Methods and apparatus for self-similar computation in fixed precision systems

Abstract

Methods and apparatus for accelerating self-similar computations. In one implementation, an input operand is divided into portions, and conditional shift logic determines a shift amount based on leading bits. A look-up table stores pre-computed values at reduced precision, and an arithmetic unit modifies the retrieved value based on the shift amount or remaining operand portion to generate a fixed precision result. The techniques reduce memory and computation requirements while preserving accuracy for operations such as logarithms, monomial expansions, and norm functions. Implementations may be applied to sensor preprocessing, audio and image compression, and neural network processing, enabling efficient handling of wide dynamic range data in embedded and low-power systems. The disclosed approaches provide scalable hardware and firmware architectures that reduce lookup table size, power consumption, and silicon area while supporting advanced signal and machine learning computations.

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