Double-double Date

Sources/FoundationEssentials/CMakeLists.txt

@@ -21,6 +21,7 @@ add_library(FoundationEssentials
     ComparisonResult.swift
     Date.swift
     DateInterval.swift
+    DoubleDouble.swift
     FoundationEssentials.swift
     IndexPath.swift
     LockedState.swift

Sources/FoundationEssentials/Calendar/Calendar_Gregorian.swift

@@ -1448,30 +1448,39 @@ internal final class _CalendarGregorian: _CalendarProtocol, @unchecked Sendable
     }
 
     func dateInterval(of component: Calendar.Component, for date: Date) -> DateInterval? {
-        let time = date.timeIntervalSinceReferenceDate
+        let approximateTime = date._time.head
         var effectiveUnit = component
         switch effectiveUnit {
         case .calendar, .timeZone, .isLeapMonth, .isRepeatedDay:
             return nil
         case .era:
-            if time < -63113904000.0 {
+            if approximateTime < -63113904000.0 {
                 return DateInterval(start: Date(timeIntervalSinceReferenceDate: -63113904000.0 - inf_ti), duration: inf_ti)
             } else {
                 return DateInterval(start: Date(timeIntervalSinceReferenceDate: -63113904000.0), duration: inf_ti)
             }
 
         case .hour:
-            let ti = Double(timeZone.secondsFromGMT(for: date))
-            var fixedTime = time + ti // compute local time
-            fixedTime = floor(fixedTime / 3600.0) * 3600.0
-            fixedTime = fixedTime - ti // compute GMT
-            return DateInterval(start: Date(timeIntervalSinceReferenceDate: fixedTime), duration: 3600.0)
+            // Local hours may not be aligned to GMT hours, so we have to apply
+            // the time zone adjustment before rounding down, then unapply it.
+            let offset = Double(timeZone.secondsFromGMT(for: date))
+            let start = ((date._time + offset)/3600).floor() * 3600 - offset
+            return DateInterval(
+                start: Date(start),
+                duration: 3600
+            )
         case .minute:
-            return DateInterval(start: Date(timeIntervalSinceReferenceDate: floor(time / 60.0) * 60.0), duration: 60.0)
+            return DateInterval(
+                start: Date((date._time/60).floor() * 60),
+                duration: 60
+            )
         case .second:
-            return DateInterval(start: Date(timeIntervalSinceReferenceDate: floor(time)), duration: 1.0)
+            return DateInterval(start: Date(date._time.floor()), duration: 1)
         case .nanosecond:
-            return DateInterval(start: Date(timeIntervalSinceReferenceDate: floor(time * 1.0e+9) * 1.0e-9), duration: 1.0e-9)
+            return DateInterval(
+                start: Date((date._time*1e9).floor() / 1e9),
+                duration: 1e-9
+            )
         case .year, .yearForWeekOfYear, .quarter, .month, .day, .dayOfYear, .weekOfMonth, .weekOfYear:
             // Continue to below
             break

Sources/FoundationEssentials/Calendar/Calendar_Recurrence.swift

@@ -93,8 +93,8 @@ extension Calendar {
             /// value is used as a lower bound for ``nextBaseRecurrenceDate()``.
             let rangeLowerBound: Date?
 
-            /// The start date's nanoseconds component
-            let startDateNanoseconds: TimeInterval
+            /// The start date's fractional seconds component
+            let fractionalSeconds: TimeInterval
 
             /// How many occurrences have been found so far
             var resultsFound = 0
@@ -131,7 +131,10 @@ extension Calendar {
                 }
                 self.recurrence = recurrence
 
-                self.start = start
+                // round start down to whole seconds, set aside fraction.
+                let wholeSeconds = start._time.floor()
+                fractionalSeconds = (start._time - wholeSeconds).head
+                self.start = Date(wholeSeconds)
                 self.range = range
 
                 let frequency = recurrence.frequency
@@ -233,9 +236,7 @@ extension Calendar {
                     case .monthly:  [.second, .minute, .hour, .day]
                     case .yearly:   [.second, .minute, .hour, .day, .month, .isLeapMonth]
                 }
-                var componentsForEnumerating = recurrence.calendar._dateComponents(components, from: start) 
-
-                startDateNanoseconds = start.timeIntervalSinceReferenceDate.truncatingRemainder(dividingBy: 1)
+                var componentsForEnumerating = recurrence.calendar._dateComponents(components, from: start)
 
                 let expansionChangesDay = dayOfYearAction == .expand || dayOfMonthAction == .expand || weekAction == .expand || weekdayAction == .expand
                 let expansionChangesMonth = dayOfYearAction == .expand || monthAction == .expand || weekAction == .expand
@@ -427,11 +428,11 @@ extension Calendar {
                     recurrence._limitTimeComponent(.second, dates: &dates, anchor: anchor)
                 }
 
