intervals.r

#' @include timespans.r
#' @include parse.r
#' @include util.r
NULL

check_interval <- function(object) {
  errors <- character()
  if (!is.numeric(object@.Data)) {
    msg <- "Span length must be numeric."
    errors <- c(errors, msg)
  }
  if (!is(object@start, "POSIXct")) {
    msg <- "Start date must be in POSIXct format."
    errors <- c(errors, msg)
  }
  if (length(object@.Data) != length(object@start)) {
    msg <- paste("Inconsistent lengths: spans = ", length(object@.Data),
      ", start dates = ", length(object@start), sep = "")
    errors <- c(errors, msg)
  }
  if (length(errors) == 0)
    TRUE
  else
    errors
}

.units_within_seconds <- function(secs, unit = "second") {
  ## return a list suitable to pass to new("Period", ...)
  switch(unit,
         second = list(secs),
         minute = list(secs %% 60, minute = secs %/% 60),
         hour =
           c(.units_within_seconds(secs %% 3600, "minute"),
             list(hour = secs %/% 3600)),
         day =
           c(.units_within_seconds(secs %% 86400, "hour"),
             list(day = secs %/% 86400)),
         stop("Unsuported unit ", unit))
}

#' Interval class
#'
#' Interval is an S4 class that extends the [Timespan-class] class. An
#' Interval object records one or more spans of time. Intervals record these
#' timespans as a sequence of seconds that begin at a specified date. Since
#' intervals are anchored to a precise moment of time, they can accurately be
#' converted to [Period-class] or [Duration-class] class objects. This
#' is because we can observe the length in seconds of each period that begins on a
#' specific date. Contrast this to a generalized period, which may not have a
#' consistent length in seconds (e.g. the number of seconds in a year will change
#' if it is a leap year).
#'
#' Intervals can be both negative and positive. Negative intervals progress
#' backwards from the start date; positive intervals progress forwards.
#'
#' Interval class objects have two slots: .Data, a numeric object equal to the number
#' of seconds in the interval; and start, a POSIXct object that specifies the time
#' when the interval starts.
#'
#' @aliases intervals
#' @export
setClass("Interval", contains = c("Timespan", "numeric"),
  slots = c(start = "POSIXct",   tzone = "character"), validity = check_interval)

#' @export
setMethod("show", signature(object = "Interval"), function(object) {
  if (length(object@.Data) == 0) {
    cat("<Interval[0]>\n")
  } else {
    print(format(object), quote = FALSE)
  }
})

#' @export
format.Interval <- function(x, ...) {
  paste(
    format(x@start, tz = x@tzone, usetz = TRUE),
    format(x@start + x@.Data, tz = x@tzone, usetz = TRUE),
    sep = "--"
  )
}

#' @export
setMethod("c", signature(x = "Interval"), function(x, ...) {
  elements <- lapply(list(...), as.interval)
  spans <- c(x@.Data, unlist(elements@.Data))
  starts <- c(x@start, lapply(elements, int_start))
  new("Interval", spans, start = starts, tzone = x@tzone)
})

#' @export
setMethod("rep", signature(x = "Interval"), function(x, ...) {
  new("Interval", rep(x@.Data, ...), start = rep(x@start, ...), tzone = x@tzone)
})

#' @export
setMethod("[", signature(x = "Interval"),
  function(x, i, j, ..., drop = TRUE) {
      new("Interval", x@.Data[i], start = x@start[i], tzone = x@tzone)
  }
)

#' @export
setMethod("[[", signature(x = "Interval"),
  function(x, i, j, ..., exact = TRUE) {
    new("Interval", x@.Data[i], start = x@start[i], tzone = x@tzone)
  }
)

#' @export
setMethod("[<-", signature(x = "Interval"), function(x, i, j, ..., value) {
    if (is.interval(value)) {
      x@.Data[i] <- value@.Data
      x@start[i] <- value@start
      new("Interval", x@.Data, start = x@start, tzone = x@tzone)
    }
    else {
      x@.Data[i] <- value
    new("Interval", x@.Data, start = x@start, tzone = x@tzone)
  }
})

#' @export
setMethod("[[<-", signature(x = "Interval"), function(x, i, j, ..., value) {
  if (is.interval(value)) {
    x@.Data[i] <- value@.Data
    x@start[i] <- value@start
    new("Interval", x@.Data, start = x@start, tzone = x@tzone)
  }
  else {
    x@.Data[i] <- value
    new("Interval", x@.Data, start = x@start, tzone = x@tzone)
  }
})

