Cython¶

Christian Elsasser (che@physik.uzh.ch)

The content of this lecture might be distributed under CC by-sa.

An introductionnary example - Fibonacci numbers¶

Pure Python¶

In [1]:
def fib0(n):
    a,b=1,1
    for i in range(n):
        a,b=a+b,a
    return a
In [2]:
fib0(5)
Out[2]:
13
In [3]:
fib0(6)
Out[3]:
21
In [4]:
%timeit fib0(10000)

1.8 ms ± 47.6 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)

Cython: Compile unmodified¶

In [5]:
import cython
In [6]:
%load_ext Cython
In [7]:
%%cython
def helloWorld():
    print("Hello, World!")
In [8]:
helloWorld
Out[8]:
<cyfunction helloWorld at 0x10d3b9f00>
In [9]:
helloWorld()

Hello, World!
In [10]:
%%cython
def fib1(n):
    a,b=1,1
    for i in range(n):
        a,b=a+b,a
    return a
In [11]:
fib1
Out[11]:
<cyfunction fib1 at 0x10c493ac0>
In [12]:
fib0
Out[12]:
<function __main__.fib0(n)>
In [13]:
fib1(5)
Out[13]:
13
In [14]:
%timeit fib1(10000)

1.72 ms ± 20.8 μs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)

Cython: Declaring Types¶

In [15]:
%%cython
def fib2(int n):
    cdef int a,b,i
    a,b=1,1
    for i in range(n):
        a,b=a+b,a
    return a
In [16]:
fib2(5)
Out[16]:
13
In [17]:
fib0("a")

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In[17], line 1
----> 1 fib0("a")

Cell In[1], line 3, in fib0(n)
      1 def fib0(n):
      2     a,b=1,1
----> 3     for i in range(n):
      4         a,b=a+b,a
      5     return a

TypeError: 'str' object cannot be interpreted as an integer
In [ ]:
In [18]:
fib2("a")

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In[18], line 1
----> 1 fib2("a")

File _cython_magic_96d7e16e39d458e7c4870bb106554519402e4a817f2d9742cf8f56c93bddd81d.pyx:1, in _cython_magic_96d7e16e39d458e7c4870bb106554519402e4a817f2d9742cf8f56c93bddd81d.fib2()

TypeError: an integer is required
In [19]:
%timeit fib2(10000)

2.43 μs ± 96.5 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)

Impressive, but¶

In [20]:
print("python result: ", fib0(500))
print("cython result: ", fib2(500))

python result:  365014740723634211012237077906479355996081581501455497852747829366800199361550174096573645929019489792751
cython result:  -1583205649
In [21]:
print("python result: ", fib0(40))
print("cython result: ", fib2(40))

python result:  267914296
cython result:  267914296
In [22]:
%timeit fib0(40)
%timeit fib2(40)

1.11 μs ± 12.2 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)
43.1 ns ± 0.499 ns per loop (mean ± std. dev. of 7 runs, 10,000,000 loops each)

Use better data types¶

In [23]:
%%cython
def fib3(int n):
    cdef long a,b
    cdef int i
    a,b=1,1
    for i in range(n):
        a,b=a+b,a
    return a
In [24]:
print("python result:     ", fib0(50))
print("cython int result: ", fib2(50))
print("cython long result:", fib3(50))

python result:      32951280099
cython int result:  -1408458269
cython long result: 32951280099
In [25]:
%timeit fib3(40)

42.1 ns ± 0.338 ns per loop (mean ± std. dev. of 7 runs, 10,000,000 loops each)

Conclusion: The speedup is real, but we pay with new potential errors.

Second Example - Numerical integration¶

start with declaring types¶

In [27]:
%%cython -a

from math import sin,exp

def f0(double x):
    return sin(x)*exp(-x)

def integrate0(double a,double b,int N):
    cdef double dx,x,s
    cdef int _
    dx = (b-a)/N
    x = a+dx/2
    s = 0.0
    for _ in range(N):
        s+=f0(x)
        x += dx
    return s*dx
Out[27]:

Generated by Cython 3.1.2

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 [28]:
from math import pi
In [29]:
integrate0(0.0,pi,1_000_000)
Out[29]:
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In [30]:
%timeit integrate0(0.0,pi,1_000_000)

150 ms ± 1.1 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)

turn f into a c-function¶

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%%cython -a

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Out[31]:

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In [32]:
%timeit integrate1(0.0,pi,1_000_000)

103 ms ± 453 μs per loop (mean ± std. dev. of 7 runs, 10 loops each)

f is now not visible in Python anymore

In [33]:
f1(5)

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[33], line 1
----> 1 f1(5)

NameError: name 'f1' is not defined

use cpdef to keep f in Python

use math functions from c¶

In [34]:
%%cython -a

from libc.math cimport sin,exp

cpdef double f2(double x):
    return sin(x)*exp(-x)

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    cdef int i
    dx = (b-a)/N
    s = 0.0
    for i in range(N):
        s+=f2(a+(i+0.5)*dx)
    return s*dx
Out[34]:

Generated by Cython 3.1.2

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In [35]:
%timeit integrate2(0.0,pi,1_000_000)

11.8 ms ± 87.6 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)

Line 10 is yellow, due to checking for ZeroDivisionError. We can deactivate this with

import cython

@cython.cdivision(True)
def integrate(...

