module test
implicit none
private
public fib

contains

! Fibonacci function
integer recursive function fib(n) result(r)
    integer, intent(in) :: n
    if (n < 2) then
        r = n
    else
        r = fib(n-1) + fib(n-2)
    end if
end function  ! end of Fibonacci function
end module

program fibonacci
use test, only: fib
implicit none
integer :: r,i
integer :: n = 1e09
real(8) :: start, finish, cum_time

cum_time=0
do i= 1,n
    call cpu_time(start)
    r = fib(20)
    call cpu_time(finish)
    cum_time = cum_time + (finish - start)
    if (cum_time >0.5) exit
enddo

print*,i,'runs, average elapsed time is', cum_time/i/1e-06, 'us'
end program

gfortran -O3 -march=native

#include <iostream>
#include <chrono>
using namespace std;

// Fib function
int fib(const int n)
{
    int r;
    if (n < 2)
        r = n;
    else
        r = fib(n-1) + fib(n-2);
    return r;
} // end of fib

template<typename T, typename ... Args>
double timeit(T (*func)(Args...), Args...args)
{
    double counter = 1.0;
    double mean_time = 0.0;
    for (auto iter=0; iter<1e09; ++iter){
        std::chrono::time_point<std::chrono::system_clock> start, end;
        start = std::chrono::system_clock::now();

        func(args...);

        end = std::chrono::system_clock::now();
        std::chrono::duration<double> elapsed_seconds = end-start;

        mean_time += elapsed_seconds.count();
        counter++;

        if (mean_time > 0.5){
            mean_time /= counter;
            std::cout << static_cast<long int>(counter)
            << " runs, average elapsed time is "
            << mean_time/1.0e-06 << " xC2xB5s" << std::endl;
            break;
        }
    }
    return mean_time;
}

int main(){
    timeit(fib,20);
    return 0;
}

g++ -O3 -march=native

Fortran: 24991 runs, average elapsed time is 20.087 us
C++    : 12355 runs, average elapsed time is 40.471 µs

.L28:
    cmpl    $1, %r13d
    jle .L29
    leal    -8(%rbx), %eax
    movl    %ecx, 12(%rsp)
    movl    %eax, 48(%rsp)
    leaq    48(%rsp), %rdi
    leal    -9(%rbx), %eax
    movl    %eax, 16(%rsp)
    call    __bench_MOD_fib
    leaq    16(%rsp), %rdi
    movl    %eax, %r13d
    call    __bench_MOD_fib
    movl    12(%rsp), %ecx
    addl    %eax, %r13d

.L28:
    movl    72(%rsp), %edx
    cmpl    $1, %edx
    movl    %edx, %eax
    jle .L33
    subl    $3, %eax
    movl    $0, 52(%rsp)
    movl    %eax, %esi
    movl    %eax, 96(%rsp)
    movl    92(%rsp), %eax
    shrl    %eax
    movl    %eax, 128(%rsp)
    addl    %eax, %eax
    subl    %eax, %esi
    movl    %edx, %eax
    subl    $1, %eax
    movl    %esi, 124(%rsp)
    movl    %eax, 76(%rsp)

// Fib function
int fib(const int n)
{
    int r;
    if (n < 2)
        r = n;
    else
        r = fib(n-1) + fib(n-2);
    asm("");
    return r;
} // end of fib

.L7:
    cmpl    $1, %edx
    jle .L17
    leal    -4(%rbx), %r13d
    leal    -5(%rbx), %edx
    cmpl    $1, %r13d
    jle .L19
    leal    -5(%rbx), %r14d
    cmpl    $1, %r14d
    jle .L55
    leal    -6(%rbx), %r13d
    movl    %r13d, %edi
    call    _Z3fibi
    leal    -7(%rbx), %edi
    movl    %eax, %r15d
    call    _Z3fibi
    movl    %r13d, %edi
    addl    %eax, %r15d

Fortran: 24991 runs, average elapsed time is 20.087 us
C++    : 25757 runs, average elapsed time is 19.412 µs