nx_alu_divider_floor_test.nx

nx_alu_divider_floor_test.nx -- COMPLETE THE FLOOR (honest step 0 toward the real divider exceed). The original floor was incomplete: it used a SIGNED compare for an unsigned remainder, so it broke for large operands (the rem<<1 overflow into the sign bit). Now the divider uses LTU (true unsigned compare), so it is correct over the FULL non-negative i64 range, INCLUDING the large-b overflow cases the signed compare got wrong. Verified here at width 63 over the whole non-negative range: 200000 randomized (a,b) in [0, 2^63) via an LCG -- which naturally exercises b in (2^62, 2^63) where rem<<1 overflows the sign bit and LTU is REQUIRED -- plus a few edges, each checked 1:1 vs behavioral a/b + a%b (signed `/` is a valid oracle since both operands are < 2^63). HONEST: this is heavy RANDOMIZED testing over the full range (exhaustive is impossible at 63-bit) -- a completed FLOOR, NOT yet the machine-checked-proof EXCEED (that needs a sovereign BMC/equivalence engine; full 64-bit unsigned with b>=2^63 needs >64-bit intermediates; signed division also still owed). Known answer (FAIL LOUD): "200003 200003 " (ok, total). exit 0 iff ok==total.