Cyclical Calendars for the HP-41
Overview
0°) Useful Formulae
1°) Solar Calendars
2°) Luni-Solar Calendars
a) Program#1
b) 2 M-Code Routines
c) Program#2 ( with M-Code Routines
)
d) Program#3 ( without M-Code Routines
)
e) Program#4
f) Program#5
g) Program#6
3°) Solar & Lunar "Calendar"
-Except in §2e) & 2f) - these programs use some of the formulae
given in references [1] &[2] in the chapter "Generic Cyclical Calendars"
with dY = dM = 0
-Paragraph 1 deals with single cycle calendars whereas paragraph 2 deals
with double cycle calendars
-All these calendars are arithmetic calendars.
-They are similar to the old Hindu calendars, but the formulas are simpler
and there is no lost days:
-In the Solar calendar, months have 30 or 31 days
-In the Luni-Solar calendars, months have 29 or 30 days and years have
12 or 13 months.
-Moreover, we use the tropical year ( the Hindu calendars are based
on the sidereal year )
0°) Useful Formulae
-The following formulas are employed in these programs ( they are also given in "Hindu Calendars for the HP-41" ):
(x.y) mod b = [ x ( y
mod b ) ] mod b ( usefull when
x.y > 10^10 , provided x.b < 10^10 )
(x/y) mod (a/b) = [ (bx) mod (ay) ] / (by)
floor (x/y) = ( x - x mod y ) / y
ceil (x/y) = [ x + (-x) mod y ] / y
[ floor ( 12 x/y ) ] mod 12 = [ 12 r - ( 12 r ) mod
y ] / y with r = x mod y
1°) Solar Calendars
-This routine employs a mean tropical year = 292559 / 801 days ~
365.2421973 days
Formulae: Given a date
YYYY.MNDD in the Gregorian calendar, we first compute the number
of days N since 2000/01/01:
• Let s = N + 1863079 , the date yyyy.mndd in the Solar Calendar is obtained as follows:
y = FLOOR ( 801 s / 292559 )
m = 1 + [ FLOOR ( 6912 s / 292559 ) ] MOD 12
d = 1 + FLOOR [ s mod ( 292559 / 6912 )
]
• Given a date yyyy.mmdd in the Solar calendar,
N = Number of days since 2000/01/01 = CEIL [
-1863080 + y 292559 / 801 + (m-1) 292559 / 6912 + d ]
Data Registers: R00-R01-R02: temp
Flags: /
Subroutines: "J2" & "D2" (
cf "Julian and Gregorian Calendars for the HP-41" )
| 01 LBL "GR-SC" 02 XEQ "J2" 03 1863079 04 + 05 801 06 * 07 STO Y 08 292559 09 STO 00 10 MOD 11 STO 01 12 - 13 RCL 00 14 / 15 X<> 01 16 12 |
17 * 18 STO Y 19 RCL 00 20 MOD 21 STO 02 22 - 23 RCL 00 24 / 25 X<> 02 26 9612 27 / 28 INT 29 1 30 ST+ 02 31 ST+ Y 32 % |
33 RCL 02 34 + 35 1 36 % 37 RCL 01 38 + 39 RTN 40 LBL "SC-GR" 41 INT 42 STO 01 43 LASTX 44 FRC 45 E2 46 STO 00 47 * 48 INT |
49 STO 02 50 LASTX 51 FRC 52 ST* 00 53 RCL 01 54 2328 55 * 56 RCL 02 57 292559 58 ST* Y 59 - 60 + 61 ENTER^ 62 CHS 63 9612 64 STO 02 |
65 MOD 66 + 67 RCL 02 68 / 69 RCL 01 70 365 71 * 72 + 73 RCL 00 74 + 75 1863080 76 - 77 XEQ "D2" 78 END |
( 147 bytes / SIZE 003 )
| STACK | INPUT1 | OUTPUT1 | INPUT2 | OUTPUT2 |
| X | YYYY.MNDDGr | yyyy.mnddSC | yyyy.mnddSC | YYYY.MNDDGr |
Examples:
-3101.0123 XEQ "GR-SC" >>>>
0.0101 XEQ "SC-GR" ( or simply
R/S ) >>>> -3101.0123
1979.0716 XEQ "GR-SC" >>>>
5080.0623 XEQ "SC-GR" ( or simply R/S )
>>>> 1979.0716
2013.0210 XEQ "GR-SC" >>>>
5114.0120 XEQ "SC-GR" ( or simply R/S )
>>>> 2013.0210
Notes:
-The years yyyy must be non-negative.
