# `Calendrical.Reform.Japan`

A composite calendar that tracks the historical calendar in use in Japan.

Unlike the European reforms, Japan did not move from the Julian calendar to
the Gregorian calendar. Before 1873 Japan used the Tenpō *lunisolar* calendar
(`Calendrical.LunarJapanese`); it adopted the Gregorian calendar as part of the
Meiji reforms. This makes `Calendrical.Reform.Japan` a good example of a
composite that splices a lunisolar calendar with a solar one.

The Gregorian side uses `Calendrical.Japanese` rather than
`Calendrical.Gregorian`, so post-reform dates carry Japanese era years
(Meiji, Taishō, Shōwa, Heisei, Reiwa) when localized — 1 January 1873 is
Meiji 6.

## Transitions

* **(base)** — the Japanese lunisolar calendar (`Calendrical.LunarJapanese`).

* **1873-01-01** — Japan adopts the Gregorian calendar (as
  `Calendrical.Japanese`). The last lunisolar day, Meiji 5, month 12, day 2
  (31 December 1872 in the Gregorian calendar), is followed directly by
  1 January 1873. No physical days are skipped — only the remainder of the
  lunisolar month is dropped.

Because `Calendrical.LunarJapanese` numbers years continuously from the Taika
era (645 CE), pre-reform dates carry that year number rather than an era-based
year such as "Meiji 5".

## Examples

    # The physical day before the reform, in the lunisolar calendar
    iex> Date.convert!(~D[1873-01-01 Calendrical.Reform.Japan], Calendrical.Gregorian)
    ~D[1873-01-01 Calendrical.Gregorian]

    iex> Date.convert!(~D[1873-01-01 Calendrical.Gregorian], Calendrical.Reform.Japan)
    ~D[1873-01-01 Calendrical.Reform.Japan]

## Reference

See `Calendrical.Reform` for the reform dates of other territories and the
sources they are drawn from.

# `day`

```elixir
@type day() :: 1..31
```

# `month`

```elixir
@type month() :: 1..12
```

# `year`

```elixir
@type year() :: -9999..9999
```

# `add`

Adds whole years, quarters or months to the fields of a naive
datetime, keeping its time of day: the `add/9` callback
[`CalendarInterval`](https://hexdocs.pm/calendar_interval) steps an
interval of a year or a month with. The date moves as `shift/6`
moves it, clamping the day into a shorter month.

### Arguments

* `year`, `month` and `day` are the date's fields in this calendar.

* `hour`, `minute`, `second` and `microsecond` are the time of day,
  returned unchanged.

* `precision` is `:year`, `:quarter` or `:month`.

* `step` is the number of years, quarters or months to add, which
  may be negative.

### Returns

* `{year, month, day, hour, minute, second, microsecond}`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {year, month, day, 12, 30, 0, {0, 0}} =
    ...>   Calendrical.Reform.Japan.add(date.year, date.month, date.day, 12, 30, 0, {0, 0}, :month, 1)
    iex> {year, month, day} == Calendrical.Reform.Japan.shift(date.year, date.month, date.day, :months, 1, [])
    true

# `calendar_base`

Returns what this calendar's year is built of, `:month` or `:week`,
as its `info/0` states.

### Returns

* `:week` for a calendar whose year is built of weeks.

* `:month` otherwise.

### Examples

    iex> Calendrical.Reform.Japan.calendar_base() in [:month, :week]
    true

# `calendar_for_date`

Identify the member calendar in effect on a given date struct.

A date of this calendar is looked up by its year, month and day. A
date of any other calendar is first converted to this calendar.

### Arguments

* `date` is any date map with `:year`, `:month`, `:day` and
  `:calendar` fields, such as a `t:Date.t/0`.

### Returns

* The member calendar module in effect on the date.

* Raises if a date of another calendar cannot be converted to
  this calendar.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.calendar_for_date(date) ==
    ...>   Calendrical.Reform.Japan.calendar_for_date(date.year, date.month, date.day)
    true
    iex> Calendrical.Reform.Japan.calendar_for_date(~D[2024-06-01]) ==
    ...>   Calendrical.Reform.Japan.calendar_for_date(date)
    true

# `calendar_for_date`

Identify the base calendar for a given date.

This function derives the calendar we delegate to for a given
date based upon the configuration.

### Arguments

* `year` is a year of this calendar.

* `month` is a month of the year.

* `day` is a day of the month.

### Returns

* The member calendar module in effect on the date.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> calendar = Calendrical.Reform.Japan.calendar_for_date(date.year, date.month, date.day)
    iex> calendar in Enum.map(Calendrical.Reform.Japan.info().members, &elem(&1, 1))
    true

# `calendar_for_iso_days`

Identify the base calendar for a given iso_days.

### Arguments

* `iso_days` is an integer number of days since the ISO epoch.

### Returns

* The member calendar module in effect on that day.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> iso_days = Date.to_gregorian_days(~D[2024-06-01])
    iex> Calendrical.Reform.Japan.calendar_for_iso_days(iso_days) ==
    ...>   Calendrical.Reform.Japan.calendar_for_date(date.year, date.month, date.day)
    true

# `calendar_from_cldr_calendar_type`

Returns the calendar module whose CLDR calendar type is the one
given, whichever calendar is asked
(`Calendrical.calendar_from_cldr_calendar_type/1`).

### Arguments

* `calendar_type` is a CLDR calendar type as an atom or a string.

### Returns

* `{:ok, calendar_module}`, or

* `{:error, exception}` for a calendar type no calendar module has.

### Examples

    iex> Calendrical.Reform.Japan.calendar_from_cldr_calendar_type(:gregorian)
    {:ok, Calendrical.Gregorian}

    iex> {:error, %Localize.UnknownCalendarError{}} =
    ...>   Calendrical.Reform.Japan.calendar_from_cldr_calendar_type(:not_a_calendar)

# `cardinal_day`

Returns the day a date is written with: the day of its
`written_date/3`.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The day of the date's `written_date/3`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar
  does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {_year, _month, written_day} = Calendrical.Reform.Japan.written_date(date.year, date.month, date.day)
    iex> Calendrical.Reform.Japan.cardinal_day(date.year, date.month, date.day) == written_day
    true

# `cardinal_month`

Returns the CLDR month a month of the year names without a year
(`Calendrical.Month.cldr_month/2`).

### Arguments

* `month` is a month of this calendar.

### Returns

* The CLDR month the month is named in the year that holds
  1 January 2000, the month itself in the Hebrew calendar, whose
  names depend on the year, and the month itself where the
  reference year has no such month.

