The major issue with PyPy is that it has a radically different C API than CPython, leading to incompatibility with NumPy, Pandas, etc. to mention just a few prominent performance-critical Python packages that are written in C. PyPy works if you want to use pure Python code, but that's rarely the case in real-world high-performance Python projects.
Compatibly with CPython's C API will always be a problem for any other implementation. The only practical solution is to switch to a better FFI, like cffi.
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Except PyPy is here now and you can use it. Not necessarily perfect, but the design is sound.
The major issue with PyPy is that it has a radically different C API than CPython, leading to incompatibility with NumPy, Pandas, etc. to mention just a few prominent performance-critical Python packages that are written in C. PyPy works if you want to use pure Python code, but that's rarely the case in real-world high-performance Python projects.
Compatibly with CPython's C API will always be a problem for any other implementation. The only practical solution is to switch to a better FFI, like cffi.