;
; The original Lisp code is from ``Calendrical Calculations'' by Nachum
; Dershowitz and Edward M. Reingold, Software---Practice & Experience,
; vol. 20, no. 9 (September, 1990), pp. 899--928.
;
; scheme conversion by oz (Ozan S. Yigit).
;
; This code is in the public domain, but any use of it should
; acknowledge its source.
;
(define (nth n lst)
(list-ref lst n))
; date (month day year) accessors
(define extract-month car) ; month field
(define extract-day cadr) ; day field
(define extract-year caddr) ; year field
; Sum expression for index = initial and successive integers,
; as long as condition holds.
(macro (sum expression index initial condition)
(let* ((temp (gensym)))
`(do ((,temp 0 (+ ,temp ,expression))
(,index ,initial (1+ ,index)))
((not ,condition) ,temp))))
; Last day in Gregorian month during year.
(define (last-day-of-gregorian-month month year)
(if (and (= month 2) ; February in a leap year
(= (modulo year 4) 0)
(not (member (modulo year 400) (list 100 200 300))))
29
(nth (1- month)
(list 31 28 31 30 31 30 31 31 30 31 30 31))))
; Absolute date equivalent to the Gregorian date.
(define (gregorian->absolute date)
(let* ((month (extract-month date))
(year (extract-year date)))
(+ (extract-day date) ; days so far this month.
(sum ; Days in prior months this year.
(last-day-of-gregorian-month m year) m 1 (< m month))
(* 365 (1- year)) ; Days in prior years.
(quotient (1- year) 4) ; Julian leap days in prior years...
(- ; ...minus prior century years...
(quotient (1- year) 100))
(quotient ; ...plus prior years divisible...
(1- year) 400)))) ; ...by 400.
; Gregorian (month day year) corresponding absolute date.
(define (absolute->gregorian date)
(let* ((approx (quotient date 366)) ; Approximation from below.
(year ; Search forward from the approximation
(+ approx
(sum 1 y approx
(>= date
(gregorian->absolute
(list 1 1 (1+ y)))))))
(month ; Search forward from January.
(1+ (sum 1 m 1
(> date
(gregorian->absolute
(list m
(last-day-of-gregorian-month m year)
year))))))
(day ; Calculate the day by subtraction.
(- date (1- (gregorian->absolute
(list month 1 year))))))
(list month day year)))
; Absolute date of the k-day on or before date.
; k=0 means Sunday, k=1 means Monday, and so on.
(define (k-day-on-or-before date k)
(- date (modulo (- date k) 7)))
; Absolute date equivalent to ISO date = (week day year).
(define (iso->absolute date)
(let* ((week (car date))
(day (cadr date))
(year (caddr date)))
(+ (k-day-on-or-before
(gregorian->absolute (list 1 4 year))
1) ; Days in prior years.
(* 7 (1- week)) ; Days in prior weeks this year.
(1- day)))) ; Prior days this week.
; ISO (week day year) corresponding to the absolute date.
(define (absolute->iso date)
(let* ((approx
(extract-year (absolute->gregorian (- date 3))))
(year (if (>= date
(iso->absolute (list 1 1 (1+ approx))))
(1+ approx)
approx))
(week (1+ (quotient
(- date (iso->absolute (list 1 1 year)))
7)))
(day (if (= 0 (modulo date 7))
7
(modulo date 7))))
(list week day year)))
; Last day in Julian month during year.
(define (last-day-of-julian-month month year)
(if (and (= month 2)
(= (modulo year 4) 0)) ; February in a leap year
29
(nth (1- month) (list 31 28 31 30 31 30 31 31 30 31 30 31))))
; Absolute date equivalent to Julian date.
(define (julian->absolute date)
(let* ((month (extract-month date))
(year (extract-year date)))
(+ (extract-day date) ; Days so far this month.
(sum ; Days in prior months this year.
