//-------------------------------------------------------------------
//	sinedemo.cpp
//
//	This program shows the graphs of successive approximations 
//	to the sine function by the sequence of Taylor Polynomials   
//	of increasing degrees around zero (Maclaurin polynomials).
//
//	  compile using:  $ g++ sinedemo.cpp int86.cpp -o sinedemo 
//
//	programmer: ALLAN CRUSE
//	written on: 04 DEC 2005
//-------------------------------------------------------------------

#include <stdio.h>	// for printf(), perror() 
#include <fcntl.h>	// for open() 
#include <stdlib.h>	// for exit() 
#include <unistd.h>	// for lseek() 
#include <math.h>	// for sin(x)
#include <sys/mman.h>	// for mmap() 
#include <sys/io.h>	// for inb(), outb(), etc.
#include "int86.h"	// for init8086(), int86()

#define PI 	3.14159

unsigned char *vram = (unsigned char*)0xA0000000; 
int  vesa_mode = 0x4105, hres = 1024, vres = 768;
struct vm86plus_struct	vm; 
int	polynomial_degree = 0;

double sineterm( int n, double x )
{
	double	fact = 1.0;
	double	term = 1.0;

	for (int k = 1; k <= n; k++)
		{
		fact *= k;
		term *= x;
		}
	term /= fact;	

	if ( ( n % 2 ) == 0 ) return 0.0;	
	if ( ( n % 4 ) == 3 ) term *= -1.0;
	return	term;
}

double polynomial( double x )
{
	double	y = 0.0;

	for (int n = 0; n <= polynomial_degree; n++) 		
		y += sineterm( n, x );
	return	y;
}


void draw_pixel( int x, int y, int color )
{
	if (( x <= 1 )||( x >= hres-2 )) return;
	if (( y <= 1 )||( y >= vres-2 )) return;

	vram[ y * hres + x ] = color;
}

void draw_curve( double function( double ), int color )
{
	double	scaleX = 42, scaleY = -42;
	double	transX = hres/2, transY = vres/2;
	double	xmin = -4*PI, xmax = 4*PI, xinc = PI/720;
	
	for (double x = xmin; x <= xmax; x += xinc)
		{
		double	y = function( x );
		 
		int	h = (int)(x * scaleX + transX);
		int	v = (int)(y * scaleY + transY);

		draw_pixel( h, v, color );
		}
}

int main( int argc, char **argv )
{
	// memory-map the display-memory into user-space
	int	vd = open( "/dev/vram", O_RDWR ); 
	if ( vd < 0 ) { perror( "/dev/vram" ); exit(1); }
	int	size = lseek( vd, 0, SEEK_END ); 
	int	prot = PROT_READ | PROT_WRITE; 
	int	flag = MAP_FIXED | MAP_SHARED; 
	if ( mmap( (void*)vram, size, prot, flag, vd, 0 ) == MAP_FAILED )
		{ perror( "mmap" ); exit(1); } 
	
	// enter graphics mode 
	init8086(); 
	vm.regs.eax = 0x4F02;	
	vm.regs.ebx = vesa_mode;	
	int86( 0x10, vm );	
	
	// draw screen border 
	int	x = 0, y = 0, color = 15; 
	do { vram[ y * hres + x ] = color; ++x; } while ( x < hres-1 ); 
	do { vram[ y * hres + x ] = color; ++y; } while ( y < vres-1 ); 
	do { vram[ y * hres + x ] = color; --x; } while ( x >      0 ); 
	do { vram[ y * hres + x ] = color; --y; } while ( y >      0 ); 
	getchar();
	
	// draw coordinate axes
	y = vres/2;
	for (x = 0; x < hres; x++) draw_pixel( x, y, 7 );
	x = hres/2;
	for (y = 0; y < vres; y++) draw_pixel( x, y, 7 );
	getchar();

	// draw the sine curve
	color = 14;
	draw_curve( sin, color );
	getchar();

	// draw the Taylor Polynomial
	color = 11;
	polynomial_degree = 1;
	for (int i = 0; i < 15; i++)
		{
		draw_curve( polynomial, color ); 
		getchar();
		draw_curve( polynomial, 0 );
		polynomial_degree += 2;
		}
	
	// leave graphics mode 
	vm.regs.eax = 0x0003;	
	int86( 0x10, vm );	
	printf( "\n" );
}