//-------------------------------------------------------------------
//	shortadd.cpp
//
//	This program computes the probability that the sum of a pair
//	of randomly chosen 'short' integers (i.e., 16-bits) will not
//	fit within a 16-bit register or 'short' memory-variable.  It
//	is amusing to observe that this probability is close to 1/2.	
//	
//	And for unsigned multiplication of short integers, which can
//	be treated simply by changing '+' to '*' in this code, it is
//	almost a certainty that 16-bit register-overflow will occur,
//	a fact which beginning programmers are wise to keep in mind.  
//
//		compile using:  $ g++ shortadd.cpp -o shortadd	
//		execute using:  $ ./shortadd
//
//	NOTE: This program may take 15-20 seconds to finish running.
//
//	programmer: ALLAN CRUSE
//	written on: 29 JAN 2011
//	revised on: 04 FEB 2011 -- fix for 32-bit CPU architectures
//-------------------------------------------------------------------

#include <stdio.h>		// for printf()  

int main( int argc, char **argv )
{
	long long	samples = 0;	// for count of summand-pairs
	long long	carries = 0;	// for count of overflow-sums

	for (unsigned int x = 0; x < 65536; x++)
	for (unsigned int y = 0; y < 65536; y++)
		{
		samples += 1;
		if ( x + y > 65535 ) carries += 1;
		}
	printf( "\ncarries = %lld  \nsamples = %lld \n", carries, samples );

	float	probability = (1.0*carries) / (1.0*samples);

	printf( "\nprobability of register-overflow " );
	printf( "when adding 'short' integers " );
	printf( "= %1.5f \n\n", probability );
}