# Multi-Core Parallelism¶

```
%load_ext cython
```

```
from concurrent.futures import ThreadPoolExecutor, ProcessPoolExecutor
import multiprocessing as mp
from multiprocessing import Pool, Value, Array
import os
import time
import numpy as np
from numba import njit
```

## Vanilla Python¶

```
def mc_pi(n):
s = 0
for i in range(n):
x = np.random.uniform(-1, 1)
y = np.random.uniform(-1, 1)
if (x**2 + y**2) < 1:
s += 1
return 4*s/n
```

```
%%time
res = [mc_pi(int(1e5)) for i in range(10)]
```

```
CPU times: user 5.19 s, sys: 20.6 ms, total: 5.21 s
Wall time: 5.21 s
```

## Using `numba`

to speed up computation¶

```
@njit()
def mc_pi_numba(n):
s = 0
for i in range(n):
x = np.random.uniform(-1, 1)
y = np.random.uniform(-1, 1)
if (x**2 + y**2) < 1:
s += 1
return 4*s/n
```

```
%%time
res = [mc_pi_numba(int(1e7)) for i in range(10)]
```

```
CPU times: user 3.66 s, sys: 21.9 ms, total: 3.68 s
Wall time: 3.69 s
```

```
np.array(res)
```

```
array([ 3.1419736, 3.1417564, 3.14116 , 3.141356 , 3.141194 ,
3.1419628, 3.141704 , 3.1418208, 3.1413216, 3.1413336])
```

## Using `cython`

to speed up computation¶

Note the use of an external C library (GNU Scientific Library or
`gsl`

) to replace `numpy`

random number generators (which are slow
for generating one number at a time). The GSL has already been packaged
for use in Cython, so we just have to `pip install`

it.

Install cythongsl if necessary and restart kernel.

```
! pip install cythongsl
```

```
%%cython -lgsl
import cython
from cython_gsl cimport *
@cython.cdivision(True)
def mc_pi_cython(int n):
cdef gsl_rng_type * T
cdef gsl_rng * r
cdef double s = 0.0
cdef double x, y
cdef int i
gsl_rng_env_setup()
T = gsl_rng_default
r = gsl_rng_alloc (T)
for i in range(n):
x = 2*gsl_rng_uniform(r) - 1
y = 2*gsl_rng_uniform(r)- 1
if (x**2 + y**2) < 1:
s += 1
return 4*s/n
```

```
%%time
res = [mc_pi_cython(int(1e7)) for i in range(10)]
```

```
CPU times: user 7.61 s, sys: 41.6 ms, total: 7.65 s
Wall time: 7.62 s
```

```
np.array(res)
```

```
array([ 3.1414584, 3.1414584, 3.1414584, 3.1414584, 3.1414584,
3.1414584, 3.1414584, 3.1414584, 3.1414584, 3.1414584])
```

## The `concurrent.futures`

module¶

Concurrent processes are processes that will return the same results
regardless of the order in which they were executed. A “future” is
something that will return a result sometime in the future. The
`concurrent.futures`

module provides an event handler, which can be
fed functions to be scheduled for future execution. This provides us
with a simple model for parallel execution on a multi-core machine.

While concurrent futures provide a simpler interface, it is slower and
less flexible when compared with using `multiprocessing`

for parallel
execution.

## Using processes in parallel with `ProcessPoolExecutor`

¶

We get a linear speedup as expected.

```
%%time
with ProcessPoolExecutor(max_workers=4) as pool:
res = pool.map(mc_pi_cython, [int(1e7) for i in range(10)])
```

```
CPU times: user 19.3 ms, sys: 31.4 ms, total: 50.7 ms
Wall time: 2.33 s
```

```
np.array(list(res))
```

```
array([ 3.1414584, 3.1414584, 3.1414584, 3.1414584, 3.1414584,
3.1414584, 3.1414584, 3.1414584, 3.1414584, 3.1414584])
```

### When you have many jobs¶

The `futures`

object gives fine control over the process, such as
adding callbacks and canceling a submitted job, but is computationally
expensive. We can use the `chunksize`

argument to reduce this cost
when submitting many jobs.

