#include "mymath.h"
#include <cmath>

using namespace std;


//************************************************************************
// function to return the gcd of two integers
//
// parameter usage
//     a,b -- import the numbers to find the gcd of
//
//  Pre-Condition -- a and b are positive
// Post-Conditions -- the gcd is returned
//************************************************************************
int gcd(int a, int b) {

   while (b != 0) {
      int remainder = a % b;
      a = b;
      b = remainder;
   }
   return a;
}


//************************************************************************
// function to find and return the lowest commmom multiple of two numbers
//
// parameter usage :
//     a, b -- import the numbers to find the lcm of
// 
//  Pre-Condition -- a and b are positive
// Post-Condition -- lowest common multiple of a and b is returned
//************************************************************************
int lcm(int a, int b) { return a * b / gcd(a,b); }


//************************************************************************
// function to exchange the values stored in two integer locations
//
// parameter usage :
//     a,b  -- import the numbers to be exchanged and
//             export the exchanged values
//
// Post-condition -- the values in the locations will be exchanged
//************************************************************************
void swap(int& a, int& b) {

   int temp = a;
   a = b;
   b = temp;
}


//************************************************************************
// function to exchange the values stored in two float locations
//
// parameter usage :
//     a,b  -- import the numbers to be exchanged and
//             export the exchanged values
//
// Post-condition -- the values in the locations will be exchanged
//************************************************************************
void swap(float& a, float& b) {

   float temp = a;
   a = b;
   b = temp;
}


//***********************************************************************
// utility function to check equality of floating point numbers
//
// parameter usage :
//     x,y  -- import the numbers to compared
//
// post-condition -- function returns true if the numbers are within
//                   TOLERANCE of each other; false otherwise
//*************************************************************************
bool dEqual(double x, double y) { return fabs(x-y) < TOLERANCE; }