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Time Zones

Time zones and daylight savings time are a complicated business. The conversions to and from Julian and Unix-style dates automatically compute the correct time zone and daylight savings adjustment to use, provided they can figure out this information. This section describes Calc's time zone adjustment algorithm in detail, in case you want to do conversions in different time zones or in case Calc's algorithms can't determine the right correction to use.

Adjustments for time zones and daylight savings time are done by t U, t J, t N, and t C, but not by any other commands. In particular, `<may 1 1991> - <apr 1 1991>' evaluates to exactly 30 days even though there is a daylight-savings transition in between. This is also true for Julian pure dates: `julian(<may 1 1991>) - julian(<apr 1 1991>)'. But Julian and Unix date/times will adjust for daylight savings time: `julian(<12am may 1 1991>) - julian(<12am apr 1 1991>)' evaluates to `29.95834' (that's 29 days and 23 hours) because one hour was lost when daylight savings commenced on April 7, 1991.

In brief, the idiom `julian(date1) - julian(date2)' computes the actual number of 24-hour periods between two dates, whereas `date1 - date2' computes the number of calendar days between two dates without taking daylight savings into account.

The calc-time-zone [tzone] command converts the time zone specified by its numeric prefix argument into a number of seconds difference from Greenwich mean time (GMT). If the argument is a number, the result is simply that value multiplied by 3600. Typical arguments for North America are 5 (Eastern) or 8 (Pacific). If Daylight Savings time is in effect, one hour should be subtracted from the normal difference.

If you give a prefix of plain C-u, calc-time-zone (like other date arithmetic commands that include a time zone argument) takes the zone argument from the top of the stack. (In the case of t J and t U, the normal argument is then taken from the second-to-top stack position.) This allows you to give a non-integer time zone adjustment. The time-zone argument can also be an HMS form, or it can be a variable which is a time zone name in upper- or lower-case. For example `tzone(PST) = tzone(8)' and `tzone(pdt) = tzone(7)' (for Pacific standard and daylight savings times, respectively).

North American and European time zone names are defined as follows; note that for each time zone there is one name for standard time, another for daylight savings time, and a third for "generalized" time in which the daylight savings adjustment is computed from context.

 9    8    7    6    5    4     3.5     0     -1      -2     -2

 8    7    6    5    4    3     2.5     -1    -2      -3     -3

9/8  8/7  7/6  6/5  5/4  4/3  3.5/2.5  0/-1 -1/-2   -2/-3  -2/-3

To define time zone names that do not appear in the above table, you must modify the Lisp variable math-tzone-names. This is a list of lists describing the different time zone names; its structure is best explained by an example. The three entries for Pacific Time look like this:

( ( "PST" 8 0 )    ; Name as an upper-case string, then standard
  ( "PDT" 8 -1 )   ; adjustment, then daylight savings adjustment.
  ( "PGT" 8 "PST" "PDT" ) )   ; Generalized time zone.

With no arguments, calc-time-zone or `tzone()' obtains an argument from the Calc variable TimeZone if a value has been stored for that variable. If not, Calc runs the Unix `date' command and looks for one of the above time zone names in the output; if this does not succeed, `tzone()' leaves itself unevaluated. The time zone name in the `date' output may be followed by a signed adjustment, e.g., `GMT+5' or `GMT+0500' which specifies a number of hours and minutes to be added to the base time zone. Calc stores the time zone it finds into TimeZone to speed later calls to `tzone()'.

The special time zone name local is equivalent to no argument, i.e., it uses the local time zone as obtained from the date command.

If the time zone name found is one of the standard or daylight savings zone names from the above table, and Calc's internal daylight savings algorithm says that time and zone are consistent (e.g., PDT accompanies a date that Calc's algorithm would also consider to be daylight savings, or PST accompanies a date that Calc would consider to be standard time), then Calc substitutes the corresponding generalized time zone (like PGT).

If your system does not have a suitable `date' command, you may wish to put a `(setq var-TimeZone ...)' in your Emacs initialization file to set the time zone. The easiest way to do this is to edit the TimeZone variable using Calc's s T command, then use the s p (calc-permanent-variable) command to save the value of TimeZone permanently.

The t J and t U commands with no numeric prefix arguments do the same thing as `tzone()'. If the current time zone is a generalized time zone, e.g., EGT, Calc examines the date being converted to tell whether to use standard or daylight savings time. But if the current time zone is explicit, e.g., EST or EDT, then that adjustment is used exactly and Calc's daylight savings algorithm is not consulted.