#' @export
setMethod("$", signature(x = "Interval"), function(x, name) {
  if (name == "span") name <- ".Data"
  slot(x, name)
})

#' @export
setMethod("$<-", signature(x = "Interval"), function(x, name, value) {
  if (name == "span") name <- ".Data"
  slot(x, name) <- value
  x
})

#' @export
unique.Interval <- function(x, ...) {
  df <- unique.data.frame(data.frame(data = x@.Data, start = x@start), ...)
  new("Interval", df$data, start = df$start, tzone = x@tzone)
}

#' Utilities for creation and manipulation of `Interval` objects
#'
#' `interval()` creates an [Interval-class] object with the specified start and
#' end dates. If the start date occurs before the end date, the interval will be
#' positive. Otherwise, it will be negative. Character vectors in ISO 8601
#' format are supported from v1.7.2.
#'
#' Intervals are time spans bound by two real date-times.  Intervals can be
#' accurately converted to either period or duration objects using
#' [as.period()], [as.duration()]. Since an interval is anchored to a fixed
#' history of time, both the exact number of seconds that passed and the number
#' of variable length time units that occurred during the interval can be
#' calculated.
#'
#' @export
#' @param start,end POSIXt, Date or a character vectors. When `start` is a
#'   character vector and end is `NULL`, ISO 8601 specification is assumed but
#'   with much more permisive lubridate style parsing both for dates and periods
#'   (see examples).
#' @param tzone a recognized timezone to display the interval in
#' @param x an R object
#' @return `interval()` -- [Interval-class] object.
#' @seealso [Interval-class], [as.interval()], \code{\link{\%within\%}}
#' @examples
#' interval(ymd(20090201), ymd(20090101))
#'
#' date1 <- ymd_hms("2009-03-08 01:59:59")
#' date2 <- ymd_hms("2000-02-29 12:00:00")
#' interval(date2, date1)
#' interval(date1, date2)
#' span <- interval(ymd(20090101), ymd(20090201))
#'
#' ### ISO Intervals
#'
#' interval("2007-03-01T13:00:00Z/2008-05-11T15:30:00Z")
#' interval("2007-03-01T13:00:00Z/P1Y2M10DT2H30M")
#' interval("P1Y2M10DT2H30M/2008-05-11T15:30:00Z")
#' interval("2008-05-11/P2H30M")
#'
#' ### More permisive parsing (as long as there are no intermittent / characters)
#' interval("2008 05 11/P2hours 30minutes")
#' interval("08 05 11/P 2h 30m")
#'
#' is.interval(period(months= 1, days = 15)) # FALSE
#' is.interval(interval(ymd(20090801), ymd(20090809))) # TRUE
interval <- function(start = NULL, end = NULL, tzone = tz(start)) {
  # NB: tzone is forced and never called on NULL here

  if (is.character(start) && is.null(end)) {
    return(parse_interval(start, tzone))
  }

  if (length(start) == 0 || length(end) == 0) {
    ## We used to return UTC on NULL
    if (is.null(start) && missing(tzone)) {
      tzone <- "UTC"
    }
    start <- POSIXct(tz = tzone)
    return(new("Interval", numeric(), start = start, tzone = tzone))
  }

  if (is.Date(start)) start <- date_to_posix(start)
  if (is.Date(end)) end <- date_to_posix(end)

  force(tzone)
  start <- as_POSIXct(start, tzone)
  end <- as_POSIXct(end, tzone)

  span <- as.numeric(end) - as.numeric(start)
  starts <- start + rep(0, length(span))
  if (tzone != tz(starts)) starts <- with_tz(starts, tzone)

  new("Interval", span, start = starts, tzone = tzone)
}

parse_interval <- function(x, tz) {

  # create matrix of string parts from x: 1st column is anything before /, 2nd is anything after.
  # replicates without stringr: str_split_fixed(x, "/", 2)
  mat <- matrix(
    c(gsub('(^[^/]+)/(.+$)', '\\1', x), gsub('(^[^/]+)/(.+$)', '\\2', x)),
    ncol = 2
  )
  pstart <- grepl("^P", mat[, 1])
  pend <- grepl("^P",  mat[, 2])

  if (any(pstart & pend)) {
    stop(sprintf("Interval specified with period endpoints (%s)", x[pstart & pend][[1]]))
  }

  start <- .POSIXct(rep.int(NA_real_, length(x)), tz = tz)
  end <- .POSIXct(rep.int(NA_real_, length(x)), tz = tz)

  start[!pstart] <- .parse_iso_dt(mat[!pstart, 1], tz)
  end[!pend] <- .parse_iso_dt(mat[!pend, 2], tz = tz)
  end[pend] <- start[pend] + parse_period(mat[pend, 2])
  start[pstart] <- end[pstart] - parse_period(mat[pstart, 1])
  interval(start, end, tz)
}

