Date Rounding (#17037)

* Added floor, ceil, round for Date and DateTime.

* Refactoring and documentation for date rounding.

* Added PR reference in NEWS.md.

* Bugfix for date rounding test in 32-bit. Doc clarifications.

* Round to nonpositive resolution throws DomainError

Throw DomainError on rounding to an invalid (non-positive) resolution
Clean up test cases for rounding dates that don't need rounding
Add test cases for rounding to invalid (non-positive) resolutions

NEWS.md

@@ -206,6 +206,9 @@ Library improvements
   * Prime number related functions have been moved from `Base` to the
     [Primes.jl package](https://github.com/JuliaMath/Primes.jl) ([#16481]).
 
+  * `Date` and `DateTime` values can now be rounded to a specified resolution (e.g., 1 month or
+    15 minutes) with `floor`, `ceil`, and `round` ([#17037]).
+
 Deprecated or removed
 ---------------------
 
@@ -297,3 +300,4 @@ Deprecated or removed
 [#16731]: https://github.com/JuliaLang/julia/issues/16731
 [#16972]: https://github.com/JuliaLang/julia/issues/16972
 [#17266]: https://github.com/JuliaLang/julia/issues/17266
+[#17037]: https://github.com/JuliaLang/julia/issues/17037

base/dates/Dates.jl

@@ -12,6 +12,7 @@ include("arithmetic.jl")
 include("conversions.jl")
 include("ranges.jl")
 include("adjusters.jl")
+include("rounding.jl")
 include("io.jl")
 
