX& x, long b)
   { add(x, x, b); return x; }

inline zz_pEX& operator-=(zz_pEX& x, const zz_pEX& b)
   { sub(x, x, b); return x; }

inline zz_pEX& operator-=(zz_pEX& x, const zz_pE& b)
   { sub(x, x, b); return x; }

inline zz_pEX& operator-=(zz_pEX& x, const zz_p& b)
   { sub(x, x, b); return x; }

inline zz_pEX& operator-=(zz_pEX& x, long b)
   { sub(x, x, b); return x; }


inline zz_pEX operator-(const zz_pEX& a) 
   { zz_pEX x; negate(x, a); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX& operator++(zz_pEX& x) { add(x, x, 1); return x; }
inline void operator++(zz_pEX& x, int) { add(x, x, 1); }
inline zz_pEX& operator--(zz_pEX& x) { sub(x, x, 1); return x; }
inline void operator--(zz_pEX& x, int) { sub(x, x, 1); }



/*****************************************************************

                        Multiplication

******************************************************************/


void mul(zz_pEX& x, const zz_pEX& a, const zz_pEX& b);
// x = a * b

void sqr(zz_pEX& x, const zz_pEX& a);
inline zz_pEX sqr(const zz_pEX& a) 
   { zz_pEX x; sqr(x, a); NTL_OPT_RETURN(zz_pEX, x); }
// x = a^2


void mul(zz_pEX & x, const zz_pEX& a, long b); 
void mul(zz_pEX & x, const zz_pEX& a, const zz_p& b); 
void mul(zz_pEX & x, const zz_pEX& a, const zz_pE& b); 

inline void mul(zz_pEX& x, long a, const zz_pEX& b)
   { mul(x, b, a); }
inline void mul(zz_pEX& x, const zz_p& a, const zz_pEX& b)
   { mul(x, b, a); }
inline void mul(zz_pEX& x, const zz_pE& a, const zz_pEX& b)
   { mul(x, b, a); }

void MulTrunc(zz_pEX& x, const zz_pEX& a, const zz_pEX& b, long n);
inline zz_pEX MulTrunc(const zz_pEX& a, const zz_pEX& b, long n)
   { zz_pEX x; MulTrunc(x, a, b, n); NTL_OPT_RETURN(zz_pEX, x); }
// x = a * b % X^n

void SqrTrunc(zz_pEX& x, const zz_pEX& a, long n);
inline zz_pEX SqrTrunc(const zz_pEX& a, long n)
   { zz_pEX x; SqrTrunc(x, a, n); NTL_OPT_RETURN(zz_pEX, x); }
// x = a*a % X^n


inline zz_pEX operator*(const zz_pEX& a, const zz_pEX& b)
   { zz_pEX x; mul(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX operator*(const zz_pEX& a, const zz_pE& b)
   { zz_pEX x; mul(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX operator*(const zz_pEX& a, const zz_p& b)
   { zz_pEX x; mul(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX operator*(const zz_pEX& a, long b)
   { zz_pEX x; mul(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX operator*(const zz_pE& a, const zz_pEX& b)
   { zz_pEX x; mul(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX operator*(const zz_p& a, const zz_pEX& b)
   { zz_pEX x; mul(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX operator*(long a, const zz_pEX& b)
   { zz_pEX x; mul(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX& operator*=(zz_pEX& x, const zz_pEX& b)
   { mul(x, x, b); return x; }

inline zz_pEX& operator*=(zz_pEX& x, const zz_pE& b)
   { mul(x, x, b); return x; }

inline zz_pEX& operator*=(zz_pEX& x, const zz_p& b)
   { mul(x, x, b); return x; }

inline zz_pEX& operator*=(zz_pEX& x, long b)
   { mul(x, x, b); return x; }


void power(zz_pEX& x, const zz_pEX& a, long e);
inline zz_pEX power(const zz_pEX& a, long e)
   { zz_pEX x; power(x, a, e); NTL_OPT_RETURN(zz_pEX, x); }





