MPI Taylor series tan(x) function

Since tan(x) = sine(x)/cosine(x), we could combine the Taylor series formula of the sine(x) and cos(x) to construct the tangent function as follows:

Write, compile, and run this Serial tangent(x) code (see the following serial  tangent(x) code) to get a feel of the program:

/**********************************  
 * Serial tangent(x) code.        * 
 *                                * 
 * Taylor series representation   * 
 * of the trigonometric tan(x).   *  
 *                                * 
 * Author: Carlos R. Morrison     * 
 *                                * 
 * Date: 1/10/2017                * 
 **********************************/ 
#include <math.h> 
#include <stdio.h> 
 
int main(void) 
{ 
/************************************************/ 
  unsigned int i,j,l; 
  unsigned long int k; 
  long long int B,D,G,I;  
  int num_loops = 17; 
  float y; 
  double x; 
  double sum=0,sum01=0,sum02=0; 
  double A,C,E,F,H,J...