/*************************    Program 2.5    ****************************/
/*                                                                      */
/************************************************************************/
/* Please Note:                                                         */
/*                                                                      */
/* (1) This computer program is written by Tao Pang in conjunction with */
/*     his book, "An Introduction to Computational Physics," published  */
/*     by Cambridge University Press in 1997.                           */
/*                                                                      */
/* (2) No warranties, express or implied, are made for this program.    */
/*                                                                      */
/************************************************************************/

#include <stdio.h>
#include <math.h>
#define NMAX 12

main()
/* Main program for evaluation of an integral with integrand
   sin(x) in the region of [0,pi/2].  Copyright (c) Tao Pang 1997. */
{
int i,n;
double pi,h,s;
double x[NMAX],f[NMAX];
void simp();

n = NMAX;
pi = 4.0*atan(1.0);
h  = pi/(2*(n-1));
for (i = 0; i < n; ++i)
  {
  x[i] = h*i;
  f[i] = sin(x[i]);
  }
simp (n,h,f,&s);
printf("%16.8lf\n",s);
}

void simp (n,h,f,s)
/* Subroutine for integration over f(x) with the Simpson rule.
   f: integrand f(x); h: interval; s: integral.
   Copyright (c) Tao Pang 1997. */
int n;
double h,*s;
double f[];
{
int i;
double s0,s1,s2;

s0 = 0;
s1 = 0;
s2 = 0;
for (i = 1; i < n-1; i = i+2)
  {
  s0 = s0+f[i];
  s1 = s1+f[i-1];
  s2 = s2+f[i+1];
  }
*s = h*(s1+4*s0+s2)/3;

/* If n is even, add the last slice separately */

if (n%2 == 0) *s = *s+h*(5*f[n-1]+8*f[n-2]-f[n-3])/12;
}