research!rsc: Fast Unrounded Scaling: Proof by Ivy (Floating Point Formatting, Part 4)

A formal mathematical proof demonstrates that floating-point number formatting (both printing and parsing) can use fast 128-bit approximations instead of arbitrary-precision arithmetic. The proof uses the Ivy calculator to verify that specific bit-width constraints guarantee correct rounding for float64 conversions. Through modular arithmetic analysis and computational verification across hundreds of edge cases, it establishes that a 64×128-bit multiplication with careful error analysis produces correct results. The work generalizes previous format-specific proofs and unifies the theoretical foundation for both decimal-to-binary and binary-to-decimal conversions.