 export Period, DatePeriod, TimePeriod,

base/dates/rounding.jl

@@ -0,0 +1,178 @@
+# The epochs used for date rounding are based ISO 8601's "year zero" notation
+const DATEEPOCH = value(Date(0))
+const DATETIMEEPOCH = value(DateTime(0))
+
+# According to ISO 8601, the first day of the first week of year 0000 is 0000-01-03
+const WEEKEPOCH = value(Date(0, 1, 3))
+
+"""
+    epochdays2date(days) -> Date
+
+Takes the number of days since the rounding epoch (`0000-01-01T00:00:00`) and returns the
+corresponding `Date`.
+"""
+epochdays2date(i) = Date(UTD(DATEEPOCH + Int64(i)))
+
+"""
+    epochms2datetime(milliseconds) -> DateTime
+
+Takes the number of milliseconds since the rounding epoch (`0000-01-01T00:00:00`) and
+returns the corresponding `DateTime`.
+"""
+epochms2datetime(i) = DateTime(UTM(DATETIMEEPOCH + Int64(i)))
+
+"""
+    date2epochdays(dt::Date) -> Int64
+
+Takes the given `Date` and returns the number of days since the rounding epoch
+(`0000-01-01T00:00:00`) as an `Int64`.
+"""
+date2epochdays(dt::Date) = value(dt) - DATEEPOCH
+
+"""
+    datetime2epochms(dt::DateTime) -> Int64
+
+Takes the given `DateTime` and returns the number of milliseconds since the rounding epoch
+(`0000-01-01T00:00:00`) as an `Int64`.
+"""
+datetime2epochms(dt::DateTime) = value(dt) - DATETIMEEPOCH
+
+function Base.floor(dt::Date, p::Year)
+    value(p) < 1 && throw(DomainError())
+    years = year(dt)
+    return Date(years - mod(years, value(p)))
+end
+
+function Base.floor(dt::Date, p::Month)
+    value(p) < 1 && throw(DomainError())
+    y, m = yearmonth(dt)
+    months_since_epoch = y * 12 + m - 1
+    month_offset = months_since_epoch - mod(months_since_epoch, value(p))
+    target_month = mod(month_offset, 12) + 1
+    target_year = div(month_offset, 12) - (month_offset < 0 && target_month != 1)
+    return Date(target_year, target_month)
+end
+
+function Base.floor(dt::Date, p::Week)
+    value(p) < 1 && throw(DomainError())
+    days = value(dt) - WEEKEPOCH
+    days = days - mod(days, value(Day(p)))
+    return Date(UTD(WEEKEPOCH + Int64(days)))
+end
+
+function Base.floor(dt::Date, p::Day)
+    value(p) < 1 && throw(DomainError())
+    days = date2epochdays(dt)
+    return epochdays2date(days - mod(days, value(p)))
+end
+
+Base.floor(dt::DateTime, p::DatePeriod) = DateTime(Base.floor(Date(dt), p))
+
+function Base.floor(dt::DateTime, p::TimePeriod)
+    value(p) < 1 && throw(DomainError())
+    milliseconds = datetime2epochms(dt)
+    return epochms2datetime(milliseconds - mod(milliseconds, value(Millisecond(p))))
+end
+
+"""
+    floor(dt::TimeType, p::Period) -> TimeType
+
+Returns the nearest `Date` or `DateTime` less than or equal to `dt` at resolution `p`.
+
+For convenience, `p` may be a type instead of a value: `floor(dt, Dates.Hour)` is a shortcut
+for `floor(dt, Dates.Hour(1))`.
+
+```jldoctest
+julia> floor(Date(1985, 8, 16), Dates.Month)
+1985-08-01
+
+julia> floor(DateTime(2013, 2, 13, 0, 31, 20), Dates.Minute(15))
+2013-02-13T00:30:00
+
+julia> floor(DateTime(2016, 8, 6, 12, 0, 0), Dates.Day)
+2016-08-06T00:00:00
+```
+"""
+Base.floor(::Dates.TimeType, ::Dates.Period)
+
+"""
+    ceil(dt::TimeType, p::Period) -> TimeType
+
+Returns the nearest `Date` or `DateTime` greater than or equal to `dt` at resolution `p`.
+
+For convenience, `p` may be a type instead of a value: `ceil(dt, Dates.Hour)` is a shortcut
+for `ceil(dt, Dates.Hour(1))`.
+
+```jldoctest
+julia> ceil(Date(1985, 8, 16), Dates.Month)
+1985-09-01
+
+julia> ceil(DateTime(2013, 2, 13, 0, 31, 20), Dates.Minute(15))
+2013-02-13T00:45:00
+
+julia> ceil(DateTime(2016, 8, 6, 12, 0, 0), Dates.Day)
+2016-08-07T00:00:00
+```
+"""
+function Base.ceil(dt::TimeType, p::Period)
+    f = floor(dt, p)
+    return (dt == f) ? f : f + p
+end
+
+"""
+    floorceil(dt::TimeType, p::Period) -> (TimeType, TimeType)
+
+Simultaneously return the `floor` and `ceil` of a `Date` or `DateTime` at resolution `p`.
+More efficient than calling both `floor` and `ceil` individually.
+"""
+function floorceil(dt::TimeType, p::Period)
+    f = floor(dt, p)
+    return f, (dt == f) ? f : f + p
+end
+
+"""
+    round(dt::TimeType, p::Period, [r::RoundingMode]) -> TimeType
+
+Returns the `Date` or `DateTime` nearest to `dt` at resolution `p`. By default
+(`RoundNearestTiesUp`), ties (e.g., rounding 9:30 to the nearest hour) will be rounded up.
+
+For convenience, `p` may be a type instead of a value: `round(dt, Dates.Hour)` is a shortcut
+for `round(dt, Dates.Hour(1))`.
+
+```jldoctest
+julia> round(Date(1985, 8, 16), Dates.Month)
+1985-08-01
+
+julia> round(DateTime(2013, 2, 13, 0, 31, 20), Dates.Minute(15))
+2013-02-13T00:30:00
+
+julia> round(DateTime(2016, 8, 6, 12, 0, 0), Dates.Day)
+2016-08-07T00:00:00
+```
+
+Valid rounding modes for `round(::TimeType, ::Period, ::RoundingMode)` are
+`RoundNearestTiesUp` (default), `RoundDown` (`floor`), and `RoundUp` (`ceil`).
+"""
+function Base.round(dt::TimeType, p::Period, r::RoundingMode{:NearestTiesUp})
+    f, c = floorceil(dt, p)
+    return (dt - f) < (c - dt) ? f : c
+end
+
+Base.round(dt::TimeType, p::Period, r::RoundingMode{:Down}) = Base.floor(dt, p)
+Base.round(dt::TimeType, p::Period, r::RoundingMode{:Up}) = Base.ceil(dt, p)
+
+# No implementation of other `RoundingMode`s: rounding to nearest "even" is skipped because
+# "even" is not defined for Period; rounding toward/away from zero is skipped because ISO
+# 8601's year 0000 is not really "zero".
+Base.round(::TimeType, ::Period, ::RoundingMode) = throw(DomainError())
+
+# Default to RoundNearestTiesUp.
+Base.round(dt::TimeType, p::Period) = Base.round(dt, p, RoundNearestTiesUp)
+
+# Make rounding functions callable using Period types in addition to values.
+Base.floor{T <: Period}(dt::TimeType, p::Type{T}) = Base.floor(dt, p(1))
+Base.ceil{T <: Period}(dt::TimeType, p::Type{T}) = Base.ceil(dt, p(1))
+
+function Base.round{T<:Period}(dt::TimeType, p::Type{T}, r::RoundingMode=RoundNearestTiesUp)
+    return Base.round(dt, p(1), r)
+end

doc/manual/dates.rst

@@ -367,4 +367,95 @@ Periods are a human view of discrete, sometimes irregular durations of time. Con
   3 years
 
