static vector much slower than global in recursive function - c++

Question

I want to use static variables instead of global variables, found it was much slower than before. The original code took less than 0.01 seconds, now it takes about 1.6 seconds.
I am not familiar with vector. Is there a simple way to get the same performance as before?
#include <cstdio>
#include <cmath>
#include <ctime>
#include <vector>
using namespace std;
vector<double> fun(double x1, double y1, double x5, double y5, int i)
{
static vector<double> vec;
double x2 = (2 * x1 + x5) / 3;
double y2 = (2 * y1 + y5) / 3;
double x3 = (x1 + x5) / 2. + (y1 - y5) / (2. * sqrt(3));
double y3 = (-x1 + x5) / (2. * sqrt(3)) + (y1 + y5) / 2.;
double x4 = (x1 + 2 * x5) / 3;
double y4 = (y1 + 2 * y5) / 3.;
if (i <= 1)
{
vec.push_back(x1);
vec.push_back(y1);
vec.push_back(x2);
vec.push_back(y2);
vec.push_back(x3);
vec.push_back(y3);
vec.push_back(x4);
vec.push_back(y4);
vec.push_back(x5);
vec.push_back(y5);
}
else
{
fun(x1, y1, x2, y2, i - 1);
fun(x2, y2, x3, y3, i - 1);
fun(x3, y3, x4, y4, i - 1);
fun(x4, y4, x5, y5, i - 1);
}
return vec;
}
int main(int argC, char** argV)
{
clock_t t0 = clock();
int n = 8;
vector<double> vec = fun(0, 0, 1, 0, n);
printf("%d\n", vec.size());
printf("time %0.4fs\n", (clock() - t0) / 1000.0);
return 0;
}

Answer 1

There are two factors,
The minor factor is that every time the function enters, the program checks whether the variable has been initialized (and this must be thread safe)
The major factor is that you're returning a copy of the vector from every call, even though you ignore almost all of them. (There are 21,845 vector copies, each involving a memory allocation and deallocation, with a total of 1,790,197,760 doubles being copied. That's almost 15 gigabytes.)
The simple way to solve both the performance issue and the issue of only being able to solve the problem once is to accumulate the result in a reference argument:
void fun(double x1, double y1, double x5, double y5, int i, vector<double>& vec)
and remove the local vec from fun, and then in main,
vector<double> vec;
fun(0, 0, 1, 0, n, vec);
No other changes should be necessary.