  We state and analyze a generalization of the "truncation trick" suggested by
Gourdon and Sebah to improve the performance of power series evaluation by
binary splitting. It follows from our analysis that the values of D-finite
functions (i.e., functions described as solutions of linear differential
equations with polynomial coefficients) may be computed with error bounded by
2^(-p) in time O(p*(lg p)^(3+o(1))) and space O(p). The standard fast algorithm
for this task, due to Chudnovsky and Chudnovsky, achieves the same time
complexity bound but requires \Theta(p*lg p) bits of memory.
