Conversion between 'std::function<double(double)>’ to ‘double (*)(double)’ - c++

Question

I am trying to pass a custom lambda to a function that expects a function pointer (more precisely the zero function in Brent library).
The idea is that I would create the lambda once with the parameters and then it would be evaluated at several values x inside this function.
I have tried the steps in this thread with no success and I am getting an error of no known conversion for argument 4 from ‘Function {aka std::function<double(double)>}’ to ‘double (*)(double)’. As far as I understand the compiler does not know how to cast from those 2 types.
Is there a workaround around this error? It would be better if no modifications had to be made to the library and it could be solved within my program. Here is a snippet of code to show the problem.
# include <functional>
# include "brent.hpp"
using namespace brent;
typedef std::function<double(double)> Function;
Function function_builder (double a, double b)
{
return [a,b](double x) {
return ( a * x + b );
};
}
int main ( )
{
Function func = function_builder ( 2.0, -1.0 );
double z = zero (0, 1, 0.001, func ); //func should be a function pointer of type double (*)(double)
return 0;
}

Answer 1

In your case, your lambda function has state - the captured a, b variables. There is no way to convert a stateful lambda to a pointer to function, but...
The Brent library does not expect a pointer to function. The zero function is declared as:
double zero ( double a, double b, double t, func_base& f )
and has an overload defined as:
// This is the overload you asked about, but....
double zero ( double a, double b, double t, double f ( double x ) ){
func_wrapper foo(f);
return zero(a, b, t, foo);
}
But you should use the first variant for your needs, which expects:
class func_base{
public:
virtual double operator() (double) = 0;
};
which is good news, since you simply have to derive from func_base, and put a lambda in there:
template <class Lambda>
class FunctionWithState : public func_base, public Lambda {
public:
FunctionWithState(const Lambda & lambda): Lambda(lambda) {}
double operator()(double x) override
{ return Lambda::operator()(x); }
};
template<class Lambda>
auto function_builder_base (Lambda lambda)
{
return FunctionWithState<decltype(lambda)>(lambda);
}
auto function_builder(double a, double b)
{
return function_builder_base([a,b](double x) {
return ( a * x + b );
});
}
The implementation details are a bit ugly, but the usage is reasonable:
main ( )
{
// func must be "auto" because the type depends on lambda, whose type is unknown.
auto func = function_builder ( 2.0, -1.0 );
double z = zero (0, 1, 0.001, func );
return 0;
}
Of course, it is possible to get rid of the lambda function altogether, and to manage state inside a non-templated object. But on the other hand, inheriting from lambda makes it easy to define many other function builders such as:
auto function_builder3(double a, double b, double c)
{
return function_builder_base([a,b,c](double x) {
return ( a*x*x + b*x + c );
});
}
In fact, you can use function_builder_base directly everywhere, eliminating the need for a function_builder middleman.

Answer 2

You won't have much luck without ugly hack (like using a global object of sorts) of passing a std::function<double(double)> to a double(*)(double). The key difference is that function pointer genuinely only abstract stateless functions while std::function<double(double)> or lambda functions with non-empty capture contain state.
Specifically for the Brent library mentioned there is, however, a way! The library doesn't really take function pointer but travels in terms of func_base objects. You can get one of these with a simple adapter:
struct brent_fun: func_base {
std::function<double(double)> fun;
template <typename Fun>
explicit brent_fun(Fun&& fun): fun(std::move(fun)) {}
double operator()(double value) override { return this->fun(value); }
};