Partial update to IntervalArithmetic v0.21

[schillic]

I tried to upgrade IntervalArithmetic to v0.21 but failed with several blockers. I pushed this so somebody with more knowledge can continue. Below are the blocking problems I found.

Problems

• StaticArrays matrix multiplication is broken (reported in Matrix multiplication with mixed Interval SMatrix and SMatrix broken IntervalArithmetic.jl#573).
• Conversion to Compl uses fallback methods that require an Interval constructor.
• setprecision was removed (it is unclear to me how the behavior is imitated).
• No method matching BigFloat(::Interval{BigFloat}).

[OlivierHnt]

Sorry I do not know this repository well. Where is the issue with the conversion with Compl? Typically, for compatibility with 0.21, convert(Interval, a) should be interval(a) and, similarly, convert(Interval{T}, a) should read interval(T, a).

About the third item in your list, is it about

IntervalRootFinding.jl/test/slopes.jl

Lines 12 to 24 in 754c005

	@testset "Automatic slope expansion" begin
	for T in [Float64, BigFloat]
	s = interval(T(0.75), T(1.75))
	example = Slopes{T}[]
	push!(example, Slopes(x->((x + sin(x)) * exp(-x^2)), s, mid(s), interval(T(-2.8), T(0.1))))
	push!(example, Slopes(x->(x^4 - 10x^3 + 35x^2 - 50x + 24), s, mid(s), interval(T(-44), T(38.5))))
	push!(example, Slopes(x->((log(x + 1.25) - 0.84x) ^ 2), s, mid(s), interval(T(-0.16), T(0.44))))
	push!(example, Slopes(x->(0.02x^2 - 0.03exp(-(20(x - 0.875))^2)), s, mid(s), interval(T(0.03), T(0.33))))
	push!(example, Slopes(x->(exp(x^2)), s, mid(s), interval(T(6.03), T(33.23))))
	push!(example, Slopes(x->(x^4 - 12x^3 + 47x^2 - 60x - 20exp(-x)), s, mid(s), interval(T(-39), T(65.56))))
	push!(example, Slopes(x->(x^6 - 15x^4 + 27x^2 + 250), s, mid(s), interval(T(-146.9), T(67.1))))
	push!(example, Slopes(x->(atan(cos(tan(x)))), s, mid(s), interval(T(1), T(2))))
	push!(example, Slopes(x->(asin(cos(acos(sin(x))))), s, mid(s), interval(T(1.36), T(∞))))

? If so, things like interval(T(...), T(...)) should be written interval(T, ..., ...).

[schillic]

About the third item in your list, is it about

IntervalRootFinding.jl/test/slopes.jl

Lines 12 to 24 in 754c005

	@testset "Automatic slope expansion" begin
	for T in [Float64, BigFloat]
	s = interval(T(0.75), T(1.75))
	example = Slopes{T}[]
	push!(example, Slopes(x->((x + sin(x)) * exp(-x^2)), s, mid(s), interval(T(-2.8), T(0.1))))
	push!(example, Slopes(x->(x^4 - 10x^3 + 35x^2 - 50x + 24), s, mid(s), interval(T(-44), T(38.5))))
	push!(example, Slopes(x->((log(x + 1.25) - 0.84x) ^ 2), s, mid(s), interval(T(-0.16), T(0.44))))
	push!(example, Slopes(x->(0.02x^2 - 0.03exp(-(20(x - 0.875))^2)), s, mid(s), interval(T(0.03), T(0.33))))
	push!(example, Slopes(x->(exp(x^2)), s, mid(s), interval(T(6.03), T(33.23))))
	push!(example, Slopes(x->(x^4 - 12x^3 + 47x^2 - 60x - 20exp(-x)), s, mid(s), interval(T(-39), T(65.56))))
	push!(example, Slopes(x->(x^6 - 15x^4 + 27x^2 + 250), s, mid(s), interval(T(-146.9), T(67.1))))
	push!(example, Slopes(x->(atan(cos(tan(x)))), s, mid(s), interval(T(1), T(2))))
	push!(example, Slopes(x->(asin(cos(acos(sin(x))))), s, mid(s), interval(T(1.36), T(∞))))

? If so, things like interval(T(...), T(...)) should be written interval(T, ..., ...).

No, that part was fine. I changed it anyway now. And also added some more fixes.

Where is the issue with the conversion with Compl? Typically, for compatibility with 0.21, convert(Interval, a) should be interval(a) and, similarly, convert(Interval{T}, a) should read interval(T, a).

This all happens internally in automatic promotion. Below is an example from a failing test:

Xc = Complex(X, X)
f(z) = z^3 - 1

# Default
rts = roots(f, Xc)

In the call to roots the function f is executed with a IntervalRootFinding.Compl{Interval{Float64}}, argument . Then f says to subtract 1. So Julia calls the method
-(x::IntervalRootFinding.Compl{Interval{Float64}}, y::Int64),
which itself calls the promotion rule.
I tried to fix this by adding another promotion rule, but then got stuck in ForwardDiff with yet another promotion issue.

[OlivierHnt]

Mhmm so since promotion between Number and interval types are disallowed, the fix may be to define f(z) = z^2 - interval(1) (since promotion between Compl and interval seems to work).

[schillic]

Mhmm so since promotion between Number and interval types are disallowed, the fix may be to define f(z) = z^2 - interval(1) (since promotion between Compl and interval seems to work).

To me the whole point of interval arithmetic is that you can plug an interval into a function that expects a number and it will just work. Having to explicitly write interval(1) means I have to define a new function for that purpose. This is not convenient, and often not even possible if the code lives in another package.

But since this is not my package, I let you decide how to fix things. As I said, feel free to continue from this branch if you want.

[OlivierHnt]

Thank you very much for your input on this and taking the time to open this draft 🙂

We do allow the mixing +,*,-(::Interval, ::Number), so instead of redefining f, what could be done is to define the methods +,*,-(::Compl{<:Interval}, ::Number)...
That being said, since I do not know this package well, I am also not sure what is the exact purpose of Compl. @lbenet, @Kolaru, would defining a ComplexInterval type in IntervalArithmetic.jl be better in the long run? In particular, can such a struct completely replace the need of Compl?