-If you want to use another origin, change lines 03 and 75.
2°) Luni-Solar Calendars
a) Program#1
-This first program employs the same value for the mean tropical year:
292559 / 801 days ~ 365.2421973 days
-And for the mean Lunar month: 23654 / 801 days ~ 29.53058677
days
-A Full Moon occurs - theoretically - on the last day of each month.
-Of course, this is just an approximation since the duration of the lunations
is not constant.
Formulae: Given a date
YYYY.MNDD in the Gregorian calendar, we calculate the number
of days N since 2000/01/01:
• Let s = N + 1863079 , the date yyyy.mndd in the Luni-Solar Calendar is obtained as follows:
With m' = FLOOR ( 801 s / 23654 ) + 1
y = CEIL ( 23654 m' / 292559 ) - 1
m = m' - [ FLOOR ( 292559 y / 23654 ) ]
d = s - CEIL [ ( m' - 1 ) ( 23654 / 801
) ] + 1
• Given a date yyyy.mmdd in the Luni-Solar calendar,
N = Number of days since 2000/01/01 = CEIL
[ -1863080 + { FLOOR ( y 292559 / 23654 + (m-1) } 23654 / 801 + d ]
Data Registers: R00 to R03: temp
Flags: /
Subroutines: "J2" & "D2" (
cf "Julian and Gregorian Calendars for the HP-41" )
| 01 LBL "GR-LS" 02 XEQ "J2" 03 1863079 04 + 05 STO Y 06 801 07 STO 01 08 * 09 RCL X 10 23654 11 STO 00 12 STO 02 13 MOD 14 - 15 ST+ 00 16 ENTER 17 CHS 18 RCL 01 19 MOD |
20 + 21 RCL 01 22 / 23 - 24 1 25 ST+ Y 26 % 27 RCL 00 28 ENTER 29 CHS 30 292559 31 STO 03 32 MOD 33 + 34 RCL 03 35 - 36 ENTER 37 STO 01 38 RCL 02 |
39 MOD 40 - 41 RCL 00 42 - 43 RCL 02 44 / 45 - 46 1 47 % 48 RCL 01 49 SIGN 50 * 51 RCL 01 52 RCL 03 53 / 54 + 55 RTN 56 LBL "LS-GR" 57 STO 00 |
58 INT 59 292559 60 * 61 STO Y 62 23654 63 STO 01 64 MOD 65 - 66 RCL 00 67 ABS 68 FRC 69 E2 70 * 71 STO 00 72 INT 73 RCL 01 74 ST* Y 75 - |
76 + 77 ENTER 78 CHS 79 801 80 STO 01 81 MOD 82 + 83 RCL 01 84 / 85 RCL 00 86 FRC 87 E2 88 * 89 + 90 1863080 91 - 92 XEQ "D2" 93 END |
( 159 bytes / SIZE 004 )
| STACK | INPUT1 | OUTPUT1 | INPUT2 | OUTPUT2 |
| X | YYYY.MNDDGr | yyyy.mnddLS | yyyy.mnddLS | YYYY.MNDDGr |
Examples:
-3101.0123 XEQ "GR-LS" >>>>
0.0101 XEQ "LS-GR" ( or simply
R/S ) >>>> -3101.0123
1979.0716 XEQ "GR-LS" >>>>
5080.0722 XEQ "LS-GR" ( or simply R/S )
>>>> 1979.0716
2012.1221 XEQ "GR-LS" >>>>
5113.1308 XEQ "LS-GR" ( or simply R/S )
>>>> 2012.1221
2013.0210 XEQ "GR-LS" >>>>
5114.0129 XEQ "LS-GR" ( or simply R/S )
>>>> 2013.0210
Notes:
-The years yyyy may be negative.
-If you want to use another origin, change lines 03 and 90.
-With different definitions, we can use "integer part" instead of "ceil":
it will save bytes since the HP41 doesn't have a CEIL function.
