`Float.Extra.aboutEqual` weirdnesses

[sebsheep]

Describe the bug
The test for aboutEqual doesn't pass, plus it makes some floats equal whereas there are clearly not.

To Reproduce

Running 1 test. To reproduce these results, run: elm-test --fuzz 10000 --seed 225971905022788

↓ FloatTests
✗ makes numbers about equal even after some operations

Given 8.98846567431158e+307

    False
    ╷
    │ Expect.equal
    ╵
    True

in the repl:

> (1.00002 + 1.00002) |> Float.Extra.aboutEqual 2.00003
True : Bool

Expected behavior
I'm not sure about what should be the "good behavior". The fuzz test shows that aboutEqual is "too strict", whereas the 1.00002 + 1.00002 is "too loose".

Maybe we should provide multiple functions aboutEqual function like aboutEqualReallyStrict/aboutEqualStrict/aboutEqualLoose/aboutEqualReallyLoose, or adding an integer parameter indicating the "strictness" of this function.

Maybe it's even not a core lib's library to make such choices, so we shouldn't provide this function at all.

Additional context

We could consider the following implementation : https://github.com/sindresorhus/float-equal/blob/main/index.js

Translated in elm with the "strictness" parameter (which we can be the number of significant bits, with 52 as the maximum precision):

{-| Corresponds to Number.EPSILON.
See: <https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number/EPSILON>
-}
epsilon : Float
epsilon =
    2 ^ -52

aboutEqual : { significantBits : Int } -> Float -> Float -> Bool
aboutEqual { significantBits } a b =
    if isInfinite a then
        isInfinite b

    else if isInfinite b then
        False

    else
        let
            diff =
                abs (a - b)
        in
        (diff < epsilon)
            || (diff <= (2.0 ^ toFloat (52 - significantBits)) * epsilon * min (abs a) (abs b))

[gampleman]

(1.00002 + 1.00002) |> Float.Extra.aboutEqual 2.00003

This is expected. That's what "about equality" is about (sorry).

You can also read in the docs:

Note: this is unlikely to be appropriate if you are performing computations much smaller than one.

Although that could be phrased a bit more clearly. Either way, we should probably also expose a function that allows you to control the relevant parameters. In our implementation there are 2 - the absolute and relative difference. They are set to 1e-5 and 1e-8 respectively, but if you wanted to detect 1.00002 + 1.00002 /= 2.00003, you would probably need to set the absolute to 1e-7 or so.

I'll look into the failing test, seems like you found a good seed.

[gampleman]

OK, looked into the test. The value it finds is very high and generally above the sort of common range this function is designed. I'll modify it to be something like:

testAboutEqual : Test
testAboutEqual =
    Test.only <|
        fuzz (Fuzz.floatRange -1.0e100 1.0e100) "makes numbers about equal even after some operations" <|
            \a ->
                ((a + 10 + a - 10 - a) * 2 / 2)
                    |> aboutEqual a
                    |> Expect.equal True