 
+Rounding
+--------
+
+:class:`Date` and :class:`DateTime` values can be rounded to a specified resolution (e.g.,
+1 month or 15 minutes) with :func:`floor`, :func:`ceil`, or :func:`round`:
+
+.. doctest::
+
+    julia> floor(Date(1985, 8, 16), Dates.Month)
+    1985-08-01
+
+    julia> ceil(DateTime(2013, 2, 13, 0, 31, 20), Dates.Minute(15))
+    2013-02-13T00:45:00
+
+    julia> round(DateTime(2016, 8, 6, 20, 15), Dates.Day)
+    2016-08-07T00:00:00
+
+Unlike the numeric :func:`round` method, which breaks ties toward the even number by
+default, the :class:`TimeType` :func:`round` method uses the ``RoundNearestTiesUp``
+rounding mode. (It's difficult to guess what breaking ties to nearest "even"
+:class:`TimeType` would entail.) Further details on the available ``RoundingMode`` s can
+be found in the
+`API reference <http://docs.julialang.org/en/latest/stdlib/dates/#rounding-functions>`_.
+
+Rounding should generally behave as expected, but there are a few cases in which the
+expected behaviour is not obvious.
+
+Rounding Epoch
+~~~~~~~~~~~~~~
+
+In many cases, the resolution specified for rounding (e.g., ``Dates.Second(30)``) divides
+evenly into the next largest period (in this case, ``Dates.Minute(1)``). But rounding
+behaviour in cases in which this is not true may lead to confusion. What is the expected
+result of rounding a :class:`DateTime` to the nearest 10 hours?
+
+.. doctest::
+
+    julia> round(DateTime(2016, 7, 17, 11, 55), Dates.Hour(10))
+    2016-07-17T12:00:00
+
+That may seem confusing, given that the hour (12) is not divisible by 10. The reason that
+``2016-07-17T12:00:00`` was chosen is that it is 17,676,660 hours after
+``0000-01-01T00:00:00``, and 17,676,660 is divisible by 10.
+
+As Julia :class:`Date` and :class:`DateTime` values are represented according to the ISO
+8601 standard, ``0000-01-01T00:00:00`` was chosen as base (or "rounding epoch") from
+which to begin the count of days (and milliseconds) used in rounding calculations. (Note
+that this differs slightly from Julia's internal representation of :class:`Date` s using
+Rata Die notation; but since the ISO 8601 standard is most visible to the end user,
+``0000-01-01T00:00:00`` was chosen as the rounding epoch instead of the
+``0000-12-31T00:00:00`` used internally to minimize confusion.)
+
+The only exception to the use of ``0000-01-01T00:00:00`` as the rounding epoch is when
+rounding to weeks. Rounding to the nearest week will always return a Monday (the first day
+of the week as specified by ISO 8601). For this reason, we use ``0000-01-03T00:00:00``
+(the first day of the first week of year 0000, as defined by ISO 8601) as the base when
+rounding to a number of weeks.
+
+Here is a related case in which the expected behaviour is not necessarily obvious: What
+happens when we round to the nearest ``P(2)``, where ``P`` is a :class:`Period` type? In
+some cases (specifically, when ``P <: Dates.TimePeriod``) the answer is clear:
+
+.. doctest::
+
+    julia> round(DateTime(2016, 7, 17, 8, 55, 30), Dates.Hour(2))
+    2016-07-17T08:00:00
+
+    julia> round(DateTime(2016, 7, 17, 8, 55, 30), Dates.Minute(2))
+    2016-07-17T08:56:00
+
+This seems obvious, because two of each of these periods still divides evenly into the
+next larger order period. But in the case of two months (which still divides evenly into
+one year), the answer may be surprising:
+
+.. doctest::
+
+    julia> round(DateTime(2016, 7, 17, 8, 55, 30), Dates.Month(2))
+    2016-07-01T00:00:00
+
+Why round to the first day in July, even though it is month 7 (an odd number)? The key is
+that months are 1-indexed (the first month is assigned 1), unlike hours, minutes, seconds,
+and milliseconds (the first of which are assigned 0).
+
+This means that rounding a :class:`DateTime` to an even multiple of seconds, minutes,
+hours, or years (because the ISO 8601 specification includes a year zero) will result in
+a :class:`DateTime` with an even value in that field, while rounding a :class:`DateTime`
+to an even multiple of months will result in the months field having an odd value. Because
+both months and years may contain an irregular number of days, whether rounding to an even
+number of days will result in an even value in the days field is uncertain.
+
+
 See the `API reference <http://docs.julialang.org/en/latest/stdlib/dates/>`_ for additional information on methods exported from the :mod:`Dates` module.