Holidays related to Easter
Calculate the date of Easter, Ascension Thursday, Pentecost, Trinity Sunday & Corpus Christi feast.
You are encouraged to solve this task according to the task description, using any language you may know.
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
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