psh-fractional/division/div

#!/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"
}
countd() { # count decimal places
  m="$1"; n=${2:-0}; while [ "$m" ]; do
    : $((n+=1))
    next="${m%?}"
    [ "${m#$next}" = "." ] && {
      break
    } || {
      m="$next"
    }
  done
  echo "$n"
}
ld() { # $1/$2

  if [ ! -z "${1##*.*}" -a -z "${2##*.*}" ]; then
    di="${1}."; until [ "${#di}" -eq "$((${#2}+1))" ]; do
      di="${di}0"
    done
    set -- "$di" "$2" "$3"
  elif [ ! -z "${2##*.*}" -a -z "${1##*.*}" ]; then
    div="${2}."; until [ "${#div}" -eq "$((${#1}+1))" ]; do
      div="${div}0"
    done
    set -- "$1" "$div" "$3"
  fi

  [ -z "${1##*.*}" -o -z "${2##*.*}" ] || {
    set -- "$1.00" "$2.00" "$3"
  }

  di="${1##*.}"; div="${2##*.}"
  until [ "${#di}" -ge "${#div}" ]; do
    di="${di}0"
  done
  until [ "${#div}" -ge "${#di}" ]; do
    div="${div}0"
  done
  set -- "${1%%.*}.$di" "${2%%.*}.$div" "$3"
  # handle decimal less numbers

  #echo "$1/$2"

  di="$1"; div="$2"; count="$3"
  case "$div" in
    *'.'*) # if $2 has a decimal we must shift
      set -- "${1%.*}${1#*.}" "${2%.*}${2#*.}" "$3" # shift $2 # simply remove the decimal point
      until [ "${#1}" -ge "${#2}" ]; do
        set -- "${1}0" "$2" "$3"
      done
      set -- "$1.00" "$2" "$3" # add decimals back in for $1 only
  esac
  #echo "$1 $2"
  di="$1"; div="$2"; count="$3" # redeclare
  #echo "$sp $div ${di}/${#di} | $1/$2 | $di/$div"
  o="$((${di%.*}/${div%.*}))"; [ "${#o}" -eq 0 ] && : $((count+=2)); : $((count+=${#o}))
  sd="${di%.*}"; : $((count+=${#sd}));
  until [ "${#di}" -eq "$((count+1))" ]; do
    di="${di}0"
  done
  : $((count-=1)) && di="${di%0}"
  set -- "$1" "$2" "${3:-9}" "$di"
  unset IFS o; n=0; for i in $(s 1 $count); do
    fd="$(fd $di)" # fd is needed later
    [ "$fd" = '.' ] && {
      dp="$n"
      di="${di#?}"; fd="$(fd $di)" 
    }
    [ "$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 -- $i"
    di="${di#?}" # $fd$sd
    : $((n+=1))
  done
  n=0; sd="$o"; while [ "$sd" ]; do
    next="${sd#?}"
    [ "$n" -eq "$dp" ] && {
      o="${o%$sd}.$sd"
      break
    }
    sd="$next"
    : $((n+=1))
  done
  #until [ "${o#0}" = "$o" ]; do
  #  o="${o#0}"
  #done
  #echo "$o"
  if [ ! -z "${o##*.*}" -a "$dp" -gt 0 ]; then # missing decimal place
    do="$o"; [ "${#do}" -gt "$dp" ] && until [ "${#do}" -eq "$dp" ]; do
      do="${do%?}"
    done
    o="${do:-0}.${o#$do}"
  fi
  [ "$(fd $o)" = '.' ] && o="0$o"
  until [ "${o#0}" = "$o" ]; do
    o="${o#0}"
  done
  [ "$(fd $o)" = '.' ] && o="0${o}"
  echo "$o" # | $1/$2 | $dp | $do || $fd $1"
}
# 19 decimal points unless $3 is passed # bc uses 19
[ "$1" -a "$2" ] && ld "$1" "$2" "${3:-20}"