### Examples

    iex> {:ok, date} = Date.convert(~D[2000-01-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.cardinal_month(1) == Calendrical.Reform.Japan.cldr_month(date.year, 1)
    true

# `cardinal_year`

Returns the year a date is written with: the year of its
`written_date/3`.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The year of the date's `written_date/3`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar
  does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {written_year, _month, _day} = Calendrical.Reform.Japan.written_date(date.year, date.month, date.day)
    iex> Calendrical.Reform.Japan.cardinal_year(date.year, date.month, date.day) == written_year
    true

# `cldr_calendar_type`

Returns the CLDR calendar type whose data names this calendar's
months, days and quarters, as its `info/0` states.

### Returns

* A CLDR calendar type such as `:gregorian` or `:hebrew`.

### Examples

    iex> Calendrical.Reform.Japan.cldr_calendar_type() == Calendrical.Reform.Japan.info().cldr_calendar_type
    true

# `cldr_calendar_type`

Returns the CLDR calendar type whose data names a date's months and
days: the member in effect on the date in a composite calendar, and
this calendar's own otherwise (`Calendrical.Info.cldr_calendar_type/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* A CLDR calendar type.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> in_effect = Calendrical.Info.in_effect(Calendrical.Reform.Japan, date.year, date.month, date.day)
    iex> Calendrical.Reform.Japan.cldr_calendar_type(date.year, date.month, date.day) == in_effect.cldr_calendar_type()
    true

# `cldr_month`

Returns the CLDR month of a month of a year
(`Calendrical.Month.cldr_month/3`).

### Arguments

* `year` and `month` are a month of this calendar.

### Returns

* A CLDR month number, or `{month, :leap}` where the month's name
  has a leap form, or

* `{:error, exception}` for a month the year does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> cldr_month = Calendrical.Reform.Japan.cldr_month(date.year, date.month)
    iex> Calendrical.Reform.Japan.written_month_from_cldr_month(date.year, cldr_month) ==
    ...>   Calendrical.Reform.Japan.numeric_month(date.year, date.month, date.day)
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidMonthError{}} = Calendrical.Reform.Japan.cldr_month(date.year, 99)

# `cyclic_year`

Returns the cyclic year of a date (`Calendrical.Era.cyclic_year/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The date's place in the sexagenary cycle, `1` to `60`, in an East
  Asian calendar, and its year in a calendar whose years run in no
  such cycle, or

* `{:error, %Calendrical.InvalidDateError{}}` for a year the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for no
  year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> cyclic_year = Calendrical.Reform.Japan.cyclic_year(date.year, date.month, date.day)
    iex> cyclic_year in 1..60 or cyclic_year == date.year
    true

    iex> {:error, %Calendrical.MissingFieldsError{}} = Calendrical.Reform.Japan.cyclic_year(nil, 1, 1)

# `date_from_cardinal_date`

Returns the date of this calendar that written figures name
(`date_from_written_date/3`), as fields.

### Arguments

* `year`, `month` and `day` are the figures a date is written with,
  as `written_date/3` returns them.

### Returns

* `{year, month, day}`, the date of this calendar, or

* `{:error, %Calendrical.InvalidDateError{}}` where the figures name no date.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {year, month, day} = Calendrical.Reform.Japan.written_date(date.year, date.month, date.day)
    iex> Calendrical.Reform.Japan.date_from_cardinal_date(year, month, day) == {date.year, date.month, date.day}
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Reform.Japan.date_from_cardinal_date(date.year, 0, 1)

# `date_from_day_of_year`

Returns the date of a day of a year, counted from the year's first
day.

### Arguments

* `year` is a year of this calendar.

* `day_of_year` is the day of the year, counted from 1.

### Returns

* A `t:Date.t/0` of this calendar, or

* `{:error, %Calendrical.InvalidDateError{}}` for a day the year does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> day_of_year = Calendrical.Reform.Japan.day_of_year(date.year, date.month, date.day)
    iex> Calendrical.Reform.Japan.date_from_day_of_year(date.year, day_of_year) == date
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Reform.Japan.date_from_day_of_year(date.year, 1000)

# `date_from_iso_days`

Returns `{year, month, day}` calculated from the number of
`iso_days`.

A day whose date is another day's, where two stretches of days carry
the same dates, has no date of its own and is written as the first
later day that has one, as a shift into the days a reform took out
reaches the day after them: England's 1 January to 24 March 1156,
whose dates are 1155's, are written as 25 March 1156.

### Arguments

* `iso_days` is an integer number of days since the ISO epoch.

### Returns

* `{year, month, day}`, the date of this calendar for the day, as
  the member calendar in effect on it writes it.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.date_from_iso_days(Date.to_gregorian_days(~D[2024-06-01]))
    {date.year, date.month, date.day}

# `date_from_week_date`

Returns the date of a day of a week of a week-year
(`Calendrical.Week.date_from_week_date/4`).

### Arguments

* `week_year` is a week-year of this calendar.

* `week` is a week of the week-year.

* `day` is the day of the week, numbered from 1 for the day the
  calendar's weeks begin on.

### Returns

* A `t:Date.t/0` of this calendar, or

* `{:error, %Calendrical.InvalidDateError{}}` where the week has no such day.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {week_year, week, day} = Calendrical.Reform.Japan.week_date_from_date(date.year, date.month, date.day)
    iex> Calendrical.Reform.Japan.date_from_week_date(week_year, week, day) == date
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Reform.Japan.date_from_week_date(date.year, 1, 8)

# `date_from_written_date`

Returns the date of this calendar that written figures name: the
date of the member calendar in effect on the day they name, in this
calendar's own fields.

### Arguments

* `year` is the written year.

* `month` is the written month, an integer or `{number, :leap}`
  for the leap month of a lunisolar member.

* `day` is the written day.

### Returns

* `{:ok, {year, month, day}}` with the date of this calendar the
  figures name.

* `{:error, :invalid_date}` if no member calendar in effect on the day
  reads the figures as a date, an atom as
  `c:Calendrical.date_from_written_date/3` answers.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {year, month, day} = Calendrical.Reform.Japan.written_date(date.year, date.month, date.day)
    iex> Calendrical.Reform.Japan.date_from_written_date(year, month, day)
    {:ok, {date.year, date.month, date.day}}
    iex> Calendrical.Reform.Japan.date_from_written_date(date.year, 13, 40)
    {:error, :invalid_date}

# `date_to_iso_days`

Returns the number of days since the ISO epoch for the
given `year-month-day`.

### Arguments

* `year` is a year of this calendar.

* `month` is a month of the year.

* `day` is a day of the month.

