Re: Calendar resources

["Charles P. Schaum" <verbo.solo@sbcglobal.net>]

Here's the main bit of code; the two documents from which I derived it
are over the 40k limit. One is the calendar FAQ text version. The other
is a file easter_date.txt that is a thread from:

Newsgroups: soc.religion.christian
From: mls@sfsup.att.com (Mike Siemon)
Subject: Easter algorithms I
Organization: AT&T Bell Laboratories
Approved: christian@aramis.rutgers.edu

Does anyone want such files?

Anyway, the implemented formulas are below. The header files are just
for keeping track of Palm-specific variables for different modules.

/*****************************************************************************
 *
 * Created with Falch.net DeveloperStudio
 * http://www.falch.net/
 * 
 * Created : 4/11/01 12:18:42 AM
 * Creator : (Unknown)
 *

****************************************************************************/
#include <Pilot.h>
#include "Easter.h"
#include "Easter_res.h"   

extern Boolean England;
extern UInt16 YearAD;
Char Orthodox_Julian[20], Orthodox_Gregorian[20], Western[20];

typedef enum {Julian,Gregorian} calendar;

/*	The "Golden Number" is the order of the year in the 19-year lunar
cycle.
 *	It is the same in Julian or Gregorian calendars, and is listed in the
 *	output of this program under the heading GN.
 */

int	GoldenNumber(int year)
{
	return ((year % 19) + 1);
}

/*	All dates in this program are referred to March 1st; so 32 means
 *	April 1 and 0 means February 28th or 29th.  Leap years are needed
 *	for printing February dates (and for dominical letters).
 */

int	Leap(int year, calendar style)
{
	if (year % 4)
		return 0;
	else switch(style) {
		case Julian:	return 1;
		case Gregorian: return (year % 100 || year % 400 == 0);
	}
}

#define	century	(year/100)

/*	Gregorian solar correction -- this is the number of days difference
 *	between Julian and Gregorian civil dates, in effect the number of
 *	excess leap years in the Julian calendar since the time of Nicea.
 *	This correction derives from the Gregorian introduction of non-leap
 *	century years, giving mean tropical year = 365.2425 days.
 */

int	Solar(int year)
{
	return (century - century/4 - 2);
}

/*	Gregorian lunar correction -- this is only used for the computation
of
 *	the paschal new moon (via epact), but might as well be pulled out on
 *	its own.  I give the pedantically correct version.
 *	This correction derives from the mean lunar month being 29.53059 days
 *	instead of the 6939.75/235 assumed in the Julian calendar.  It is one
 *	days in (roughly) 312.5 years, or 8 days in 2500 years.
 */

int	Lunar(int year)
{
	return ((century - 15 - (century-17)/25)/3);
}

/*	Epact is the "age" of the moon on March 1st (same as January 1st);
 *	It (may have) derived from Greek methods of calculating the extra
 *	("epagomenal") months intercalated into the regular 12 at 7 points
 *	of the 19-year Metonic cycle.  However, it is not used in Julian
 *	easter calculations and is provided here only for Gregorian NewMoon.
 */

int	Epact(int year)
{
	int	epact;

	epact = (11*GoldenNumber(year) - Solar(year) + Lunar(year)) % 30;
	if (epact < 0)
		epact += 30;
	return epact;
}

/*	Here's the hard one.  Keep in mind that there are several artificial
 *	conventions -- the equinox is ALWAYS March 21; new moon is ALWAYS the
 *	date on which a fictitious "average" moon is one day old, and the
full
 *	moon is 13 days later, on the 14th of the month.  In the Julian
version
 *	(and MOSTLY in the Gregorian) the pre-paschal month has 30 days.  All
 *	of this works out keeping fairly close to astronomical reality in the
 *	Gregorian case, but it is not necessarily exact.
 */

int	NewMoon(int year, calendar style)
{
	int	new_moon, epact;

	switch (style) {
		case Julian:
			new_moon = (4 - 11*GoldenNumber(year)) % 30;
			while (new_moon < 8)
				new_moon += 30;
			return new_moon;
		case Gregorian:
			epact = Epact(year);
			new_moon = 31-epact;
			if (new_moon < 8) {
				new_moon += 30;
				if (epact == 24 || epact == 25 && year%19 > 10)
					new_moon--;
			}
			return new_moon;
	}
}

int	WeekDay(int date, int year, calendar style)
{
	int	d;

	d = date + year + year/4;
	if (style == Gregorian)
		d -= Solar(year);
	return  (d % 7);
}

/*	Given the Paschal full moon, we just step to the next Sunday ...
 */

int	Easter(int year, calendar style)
{
	int	paschal_moon;

	paschal_moon = NewMoon(year, style) + 13;
	return (paschal_moon + 7 - WeekDay(paschal_moon, year, style));
}


