▁to ▁the ▁final ▁precision . ▁Double ▁round ing ▁can ▁be ▁avoided ▁by ▁choosing ▁an ▁ade qu ate ▁round ing ▁for ▁the ▁intermediate ▁computation . ▁This ▁consists ▁in ▁avoid ing ▁to ▁round ▁to ▁mid points ▁for ▁the ▁final ▁round ing ▁( except ▁when ▁the ▁mid point ▁is ▁exact ). ▁In ▁binary ▁arithmetic , ▁the ▁idea ▁is ▁to ▁round ▁the ▁result ▁toward ▁zero , ▁and ▁set ▁the ▁least ▁significant ▁bit ▁to ▁ 1 ▁if ▁the ▁rounded ▁result ▁is ▁in ex act ; ▁this ▁round ing ▁is ▁called ▁stick y ▁round ing . ▁Equ ival ently , ▁it ▁consists ▁in ▁returning ▁the ▁intermediate ▁result ▁when ▁it ▁is ▁exactly ▁represent able , ▁and ▁the ▁nearest ▁floating - point ▁number ▁with ▁an ▁odd ▁signific and ▁otherwise ; ▁this ▁is ▁why ▁it ▁is ▁also ▁known ▁as ▁round ing ▁to ▁odd . ▁ ▁Table - maker ' s ▁d ile m ma ▁William ▁M . ▁K ah an ▁co ined ▁the ▁term ▁" The ▁Table - M aker ' s ▁D ile m ma " ▁for ▁the ▁unknown ▁cost ▁of ▁round ing ▁trans c endent al ▁functions : ▁" N ob ody ▁knows ▁how ▁much ▁it ▁would ▁cost ▁to ▁compute ▁ ▁correctly ▁rounded ▁for ▁ ▁two ▁floating - point ▁arguments ▁at ▁which ▁it ▁does ▁not ▁over / under flow . ▁Instead , ▁re put able ▁math ▁libraries ▁compute ▁elementary ▁trans c endent al ▁functions ▁mostly ▁within ▁slightly ▁more ▁than ▁half ▁an ▁ul p ▁and ▁almost ▁always ▁well ▁within ▁one ▁ul p . ▁Why ▁can ' t ▁ ▁be ▁rounded ▁within