local p = {}

function LastDayOfGregorianMonth(month, year)

    if month == 2 then    if ((((year % 4) == 0) and ((year % 100) ~= 0)) or ((year % 400) == 0)) then      return 29;    else      return 28;    end  elseif month == 2 or month == 4 or month == 6 or month == 9 or month == 11 then    return 30;  else     return 31;  end

end

GregorianDate = {}

GregorianDate.__index = GregorianDate

function GregorianDate.create(month, day, year)

   local gregoriandate = {}             -- our new object   setmetatable(gregoriandate,GregorianDate)  -- make GregorianDate handle lookup   -- initialize our object    gregoriandate.month = month --  1 == January, ..., 12 == December    gregoriandate.day = day     -- 1..LastDayOfGregorianMonth(month, year)    gregoriandate.year = year   --    return gregoriandate

end

function GregorianDateFromAbsolute(d)

  -- Computes the Gregorian date from the absolute date.        -- Search forward year by year from approximate year    local year = math.floor(d/366);    while (d >= AbsoluteFromGregorianDate(GregorianDate.create(1,1,year+1))) do      year = year + 1;    end        -- Search forward month by month from January    local month = 1;    while (d > AbsoluteFromGregorianDate(GregorianDate.create(month, LastDayOfGregorianMonth(month,year), year))) do      month = month + 1;    end        local day = d - AbsoluteFromGregorianDate(GregorianDate.create(month,1,year)) + 1;        return GregorianDate.create(month, day, year)

end

function AbsoluteFromGregorianDate(gregoriandate)

    local N = gregoriandate.day;           -- days this month        -- days in prior months this year    local m = gregoriandate.month - 1;    while (m > 0) do       N = N + LastDayOfGregorianMonth(m, gregoriandate.year);      m = m - 1;    end        return (N                    -- days this year       + 365 * (gregoriandate.year - 1)   -- days in previous years ignoring leap days       + math.floor((gregoriandate.year - 1)/4)       -- Julian leap days before this year...       - math.floor((gregoriandate.year - 1)/100)     -- ...minus prior century years...       + math.floor((gregoriandate.year - 1)/400));   -- ...plus prior years divisible by 400

end

HebrewEpoch = -1373429 -- Absolute date of start of Hebrew calendar

function HebrewLeapYear(year)

  if ((((7 * year) + 1) % 19) < 7)  then    return 1;  else    return 0;  end

end

function LastMonthOfHebrewYear(year)

  if (HebrewLeapYear(year) == 1) then    return 13;  else    return 12;  end

end

function HebrewCalendarElapsedDays(year)

    local MonthsElapsed =    (235 * math.floor((year - 1) / 19))           -- Months in complete cycles so far.    + (12 * ((year - 1) % 19))          -- Regular months in this cycle.    + math.floor((7 * ((year - 1) % 19) + 1) / 19); -- Leap months this cycle  local PartsElapsed = 204 + 793 * (MonthsElapsed % 1080);  local HoursElapsed =    5 + 12 * MonthsElapsed + 793 * math.floor(MonthsElapsed  / 1080)    + math.floor(PartsElapsed / 1080);  local ConjunctionDay = 1 + 29 * MonthsElapsed + math.floor(HoursElapsed / 24);  local ConjunctionParts = 1080 * (HoursElapsed % 24) + PartsElapsed % 1080;  local AlternativeDay = 0;  if ((ConjunctionParts >= 19440)        -- If new moon is at or after midday,      or (((ConjunctionDay % 7) == 2)    -- ...or is on a Tuesday...          and (ConjunctionParts >= 9924)  -- at 9 hours, 204 parts or later...          and (HebrewLeapYear(year)) == 0)   -- ...of a common year,      or (((ConjunctionDay % 7) == 1)    -- ...or is on a Monday at...          and (ConjunctionParts >= 16789) -- 15 hours, 589 parts or later...          and (HebrewLeapYear(year - 1) == 1))) then -- at the end of a leap year    -- Then postpone Rosh HaShanah one day    AlternativeDay = ConjunctionDay + 1;  else    AlternativeDay = ConjunctionDay;  end    if (((AlternativeDay % 7) == 0)-- If Rosh HaShanah would occur on Sunday,      or ((AlternativeDay % 7) == 3)     -- or Wednesday,      or ((AlternativeDay % 7) == 5))    -- or Friday    -- Then postpone it one (more) day  then    return (1+ AlternativeDay);  else    return AlternativeDay;  end

end

function DaysInHebrewYear(year)

    return ((HebrewCalendarElapsedDays(year + 1)) -          (HebrewCalendarElapsedDays(year)));

end

function LongHeshvan(year)

    if ((DaysInHebrewYear(year) % 10) == 5)  then    return 1;  else    return 0;  end

end

function ShortKislev(year)

    if ((DaysInHebrewYear(year) % 10) == 3)  then    return 1;  else    return 0;  end

end

function LastDayOfHebrewMonth(month, year)

    if ((month == 2)      or (month == 4)      or (month == 6)      or ((month == 8) and LongHeshvan(year) == 0)      or ((month == 9) and ShortKislev(year) == 1)      or (month == 10)      or ((month == 12) and (HebrewLeapYear(year) == 0))      or (month == 13))  then    return 29;  else    return 30;  end

end

HebrewDate = {}

HebrewDate.__index = HebrewDate

function HebrewDate.create(month, day, year)

   local hebrewdate = {}             -- our new object   setmetatable(hebrewdate,HebrewDate)  -- make HebrewDate handle lookup   -- initialize our object    hebrewdate.month = month -- 1...    hebrewdate.day = day     -- 1..LastMonthOfHebrewYear(year)    hebrewdate.year = year   -- 1..LastDayOfHebrewMonth(month, year)        return hebrewdate

end

function HebrewDateFromAbsolute(d)