-Here is an unorthodox version that employs the following formulae:
m' = INT ( s/M ) ; y = INT ( m'/L ) ; d = INT ( s MOD M ) + 1 ; m = INT ( m' MOD L ) + 1
with M = 51649/1749 = 29.53058891... &
L = 12628/1021 = 12.36826641...
| 01 LBL "YMD" 02 XEQ "J2" 03 1863079 04 + 05 1749 06 STO 01 07 * |
08 STO 00 09 51649 10 ST/ 00 11 MOD 12 RCL 01 13 / 14 INT |
15 1 16 ST+ Y 17 % 18 RCL 00 19 INT 20 1021 21 STO 01 |
22 * 23 STO 00 24 12628 25 ST/ 00 26 MOD 27 RCL 01 28 / 29 INT |
30 + 31 1 32 ST+ Y 33 % 34 RCL 00 35 INT 36 + 37 END |
( 72 bytes / SIZE 002 )
| STACK | INPUT | OUTPUT |
| X | YYYY.MNDDGr | yyyy.mnddLS |
Examples:
-3101.0123 XEQ "YMD" >>>>
0.0101
1979.0716
R/S >>>>
5080.0621
2012.1221
R/S >>>>
5113.1208
2013.0210
R/S >>>>
5113.1329
2020.0126
R/S >>>>
5121.0101
2020.0314
R/S >>>>
5121.0220
Notes:
>>> yyyy must be non-negative
-For current dates, these results are often about 1 month before the results
given by the previous version.
-With "YMD", the New Years are often very close to the Chinese calendar
New Years.
-The reverse operation employs the CEIL function:
m' = CEIL ( L.yyyy ) + mn - 1
s = CEIL ( M.m' ) + dd - 1863080
| 01 LBL "YMDR" 02 STO 00 03 INT 04 ST- 00 05 12628 06 * 07 ENTER 08 CHS |
09 1021 10 STO 01 11 MOD 12 + 13 RCL 01 14 / 15 RCL 00 16 E2 |
17 * 18 STO 00 19 INT 20 ST- 00 21 + 22 1 23 - 24 51649 |
25 * 26 ENTER 27 CHS 28 1749 29 STO 01 30 MOD 31 + 32 RCL 01 |
33 / 34 RCL 00 35 E2 36 * 37 + 38 1863080 39 - 40 XEQ "D2" 41 END |
( 77 bytes / SIZE 002 )
| STACK | INPUT | OUTPUT |
| X | yyyy.mnddLS | YYYY.MNDDGr |
Examples:
0.0101
XEQ "YMDR" >>>> -3101.0123
5080.0621
R/S
>>>> 1979.0716
5113.1208
R/S
>>>> 2012.1221
5113.1329
R/S
>>>> 2013.0210
5121.0101
R/S
>>>> 2020.0126
5121.0220
R/S
>>>> 2020.0314
Note:
>>> yyyy must be non-negative
b) 2 M-Code-Routines
-In calendrical calculations, we often have to compute floor(y.z/x)
or ceil(y.z/x) where x , y , z are integers
-We can take advantage of the 13-digit routines to use these formulas even
if y.z > E10 provided y.z/x remains < E10
-FMD & CMD compute these functions.
-There is no check for alpha data, overflow and underflow.
084 "D"
00D "M"
003 "C" Ceil (y.z/x)
108 SETF 8
02B JNC+05
084 "D"
00D "M"
006 "F" Floor (y.z/x)
104 CLRF 8
2A0 SETDEC
078 C=Z
10E A=C ALL
0B8 C=Y
135 C=
060 A*C
0F8 C=X
128 L=C
10C ?FSET 8
013 JNC+02
2BE C=-C
000 NOP
269 C=
060 AB/C
2EE ?C#0 ALL
10B JNC+ 33d
130 LDI S&X
200 200h
306 ?A<C S&X
02F JC+05
01A A=0 M
006 A=0 S&X
02E B=0 ALL
073 JNC+14d
130 LDI S&X
010 010h
306 ?A<C S&X
06B JNC+13d
0A6 A<>C S&X
106 A=C S&X
35C PT=12
3D4 PT=PT-1
266 C=C-1 S&X
3F3 JNC-02
2CA ?B#0 PT <-
02B JNC+05
02A B=0 PT <-
35E ?A#0 MS
009 C=
061 AB-1 if carry
04E C= 0 ALL
025 C=
060 AB+C
2EE ?C#0 ALL
023 JNC+04
10C ?FSET 8
013 JNC+02
2BE C=-C
0E8 X=C
046 C
270 =
038 T
068 Z=C
0A8 Y=C
3E0 RTN
( 64 words )
| STACK | INPUTS | OUTPUTS |
| T | T | T |
| Z | z | T |
| Y | y | T |
| X | x | F(x,y,z) |
| L | L | x |
where F(x,y,z) = Floor (y.z/x) with
FMD
and F(x,y,z) = Ceil
(y.z/x) with CMD
Examples:
• 123456789 ENTER^
12345
ENTER^
654321
XEQ "FMD" >>>> FLOOR ( 123456789*12345 / 654321)
= 2329245
• 123456789 ENTER^
12345
ENTER^
654321
XEQ "CMD" >>>> CEIL ( 123456789*12345 / 654321) =
2329246
Notes:
-These routines also work with negative arguments
-We have used ceil(x) = - floor(-x)
-The results may be wrong if y.z has more than 13 digits and
/ or if x is too large.
