import math
import datetime
import threading
 
print ("###### С потоками ######")
now_time = datetime.datetime.now()
print ("Начало в ", now_time)
 
sum1=[0.0, 0.0, 0.0, 0.0]
h=sum=0.0
def Inthread(a, b, n):
    h=(b-a)/n
    
    def Sintegral (fe, se, si):
        global sum1
        for i in range(int(fe), int(se)):
            t=a+i*h
            sum1[si]=sum1[si]+abs(math.sin(t))
 
    th1=threading.Thread(target=Sintegral, args=(1, n/4, 0))
    th2=threading.Thread(target=Sintegral, args=(n/4, n/2, 1))
    th3=threading.Thread(target=Sintegral, args=(n/2, 3*n/4, 2))
    th4=threading.Thread(target=Sintegral, args=(3*n/4, n, 3))
    
    th1.start()
    th2.start()
    th3.start()
    th4.start()
    th1.join()
    th2.join()
    th3.join()
    th4.join()
    
    global sum
    for i in range(4):
        sum=sum+sum1[i]
    integral = h*((math.sin(a)+math.sin(b))/2+sum)
    print("Integral:", float(integral))
    return integral
 
a=Inthread(0, math.pi/2, 10000000)
print ("Конец в " + str(datetime.datetime.now()))
now_time = datetime.datetime.now() - now_time
print ("Затрачено времени: " + str(now_time))
input()

➜  python.su  python3 t_24211_ask.py 
###### С потоками ######
Integral: 1.000000000000041
Затрачено времени: 0:00:08.956972
➜  python.su  python3 t_24211_answ.py
###### С потоками multiprocessing ######
Integral: 1.000000000000041
Затрачено времени: 0:00:01.779728
➜  python.su  pypy3 t_24211_ask.py 
###### С потоками ######
Integral: 1.000000000000041
Затрачено времени: 0:00:00.390492
➜  python.su  pypy3 t_24211_answ.py
###### С потоками multiprocessing ######
Integral: 1.000000000000041
Затрачено времени: 0:00:00.291700

import math
import datetime
from multiprocessing import Process, Manager
print ("###### С потоками multiprocessing ######")
now_time = datetime.datetime.now()
print ("Начало в ", now_time)
sum1=[0.0, 0.0, 0.0, 0.0]
h=sum=0.0
def Inthread(a, b, n):
    h=(b-a)/n
    def Sintegral (fe, se, sum1, out):
        for i in range(int(fe), int(se)):
            t=a+i*h
            sum1=sum1+abs(math.sin(t))
        out[0] = sum1
        return
    global sum1
    manager = Manager()
    out_sum = []
    for i in range(4):
        out_sum.append(manager.list([sum1[i],]))
    processes = []
    for i, j in zip(range(4), [(1, n/4), (n/4, n/2),
                 (n/2, 3*n/4), (3*n/4, n)]):
        processes.append(Process(target=Sintegral,
            args=(j[0], j[1], sum1[i], out_sum[i])))
    for p in processes:
        p.start()
    for p in processes:
        p.join()
    global sum
    for i in range(4):
        sum=sum+out_sum[i][0]
    integral = h*((math.sin(a)+math.sin(b))/2+sum)
    print("Integral:", float(integral))
    return integral
a=Inthread(0, math.pi/2, 10000000)
print ("Конец в " + str(datetime.datetime.now()))
now_time = datetime.datetime.now() - now_time
print ("Затрачено времени: " + str(now_time))

import numpy as np
from scipy.integrate import quad,simps
from time import clock
def integrand(x):
    return np.abs(np.sin(x))
t0=clock()
npoint=13
x=np.linspace(0, np.pi/2,npoint)
ans = simps(np.abs(np.sin(x)), dx=np.pi/2/(npoint-1))
t1=clock()
print "simps 1",ans,t1-t0
t0=clock()
ans, err = quad(integrand, 0, np.pi/2)
t1=clock()
print "quad",ans,t1-t0
t0=clock()
npoint=10000000
x=np.linspace(0, np.pi/2,npoint)
ans = simps(np.abs(np.sin(x)), dx=np.pi/2/(npoint-1))
t1=clock()
print "simps 0",ans,t1-t0
simps 1 1.00000163444 0.000127365258906
quad 1.0 0.000169417306416
simps 0 1.0 0.966470488785

