%------------------hebcal.sty------------------------------
%
% TeX & LaTeX MACROS FOR COMPUTING HEBREW DATE FROM GREGORIAN ONE
% ( Released: Tammuz 12, 5751 -- June 24, 1991 )
% Corrected: 15 January, 1992. Rama.
% by Michail Rozman, misha@iop.tartu.ew.su
% Translated to Hebrew by Rama.
%
% Please direct any comments, bugfixed, questions, etc.
% to the address above.
%
% TABLE OF CONTENTS
%
% INTRODUCTION
% REGISTERS, COMMANDS AND MACROS FOR HEBREW DATE FORMATTING
% AUXILIARY MACROS
% GREGORIAN PART
% HEBREW PART
%
% *******************************************
% * INTRODUCTION *
% *******************************************
%
% The Hebrew calendar is inherently complicated:
% It is lunisolar -- each year starts close to the
% autumn equinox, but each month must strictly start
% at a new moon. Thus Hebrew calendar must be harmonized
% simultaneously with both lunar and solar events.
% In addition, for reasons of the religious practice, the
% year cannot start on Sunday, Wednesday or Friday.
%
% For the full description of Hebrew calendar and for
% the list of references see:
%
% Nachum Dershowitz and Edward M. Reingold,
% "Calendrical Calculations", Software--Pract.Exper.,
% vol. 20 (9), pp.899--928 (September 1990)
% C translation of LISP programs from the above article
% available from Mr. Wayne Geiser, geiser%pictel@uunet.uu.net
%
% The 4th distribution ( July 1989 ) of hdate/hcal ( Hebrew
% calendar programs similar to UNIX date/cal ) by
% Mr. Amos Shapir, amos@shum.huji.ac.il , contains short
% and very clear description of algorithms.
%
\catcode`@=11
% *******************************************
% * REGISTERS, COMMAND, FORMATTING MACROS *
% *******************************************
%
% The command \Hebrewtoday produces today's date for Hebrew
% calendar. It is similar to the \today command of the LETTER
% style. In addition three numerical registers \Hebrewday
% \Hebrewmonth and \Hebrewyear are set.
% For setting this registers without producing of date string
% command \Hebrewsetreg can be used.
% The command \Hebrewdate{Gday}{Gmonth}{Gyear} produces Hebrew
% calendar date corresponding to Gregorian date Gday.Gmonth.Gyear.
% Three numerical registers \Hebrewday \Hebrewmonth and
% \Hebrewyear are set.
% For converting arbitrary Gregorian date Gday.Gmonth.Gyear
% to Hebrew date Hday.Hmonth.Hyear without producing date string
% the command:
% \HebrewFromGregorian{Gday}{Gmonth}{Gyear}{Hday}{Hmonth}{Hyear}
% can be used.
%
\newcount\Hebrewday \newcount\Hebrewmonth \newcount\Hebrewyear
%
%
% \Hebrewtoday
% ============
% Today's date in hebrew calendar
\def\Hebrewtoday{%
\HebrewFromGregorian{\day}{\month}{\year}
{\Hebrewday}{\Hebrewmonth}{\Hebrewyear}%
\HebrewDayName{\Hebrewday} \HebrewMonthName{\Hebrewmonth}{\Hebrewyear}, zyp"a%
% \HebrewMonthName{\Hebrewmonth}{\Hebrewyear} \number\Hebrewday, \ %
% \number\Hebrewyear%
}%
\let\hebrewtoday=\Hebrewtoday
%
% \Hebrewsetreg
% ============
% Set registers: today's date in hebrew calendar
\def\Hebrewsetreg{%
\HebrewFromGregorian{\day}{\month}{\year}
{\Hebrewday}{\Hebrewmonth}{\Hebrewyear}%
}%
%
% \Hebrewdate{Gday}{Gmonth}{Gyear}
% ================================
% Hebrew calendar date corresponding to Gregorian Gday.Gmonth.Gyear
\def\Hebrewdate #1#2#3{%
\HebrewFromGregorian{#1}{#2}{#3}
{\Hebrewday}{\Hebrewmonth}{\Hebrewyear}%
\HebrewDayName{\Hebrewday} \HebrewMonthName{\Hebrewmonth}{\Hebrewyear}, $\number\Hebrewyear$%
% \HebrewMonthName{\Hebrewmonth}{\Hebrewyear} \number\Hebrewday, \ %
% \number\Hebrewyear%
}%
%
% TO PREPARE ANOTHER LANGUAGE VERSION CHANGE HERE !!!
