Using static typing

Python is both a strongly typed and a dynamically typed language.

Strong typing means that variables do have a type and that the type matters when performing operations on a variable. Dynamic typing means that the type of the variable is determined only during runtime.

Due to strong typing, types need to be compatible with respect to the operand when performing operations. For example Python allows one to add an integer and a floating point number, but adding an integer to a string produces error.

Due to dynamic typing, in Python the same variable can have a different type at different times during the execution. Dynamic typing allows for flexibility in programming, but with a price in performance.

Everything is an object

One of the key features of Python is that everything is an object, and the type is just one attribute of an object. As an illustration, we can assign a single integer to a variable, and use the Python built-in function dir for
finding out the attributes of the object. If you execute the following two
lines in an interactive interpreter, it should become clear that a Python
integer is much more complex than just a number. Please feel free to
experiment also with other types!

n = 5
dir(n)

The fact that everything is an object means that there is a lot of “unboxing”
and “boxing” involved when Python performs operations with variables. For
example, when just adding two integers

a = 7
b = 6
c = a + b

there are several steps Python needs to do:

1. Check the types of both operands
2. Check whether they both support the + operation
3. Extract the function that performs the + operation (due to operator
   overloading objects can have a custom definition for addition)
4. Extract the actual values of the objects
5. Perform the + operation
6. Construct a new integer object for the result

Due to the fact that Python is dynamically typed, the interpreter cannot know
beforehand what type of objects one is dealing with, and everytime two
variables are added one needs to perform all the above steps.

Adding static type information

What if one knows that e.g. in a certain function the variables have always
the same type? That’s where Cython steps in: Cython allows one to add static
typing information so that boxing and unboxing are not needed, and one can
operate directly with the actual values.

When Cythonizing a Python code, static type information can be added either:

• In function signatures by prefixing the formal arguments by their type
• By declaring variables with the cdef Cython keyword, followed by the
  the type

For example, a simple Python function adding two objects could be Cythonized
as follows:

def add (int x, int y):
 cdef int result
 result = x + y
 return result

The function works now only with integers but with less boxing/unboxing
overheads.

The types provided in Cython code are C types, and the variables with type
information are pure C variables and not Python objects. When calling a
Cythonized function from Python, there is an automatic conversion from the
Python object of actual arguments to the C value of formal argument, and when
returning a C variable it is converted to corresponding Python object.
Automatic conversions are carried out also in most cases within the Cython
code where both Python objects and C variables are involved.

The table below lists the most common C types and their corresponding Python
types. More information can be found in the
Cython documentation.

Static typing in Mandelbrot kernel

In week 1 we did a performance analysis of Mandelbrot fractal in Step 1.11. The analysis revealed
that the kernel function in module mandelbrot.py was the most time critical one. Thus, let’s make mandelbrot.py into Cython module mandelbrot.pyx and introducing static typing to the
function kernel.

Pure Python version was:

def kernel(zr, zi, cr, ci, lim, cutoff):
 ''' Computes the number of iterations `n` such that
 |z_n| > `lim`, where `z_n = z_{n-1}**2 + c`.
 '''
 count = 0
 while ((zr*zr + zi*zi) < (lim*lim)) and count < cutoff:
 zr, zi = zr * zr - zi * zi + cr, 2 * zr * zi + ci
 count += 1
 return count

We can add type information both to the function signature and to the function
body:

def kernel(double zr, double zi, double cr, double ci, double lim, int cutoff):
 ''' Computes the number of iterations `n` such that
 |z_n| > `lim`, where `z_n = z_{n-1}**2 + c`.
 '''
 cdef int count = 0
 while ((zr*zr + zi*zi) < (lim*lim)) and count < cutoff:
 zr, zi = zr * zr - zi * zi + cr, 2 * zr * zi + ci
 count += 1
 return count

When comparing the performance of pure Python and Cythonized versions, we obtain the following results:

• Pure Python: 0.57 s
• Static type declarations in the kernel: 14 ms

Thus, we obtained a speed up of ~40 !