def twofilter_smoothing(self, t, info, phi, loggamma, linear_cost=False,
                            return_ess=False, modif_forward=None,
                            modif_info=None):
        """Two-filter smoothing.

        Parameters
        ----------
        t: time, in range 0 <= t < T-1
        info: SMC object 
            the information filter
        phi: function
            test function, a function of (X_t,X_{t+1})
        loggamma: function
            a function of (X_{t+1})
        linear_cost: bool
            if True, use the O(N) variant (basic version is O(N^2))

        Returns
        -------
        Two-filter estimate of the smoothing expectation of phi(X_t,x_{t+1})
        """
        ti = self.T - 2 - t  # t+1 in reverse
        if t < 0 or t >= self.T - 1:
            raise ValueError(
                'two-filter smoothing: t must be in range 0,...,T-2')
        lwinfo = info.hist.wgt[ti].lw - loggamma(info.hist.X[ti])
        if linear_cost:
            return self._twofilter_smoothing_ON(t, ti, info, phi, lwinfo,
                                               return_ess,
                                               modif_forward, modif_info)
        else:
            return self._twofilter_smoothing_ON2(t, ti, info, phi, lwinfo)