`UndefRefError: access to undefined reference` for large `t`

[DanielVandH]

Maybe this t is so large that this is not realistic to work with / even expect to work, but while experimenting with it I found some errors. With BigFloat, the error is

julia> using SemiclassicalOrthogonalPolynomials

julia> t = big"1.599999999999999936381138676922222877671819028324835445962612546449591618087544e+17"
1.599999999999999936381138676922222877671819028324835445962612546449591618087544e+17

julia> T = BigFloat;

julia> a, b, c = -one(T)/2, -one(T), -one(T)/2
(-0.5, -1.0, -0.5)

julia> SemiclassicalJacobi(t, a, b, c)
ERROR: UndefRefError: access to undefined reference
Stacktrace:
  [1] getindex
    @ .\essentials.jl:917 [inlined]
  [2] getindex
    @ .\array.jl:930 [inlined]
  [3] getindex
    @ .\subarray.jl:320 [inlined]
  [4] _getindex
    @ .\abstractarray.jl:1358 [inlined]
  [5] getindex
    @ .\abstractarray.jl:1312 [inlined]
  [6] macro expansion
    @ C:\Users\djv23\.julia\juliaup\julia-1.11.3+0.x64.w64.mingw32\share\julia\stdlib\v1.11\LinearAlgebra\src\generic.jl:189 [inlined]
  [7] macro expansion
    @ .\simdloop.jl:77 [inlined]
  [8] rmul!(X::SubArray{BigFloat, 2, Matrix{BigFloat}, Tuple{UnitRange{Int64}, UnitRange{Int64}}, false}, s::BigFloat)
    @ LinearAlgebra C:\Users\djv23\.julia\juliaup\julia-1.11.3+0.x64.w64.mingw32\share\julia\stdlib\v1.11\LinearAlgebra\src\generic.jl:188
  [9] _banded_rmul!
    @ C:\Users\djv23\.julia\packages\BandedMatrices\rDdVw\src\generic\broadcast.jl:943 [inlined]
 [10] banded_rmul!
    @ C:\Users\djv23\.julia\packages\BandedMatrices\rDdVw\src\generic\broadcast.jl:948 [inlined]
 [11] materialize!
    @ C:\Users\djv23\.julia\packages\BandedMatrices\rDdVw\src\generic\broadcast.jl:951 [inlined]
 [12] rmul!
    @ C:\Users\djv23\.julia\packages\ArrayLayouts\QgP9t\src\lmul.jl:48 [inlined]
 [13] default_blasmul!(α::BigFloat, A::LinearAlgebra.Adjoint{…}, B::SubArray{…}, β::BigFloat, C::SubArray{…})
    @ ArrayLayouts C:\Users\djv23\.julia\packages\ArrayLayouts\QgP9t\src\muladd.jl:178
 [14] materialize!
    @ C:\Users\djv23\.julia\packages\ArrayLayouts\QgP9t\src\muladd.jl:264 [inlined]
 [15] muladd!
    @ C:\Users\djv23\.julia\packages\ArrayLayouts\QgP9t\src\muladd.jl:75 [inlined]
 [16] partialcholesky!(F::InfiniteLinearAlgebra.AdaptiveCholeskyFactors{…}, n::Int64)
    @ InfiniteLinearAlgebra C:\Users\djv23\.julia\packages\InfiniteLinearAlgebra\qfWao\src\infcholesky.jl:38
 [17] ClassicalOrthogonalPolynomials.CholeskyJacobiData(U::LinearAlgebra.UpperTriangular{…}, P::Normalized{…})
    @ ClassicalOrthogonalPolynomials C:\Users\djv23\.julia\packages\ClassicalOrthogonalPolynomials\LOdoJ\src\choleskyQR.jl:82
 [18] cholesky_jacobimatrix(W::LinearAlgebra.Symmetric{…}, Q::Normalized{…})
    @ ClassicalOrthogonalPolynomials C:\Users\djv23\.julia\packages\ClassicalOrthogonalPolynomials\LOdoJ\src\choleskyQR.jl:62
 [19] cholesky_jacobimatrix(w::QuasiArrays.BroadcastQuasiVector{…}, P::Normalized{…})
    @ ClassicalOrthogonalPolynomials C:\Users\djv23\.julia\packages\ClassicalOrthogonalPolynomials\LOdoJ\src\choleskyQR.jl:57
 [20] semiclassical_jacobimatrix(t::BigFloat, a::BigFloat, b::BigFloat, c::BigFloat)
    @ SemiclassicalOrthogonalPolynomials C:\Users\djv23\.julia\packages\SemiclassicalOrthogonalPolynomials\MxMOu\src\SemiclassicalOrthogonalPolynomials.jl:171
 [21] semiclassical_jacobimatrix(t::BigFloat, a::BigFloat, b::BigFloat, c::BigFloat)
    @ SemiclassicalOrthogonalPolynomials C:\Users\djv23\.julia\packages\SemiclassicalOrthogonalPolynomials\MxMOu\src\SemiclassicalOrthogonalPolynomials.jl:154
 [22] SemiclassicalJacobi(t::BigFloat, a::BigFloat, b::BigFloat, c::BigFloat)
    @ SemiclassicalOrthogonalPolynomials C:\Users\djv23\.julia\packages\SemiclassicalOrthogonalPolynomials\MxMOu\src\SemiclassicalOrthogonalPolynomials.jl:127
 [23] top-level scope
    @ REPL[23]:1
Some type information was truncated. Use `show(err)` to see complete types.

