Integer based date class

Classes (IDate and ITime) with integer storage for fast sorting and grouping.

IDate inherits from the base class Date; the main difference is that the latter uses double storage, allowing e.g. for fractional dates at the cost of storage & sorting inefficiency.

Using IDate, if sub-day granularity is needed, use a second ITime column. IDateTime() facilitates building such paired columns.

Lastly, there are date-time helpers for extracting parts of dates as integers, for example the year (year()), month (month()), or day in the month (mday()); see Usage and Examples.

Usage

as.IDate(x, ...)
# Default S3 method
as.IDate(x, ..., tz = attr(x, "tzone", exact=TRUE))
# S3 method for class 'Date'
as.IDate(x, ...)
# S3 method for class 'IDate'
as.Date(x, ...)
# S3 method for class 'IDate'
as.POSIXct(x, tz = "UTC", time = 0, ...)
# S3 method for class 'IDate'
round(x, digits = c("weeks", "months", "quarters","years"), ...)

as.ITime(x, ...)
# Default S3 method
as.ITime(x, ...)
# S3 method for class 'POSIXlt'
as.ITime(x, ms = 'truncate', ...)
# S3 method for class 'ITime'
round(x, digits = c("hours", "minutes"), ...)
# S3 method for class 'ITime'
trunc(x, units = c("hours", "minutes"), ...)

# S3 method for class 'ITime'
as.POSIXct(x, tz = "UTC", date = Sys.Date(), ...)
# S3 method for class 'ITime'
as.character(x, ...)
# S3 method for class 'ITime'
format(x, ...)

IDateTime(x, ...)
# Default S3 method
IDateTime(x, ...)

second(x)
minute(x)
hour(x)
yday(x)
wday(x)
mday(x)
week(x)
isoweek(x)
isoyear(x)     
month(x)
quarter(x)
year(x)
yearmon(x)
yearqtr(x)

Arguments

x: an object
...: arguments to be passed to or from other methods. For as.IDate.default, arguments are passed to as.Date. For as.ITime.default, arguments are passed to as.POSIXlt.
tz: time zone (see strptime).
date: date object convertible with as.IDate.
time: time-of-day object convertible with as.ITime.
digits: really units; one of the units listed for rounding. May be abbreviated. Named digits for consistency with the S3 generic.
units: one of the units listed for truncating. May be abbreviated.
ms: For as.ITime methods, what should be done with sub-second fractions of input? Valid values are 'truncate' (floor), 'nearest' (round), and 'ceil' (ceiling). See Details.

Details

IDate is a date class derived from Date. It has the same internal representation as the Date class, except the storage mode is integer. IDate is a relatively simple wrapper, and it should work in almost all situations as a replacement for Date. The main limitations of integer storage are (1) fractional dates are not supported (use IDateTime() instead) and (2) the range of supported dates is bounded by .Machine$integer.max dates away from January 1, 1970 (a rather impractical limitation as these dates are roughly 6 million years in the future/past, but consider this your caveat).

Functions that use Date objects generally work for IDate objects. This package provides specific methods for IDate objects for mean, cut, seq, c, rep, and split to return an IDate object.

ITime is a time-of-day class stored as the integer number of seconds in the day. as.ITime does not allow days longer than 24 hours. Because ITime is stored in seconds, you can add it to a POSIXct object, but you should not add it to a Date object.

For as.ITime, note that the string "24:00:00" is parsed as "00:00:00". This is because the conversion uses as.POSIXct, which treats "24:00:00" as midnight of the next day. This differs from ISO 8601 (which allows "24:00:00" to represent end-of-day), but aligns with POSIX standards. To represent end-of-day intervals, use "23:59:59" or arithmetic (e.g., as.ITime("23:59:59") + 1L).

We also provide S3 methods to convert to and from Date and POSIXct.

ITime is time zone-agnostic. When converting ITime and IDate to POSIXct with as.POSIXct, a time zone may be specified.

