// Test for boost.polynomial

#include <iostream>

#include <boost/operators.hpp>
#include <boost/polynomial.hpp>

typedef unsigned char BYTE;

namespace
{
// The binary Galois field for the range of the code is generated by
// the following generator polynomial;
//    x^8 + x^4 + x^3 + x^2 + 1
static BYTE m_to_a[255] = { 0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80,
                            0x1d, 0x3a, 0x74, 0xe8, 0xcd, 0x87, 0x13, 0x26,
                            0x4c, 0x98, 0x2d, 0x5a, 0xb4, 0x75, 0xea, 0xc9,
                            0x8f, 0x03, 0x06, 0x0c, 0x18, 0x30, 0x60, 0xc0,
                            0x9d, 0x27, 0x4e, 0x9c, 0x25, 0x4a, 0x94, 0x35,
                            0x6a, 0xd4, 0xb5, 0x77, 0xee, 0xc1, 0x9f, 0x23,
                            0x46, 0x8c, 0x05, 0x0a, 0x14, 0x28, 0x50, 0xa0,
                            0x5d, 0xba, 0x69, 0xd2, 0xb9, 0x6f, 0xde, 0xa1,
                            0x5f, 0xbe, 0x61, 0xc2, 0x99, 0x2f, 0x5e, 0xbc,
                            0x65, 0xca, 0x89, 0x0f, 0x1e, 0x3c, 0x78, 0xf0,
                            0xfd, 0xe7, 0xd3, 0xbb, 0x6b, 0xd6, 0xb1, 0x7f,
                            0xfe, 0xe1, 0xdf, 0xa3, 0x5b, 0xb6, 0x71, 0xe2,
                            0xd9, 0xaf, 0x43, 0x86, 0x11, 0x22, 0x44, 0x88,
                            0x0d, 0x1a, 0x34, 0x68, 0xd0, 0xbd, 0x67, 0xce,
                            0x81, 0x1f, 0x3e, 0x7c, 0xf8, 0xed, 0xc7, 0x93,
                            0x3b, 0x76, 0xec, 0xc5, 0x97, 0x33, 0x66, 0xcc,
                            0x85, 0x17, 0x2e, 0x5c, 0xb8, 0x6d, 0xda, 0xa9,
                            0x4f, 0x9e, 0x21, 0x42, 0x84, 0x15, 0x2a, 0x54,
                            0xa8, 0x4d, 0x9a, 0x29, 0x52, 0xa4, 0x55, 0xaa,
                            0x49, 0x92, 0x39, 0x72, 0xe4, 0xd5, 0xb7, 0x73,
                            0xe6, 0xd1, 0xbf, 0x63, 0xc6, 0x91, 0x3f, 0x7e,
                            0xfc, 0xe5, 0xd7, 0xb3, 0x7b, 0xf6, 0xf1, 0xff,
                            0xe3, 0xdb, 0xab, 0x4b, 0x96, 0x31, 0x62, 0xc4,
                            0x95, 0x37, 0x6e, 0xdc, 0xa5, 0x57, 0xae, 0x41,
                            0x82, 0x19, 0x32, 0x64, 0xc8, 0x8d, 0x07, 0x0e,
                            0x1c, 0x38, 0x70, 0xe0, 0xdd, 0xa7, 0x53, 0xa6,
                            0x51, 0xa2, 0x59, 0xb2, 0x79, 0xf2, 0xf9, 0xef,
                            0xc3, 0x9b, 0x2b, 0x56, 0xac, 0x45, 0x8a, 0x09,
                            0x12, 0x24, 0x48, 0x90, 0x3d, 0x7a, 0xf4, 0xf5,
                            0xf7, 0xf3, 0xfb, 0xeb, 0xcb, 0x8b, 0x0b, 0x16,
                            0x2c, 0x58, 0xb0, 0x7d, 0xfa, 0xe9, 0xcf, 0x83,
                            0x1b, 0x36, 0x6c, 0xd8, 0xad, 0x47, 0x8e };
static BYTE a_to_m[256] = { 0x00, 0x00, 0x01, 0x19, 0x02, 0x32, 0x1a, 0xc6,
                            0x03, 0xdf, 0x33, 0xee, 0x1b, 0x68, 0xc7, 0x4b,
                            0x04, 0x64, 0xe0, 0x0e, 0x34, 0x8d, 0xef, 0x81,
                            0x1c, 0xc1, 0x69, 0xf8, 0xc8, 0x08, 0x4c, 0x71,
                            0x05, 0x8a, 0x65, 0x2f, 0xe1, 0x24, 0x0f, 0x21,
                            0x35, 0x93, 0x8e, 0xda, 0xf0, 0x12, 0x82, 0x45,
                            0x1d, 0xb5, 0xc2, 0x7d, 0x6a, 0x27, 0xf9, 0xb9,
                            0xc9, 0x9a, 0x09, 0x78, 0x4d, 0xe4, 0x72, 0xa6,
                            0x06, 0xbf, 0x8b, 0x62, 0x66, 0xdd, 0x30, 0xfd,
                            0xe2, 0x98, 0x25, 0xb3, 0x10, 0x91, 0x22, 0x88,
                            0x36, 0xd0, 0x94, 0xce, 0x8f, 0x96, 0xdb, 0xbd,
                            0xf1, 0xd2, 0x13, 0x5c, 0x83, 0x38, 0x46, 0x40,
                            0x1e, 0x42, 0xb6, 0xa3, 0xc3, 0x48, 0x7e, 0x6e,
                            0x6b, 0x3a, 0x28, 0x54, 0xfa, 0x85, 0xba, 0x3d,
                            0xca, 0x5e, 0x9b, 0x9f, 0x0a, 0x15, 0x79, 0x2b,
                            0x4e, 0xd4, 0xe5, 0xac, 0x73, 0xf3, 0xa7, 0x57,
                            0x07, 0x70, 0xc0, 0xf7, 0x8c, 0x80, 0x63, 0x0d,
                            0x67, 0x4a, 0xde, 0xed, 0x31, 0xc5, 0xfe, 0x18,
                            0xe3, 0xa5, 0x99, 0x77, 0x26, 0xb8, 0xb4, 0x7c,
                            0x11, 0x44, 0x92, 0xd9, 0x23, 0x20, 0x89, 0x2e,
                            0x37, 0x3f, 0xd1, 0x5b, 0x95, 0xbc, 0xcf, 0xcd,
                            0x90, 0x87, 0x97, 0xb2, 0xdc, 0xfc, 0xbe, 0x61,
                            0xf2, 0x56, 0xd3, 0xab, 0x14, 0x2a, 0x5d, 0x9e,
                            0x84, 0x3c, 0x39, 0x53, 0x47, 0x6d, 0x41, 0xa2,
                            0x1f, 0x2d, 0x43, 0xd8, 0xb7, 0x7b, 0xa4, 0x76,
                            0xc4, 0x17, 0x49, 0xec, 0x7f, 0x0c, 0x6f, 0xf6,
                            0x6c, 0xa1, 0x3b, 0x52, 0x29, 0x9d, 0x55, 0xaa,
                            0xfb, 0x60, 0x86, 0xb1, 0xbb, 0xcc, 0x3e, 0x5a,
                            0xcb, 0x59, 0x5f, 0xb0, 0x9c, 0xa9, 0xa0, 0x51,
                            0x0b, 0xf5, 0x16, 0xeb, 0x7a, 0x75, 0x2c, 0xd7,
                            0x4f, 0xae, 0xd5, 0xe9, 0xe6, 0xe7, 0xad, 0xe8,
                            0x74, 0xd6, 0xf4, 0xea, 0xa8, 0x50, 0x58, 0xaf };

