# Cython¶

Cython can be viewed as an extension of Python where variables and functions are annotated with extra information, in particular types. The resulting Cython source code will be compiled into optimized C or C++ code, and thereby yielding substantial speed-up of slow Python code. In other words, Cython provides a way of writing Python with comparable performance to that of C/C++.

## Start Coding in Cython¶

Cython code must, unlike Python, be compiled. This happens in the following stages:

• The cython code in .pyx file will be translated to a C file.

• The C file will be compiled by a C compiler into a shared library, which will be directly loaded into Python.

In a Jupyter notebook, everything is a lot easier. One needs only to load the Cython extension (%load_ext Cython) at the beginning and put %%cython mark in front of cells of Cython code. Cells with Cython mark will be treated as a .pyx code and consequently, compiled into C.

For details, please see Building Cython Code.

### Pure python Mandelbrot set:¶

xmin = -1.5
ymin = -1.0
xmax = 0.5
ymax = 1.0
resolution = 300
xstep = (xmax - xmin) / resolution
ystep = (ymax - ymin) / resolution
xs = [(xmin + (xmax - xmin) * i / resolution) for i in range(resolution)]
ys = [(ymin + (ymax - ymin) * i / resolution) for i in range(resolution)]

def mandel(position, limit=50):
value = position
while abs(value) < 2:
limit -= 1
value = value ** 2 + position
if limit < 0:
return 0
return limit


### Compiled by Cython:¶

%load_ext Cython

%%cython

def mandel_cython(position, limit=50):
value = position
while abs(value) < 2:
limit -= 1
value = value ** 2 + position
if limit < 0:
return 0
return limit


Let’s verify the result

data_python = [[mandel(complex(x, y)) for x in xs] for y in ys]
data_cython = [[mandel_cython(complex(x, y)) for x in xs] for y in ys]

from matplotlib import pyplot as plt

%matplotlib inline
f, axarr = plt.subplots(1, 2)
axarr[0].imshow(data_python, interpolation="none", extent=[xmin, xmax, ymin, ymax])
axarr[0].set_title("Pure Python")
axarr[1].imshow(data_cython, interpolation="none", extent=[xmin, xmax, ymin, ymax])
axarr[1].set_title("Cython")

Text(0.5, 1.0, 'Cython')

%timeit [[mandel(complex(x,y)) for x in xs] for y in ys] # pure python
%timeit [[mandel_cython(complex(x,y)) for x in xs] for y in ys] # cython

665 ms ± 30.2 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

513 ms ± 5.77 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)


We have improved the performance of a factor of 1.5 by just using the Cython compiler, without changing the code!

### Cython with C Types¶

But we can do better by telling Cython what C data type we would use in the code. Note we’re not actually writing C, we’re writing Python with C types.

typed variable

%%cython
def var_typed_mandel_cython(position, limit=50):
cdef double complex value # typed variable
value = position
while abs(value) < 2:
limit -= 1
value = value**2 + position
if limit < 0:
return 0
return limit


typed function + typed variable

%%cython
cpdef call_typed_mandel_cython(double complex position, int limit=50): # typed function
cdef double complex value # typed variable
value = position
while abs(value)<2:
limit -= 1
value = value**2 + position
if limit < 0:
return 0
return limit


performance of one number:

# pure python
%timeit a = mandel(complex(0, 0))

14.7 µs ± 284 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)

# primitive cython
%timeit a = mandel_cython(complex(0, 0))

10.6 µs ± 263 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)

# cython with C type variable
%timeit a = var_typed_mandel_cython(complex(0, 0))

4.09 µs ± 121 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)

# cython with typed variable + function
%timeit a = call_typed_mandel_cython(complex(0, 0))

793 ns ± 11.2 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)


### Cython with numpy ndarray¶

You can use NumPy from Cython exactly the same as in regular Python, but by doing so you are losing potentially high speedups because Cython has support for fast access to NumPy arrays.

import numpy as np

ymatrix, xmatrix = np.mgrid[ymin:ymax:ystep, xmin:xmax:xstep]
values = xmatrix + 1j * ymatrix

%%cython
import numpy as np
cimport numpy as np

cpdef numpy_cython_1(np.ndarray[double complex, ndim=2] position, int limit=50):
cdef np.ndarray[long,ndim=2] diverged_at
cdef double complex value
cdef int xlim
cdef int ylim
cdef double complex pos
cdef int steps
cdef int x, y

xlim = position.shape[1]
ylim = position.shape[0]
diverged_at = np.zeros([ylim, xlim], dtype=int)
for x in xrange(xlim):
for y in xrange(ylim):
steps = limit
value = position[y,x]
pos = position[y,x]
while abs(value) < 2 and steps >= 0:
steps -= 1
value = value**2 + pos
diverged_at[y,x] = steps

return diverged_at


Note the double import of numpy: the standard numpy module and a Cython-enabled version of numpy that ensures fast indexing of and other operations on arrays. Both import statements are necessary in code that uses numpy arrays. The new thing in the code above is declaration of arrays by np.ndarray.

%timeit data_cy = [[mandel(complex(x,y)) for x in xs] for y in ys] # pure python

666 ms ± 13.1 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

%timeit data_cy = [[call_typed_mandel_cython(complex(x,y)) for x in xs] for y in ys] # typed cython

52.7 ms ± 337 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

%timeit numpy_cython_1(values) # ndarray

33.1 ms ± 868 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)


#### A trick of using np.vectorize¶

numpy_cython_2 = np.vectorize(call_typed_mandel_cython)

%timeit numpy_cython_2(values) #  vectorize

43.4 ms ± 269 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)


### Calling C functions from Cython¶

#### Example: compare sin() from Python and C library¶

%%cython
import math
cpdef py_sin():
cdef int x
cdef double y
for x in range(1e7):
y = math.sin(x)

%%cython
from libc.math cimport sin as csin # import from C library
cpdef c_sin():
cdef int x
cdef double y
for x in range(1e7):
y = csin(x)

%timeit [math.sin(i) for i in range(int(1e7))] # python

2.02 s ± 31.7 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

%timeit py_sin()                                # cython call python library

1.21 s ± 16.3 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

%timeit c_sin()                                 # cython call C library

5.73 ms ± 126 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)