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Hi guys, I just released a new version of the Dragonbox algorithm, which is a fast float-to-string conversion algorithm that fmt uses for shortest round-trip floating-point formatting internally.
Faster digit generation, based on a jeaiii-style digit generation routine.
At the very core of all these theoretical stuffs, there is the theory of continued fractions. This is an immensely useful monster which I even dare call as the ultimate tool for floating-point formatting/parsing that everyone who wants to contribute in this field should learn. Before I learned continued fractions, my main tool for proving stuffs was the minmax Euclid algorithm (which is one of the greatest contributions of the wonderful Ryu paper), but it turns out that it is actually just a quite straightforward application of the theory of continued fractions. The main role minmax Euclid algorithm played was to estimate the maximum size of possible errors, but with continued fractions it is even possible to find the list of all examples that generate errors above a given threshold. This is something I desperately wanted but really couldn't do back in 2020.