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Scientific Programming in Python

Topic 5: Accelerating Python with Cython: Writting C in Python

Notebook created by Martín Villanueva - martin.villanueva@usm.cl - DI UTFSM - May2017.





In [5]:



    


%matplotlib inline

import numpy as np
import numexpr as ne
import numba
import math
import random
import matplotlib.pyplot as plt
import scipy as sp
import sys

%load_ext Cython

Table of Contents

1.- Cython Basic Usage

Cython is both a Superset of Python and a Python Library that lets you combine C and Python in various ways. There are two main use-cases:

  1. Optimizing your Python code by statically compiling it to C.
  2. Wrapping a C/C++ library in Python.

In order to get it properly working, you need Cython and a C compiler:

  1. Cython: conda install cython
  2. C compiler: Install GNU C compiler with your package manager (Unix/Linux) or install Xcode (OSX).

We will introduce the basic Cython usage by impementing the Eratosthenes Sieve Algorithm, which is an algorithm to find all prime numbers smaller than a given number.





In [1]:



    


def primes_python(n):
    primes = [False, False] + [True] * (n - 2)
    i= 2
    while i < n:
        # We do not deal with composite numbers.
        if not primes[i]:
            i += 1
            continue 
        k= i+i
        # We mark multiples of i as composite numbers.
        while k < n:
            primes[k] = False
            k += i 
        i += 1
    # We return all numbers marked with True.
    return [i for i in range(2, n) if primes[i]]



    











In [2]:



    


primes_python(20)



    


















    
Out[2]:








[2, 3, 5, 7, 11, 13, 17, 19]

Let's evaluate the performance for the first version:





In [3]:



    


tp = %timeit -o primes_python(10000)



    


















    






100 loops, best of 3: 4.57 ms per loop

And now we write our first Cython version, by just adding %%cython magic in the first line of the cell:





In [6]:



    


%%cython
def primes_cython1(n):
    primes = [False, False] + [True] * (n - 2)
    i= 2
    while i < n:
        # We do not deal with composite numbers.
        if not primes[i]:
            i += 1
            continue 
        k= i+i
        # We mark multiples of i as composite numbers.
        while k < n:
            primes[k] = False
            k += i 
        i += 1
    # We return all numbers marked with True.
    return [i for i in range(2, n) if primes[i]]



    











In [7]:



    


tc1 = %timeit -o primes_cython1(10000)



    


















    






100 loops, best of 3: 2.67 ms per loop

We achieve x2 speed improvement doing (practically) nothing!.

When we add %%cython at the beginning of the cell, the code gets compiled by Cython into a C extension. Then, this extension is loaded, and the compiled function is readily available in the interactive namespace.

Lets help the compiler by explicitly defining the type of the variables with the cdef macro/keyword:





In [8]:



    


%%cython
def primes_cython2(int n):
    # Note the type declarations below
    cdef list primes = [False, False] + [True] * (n - 2)
    cdef int i = 2
    cdef int k = 0
    # The rest of the functions is unchanged
    while i < n:
        # We do not deal with composite numbers.
        if not primes[i]:
            i += 1
            continue 
        k= i+i
        # We mark multiples of i as composite numbers.
        while k < n:
            primes[k] = False
            k += i 
        i += 1
    # We return all numbers marked with True.
    return [i for i in range(2, n) if primes[i]]



    











In [9]:



    


tc2 = %timeit -o primes_cython2(10000)



    


















    






1000 loops, best of 3: 320 µs per loop

















In [10]:



    


print("Cython version 1 speedup: {0}".format(tp.best/tc1.best))
print("Cython version 2 speedup: {0}".format(tp.best/tc2.best))



    


















    






Cython version 1 speedup: 1.7089263650919428
Cython version 2 speedup: 14.255755129764186

Then: In general, Cython will be the most efficient when it can compile data structures and operations directly to C by making as few CPython API calls as possible. Specifying the types of the variables often leads to greater speed improvements.