%
% \HebrewMonthName{month}{year}
% ===============================
% Name of month in the `year'
\def\HebrewMonthName #1#2{%
\ifnum #1 = 7%
\CheckLeapHebrewYear{#2}%
\if@HebrewLeap `cx a' \else `cx \fi%
\else%
\ifcase #1%
Dummy \or%
zyxi \or%
gyeo \or%
kqle \or%
haz \or%
yah \or%
`cx `' \or%
`cx a' \or%
piqo \or%
`iix \or%
qieo \or%
znef \or%
`a \or%
`lel %
\fi %
\fi %
}%
%
% \HebrewDayName{day}
% ===============================
% Name of day in Hebrew letters.
%
\def\HebrewDayName #1{
\ifcase #1%
Dummy \or%
%Dummy \or%
`' \or%
a' \or%
b' \or%
c' \or%
d' \or%
e' \or%
f' \or%
g' \or%
h' \or%
i' \or%
i`' \or%
ia' \or%
ib' \or%
ic' \or%
he' \or%
hf' \or%
if' \or%
ig' \or%
ih' \or%
k' \or%
k`' \or%
ka' \or%
kb' \or%
kc' \or%
kd' \or%
ke' \or%
kf' \or%
kg' \or%
kh' \or%
l' \or%
l`'%
\fi
}
%\def\HebrewMonthName #1#2{%
%\ifnum #1 = 7%
%\CheckLeapHebrewYear{#2}%
%\if@HebrewLeap Adar II \else Adar \fi%
%\else%
%\ifcase #1%
%Dummy \or%
%Tishri \or%
%Heshvan \or%
%Kislev \or%
%Tebeth \or%
%Shebat \or%
%Adar I \or%
%Adar II \or%
%Nisan \or%
%Iyar \or%
%Sivan \or%
%Tammuz \or%
%Av \or%
%Ellul%
%\fi %
%\fi %
%}%
% *******************************************
% * AUXILIARY MACROS *
% *******************************************
%
\newcount\@common
%
% \Remainder{a}{b}{c}
% ===================
% c = a%b == a - b(a/b)
\def\Remainder #1#2#3{%
#3 = #1% % c = a
\divide #3 by #2% % c = a/b
\multiply #3 by -#2% % c = -b(a/b)
\advance #3 by #1% % c = a - b(a/b)
}%
%
\newif\if@Divisible
%
% \CheckIfDivisible{a}{b}
% ==================
% Set \@Divisibletrue if a%b == 0
\def\CheckIfDivisible #1#2{%
{%
\countdef\tmp = 0% % \tmp == \count0 - temporary variable
\Remainder{#1}{#2}{\tmp}%
\ifnum \tmp = 0%
\global\@Divisibletrue%
\else%
\global\@Divisiblefalse%
\fi%
}%
}%
% *******************************************
% * GREGORIAN PART *
% *******************************************
%
\newif\if@GregorianLeap
%
% \IfGregorianLeap{year}
% ======================
% Conditional which is true if Gregorian `year' is
% a leap year:
% ( ( year%4 == 0 ) && ( year%100 != 0 ) || ( year%400 == 0 ) )
\def\IfGregorianLeap #1{%
\CheckIfDivisible{#1}{4}%
\if@Divisible%
\CheckIfDivisible{#1}{100}%
\if@Divisible%
\CheckIfDivisible{#1}{400}%
\if@Divisible%
\@GregorianLeaptrue%
\else%
\@GregorianLeapfalse%
\fi%
\else%
\@GregorianLeaptrue%
\fi%
\else%
\@GregorianLeapfalse%
\fi%
\if@GregorianLeap%
}%
%
% \GregorianDaysInPriorMonths{month}{year}{days}
% ===============================
% Number of days in months prior to `month' in the `year'
\def\GregorianDaysInPriorMonths #1#2#3{%
{%
#3 = \ifcase #1%
0 \or % % no month number 0
0 \or 31 \or 59 \or 90 \or 120 \or 151 \or %
181 \or 212 \or 243 \or 273 \or 304 \or 334%
\fi%
\IfGregorianLeap{#2}% % in leap year ...
\ifnum #1 > 2% % if month after February ...
