What if we Initializing variable with 'double' instead of 'integer' while using pow() function as equation in c++?

Question

I have been trying to solve a basic Armstrong problem in C++ using the pow() function.

I'm encountering unexpected behavior while implementing a solution to compute Armstrong numbers in C++ using the pow() function. An Armstrong number is defined as a number that is equal to the sum of its digits raised to the power of the number of digits. While my code successfully identifies Armstrong numbers in most cases, it fails to do so for certain inputs, notably when the number 153 is entered.

Specific Issues Encountered:

• Unexpected Output: When inputting the number 153, the program produces unexpected results during the calculation process.

• Incorrect Sum: The calculated sum of digits raised to the power of the number of digits does not match the expected result for the number 153.

• Observations: Upon debugging and researching, I've observed discrepancies in the output generated by the pow() function, particularly when used with integral arguments.

Proposed Solutions Investigated:

1. Truncation Issue: I explored the possibility of truncation errors occurring due to the conversion of double results to int.

2. Alternative Implementations: I considered alternative computation methods, such as using std::pow from <cmath> or manually calculating powers to mitigate potential issues with pow().

While calculating the pow() function, I encountered a problem the function gives unexpected output while solving a specific number -> '153' as: (But giving correct result while solving other Armstrong numbers like 4, 9, 370, 371, etc)

---

Enter a number: 153

Sum: 27

Sum: 151

Sum: 152

153 is not an armstrong number.

CODE: -

#include <iostream>
#include <cmath>

using namespace std;

int main()
{
    int num, temp, digit, sum = 0;

    cout << "\nEnter a number: ";
    cin >> num;
    temp = num;
    digit = log10(num) + 1;

    while (temp > 0)
    {
        sum += pow((temp % 10), (digit));
        temp /= 10;
        cout << "\nSum: " << sum;
    }

    if (sum == num) {
        cout << endl << num << " is an armstrong number.";
    } else {
        cout << endl << num << " is not an armstrong number.";
    }

    cout << "\n\n";
    return 0;
}

---

There is a solution I found on stack overflow:

Although it's fashionable to expect pow to return the best possible result, particularly with integral arguments1, neither the C++ standard nor the IEEE754 floating point standard insists on that.

And with a truncation of the double result to an int, your result could be 1 less than expected.

The solution is to write out small powers in longhand: temp * temp * temp in your case.

You might get a better result with std::pow from <cmath> as then your compiler will pick an overload more suitable for your calculation. – @Bathsheba

Also,

If you put a cout << pow(temp,3) just after sum = sum + pow(temp,3) you will see expected result i.e 27, 125 and 1 on passing 153 and 153 as argument. But if you put cout << sum just after sum = sum + pow(temp,3) then unexpected result are shown i.e. 27, 151 and 152 . Instead of 151 there must be 152. – @Jayant Sharma

---

But after trial and error, there is a solution I came up with.

If we initialize the variable with double where we storing the pow() function equation will result the correct output.

Like in above code if we initialize double sum = 0;, the output will be expected as:

Enter a number: 153

Sum: 27

Sum: 152

Sum: 153

153 is an armstrong number.

CODE: -

#include <iostream>
#include <cmath>

using namespace std;

int main()
{
    int num, temp, digit;
    double sum = 0;

    cout << "\nEnter a number: ";
    cin >> num;
    temp = num;
    digit = log10(num) + 1;

    while (temp > 0)
    {
        sum += pow((temp % 10), (digit));
        temp /= 10;
        cout << "\nSum: " << sum << endl;
    }

    if (sum == num) {
        cout << endl << num << " is an armstrong number.";
    } else {
        cout << endl << num << " is not an armstrong number.";
    }

    cout << "\n\n";
    return 0;
}

Resolution Attempted:

After experimentation, I found that initializing the sum variable as a double instead of an int yielded the expected output for Armstrong numbers, including 153.

Request for Assistance:

I seek insights into the root cause of the unexpected behavior and recommendations for optimizing the computation of Armstrong numbers using the pow() function in C++.