Computing PI using Serial Code

Program serialPi

• The serial version of our program to compute PI, written in C, is displayed below:

  #include <stdio.h>
  #include <stdlib.h>
  #include <math.h>
  
  const double pi = 3.1415926535897932385;
  
  int main( int argc, char *argv[] ) {
    /*  Arguments required for executing serialPi:     */
    /*  0                         -> serialPi          */
    /*  1                         -> numberOfIntervals */
  
    int numberOfIntervals, interval;
    double intervalWidth, intervalMidPoint, area = 0.0;
  
    /*  The number of intervals is a command line argument. */
    numberOfIntervals = atoi( argv[1] );
  
    /*  Compute the interval width. */
    intervalWidth = 1.0 / numberOfIntervals;
  
    /*  Now compute the area. */
    for ( interval = 0; interval < numberOfIntervals; interval++ ) {
        intervalMidPoint = (interval + 0.5) * intervalWidth;
        area += 4.0 / ( 1.0 + intervalMidPoint*intervalMidPoint );
    }
    area *= intervalWidth;
  
    /*  Print the results. */
    printf( "The computed value of the integral is %.15f\n", area );
    printf( "The exact value of the integral is    %.15f\n", pi );
  
    return 0;
  }
        

  Note: If you did not copy example programs from HPC's account in the initial section of this workshop, then copy the above source code as serialPi.c to your SerialPi directory.

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• Exercise: Do this!

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  To compile the serialPi program, at your shell prompt in the SerialPi directory, do:

   [agopu@bh2 agopu]$ cd ~/MPI_Tutorial/SerialPi/
   [agopu@bh2 SerialPi]$ icc -o serialPi serialPi.c 

  Then to run the program on interactive nodes you got through qsub -I (bcXX), do:

   [agopu@bc81 agopu]$ cd ~/MPI_Tutorial/SerialPi/
   [agopu@bc81 SerialPi]$ ./serialPi 20000
    The computed value of the integral is 3.141592654423135
    The exact value of the integral is    3.141592653589793 

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  Note: Since this is not a MPI program, we've not used the Makefile. We could have if we'd wanted to, but we would have needed to change the compiler to icc or gcc.

• Since the command line argument used above is 20000, the domain would have been divided into 20,000 intervals.