rewrote the initial tutorial on calling into C libraries

src/tutorial/external.rst

+Calling C functions
+====================
+
+This tutorial describes shortly what you need to know in order to call
+C library functions from Cython code.  For a longer and more
+comprehensive tutorial about using external C libraries, wrapping them
+and handling errors, see :doc:`clibraries`.
+
+For simplicity, let's start with a function from the standard C
+library.  This does not add any dependencies to your code, and it has
+the additional advantage that Cython already defines many such
+functions for you. So you can just cimport and use them.
+
+For example, let's say you need a low-level way to parse a number from
+a ``char*`` value.  You could use the ``atoi()`` function, as defined
+by the ``stdlib.h`` header file.  This can be done as follows::
+
+  from libc.stdlib cimport atoi
+
+  cdef parse_charptr_to_py_int(char* s):
+      assert s is not NULL, "byte string value is NULL"
+      return atoi(s)   # note: atoi() has no error detection!
+
+You can find a complete list of these standard cimport files in
+Cython's source package ``Cython/Includes/``.  It also has a complete
+set of declarations for CPython's C-API.  For example, to test at C
+compilation time which CPython version your code is being compiled
+with, you can do this::
+
+  from cpython.version cimport PY_VERSION_HEX
+
+  print PY_VERSION_HEX >= 0x030200F0 # Python version >= 3.2 final
+
+Cython also provides declarations for the C math library::
+
+  from libc.math cimport sin
+
+  cdef double f(double x):
+      return sin(x*x)
+
+However, this is a library that is not linked by default on Unix-like
+systems, such as Linux or MacOS-X. In addition to cimporting the
+declarations, you must configure your build system to link against the
+shared library ``m``.  For distutils, it is enough to add it to the
+``libraries`` parameter of the ``Extension()`` setup::
+
+  from distutils.core import setup
+  from distutils.extension import Extension
+  from Cython.Distutils import build_ext
+
+  ext_modules=[ 
+      Extension("demo",
+                ["demo.pyx"], 
+                libraries=["m"]) # Unix-like specific
+  ]
+
+  setup(
+    name = "Demos",
+    cmdclass = {"build_ext": build_ext},
+    ext_modules = ext_modules
+  )
+
+If you want to access C code for which Cython does not provide a ready
+to use declaration, you must declare them yourself.  For example, the
+above ``sin()`` function is defined as follows::
+
+  cdef extern from "math.h":
+      double sin(double)
+
+This instructs Cython to generate code that imports the ``math.h``
+header file and declares the ``sin()`` function in a way that makes it
+available to Cython code.  The C compiler will see the original
+declaration in ``math.h`` at compile time, but Cython does not parse
+"math.h" and requires a separate definition.
+
+Just like the ``sin()`` function from the math library, it is possible
+to declare and call into any C library as long as the module that
+Cython generates is properly linked against the shared or static
+library.

src/tutorial/index.rst

@@ -4,6 +4,7 @@ Tutorials
 .. toctree::
    :maxdepth: 2
 
+   external
    clibraries
    cdef_classes
    pxd_files