Function SWAPI

IntegerProgramming/LLL.cc:97–131

void SWAPI(const short& k, const short& k_max, BigInt** b, BigInt* d,
           BigInt** lambda)
// the SWAPI procedure of algorithm 2.6.7
{

  // exchange b[k] and b[k-1]
  // This can be done efficiently by swapping pointers (not entries).
  BigInt* swap=b[k];
  b[k]=b[k-1];
  b[k-1]=swap;

  if(k>1)
    for(short j=0;j<=k-2;j++)
    {
      // exchange lambda[k][j] and lambda[k-1][j]
      BigInt swap=lambda[k][j];
      lambda[k][j]=lambda[k-1][j];
      lambda[k-1][j]=swap;
    }

  BigInt _lambda=lambda[k][k-1];

  BigInt B=(d[k-1]*d[k+1] + _lambda*_lambda)/d[k];
  // It might be better to choose another evaluation order for this formula,
  // see below.

  for(short i=k+1;i<=k_max;i++)
  {
    BigInt t=lambda[i][k];
    lambda[i][k]=(d[k+1]*lambda[i][k-1] - _lambda*t)/d[k];
    lambda[i][k-1]=(B*t + _lambda*lambda[i][k])/d[k+1];
  }

  d[k]=B;
}