-                if startDateNanoseconds > 0 {
+                if fractionalSeconds != 0 {
                     // `_dates(startingAfter:)` above returns whole-second dates,
                     // so we need to restore the nanoseconds value present in the original start date.
                     for idx in dates.indices {
-                        dates[idx] += startDateNanoseconds
+                        dates[idx] += fractionalSeconds
                     }
                 }
                 dates = dates.filter { $0 >= self.start }

Sources/FoundationEssentials/Date.swift

@@ -34,12 +34,64 @@ public typealias TimeInterval = Double
  A `Date` is independent of a particular calendar or time zone. To represent a `Date` to a user, you must interpret it in the context of a `Calendar`.
 */
 @available(macOS 10.10, iOS 8.0, watchOS 2.0, tvOS 9.0, *)
-public struct Date : Comparable, Hashable, Equatable, Sendable {
-
-    internal var _time : TimeInterval
+public struct Date: Comparable, Hashable, Equatable, Sendable {
+    /* Date is internally represented as a sum of two Doubles.
+
+     Previously Date was backed by a single Double measuring time since
+     Jan 1 2001 in seconds. Because Double's precision is non-uniform, this
+     means that times within a hundred days of the epoch are represented
+     with approximately nanosecond precision, but as you get farther away
+     from that date the precision decreases. For times close to the time
+     at which this comment was written, accuracy has been reduced to about
+     100ns.
+
+     The obvious thing would be to adopt an integer-based representation
+     similar to C's timespec (32b nanoseconds, 64b seconds) or Swift's
+     Duration (128b attoseconds). These representations suffer from a few
+     difficulties:
+
+     - Existing API on Date takes and produces `TimeInterval` (aka Double).
+       Making Date use an integer representation internally would mean that
+       existing users of the public API would suddently start getting
+       different results for computations that were previously exact; even
+       though we could add new API, and the overall system would be more
+       precise, this would be a surprisingly subtle change for users to
+       navigate.
+
+     - We have been told that some software interprets the raw bytes of Date
+       as a Double for the purposes of fast serialization. These packages
+       formally violate Foundation's API boundaries, but that doesn't help
+       users of those packages who would abruptly be broken by switching to
+       an integer representation.
+
+     Using DoubleDouble instead navigates these problems fairly elegantly.
+
+     - Because DoubleDouble is still a floating-point type, it still suffers
+       from non-uniform precision. However, because DoubleDouble is so
+       fantastically precise, it can represent dates out to ±2.5 quadrillion
+       years at ~nanosecond or better precision, so in practice this won't
+       be much of an issue.
+
+     - Existing API on Date will produce exactly the same result as it did
+       previously in cases where those results were exact, minimizing
+       surprises. In cases where the existing API was not exact, it will
+       produce much more accurate results, even if users do not adopt new
+       API, because its internal calculations are now more precise.
+
+     - Software that (incorrectly) interprets the raw bytes of Date as a
+       Double will get at least as accurate of a value as it did previously
+       (and often a more accurate value).                                     */
+    internal var _time: DoubleDouble
+
+    internal init(_ time: DoubleDouble) {
+        self._time = time
+    }
+}
 
+@available(macOS 10.10, iOS 8.0, watchOS 2.0, tvOS 9.0, *)
+extension Date {
     /// The number of seconds from 1 January 1970 to the reference date, 1 January 2001.
-    public static let timeIntervalBetween1970AndReferenceDate : TimeInterval = 978307200.0
+    public static let timeIntervalBetween1970AndReferenceDate: TimeInterval = 978307200.0
 
     /// The number of seconds from 1 January 1601 to the reference date, 1 January 2001.
     internal static let timeIntervalBetween1601AndReferenceDate: TimeInterval = 12622780800.0
@@ -51,17 +103,23 @@ public struct Date : Comparable, Hashable, Equatable, Sendable {
 
