Relax complex function signatures to make them ForwardDiff compatible

[YingboMa]

This PR relaxes complex math function signatures so log(::Complex{<:Dual}) can work.

Ref: JuliaDiff/ForwardDiff.jl#455

[YingboMa]

Example:

using ForwardDiff
Base.float(d::ForwardDiff.Dual{T}) where T = ForwardDiff.Dual{T}(float(d.value), d.partials)
Base.prevfloat(d::ForwardDiff.Dual{T,V,N}) where {T,V,N} = ForwardDiff.Dual{T}(prevfloat(float(d.value)), d.partials)
Base.nextfloat(d::ForwardDiff.Dual{T,V,N}) where {T,V,N} = ForwardDiff.Dual{T}(nextfloat(float(d.value)), d.partials)
function Base.ldexp(x::T, e::Integer) where T<:ForwardDiff.Dual
    if e >=0
        x * (1<<e)
    else
        x / (1<<-e)
    end
end

julia> using Test

julia> for f in [atanh, tanh, acos, x->2^x, x->(2+im)^x, exp10, exp2, expm1, log, sqrt]
           @inferred f(ForwardDiff.Dual(1, 1) + im)
       end

[jebej]

Any potential performance impacts?

[YingboMa]

channels                        |      225     1               226

I don't think the CI failure is related.

[arm61]

Even running on the nightly I am still having an error thrown with some of the examples in @YingboMa's comment (#36030 (comment)). i.e.

julia> using ForwardDiff
julia> sqrt(ForwardDiff.Dual(1., 1.) + 0im)
ERROR: MethodError: no method matching nextfloat(::ForwardDiff.Dual{Nothing, Float64, 1})
Closest candidates are:
  nextfloat(::Union{Float16, Float32, Float64}, ::Integer) at float.jl:595
  nextfloat(::BigFloat) at mpfr.jl:911
  nextfloat(::AbstractFloat) at float.jl:639
  ...
Stacktrace:
 [1] ssqs(x::ForwardDiff.Dual{Nothing, Float64, 1}, y::ForwardDiff.Dual{Nothing, Float64, 1})
   @ Base ./complex.jl:472
 [2] sqrt(z::Complex{ForwardDiff.Dual{Nothing, Float64, 1}})
   @ Base ./complex.jl:487
 [3] top-level scope
   @ REPL[19]:1

Any help/advice would be great! I am new to julia but keen to learn.

[baggepinnen]

You must define the functions listed above, the following works on a 14 day old nightly.

julia> using ForwardDiff

julia> Base.float(d::ForwardDiff.Dual{T}) where T = ForwardDiff.Dual{T}(float(d.value), d.partials)

julia> Base.prevfloat(d::ForwardDiff.Dual{T,V,N}) where {T,V,N} = ForwardDiff.Dual{T}(prevfloat(float(d.value)), d.partials)

julia> Base.nextfloat(d::ForwardDiff.Dual{T,V,N}) where {T,V,N} = ForwardDiff.Dual{T}(nextfloat(float(d.value)), d.partials)

julia> function Base.ldexp(x::T, e::Integer) where T<:ForwardDiff.Dual
           if e >=0
               x * (1<<e)
           else
               x / (1<<-e)
           end
       end

julia> sqrt(ForwardDiff.Dual(1., 1.) + 0im)
Dual{Nothing}(1.0,0.5) + Dual{Nothing}(0.0,0.0)*im

[arm61]

Amazing! It is working now for me.

[kapple19]

Am I doing something wrong?

julia> using ForwardDiff

julia> Base.float(d::ForwardDiff.Dual{T}) where T = ForwardDiff.Dual{T}(float(d.value), d.partials)

julia> Base.prevfloat(d::ForwardDiff.Dual{T,V,N}) where {T,V,N} = ForwardDiff.Dual{T}(prevfloat(float(d.value)), d.partials)

julia> Base.nextfloat(d::ForwardDiff.Dual{T,V,N}) where {T,V,N} = ForwardDiff.Dual{T}(nextfloat(float(d.value)), d.partials)

julia> function Base.ldexp(x::T, e::Integer) where T<:ForwardDiff.Dual
                  if e >=0
                                 x * (1<<e)
                                            else
                                                           x / (1<<-e)
                                                                      end
                                                                             end

julia> sqrt(ForwardDiff.Dual(1., 1.) + 0im)
ERROR: StackOverflowError:
Stacktrace:
 [1] sqrt(::Complex{ForwardDiff.Dual{Nothing,Float64,1}}) at .\complex.jl:506 (repeats 79984 times)

[arm61]

Are you using the nightly 1.6.x build? That's what I needed.