%
% \DayOfWeek expands to the day of the week ("Sunday", etc.)
% \PhaseOfMoon expands to the phase of the moon
%
% Written by Martin Minow of DEC (minow%bolt.dec@decwrl.dec.com).
%
\def\DayOfWeek{%
%
% Calculate day of the week, return "Sunday", etc.
%
\newcount\dow % Gets day of the week
\newcount\leap % Leap year fingaler
\newcount\x % Temp register
\newcount\y % Another temp register
% leap = year + (month - 14)/12;
\leap=\month \advance\leap by -14 \divide\leap by 12
\advance\leap by \year
% dow = (13 * (month + 10 - (month + 10)/13*12) - 1)/5
\dow=\month \advance\dow by 10
\y=\dow \divide\y by 13 \multiply\y by 12
\advance\dow by -\y \multiply\dow by 13 \advance\dow by -1 \divide\dow by 5
% dow += day + 77 + 5 * (leap % 100)/4
\advance\dow by \day \advance\dow by 77
\x=\leap \y=\x \divide\y by 100 \multiply\y by 100 \advance\x by -\y
\multiply\x by 5 \divide\x by 4 \advance\dow by \x
% dow += leap / 400
\x=\leap \divide\x by 400 \advance\dow by \x
% dow -= leap / 100 * 2;
% dow = (dow % 7)
\x=\leap \divide\x by 100 \multiply\x by 2 \advance\dow by -\x
\x=\dow \divide\x by 7 \multiply\x by 7 \advance\dow by -\x
\ifcase\dow Sunday\or Monday\or Tuesday\or Wednesday\or
Thursday\or Friday\or Saturday\fi
}
%%
%%
%%
\def\PhaseOfMoon{% Calculate the phase of the (civil) moon.
%
% The routine calculates the year's epact (the age of the moon on Jan 1.),
% adds this to the number of days in the year, and calculates the phase
% of the moon for this date. It returns the phase as a string, e.g.,
% "new", "full", etc.
%
% In the algorithm:
%
% diy Is the day of the year - 1 (i.e., Jan 1 is day 0).
%
% golden Is the number of the year in the Mentonic cycle, used to
% determine the position of the calender moon.
%
% epact Is the age of the calender moon (in days) at the beginning
% of the year. To calculate epact, two century-based
% corrections are applied:
% Gregorian: (3 * cent)/4 - 12
% is the number of years such as 1700, 1800 when
% leap year was not held.
% Clavian: (((8 * cent) + 5) / 25) - 5
% is a correction to the Mentonic cycle of about
% 8 days every 2500 years. Note that this will
% overflow 16 bits in the year 409600. Beware.
%
% The algorithm is accurate for the Gregorian calender only.
%
% The magic numbers used in the phase calculation are as follows:
% 29.5 The moon's period in days.
% 177 29.5 scaled by 6
% 22 (29.5 / 8) scaled by 6 (this gets the phase)
% 11 ((29.5 / 8) / 2) scaled by 6
%
% Theoretically, this should yield a number in the range 0 .. 7. However,
% two days per year, things don't work out too well.
%
% Epact is calculated by the algorithm given in Knuth vol. 1 (calculation
% of Easter). See also the article on Calenders in the Encyclopaedia
% Britannica and Knuth's algorithm in CACM April 1962, page 209.
%
\newcount\cent % Century number (1979 == 20)
\newcount\epact % Age of the moon on Jan. 1
\newcount\diy % Day in the year
\newcount\golden % Moon's golden number
\newcount\x % Temp
\newcount\m % Temp for modulus
\diy=\day \advance\diy by \ifcase\month % Jan 1 == 0
-1\or -1\or 30\or 58\or 89\or 119\or 150\or % Jan .. Jun
180\or 211\or 241\or 272\or 303\or 333\fi % Jul .. Dec
% if ((month > 2) && ((year % 4 == 0) &&
% ((year % 400 == 0) || (year % 100 != 0))))
% diy++; /* Leapyear fixup */
\ifnum \month>2
\x=\year \m=\x \divide\m by 4 \multiply\m by 4 \advance\x by -\m
\ifnum \x=0 % month > 2 and maybe leapyear
\x=\year \m=\x \divide\m by 400 \multiply\m by 400 \advance\x by -\m
\ifnum \x=0 % 2000 is a leap year
\advance\diy by 1 % so it's one day later
\else % not 2000, check other '00's
\x=\year \m=\x \divide\m by 100 \multiply\m by 100 \advance\x by -\m
\ifnum \x>0 % not some other '00' year
\advance\diy by 1 % it's still one day later
\fi % not odd century
\fi % not 2000-type century
\fi % not leapish year
\fi % not march or later
% cent = (year / 100) + 1; /* Century number */
% golden = (year % 19) + 1; /* Golden number */
\cent=\year \divide\cent by 100 \advance\cent by 1
\golden=\year
\m=\year \divide\m by 19 \multiply\m by 19 \advance\golden by -\m
\advance\golden by 1
% epact = ((11 * golden) + 20 /* Golden number */
% + (((8 * cent) + 5) / 25) - 5 /* 400 year cycle */
% - (((3 * cent) / 4) - 12)) % 30;/* Leap year correction */
\epact=11 \multiply\epact by \golden
\advance\epact by 20
\x=8 \multiply\x by \cent \advance\x by 5
\divide\x by 25 \advance\x by -5
\advance\epact by \x
\x=3 \multiply\x by \cent \divide\x by 4 \advance\x by -12
\advance\epact by -\x
\m=\epact \divide\m by 30 \multiply\m by 30 \advance\epact by -\m
% if (epact <= 0)
% epact += 30; /* Age range is 1 .. 30 */
% if ((epact == 25 && golden > 11) || epact == 24)
% epact++;
\ifnum \epact<0
\advance\epact by 30
\fi
\ifnum \epact=25
\ifnum \golden>11
\advance \epact by 1
\fi
\else
\ifnum \epact=24
\advance \epact by 1
\fi
\fi
%
% Calculate the phase, using the magic numbers defined above.
% Note that phase may be equal to 8 (== 0) on two days of the year
% due to the way the algorithm was implemented.
% phase = (((((diy + epact) * 6) + 11) % 177) / 22) & 7;
%
\x=\diy \advance\x by \epact \multiply\x by 6 \advance\x by 11
\m=\x \divide\m by 177 \multiply\m by 177 \advance\x by -\m
\divide\x by 22
\ifcase\x new\or waxing crescent\or in its first quarter\or
waxing gibbous\or full\or waning gibbous\or
in its last quarter\or waning crescent\or new\fi
}