Just for curiosity let's see the performance Numba's JIT achieves:





In [11]:



    


@numba.jit(nopython=True)
def primes_numba(n):
    primes = [False, False] + [True] * (n - 2)
    i= 2
    while i < n:
        # We do not deal with composite numbers.
        if not primes[i]:
            i += 1
            continue 
        k= i+i
        # We mark multiples of i as composite numbers.
        while k < n:
            primes[k] = False
            k += i 
        i += 1
    # We return all numbers marked with True.
    res = []
    for i in range(2,n):
        if primes[i]: res.append(i)
    return res



    











In [12]:



    


tn = %timeit -o primes_numba(10000)



    


















    






The slowest run took 2398.70 times longer than the fastest. This could mean that an intermediate result is being cached.
1 loop, best of 3: 143 µs per loop

Numba wins this time! but: This is not the final form of Cython...

Inspecting Cython bottlenecks with annotations

We can inspect the C code generated by Cython with the -a argument. Let's inspect the code used above.

The non-optimized lines will be shown in a gradient of yellow (white lines are faster, yellow lines are slower), telling you which lines are the least efficiently compiled to C. By clicking on a line, you can see the generated C code corresponding to that line.





In [13]:



    


%%cython -a
def primes_cython1(n):
    primes = [False, False] + [True] * (n - 2)
    i= 2
    while i < n:
        # We do not deal with composite numbers.
        if not primes[i]:
            i += 1
            continue 
        k= i+i
        # We mark multiples of i as composite numbers.
        while k < n:
            primes[k] = False
            k += i 
        i += 1
    # We return all numbers marked with True.
    return [i for i in range(2, n) if primes[i]]



    


















    
Out[13]:











    
    Cython: _cython_magic_7ce427e7ceb040e959d167c66d2f6928.pyx
    
    



Generated by Cython 0.25.2



    Yellow lines hint at Python interaction.

    Click on a line that starts with a "+" to see the C code that Cython generated for it.



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In [14]:



    


%%cython -a
def primes_cython2(int n):
    # Note the type declarations below
    cdef list primes = [False, False] + [True] * (n - 2)
    cdef int i = 2
    cdef int k = 0
    # The rest of the functions is unchanged
    while i < n:
        # We do not deal with composite numbers.
        if not primes[i]:
            i += 1
            continue 
        k= i+i
        # We mark multiples of i as composite numbers.
        while k < n:
            primes[k] = False
            k += i 
        i += 1
    # We return all numbers marked with True.
    return [i for i in range(2, n) if primes[i]]



    


















    
Out[14]:











    
    Cython: _cython_magic_7faed0e5d5b89d29eea1f4d95c47da28.pyx
    
    



Generated by Cython 0.25.2



    Yellow lines hint at Python interaction.

    Click on a line that starts with a "+" to see the C code that Cython generated for it.



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gcc -shared -fPIC -fwrapv -O3 -fno-strict-aliasing -I/home/mavillan/anaconda3/include/python3.6m -o primes.so primes.c

2.- Advanced usage

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NumPy Arrays

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%timeit distance_matrix_python(A,B)



    


















    






1 loop, best of 3: 1min 50s per loop

















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In [63]:



    


%timeit distance_matrix_cython0(A,B)



    


















    






1 loop, best of 3: 1min 51s per loop

Now let's improve this naive Cython implementation by statically defining the types of the variables:





In [15]:



    


%%cython -a
import numpy as np
cimport numpy as cnp

ctypedef cnp.float64_t float64_t

def dist(cnp.ndarray[float64_t, ndim=1] a, cnp.ndarray[float64_t, ndim=1] b):
    return np.sqrt(np.sum((a-b)**2))

def distance_matrix_cython1(cnp.ndarray[float64_t, ndim=2] A, cnp.ndarray[float64_t, ndim=2] B):
    cdef:
        int m = A.shape[0]
        int n = B.shape[0]
        int i,j
        cnp.ndarray[float64_t, ndim=2] D = np.empty((m,n))
    for i in range(m):
        for j in range(n):
            D[i,j] = dist(A[i], B[j])
    return D



    


















    
Out[15]:











    
    Cython: _cython_magic_ed6bc794487e0d219dae0b68e7bdb406.pyx
    
    



Generated by Cython 0.25.2



    Yellow lines hint at Python interaction.