/* The rest of the code turns numbers into human-readable output */

static Boolean frmDates_fldOrthodoxJulian_OnSelect(EventPtr event)
{
	// Insert code for fldOrthodoxJulian
	FormPtr form;
	FieldPtr field;

	form = FrmGetActiveForm();
	field =
FrmGetObjectPtr(form,FrmGetObjectIndex(form,fldOrthodoxJulian));
	FldCopy(field);	
	return true;
}

static Boolean frmDates_fldOrthodoxGregorian_OnSelect(EventPtr event)
{
	// Insert code for fldOrthodoxGregorian
	FormPtr form;
	FieldPtr field;

	form = FrmGetActiveForm();
	field =
FrmGetObjectPtr(form,FrmGetObjectIndex(form,fldOrthodoxGregorian));
	FldCopy(field);	
	return true;
}

static Boolean frmDates_fldWesternGregorian_OnSelect(EventPtr event)
{
	// Insert code for fldWesternGregorian
	FormPtr form;
	FieldPtr field;

	form = FrmGetActiveForm();
	field =
FrmGetObjectPtr(form,FrmGetObjectIndex(form,fldWesternGregorian));
	FldCopy(field);	
	return true;
}

static Boolean frmDates_cmdNewYear_OnSelect(EventPtr event)
{
	// Insert code for cmdNewYear
	FrmGotoForm(frmMain);
	return true;
}

Boolean frmDates_HandleEvent(EventPtr event)
{
	FormPtr form;
	FieldPtr J1, J2, G;
	Boolean handled = false;
	int year, easterJ1, easterJ2, easterG;

	switch (event->eType)
	{
		case ctlSelectEvent:
			switch (event->data.ctlSelect.controlID)
			{
				// fldOrthodoxJulian receives an event
				case fldOrthodoxJulian:
					handled = frmDates_fldOrthodoxJulian_OnSelect(event);
					break;
				// fldOrthodoxGregorian receives an event
				case fldOrthodoxGregorian:
					handled = frmDates_fldOrthodoxGregorian_OnSelect(event);
					break;
				// fldWesternGregorian receives an event
				case fldWesternGregorian:
					handled = frmDates_fldWesternGregorian_OnSelect(event);
					break;
				// cmdNewYear receives an event
				case cmdNewYear:
					handled = frmDates_cmdNewYear_OnSelect(event);
					break;
			}
			break;
		case frmOpenEvent:
			form = FrmGetActiveForm();
			J1 = FrmGetObjectPtr(form,FrmGetObjectIndex(form,fldOrthodoxJulian));
			J2 =
FrmGetObjectPtr(form,FrmGetObjectIndex(form,fldOrthodoxGregorian));
			G  =
FrmGetObjectPtr(form,FrmGetObjectIndex(form,fldWesternGregorian));
			
			// Calculate the necessary dates
			year = (int) YearAD;
			easterJ1 = Easter(year, Julian);
			easterJ2 = easterJ1 + Solar(year);
			easterG  = Easter(year, Gregorian);

			if (easterJ1 > 31)
				StrPrintF(Orthodox_Julian, "%2d April AD %d", easterJ1-31, year);
			else
				StrPrintF(Orthodox_Julian, "%2d March AD %d", easterJ1, year);

			if (easterJ2 > 92)
				StrPrintF(Orthodox_Gregorian, "%2d June AD %d", easterJ2-92, year);
			else if (easterJ2 > 61)
				StrPrintF(Orthodox_Gregorian, "%2d May AD %d", easterJ2-61, year);
			else if (easterJ2 > 31)
				StrPrintF(Orthodox_Gregorian, "%2d April AD %d", easterJ2-31, year);
			else
				StrPrintF(Orthodox_Gregorian, "%2d March AD %d", easterJ2, year);

			if (easterG > 31)
				StrPrintF(Western, "%2d April AD %d", easterG-31, year);
			else
				StrPrintF(Western, "%2d March AD %d", easterG, year);

			if (year < 1583)
			{
				FldSetTextPtr(J1,Orthodox_Julian);
				FldSetTextPtr(J2,"");
				FldSetTextPtr(G,"");
			}
			else if (year < 1753 && England)
			{
				FldSetTextPtr(J1,Orthodox_Julian);
				FldSetTextPtr(J2,Orthodox_Gregorian);
				FldSetTextPtr(G,"");
			}
			else
			{
				FldSetTextPtr(J1,Orthodox_Julian);
				FldSetTextPtr(J2,Orthodox_Gregorian);
				FldSetTextPtr(G,Western);
			}

			// Repaint form on open
			FrmDrawForm(form);
			handled = true;
			break;
	}

	return handled;
}

On Sun, 2008-06-22 at 19:38 +0200, Hans Hagen wrote:
> Charles P. Schaum wrote:
> > Some calendar links, FYI:
> > 
> > http://astro.nmsu.edu/~lhuber/leaphist.html
> > http://www.smart.net/~mmontes/ec-cal.html
> > http://www.tondering.dk/claus/calendar.html
> > http://tycho.usno.navy.mil/vphase.html
> > 
> > I would be happy to make available the C code for an Easter date
> > calculator that I implemented on the Palm III. I used the complex
> > algorithm that figures the "age" of the moon at New Year's. It
> > originally came from Bell Labs, I think.
> 
> well, we can make a nice l-calendar.lua module together
> 
> just provide me the calculations (i can implement to lua code but i have 
> no time to figure out all the logic)
> 
> 
> Hans
> 
> -----------------------------------------------------------------
>                                            Hans Hagen | PRAGMA ADE
>                Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
>       tel: 038 477 53 69 | fax: 038 477 53 74 | www.pragma-ade.com
>                                               | www.pragma-pod.nl
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