c) Program#2 (
With M-Code Routines )
-Focal programs are limited by 10-digit arithmetic, but with the 2 M-Code
routines above FMD & CMD,
we can use better approximations to the mean lunar month and the
mean tropical year
-In the following routine:
1 Lunar month = 334995
/ 11344 days ~ 29.53058886 days
and 1 tropical year / 1 lunar month = 774439 / 62615
~ 12.36826639
which leads to 1 tropical year ~ 365.2421896 days
Data Registers: R00 to R03: temp
Flags: /
Subroutines: "J2" & "D2" (
cf "Julian and Gregorian Calendars for the HP-41" )
| 01 LBL "GR-LS" 02 XEQ "J2" 03 1863079 04 + 05 STO Y 06 11344 07 STO 01 08 334995 09 STO 02 10 FMD 11 STO 00 12 RCL 02 13 RCL 01 14 CMD 15 - |
16 1 17 ST+ 00 18 ST+ Y 19 % 20 RCL 00 21 62615 22 STO 01 23 774439 24 STO 02 25 CMD 26 1 27 - 28 STO 03 29 RCL 02 30 RCL 01 |
31 FMD 32 RCL 00 33 X<>Y 34 - 35 + 36 1 37 % 38 RCL 03 39 SIGN 40 * 41 RCL 03 42 + 43 RTN 44 LBL "LS-GR" 45 INT |
46 STO 01 47 LASTX 48 ABS 49 FRC 50 E2 51 STO 00 52 * 53 INT 54 STO 02 55 LASTX 56 FRC 57 ST* 00 58 RCL 01 59 774439 60 62615 |
61 FMD 62 RCL 02 63 + 64 1 65 - 66 334995 67 11344 68 CMD 69 RCL 00 70 + 71 1863080 72 - 73 XEQ "D2" 74 END |
( 159 bytes / SIZE 004 )
| STACK | INPUT1 | OUTPUT1 | INPUT2 | OUTPUT2 |
| X | YYYY.MNDDGr | yyyy.mnddLS | yyyy.mnddLS | YYYY.MNDDGr |
Examples:
-3101.0123 XEQ "GR-LS" >>>>
0.0101 XEQ "LS-GR" ( or simply
R/S ) >>>> -3101.0123
1979.0716 XEQ "GR-LS" >>>>
5080.0721 XEQ "LS-GR" ( or simply R/S )
>>>> 1979.0716
2012.1221 XEQ "GR-LS" >>>>
5113.1308 XEQ "LS-GR" ( or simply R/S )
>>>> 2012.1221
2013.0210 XEQ "GR-LS" >>>>
5114.0129 XEQ "LS-GR" ( or simply R/S )
>>>> 2013.0210
Notes:
-Here, the years yyyy may also be negative ( otherwise, delete lines 48-40-39-38 ).
-All these programs take the onset of the Kali-Yuga as origin i-e
-3101.0123 ( Gregorian Calendar ) -3101 = 3102 B.C.
-If you want to use another origin, change lines 03 and 71.
-For example, assuming Lord Jesus was born near the New Moon on -1.1225
(???) ( Gregorian ),
replace 1863079 ( line 03 ) by 730492 and replace line
71 by 730493
-With these modifications, you will have a Christian Luni-Solar Calendar and, for instance:
-1.1224 XEQ "GR-LS"
>>>> -1.1329
XEQ "LS-GR" ( or simply R/S ) >>>>
-1.1224
-1.1225 XEQ "GR-LS"
>>>> 0.0101
XEQ "LS-GR" ( or simply R/S ) >>>>
-1.1225
2013.0210 XEQ "GR-LS" >>>>
2013.0229 XEQ "LS-GR" ( or simply R/S )
>>>> 2013.0210
d) Program#3 (
Without M-Code Routines )
-In fact, we can use the same approximations for the mean lunar months
and solar years without using M-Code routines.
