Howto grep over months with defined start and end date - regex

Question

so here's my problem: I have big log files and want a script to grep certain periods of time and safe them to a file (sorted), basically
bash script.sh Jul 4 Sep 30
will return for example
Sep 30 user0 logged in
Sep 15 user1 logged in
Aug 6 user0 logged in
Aug 3 user1 logged in
Jul 28 user2 logged in
Jul 27 user2 logged in
Jul 4 user0 logged in
My first attempt was that every month and date gets his own variable like
bash script.sh Jul 4 Sep 3 0
so I can use $1 for start month (July), $2 for start date (4) and so on in grep like
for logs in logs*
do
grep -qEe "^\"$1\" [\"$2\"-9]\s" $messages >> result.txt
done
to get all logs from July 4 to 9 but I don't know how to get logs from the entire time period that aren't in the same month nor in a period like 1-9 or 10-19 and so on
Any help greatly appreciated!
EDIT:
As some people asked, here's how my log files look like (just much bigger and not sorted):
Sep 30 user0 logged in
Jul 27 user2 logged in
Aug 6 user0 logged in
Aug 31 user1 logged in
Jul 8 user2 logged in
Sep 5 user1 logged in
Jul 27 user2 logged in
Jul 14 user0 logged in
[...]

Answer 1

Here's my take:
#/bin/bash
year="$(date +"%Y")"
start="$(date -d"$1 $2, $year" +'%s')"
end="$(($(date -d"$3 $4, $year" +'%s')+86400))"
for log in logs*; do
while IFS= read -r line; do
d="$(date -d"$(cut -d' ' -f1,2 <<< "$line"), $year" +'%s')"
if (( $start <= $d && $d < $end )); then
echo "$s"
fi
done < "$log"
done
You run it like that: ./script.sh Jul 04 Sep 03. Since no year is included in the logs, it assumes that all dates (including the ones in the command line) are for the current year. It's probably not the most optimal solution but it works. It relies on date which it repeatedly calls to parse dates into a unix timestamp. unix timestamps are nice because they are just numbers and thus can be used in numeric comparisons.

Answer 2

$ range="Jul 4 Sep 30"
$ awk -v range="$range" '
BEGIN {
numMths = split("Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec",m)
for (i in m) {
mths[m[i]] = i
}
split(range,r)
beg = sprintf("%02d%02d", mths[r[1]], r[2])
end = sprintf("%02d%02d", mths[r[3]], r[4])
}
{ cur = sprintf("%02d%02d", mths[$1], $2) }
(cur >= beg) && (cur <= end) { vals[$1,$2] = $0 }
END {
for (mthNr=numMths; mthNr>0; mthNr--) {
for (dayNr=31; dayNr>0; dayNr--) {
date = m[mthNr] SUBSEP dayNr
if (date in vals) {
print vals[date]
}
}
}
}
' file
Sep 30 user0 logged in
Sep 5 user1 logged in
Aug 31 user1 logged in
Aug 6 user0 logged in
Jul 27 user2 logged in
Jul 14 user0 logged in
Jul 8 user2 logged in