\advance #3 by 1% % add leap day
\fi%
\fi%
\global\@common = #3%
}%
#3 = \@common%
}%
%
% \GregorianDaysInPriorYears{year}{days}
% ===============================
% Number of days since 01.01.01 in years prior to the `year'
\def\GregorianDaysInPriorYears #1#2{%
{%
\countdef\tmpc = 4% % \tmpc==\count4
\countdef\tmpb = 2% % \tmpb==\count2
\tmpb = #1%
\advance \tmpb by -1%
\tmpc = \tmpb% % \tmpc = \tmpb = year-1
\multiply \tmpc by 365% % Days in prior years =
#2 = \tmpc% % = 365*(year-1) ...
\tmpc = \tmpb%
\divide \tmpc by 4% % \tmpc = (year-1)/4
\advance #2 by \tmpc% % ... plus Julian leap days ...
\tmpc = \tmpb% %
\divide \tmpc by 100% % \tmpc = (year-1)/100
\advance #2 by -\tmpc% % ... minus century years ...
\tmpc = \tmpb%
\divide \tmpc by 400% % \tmpc = (year-1)/400
\advance #2 by \tmpc% % ... plus 4-century years.
\global\@common = #2%
}%
#2 = \@common%
}%
%
% \AbsoluteFromGregorian{day}{month}{year}{absdate}
% ======================
% Calculation of absolute date ( days since 01.01.01 ) from
% Gregorian date day.month.year
\def\AbsoluteFromGregorian #1#2#3#4{%
{%
\countdef\tmpd = 0% % \tmpd==\count0
#4 = #1% % days so far this month
\GregorianDaysInPriorMonths{#2}{#3}{\tmpd}%
\advance #4 by \tmpd% % add days in prior months
\GregorianDaysInPriorYears{#3}{\tmpd}%
\advance #4 by \tmpd% % add days in prior years
\global\@common = #4%
}%
#4 = \@common%
}%
%
\newif\if@GregorianLeap
%
% \IfGregorianLeap{year}
% ======================
% Conditional which is true if Gregorian `year' is
% a leap year:
% ( ( year%4 == 0 ) && ( year%100 != 0 ) || ( year%400 == 0 ) )
\def\IfGregorianLeap #1{%
\CheckIfDivisible{#1}{4}%
\if@Divisible%
\CheckIfDivisible{#1}{100}%
\if@Divisible%
\CheckIfDivisible{#1}{400}%
\if@Divisible%
\@GregorianLeaptrue%
\else%
\@GregorianLeapfalse%
\fi%
\else%
\@GregorianLeaptrue%
\fi%
\else%
\@GregorianLeapfalse%
\fi%
\if@GregorianLeap%
}%
%
% \GregorianDaysInPriorMonths{month}{year}{days}
% ===============================
% Number of days in months prior to `month' in the `year'
\def\GregorianDaysInPriorMonths #1#2#3{%
{%
#3 = \ifcase #1%
0 \or% % no month number 0
0 \or%
31 \or%
59 \or%
90 \or%
120 \or%
151 \or%
181 \or%
212 \or%
243 \or%
273 \or%
304 \or%
334%
\fi%
\IfGregorianLeap{#2}%
\ifnum #1 > 2% % if month after February
\advance #3 by 1% % add leap day
\fi%
\fi%
\global\@common = #3%
}%
#3 = \@common%
}%
%
% \GregorianDaysInPriorYears{year}{days}
% ===============================
% Number of days in years prior to the `year'
\def\GregorianDaysInPriorYears #1#2{%
{%
\countdef\tmpc = 4% % \tmpc==\count4
\countdef\tmpb = 2% % \tmpb==\count2
\tmpb = #1% %
\advance \tmpb by -1% %
\tmpc = \tmpb% % \tmpc = \tmpb = year-1
\multiply \tmpc by 365% % Days in prior years =
#2 = \tmpc% % = 365*(year-1) ...
\tmpc = \tmpb% %
\divide \tmpc by 4% % \tmpc = (year-1)/4
\advance #2 by \tmpc% % ... plus Julian leap days ...
\tmpc = \tmpb% %
\divide \tmpc by 100% % \tmpc = (year-1)/100
\advance #2 by -\tmpc% % ... minus century years ...
\tmpc = \tmpb% %
\divide \tmpc by 400% % \tmpc = (year-1)/400
\advance #2 by \tmpc% % ... plus 4-century years.