### Returns

* The number of days since the ISO epoch, as an integer, computed by
  the member calendar in effect on the date.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.date_to_iso_days(date.year, date.month, date.day) ==
    ...>   Date.to_gregorian_days(~D[2024-06-01])
    true

# `dates_in_gregorian_year`

Returns the dates of this calendar, earliest first, whose month and
day are those given and that fall in a Gregorian year.

### Arguments

* `gregorian_year` is the Gregorian year to search within.

* `month` and `day` are a month and a day of this calendar.

### Returns

* A list of zero, one or two `t:Date.t/0` of this calendar, earliest
  first, since this calendar's years and the Gregorian years drift.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> date in Calendrical.Reform.Japan.dates_in_gregorian_year(2024, date.month, date.day)
    true

# `day_numbers`

Returns the days a month of a year has, as runs of their numbers
(`Calendrical.Month.day_numbers/3`).

### Arguments

* `year` and `month` are a month of this calendar.

### Returns

* A list of ranges: one from 1 in every month of every calendar but
  a composite, whose month a change of calendar falls in has the
  days that are left, and `[]` for a month the year does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.day_numbers(date.year, date.month) ==
    ...>   [1..Calendrical.Reform.Japan.days_in_month(date.year, date.month)//1]
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.day_numbers(date.year, 99)
    []

# `day_of_era`

Calculates the day and era for the given date.

The era is the one the calendar in effect on the date gives, and
its days are counted in one count through every change of calendar
the era runs through: that of the calendar in effect where the era
begins, or where it ends for an era whose days are counted back from
its last. So the day after 2 September 1752 in England, 14
September, is the next day of the era.

### Arguments

* `year` is a year of this calendar.

* `month` is a month of the year.

* `day` is a day of the month.

### Returns

* `{day_of_era, era}` where `day_of_era` is the day within the era
  and `era` is the era's index, the same era `year_of_era/3` gives.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {day_of_era, era} = Calendrical.Reform.Japan.day_of_era(date.year, date.month, date.day)
    iex> {_year_of_era, year_era} = Calendrical.Reform.Japan.year_of_era(date.year, date.month, date.day)
    iex> day_of_era >= 1 and era == year_era
    true

# `day_of_week`

Returns the day of the week of a date (`Calendrical.Week.day_of_week/5`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

* `starting_on` is `:default` for the day this calendar's weeks
  begin on, or the name of a weekday, `:monday` to `:sunday`.

### Returns

* `{day_of_week, 1, 7}`, the day numbered from the day the week
  begins on, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for a
  missing field.

### Examples

    # 1 June 2024 is a Saturday
    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.day_of_week(date.year, date.month, date.day, :monday)
    {6, 1, 7}

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Reform.Japan.day_of_week(date.year, date.month, 0, :monday)

# `day_of_year`

Returns the day of the year of a date (`Calendrical.Period.day_of_year/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The day of the year, counted from 1 for its first day, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for a
  missing field.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> first_day = Calendrical.Reform.Japan.year(date.year).first
    iex> Calendrical.Reform.Japan.day_of_year(date.year, date.month, date.day) == Date.diff(date, first_day) + 1
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Reform.Japan.day_of_year(date.year, date.month, 0)

# `days_in_month`

Returns the number of days in a month without a year
(`Calendrical.Month.days_in_month/2`).

### Arguments

* `month` is a month of this calendar.

### Returns

* The number of days where the month has as many in every year, or

* `{:ambiguous, lengths}` where its length depends on the year, the
  lengths a range or, where they are not consecutive, a list, or

* `{:error, %Calendrical.NotDefinedError{}}` for a month the calendar has in no year, or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, where
  the month is `nil`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {fewest, most} = Calendrical.Reform.Japan.days_in_month_bounds(date.month)
    iex> case Calendrical.Reform.Japan.days_in_month(date.month) do
    ...>   days when is_integer(days) -> fewest == days and most == days
    ...>   {:ambiguous, lengths} -> Enum.min(lengths) == fewest and Enum.max(lengths) == most
    ...> end
    true

    iex> {:error, %Calendrical.NotDefinedError{}} = Calendrical.Reform.Japan.days_in_month(99)

# `days_in_month`

```elixir
@spec days_in_month(Calendar.year(), Calendar.month()) ::
  Calendar.day() | {:error, Exception.t()}
```

Returns the number of days in the given year and month.

A month a transition cuts short, or splits between two calendars,
counts only the days that carry its label: England's September
1752 has 19 days (1 and 2, then 14 to 30). A month no day carries
has none: England's January and February 1751, since its 1751 began
on 25 March.

### Arguments

* `year` is a year of this calendar.

* `month` is a month of the year.

### Returns

* The number of days that carry the label of `year` and `month`, or

* `{:error, %Calendrical.InvalidMonthError{}}` for a month no day
  carries, or

* `{:error, %Calendrical.MissingFieldsError{}}` where `year` or
  `month` is `nil`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.days_in_month(date.year, date.month) >= date.day
    true
    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidMonthError{month: 0}} = Calendrical.Reform.Japan.days_in_month(date.year, 0)

# `days_in_month_bounds`

Returns the fewest and the most days a month has in any year
(`Calendrical.Month.days_in_month_bounds/2`).

### Arguments

* `month` is a month of this calendar.

### Returns

* `{fewest, most}`, or

* `{:error, exception}` for a month the calendar has in no year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {fewest, most} = Calendrical.Reform.Japan.days_in_month_bounds(date.month)
    iex> Calendrical.Reform.Japan.days_in_month(date.year, date.month) in fewest..most
    true

    iex> {:error, %Calendrical.InvalidMonthError{}} = Calendrical.Reform.Japan.days_in_month_bounds(99)

# `days_in_week`

Returns the number of days in a week.

### Returns

* `7`.

### Examples

    iex> Calendrical.Reform.Japan.days_in_week()
    7

# `days_in_year`

Returns the number of days in a year (`Calendrical.Period.days_in_year/2`).

### Arguments

* `year` is a year of this calendar.

### Returns

* The number of days, or

* `{:error, %Calendrical.InvalidDateError{}}` for a year the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for no
  year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.days_in_year(date.year) == Enum.count(Calendrical.Reform.Japan.year(date.year))
    true

    iex> {:error, %Calendrical.MissingFieldsError{}} = Calendrical.Reform.Japan.days_in_year(nil)

# `diff`

Returns the whole number of `date_part`s from one
`{year, month, day}` to another, as `shift/6` adds them,
counted through each calendar a span crosses.

### Arguments

* `from` is the `{year, month, day}` the count starts from.

* `to` is the `{year, month, day}` the count ends at.