(last-day-of-julian-month m year) m 1 (< m month))
(* 365 (1- year)) ; Days in prior years.
(quotient (1- year) 4) ; Leap days in prior years.
-2))) ; Days elapsed before absolute date 1.
; Julian (month day year) corresponding to absolute date.
(define (absolute->julian date)
(let*
((approx ; Approximation from below.
(quotient (+ date 2) 366))
(year ; Search forward from the approximation
(+ approx
(sum 1 y approx
(>= date
(julian->absolute (list 1 1 (1+ y)))))))
(month ; Search forward from January.
(1+ (sum 1 m 1
(> date
(julian->absolute
(list m
(last-day-of-julian-month m year)
year))))))
(day ; Calculate the day by subtraction.
(- date (1- (julian->absolute (list month 1 year))))))
(list month day year)))
; true if year is an Islamic leap year.
(define (islamic-leap-year? year)
(< (modulo (+ 14 (* 11 year)) 30) 11))
; Last day in month during year on the Islamic calendar.
(define (last-day-of-islamic-month month year)
(if (or (odd? month)
(and (= month 12)
(islamic-leap-year? year)))
30
29))
; Absolute date equivalent to Islamic date.
(define (islamic->absolute date)
(let* ((month (extract-month date))
(year (extract-year date)))
(+ (extract-day date) ; Days so far this month.
(* 29 (1- month)) ; Days so far...
(quotient month 2) ; ...this year.
(* (1- year) 354) ; Non-leap days in prior years.
(quotient ; Leap days in prior years.
(+ 3 (* 11 year)) 30)
227014))) ; Days before start of calendar.
; Islamic date (month day year) corresponding to absolute date.
(define (absolute->islamic date)
(if (<= date 227014) ; Pre-Islamic date.
(list 0 0 0)
(let* ((approx ; Approximation from below.
(quotient (- date 227014) 355))
(year ; Search forward from the approximation
(+ approx
(sum 1 y approx
(>= date
(islamic->absolute
(list 1 1 (1+ y)))))))
(month ; Search forward from Muharram.
(1+ (sum 1 m 1
(> date
(islamic->absolute
(list m
(last-day-of-islamic-month m year)
year))))))
(day ; Calculate the day by subtraction.
(- date (1- (islamic->absolute
(list month 1 year))))))
(list month day year))))
; true if year is a leap year.
(define (hebrew-leap-year? year)
(< (modulo (1+ (* 7 year)) 19) 7))
; Last month of Hebrew year.
(define (last-month-of-hebrew-year year)
(if (hebrew-leap-year? year)
13
12))
; Last day of month in Hebrew year.
(define (last-day-of-hebrew-month month year)
(if (or (member month (list 2 4 6 10 13))
(and (= month 12)
(not (hebrew-leap-year? year)))
(and (= month 8)
(not (long-heshvan year)))
(and (= month 9)
(short-kislev year)))
29
30))
; Number of days elapsed from the Sunday prior to the start of the
; Hebrew calendar to the mean conjunction of Tishri of Hebrew year.
(define (hebrew-calendar-elapsed-days year)
(let*
((months-elapsed
(+
(* 235 ; Months in complete cycles so far.
(quotient (1- year) 19))
(* 12 ; Regular months in this cycle.
(modulo (1- year) 19))
(quotient ; Leap months this cycle
(1+ (* 7 (modulo (1- year) 19)))
19)))
;;
;; (parts-elapsed (+ 5604 (* 13753 months-elapsed)))
;; (day ; Conjunction day
;; (+ 1 (* 29 months-elapsed) (quotient parts-elapsed 25920)))
;; (parts (modulo parts-elapsed 25920)) ; Conjunction parts
;;
;; The above lines of code are correct, but can have intermediate
;; values that are too large for a 32-bit machine. The following
;; lines of code that replace them are equivalent, but avoid the
;; problem.
