Why doesn't pow() function gives correct result to print armstrong number between two intervals but num*num*num gives in C++?

Question

I have tried to print Armstrong number between 100 and 1000; my code with pow() function print all numbers except 153. But when I tried to run the code temp*temp*temp it gives all numbers including 153. How?

#include<iostream>
#include <math.h>
using namespace std;
int main() {
    int lower, upper;
    cout << "enter the lower and upper bound number";
    cin >> lower >> upper;
    cout<< "armstrong number are " << endl;
    for(int num = lower; num <= upper; num++) {
       int sum = 0, num1 =num,temp;
        while(num1 != 0) {
            temp = num1 % 10;
            // sum = sum + temp * temp * temp; [this gives a correct result]
            sum = sum + pow(temp,3);
            num1 = num1 / 10;
        }
        if(num == sum) 
            cout << num << endl;1
    }
    return 0;
}

Answer 1

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 insist 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 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.

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¹In fact I'd consider an implementation of pow that gave an incorrect result for a third power of an integral argument defective.