* `date_part` is one of `:years`, `:quarters`, `:months`, `:weeks`
  or `:days`.

### Returns

* The largest whole number of `date_part`s `shift/6` can add to the
  earlier date without passing the later one, as an integer. It is
  negative when `to` is before `from`.

* `{:error, %Calendrical.InvalidDateError{}}` for a `from` or `to` the
  calendar does not have, `{:error, %Calendrical.MissingFieldsError{}}`
  for one missing a field, or `{:error, %Calendrical.InvalidPartError{}}`
  for a `date_part` other than the five.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> from = {date.year, date.month, date.day}
    iex> to = Calendrical.Reform.Japan.shift(date.year, date.month, date.day, :months, 3)
    iex> Calendrical.Reform.Japan.diff(from, to, :months)
    3
    iex> Calendrical.Reform.Japan.diff(to, from, :months)
    -3

# `era_calendar_type`

Returns the CLDR calendar type that names this calendar's eras, as
its `info/0` states.

### Returns

* A CLDR calendar type such as `:gregorian` or `:japanese`.

### Examples

    iex> Calendrical.Reform.Japan.era_calendar_type() == Calendrical.Reform.Japan.info().era_calendar_type
    true

# `extended_year`

Returns the extended year of a date (`Calendrical.Era.extended_year/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The year numbered without a gap at 0, so that in a calendar with
  no year 0 the year before 1 is 0, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar does not have, or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for no
  year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.extended_year(date.year, date.month, date.day) == date.year
    true

    iex> {:error, %Calendrical.MissingFieldsError{}} = Calendrical.Reform.Japan.extended_year(nil, 1, 1)

# `info`

Returns the static facts about this calendar, as
`t:Calendrical.Info.t/0`: its members, each with the first day it
is in effect on, its base member's year 0 and the weeks of the
member in effect last.

### Returns

* A `t:Calendrical.Info.t/0` describing this calendar, whose
  `:members` are `{first_iso_day, calendar}` tuples in the order the
  member calendars take effect, the base calendar's first day being
  `nil`.

### Examples

    iex> Calendrical.Reform.Japan.info().calendar
    Calendrical.Reform.Japan
    iex> match?([{nil, _base_calendar} | _], Calendrical.Reform.Japan.info().members)
    true

# `iso_week_of_year`

Returns the ISO 8601 week-year and week of the day a date names
(`Calendrical.Week.iso_week_of_year/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* `{week_year, week}` of ISO 8601, or

* `{:error, exception}` for a date the calendar does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.iso_week_of_year(date.year, date.month, date.day)
    {2024, 22}

# `leap_month`

Returns the position of a year's leap month, or `nil` where the
year has none.

### Arguments

* `year` is a year of this calendar.

### Returns

* The leap month's position in the year, or

* `nil` where the year has no leap month, as for anything but an
  integer year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> leap_month = Calendrical.Reform.Japan.leap_month(date.year)
    iex> is_nil(leap_month) or leap_month in 1..Calendrical.Reform.Japan.months_in_year(date.year)
    true

# `leap_year?`

Returns whether the given year is a leap year: the calendar in
effect on its first day counts it one, and the day the leap year
adds is a date of this calendar.

### Arguments

* `year` is a year of this calendar.

### Returns

* `true` if the member calendar in effect on the first day of
  `year` counts it a leap year and the day its leap year adds, the
  last day of a lengthened month or the first day of a leap month,
  is a date of this calendar; otherwise `false`, as for a year with
  no days of its own (`months_in_year/1` is `0`) and for a year a
  change of calendar took the leap day from, as Sweden's 1700 has
  no 29 February.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> calendar = Calendrical.Reform.Japan.calendar_for_date(date.year, 1, 1)
    iex> Calendrical.Reform.Japan.leap_year?(date.year) == calendar.leap_year?(date.year)
    true

# `lunar_month_of_year`

Returns the traditional month at a position in a year
(`Calendrical.Month.traditional_month/3`), or an error for a place
the year does not have.

### Arguments

* `year` and `month` are a month of this calendar.

### Returns

* The month's traditional number, or `{month, :leap}` for a leap
  month, or

* `{:error, %Calendrical.InvalidMonthError{}}` for a month the year does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.lunar_month_of_year(date.year, date.month) ==
    ...>   Calendrical.Reform.Japan.traditional_month(date.year, date.month)
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidMonthError{}} = Calendrical.Reform.Japan.lunar_month_of_year(date.year, 99)

# `month`

Returns the days of a month of a year (`Calendrical.Period.month/3`).

### Arguments

* `year` and `month` are a month of this calendar.

### Returns

* A `t:Date.Range.t/0`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a month the year does not have, or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for a
  missing year or month.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> date in Calendrical.Reform.Japan.month(date.year, date.month)
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Reform.Japan.month(date.year, 99)

# `month_from_traditional`

Returns the position of a traditional month in a year
(`Calendrical.Month.month_from_traditional/3`).

### Arguments

* `year` is a year of this calendar.

* `traditional_month` is a month's traditional number, or
  `{month, :leap}` for a leap month.

### Returns

* The month's position in the year, or

* `{:error, exception}` where the year has no such month.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> traditional_month = Calendrical.Reform.Japan.traditional_month(date.year, date.month)
    iex> Calendrical.Reform.Japan.month_from_traditional(date.year, traditional_month) == date.month
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidMonthError{}} = Calendrical.Reform.Japan.month_from_traditional(date.year, 99)

# `month_numbers`

Returns the months a year has, as runs of their numbers
(`Calendrical.Month.month_numbers/2`).

### Arguments

* `year` is a year of this calendar.

### Returns

* A list of ranges: one from 1 in every year of every calendar but a
  composite, whose year a change of calendar falls in has the months
  that are left, and `[]` for a year the calendar does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.month_numbers(date.year) == [1..Calendrical.Reform.Japan.months_in_year(date.year)//1]
    true

# `month_of_year`

Returns the CLDR month of a month of a year: the index of its name
in this calendar's CLDR data, with `{month, :leap}` where the name
has a leap form (`Calendrical.Month.cldr_month/3`).

### Arguments

* `year`, `month` and `day` are a date of this calendar. The year
  and the day may be `nil`: a month's name needs only the month.

### Returns

* A CLDR month number, or `{month, :leap}`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a day the month does not have, or

* `{:error, exception}` for a month the year does not have, or a
  `Calendrical.MissingFieldsError` where the month is `nil`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.month_of_year(date.year, date.month, date.day) == Calendrical.Reform.Japan.cldr_month(date.year, date.month)
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Reform.Japan.month_of_year(date.year, date.month, 0)

# `months_in_leap_year`

Returns the number of months in a leap year: the most months a year
of this calendar has.

