Calendar_sig.S.Date

# Module Calendar_sig.S.Date

    module Date: Date_sig.S

Date implementation used by this calendar.
Since 2.0

## Datatypes

    type field = Period.date_field

The different fields of a date.
Since 2.02

    type -[< field ] date

Type of a date, without specifying any precision level.
Since 2.02

    type t = field date

Type of a date.

    type day =

`|` | `Sun`
`|` | `Mon`
`|` | `Tue`
`|` | `Wed`
`|` | `Thu`
`|` | `Fri`
`|` | `Sat`

Days of the week.

    type month =

`|` | `Jan`
`|` | `Feb`
`|` | `Mar`
`|` | `Apr`
`|` | `May`
`|` | `Jun`
`|` | `Jul`
`|` | `Aug`
`|` | `Sep`
`|` | `Oct`
`|` | `Nov`
`|` | `Dec`

Months of the year.

    type year = int

Year as an `int`.

## Exceptions

    exception Out_of_bounds

Raised when a date is outside the Julian period.

    exception Undefined

Raised when a date belongs to `[October 5th, 1582; October 14th, 1582]`.

## Constructors

    val make : year -> int -> int -> t

`make year month day` makes the date year-month-day. A BC year `y` corresponds to the year `-(y+1)`.
Raises

- `Out_of_bounds` when a date is outside the Julian period.
- `Undefined` when a date belongs to `[October 5th, 1582; October 14th, 1582]`.

Example: years (5 BC) and (1 BC) respectively correspond to years (-4) and 0.

    val lmake : year:year -> ?month:int -> ?day:int -> unit -> t

Labelled version of `make`. The default value of `month` and `day` is `1`.
Since 1.05
Raises

- `Out_of_bounds` when a date is outside the Julian period.
- `Undefined` when a date belongs to `[October 5th, 1582; October 14th, 1582]`.

    val make_year : int -> [< `Year ] date

`make_year y` makes a date only represented by its year `y`. The month and the day of such a date are not relevant.
Since 2.02

    val make_year_month : int -> int -> [< `Month | `Year ] date

`make_year_month y m` makes a date only represented by its year `y` and its month `m`. The day of such a date is not relevant.
Since 2.02

    val today : unit -> t

Date of the current day (based on `Time_Zone.current ()`).

    val from_jd : int -> t

Make a date from its Julian day.
Example: `from_jd 0` returns the date 4713 BC-1-1.

    val from_mjd : int -> t

Make a date from its modified Julian day (i.e. Julian day - 2 400 001). The Modified Julian day is more manageable than the Julian day.
Example: `from_mjd 0` returns the date 1858-11-17.

    val from_day_of_year : year -> int -> t

Make a date from a year and its day of the year.
Since 2.0
Example: `from_day_of_year 2008 39` returns the date 2008-2-8.

## Getters

    val days_in_month : [< field > `Month `Year ] date -> int

Number of days in the month of a date.
Example: `days_in_month (make 2003 6 26)` returns `30`.

    val day_of_week : t -> day

Day of the week.
Example: `day_of_week (make 2003 6 26)` returns `Thu`.

    val day_of_month : t -> int

Day of the month.
Example: `day_of_month (make 2003 6 26)` returns `26`.

    val day_of_year : t -> int

Day of the year.
Examples:

- `day_of_year (make 2003 12 28)` returns `362`.
- `day_of_year (make 2003 1 5)` returns `5`

    val week : t -> int

Week.
Examples:

- `week (make 2003 12 29)` returns `1`.
- `week (make 2003 12 28)` returns `52`.
- `week (make 2000 1 2)` returns `52`.
- `week (make 2000 1 3)` returns `1`.

    val month : [< field > `Month ] date -> month

Month.
Example: `month (make 2003 6 26)` returns `Jun`.

    val year : [< field > `Year ] date -> year

Year.
Example: `year (make 2003 6 26)` returns `2003`.

    val to_jd : t -> int

Julian day.
Example: `to_jd (make (-4712) 1 1)` returns 0.

    val to_mjd : t -> int

Modified Julian day (i.e. Julian day - 2 400 001). The Modified Julian day is more manageable than the Julian day.
Example: `to_mjd (make 1858 11 17)` returns 0.

