Get three-letter day name from date command

Some time ago I had similar issue. There is my solution:

 $ ./get_dates.sh 2012 07
The first day is 01.2012.07, Sunday
The last day is 31.2012.07, Tuesday
 $ cal
 July 2012
Su Mo Tu We Th Fr Sa
 1  2  3  4  5  6  7
 8  9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31

Script itself:

#!/bin/bash
# last day for month
lastday()  {
#                ja   fe   ma   ap   ma   jn   jl   ag   se   oc   no   de
  mlength=('xx' '31' '28' '31' '30' '31' '30' '31' '31' '30' '31' '30' '31')

  year=$1
  month=$2

  if [ $month -ne 2 ] ; then
    echo ${mlength[$month]}
    return 0
  fi

  leap=0
  ((!(year%100))) && { ((!(year%400))) && leap=1 ; } || { ((!(year%4))) && leap=1 ; }

  feblength=28
  ((leap)) && feblength=29
  echo $feblength
}

# date to Julian date
date2jd() {

  year=$1
  month=$2
  day=$3
  lday=$(lastday $year $month) || exit $?

  if ((day<1 || day> lday)) ; then
    echo day out of range
    exit 1
  fi

  echo $(( jd = day - 32075
                + 1461 * (year + 4800 - (14 - month)/12)/4
                        + 367 * (month - 2 + (14 - month)/12*12)/12
                    - 3 * ((year + 4900 - (14 - month)/12)/100)/4
                - 2400001 ))
}

jd2dow()
{
  days=('Sunday' 'Monday' 'Tuesday' 'Wednesday' 'Thursday' 'Friday' 'Saturday')

  jd=$1
  if ((jd<1 || jd>782028)) ; then
    echo julian day out of range
    return 1
  fi

  ((dow=(jd+3)%7))

  echo ${days[dow]}
}


echo -n "The first day is 01.$1.$2, "
jd2dow $(date2jd $1 $2 01)
echo -n "The last day is $(lastday $1 $2).$1.$2, "
jd2dow $(date2jd $1 $2 $(lastday $1 $2))

I didn't have GNU date on machines I need it, therefore I didn't solve it with date. May be there is more beautiful solution.

- 1 month will subtract one from the month number, and then if the resulting date is not valid (February 30, for example), adjust it so that it is valid. So December 31 - 1 month is December 1, not a day in November, and March 31 - 1 month is March 3 (unless executed in a leap year).

Here's quote from the info page for Gnu date (which is the date version which implements this syntax), which includes a good suggestion to make the arithmetic more robust:

The fuzz in units can cause problems with relative items. For example, 2003-07-31 -1 month might evaluate to 2003-07-01, because 2003-06-31 is an invalid date. To determine the previous month more reliably, you can ask for the month before the 15th of the current month. For example:

    $ date -R
    Thu, 31 Jul 2003 13:02:39 -0700
    $ date --date='-1 month' +'Last month was %B?'
    Last month was July?
    $ date --date="$(date +%Y-%m-15) -1 month" +'Last month was %B!'
    Last month was June!

Another warning, also quoted from the info page:

Also, take care when manipulating dates around clock changes such as daylight saving leaps. In a few cases these have added or subtracted as much as 24 hours from the clock, so it is often wise to adopt universal time by setting the TZ environment variable to UTC0 before embarking on calendrical calculations.