### Returns

* A positive integer.

### Examples

    iex> Calendrical.Reform.Japan.months_in_leap_year() >= Calendrical.Reform.Japan.months_in_ordinary_year()
    true

# `months_in_ordinary_year`

Returns the number of months in an ordinary year: the fewest months
a year of this calendar has.

### Returns

* A positive integer.

### Examples

    iex> Calendrical.Reform.Japan.months_in_ordinary_year() <= Calendrical.Reform.Japan.months_in_leap_year()
    true

# `months_in_year`

Returns the number of months in a year without a year: the count
where every year has as many, `{:ambiguous, range}` where a leap
year has more, and `{:error, %Calendrical.NotDefinedError{}}` for a composite calendar
(`Calendrical.Info.months_in_year/1`).

### Returns

* The number of months where every year has as many, or

* `{:ambiguous, fewest..most}` where a leap year has more, or

* `{:error, %Calendrical.NotDefinedError{}}` for a composite calendar, whose bounds
  `months_in_year_bounds/0` gives.

### Examples

    iex> case Calendrical.Reform.Japan.months_in_year() do
    ...>   months when is_integer(months) -> months == Calendrical.Reform.Japan.months_in_leap_year()
    ...>   {:ambiguous, fewest..most//1} -> {fewest, most} == Calendrical.Reform.Japan.info().months_in_year
    ...>   {:error, %Calendrical.NotDefinedError{}} -> is_list(Calendrical.Reform.Japan.info().members)
    ...> end
    true

# `months_in_year`

Returns the number of the last month of the given year that has
days, which is the number of months in a year a transition does not
cut short.

England's 1751, which began on 25 March, has months 3 to 12 and
answers 12; Russia's 1492, which ended on 31 August, answers 8. A
year no day carries answers `0`.

### Arguments

* `year` is a year of this calendar.

### Returns

* The number of the last month of the year that has days, as a
  non-negative integer. It is `0` for a year no day carries, or

* `{:error, %Calendrical.MissingFieldsError{}}` where `year` is `nil`, or

* `{:error, %Calendrical.InvalidDateError{}}` where `year` is no integer.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.months_in_year(date.year) >= date.month
    true

# `months_in_year_bounds`

Returns the fewest and the most months a year has
(`Calendrical.Month.months_in_year_bounds/1`).

### Returns

* `{fewest, most}`, which in a composite calendar counts the months
  left in a year a change of calendar falls in.

### Examples

    iex> {fewest, most} = Calendrical.Reform.Japan.months_in_year_bounds()
    iex> fewest <= Calendrical.Reform.Japan.months_in_ordinary_year() and
    ...>   most >= Calendrical.Reform.Japan.months_in_leap_year()
    true

# `naive_datetime_from_iso_days`

Converts ISO days and a day fraction to a naive datetime of this
calendar, as `c:Calendar.naive_datetime_from_iso_days/1` asks.

### Arguments

* `iso_days` is `{days, {parts_in_day, parts_per_day}}`, a day and a
  fraction of it.

### Returns

* `{year, month, day, hour, minute, second, microsecond}` of this
  calendar.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {year, month, day, 12, 0, 0, {0, 6}} =
    ...>   Calendrical.Reform.Japan.naive_datetime_from_iso_days({739403, {43200000000, 86400000000}})
    iex> {year, month, day} == {date.year, date.month, date.day}
    true

# `naive_datetime_to_iso_days`

Converts a naive datetime of this calendar to ISO days and a day
fraction, as `c:Calendar.naive_datetime_to_iso_days/7` asks.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

* `hour`, `minute`, `second` and `microsecond` are a time of day,
  the microsecond as `{microseconds, precision}`.

### Returns

* `{iso_days, {parts_in_day, parts_per_day}}`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.naive_datetime_to_iso_days(date.year, date.month, date.day, 12, 0, 0, {0, 6})
    {739403, {43200000000, 86400000000}}

# `named_month`

Returns the days of a named month in a year
(`Calendrical.Month.named_month/3`).

### Arguments

* `year` is a year of this calendar.

* `named_month` is the CLDR month that names the month.

### Returns

* A list of `t:Date.Range.t/0`, one for each counted month that
  carries the name, earliest first, and `[]` where none does.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> cldr_month = Calendrical.Reform.Japan.cldr_month(date.year, date.month)
    iex> Calendrical.Reform.Japan.named_month(date.year, cldr_month) |> Enum.any?(&(date in &1))
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.named_month(date.year, 99)
    []

# `numeric_month`

Returns the number a date's month is written with in figures: the
month of its `written_date/3`.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The month of the date's `written_date/3`: a month number, or
  `{month, :leap}` for a leap month of a lunisolar calendar, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar
  does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {_year, written_month, _day} = Calendrical.Reform.Japan.written_date(date.year, date.month, date.day)
    iex> Calendrical.Reform.Japan.numeric_month(date.year, date.month, date.day) == written_month
    true

# `ordinal_month_from_traditional`

Returns the position in a year of a traditional month
(`Calendrical.Month.month_from_traditional/3`), as `{:ok, month}`.

### Arguments

* `year` is a year of this calendar.

* `traditional_month` is a month's traditional number, or
  `{month, :leap}` for a leap month.

### Returns

* `{:ok, month}`, the month's position in the year, or

* `{:error, %Calendrical.InvalidMonthError{}}` for a month or a leap
  month the year does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> traditional_month = Calendrical.Reform.Japan.traditional_month(date.year, date.month)
    iex> Calendrical.Reform.Japan.ordinal_month_from_traditional(date.year, traditional_month) == {:ok, date.month}
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidMonthError{}} = Calendrical.Reform.Japan.ordinal_month_from_traditional(date.year, 99)

# `parse_date`

Parses a date written in this calendar's own notation.

### Arguments

* `string` is a date written `YYYY-MM-DD`, with a leading `-` for a
  year before 1, or, in a calendar of weeks, `YYYY-Www-D`.

### Returns

* `{:ok, {year, month, day}}`, or

* `{:error, :invalid_format}` where the text is not in that form or
  its fields are not digits, or

* `{:error, :invalid_date}` where the text names no date of this
  calendar.

The reason is an atom, not an exception, because `c:Calendar.parse_date/1`
requires one: `Date.from_iso8601/2` reads it.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.parse_date(Date.to_string(date)) == {:ok, {date.year, date.month, date.day}}
    true

    iex> Calendrical.Reform.Japan.parse_date("not a date")
    {:error, :invalid_format}

# `parse_naive_datetime`

Parses a naive datetime written in this calendar's own notation.

