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{ Uncertainty } = require './uncertainty'
{ ThreeValuedLogic } = require './logic'
{ successor, predecessor, maxValueForInstance, minValueForInstance } = require '../util/math'
cmp = require '../util/comparison'
module.exports.Interval = class Interval
constructor: (@low, @high, @lowClosed = true, @highClosed = true) ->
# Define a simple getter to allow type-checking of this class without instanceof
# and in a way that survives minification (as opposed to checking constructor.name)
Object.defineProperties @prototype,
isInterval:
get: -> true
copy: ->
newLow = @low
newHigh = @high
if @low? and typeof @low.copy == 'function'
newLow = @low.copy()
if @high? and typeof @high.copy == 'function'
newHigh = @high.copy();
new Interval(newLow, newHigh, @lowClosed, @highClosed)
contains: (item, precision) ->
if item instanceof Interval then throw new Error("Argument to contains must be a point")
closed = @toClosed()
ThreeValuedLogic.and(
cmp.lessThanOrEquals(closed.low, item, precision),
cmp.greaterThanOrEquals(closed.high, item, precision)
)
properlyIncludes: (other, precision) ->
if not (other instanceof Interval) then throw new Error("Argument to properlyIncludes must be an interval")
ThreeValuedLogic.and(
@includes(other, precision),
ThreeValuedLogic.not(other.includes(@, precision))
)
includes: (other, precision) ->
if not (other instanceof Interval)
return @.contains(other,precision)
a = @toClosed()
b = other.toClosed()
ThreeValuedLogic.and(
cmp.lessThanOrEquals(a.low, b.low, precision),
cmp.greaterThanOrEquals(a.high, b.high, precision)
)
includedIn: (other, precision) ->
# For the point overload, this operator is a synonym for the in operator
if not (other instanceof Interval)
@.contains(other, precision)
else
other.includes @
overlaps: (item, precision) ->
closed = @toClosed()
[low, high] = if item instanceof Interval
itemClosed = item.toClosed()
[itemClosed.low, itemClosed.high]
else
[item, item]
ThreeValuedLogic.and(
cmp.lessThanOrEquals(closed.low, high, precision),
cmp.greaterThanOrEquals(closed.high, low, precision)
)
overlapsAfter: (item, precision) ->
closed = @toClosed()
high = if item instanceof Interval then item.toClosed().high else item
ThreeValuedLogic.and(
cmp.lessThanOrEquals(closed.low, high, precision),
cmp.greaterThan(closed.high, high, precision)
)
overlapsBefore: (item, precision) ->
closed = @toClosed()
low = if item instanceof Interval then item.toClosed().low else item
ThreeValuedLogic.and(
cmp.lessThan(closed.low, low, precision),
cmp.greaterThanOrEquals(closed.high, low, precision)
)
areDateTimes = (x, y) ->
[x, y].every (z) -> z instanceof DateTime
areNumeric = (x, y) ->
[x, y].every (z) -> typeof z is 'number' or (z instanceof Uncertainty and typeof z.low is 'number')
lowestNumericUncertainty = (x, y) ->
if not(x instanceof Uncertainty) then x = new Uncertainty(x)
if not(y instanceof Uncertainty) then y = new Uncertainty(y)
low = if x.low < y.low then x.low else y.low
high = if x.high < y.high then x.high else y.high
if low != high then return new Uncertainty(low, high) else return low
highestNumericUncertainty = (x, y) ->
if not(x instanceof Uncertainty) then x = new Uncertainty(x)
if not(y instanceof Uncertainty) then y = new Uncertainty(y)
low = if x.low > y.low then x.low else y.low
high = if x.high > y.high then x.high else y.high
if low != high then return new Uncertainty(low, high) else return low
union: (other) ->
if not (other instanceof Interval) then throw new Error("Argument to union must be an interval")
