Can you call a C function that takes function pointers as arguments?

Question

I want to use MathLink to call a function I wrote in C. However, similar to an integrator, it takes a function pointer as an argument and applies it on numbers depending on the other arguments. I know how to pass lists of reals and so on, but can you also pass pointers to functions defined in Mathematica? In the end, it should look something like this:

f[x_,y_] := x*y; Install["mycprogram"]; MyCFunction[f,1,2]

f is a function that takes two doubles and returns a double. It's fairly simple and should always be some combination of polynomials, fractions, Log and Exp.

Answer 1

I think there are several approaches to achieve the behavior you want but first let me point out that it is not possible to get a function pointer of a normal Mathematica function. A function pointer would require that the function was compiled but when you define a function inside Mathematica with e.g.

f[x_,y_] := x+y;

this is not the case as Oleksandr already pointed out.

Therefore, let me first give a solution which emulates the behavior you try to achieve. If you have a MathLink program or a library function which can be used inside Mathematica you can always evaluate any kind of expressions through MathLink-communication.

The idea now is to give your C-function the name of the Mathematica function (f) you want to call together with the numeric input. The you call inside your C-function the MathKernel and evaluate the call f[x,y] and use the result in the further computation.

Assume the following short library function (it is very similar to what you have to use in your MathLink program)

#include "mathlink.h"
#include "WolframLibrary.h"

DLLEXPORT mint WolframLibrary_getVersion( ) {
    return WolframLibraryVersion;
}

DLLEXPORT int WolframLibrary_initialize( WolframLibraryData libData) {
    return 0;
}

DLLEXPORT int func(WolframLibraryData libData, mint argc, MArgument *args, MArgument res)
{
    int pkt;
    mreal parm1, parm2, calc_result;
    char *f;

    f = MArgument_getUTF8String(args[0]);
    parm1 = MArgument_getReal(args[1]);
    parm2 = MArgument_getReal(args[2]);

    MLINK mlp = libData->getMathLink(libData);
    MLPutFunction(mlp, "EvaluatePacket", 1);
    MLPutFunction(mlp, f, 2);
    MLPutReal(mlp, parm1);
    MLPutReal(mlp, parm2);
    libData->processMathLink(mlp);
    pkt = MLNextPacket(mlp);
    if (pkt == RETURNPKT) MLGetReal(mlp, &calc_result);
    libData->UTF8String_disown(f);
    MArgument_setReal(res, calc_result);        
    return LIBRARY_NO_ERROR;

}

Assuming you have stored this inside the file "myfunc.c" then you can create the ready-to-use library with

<< CCompilerDriver`
CreateLibrary[{"myfunc.c"}, "myfunc", "ShellOutputFunction" :> Print]

The library is automatically put to a location where it can be found by Mathematica. When you have a closer look at the func function, you see that it expects a string and two double arguments. Then it simply uses a MathLink to evaluate the function-call f[parm1,parm2] and takes the result and just passes it back.

You can load and use this function inside your current session with

f[x_, y_] := x + y;
fun = LibraryFunctionLoad["myfunc", "func", {"UTF8String", _Real, _Real}, _Real]
fun["f", 1., 4.]

(*
    Out[4]= 5.
*)