Add Ethiopian and Coptic calendars (#8)

* Add Ethiopian and Coptic calendars

* Fix month names

* Fix Coptic and Ethiopian leap year computation

* Add Ethiopian and Coptic limits

* Alphabetize

* Move note

* Move note again

README.md

@@ -1,11 +1,13 @@
 # JulianDayNumber
 
 Julian day number (JDN) and Julian date (JD) calculations supporting the following calendars:
-- Julian
-- Gregorian
 - Astronomical
-- Islamic
+- Coptic
 - Egyptian
+- Ethiopian
+- Gregorian
+- Islamic
+- Julian
 
 The JDN conversion algorithms are adapted from Richards, E.G. 2012, "[Calendars](https://aa.usno.navy.mil/downloads/c15_usb_online.pdf)," from the *Explanatory Supplement to the Astronomical Almanac, 3rd edition*, S.E Urban and P.K. Seidelmann eds., (Mill Valley, CA: University Science Books), Chapter 15, pp. 585-624.
 
@@ -32,7 +34,7 @@ let jd = AstronomicalCalendar.dateToJulianDate(year: 1919, month: 5, day: 29)
 ```
 
 > [!NOTE]
-> `AstronomicalCalendar` uses the Julian calendar for dates before 1582-10-15 and the Gregorian calendar for later dates.
+> The astronomical calendar is a hybrid calendar using the Julian calendar for dates before October 15, 1582 and the Gregorian calendar for later dates.
 
 2. Convert the Julian date 2422107.5 to a `Date` instance.
 
@@ -57,21 +59,25 @@ The following table summarizes the **absolute limit** for 64-bit integer Julian
 
 | Calendar | Minimum JDN | Maximum JDN |
 | --- | --- | --- |
-| Julian | -9223372036854775664 | 2305843009213692550 |
+| Coptic | -9223372036854775664 | 2305843009213693827 |
+| Egyptian | -9223372036854775514 | 9223372036854775760 |
+| Ethiopian | -9223372036854775664 | 2305843009213693827 |
 | Gregorian | -9223372036854719351 | 2305795661307959247 |
 | Islamic | -9223372036854775352 | 307445734561818195 |
-| Egyptian | -9223372036854775514 | 9223372036854775760 |
+| Julian | -9223372036854775664 | 2305843009213692550 |
 
 ### Julian Dates
 
 The following table summarizes the **absolute limit** for 64-bit floating-point Julian dates. Julian dates outside these values will cause an arithmetic overflow in `julianDateToDate`.
 
 | Calendar | Minimum JD | Maximum JD |
 | --- | --- | --- |
-| Julian | -0x1.fffffffffffffp+62 | 0x1.ffffffffffffap+60 |
+| Coptic | -0x1.fffffffffffffp+62 | 0x1.fffffffffffffp+60 |
+| Egyptian | -0x1.fffffffffffffp+62 | 0x1.fffffffffffffp+62 |
+| Ethiopian | -0x1.fffffffffffffp+62 | 0x1.fffffffffffffp+60 |
 | Gregorian | -0x1.fffffffffffc8p+62 | 0x1.fffd4eff4e5d7p+60 |
 | Islamic | -0x1.fffffffffffffp+62 | 0x1.1111111111099p+58 |
-| Egyptian | -0x1.fffffffffffffp+62 | 0x1.fffffffffffffp+62 |
+| Julian | -0x1.fffffffffffffp+62 | 0x1.ffffffffffffap+60 |
 
 ## License
 

Sources/JulianDayNumber/CopticCalendar+JDN.swift

@@ -0,0 +1,104 @@
+//
+// Copyright © 2021-2023 Stephen F. Booth <[email protected]>
+// Part of https://github.com/sbooth/JulianDayNumber
+// MIT license
+//
+
+import Foundation
+
+// Algorithm from the Explanatory Supplement to the Astronomical Almanac, 3rd edition, S.E Urban and P.K. Seidelmann eds., (Mill Valley, CA: University Science Books), Chapter 15, pp. 585-624.
+
+/// The number of years in a cycle of the Coptic calendar.
+///
+/// A cycle in the Coptic calendar consists of 3 common years and 1 leap year.
+let copticCalendarCycleYears = 4
+
+/// The number of days in a cycle of the Coptic calendar.
+///
+/// A cycle in the Coptic calendar consists of 3 years of 365 days and 1 leap year of 366 days.
+let copticCalendarCycleDays = 1461
+
+extension CopticCalendar: JulianDayNumberConverting {
+	/// Converts a year, month, and day in the Coptic calendar to a Julian day number.
+	///
+	/// - note: No validation checks are performed on the date values.
+	///
+	/// - parameter Y: A year number.
+	/// - parameter M: A month number between `1` (Tut) and `13` (Nissieh).
+	/// - parameter D: A day number between `1` and the maximum number of days in month `M` for year `Y`.
+	///
+	/// - returns: The Julian day number corresponding to the specified year, month, and day.
+	public static func dateToJulianDayNumber(year Y: Int, month M: Int, day D: Int) -> JulianDayNumber {
+		var Y = Y
+		var ΔcalendarCycles = 0
+
+		// Richards' algorithm is only valid for positive JDNs.
+		// JDN 0 is -4996-05-05 in the Coptic calendar.
