galoisfieldpolynomial.cpp

心电图小波零树压缩演算法的研究

      {
         poly.resize(0,GaloisFieldElement(gf,0));
      }
      return *this;
   }


   const GaloisFieldElement& GaloisFieldPolynomial::operator[](const unsigned int& term) const
   {
      assert(term < poly.size());
      return poly[term];
   }


   GaloisFieldElement& GaloisFieldPolynomial::operator[](const unsigned int& term)
   {
      assert(term < poly.size());
      return poly[term];
   }


   GaloisFieldElement GaloisFieldPolynomial::operator()(const GaloisFieldElement& value)
   {
      GaloisFieldElement result(gf,0);

      if (poly.size() > 0)
      {
         result = poly[poly.size() - 1];
         for(size_t i = poly.size() - 2; ((int)i) >= 0; i--)
         {
            result = poly[i] + (result * value);
         }
      }
      return result;
   }


   const GaloisFieldElement GaloisFieldPolynomial::operator()(const GaloisFieldElement& value) const
   {
      GaloisFieldElement result(gf,0);

      if (poly.size() > 0)
      {
         result = poly[poly.size() - 1];
         for(size_t i = poly.size() - 2; static_cast<int>(i) >= 0; i--)
         {
            result = poly[i] + (result * value);
         }
      }
      return result;
   }


   GaloisFieldElement GaloisFieldPolynomial::operator()(GFSymbol value)
   {
      return (*this)(GaloisFieldElement(gf,value));
   }


   const GaloisFieldElement GaloisFieldPolynomial::operator()(GFSymbol value) const
   {
      return (*this)(GaloisFieldElement(gf,value));
   }


   bool GaloisFieldPolynomial::operator==(const GaloisFieldPolynomial& polynomial) const
   {
      if (gf == polynomial.gf)
      {
         if (poly.size() != polynomial.poly.size())
           return false;
         else
         {
            for (unsigned int i = 0; i < poly.size(); i++)
            {
               if (poly[i] != polynomial.poly[i])
                 return false;
            }
            return true;
         }
      }
      else
        return false;
   }


   bool GaloisFieldPolynomial::operator!=(const GaloisFieldPolynomial& polynomial) const
   {
      return !(*this == polynomial);
   }


   GaloisFieldPolynomial GaloisFieldPolynomial::derivative()
   {
      if ((*this).poly.size() > 1)
      {
         GaloisFieldPolynomial deriv(gf,deg());
         for (unsigned int i = 0; i < poly.size() - 1; i++)
         {
            if (((i + 1) & 1) == 1)
              deriv.poly[i] = poly[i + 1];
            else
              deriv.poly[i] = 0;
         }
         simplify(deriv);
         return deriv;
      }
      return GaloisFieldPolynomial(gf,0);
   }


   void GaloisFieldPolynomial::simplify()
   {
      simplify(*this);
   }


   void GaloisFieldPolynomial::simplify(GaloisFieldPolynomial& polynomial)
   {
      if (poly.size() > 0)
      {
         size_t last = polynomial.poly.size() - 1;

         while((last >= 0) && (polynomial.poly.size() > 0))
         {
            if (polynomial.poly[last] == 0)
              polynomial.poly.pop_back();
            else
              break;

            last = polynomial.poly.size() - 1;
         }
      }
   }


   GaloisFieldPolynomial operator+(const GaloisFieldPolynomial& a, const GaloisFieldPolynomial& b)
   {
      GaloisFieldPolynomial result = a;
      result += b;
      return result;
   }


   GaloisFieldPolynomial operator + (const GaloisFieldPolynomial& a, const GaloisFieldElement& b)
   {
      GaloisFieldPolynomial result = a;
      result += b;
      return result;
   }


   GaloisFieldPolynomial operator + (const GaloisFieldElement& a, const GaloisFieldPolynomial& b)
   {
      GaloisFieldPolynomial result = b;
      result += a;
      return result;
   }


   GaloisFieldPolynomial operator + (const GaloisFieldPolynomial& a, const GFSymbol& b)
   {
      return a + GaloisFieldElement(a.field(),b);
   }


   GaloisFieldPolynomial operator + (const GFSymbol& a, const GaloisFieldPolynomial& b)
   {
      return b + GaloisFieldElement(b.field(),a);
   }


