I do not seem to understand the use of @evalpoly (doc)

julia> @evalpoly(3.0, 1)
ERROR: BoundsError: attempt to access (1,)
  at index [0]

julia> f(p) = @evalpoly(3.0, p)
ERROR: BoundsError: attempt to access (:p,)
  at index [0]

julia> f(p) = @evalpoly(1, p...)
ERROR: BoundsError: attempt to access (:(p...),)
  at index [0]

From what I understand, the first error comes from https://github.com/JuliaLang/julia/blob/e976e63cc791411b1e7d88b7ca705e87e10d8574/base/math.jl#L110.

As for the second and third, is there a way to delay the evaluation of the macro until p is passed to the function f? Or is this not the way the macro is intended to be used?


The whole point of this macro is to inline the evaluation of a polynomial whose degree (and usually its coefficients) is known at compile time. This allows things like polynomial approximations of special-function implementations to be extremely efficient. Hence, the arguments must be an explicit list of coefficients.

(The case of a single coefficient, i.e. a degree-0 polynomial, is so pointless that we never implemented it. i.e. you might as well just write 1 instead of @evalpoly 3.0 1. We might as well implement it for completeness, I suppose.)

So, for example, if you knew that p was an array of length 4, you could do:

julia> f(p) = @evalpoly(1, p[1], p[2], p[3], p[4])
f (generic function with 1 method)

julia> f([2,3,4,5])

In practice, @evalpoly is mainly used in cases where the coefficients are compile-time constants as well, mainly in the implementation of special functions like erfinv and polygamma.

If you have an array p whose length is not known, there is no point in using a macro to evaluate the polynomial. It will need an explicit loop that is evaluated at runtime, rather than at compile-time as in @evalpoly.

At one point, I suggested that we have an evalpoly function for runtime evaluation of polynomials (RFC: add evalpoly function, mirroring @evalpoly macro by stevengj · Pull Request #7186 · JuliaLang/julia · GitHub), but there wasn’t much interest. In most such cases you probably want to use the Polynomials.jl package.


Thank you for the reply and the example.

I remember that at a certain point, you (most likely) implemented a horner method (or a macro) and I could not find it anymore. The @evalpoly is what came up when I searched the latest documentation for horner.

I completely agree with you that the evaluation of a 0th order polynomial is useless for the specialized cases of special functions.

I believe Stefan Karpinski addressed this specific macro at about 50m in the Julia - To Lisp or not to Lisp talk on YouTube.
Hope it helps.


Interesting presentation, @evalpoly macro aside. Thank you.

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My pleasure - but we should probably be thanking Stefan!