## Dates are comparable

    val equal : [< field ] date ->
           [< field ] date -> bool

Equality function between two dates.
Since 1.09.0
See also Utils.Comparable.equal

    val compare : [< field ] date ->
           [< field ] date -> int

Comparison function between two dates.
See also Utils.Comparable.compare

    val hash : [< field ] date -> int

Hash function for dates.
Since 2.0
See also Utils.Comparable.hash

## Boolean operations on dates

    val is_valid_date : year -> int -> int -> bool

Check if a date is valid, that is the date has not been coerced to look like a real date.
Since 2.0
Examples:

- `is_valid_date 2008 2 30` returns `false`
- `is_valid_date 2008 2 8` returns `true`

    val is_leap_day : t -> bool

Return `true` if a date is a leap day (i.e. February, 24th of a leap year); `false` otherwise.

    val is_gregorian : t -> bool

Return `true` if a date belongs to the Gregorian calendar; `false` otherwise.

    val is_julian : t -> bool

Return `true` iff a date belongs to the Julian calendar; `false` otherwise.

## Coercions

    val to_unixtm : t -> Unix.tm

Convert a date into the `Unix.tm` type. The field `is_isdst` is always `false`. The fields `Unix.tm_sec`, `Unix.tm_min` and `Unix.tm_hour` are irrelevant.
Since 1.01

    val from_unixtm : Unix.tm -> t

Inverse of `to_unixtm`. Assume the current time zone.
Since 1.01

    val to_unixfloat : t -> float

Convert a date to a float such than `to_unixfloat (make 1970 1 1)` returns `0.0`. So such a float is convertible with those of the `Unix` module. The fractional part of the result is always `0`.
Since 1.01

    val from_unixfloat : float -> t

Inverse of `to_unixfloat`. Ignore the fractional part of the argument. Assume the current time zone.
Since 1.01

    val to_business : t -> year * int * day

Return the "business week" and the day in this week respecting ISO 8601. Notice that business weeks at the beginning and end of the year can sometimes have year numbers which don't match the real year.
Since 1.09.0
Examples:

- `to_business (make 2003 12 29)` returns `2004, 1, Mon`.
- `to_business (make 2003 12 28)` returns `2003, 52, Sun`
- `to_business (make 2000 1 2)` returns `1999, 52, Sun`
- `to_business (make 2000 1 3)` returns `2000, 1, Mon`

    val from_business : year -> int -> day -> t

Inverse of `to_business` respecting ISO-8601. Notice that business weeks at the beginning and end of the year can sometimes have year numbers which don't match the real year.
Since 1.09.0
Raises `Invalid_argument` if the date is bad.

    val int_of_day : day -> int

Convert a day to an integer respecting ISO-8601. So, Monday is 1, Tuesday is 2, ..., and sunday is 7.

    val day_of_int : int -> day

Inverse of `int_of_day`.
Raises `Invalid_argument` if the argument does not belong to `1; 7`.

    val int_of_month : month -> int

Convert a month to an integer respecting ISO-8601. So, January is 1, February is 2 and so on.

    val month_of_int : int -> month

Inverse of `int_of_month`.
Raises `Invalid_argument` if the argument does not belong to `1; 12`.

## Period

    module Period: sig .. end

A period is the number of days between two dates.

## Arithmetic operations on dates and periods

    val add : ([< field ] as 'a) date ->
           'a Period.period -> 'a date

`add d p` returns `d + p`.
Raises

- `Out_of_bounds` when the resulting date is outside the Julian period.
- `Undefined` when the resulting date belongs to `[October 5th, 1582; October 14th, 1582]`.

Examples:

- `add (make 2003 12 31) (Period.month 2)` returns the date 2004-3-2 (following the coercion rule describes in the introduction).
- `add (make 2003 12 31) (Period.month 1)` returns the date 2004-1-31

    val sub : ([< field ] as 'a) date ->
           'a date ->
           [< field > `Day `Week ] Period.period

`sub d1 d2` returns the period between `d1` and `d2`.

    val precise_sub : ([< field ] as 'a) date ->
           'a date -> Period.t

`precise_sub d1 d2` returns the period between `d1` and `d2`. It is equivalent to `sub`, but:

- the period is expressed with a number of years, months and days, not only with a number of days;
- it is less efficient.

