Compute pi

compute_pi.jl

function compute_pi(N::Int)
    """
    Compute pi with a Monte Carlo simulation of N darts thrown in [-1,1]^2
    Returns estimate of pi
    """
    n_landed_in_circle = 0  # counts number of points that have radial coordinate < 1, i.e. in circle
    for i = 1:N
        x = rand() * 2 - 1  # uniformly distributed number on x-axis
        y = rand() * 2 - 1  # uniformly distributed number on y-axis

        r2 = x*x + y*y  # radius squared, in radial coordinates
        if r2 < 1.0
            n_landed_in_circle += 1
        end
    end

    return n_landed_in_circle / N * 4.0    
end

everywhere.jl

@everywhere function compute_pi(N::Int)
    """
    Compute pi with a Monte Carlo simulation of N darts thrown in [-1,1]^2
    Returns estimate of pi
    """
    n_landed_in_circle = 0  # counts number of points that have radial coordinate < 1, i.e. in circle
    for i = 1:N
        x = rand() * 2 - 1  # uniformly distributed number on x-axis
        y = rand() * 2 - 1  # uniformly distributed number on y-axis
 
        r2 = x*x + y*y  # radius squared, in radial coordinates
        if r2 < 1.0
            n_landed_in_circle += 1
        end
    end
 
    return n_landed_in_circle / N * 4.0    
end

parallel_pi.jl

function parallel_pi_computation(N::Int; ncores::Int=8)
    """
    Compute pi in parallel, over ncores cores, with a Monte Carlo simulation throwing N total darts
    """
     
    # compute sum of pi's estimated among all cores in parallel
    sum_of_pis = @parallel (+) for i=1:ncores
        compute_pi(int(N/8))
    end
    
    return sum_of_pis / ncores  # average value
end

parallel_plot.jl

function parallel_estimate_of_N()
    """
    Computes estimate of pi for an array of N
    """
    N = logspace(4, 8)
    return pmap(compute_pi, int(N))
end

pmap.jl

N = logspace(0,7)
estimates = pmap(compute_pi, N)

remotecall.jl

job = @spawn compute_pi(1000000000)
fetch(job)

serial_plot.jl

function serial_estimate_of_N()
    """
    Computes estimate of pi for an array of N
    """
    N = logspace(4,8)
    pi_estimate = zeros(length(N))

    for i = 1:length(N)
        pi_estimate[i] = compute_pi(int(N[i]))
    end
    
    return pi_estimate
end

start.sh

julia -p 8