Easter Calculation

Ian Cairns replied

10 May 2000, 08:26 AM

Code:

'######################################################################################
' Difference between Date/Time combinations using Date$ and Time$ style data strings
'
' Thanks to Egbert for the Julian Date routines.
' I changed the routine declarations slightly to use LONGs rather than INTEGERs
'######################################################################################
#COMPILE EXE
#INCLUDE "WIN32API.INC"

' One TYPE declaration required
TYPE ElapsedTimeStruc
  hours   AS LONG
  minutes AS LONG
  seconds AS LONG
END TYPE
'######################################################################################
FUNCTION DateToJulian(inDate AS STRING) AS LONG
' Returns Julian Date (Long Integer) from "String" Date formatted as: MM/DD/YYYY.
  LOCAL year         AS LONG, _
        month        AS LONG, _
        day          AS LONG, _
        Elapsed      AS LONG, _
        InvalidLeaps AS LONG, _
        ValidLeaps   AS LONG, _
        dMonths      AS LONG

  month = VAL(LEFT$(inDate,2))
  day   = VAL(MID$(inDate,4,2))
  year  = VAL(MID$(inDate,7,4))

  IF month < 3 THEN                      ' January or February?
    month = month + 12                   ' 13th or 14th month ....
    DECR year                            ' .... of prev. year
  END IF

  Elapsed = INT((year + 4712) * 365.25)  ' days in years elapsed
  InvalidLeaps = year \ 100              ' substract century leapdays
  ValidLeaps = year \ 400                ' re-add valid ones
  dMonths = INT(30.6 * (month - 1) + .2) ' days of months elapsed + adjustment
  FUNCTION = Elapsed - InvalidLeaps + ValidLeaps + dMonths + day

END FUNCTION
'######################################################################################
FUNCTION JulToDate(BYVAL Jul AS LONG) AS STRING
' Returns "String" Date formatted as: MM/DD/YYYY from Julian Date (Long Integer)

  LOCAL help      AS LONG, _
        Year  AS LONG,_
        Month AS LONG,_
        Day   AS LONG,_
        oText AS STRING * 10

  Jul = Jul + 68569
  help = 4 * Jul \ 146097
  Jul = Jul - ((146097 * help + 3) \ 4)
  Year = 4000 * (Jul + 1) \ 1461001
  Jul = Jul - (1461 * Year \ 4) + 31
  Month = 80 * Jul \ 2447
  Day = Jul - (2447 * Month \ 80)
  Month = Month + 2 - (12 * (Month \ 11))
  Year = 100 * (help - 49) + Year + (Month \ 11)

  oText = RIGHT$(STR$(Month),2) + "/" _
          +RIGHT$(STR$(Day),2) + "/" _
          +RIGHT$(STR$(Year),4) + "/"
  REPLACE " " WITH "0" IN oText
  FUNCTION = oText
END FUNCTION
'######################################################################################
FUNCTION SecondsSinceMidnight(inTime AS STRING) AS LONG
' accepts time "hh:mm:ss" and converts it to elapsed seconds since previous midnight
  LOCAL inHours   AS LONG,_
        inMinutes AS LONG,_
        inSeconds AS LONG
  inHours   = VAL(LEFT$(inTime,2))
  inMinutes = VAL(MID$(inTime,4,2))
  inSeconds = VAL(MID$(inTime,7,2))
  FUNCTION = inHours * 3600 + inMinutes * 60 + inSeconds

END FUNCTION
'######################################################################################
SUB TimeDifference(inDate1 AS STRING, inTime1 AS STRING, _
                     inDate2 AS STRING, inTime2 AS STRING, _
                     tStruc AS elapsedTimeStruc)
  ' accepts 2 dates/times and calculates the absolute time elapsed.

