Isn't the sum of a series of integers always an integer? (Stroustrup PPP - Chapter 5, Question 9)

Question

Question 9:

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

To give more context to question 9, here's Question 8:

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.

So my question is:

If I have a vector of integers, and I sum the elements in the vector, won't my result always be an integer? If so, what is question 9 in Stroustrup PPP asking for?

*if it helps, here's a link to my code for question 8.

Answer 1

Yes, the result will always be an integer, but it may not be the "correct" solution because there was an overflow.

For instance if your integer type can only represent from -3 to 4, and you sum 2 and 3, what's the correct result? 5, but your integer result could be -3 instead (assuming 2-complement signed integers). That's what you need to detect.

Just an indication for the solution. numeric_limits<T>::max() is the max you can represent. If your current sum is sum and the new value value, what can you say about max - value and sum with regard to the overflow?

Answer 2

Indeed mathematically speaking the set of integers is closed under addition.

But the int of C++ is bound by numeric_limits<int>::min() and numeric_limits<int>::max(). The behaviour on exceeding this range is undefined.