;;
(parts-elapsed
(+ 204
(* 793 (modulo months-elapsed 1080))))
(hours-elapsed
(+ 5
(* 12 months-elapsed)
(* 793 (quotient months-elapsed 1080))
(quotient parts-elapsed 1080)))
(day ; Conjunction day
(+ 1
(* 29 months-elapsed)
(quotient hours-elapsed 24)))
(parts ; Conjunction parts
(+ (* 1080 (modulo hours-elapsed 24))
(modulo parts-elapsed 1080)))
(alternative-day
(if (or
(>= parts 19440) ; If new moon is at or after midday,
(and
(= (modulo day 7) 2) ; ...or is on a Tuesday...
(>= parts 9924) ; at 9 hours, 204 parts or later...
(not (hebrew-leap-year? year))) ; of a common year,
(and
(= (modulo day 7) 1) ; ...or is on a Monday at...
(>= parts 16789) ; 15 hours, 589 parts or later...
(hebrew-leap-year? ; at the end of a leap year
(1- year))))
(1+ day) ; Then postpone Rosh HaShanah one day
day)))
; If Rosh HaShanah would occur on Sunday, Wednesday, or Friday
(if (member (modulo alternative-day 7) (list 0 3 5))
(1+ alternative-day) ; Then postpone it one (more) day
alternative-day)))
; Number of days in Hebrew year.
(define (days-in-hebrew-year year)
(- (hebrew-calendar-elapsed-days (1+ year))
(hebrew-calendar-elapsed-days year)))
; true if Heshvan is long in Hebrew year.
(define (long-heshvan? year)
(= (modulo (days-in-hebrew-year year) 10) 5))
; true if Kislev is short in Hebrew year.
(define (short-kislev? year)
(= (modulo (days-in-hebrew-year year) 10) 3))
; absolute date of Hebrew date.
(define (hebrew->absolute date)
(let* ((month (extract-month date))
(day (extract-day date))
(year (extract-year date)))
(+ day ; Days so far this month.
(if (< month 7) ; before Tishri
; add days in prior months this year before and after Nisan.
(+ (sum (last-day-of-hebrew-month m year)
m 7 (<= m (last-month-of-hebrew-year year)))
(sum (last-day-of-hebrew-month m year)
m 1 (< m month)))
; add days in prior months this year
(sum (last-day-of-hebrew-month m year) m 7 (< m month)))
(hebrew-calendar-elapsed-days year) ; Days in prior years.
-1373429))) ; Days elapsed before absolute date 1.
; hebrew (month day year) corresponding to absolute date.
(define (absolute->hebrew date)
(let* ((approx ; Approximation from below.
(quotient (+ date 1373429) 366))
(year ; Search forward from the approximation
(+ approx (sum 1 y approx
(>= date
(hebrew->absolute
(list 7 1 (1+ y)))))))
(start ; Starting month for search for month.
(if (< date (hebrew->absolute (list 1 1 year)))
7 ; start at Tishri
1)) ; start at Nisan
(month ; Search forward from either Tishri or Nisan.
(+ start
(sum 1 m start
(> date
(hebrew->absolute
(list m
(last-day-of-hebrew-month m year)
year))))))
(day ; Calculate the day by subtraction.
(- date (1- (hebrew->absolute (list month 1 year))))))
(list month day year)))
; Absolute date of American Independence Day in Gregorian year.
(define (independence-day year)
(gregorian->absolute (list 7 4 year)))
; Absolute date of the n-th k-day in Gregorian month, year.
; If n<0, the n-th k-day from the end of month is returned
; (that is, -1 is the last k-day, -2 is the penultimate k-day,
; and so on). k=0 means Sunday, k=1 means Monday, and so on.
(define (nth-k-day n k month year)
(if (> n 0)
(+ (k-day-on-or-before ; First k-day in month.
(gregorian->absolute
(list month 7 year)) k)
(* 7 (1- n))) ; Advance n-1 k-days.
