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Using a multibyte codec and a custom error handler that ignores errors to encode a string that contains characters not representable in said encoding causes exponential growth of the output buffer, raising MemoryError.
The problem is in multibytecodec_encerror() and REQUIRE_ENCODEBUFFER() in Modules/cjkcodecs/multibytecodec.c. multibytecodec_encerror() always uses REQUIRE_ENCODEBUFFER() to ensure there's enough space for the replacement string, and if more space is needed, REQUIRE_ENCODEBUFFER() calls expand_encodebuffer(), which in turn always grows the buffer by at least 50%. However, if size < 1, REQUIRE_ENCODEBUFFER() doesn't check if more space is actually needed. (It's used with negative values in other places)
I have no idea why the condition was originally size < 1 instead of size < 0, but changing it seems to fix this. The replacement string case is also the only use of the macro that may use 0 as the argument. 
In the patch, I've instead wrapped the REQUIRE_ENCODEBUFFER() (and memcpy) in a if(size > 0), since that's what the corresponding part in multibytecodec_decerror() did in the past:
https://hg.python.org/cpython/file/1c3f8d044589/Modules/cjkcodecs/multibytecodec.c#l438
Not sure which one makes more sense.
As for the tests, I'm not sure if 1) all of the affected encodings should be tested or only one (or even all encodings, affected or not?) and 2) whether it should be a new test or if I should just add it to test_longstrings in Lib/test/test_codeccallbacks.py. (Structurally it's a perfect fit, but it really isn't a "long string" test as it can happen with <50 characters) At the moment, the patch is testing affected encodings in a separate test.
Is the test philosophy "as thorough as possible" or "as fast as possible"?

New changeset 3a9b1e5fe179 by R David Murray in branch '3.4':
#23215: reflow paragraph.
https://hg.python.org/cpython/rev/3a9b1e5fe179
New changeset 52a06812d5da by R David Murray in branch 'default':
Merge: #23215: note that time.sleep affects the current thread only.
https://hg.python.org/cpython/rev/52a06812d5da 

Oops, typoed the issue number. That should have been 23251.

Thank you for your patch Aleksi. It LGTM in general. Updated patch just moves the test to Lib/test/test_multibytecodec.py where it can reuse ALL_CJKENCODINGS and fixes few other minor bugs in multibyte codecs.

New changeset af8089217cc6 by Serhiy Storchaka in branch '2.7':
Issue #23215: Multibyte codecs with custom error handlers that ignores errors
https://hg.python.org/cpython/rev/af8089217cc6
New changeset 4dc8b7ed8973 by Serhiy Storchaka in branch '3.4':
Issue #23215: Multibyte codecs with custom error handlers that ignores errors
https://hg.python.org/cpython/rev/4dc8b7ed8973
New changeset 5620691ce26b by Serhiy Storchaka in branch 'default':
Issue #23215: Multibyte codecs with custom error handlers that ignores errors
https://hg.python.org/cpython/rev/5620691ce26b