Question about intervals of exp

[FavioVazquez]

Hello, I have a question about using the implemented function exp and the e number in Julia. I was trying some stuff and I found this,

julia> println(@interval(e))
[2.718281828459045, 2.7182818284590455]

julia> println(exp(@interval(1)))
[2.718281828459045, 2.718281828459045]

And of course:

julia> @interval(e) == exp(@interval(1))
false

There is an extra 5 in the the println(@interval(e)) as you can see.

So I was wondering, shouldn't this be equal? or this I'm thinking the wrong way about this.

[lbenet]

Thanks for reporting! I get the same as you using the tagged version v0.1.3.

Switch to master and you get the expected tight interval. Lot is going on at the moment, and we are getting close to full compliance with the ITF1788 Std for interval arithmetic; then, a new version will be released (see #31).

This is what I get in master:

julia> Pkg.checkout("ValidatedNumerics")
INFO: Checking out ValidatedNumerics master...
INFO: Pulling ValidatedNumerics latest master...
INFO: No packages to install, update or remove

julia> Pkg.status("ValidatedNumerics")
 - ValidatedNumerics             0.1.3+             master

julia> using ValidatedNumerics
INFO: Recompiling stale cache file /Users/benet/.julia/lib/v0.5/ValidatedNumerics.ji for module ValidatedNumerics.

julia> println(@interval(eu))
[2.718281828459045, 2.7182818284590455]

julia> println(exp(@interval(1)))
[2.718281828459045, 2.7182818284590455]

[FavioVazquez]

Great thanks for answering, switching to master

[dpsanders]

Thanks for trying out the package.

Note that in Julia, every expression returns an answer, so you don't need to use println. Also, since v0.1 you can use @interval outside an expression and it will replace all literal values, e.g. the 1 above, with interval versions. Using the current master branch:

julia> @interval(eu)
[2.718281828459045, 2.7182818284590455]

julia> @interval exp(1)
[2.718281828459045, 2.7182818284590455]

[dpsanders]

[We have used the (built-in) name eu instead of e for the Euler constant since you often want to define a variable called e in your code, which will override the built-in e, whereas you (almost) never want to define something called eu. In any case, it is safer to use exp(1).]

[FavioVazquez]

Oh I see. Thanks for the tip! I'll let you know later about what I'm doing with it and the results.