(+ (k-day-on-or-before ; Last k-day in month.
(gregorian->absolute
(list month
(last-day-of-gregorian-month month year)
year))
k)
(* 7 (1+ n))))) ; Go back -n-1 k-days.
; Absolute date of American Labor Day in Gregorian year.
(define (labor-day year)
(nth-k-day 1 1 9 year)) ; First Monday in September.
; Absolute date of American Memorial Day in Gregorian year.
(define (memorial-day year)
(nth-k-day -1 1 5 year)) ; Last Monday in May.
; Absolute date of the start of American daylight savings time
; in Gregorian year.
(define (daylight-savings-start year)
(nth-k-day 1 0 4 year)) ; First Sunday in April.
; Absolute date of the end of American daylight savings time
; in Gregorian year.
(define (daylight-savings-end year)
(nth-k-day -1 0 10 year)) ; Last Sunday in October.
; Absolute date of Christmas in Gregorian year.
(define (christmas year)
(gregorian->absolute (list 12 25 year)))
; Absolute date of Advent in Gregorian year.
(define (advent year)
(k-day-on-or-before (gregorian->absolute (list 12 3 year)) 0))
; Absolute date of Epiphany in Gregorian year.
(define (epiphany year)
(+ 12 (christmas year)))
; List of zero or one absolute dates of Eastern Orthodox
; Christmas in Gregorian year.
(define (eastern-orthodox-christmas year)
(let* ((jan1 (gregorian->absolute (list 1 1 year)))
(dec31 (gregorian->absolute (list 12 31 year)))
(y (extract-year (absolute->julian jan1)))
(c1 (julian->absolute (list 12 25 y)))
(c2 (julian->absolute (list 12 25 (1+ y)))))
(append
(if (<= jan1 c1 dec31) ; c1 occurs in current year
(list c1) ; that date; otherwise, none
nil)
(if (<= jan1 c2 dec31) ; c2 occurs in current year
(list c2) ; that date; otherwise, none
nil))))
; Absolute date of Easter in Julian year, according to the rule
; of the Council of Nicaea.
(define (nicaean-rule-easter year)
(let* ((shifted-epact ; Age of moon for April 5.
(modulo (+ 14
(* 11 (modulo year 19)))
30))
(paschal-moon ; Day after full moon on or after March
21.
(- (julian->absolute (list 4 19 year))
shifted-epact)))
; Return the Sunday following the Paschal moon
(k-day-on-or-before (+ paschal-moon 7) 0)))
; Absolute date of Easter in Gregorian year.
(define (easter year)
(let* ((century (1+ (quotient year 100)))
(shifted-epact ; Age of moon for April 5...
(modulo
(+ 14 (* 11 (modulo year 19)); ...by Nicaean rule
(- ; ...corrected for the Gregorian century rule
(quotient (* 3 century) 4))
(quotient ; ...corrected for Metonic cycle inaccuracy.
(+ 5 (* 8 century)) 25)
(* 30 century)) ; Keeps value positive.
30))
(adjusted-epact ; Adjust for 29.5 day month..
(if (or (= shifted-epact 0)
(and (= shifted-epact 1)
(< 10 (modulo year 19))))
(1+ shifted-epact)
shifted-epact))
(paschal-moon ; Day after full moon on or after March 21.
(- (gregorian->absolute (list 4 19 year))
adjusted-epact)))
; Return the Sunday following the Paschal moon.
(k-day-on-or-before (+ paschal-moon 7) 0)))
; Absolute date of Pentecost in Gregorian year.
(define (pentecost year)
(+ 49 (easter year)))
; List of the absolute dates of Islamic month, day
; that occur in Gregorian year.