-We simply have to re-write some formulas and employ the RND function in
FIX 0 mode.
-The "interesting formulae" given in paragraph 2°) a) are also very
useful.
Formula: Given a date
YYYY.MNDD in the Gregorian calendar, we calculate the number
of days N since 2000/01/01:
• Let s = N + 1863079 , the date yyyy.mndd in the Luni-Solar Calendar is obtained as follows:
With m' = FLOOR ( 11344 s / 334995 ) + 1
d = FLOOR [ s mod ( 334995 / 11344 ) ]
+ 1
m = CEIL [ m' amod ( 774439 / 62615 ) ]
where y amod x = y mod x if y mod x # 0
y = CEIL ( 62615 m' / 774439 ) - 1
and y amod x = x
if y mod x = 0
Data Registers: R00 to R03: temp
Flags: /
Subroutines: "J2" & "D2" (
cf "Julian and Gregorian Calendars for the HP-41" )
| 01 LBL "GR-LS" 02 XEQ "J2" 03 1863079 04 + 05 11344 06 STO 01 07 * 08 STO 00 09 334995 10 STO 02 11 MOD 12 ENTER^ 13 ST- 00 14 RCL 01 15 MOD 16 - 17 RCL 01 18 / 19 FIX 0 20 RND 21 1 22 ST+ Y 23 % |
24 RCL 00 25 RCL 02 26 / 27 RND 28 1 29 + 30 62615 31 STO 01 32 * 33 STO 00 34 774439 35 STO 02 36 MOD 37 X=0? 38 X<> L 39 ENTER^ 40 CHS 41 RCL 01 42 MOD 43 + 44 RCL 01 45 / 46 RND |
47 + 48 1 49 % 50 RCL 00 51 ENTER^ 52 CHS 53 RCL 02 54 MOD 55 + 56 RCL 02 57 / 58 RND 59 1 60 - 61 STO Z 62 SIGN 63 * 64 + 65 FIX 4 66 RTN 67 LBL "LS-GR" 68 INT 69 STO 01 |
70 LASTX 71 ABS 72 FRC 73 E2 74 STO 00 75 * 76 INT 77 STO 02 78 LASTX 79 FRC 80 ST* 00 81 RCL 01 82 774439 83 * 84 STO Y 85 62615 86 STO 03 87 MOD 88 - 89 RCL 03 90 / 91 FIX 0 92 RND |
93 RCL 02 94 + 95 1 96 - 97 334995 98 * 99 ENTER^ 100 CHS 101 11344 102 STO 03 103 MOD 104 + 105 RCL 03 106 / 107 RND 108 RCL 00 109 + 110 1863080 111 - 112 XEQ "D2" 113 FIX 4 114 END |
( 197 bytes / SIZE 004 )
| STACK | INPUT1 | OUTPUT1 | INPUT2 | OUTPUT2 |
| X | YYYY.MNDDGr | yyyy.mnddLS | yyyy.mnddLS | YYYY.MNDDGr |
Examples:
-5724.1214 XEQ "GR-LS" >>>>
-2623.1201 XEQ "LS-GR" ( or simply R/S )
>>>> -5724.1214
-3101.0123 XEQ "GR-LS" >>>>
0.0101 XEQ "LS-GR" ( or simply
R/S ) >>>> -3101.0123
1979.0716 XEQ "GR-LS" >>>>
5080.0721 XEQ "LS-GR" ( or simply R/S )
>>>> 1979.0716
2012.1221 XEQ "GR-LS" >>>>
5113.1308 XEQ "LS-GR" ( or simply R/S )
>>>> 2012.1221
2013.0210 XEQ "GR-LS" >>>>
5114.0129 XEQ "LS-GR" ( or simply R/S )
>>>> 2013.0210
Notes:
-The results are of course identical to those of the previous version.
-In fact, several RND are superfluous in most cases.
e) Program#4
-This routine also employs the formulae given in references [1] &[2]
- page 167 - but with dY = dM = 1/2
-And with M = 51649/1749 = 29.53058891... &
L = 12628/1021 = 12.36826641...
