Copy of Stefan Behnel's msg345305 in bpo-37221:
"""
Note that PyCode_New() is not the only change in 3.8 beta1 that breaks Cython generated code. The renaming of "tp_print" to "tp_vectorcall" is equally disruptive, because Cython has (or had) a work-around for CPython (mis-)behaviour that reset the field explicitly to NULL after calling PyType_Ready(), which could set it arbitrarily without good reason.

So, either revert that field renaming, too, or ignore Cython generated modules for the reasoning about the change in this ticket.

I'm fine with keeping things as they are now in beta-1, but we could obviously adapt to whatever beta-2 wants to change again.
"""

There are 2 problems:

* source compatibility
* ABI compatibility

The following change removed PyTypeObject.tp_print and replaced it with PyTypeObject.tp_vectorcall_offset:

commit aacc77fbd77640a8f03638216fa09372cc21673d
Author: Jeroen Demeyer <J.Demeyer@UGent.be>
Date:   Wed May 29 20:31:52 2019 +0200

    bpo-36974: implement PEP 590 (GH-13185)
    
    
    Co-authored-by: Jeroen Demeyer <J.Demeyer@UGent.be>
    Co-authored-by: Mark Shannon <mark@hotpy.org>


== ABI compatibility ==

In term of ABI, it means that C extensions using static type ("static PyTypeObject mytype = { .... };") is broken by this change.

Honestly, I'm not sure if we ever provided any forward compatibility for static types. bpo-32388 removed "cross-version binary compatibility" on purpose in Python 3.8. It's an on-going topic, see also my notes about ABI and PyTypeObject:
https://pythoncapi.readthedocs.io/type_object.html

Maybe we can simply ignore this part of the problem.


== Source compatibility ==

Cython generates C code setting tp_print explicitly to NULL.

To avoid depending on Cython at installation, most (if not all) projects using Cython include C files generated by Cython in files they distribute (like tarballs). Because of that, the commit aacc77fbd77640a8f03638216fa09372cc21673d requires all these projects to regenerate their C files using Cython.

In Fedora, we fixed many Python packages to always re-run Cython to regenerate all C files. But Fedora is just one way to distribute packages, it doesn't solve the problem of files distributed on PyPI, nor other Linux distribution (for example).

Jeroen Demeyer proposed PR 14009 to fix the source compatibility:

   #define tp_print tp_vectorcall