### Arguments

* `string` is a date as `parse_date/1` reads it, then `T` or a
  space and a time of day.

### Returns

* `{:ok, {year, month, day, hour, minute, second, microsecond}}`, or

* `{:error, reason}`, such as `:invalid_format` or `:invalid_date`,
  where the text is no such datetime.

The reason is an atom, not an exception, because
`c:Calendar.parse_naive_datetime/1` requires one:
`NaiveDateTime.from_iso8601/2` reads it.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.parse_naive_datetime(Date.to_string(date) <> "T12:00:00") ==
    ...>   {:ok, {date.year, date.month, date.day, 12, 0, 0, {0, 0}}}
    true

    iex> Calendrical.Reform.Japan.parse_naive_datetime("2024-06-01")
    {:error, :invalid_format}

# `parse_utc_datetime`

Parses a UTC datetime written in this calendar's own notation.

### Arguments

* `string` is a date as `parse_date/1` reads it, then `T` or a
  space, a time of day and an offset from UTC, `Z` or `±HH:MM`.

### Returns

* `{:ok, {year, month, day, hour, minute, second, microsecond}, offset}`,
  the datetime in UTC and the offset in seconds it was written with,
  or

* `{:error, reason}`, such as `:invalid_format`, `:invalid_date` or
  `:missing_offset`, where the text is no such datetime.

The reason is an atom, not an exception, because
`c:Calendar.parse_utc_datetime/1` requires one:
`DateTime.from_iso8601/2` reads it.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.parse_utc_datetime(Date.to_string(date) <> "T12:00:00Z") ==
    ...>   {:ok, {date.year, date.month, date.day, 12, 0, 0, {0, 0}}, 0}
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.parse_utc_datetime(Date.to_string(date) <> "T12:00:00")
    {:error, :missing_offset}

# `parsing_calendar`

Returns the calendar a date written for this calendar is parsed in,
as its `info/0` states.

### Returns

* A calendar module.

### Examples

    iex> Calendrical.Reform.Japan.parsing_calendar() == Calendrical.Reform.Japan.info().parsing_calendar
    true

# `parsing_calendars`

Returns the calendars a date written for this calendar may be
written in: the members of a composite calendar, and this calendar
alone otherwise (`Calendrical.Info.parsing_calendars/1`).

### Returns

* A non-empty list of calendar modules, the members of a composite
  calendar in the order they take effect.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> in_effect = Calendrical.Info.in_effect(Calendrical.Reform.Japan, date.year, date.month, date.day)
    iex> in_effect in Calendrical.Reform.Japan.parsing_calendars()
    true

# `periods_in_year`

Returns the number of periods in a year: its months.

### Arguments

* `year` is a year of this calendar.

### Returns

* The number of months in the year, as `months_in_year/1` returns
  it.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.periods_in_year(date.year) == Calendrical.Reform.Japan.months_in_year(date.year)
    true

# `quadrimester`

Returns the days of a quadrimester of a year
(`Calendrical.Period.quadrimester/3`).

### Arguments

* `year` is a year of this calendar.

* `quadrimester` is the quadrimester, `1` to `3`.

### Returns

* A `t:Date.Range.t/0`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a quadrimester or a year the
  calendar does not have, or

* `{:error, %Calendrical.MissingFieldsError{}}` where the year or the
  quadrimester is `nil`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.quadrimester(date.year, 1).first == Calendrical.Reform.Japan.year(date.year).first
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Reform.Japan.quadrimester(date.year, 4)

# `quarter`

Returns the days of a quarter of a year (`Calendrical.Period.quarter/3`).

### Arguments

* `year` is a year of this calendar.

* `quarter` is the quarter, `1` to `4`.

### Returns

* A `t:Date.Range.t/0`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a quarter or a year the calendar
  does not have, or

* `{:error, %Calendrical.MissingFieldsError{}}` where the year or the
  quarter is `nil`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> quarter = Calendrical.Reform.Japan.quarter_of_year(date.year, date.month, date.day)
    iex> date in Calendrical.Reform.Japan.quarter(date.year, quarter)
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Reform.Japan.quarter(date.year, 5)

# `quarter_of_year`

Returns the quarter of the year a date falls in
(`Calendrical.Period.quarter_of_year/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The quarter, `1` to `4`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for a
  missing year or month.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.quarter_of_year(date.year, date.month, date.day) in 1..4
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Reform.Japan.quarter_of_year(date.year, date.month, 0)

# `related_gregorian_year`

Returns the related Gregorian year of a date
(`Calendrical.Era.related_gregorian_year/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The Gregorian year the date's calendar year begins in, or

* `{:error, %Calendrical.InvalidDateError{}}` for a year the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for no
  year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:ok, first_day} = Date.convert(Calendrical.Reform.Japan.year(date.year).first, Calendrical.Gregorian)
    iex> Calendrical.Reform.Japan.related_gregorian_year(date.year, date.month, date.day) == first_day.year
    true

# `semester`

Returns the days of a semester of a year (`Calendrical.Period.semester/3`).

### Arguments

* `year` is a year of this calendar.

* `semester` is the semester, `1` or `2`.

### Returns

* A `t:Date.Range.t/0`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a semester or a year the calendar
  does not have, or

* `{:error, %Calendrical.MissingFieldsError{}}` where the year or the
  semester is `nil`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.semester(date.year, 1).first == Calendrical.Reform.Japan.year(date.year).first
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Reform.Japan.semester(date.year, 3)

# `shift`

Adds an `increment` number of `date_part`s to the given
`year-month-day`, always returning a date of this calendar.

Years, quarters and months are added in the calendar in effect on
the date, a year being as many months as that calendar counts.
When the result falls under another calendar the months
are counted on through each calendar's own months, so one month
after 20 August 1752 in England is 20 September 1752. A day the
resulting month does not have becomes the month's next day that
exists, or its last day: one month after 5 August 1752 is
14 September 1752 and one month after 31 January is the last day
of February. Weeks and days count days.

### Arguments

* `year` is a year of this calendar.

* `month` is a month of the year.

* `day` is a day of the month.

* `date_part` is one of `:years`, `:quarters`, `:months`, `:weeks`
  or `:days`.

* `increment` is the positive or negative integer number of
  `date_part`s to add.

* `options` is a keyword list of options.

### Options

* `:clamp` is accepted for the `c:Calendrical.shift/6` callback but
  has no effect: a day the resulting month does not have is always
  brought into it as described above.