-With N = number of days since 2000/01/01 ( Gregorian )
• Let s = N + 1863079 , the date yyyy.mndd in the Luni-Solar Calendar is obtained as follows:
With n = N + 1/2 and m' = FLOOR ( n / M ) + 1/2
d = FLOOR ( n mod M ) + 1
m = CEIL ( m' amod
L )
where y amod x = y mod x if y mod x # 0
y = CEIL
( m' / L ) - 1
and y amod x = x
if y mod x = 0
• And for the reverse conversion:
-With m' = FLOOR ( y L + 1/2 ) + m - 1
N = CEIL ( m' M - 1/2 ) + d - 1
Data Registers: R00 to R02: temp
Flags: /
Subroutines: "J2" & "D2" (
cf "Julian and Gregorian Calendars for the HP-41" )
| 01 LBL "GRLS" 02 XEQ "J2" 03 1863079 04 + 05 ST+ X 06 1749 07 STO 01 08 ST+ 01 09 ST* Y 10 + 11 STO 00 12 51649 13 STO 02 14 ST+ X 15 MOD 16 ENTER 17 ST- 00 18 RCL 01 19 MOD 20 - 21 RCL 01 22 / |
23 1 24 ST+ Y 25 % 26 RCL 00 27 RCL 02 28 ST+ Y 29 ST+ X 30 / 31 2042 32 STO 01 33 * 34 STO 00 35 25256 36 STO 02 37 MOD 38 X=0? 39 X<> L 40 ENTER 41 CHS 42 RCL 01 43 MOD 44 + |
45 RCL 01 46 / 47 + 48 1 49 % 50 RCL 00 51 ENTER 52 CHS 53 RCL 02 54 MOD 55 + 56 RCL 02 57 ST- Y 58 / 59 STO Z 60 SIGN 61 * 62 + 63 RTN 64 LBL "LSGR" 65 STO 00 66 INT |
67 25256 68 * 69 1021 70 + 71 RCL X 72 LASTX 73 ST+ X 74 STO 01 75 MOD 76 - 77 RCL 01 78 / 79 RCL 00 80 ABS 81 FRC 82 E2 83 * 84 STO 00 85 INT 86 + 87 1 88 - |
89 103298 90 * 91 1749 92 STO 01 93 ST+ 01 94 - 95 ENTER 96 CHS 97 RCL 01 98 MOD 99 + 100 RCL 01 101 / 102 RCL 00 103 FRC 104 E2 105 * 106 + 107 1863080 108 - 109 XEQ "D2" 110 END |
( 189 bytes / SIZE 003 )
| STACK | INPUT1 | OUTPUT1 | INPUT2 | OUTPUT2 |
| X | YYYY.MNDDGr | yyyy.mnddLS | yyyy.mnddLS | YYYY.MNDDGr |
Examples:
-5724.1214 XEQ "GRLS" >>>>
-2623.1202 XEQ "LSGR" ( or simply R/S )
>>>> -5724.1214
-3101.0123 XEQ "GRLS" >>>>
0.0101 XEQ "LSGR" ( or simply
R/S ) >>>> -3101.0123
1979.0716 XEQ "GRLS" >>>>
5080.0622 XEQ "LSGR" ( or simply R/S )
>>>> 1979.0716
2012.1221 XEQ "GRLS" >>>>
5113.1208 XEQ "LSGR" ( or simply R/S )
>>>> 2012.1221
2020.0404 XEQ "GRLS" >>>>
5121.0311 XEQ "LSGR" ( or simply R/S )
>>>> 2020.0404
Notes:
-To avoid numbers > E10, the Gregorian date should not exceed
4726/02/07
-If yyyyLS is non-negative, lines 80-61-60-59
are superfluous and may be deleted.
f) Program#5
-This routine also employs the formulae given in references [1] &[2]
- page 167 - but with dY = 1/2
& dM = 0
-And with M = 51649/1749 = 29.53058891... &
L = 12628/1021 = 12.36826641...
