program main

c*********************************************************************72
c
cc MAIN is the main program for QUAD.
c
c  Discussion:
c
c    QUAD is a FORTRAN77 program to estimate the integral of
c      f = 50.0 / ( pi * ( 2500.0 * x(i) * x(i) + 1.0 ) )
c    from 0 to 10.
c
c    If you modify the program in 4 places, it should run correctly
c    under OpenMP.
c
c    If you can do that, then compare the execution time when you
c    use 1, 2, 4 or 8 threads.
c
c  Licensing:
c
c    This code is distributed under the GNU LGPL license.
c
c  Modified:
c
c    03 September 2013
c
c  Author:
c
c    John Burkardt
c

c
c  CHANGE 1) Activate the following INCLUDE statement.
c
c     include 'omp_lib.h'

      double precision a
      double precision b
      double precision error
      double precision exact
      integer i
      integer n
      double precision pi
      double precision total
      double precision wtime
      double precision x(1000000)

      a =  0.0
      b = 10.0
      exact = 0.49936338107645674464D+00
      n = 1000000
      pi = 3.141592653589793D+00
      wtime = 0.0D+00

      write ( *, * ) ' '
      write ( *, * ) 'QUAD:'
      write ( *, * ) '  FORTRAN77 version'
      write ( *, * ) ' '
      write ( *, * ) '  Estimate the integral of f(x) from A to B.'
      write ( *, * ) '  f(x) = 50 / (pi * ( 2500 * x * x + 1 ) ).'
      write ( *, * ) '  A = ', a
      write ( *, * ) '  B = ', b
      write ( *, * ) '  Exact integral is 0.49936338107645674464...'
c
c  Load the array X with evenly spaced values between A and B.
c
      do i = 1, n
        x(i) =  ( dble ( n - i     ) * a   
     &          + dble (     i - 1 ) * b ) 
     &          / dble ( n     - 1 )
      end do
c
c  Evaluate F at each node, sum and average.
c
c
c  CHANGE 2) Use the OpenMP timer here to initialize WTIME.
c
c     wtime = ???
c
      total = 0.0D+00
c
c  CHANGE 3) Fill in these two OpenMP directives here
c
c$omp parallel private ( ??? ) shared ( ??? )
c$omp do ???
      do i = 1, n
        total = total + 50.0D+00 
     &    / ( pi * ( 2500.0D+00 * x(i) * x(i) + 1.0D+00 ) )
      end do
c
c  CHANGE 3.1) Insert "closing" OpenMP directives after the loop
c
c$omp end do
c$omp end parallel
c
      total = ( b - a ) * total / dble ( n )
c
c  CHANGE 4) Call the OpenMP timer here to update WTIME.
c
c      wtime = ???
c
c  Print quadrature estimate, error, time
c
      error = abs ( total - exact )

      write ( *, * ) ' '
      write ( *, * ) '  Estimate = ', total
      write ( *, * ) '  Error    = ', error
      write ( *, * ) '  Wallclock time   = ', wtime

      stop
      end
      function f ( x )

      double precision f
      double precision pi
      double precision x

      pi = 3.141592653589793D+00
c
c  Write the formula for the function here.
c
      f = 50.0 / (pi * ( 2500.0 * x * x + 1.0 ) )

      return
      end