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Python Codec Registry and support functions are well documented in codecs.h header file. It should be easy to convert that to reST.

I will write a codecs.rst for this. Any suggestion of where in c-api/index.html it should be linked?

Please call it codec.rst. It is probably best placed under "utilities".

While preparing a .rst document for this, I ran into a possible inaccuracy in a comment in codecs.h:
/* Lookup the error handling callback function registered under the
 name error. As a special case NULL can be passed, in which case
 the error handling callback for "strict" will be returned. */
PyAPI_FUNC(PyObject *) PyCodec_LookupError(const char *name);
----
The problem may be with the phrase "under the name error". Shouldn't it be just "under *name*"?

Yes, apparently the parameter was (intended to be) called "error" at some point. Can you put the correction in your patch?

Submitting a patch. What was touched:
1. Include/codecs.h - minor inaccuracy and inconsistency in a comment
2. Doc/c-api/codec.rst - new reST documentation file for the codecs.h C API
3. Doc/c-api/utilities.rst - for linking to codec.rst, per Georg's suggestion

Thanks for the patch, it looks good, I have 2 remarks though:
- "under the name name" could be replaced by "under the given name".
- "The *search_function*'s refcount is incremented by this function."
This information is not useful to the caller - she just wants to know whether she still owns the reference she had before. Most probably here, the refcount is incremented because the object is stored in a list; the caller still owns the reference to the parameter, like most functions of the API, and there is nothing to say about refcounts here.

Amaury,
Thanks for the review & comments.
I'm attaching a fixed patch.

Please also keep to 3-space indentation in directives.

Georg,
Thanks. Submitting fixed patch with 3-space indentation in directives.

Reviewed and applied in r86562. Thanks!