Inputs like '2018-05-15 12:34:56.789' are ambiguous from the perspective of an ITime object – the method of coercion of the 789 milliseconds is controlled by the ms argument to relevant methods. The default behavior (ms = 'truncate') is to use as.integer, which has the effect of truncating anything after the decimal. Alternatives are to round to the nearest integer (ms = 'nearest') or to round up (ms = 'ceil').

In as.POSIXct methods for ITime and IDate, the second argument is required to be tz based on the generic template, but to make converting easier, the second argument is interpreted as a date instead of a time zone if it is of type IDate or ITime. Therefore, you can use either of the following: as.POSIXct(time, date) or as.POSIXct(date, time).

IDateTime takes a date-time input and returns a data table with columns date and time.

Using integer storage allows dates and/or times to be used as data table keys. With positive integers with a range less than 100,000, grouping and sorting is fast because radix sorting can be used (see sort.list).

Several convenience functions like hour and quarter are provided to group or extract by hour, month, and other date-time intervals. as.POSIXlt is also useful. For example, as.POSIXlt(x)$mon is the integer month. The R base convenience functions weekdays, months, and quarters can also be used, but these return character values, so they must be converted to factors for use with data.table. isoweek is ISO 8601-consistent.

The round method for IDate's is useful for grouping and plotting. It can round to weeks, months, quarters, and years. Similarly, the round and trunc methods for ITime's are useful for grouping and plotting. They can round or truncate to hours and minutes. Note for ITime's with 30 seconds, rounding is inconsistent due to rounding off a 5. See 'Details' in round for more information.

Functions like week() and isoweek() provide week numbering functionality. week() computes completed or fractional weeks within the year, while isoweek() calculates week numbers according to ISO 8601 standards, which specify that the first week of the year is the one containing the first Thursday. This convention ensures that week boundaries align consistently with year boundaries, accounting for both year transitions and varying day counts per week.

Similarly, isoyear() returns the ISO 8601 year corresponding to the ISO week.

Value

For as.IDate, a class of IDate and Date with the date stored as the number of days since some origin.

For as.ITime, a class of ITime stored as the number of seconds in the day.

For IDateTime, a data table with columns idate and itime in IDate and ITime format.

second, minute, hour, yday, wday, mday, week, isoweek, isoyear, month, quarter, and year return integer values for second, minute, hour, day of year, day of week, day of month, week, month, quarter, and year, respectively. yearmon and yearqtr return double values representing respectively year + (month-1) / 12 and year + (quarter-1) / 4.

second, minute, hour are taken directly from the POSIXlt representation. All other values are computed from the underlying integer representation and comparable with the values of their POSIXlt representation of x, with the notable difference that while yday, wday, and mon are all 0-based, here they are 1-based.

References

G. Grothendieck and T. Petzoldt, “Date and Time Classes in R”, R News, vol. 4, no. 1, June 2004.

H. Wickham, https://gist.github.com/hadley/10238.

ISO 8601, https://www.iso.org/iso/home/standards/iso8601.htm

Author

Tom Short, t.short@ieee.org

Examples


# create IDate:
(d <- as.IDate("2001-01-01"))
#> [1] "2001-01-01"

# S4 coercion also works
identical(as.IDate("2001-01-01"), methods::as("2001-01-01", "IDate"))
#> [1] TRUE

# create ITime:
(t <- as.ITime("10:45"))
#> [1] "10:45:00"

# S4 coercion also works
identical(as.ITime("10:45"), methods::as("10:45", "ITime"))
#> [1] TRUE

(t <- as.ITime("10:45:04"))
#> [1] "10:45:04"

(t <- as.ITime("10:45:04", format = "%H:%M:%S"))
#> [1] "10:45:04"