#### Using default chunksize of 1 for 10000 jobs¶

The total amount of computation whether you have 10 jobs of size 10,000,000 or 10,000 jobs of size 10,000 is essentially the same, so we would expect them both to take about the same amount of time.

```
%%time
with ProcessPoolExecutor(max_workers=4) as pool:
res = pool.map(mc_pi_cython, [int(1e4) for i in range(int(1e4))])
```

```
CPU times: user 4.52 s, sys: 1.67 s, total: 6.19 s
Wall time: 5.61 s
```

#### Using chunksize of 100¶

```
%%time
with ProcessPoolExecutor(max_workers=4) as pool:
res = pool.map(mc_pi_cython, [int(1e4) for i in range(int(1e4))], chunksize=100)
```

```
CPU times: user 105 ms, sys: 81 ms, total: 186 ms
Wall time: 2.11 s
```

### Functions with multiple arguments¶

```
def f(a, b):
return a + b
```

#### Using a function adapter¶

```
def f_(args):
return f(*args)
```

```
xs = np.arange(24)
chunks = np.array_split(xs, xs.shape[0]//2)
```

```
chunks
```

```
[array([0, 1]),
array([2, 3]),
array([4, 5]),
array([6, 7]),
array([8, 9]),
array([10, 11]),
array([12, 13]),
array([14, 15]),
array([16, 17]),
array([18, 19]),
array([20, 21]),
array([22, 23])]
```

```
with ProcessPoolExecutor(max_workers=4) as pool:
res = pool.map(f_, chunks)
list(res)
```

```
[1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45]
```

## Using processes in parallel with ThreadPoolExecutor¶

We do not get any speedup because the GIL only allows one thread to run at one time.

```
%%time
with ThreadPoolExecutor(max_workers=4) as pool:
res = pool.map(mc_pi_cython, [int(1e7) for i in range(10)])
```

```
CPU times: user 7.62 s, sys: 88.8 ms, total: 7.71 s
Wall time: 7.62 s
```

```
np.array(list(res))
```

```
array([ 3.1414584, 3.1414584, 3.1414584, 3.1414584, 3.1414584,
3.1414584, 3.1414584, 3.1414584, 3.1414584, 3.1414584])
```

## Turning off the GIL in `cython`

¶

```
%%cython -lgsl
import cython
from cython_gsl cimport *
@cython.cdivision(True)
def mc_pi_cython_nogil(int n):
cdef gsl_rng_type * T
cdef gsl_rng * r
cdef double s = 0.0
cdef double x, y
cdef int i
gsl_rng_env_setup()
T = gsl_rng_default
r = gsl_rng_alloc (T)
with cython.nogil:
for i in range(n):
x = 2*gsl_rng_uniform(r) - 1
y = 2*gsl_rng_uniform(r)- 1
if (x**2 + y**2) < 1:
s += 1
return 4*s/n
```

## Using processes in parallel with `ThreadPoolExecutor`

and `nogil`

¶

We finally get the linear speedup expected. Note that threads are actually faster than processes because there is less overhead to using a thread.

```
%%time
with ThreadPoolExecutor(max_workers=4) as pool:
res = pool.map(mc_pi_cython_nogil, [int(1e7) for i in range(10)])
```

```
CPU times: user 7.61 s, sys: 7.57 ms, total: 7.62 s
Wall time: 2.28 s
```

```
np.array(list(res))
```

```
array([ 3.1414584, 3.1414584, 3.1414584, 3.1414584, 3.1414584,
3.1414584, 3.1414584, 3.1414584, 3.1414584, 3.1414584])
```

## Using `multiprocessing`

¶

One nice thing about using `multiprocessing`

is that it works equally
well for small numbers of large jobs, or large numbers of small jobs out
of the box.

```
%%time
with mp.Pool(processes=4) as pool:
res = pool.map(mc_pi_cython, [int(1e7) for i in range(10)])
```

```
CPU times: user 16 ms, sys: 34 ms, total: 50.1 ms
Wall time: 2.41 s
```

```
%%time
with mp.Pool(processes=4) as pool:
res = pool.map(mc_pi_cython, [int(1e4) for i in range(int(1e4))])
```

```
CPU times: user 18.1 ms, sys: 32.5 ms, total: 50.6 ms
Wall time: 2.11 s
```

### Creating individual processes¶

```
def f(i):
time.sleep(np.random.random())
print(os.getpid(), i)
```

```
for i in range(10):
p = mp.Process(target=f, args=(i,))
p.start()
p.join()
```

```
27826 0
27827 1
27828 2
27829 3
27830 4
27831 5
27832 6
27833 7
27834 8
27835 9
```

### Functions with multiple arguments¶

Multiprocessing `Pool`

has a `starmap`

method that removes the need
to write a wrapper function.

```
def f(a, b):
return a + b
```

```
xs = np.arange(24)
with Pool(processes=4) as pool:
res = pool.starmap(f, np.array_split(xs, xs.shape[0]//2))
list(res)
```

```
[1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45]
```

#### Partial application¶

Sometimes, `functools.partial`

can be used to reduce the number of
arguments needed to just one.

```
def f(a, b):
return a * b
```

```
from functools import partial
fp = partial(f, b=2)
```

```
xs = np.arange(24)
with Pool(processes=4) as pool:
res = pool.map(fp, xs)
np.array(list(res))
```

```
array([ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32,
34, 36, 38, 40, 42, 44, 46])
```

