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Gregorian Calendar for the HP-33S & HP-35S

For the HP-32SII version, go here.

Written by Dave Coffin in March 2006.
(Program E was written on Easter 2006)

Overview

Program C converts a calendar date from the format yyyy.mmdd to a simple day number. Program G does the exact opposite. Months go from 01 to 12, and days from 01 to 31. Years must not be truncated to two digits!!

These operations are useful for any problem that depends on the exact interval between two dates.

Program E calculates the date of Easter Sunday in any given year.

Usage

2006.0310       Today's date (Mar 10, 2006)
XEQ C
732685
1965.0927       Your birthdate (Sep 27, 1965)
XEQ C
717911
-
14774           Your age in days
LASTx
717911		When will you be 20000 days old?
20000
+
737911
XEQ G
2020.063
FIX 4
2020.0630	June 30, 2020
XEQ E		When's Easter Sunday that year?
737832		subtract 46 for Ash Wednesday, for example.
XEQ G
2020.0412	Easter Sunday is April 12, 2020

In my system, Day 0 is March 1, 0 A.D (better known as 1 B.C.), or Julian day 1721120. Thus at 12:00 noon Universal Time on March 10, 2006, the Julian day was 1721120 + 732685 = 2453805.0.

Divide a day number by seven and take the remainder to determine the weekday. Zero is Wednesday.

Listing of Program C

C0001 LBL C
C0002 0.88		; stash this for RCL+ later
C0003 STO Y
C0004 R↓
C0005 ENTER		; copy the whole date
C0006 FP		; discard the year
C0007 0.0301
C0008 x>y?		; move New Year's Day from January 1 to March 1
C0009 RCL+ Y
C0010 x<>y
C0011 R↓
C0012 -	
C0013 STO Y		; save the new date
C0014 FP		; month and day in Xreg
C0015 STO- Y		; keep year only in Y
C0016 100
C0017 ×
C0018 ENTER		; split month and day
C0019 FP
C0020 100
C0021 ×
C0022 x<>y
C0023 IP		; Yreg = day, Xreg = month
C0024 30.6		; convert month to days
C0025 ×
C0026 0.5
C0027 +
C0028 IP
C0029 +
C0030 365.25		; convert year to days
C0031 RCL× Y
C0032 IP
C0033 +
C0034 RCL Y		; centuries are not leap years...
C0035 100
C0036 INT÷
C0037 -
C0038 LASTx		; ...except those divisible by 400
C0039 4
C0040 INT÷
C0041 +
C0042 RTN

HP-33s: checksum = 6543, length = 234
HP-35s: checksum = 9B9B, length = 159

Listing of Program G

G0001 LBL G
G0002 ENTER
G0003 ENTER
G0004 0.9
G0005 +
G0006 36524.25		; how many whole centuries?
G0007 ÷
G0008 IP		; add one missing leap day per century
G0009 +
G0010 LASTx		; except for centuries divisible by 400
G0011 4
G0012 INT÷
G0013 -
G0014 ENTER
G0015 ENTER
G0016 0.9
G0017 +
G0018 365.25		; compute the year
G0019 ÷
G0020 IP
G0021 STO Y
G0022 365.25		; keep the remaining days
G0023 ×
G0024 IP
G0025 -
G0026 0.5		; determine month and day
G0027 +
G0028 30.6
G0029 ÷
G0030 ENTER
G0031 FP
G0032 30.6
G0033 ×
G0034 IP
G0035 100
G0036 ÷
G0037 x<>y
G0038 IP
G0039 +			; Xreg contains mm.dd
G0040 88
G0041 x<> Y		; move New Year's Day from March 1 to January 1
G0042 x<>y
G0043 10
G0044 x≤y?		; "≤" means "less than or equal to"
G0045 RCL+ Y
G0046 +
G0047 6.99
G0048 -
G0049 100		; combine mm.dd value with year
G0050 ÷
G0051 +
G0052 RTN

HP-33s: checksum = 72FE, length = 324
HP-35s: checksum = 94BD, length = 208

Listing of Program E

E0001 LBL E
E0002 IP		; save the integer year
E0003 STO Y
E0004 19		; apply the Meeus/Jones/Butcher algorithm
E0005 RMDR
E0006 19
E0007 ×
E0008 RCL Y
E0009 100
E0010 INT÷
E0011 +
E0012 LASTx
E0013 LASTx
E0014 8
E0015 +
E0016 25
E0017 INT÷
E0018 -
E0019 1
E0020 +
E0021 3
E0022 INT÷
E0023 -
E0024 RCL Y
E0025 400
E0026 INT÷
E0027 -
E0028 15
E0029 +
E0030 30
E0031 RMDR		; days from March 22 to ecclesiastical full moon
E0032 STO Z
E0033 0.0322
E0034 RCL+ Y
E0035 XEQ C		; day number for March 22, year Y
E0036 +			; day number for full moon
E0037 ENTER
E0038 ENTER
E0039 4
E0040 x<>y
E0041 -
E0042 7
E0043 RMDR		; days from full moon to the following Sunday
E0044 x<> Z
E0045 11
E0046 ×
E0047 22
E0048 RCL× Z
E0049 +
E0050 RCL Y
E0051 19
E0052 RMDR
E0053 +
E0054 451		; for April 26 and sometimes April 25,
E0055 INT÷		; go back seven days
E0056 -7
E0057 ×
E0058 RCL+ Z
E0059 +
E0060 RTN		; GTO G instead converts day number to date

HP-33s: checksum = E175, length = 396
HP-33s: checksum = 6084 if the last line is "GTO G"

HP-35s: checksum = 01F0, length = 218
HP-35s: checksum = 9DEA, length = 248 if the last line is "GTO G"