RFC: add evalpoly function, mirroring @evalpoly macro

[stevengj]

As mentioned in #7146, since we have an @evalpoly(z, c...) it makes sense to also have a evalpoly(z, c), analogous to Matlab's polyval but with the arguments in reverse order and the coefficients in ascending order by power of z.

We could alternatively mirror Matlab and store the coefficients in descending order, in which case we might as well swap the arguments and call it polyval. However, this issue seems to have been discussed in vtjnash/Polynomial.jl#5, and the consensus seems to have been to reject Matlab's ordering, resulting in @Keno's Polynomials.jl fork.

[stevengj]

There's also the question of whether this should use * or .*, where the latter is used in Polynomial.jl. Using .* (and presumably .+ for consistency) allows us to evaluate a polynomial with vector-valued coefficients at a vector of points, but I was uncomfortable with using it in a generic evalpoly. First, my feeling is that evalpoly should work for any types that define + and * in such a way as to form a field (i.e. satisfying a distributive law); they shouldn't have to define .* (which has no default meaning for non-Number types). Second, this isn't Matlab and I'm not sure it's a good idea to vectorize evaluation of multiple polynomials in that way (on the other hand, it is convenient to evaluate a single scalar-coefficient polynomial at a vector of points, and I added a method for that).

[doy]

Any progress on this?

[stevengj]

There doesn't seem to be much demand for such a function.

[IainNZ]

Cross-reference to Stackoverflow question along these lines: http:https://stackoverflow.com/questions/28077057/julia-evalpoly-macro-with-varargs/

[stevengj]

Rebased this in case anyone is still interested. (Probably should be updated to use muladd too.)

[stevengj]

Updated to use muladd.

[stevengj]

Travis failure on OSX seems unrelated: "The job exceeded the maxmimum time limit for jobs, and has been terminated."

[vtjnash]

As @stevengj said, doesn't seem like interest in having this in Base. To me, seems like a better match for a package, so I've opened JuliaMath/Polynomials.jl#169. I assume Nemo (http:https://nemocas.org/index.html) already has it?