//---------------------------------------------------------------------
//	stdnorml.cpp
//
//	This program displays a table showing areas under the standard
//	normal distribution from  0  to  z > 0  in increments of 1/10.
//
//		to compile:  $ g++ stdnorml.cpp -o stdnorml
//		to execute:  $ ./stdnorml
//
//	programmer: ALLAN CRUSE
//	written on: 22 FEB 2011
//---------------------------------------------------------------------

#include <stdio.h>	// for printf()  
#include <math.h>	// for sqrt(), exp()

#define	PI	3.14159

double func( double x )
{
	// returns the value  y = ( 1 / sqrt(2*pi) ) * (exp( - x*x / 2 )
	double	root_2pi = sqrt( 2.0 * PI );
	double	den = root_2pi * exp( x*x / 2.0 );
	return	1.0 / den; 
}

double area( double z )
{
	// returns the area from  0  to  z > 0  under the graph of
	// the curve  y = ( 1 / sqrt( 2*pi ) ) * exp( - x*x / 2 ).
	// computed using the trapezoid rule with 100 subintervals
	double	delta_x = z / 100.0;
	double	areasum = 0.0;
	double	x0 = 0.0;
	double	x1 = delta_x;
	for (int i = 0; i < 100; i++)
		{
		double	y_value_L = func( x0 ); 
		double	y_value_R = func( x1 );
		areasum += (y_value_L + y_value_R) * delta_x / 2.0;
		x0 += delta_x;
		x1 += delta_x;
		}
	return	areasum;
}

int main( int argc, char **argv )
{
	// display the table's title and headline
	printf( "\n\n         " );
	printf( "Table of areas under the standard normal curve " );
	printf( "from  0  to  z  \n\n" );
	printf( "\n  z    " );
	for (int i = 0; i < 10; i++) printf( "  %d    ", i );

	// display the table's sideline and body
	double	z = 0.0, delta_z = 0.10;
	for (int i = 0; i < 40; i++)
		{
		if ( (i % 10) == 0 ) printf( "\n %1.1f: ", z );
		printf( " %1.3f ", area( z ) );
		z += delta_z;
		}
	printf( "\n\n\n" );
}