Holidays related to Easter
You are encouraged to solve this task according to the task description, using any language you may know.
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
Note: 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")$,
INT year months = 12;
PROC year days = (YEAR year)DAY: # Ignore 1752 for the moment #
IF month days(year, 2) = 28 THEN 365 ELSE 366 FI;
PROC month days = (YEAR year, MONTH month) INT:
(month | 31,
28 + (year %* 4 = 0 AND year %* 400 /= 0 | 1 | 0),
31, 30, 31, 30, 31, 31, 30, 31, 30, 31);
INT week days = 7; # France 1793 to 1805 had 10 day weeks! #
OP + = (DATE in date, DAY in days)DATE:
BEGIN
DAY days := in days;
DATE date := in date;
month day OF date +:= days;
WHILE days < 0 DO
year OF date -:= 1;
days +:= year days(year OF date)
OD;
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;
FORMAT week day fmt = $c("Sat", "Sun", "Mon", "Tue", "Wed", "Thu", "Fri")$; 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;
FORMAT easter related fmt = $zzzd" Easter: "f(wdmdm fmt) ", Ascension: "f(wdmdm fmt)
", Pentecost: "f(wdmdm fmt) ", Trinity: "f(wdmdm fmt)", Corpus: "f(wdmdm fmt)$;
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 (($"Christian holidays, related to Easter, for each centuary start from 400 to 2100:"l$)); FOR year FROM 400 BY 100 TO 2100 DO easter related print(year) OD;
printf (($l"Christian holidays, related to Easter, for years from 2010 to 2020:"l$)); FOR year FROM 2010 TO 2020 DO easter related print(year) OD</lang> Output:
Christian holidays, related to Easter, for each centuary start from 400 to 2100: 0400 Easter: Sun 2 Apr, Ascension: Thu 11 May, Pentecost: Sun 21 May, Trinity: Sun 28 May, Corpus: Thu 1 Jun 0500 Easter: Sun 4 Apr, Ascension: Thu 13 May, Pentecost: Sun 23 May, Trinity: Sun 30 May, Corpus: Thu 3 Jun 0600 Easter: Sun 13 Apr, Ascension: Thu 22 May, Pentecost: Sun 1 Jun, Trinity: Sun 8 Jun, Corpus: Thu 12 Jun 0700 Easter: Sun 15 Apr, Ascension: Thu 24 May, Pentecost: Sun 3 Jun, Trinity: Sun 10 Jun, Corpus: Thu 14 Jun 0800 Easter: Sun 23 Apr, Ascension: Thu 1 Jun, Pentecost: Sun 11 Jun, Trinity: Sun 18 Jun, Corpus: Thu 22 Jun 0900 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: 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