Holidays related to Easter: Difference between revisions

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Calculate the date of Easter, Ascension Thursday, Pentecost, Trinity Sunday & Corpus Christi feast.

As the example calculate for the first year of each century from 400 to 2100 CE and also for years 2010 to 2020 CE.

Note: From year 325 CE on, Easter Sunday is the Sunday following the ﬁrst Ecclesiastical full moon not earlier than the equinox date in 325 — 21 March. The Ecclesiastical full moon does not always correspond to the astronomical full moon since in 325 ﬁne details of Lunar dynamics were not yet fully understood.

ALGOL 68

Works with: ALGOL 68 version Revision 1 - no extensions to language used

Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny

Note: Base code specimen extracted from Algol 68 Genie Documentation Part III - Example a68g programs. <lang algol68>MODE YEAR = INT, MONTH = INT, WEEK = INT, DAY = INT;

MODE DATE = STRUCT(

 YEAR year,  #DAY year day, #
 MONTH month, DAY month day,#
 WEEK week,  #DAY week day);

FORMAT mon fmt = $c("Jan", "Feb", "Mar", "Apr", "May", "Jun",

                        "Jul", "Aug", "Sep", "Oct", "Nov", "Dec")$,

FORMAT week day fmt = $c("Sat", "Sun", "Mon", "Tue", "Wed", "Thu", "Fri")$;

PROC year days = (YEAR year)DAY: # Ignore 1752 CE for the moment #

 ( month days(year, 2) = 28 | 365 | 366 );

PROC month days = (YEAR year, MONTH month) INT:

 ( month | 31,
           28 + ABS(year MOD 4 NE 0 OR year MOD 400 EQ 0),
           31, 30, 31, 30, 31, 31, 30, 31, 30, 31);

INT year months = 12; INT week days = 7; # France 1793 to 1805 had 10 day weeks! #

OP + = (DATE in date, DAY in days)DATE:

   BEGIN # todo: eliminate loops, handle year <= 1752 #
      DAY days := in days;
      DATE date := in date;
   # Normalize the days to be less then 1 year #
      WHILE days < 0 DO
        year OF date -:= 1;
        days +:= year days(year OF date)
      OD;
      WHILE days > year days(year OF date) DO
        days -:= year days(year OF date);
        year OF date +:= 1
      OD;
      month day OF date +:= days;
   # Normalize the days to be the same month #
      WHILE month day OF date > month days(year OF date, month OF date) DO
         month day OF date -:= month days(year OF date, month OF date);
         month OF date +:= 1;
         IF month OF date > year months THEN
            month OF date -:= year months;
            year OF date +:= 1
         FI
      OD;
      week day OF date := week day(date);
      date
   END;

OP +:= = (REF DATE date, DAY in days)DATE:

  date := date + in days;

PROC easter = (YEAR year)DATE:

  BEGIN
     COMMENT
        Easter date algorithm from J.M. Oudin (1940), reprinted in:
        P.K. Seidelmann ed., "Explanatory Supplement to the Astronomical
        Almanac" [1992] (Chapter 12, "Calendars", by L.E. Doggett)
     COMMENT
     DATE date; year OF date := year;
     INT c = year % 100, n = year %* 19;
     INT i := (c - c % 4 - (c - (c - 17) % 25) % 3 + 19 * n + 15) %* 30;
     i -:= (i % 28) * (1 - (i % 28) * (29 % (i + 1)) * ((21 - n) % 11));
     INT l = i - (year + year % 4 + i + 2 - c + c % 4) %* 7;
     month OF date := 3 + (l + 40) % 44;
     month day OF date := l + 28 - 31 * (month OF date % 4);
     week day OF date := week day(date);
     date
  END;

PROC week day = (DATE date)DAY:

  # Zeller’s Congruence algorithm from 1887. #
  BEGIN
     INT year := year OF date, month := month OF date, month day := month day OF date, c;
     (month <= 2 | (month +:= 12, year -:= 1));
     c := year OVER 100;
     year %*:= 100;
     1 + (month day + ((month + 1) * 26) OVER 10
        + year + year OVER 4 + c OVER 4 - 2 * c) %* 7
  END;

FORMAT wdmdm fmt = $f(week day fmt)z-dxf(mon fmt)$,

MODE EASTERRELATED = STRUCT(DATE easter, ascension, pentecost, trinity, corpus christi);

PROC easter related init = (YEAR year)EASTERRELATED: BEGIN

 DATE date;
 EASTERRELATED holidays;

Easter date, always a Sunday. #

  easter OF holidays := date := easter(year);

Ascension day is 39 days after Easter.#

  ascension OF holidays := ( date +:= 39);