  -- Computes the Hebrew date from the absolute date.    local year = math.floor((d + HebrewEpoch) / 366); -- Approximation from below.    -- Search forward for year from the approximation.    while (d >= AbsoluteFromHebrewDate(HebrewDate.create(7,1,year + 1)))    do      year = year + 1;    end    -- Search forward for month from either Tishri or Nisan.    local month = 0    if (d < AbsoluteFromHebrewDate(HebrewDate.create(1, 1, year))) then        month = 7;  --  Start at Tishri    else      month = 1;  --  Start at Nisan    end        while (d > AbsoluteFromHebrewDate(HebrewDate.create(month, (LastDayOfHebrewMonth(month,year)), year))) do        month = month + 1;      end    -- Calculate the day by subtraction.    local day = d - AbsoluteFromHebrewDate(HebrewDate.create(month, 1, year)) + 1;    return HebrewDate.create(month, day, year)  end

function AbsoluteFromHebrewDate(hebrewdate)

    -- Computes the absolute date of Hebrew date.    local DayInYear = hebrewdate.day; -- Days so far this month.    if (hebrewdate.month < 7) then -- Before Tishri, so add days in prior months                     -- this year before and after Nisan.      local m = 7;      while (m <= (LastMonthOfHebrewYear(hebrewdate.year))) do        DayInYear = DayInYear + LastDayOfHebrewMonth(m, hebrewdate.year);        m = m + 1;      end            m = 1;      while (m < hebrewdate.month) do        DayInYear = DayInYear + LastDayOfHebrewMonth(m, hebrewdate.year);        m = m + 1;      end          else  -- Add days in prior months this year      local m = 7;      while (m < hebrewdate.month) do        DayInYear = DayInYear + LastDayOfHebrewMonth(m, hebrewdate.year);        m = m + 1;      end    end    return (DayInYear +            (HebrewCalendarElapsedDays(hebrewdate.year)-- Days in prior years.             + HebrewEpoch));         -- Days elapsed before absolute date 1.

end

function find_gregorian_for_next_hebrew_date_occurrence(greg_year, greg_month, greg_day, heb_month, heb_day)

    local greg_absolute = AbsoluteFromGregorianDate(GregorianDate.create(greg_month, greg_day, greg_year))    local hebrew_date = HebrewDateFromAbsolute(greg_absolute)        local heb_year = hebrew_date.year        -- Check if we already passed that date this year. If we have, increase the year by 1    local this_years_hebrew_absolute = AbsoluteFromHebrewDate(HebrewDate.create(heb_month, heb_day, heb_year))    if (greg_absolute > this_years_hebrew_absolute) then        heb_year = heb_year + 1    end        -- Certain months only have 29 days. Advance years until we find a year with 30 days that month.    if heb_day == 30 then        while ((heb_month == 8) and not(LongHeshvan(heb_year))) or ((heb_month == 9) and ShortKislev(heb_year)) or ((heb_month == 12) and (HebrewLeapYear(heb_year) == 0)) do            heb_year = heb_year + 1        end    end

    -- The year we're in has the date. Get the absolute and convert it back to a Gregorian date    local absolute = AbsoluteFromHebrewDate(HebrewDate.create(heb_month, heb_day, heb_year))    local gregorian = GregorianDateFromAbsolute(absolute)    return gregorian

end

function GregorianMonthToName(monthNumber)

    if monthNumber == 1 then        return "January"    elseif monthNumber == 2 then        return "February"    elseif monthNumber == 3 then        return "March"    elseif monthNumber == 4 then        return "April"    elseif monthNumber == 5 then        return "May"    elseif monthNumber == 6 then        return "June"    elseif monthNumber == 7 then        return "July"    elseif monthNumber == 8 then        return "August"    elseif monthNumber == 9 then        return "September"    elseif monthNumber == 10 then        return "October"    elseif monthNumber == 11 then        return "November"    elseif monthNumber == 12 then        return "December"    end

end

function p.next_occurrence_of_hebrew_date_from_date(frame)

local greg_year = tonumber(frame.args[1])

local greg_month = tonumber(frame.args[2])

local greg_day = tonumber(frame.args[3])

local heb_month = tonumber(frame.args[4])

local heb_day = tonumber(frame.args[5])

    gregorian = find_gregorian_for_next_hebrew_date_occurrence(greg_year, greg_month, greg_day, heb_month, heb_day)    month_name = GregorianMonthToName(gregorian.month)    return month_name.." ".. gregorian.day..", "..gregorian.year

end

function p.next_occurrence_of_hebrew_date(frame)

local greg_year = tonumber(os.date("%Y"))

local greg_month = tonumber(os.date("%m"))

local greg_day = tonumber(os.date("%d"))

local heb_month = tonumber(frame.args[1])

local heb_day = tonumber(frame.args[2])

    gregorian = find_gregorian_for_next_hebrew_date_occurrence(greg_year, greg_month, greg_day, heb_month, heb_day)    month_name = GregorianMonthToName(gregorian.month)    return month_name.." ".. gregorian.day..", "..gregorian.year

end

return p

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