Friday the 13th? @xref{Types Answer 5, 5}. (@bullet{})
(@bullet{}) @strong{Exercise 6.} How many leap years will there be
-between now and the year 10001 A.D.? @xref{Types Answer 6, 6}. (@bullet{})
+between now and the year 10001 AD@? @xref{Types Answer 6, 6}. (@bullet{})
@cindex Slope and angle of a line
@cindex Angle and slope of a line
apply to any product-of-sum it encounters---this rule may surprise
you if you put it into @code{EvalRules}!
-In the second rule, the sum of two O's is changed to the smaller O.
+In the second rule, the sum of two O's is changed to the smaller O@.
The optional constant coefficients are there mostly so that
@samp{O(x^2) - O(x^3)} and @samp{O(x^3) - O(x^2)} are handled
as well as @samp{O(x^2) + O(x^3)}.
notations for dates and times. @xref{Date Formats}.
Date forms are stored internally as numbers, specifically the number
-of days since midnight on the morning of January 1 of the year 1 AD.
+of days since midnight on the morning of December 31 of the year 1 BC@.
If the internal number is an integer, the form represents a date only;
if the internal number is a fraction or float, the form represents
-a date and time. For example, @samp{<6:00am Wed Jan 9, 1991>}
+a date and time. For example, @samp{<6:00am Thu Jan 10, 1991>}
is represented by the number 726842.25. The standard precision of
12 decimal digits is enough to ensure that a (reasonable) date and
time can be stored without roundoff error.
of a date form. @xref{Packing and Unpacking}.
Date forms can go arbitrarily far into the future or past. Negative
-year numbers represent years BC@. Calc uses a combination of the
-Gregorian and Julian calendars, following the history of Great
-Britain and the British colonies. This is the same calendar that
-is used by the @code{cal} program in most Unix implementations.
+year numbers represent years BC@. There is no ``year 0''; the day
+before @samp{<Mon Jan 1, +1>} is @samp{<Sun Dec 31, -1>}. These are
+days 1 and 0 respectively in Calc's internal numbering scheme. The
+Gregorian calendar is used for all dates, including dates before the
+Gregorian calendar was invented (although that can be configured; see
+below). Thus Calc's use of the day number @mathit{-10000} to
+represent August 15, 28 BC should be taken with a grain of salt.
@cindex Julian calendar
@cindex Gregorian calendar
Some historical background: The Julian calendar was created by
-Julius Caesar in the year 46 BC as an attempt to fix the gradual
-drift caused by the lack of leap years in the calendar used
-until that time. The Julian calendar introduced an extra day in
-all years divisible by four. After some initial confusion, the
-calendar was adopted around the year we call 8 AD@. Some centuries
-later it became apparent that the Julian year of 365.25 days was
-itself not quite right. In 1582 Pope Gregory XIII introduced the
-Gregorian calendar, which added the new rule that years divisible
-by 100, but not by 400, were not to be considered leap years
-despite being divisible by four. Many countries delayed adoption
-of the Gregorian calendar because of religious differences;
-in Britain it was put off until the year 1752, by which time
-the Julian calendar had fallen eleven days behind the true
-seasons. So the switch to the Gregorian calendar in early
-September 1752 introduced a discontinuity: The day after
-Sep 2, 1752 is Sep 14, 1752. Calc follows this convention.
-To take another example, Russia waited until 1918 before
-adopting the new calendar, and thus needed to remove thirteen
-days (between Feb 1, 1918 and Feb 14, 1918). This means that
-Calc's reckoning will be inconsistent with Russian history between
-1752 and 1918, and similarly for various other countries.
-
-Today's timekeepers introduce an occasional ``leap second'' as
-well, but Calc does not take these minor effects into account.
-(If it did, it would have to report a non-integer number of days
-between, say, @samp{<12:00am Mon Jan 1, 1900>} and
+Julius Caesar in the year 46 BC as an attempt to fix the confusion
+caused by the irregular Roman calendar that was used before that time.
+The Julian calendar introduced an extra day in all years divisible by
+four. After some initial confusion, the calendar was adopted around
+the year we call 8 AD@. Some centuries later it became
+apparent that the Julian year of 365.25 days was itself not quite
+right. In 1582 Pope Gregory XIII introduced the Gregorian calendar,
+which added the new rule that years divisible by 100, but not by 400,
+were not to be considered leap years despite being divisible by four.
