#include "stdafx.h"											/* Libarary Definitions - Used for printf, scanf, etc */
#include "math.h"											/* Math Libarary for C - Used for Abs() = Absolute Value */


/* User Created Function 1 - Print Error "Integration Cannot Be Done"  */
void Print_Integration_Error (int B, int C, int D, double X_Initial, double X_Final)
{
			printf("  %d  %d  %d  %lf  %lf \n\n ", B, C, D, X_Initial, X_Final);					/* If X_Initial is Less Than or Equal to 0.0 and X_Final is Greater or Equal to 0.0 */
			printf("===================================================================\n");		/* It Will Print The Data Values and Message Explaining Integration Cannot Be Done */
			printf("  Integration Cannot Be Done As The Function Is Not Defined For X=0 \n" );
			printf(" ===================================================================\n");
}

/* User Created Function 2 - Prints Data Values and The Heading For Results */
void Print_Top_Half_of_Table (int B, int C, int D, double X_Initial, double X_Final)
{
		printf("\n");
		printf("  %d  %d  %d  %lf  %lf \n\n ", B, C, D, X_Initial, X_Final);				/* If X_Initial isn't Less Than or Equal to 0.0 and X_Final isn't Greater or Equal to 0.0 */
		printf("===================================================\n");					/* It Will Print The Data Values and The Table for The Results of H, N and Total Area */
		printf(" |      N      |        H        |       AREA      |\n");
		printf(" |=================================================|\n");
}

/* User Created Function 3 - Prints The Results In a Table */
void Print_Results_In_Table (int N, double Height, double Area_Total)
{
	printf(" |   %6d    |    %8.5f     |    %8.5f     |\n\n", N, Height, Area_Total);	/* User Created Function 3 - Prints The Results in a Table With The N, Height and Area Total for Each Data Set */
}
/* User Created Function - Calculates Area_i */
void Area_i_Calculate (double Height, double X_a, double X_b, int B, int C, int D)
{
	double Area_i;
	Area_i = Height * (abs(X_a*X_a + B*X_a + C + D/X_a) + abs(X_b*X_b + B*X_b + C + D/X_b)) * 0.5;
}

/* User Created Function - Calculates N = Number of Trapziums */
void N_Calculate (double X_Final, double X_Initial, double Height)
{
	int N;
	N = (int) ( (X_Final - X_Initial) / (Height + 0.5 ));

}

/* User Created Function - Calculates The Total Area Under The Curve */
void Area_Total_Calculate (double Area_i)
{
	double Area_Total;

		   Area_Total = Area_i + Area_Total;

}

/* User Created Function - Calculates X_b*/
void X_b_Calculate (double X_a, double Height)
{
	double X_b;

	X_b = X_a + Height;
}

/* User Created Function - Calculates X_a */
void X_a_Calculate (double X_b)
{
	double X_a;
	X_a = X_b;
}


int
	main (void)
{
	FILE *inp;													/* Input File Pointer - The Variable inp will hold a descriptor for the file once it is open for input*/
	inp = fopen("C:\\input1.dat", "r");							/* The File Location/Path Directory - And The Selected Mode is Read Input File*/

	int	N,														/* Output - The Number of Trapezium Calculations Required */
		B,														/* Scanned Value - The B Value From The File - input1.dat */
		C,														/* Scanned Value - The C Value From The File - input1.dat */
		D,														/* Scanned Value - The D Value From The File - input1.dat */
		input_status;											/* Status Value Returned by fscanf - Either Success or EOF */

	double X_Initial,											/* Scanned Value - The Read X Initial Value From The File - input1.dat */
		   X_Final,												/* Scanned Value - The Read X Final Value From The File - input1.dat */
		   Height,												/* Output - The Calculated Height Value for The Trapizium Rule */
		   Area_Total,											/* Output - The Calculated Total Area Under The Curve */
		   Area_i,												/* Calculated Value - The Mathematical Relationships Associated With Numerical Integration (Trapzium Rule) */
		   X_a,													/* Calculated Value - The X_a Value is X_Initial ( Xi ) */
		   X_b;													/* Calculated Value - The X_b Value is X_Initial + Height ( Xi + h ) */


	printf("\n");												/* Creates New Line - Purpose to Make the End Result Clearer */

	if (inp == NULL) {											/* If inp (Input File Pointer) Cannot Locate or Open the File */
		printf("Cannot Find or Open input1.dat File! \n");		/* It will Display a Error Message for The User */
	}
	else
		printf("The File Was Found \n\n");						/* If the file was found it will Display a Success Message And Print a Heading for The Data Inputs */

		printf("The Following are The Data Inputs: \n");

		printf("\n");											/* Creates New Line - Purpose to Make the End Result Clearer */


	input_status = fscanf(inp, "%d %d %d %lf %lf", &B, &C, &D, &X_Initial, &X_Final);			/* Scans The File for Data Values and Stores Them at a Given Location */
	while (input_status != EOF){																/* Status Value Returned by fscanf - Either Success or EOF */

		if( X_Initial <= 0.0 && X_Final >= 0.0){												/* If X_Initial is Less Than or Equal to 0.0 and X_Final is Greater or Equal to 0.0 */
			Print_Integration_Error (B, C, D, X_Initial, X_Final);								/* User Created Function 1 - It Will Print The Data Values and Message Explaining Integration Cannot Be Done */
		}
			else
		{
			Print_Top_Half_of_Table (B, C, D, X_Initial, X_Final);								/* User Created Function 2 - It Will Print The Data Values and Top Half of The Table if Integration Cannot Be Done */

			for ( Height = 0.1; Height >= 0.00001; Height = Height * 0.1 ){						/* Starting with an h value of 0.1 and then continuing with h = 0.01, 0.001, etc. until the latest two calculations are within 0.0005 of each other, or h becomes 0.00001. */
					                                                                            /* You can see that as h is reduced and the number of trapeziums increases, we will get a better estimate. */
					N = (X_Final - X_Initial) / ( Height ) + ( 0.5 );							/* Calculating The Value N */

					X_a = X_Initial;															/* X_a = Xi - Used in The Area_i Calculation */
					Area_Total = 0;

					for ( int i = 0 ; i < N ; i++){

						X_b = X_a + Height;																				/* X_b = Xi + h - (X_initial + Height) Used in The Area_i Calculation */

						Area_i = Height * (abs(X_a*X_a + B*X_a + C + D/X_a) + abs(X_b*X_b + B*X_b + C + D/X_b)) * 0.5;  /* Calculating Area_i  */

						Area_Total = Area_i + Area_Total;																/* The Estimate of the Total Area Under The Curve is Simply The Sum of all the Trapezium Area Calculations. */

						X_a = X_b;

							}

						Print_Results_In_Table (N, Height, Area_Total);													/* User Created Function 3 - Prints The Results in a Table With The N, Height and Area Total for Each Data Set */

					}

			}

			input_status = fscanf(inp, "%d %d %d %lf %lf", &B, &C, &D, &X_Initial, &X_Final);							/* Once The First Data Has Been Done It Will Reloop Untill EOF */

	}

	fclose(inp);																										/* Closes The File */

	printf("\n");																										/* Creates New Line - Purpose to Make the End Result Clearer */

	return 0;

}