Fixed basejoin. There were two main problems:

- basejoin('some/url', '#name') would strip the last component of
  some/url and resturn some/#name.
- basejoin('file.html', 'relative/path') would return something like
  file:/relative/path, making a relative path into an absolute one.
These bugs are fixed by some drastic changes.  No scheme is added when
none is present (i.e. it works as replacement for posix.joinpath).
If a scheme is present in the second argument, it is returned
unprocessed.  No hostname are added in this case.  If no scheme is
present, the scheme of the first argument, if present, is used.
The algorithm is commented profusely.
Also fixed a typo in a comment.

Lib/urllib.py

@@ -482,25 +482,49 @@ class addinfo(addbase):
 
 def basejoin(base, url):
 	type, path = splittype(url)
+	if type:
+		# if url is complete (i.e., it contains a type), return it
+		return url
 	host, path = splithost(path)
-	if type and host: return url
-	basetype, basepath = splittype(base)
-	basehost, basepath = splithost(basepath)
-	basepath, basetag = splittag(basepath)
-	basepath, basequery = splitquery(basepath)
-	if not type: type = basetype or 'file'
+	type, basepath = splittype(base) # inherit type from base
+	if host:
+		# if url contains host, just inherit type
+		if type: return type + '://' + host + path
+		else:
+			# no type inherited, so url must have started with //
+			# just return it
+			return url
+	host, basepath = splithost(basepath) # inherit host
+	basepath, basetag = splittag(basepath) # remove extraneuous cruft
+	basepath, basequery = splitquery(basepath) # idem
 	if path[:1] != '/':
-		i = string.rfind(basepath, '/')
-		if i < 0: basepath = '/'
-		else: basepath = basepath[:i+1]
+		# non-absolute path name
+		if path[:1] in ('#', '?'):
+			# path is just a tag or query, attach to basepath
+			i = len(basepath)
+		else:
+			# else replace last component
+			i = string.rfind(basepath, '/')
+		if i < 0:
+			# basepath not absolute
+			if host:
+				# host present, make absolute
+				basepath = '/'
+			else:
+				# else keep non-absolute
+				basepath = ''
+		else:
+			# remove last file component
+			basepath = basepath[:i+1]
 		path = basepath + path
-	if not host: host = basehost
-	if host: return type + '://' + host + path
-	else: return type + ':' + path
+	if type and host: return type + '://' + host + path
+	elif type: return type + ':' + path
+	elif host: return '//' + host + path # don't know what this means
+	else: return path
 
 
 # Utilities to parse URLs (most of these return None for missing parts):
-# unwrap('<URL:type//host/path>') --> 'type//host/path'
+# unwrap('<URL:type://host/path>') --> 'type://host/path'
 # splittype('type:opaquestring') --> 'type', 'opaquestring'
 # splithost('//host[:port]/path') --> 'host[:port]', '/path'
 # splituser('user[:passwd]@host[:port]') --> 'user[:passwd]', 'host[:port]'