days_from_civil implemented in Lua

days_from_civil.lua

--[[
 http://howardhinnant.github.io/date_algorithms.html

 Returns number of days since civil 1970-01-01.  Negative values indicate
    days prior to 1970-01-01.
 Preconditions:  y-m-d represents a date in the civil (Gregorian) calendar
                 m is in [1, 12]
                 d is in [1, last_day_of_month(y, m)]
                 y is "approximately" in
                   [numeric_limits<Int>::min()/366, numeric_limits<Int>::max()/366]
                 Exact range of validity is:
                 [civil_from_days(numeric_limits<Int>::min()),
                  civil_from_days(numeric_limits<Int>::max()-719468)]
]]
function days_from_civil(y, m, d)
    if m <= 2 then -- adjust so that leap days are at the end of leap years
      y = y - 1
      m = m + 9
    else
      m = m - 3
    end
    local era = math.floor(y / 400)
    local yoe = y - era * 400                                           -- [0, 399]
    local doy = math.modf((153*m + 2)/5) + d-1                          -- [0, 365]
    local doe = yoe * 365 + math.modf(yoe/4) - math.modf(yoe/100) + doy -- [0, 146096]
    return era * 146097 + doe - 719468
end

local reference_date = {year=2001, month = 1, day = 1}
local date = os.date("*t")

local reference_days = days_from_civil(reference_date.year, reference_date.month, reference_date.day)
local days = days_from_civil(date.year, date.month, date.day)

print(string.format("Today is %d days into the 21st century.",days-reference_days))


-- Returns: true if y is a leap year in the civil calendar, else false
function is_leap(y)
    return math.fmod(y, 4) == 0 and (math.fmod(y, 100) ~= 0 or  math.fmod(y, 400) == 0)
end

--[[
 Preconditions: m is in [1, 12]
 Returns: The number of days in the month m of common year
 The result is always in the range [28, 31].
]]
function last_day_of_month_common_year(m)
    local a = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}
    return a[m]
end

--[[
 Preconditions: m is in [1, 12]
 Returns: The number of days in the month m of year y
 The result is always in the range [28, 31].
]]
function last_day_of_month(y, m)
    return (m ~= 2 or not is_leap(y)) and last_day_of_month_common_year(m) or 29
end

local previous_days = days_from_civil(-1001, 12, 31)

for year = -1000, 3000 do
  for month = 1, 12 do
    for day = 1, last_day_of_month(year, month) do
      local days = days_from_civil(year, month, day)
      if previous_days + 1 ~= days then
        print("Error", year, month, day)
      end
      previous_days = days
    end
  end
end