Python multiprocessing performance only improves with the square root of the number of cores used

Question

I am attempting to implement multiprocessing in Python (Windows Server 2012) and am having trouble achieving the degree of performance improvement that I expect. In particular, for a set of tasks which are almost entirely independent, I would expect a linear improvement with additional cores.

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I understand that--especially on Windows--there is overhead involved in opening new processes [1], and that many quirks of the underlying code can get in the way of a clean trend. But in theory the trend should ultimately still be close to linear for a fully parallelized task [2]; or perhaps logistic if I were dealing with a partially serial task [3].

However, when I run multiprocessing.Pool on a prime-checking test function (code below), I get a nearly perfect square-root relationship up to N_cores=36 (the number of physical cores on my server) before the expected performance hit when I get into the additional logical cores.

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Here is a plot of my performance test results :
_{( "Normalized Performance" is [ a run time with 1 CPU-core ] divided by [ a run time with N CPU-cores ] ).}

Is it normal to have this dramatic diminishing of returns with multiprocessing? Or am I missing something with my implementation?

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import numpy as np
from multiprocessing import Pool, cpu_count, Manager
import math as m
from functools import partial
from time import time

def check_prime(num):

    #Assert positive integer value
    if num!=m.floor(num) or num<1:
        print("Input must be a positive integer")
        return None

    #Check divisibility for all possible factors
    prime = True
    for i in range(2,num):
        if num%i==0: prime=False
    return prime

def cp_worker(num, L):
    prime = check_prime(num)
    L.append((num, prime))


def mp_primes(omag, mp=cpu_count()):
    with Manager() as manager:
        np.random.seed(0)
        numlist = np.random.randint(10**omag, 10**(omag+1), 100)

        L = manager.list()
        cp_worker_ptl = partial(cp_worker, L=L)

        try:
            pool = Pool(processes=mp)   
            list(pool.imap(cp_worker_ptl, numlist))
        except Exception as e:
            print(e)
        finally:
            pool.close() # no more tasks
            pool.join()

        return L


if __name__ == '__main__':
    rt = []
    for i in range(cpu_count()):
        t0 = time()
        mp_result = mp_primes(6, mp=i+1)
        t1 = time()
        rt.append(t1-t0)
        print("Using %i core(s), run time is %.2fs" % (i+1, rt[-1]))

Note: I am aware that for this task it would likely be more efficient to implement multithreading, but the actual script for which this one is a simplified analog is incompatible with Python multithreading due to GIL.

Answer 1

_{@KellanM deserved [+1] for quantitative performance monitoring}

am I missing something with my implementation?

Yes, you abstract from all add-on costs of the process-management.

While you have expressed an expectation of " a linear improvement with additional cores. ", this would hardly appear in practice for several reasons ( even the hype of communism failed to deliver anything for free ).

Gene AMDAHL has formulated the inital law of diminishing returns.
A more recent, re-formulated version, took into account also the effects of process-management {setup|terminate}-add-on overhead costs and tried to cope with atomicity-of-processing ( given large workpackage payloads cannot get easily re-located / re-distributed over available pool of free CPU-cores in most common programming systems ( except some indeed specific micro-scheduling art, like the one demonstrated in Semantic Design's PARLANSE or LLNL's SISAL have shown so colourfully in past ).

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A best next step?

If indeed interested in this domain, one may always experimentally measure and compare the real costs of process management ( plus data-flow costs, plus memory-allocation costs, ... up until the process-termination and results re-assembly in the main process ) so as to quantitatively fair record and evaluate the add-on costs / benefit ratio of using more CPU-cores ( that will get, in python, re-instated the whole python-interpreter state, including all its memory-state, before a first usefull operation will get carried out in a first spawned and setup process ).

Underperformance ( for the former case below )
if not disastrous effects ( from the latter case below ),
of either of ill-engineered resources-mapping policy, be it
an "under-booking"-resources from a pool of CPU-cores
or
an "over-booking"-resources from a pool of RAM-space
are discussed also here

The link to the re-formulated Amdahl's Law above will help you evaluate the point of diminishing returns, not to pay more than will ever receive.

Hoefinger et Haunschmid experiments may serve as a good practical evidence, how a growing number of processing-nodes ( be it a local O/S managed CPU-core, or a NUMA distributed architecture node ) will start decreasing the resulting performance,
where a Point of diminishing returns ( demonstrated in overhead agnostic Amdahl's Law )
will actually start to become a Point after which you pay more than receive. :

Good luck on this interesting field!

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Last, but not least,

NUMA / non-locality issues get their voice heard, into the discussion of scaling for HPC-grade tuned ( in-Cache / in-RAM computing strategies ) and may - as a side-effect - help detect the flaws ( as reported by @eryksun above ). One may feel free to review one's platform actual NUMA-topology by using lstopo tool, to see the abstraction, that one's operating system is trying to work with, once scheduling the "just"-[CONCURRENT] task execution over such a NUMA-resources-topology: