//this simply calucaltes the exponent with a Taylor's expansion
//	to demonstrate the negative aspect of alternating series
#include <stdio.h>
#include <math.h>
#include <stdlib.h>

main()
{
	int i;
	double x;
	double xprod,factorial,sexp;
	double actualvalue;
	int flag;

	char filename[25];
	FILE *outfile;

	printf("Enter x value\n");
	scanf("%lg",&x);
	
	printf("Name of output file\n");
	scanf("%s",filename);
	outfile=fopen(filename,"w");
	fprintf(outfile,"N\tPsum\tFacErr\n");


	//xprod is used to keep track of the power of x^i
	//sexp is the Taylor's estimates of exp(x)
	//factorial is the i! - i should not be much larger than 50 in this case
	factorial=1.0;
	xprod=1.0;
	sexp=1.0;
	actualvalue=exp(x);

	//this part deal with problem with negative x
	if(x<0)
	{
		flag=1;
		x=-x;
	}
	else
		flag=0;



	for(i=1;i<=30;i++)
	{
		//increment variables
		factorial*=i;
		xprod*=x;

		sexp+=xprod/factorial;
		//if x<0, Taylor's series can be use effectively with 1/sexp.
		if(flag)
			fprintf(outfile,"%d\t%lg\t%lg\n",i,1.0/sexp,log10(fabs(1.0/sexp-actualvalue)/actualvalue));
		else
			fprintf(outfile,"%d\t%lg\t%lg\n",i,sexp,log10(fabs(sexp-actualvalue)/actualvalue));

	}

	return 0;
}