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In [18]:



    


%timeit -n 10 distance_matrix_cython1(A,B)



    


















    






10 loops, best of 3: 4.96 s per loop

















In [121]:



    


%%cython -a
import numpy as np
cimport numpy as cnp

ctypedef cnp.float64_t float64_t
from libc.math cimport sqrt

def dist(cnp.ndarray[float64_t, ndim=1] a, cnp.ndarray[float64_t, ndim=1] b):
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        int n = a.shape[0]
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def distance_matrix_cython2(cnp.ndarray[float64_t, ndim=2] A, cnp.ndarray[float64_t, ndim=2] B):
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    for i in range(m):
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    return D



    


















    
Out[121]:











    
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Generated by Cython 0.25.2



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In [122]:



    


%timeit -n 10 distance_matrix_cython2(A,B)



    


















    






10 loops, best of 3: 1.17 s per loop

Typed Memory Views

Typed memoryviews allow efficient access to memory buffers, such as those underlying NumPy arrays, without incurring any Python overhead. Memoryviews are similar to the current NumPy array buffer support (np.ndarray[np.float64_t, ndim=2]), but they have more features and cleaner syntax.

They can handle a wider variety of sources of array data. For example, they can handle C arrays and the Cython array type (Cython arrays).

Syntaxis: dtype[:,::1] where ::1 indicates the axis where elements are contiguous.





In [19]:



    


%%cython -a
import numpy as np
cimport numpy as cnp

ctypedef cnp.float64_t float64_t
from libc.math cimport sqrt

def dist(float64_t[::1] a, float64_t[::1] b):
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        int n = a.shape[0]
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def distance_matrix_cython3(float64_t[:,::1] A, float64_t[:,::1] B):
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        int n = B.shape[0]
        int i,j
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    for i in range(m):
        for j in range(n):
            D[i,j] = dist(A[i], B[j])
    return D



    


















    
Out[19]:











    
    Cython: _cython_magic_0b434337ca1aa0c18339dae232dd3e72.pyx
    
    



Generated by Cython 0.25.2



    Yellow lines hint at Python interaction.

    Click on a line that starts with a "+" to see the C code that Cython generated for it.



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In [20]:



    


%timeit -n 10 distance_matrix_cython3(A,B)



    


















    






10 loops, best of 3: 370 ms per loop

Compiler optimization

With the -c option we can pass the compiler (gcc) optimization options. Below we use the most common of them:





In [21]:



    


%%cython -a -c=-fPIC -c=-fwrapv -c=-O3 -c=-fno-strict-aliasing
import numpy as np
cimport numpy as cnp

ctypedef cnp.float64_t float64_t
from libc.math cimport sqrt

def dist(float64_t[::1] a, float64_t[::1] b):
    cdef:
        int i = 0
        int n = a.shape[0]
        float ret = 0
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def distance_matrix_cython4(float64_t[:,::1] A, float64_t[:,::1] B):
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        int n = B.shape[0]
        int i,j
        float64_t[:,::1] D = np.empty((m,n))
    for i in range(m):
        for j in range(n):
            D[i,j] = dist(A[i], B[j])
    return D



    


















    
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Generated by Cython 0.25.2



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In [22]:



    


%timeit -n 10 distance_matrix_cython4(A,B)



    


















    






10 loops, best of 3: 368 ms per loop

Compiler directives

Compiler directives are instructions which affect the behavior of Cython code.

cdivision (True / False)

  • If set to False, Cython will adjust the remainder and quotient operators C types to match those of Python ints (which differ when the operands have opposite signs) and raise a ZeroDivisionError when the right operand is 0. This has up to a 35% speed penalty. If set to True.

boundscheck (True / False)

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nonecheck (True / False)

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wraparound (True / False)

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initializedcheck (True / False)

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For all the compilation directives see here.





