There is a lot happening in this recipe, so let's start by explaining the overall process. Cython takes code that is written in an extension of the Python language and compiles it into C code, which is then used to produce a C extension library that can be imported into a Python session. In fact, you can even use Cython to compile ordinary Python code directly to an extension, although the results are not as good as when using the modified language. The first few steps in this recipe define the new version of the Python code in the modified language (saved as a .pyx file), which includes type information in addition to the regular Python code. In order to build the C extension using Cython, we need to define a setup file, and then we create a file that we run to produce the results.
The final compiled version of the Cython code runs considerably faster than its Python equivalent. The Cython compiled Python code (hybrid, as we called it in this recipe...