# L-11 MCS 507 Fri 15 Sep 2023 : estimatepidp.jl

# Runs a Monte Carlo simulation with multiprocessing,
# using the Distributed module of Julia.
# Launch this script as julia -p estimatepidp.jl,
# or as time julia -p N estimatepidp.jl to get also
# the wall clock time, where N is the total number
# of workers, the number of processes is then N+1.

using Distributed, Statistics

# @everywhere function estimatepi(n)
# 
# Runs a simple Monte Carlo method
# to estimate pi with n samples.

@everywhere function estimatepi(n)
   count = 0
   for i=1:n
       x = rand()
       y = rand()
       count += (x^2 + y^2) <= 1
   end
   return 4*count/n
end

parallelpi(N) = mean(pmap(n->estimatepi(n),
          [N/nworkers() for i=1:nworkers()]));

np = nprocs()
nw = nworkers()
println("number of processes : $np")
println("number of workers : $nw")

timestart = time()
estpi = parallelpi(10_000_000_000) 
elapsed = time() - timestart
println("The estimate for Pi : $estpi")
println("The elapsed time : $elapsed seconds")