#include <iostream>
#include <iomanip>
#include <limits>
#include <math.h>
#include <numbers>

using namespace std;

int main()  {

    float f; 
    long double bigNumber;
    numeric_limits<float>floatInfo;
    numeric_limits<long double>ldInfo;

    cout << "\tThe size of a float is " << sizeof(float) << endl; 
    cout << "\tThe size of a float is " << sizeof(f) << endl; 
    cout << "\tThe size of a double is " << sizeof(double) << endl; 
    cout << "\tThe size of a long double is " << sizeof(long double) << endl; 
    cout << endl;

   
    // limits

    cout << "The smallest float is " << floatInfo.min() << endl;
    cout << "The largest float is " << floatInfo.max() << endl;

    bigNumber = floatInfo.max();

    // overflow
    cout << bigNumber << " +  1 = " << bigNumber+1 << endl;

    cout << "An exmpal of gap " << endl;
    long double biggerNumber = bigNumber  + 1;
    cout << bigNumber << " - " << biggerNumber
         << " = " << bigNumber-biggerNumber << endl;

    cout << endl << endl;

    cout << "At 1, the next float is " << floatInfo.epsilon() << endl;
    cout << "At 1, the next ld is " << ldInfo.epsilon() << endl;
    cout << "Everything between this and 1 is in the GAP" << endl;

    cout << endl << endl;
    cout << "The largest long double is " << ldInfo.max() << endl;
    cout << "The smallest long double is " << ldInfo.min() << endl;
    cout << "The closest to zero long double is " << ldInfo.denorm_min() << endl;

    cout << endl;
    cout << "minimum exponent for ld " << ldInfo.min_exponent << endl ;
    cout << "minimum exponent for float " << floatInfo.min_exponent << endl;
    cout << endl << endl;

    cout << "0/0 " << float(0) / float(0) << endl;
    cout << "7/0 " << 7.0/0.0 << endl;
    cout << "-7/0 " << -7.0/0.0 << endl;

    cout << endl << endl;
    cout << "Pi = " << M_PI << endl;

    return 0;
}