Time Arithmetic

September 15, 2015

We’ll write new functions julian-time and gregorian-time that call julian and gregorian for the date part of the calculation; it’s always easier to let somebody else do the hard work.

We represent a date-time stamp as an integer date with an added fraction for the time, which is the number of seconds since midnight divided by 24 * 60 * 60 = 86400, the number of seconds in a full day. The number of seconds since midnight is 60 * 60 = 3600 times the number of hours since midnight, plus 60 times the number of minutes since the hour, plus the number of seconds since the minute:

(define (julian-time year month day hour minute second)
  (+ (julian year month day)
    (/ (+ (* hour 60 60) (* minute 60) second) 86400)))

Extracting hours, minutes and seconds from the time-stamp is just the reverse calculation:

(define (gregorian-time time-stamp)
  (let* ((date (floor time-stamp))
         (time (* (- time-stamp date) 86400))
         (hour (quotient time 3600))
         (minute (modulo (quotient time 60) 60))
         (second (modulo time 60)))
    (call-with-values
      (lambda () (gregorian date))
      (lambda (year month day)
        (values year month day hour minute second)))))

Here are some examples:

> (julian-time 2015 9 14 10 39 42)
35384838397/14400
> (gregorian-time (julian-time 2015 9 14 10 39 42))
2015
9
14
10
39
42

We used the julian and gregorian functions from the Standard Prelude. You can run the program at http://ideone.com/Woug7l.

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