  LOCAL Julian1 AS LONG,_
        Julian2 AS LONG,_
        Seconds1 AS LONG,_
        Seconds2 AS LONG

  Julian1 = DateToJulian(inDate1)
  Julian2 = DateToJulian(inDate2)
  Seconds1 = SecondsSinceMidnight(inTime1)
  Seconds2 = SecondsSinceMidnight(inTime2)

  IF Julian1 > Julian2 OR (julian1 = Julian2 AND Seconds1 > Seconds2) THEN
    SWAP Julian1, Julian2
    SWAP Seconds1, Seconds2
  END IF
  IF Julian1 = Julian2 THEN
    tStruc.seconds = Seconds2 - Seconds1
  ELSE
    tStruc.seconds =  (60*60*24) - Seconds1 + Seconds2
    tStruc.hours = (Julian2 - Julian1-1) * 24
  END IF
  WHILE tStruc.seconds >= 60
    INCR tStruc.minutes
    tStruc.seconds = tStruc.seconds - 60
  LOOP
  WHILE tStruc.minutes >= 60
    INCR tStruc.hours
    tStruc.minutes = tStruc.minutes - 60
  LOOP

END SUB
'######################################################################################
FUNCTION PBMAIN() AS LONG
 LOCAL  inDate1 AS STRING, _
        inTime1 AS STRING, _
        inDate2 AS STRING, _
        inTime2 AS STRING, _
        elapsedTime AS elapsedTimeStruc


  inDate1 = "05/09/2000"
  inTime1 = "18:11:35"
  inDate2 = "05/11/2000"
  inTime2 = "03:15:45"
  CALL TimeDifference(inDate1, inTime1, inDate2, inTime2, elapsedTime)

  CALL MessageBox (BYVAL %NULL,"From: " + inDate1 + " " + inTime1 + CHR$(13) + _
                        "  To: " + inDate2 + " " + inTime2 + CHR$(13) + _
                        "elapsed time: " + CHR$(13) + _
                        "Hrs: " + STR$(elapsedTime.hours) + CHR$(13) + _
                        "Min: " + STR$(elapsedTime.minutes) + CHR$(13) + _
                        "Sec: " + STR$(elapsedTime.seconds), _
                        "Time Difference", %MB_ICONEXCLAMATION OR %MB_OK)
  
END FUNCTION

------------------
[email protected]

Easter date or Easter Sunday is the Sunday, following the first full moon after the Vernal Equinox (= the 21st of March). This full moon is also referred to as: PASCHAL FULL MOON.

This Easter-routine uses Julian Day Number calculations, which has 3 advantages:
1. Easter-related holidays can easily be found too, e.g. Good Friday = Easter minus 2.
2. Once we have found the Julian Day Number for Paschal Full Moon, it's easy to find the next Sunday. Don't use difficult 'algebraic' formulas here, but simply add 1 (day) until the result is a Sunday.
3. Initially PFM is returned as the number of days elapsed since March 1. If this number is greater than 31, PFM is in April. However, using JDN you don't need to care about this. Simply pretend that March has more than 31 days. Example: 'March 32', written as Julian(year, 3, 32), equals April 1 or Julian(year, 4, 1)

Code:

' ===============================================================================
'      Source code: PowerBASIC for Windows
'         Compiler: PBDLL60
'           Author: [email protected]
' Copyright status: Public Domain
'          Purpose: Calculate Easter for a given year
' ===============================================================================
 
#COMPILE EXE
#INCLUDE "WIN32API.INC"
 
FUNCTION Julian(BYVAL year AS INTEGER, _
                BYVAL month AS INTEGER, _
                BYVAL day AS INTEGER) AS LONG
  LOCAL Elapsed AS LONG, InvalidLeaps AS INTEGER, ValidLeaps AS INTEGER, dMonths AS INTEGER
 
  IF month < 3 THEN                      ' January or February?
    month = month + 12                   ' 13th or 14th month ....
    DECR year                            ' .... of prev. year
  END IF
 
  Elapsed = INT((year + 4712) * 365.25)  ' days in years elapsed
  InvalidLeaps = year \ 100              ' substract century leapdays
  ValidLeaps = year \ 400                ' re-add valid ones
  dMonths = INT(30.6 * (month - 1) + .2) ' days of months elapsed + adjustment
  FUNCTION = Elapsed - InvalidLeaps + _
             ValidLeaps + dMonths + day
END FUNCTION
 