# "24:00:00" is parsed as "00:00:00"
as.ITime("24:00:00")
#> [1] "00:00:00"

# Workaround for end-of-day: add 1 second to "23:59:59"
as.ITime("23:59:59") + 1L
#> [1] "24:00:00"

as.POSIXct("2001-01-01") + as.ITime("10:45")
#> [1] "2001-01-01 10:45:00 UTC"

datetime <- seq(as.POSIXct("2001-01-01"), as.POSIXct("2001-01-03"), by = "5 hour")
(af <- data.table(IDateTime(datetime), a = rep(1:2, 5), key = c("a", "idate", "itime")))
#> Key: <a, idate, itime>
#>          idate    itime     a
#>         <IDat>  <ITime> <int>
#>  1: 2001-01-01 00:00:00     1
#>  2: 2001-01-01 10:00:00     1
#>  3: 2001-01-01 20:00:00     1
#>  4: 2001-01-02 06:00:00     1
#>  5: 2001-01-02 16:00:00     1
#>  6: 2001-01-01 05:00:00     2
#>  7: 2001-01-01 15:00:00     2
#>  8: 2001-01-02 01:00:00     2
#>  9: 2001-01-02 11:00:00     2
#> 10: 2001-01-02 21:00:00     2

af[, mean(a), by = "itime"]
#>        itime    V1
#>      <ITime> <num>
#>  1: 00:00:00     1
#>  2: 10:00:00     1
#>  3: 20:00:00     1
#>  4: 06:00:00     1
#>  5: 16:00:00     1
#>  6: 05:00:00     2
#>  7: 15:00:00     2
#>  8: 01:00:00     2
#>  9: 11:00:00     2
#> 10: 21:00:00     2
af[, mean(a), by = list(hour = hour(itime))]
#>      hour    V1
#>     <int> <num>
#>  1:     0     1
#>  2:    10     1
#>  3:    20     1
#>  4:     6     1
#>  5:    16     1
#>  6:     5     2
#>  7:    15     2
#>  8:     1     2
#>  9:    11     2
#> 10:    21     2
af[, mean(a), by = list(wday = factor(weekdays(idate)))]
#>       wday    V1
#>     <fctr> <num>
#> 1:  Monday   1.4
#> 2: Tuesday   1.6
af[, mean(a), by = list(wday = wday(idate))]
#>     wday    V1
#>    <int> <num>
#> 1:     2   1.4
#> 2:     3   1.6

as.POSIXct(af$idate)
#>  [1] "2001-01-01 UTC" "2001-01-01 UTC" "2001-01-01 UTC" "2001-01-02 UTC"
#>  [5] "2001-01-02 UTC" "2001-01-01 UTC" "2001-01-01 UTC" "2001-01-02 UTC"
#>  [9] "2001-01-02 UTC" "2001-01-02 UTC"
as.POSIXct(af$idate, time = af$itime)
#>  [1] "2001-01-01 00:00:00 UTC" "2001-01-01 10:00:00 UTC"
#>  [3] "2001-01-01 20:00:00 UTC" "2001-01-02 06:00:00 UTC"
#>  [5] "2001-01-02 16:00:00 UTC" "2001-01-01 05:00:00 UTC"
#>  [7] "2001-01-01 15:00:00 UTC" "2001-01-02 01:00:00 UTC"
#>  [9] "2001-01-02 11:00:00 UTC" "2001-01-02 21:00:00 UTC"
as.POSIXct(af$idate, af$itime)
#>  [1] "2001-01-01 00:00:00 UTC" "2001-01-01 10:00:00 UTC"
#>  [3] "2001-01-01 20:00:00 UTC" "2001-01-02 06:00:00 UTC"
#>  [5] "2001-01-02 16:00:00 UTC" "2001-01-01 05:00:00 UTC"
#>  [7] "2001-01-01 15:00:00 UTC" "2001-01-02 01:00:00 UTC"
#>  [9] "2001-01-02 11:00:00 UTC" "2001-01-02 21:00:00 UTC"
as.POSIXct(af$idate, time = af$itime, tz = "GMT")
#>  [1] "2001-01-01 00:00:00 GMT" "2001-01-01 10:00:00 GMT"
#>  [3] "2001-01-01 20:00:00 GMT" "2001-01-02 06:00:00 GMT"
#>  [5] "2001-01-02 16:00:00 GMT" "2001-01-01 05:00:00 GMT"
#>  [7] "2001-01-01 15:00:00 GMT" "2001-01-02 01:00:00 GMT"
#>  [9] "2001-01-02 11:00:00 GMT" "2001-01-02 21:00:00 GMT"