Pentecost is 10 days after Ascension day.#

  pentecost OF holidays := date +:= 10;

Trinity is 7 days after Pentecost.#

  trinity OF holidays := date +:= 7;

Corpus Christi is 4 days after Trinity.#

  corpus christi OF holidays := date +:= 4;
  holidays

END;

Note: Y10K bug here... :-) #

FORMAT easter related fmt = $g(-4)" Easter: "f(wdmdm fmt) ", Ascension: "f(wdmdm fmt)

   ", Pentecost: "f(wdmdm fmt) ", Trinity: "f(wdmdm fmt)", Corpus: "f(wdmdm fmt)$;

PROC easter related print = (YEAR year)VOID: BEGIN

 EASTERRELATED holidays = easter related init(year);
 PROC wdmdm = (DATE date)STRUCT(DAY week day, DAY month day, MONTH month):
   (week day OF date, month day OF date, month OF date);
 printf((easter related fmt, year,
    wdmdm(easter OF holidays),  wdmdm(ascension OF holidays), wdmdm(pentecost OF holidays),
    wdmdm(trinity OF holidays), wdmdm(corpus christi OF holidays),
 $l$))

END;

printf (($"Christian holidays, related to Easter, for each centennial from 400 to 2100 CE:"l$)); FOR year FROM 400 BY 100 TO 2100 DO easter related print(year) OD;

printf (($l"Christian holidays, related to Easter, for years from 2010 to 2020 CE:"l$)); FOR year FROM 2010 TO 2020 DO easter related print(year) OD</lang> Output:

Christian holidays, related to Easter, for each centennial from 400 to 2100 CE:
 400 Easter: Sun  2 Apr, Ascension: Thu 11 May, Pentecost: Sun 21 May, Trinity: Sun 28 May, Corpus: Thu  1 Jun
 500 Easter: Sun  4 Apr, Ascension: Thu 13 May, Pentecost: Sun 23 May, Trinity: Sun 30 May, Corpus: Thu  3 Jun
 600 Easter: Sun 13 Apr, Ascension: Thu 22 May, Pentecost: Sun  1 Jun, Trinity: Sun  8 Jun, Corpus: Thu 12 Jun
 700 Easter: Sun 15 Apr, Ascension: Thu 24 May, Pentecost: Sun  3 Jun, Trinity: Sun 10 Jun, Corpus: Thu 14 Jun
 800 Easter: Sun 23 Apr, Ascension: Thu  1 Jun, Pentecost: Sun 11 Jun, Trinity: Sun 18 Jun, Corpus: Thu 22 Jun
 900 Easter: Sun 28 Mar, Ascension: Thu  6 May, Pentecost: Sun 16 May, Trinity: Sun 23 May, Corpus: Thu 27 May
1000 Easter: Sun 30 Mar, Ascension: Thu  8 May, Pentecost: Sun 18 May, Trinity: Sun 25 May, Corpus: Thu 29 May
1100 Easter: Sun  8 Apr, Ascension: Thu 17 May, Pentecost: Sun 27 May, Trinity: Sun  3 Jun, Corpus: Thu  7 Jun
1200 Easter: Sun  9 Apr, Ascension: Thu 18 May, Pentecost: Sun 28 May, Trinity: Sun  4 Jun, Corpus: Thu  8 Jun
1300 Easter: Sun 18 Apr, Ascension: Thu 27 May, Pentecost: Sun  6 Jun, Trinity: Sun 13 Jun, Corpus: Thu 17 Jun
1400 Easter: Sun 20 Apr, Ascension: Thu 29 May, Pentecost: Sun  8 Jun, Trinity: Sun 15 Jun, Corpus: Thu 19 Jun
1500 Easter: Sun  1 Apr, Ascension: Thu 10 May, Pentecost: Sun 20 May, Trinity: Sun 27 May, Corpus: Thu 31 May
1600 Easter: Sun  2 Apr, Ascension: Thu 11 May, Pentecost: Sun 21 May, Trinity: Sun 28 May, Corpus: Thu  1 Jun
1700 Easter: Sun 11 Apr, Ascension: Thu 20 May, Pentecost: Sun 30 May, Trinity: Sun  6 Jun, Corpus: Thu 10 Jun
1800 Easter: Sun 13 Apr, Ascension: Thu 22 May, Pentecost: Sun  1 Jun, Trinity: Sun  8 Jun, Corpus: Thu 12 Jun
1900 Easter: Sun 15 Apr, Ascension: Thu 24 May, Pentecost: Sun  3 Jun, Trinity: Sun 10 Jun, Corpus: Thu 14 Jun
2000 Easter: Sun 23 Apr, Ascension: Thu  1 Jun, Pentecost: Sun 11 Jun, Trinity: Sun 18 Jun, Corpus: Thu 22 Jun
2100 Easter: Sun 28 Mar, Ascension: Thu  6 May, Pentecost: Sun 16 May, Trinity: Sun 23 May, Corpus: Thu 27 May

