// 
// Copyright  (C) 2005 Intel Corporation.  All rights reserved.
// 
// The information and source code contained herein is the exclusive property
// of Intel Corporation and may not be disclosed, examined, or reproduced in
// whole or in part without explicit written authorization from the Company.
// 
// 


// Integrate a function over a given interval using the well-known
// midpoint rule:
// Given height = f(x_i), compute the area of the
// rectangle of width "step"
// Simply sum the areas of internal rectangles: f(xi + step) * step 

#include <stdio.h>
#include <stdlib.h> 
#include <time.h> 
//// #include <mathimf.h> <- intel proprietary math.h, commented out for compatibility with VC++ 6 compiler
#include <math.h>

// Function to be integrated
// Define and prototype it here
// | sin(x) |
#define INTEG_FUNC(x)  fabs(sin(x))

// Prototype timing function
double dclock(void);

int main(void)
{
   // Loop counters and number of interior points
   unsigned int i, j, N;
   // Stepsize, independent variable x, and accumulated sum
   double step, x_i, sum;
   // Timing variables for evaluation   
   double start, finish, duration, clock_t;
   // Start integral from 
   double interval_begin = 0.0;
   // Complete integral at 
   double interval_end = 2.0 * 3.141592653589793238;

   // Start timing for the entire application
   start = clock();

   printf("     \n");
   printf("    Number of    | Computed Integral | \n");
   printf(" Interior Points |                   | \n");
   for (j=2;j<27;j++)
   {
    printf("------------------------------------- \n");

     // Compute the number of (internal rectangles + 1)
     N =  1 << j;

     // Compute stepsize for N-1 internal rectangles 
     step = (interval_end - interval_begin) / N;

     // Approx. 1/2 area in first rectangle: f(x0) * [step/2] 
     sum = INTEG_FUNC(interval_begin) * step / 2.0;

     // Apply midpoint rule:
     // Given length = f(x), compute the area of the
     // rectangle of width step
     // Sum areas of internal rectangle: f(xi + step) * step 

     for (i=1;i<N;i++)
     {
        x_i = i * step;
        sum += INTEG_FUNC(x_i) * step;
     }

     // Approx. 1/2 area in last rectangle: f(xN) * [step/2] 
     sum += INTEG_FUNC(interval_end) * step / 2.0;

     printf(" %10d      |  %14e   | \n", N, sum);
   }
   finish = clock();
   duration = (finish - start);
   printf("     \n");
   printf("   Application Clocks   = %10e  \n", duration);
   printf("     \n");
}