//
// Apr. 8, 1999
// Dr. Ken Vollmar      KenVollmar@mail.smsu.edu     (417)836-5789
// Dept. of Computer Science                 www.cs.smsu.edu/~vollmar
// Southwest Missouri State University
// 901 S. National Ave.
// Springfield, MO 65804
//
// Problem: Show the hexadecimal representation of an IEEE 754 32-bit
// floating point number.
// It is not possible to examine the bits of a floating point data type, 
// nor to print the value of a f.p. type in hex. Also, if the f.p. value is
// assigned to an integer type, then the bits are rearranged so that the
// numeric represented value is maintained.
// 
// Solution: Define storage space such that the same space is used for both
// the f.p. data type and the integer type. Initialize the f.p. form of the
// storage location, but operate on the integer form of the location.
// Look at the integer form four bits at a time in a loop. At each group 
// of four bits, print the corresponding hexadecimal digit.

#include <math.h>
#include <iostream.h>
#include <assert.h>

main()
{
   // "union" declares the members to be stored in the same memory space.
   union {
     unsigned long l;
     float f;
     } input, temporary;

   int denominator = 2;
   unsigned long mask = 0x400000;  // Set to MSBit of significand
   unsigned long significand;
            long exponent;  // exponent is signed (may be neg.)
   unsigned long sign;
   char dummy;

   // Verify that union contains equal-sized data items.
   // This is critical because the two types must be
   // stored in the same memory location.
   assert (sizeof(unsigned long) == sizeof(float));

   cout << endl << "Default precision value for cout stmts is ";
   cout << cout.precision() << endl << endl;

   cout << endl << "Input a float value? ";
   cin >> input.f;

   cout << "\n\nThe original float value: " << input.f << endl;
   cout << "        " << endl;

   cout << hex;  // Format the output in hexadecimal
   cout << "\n\nThe hex form of original float value: " << input.l << endl;
   cout << "        " << endl;
   cout << dec;  // Restore data output format to decimal

   significand = input.l & 0x7fffff; // Isolate the significand
   exponent = ((input.l >> 23) & 0xff) - 127;  // Isolate the exponent
   sign = (input.l & 0x80000000);  // Isolate the sign

   // Show the value in the form (-1)^^s x (1 + 1/2 + ... ) x 2^^exponent.
   // Show only the fractions actually present in the number. 
   cout << "Value is (-1)^^";
   if (sign)
      cout << "1";
   else
      cout << "0";

   cout << "* ( 1 ";  // Hidden bit -- always present

   mask = 0x400000;  // Initial value of bit mask is the position of the MSBit in significand

   // Go through each bit of the significand, beginning at the Most Significant Bit.
   for (int i = 1; i <= 23; i++) // 23 bits in significand
   {
     if (significand & mask)    // if the bit at the current position is a 1
     {
        cout << " + 1/";
        cout << denominator;
     }

     denominator = denominator * 2;  // Update for next bit position
     mask >>= 1;  // Mask is rotated (shifted) right by 1 position

   } // end for i

   cout << ") * 2^^(" << exponent << ")";
   
   cout << endl << endl;



   mask = 0x400000;  // Set to MSBit of significand
   significand = input.l & 0x7fffff;
   exponent = ((input.l >> 23) & 0xff) - 127;
   sign = (input.l & 0x80000000);

   cout << "Contribution to value, bit by bit. " << endl;
   cout.precision(20);

   // The value of temporary is initially that given by the hidden bit only
   // of the original input. As each bit is examined, the value of temporary
   // will increase based on the contribution from each bit of the significand.
   temporary.l = input.l & 0xff800000; // Retain only sign, exponent, and hidden bit
   
   cout << "Hidden bit:  " << temporary.f << endl;

   for (int i = 1; i <= 23; i++)   // 23 bits in significand
   {
     cout << "     Bit " << i << ":  ";

     temporary.l |= (significand & mask);  // Duplicate current bit

     if (significand & mask)    // if current bit position is set
        cout << temporary.f << endl;  // show the cumulative value
     else 
        cout << "               (bit not set)" << endl;

     mask >>= 1;  // Mask is rotated (shifted) right by 1 position

   } // end for i
     

}