To contribute something more substantial than "pseudo-hints": On my aged Windows computer one 9x9 determinant takes ~ 6.2e-7 s, using 8 byte floats and Gauss elimination from LAPACK running on one core with PARI checking ispseudoprime on a second core. I.e. 10^9 determinants in 10 minutes CPU. For comparison of machine speed: yafu-1.34 tune tells me:
Code:
SIQS on c100: ...
elapsed time for ~10k relations of c100 = 54.6251 seconds.
extrapolated time for complete factorization = 8707.0082 seconds
... WIN64 - Intel(R) Core(TM) i5-2400 CPU @ 3.10GHz