### Returns

* `{year, month, day}`, the date of this calendar reached, or

* `{:error, %Calendrical.InvalidDateError{}}` where `year`, `month` and
  `day` are no date of this calendar, or

* `{:error, %Calendrical.MissingFieldsError{}}` where a field is `nil`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {year, month, day} = Calendrical.Reform.Japan.shift(date.year, date.month, date.day, :days, 10)
    iex> Calendrical.Reform.Japan.date_to_iso_days(year, month, day) -
    ...>   Calendrical.Reform.Japan.date_to_iso_days(date.year, date.month, date.day)
    10
    iex> to = Calendrical.Reform.Japan.shift(date.year, date.month, date.day, :years, 1)
    iex> Calendrical.Reform.Japan.diff({date.year, date.month, date.day}, to, :years)
    1

# `shift_date`

Shifts a date by a duration: its years and months together, as
`shift/6` adds months, and then its weeks and days.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

* `duration` is a `t:Duration.t/0`.

### Returns

* `{year, month, day}` of this calendar.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {year, month, day} = Calendrical.Reform.Japan.shift_date(date.year, date.month, date.day, Duration.new!(day: 7))
    iex> Date.new!(year, month, day, Calendrical.Reform.Japan) == Date.add(date, 7)
    true

# `shift_naive_datetime`

Shifts a naive datetime by a duration: its date as `shift_date/4`
shifts it, and its time as `Calendar.ISO` does.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

* `hour`, `minute`, `second` and `microsecond` are a time of day,
  the microsecond as `{microseconds, precision}`.

* `duration` is a `t:Duration.t/0`.

### Returns

* `{year, month, day, hour, minute, second, microsecond}` of this
  calendar.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> next_day = Date.add(date, 1)
    iex> Calendrical.Reform.Japan.shift_naive_datetime(date.year, date.month, date.day, 23, 0, 0, {0, 0}, Duration.new!(hour: 2)) ==
    ...>   {next_day.year, next_day.month, next_day.day, 1, 0, 0, {0, 0}}
    true

# `shift_time`

Shifts a time by a duration, as `Calendar.ISO` does.

### Arguments

* `hour`, `minute`, `second` and `microsecond` are a time of day,
  the microsecond as `{microseconds, precision}`.

* `duration` is a `t:Duration.t/0` of time units.

### Returns

* `{hour, minute, second, microsecond}`, wrapped around midnight.

### Examples

    iex> Calendrical.Reform.Japan.shift_time(23, 0, 0, {0, 0}, Duration.new!(hour: 2))
    {1, 0, 0, {0, 0}}

# `solar_term`

Returns the day of a solar term of a Gregorian year, reckoned at the
place this calendar's `info/0` names, or at the Chinese calendar's
meridian, the traditional reference, where it names none.

### Arguments

* `index` is the solar term's number, `1` (lichun, 315° of solar
  longitude) to `24`, every 15° on.

* `gregorian_year` is a Gregorian year.

### Returns

* `{:ok, date}`, a `t:Date.t/0` in `Calendrical.Gregorian`, or

* `{:error, %Calendrical.InvalidSolarTermError{}}` where `index` is not
  `1` to `24`.

### Examples

    # Qingming, the fifth solar term
    iex> Calendrical.Reform.Japan.solar_term(5, 2025)
    {:ok, ~D[2025-04-04 Calendrical.Gregorian]}

    iex> Calendrical.Reform.Japan.solar_term(25, 2025)
    {:error, %Calendrical.InvalidSolarTermError{index: 25}}

# `traditional_leap_month`

Returns the traditional number of the month a year's leap month
follows, or `nil` (`Calendrical.Month.traditional_leap_month/2`).

### Arguments

* `year` is a year of this calendar.

### Returns

* The traditional number of the month the leap month follows, or

* `nil` where the year has no leap month.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> is_nil(Calendrical.Reform.Japan.traditional_leap_month(date.year)) ==
    ...>   is_nil(Calendrical.Reform.Japan.leap_month(date.year))
    true

# `traditional_month`

Returns a month of a year as this calendar names it
(`Calendrical.Month.traditional_month/3`).

### Arguments

* `year` and `month` are a month of this calendar.

### Returns

* The month's traditional number, or `{month, :leap}` for a leap
  month, or

* `{:error, exception}` for a month the year does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.traditional_month(date.year, date.month) ==
    ...>   Enum.at(Calendrical.Reform.Japan.traditional_months(date.year), date.month - 1)
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidMonthError{}} = Calendrical.Reform.Japan.traditional_month(date.year, 99)

# `traditional_months`

Returns a year's months in order, named traditionally
(`Calendrical.Month.traditional_months/2`).

### Arguments

* `year` is a year of this calendar.

### Returns

* A list of traditional months, the nth naming the year's nth month,
  with `{month, :leap}` for a leap month, and `[]` for a year the
  calendar does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> length(Calendrical.Reform.Japan.traditional_months(date.year)) ==
    ...>   Calendrical.Reform.Japan.months_in_year(date.year)
    true

# `valid_date?`

Determines if the date given is valid according to this calendar.

A date is valid when the member calendar in effect on it accepts it
and the day it names is one that calendar governs, so a date a
change of calendar took out is not valid.

### Arguments

* `year` is a year of this calendar.

* `month` is a month of the year.

* `day` is a day of the month.

### Returns

* `true` if the year, month and day are a date of this calendar,
  otherwise `false`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.valid_date?(date.year, date.month, date.day)
    true
    iex> Calendrical.Reform.Japan.valid_date?(date.year, date.month, 0)
    false

# `week`

Returns the seven days of a week of a year (`Calendrical.Week.week/3`).

### Arguments

* `year` is a year of this calendar.

* `week` is a week of the year.

