Ensure correct rounding for irrationals

[OlivierHnt]

Fixes #616.

[codecov-commenter]

Codecov Report

Attention: 1 lines in your changes are missing coverage. Please review.

Comparison is base (946493a) 84.07% compared to head (69236c0) 84.33%.

❗ Current head 69236c0 differs from pull request most recent head 885ce8c. Consider uploading reports for the commit 885ce8c to get more accurate results

Files	Patch %	Lines
src/intervals/construction.jl	94.44%	1 Missing ⚠️

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Additional details and impacted files

@@            Coverage Diff             @@
##           master     #617      +/-   ##
==========================================
+ Coverage   84.07%   84.33%   +0.26%     
==========================================
  Files          24       25       +1     
  Lines        2091     2088       -3     
==========================================
+ Hits         1758     1761       +3     
+ Misses        333      327       -6     

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[Joel-Dahne]

I took a quick look at the code and didn't spot anything odd. I don't understand the distinction between _unsafe_bareinterval and __unsafe_bareinterval though?

You could also support Irrational{:ℯ} by simply evaluating exp(BareInterval{T}(1)) and taking those endpoints.

It would of course be possible to support more irrationals by simply evaluating them with interval arithmetic. They would in general not be correctly (but faithfully) rounded in those cases though. I don't know what guarantees you give on correct rounding outside of the standard though (and the standard clearly doesn't covers these types of irrationals).

[OlivierHnt]

I took a quick look at the code and didn't spot anything odd. I don't understand the distinction between _unsafe_bareinterval and __unsafe_bareinterval though?

Oh just a way to fix method ambiguities when we introduce Irrational in the functions type signature.

You could also support Irrational{:ℯ} by simply evaluating exp(BareInterval{T}(1)) and taking those endpoints.

It would of course be possible to support more irrationals by simply evaluating them with interval arithmetic. They would in general not be correctly (but faithfully) rounded in those cases though. I don't know what guarantees you give on correct rounding outside of the standard though (and the standard clearly doesn't covers these types of irrationals).

Indeed, same for :φ. Well for such cases, I think it suffices for the returned interval to contain the true value without necessarily be tight.

[Joel-Dahne]

For :ℯ it would even be tight!

I think non-tight enclosures would be perfectly fine for irrationals. Personally I don't care much for correct rounding (faithful rounding is of course necessary though!), you lose it after doing two operations anyway.

In that case I think it would make sense to also implement :φ in this PR! Then all irrationals in Base are covered at least.

[OlivierHnt]

Sounds good, I'll find time to make the changes. Thx for looking over this PR btw!