/*************************************************************

                      Division

**************************************************************/

void DivRem(zz_pEX& q, zz_pEX& r, const zz_pEX& a, const zz_pEX& b);
// q = a/b, r = a%b

void div(zz_pEX& q, const zz_pEX& a, const zz_pEX& b);
void div(zz_pEX& q, const zz_pEX& a, const zz_pE& b);
void div(zz_pEX& q, const zz_pEX& a, const zz_p& b);
void div(zz_pEX& q, const zz_pEX& a, long b);
// q = a/b

void rem(zz_pEX& r, const zz_pEX& a, const zz_pEX& b);
// r = a%b

long divide(zz_pEX& q, const zz_pEX& a, const zz_pEX& b);
// if b | a, sets q = a/b and returns 1; otherwise returns 0

long divide(const zz_pEX& a, const zz_pEX& b);
// if b | a, sets q = a/b and returns 1; otherwise returns 0

void InvTrunc(zz_pEX& x, const zz_pEX& a, long m);
inline zz_pEX InvTrunc(const zz_pEX& a, long m)
   { zz_pEX x; InvTrunc(x, a, m); NTL_OPT_RETURN(zz_pEX, x); }
// computes x = a^{-1} % X^m 
// constant term must be invertible


inline zz_pEX operator/(const zz_pEX& a, const zz_pEX& b)
   { zz_pEX x; div(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX operator/(const zz_pEX& a, const zz_pE& b)
   { zz_pEX x; div(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX operator/(const zz_pEX& a, const zz_p& b)
   { zz_pEX x; div(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX operator/(const zz_pEX& a, long b)
   { zz_pEX x; div(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX& operator/=(zz_pEX& x, const zz_pEX& b)
   { div(x, x, b); return x; }

inline zz_pEX& operator/=(zz_pEX& x, const zz_pE& b)
   { div(x, x, b); return x; }

inline zz_pEX& operator/=(zz_pEX& x, const zz_p& b)
   { div(x, x, b); return x; }

inline zz_pEX& operator/=(zz_pEX& x, long b)
   { div(x, x, b); return x; }


inline zz_pEX operator%(const zz_pEX& a, const zz_pEX& b)
   { zz_pEX x; rem(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX& operator%=(zz_pEX& x, const zz_pEX& b)
   { rem(x, x, b); return x; }



/***********************************************************

                         GCD's

************************************************************/


void GCD(zz_pEX& x, const zz_pEX& a, const zz_pEX& b);
inline zz_pEX GCD(const zz_pEX& a, const zz_pEX& b)
   { zz_pEX x; GCD(x, a, b); NTL_OPT_RETURN(zz_pEX, x); }
// x = GCD(a, b),  x is always monic (or zero if a==b==0).

void XGCD(zz_pEX& d, zz_pEX& s, zz_pEX& t, const zz_pEX& a, const zz_pEX& b);
// d = gcd(a,b), a s + b t = d 


/*************************************************************

             Modular Arithmetic without pre-conditioning

**************************************************************/

// arithmetic mod f.
// all inputs and outputs are polynomials of degree less than deg(f).
// ASSUMPTION: f is assumed monic, and deg(f) > 0.
// NOTE: if you want to do many computations with a fixed f,
//       use the zz_pEXModulus data structure and associated routines below.