Christian holidays, related to Easter, for years from 2010 to 2020 CE:
2010 Easter: Sun  4 Apr, Ascension: Thu 13 May, Pentecost: Sun 23 May, Trinity: Sun 30 May, Corpus: Thu  3 Jun
2011 Easter: Sun 24 Apr, Ascension: Thu  2 Jun, Pentecost: Sun 12 Jun, Trinity: Sun 19 Jun, Corpus: Thu 23 Jun
2012 Easter: Sun  8 Apr, Ascension: Thu 17 May, Pentecost: Sun 27 May, Trinity: Sun  3 Jun, Corpus: Thu  7 Jun
2013 Easter: Sun 31 Mar, Ascension: Thu  9 May, Pentecost: Sun 19 May, Trinity: Sun 26 May, Corpus: Thu 30 May
2014 Easter: Sun 20 Apr, Ascension: Thu 29 May, Pentecost: Sun  8 Jun, Trinity: Sun 15 Jun, Corpus: Thu 19 Jun
2015 Easter: Sun  5 Apr, Ascension: Thu 14 May, Pentecost: Sun 24 May, Trinity: Sun 31 May, Corpus: Thu  4 Jun
2016 Easter: Sun 27 Mar, Ascension: Thu  5 May, Pentecost: Sun 15 May, Trinity: Sun 22 May, Corpus: Thu 26 May
2017 Easter: Sun 16 Apr, Ascension: Thu 25 May, Pentecost: Sun  4 Jun, Trinity: Sun 11 Jun, Corpus: Thu 15 Jun
2018 Easter: Sun  1 Apr, Ascension: Thu 10 May, Pentecost: Sun 20 May, Trinity: Sun 27 May, Corpus: Thu 31 May
2019 Easter: Sun 21 Apr, Ascension: Thu 30 May, Pentecost: Sun  9 Jun, Trinity: Sun 16 Jun, Corpus: Thu 20 Jun
2020 Easter: Sun 12 Apr, Ascension: Thu 21 May, Pentecost: Sun 31 May, Trinity: Sun  7 Jun, Corpus: Thu 11 Jun

Tcl

<lang tcl>package require Tcl 8.5; # Advanced date handling engine

Easter computation code from http://www.assa.org.au/edm.html

proc EasterDate year {

   set FirstDig [expr {$year / 100}]
   set Remain19 [expr {$year % 19}]

   # calculate Paschal Full Moon date
   set temp [expr {($FirstDig - 15)/2 + 202 - 11*$Remain19}]
   if {$FirstDig in {21 24 25 27 28 29 30 31 32 34 35 38}} {

incr temp -1

   } elseif {$FirstDig in {33 36 37 39 40}} {

incr temp -2

   }
   set temp [expr {$temp % 30}]

   set tA [expr {$temp + 21}]
   if {$temp == 29} {incr tA -1}
   if {$temp == 28 && $Remain19 > 10} {incr tA -1}

   # find the next Sunday
   set tB [expr {($tA - 19) % 7}]

   set tC [expr {(40 - $FirstDig) % 4}]
   if {$tC == 3} {incr tC}
   if {$tC > 1} {incr tC}

   set temp [expr {$year % 100}]
   set tD [expr {($temp + $temp/4) % 7}]

   set tE [expr {((20 - $tB - $tC - $tD) % 7) + 1}]
   set d [expr {$tA + $tE}]

   # return the date
   if {$d > 31} {

return [format "%02d April %04d" [expr {$d - 31}] $year]

   } else {

return [format "%02d March %04d" $d $year]

}

Use the Easter calculator to work out the data for the feasts

proc DateInfo year {

   set fields [format %4d: $year]
   set easter [clock scan [EasterDate $year] -format "%d %B %Y"]
   foreach {name delta} {

Easter 0 Ascension 39 Pentecost 49 Trinity 56 Corpus 60

} {

set when [clock add $easter $delta days] lappend fields [clock format $when -format "${name}: %d %b"]

   }
   return [join $fields \t]

}

Print the required info

puts "Christian holidays, related to Easter, for each centennial from 400 to 2100 CE:" for {set year 400} {$year <= 2100} {incr year 100} {

   puts [DateInfo $year]

