#include <stdio.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_sum.h>

#define N 20

int

main (void)

{

  double t[N];

  double sum_accel, err;

  double sum = 0;

  int n;

  gsl_sum_levin_u_workspace * w 

    = gsl_sum_levin_u_alloc (N);

  const double zeta_2 = M_PI * M_PI / 6.0;

  /* terms for zeta(2) = \sum_{n=1}^{\infty} 1/n^2 */

  for (n = 0; n < N; n++)

    {

      double np1 = n + 1.0;

      t[n] = 1.0 / (np1 * np1);

      sum += t[n];

    }

  gsl_sum_levin_u_accel (t, N, w, &sum_accel, &err;;

  printf ("term-by-term sum = % .16f using %d terms\n", 

          sum, N);

  printf ("term-by-term sum = % .16f using %zu terms\n", 

          w->sum_plain, w->terms_used);

  printf ("exact value      = % .16f\n", zeta_2);

  printf ("accelerated sum  = % .16f using %zu terms\n", 

          sum_accel, w->terms_used);

  printf ("estimated error  = % .16f\n", err);

  printf ("actual error     = % .16f\n", 

          sum_accel - zeta_2);

  gsl_sum_levin_u_free (w);

  return 0;

}