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C
C Copyright (C) by Argonne National Laboratory
C See COPYRIGHT in top-level directory
C
C****************************************************************************
C pi.f - compute pi by integrating f(x) = 4/(1 + x**2)
C Each node:
C 1) receives the number of rectangles used in the approximation.
C 2) calculates the areas of it's rectangles.
C 3) Synchronizes for a global summation.
C Node 0 prints the result.
C
C Variables:
C
C pi the calculated result
C n number of points of integration.
C x midpoint of each rectangle's interval
C f function to integrate
C sum,pi area of rectangles
C tmp temporary scratch space for global summation
C i do loop index
C****************************************************************************
program main
include 'mpif.h'
double precision PI25DT
parameter (PI25DT = 3.141592653589793238462643d0)
double precision mypi, pi, h, sum, x, f, a
integer n, myid, numprocs, i, rc
C function to integrate
f(a) = 4.d0 / (1.d0 + a*a)
call MPI_INIT( ierr )
call MPI_COMM_RANK( MPI_COMM_WORLD, myid, ierr )
call MPI_COMM_SIZE( MPI_COMM_WORLD, numprocs, ierr )
print *, "Process ", myid, " of ", numprocs, " is alive"
sizetype = 1
sumtype = 2
10 if ( myid .eq. 0 ) then
write(6,98)
98 format('Enter the number of intervals: (0 quits)')
read(5,99) n
99 format(i10)
endif
call MPI_BCAST(n,1,MPI_INTEGER,0,MPI_COMM_WORLD,ierr)
C check for quit signal
if ( n .le. 0 ) goto 30
C calculate the interval size
h = 1.0d0/n
sum = 0.0d0
do 20 i = myid+1, n, numprocs
x = h * (dble(i) - 0.5d0)
sum = sum + f(x)
20 continue
mypi = h * sum
C collect all the partial sums
call MPI_REDUCE(mypi,pi,1,MPI_DOUBLE_PRECISION,MPI_SUM,0,
$ MPI_COMM_WORLD,ierr)
C node 0 prints the answer.
if (myid .eq. 0) then
write(6, 97) pi, abs(pi - PI25DT)
97 format(' pi is approximately: ', F18.16,
+ ' Error is: ', F18.16)
endif
goto 10
30 call MPI_FINALIZE(rc)
stop
end
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