Module:Sandbox/DixonD/Datetime/Julian

local Error = require('Module:Error');

local this = {};

function this.julianDayOfDate(date)

-- http://www.tondering.dk/claus/cal/julperiod.php#formula

local y = date.year + 4799; -- Set epoch in 1 March -4800, but counting months from January as the 10th month of previous year.

local m = y * 12 + date.month + 9; -- Total number of months since epoch (January = 10, December = 21).

y = math.floor(m / 12); m = m - y * 12; -- Split total months into relative months...

return

math.floor(y * 1461 / 4) -- Julian cycle of 1461 days every 4 years.

+ math.floor((m + 4) * 153 / 5) -- Days in relative month (need to substract 122 at end).

+ date.day -- Additional days (need to substract 1 at end).

+ (date.hour - 12) / 24 -- The time part.

+ date.minute / 1440

+ date.second / 86400 -- (leap seconds ignored, every day assumed to be 86400 seconds exactly).

- 32204; -- Final substractive constant 32204 == 32081 + 122 + 1.

end;

function this.dateOfJulianDay(JD)

-- Check parameters.

if JD == nil then

return Error.error{"Parameter 1=Julian day is either missing or has wrong format!"};

end;

local date = {};

date.weekday = JD + 0.5 - math.floor((JD + 0.5) / 7) * 7; -- 0 = Monday, 6 = Sunday.

-- See fr:Formules de calcul du calendrier grégorien on Wikipedia for explained details and intermediate values in test cases.

JD = JD + 32081.5;

local j = math.floor(JD); -- no rounding performed for the precision of time; if you need it, round the JD before calling this method.

-- 1461 days per cycle of 4 years (no adjustment needed).

local b = math.floor(dc / 1461);

local db = dc - b * 1461;

-- 365 days per cycle of 1 year (cycle numbers: 0 to 4; but 4 is reduced to 3, making sometimes the last cycle longer longer by 1 day).

-- Note: for a in 0..4: math.min(a, 3) is equal to math.floor((a * 3 + 1) / 4); this avoids conditional branches:

-- 0 -> 0 = floor(1 / 4); 1 -> 1 = floor(4 / 4); 2 -> 2 = floor(7 / 4); 3 -> 3 = floor(10 / 4); 4 -> 4 = floor(13 / 4)

local a = math.floor((math.floor(db / 365) * 3 + 1) / 4);

local da = db - a * 365;

-- Relative date since epoch (1 March -4800).

local y = b * 4 + a;

local m = math.floor((da * 5 + 308) / 153) - 2;

local d = da - math.floor((m + 4) * 153 / 5) + 122;

-- Actual Julian date.

date.year = y - 4800 + math.floor((m + 2) / 12);

date.month = m - math.floor((m + 2) / 12) * 12 + 3;

date.day = d + 1;--//Test:1

-- Actual time of day (leap seconds ignored, every day assumed to be 86400 seconds exactly).

j = (JD + 0.5 - math.floor(JD + 0.5)) * 24;

date.hour = math.floor(j);

j = (j - date.hour) * 60;

date.minute = math.floor(j);

date.second = (j - date.minute) * 60; -- No rounding performed; this includes fractions of seconds.

return date;

end;

function this.julianDay(year, month, day, hour, minute, second)

-- Check parameters and set defaults.

if year == nil then

return Error.error{"Parameter 1=year is either missing or has wrong format!"};

end;

if month == nil then month = 1; end;

if day == nil then day = 1; end;

if hour == nil then hour = 12; end;

if minute == nil then minute = 0; end;

if second == nil then second = 0; end;

return this.julianDayOfDate({year = year, month = month, day = day, hour = hour, minute = minute, second = second});

end;

-- Basic formatting (for debugging only ?).

function this.wikiDateOfJulianDay(JD)

-- Check parameters.

if JD == nil then

return Error.error{"Parameter 1=Julian day is either missing or has wrong format!"};

end;

local date = this.dateOfJulianDay(JD);

return tostring(date.year)

.. "|" .. tostring(date.month)

.. "|" .. tostring(date.day)

.. "|" .. tostring(date.hour)

.. "|" .. tostring(date.minute)

.. "|" .. tostring(date.second);

end;

-- English formatting (for display or tests ? not internationalized).

function this.EnglishDateOfJulianDay(JD)

-- Check parameters.

if JD == nil then

return Error.error{"Parameter 1=Julian day is either missing or has wrong format!"};

end;

local date = this:dateOfJulianDay(JD);

local s = "";

if (date >= 0 and date.day < 10) then

s = s .. "0" .. tostring(date.day);

else

s = s .. tostring(date.day);

end

local months = {

"January", "February", "March", "April", "May", "June",

"July", "August", "September", "October", "November", "December"

};

s = s .. " " .. months[date.month - 1] .. " ";

if (date.year < 0) then

s = s .. tostring(1 - date.year) .. " BC ";

else

s = s .. tostring(date.year) .. " AD ";

end

if (date.hour >= 0 and date.hour < 10) then

s = s .. "0" .. tostring(date.hour) .. ":";

else

s = s .. tostring(date.hour) .. ":";

end

if (date.minute >= 0 and date.minute < 10) then

s = s .. "0" .. tostring(date.minute) .. ":";

else

s = s .. tostring(date.minute) .. ":";

end

if (date.second >= 0 and date.second < 10) then

s = s .. "0" .. tostring(date.second);

else

s = s .. tostring(date.second);

end

return s .. " UTC";

end;

function this.yearOfJulianDay(JD)

-- Check parameters.

if JD == nil then

return Error.error{"Parameter 1=Julian day is either missing or has wrong format!"};

end;

return this.dateOfJulianDay(JD).year;

end;

function this.monthOfJulianDay(JD)

-- Check parameters.

if JD == nil then

return Error.error{"Parameter 1=Julian day is either missing or has wrong format!"};

end;

return this.dateOfJulianDay(JD).month;

end;

function this.dayOfJulianDay(JD)

-- Check parameters.

if JD == nil then

return Error.error{"Parameter 1=Julian day is either missing or has wrong format!"};

end;

return this.dateOfJulianDay(JD).day;

end;

function this.weekdayOfJulianDay(JD)

-- Check parameters.

if JD == nil then

return Error.error{"Parameter 1=Julian day is either missing or has wrong format!"};

end;

return this.dateOfJulianDay(JD).weekday;

end;

function this.hourOfJulianDay(JD)

-- Check parameters.

if JD == nil then

return Error.error{"Parameter 1=Julian day is either missing or has wrong format!"};

end;

return this.dateOfJulianDay(JD).hour;

end;

function this.minuteOfJulianDay(JD)

-- Check parameters.

if JD == nil then

return Error.error{"Parameter 1=Julian day is either missing or has wrong format!"};

end;

return this.dateOfJulianDay(JD).minute;

end;

function this.secondOfJulianDay(JD)

-- Check parameters.

if JD == nil then

return Error.error{"Parameter 1=Julian day is either missing or has wrong format!"};

end;

return this.dateOfJulianDay(JD).second;

end;

return this;