Traceback (most recent call last):
  File "<string>", line 1, in <module>
  File "C:\comp\Python33\lib\multiprocessing\forking.py", line 350, in main
    prepare(preparation_data)
  File "C:\comp\Python33\lib\multiprocessing\forking.py", line 457, in prepare
    '__parents_main__', file, path_name, etc
  File "C:\comp\Python33\lib\imp.py", line 180, in load_module
    return load_source(name, filename, file)
  File "C:\comp\Python33\lib\imp.py", line 119, in load_source
    _LoadSourceCompatibility(name, pathname, file).load_module(name)
  File "<frozen importlib._bootstrap>", line 584, in _check_name_wrapper
  File "<frozen importlib._bootstrap>", line 1022, in load_module
  File "<frozen importlib._bootstrap>", line 1003, in load_module
  File "<frozen importlib._bootstrap>", line 560, in module_for_loader_wrapper
  File "<frozen importlib._bootstrap>", line 868, in _load_module
  File "<frozen importlib._bootstrap>", line 313, in _call_with_frames_removed
  File "C:\PROJECTS\prjdocs\and\social\solution_method\simulation\cpp\bbb.py", line 39, in <module>
    a=Inthread(0, math.pi/2, 10000)
  File "C:\PROJECTS\prjdocs\and\social\solution_method\simulation\cpp\bbb.py", line 20, in Inthread
    manager = Manager()
  File "C:\comp\Python33\lib\multiprocessing\__init__.py", line 73, in Manager
    m.start()
  File "C:\comp\Python33\lib\multiprocessing\managers.py", line 486, in start
    self._process.start()
  File "C:\comp\Python33\lib\multiprocessing\process.py", line 111, in start
    self._popen = Popen(self)
  File "C:\comp\Python33\lib\multiprocessing\forking.py", line 216, in __init__
    cmd = ' '.join('"%s"' % x for x in get_command_line())
  File "C:\comp\Python33\lib\multiprocessing\forking.py", line 328, in get_command_line
    is not going to be frozen to produce a Windows executable.''')
RuntimeError: 
            Attempt to start a new process before the current process
            has finished its bootstrapping phase.
            This probably means that you are on Windows and you have
            forgotten to use the proper idiom in the main module:
                if __name__ == '__main__':
                    freeze_support()
                    ...
            The "freeze_support()" line can be omitted if the program
            is not going to be frozen to produce a Windows executable.
Traceback (most recent call last):
  File "C:\PROJECTS\prjdocs\and\social\solution_method\simulation\cpp\bbb.py", line 39, in <module>
    a=Inthread(0, math.pi/2, 10000)
  File "C:\PROJECTS\prjdocs\and\social\solution_method\simulation\cpp\bbb.py", line 20, in Inthread
    manager = Manager()
  File "C:\comp\Python33\lib\multiprocessing\__init__.py", line 73, in Manager
    m.start()
  File "C:\comp\Python33\lib\multiprocessing\managers.py", line 490, in start
    self._address = reader.recv()
  File "C:\comp\Python33\lib\multiprocessing\connection.py", line 251, in recv
    buf = self._recv_bytes()
  File "C:\comp\Python33\lib\multiprocessing\connection.py", line 307, in _recv_bytes
    [ov.event], False, INFINITE)
KeyboardInterrupt

if __name__ == "__main__":
    pass

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
from multiprocessing import Process, Manager,freeze_support
import math
import datetime
import threading
print ("###### С потоками multiprocessing ######")
now_time = datetime.datetime.now()
print ("Начало в ", now_time)
sum1=[0.0, 0.0, 0.0, 0.0]
h=sum=0.0
def Sintegral (a,h,fe, se, sum1, out):
    for i in range(int(fe), int(se)):
        t=a+i*h
        sum1=sum1+abs(math.sin(t))
    out[0] = sum1
    return
def Inthread(a, b, n):
    h=(b-a)/n
    manager = Manager()
    out_sum = []
    for i in range(4):
        out_sum.append(manager.list([0,]))
    processes = []
    for i, j in zip(range(4), [(1, n/4), (n/4, n/2),
                 (n/2, 3*n/4), (3*n/4, n)]):
        processes.append(Process(target=Sintegral,
            args=(a,h,j[0], j[1], sum1[i], out_sum[i])))
    for p in processes:
        p.start()
    for p in processes:
        p.join()
    global sum
    for i in range(4):
        sum=sum+out_sum[i][0]
    integral = h*((math.sin(a)+math.sin(b))/2+sum)
    print("Integral:", float(integral))
    return integral
if __name__ == "__main__":
    freeze_support()
    a=Inthread(0, math.pi/2, 10000)
    print ("Конец в " + str(datetime.datetime.now()))
    now_time = datetime.datetime.now() - now_time
    print ("Затрачено времени: " + str(now_time))
###### С потоками multiprocessing ######
Начало в  2014-08-18 23:13:54.671875
###### С потоками multiprocessing ######
Начало в  2014-08-18 23:13:54.687500
###### С потоками multiprocessing ######
Начало в  2014-08-18 23:13:54.671875
###### С потоками multiprocessing ######
Начало в  2014-08-18 23:13:54.687500
###### С потоками multiprocessing ######
Начало в  2014-08-18 23:13:54.500000
###### С потоками multiprocessing ######
Начало в  2014-08-18 23:13:54.343750
Integral: 0.9999999979438331
Конец в 2014-08-18 23:13:54.828125
Затрачено времени: 0:00:00.484375

('simps 1', 1.0000016344385796, 0.00011400000000000299)
('quad', 0.9999999999999999, 0.000126000000000015)
('simps 0', 1.0000000000000291, 1.494825)