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The GNU libc atanh is correctly rounded

89 points by matt_d

by RyJones

2 subcomments

Interesting: https://youtu.be/cb5r3r38O9c
Guy's world records get deleted due to changes in atanh over time

by jcranmer

2 subcomments

One of the major projects that's ongoing in the current decade is moving the standard math library functions to fully correctly-rounded, as opposed to the traditional accuracy target of ~1 ULP (the last bit is off).
For single-precision unary functions, it's easy enough to just exhaustively test every single input (there's only 4 billion of them). But double precision has prohibitively many inputs to test, so you have to resort to actual proof techniques to prove correct rounding for double-precision functions.

by kergonath

1 subcomments

I don’t think I ever used atanh, but I always love some floating-point nerdery. These other documents by the same team are fantastic resources: https://inria.hal.science/hal-04714173v2/document for complex values and https://members.loria.fr/PZimmermann/papers/accuracy.pdf for real values.
Lots of good stuff here: https://members.loria.fr/PZimmermann/papers/ .

0 subcomment

by jonathrg

0 subcomment

by brcmthrowaway

2 subcomments

by RandomTeaParty

1 subcomments