Some places don't follow the usual rules for daylight savings time. The state of Arizona, for example, does not observe daylight savings time. If you run Calc during the winter season in Arizona, the Unix date command will report MST time zone, which Calc will change to MGT. If you then convert a time that lies in the summer months, Calc will apply an incorrect daylight savings time adjustment. To avoid this, set your TimeZone variable explicitly to MST to force the use of standard, non-daylight-savings time.

By default Calc always considers daylight savings time to begin at 2 a.m. on the first Sunday of April, and to end at 2 a.m. on the last Sunday of October. This is the rule that has been in effect in North America since 1987. If you are in a country that uses different rules for computing daylight savings time, you have two choices: Write your own daylight savings hook, or control time zones explicitly by setting the TimeZone variable and/or always giving a time-zone argument for the conversion functions.

The Lisp variable math-daylight-savings-hook holds the name of a function that is used to compute the daylight savings adjustment for a given date. The default is math-std-daylight-savings, which computes an adjustment (either 0 or -1) using the North American rules given above.

The daylight savings hook function is called with four arguments: The date, as a floating-point number in standard Calc format; a six-element list of the date decomposed into year, month, day, hour, minute, and second, respectively; a string which contains the generalized time zone name in upper-case, e.g., "WEGT"; and a special adjustment to be applied to the hour value when converting into a generalized time zone (see below).

The Lisp function math-prev-weekday-in-month is useful for daylight savings computations. This is an internal version of the user-level pwday function described in the previous section. It takes four arguments: The floating-point date value, the corresponding six-element date list, the day-of-month number, and the weekday number (0-6).

The default daylight savings hook ignores the time zone name, but a more sophisticated hook could use different algorithms for different time zones. It would also be possible to use different algorithms depending on the year number, but the default hook always uses the algorithm for 1987 and later. Here is a listing of the default daylight savings hook:

(defun math-std-daylight-savings (date dt zone bump)
  (cond ((< (nth 1 dt) 4) 0)
        ((= (nth 1 dt) 4)
         (let ((sunday (math-prev-weekday-in-month date dt 7 0)))
           (cond ((< (nth 2 dt) sunday) 0)
                 ((= (nth 2 dt) sunday)
                  (if (>= (nth 3 dt) (+ 3 bump)) -1 0))
                 (t -1))))
        ((< (nth 1 dt) 10) -1)
        ((= (nth 1 dt) 10)
         (let ((sunday (math-prev-weekday-in-month date dt 31 0)))
           (cond ((< (nth 2 dt) sunday) -1)
                 ((= (nth 2 dt) sunday)
                  (if (>= (nth 3 dt) (+ 2 bump)) 0 -1))
                 (t 0))))
        (t 0))

The bump parameter is equal to zero when Calc is converting from a date form in a generalized time zone into a GMT date value. It is -1 when Calc is converting in the other direction. The adjustments shown above ensure that the conversion behaves correctly and reasonably around the 2 a.m. transition in each direction.

There is a "missing" hour between 2 a.m. and 3 a.m. at the beginning of daylight savings time; converting a date/time form that falls in this hour results in a time value for the following hour, from 3 a.m. to 4 a.m. At the end of daylight savings time, the hour from 1 a.m. to 2 a.m. repeats itself; converting a date/time form that falls in in this hour results in a time value for the first manifestion of that time (not the one that occurs one hour later).

If math-daylight-savings-hook is nil, then the daylight savings adjustment is always taken to be zero.

In algebraic formulas, `tzone(zone, date)' computes the time zone adjustment for a given zone name at a given date. The date is ignored unless zone is a generalized time zone. If date is a date form, the daylight savings computation is applied to it as it appears. If date is a numeric date value, it is adjusted for the daylight-savings version of zone before being given to the daylight savings hook. This odd-sounding rule ensures that the daylight-savings computation is always done in local time, not in the GMT time that a numeric date is typically represented in.

The `dsadj(date, zone)' function computes the daylight savings adjustment that is appropriate for date in time zone zone. If zone is explicitly in or not in daylight savings time (e.g., PDT or PST) the date is ignored. If zone is a generalized time zone, the algorithms described above are used. If zone is omitted, the computation is done for the current time zone.

See section Reporting Bugs, for the address of Calc's author, if you should wish to contribute your improved versions of math-tzone-names and math-daylight-savings-hook to the Calc distribution.

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