Coding in Cython

This chapter discusses Cython, which is a compiled language based on Python. The major advantage it has over Python is that code can be much faster (sometimes orders of magnitude) and can directly call C and C++ code. As Cython is essentially a superset of the Python language, one often doesn’t make a distinction between Cython and Python code in Sage (e.g. one talks of the “Sage Python Library” and “Python Coding Conventions”).

Python is an interpreted language and has no declared data types for variables. These features make it easy to write and debug, but Python code can sometimes be slow. Cython code can look a lot like Python, but it gets translated into C code (often very efficient C code) and then compiled. Thus it offers a language which is familiar to Python developers, but with the potential for much greater speed. Cython also allows Sage developers to interface with C and C++ much easier than using the Python C API directly.

Cython is a compiled version of Python. It was originally based on Pyrex but has changed based on what Sage’s developers needed; Cython has been developed in concert with Sage. However, it is an independent project now, which is used beyond the scope of Sage. As such, it is a young, but developing language, with young, but developing documentation. See its web page,, for the most up-to-date information or check out the Language Basics to get started immediately.

Writing Cython Code in Sage

There are several ways to create and build Cython code in Sage.

  1. In the Sage Notebook, begin any cell with %cython. When you evaluate that cell,

    1. It is saved to a file.

    2. Cython is run on it with all the standard Sage libraries automatically linked if necessary.

    3. The resulting shared library file (.so / .dll / .dylib) is then loaded into your running instance of Sage.

    4. The functionality defined in that cell is now available for you to use in the notebook. Also, the output cell has a link to the C program that was compiled to create the .so file.

    5. A cpdef or def function, say testfunction, defined in a %cython cell in a worksheet can be imported and made available in a different %cython cell within the same worksheet by importing it as shown below:

      from __main__ import testfunction
  2. Create an .spyx file and attach or load it from the command line. This is similar to creating a %cython cell in the notebook but works completely from the command line (and not from the notebook).

  3. Create a .pyx file and add it to the Sage library.

    1. First, add a listing for the Cython extension to the variable ext_modules in the file SAGE_ROOT/src/ See the distutils.extension.Extension class for more information on creating a new Cython extension.
    2. Run sage -b to rebuild Sage.

    For example, in order to compile SAGE_ROOT/src/sage/graphs/chrompoly.pyx, we see the following lines in

              sources = ['sage/graphs/chrompoly.pyx'],
              libraries = ['gmp']),

Special Pragmas

If Cython code is either attached or loaded as a .spyx file or loaded from the notebook as a %cython block, the following pragmas are available:

  • clang — may be either c or c++ indicating whether a C or C++ compiler should be used.
  • clib — additional libraries to be linked in, the space separated list is split and passed to distutils.
  • cinclude — additional directories to search for header files. The space separated list is split and passed to distutils.
  • cfile – additional C or C++ files to be compiled
  • cargs – additional parameters passed to the compiler

For example:

#clang C++
#clib givaro
#cinclude /usr/local/include/
#cargs -ggdb
#cfile foo.c

Attaching or Loading .spyx Files

The easiest way to try out Cython without having to learn anything about distutils, etc., is to create a file with the extension spyx, which stands for “Sage Pyrex”:

  1. Create a file power2.spyx.

  2. Put the following in it:

    def is2pow(n):
        while n != 0 and n%2 == 0:
            n = n >> 1
        return n == 1
  3. Start the Sage command line interpreter and load the spyx file (this will fail if you do not have a C compiler installed).

    sage: load("power2.spyx")
    Compiling power2.spyx...
    sage: is2pow(12)

Note that you can change power2.spyx, then load it again and it will be recompiled on the fly. You can also attach power2.spyx so it is reloaded whenever you make changes:

sage: attach("power2.spyx")

Cython is used for its speed. Here is a timed test on a 2.6 GHz Opteron:

sage: %time [n for n in range(10^5) if is2pow(n)]
[1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536]
CPU times: user 0.60 s, sys: 0.00 s, total: 0.60 s
Wall time: 0.60 s

Now, the code in the file power2.spyx is valid Python, and if we copy this to a file and load that, we get the following:

sage: load("")
sage: %time [n for n in range(10^5) if is2pow(n)]
[1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536]
CPU times: user 1.01 s, sys: 0.04 s, total: 1.05 s
Wall time: 1.05 s

By the way, we could gain even a little more speed with the Cython version with a type declaration, by changing def is2pow(n): to def is2pow(unsigned int n):.

Interrupt and Signal Handling

When writing Cython code for Sage, special care must be taken to ensure that the code can be interrupted with CTRL-C.

Sage uses the cysignals package for this, see the cysignals documentation for more information.

Unpickling Cython Code

Pickling for Python classes and extension classes, such as Cython, is different. This is discussed in the Python pickling documentation. For the unpickling of extension classes you need to write a __reduce__() method which typically returns a tuple (f, args, ...) such that f(*args) returns (a copy of) the original object. As an example, the following code snippet is the __reduce__() method from sage.rings.integer.Integer:

def __reduce__(self):
    This is used when pickling integers.


        sage: n = 5
        sage: t = n.__reduce__(); t
        (<built-in function make_integer>, ('5',))
        sage: t[0](*t[1])
        sage: loads(dumps(n)) == n
    # This single line below took me HOURS to figure out.
    # It is the *trick* needed to pickle Cython extension types.
    # The trick is that you must put a pure Python function
    # as the first argument, and that function must return
    # the result of unpickling with the argument in the second
    # tuple as input. All kinds of problems happen
    # if we don't do this.
    return sage.rings.integer.make_integer, (self.str(32),)