Multithreading python

import time
import pandas as pd
import multiprocessing


results = []

def processData(df):  
    """Does some compute intensive operation on the data frame.
       Returns a list."""
       
    for i in range(100000):
        df = df * 1.0
    return df.values.tolist()

def collect_results(result):
    """Uses apply_async's callback to setup up a separate Queue for each process"""
    results.extend(result)
    
if __name__ == "__main__":
    start_time = time.time()  
    
    # Repeats the compute intensive operation on 10 data frames concurrently
    pool = multiprocessing.Pool(processes=multiprocessing.cpu_count())
    for i in range(2): 
        pool.apply_async(processData, args=(123, ), callback=collect_results)
    pool.close()
    pool.join()
    
    # Converts list of lists to a data frame
    df = pd.DataFrame(results)
    print(df.shape)
    print("--- %s seconds ---" % (time.time() - start_time))

import time
import multiprocessing

def processData(D,F):
    print("d:",D, F)
    P=0
    v=1+4*D
    for k in range(D,F):
        P=P+(4/v)-(4/(v+2))
        v=v+4
    print("f:",D,F)
    return P

def collect_results(result):
    """Uses apply_async's callback to setup up a separate Queue for each process"""
    global results
    print(result)
    results+=result

if __name__ == "__main__":
    results = 0
    start_time = time.time()
    boucles=float(100000000)
    procs=4
    C=int(boucles/procs)
    pool = multiprocessing.Pool(processes=multiprocessing.cpu_count())
    for i in range(procs):
        pool.apply_async(processData, args=(i*C,(i+1)*C), callback=collect_results)
    pool.close()
    pool.join()
    print("total:",results)
    print("--- %s seconds ---" % (time.time() - start_time))

P

v_k

k

1

4

P

k

import functools, multiprocessing

def p(k):
    return 4 / (4 * k + 1) - 4 / (4 * k + 3)

pool = multiprocessing.Pool(processes=multiprocessing.cpu_count())
with multiprocessing.Pool(multiprocessing.cpu_count()) as pool:
     pks = pool.map(p, range(10))
print(sum(pks))

test()