get 1 solid answer from gmpy2 maintainer.

One last comment: the values of precision, emax and emin are slight different between the IEEE standards and the MPFR library. If e is the exponent size and p is the precision (in IEEE terms), then precision should be p+1,emax should be 2**(e-1) and emin should be 4-emax-precision. This doesn't impact your question since it only changes emax.

but in which document can i find this? i take a glance and do search in official gmpy document https://gmpy2.readthedocs.io/en/latest/mpfr.html, find nothing regarding this. why emin/emax/precision set that value? why not directly as emax=15, emin as -14, precison as 11 directly?