Modular Computation for Simulation and Physics

Modern simulations in physics—particularly those involving chaotic systems, long-duration integration, or finely-tuned constants—often demand numerical precision far beyond what standard IEEE floating-point formats can provide. As highlighted in research on arbitrary-precision libraries, certain models quickly degrade without hundreds or even thousands of bits of precision, leading to divergence, error accumulation, and instability.

RNS-based modular computation offers a compelling alternative. By using a carry-free architecture, ultra-high precision formats like 128.128 fixed-point RNS can perform massively parallel arithmetic with no loss in accuracy and significantly higher throughput than traditional bignum libraries. Unlike binary systems, where increasing precision leads to quadratic growth in resource and timing costs, RNS arithmetic scales linearly with the number of moduli. This makes RNS ideally suited for:

• Long-running orbital mechanics or N-body problems requiring constant precision over billions of iterations.

• Quantum physics simulations where irrational constants and minute perturbations demand exact fractional representation.

• Climate modeling and finite-element analysis, where small rounding errors can destabilize entire systems over time.

• Symbolic or algebraic solvers embedded in high-fidelity numeric workflows.

By combining precision and performance, RNS-based modular computation bridges the gap between simulation fidelity and computational efficiency—unlocking simulations previously constrained by floating-point limits.