Since 2.03

    val rem : ([< field ] as 'a) date ->
           'a Period.period -> 'a date

`rem d p` is equivalent to `add d (Period.opp p)`.
Raises

- `Out_of_bounds` when the resulting date is outside the Julian period.
- `Undefined` when the resulting date belongs to `[October 5th, 1582; October 14th, 1582]`.

    val next : ([< field ] as 'a) date -> 'a -> 'a date

`next d f` returns the date corresponding to the next specified field.
Raises

- `Out_of_bounds` when the resulting date is outside the Julian period.
- `Undefined` when the resulting date belongs to `[October 5th, 1582; October 14th, 1582]`.

Example: `next (make 2003 12 31) `Month` returns the date 2004-1-31 (i.e. one month later).

    val prev : ([< field ] as 'a) date -> 'a -> 'a date

`prev d f` returns the date corresponding to the previous specified field.
Raises

- `Out_of_bounds` when the resulting date is outside the Julian period.
- `Undefined` when the resulting date belongs to `[October 5th, 1582; October 14th, 1582]`.

Example: `prev (make 2003 12 31) `Year` returns the date 2002-12-31 (i.e. one year ago).

## Operations on years

    val is_leap_year : year -> bool

Return `true` if a year is a leap year; `false` otherwise.

    val same_calendar : year -> year -> bool

Return `true` if two years have the same calendar; `false` otherwise.

    val days_in_year : ?month:month -> year -> int

Number of days in a year.

`days_in_year ~month y` returns the number of days in the year `y` up to the end of the given month. Thus `days_in_year ~month:Dec y` is the same as `days_in_year y`.

    val weeks_in_year : year -> int

Number of weeks in a year.

    val week_first_last : int -> year -> t * t

Return the first and last days of a week in a year.
Since 1.08

    val nth_weekday_of_month : year -> month -> day -> int -> t

`nth_weekday_of_month y m d n` returns the `n`-th day `d` in the month `m` of the year `y` (for instance the 3rd Thursday of the month).
Since 1.09.0

    val century : year -> int

Century of a year.
Examples:

- `century 2001` returns 21.
- `century 2000` returns 20

    val millenium : year -> int

Millenium of a year.
Examples:

- `millenium 2001` returns 3.
- `millenium 2000` returns 2

    val solar_number : year -> int

Solar number.

In the Julian calendar there is a one-to-one relationship between the Solar number and the day on which a particular date falls.

    val indiction : year -> int

Indiction.

The Indiction was used in the middle ages to specify the position of a year in a 15 year taxation cycle. It was introduced by emperor Constantine the Great on 1 September 312 and ceased to be used in 1806.

The Indiction has no astronomical significance.

    val golden_number : year -> int

Golden number.

Considering that the relationship between the moon's phases and the days of the year repeats itself every 19 years, it is natural to associate a number between 1 and 19 with each year. This number is the so-called Golden number.

    val epact : year -> int

Epact.

The Epact is a measure of the age of the moon (i.e. the number of days that have passed since an "official" new moon) on a particular date.

    val easter : year -> t

Easter Sunday.

In the Christian world, Easter (and the days immediately preceding it) is the celebration of the death and resurrection of Jesus in (approximately) AD 30.

    val carnaval : year -> t

Carnaval Monday. `carnaval y` is `easter y - 48`.
Since 1.09.0

    val mardi_gras : year -> t

Mardi Gras. `mardi_gras y` is `easter y - 47`.
Since 1.09.0

    val ash : year -> t

Ash Wednesday. `ash y` is `easter y - 46`.
Since 1.09.0

    val palm : year -> t

Palm Sunday. `palm y` is `easter y - 7`.
Since 1.09.0

    val easter_friday : year -> t

Easter Friday. `easter_friday y` is `easter y - 2`.
Since 1.09.0

    val easter_saturday : year -> t

Easter Saturday. `easter_saturday y` is `easter y - 1`.
Since 1.09.0

    val easter_monday : year -> t

Easter Monday. `easter_monday y` is `easter y + 1`.
Since 1.09.0

    val ascension : year -> t

Ascension. `ascension y` is `easter y + 39`.
Since 1.09.0

    val withsunday : year -> t

Withsunday. `withsunday y` is `easter y + 49`.
Since 1.09.0

    val withmonday : year -> t

Withmonday. `withmonday y` is `easter y + 50`.
Since 1.09.0

    val corpus_christi : year -> t

Feast of Corpus Christi. `corpus_christi y` is `easter + 60`.
Since 1.09.0