bug(?) on round/floor/ceil

[Moelf]

this is probably edge case but:

julia> central_fdm(5, 1)(ceil, 0.1)
5.833333333333332

julia> central_fdm(5, 1)(ceil, 0.2)
-0.8333333333333333

JuliaDiff/ChainRules.jl#277

[oxinabox]

Does this happen on FiniteDifference v0.10?

[oxinabox]

It does happen in v0.10 also.

Finite differencing near discontinualities is hard.
I would hope we do a bit better that that though.

Probably though the right solution is to do forward_fdm for ciel and backward_fdm for floor
and the appropriate one depending on which side of 0.5 you are on for round
(You can pass the fdm method into the test_X functions from ChainRulesTestUtils as a kwarg)

julia> forward_fdm(5, 1)(ceil, 0.2)  # do this
-2.220446049250313e-15

julia> backward_fdm(5, 1)(ceil, 0.2)  # don't do this
-19.166666666666664

[wesselb]

In v0.12, another way of doing this is by setting the max_range keyword appropriately:

julia> central_fdm(5, 1, max_range=9e-1)(ceil, 0.2)
6.085449991639748e-14