HP 12C Platinum: Finding the Day of Easter
An Easter Algorithm
One can figure
out when Easter is by the following algorithm:
“ c = y / 100
n =
y - 19 * ( y / 19 )
k =
( c - 17 ) / 25
i =
c - c / 4 - ( c - k ) / 3 + 19 * n + 15
i =
i - 30 * ( i / 30 )
i =
i - ( i / 28 ) * ( 1 - ( i / 28 ) * ( 29 / ( i + 1 ) )
* ( ( 21 - n ) / 11 ) )
j =
y + y / 4 + i + 2 - c + c / 4
j =
j - 7 * ( j / 7 )
l =
i - j
m =
3 + ( l + 40 ) / 44
d =
l + 28 - 31 * ( m / 4 )
“ (see the Source below, http://aa.usno.navy.mil/faq/docs/easter.php
)
The only input
is y, the four digit year (1997, 2015, etc).
Each of the slashes “/” in the above text refers to integer division. Hence in this case: a/b refers
to INTG(a ÷ b).
Other things I
noticed while porting this algorithm to the HP 12C Platinum:
The line y - 19 * ( y / 19 ) can be expressed as y MOD 19 and 19 *
fPart(y ÷ 19). This happens in
three other lines (2nd, 5th, and 8th). See how to calculate the MOD function, when
both arguments are positive on the HP 12C here:
http://edspi31415.blogspot.com/2016/07/hp-12c-programming-part-i-modulus-gcd.html
On the HP 12C Platinum, the LSTx
function moved to [ g ] [ + ]. (Code 43,
40)
After the 5th line, the
variable i will between 0 and 29. If i ≤
27, the 6th line can be skipped entirely since iPart(i/28) = 0. Otherwise, iPart(i/28) = 1. This cuts on down the number of steps needed.
I was also to combine some steps in
the beginning by computing c and k while building i at the same time.
Storage arithmetic is allowed on R0
– R4 on both the HP 12C Platinum and the classic HP 12C. By the way, the reason why I mention the HP
12C Platinum is that this program is 133 steps. Only 99 steps are possible on the classic HP
12C.
Store registers:
R0: four digit year
R1:
c, m (result: month)
R2:
n, j, d (result: day)
R3: k, l
R4: i
Instructions: Enter the four digit year. Press [ R/S ]. The month will be displayed (stored in
R1). Press [ R/S ] to get the day
(stored in R2).
HP12C Platinum Program: Easter
|
STEP
|
CODE
|
KEY
|
Notes
|
|
001
|
44, 0
|
STO 0
|
Store year (y)
|
|
002
|
1
|
1
|
|
|
003
|
25
|
%
|
|
|
004
|
43, 25
|
INTG
|
|
|
005
|
44, 1
|
STO 1
|
Store c
|
|
006
|
44, 4
|
STO 4
|
Start i
|
|
007
|
36
|
ENTER
|
To fill the stack
|
|
008
|
36
|
ENTER
|
|
|
009
|
4
|
4
|
|
|
010
|
10
|
÷
|
|
|
011
|
43, 25
|
INTG
|
|
|
012
|
44, 30, 4
|
STO- 4
|
|
|
013
|
33
|
R↓
|
|
|
014
|
36
|
ENTER
|
|
|
015
|
36
|
ENTER
|
|
|
016
|
1
|
1
|
|
|
017
|
7
|
7
|
|
|
018
|
30
|
-
|
|
|
019
|
2
|
2
|
|
|
020
|
5
|
5
|
|
|
021
|
10
|
÷
|
|
|
022
|
43, 25
|
INTG
|
|
|
023
|
44, 3
|
STO 3
|
Store k
|
|
024
|
30
|
-
|
|
|
025
|
3
|
3
|
|
|
026
|
10
|
÷
|
|
|
027
|
43, 25
|
INTG
|
|
|
028
|
44, 30, 4
|
STO- 4
|
|
|
029
|
1
|
1
|
|
|
030
|
5
|
5
|
|
|
031
|
44, 40, 4
|
STO+ 4
|
|
|
032
|
45, 0
|
RCL 0
|
|
|
033
|
1
|
1
|
|
|
034
|
9
|
9
|
|
|
035
|
10
|
÷
|
|
|
036
|
43, 40
|
LSTx
|
LSTx is [ g ] [ + ] on the Platinum
|
|
037
|
34
|
X<>Y
|
|
|
038
|
43, 24
|
FRAC
|
|
|
039
|
20
|
*
|
y MOD 19
|
|
040
|
44, 2
|
STO 2
|
Store n
|
|
041
|
1
|
1
|
|
|
042
|
9
|
9
|
|
|
043
|
20
|
*
|
|
|
044
|
44, 40, 4
|
STO+ 4
|
|
|
045
|
45, 4
|
RCL 4
|
|
|
046
|
3
|
3
|
|
|
047
|
0
|
0
|
|
|
048
|
10
|
÷
|
|
|
049
|
43, 40
|
LSTx
|
|
|
050
|
34
|
X<>Y
|
|
|
051
|
43, 24
|
FRAC
|
|
|
052
|
20
|
*
|
|
|
053
|
44, 4
|
STO 4
|
i MOD 30
|
|
054
|
2
|
2
|
|
|
055
|
7
|
7
|
|
|
056
|
45, 4
|
RCL 4
|
|
|
057
|
43, 44
|
x≤y
|
Is i≤27?
