Typing Variables

Consider the following pure Python code:

def f(x):
    return x**2-x

def integrate_f(a, b, N):
    s = 0
    dx = (b-a)/N
    for i in range(N):
        s += f(a+i*dx)
    return s * dx

Simply compiling this in Cython merely gives a 35% speedup. This is better than nothing, but adding some static types can make a much larger difference.

With additional type declarations, this might look like:

def f(double x):
    return x**2-x

def integrate_f(double a, double b, int N):
    cdef int i
    cdef double s, dx
    s = 0
    dx = (b-a)/N
    for i in range(N):
        s += f(a+i*dx)
    return s * dx

Since the iterator variable i is typed with C semantics, the for-loop will be compiled to pure C code. Typing a, s and dx is important as they are involved in arithmetic withing the for-loop; typing b and N makes less of a difference, but in this case it is not much extra work to be consistent and type the entire function.

This results in a 4 times speedup over the pure Python version.

Typing Functions

Python function calls can be expensive – in Cython doubly so because one might need to convert to and from Python objects to do the call. In our example above, the argument is assumed to be a C double both inside f() and in the call to it, yet a Python float object must be constructed around the argument in order to pass it.

Therefore Cython provides a syntax for declaring a C-style function, the cdef keyword:

cdef double f(double x) except? -2:
    return x**2-x

Some form of except-modifier should usually be added, otherwise Cython will not be able to propagate exceptions raised in the function (or a function it calls). The except? -2 means that an error will be checked for if -2 is returned (though the ? indicates that -2 may also be used as a valid return value). Alternatively, the slower except * is always safe. An except clause can be left out if the function returns a Python object or if it is guaranteed that an exception will not be raised within the function call.

A side-effect of cdef is that the function is no longer available from Python-space, as Python wouldn’t know how to call it. It is also no longer possible to change ``f` at runtime.

Using the cpdef keyword instead of cdef, a Python wrapper is also created, so that the function is available both from Cython (fast, passing typed values directly) and from Python (wrapping values in Python objects). In fact, cpdef does not just provide a Python wrapper, it also installs logic to allow the method to be overridden by python methods, even when called from within cython. This does add a tiny overhead compared to cdef methods.

Speedup: 150 times over pure Python.

Determining where to add types

Because static typing is often the key to large speed gains, beginners often have a tendency to type everything in sight. This cuts down on both readability and flexibility, and can even slow things down (e.g. by adding unnecessary type checks, conversions, or slow buffer unpacking). On the other hand, it is easy to kill performance by forgetting to type a critical loop variable. Two essential tools to help with this task are profiling and annotation. Profiling should be the first step of any optimization effort, and can tell you where you are spending your time. Cython’s annotation can then tell you why your code is taking time.

Using the -a switch to the cython command line program (or following a link from the Sage notebook) results in an HTML report of Cython code interleaved with the generated C code. Lines are colored according to the level of “typedness” – white lines translates to pure C without any Python API calls. This report is invaluable when optimizing a function for speed.