Bit-Exact Absorption of Underflowing Summands under IEEE 754 Round-to-Nearest-Even

Abstract

Preprint. A local IEEE 754 binary64 criterion is given under which an addend may be replaced by 0 without changing a bit of a fixed addition tree (round-to-nearest-even). A second theorem lifts a bound on the omitted impulse to an observable such as an integrated coordinate, when that impulse lies below half an ulp of the observable. A warp-uniform three-path GPU kernel is described. Force-bit identity and the observable split are reported on an NVIDIA GeForce RTX 3090 up to N = 65536. The kernel is not claimed to be faster than the classical sequential sum. This manuscript is a new work. It does not restore the global force-identity claim of the withdrawn ACM TOMS submission TOMS-2026-0141. Reproduction scripts are in the attached archive apm_verify.zip.