Use dual-like type to reimplement cauchy(f,x,s)

[dlfivefifty]

The current usage of s to indicate left/right limit is error prone. It should be replaced by a special type DirectedNumber, which special functions like log, etc. override.

(I want to think about whether a more general notion of choice of branch would be better.)

[dlfivefifty]

This works:

"""
`Directed` represents a number that is a limit from either left (s=true) or right (s=false)
"""
immutable Directed{s,T}
    x::T
end

Base.convert{s}(::Type{Directed{s}},x) = Directed{s,eltype(x)}(x)
*{s}(a::Directed{s},b::Number) = Directed{s}(a.x*b)
*{s}(b::Number,a::Directed{s}) = a*b

const ⁺ = Directed{true}(true)
const ⁻ = Directed{false}(true)

1⁺
1⁻

I think all it takes then is to consider log, etc. oriented from [0,-∞) not (-∞,0], at least for _2F1 where we need to use -z.

[dlfivefifty]

Implemented and merged!