  This paper provides an introduction to the design of augmented data
structures that offer an efficient representation of a mathematical sequence
and fast sequential summation algorithms, which guarantee both logarithmic
running time and logarithmic computational cost in terms of the total number of
operations. In parallel summation algorithms, logarithmic running time is
achieved by high linear computational cost with a linear number of processors.
The important practical advantage of the fast sequential summation algorithms
is that they do not require supercomputers and can run on the cheapest single
processor systems.
