CS 210

PROJECT #3                                   Due: Noon Friday 03/30/2007

     This project offers the student some experience with mixed-language
programming, and with using assembly language to implement a 'recursive'
function.

                           PROBLEM STATEMENT

     On the back of this page is the C++ source-code for a program which
prints some of the upper rows in the famous PASCAL TRIANGLE of so-called
'binomial coefficients' that were studied in High School algebra.  There
is a formula for calculating these binomial coeffieients using values of
the factorial function:

		    bin( n, k ) = n! / k!(n-k)! 

But this formula is not very useful in practical computations, even with
a computer, because of the large sizes of the numerator and denominator,
even when the arguments  n  and  k  are fairly small.  These values will
quickly "overflow" the size of the CPU's general registers, so a program 
cannot make direct use of the built-in circuits for doing multiplication 
and division based on this formula. 

Fortunately there is another way to obtain the values for these binomial
coefficients, based on 'recursion', as shown in the source-code for this
'triangle.cpp' application.  Your task is to design an implementation of
that function in assembly language, and then link your assembly language
file (named 'binary.s') with a modfified version of 'triangle.cpp' where
the body of the 'bin' function has been removed (or just commented out),
and only the function's prototye is retained, like this:

		extern "C" int bin( int n, int k ); 

The commands for assembling your 'binary.s' file, and then compiling and
linking your 'triangle.cpp' program, are these:

		$ as binary.s -o binary.o
		$ g++ triangle.cpp triangle.o -o triangle


			   WHAT TO SUBMIT
     
     Copy all of your project files into your CS210 '/submit' directory
where your Instructor can find them for testing purposes.  Also turn in
printouts of your source-files ('binary.s' and 'triangle.cpp') that you
produce using the 'ljpages' printing-utility (from our course website).
Finally turn in a printout of the screen-output your program generates,
which you 'captured' in a file (by using i/o-redirection), like this:

		$ triangle > triangle.out

(These printed submissions should be turned in at Room 222 in Harney.)
________________________________________________________________________
Allan B. Cruse          University of San Francisco          Spring 2007