Replace error functions in DifficultyCalculationUtils with good-enough approximations #33717
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tsunyoku
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Jun 18, 2025
Finadoggie
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Aug 18, 2025
…h approximations (ppy#33717) * Reimplement error functions * Fix bug with adjustment for negative values * Formatting --------- Co-authored-by: tsunyoku <[email protected]>
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For an acceptable loss in precision, we can speed up the error function implementations by around 5x. This affects both standard and taiko, as both modes use DifficultyCalculationUtils.Erf for their accuracy scaling. In standard, this necessitates a change to the maximum tested precision, however taiko's calculation is not precision-sensitive and is therefore fine without any changes.
This massively speeds up the standard performance calculator, by around 2x.
Old:
New:
Erf approximation delta visualization:
https://www.desmos.com/calculator/lyg8opgpej
ErfInv approximation delta visualization:
https://www.desmos.com/calculator/npbyvxpwtw