# Note that interval union is only defined if the arguments overlap or meet.
if @overlaps(other) or @meets(other)
[a, b] = [@toClosed(), other.toClosed()]
[l, lc] = switch
when cmp.lessThanOrEquals(a.low, b.low) then [@low, @lowClosed]
when cmp.greaterThanOrEquals(a.low, b.low) then [other.low, other.lowClosed]
when areNumeric(a.low, b.low) then [lowestNumericUncertainty(a.low, b.low), true]
# TODO: Do we need to support quantities here?
when areDateTimes(a.low, b.low) and a.low.isMorePrecise(b.low) then [other.low, other.lowClosed]
else [@low, @lowClosed]
[h, hc] = switch
when cmp.greaterThanOrEquals(a.high, b.high) then [@high, @highClosed]
when cmp.lessThanOrEquals(a.high, b.high) then [other.high, other.highClosed]
when areNumeric(a.high, b.high) then [highestNumericUncertainty(a.high, b.high), true]
# TODO: Do we need to support quantities here?
when areDateTimes(a.high, b.high) and a.high.isMorePrecise(b.high) then [other.high, other.highClosed]
else [@high, @highClosed]
new Interval(l, h, lc, hc)
else
null
intersect: (other) ->
if not (other instanceof Interval) then throw new Error("Argument to union must be an interval")
# Note that interval union is only defined if the arguments overlap.
if @overlaps(other)
[a, b] = [@toClosed(), other.toClosed()]
[l, lc] = switch
when cmp.greaterThanOrEquals(a.low, b.low) then [@low, @lowClosed]
when cmp.lessThanOrEquals(a.low, b.low) then [other.low, other.lowClosed]
when areNumeric(a.low, b.low) then [highestNumericUncertainty(a.low, b.low), true]
# TODO: Do we need to support quantities here?
when areDateTimes(a.low, b.low) and b.low.isMorePrecise(a.low) then [other.low, other.lowClosed]
else [@low, @lowClosed]
[h, hc] = switch
when cmp.lessThanOrEquals(a.high, b.high) then [@high, @highClosed]
when cmp.greaterThanOrEquals(a.high, b.high) then [other.high, other.highClosed]
when areNumeric(a.high, b.high) then [lowestNumericUncertainty(a.high, b.high), true]
# TODO: Do we need to support quantities here?
when areDateTimes(a.high, b.high) and b.high.isMorePrecise(a.high) then [other.high, other.highClosed]
else [@high, @highClosed]
new Interval(l, h, lc, hc)
else
null
except: (other) ->
if (other == null) then return null
if not (other instanceof Interval) then throw new Error("Argument to except must be an interval")
ol = @overlaps other
if ol is true
olb = @overlapsBefore other
ola = @overlapsAfter other
if olb is true and ola is false then new Interval(@low, other.low, @lowClosed, not other.lowClosed)
else if ola is true and olb is false then new Interval(other.high, @high, not other.highClosed, @highClosed)
else null
else if ol is false
@
else # ol is null
null
sameAs: (other, precision) ->
# This large if and else if block handles the scenarios where there is an open ended null
# If both lows or highs exists, it can be determined that intervals are not Same As
if (@low? and other.low? and !@high? and other.high? and !@highClosed) or
(@low? and other.low? and @high? and !other.high? and !other.highClosed) or
(@low? and other.low? and !@high? and !other.high? and !other.highClosed and !@highClosed)
if typeof @low == 'number'
if !(@.start() == other.start()) then return false
else
if !(@.start().sameAs(other.start(), precision)) then return false
else if (@low? and !other.low? and @high? and other.high?) or
(!@low? and other.low? and @high? and other.high?) or
(!@low? and !other.low? and @high? and other.high?)
if typeof @high == 'number'
if !(@.end() == other.end()) then return false
else
if !(@.end().sameAs(other.end(), precision)) then return false
# Checks to see if any of the Intervals have a open, null boundary
if (!@low? and !@lowClosed) or
(!@high? and !@highClosed) or
(!other.low? and !other.lowClosed) or
(!other.high? and !other.highClosed)
return null
# For the special cases where @ is Interval[null,null]
if @lowClosed and !@low? and @highClosed and !@high?
return other.lowClosed and !other.low? and other.highClosed and !other.high?