\global\@common = #2%
}%
#2 = \@common%
}%
%
% \AbsoluteFromGregorian{day}{month}{year}{absdate}
% ======================
% Calculation of absolute date ( days since 01.01.0001 ) from
% Gregorian date day.month.year
\def\AbsoluteFromGregorian #1#2#3#4{%
{%
\countdef\tmpd = 0% % \tmpd==\count0
#4 = #1% % days so far this month
\GregorianDaysInPriorMonths{#2}{#3}{\tmpd}%
\advance #4 by \tmpd% % add days in prior months
\GregorianDaysInPriorYears{#3}{\tmpd}%
\advance #4 by \tmpd% % add days in prior years
\global\@common = #4%
}%
#4 = \@common%
}%
% *******************************************
% * HEBREW PART *
% *******************************************
%
\newif\if@HebrewLeap
%
% \CheckLeapHebrewYear{year}
% ======================
% Set \@HebrewLeaptrue if Hebrew `year' is
% a leap year: if (1+7*year)%19 < 7 then true else false
\def\CheckLeapHebrewYear #1{%
{%
\countdef\tmpa = 0% % \tmpa==\count0
\countdef\tmpb = 1% % \tmpb==\count1
%
\tmpa = #1%
\multiply \tmpa by 7%
\advance \tmpa by 1%
\Remainder{\tmpa}{19}{\tmpb}%
\ifnum \tmpb < 7% % \tmpb = (7*year+1)%19
\global\@HebrewLeaptrue%
\else%
\global\@HebrewLeapfalse%
\fi%
}%
}%
%
% \HebrewElapsedMonths{year}{months}
% ==============================
% Number of months elapsed from the Sunday prior to the start
% of the Hebrew calendar to the mean conjunction of Tishri
% of Hebrew `year'
\def\HebrewElapsedMonths #1#2{%
{%
\countdef\tmpa = 0% % \tmpa==\count0
\countdef\tmpb = 1% % \tmpb==\count1
\countdef\tmpc = 2% % \tmpc==\count2
%
\tmpa = #1% %
\advance \tmpa by -1% %
#2 = \tmpa% % #2 = \tmpa = year-1
\divide #2 by 19% % Number of complete Meton cycles
\multiply #2 by 235% % #2 = 235*((year-1)/19)
%
\Remainder{\tmpa}{19}{\tmpb}% % \tmpa = years%19 - years this cycle
\tmpc = \tmpb% %
\multiply \tmpb by 12% %
\advance #2 by \tmpb% % add regular months this cycle
%
\multiply \tmpc by 7% %
\advance \tmpc by 1% %
\divide \tmpc by 19% % \tmpc = (1+7*((year-1)%19))/19 -
% % number of leap months this cycle
\advance #2 by \tmpc% % add leap months
%
\global\@common = #2%
}%
#2 = \@common%
}%
%
% \HebrewElapsedDays{year}{days}
% ==============================
% Number of days elapsed from the Sunday prior to the start
% of the Hebrew calendar to the mean conjunction of Tishri
% of Hebrew `year'
\def\HebrewElapsedDays #1#2{%
{%
\countdef\tmpa = 0% % \tmpa==\count0
\countdef\tmpb = 1% % \tmpb==\count1
\countdef\tmpc = 2% % \tmpc==\count2
%
\HebrewElapsedMonths{#1}{#2}% %
\tmpa = #2% %
\multiply \tmpa by 13753% %
\advance \tmpa by 5604% % \tmpa=MonthsElapsed*13758 + 5604
\Remainder{\tmpa}{25920}{\tmpc}% % \tmpc == ConjunctionParts
\divide \tmpa by 25920%
%
\multiply #2 by 29%
\advance #2 by 1%
\advance #2 by \tmpa% % #2 = 1 + MonthsElapsed*29 +
% % PartsElapsed/25920
\Remainder{#2}{7}{\tmpa}% % \tmpa == DayOfWeek
\ifnum \tmpc < 19440%
\ifnum \tmpc < 9924%
\else% % New moon at 9 h. 204 p. or later ...
\ifnum \tmpa = 2% % on Tuesday ...
\CheckLeapHebrewYear{#1}% % of a common year
\if@HebrewLeap%
\else%
\advance #2 by 1%
\fi%
\fi%
\fi%
\ifnum \tmpc < 16789%
\else% % New moon at 15 h. 589 p. or later ...
\ifnum \tmpa = 1% % on Monday ...
\advance #1 by -1%
\CheckLeapHebrewYear{#1}% % at the end of leap year
\if@HebrewLeap%
\advance #2 by 1%
\fi%
\fi%
\fi%
\else%
\advance #2 by 1% % new moon at or after midday
\fi%
%
\Remainder{#2}{7}{\tmpa}% % \tmpa == DayOfWeek
\ifnum \tmpa = 0% % if Sunday ...
