Trigonometric functions at infinity

[isa...@gmail.com]

I have recently become aware of Julia and have been impressed with its ease of use and speed.  While I was converting my previous code to Julia, I noticed that trigonometric functions at infinity yield DomainError and abort the program. Try sin(Inf), sin(-Inf), cos(Inf), tan(Inf), etc.  I checked the behavior of Numpy and it returns a NaN and a warning of invalid value to the function. I remember Matlab was yielding a NaN too. But they both wouldn't abort the program.

Returning a NaN instead of aborting the program might be useful when the following computations don't depend on only this result of NaN.  For example, consider finding the smallest element of x =cos( [1.0, 2.0, Inf]) which would have given the number I am interested in if cos(Inf) gives a NaN.  Here I cos(2.0) < NaN would be false nevertheless findmin cleverly finds the correct answer 2.0 ( so does Numpy). Note that Inf is usually a result of an intermediate step of an algorithm.

If the following computations involve NaN and yield compilation error than checking elements of x being not NaN is necessary. But since it does occur rarely, avoiding this check might be useful for speed.

What would be your thoughts?  Thanks.

[John Myles White]

My personal preference is for code to never raise warnings if you might ever use it in a system that has more than 10 lines of code. So I'm personally a believer in either returning NaN without a warning (which seems a little risky) or maintaining the current behavior, which seems wisest to me.

-- John

[Milan Bouchet-Valat]

Le mardi 04 novembre 2014 à 09:22 -0800, isa...@gmail.com a écrit :
> I have recently become aware of Julia and have been impressed with its
> ease of use and speed. While I was converting my previous code to
> Julia, I noticed that trigonometric functions at infinity yield
> DomainError and abort the program. Try sin(Inf), sin(-Inf), cos(Inf),
> tan(Inf), etc. I checked the behavior of Numpy and it returns a NaN
> and a warning of invalid value to the function. I remember Matlab was
> yielding a NaN too. But they both wouldn't abort the program.
>
> Returning a NaN instead of aborting the program might be useful when
> the following computations don't depend on only this result of NaN.
> For example, consider finding the smallest element of x =cos( [1.0,
> 2.0, Inf]) which would have given the number I am interested in if
> cos(Inf) gives a NaN. Here I cos(2.0) < NaN would be false
> nevertheless findmin cleverly finds the correct answer 2.0 ( so does
> Numpy). Note that Inf is usually a result of an intermediate step of
> an algorithm.

You'll probably be interested in this discussion:
https://github.com/JuliaLang/julia/issues/7866

[isa...@gmail.com]

In order to avoid exiting the program, I am checking for Inf and setting the result to Nan manually for each trigonometric function.  I agree with John's comments and hope that something like this would become default behavior.
@Milan: Thanks for the link, it was a good one.

[Simon Byrne]

Alternatively, you could just redefine sin without the nan_dom_err call:

https://github.com/JuliaLang/julia/blob/cdcdc7ae5a79d5f8232a14e6e072123dd178cf9e/base/math.jl#L123

Something like the following should work:

import Base.sin
sin(x::Float64) = ccall((:sin,Base.Math.libm), Float64, (Float64,), x)

[isa...@gmail.com]

Nice solution! Thanks.