With Float64,

julia> SemiclassicalJacobi(1.6e17, -1/2, -1, -1/2)
ERROR: BoundsError: attempt to access 0-element UnitRange{Int64} at index [1]
Stacktrace:
  [1] throw_boundserror(A::UnitRange{Int64}, I::Int64)
    @ Base .\essentials.jl:14
  [2] _getindex
    @ .\range.jl:939 [inlined]
  [3] getindex
    @ .\array.jl:3076 [inlined]
  [4] _shift
    @ C:\Users\djv23\.julia\packages\BandedMatrices\rDdVw\src\banded\BandedMatrix.jl:904 [inlined]
  [5] similar
    @ C:\Users\djv23\.julia\packages\BandedMatrices\rDdVw\src\banded\BandedMatrix.jl:911 [inlined]
  [6] _convert_common_container
    @ C:\Users\djv23\.julia\packages\BandedMatrices\rDdVw\src\banded\BandedMatrix.jl:145 [inlined]
  [7] convert(::Type{…}, M::SubArray{…})
    @ BandedMatrices C:\Users\djv23\.julia\packages\BandedMatrices\rDdVw\src\banded\BandedMatrix.jl:154
  [8] convert
    @ C:\Users\djv23\.julia\packages\BandedMatrices\rDdVw\src\banded\BandedMatrix.jl:164 [inlined]
  [9] materialize!(M::ArrayLayouts.MulAdd{…})
    @ BandedMatrices C:\Users\djv23\.julia\packages\BandedMatrices\rDdVw\src\generic\matmul.jl:182
 [10] muladd!
    @ C:\Users\djv23\.julia\packages\ArrayLayouts\QgP9t\src\muladd.jl:75 [inlined]
 [11] partialcholesky!(F::InfiniteLinearAlgebra.AdaptiveCholeskyFactors{…}, n::Int64)
    @ InfiniteLinearAlgebra C:\Users\djv23\.julia\packages\InfiniteLinearAlgebra\qfWao\src\infcholesky.jl:38
 [12] ClassicalOrthogonalPolynomials.CholeskyJacobiData(U::LinearAlgebra.UpperTriangular{…}, P::Normalized{…})
    @ ClassicalOrthogonalPolynomials C:\Users\djv23\.julia\packages\ClassicalOrthogonalPolynomials\LOdoJ\src\choleskyQR.jl:82
 [13] cholesky_jacobimatrix(W::LinearAlgebra.Symmetric{…}, Q::Normalized{…})
    @ ClassicalOrthogonalPolynomials C:\Users\djv23\.julia\packages\ClassicalOrthogonalPolynomials\LOdoJ\src\choleskyQR.jl:62
 [14] cholesky_jacobimatrix(w::QuasiArrays.BroadcastQuasiVector{…}, P::Normalized{…})
    @ ClassicalOrthogonalPolynomials C:\Users\djv23\.julia\packages\ClassicalOrthogonalPolynomials\LOdoJ\src\choleskyQR.jl:57
 [15] semiclassical_jacobimatrix(t::Float64, a::Float64, b::Int64, c::Float64)
    @ SemiclassicalOrthogonalPolynomials C:\Users\djv23\.julia\packages\SemiclassicalOrthogonalPolynomials\MxMOu\src\SemiclassicalOrthogonalPolynomials.jl:171
 [16] semiclassical_jacobimatrix(t::Float64, a::Float64, b::Int64, c::Float64)
    @ SemiclassicalOrthogonalPolynomials C:\Users\djv23\.julia\packages\SemiclassicalOrthogonalPolynomials\MxMOu\src\SemiclassicalOrthogonalPolynomials.jl:154
 [17] SemiclassicalJacobi(t::Float64, a::Float64, b::Int64, c::Float64)
    @ SemiclassicalOrthogonalPolynomials C:\Users\djv23\.julia\packages\SemiclassicalOrthogonalPolynomials\MxMOu\src\SemiclassicalOrthogonalPolynomials.jl:127
 [18] top-level scope
    @ REPL[32]:1
Some type information was truncated. Use `show(err)` to see complete types.