Here's my attempt to encode the bisection method in C (give me a bit of a break veteran C people, I am but a mere high-level language user and might have designed it poorly). The crucial feature is that it takes a function as an argument, some of the details of which perhaps I don't understand perfectly (still figuring out pointers - although I'm told we're all still figuring out pointers):

#include <iostream>
#include <cmath>

double bisectionMethod(double (*f)(double), double a, double b, double eps)
{
    if (b <= a) {
        double switchVal = a;
        a = b;
        b = switchVal;
    }
    if ((*f)(a)*((*f)(b)) > 0) {
        return -999.0;
    }
    while ((b-a) > eps) {
        double middle = ((b a)/2.0);
        if (((*f)(middle)) * ((*f)(b)) > 0) {
            b = middle;
        }
        else if (((*f)(middle)) * ((*f)(a)) > 0) {
            a = middle;
        }
        else if (((*f)(middle)) == 0.0) {
            return middle;
        }
    }
    return ((b a)/2.0);
}

This function works on its own in a C file, and as an example, you may use the above function with the following example so that you can reproduce its functioning (the answer it outputs should be a decent approximation of ln(2)):

double fexample(double x)
{
    double y = (std::exp(x)-2);
    return y;
}

int main()
{
    std::cout << bisectionMethod(fexample, 0, 3, 0.0000001) << std::endl; 
    return 0;
}

Now, I'm using the Rcpp package to try and make this function callable in R (if I don't get any answer here I will do the circuit of R help subreddits/email lists). However that has so far failed, and the reason Rcpp gave was that f was an undeclared identifier, which is not a problem it had when I ran the function separately.

That requires:

// [[Rcpp::export]]

Directly above the function and:

#include <Rcpp.h>
using namespace Rcpp;

Added to the include statements at the top.

So my question is, what am I doing wrong? What do I change? And I guess, how do you make functional programming in C and R speak with each other since that seems to be the root of the problem.

EDIT: Previously when people have asked similar questions, people seem to get caught up on the fact that the post is implementing a very simple function with better implementations in both languages. You're right, there's probably a bisection method in some C package and another already implemented using Rcpp in some R package somewhere. But I am learning, not trying to provide a service to the R/C community, so my purpose was not to try to 'fix something that isn't broken'.

Since implementing the bisection method is a super common homework question for people learning C in classes, I might censor the function after there's a useful answer to my query if others think that's a good idea.