Grisu is accurate, but not always optimal. However, it figures out when that happens and lets you bail out to a slower algorithm when that happens. If you want full speed you should use Grisu, and then use Errol as a bailout.
A bit more context: there are 3 important properties when printing floating-point numbers.
- accurateness: you want the printed number to read back to the same number.
- shortness: often you want the shortest decimal representation: "0.3" and not "0.2999999999999999889". The latter is more precise, but reads back to the same number as "0.3".
- closeness: given two decimal representations of the same length, you prefer the one that is closer to the actual number.
I call the combination of these three properties "optimal".
Note that shortness and closeness are not always crucial. For example, a json-encoder could easily drop those, if the encoding is faster without them.
Also, some languages drop shortness in favor of printing something closer to the input.
Grisu always produces accurate results. However, it sometimes can't tell if it already has the shortest and closest number. However (by being conservative) it can tell the user when that happens. In that case, one can fall back to another complete algorithm.
