A Constant-Time Approximate Multiplication Algorithm for Arbitrarily Large Integers.

This dataset contains the implementation and experimental results of a linear-time algorithm for approximate multiplication of arbitrarily large integers. The method is based on power-of-two decomposition, mantissa truncation, and controlled rounding, with a precision parameter t that regulates the approximation error. We show that the relative error is bounded by 2¹⁻ᵗ, and that values of t between 1000 and 10000 yield errors on the order of 10⁻³⁰⁰ to 10⁻³⁰⁰⁰. Benchmarks demonstrate speedups of up to 1300× on inputs with millions of digits. The included code allows full reproduction of all experiments.