} puts "" puts "Christian holidays, related to Easter, for years from 2010 to 2020 CE:" for {set year 2010} {$year <= 2020} {incr year} {

   puts [DateInfo $year]

}</lang> Output:

Christian holidays, related to Easter, for each centennial from 400 to 2100 CE:
400:	Easter: 02 Apr	Ascension: 11 May	Pentecost: 21 May	Trinity: 28 May	Corpus: 01 Jun
500:	Easter: 04 Apr	Ascension: 13 May	Pentecost: 23 May	Trinity: 30 May	Corpus: 03 Jun
600:	Easter: 13 Apr	Ascension: 22 May	Pentecost: 01 Jun	Trinity: 08 Jun	Corpus: 12 Jun
700:	Easter: 15 Apr	Ascension: 24 May	Pentecost: 03 Jun	Trinity: 10 Jun	Corpus: 14 Jun
800:	Easter: 23 Apr	Ascension: 01 Jun	Pentecost: 11 Jun	Trinity: 18 Jun	Corpus: 22 Jun
900:	Easter: 28 Mar	Ascension: 06 May	Pentecost: 16 May	Trinity: 23 May	Corpus: 27 May
1000:	Easter: 30 Mar	Ascension: 08 May	Pentecost: 18 May	Trinity: 25 May	Corpus: 29 May
1100:	Easter: 08 Apr	Ascension: 17 May	Pentecost: 27 May	Trinity: 03 Jun	Corpus: 07 Jun
1200:	Easter: 09 Apr	Ascension: 18 May	Pentecost: 28 May	Trinity: 04 Jun	Corpus: 08 Jun
1300:	Easter: 18 Apr	Ascension: 27 May	Pentecost: 06 Jun	Trinity: 13 Jun	Corpus: 17 Jun
1400:	Easter: 20 Apr	Ascension: 29 May	Pentecost: 08 Jun	Trinity: 15 Jun	Corpus: 19 Jun
1500:	Easter: 01 Apr	Ascension: 10 May	Pentecost: 20 May	Trinity: 27 May	Corpus: 31 May
1600:	Easter: 02 Apr	Ascension: 11 May	Pentecost: 21 May	Trinity: 28 May	Corpus: 01 Jun
1700:	Easter: 11 Apr	Ascension: 20 May	Pentecost: 30 May	Trinity: 06 Jun	Corpus: 10 Jun
1800:	Easter: 13 Apr	Ascension: 22 May	Pentecost: 01 Jun	Trinity: 08 Jun	Corpus: 12 Jun
1900:	Easter: 15 Apr	Ascension: 24 May	Pentecost: 03 Jun	Trinity: 10 Jun	Corpus: 14 Jun
2000:	Easter: 23 Apr	Ascension: 01 Jun	Pentecost: 11 Jun	Trinity: 18 Jun	Corpus: 22 Jun
2100:	Easter: 28 Mar	Ascension: 06 May	Pentecost: 16 May	Trinity: 23 May	Corpus: 27 May

Christian holidays, related to Easter, for years from 2010 to 2020 CE:
2010:	Easter: 04 Apr	Ascension: 13 May	Pentecost: 23 May	Trinity: 30 May	Corpus: 03 Jun
2011:	Easter: 24 Apr	Ascension: 02 Jun	Pentecost: 12 Jun	Trinity: 19 Jun	Corpus: 23 Jun
2012:	Easter: 08 Apr	Ascension: 17 May	Pentecost: 27 May	Trinity: 03 Jun	Corpus: 07 Jun
2013:	Easter: 31 Mar	Ascension: 09 May	Pentecost: 19 May	Trinity: 26 May	Corpus: 30 May
2014:	Easter: 20 Apr	Ascension: 29 May	Pentecost: 08 Jun	Trinity: 15 Jun	Corpus: 19 Jun
2015:	Easter: 05 Apr	Ascension: 14 May	Pentecost: 24 May	Trinity: 31 May	Corpus: 04 Jun
2016:	Easter: 27 Mar	Ascension: 05 May	Pentecost: 15 May	Trinity: 22 May	Corpus: 26 May
2017:	Easter: 16 Apr	Ascension: 25 May	Pentecost: 04 Jun	Trinity: 11 Jun	Corpus: 15 Jun
2018:	Easter: 01 Apr	Ascension: 10 May	Pentecost: 20 May	Trinity: 27 May	Corpus: 31 May
2019:	Easter: 21 Apr	Ascension: 30 May	Pentecost: 09 Jun	Trinity: 16 Jun	Corpus: 20 Jun
2020:	Easter: 12 Apr	Ascension: 21 May	Pentecost: 31 May	Trinity: 07 Jun	Corpus: 11 Jun