text: /*
   * BSD 2-Clause License
   * 
   * Copyright (c) 2020, Alessandro Capotondi
   * All rights reserved.
   * 
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions are met:
   * 
   * * Redistributions of source code must retain the above copyright notice, this
   *   list of conditions and the following disclaimer.
   * 
   * * Redistributions in binary form must reproduce the above copyright notice,
   *   this list of conditions and the following disclaimer in the documentation
   *   and/or other materials provided with the distribution.
   * 
   * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
   * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
   * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
   * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
   * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
   * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
   * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
   * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
   * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
   * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
   */
  
  /**
   * @file exercise7.c
   * @author Alessandro Capotondi
   * @date 27 Mar 2020
   * @brief Exercise 8
   * 
   * Pi calculation
   * @see https://dolly.fim.unimore.it/2019/course/view.php?id=152
   */
  
  #include <stdio.h>
  #include <omp.h>
  
  #include "utils.h"
  
  /**
   * @brief EX 8- Pi Calculation
   * 
   * This program computes pi as
   * \pi = 4 arctan(1)
   *     = 4 \int _0 ^1 \frac{1} {1 + x^2} dx
   * 
   * @return void
   */
  #include <stdio.h>
  #include <math.h>
  #include <omp.h>
  
  #define NSTEPS 134217728
  
  void exercise()
  {
      long i;
      double dx = 1.0 / NSTEPS;
      double pi = 0.0;
  
      double start_time = omp_get_wtime();
  
  #pragma omp parallel for reduction(+ \
                                     : pi)
      for (i = 0; i < NSTEPS; i++)
      {
          double x = (i + 0.5) * dx;
          pi += 1.0 / (1.0 + x * x);
      }
      pi *= 4.0 * dx;
  
      double run_time = omp_get_wtime() - start_time;
      double ref_pi = 4.0 * atan(1.0);
      printf("pi with %ld steps is %.10f in %.6f seconds (error=%e)\n",
             NSTEPS, pi, run_time, fabs(ref_pi - pi));
  }
  