Errors with BigFloat boundaries

[araujoms]

The following function errors when I call it as erf(BigFloat). It should work, no? It doesn't complain if I call it with other funny types that are nevertheless isbits.

function erf(T)
    lb, ub = T(0), T(1)
    f(x) = exp(-x^2)
    sol = hquadrature(f, lb, ub)
    return sol[1] 
end

[stevengj]

If you want to do 1d BigFloat quadrature, I would highly recommend using QuadGK instead, since QuadGK lets you increase the quadrature order (it is a good idea to increase the order roughly in proportion to the precision).

That being said, I agree that this should work (even if it is suboptimal). Maybe we can make use of JuliaArrays/StaticArrays.jl#799

[araujoms]

The actual integral I need to solve is 2d, I only simplified it for the MWE.

Do you mean for example, in line 67 of HCubature.jl, declare ma = similar(a) instead of ma = MVector(a)?

[stevengj]

Yes. similar is defined to return a mutable type, and apparently it should nowadays do the right thing with SVector:

julia> a = SA[1,2,3]
3-element SVector{3, Int64} with indices SOneTo(3):
 1
 2
 3

julia> ma = similar(a)
3-element MVector{3, Int64} with indices SOneTo(3):
 4537519120
  167772160
          0

julia> a = SA[big(1),2,3]
3-element SVector{3, BigInt} with indices SOneTo(3):
 1
 2
 3

julia> ma = similar(a)
3-element SizedVector{3, BigInt, Vector{BigInt}} with indices SOneTo(3):
 #undef
 #undef
 #undef

[stevengj]

Sorry, not similar because we need to copy the contents. Maybe Base.copymutable(a)?

[stevengj]

The annoyance here is that Base.copymutable(a), which calls similar and then copyto!, may be less efficient than MVector(a) for the cases where MVector does work.

It seems like StaticArrays.jl should ideally implement a specialized Base.copymutable method? JuliaArrays/StaticArrays.jl#1247

But for now Base.copymutable seems like the most reliable method. Would be good to benchmark it to check for regressions for Float64 integration — I doubt it is noticeable.

[araujoms]

StaticArrays is above my pay grade.

But if this is the only place then I'm sure there will be no difference in performance. Looking around a bit, line 15 of genz-malik.jl will also certainly cause trouble. But there similar is enough, no copying is needed.

I can give it a try tomorrow; to see if I can fix it and benchmark it. Can you suggest a test case for benchmarking?