FUNCTION JulToDate(BYVAL Jul AS LONG) AS STRING
  LOCAL st AS SYSTEMTIME, szText AS ASCIIZ * 255
 
  Jul = Jul + 68569
  help& = 4 * Jul \ 146097
  Jul = Jul - ((146097 * help& + 3) \ 4)
  TempYear& = 4000 * (Jul + 1) \ 1461001
  Jul = Jul - (1461 * TempYear& \ 4) + 31
  TempMonth& = 80 * Jul \ 2447
  st.wDay = Jul - (2447 * TempMonth& \ 80)
  st.wMonth = TempMonth& + 2 - (12 * (TempMonth& \ 11))
  st.wYear = 100 * (help& - 49) + TempYear& + (TempMonth& \ 11)
  GetDateFormat %LOCALE_USER_DEFAULT, %DATE_LONGDATE, st, BYVAL %NULL, szText, SIZEOF(szText)
  FUNCTION = szText
END FUNCTION
 
FUNCTION PaschalFullMoon(year AS INTEGER) AS LONG
  LOCAL Century AS INTEGER, temp AS INTEGER, PFM AS INTEGER
 
  Century = year \ 100
  temp    = (Century - 15) \ 2
  temp    = temp + 202
  temp    = temp - 11 * (year MOD 19)
  SELECT CASE Century
    CASE 21, 24, 25, 27 TO 32, 34, 35
      DECR temp
    CASE 33, 36, 37, >38
      temp = temp - 2
  END SELECT
  temp = temp MOD 30
  PFM = temp + 21
  IF (temp = 29) OR _
     (temp = 28 AND year MOD 19 > 10) THEN DECR PFM
  FUNCTION = Julian(year, 3, PFM)
END FUNCTION                  
  
FUNCTION EasterSunday(year AS INTEGER) AS LONG
  LOCAL start AS LONG, Sun AS BYTE
 
  Sun = 6
  start = PaschalFullMoon(year)
  DO
    INCR start
  LOOP UNTIL start MOD 7 = Sun
  FUNCTION = start
END FUNCTION
 
FUNCTION GoodFriday(year AS INTEGER) AS LONG
  FUNCTION = EasterSunday(year) - 2
END FUNCTION
 
FUNCTION EasterMonday(year AS INTEGER) AS LONG
  FUNCTION = EasterSunday(year) + 1
END FUNCTION
 
FUNCTION AscensionDay(year AS INTEGER) AS LONG
  FUNCTION = EasterSunday(year) + 39
END FUNCTION
 
FUNCTION WhitSunday(year AS INTEGER) AS LONG
  FUNCTION = EasterSunday(year) + 49
END FUNCTION
 
FUNCTION WhitMonday(year AS INTEGER) AS LONG
  FUNCTION = EasterSunday(year) + 50
END FUNCTION
 
FUNCTION PBMAIN() AS LONG
  LOCAL WhichYear AS INTEGER, caption AS STRING
  WhichYear = 2000
  caption = "Easter " + TRIM$(STR$(WhichYear)) + " by Egbert Zijlema"
  MSGBOX "Paschal Full Moon in " + TRIM$(STR$(WhichYear)) + " is " + _
         JulToDate(PaschalFullMoon(WhichYear)) + CHR$(46, 13) + _
         "The first Sunday after this date - " + _
         JulToDate(EasterSunday(WhichYear)) + " - is Easter" + CHR$(46, 13) + _
         "Other Easter-related holidays are:" + CHR$(13, 9) + _
         "Good Friday: " + JulToDate(GoodFriday(WhichYear)) + CHR$(46, 13, 9) + _
         "Easter Monday: " + JulToDate(EasterMonday(WhichYear)) + CHR$(46, 13, 9) + _
         "Ascension Day: " + JulToDate(AscensionDay(WhichYear)) + CHR$(46, 13, 9) + _
         "Whit Sunday: " + JulToDate(WhitSunday(WhichYear)) + CHR$(46, 13, 9) + _
         "Whit Monday: " + JulToDate(WhitMonday(WhichYear)) + ".", 64, caption
END FUNCTION

[This message has been edited by Egbert Zijlema (edited April 22, 2000).]

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