Docs: Migrate profiling tutorial to pure Python (GH-4311)

docs/examples/tutorial/profiling_tutorial/calc_pi.py

-# calc_pi.py
-
 def recip_square(i):
     return 1. / i ** 2
 

docs/examples/tutorial/profiling_tutorial/calc_pi_2.py

+# cython: profile=True
+import cython
+
+def recip_square(i: cython.longlong):
+    return 1. / i ** 2
+
+def approx_pi(n: cython.int = 10000000):
+    val: cython.double = 0.
+    k: cython.int
+    for k in range(1, n + 1):
+        val += recip_square(k)
+    return (6 * val) ** .5

docs/examples/tutorial/profiling_tutorial/calc_pi_2.pyx

 # cython: profile=True
 
-# calc_pi.pyx
-
 def recip_square(int i):
     return 1. / i ** 2
 

docs/examples/tutorial/profiling_tutorial/calc_pi_3.py

+# cython: profile=True
+import cython
+
+@cython.cfunc
+@cython.inline
+@cython.exceptval(-1.0)
+def recip_square(i: cython.longlong) -> cython.double:
+    return 1. / (i * i)
+
+def approx_pi(n: cython.int = 10000000):
+    val: cython.double = 0.
+    k: cython.int
+    for k in range(1, n + 1):
+        val += recip_square(k)
+    return (6 * val) ** .5

docs/examples/tutorial/profiling_tutorial/calc_pi_3.pyx

 # cython: profile=True
 
-# calc_pi.pyx
 
-cdef inline double recip_square(int i) except -1.0:
+
+
+cdef inline double recip_square(long long i) except -1.0:
     return 1. / (i * i)
 
 def approx_pi(int n=10000000):

docs/examples/tutorial/profiling_tutorial/calc_pi_4.py

+# cython: profile=True
+
+import cython
+
+@cython.profile(False)
+@cython.cfunc
+@cython.inline
+@cython.exceptval(-1.0)
+def recip_square(i: cython.longlong) -> float:
+    return 1. / (i * i)
+
+def approx_pi(n: cython.int = 10000000):
+    val: cython.double = 0.
+    k: cython.int
+    for k in range(1, n + 1):
+        val += recip_square(k)
+    return (6 * val) ** .5

docs/examples/tutorial/profiling_tutorial/calc_pi_4.pyx

 # cython: profile=True
 
-# calc_pi.pyx
-
 cimport cython
 
+
+
+
 @cython.profile(False)
-cdef inline double recip_square(int i) except -1.0:
+cdef inline double recip_square(long long i) except -1.0:
     return 1. / (i * i)
 
 def approx_pi(int n=10000000):

docs/examples/tutorial/profiling_tutorial/often_called.py

+import cython
+
+@cython.profile(False)
+def my_often_called_function():
+    pass

docs/examples/tutorial/profiling_tutorial/profile.py

-# profile.py
-
 import pstats, cProfile
 
 import calc_pi

docs/examples/tutorial/profiling_tutorial/profile_2.py

-# profile.py
-
 import pstats, cProfile
 
 import pyximport