+Many countries delayed adoption of the Gregorian calendar
+because of religious differences. For example, Great Britain and the
+British colonies switched to the Gregorian calendar in September
+1752, when the Julian calendar was eleven days behind the
+Gregorian calendar. That year in Britain, the day after September 2
+was September 14. To take another example, Russia did not adopt the
+Gregorian calendar until 1918, and that year in Russia the day after
+January 31 was February 14. Calc's reckoning therefore matches English
+practice starting in 1752 and Russian practice starting in 1918, but
+disagrees with earlier dates in both countries.
+
+When the Julian calendar was introduced, it had January 1 as the first
+day of the year. By the Middle Ages, many European countries
+had changed the beginning of a new year to a different date, often to
+a religious festival. Almost all countries reverted to using January 1
+as the beginning of the year by the time they adopted the Gregorian
+calendar.
+
+Some calendars attempt to mimic the historical situation by using the
+Gregorian calendar for recent dates and the Julian calendar for older
+dates. The @code{cal} program in most Unix implementations does this,
+for example. While January 1 wasn't always the beginning of a calendar
+year, these hybrid calendars still use January 1 as the beginning of
+the year even for older dates. The customizable variable
+@code{calc-gregorian-switch} (@pxref{Customizing Calc}) can be set to
+have Calc's date forms switch from the Julian to Gregorian calendar at
+any specified date.
+
+Today's timekeepers introduce an occasional ``leap second''.
+These do not occur regularly and Calc does not take these minor
+effects into account. (If it did, it would have to report a
+non-integer number of days between, say,
+@samp{<12:00am Mon Jan 1, 1900>} and
@samp{<12:00am Sat Jan 1, 2000>}.)
-Calc uses the Julian calendar for all dates before the year 1752,
-including dates BC when the Julian calendar technically had not
-yet been invented. Thus the claim that day number @mathit{-10000} is
-called ``August 16, 28 BC'' should be taken with a grain of salt.
-
-Please note that there is no ``year 0''; the day before
-@samp{<Sat Jan 1, +1>} is @samp{<Fri Dec 31, -1>}. These are
-days 0 and @mathit{-1} respectively in Calc's internal numbering scheme.
-
@cindex Julian day counting
Another day counting system in common use is, confusingly, also called
-``Julian.'' The Julian day number is the numbers of days since
-12:00 noon (GMT) on Jan 1, 4713 BC, which in Calc's scheme (in GMT)
-is @mathit{-1721423.5} (recall that Calc starts at midnight instead
-of noon). Thus to convert a Calc date code obtained by unpacking a
-date form into a Julian day number, simply add 1721423.5 after
+``Julian.'' Julian days go from noon to noon. The Julian day number
+is the numbers of days since 12:00 noon (GMT) on November 24, 4714 BC
+in the Gregorian calendar (i.e., January 1, 4713 BC in the Julian
+calendar). In Calc's scheme (in GMT) the Julian day origin is
+@mathit{-1721422.5}, because Calc starts at midnight instead of noon.
+Thus to convert a Calc date code obtained by unpacking a
+date form into a Julian day number, simply add 1721422.5 after
compensating for the time zone difference. The built-in @kbd{t J}
command performs this conversion for you.
up by other astronomers. (At the time, noon was the start of the
astronomical day. Herschel originally suggested counting the days
since Jan 1, 4713 BC at noon Alexandria time; this was later amended to
-noon GMT.) Julian day numbering is largely used in astronomy.
+noon GMT@.) Julian day numbering is largely used in astronomy.
@cindex Unix time format
The Unix operating system measures time as an integer number of
match exactly; letter fields must correspond to suitable text in
the input. If this doesn't work, Calc checks if the input is a
simple number; if so, the number is interpreted as a number of days
-since Jan 1, 1 AD@. Otherwise, Calc tries a much more relaxed and
+since Dec 31, 1 BC@. Otherwise, Calc tries a much more relaxed and
flexible algorithm which is described in the next section.
Weekday names are ignored during reading.
be preserved. The default value of @code{calc-undo-length} is @expr{100}.
@end defvar
+@defvar calc-gregorian-switch
+See @ref{Date Forms}.@*
+The variable @code{calc-gregorian-switch} is either a list of integers
+@code{(@var{YEAR} @var{MONTH} @var{DAY})} or @code{nil}.
+If it is @code{nil}, then Calc's date forms always represent Gregorian dates.
+Otherwise, @code{calc-gregorian-switch} represents the date that the
+calendar switches from Julian dates to Gregorian dates;
+@code{(@var{YEAR} @var{MONTH} @var{DAY})} will be the first Gregorian
+date. The customization buffer will offer several standard dates to
+choose from, or the user can enter their own date.
+
+The default value of @code{calc-gregorian-switch} is @code{nil}.
+@end defvar
+
@node Reporting Bugs, Summary, Customizing Calc, Top
@appendix Reporting Bugs