   GaloisFieldPolynomial operator - (const GaloisFieldPolynomial& a, const GaloisFieldPolynomial& b)
   {
      GaloisFieldPolynomial result = a;
      result -= b;
      return result;
   }

   GaloisFieldPolynomial operator - (const GaloisFieldPolynomial& a, const GaloisFieldElement& b)
   {
      GaloisFieldPolynomial result = a;
      result -= b;
      return result;
   }


   GaloisFieldPolynomial operator - (const GaloisFieldElement& a, const GaloisFieldPolynomial& b)
   {
      GaloisFieldPolynomial result = b;
      result -= a;
      return result;
   }


   GaloisFieldPolynomial operator - (const GaloisFieldPolynomial& a, const GFSymbol& b)
   {
      return a - GaloisFieldElement(a.field(),b);
   }


   GaloisFieldPolynomial operator - (const GFSymbol& a, const GaloisFieldPolynomial& b)
   {
      return b - GaloisFieldElement(b.field(),a);
   }


   GaloisFieldPolynomial operator * (const GaloisFieldPolynomial& a, const GaloisFieldPolynomial& b)
   {
      GaloisFieldPolynomial result = a;
      result *= b;
      return result;
   }


   GaloisFieldPolynomial operator * (const GaloisFieldElement& a, const GaloisFieldPolynomial& b)
   {
      GaloisFieldPolynomial result = b;
      result *= a;
      return result;
   }


   GaloisFieldPolynomial operator * (const GaloisFieldPolynomial& a, const GaloisFieldElement& b)
   {
      GaloisFieldPolynomial result = a;
      result *= b;
      return result;
   }

   GaloisFieldPolynomial operator / (const GaloisFieldPolynomial& a, const GaloisFieldPolynomial& b)
   {
      GaloisFieldPolynomial result = a;
      result /= b;
      return result;
   }


   GaloisFieldPolynomial operator / (const GaloisFieldPolynomial& a, const GaloisFieldElement& b)
   {
      GaloisFieldPolynomial result = a;
      result /= b;
      return result;
   }


   GaloisFieldPolynomial operator % (const GaloisFieldPolynomial& a, const GaloisFieldPolynomial& b)
   {
      GaloisFieldPolynomial result = a;
      result %= b;
      return result;
   }

   GaloisFieldPolynomial operator % (const GaloisFieldPolynomial& a, const unsigned int& power)
   {
      GaloisFieldPolynomial result = a;
      result %= power;
      return result;
   }

   GaloisFieldPolynomial operator ^ (const GaloisFieldPolynomial& a, const int& n)
   {
      GaloisFieldPolynomial result = a;
      result ^= n;
      return result;
   }


   GaloisFieldPolynomial operator<<(const GaloisFieldPolynomial& a, const unsigned int& n)
   {
      GaloisFieldPolynomial result = a;
      result <<= n;
      return result;
   }


   GaloisFieldPolynomial operator>>(const GaloisFieldPolynomial& a, const unsigned int& n)
   {
      GaloisFieldPolynomial result = a;
      result >>= n;
      return result;
   }


   GaloisFieldPolynomial gcd(const GaloisFieldPolynomial& a, const GaloisFieldPolynomial& b)
   {
      if ((*a.field()) == (*b.field()))
      {
         if ((!a.valid()) && (!b.valid())) return GaloisFieldPolynomial();
         if (!a.valid()) return b;
         if (!b.valid()) return a;

         GaloisFieldPolynomial x = a % b;
         GaloisFieldPolynomial y = b;
         GaloisFieldPolynomial z = x;

         while ((z = y % x).valid())
         {
            y = x;
            x = z;
         }
         return x;
      }
      else
        return GaloisFieldPolynomial();
   }


   std::ostream& operator << (std::ostream& os, const GaloisFieldPolynomial& polynomial)
   {

      if (polynomial.deg() >= 0)
      {
/*
         for (unsigned int i = 0; i < polynomial.poly.size(); i++)
         {
            os << polynomial.poly[i].index()
               << ((i != (polynomial.deg())) ? " " : "");
         }

         std::cout << " poly form: ";
*/
         for (unsigned int i = 0; i < polynomial.poly.size(); i++)
         {
            os << polynomial.poly[i].poly()
               << " "
               << "x^"
               << i
               << ((i != (polynomial.deg())) ? " + " : "");
         }
      }
      return os;
   }

}