Hindu Calendars for the HP-41
Overview
1°) Old Hindu Solar Calendars
a) Traditional Calendar
b) "New-Old" Hindu Solar
2°) Old Hindu Luni-Solar Calendars
a) "New-Old" Hindu Luni-Solar (
program #1 )
b) "New-Old" Hindu Luni-Solar (
program #2 )
c) "New-Old" Hindu Luni-Solar (
program #3 )
1°) Old Hindu Solar Calendars
a) Traditional Calendar
-The following programs use the Old Hindu Calendars
that began on -3101 January 23rd ( Gregorian ) = -3101 February
18th ( Julian ) = 0.0101 ( Kali Yuga )
( -3101 = 3102 BC )
-It is based on a mean sidereal year = 1577917500 / 4320000 =
210389 / 576 = 365 + 149/576 ~ 365.25868 days
-A variant is suggested below to replace this value by a more accurate
approximation.
-Months have 30 or 31 days.
-Mean month = (1/12) x one sidereal year = 210389 / 6912 ~ 30.43822
days
Formulae: Given a date
YYYY.MNDD in the Gregorian or Julian calendar, we first compute
the number of days N since 2000/01/01 , then:
Let s = N + 1863079.25 , the date yyyy.mndd in the Hindu Calendar is obtained as follows:
y = FLOOR ( 576 s / 210389 )
m = 1 + [ FLOOR ( 6912 s / 210389 ) ] MOD
12
d = 1 + FLOOR [ s mod ( 210389 / 6912
) ]
Data Registers: R00-R01-R02: temp
Flag:
F04 if are using "J1"
Subroutine:
"J0" or "J1" or "J2" - cf "Julian & Gregorian Calendar for the HP-41"
| 01 LBL "DT-KY"
02 XEQ "J0" 03 4 04 * 05 7452317 06 + 07 144 08 * 09 STO Y |
10 210389
11 STO 00 12 MOD 13 STO 01 14 - 15 RCL 00 16 / 17 X<> 01 18 12 |
19 *
20 STO Y 21 RCL 00 22 MOD 23 STO 02 24 - 25 RCL 00 26 / 27 X<> 02 |
28 6912
29 / 30 INT 31 1 32 ST+ 02 33 ST+ Y 34 % 35 RCL 02 36 + |
37 1
38 % 39 RCL 01 40 + 41 END |
( 77 bytes / SIZE 003 )
| STACK | INPUT | OUTPUT |
| X | YYYY.MNDDGr/Ju | YYYY.MNDDKy |
Examples:
-3101.0218 XEQ "DT-KY" >>>>
0.0101
1979.0716
R/S >>>>
5080.0331
2009.1225
R/S >>>>
5110.0910
Notes:
-In the Hindu calendar, the day begins at 6 a.m.
-So we also assume that a date written yyyy.mndd in the Julian
or Gregorian calendar represents a time after 6 a.m. ( in fact between
6h and 30h )
-With another convention like "civil days begin at 0h" , lines 03 to
08 could be replaced by 1863079 + 576 *
-This routine does not work before -3101.0218 ( Julian
)
-Simply add RCL 01 SIGN * after line
38 and it will work in this case too.
-We can create a "new-old" Hindu calendar by changing the value of the
mean sidereal year:
-For instance, 1577907500 / 4320000 = 631163 / 1728 = 365 + 443
/ 1728 ~ 365.2563657... days is a better approximation.
-If you want to use this value, replace lines 07-10-28 by 432 , 631163 , 20736 and the 3 examples above become:
-3101.0218 XEQ "DT-KY" >>>>
0.0101
( of course unchanged )
1979.0716
R/S >>>>
5080.0412
2009.1225
R/S >>>>
5110.0922 thus a difference
of about 12 days nowadays.
Reverse conversion:
Formula: Given a date yyyy.mmdd in the old Hindu solar calendar,
Number of days since 2000/01/01
= CEIL [ -1863080.25 + y 210389 / 576 + (m-1) 210389 / 6912 + d
]
Data Registers: R00-R01-R02: temp
Flag:
F04 if are using "D1"
Subroutine:
"DT" or "D1" or "D2" - cf "Julian & Gregorian Calendar for the HP-41"
| 01 LBL "KY-DT"
02 INT 03 STO 01 04 LASTX 05 FRC 06 E2 07 STO 00 08 * 09 INT |
10 STO 02
11 LASTX 12 FRC 13 ST* 00 14 RCL 01 15 1788 16 * 17 RCL 02 18 210389 |
19 ST* Y
20 - 21 + 22 6912 23 STO 02 24 4 25 / 26 - 27 ENTER^ |
28 CHS
29 RCL 02 30 MOD 31 + 32 RCL 02 33 / 34 RCL 01 35 365 36 * |
37 +
38 RCL 00 39 + 40 1863080 41 - 42 XEQ "DT" 43 END |
( 78 bytes / SIZE 003 )
| STACK | INPUT | OUTPUT |
| X | YYYY.MNDDKy | YYYY.MNDDGr/Ju |
Examples:
0.0101
XEQ "KY-DT" >>>> -3101.0218
( or -3101.0123 Gregorian )
5080.0331
R/S >>>>
1979.0716
5110.0910
R/S >>>>
2009.1225
Notes:
-This routine does not work before 0.0101 ( Kali
Yuga )
-Simply add ABS after line 04 and it will work in this
case too.
