Structured broadcasting doesn't work with functions that may not preserve structure conditionally

[jishnub]

This might be too ambitious, but broadcasting a function that may conditionally preserve zeros fails currently:

julia> (x -> rand() < 0.5 ? 0 : 1).(Diagonal([1,2]))
ERROR: ArgumentError: cannot set off-diagonal entry (2, 1) to a nonzero value (1)
Stacktrace:
  [1] setindex!
    @ ~/.julia/juliaup/julia-nightly/share/julia/stdlib/v1.12/LinearAlgebra/src/diagonal.jl:206 [inlined]
  [2] _setindex!
    @ ./abstractarray.jl:1472 [inlined]
  [3] setindex!
    @ ./abstractarray.jl:1442 [inlined]
  [4] macro expansion
    @ ./broadcast.jl:974 [inlined]
  [5] macro expansion
    @ ./simdloop.jl:77 [inlined]
  [6] copyto!
    @ ./broadcast.jl:973 [inlined]
  [7] copyto!(dest::Diagonal{…}, bc::Base.Broadcast.Broadcasted{…})
    @ LinearAlgebra ~/.julia/juliaup/julia-nightly/share/julia/stdlib/v1.12/LinearAlgebra/src/structuredbroadcast.jl:206
  [8] copy
    @ ./broadcast.jl:898 [inlined]
  [9] materialize(bc::Base.Broadcast.Broadcasted{LinearAlgebra.StructuredMatrixStyle{…}, Nothing, var"#35#36", Tuple{…}})
    @ Base.Broadcast ./broadcast.jl:873
 [10] top-level scope
    @ REPL[2]:1
Some type information was truncated. Use `show(err)` to see complete types.

julia> (x -> rand() < 0.5 ? 0 : 1).(Diagonal([1,2]))
2×2 Matrix{Int64}:
 0  0
 1  0

julia> versioninfo()
Julia Version 1.12.0-DEV.1127
Commit ca72e28f26b (2024-08-31 11:47 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 8 × Intel(R) Core(TM) i5-10310U CPU @ 1.70GHz
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, skylake)
Threads: 1 default, 0 interactive, 1 GC (on 8 virtual cores)
Environment:
  JULIA_EDITOR = subl

This is because the function is evaluated once to check if it does preserve a zero, and the destination type is chosen based on this. In the first case, the destination is chosen to be a Diagonal, which fails, while in the second case, it is chosen to be a Matrix and the copyto! succeeds. This approach of choosing the destination by evaluating the function only works if the function always produces the same output for a zero input. I wonder if there might be some introspection tools that might help us assess this? Or at least, this should consistently error, so that a working code doesn't break on being run a second time.

[Seelengrab]

This is because the function is evaluated once to check if it does preserve a zero, and the destination type is chosen based on this.

I think this is basically the same as requiring the function to be :consistent. Unfortunately, that's not dispatchable information...