Fixes https://github.com/cython/cython/issues/3647

Use newer test dependencies in Py3.6+. (Excluding 3.10 for now to give the projects a bit more time.)

Disable some plain Python (non Cython related) tests that fail in Py3.10 due to changed error messages.

Originally discussed here:
https://groups.google.com/g/cython-users/c/rU0_mt3Vgn0

The function `(cython-current-defun)` of `cython-mode.el` had some issues:

* ran into an endless loop
* for `cdef`s and `cpdef`s it picked the function type rather than the function name.
* did not properly handle nested functions

Closes https://github.com/cython/cython/issues/3218

Tests are disabled on macOS+clang (failing with Apple clang++ 12) but appear to work fine on gcc-11.

Use the accessor function instead of the direct struct member (which is now the wrong type).

Closes https://github.com/cython/cython/issues/4416

Make coverage.py handle "stringsource" better by making it clear that it is not a file name (GH-4440)

Having a code object with `co_filename` set to just "stringsource" (e.g. when using memory views or auto-pickling), causes coverage.py to think that "stringsource" is a relative path to an actual file. The convention is to wrap such fake paths with angle brackets, which coverage.py correctly recognizes.

You will recognize this as the following error, e.g. when running "coverage html":
    No source for code: '.../stringsource'.
    Aborting report output, consider using -i.

Replace a mutable default argument with a None default and check since it is not intended to be mutated (GH-4435)

Avoid "possible loss of data" warning in MSVC by adding redundant casts to code that gets discarded later.

Still requires the more conservative __index__ here rather than a possibly
truncating __int__ because this is used in a context where floating point
values should probably be treated specially.

This fixes Github issue #2752.

PyContextVar_Get() was added in PyPy 7.3.6.
https://foss.heptapod.net/pypy/pypy/-/blob/branch/default/pypy/doc/release-v7.3.6.rst

Some overloaded methods are commented out as they currently result in incorrect C++ code.
See https://github.com/cython/cython/pull/4423#issuecomment-953685310

Repair coverage tests to make them work with coverage 6.1, which changed the HTML output format that the tests parse.

Arguably, it's unnecessary if the auto-call works correctly, but if we're still advising users to do it themselves then it probably should be in the docs.

Repair coverage tests to make them work with coverage 6.1, which changed the HTML output format that the tests parse.

See https://github.com/python/cpython/pull/28968/8e5de40f90476249e9a2e5ef135143b5c6a0b512
which is part of implementing
https://bugs.python.org/issue35134
moved the header "longintrepr.h" into a sub-folder.
The notes on this change suggested to include "Python.h" instead.

See https://github.com/python/cpython/pull/28968/8e5de40f90476249e9a2e5ef135143b5c6a0b512
which is part of implementing
https://bugs.python.org/issue35134
moved the header "longintrepr.h" into a sub-folder.
The notes on this change suggested to include "Python.h" instead.

* Utils.py: add _find_cache_attributes, clear_method_caches

* TestCythonUtils.py: add tests for Cached Methods

* Utils.py: add constants

* Utils.py: update comment

* TestCythonUtils.py: remove excess blank line

* Change names to `_CACHE_NAME` and `_CACHE_NAME_PATTERN`

* ci.yml: extend timeout to 40 minutes

* _CACHE_NAME -> _build_cache_name

See https://github.com/cython/cython/pull/3782

Use newer test dependencies in Py3.6+. (Excluding 3.10 for now to give the projects a bit more time.)