#### How do we get a return value from a process?¶

```
def f1(q, i):
time.sleep(np.random.random())
q.put((os.getpid(), i))
```

```
q = mp.Queue()
res = []
for i in range(10):
p = mp.Process(target=f1, args=(q,i,))
p.start()
res.append(q.get())
p.join()
res
```

```
[(27844, 0),
(27845, 1),
(27846, 2),
(27847, 3),
(27848, 4),
(27849, 5),
(27850, 6),
(27851, 7),
(27852, 8),
(27853, 9)]
```

#### Counting number of jobs (1)¶

```
def f2(i):
global counter
counter = counter + 1
print(os.getpid(), i)
```

#### Checking¶

```
counter = 0
f2(10)
print(counter)
```

```
27789 10
1
```

```
counter = 0
for i in range(10):
p = mp.Process(target=f2, args=(i,))
p.start()
p.join()
```

```
27854 0
27855 1
27856 2
27857 3
27858 4
27859 5
27860 6
27861 7
27862 8
27863 9
```

#### Counting number of jobs (2)¶

We can use shared memory to do this, but it is slow because multiprocessing has to ensure that only one process gets to use counter at any one time. Multiprocesing provides Value and Array shared memory variables, but you can also convert arbitrary Python variables into shared memory objects (less efficient).

```
def f3(i, counter, store):
counter.value += 1
store[os.getpid() % 10] += i
```

```
%%time
counter = mp.Value('i', 0)
store = mp.Array('i', [0]*10)
for i in range(int(1e2)):
p = mp.Process(target=f3, args=(i, counter, store))
p.start()
p.join()
print(counter.value)
print(store[:])
```

```
100
[510, 520, 530, 540, 450, 460, 470, 480, 490, 500]
CPU times: user 120 ms, sys: 436 ms, total: 556 ms
Wall time: 1.25 s
```

#### Counting number of jobs (3)¶

We should try to avoid using shared memory as much as possible in
parallel jobs as they drastically reduce efficiency. One useful approach
is to use the `map-reduce`

pattern. We should also use Pool to reuse
processes rather than spawn too many of them. We will see much more of
the `map-reduc`

approach when we work with Spark.

```
def f4(i):
return (os.getpid(), 1, i)
```

```
%%time
# map step
with mp.Pool(processes=10) as pool:
res = pool.map(f4, range(int(1e2)))
#reeduce step
res = np.array(res)
counter = res[:, 1].sum()
print(counter)
store = np.zeros(10)
idx = res[:, 0] % 10
for i in range(10):
store[i] = res[idx==i, 2].sum()
print(store)
```

```
100
[ 423. 486. 531. 303. 579. 552. 615. 633. 414. 414.]
CPU times: user 25.7 ms, sys: 70.1 ms, total: 95.8 ms
Wall time: 197 ms
```

### Using decorators with multiprocessing¶

```
@njit()
def mc_pi_numba(n):
s = 0
for i in range(n):
x = np.random.uniform(-1, 1)
y = np.random.uniform(-1, 1)
if (x**2 + y**2) < 1:
s += 1
return 4*s/n
def get_pis(n1, n2):
results = [mc_pi_numba(int(n1)) for i in range(n2)]
return results
```

```
%%time
get_pis(1e7, 10)
```

```
CPU times: user 3.65 s, sys: 17.1 ms, total: 3.67 s
Wall time: 3.67 s
```

```
[3.1412004,
3.142614,
3.1412916,
3.1415904,
3.1416708,
3.14172,
3.141886,
3.141906,
3.1419364,
3.1418736]
```

### Using `joblib`

for simple parallelism¶

```
from joblib import Parallel, delayed
@njit
def mc_pi(n):
s = 0
for i in range(n):
x = np.random.uniform(-1, 1)
y = np.random.uniform(-1, 1)
if (x**2 + y**2) < 1:
s += 1
return 4*s/n
def get_pis(n1, n2, k):
n1, n2 = int(n1), int(n2)
results = Parallel(n_jobs=k)(delayed(mc_pi)(n1) for i in range(n2))
return results
```

```
%%time
get_pis(1e7, 10, 1)
```

```
CPU times: user 3.5 s, sys: 46.3 ms, total: 3.54 s
Wall time: 3.5 s
```

```
[3.1414168,
3.1419008,
3.1421364,
3.1421516,
3.1421732,
3.1422248,
3.1412356,
3.1419928,
3.1413028,
3.1416204]
```

```
%%time
get_pis(1e7, 10, 8)
```

```
CPU times: user 95.1 ms, sys: 60.3 ms, total: 155 ms
Wall time: 947 ms
```

```
[3.141658,
3.141658,
3.141658,
3.141658,
3.141658,
3.141658,
3.141658,
3.141658,
3.1405908,
3.1405908]
```