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mid-14c., "speedy, quick," by 1500s replacing or nativizing earlier hastif (c.1300) "eager, impetuous," from Old French hastif "speedy, rapid; forward, advanced; rash, impetuous" (12c., Modern French hâtif), from haste (see haste). Meaning "requiring haste" is late 14c. (the sense in hasty pudding, 1590s, so called because it was made quickly); that of "rash" is from early 15c. Related: Hastiness. Old French also had a form hasti (for loss of terminal -f, cf. joli/jolif, etc.), which may have influenced the form of the English word.
The termination was doubtless from the first identified with native -i, -y, from OE -ig; and it is noticeable that the other Teutonic langs. have formed corresponding adjs. of that type: Du. haastig, Ger., Da., Sw. hastig. [OED]