# For the special case where Interval[...] same as Interval[null,null] should return false
# This accounts for the inverse of the if statement above: where the second Interval is [null,null] and not the first Interval
# The reason why this isn't caught below is due to how start() and end() work
# There is no way to tell the datatype for MIN and MAX if both boundaries are null
if other.lowClosed and !other.low? and other.highClosed and !other.high?
return false
if typeof @low == 'number'
@.start() == other.start() and @.end() == other.end()
else
@.start().sameAs(other.start(), precision) and @.end().sameAs(other.end(), precision)
equals: (other) ->
if other instanceof Interval
[a, b] = [@toClosed(), other.toClosed()]
ThreeValuedLogic.and(
cmp.equals(a.low, b.low),
cmp.equals(a.high, b.high)
)
else
false
after: (other, precision) ->
closed = @toClosed()
# Meets spec, but not 100% correct (e.g., (null, 5] after [6, 10] --> null)
# Simple way to fix it: and w/ not overlaps
if !!other.toClosed
cmp.greaterThan closed.low, other.toClosed().high, precision
else
cmp.greaterThan closed.low, other, precision
before: (other, precision) ->
closed = @toClosed()
# Meets spec, but not 100% correct (e.g., (null, 5] after [6, 10] --> null)
# Simple way to fix it: and w/ not overlaps
if !!other.toClosed
cmp.lessThan closed.high, other.toClosed().low, precision
else
cmp.lessThan closed.high, other, precision
meets: (other, precision) ->
ThreeValuedLogic.or(
@meetsBefore(other, precision),
@meetsAfter(other, precision)
)
meetsAfter: (other, precision) ->
try
if precision? and @low instanceof DateTime
@toClosed().low.sameAs(other.toClosed().high?.add(1, precision), precision)
else
cmp.equals @toClosed().low, successor(other.toClosed().high)
catch
false
meetsBefore: (other, precision) ->
try
if precision? and @high instanceof DateTime
@toClosed().high.sameAs(other.toClosed().low?.add(-1, precision), precision)
else
cmp.equals @toClosed().high, predecessor(other.toClosed().low)
catch
false
start: () ->
if !@low?
if @lowClosed
return minValueForInstance(@high)
else
return @low
return @toClosed().low
end: () ->
if !@high?
if @highClosed
return maxValueForInstance(@low)
else
return @high
return @toClosed().high
starts: (other, precision) ->
if precision? and @low instanceof DateTime
startEqual = @low.sameAs(other.low, precision)
else
startEqual = cmp.equals(@low, other.low)
endLessThanOrEqual = cmp.lessThanOrEquals(@high, other.high, precision)
startEqual and endLessThanOrEqual
ends: (other, precision) ->
startGreaterThanOrEqual = cmp.greaterThanOrEquals(@low, other.low, precision)
if precision? and @low instanceof DateTime
endEqual = @high.sameAs(other.high, precision)
else
endEqual = cmp.equals(@high, other.high)
startGreaterThanOrEqual && endEqual
width: () ->
if @low instanceof DateTime or @high instanceof DateTime
throw new Error("Width of DateTime intervals is not supported")
closed = @toClosed()
if closed.low instanceof Uncertainty or closed.high instanceof Uncertainty
null
else
# TODO: Fix precision to 8 decimals in other places that return numbers
diff = Math.abs(closed.high - closed.low)
Math.round(diff * Math.pow(10, 8)) / Math.pow(10, 8)
toClosed: () ->
point = @low ? @high
if typeof(point) is 'number' or point instanceof DateTime or point?.isQuantity or point?.isDate
low = switch
when @lowClosed and not @low? then minValueForInstance point
when not @lowClosed and @low? then successor @low
else @low
high = switch
when @highClosed and not @high? then maxValueForInstance point
when not @highClosed and @high? then predecessor @high
else @high
if not low? then low = new Uncertainty(minValueForInstance(point), high)
if not high? then high = new Uncertainty(low, maxValueForInstance(point))
new Interval(low, high, true, true)
else
new Interval(@low, @high, true, true)
toString: () ->
start = if @lowClosed then '[' else '('
end = if @highClosed then ']' else ')'
return start + @low.toString() + ', ' + @high.toString() + end
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