static double

rat_eval (const double a[], const size_t na,

          const double b[], const size_t nb, const double x)

{

  size_t i, j;

  double u, v, r;

  u = a[na - 1];

  for (i = na - 1; i > 0; i--)

    {

      u = x * u + a[i - 1];

    }

  v = b[nb - 1];

  for (j = nb - 1; j > 0; j--)

    {

      v = x * v + b[j - 1];

    }

  r = u / v;

  return r;

}