diff --git a/cython_test.pyx b/cython_test.pyx
new file mode 100644
index 0000000..b924c83
--- /dev/null
+++ b/cython_test.pyx
@@ -0,0 +1,16 @@
+def say_hello_to(name):
+  print("Hello %s!" % name)
+
+from math import sin
+
+def f(double x):
+    return sin(x**2)
+
+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
diff --git a/cython_test_test.py b/cython_test_test.py
new file mode 100644
index 0000000..672c3a3
--- /dev/null
+++ b/cython_test_test.py
@@ -0,0 +1,45 @@
+from __future__ import division, print_function
+from math import sin
+from random import uniform, randint
+from timeit import timeit
+
+import pyximport
+pyximport.install()
+
+import cython_test
+
+
+# as defined in cython_test.pyx, but in pure python:
+def f(x):
+    return sin(x**2)
+
+
+# as defined in cython_test.pyx, but in pure python:
+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
+
+if __name__ == "__main__":
+    cython_test.say_hello_to("schweini")
+
+    assert(cython_test.f(0.5) == f(0.5))
+    assert(cython_test.f(1.7) == f(1.7))
+
+    for i in range(10):
+        a = uniform(-3.14, 3.14)
+        b = uniform(-3.14, 3.14)
+        N = randint(10, 1000)
+        assert(integrate_f(a, b, N)
+               == cython_test.integrate_f(a, b, N))
+
+    print("Python:",
+          timeit('integrate_f(0.0, 0.25, 1000)',
+                 'from cython_test_test import integrate_f',
+                 number=10000))
+    print("Cython:",
+          timeit('cython_test.integrate_f(0.0, 0.25, 1000)',
+                 'import pyximport; pyximport.install(); import cython_test',
+                 number=10000))