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.

*ˁaday - up to, until (DUL 142)

It is not obvious that forms of the type (wV)d meaning “to, towards” are related to this preposition (Arakelova 2001:22). They are united into a separate lexeme, see *ˀVd/d.