/**************************************************************************
Function Name: Simpsonthree
Description: The simpsonthree works using the 3/8th rule of simpson that 
replicates the number of bins using the formula for simpsons rule.
output: Double value corresponding to the sum of the individual integral 
results from the bins
Input: Function to be integrated, upper limit, lower limit, number of bins
***********************************************************************/


#include<stdio.h>
#include<math.h>

double simpsonthree(double (*func)(double),double a,double b,int n)
	{
		double dH,dRes;
		int N=n;
	//This is the number of intervals
	
		double *x;
		x=malloc((N+1)*sizeof(double));
//malloc to allocate the memory for the size of the output to be summed
		int i;	
//loop variable
		x[0]=a;
//intial value at which function is evaluated
		x[N]=b;
//Final value at which function is evaluated
		dH=(b-a)/(double)N;
//bin size
		dRes=3*dH/8*func(a);
//variable initialized to integral value
	omp_set_num_threads(100);
/*this sets the number of threads that will be used for
the program*/
        #pragma omp parallel //pragma!!
        #pragma omp for
	//for loop is being parallized
		for(i=1;i<N;i+=3)
		{
			x[i]=a+i*dH;
			//split the bins
			dRes+=3*dH/8*(3*func(x[i])+3*func(x[i])+2*func(x[i]));
			/*compute integral at all the values summing up 
all the bins*/
		}
		return dRes;
	}