get rid of test_approx_eq_*

[StefanKarpinski]

These are not really fundamental testing primitives and should be replaced with @test isapprox(...) or something similar.

[JeffBezanson]

The point of this is it knows more about what is being tested, so it can print the compared values and their difference compared to the requested tolerance, instead of just a boolean result.

[StefanKarpinski]

Well, we need a better general way of printing more information when tests fail. As it is, these fail incorrectly: they throw an error instead of failing.

[JeffBezanson]

Ah, well failing incorrectly is certainly a problem.

[StefanKarpinski]

Can't tell if serious...

[JeffBezanson]

I was actually serious, but you have a point.

[andreasnoack]

I have aggressively changed @test to @test_approx_eq in the test code I have met because of the extra output. In the linalg test code the line numbers relate to the end of the loop that goes through all the BlasTypes. Therefore it can be difficult to know which test is failing unless you can see some output.

[StefanKarpinski]

Well, I'm working on improving the @test macro to be more informative when tests fail, which should eliminate the need for these things.

[IainNZ]

Having @test display more would be great! We do currently use test_approx_eq_eps in @JuliaOpt code but any reasonable replacement will be fine.

[simonbyrne]

I support getting rid of @test_approx_eq_*, as they're kind of confusing: @test_approx_eq is relative-error based (but at a fixed threshold), and @test_approx_eq_eps is absolute-error based. Forcing use of isapprox would make it easier to set more reasonable thresholds in tests.

I also agree that @test output needs to be improved, ideally outputting the values of all inputs into the failed test.

[stevengj]

Given #12472, you can now do @test foo ≈ bar and you will get the nice test output, as long as you are happy with the default tolerance.

It would be fairly easy to update the @test macro to look for @test isapprox(...) too, for the cases where a non-default tolerance is used.

[kshyatt]

@StefanKarpinski didn't your great Regex-fest (mostly) do this?

[tkelman]

They're not used much in base any more, but they should be deprecated to really close this if we want to finish getting rid of them all the way.

[timholy]

Related: #15477

[IainNZ]

I really did want to kill these during the at-testset change, but failed to find a solution I liked at the time.

[StefanKarpinski]

Bump?

[stevengj]

A good solution would be to recognize @test isapprox(...) and give extra output for it (e.g. the two things being compared, and the relative error encountered vs. the error tolerance requested).

[StefanKarpinski]

I have a PR for most of this (#19901), the remaining special printing of failures for @test a ≈ b is split out into #19898, which can be handled whenever since it's just a display improvement.

[KristofferC]

This is done