Get Shrove Tuesday in Lua - date

Question

How can I get the date of Shrove Tuesday (12/02/2013, 04/03/2014, 17/02/2015, etc.) in Lua from a supplied year? If possible, could it be explained clearly so that it can be adapted for Easter, Mother's Day, and other holidays that change each year? There are scripts available online that get Easter, but they're not explained very clearly and I don't understand how I can change them for Shrove Tuesday and other holidays.

Answer 1

According to Wikipedia, Shrove Tuesday is exactly 47 days before Easter Sunday. So the key is really just how to calculate Easter Day, a movable feast. You can modify the code to calculate Easter to get Shrove Tuesday.
function shrove_tuesday(year)
local leap_year
if year % 4 == 0 then
if year % 100 == 0 then
if year % 400 == 0 then
leap_year = true
else
leap_year = false
end
else
leap_year = true
end
else
leap_year = false
end
local a = year % 19
local b = math.floor(year / 100)
local c = year % 100
local d = math.floor(b / 4)
local e = b % 4
local f = math.floor((b + 8) / 25)
local g = math.floor((b - f + 1) / 3)
local h = (19 * a + b - d - g + 15) % 30
local i = math.floor(c / 4)
local k = c % 4
local L = (32 + 2 * e + 2 * i - h - k) %7
local m = math.floor((a + 11 * h + 22 * L) / 451)
local month = math.floor((h + L - 7 * m + 114 - 47) / 31)
local day = (h + L - 7 * m + 114 - 47) % 31 + 1
if month == 2 then --adjust dates in February
day = leap_year and day - 2 or day - 3
end
return day, month
end
The calculation seems complicated, that's because calculating Easter Day is complicated, this function is following the algorithm of Computus.
Test:
print(shrove_tuesday(2012))
print(shrove_tuesday(2013))
print(shrove_tuesday(2014))
print(shrove_tuesday(2015))
Output:
21 2
12 2
4 3
17 2
You can easily use the day and month to get formatted string using string.format("%02d/%02d/%04d", day, month, year) or whatever you need.