sinpi returns unnecessarily wide intervals

[fph]

It looks like sinpi(x), where x is an interval, is defined internally as sin(x*\pi). Unfortunately this yields intervals that could be tightened; for instance:

julia> sinpi(1..1)
[-3.21625e-16, 1.22465e-16]

while it should be possible to determine that the result is exactly 0.

If sin were defined in terms of sinpi, instead of the opposite, with an implementation analogous to the current one, then this problem would disappear. I tried to submit a PR, but some tests fail because of a related issue I just reported in CRlibm (JuliaIntervals/CRlibm.jl#39).

[dpsanders]

sin should definitely not be defined in terms of sinpi, since this will also widen the resulting interval.

But yes it should be possible to implement sinpi for Interval{Float64} in a similar, but easier way to sin.

[dpsanders]

Please feel free to file the PR and we can try and find what's going wrong.

[fph]

Filed the PR. With the implementation in the PR all tests pass, but cospi(@biginterval(0.5)) fails (because now it relies on calling CRlibm.cospi on a BigFloat, and that is undefined).

[fph]

..oops; all tests pass on my machine, but apparently not in the CI environment, where the same stack overflow bug pops up. So there is indeed something still to fix.