Overview
-3 programs are listed hereafter:
"EASTR1" calculates the date of the Christian Easter Sunday in
the Gregorian calendar.
"EASTR2" calculates the date of the Christian Easter Sunday
in the Julian calendar.
"EASTER" calculates the date of the Christian Easter Sunday
in both calendars.
-Dates are given in YMD format.
-Synthetic registers M N may be replaced by any data registers ( like
R00 R01 )
1°) Gregorian Calendar ( from 1583 )
Data Registers: /
Flags: /
Subroutines: /
| 01 LBL "EASTR1"
02 INT 03 STO M 04 1 05 % 06 INT 07 ENTER^ 08 STO Z 09 8 10 + 11 25 12 / 13 INT 14 - 15 1 16 + 17 3 |
18 /
19 INT 20 - 21 X<>Y 22 4 23 / 24 INT 25 - 26 RCL M 27 19 28 MOD 29 STO N 30 LASTX 31 * 32 + 33 15 34 + |
35 30
36 MOD 37 X<>Y 38 4 39 MOD 40 RCL M 41 E2 42 MOD 43 4 44 / 45 INT 46 + 47 ST+ X 48 X<>Y 49 - 50 RCL M 51 4 |
52 ST+ Z
53 MOD 54 - 55 7 56 MOD 57 + 58 ST+ L 59 LASTX 60 11 61 * 62 RCL N 63 + 64 451 65 / 66 INT 67 7 68 * |
69 -
70 9 71 - 72 69 73 X<>Y 74 X>0? 75 + 76 331 77 + 78 E4 79 / 80 RCL M 81 + 82 CLA 83 END |
( 117 bytes / SIZE 000 )
| STACK | INPUTS | OUTPUTS |
| X | YYYY | YYYY.MNDD |
| L | / | YYYY |
Example: 2005 XEQ "EASTR1"
>>>> 2005.0327 ( March 27th )
2°) Julian Calendar
Data Registers: /
Flags: /
Subroutines: /
| 01 LBL "EASTR2"
02 INT 03 ENTER^ 04 ENTER^ 05 STO M 06 4 07 MOD 08 X<>Y 09 7 |
10 MOD
11 ST+ X 12 + 13 ST+ X 14 X<>Y 15 19 16 MOD 17 LASTX 18 * |
19 15
20 + 21 30 22 MOD 23 ST- Y 24 X<>Y 25 1 26 - 27 7 |
28 MOD
29 + 30 9 31 - 32 69 33 X<>Y 34 X>0? 35 + 36 331 |
37 +
38 E4 39 / 40 0 41 X<> M 42 + 43 END |
( 66 bytes / SIZE 000 )
| STACK | INPUTS | OUTPUTS |
| X | YYYY | YYYY.MNDD |
| L | / | YYYY |
Example: 1243 XEQ "EASTR2"
>>>> 1243.0412 ( April 12th
)
-This program works for positive years only.
-However, the rules for finding the date of Easter Sunday were fixed
in the 4th century, and only gradually adopted,
therefore, applying this program to years of the first centuries
may be hazardous...
3°) Gregorian & Julian Calendars
-These 2 programs may be reduced to a single routine.
-A flag is used to select the calendar.
Data Registers: /
Flag: F01
CF 01 = Gregorian calendar
SF 01 = Julian calendar
Subroutines: /
| 01 LBL "EASTER"
02 INT 03 STO M 04 1 05 % 06 INT 07 ENTER^ 08 STO Z 09 8 10 + 11 25 12 / 13 INT 14 - 15 1 16 + 17 3 18 / 19 INT 20 - |
21 X<>Y
22 4 23 / 24 INT 25 - 26 RCL M 27 19 28 MOD 29 STO N 30 LASTX 31 * 32 FC? 01 33 + 34 15 35 + 36 30 37 MOD 38 X<>Y 39 4 40 MOD |
41 RCL M
42 E2 43 MOD 44 4 45 / 46 INT 47 + 48 FS? 01 49 SIGN 50 ST+ X 51 X<>Y 52 - 53 RCL M 54 4 55 ST+ Z 56 MOD 57 FS? 01 58 ST+ X 59 FS? 01 60 CHS |
61 -
62 RCL M 63 7 64 MOD 65 4 66 * 67 FC? 01 68 CLX 69 + 70 7 71 MOD 72 + 73 ST+ L 74 LASTX 75 11 76 * 77 RCL N 78 + 79 451 80 / |
81 INT
82 7 83 * 84 FS? 01 85 CLX 86 - 87 9 88 - 89 69 90 X<>Y 91 X>0? 92 + 93 331 94 + 95 E4 96 / 97 RCL M 98 + 99 CLA 100 END |
( 142 bytes / SIZE 000 )
| STACK | INPUTS | OUTPUTS |
| X | YYYY | YYYY.MNDD |
| L | / | YYYY |
( execution time = 4 seconds )
Examples:
CF 01 2005
XEQ "EASTER" >>>> 2005.0327
SF 01 1243
R/S
>>>> 1243.0412
References:
[1] Jean Meeus , "Astronomical Algorithms" - Willmann-Bell -
ISBN 0-943396-61-1
[2] Jean Meeus , "Mathematical Astronomy Morsels" - Willmann-Bell
- ISBN 0-943396-51-4