+		// Adjust the year of earlier dates forward in time by a multiple of
+		// the calendar's cycle before calculating the JDN, and then translate
+		// the result backward in time by the period of adjustment.
+		if Y < -4996 || (Y == -4996 && (M < 5 || (M == 5 && D < 5))) {
+			ΔcalendarCycles = (-4997 - Y) / copticCalendarCycleYears + 1
+			Y += ΔcalendarCycles * copticCalendarCycleYears
+		}
+
+		let h = M - m
+		let g = Y + y - (n - h) / n
+		let f = (h - 1 + n) % n
+		let e = (p * g + q) / r + D - 1 - j
+		var J = e + (s * f + t) / u
+
+		if ΔcalendarCycles > 0 {
+			J -= ΔcalendarCycles * copticCalendarCycleDays
+		}
+
+		return J
+	}
+
+	/// Converts a Julian day number to a year, month, and day in the Coptic calendar.
+	///
+	/// - parameter J: A Julian day number.
+	///
+	/// - returns: The year, month, and day corresponding to the specified Julian day number.
+	public static func julianDayNumberToDate(_ J: JulianDayNumber) -> (year: Int, month: Int, day: Int) {
+		var J = J
+		var ΔcalendarCycles = 0
+
+		// Richards' algorithm is only valid for positive JDNs.
+		// Adjust negative JDNs forward in time by a multiple of
+		// the calendar's cycle before calculating the JDN, and then translate
+		// the result backward in time by the period of adjustment.
+		if J < 0 {
+			ΔcalendarCycles = -J / copticCalendarCycleDays + 1
+			J += ΔcalendarCycles * copticCalendarCycleDays
+		}
+
+		let f = J + j
+		let e = r * f + v
+		let g = (e % p) / r
+		let h = u * g + w
+		let D = (h % s) / u + 1
+		let M = ((h / s + m) % n) + 1
+		var Y = e / p - y + (n + m - M) / n
+
+		if ΔcalendarCycles > 0 {
+			Y -= ΔcalendarCycles * copticCalendarCycleYears
+		}
+
+		return (Y, M, D)
+	}
+}
+
+// Constants for Coptic calendar conversions
+private let y = 4996
+private let j = 124
+private let m = 0
+private let n = 13
+private let r = 4
+private let p = 1461
+private let q = 0
+private let v = 3
+private let u = 1
+private let s = 30
+private let t = 0
+private let w = 0

Sources/JulianDayNumber/CopticCalendar.swift

@@ -0,0 +1,76 @@
+//
+// Copyright © 2021-2023 Stephen F. Booth <[email protected]>
+// Part of https://github.com/sbooth/JulianDayNumber
+// MIT license
+//
+
+import Foundation
+
+/// The Coptic calendar.
+///
+/// The Coptic calendar is a solar calendar of 365 days in every year.
+///
+/// The Coptic calendar epoch in the Coptic calendar is 1 Tut 1.
+/// The Coptic calendar epoch in the Julian calendar is August 29, 284 AD.
+///
+/// - seealso: [Coptic calendar](https://en.wikipedia.org/wiki/Coptic_calendar)
+public struct CopticCalendar {
+	/// The year, month, and day of the epoch of the Coptic calendar.
+	///
+	/// The Coptic calendar epoch in the Coptic calendar is 1 Tut 1.
+	/// The Coptic calendar epoch in the Julian calendar is August 29, 284 AD.
+	public static let epochDate = (year: 1, month: 1, day: 1)
+
+	/// The Julian day number of the epoch of the Coptic calendar.
+	///
+	/// This JDN corresponds to noon on 1 Tut 1 in the Coptic calendar.
+	public static let epochJulianDayNumber: JulianDayNumber = 1825030
+
+	/// The Julian date of the epoch of the Coptic calendar.
+	///
+	/// This JD corresponds to midnight on 1 Tut 1 in the Coptic calendar.
+	public static let epochJulianDate: JulianDate = 1825029.5
+
+	/// Returns `true` if the specified year, month, and day form a valid date in the Coptic calendar.
+	///
+	/// - parameter Y: A year number.
+	/// - parameter M: A month number between `1` (Tut) and `13` (Nissieh).
+	/// - parameter D: A day number between `1` and the maximum number of days in month `M` for year `Y`.
+	///
+	/// - returns: `true` if the specified year, month, and day form a valid date in the Coptic calendar.
+	public static func isDateValid(year Y: Int, month M: Int, day D: Int) -> Bool {
+		M > 0 && M <= 13 && D > 0 && D <= daysInMonth(year: Y, month: M)
+	}
+
+	/// Returns `true` if the specified year is a leap year in the Coptic calendar.
+	///
+	/// A Coptic year is a leap year if its numerical designation plus one is divisible by 4.
+	///
+	/// - parameter Y: A year number.
+	///
+	/// - returns: `true` if the specified year is a leap year in the Coptic calendar.
+	public static func isLeapYear(_ Y: Int) -> Bool {
+		(Y + 1) % 4 == 0
+	}
+