In [23]:



    


%%cython -a -c=-fPIC -c=-fwrapv -c=-O3 -c=-fno-strict-aliasing
#!python
#cython: cdivision=True, boundscheck=False, nonecheck=False, wraparound=False, initializedcheck=False

import numpy as np
cimport numpy as cnp

ctypedef cnp.float64_t float64_t
from libc.math cimport sqrt

def dist(float64_t[::1] a, float64_t[::1] b):
    cdef:
        int i = 0
        int n = a.shape[0]
        float ret = 0
    for i in range(n):
        ret += (a[i]-b[i])**2
    return sqrt(ret)


def distance_matrix_cython5(float64_t[:,::1] A, float64_t[:,::1] B):
    cdef:
        int m = A.shape[0]
        int n = B.shape[0]
        int i,j
        float64_t[:,::1] D = np.empty((m,n))
    for i in range(m):
        for j in range(n):
            D[i,j] = dist(A[i,:], B[j,:])
    return D



    


















    
Out[23]:











    
    Cython: _cython_magic_9c0c3b17c4f6bac0815df807cbf0eead.pyx
    
    



Generated by Cython 0.25.2



    Yellow lines hint at Python interaction.

    Click on a line that starts with a "+" to see the C code that Cython generated for it.



+01: #!python


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 02: #cython: cdivision=True, boundscheck=False, nonecheck=False, wraparound=False, initializedcheck=False


 03: 


+04: import numpy as np


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In [24]:



    


%timeit -n 10 distance_matrix_cython5(A,B)



    


















    






10 loops, best of 3: 365 ms per loop

Pure C functions

With the cdef keywork we can realy define C function, as we shown below. In such functions all variable types should be defined and should have a return type, and can't be called directly in Python, i.e, only can be called by functions defined in the same module.

There is a midpoint between def and cdef which automatically creates a Python function with the same name, so the function can be called directly.





In [25]:



    


%%cython -a -c=-fPIC -c=-fwrapv -c=-O3 -c=-fno-strict-aliasing
#!python
#cython: cdivision=True, boundscheck=False, nonecheck=False, wraparound=False, initializedcheck=False

import numpy as np
cimport numpy as cnp

ctypedef cnp.float64_t float64_t
from libc.math cimport sqrt

cdef float64_t dist(float64_t[::1] a, float64_t[::1] b):
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        int i = 0
        int n = a.shape[0]
        float ret = 0
    for i in range(n):
        ret += (a[i]-b[i])**2
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def distance_matrix_cython6(float64_t[:,::1] A, float64_t[:,::1] B):
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        int m = A.shape[0]
        int n = B.shape[0]
        int i,j
        float64_t[:,::1] D = np.empty((m,n))
    for i in range(m):
        for j in range(n):
            D[i,j] = dist(A[i,:], B[j,:])
    return D



    


















    
Out[25]:











    
    Cython: _cython_magic_55f47f37023751be50bd87c6d8f78ec3.pyx
    
    



Generated by Cython 0.25.2



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In [26]:



    


%timeit -n 10 distance_matrix_cython6(A,B)



    


















    






10 loops, best of 3: 17.7 ms per loop

Example of cdef and cpdef





In [29]:



    


%%cython  -c=-fPIC -c=-fwrapv -c=-O3 -c=-fno-strict-aliasing
#!python
#cython: cdivision=True, boundscheck=False, nonecheck=False, wraparound=False, initializedcheck=False

cimport numpy as cnp
ctypedef cnp.float64_t float64_t

cdef float64_t test1(float64_t a, float64_t b):
    return a+b



    











In [31]:



    


test1(1.,1.)



    


















    






---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
<ipython-input-31-f4ee9cdb0154> in <module>()
----> 1 test1(1.,1.)

