RFC: add complex-valued tests

[simonbyrne]

I've started adding some tests for complex valued functions, to deal with branch cut issues (see #2843).

Currently just has tests for sqrt. All tests are taken from the mac csqrt man page (it was the most specific).

Some of these tests currently fail (which I guess is the point of doing them). I'm happy to add more functions (log, trig/inverse trig, etc.).

[ViralBShah]

Thanks. Please add as many as you can. Let's fix all the uncovered issues in here and then merge.

[simonbyrne]

Okay, there's a few more. I'll add more as I get time.

[simonbyrne]

I've included the ones which are supposed to "raise an invalid flag": some of these currently raise an error, e.g.

julia> sinh(complex(0.0,Inf))
ERROR: DomainError()
 in sinh at complex.jl:332

Is there a standard method for asserting an error in the tests?

[aviks]

julia> using Base.Test

julia> @test_fails sinh(complex(0.0,Inf))

julia>

[ViralBShah]

Ideally we need a way to check that the particular exception was raised, rather than a generic error.

[ViralBShah]

Here, we really need the feature that was requested earlier (was it @johnmyleswhite ?) that the tests should continue running even if certain tests fail, so that we can see all the failures. This would be especially useful in travis.

[andrioni]

This could be solved by using a more appropriate handler when needed, in fact this was exactly my reason for #2680.

[ViralBShah]

@andrioni Good point.

[simonbyrne]

Okay, that should be all of the functions. The only one which is incomplete is ^: this is a bit tricky, as it's a binary function, and not really clearly defined in the standard.

To make this a bit easier to incorporate, I could remove it from runtests.jl so it won't be called by travis? It could still be called manually by make test-complex.

[ViralBShah]

We can't merge this before all of these pass. Do you have time to look at and fix the implementations too?

Also cc: @jiahao to help out.

[ViralBShah]

An alternate thing to do would be to put all these new tests in a new file. We certainly do not want to disable existing tests. Then we can keep fixing them and moving them to test/complex.jl.

[ViralBShah]

This also needs a rebase before merging, once the new tests are put in say, complex-bc.jl.

[simonbyrne]

complex.jl is a new file, so disabling it won't disable any existing tests.

I'm happy to help out with the implementations where I can, but some of them may be beyond my skill set.

[simonbyrne]

Okay, I've rebased, and removed the new tests from make testall (but they can still be run by make test-complex).

[simonbyrne]

To keep the consistency of the limits:

julia> complex(1e-10,1e-10)^complex(1e-10,1e-10)
0.9999999976535324 - 2.189387912488976e-9im

[simonbyrne]

But as I said, ^ isn't really specified that clearly: the mac documentations for cpow says that cpow(x,y) == cexp(y * clog(x)). However for x=0 + i0, clog(x) == -Inf + 0i, which means that the term inside the y*clog(x) would have an NaN.

The C99 standard isn't really specific, just saying (in a footnote):

This allows cpow(z, c) to be implemented as cexp(c clog(z)) without precluding
implementations that treat special cases more carefully.

[andrioni]

These lines lack closing parentheses.

[simonbyrne]

Yes, these were fixed by #2878.