static void balance_companion_matrix (double *m, size_t n);

#define RADIX 2
#define RADIX2 (RADIX*RADIX)

static void
balance_companion_matrix (double *m, size_t nc)
{
  int not_converged = 1;

  double row_norm = 0;
  double col_norm = 0;

  while (not_converged)
    {
      size_t i, j;
      double g, f, s;

      not_converged = 0;

      for (i = 0; i < nc; i++)
	{
	  /* column norm, excluding the diagonal */

	  if (i != nc - 1)
	    {
	      col_norm = fabs (MAT (m, i + 1, i, nc));
	    }
	  else
	    {
	      col_norm = 0;

	      for (j = 0; j < nc - 1; j++)
		{
		  col_norm += fabs (MAT (m, j, nc - 1, nc));
		}
	    }

	  /* row norm, excluding the diagonal */

	  if (i == 0)
	    {
	      row_norm = fabs (MAT (m, 0, nc - 1, nc));
	    }
	  else if (i == nc - 1)
	    {
	      row_norm = fabs (MAT (m, i, i - 1, nc));
	    }
	  else
	    {
	      row_norm = (fabs (MAT (m, i, i - 1, nc)) 
                          + fabs (MAT (m, i, nc - 1, nc)));
	    }

	  if (col_norm == 0 || row_norm == 0)
	    {
	      continue;
	    }

	  g = row_norm / RADIX;
	  f = 1;
	  s = col_norm + row_norm;

	  while (col_norm < g)
	    {
	      f *= RADIX;
	      col_norm *= RADIX2;
	    }

	  g = row_norm * RADIX;

	  while (col_norm > g)
	    {
	      f /= RADIX;
	      col_norm /= RADIX2;
	    }

	  if ((row_norm + col_norm) < 0.95 * s * f)
	    {
	      not_converged = 1;

	      g = 1 / f;

	      if (i == 0)
		{
		  MAT (m, 0, nc - 1, nc) *= g;
		}
	      else
		{
		  MAT (m, i, i - 1, nc) *= g;
		  MAT (m, i, nc - 1, nc) *= g;
		}

	      if (i == nc - 1)
		{
		  for (j = 0; j < nc; j++)
		    {
		      MAT (m, j, i, nc) *= f;
		    }
		}
	      else
		{
		  MAT (m, i + 1, i, nc) *= f;
		}
	    }
	}
    }
}