Notes on FUNCTIONS

Let's try to clarify the difference between 

  function (a division of your program code)
    and
  function call (causing a function to execute and compute something)

  physical real-world example
    if you are a painter, you can paint a room any color, not just one color
      someone gives you a can of yellow paint, you paint the room yellow
      someone gives you a can of beige paint, you paint the room beige
      someone gives you a can of blue paint, you paint the room blue 

    we do not have to hire a blue painter to paint the living room, 
      and a different yellow painter to paint the family room
      we hire one painter, and give him/her different cans 
        for different rooms
      the painter "executes" the paint function in each room, and the
        can of paint is the "parameter" we pass to make the "computation"
        vary from room to room

    function is the same way... it does some general activity (as defined
      in the function body) and you pass to it the specific data it will 
      act upon (when you call the function).

    so we define a function to load an array with random numbers
      we call it, and pass it array "first", and "first" gets loaded
      we call it, and pass it array "second", and "second" gets loaded

    so we define a function to compute 2 raised to a power
      we call it, and pass it 5 and it produces 2^5 and returns  32
      we call it, and pass it 7 and it produces 2^5 and returns 128
   
    we define a function once (we write the code that tells the 
      parameter names and order, the local variable inside the function, 
      the code for the function body, and what the function returns, 
      if anything)

       function pow2 ( exponent ) {
          var i;
          var result=1;
          for (i=1; i<=exponent; i++) {
             result=2*result;
          }
          return result;
       } 

    We can call a function (make a function execute and compute something)
    as many times as we need.  We pass the data to it that we want to have
    worked on

       quant = pow2(4);
       alert(quant);

       var n = 6;
       quant = pow2(n);
       alert(quant);

       alert(pow2(10));

       quant = 17 + pow2(5);
       alert(quant);
 

    Functions provide several advantages in writing programs.

      First, by calling a function in different places, we do not
         have to have repeated copies of the body of the function 
         code in our program in different places... we prevent errors
         that come from replicating code
         Here is the code above without writing a function "pow2"

           var i;
           var quant;

           exponent = 4;
           quant=1;
           for (i=1; i<=exponent; i++) {
             quant=2*quant;
           }
           alert(quant);

           exponent = 6;
           quant=1;
           for (i=1; i<=exponent; i++) {
             quant=2*quant;
           }
           alert(quant);

           exponent = 10;
           quant=1;
           for (i=1; i<=exponent; i++) {
             quant=2*quant;
           }
           alert(quant);

           exponent = 5;
           quant=1;
           for (i=1; i<=exponent; i++) {
             quant=2*quant;
           }
           quant = 17 + quant;
           alert(quant);

      Second, we get the advantage of abstraction... we see the name
         of the function only at the call, and do not have to look
         at all the details of the body of the function code, so we
         have a higher-level understanding of the computation where
         the function is called

      Third, using functions allows us to write our programs in modular
         fashion, breaking a large problem down into interacting smaller
         problems, solving each smaller problem one at a time, and using
         "stubs" for our functions until they are fleshed out fully.