Information bounds and exact indices for ordered floating-point addition
Year: 2026
Type: preprint
Abstract: This preprint studies the exact input-output functions defined by fixed blocks of sequential floating-point additions, with each addition rounded separately to nearest, ties to even. The incoming accumulator is unknown when a standalone description of the block is prepared. The manuscript presents constructive information lower bounds and matching description bounds on a specified query grid under fixed-binade corridor restrictions. It also develops a two-threshold normal form and an exact index over all finite numerical inputs of a binary format, including subnormals and absorbing overflow. Signed zeros are identified numerically; NaNs, nonfinite operands, and exception flags are excluded from this whole-format contract. Exact arithmetic, symbolic checks, and retained native arithmetic results support the constructions. No practical speedup or lower bound on unrestricted parallel running time is claimed. This is a preprint; it has not undergone external peer review. The accompanying code, data, and reproduction instructions are published separately at https://doi.org/10.5281/zenodo.24044237.
Author: Popkov, Artem D.
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225463132