I have made a new version of levin (www.bertold.org/levin)
Changes:
Faster for series with terms that take only rational values.
Since levin can now compute propagation of rounding errors it is possible
to sum series with terms that take non-rational values with
predetermined precision.
Example
fpprec:50;
bflevin_u_sum(1/n-log(1+1/n),n,1);
5.7721566490153286060651209008240243104215933593992b-1
bfloat(%-%gamma);
0.0b0
Note 0: To see the algorithm in action put
levin_options["debug"]:true;
Note 1: Summing series with terms that take non-rational values is
generally
slower than summing terms that take rational values.
Note 2: The code is not optimized yet. For now I was mainly aiming for
correctness.
Note 3: Levin seems to converge rather slowly for series with wildly
oscilating terms.
It is of course still better than summing the series naively.
Michel