But:

  • we would again open another door for errors
  • this line is only executed once
In [36]:
%%cython -a

from libc.math cimport sin,exp
import cython

cpdef double f3(double x):
    return sin(x)*exp(-x)

@cython.cdivision(True)
def integrate3(double a,double b,int N):
    cdef double dx,s
    cdef int i
    dx = (b-a)/N
    s = 0.0
    for i in range(N):
        s+=f3(a+(i+0.5)*dx)
    return s*dx
Out[36]:

Generated by Cython 3.1.2

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  }

+16:     return s*dx
  __Pyx_XDECREF(__pyx_r);
  __pyx_t_5 = PyFloat_FromDouble((__pyx_v_s * __pyx_v_dx)); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 16, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __pyx_r = __pyx_t_5;
  __pyx_t_5 = 0;
  goto __pyx_L0;
In [37]:
%timeit integrate3(0.0,pi,1_000_000)

11.5 ms ± 118 μs per loop (mean ± std. dev. of 7 runs, 100 loops each)

Was it worth it?¶

In [38]:
import numpy as np

def f4(x):
    return np.sin(x)*np.exp(-x)

def integrate4(a,b,N):
    dx = (b-a)/N
    x = (np.arange(N)+0.5)*dx+a
    return np.sum(f4(x))*dx
In [39]:
%timeit integrate4(0.0,pi,1_000_000)

21.5 ms ± 1.2 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)

C function wrapping¶

In [40]:
# %load fastinvsqrt/c_func.c
#include <stdio.h>

double fast_inv_sqrt( double number )
  {
      double y = number;
      double x2 = y * 0.5;
      long long i = *(long long*) &y;
      // The magic number is for doubles is from https://cs.uwaterloo.ca/~m32rober/rsqrt.pdf
      i = 0x5fe6eb50c7b537a9 - (i >> 1);
      y = *(double *) &i;
      y = y * (1.5 - (x2 * y * y));   // 1st iteration
      //      y  = y * ( 1.5 - ( x2 * y * y ) );   // 2nd iteration, this can be removed
      return y;
  }
In [41]:
%%cython -I.
# -I followed by include directory i.e. root directory where the files specified 
cdef extern from "fastinvsqrt/c_func.c":
    double fast_inv_sqrt(double number)

def py_fis(number:double) -> double:
    """Function to calculate 1/x**0.5 and hence helpful for normalising vectors
    
    Parameters
    ----------
    number : double
        
    Returns
    -------
    double :
        Inverse of the square root
    """
    return fast_inv_sqrt(number)

def norm_vector(values:list) -> list:
    """Calculates the normalised vector with length 1
    
    Parameters
    ----------
    values : list
        Components of the vector
    
    Returns
    -------
    list :
        Components of the normalised vector
    """
    length_squared = sum([x**2 for x in values])
    return [x*fast_inv_sqrt(length_squared) for x in values]
In [42]:
py_fis(100)
Out[42]:
0.09984476108311886
In [43]:
norm_vector([1,2,2])
Out[43]:
[0.3329527851243409, 0.6659055702486818, 0.6659055702486818]

Appendix¶

Cython and STL containers¶

In [ ]:
%%cython -+
#distutils: language = c++
from libcpp.vector cimport vector
def manipulateVector(vector[double] v):
    v.push_back(42.0) # Equivalent to append for list in python
    return v
In [ ]:
manipulateVector([1,2,3,4])

Cython and exceptions¶

In [ ]:
%%cython
cpdef int raiseError():
    raise RuntimeError("A problem!")
    return 1
In [ ]:
raiseError()
print("Still going strong!")
In [ ]:
%%cython
cpdef int raiseErrorBetter() except *:
    raise RuntimeError("A problem!")
    return 1
In [ ]:
raiseErrorBetter()
print("Still going strong!")
In [ ]:
try:
    raiseErrorBetter()
except RuntimeError:
    print("Error caught")
In [ ]:
%%cython
cpdef int raiseException(int n) except -1:
    # Assuming C function returning an integer; if -1 --> Error appeared
    return n
In [ ]:
raiseException(1)
In [ ]:
raiseException(-1)

Back to integration - Cython and Classes¶

In [ ]:
%%cython

from libc.math cimport sin,exp

cdef class Integrand(object):
    cpdef double evaluate(self,double x):
        raise NotImplementedError()
        
cdef class SinExpFunction(Integrand):
    cpdef double evaluate(self,double x):
        return sin(x)*exp(-x)
    
def integrate(Integrand f, double a, double b, int N):
    cdef int i
    cdef double dx,s
    dx = (b-a)/N
    s = 0.0
    for i in range(N):
        s += f.evaluate(a+(i+0.5)*dx)
    return s*dx
In [ ]:
f = SinExpFunction()
In [ ]:
import math
In [ ]:
%timeit integrate(f,0,math.pi,1000000)
In [ ]:
class Poly(Integrand):
    def evaluate(self,x):
        return 3*x-x**3
In [ ]:
g = Poly()
integrate(g,0,math.pi,10000)
In [ ]:
%timeit integrate(g,0,math.pi,1000000)