\advance #2 by 1%
\else% %
\ifnum \tmpa = 3% % Wednesday ...
\advance #2 by 1%
\else%
\ifnum \tmpa = 5% % or Friday
\advance #2 by 1%
\fi%
\fi%
\fi%
\global\@common = #2%
}%
#2 = \@common%
}%
%
% \DaysInHebrewYear{year}{days}
% ==============================
% Number of days in Hebrew `year'
\def\DaysInHebrewYear #1#2{%
{%
\countdef\tmpe = 12% % \tmpe==\count12
%
\HebrewElapsedDays{#1}{\tmpe}%
\advance #1 by 1%
\HebrewElapsedDays{#1}{#2}%
\advance #2 by -\tmpe%
\global\@common = #2%
}%
#2 = \@common%
}%
%
% \HebrewDaysInPriorMonths{month}{year}{days}
% ===============================
% Number of days in months prior to `month' in the `year'
\def\HebrewDaysInPriorMonths #1#2#3{%
{%
\countdef\tmpf= 14% % \tmpf==\count14
%
#3 = \ifcase #1% % Days in prior month of regular year
0 \or% % no month number 0
0 \or% % Tishri
30 \or% % Heshvan
59 \or% % Kislev
89 \or% % Tebeth
118 \or% % Shebat
148 \or% % Adar I
148 \or% % Adar II
177 \or% % Nisan
207 \or% % Iyar
236 \or% % Sivan
266 \or% % Tammuz
295 \or% % Av
325 \or% % Elul
400% % Dummy
\fi%
\CheckLeapHebrewYear{#2}%
\if@HebrewLeap% % in leap year
\ifnum #1 > 6% % if month after Adar I
\advance #3 by 30% % add 30 days
\fi%
\fi%
\DaysInHebrewYear{#2}{\tmpf}%
\ifnum #1 > 3%
\ifnum \tmpf = 353% %
\advance #3 by -1% %
\fi% % Short Kislev
\ifnum \tmpf = 383% %
\advance #3 by -1% %
\fi% %
\fi%
%
\ifnum #1 > 2%
\ifnum \tmpf = 355% %
\advance #3 by 1% %
\fi% % Long Heshvan
\ifnum \tmpf = 385% %
\advance #3 by 1% %
\fi% %
\fi%
\global\@common = #3%
}%
#3 = \@common%
}%
%
% \AbsoluteFromHebrew{day}{month}{year}{days}
% ===============================
% Absolute date of Hebrew day,month,year
\def\AbsoluteFromHebrew #1#2#3#4{%
{%
#4 = #1%
\HebrewDaysInPriorMonths{#2}{#3}{#1}%
\advance #4 by #1% % Add days in prior months this year
\HebrewElapsedDays{#3}{#1}%
\advance #4 by #1% % Add days in prior years
\advance #4 by -1373429% % Subtract days before Gregorian 1.1.1
\global\@common = #4%
}%
#4 = \@common%
}%
%
% \HebrewFromGregorian{Gday}{Gmonth}{Gyear}{Hday}{Hmonth}{Hyear}
% ===============================
% Evaluating Hebrew date Hday,Hmonth,Hyear from
% Gregorian date Gday,Gmonth,Gyear
\def\HebrewFromGregorian #1#2#3#4#5#6{%
{%
\countdef\tmpx= 17% % \tmpx==\count17
\countdef\tmpy= 18% % \tmpy==\count18
\countdef\tmpz= 19% % \tmpz==\count19
%
#6 = #3% %
\global\advance #6 by 3761% % approximation from above
\AbsoluteFromGregorian{#1}{#2}{#3}{#4} %
\tmpz = 1 \tmpy = 1%
\AbsoluteFromHebrew{\tmpz}{\tmpy}{#6}{\tmpx}%
\ifnum \tmpx > #4% %
\global\advance #6 by -1% % Hyear = Gyear + 3760
\AbsoluteFromHebrew{\tmpz}{\tmpy}{#6}{\tmpx}%
\fi% %
\advance #4 by -\tmpx% % Days in this year
\advance #4 by 1% %
#5 = #4% %
\divide #5 by 30% % Approximation for month from below
\loop% % Search for month
\HebrewDaysInPriorMonths{#5}{#6}{\tmpx}%
\ifnum \tmpx < #4%
\advance #5 by 1%
\tmpy = \tmpx%
\repeat%
\global\advance #5 by -1%
\global\advance #4 by -\tmpy%
}%
}%
\catcode`@=12