(define (islamic-date month day year)
(let* ((jan1 (gregorian->absolute (list 1 1 year)))
(dec31 (gregorian->absolute (list 12 31 year)))
(y (extract-year (absolute->islamic jan1)))
; The possible occurrences in one year are
(date1 (islamic->absolute (list month day y)))
(date2 (islamic->absolute (list month day (1+ y))))
(date3 (islamic->absolute (list month day (+ 2 y)))))
; Combine in one list those that occur in current year
(append
(if (<= jan1 date1 dec31)
(list date1) nil)
(if (<= jan1 date2 dec31)
(list date2) nil)
(if (<= jan1 date3 dec31)
(list date3) nil))))
; List of absolute dates of Mulad-al-Nabi occurring in
; Gregorian year.
(define (mulad-al-nabi year)
(islamic-date 3 12 year))
; Absolute date of Yom Kippur occurring in Gregorian year.
(define (yom-kippur year)
(hebrew->absolute (list 7 10 (+ year 3761))))
; Absolute date of Passover occurring in Gregorian year.
(define (passover year)
(hebrew->absolute (list 1 15 (+ year 3760))))
; Absolute date of Purim occurring in Gregorian year.
(define (purim year)
(hebrew->absolute
(list
(last-month-of-hebrew-year (+ year 3760)) ; Adar or Adar II
14
(+ year 3760))))
; Absolute date of Ta'anith Esther occurring in Gregorian year.
(define (ta-anit-esther year)
(let* ((purim-date (purim year))) ; absolute date of Purim
(if (= (modulo purim-date 7) 0) ; Purim is on Sunday
(- purim-date 3) ; return prior Thursday
(1- purim-date)))) ; return previous day
; Absolute date of Tisha B'Av occurring in Gregorian year.
(define (tisha-b-av year)
(let* ((ninth-of-av
(hebrew->absolute (list 5 9 (+ year 3760)))))
(if
(= (modulo ninth-of-av 7) 6) ; Ninth of Av is Saturday
(1+ ninth-of-av) ; return the next day
ninth-of-av)))
; Absolute date of the anniversary of Hebrew birthdate
; occurring in Hebrew year.
(define (hebrew-birthday birthdate year)
(let* ((birth-day (extract-day birthdate))
(birth-month (extract-month birthdate))
(birth-year (extract-year birthdate)))
; It's Adar in a normal year or Adar II in a leap year
; then use the same day in last month of year.
(if (= birth-month (last-month-of-hebrew-year birth-year))
(hebrew->absolute
(list (last-month-of-hebrew-year year) birth-day year))
; else use the normal anniversary of the birth date,
; or the corresponding day in years without that date
(hebrew->absolute (list birth-month birth-day year)))))
; Absolute date of the anniversary of Hebrew death-date
; occurring in Hebrew year.
(define (yahrzeit death-date year)
(let* ((death-day (extract-day death-date))
(death-month (extract-month death-date))
(death-year (extract-year death-date)))
(cond
; If it's Heshvan 30 it depends on the first anniversary.
; If that was not Heshvan 30, use the day before Kislev 1.
((and (= death-month 8)
(= death-day 30)
(not (long-heshvan? (1+ death-year))))
(1- (hebrew->absolute (list 9 1 year))))
; If it's Kislev 30 it depends on the first anniversary.
; If that was not Kislev 30, use the day before Teveth 1.
((and (= death-month 9)
(= death-day 30)
(short-kislev? (1+ death-year)))
(1- (hebrew->absolute (list 10 1 year))))
; If it's Adar II, use the same day in last month of
; year (Adar or Adar II).
((= death-month 13)
(hebrew->absolute
(list (last-month-of-hebrew-year year) death-day year)))
; If it's the 30th in Adar I and year is not a leap year
; (so Adar has only 29 days), use the last day in Shevat.
((and (= death-day 30)
(= death-month 12)
(not (hebrew-leap-year? death-year)))
(hebrew->absolute (list 11 30 year)))
; In all other cases, use the normal anniversary of the
; date of death.
(t (hebrew->absolute
(list death-month death-day year))))))