Scaled Fenwick Trees

A novel data structure that enables the storage and retrieval of linear array numeric with logarithmic time complexity updates, range sums, rescaling is introduced studied. Computing sums ranges arrays numbers a common computational problem encountered in compression, coding, machine learning, vision, finance, among other fields. Efficient structures enabling log n updates underlying (including updates), queries over ranges, searches for given sum have been extensively studied (n being length array). Two solutions to this are well-known: Fenwick trees (also known as Binary Indexed Trees) Segment Trees. The new extends capabilities first further enable multiplying (rescaling) by scalar well n. Scaling 0 can be enabled, effect subsequent may take (log n) 2 time. here consists pair interacting tree-like structures, one which holds unscaled values scalars. Experimental results demonstrating performance improvements multiplication operation on from few dozen 30 million points discussed. This research was done part Ajna Labs course developing decentralized finance protocol. It an efficient on-chain encoding processing order book-like used manage lending, interest, collateral.