adi - up to, as far as; until, up to (connoting time); concerning, as to
(CAD A₁ 115, AHw. 12)
Also adu, gadu, ḳаdu, ḫadu, ad. The background of variants with initial ḳ and g is difficult to establish.
GAG § 114 j analyzes adīni and adīšu as lexicalized combinations of adi and pronominal suffixes.
It is hard to avoid thinking that adīni ‘until now; not yet’, has something to do with PWS *ˁād- ‘(he is) still’ also in terms of etymology (Kogan 2015: 76).
Akkadian
adīšu - meanwhile, until then
(CAD A₁ 128, AHw. 13)