Move general utility functions and errors from DiffEqBase to SciMLBase

[jClugstor]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

We want to move the solve dispatches for Nonlinear problems to NonlinearSolveBase from DiffEqBase. In order to do that we need to move some of the things from DiffEqBase to SciMLBase so that NonlinearSolveBase can use them.

[jClugstor]

@ChrisRackauckas this moves the general utility functions used for the solve dispatches to SciMLBase, the extensions needed for those, and most of the errors that were in DiffEqBase before.

I have a branch of DiffEqBase that imports and uses these from SciMLBase, which also means that for example DiffEqBase.anyeltypedual will still work even though it's defined in SciMLBase. I think that should make this non-breaking and allow us to gradually move to using SciMLBase instead of DiffEqBase for these.

[ChrisRackauckas]

What's the load time impact of this?

[jClugstor]

I did

@time using SciMLBase

Current master: 0.367625 seconds (470.92 k allocations: 41.653 MiB, 2.65% gc time, 12.92% compilation time)

This PR: 0.364500 seconds (385.76 k allocations: 37.483 MiB, 2.90% gc time)

I also looked at loading OrdinaryDiffEq:

@time using OrdinaryDiffEq

Current master: 5.729929 seconds (12.34 M allocations: 696.356 MiB, 2.83% gc time, 11.45% compilation time: 4% of which was recompilation)

This PR: 5.783470 seconds (12.33 M allocations: 695.451 MiB, 3.04% gc time, 11.07% compilation time: 4% of which was recompilation)

Any better way to see how this affects load times?

[ChrisRackauckas]

oh shit, that shouldn't be there... why is static needed? Just noticed this too late. This should not be in SciMLBase!

[jClugstor]

reduce_tup is used for the Dual type checking, anyeltypedual.

[ChrisRackauckas]

can that be isolated from the rest of Static?

[jClugstor]

I think so, I don't see anything in the definition that uses anything besides Base functions. Should I just copy paste this?

@generated function reduce_tup(f::F, inds::Tuple{Vararg{Any, N}}) where {F, N}
    q = Expr(:block, Expr(:meta, :inline, :propagate_inbounds))
    if N == 1
        push!(q.args, :(inds[1]))
        return q
    end
    syms = Vector{Symbol}(undef, N)
    i = 0
    for n in 1:N
        syms[n] = iₙ = Symbol(:i_, (i += 1))
        push!(q.args, Expr(:(=), iₙ, Expr(:ref, :inds, n)))
    end
    W = 1 << (8sizeof(N) - 2 - leading_zeros(N))
    while W > 0
        _N = length(syms)
        for _ in (2W):W:_N
            for w in 1:W
                new_sym = Symbol(:i_, (i += 1))
                push!(q.args, Expr(:(=), new_sym, Expr(:call, :f, syms[w], syms[w + W])))
                syms[w] = new_sym
            end
            deleteat!(syms, (1 + W):(2W))
        end
        W >>>= 1
    end
    q
end