-With N = number of days since 2000/01/01 ( Gregorian )
• Let s = N + 1863079 , the date yyyy.mndd in the Luni-Solar Calendar is obtained as follows:
With m' = FLOOR ( s / M ) + 1/2
d = FLOOR ( s mod M ) + 1
m = CEIL ( m' amod
L )
where y amod x = y mod x if y mod x # 0
y = CEIL
( m' / L ) - 1
and y amod x = x
if y mod x = 0
• And for the reverse conversion:
-With m' = FLOOR ( y L + 1/2 ) + m - 1
N = CEIL ( m' M ) + d - 1
Data Registers: R00 to R02: temp
Flags: /
Subroutines: "J2" & "D2" (
cf "Julian and Gregorian Calendars for the HP-41" )
| 01 LBL "GRLS" 02 XEQ "J2" 03 1863079 04 + 05 1749 06 STO 01 07 * 08 STO 00 09 51649 10 STO 02 11 MOD 12 ENTER 13 ST- 00 14 RCL 01 15 MOD 16 - 17 RCL 01 18 / 19 1 20 ST+ Y 21 % |
22 RCL 00 23 ST+ X 24 RCL 02 25 ST+ Y 26 / 27 1021 28 STO 01 29 ST+ 01 30 * 31 STO 00 32 25256 33 STO 02 34 MOD 35 X=0? 36 X<> L 37 ENTER 38 CHS 39 RCL 01 40 MOD 41 + 42 RCL 01 |
43 / 44 + 45 1 46 % 47 RCL 00 48 ENTER 49 CHS 50 RCL 02 51 MOD 52 + 53 RCL 02 54 ST- Y 55 / 56 STO Z 57 SIGN 58 * 59 + 60 RTN 61 LBL "LSGR" 62 STO 00 63 INT |
64 25256 65 * 66 1021 67 + 68 RCL X 69 LASTX 70 ST+ X 71 STO 01 72 MOD 73 - 74 RCL 01 75 / 76 RCL 00 77 ABS 78 FRC 79 E2 80 * 81 STO 00 82 INT 83 + 84 1 |
85 - 86 51649 87 * 88 ENTER 89 CHS 90 1749 91 STO 01 92 MOD 93 + 94 RCL 01 95 / 96 RCL 00 97 FRC 98 E2 99 * 100 + 101 1863080 102 - 103 XEQ "D2" 104 END |
( 178 bytes / SIZE 003 )
| STACK | INPUT1 | OUTPUT1 | INPUT2 | OUTPUT2 |
| X | YYYY.MNDDGr | yyyy.mnddLS | yyyy.mnddLS | YYYY.MNDDGr |
Examples:
-5724.1214 XEQ "GRLS" >>>>
-2623.1201 XEQ "LSGR" ( or simply R/S )
>>>> -5724.1214
-3101.0123 XEQ "GRLS" >>>>
0.0101 XEQ "LSGR" ( or simply
R/S ) >>>> -3101.0123
1979.0716 XEQ "GRLS" >>>>
5080.0621 XEQ "LSGR" ( or simply R/S )
>>>> 1979.0716
2012.1221 XEQ "GRLS" >>>>
5113.1208 XEQ "LSGR" ( or simply R/S )
>>>> 2012.1221
2020.0404 XEQ "GRLS" >>>>
5121.0311 XEQ "LSGR" ( or simply R/S )
>>>> 2020.0404
Note:
-If yyyyLS is non-negative, lines 77-58-57-56
are superfluous and may be deleted.
g) Program#6
-If dY = dM = 0, the routine becomes a little simpler
-And with M = 51649/1749 = 29.53058891... &
L = 12628/1021 = 12.36826641...
