/* File:    omp_trap1.c
 * Purpose: Calculate definite integral using trapezoidal 
 *          rule.
 *
 * Input:   a, b, n
 * Output:  estimate of integral from a to b of f(x)
 *          using n trapezoids.
 *
 * Compile: gcc -g -Wall -fopenmp -o omp_trap1 omp_trap1.c
 * Usage:   ./omp_trap1 <number of threads>
 *
 * Notes:   
 *   1.  The function f(x) is hardwired.
 *   2.  In this version, each thread explicitly computes the integral
 *       over its assigned subinterval, and the return value of the
 *       function is computed by a reduction directive.
 *   3.  This version assumes that n is evenly divisible by the 
 *       number of threads
 */

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

void Usage(char* prog_name);
double f(double x);    /* Function we're integrating */
double Trap(double a, double b, int n);

int main(int argc, char* argv[]) {
   double  integral = 0;  /* Store result in integral      */
   double  a, b;          /* Left and right endpoints      */
   int     n;             /* Total number of trapezoids    */
   int     thread_count;
   double  elapsed = 0.0;

   if (argc != 2) Usage(argv[0]);
   thread_count = strtol(argv[1], NULL, 10);

   printf("Enter a, b, and n\n");
   scanf("%lf %lf %d", &a, &b, &n);
   
#  pragma omp parallel num_threads(thread_count) reduction(+: integral) 
   {
      double start, finish, my_elapsed;
#     pragma omp barrier
      start = omp_get_wtime();
      integral = Trap(a, b, n);   /* Can also do += */
      finish = omp_get_wtime();
      my_elapsed = finish-start;
#     pragma omp critical
      if (my_elapsed > elapsed) elapsed = my_elapsed;
   }

   printf("With n = %d trapezoids, our estimate\n", n);
   printf("of the integral from %f to %f = %.15e\n",
      a, b, integral);
   printf("Elapsed time = %e seconds\n", elapsed);

   return 0;
}  /* main */

/*--------------------------------------------------------------------
 * Function:    Usage
 * Purpose:     Print command line for function and terminate
 * In arg:      prog_name
 */
void Usage(char* prog_name) {

   fprintf(stderr, "usage: %s <number of threads>\n", prog_name);
   exit(0);
}  /* Usage */

/*------------------------------------------------------------------
 * Function:    f
 * Purpose:     Compute value of function to be integrated
 * Input arg:   x
 * Return val:  f(x)
 */
double f(double x) {
   double return_val;

   return_val = sin(exp(x));
   return return_val;
}  /* f */

/*------------------------------------------------------------------
 * Function:    Trap
 * Purpose:     Use trapezoidal rule to compute definite integral
 * Input args:  
 *    a: left endpoint
 *    b: right endpoint
 *    n: number of trapezoids
 * Return value:  Estimate of Integral from a to b of f(x)
 */
double Trap(double a, double b, int n) {
   double  h, x, integral;
   double  local_a, local_b;
   int  i, local_n;
   int my_rank = omp_get_thread_num();
   int thread_count = omp_get_num_threads();

   h = (b-a)/n;
   local_n = n/thread_count;
   local_a = a + my_rank*local_n*h;
   local_b = local_a + local_n*h;
   integral = (f(local_a) + f(local_b))/2.0;
   for (i = 1; i <= local_n-1; i++) {
     x = local_a + i*h;
     integral += f(x);
   }
   integral = integral*h;

#  ifdef DEBUG
   printf("Thread %d:  integral = %e\n", my_rank, integral);
   fflush(stdout);
#  endif

   return integral;
}  /* Trap */