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This checks whether
hypot
of the value component is zero,and if so switches to a next-order method.
This may be slightly controversial since it exploits the difference between 0.0 and -0.0 to give the correct sign behavior at the origin.This exploits the difference between 0.0 and -0.0 to provide the same behavior exhibited forabs
:This implementation is consistent with the limit -> 0, e.g.,
Note this only covers the 3-arg version. For the 2-arg version I think a similar fix must be made in DiffRules.