> ... to see `pow(a, p-2, p)` beat a pure Python xgcd for computing the inverse.

OK, I'm indeed assuming that modinv() is implemented efficiently, in CPython, like pow() is. Then, it should be considerably faster, maybe like this:

>>> timeit.timeit("gmpy2.invert(1023,p)", "import gmpy2; p=2**61-1")
0.18928535383349754
>>> timeit.timeit("gmpy2.invert(1023,p)", "import gmpy2; p=2**127-1")
0.290736872836419
>>> timeit.timeit("gmpy2.invert(1023,p)", "import gmpy2; p=2**521-1")
0.33174844290715555
>>> timeit.timeit("gmpy2.powmod(1023,p-2,p)", "import gmpy2; p=2**61-1")
0.8771009990597349
>>> timeit.timeit("gmpy2.powmod(1023,p-2,p)", "import gmpy2; p=2**127-1")
3.460449585430979
>>> timeit.timeit("gmpy2.powmod(1023,p-2,p)", "import gmpy2; p=2**521-1")
84.38728888797652