     /// Returns a `Date` initialized to the current date and time.
     public init() {
-        _time = Self.getCurrentAbsoluteTime()
+        _time = .init(uncheckedHead: Self.getCurrentAbsoluteTime(), tail: 0)
     }
 
     /// Returns a `Date` initialized relative to the current date and time by a given number of seconds.
     public init(timeIntervalSinceNow: TimeInterval) {
-        self.init(timeIntervalSinceReferenceDate: timeIntervalSinceNow + Self.getCurrentAbsoluteTime())
+        self.init(.sum(
+            Self.getCurrentAbsoluteTime(),
+            timeIntervalSinceNow
+        ))
     }
 
     /// Returns a `Date` initialized relative to 00:00:00 UTC on 1 January 1970 by a given number of seconds.
     public init(timeIntervalSince1970: TimeInterval) {
-        self.init(timeIntervalSinceReferenceDate: timeIntervalSince1970 - Date.timeIntervalBetween1970AndReferenceDate)
+        self.init(.sum(
+            timeIntervalSince1970,
+            -Date.timeIntervalBetween1970AndReferenceDate
+        ))
     }
 
     /**
@@ -71,12 +129,12 @@ public struct Date : Comparable, Hashable, Equatable, Sendable {
     - Parameter date: The reference date.
     */
     public init(timeInterval: TimeInterval, since date: Date) {
-        self.init(timeIntervalSinceReferenceDate: date.timeIntervalSinceReferenceDate + timeInterval)
+        self.init(date._time + timeInterval)
     }
 
     /// Returns a `Date` initialized relative to 00:00:00 UTC on 1 January 2001 by a given number of seconds.
     public init(timeIntervalSinceReferenceDate ti: TimeInterval) {
-        _time = ti
+        _time = .init(uncheckedHead: ti, tail: 0)
     }
 
     /**
@@ -85,7 +143,7 @@ public struct Date : Comparable, Hashable, Equatable, Sendable {
     This property's value is negative if the date object is earlier than the system's absolute reference date (00:00:00 UTC on 1 January 2001).
     */
     public var timeIntervalSinceReferenceDate: TimeInterval {
-        return _time
+        return _time.head
     }
 
     /**
@@ -100,7 +158,7 @@ public struct Date : Comparable, Hashable, Equatable, Sendable {
     - SeeAlso: `timeIntervalSinceReferenceDate`
     */
     public func timeIntervalSince(_ date: Date) -> TimeInterval {
-        return self.timeIntervalSinceReferenceDate - date.timeIntervalSinceReferenceDate
+        return (self._time - date._time).head
     }
 
     /**
@@ -173,9 +231,9 @@ public struct Date : Comparable, Hashable, Equatable, Sendable {
 
     /// Compare two `Date` values.
     public func compare(_ other: Date) -> ComparisonResult {
-        if _time < other.timeIntervalSinceReferenceDate {
+        if _time < other._time {
             return .orderedAscending
-        } else if _time > other.timeIntervalSinceReferenceDate {
+        } else if _time > other._time {
             return .orderedDescending
         } else {
             return .orderedSame
@@ -184,27 +242,27 @@ public struct Date : Comparable, Hashable, Equatable, Sendable {
 
     /// Returns true if the two `Date` values represent the same point in time.
     public static func ==(lhs: Date, rhs: Date) -> Bool {
-        return lhs.timeIntervalSinceReferenceDate == rhs.timeIntervalSinceReferenceDate
+        return lhs._time == rhs._time
     }
 
     /// Returns true if the left hand `Date` is earlier in time than the right hand `Date`.
     public static func <(lhs: Date, rhs: Date) -> Bool {
-        return lhs.timeIntervalSinceReferenceDate < rhs.timeIntervalSinceReferenceDate
+        return lhs._time < rhs._time
     }
 
     /// Returns true if the left hand `Date` is later in time than the right hand `Date`.
     public static func >(lhs: Date, rhs: Date) -> Bool {
-        return lhs.timeIntervalSinceReferenceDate > rhs.timeIntervalSinceReferenceDate
+        return lhs._time > rhs._time
     }
 
     /// Returns a `Date` with a specified amount of time added to it.
     public static func +(lhs: Date, rhs: TimeInterval) -> Date {
-        return Date(timeIntervalSinceReferenceDate: lhs.timeIntervalSinceReferenceDate + rhs)
+        return Date(lhs._time + rhs)
     }
 
