pi

pi.jl

@everywhere const exact = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092

@everywhere function approx_pi(n::Integer)
    current_term = 0.5 
    sum = current_term
    for i=1:n
        current_term *= (2 * i) * (2 * i - 1) / (16 * i * i) * (2 * (i - 1) + 1) / (2 * i + 1)
        sum += current_term
    end 
    return 6 * sum 
end

function main()
    ns = 0:29
    function get_error(n::Integer)
        pi_approx = approx_pi(n)
        rel_error = abs((exact - pi_approx) / exact)
        return (n, rel_error)
    end 
    results = pmap(get_error, ns)
    for details=results
        @printf("%10li %+20.12e \n", 
          details[1], details[2])
    end
end

main()