基本教程 ¶

def primes(int nb_primes):
    cdef int n, i, len_p
    cdef int p[1000]
    if nb_primes > 1000:
        nb_primes = 1000
    len_p = 0  # The current number of elements in p.
    n = 2
    while len_p < nb_primes:
        # Is n prime?
        for i in p[:len_p]:
            if n % i == 0:
                break
        # If no break occurred in the loop, we have a prime.
        else:
            p[len_p] = n
            len_p += 1
        n += 1
    # Let's return the result in a python list:
    result_as_list  = [prime for prime in p[:len_p]]
    return result_as_list
									

You’ll see that it starts out just like a normal Python function definition, except that the parameter nb_primes is declared to be of type int . This means that the object passed will be converted to a C integer (or a TypeError. will be raised if it can’t be).

Now, let’s dig into the core of the function:

cdef int n, i, len_p
cdef int p[1000]
						

Lines 2 and 3 use the cdef statement to define some local C variables. The result is stored in the C array p during processing, and will be copied into a Python list at the end (line 22).

注意

You cannot create very large arrays in this manner, because they are allocated on the C function call stack, which is a rather precious and scarce resource. To request larger arrays, or even arrays with a length only known at runtime, you can learn how to make efficient use of C 内存分配 , Python 数组 or NumPy 数组 采用 Cython。

if nb_primes > 1000:
    nb_primes = 1000
						

As in C, declaring a static array requires knowing the size at compile time. We make sure the user doesn’t set a value above 1000 (or we would have a segmentation fault, just like in C).

len_p = 0  # The number of elements in p
n = 2
while len_p < nb_primes:
						

Lines 7-9 set up for a loop which will test candidate numbers for primeness until the required number of primes has been found.

# Is n prime?
for i in p[:len_p]:
    if n % i == 0:
        break
						

Lines 11-12, which try dividing a candidate by all the primes found so far, are of particular interest. Because no Python objects are referred to, the loop is translated entirely into C code, and thus runs very fast. You will notice the way we iterate over the p C array.

for i in p[:len_p]:
						

The loop gets translated into a fast C loop and works just like iterating over a Python list or NumPy array. If you don’t slice the C array with [:len_p] , then Cython will loop over the 1000 elements of the array.

# If no break occurred in the loop
else:
    p[len_p] = n
    len_p += 1
n += 1
						

If no breaks occurred, it means that we found a prime, and the block of code after the else line 16 will be executed. We add the prime found to p . If you find having an else after a for-loop strange, just know that it’s a lesser known features of the Python language, and that Cython executes it at C speed for you. If the for-else syntax confuses you, see this excellent blog post .

# Let's put the result in a python list:
result_as_list  = [prime for prime in p[:len_p]]
return result_as_list
						

In line 22, before returning the result, we need to copy our C array into a Python list, because Python can’t read C arrays. Cython can automatically convert many C types from and to Python types, as described in the documentation on 类型转换 , so we can use a simple list comprehension here to copy the C int values into a Python list of Python int objects, which Cython creates automatically along the way. You could also have iterated manually over the C array and used result_as_list.append(prime) , the result would have been the same.

You’ll notice we declare a Python list exactly the same way it would be in Python. Because the variable result_as_list hasn’t been explicitly declared with a type, it is assumed to hold a Python object, and from the assignment, Cython also knows that the exact type is a Python list.

Finally, at line 18, a normal Python return statement returns the result list.

Compiling primes.pyx with the Cython compiler produces an extension module which we can try out in the interactive interpreter as follows:

>>> import primes
>>> primes.primes(10)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
						

See, it works! And if you’re curious about how much work Cython has saved you, take a look at the C code generated for this module.

Cython has a way to visualise where interaction with Python objects and Python’s C-API is taking place. For this, pass the annotate=True 参数用于 cythonize() . It produces a HTML file. Let’s see:

If a line is white, it means that the code generated doesn’t interact with Python, so will run as fast as normal C code. The darker the yellow, the more Python interaction there is in that line. Those yellow lines will usually operate on Python objects, raise exceptions, or do other kinds of higher-level operations than what can easily be translated into simple and fast C code. The function declaration and return use the Python interpreter so it makes sense for those lines to be yellow. Same for the list comprehension because it involves the creation of a Python object. But the line if n % i == 0: , why? We can examine the generated C code to understand:

We can see that some checks happen. Because Cython defaults to the Python behavior, the language will perform division checks at runtime, just like Python does. You can deactivate those checks by using the 编译器指令 .

Now let’s see if, even if we have division checks, we obtained a boost in speed. Let’s write the same program, but Python-style:

def primes_python(nb_primes):
    p = []
    n = 2
    while len(p) < nb_primes:
        # Is n prime?
        for i in p:
            if n % i == 0:
                break
        # If no break occurred in the loop
        else:
            p.append(n)
        n += 1
    return p
						

It is also possible to take a plain .py file and to compile it with Cython. Let’s take primes_python , change the function name to primes_python_compiled and compile it with Cython (without changing the code). We will also change the name of the file to example_py_cy.py to differentiate it from the others. Now the setup.py 看起来像这样：

from distutils.core import setup
from Cython.Build import cythonize
setup(
    ext_modules=cythonize(['example.pyx',        # Cython code file with primes() function
                           'example_py_cy.py'],  # Python code file with primes_python_compiled() function
                          annotate=True),        # enables generation of the html annotation file
)
						

Now we can ensure that those two programs output the same values:

>>> primes_python(1000) == primes(1000)
True
>>> primes_python_compiled(1000) == primes(1000)
True
						

It’s possible to compare the speed now:

python -m timeit -s 'from example_py import primes_python' 'primes_python(1000)'
10 loops, best of 3: 23 msec per loop
python -m timeit -s 'from example_py_cy import primes_python_compiled' 'primes_python_compiled(1000)'
100 loops, best of 3: 11.9 msec per loop
python -m timeit -s 'from example import primes' 'primes(1000)'
1000 loops, best of 3: 1.65 msec per loop
						

The cythonize version of primes_python is 2 times faster than the Python one, without changing a single line of code. The Cython version is 13 times faster than the Python version! What could explain this?

Multiple things:

• In this program, very little computation happen at each line. So the overhead of the python interpreter is very important. It would be very different if you were to do a lot computation at each line. Using NumPy for example.
• Data locality. It’s likely that a lot more can fit in CPU cache when using C than when using Python. Because everything in python is an object, and every object is implemented as a dictionary, this is not very cache friendly.

Usually the speedups are between 2x to 1000x. It depends on how much you call the Python interpreter. As always, remember to profile before adding types everywhere. Adding types makes your code less readable, so use them with moderation.

Primes with C++ ¶

With Cython, it is also possible to take advantage of the C++ language, notably, part of the C++ standard library is directly importable from Cython code.

Let’s see what our primes.pyx becomes when using vector from the C++ standard library.

注意

Vector in C++ is a data structure which implements a list or stack based on a resizeable C array. It is similar to the Python array 类型在 array standard library module. There is a method reserve available which will avoid copies if you know in advance how many elements you are going to put in the vector. For more details see this page from cppreference .

# distutils: language=c++
from libcpp.vector cimport vector
def primes(unsigned int nb_primes):
    cdef int n, i
    cdef vector[int] p
    p.reserve(nb_primes)  # allocate memory for 'nb_primes' elements.
    n = 2
    while p.size() < nb_primes:  # size() for vectors is similar to len()
        for i in p:
            if n % i == 0:
                break
        else:
            p.push_back(n)  # push_back is similar to append()
        n += 1
    # Vectors are automatically converted to Python
    # lists when converted to Python objects.
    return p