Converting Binary Floating-Point Numbers to Shortest Decimal Strings: An Experimental Review

Résumé

When sharing or logging numerical data, we must convert binary floating-point numbers into their decimal string representations. For example, the number $\pi$ might become 3.1415927. Engineers have perfected many algorithms for producing such accurate, short strings. We present an empirical comparison across diverse hardware architectures and datasets. Cutting-edge techniques like Schubfach and Dragonbox achieve up to a tenfold speedup over Steele and White’s Dragon4, executing as few as 210 instructions per conversion compared to Dragon4’s 1500–5000 instructions. Maybe surprisingly, none of the implementations we surveyed consistently produced the shortest possible strings—some generate outputs up to 30% longer than optimal. We find that standard library implementations in languages such as C++ and Swift execute significantly more instructions than the fastest methods, with performance gaps varying across CPU architectures and compilers. We suggest some optimization targets for future research.

Jaël Champagne Gareau

Chercheur postdoctoral en informatique

Mes intérêts de recherche incluent l’intelligence artificielle et l’exploitation de l’architecture moderne des ordinateurs lors de la conception et de l’implémentation d’algorithmes et de structures de données.