+	/// The number of days in each month indexed from `0` (Tut) to `12` (Nissieh).
+	static let monthLengths = [ 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 5 ]
+
+	/// Returns the number of days in the specified month and year in the Coptic calendar.
+	///
+	/// - parameter Y: A year number.
+	/// - parameter M: A month number between `1` (Tut) and `13` (Nissieh).
+	///
+	/// - returns: The number of days in the specified month and year.
+	public static func daysInMonth(year Y: Int, month M: Int) -> Int {
+		guard M > 0, M <= 13 else {
+			return 0
+		}
+
+		if M == 13 {
+			return isLeapYear(Y) ? 6 : 5
+		} else {
+			return monthLengths[M - 1]
+		}
+	}
+}

Sources/JulianDayNumber/EthiopianCalendar+JDN.swift

@@ -0,0 +1,104 @@
+//
+// Copyright © 2021-2023 Stephen F. Booth <[email protected]>
+// Part of https://github.com/sbooth/JulianDayNumber
+// MIT license
+//
+
+import Foundation
+
+// Algorithm from the Explanatory Supplement to the Astronomical Almanac, 3rd edition, S.E Urban and P.K. Seidelmann eds., (Mill Valley, CA: University Science Books), Chapter 15, pp. 585-624.
+
+/// The number of years in a cycle of the Ethiopian calendar.
+///
+/// A cycle in the Ethiopian calendar consists of 3 common years and 1 leap year.
+let ethiopianCalendarCycleYears = 4
+
+/// The number of days in a cycle of the Ethiopian calendar.
+///
+/// A cycle in the Ethiopian calendar consists of 3 years of 365 days and 1 leap year of 366 days.
+let ethiopianCalendarCycleDays = 1461
+
+extension EthiopianCalendar: JulianDayNumberConverting {
+	/// Converts a year, month, and day in the Ethiopian calendar to a Julian day number.
+	///
+	/// - note: No validation checks are performed on the date values.
+	///
+	/// - parameter Y: A year number.
+	/// - parameter M: A month number between `1` (Mäskäräm) and `13` (Ṗagumen).
+	/// - parameter D: A day number between `1` and the maximum number of days in month `M` for year `Y`.
+	///
+	/// - returns: The Julian day number corresponding to the specified year, month, and day.
+	public static func dateToJulianDayNumber(year Y: Int, month M: Int, day D: Int) -> JulianDayNumber {
+		var Y = Y
+		var ΔcalendarCycles = 0
+
+		// Richards' algorithm is only valid for positive JDNs.
+		// JDN 0 is -4720-05-05 in the Ethiopian calendar.
+		// Adjust the year of earlier dates forward in time by a multiple of
+		// the calendar's cycle before calculating the JDN, and then translate
+		// the result backward in time by the period of adjustment.
+		if Y < -4720 || (Y == -4720 && (M < 5 || (M == 5 && D < 5))) {
+			ΔcalendarCycles = (-4721 - Y) / ethiopianCalendarCycleYears + 1
+			Y += ΔcalendarCycles * ethiopianCalendarCycleYears
+		}
+
+		let h = M - m
+		let g = Y + y - (n - h) / n
+		let f = (h - 1 + n) % n
+		let e = (p * g + q) / r + D - 1 - j
+		var J = e + (s * f + t) / u
+
+		if ΔcalendarCycles > 0 {
+			J -= ΔcalendarCycles * ethiopianCalendarCycleDays
+		}
+
+		return J
+	}
+
+	/// Converts a Julian day number to a year, month, and day in the Ethiopian calendar.
+	///
+	/// - parameter J: A Julian day number.
+	///
+	/// - returns: The year, month, and day corresponding to the specified Julian day number.
+	public static func julianDayNumberToDate(_ J: JulianDayNumber) -> (year: Int, month: Int, day: Int) {
+		var J = J
+		var ΔcalendarCycles = 0
+
+		// Richards' algorithm is only valid for positive JDNs.
+		// Adjust negative JDNs forward in time by a multiple of
+		// the calendar's cycle before calculating the JDN, and then translate
+		// the result backward in time by the period of adjustment.
+		if J < 0 {
+			ΔcalendarCycles = -J / ethiopianCalendarCycleDays + 1
+			J += ΔcalendarCycles * ethiopianCalendarCycleDays
+		}
+
+		let f = J + j
+		let e = r * f + v
+		let g = (e % p) / r
+		let h = u * g + w
+		let D = (h % s) / u + 1
+		let M = ((h / s + m) % n) + 1
+		var Y = e / p - y + (n + m - M) / n
+
+		if ΔcalendarCycles > 0 {
+			Y -= ΔcalendarCycles * ethiopianCalendarCycleYears
+		}
+
+		return (Y, M, D)
+	}
+}
+
+// Constants for Ethiopian calendar conversions
+private let y = 4720
+private let j = 124
+private let m = 0
+private let n = 13
+private let r = 4
+private let p = 1461
+private let q = 0
+private let v = 3
+private let u = 1
+private let s = 30
+private let t = 0
+private let w = 0