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

Abstract

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. Often per their specification, 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.