|
|
058
|
43, 33, 080
|
GTO 080
|
If so, go to step 080
|
|
059
|
2
|
2
|
|
|
060
|
9
|
9
|
|
|
061
|
45, 4
|
RCL 4
|
|
|
062
|
1
|
1
|
|
|
063
|
40
|
+
|
|
|
064
|
10
|
÷
|
|
|
065
|
43, 25
|
INTG
|
|
|
066
|
20
|
*
|
|
|
067
|
1
|
1
|
|
|
068
|
34
|
X<>Y
|
|
|
069
|
30
|
-
|
|
|
070
|
2
|
2
|
|
|
071
|
1
|
1
|
|
|
072
|
45, 2
|
RCL 2
|
|
|
073
|
30
|
-
|
|
|
074
|
1
|
1
|
|
|
075
|
1
|
1
|
|
|
076
|
10
|
÷
|
|
|
077
|
43, 25
|
INTG
|
|
|
078
|
20
|
*
|
|
|
079
|
44, 30, 4
|
STO- 4
|
|
|
080
|
45, 0
|
RCL 0
|
|
|
081
|
45, 2
|
STO 2
|
Start j
|
|
082
|
4
|
4
|
|
|
083
|
10
|
÷
|
|
|
084
|
43, 25
|
INTG
|
|
|
085
|
44, 40, 2
|
STO+ 2
|
|
|
086
|
45, 4
|
RCL 4
|
|
|
087
|
2
|
2
|
|
|
088
|
40
|
+
|
|
|
089
|
45, 1
|
RCL 1
|
|
|
090
|
30
|
-
|
|
|
091
|
44, 40, 2
|
STO+ 2
|
|
|
092
|
45, 1
|
RCL 1
|
|
|
093
|
4
|
4
|
|
|
094
|
10
|
÷
|
|
|
095
|
43, 25
|
INTG
|
|
|
096
|
44, 40, 2
|
STO+ 2
|
|
|
097
|
45, 2
|
RCL 2
|
|
|
098
|
7
|
7
|
|
|
099
|
10
|
÷
|
|
|
100
|
43, 40
|
LSTx
|
|
|
101
|
34
|
X<>Y
|
|
|
102
|
43, 24
|
FRAC
|
|
|
103
|
20
|
*
|
|
|
104
|
44, 2
|
STO 2
|
j MOD 7
|
|
105
|
45, 4
|
RCL 4
|
|
|
106
|
34
|
X<>Y
|
|
|
107
|
30
|
-
|
|
|
108
|
44, 3
|
STO 3
|
Store l
|
|
109
|
4
|
4
|
|
|
110
|
0
|
0
|
|
|
111
|
40
|
+
|
|
|
112
|
4
|
4
|
|
|
113
|
4
|
4
|
|
|
114
|
10
|
÷
|
|
|
115
|
43, 25
|
INTG
|
|
|
116
|
3
|
3
|
|
|
117
|
40
|
+
|
|
|
118
|
44, 1
|
STO 1
|
Store month (m)
|
|
119
|
31
|
R/S
|
Displays m
|
|
120
|
4
|
4
|
|
|
121
|
10
|
÷
|
|
|
122
|
43, 25
|
INTG
|
|
|
123
|
3
|
3
|
|
|
124
|
1
|
1
|
|
|
125
|
20
|
*
|
|
|
126
|
16
|
CHS
|
|
|
127
|
2
|
2
|
|
|
128
|
8
|
8
|
|
|
129
|
40
|
+
|
|
|
130
|
45, 3
|
RCL 3
|
|
|
131
|
40
|
+
|
|
|
132
|
44 , 2
|
STO 2
|
Store day (d)
|
|
133
|
43, 33, 000
|
GTO 000
|
Stop, display d
|
Examples and
Test Data:
2016: 3, 27
Keystrokes: 2016 [R/S] [R/S]
1995: 4, 16
2124: 4, 2
1977: 4, 10
2017: 4, 16
1826: 3, 26
These results
have been verified.
Now we can
determine when is Easter at any year.
Happy Easter in advance!
Eddie
Source: The United States Naval Observatory “The Date of Easter” March 11, 2016. http://aa.usno.navy.mil/faq/docs/easter.php Retrieved September 2, 2016
This blog is
property of Edward Shore, 2016.