CS 210                                 

PROJECT 2		              Due Date: Noon Thursday 03/12/2009

     This project acquaints students with some numeric formatting issues 
that arise when presenting a mathematical table and with design steps in
implementing an algorithm based on formulas from elementary algebra. 

                          PROJECT STATEMENT
    
     Enhance the 'squares.s' example-program which we discussed in class
so that, in addition to showing the squares of the first twenty positive
integers, computed without using any x86 multiplication instructions, it 
also shows the cubes of these integers, but once again without using any 
multiplication instructions.  Your revised program source-file should be 
named 'powers.s', and it should display its numerical output arranged in
columns whose fields are right-justified, so it looks like this:


                    Table of Squares and Cubes

                  number       square       cube
		  ------------------------------
		     1            1           1
		     2            4           8
		     3            9          27
		     4           16          64
		     5           25         125
		     .            .           .
		     .            .           .
		     .            .           .
		    20         	400        8000 
		  ------------------------------

You can redirect your program's output to a file (so it can be printed).
For example, if your executable file is named 'powers', you can use the
command-syntax:		
			$ ./powers > powers.out 
			$ ./ljpages powers.out

     To avoid using multiplication operations in 'squares.s', we applied
ideas from elementary algebra, described by these two formulas:

			 twice( x ) = x + x

	    square( n+1 ) = square( n ) + twice( n ) + 1		

In a similar manner, you can calculate the cubes of positive integers by
using this additional pair of formulas from algebra:

	               thrice( x ) = x + x + x 

    cube( n+1 ) = cube( n ) + thrice( square( n ) ) + thrice( n ) + 1

Copy your (four) project-files to your '/submit' directory, and hand in  
printouts of your 'powers.s' and 'powers.out' files to your Instructor.
_______________________________________________________________________
Allan B. Cruse        University of San Francisco           Spring 2009