Henceforth, starts another exciting week of coding. This week I look forward to implementing arbitrary precision floating point LLL using the mpf_t data type provided by GMP (which is dependency for installing FLINT). According to the discussion on the mailing list, as it isn't a big issue, I've decided to get the code working with mpf for now as some helper functions are already implemented in the mpf_vec and mpf_mat modules (The other option is Arb which will be used eventually).
Last week, I wrote the heuristic version of LLL (which always uses heuristic dot products that attempt to detect cancellation) over doubles and worked on improving the textbook L^2 and Gram matrix variants. I think the textbook L^2 implementation needs more work before it can be proclaimed ready for use. Though it works on most of the test cases, there are still some corner cases to consider. For use in fmpz_lll_check_babai_heuristic, some changes were also made to the mpf_vec, fmpz, fmpz_vec modules to help facilitate conversion between fmpz and mpf and vice versa. Also, _mpf_vec_dot2 now signals possible cancellation through an integer return value.
Last week, I wrote the heuristic version of LLL (which always uses heuristic dot products that attempt to detect cancellation) over doubles and worked on improving the textbook L^2 and Gram matrix variants. I think the textbook L^2 implementation needs more work before it can be proclaimed ready for use. Though it works on most of the test cases, there are still some corner cases to consider. For use in fmpz_lll_check_babai_heuristic, some changes were also made to the mpf_vec, fmpz, fmpz_vec modules to help facilitate conversion between fmpz and mpf and vice versa. Also, _mpf_vec_dot2 now signals possible cancellation through an integer return value.
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