The Museum of HP Calculators

Date of Easter for the HP-41

This program is supplied without representation or warranty of any kind. Jean-Marc Baillard and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

Overview

-3 programs are listed hereafter:

1°) "EASTER1" calculates the date of the Christian Easter Sunday in the Gregorian calendar.
2°) "EASTER2" ----------------------------------------------------- Julian calendar.
3°) "EASTER" ----------------------------------------------------- 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 "EASTER1"
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

( 118 bytes / SIZE 000 )

      STACK        INPUTS      OUTPUTS

           X         YYYY YYYY.MNDD

           L             /        YYYY

Example: 2005 XEQ "EASTER1" >>>> 2005.0327 ( March 27th )

2°) Julian Calendar

Data Registers: /
Flags: /
Subroutines: /

01 LBL "EASTER2"
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

( 67 bytes / SIZE 000 )

      STACK        INPUTS      OUTPUTS

           X         YYYY YYYY.MNDD

           L             /        YYYY

Example: 1243 XEQ "EASTER2" >>>> 1243.0412 ( April 12th )

Notes: -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 distinguish between the 2 calendars.

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: Jean Meeus , "Astronomical Algorithms" - Willmann-Bell - ISBN 0-943396-35-2
Jean Meeus , "Mathematical Astronomy Morsels" - Willmann-Bell - ISBN 0-943396-51-4

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