diff --git a/multiplication/python/karatsuba.py b/multiplication/python/karatsuba.py
index 00dd49a2..e117db47 100644
--- a/multiplication/python/karatsuba.py
+++ b/multiplication/python/karatsuba.py
@@ -1,4 +1,18 @@
+"""
+https://en.wikipedia.org/wiki/Karatsuba_algorithm
+"""
+
+
 def equalize_strings(x, y):
+  """
+  >>> def eq_str(x, y):
+  ...   max_len = max(len(x), len(y))
+  ...   return x.zfill(max_len), y.zfill(max_len), max_len
+  >>>
+  >>> all(equalize_strings(x, y) == eq_str(x, y) for x, y
+  ...   in (('x' * i, 'y' * (i // 2)) for i in range(10)))
+  True
+  """
   n = len(x)
   m = len(y)
   zeros = abs(n - m) * '0'
@@ -8,7 +22,13 @@ def equalize_strings(x, y):
     x = zeros + x
   return x, y, len(x)
 
-def sum(x, y):
+
+def add(x, y):
+  """
+  >>> all(add(str(x), str(y)) == str(x + y) for x, y
+  ...   in ((0, 0), (0, 1), (1, 0), (1, 1234567890), (543210, 9876543)))
+  True
+  """
   x, y, size = equalize_strings(x, y)
   carry = 0
   result = ''
@@ -25,7 +45,13 @@ def sum(x, y):
     result = '1' + result
   return result
 
-def subtract(x, y):
+
+def absolute_difference(x, y):
+  """
+  >>> all(absolute_difference(str(x), str(y)) == str(abs(x - y)) for x, y
+  ...   in ((0, 0), (0, 1), (1, 0), (1, 1234567890), (543210, 9876543)))
+  True
+  """
   x, y, size = equalize_strings(x, y)
   carry = 0
   result = ""
@@ -50,7 +76,13 @@ def subtract(x, y):
     result = str(dgt3) + result
   return result
 
+
 def kmul(x ,y):
+  """
+  >>> all(kmul(str(x), str(y)) == str(x * y) for x, y
+  ...   in ((0, 0), (0, 1), (1, 0), (1, 1234567890), (543210, 9876543)))
+  True
+  """
   x, y, size = equalize_strings(x, y)
   if size == 1:
     return str(int(x) * int(y))
@@ -61,15 +93,17 @@ def kmul(x ,y):
   d = y[mid:]
   ac = kmul(a, c)
   bd = kmul(b, d)
-  ab_cd = kmul(sum(a, b), sum(c, d))
-  ad_bc = subtract(ab_cd, sum(ac, bd))
+  ab_cd = kmul(add(a, b), add(c, d))
+  ad_bc = absolute_difference(ab_cd, add(ac, bd))
   zeros = "0" * (size - mid)
 
-  result = sum(ac + 2 * zeros, ad_bc + zeros)
-  result = sum(result, bd)
+  result = add(ac + 2 * zeros, ad_bc + zeros)
+  result = add(result, bd)
   result = result.lstrip('0')
   return result
 
-x = "134231412"
-y = "141324"
-print(kmul(x, y))
+
+if __name__ == "__main__":
+  x = "134231412"
+  y = "141324"
+  print(kmul(x, y))