How do I specify a function's type/signature in Julia?

Question

I'm implementing Newton's method for finding roots in a precompiled library. The common case will be to work with functions from Float64 to Float64, and I want an optimized compiled version of it to exist in the library. I will, of course, implement a type generic version, too, but Julia will need some way of differentiating the methods by signature so it knows which one to call at runtime. Presently, the implementation is:

#Float64 optimized version
function findrootNewton( func, funcder, guess::Float64,
                        rtol::Float64=1e-12, abstol::Float64=1e-12, maxiter::Int=100 )
    #make sure tolerances are positive
    if rtol <= 0.0
        error("findrootNewton: rtol must be a positive number")
    end

    if abstol <= 0.0
        error("findrootNewton: abstol must be a positive number")
    end

    if maxiter <= 0.0
        error("findrootNewton: maxiter must be a positive integer")
    end

    converged::Bool = false

    oldx::Float64 = guess
    newx::Float64 = oldx - ((func(oldx) / funcder(oldx))::Float64)
    absdiff = abs(oldx - newx)

    iter = 2
    while (absdiff < abstol || absdiff < rtol * abs(newx)) && iter <= maxiter
        oldx = newx
        newx = oldx - func(oldx) / funcder(oldx)
        absdiff = abs(oldx - newx)

        iter += 1
    end #while (absdiff < abstol || absdiff < rtol * abs(newx)) && newxiter <= maxiter

    if iter <= maxiter
        converged = true
    end

    return (newx, converged)
end #findzeroNewton

#Generic version
function findrootNewton( func, funcder, guess::Number,
                        rtol::Real=1e-12, abstol::Real=1e-12, maxiter::Int=100 )
    #make sure tolerances are positive
    if rtol <= 0
        error("findrootNewton: rtol must be a positive number")
    end

    if abstol <= 0
        error("findrootNewton: abstol must be a positive number")
    end

    if maxiter <= 0
        error("findrootNewton: maxiter must be a positive integer")
    end

    converged::Bool = false

    newx = oldx - func(oldx) / funcder(oldx)
    oldx = convert(typeof(newx), guess)
    absdiff = abs(oldx - newx)

    iter = 2
    while (absdiff < abstol || absdiff < rtol * abs(newx)) && iter <= maxiter
        oldx = newx
        newx = oldx - func(oldx) / funcder(oldx)
        absdiff = abs(oldx - newx)

        iter += 1
    end #while (absdiff < abstol || absdiff < rtol * abs(newx)) && newxiter <= maxiter

    if iter <= maxiter
        converged = true
    end

    return (newx, converged)
end #findzeroNewton

This has not been used/debugged, yet. For example, I'm not checking for the derivative hitting zero because the particular case I'm coding this for does not need it.

Notice that if guess, rtol, and abstol arguments are given as Float64, but the functions don't return Float64 but BigFloat, then the code will fail at the point of the type assertion in the definition of newx, even though there is a method appropriate to generic functions available. Is there a way to avoid this problem?

Edit: I can specify the type of data a variable stores in Julia, for example:

x::Float64 = 2.5

Is it possible to similarly specify the signature of a variable that can store (pointers to) functions?

Answer 1

For clarity I will write my comment as an answer: You don't need to specialize function signatures on types in Julia, unless it is to implement a specialized handling in the function body. Argument type assertion has no impact on code speed or compilability. See http://docs.julialang.org/en/latest/manual/performance-tips/

Type assertions in function arguments in julia are mainly used to control multiple dispatch, i.e. different function behaviour for different types of the input arguments. When not asserting a type, the compiler will automatically compile a type-specialized version for each combination of input arguments.

If you need for another reason, e.g. to ensure type stability, to assert that the return type of a function is the same as the input, you can do

function foo(x::T)::T where T
...
end