### Returns

* A `t:Date.Range.t/0` of the week's seven days, which may begin in
  the year before or end in the year after, or

* `{:error, %Calendrical.InvalidDateError{}}` for a week the year does not have, or

* `{:error, %Calendrical.MissingFieldsError{}}` where the year or the
  week is `nil`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {week_year, week} = Calendrical.Reform.Japan.week_of_year(date.year, date.month, date.day)
    iex> days = Calendrical.Reform.Japan.week(week_year, week)
    iex> {Enum.count(days), date in days}
    {7, true}

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Reform.Japan.week(date.year, 0)

# `week_date_from_date`

Returns the week-year, the week and the day of the week of a date
(`Calendrical.Week.week_date_from_date/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* `{week_year, week, day_of_week}`, the day numbered from the day
  the calendar's weeks begin on, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {week_year, week, day} = Calendrical.Reform.Japan.week_date_from_date(date.year, date.month, date.day)
    iex> {week_year, week} == Calendrical.Reform.Japan.week_of_year(date.year, date.month, date.day) and day in 1..7
    true

# `week_of_month`

Returns the month and the week of the month a date is in
(`Calendrical.Week.week_of_month/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* `{month, week}`, where the month is the one before or after where
  the date falls in that month's last or first week, or

* `{:error, exception}` for a date the calendar does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {month, week} = Calendrical.Reform.Japan.week_of_month(date.year, date.month, date.day)
    iex> month in (date.month - 1)..(date.month + 1) and week >= 1
    true

# `week_of_year`

Returns the week-year and the week of the year a date is in
(`Calendrical.Week.week_of_year/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* `{week_year, week}`, where the week-year is the year before or
  after where the date falls in that year's last or first week, or

* `{:error, exception}` for a date the calendar does not have: a
  `Calendrical.MissingFieldsError` for a date missing a field, and a
  `Calendrical.InvalidDateError` otherwise.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {week_year, week} = Calendrical.Reform.Japan.week_of_year(date.year, date.month, date.day)
    iex> date in Calendrical.Reform.Japan.week(week_year, week)
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Reform.Japan.week_of_year(date.year, date.month, 0)

# `weeks_in_week_year`

Returns the number of weeks in a week-year
(`Calendrical.Week.weeks_in_week_year/2`).

### Arguments

* `week_year` is a week-year of this calendar.

### Returns

* The number of weeks, or

* `{:error, %Calendrical.InvalidDateError{}}` for a year the calendar does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {week_year, week, _day} = Calendrical.Reform.Japan.week_date_from_date(date.year, date.month, date.day)
    iex> week <= Calendrical.Reform.Japan.weeks_in_week_year(week_year)
    true

# `weeks_in_year`

Returns the number of weeks in a year (`Calendrical.Week.weeks_in_year/2`).

### Arguments

* `year` is a year of this calendar.

### Returns

* The number of weeks, or

* `{:error, exception}` for a year the calendar does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {week_year, week} = Calendrical.Reform.Japan.week_of_year(date.year, date.month, date.day)
    iex> week <= Calendrical.Reform.Japan.weeks_in_year(week_year)
    true

# `weeks_of_month`

Returns the weeks of a month of a year in order
(`Calendrical.Week.weeks_of_month/3`).

### Arguments

* `year` and `month` are a month of this calendar.

### Returns

* A list of `t:Date.Range.t/0`, one for each week `week_of_month/3`
  names for the month, the first of which may begin in the month
  before and the last run into the month after, or

* `{:error, exception}` for a month the year does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.weeks_of_month(date.year, date.month) |> Enum.all?(&(Enum.count(&1) == 7))
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {:error, %Calendrical.InvalidMonthError{}} = Calendrical.Reform.Japan.weeks_of_month(date.year, 99)

# `written_date`

Returns the figures a date is written with: the member calendar's.

### Arguments

* `year` is a year of this calendar.

* `month` is a month of the year.

* `day` is a day of the month.

### Returns

* `{year, month, day}` as the member calendar in effect on the date
  writes it, where `month` may be `{number, :leap}` for the leap
  month of a lunisolar member.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {year, month, day} = Calendrical.Reform.Japan.written_date(date.year, date.month, date.day)
    iex> Calendrical.Reform.Japan.date_from_written_date(year, month, day)
    {:ok, {date.year, date.month, date.day}}

# `written_month_from_cldr_month`

Returns the month a CLDR month is written with in a year
(`Calendrical.Month.written_month_from_cldr_month/3`).

### Arguments

* `year` is a year of this calendar.

* `cldr_month` is a CLDR month number, or `{month, :leap}`.

### Returns

* The month as `written_date/3` writes it, or

* `{:error, :invalid_month}` where the year has no month of that
  name. The reason is an atom, not an exception: Localize's date parser
  reads it, where `Calendrical.Month.written_month_from_cldr_month/3`
  answers with an exception.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {_year, written_month, _day} = Calendrical.Reform.Japan.written_date(date.year, date.month, date.day)
    iex> cldr_month = Calendrical.Reform.Japan.cldr_month(date.year, date.month)
    iex> Calendrical.Reform.Japan.written_month_from_cldr_month(date.year, cldr_month) == written_month
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.written_month_from_cldr_month(date.year, 99)
    {:error, :invalid_month}

# `year`

Returns the days of a year (`Calendrical.Period.year/2`).

### Arguments

* `year` is a year of this calendar.

### Returns

* A `t:Date.Range.t/0`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a year the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for
  no year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> date in Calendrical.Reform.Japan.year(date.year)
    true

    iex> {:error, %Calendrical.MissingFieldsError{}} = Calendrical.Reform.Japan.year(nil)

# `year_of_era`

Returns the year of era and era of a year (`Calendrical.Era.year_of_era/2`).

### Arguments

* `year` is a year of this calendar.

### Returns

* `{year_of_era, era}`, the era in effect on the year's first day,
  or

* `{:error, %Calendrical.InvalidDateError{}}` for a year the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for no
  year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> Calendrical.Reform.Japan.year_of_era(date.year) ==
    ...>   Calendrical.Reform.Japan.year_of_era(date.year, date.month, date.day)
    true

# `year_of_era`

```elixir
@spec year_of_era(year(), month(), day()) :: {year(), era :: non_neg_integer()}
```

Calculates the year and era from the given `year`, `month`,
and `day`. The result is in the context of the calendar in
effect on that date.

### Arguments

* `year` is a year of this calendar.

* `month` is a month of the year.

* `day` is a day of the month.

### Returns

* `{year_of_era, era}` where `year_of_era` is the year within the
  era and `era` is the era's index, as the member calendar in effect
  on the date gives them.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> {year_of_era, era} = Calendrical.Reform.Japan.year_of_era(date.year, date.month, date.day)
    iex> is_integer(year_of_era) and is_integer(era)
    true

# `years_in_cycle`

Returns the number of years after which this calendar's years
repeat, as its `info/0` states, or `{:error, %Calendrical.NotDefinedError{}}`.

### Returns

* The number of years in the cycle, or

* `{:error, %Calendrical.NotDefinedError{}}` where the calendar states none.

### Examples

    # A year has as many days as the year one cycle later
    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Reform.Japan)
    iex> case Calendrical.Reform.Japan.years_in_cycle() do
    ...>   {:error, %Calendrical.NotDefinedError{}} -> true
    ...>   years -> Calendrical.Reform.Japan.days_in_year(date.year) == Calendrical.Reform.Japan.days_in_year(date.year + years)
    ...> end
    true

---

*Consult [api-reference.md](api-reference.md) for complete listing*