as.POSIXct(af$itime, af$idate)
#>  [1] "2001-01-01 00:00:00 UTC" "2001-01-01 10:00:00 UTC"
#>  [3] "2001-01-01 20:00:00 UTC" "2001-01-02 06:00:00 UTC"
#>  [5] "2001-01-02 16:00:00 UTC" "2001-01-01 05:00:00 UTC"
#>  [7] "2001-01-01 15:00:00 UTC" "2001-01-02 01:00:00 UTC"
#>  [9] "2001-01-02 11:00:00 UTC" "2001-01-02 21:00:00 UTC"
as.POSIXct(af$itime) # uses today's date
#>  [1] "2025-10-29 00:00:00 UTC" "2025-10-29 10:00:00 UTC"
#>  [3] "2025-10-29 20:00:00 UTC" "2025-10-29 06:00:00 UTC"
#>  [5] "2025-10-29 16:00:00 UTC" "2025-10-29 05:00:00 UTC"
#>  [7] "2025-10-29 15:00:00 UTC" "2025-10-29 01:00:00 UTC"
#>  [9] "2025-10-29 11:00:00 UTC" "2025-10-29 21:00:00 UTC"

(seqdates <- seq(as.IDate("2001-01-01"), as.IDate("2001-08-03"), by = "3 weeks"))
#>  [1] "2001-01-01" "2001-01-22" "2001-02-12" "2001-03-05" "2001-03-26"
#>  [6] "2001-04-16" "2001-05-07" "2001-05-28" "2001-06-18" "2001-07-09"
#> [11] "2001-07-30"
round(seqdates, "months")
#>  [1] "2001-01-01" "2001-01-01" "2001-02-01" "2001-03-01" "2001-03-01"
#>  [6] "2001-04-01" "2001-05-01" "2001-05-01" "2001-06-01" "2001-07-01"
#> [11] "2001-07-01"