NameError: name 'test1' is not defined
















In [32]:



    


%%cython  -c=-fPIC -c=-fwrapv -c=-O3 -c=-fno-strict-aliasing
#!python
#cython: cdivision=True, boundscheck=False, nonecheck=False, wraparound=False, initializedcheck=False

cimport numpy as cnp
ctypedef cnp.float64_t float64_t

cpdef float64_t test2(float64_t a, float64_t b):
    return a+b



    











In [33]:



    


test2(1,1)



    


















    
Out[33]:








2.0

Function inlining

In computing, inline expansion, or inlining, is a manual or compiler optimization that replaces a function call site with the body of the called function.

As a rule of thumb: Some inlining will improve speed at very minor cost of space, but excess inlining will hurt speed, due to inlined code consuming too much of the instruction cache, and also cost significant space.





In [34]:



    


%%cython -a -c=-fPIC -c=-fwrapv -c=-O3 -c=-fno-strict-aliasing
#!python
#cython: cdivision=True, boundscheck=False, nonecheck=False, wraparound=False, initializedcheck=False

import numpy as np
cimport numpy as cnp

ctypedef cnp.float64_t float64_t
from libc.math cimport sqrt

cdef inline float64_t dist(float64_t[::1] a, float64_t[::1] b):
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def distance_matrix_cython7(float64_t[:,::1] A, float64_t[:,::1] B):
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        int n = B.shape[0]
        int i,j
        float64_t[:,::1] D = np.empty((m,n))
    for i in range(m):
        for j in range(n):
            D[i,j] = dist(A[i,:], B[j,:])
    return D



    


















    
Out[34]:











    
    Cython: _cython_magic_4f7592de4881141d314a4e9ccb0eb6e6.pyx
    
    



Generated by Cython 0.25.2



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In [35]:



    


%timeit -n 10 distance_matrix_cython7(A,B)



    


















    






10 loops, best of 3: 17.7 ms per loop

What about Numba?





In [36]:



    


@numba.jit(nopython=True)
def dist(a, b):
    n = a.shape[0]
    ret = 0
    for i in range(n):
        ret += (a[i]-b[i])**2
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@numba.jit(nopython=True)
def distance_matrix_numba(A, B):
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    n = B.shape[0]
    D = np.empty((m,n))
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    return D



    











In [37]:



    


%timeit -n 10 distance_matrix_numba(A,B)



    


















    






10 loops, best of 3: 38.7 ms per loop

4.- Other advanced things you can do with Cython

We have seen that with Cython we can implement our algorithms achieving C performance. Moreover it is very versatile and we can do some other advanced thing with it:

Object-oriented programming: Classes and methods

To support object-oriented programming, Cython supports writing normal Python classes exactly as in Python.





In [38]:



    


%%cython -a -c=-fPIC -c=-fwrapv -c=-O3 -c=-fno-strict-aliasing
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#cython: cdivision=True, boundscheck=False, nonecheck=False, wraparound=False, initializedcheck=False

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    def test_cpdef(self, long num):
        while num > 0:
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            num -= 1



    


















    
Out[38]:











    
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Generated by Cython 0.25.2



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In [39]:



    


%%timeit n = 1000000
a1 = A()
a1.test_def(n)



    


















    






10 loops, best of 3: 40.2 ms per loop

















In [40]:



    


%%timeit n = 1000000
a1 = A()
a1.test_cdef(n)



    


















    






100 loops, best of 3: 2.01 ms per loop

















In [41]:



    


%%timeit n = 1000000
a1 = A()
a1.test_cpdef(n)



    


















    






100 loops, best of 3: 3.11 ms per loop

C library Wrapping

Wrapper libraries (or library wrappers) consist of a thin layer of code which translates a library's existing interface into a compatible interface. Cython allows us to do this with C libraries... In fact many important project use Cython to do that:

  • Scikit-Learn use Cython to wrap many machine learning routines written in C (LibSVM).
  • OpenCV for python.
  • Scikit-Image.
  • SciPy Wraps BLAS, LAPACK and others.
  • Etc.

Content source: mavillan/SciProg

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