cumsum loses the sign of zero imaginary part

[stevengj]

julia> cumsum(1.7 - 0.0im + (0:7))
8-element Array{Complex{Float64},1}:
  1.7+0.0im
  4.4+0.0im
  8.1+0.0im
 12.8+0.0im
 18.5+0.0im
 25.2+0.0im
 32.9+0.0im
 41.6+0.0im

(I would have expected -0.0im imaginary parts.)

Similarly for cumprod.

[jiahao]

Similarly for cumprod. Probably a zero issue?

julia> cumprod!(Array{Complex128}(1), -0.0im + (0:0))
1-element Array{Complex{Float64},1}:
 0.0+0.0im

[jiahao]

Is it too horrible a hack to simply change zero(...) to -zero(...) in this line

julia/base/arraymath.jl

Line 445 in 40c0fc6

($fp)(v, result, $(op==:+ ? :(zero(first(v))) : :(one(first(v)))), first(indices(v,1)), n)

?

[stevengj]

Or we could just use @inbounds c[i1] = v[i1]. I don't think calling op accomplishes anything there. Even if 0+v[i1] is of a different type than v[i1], the assignment to c[i1] should do any necessary conversion.

[TotalVerb]

Would it be really breaking if zero(Float) returned -0.0? Technically, the real floating point additive identity is -0.0... See #18341.

[stevengj]

Note that this is not specific to complex arithmetic:

julia> cumsum([-0.0])
1-element Array{Float64,1}:
 0.0

[eschnett]

Well -- if we're not changing zero to return the additive identity, then we can either special-case IEEE numbers here, or introduce a new function additive_identity that falls back to zero, but handles representations with negative zeros correctly.

Another option would be to change cumsum's algorithm to work in the same way as sum, probably by special-casing empty arrays.

By the way:

julia> cumsum([])
ERROR: BoundsError: attempt to access 0-element Array{Any,1} at index [1]
 in cumsum(::Array{Any,1}) at ./arraymath.jl:480

[stevengj]

@eschnett, see my comment above for a simple fix. Oh, nevermind, it's not that simple, because that extra $op is required for the cumsum logic.

[stevengj]

cumsum already special-cases empty arrays. It looks sufficient to special-case length-1 arrays as well.

[eschnett]

2-element arrays also don't work correctly:

julia> cumsum([-0.0, -0.0])
2-element Array{Float64,1}:
 0.0
 0.0
julia> sum([-0.0, -0.0])
-0.0

[TotalVerb]

That definitely is an argument to start at the additive identity, whether or not zero is changed to return it.

[oscardssmith]

I think I should probably mention that there is an argument over whether isequal(-0.0, 0.0) should return true. #18485

[timholy]

I'm not sure one can unambiguously say this was wrong. For example:

julia> 1.7 - 0.0im + convert(Vector{Complex128}, [0:7;])
8-element Array{Complex{Float64},1}:
 1.7+0.0im
 2.7+0.0im
 3.7+0.0im
 4.7+0.0im
 5.7+0.0im
 6.7+0.0im
 7.7+0.0im
 8.7+0.0im

If one considers that promotion should happen before arithmetic, then the given result is simply a consequence of the fact that -0.0 + 0.0 === 0.0.