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(y / 100) + math.floor(y / 400) -- Gregorian adjustement for non-leap 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).
        - 32167;                                    -- Final substractive constant 32167 == 32044 + 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 + 32044.5;
    local j = math.floor(JD); -- No rounding performed for the precision of time; if you need it, round the JD before calling this method.
    
    -- 146097 days per cycle of 400 years
    local g  = math.floor(j / 146097);
    local dg = j - g * 146097;
    
    -- 36524 days per cycle of 100 years (cycle numbers: 0 to 4; but 4 is reduced to 3, making sometimes the last cycle longer by 1 day).
    -- Note: for c in 0..4: math.min(c, 3) is equal to math.floor((c * 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 c  = math.floor((math.floor(dg / 36524) * 3 + 1) / 4);
    local dc = dg - c * 36524;
    
    -- 1461 days per cycle of 4 years (cycle numbers: 0 to 24; 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:
    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 = g * 400 + c * 100 + b * 4 + a;
    local m = math.floor((da * 5 + 308) / 153) - 2;
    local d = da - math.floor((m + 4) * 153 / 5) + 122;
    
    -- Actual Gregorian 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;