#'
#' \code{\%--\%} Creates an interval that covers the range spanned by two
#' dates. It replaces the original behavior of \pkg{lubridate}, which created an
#' interval by default whenever two date-times were subtracted.
#'
#' @export
#' @rdname interval
"%--%" <- function(start, end) interval(start, end)

#' @rdname interval
#' @export
is.interval <- function(x) is(x, c("Interval"))


#'
#'
#' `int_start()` and `int_start<-()` are accessors the start date of an
#' interval. Note that changing the start date of an interval will change the
#' length of the interval, since the end date will remain the same.
#'
#' @rdname interval
#' @param int an interval object
#' @return `int_start()` and `int_end()` return a POSIXct date object when
#'   used as an accessor. Nothing when used as a setter.
#' @examples
#' int <- interval(ymd("2001-01-01"), ymd("2002-01-01"))
#' int_start(int)
#' int_start(int) <- ymd("2001-06-01")
#' int
#'
#' int <- interval(ymd("2001-01-01"), ymd("2002-01-01"))
#' int_end(int)
#' int_end(int) <- ymd("2002-06-01")
#' int
#' @export
int_start <- function(int) int@start

#' @rdname interval
#' @param value interval's start/end to be assigned to `int`
#' @export
"int_start<-" <- function(int, value) {
  value <- as.POSIXct(value)
  span <- as.numeric(int@start + int@.Data - value, "secs")
  equal.lengths <- data.frame(span, value)
  int <- new("Interval", span, start = equal.lengths$value,
    tzone = int@tzone)
}

#' @description
#' `int_end()` and `int_end<-()` are accessors the end date of an
#' interval. Note that changing the end date of an interval will change the
#' length of the interval, since the start date will remain the same.
#'
#' @rdname interval
#' @export
int_end <- function(int) int@start + int@.Data

#' @rdname interval
#' @export
"int_end<-" <- function(int, value) {
  value <- as.POSIXct(value)
  span <- as.numeric(value - int@start, "secs")
  int <- new("Interval", span, start = int@start,
    tzone = int@tzone)
}

#' @rdname interval
#' @return `int_length()` -- numeric length of the interval in
#'   seconds. A negative number connotes a negative interval.
#' @examples
#' int <- interval(ymd("2001-01-01"), ymd("2002-01-01"))
#' int_length(int)
#' @export
int_length <- function(int) int@.Data

#' @description
#' `int_flip()` reverses the order of the start date and end date in an
#' interval. The new interval takes place during the same timespan as the
#' original interval, but has the opposite direction.
#'
#' @rdname interval
#' @return `int_flip()` -- flipped interval object
#' @examples
#' int <- interval(ymd("2001-01-01"), ymd("2002-01-01"))
#' int_flip(int)
#' @export
int_flip <- function(int) {
  new("Interval", -int@.Data, start = int@start + int@.Data, tzone = int@tzone)
}


#' @description
#' `int_shift()` shifts the start and end dates of an interval up or down the
#' timeline by a specified amount. Note that this may change the exact length of
#' the interval if the interval is shifted by a Period object. Intervals shifted
#' by a Duration or difftime object will retain their exact length in seconds.
#'
#' @rdname interval
#' @param by A period or duration object to shift by (for `int_shift`)
#' @return `int_shift()` -- an Interval object
#' @examples
#' int <- interval(ymd("2001-01-01"), ymd("2002-01-01"))
#' int_shift(int, duration(days = 11))
#' int_shift(int, duration(hours = -1))
#' @export
int_shift <- function(int, by) {
  if (!is.timespan(by)) stop("by is not a recognized timespan object")
  if (is.interval(by)) stop("an interval cannot be shifted by another interval.
    Convert second interval to a period or duration.")
  interval(int@start + by, int_end(int) + by)
}


