With this change, _statistics._normal_dist_inv_cdf() uses less efficient code to parse its arguments:

• Use METH_VARARGS calling convention (pass arguments as a tuple), instead of METH_FASTCALL (no Python object needed to pass arguments)
• Use PyArg_ParseTuple() to parse arguments with the "ddd:_normal_dist_inv_cdf" string. PyArg_ParseTuple() has to parse the format string. Instead of using inlined code _PyArg_CheckPositional(), PyFloat_CheckExact() / PyFloat_AsDouble() and PyFloat_AS_DOUBLE().

Micro-benchmark on Linux with CPU isolation, Python built with -O3 (without LTO, without PGO):

$ python -m pyperf compare_to ref.json limited.json 
Mean +- std dev: [ref] 88.6 ns +- 1.5 ns -> [limited] 160 ns +- 1 ns: 1.81x slower

Code:

import _statistics
import pyperf

p = 0.5
mu = 0.0
sigma = 1.0

runner = pyperf.Runner()
runner.bench_func('inv_cdf', _statistics._normal_dist_inv_cdf, p, mu, sigma)

I'm not sure if the _statistics is a good candidate for this work on converting stdlib extensions to the limited C API. The Lib/statistics.py module has a pure Python implementation, and the C code is there for optimization. So I would expect best performance for that. Moreover, the function is quite fast, around 100 ns, so the cost of argument parsing is significant.