#include <iostream>

// This program queries the user for two integers 'm'
// and 'n' and calculates their greatest common divisor
// using the Euclidean algorithm.
//
// By convention, the greatest common divisor is
// non-negative. In particular,
//
//     gcd(m, 0) = |m|,
//     gcd(0, n) = |n|,
//
// and we will define
//
//     gcd(0, 0) = 0.
//
// Exercises:
//
// 1. This code does not work if at least one of the
//    arguments is 0. In particular, it may attempt
//    to calculate a remainder after division by 0.
//
//    Modify the code so that it correctly handles
//    cases where either or both arguments are 0.
//
// 2. If the program crashes with the message
//
//        Floating point exception (core dumped)
//
//    what exact operation in this program causes the
//    error?
//
//    Is the program actually performing any
//    floating-point arithmetic?
//
// 3. Trace the Euclidean algorithm by hand for
//
//        m = 112
//        n = 42.
//
//    What are the successive values of 'm', 'n',
//    and 'rem'?

// Function declarations
int main();

// Function definitions
int main() {
    int m{};
    int n{};

    std::cout << "Enter the first integer: ";
    std::cin  >> m;

    if ( m < 0 ) {
        m = -m;
    }

    std::cout << "Enter the second integer: ";
    std::cin  >> n;

    if ( n < 0 ) {
        n = -n;
    }

    // Make sure m >= n.
    if ( m < n ) {
        int tmp{ m };
        m = n;
        n = tmp;
    }

    // Perform the Euclidean algorithm.
    while ( m%n != 0 ) {
        int rem{ m%n };
        m = n;
        n = rem;
    }

    std::cout << "The gcd is " << n << "."
              << std::endl;

    return 0;
}



























// Hint for Exercise 1:
//
// After making both integers non-negative and
// ensuring that m >= n, what can you immediately
// conclude if
//
//     n == 0?
//
// In that case, should the Euclidean algorithm
// even be executed?



























// Hint for Exercise 2:
//
// Consider the condition of the while loop:
//
//     m%n != 0
//
// What operation is performed before the result
// can be compared with 0?
//
// What happens if n == 0?



























// Here is one solution:
/*
int main() {
    int m{};
    int n{};

    std::cout << "Enter the first integer: ";
    std::cin  >> m;

    if ( m < 0 ) {
        m = -m;
    }

    std::cout << "Enter the second integer: ";
    std::cin  >> n;

    if ( n < 0 ) {
        n = -n;
    }

    // Make sure m >= n.
    if ( m < n ) {
        int tmp{ m };
        m = n;
        n = tmp;
    }

    // If n == 0, then gcd(m, 0) == m. Otherwise,
    // perform the Euclidean algorithm.
    if ( n != 0 ) {
        while ( m%n != 0 ) {
            int rem{ m%n };
            m = n;
            n = rem;
        }
    } else {
        n = m;
    }

    std::cout << "The gcd is " << n << "."
              << std::endl;

    return 0;
}
*/

























// Explanation of Exercise 2:
//
// The operation that causes the error is
//
//     m%n
//
// when
//
//     n == 0.
//
// The '%' operator calculates the remainder after
// integer division. There is no remainder after
// division by zero because integer division by zero
// is undefined.
//
// Despite the message
//
//     Floating point exception (core dumped)
//
// no floating-point calculation occurs in this
// program. On some systems, integer division or
// remainder by zero generates the same kind of
// processor signal that is reported using this
// historical message.