• Let s = N + 1863079 , the date yyyy.mndd in the Luni-Solar Calendar is obtained as follows:
With m' = FLOOR ( s / M ) + 1
y = CEIL ( m' / L ) - 1
m = m' - [ FLOOR ( y L ) ]
d = s - CEIL [ ( m' - 1 ) M ] + 1
• Given a date yyyy.mmdd in the Luni-Solar calendar,
N = Number of days since 2000/01/01 = CEIL
[ -1863080 + { FLOOR ( y L + (m-1) } M + d ]
Data Registers: R00 to R03: temp
Flags: /
Subroutines: "J2" & "D2" (
cf "Julian and Gregorian Calendars for the HP-41" )
| 01 LBL "GRLS" 02 XEQ "J2" 03 1863079 04 + 05 STO Y 06 1749 07 STO 01 08 * 09 RCL X 10 51649 11 STO 02 12 MOD 13 - 14 STO 00 15 ENTER 16 CHS 17 RCL 01 18 MOD 19 + 20 RCL 01 |
21 / 22 - 23 1 24 ST+ Y 25 % 26 RCL 00 27 RCL 02 28 ST+ Y 29 / 30 STO 00 31 1021 32 STO 01 33 * 34 ENTER 35 CHS 36 12628 37 STO 02 38 MOD 39 + 40 RCL 02 |
41 - 42 ENTER 43 STO 03 44 RCL 01 45 MOD 46 - 47 RCL 01 48 / 49 RCL 00 50 - 51 - 52 1 53 % 54 RCL 03 55 RCL 02 56 / 57 STO Z 58 SIGN 59 * 60 + |
61 RTN 62 LBL "LSGR" 63 STO 00 64 INT 65 12628 66 * 67 STO Y 68 1021 69 STO 01 70 MOD 71 - 72 RCL 01 73 / 74 RCL 00 75 ABS 76 FRC 77 E2 78 * 79 STO 00 80 INT |
81 + 82 51649 83 ST* Y 84 - 85 ENTER 86 CHS 87 1749 88 STO 01 89 MOD 90 + 91 RCL 01 92 / 93 RCL 00 94 FRC 95 E2 96 * 97 + 98 1863080 99 - 100 XEQ "D2" 101 END |
( 172 bytes / SIZE 004 )
| STACK | INPUT1 | OUTPUT1 | INPUT2 | OUTPUT2 |
| X | YYYY.MNDDGr | yyyy.mnddLS | yyyy.mnddLS | YYYY.MNDDGr |
Examples:
-5724.1214 XEQ "GRLS" >>>>
-2623.1201 XEQ "LSGR" ( or simply R/S )
>>>> -5724.1214
-3101.0123 XEQ "GRLS" >>>>
0.0101 XEQ "LSGR" ( or simply
R/S ) >>>> -3101.0123
1979.0716 XEQ "GRLS" >>>>
5080.0721 XEQ "LSGR" ( or simply R/S )
>>>> 1979.0716
2012.1221 XEQ "GRLS" >>>>
5113.1308 XEQ "LSGR" ( or simply R/S )
>>>> 2012.1221
2020.0407 XEQ "GRLS" >>>>
5121.0414 XEQ "LSGR" ( or simply R/S )
>>>> 2020.0407
Note:
-If yyyyLS is non-negative, lines 75-59-58-57
are superfluous and may be deleted.
3°) Solar & Lunar "Calendar"
-"YDMD" calculates the year and the day of the year + the month and the
day of the month for a given date of the Gregorian calendar.
Formulae:
• With s = N + 1863079 >= 0 where N = the number of days N since 2000/01/01
YYYY = Int ( 801.s / 292559 ) DDD1 = 1 +
Int ( s Mod (292559/801) )
MM = Int ( 801.s / 23654 )
DD2 = 1 + Int ( s Mod (23654/801) )
Data Registers: R00-R01-R02: temp
Flags: /
Subroutine: "J2" ( cf "Julian
and Gregorian Calendars for the HP-41" )
| 01 LBL "YDMD" 02 XEQ "J2" 03 1863079 04 + 05 801 06 STO 01 07 * 08 STO 02 |
09 23654 10 STO 00 11 / 12 INT 13 RCL 02 14 RCL 00 15 MOD 16 RCL 01 |
17 / 18 INT 19 1 20 + 21 E2 22 / 23 + 24 RCL 02 |
25 292559 26 STO 00 27 / 28 INT 29 RCL 02 30 RCL 00 31 MOD 32 RCL 01 |
33 / 34 INT 35 1 36 + 37 E3 38 / 39 + 40 END |
( 71 bytes / SIZE 003 )
| STACK | INPUT | OUTPUTS |
| Y | / | MM.DD2 |
| X | yyyy.mnddGr | YYYY.DDD1 |
Examples:
-3101.0123 XEQ "YMD" >>>>
0.001 X<>Y
0.01
2000.0101
R/S >>>>
5100.344 X<>Y 63089.24
2020.0314
R/S >>>>
5121.052 X<>Y 63339.20
-Thus, 2020/03/14 is the 52nd day of the 5121st year and
the 20th day of the 63339th month since -3101/01/23
Notes:
-The day of the year is the first 3 decimals of YYYY.DDD1
( between 365 & 366 )
-The day of the month is the first 2 decimald of MM.DD2
( between 29 & 30 )
-These results are only based on the mean solar year & mean
lunar month. YYYY must be non-negative.
References:
[1] Nachum Dershowitz & Edward M. Reingold - "Calendrical Calculations"
- Cambridge University Press - ISBN 978-0-521-70238-6
[2] Nachum Dershowitz & Edward M. Reingold - "Indian
Calendrical Calculations"