psh-fractional/division/div

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#!/bin/sh
s() {
n=$1; i=1; while [ "$n" -le $2 ]; do
echo "$n"; : $((n+=i))
done
} # seq
fd() { # return first digit of $1
x="$1"; until [ "${#x}" -eq 1 ]; do
x="${x%?}"
done
echo "$x"
}
ld() { # $1/$2
di="$1"; div="$2"; count="$3"
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case "$div" in
*'.'*)
sp=0; sdiv="${div%%.*}"; IFS="."; set -- ${div}; div="${1}${2}"; unset IFS
sp="$((${#div}-${#sdiv}))"
esac
# determine where the decimal point is -- if present
case "$di" in
*'.'*)
dp=0; t="$di"; while :; do # use while true + case/break
t="${t#?}"; : $((dp+=1))
case "$t" in
'.'*) break
esac
done
;;
*) dp=0
esac
[ "$dp" -gt 0 ] && {
IFS="."; set -- ${di}; di="${1}${2}"; unset IFS
}
#echo "$sp $div ${di}/${#di}"
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[ "$sp" ] && {
ss="${#di}"; : $((ss-=dp)); : $((ss+=sp)); : $((ss+=1))
until [ "${#div}" -eq "$ss" ]; do
div="${div}0"
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done
}
#echo "-"
o="$((di/div))"; dp="${#o}"
[ "${#o}" -eq 0 ] && : $((count+=2))
: $((count+=${#o}))
until [ "${#di}" -eq "$count" ]; do
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di="${di}0"
done
set -- "$1" "$2" "${3:-9}" "$di" "$sd"
unset IFS o; n=0; for i in $(s 1 $count); do
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fd="$(fd $di)" # fd is needed later
#echo "$fd";
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[ "$i" -gt 1 ] && {
fd="${sd}${fd}"
#echo "$fd"
}
sd="$((fd/div))"; [ "$sd" -eq 0 ] && : $((count+=1))
o="${o}${sd}"; sd="$((sd*div))"
#printf " %s\n- %s\n" "$fd" "$sd"
sd="$((fd-sd))"
#echo "| $sd"
[ "$sd" -eq 0 ] && {
n=0
break
}
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# now pull down # redefine $di
di="${di#?}" # $fd$sd
: $((n+=1))
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done
[ "$n" -gt 0 ] && {
count=$((count+n))
} || count=0
#echo "$fd $di/$4 - $div / $dp -- $sp | $count"
# do again if $((count-n)) is > 0
[ "$count" -gt 0 ] && {
di="$4"; sd="$5"; o=""; until [ "${#di}" -eq "$count" ]; do
di="${di}0"
done
for i in $(s 1 $count); do
fd="$(fd $di)" # fd is needed later
[ "$i" -gt 1 ] && fd="${sd}${fd}"
sd="$((fd/div))"; o="${o}${sd}"; sd="$((sd*div))"; sd="$((fd-sd))"
[ "$sd" -eq 0 ] && break
di="${di#?}"
done
}
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until [ "${o#0}" = "$o" ]; do
o="${o#0}"
done
[ "$dp" -gt 0 -a "$fd" -ne "$1" ] && {
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[ "$t" ] || : $((dp+=1))
[ "$t" ] && : $((dp-=1))
[ "$sp" ] && : $((dp+=1))
[ "${sp:-0}" -gt 1 ] && : $((dp+=1))
#echo "$o $dp/$sp | ${#o}"
do="$o"; [ "${#do}" -gt "$dp" ] && until [ "${#do}" -eq "$dp" ]; do
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do="${do%?}"
done
[ "$1" -lt "$2" ] && do="${do%?}"
o="${do:-0}.${o#$do}"
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}
[ "$1" -lt "$2" ] || until [ "${o#0}" = "$o" ]; do
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o="${o#0}"
done
echo "$o" # | $dp | $do"
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}
# 9 decimal points unless $3 is passed
[ "$1" -a "$2" ] && ld "$1" "$2" "${3:-9}"