#' @description
#' `int_overlaps()` tests if two intervals overlap.
#'
#' @rdname interval
#' @param int1 an Interval object (for `int_overlaps()`, `int_aligns()`)
#' @param int2 an Interval object (for `int_overlaps()`, `int_aligns()`)
#' @return `int_overlaps()` -- logical, TRUE if int1 and int2 overlap by at
#'   least one second. FALSE otherwise
#' @examples
#' int1 <- interval(ymd("2001-01-01"), ymd("2002-01-01"))
#' int2 <- interval(ymd("2001-06-01"), ymd("2002-06-01"))
#' int3 <- interval(ymd("2003-01-01"), ymd("2004-01-01"))
#'
#' int_overlaps(int1, int2) # TRUE
#' int_overlaps(int1, int3) # FALSE
#' @export
int_overlaps <- function(int1, int2) {
  stopifnot(c(is.interval(int1), is.interval(int2)))
  int1 <- int_standardize(int1)
  int2 <- int_standardize(int2)
  int1@start <= int2@start + int2@.Data & int2@start <= int1@start + int1@.Data
}


#' @description
#' `int_standardize()` ensures all intervals in an interval object are
#' positive. If an interval is not positive, flip it so that it retains its
#' endpoints but becomes positive.
#'
#' @rdname interval
#' @examples
#' int <- interval(ymd("2002-01-01"), ymd("2001-01-01"))
#' int_standardize(int)
#' @export
int_standardize <- function(int) {
  negs <- !is.na(int@.Data) & int@.Data < 0
  int[negs] <- int_flip(int[negs])
  int
}


#' @description
#' `int_aligns()` tests if two intervals share an endpoint. The direction of
#' each interval is ignored. int_align tests whether the earliest or latest
#' moments of each interval occur at the same time.
#'
#' @rdname interval
#' @return `int_aligns()` -- logical, TRUE if int1 and int2 begin or end on the
#'   same moment. FALSE otherwise
#' @examples
#' int1 <- interval(ymd("2001-01-01"), ymd("2002-01-01"))
#' int2 <- interval(ymd("2001-06-01"), ymd("2002-01-01"))
#' int3 <- interval(ymd("2003-01-01"), ymd("2004-01-01"))
#'
#' int_aligns(int1, int2) # TRUE
#' int_aligns(int1, int3) # FALSE
#' @export
int_aligns <- function(int1, int2) {
  int1 <- int_standardize(int1)
  int2 <- int_standardize(int2)

  int1@start == int2@start | (int1@start + int1@.Data) == (int2@start + int2@.Data)
}

#' @description
#' `int_diff()` returns the intervals that occur between the elements of a
#' vector of date-times. `int_diff()` is similar to the POSIXt and Date
#' methods of [diff()], but returns an [Interval-class] object instead
#' of a difftime object.
#'
#' @rdname interval
#' @param times A vector of POSIXct, POSIXlt or Date class date-times (for
#'   `int_diff()`)
#' @return `int_diff()` -- interval object that contains the n-1 intervals
#'   between the n date-time in times
#' @examples
#' dates <- now() + days(1:10)
#' int_diff(dates)
#' @export
int_diff <- function(times) {
  interval(times[-length(times)], times[-1])
}


#' @importFrom generics intersect
#' @export
generics::intersect

#' @export
intersect.Interval <- function(x, y, ...) {
  int1 <- int_standardize(x)
  int2 <- int_standardize(y)

  starts <- pmax(int1@start, int2@start)
  ends <- pmin(int1@start + int1@.Data, int2@start + int2@.Data)
  spans <- as.numeric(ends) - as.numeric(starts)

  no.int <- ends < starts
  no.int <- is.na(no.int) | no.int
  spans[no.int] <- NA
  starts[no.int] <- NA

  new.int <- new("Interval", spans, start = starts, tzone = x@tzone)
  negix <- !is.na(x@.Data) & (sign(x@.Data) == -1)
  new.int[negix] <- int_flip(new.int[negix])
  new.int
}

#' @importFrom generics union
#' @export
generics::union

#' @export
union.Interval <- function(x, y, ...) {
  int1 <- int_standardize(x)
  int2 <- int_standardize(y)

  starts <- pmin(int1@start, int2@start)
  ends <- pmax(int1@start + int1@.Data, int2@start + int2@.Data)

  spans <- as.numeric(ends) - as.numeric(starts)

  if (any(!int_overlaps(int1, int2)) && is_verbose()) {
    message("Union includes intervening time between intervals.")
  }

  tz(starts) <- x@tzone
  new.int <- new("Interval", spans, start = starts, tzone = x@tzone)
  new.int[sign(x@.Data) == -1] <- int_flip(new.int[sign(x@.Data) == -1])
  new.int
}

