What happened to "Modexp, bᵈ mod m" topic from (last updted 2016) "Itemised plans for GMP"

[hermann at stamm-wilbrandt.de]

Last updated in 2016:
https://gmplib.org/devel/GMPng

What happened to "Modexp, bᵈ mod m" section topic: "Use special code for 
when b is much smaller than m, avoiding REDC representation and table 
precomputation."


For my application m is a 100Ks digits prime "=1 (mod 4)", d=p/4, and b 
is smallest quadratic non-resiidue of m. That can be computed quickly 
with kronecker symbol:
https://github.com/Hermann-SW/RSA_numbers_factored/blob/main/c%2B%2B/sqrtm1.cc

     // deterministic fast search for smallest quadratic non-residue
     b = 2;
     while (mpz_kronecker(b.get_mpz_t(), p.get_mpz_t()) != -1) {
         mpz_nextprime(b.get_mpz_t(), b.get_mpz_t());
     }
     std::cerr << "smallest quadratic non-residue prime: " << b << "\n";

Most times smallest quadratic non-residue is single digit, or lower 
2-digit prime.


It took 26h to compute that "powm()" for smallest known 1million digit 
prime with i7_11850H; expected runtime with 7600X CPU is 19.2h.

https://github.com/Hermann-SW/QuadraticRegression/blob/master/sqrtm1___.py
pi at pi400-64:~/QuadraticRegression $ python sqrtm1___.py
y = 7.950524562496551e-08x² - 0.011528213946191843x + 914.8718066871961

? f(x) = 7.950524562496551e-08*x^2 - 0.011528213946191843*x + 
914.8718066871961 %11 = 
(x)->7.950524562496551e-08*x^2-0.011528213946191843*x+914.8718066871961
? f(1000000)/3600
%12 = 19.136639857072461972222222222222222222
?


But the number I am really interested in (largest known prime "=1 (mod 
4)", rank 9: https://t5k.org/primes/lists/all.txt)

     8  2^32582657-1                     9808358 G9    2006 Mersenne 44
     9  10223*2^31172165+1               9383761 SB12  2016
    10  2^30402457-1                     9152052 G9    2005 Mersenne 43

would take roughly 80 days to compute sqrtm1 (above "powm()") 
sequentially with 7600X ...

? f(9383761)/3600
%13 = 1914.8802571909706918476056601972222222
? f(9383761)/3600/24
%14 = 79.786677382957112160316902508217592593
?


Any other ideas on speeding up "powm(_, qnr, p/4, p)" with millions 
digits prime p somehow?


Regards,

Hermann.