;;  constants
;; Fixed second counts and calendar facts.
   
(define seconds-in-a-normal-year 31536000)

   
(define seconds-in-a-leap-year 31622400)

  
(define seconds-in-a-week 604800)

   
(define seconds-in-a-day 86400)

   
(define seconds-in-an-hour 3600)

   
(define base-year 1970)

   
(define month-length-normal-year
  (vector 31 28 31 30 31 30 31 31 30 31 30 31))

  
;;  functions
;; The section of functions.
; Return whether y is a leap year
   
(define (leap-year y)
  (cond ((= (modulo y 400) 0) #t)
        ((= (modulo y 100) 0) #f)
        ((= (modulo y 4) 0) #t)
        (else #f)))

; Return a list of year and remainding seconds of the second
; counter n.
    
(define (years-and-seconds n)
  (cycle-years 0 base-year n))

; Count years by increasing n and decreasing u until u is less than the seconds in a year.
; Both n and u are integeres representing a number of seconds.
; Returns a list of year and remaining seconds (less than a year).
   
(define (cycle-years n year u)
  (let ((year-length (if (leap-year year)
                          seconds-in-a-leap-year
                          seconds-in-a-normal-year)))
    (if (< u year-length) 
        (list year u)
        (cycle-years (+ n year-length) (+ 1 year) (- u year-length)))))

; Return the number days, hours, minutes and seconds in second count n.
; n is less than the number of seconds in a year
    
(define (how-many-days-hours-minutes-seconds n)
  (let* ((days (quotient n seconds-in-a-day))    ;  
         (n-rest-1 (modulo n seconds-in-a-day))  ;  
         (hours (quotient n-rest-1 seconds-in-an-hour))  ;  
         (n-rest-2 (modulo n-rest-1 seconds-in-an-hour)) ;  
         (minutes (quotient n-rest-2 60)) ;  
         (seconds (modulo n-rest-2 60)))  ;  
    (list days hours minutes seconds)))

; Return a list of day and moth given a number of days in year.
; Day-count is a number of days in a year. 
    
(define (day-and-month day-count year)
  (day-and-month-help 0 1 year (+ 1 day-count)) )

   
(define (day-and-month-help n m y c)
  (if (<= c (days-in-month m y)) 
      (list c m)
      (day-and-month-help (+ n (days-in-month m y)) (+ m 1)
                          y (- c (days-in-month m y)))))

; Return the number of days in month and year
   
(define (days-in-month month year)
   (if (= month 2)
       (if (leap-year year) 29 28)
       (vector-ref month-length-normal-year (- month 1))))

; Return a list of year month day hours minutes seconds from n,
; which represents the number of seconds elapsed since January 1, 1970.
      
(define (time-decode n)
  (let* ((year-seconds 
           (years-and-seconds n)) ;  
         (year (car year-seconds))
         (days-hours-minutes-seconds   ;  
             (how-many-days-hours-minutes-seconds (cadr year-seconds)))
         (hours (second days-hours-minutes-seconds))
         (minutes (third days-hours-minutes-seconds))
         (seconds (fourth days-hours-minutes-seconds))
         (day-month
             (day-and-month (first days-hours-minutes-seconds) year)) ;  
         (day (first day-month))
         (month (second day-month)))
     (list year month day hours minutes seconds)))