#' @importFrom generics setdiff
#' @export
generics::setdiff

#' @export
setdiff.Interval <- function(x, y, ...) {

  if (length(x) != length(y)) {
    xy <- match_lengths(x, y)
    x <- xy[[1]]
    y <- xy[[2]]
  }

  aligned <- int_aligns(x, y)
  inside <- y %within% x
  makes2 <- !aligned & inside

  if (sum(makes2)) {
    stop(paste("Cases", which(makes2),
      "result in discontinuous intervals."))
  }

  int1 <- int_standardize(x)
  int2 <- int_standardize(y)

  first.y <- int_start(int2)
  last.y <- int_end(int2)

  starts <- int_start(int1)

  starts[(last.y + 1) %within% int1] <- last.y[(last.y + 1) %within% int1]

  ends <- int_end(int1)
  ends[(first.y - 1) %within% int1] <- first.y[(first.y - 1) %within% int1]

  spans <- as.numeric(ends) - as.numeric(starts)

  new.int <- new("Interval", spans, start = starts, tzone = x@tzone)
  new.int[sign(x@.Data) == -1] <- int_flip(new.int[sign(x@.Data) == -1])
  new.int
}


#' Does a date (or interval) fall within an interval?
#'
#' Check whether `a` lies within the interval `b`, inclusive of the endpoints.
#'
#' @export
#' @rdname within-interval
#' @aliases %within%,Interval,Interval-method %within%,ANY,Interval-method
#'   %within%,Date,list-method %within%,POSIXt,list-method
#' @param a An interval or date-time object.
#' @param b Either an interval vector, or a list of intervals.
#'
#'   If `b` is an internal it is recycled to the same length as `a`.
#'   If `b` is a list of intervals, `a` is checked if it falls within _any_
#'   of the intervals, i.e. `a %within% list(int1, int2)` is equivalent to
#'   `a %within% int1 | a %within% int2`.
#' @return A logical vector.
#' @examples
#' int <- interval(ymd("2001-01-01"), ymd("2002-01-01"))
#' int2 <- interval(ymd("2001-06-01"), ymd("2002-01-01"))
#'
#' ymd("2001-05-03") %within% int # TRUE
#' int2 %within% int # TRUE
#' ymd("1999-01-01") %within% int # FALSE
#'
#' ## recycling
#' dates <- ymd(c("2014-12-20", "2014-12-30", "2015-01-01", "2015-01-03"))
#' blackouts<- c(interval(ymd("2014-12-30"), ymd("2014-12-31")),
#'               interval(ymd("2014-12-30"), ymd("2015-01-03")))
#' dates %within% blackouts
#'
#' ## within ANY of the intervals of a list
#' dates <- ymd(c("2014-12-20", "2014-12-30", "2015-01-01", "2015-01-03"))
#' blackouts<- list(interval(ymd("2014-12-30"), ymd("2014-12-31")),
#'                  interval(ymd("2014-12-30"), ymd("2015-01-03")))
#' dates %within% blackouts
setGeneric("%within%", useAsDefault = function(a, b) {
  stop(sprintf("No %%within%% method with signature a = %s,  b = %s",
               class(a)[[1]], class(b)[[1]]))
})

.within <- function(a, int) {
  as.numeric(a) - as.numeric(int@start) <= int@.Data & as.numeric(a) - as.numeric(int@start) >= 0
}

setMethod("%within%", signature(b = "Interval"), function(a, b) {
  if (!is.instant(a)) stop("Argument 1 is not a recognized date-time")
  a <- as.POSIXct(a)
  .within(a, b)
})

setMethod("%within%", signature(a = "Interval", b = "Interval"), function(a, b) {
  a <- int_standardize(a)
  b <- int_standardize(b)
  start.in <- as.numeric(a@start) >= as.numeric(b@start)
  end.in <- (as.numeric(a@start) + a@.Data) <= (as.numeric(b@start) + b@.Data)
  start.in & end.in
})

setMethod("%within%", signature(a = "Interval", b = "Interval"), function(a, b) {
  a <- int_standardize(a)
  b <- int_standardize(b)
  start.in <- as.numeric(a@start) >= as.numeric(b@start)
  end.in <- (as.numeric(a@start) + a@.Data) <= (as.numeric(b@start) + b@.Data)
  start.in & end.in
})

