Numerical Data Types

• Integers
  • Integers are whole numbers, no fractional part
  • There are a entire set of integer types
    • char, short, int, long
    • Each is at least as small as the one that follows.
    • sizeof function
      • Takes a type.
      • returns number of bytes for the type.
      • Can be used in other ways as well.
    • Size depends on c++ implementation, which in turn depends on the architecture.
    • ints are usually 4 bytes, or 32 bits.
    • They are numbers in twos compliment between -2³¹ and 2³¹-1
  • Things can be signed or unsigned.
    • An unsigned int would be between 0 and 2³²-1
  • declarations of constants and variables

    	    const int X = 3;
    	    const unsigned short  Y = 5;
    	    ...
    
    	    long grossPay;
    	    int bonusPay = -4;
    	    unsigned char netPay = 3;
    	

  • Usually, unless you have reasons to do otherwise, you use an int.
  • If an integer literal begins with a 0, the number is assumed to be in base 8.
  • If an integer literal begins with an 0x the number is assumed to be in base 16

    int x=0x1F;
    
    cout << "X is " << x << endl;
    x = 010;
    cout << "X is " << x << endl;
    
    output:
    X is 31
    X is 8
    	

  • The file /usr/include/limits.h has some predefined sizes

    #include <limits.h>
    
    cout << "The maximum integer is " << INT_MAX << endl;
            

  • If you try to add two really big numbers, (or really small for that matter), you will produce overflow.
    • The compiler may warn you if it occurs (and it can figure out that it will occur)
    • The operating system may do so as well when it runs

      #include <iostream>
      #include <limits.h>
      
      using namespace std;
      
      int main () {
           int x;
      
          cout << "The maximum integer is " << INT_MAX << endl;
          x = INT_MAX + 1;
          cout << "one more is " << x << endl;
          return -1;
      }
      
      WHEN COMPILED:
      
      foo.C: In function `int main()':
      foo.C:12: warning: integer overflow in expression
      
      PRODUCES:
      The maximum integer is 2147483647
      one more is -2147483648
      
      	   

• Warnings
  • Warnings are issued when the compiler finds a problem, but can go on anyway.
  • There are very few times when you should allow a warning to exist without fixing it. (NEVER?)
• Floating Point Numbers
  • Think of these as numbers in scientific notation.
  • Numbers with a decimal point.
  • types : float, double, longdouble
  • Find the sizes with sizeof
  • /usr/include/math.h for some predefined constants.
  • Declarations are the same as ints, chars, and strings.
  • Literals
    • {+|-}digit^*{.}digit^*{E{+|-}digit⁺}

      
      float x;
      
      x = -1;
      cout << "X is " << x << endl;
      x = .2;
      cout << "X is " << x << endl;
      x = -.3E22;
      cout << "X is " << x << endl;
      x = -1.2E-12;
      cout << "X is " << x << endl;
      
      Output:
      X is -1
      X is 0.2
      X is -3e+21
      X is -1.2e-12
      
      	     

  • Floats are much slower to use than integers. Use integers when you can.
  • We can not represent many numbers
    • This is known as roundoff error.
    • Actually, we can only represent a finite number of numbers, and there are infinately many real numbers.
    • We will see more of this later.