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There are several data structures which can calculate the prefix sums of anarray efficiently, while handling point updates on the array, such as SegmentTrees and Binary Indexed Trees (BIT). Both these data structures can handle thethese two operations (query and update) in $O(\log{n})$ time. In this paper, wepresent a data structure similar to the BIT, but with an even smaller constant.To do this, we use Zeckendorf's Theorem, a property of the Fibonacci sequenceof numbers. The new data structure achieves the same complexity of$O(\log{n})$, but requires about $\log_{\phi^{2}} n$ computations for the QueryOperation as opposed to the $\log_{2} n$ computations required for a BIT QueryOperation in the worst case.

A Constant Optimization of the Binary Indexed Tree Query Operation