void MulMod(zz_pEX& x, const zz_pEX& a, const zz_pEX& b, const zz_pEX& f);
inline zz_pEX MulMod(const zz_pEX& a, const zz_pEX& b, const zz_pEX& f)
   { zz_pEX x; MulMod(x, a, b, f); NTL_OPT_RETURN(zz_pEX, x); }
// x = (a * b) % f

void SqrMod(zz_pEX& x, const zz_pEX& a, const zz_pEX& f);
inline zz_pEX SqrMod(const zz_pEX& a, const zz_pEX& f)
   { zz_pEX x; SqrMod(x, a, f); NTL_OPT_RETURN(zz_pEX, x); }
// x = a^2 % f

void MulByXMod(zz_pEX& x, const zz_pEX& a, const zz_pEX& f);
inline zz_pEX MulByXMod(const zz_pEX& a, const zz_pEX& f)
   { zz_pEX x; MulByXMod(x, a, f); NTL_OPT_RETURN(zz_pEX, x); }
// x = (a * X) mod f

void InvMod(zz_pEX& x, const zz_pEX& a, const zz_pEX& f);
inline zz_pEX InvMod(const zz_pEX& a, const zz_pEX& f)
   { zz_pEX x; InvMod(x, a, f); NTL_OPT_RETURN(zz_pEX, x); }
// x = a^{-1} % f, error is a is not invertible

long InvModStatus(zz_pEX& x, const zz_pEX& a, const zz_pEX& f);
// if (a, f) = 1, returns 0 and sets x = a^{-1} % f
// otherwise, returns 1 and sets x = (a, f)





/******************************************************************

        Modular Arithmetic with Pre-conditioning

*******************************************************************/


// If you need to do a lot of arithmetic modulo a fixed f,
// build zz_pEXModulus F for f.  This pre-computes information about f
// that speeds up the computation a great deal.

class zz_pEXModulus {
public:
   zz_pEXModulus();
   ~zz_pEXModulus();

   zz_pEXModulus(const zz_pEX& ff);

   zz_pEX f;   // the modulus

   operator const zz_pEX& () const { return f; }
   const zz_pEX& val() const { return f; }

   long n; //  deg(f)

   long method;

   zz_pEX h0;
   zz_pE hlc;
   zz_pEX f0;

   vec_zz_pE tracevec; // mutable

}; 



inline long deg(const zz_pEXModulus& F) { return F.n; }


void build(zz_pEXModulus& F, const zz_pEX& f);

void rem(zz_pEX& r, const zz_pEX& a, const zz_pEXModulus& F);
   
void DivRem(zz_pEX& q, zz_pEX& r, const zz_pEX& a, const zz_pEXModulus& F);

void div(zz_pEX& q, const zz_pEX& a, const zz_pEXModulus& F);

void MulMod(zz_pEX& c, const zz_pEX& a, const zz_pEX& b, 
            const zz_pEXModulus& F);
inline zz_pEX MulMod(const zz_pEX& a, const zz_pEX& b, 
            const zz_pEXModulus& F)
   { zz_pEX x; MulMod(x, a, b, F); NTL_OPT_RETURN(zz_pEX, x); }

void SqrMod(zz_pEX& c, const zz_pEX& a, const zz_pEXModulus& F);
inline zz_pEX SqrMod(const zz_pEX& a, const zz_pEXModulus& F)
   { zz_pEX x; SqrMod(x, a, F); NTL_OPT_RETURN(zz_pEX, x); }


void PowerMod(zz_pEX& h, const zz_pEX& g, const ZZ& e, const zz_pEXModulus& F);

inline void PowerMod(zz_pEX& h, const zz_pEX& g, long e, 
                     const zz_pEXModulus& F)
   { PowerMod(h, g, ZZ_expo(e), F); }

inline zz_pEX PowerMod(const zz_pEX& g, const ZZ& e, 
                             const zz_pEXModulus& F)
   { zz_pEX x; PowerMod(x, g, e, F);  NTL_OPT_RETURN(zz_pEX, x); }

inline zz_pEX PowerMod(const zz_pEX& g, long e, const zz_pEXModulus& F)
   { zz_pEX x; PowerMod(x, g, e, F);  NTL_OPT_RETURN(zz_pEX, x); }

void PowerXMod(zz_pEX& hh, const ZZ& e, const zz_pEXModulus& F);