How to detect integer overflow?-CodePudding

Write a program that reads and stores a series of integers and then computes the sum of the first N integers. First ask for N, then read the values into a vector, then calculate the sum of the first N values. For example: “Please enter the number of values you want to sum:” 3 “Please enter some integers (press '|' to stop):” 12 23 13 24 15 | “The sum of the first 3 numbers ( 12 23 13 ) is 48.” Handle all inputs. For example, make sure to give an error message if the user asks for a sum of more numbers than there are in the vector.

Modify the program from exercise 8 to write out an error if the result cannot be represented as an int.

So in exercise 9 it says to write out an error message if the result cannot be represented as an int, but if I'm only adding up integers here the only thing I can think of here that would cause a number to not be able to be represented as an int would be if there's some integer overflow and the integer goes above INT_MAX or below INT_MIN but how exactly can I detect this?

This is my code:

#include<vector>
#include<cmath>
#include<string>
#include<iostream>
#include<algorithm>
#include<stdexcept>
using namespace std;

    int main()
    {
        int N = 0;
        vector<int> values;
        cout << "Please enter the number of values you want to sum." << '\n';
        cin >> N;
        cout << "Please enter some numbers" << '\n';
        for (int tempnum; cin >> tempnum; )
        {
    
            values.push_back(tempnum);
    
    
        }
        if (N > values.size())
        {
    
            cout << "How am I gonna add up more numbers than you gave me?" << '\n';
        }
        else
        {
            int total = 0;
            for (int i = 0; i < N; i  )
            {
                total  = values[i];
            }
            
    
        }
    
    }

But I can't just check if total is above or below INT_MAX or INT_MIN because INT_MAX 1 or something returns some random negative value so I'm not really sure how to do this

CodePudding user response：

You can do this with some arithmetic:

So you want to know if acc x > INT_MAX, where acc is the accumulator (the sum so far) and x is the next element. Adding them together may overflow though. But acc > INT_MAX - x is equivalent and x is already stored in an int. So this can also not underflow, bc. x can be at most INT_MAX.

I.e., just transform the inequation to avoid overflow. In this case, subtract x from both sides.

That only works for positive x though, thanks to user interjay for pointing this out.

With negative x, this becomes a subtraction:

acc   (-x) > INT_MAX
acc - x    > INT_MAX

This can not overflow, because we are subtracting from acc. But it may underflow, so the question becomes:

acc - x < INT_MIN
acc     < INT_MIN   x

So:

int acc = 0;
for (int i = 0; i < N;   i) {
    int x = values[i];
    if (x >= 0 && acc > (INT_MAX - x)) {
        cout << "ERROR: Overflow.";
        return 1;
    } else if (x < 0 && acc < (INT_MIN - x)) {
        cout << "ERROR: Underflow.";
        return 1;
    } else {
        acc  = x;
    }
}