Numerical Residual Compression Acceleration for Finite Truncations of the Chudnovsky Series

This paper presents a numerical acceleration technique for computing finite truncations of the Chudnovsky series, one of the most efficient algorithms for high-precision Pi computation. We introduce a residual compression method that exploits the algebraic structure of the series terms to reduce computational redundancy in iterative summation. By reorganizing the evaluation order and applying compressed intermediate representations, the proposed method achieves a significant reduction in both arithmetic operations and memory footprint compared to the standard term-by-term evaluation. We provide a detailed complexity analysis, a modular C++ implementation, and benchmark results on standard consumer hardware. The method is particularly suited for embedded systems and resource-constrained environments where full binary splitting may be impractical. This work offers a practical engineering alternative for high-precision Pi computation in memory-limited scenarios.