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codecs.charmap_decode behaves differently with native and user string as decode table.
>>> import codecs
>>> print(ascii(codecs.charmap_decode(b'\x00', 'replace', '\uFFFE')))
('\ufffd', 1)
>>> class S(str): pass
... 
>>> print(ascii(codecs.charmap_decode(b'\x00', 'replace', S('\uFFFE'))))
('\ufffe', 1)
It's because charmap decoder (function PyUnicode_DecodeCharmap in Objects/unicodeobject.c) uses different algorithms for exact strings and for other.
We need to fix it? If yes, what should return `codecs.charmap_decode(b'\x00', 'replace', {0:'\uFFFE'})`? What should return `codecs.charmap_decode(b'\x00', 'replace', {0:0xFFFE})`?

What is the use case for passing a string subclass to charmap_decode? Or in other words, how did you stumble upon the bug?

U+FFFE is documented as representing an undefined mapping, see
http://docs.python.org/dev/c-api/unicode.html?highlight=charmap#PyUnicode_DecodeCharmap
So the base string case is correct; the derived string implementation also needs to invoke the error handler.

> What is the use case for passing a string subclass to charmap_decode? Or in other words, how did you stumble upon the bug?
I stumbled upon it, rewriting the charmap decoder (issue14874). Now
charmap decoder processes the two cases -- a more effective case of
string table and a general slower case of general mapping. I proposed a
more optimized case of 256-character UCS2 string (covers all standard
charmap encodings). If processing general strings and maps was
consistent, these cases can be merged. A string subclass is just an
example that illustrates the inconsistency.

> U+FFFE is documented as representing an undefined mapping,
Yes, using U+FFFE for representing an undefined mapping in strings is
normal, the question was about string subclasses. And if we will correct
it for string subclasses, how far we go any further? How about general
mapping?

>> U+FFFE is documented as representing an undefined mapping,
>
> Yes, using U+FFFE for representing an undefined mapping in strings is
> normal, the question was about string subclasses.
What is the question? U+FFFE also represents an undefined mapping in 
string subclasses.
 > And if we will correct it for string subclasses, how far we go any
 > further?
This is a single issue, a single bug. If the bug is fixed, it is fixed. 
No need to go further (unless there is another bug somewhere).

> What is the question? U+FFFE also represents an undefined mapping in 
> string subclasses.
What about classes that not subclassed string but ducktyped string by
implementing all string method? What about list/tuple/array.array of
integers or 1-character strings? What about general mapping? Should any
of them have 0xFFFE or '\uFFFE' represent an undefined mapping?
> This is a single issue, a single bug. If the bug is fixed, it is fixed. 
> No need to go further (unless there is another bug somewhere).
My question, where is the limit of this bug.

> integers or 1-character strings? What about general mapping? Should
 > any of them have 0xFFFE or '\uFFFE' represent an undefined mapping?
The documentation says that the parameter "can be a dictionary mapping 
byte or a unicode string, which is treated as a lookup table". So 
anything that supports GetItem with a small integer index can be passed.
It then says '... U+FFFE "characters" are treated as "undefined mapping"'.
So the answer to your last question is "yes". I hope that the answer to
your other questions follows from that (strictly speaking, it's only
U+FFFE, not 0xFFFE, that is documented as indicating an undefined
mapping; a patch should probably fix that).
(I also wonder where the support for LookupError comes from - that 
appears to be undocumented)

> So the answer to your last question is "yes". I hope that the answer to
> your other questions follows from that
Thank you, this is the answer to all my questions. I've prepared a patch
to treat U+FFFE in general mapping as "undefined mapping".
> (strictly speaking, it's only
> U+FFFE, not 0xFFFE, that is documented as indicating an undefined
> mapping; a patch should probably fix that).
As both integer 0xXXXX and string '\uXXXX' denote U+XXXX, I do not think
it necessary fixes.
> (I also wonder where the support for LookupError comes from - that 
> appears to be undocumented)
I believe, this is what is meant by the words "undefined mapping".

Patch updated to resolve conflict with issue15379. Added tests. Added patches 
for 3.2 and 2.7.

Does anyone have objections against the idea or the implementation of the patch? Please review.

I no one objects I will commit this next year.

New changeset 33a8ef498b1e by Serhiy Storchaka in branch '2.7':
Issue #14850: Now a chamap decoder treates U+FFFE as "undefined mapping"
http://hg.python.org/cpython/rev/33a8ef498b1e
New changeset 13cd78a2a17b by Serhiy Storchaka in branch '3.2':
Issue #14850: Now a chamap decoder treates U+FFFE as "undefined mapping"
http://hg.python.org/cpython/rev/13cd78a2a17b
New changeset 6ac4f1609847 by Serhiy Storchaka in branch '3.3':
Issue #14850: Now a chamap decoder treates U+FFFE as "undefined mapping"
http://hg.python.org/cpython/rev/6ac4f1609847
New changeset 03e22cc9407a by Serhiy Storchaka in branch 'default':
Issue #14850: Now a chamap decoder treates U+FFFE as "undefined mapping"
http://hg.python.org/cpython/rev/03e22cc9407a 

Fixed. Thank you for your answers, Martin.