I'm trying to calculate large integers with the long long datatype but when it gets large enough (2^55), the arithmetic behavior is unpredictable. I am working in Microsoft Visual Studio 2017.
In this first case, I am subtracting 2 from the long long variable m in the initialization. This works fine for all n until I try 54, then m will simply not be subtracted by 2.
#include <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <map>
#include <set>
using namespace std;
#define LL long long
int main()
{
LL n;
cin >> n;
LL m = pow(2, n + 1) - 2;
cout << m;
return 0;
}
However, using this code m does get subtracted by 2 and is working as I would expect.
#include <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <map>
#include <set>
using namespace std;
#define LL long long
int main()
{
LL n;
cin >> n;
LL m = pow(2, n + 1);
m -= 2;
cout << m;
return 0;
}
I expect both codes to be equivalent, why is this not the case?
The issue with
LL m = pow(2, n + 1) - 2;
is that pow(2, n + 1) is not a long long. It has the type double (refer to cppreference) and because the value is so large, subtracting 2 from it will not change its value. That means that m will not have the correct value. As you have already found, you need to assign the result first and then do the subtraction. Another alternative is to write your own pow that will return a integer type when given an integer type so you can do the raising to the power and subtraction at the same time.