Harmonic Oscillator not getting oscillations - c++

Question

I am writing a harmonic oscillator program , but it does an exponential decay instead and I am not sure why. I have the code below. I use F= -k x and F = m a
I assume m = 1 and k = 1, so a = -x
So my equations to find velocity and position are
v(t) = v(t-dt) - x(t-dt) * dt
x(t) = x(t-dt) + v(t-dt) * dt
I am not sure what I am doing wrong
The code associated with this is
#include <iostream>
#include <fstream>
using namespace std;
double updateX(double intialV, double intialX, double step);
double updateV(double intialV, double intialX, double step);
int main()
{
long double position[2];long double velocity[2];
position[0] = 0.0; velocity[0] = 1.0; double time = 0.0; double step = .1;
ofstream outputFile;
outputFile.open("velo1.dat");
outputFile << time << " " << position[0] << " " << velocity[0] << "\n";
for(int i = 1; i < 50; i++)
{
time = i * step;
velocity[1] = updateV(velocity[0], position[0], step);
position[1] = updateX(velocity[0], position[0], step);
outputFile << time << " " << position[1] << " " << velocity[1] << "\n";
velocity[0] = velocity[1];
position[0] = velocity[1];
}
return 0;
outputFile.close();
}
double updateX(double intialV, double intialX, double step)
{
double stuff =(intialX + intialV * step);
return stuff;
}
double updateV(double intialV, double intialX, double step)
{
double stuff = (intialV - intialX * step) ;
return stuff;
}