Tree-lookup for partial sums or: how can I find this stuff quickly?

Suppose that you need to maintain a large list of data that is to be searched and modified frequently in the course of a computation. You can almost always arrange for both operations to be done efficiently by storing the data in a structure other than a single array. Although there are several elegant ways to do this, we present just one: a simple tree that doesn´t require a lot of thinking to implement. It can speed up execution tremendously because instead of searching through a list item after item for each update, possibly examining n items, you need only examine O(log n) items per operation. (More advanced methods can reduce this to log*n at the cost of more complex programming. Here, log*n is the number of iterations of log₂ that are required to get below 1. For numbers having less than 65K bits, log* is less than 5.)