     /// Returns a `Date` with a specified amount of time subtracted from it.
     public static func -(lhs: Date, rhs: TimeInterval) -> Date {
-        return Date(timeIntervalSinceReferenceDate: lhs.timeIntervalSinceReferenceDate - rhs)
+        return Date(lhs._time - rhs)
     }
 
     /// Add a `TimeInterval` to a `Date`.
@@ -220,7 +278,6 @@ public struct Date : Comparable, Hashable, Equatable, Sendable {
     public static func -=(lhs: inout Date, rhs: TimeInterval) {
         lhs = lhs - rhs
     }
-
 }
 
 @available(macOS 10.10, iOS 8.0, watchOS 2.0, tvOS 9.0, *)

Sources/FoundationEssentials/DateInterval.swift

@@ -12,38 +12,45 @@
 
 /// DateInterval represents a closed date interval in the form of [startDate, endDate].  It is possible for the start and end dates to be the same with a duration of 0.  DateInterval does not support reverse intervals i.e. intervals where the duration is less than 0 and the end date occurs earlier in time than the start date.
 @available(macOS 10.12, iOS 10.0, watchOS 3.0, tvOS 10.0, *)
-public struct DateInterval : Comparable, Hashable, Codable, Sendable {
+public struct DateInterval: Comparable, Hashable, Codable, Sendable {
 
     /// The start date.
-    public var start : Date
+    public var start: Date
+
+    /// Underlying storage for `duration`
+    internal var _duration: DoubleDouble
 
     /// The end date.
     ///
     /// - precondition: `end >= start`
-    public var end : Date {
+    public var end: Date {
         get {
-            return start + duration
+            return Date(start._time + _duration)
         }
         set {
             precondition(newValue >= start, "Reverse intervals are not allowed")
-            duration = newValue.timeIntervalSinceReferenceDate - start.timeIntervalSinceReferenceDate
+            _duration = (newValue._time - start._time)
         }
     }
-
-    /// The duration.
+    
+    /// The duration
     ///
     /// - precondition: `duration >= 0`
-    public var duration : TimeInterval {
-        willSet {
+    public var duration: TimeInterval {
+        get {
+            _duration.head
+        }
+        set {
             precondition(newValue >= 0, "Negative durations are not allowed")
+            _duration = DoubleDouble(uncheckedHead: newValue, tail: 0)
         }
     }
 
     /// Initializes a `DateInterval` with start and end dates set to the current date and the duration set to `0`.
     public init() {
         let d = Date()
         start = d
-        duration = 0
+        _duration = .zero
     }
 
     /// Initialize a `DateInterval` with the specified start and end date.
@@ -52,7 +59,7 @@ public struct DateInterval : Comparable, Hashable, Codable, Sendable {
     public init(start: Date, end: Date) {
         precondition(end >= start, "Reverse intervals are not allowed")
         self.start = start
-        duration = end.timeIntervalSince(start)
+        _duration = end._time - start._time
     }
 
     /// Initialize a `DateInterval` with the specified start date and duration.
@@ -61,7 +68,7 @@ public struct DateInterval : Comparable, Hashable, Codable, Sendable {
     public init(start: Date, duration: TimeInterval) {
         precondition(duration >= 0, "Negative durations are not allowed")
         self.start = start
-        self.duration = duration
+        _duration = DoubleDouble(uncheckedHead: duration, tail: 0)
     }
 
     /**
@@ -162,6 +169,24 @@ public struct DateInterval : Comparable, Hashable, Codable, Sendable {
     public static func <(lhs: DateInterval, rhs: DateInterval) -> Bool {
         return lhs.compare(rhs) == .orderedAscending
     }
+
+    enum CodingKeys: String, CodingKey {
+        case start = "start"
+        case duration = "duration"
+    }
+
+    public init(from decoder: Decoder) throws {
+        let container = try decoder.container(keyedBy: CodingKeys.self)
+        let start = try container.decode(Date.self, forKey: .start)
+        let duration = try container.decode(TimeInterval.self, forKey: .duration)
+        self.init(start: start, duration: duration)
+    }
+
+    public func encode(to encoder: Encoder) throws {
+        var container = encoder.container(keyedBy: CodingKeys.self)
+        try container.encode(start, forKey: .start)
+        try container.encode(duration, forKey: .duration)
+    }
 }
 
 @available(macOS 10.12, iOS 10.0, watchOS 3.0, tvOS 10.0, *)