If you  wish to write your  own hdate program, here  are the principles.
They are  based on  common knowledge  and a  book called  'the 6000-year
calendar' by  A.  Akavia (I  don't know if  it was ever  translated from
Hebrew).  The  given algorithm  is the one  used currently  (others were
used in different times in history), and  is in use since about the 10th
century A.D.

The  calendar is  lunisolar  -  each year  starts  close  to the  autumn
equinox, but each month starts at the new moon.  Dates change at sunset,
so the 1st day  of the month is the one following  the new moon.  Months
are alternately  30 and 29 days  long, and are named:  Tishrey, Heshvan,
Kislev, Tevet, Shvat, Adar, Nisan, Iyar, Sivan, Tamuz, Av and Elul.  (In
biblical times,  the year used  to start at  Nisan.) A standard  year is
therefore 354 days long.

In leap years, an extra month of  30 days is inserted before Adar (which
used to  be the last month),  and the 2  Adar's are called 'Adar  a' and
'Adar b'.  Leap years occur 7 times in a 19-year cycle, and are years 3,
6, 8, 11, 14, 17 and 19.  A standard leap year is 384 days long.

For various reasons  of religious practices, the year cannot  start on a
Sunday, a Wednesday or  a Friday.  If an adjustment is  needed, a day is
added to Heshvan or taken off Kislev.  Thus a regular year may be 353 to
355 days long, and a leap year - 383 to 385.

Now, to the computation:  each day starts at 6 p.m.,  and consists of 24
hours; the hour is sub-divided into 1080 'parts'.  The month is 29 days,
12 hours  and 793 parts  long (let's use  the notation 12h793).   In all
computations, we are only interested in  the time of the new moon modulu
one week; the starting point (1st new  moon of year 1) is Monday, 5h204,
i.e.   23:11:20.  To  give you  a more  recent clue,  year 5701  started
(exactly 300 cycles later) on Thursday, Oct.  3, 1940.  The new moon was
on Wednesday, 2h504.

Given a  date, find the number  of days since a  pre-calculated starting
point (preferably a new moon of Tishrey), then subtract cycles and years
to  arrive at  the new  moon of  the requested  year, and  calculate its
offset into  the week.  If one  or more of the  following conditions are
true, the new year is delayed by one (or 2, see below) days:

1) The hour >= 18 (i.e. after noon);
2) Day is a Tuesday, and the hour >= 9h204 in a non-leap year;
3) Day is a Monday, and the  hour >= 15h589 and the previous year
   is a leap year;
4) Day is a Sunday, a Wednesday or a Friday.

(Note that the  delay because of 1-3 may cause  another delay because of
4, and the new year would start 2 days after the new moon.  Rule 1 is to
make sure the  new moon is seen  after sunset on the first  day; rules 2
and 3 are to  prevent a double delay from creating a year  of 356 or 382
days).

Now do it again for the next year,  and you have the exact length of the
requested  year, by  which you  can  determine the  lengths of  Heshvan,
Kislev, and (by year number modulu  19, see above) Adar.  By what's left
of the day number within the year, you can find the exact date.

I hope this is not too confusing!