BYTE fieldMult( BYTE lhs, BYTE rhs )
{
  return ( lhs && rhs )?m_to_a[( a_to_m[lhs]+a_to_m[rhs] )%255]:( BYTE )0;
}

BYTE fieldInv( BYTE e )
{
  return ( e )?m_to_a[( 255-a_to_m[e] )%255]:( BYTE )0;
}

} // namespace

class FieldElem : boost::field_operators<FieldElem,
                                         boost::equality_comparable<FieldElem> >
{
public:
  FieldElem( BYTE b=0 ) : m( b ) {}
  // Compiler-generated copy constructor and assignment operator are fine

  FieldElem &operator+=( const FieldElem &rhs ) { m ^= rhs.m; return *this; }
  FieldElem &operator-=( const FieldElem &rhs ) { m ^= rhs.m; return *this; }
  FieldElem &operator*=( const FieldElem &rhs ) { m = fieldMult( m, rhs.m ); return *this; }
  FieldElem &operator/=( const FieldElem &rhs )
  {
    m = fieldMult( m, fieldInv( rhs.m ) ); return *this;
  }
  bool operator==( const FieldElem &rhs ) { return m == rhs.m; }

  unsigned int byte() const { return m; }

private:
  BYTE m;
};

std::ostream &operator<<( std::ostream &o, FieldElem m ) { o << m.byte(); return o; }

typedef boost::math::tools::polynomial<FieldElem> poly_t;

int main( int, char *[] )
{
  // Generator polynomial for RS code
  poly_t generator( FieldElem( 1 ) );

  {
    std::vector<FieldElem> coeffs;
    coeffs.push_back( 1 );
    coeffs.push_back( 1 );
    for ( int indx = 0; indx < 15; ++indx )
    {
      poly_t tmp( coeffs.begin(), coeffs.end() );
      generator *= tmp;
      coeffs[0] *= FieldElem( 0x02 );
    }
  }

  for ( unsigned indx = 0; indx <= generator.degree(); ++indx )
    std::cout << generator[indx] << " ";
  std::cout << std::endl;

  return 0;
}