Justin Willmert

I don't understand why the original doesn't work, but the following patch seems to solve the problem in a similar usage case. ```diff diff --git a/src/require.jl b/src/require.jl index e402421..93391bd 100644...

> @jmert that's very odd; can you send a PR and @davidanthoff can you confirm if that patch fixes things for you? Will do. PR coming shortly.

> Somewhat related is JuliaLang/julia#15648, but I like how this turns the problem on its head: instead of trying to wedge sparse matrices into a generic API, we simply "lift"...

I see the same rendering artifacts in text boxes (which seems to be "bleed through" of various bits of previously rendered UI elements). I was able to fix the issue...

Yes, this is a known issue that I haven't gotten around to sorting out — it's because the values for ℓ==m for large m and θ near the poles are...

If I'm not mistaken, Quadmath dispatches to an external C library so you have the problem of an opaque data structure/number type to Julia that it can't optimize through. So...

> Oh, I should actually try DoubleFloats, Quadmath isn't the defacto standard I thought it was. If I remember correctly, I've tried DoubleFloats and it doesn't help because you only...

All of that being said, an alternative proposal does exist in the more recent paper that `libsharp2`'s recurrence is based on (https://www.jstage.jst.go.jp/article/jmsj/96/2/96_2018-019/_article) which I haven't had time to fully digest....

> Is this problem related? > > ```julia > julia> AssociatedLegendrePolynomials.λlm(600,500,1/sqrt(2)) > 3.485220526612233e-21 > > julia> AssociatedLegendrePolynomials.λlm(600,500,Float32(1/sqrt(2))) > 6.120498f9 > ``` > > I'v realised this as for higher resolution...

It looks like [CustomUnitRanges.jl](https://github.com/JuliaArrays/CustomUnitRanges.jl) provides a `ZeroRange` type which will probably be needed to get 0-indexed `OffsetArrays` without the overhead of an unknown start index (as I expect will happen...