Evalpoly without coefficients: ugly errors, zero polynomial?

Consider calls such as these:

julia> evalpoly(3, ())
ERROR: BoundsError: attempt to access Tuple{} at index [0]
 [1] getindex(t::Tuple, i::Int64)
   @ Base ./tuple.jl:31
 [2] macro expansion
   @ ./math.jl:182 [inlined]
 [3] evalpoly(x::Int64, p::Tuple{})
   @ Base.Math ./math.jl:181
 [4] top-level scope
   @ REPL[1]:1

julia> evalpoly(0.3, Float64[])
ERROR: BoundsError: attempt to access 0-element Vector{Float64} at index [0]
 [1] getindex
   @ ./essentials.jl:13 [inlined]
 [2] _evalpoly
   @ ./math.jl:199 [inlined]
 [3] evalpoly(x::Float64, p::Vector{Float64})
   @ Base.Math ./math.jl:194
 [4] top-level scope
   @ REPL[2]:1

Some issues:

  1. The errors are not friendly/decriptive.

  2. In the case when the coefficients are an empty tuple, Tuple{}, it might make sense to fail early, that is, make this a MethodError by preventing dispatch to the method for empty tuples in the first place. This trick should work.

  3. Arguably, a polynomial with no coefficients should be interpreted as the zero polynomial. So it might make sense to special-case this instead of erroring. For tuples this might be addressed with a method like so: Base.evalpoly(::T, ::Tuple{}) where {T} = zero(T). For empty vectors an additional check would need to be included at the beginning of the relevant method.

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