Algorithmic Optimization and Regression Validation of the RPD Index Implementation

This technical report documents the development of RPDindexOptimized, a separate optimized im- plementation of the six RPD indices previously distributed through the RPDindex research-software repository. The historical implementation is intentionally preserved as the archival reference associ- ated with Zenodo DOI 10.5281/zenodo.20313771. The new implementation preserves the intended numerical semantics for finite Python int/float sequences of length at least two, while reducing the asymptotic complexity of the three global indices from O(n2 ) to O(n log n) by using coordinate compression and Fenwick trees for cumulative counts and sums. A deterministic regression suite performs 52,248 reference-versus-optimized comparisons, and an additional 4,848 checks validate progressive-prefix trajectories. All tests pass within explicit floating-point tolerances; the largest observed absolute discrepancy is approximately 1.11 × 10−15 . A preliminary benchmark confirms the expected computational advantage of the optimized global algorithms as sequence length grows. The new software is independently archived as RPDindexOptimized v1.0.0 with Zenodo DOI 10.5281/zenodo.21892420. The report also documents repository organization, licensing, reproducibility procedures, compatibility limits, and the use of generative artificial intelligence as an assistive software-engineering and drafting tool under the sole author’s responsibility.