Thanks for this reference; some readers might enjoy the experiment:
(%i33) fpprec : 20$
(%i34) l : makelist((-75)^k/k!,k,0,500)$
(%i35) bfloat(tree_reduce("+", map(lambda([s],
rationalize(bfloat(s))),l)));
(%o35) -5.3399030854116552833b10
(%i36) bfloat(tree_reduce("+", l));
(%o36) 2.6786369618080779443b-33
The reason (%o35) and (%o36) aren't close isn't subtractive
cancellation--the sum was done using rational arithmetic. The
problem is that the sum is ill-conditioned.
Barton
-----maxima-bounces at math.utexas.edu wrote: -----
>There is a brief summary of some of the many proposed ways of accurate
>summation here:
>
>http://hpcrd.lbl.gov/SCG/ocean/NRS/ECMWF/img11.htm
>