# L-12 MCS 507 Mon 18 Sep 2023 : simpson4pi2

"""
This script speeds up the simpson4pi1.py.
"""

from multiprocessing import Process, Queue
from scipy import linspace, sqrt, pi
from scipy.integrate import simps

def call_simpson(fun, a,b,n,q):
    """
    Calls Simpson rule to integrate fun
    over [a,b] using n intervals.
    Adds the result to the queue q.
    """
    x = linspace(a, b, n)
    y = fun(x)
    I = simps(y, x)
    q.put(I)

def main():
    """
    The number of processes is given at the command line.
    """
    from sys import argv
    if len(argv) < 2:
        print('Enter the number of processes at the command line.')
        return
    npr = int(argv[1])
    crc = lambda x: sqrt(1-x**2)
    nbr = 10**8
    nbrsam = nbr//npr  # integer division
    intlen = 1.0/npr
    queues = [Queue() for _ in range(npr)]
    procs = []
    (left, right) = (0, intlen)
    for k in range(1, npr+1):
        procs.append(Process(target=call_simpson, \
            args = (crc, left, right, nbrsam, queues[k-1])))
        (left, right) = (right, right+intlen)
    for process in procs:
        process.start()
    for process in procs:
        process.join()
    app = 4*sum([q.get() for q in queues])
    print(app, abs(app - pi))

main()