I am unsure whether 64-bit specific tests are fine.

We want the tests to still pass on 32 bit (gh-317).

all configured Github runners are 64-bit platforms

Since gh-318 there is the pyodide job which runs on wasm32 although it would still be good to have a proper i686 job to test things like this.

Looks like arb_poly and acb_poly have mullow but not pow_trunc.

If at least all the exact poly types have these methods now then they can be added to this typing protocol:

New proposal :

• extend pow_trunc to big integers (I believe it feels better for a Python API to not depend on hardware architecture)
• remove note from docstrings
• add missing unit tests for pow_trunc
• add methods to epoly_p

The proposal is to not use modular pow (which is not defined for fmpz/fmpq) and implement "manually" large exponents using a loop (it works even for fmpz/fmpq and it is 2x-3x faster than powmod). I hope it is not overkill (I'm not sure there is a lot of use for large powers of fmpz_poly, maybe for combinatorics?)

I hope it is not overkill (I'm not sure there is a lot of use for large powers of fmpz_poly, maybe for combinatorics?)

I'm not sure either but it is good to have an implementation that does not have an arbitrary upper limit on the exponent as long as higher powers are computable.

It took me a while to parse the code used for this but it looks good:

def pow(x, e):
    ebytes = e.to_bytes((e.bit_length() + 15) // 16 * 2, "nig")
    p = x ** (ebytes[0] * 256 + ebytes[1])
    for i in range(2, len(ebytes), 2):
        p = p ** (1 << 16)
        p = p * x ** (ebytes[i] * 256 + ebytes[i + 1])
    return p

I guess that is going to reduce the overhead a little compared to working through e one bit at a time (which is ultimately what e.g. fmpz_poly_pow_trunc ends up doing after a bit of preprocessing).

The series types can also be used for this but they also have the overflow problem so I guess the same approach could be used there:

In [1]: import flint

In [2]: f = flint.fmpz_series([1, 2, 3], prec=3)

In [3]: f
Out[3]: 1 + 2*x + 3*x^2 + O(x^3)

In [4]: f ** (5 ** 25)
Out[4]: 1 + 596046447753906250*x + 177635683940025046765804290771484375*x^2 + O(x^3)

In [5]: f ** (5 ** 30)
---------------------------------------------------------------------------
OverflowError

Looks good to me. Thanks