Floating Point

• There are three floating point types
  • float
  • double
  • long double
• Floating point math can have round off errors.
  • see floatDemo.cpp
• Most operations are supported on floats (+,-,*,/,...)
• Floats can be declared

      float normal {0.01};
      float small {1.0E-10};
      float big  {3.4e15};
          

• Coercion and Type Casting
  • When the compiler changes one type to another it is called coercion.
  • When the user performs this action, it is called type casting.

  • int num {1};
    int denom {2};
    float fraction{0}
    
    fraction = num/denom; 

  • This will produce surprising results.
    • The compiler will perform integer division.
    • And the coerce the results to a float.
  • To get the proper results, we should cast the integers to floats before the division.
  • To cast from one type to another
    • type(expression)
    • float(3) will change the integer 3 to be a float.
    • int('a') will change the character 'a' into an int.
  • But be careful

    • int num {1};
      int denom {2};
      float fraction{0}
      
      fraction = float(num/denom); 

    • Does not do what you expect either.
      • It does the integer division, then the cast.

    • int num {1};
      int denom {2};
      float fraction{0}
      
      // all three work
      //fraction = num/float(denom); 
      //fraction = float(num)/denom; 
      fraction = float(num)/float(denom); 

  • To properly round
    • Casting from a float to an int just drops the floating point part.
    • cout <<int(4.9) will produce 4.

      intVar = int(float expression + 0.5); 

  • In general, you should perform most type casts, do not let the compiler coerce.
• Write a program that converts between Fahrenheit and Celsius
  • $c = \frac{5}{9}(f-32)$
  • $f = \frac{9}{5}c + 32$