▁Index , ▁which ▁enables ▁the ▁comparison ▁of ▁the ▁numer acy ▁among ▁regions ▁possible ▁without ▁any ▁historical ▁sources ▁where ▁the ▁population ▁liter acy ▁was ▁measured . ▁ ▁R ounding ▁functions ▁in ▁programming ▁languages ▁Most ▁programming ▁languages ▁provide ▁functions ▁or ▁special ▁syntax ▁to ▁round ▁fraction al ▁numbers ▁in ▁various ▁ways . ▁The ▁earliest ▁numeric ▁languages , ▁such ▁as ▁FOR TRAN ▁and ▁C , ▁would ▁provide ▁only ▁one ▁method , ▁usually ▁trunc ation ▁( t ow ards ▁zero ). ▁This ▁default ▁method ▁could ▁be ▁imp lied ▁in ▁certain ▁context s , ▁such ▁as ▁when ▁assigning ▁a ▁fraction al ▁number ▁to ▁an ▁integer ▁variable , ▁or ▁using ▁a ▁fraction al ▁number ▁as ▁an ▁index ▁of ▁an ▁array . ▁Other ▁kinds ▁of ▁round ing ▁had ▁to ▁be ▁program med ▁explicitly ; ▁for ▁example , ▁round ing ▁a ▁positive ▁number ▁to ▁the ▁nearest ▁integer ▁could ▁be ▁implemented ▁by ▁adding ▁ 0 . 5 ▁and ▁trunc ating . ▁ ▁In ▁the ▁last ▁dec ades , ▁however , ▁the ▁syntax ▁and / or ▁the ▁standard ▁libraries ▁of ▁most ▁languages ▁have ▁commonly ▁provided ▁at ▁least ▁the ▁four ▁basic ▁round ing ▁functions ▁( up , ▁down , ▁to ▁nearest , ▁and ▁towards ▁zero ). ▁The ▁tie - bre aking ▁method ▁may ▁vary ▁depending ▁the ▁language ▁and ▁version , ▁and / or ▁may ▁be ▁select able ▁by ▁the ▁programmer . ▁Several ▁languages ▁follow ▁the ▁lead ▁of ▁the ▁IE EE ▁ 7 5 4 ▁floating - point ▁standard , ▁and ▁define ▁these ▁functions ▁as ▁taking ▁a ▁double ▁precision ▁float ▁argument ▁and ▁returning ▁the ▁result ▁of