(seqtimes <- seq(as.ITime("07:00"), as.ITime("08:00"), by = 20))
#>   [1] "07:00:00" "07:00:20" "07:00:40" "07:01:00" "07:01:20" "07:01:40"
#>   [7] "07:02:00" "07:02:20" "07:02:40" "07:03:00" "07:03:20" "07:03:40"
#>  [13] "07:04:00" "07:04:20" "07:04:40" "07:05:00" "07:05:20" "07:05:40"
#>  [19] "07:06:00" "07:06:20" "07:06:40" "07:07:00" "07:07:20" "07:07:40"
#>  [25] "07:08:00" "07:08:20" "07:08:40" "07:09:00" "07:09:20" "07:09:40"
#>  [31] "07:10:00" "07:10:20" "07:10:40" "07:11:00" "07:11:20" "07:11:40"
#>  [37] "07:12:00" "07:12:20" "07:12:40" "07:13:00" "07:13:20" "07:13:40"
#>  [43] "07:14:00" "07:14:20" "07:14:40" "07:15:00" "07:15:20" "07:15:40"
#>  [49] "07:16:00" "07:16:20" "07:16:40" "07:17:00" "07:17:20" "07:17:40"
#>  [55] "07:18:00" "07:18:20" "07:18:40" "07:19:00" "07:19:20" "07:19:40"
#>  [61] "07:20:00" "07:20:20" "07:20:40" "07:21:00" "07:21:20" "07:21:40"
#>  [67] "07:22:00" "07:22:20" "07:22:40" "07:23:00" "07:23:20" "07:23:40"
#>  [73] "07:24:00" "07:24:20" "07:24:40" "07:25:00" "07:25:20" "07:25:40"
#>  [79] "07:26:00" "07:26:20" "07:26:40" "07:27:00" "07:27:20" "07:27:40"
#>  [85] "07:28:00" "07:28:20" "07:28:40" "07:29:00" "07:29:20" "07:29:40"
#>  [91] "07:30:00" "07:30:20" "07:30:40" "07:31:00" "07:31:20" "07:31:40"
#>  [97] "07:32:00" "07:32:20" "07:32:40" "07:33:00" "07:33:20" "07:33:40"
#> [103] "07:34:00" "07:34:20" "07:34:40" "07:35:00" "07:35:20" "07:35:40"
#> [109] "07:36:00" "07:36:20" "07:36:40" "07:37:00" "07:37:20" "07:37:40"
#> [115] "07:38:00" "07:38:20" "07:38:40" "07:39:00" "07:39:20" "07:39:40"
#> [121] "07:40:00" "07:40:20" "07:40:40" "07:41:00" "07:41:20" "07:41:40"
#> [127] "07:42:00" "07:42:20" "07:42:40" "07:43:00" "07:43:20" "07:43:40"
#> [133] "07:44:00" "07:44:20" "07:44:40" "07:45:00" "07:45:20" "07:45:40"
#> [139] "07:46:00" "07:46:20" "07:46:40" "07:47:00" "07:47:20" "07:47:40"
#> [145] "07:48:00" "07:48:20" "07:48:40" "07:49:00" "07:49:20" "07:49:40"
#> [151] "07:50:00" "07:50:20" "07:50:40" "07:51:00" "07:51:20" "07:51:40"
#> [157] "07:52:00" "07:52:20" "07:52:40" "07:53:00" "07:53:20" "07:53:40"
#> [163] "07:54:00" "07:54:20" "07:54:40" "07:55:00" "07:55:20" "07:55:40"
#> [169] "07:56:00" "07:56:20" "07:56:40" "07:57:00" "07:57:20" "07:57:40"
#> [175] "07:58:00" "07:58:20" "07:58:40" "07:59:00" "07:59:20" "07:59:40"
#> [181] "08:00:00"
round(seqtimes, "hours")
#>   [1] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>   [7] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [13] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [19] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [25] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [31] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [37] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [43] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [49] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [55] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [61] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [67] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [73] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [79] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [85] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [91] "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00"
#>  [97] "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00"
#> [103] "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00"
#> [109] "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00"
#> [115] "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00"
#> [121] "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00"
#> [127] "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00"
#> [133] "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00"
#> [139] "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00"
#> [145] "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00"
#> [151] "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00"
#> [157] "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00"
#> [163] "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00"
#> [169] "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00"
#> [175] "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00" "08:00:00"
#> [181] "08:00:00"
trunc(seqtimes, "hours")
#>   [1] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>   [7] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [13] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [19] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [25] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [31] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [37] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [43] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [49] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [55] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [61] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [67] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [73] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [79] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [85] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [91] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#>  [97] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#> [103] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#> [109] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#> [115] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#> [121] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#> [127] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#> [133] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#> [139] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#> [145] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#> [151] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#> [157] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#> [163] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#> [169] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#> [175] "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00" "07:00:00"
#> [181] "08:00:00"

# Examples for isoyear() and isoweek()
d1 = as.IDate("2019-12-30")
year(d1)
#> [1] 2019
isoweek(d1)
#> [1] 1
isoyear(d1)
#> [1] 2020

d2 = as.IDate("2016-01-01")
year(d2)
#> [1] 2016
isoweek(d2)
#> [1] 53
isoyear(d2)
#> [1] 2015