XiSort: Deterministic Sorting via IEEE-754 Total Ordering and Entropy Minimization

TL;DR

XiSort addresses nondeterminism in floating-point sorting by enforcing the IEEE-754 total order and a deterministic tie-breaking policy, cast as an entropy-minimization transformation. It introduces formal disorder metrics, including a curved variant, and integrates these with an information-theoretic view to ensure a unique output for any input. The algorithm is a principled, stable, divide-and-conquer sort with an explicit tie-break, proven correct within an Alpay Algebra framework that emphasizes monotonic convergence and idempotence. Empirically, XiSort delivers competitive in-memory throughput and reliable external-memory performance while guaranteeing byte-for-byte reproducibility across runs and platforms, making it suitable for reproducible scientific computing and auditable financial pipelines.

Abstract

We introduce XiSort, a deterministic and reproducible sorting algorithm for floating-point sequences based on IEEE-754 total ordering and entropy minimization. XiSort guarantees bit-for-bit stability across runs and platforms by resolving tie-breaking via information-theoretic and symbolic methods. The algorithm supports both in-memory and external (out-of-core) operation, offering consistent performance on large datasets. We formalize a curved variant of the sorting metric that integrates into the Alpay Algebra framework, treating XiSort as a recursive operator with provable convergence and symbolic idempotence. This model preserves state-space closure while minimizing local disorder, interpretable as symbolic entropy. Empirical benchmarks demonstrate that XiSort achieves competitive throughput (e.g., sorting 10^8 doubles in approximately 12 seconds in-memory, and 100 GB at around 100 MB/s on SSDs), with applications in scientific computing, high-frequency finance, and reproducible numerical workflows. The results position XiSort as a principled tool for stable data alignment, symbolic preprocessing, and cross-platform float ordering. Keywords: deterministic sorting, IEEE-754, entropy minimization, symbolic algebra, reproducibility, external memory, Alpay Algebra, data pipelines