CS 210

PROJECT #4                                 Due: Noon Thursday 04/24/2008

     This project offers the student some experience with mixed-language
programming, and with using integer arithmetic instructions to calculate
square-roots and format numeral-strings representing decimal-fractions.  


                           PROBLEM STATEMENT

     The accompanying application-program named 'sqroots.cpp' calculates
and displays a mathematical table of square-roots to four-place accuracy
for the positive integers up to one hundred, but it relies upon calls to
to a subroutine named 'int2root()' which uses the 'sqrt()' function from 
the C/C++ math library.  That function is implemented by using floating-
point operations and data-types which we have not yet studied.  In fact,
those floating-point operations are not strictly necessary.  There is an
alternative way to compute square-roots using only integer instructions,
based on the well-known recursive identity from high school algebra:

		(n + 1)*(n + 1) = n*n + (n + n + 1)

Thus any positive integer which is a perfect square can be built up just
by adding together successive odd integers.  The number of summands will
then give the square root.

          EXAMPLE:   Compute the square-root of one-hundred    

The answer is ten, because ten successive odd integers can be subtracted
from one hundred (100 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19), and
square-roots for integers which are not perfect squares can be obtained,
approximately, using interpolations, as in the following algorithm:

	// Find  sqrt(N)  to two decimal-places
	int	product = N * 10000;
	int	nextodd = 1;
	int	counter = 0;
	char	rootbuf[ 20 ];
	while ( product >  counter )
		{
		product -= nextodd;
		nextodd += 2;
		++counter;
		}
	int	len = sprintf( rootbuf, " %d", count );
	memcpy( rootbuf, rootbuf+1, len-3 ); 
	memset( rootbuf+len-3, '.', 1 );
	printf( " square-root of %d equals %s \n", N, rootbuf );
	

Your job in this assignment is to re-implement the function 'int2root()'
as an 'external' subroutine, written in assembly language, and using the
CPU's integer operations instead of floating-point aritmetic.  Then link
your assembly language subroutine to our 'sqroots.cpp' application.  You
should turn in a printout of your two source-files, and also should copy 
all of your project's files to your '/submit' direectory.
________________________________________________________________________
Allan B. Cruse          University of San Francisco          Spring 2008