Question

What is the difference between these two function prototypes ?

void apply1(double(f)(double));
void apply2(double(*f)(double));

If the goal is to apply the provided function to an array, is there a version faster compared to the other one ?

EDIT :
An example of implementation :

#include <iostream>
#include <vector>
#include <cmath>

// First version
template<typename Type> void apply1(std::vector<Type>& v, Type(f)(Type))
{
    for (unsigned int i = 0; i < v.size(); ++i) {
        v[i] = f(v[i]);
    }
}

// Second version
template<typename Type> void apply2(std::vector<Type>& v, Type(*f)(Type))
{
    for (unsigned int i = 0; i < v.size(); ++i) {
        v[i] = f(v[i]);
    }
}

// Main
int main()
{
   std::vector<double> v = {1., 2., 3., 4., 5.};
   apply1(v, std::sin);
   apply2(v, std::sin);
   return 0;
}

Answer 1

First, the speed of the template wrapper instantiation is going to be almost entirely at the mercy of your optimizer.

That said, I’ve reduced your samples to the most basic code I can think of, specifically to check the invoke of the function parameters. You can read on, but you’ll see they invoke exactly the same. There is no benefit for one declaration vs another. Further, I included the one you left out, (reference-decl)

#include <cstdio>

int hello(int x)
{
    return x;
}

template<typename Type> 
void apply1(Type x, Type (f)(Type))
{
    f(x);
}

template<typename Type> 
void apply2(Type x, Type (*f)(Type))
{
    f(x);
}

template<typename Type> 
void apply3(Type x, Type (&f)(Type))
{
    f(x);
}

int main(int argc, char *argv[])
{
    apply1(1,hello);
    apply2(2,hello);
    apply3(3,hello);
    return 0;
}

The actual asm generated from the deductions is:

apply1

__Z6apply1IiEvT_PFS0_S0_E:
Leh_func_begin2:
    pushq   %rbp
Ltmp2:
    movq    %rsp, %rbp
Ltmp3:
    subq    $16, %rsp
Ltmp4:
    movl    %edi, -4(%rbp)
    movq    %rsi, -16(%rbp)
    movq    -16(%rbp), %rax
    movl    -4(%rbp), %ecx
    movl    %ecx, %edi
    callq   *%rax
    addq    $16, %rsp
    popq    %rbp
    ret
Leh_func_end2:

apply2

__Z6apply2IiEvT_PFS0_S0_E:
Leh_func_begin3:
    pushq   %rbp
Ltmp5:
    movq    %rsp, %rbp
Ltmp6:
    subq    $16, %rsp
Ltmp7:
    movl    %edi, -4(%rbp)
    movq    %rsi, -16(%rbp)
    movq    -16(%rbp), %rax
    movl    -4(%rbp), %ecx
    movl    %ecx, %edi
    callq   *%rax
    addq    $16, %rsp
    popq    %rbp
    ret
Leh_func_end3:

apply3

__Z6apply3IiEvT_RFS0_S0_E:
Leh_func_begin4:
    pushq   %rbp
Ltmp8:
    movq    %rsp, %rbp
Ltmp9:
    subq    $16, %rsp
Ltmp10:
    movl    %edi, -4(%rbp)
    movq    %rsi, -16(%rbp)
    movq    -16(%rbp), %rax
    movl    -4(%rbp), %ecx
    movl    %ecx, %edi
    callq   *%rax
    addq    $16, %rsp
    popq    %rbp
    ret
Leh_func_end4:

They are identical (as I suspected they would be). There is no difference that I can see whatsoever.

Note: it is worth mentioning the way the compiler saw these declarations by name mangling examination:

apply1: __Z6apply1IiEvT_PFS0_S0_E
apply2: __Z6apply2IiEvT_PFS0_S0_E
apply3: __Z6apply3IiEvT_RFS0_S0_E