.within_instant <- function(a, b) {
  if (!all(sapply(b, is.interval)))
    stop("When second argument to %within% is a list it must contain interval objects only")
  a <- as.POSIXct(a)
  out <- FALSE
  for (int in b) {
    out <- out | .within(a, int)
  }
  out
}

setMethod("%within%", signature(a = "POSIXt", b = "list"), .within_instant)
setMethod("%within%", signature(a = "Date", b = "list"), .within_instant)

#' @export
as.list.Interval <- function(x, ...) {
  lapply(seq_along(x), function(i) x[[i]])
}

#' @export
summary.Interval <- function(object, ...) {
  nas <- is.na(object)
  object <- object[!nas]
  n <- length(object)
  dates <- c(int_start(object), int_end(object))
  earliest <- as.character(min(dates))
  latest <- as.character(max(dates))
  zone <- tz(dates)

  qq <- c(n, earliest, latest, zone)
  names(qq) <- c("Intervals", "Earliest endpoint", "Latest endpoint", "Time zone")
  if (any(nas))
    c(qq, `NA's` = sum(nas))
  else qq
}

#' @rdname time_length
setMethod("time_length", signature("Interval"), function(x, unit = "second") {
  unit <- standardise_period_names(unit)
  if (unit %in% c("year", "month")) {

    periods <- as.period(x, unit = unit)
    int_part <- slot(periods, unit)

    prev_aniv <- add_with_rollback(
      int_start(x), (int_part * period(1, units = unit)),
      roll_to_first = TRUE, preserve_hms = FALSE)
    next_aniv <- add_with_rollback(
      int_start(x), ((int_part + ifelse(x@.Data < 0, -1, 1)) * period(1, units = unit)),
      roll_to_first = TRUE, preserve_hms = FALSE)

    sofar <- as.duration(int_end(x) - prev_aniv)
    total <- as.duration(next_aniv - prev_aniv)
    int_part + sign(x@.Data) * sofar / total

  } else {
    as.duration(x) / duration(num = 1, units = unit)
  }
})

#' @export
setMethod("Arith", signature(e1 = "Interval", e2 = "ANY"), function(e1, e2) {
  stop_incompatible_classes(e1, e2, .Generic)
})

#' @export
setMethod("Arith", signature(e1 = "ANY", e2 = "Interval"), function(e1, e2) {
  stop_incompatible_classes(e1, e2, .Generic)
})

#' @name hidden_aliases
#' @aliases Arith,Interval,ANY-method Arith,ANY,Interval-method
#'   intersect,Interval,Interval-method union,Interval,Interval-method
#'   setdiff,Interval,Interval-method as.numeric,Interval-method
#'   show,Interval-method c,Interval-method rep,Interval-method
#'   [,Interval-method [<-,Interval,ANY,ANY,ANY-method [[,Interval-method
#'   [[<-,Interval,ANY,ANY,ANY-method $,Interval-method $<-,Interval-method
#'   as.difftime,Interval-method as.character,Interval-method
#'   +,Interval,Duration-method +,Interval,Interval-method
#'   +,Interval,Period-method +,Interval,Date-method +,Date,Interval-method
#'   +,Interval,difftime-method +,difftime,Interval-method
#'   +,Interval,numeric-method +,numeric,Interval-method
#'   +,Interval,POSIXct-method +,POSIXct,Interval-method
#'   +,Interval,POSIXlt-method +,POSIXlt,Interval-method
#'   /,Interval,Duration-method /,Interval,Interval-method
#'   /,Interval,Period-method /,Interval,difftime-method
#'   /,difftime,Interval-method /,Interval,numeric-method
#'   /,numeric,Interval-method *,Interval,ANY-method *,ANY,Interval-method
#'   -,Interval,missing-method -,Interval,Interval-method -,Date,Interval-method
#'   -,POSIXct,Interval-method -,POSIXlt,Interval-method
#'   -,numeric,Interval-method -,Interval,Date-method -,Interval,POSIXct-method
#'   -,Interval,POSIXlt-method -,Interval,numeric-method
#'   -,Duration,Interval-method -,Period,Interval-method
#'   %%,Interval,Duration-method %%,Interval,Interval-method
#'   %%,Interval,Period-method %%,Interval,Duration %%,Interval,Interval
#'   %%,Interval,Period -,Date,Interval -,Duration,Interval -,Interval,Date
#'   -,Interval,Interval -,Interval,POSIXct -,Interval,POSIXlt
#'   -,Interval,numeric -,POSIXct,Interval -,POSIXlt,Interval -,numeric,Interval
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