Possible to add log and exp support?

[oschulz]

Would it be possible to add

Base.exp(::Zero) = One()
Base.log(::One) = Zero()

without causing unforseen trouble somewhere? If so, maybe

import Base.^
^(x::Number, ::Zero) = One()
^(x::Number, ::One) = x
Base.sqrt(::One) = One()
Base.sqrt(::Zero) = Zero()

as well?

[oschulz]

Ah, ^(x::Number, ::One) would cause some ambiguous dispatch. Would need

import Base.^

^(x::Number, ::Zero) = One()
^(x::Float16, ::Zero) = One()
^(x::Float32, ::Zero) = One()
^(x::Float64, ::Zero) = One()
^(x::BigFloat, ::Zero) = One()
^(x::AbstractFloat, ::Zero) = One()

^(x::Number, ::One) = x
^(x::Float16, ::One) = x
^(x::Float32, ::One) = x
^(x::BigFloat, ::One) = x
^(x::AbstractFloat, ::One) = x

Would that be too much "fine-tuning" resp. too fragile?

It would make things like A .^ Zero() run in constant time, with zero-sized output. :-) Not sure that's a relevant use-case, though.

[perrutquist]

Done.

^(x, p::One) doesn't need special-casing, because those methods typically start with something like p==1 && return x anyway. For example:

julia> @code_llvm 1.0^One()

;  @ math.jl:899 within `^'
define double @"julia_^_3800"(double) {
top:
;  @ math.jl:902 within `^'
  ret double %0
}

[oschulz]

Awesome, thanks!!