What question did this study set out to answer?

The aim is to highlight VDR arithmetic's ability to yield exact results in physical computation, minimizing floating-point errors.

May 18, 2026Open Access

VDR in Physical Computation: Exact Arithmetic Where It Matters

Key Points

The aim is to highlight VDR arithmetic's ability to yield exact results in physical computation, minimizing floating-point errors.
Applied VDR system based on the [V, D, R] triple for computations
Utilized Gaussian elimination for linear algebra
Employed complex pairs for quantum mechanics and signal processing
Achieved exact results for computations commonly affected by floating-point errors.
Demonstrated the effectiveness of VDR arithmetic across various applications involving transcendental functions.
Showcased improved numerical management in physical computations, avoiding the pitfalls of traditional methods.

Abstract

This paper demonstrates VDR exact arithmetic applied to physical computation. It is not a physics paper — it does not derive new physical results. It shows that computations physicists perform routinely, which accumulate floating-point error and require careful numerical management, produce exact results when performed in VDR arithmetic. Every computation here uses the VDR system described in VDR-13: the V, D, R triple where V and D are integers and R is a first-class Remainder value, the Q335 basis of 22 transcendental constants as integers over 2³³⁵, Gaussian elimination for linear algebra, complex pairs for quantum mechanics and signal processing, and functional remainders for transcendental functions. References: VDR-13 (complete system specification), VDR-1 (core axioms), MATH-4 (Q335 basis).

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