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+## Cython
+
+<br>
+
+### tl; dr
+
+<br>
+
+* **[cython](https://cython.org/)** is an **optimising static compiler** for both Python and the extended cython programming language, making writing C extensions for Python easier.
+* it turns readable Python code into plain C performance by adding static type declarations in Python syntax.
+* cython source file names consist of the name of the module followed by a `.pyx` extension.
+* the setuptools extension provided with cython allows you to pass `.pyx` files directly to the `Extension` constructor in the setup file.
+* to compile the extension for use in the current directory, you can use `python setup.py build_ext --inplace`
+
+<br>
+
+----
+
+### cythonize example
+
+<br>
+
+* for typing variables, consider the following snippet in python:
+
+<br>
+
+```python
+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
+```
+
+* compiling this in cython already gives a ~35% speedup, but adding static types can make it up to 4x faster.
+* to accomplish this, you can add type declarations, for example:
+
+```python
+def f(x: cython.double):
+    return x ** 2 - x
+
+def integrate_f(a: cython.double, b: cython.double, N: cython.int):
+
+    i: cython.int
+    s: cython.double
+    dx: cython.double
+    s = 0
+    dx = (b - a) / N
+    for i in range(N):
+        s += f(a + i * dx)
+
+    return s * dx
+```
+
+* this is converted to cython as pure C-style code:
+
+```python
+def f(double x):
+    return x ** 2 - x
+
+def integrate_f(double a, double b, int N):
+
+    cdef int i
+    cdef double s
+    cdef double dx
+    s = 0
+    dx = (b - a) / N
+    for i in range(N):
+        s += f(a + i * dx)
+
+    return s * dx
+```
+
+* since python functions can be expensive, the cython specific `cdef` statement, as well as `@cfunc` decorator can be used:
+
+```python
+cdef double f(double x) except? -2:
+    return x ** 2 -x
+```
+
+<br>
+