-If civil days began at 0h instead of 6h, we could simplify this program: replace line 29 by 6192 STO 02 and delete lines 22 thru 26
-If you want to use the "new-old" Hindu calendar mentioned in §1,
replace lines 15-18-22 by 5316 , 631163 , 20736.
b) "New-Old" Hindu Solar
-The variant suggested above uses 1 sidereal year = 365 + 443 / 1728
~ 365.2563657... days
-Actually, in 2000, one mean sidereal year = 365.256363
days
-The following routine employs this value.
Data Registers: R00-R03: temp
Flag:
F04 if are using "J1"
Subroutine:
"J0" or "J1" or "J2" - cf "Julian & Gregorian Calendar for the HP-41"
| 01 LBL "DT-KY"
02 XEQ "J0" 03 1863079.25 04 + 05 STO 00 06 STO 01 07 365.256363 |
08 STO 02
09 12 10 / 11 STO 03 12 MOD 13 ST- 01 14 INT |
15 1
16 ST+ Y 17 % 18 RCL 01 19 RCL 03 20 / 21 FIX 0 |
22 RND
23 12 24 MOD 25 + 26 1 27 ST+ Y 28 % |
29 RCL 00
30 RCL 02 31 / 32 INT 33 + 34 FIX 4 35 END |
( 73 bytes / SIZE 004 )
| STACK | INPUT | OUTPUT |
| X | YYYY.MNDDGr/Ju | YYYY.MNDDKy |
Examples:
-3101.0218 XEQ "DT-KY" >>>>
0.0101
1979.0716
R/S >>>>
5080.0412
2009.1225
R/S >>>>
5110.0922
Notes:
-Actually, one mean sidereal year =
365.2563630 days in 2000
365.2563607 days in 0
365.2563573 days in -3000
-This value of 365.256363 ( line 12 ) may be
replaced by another approximation y,
provided 1000000 y is an integer and a mulptiple
of 3: there will be no roundoff-error.
Reverse conversion:
Data Registers: R00-R03: temp
Flag:
F04 if are using "D1"
Subroutine:
"DT" or "D1" or "D2" - cf "Julian & Gregorian Calendar for the HP-41"
| 01 LBL "KY-DT"
02 INT 03 STO 01 04 LASTX 05 FRC 06 E2 07 STO 00 08 * 09 INT 10 STO 02 11 LASTX |
12 FRC
13 ST* 00 14 SIGN 15 ST- 02 16 RCL 01 17 5.256363 18 STO 03 19 FRC 20 * 21 INT 22 LASTX |
23 FRC
24 RCL 03 25 12 26 / 27 RCL 02 28 * 29 + 30 4 31 1/X 32 - 33 ENTER^ |
34 CHS
35 1 36 MOD 37 + 38 + 39 RCL 01 40 365 41 * 42 + 43 RCL 02 44 30 |
45 *
46 + 47 RCL 00 48 + 49 1863080 50 - 51 XEQ "DT" 52 END |
( 85 bytes / SIZE 004 )
| STACK | INPUT | OUTPUT |
| X | YYYY.MNDDKy | YYYY.MNDDGr/Ju |
Examples:
0.0101
XEQ "KY-DT" >>>> -3101.0218
( or -3101.0123 Gregorian )
5080.0412
R/S >>>>
1979.0716
5110.0922
R/S >>>>
2009.1225
2°) Old Hindu Luni-Solar Calendars
a) "New-Old" Hindu Luni-Solar
( program #1 )
-The Traditional Luni-Solar Calendar uses:
1 sidereal year = 365 + 149/576 ~ 365.25868 days
1 lunar month = 29 + 2362563/4452778 ~ 29.53058181
days
-It's difficult to apply the formulae given in reference [1] with such
fractions: multiprecision arithmetic would be needed.
-So, I've simplified the problem by choosing different approximations,
namely:
One sidereal year = A = 346263/948 = 365.256329...
days ( not excellent but better
than 365.25868... )
One Lunar month = B = 27995/948 = 29.53059072...
days
Formulae: Given a date
YYYY.MNDD in the Gregorian or Julian calendar, we first compute
the number of days N since 2000/01/01 , then:
Let s = N + 1863079.25 , the year y, the month m and the day d in the Hindu Calendar are obtained as follows:
Let N.M. = new-moon = s - s mod B
the month is leap iff A/12 - B >= N.M. mod ( A/12 ) > 0
m = 1 + ceil ( 12 N.M. / A ) mod 12
d = 1 + floor ( 30 s / B ) mod 30
y = -1 + ceil [ ( N.M. + A/12 ) / A ]
Data Registers: R00-R04: temp
Flag:
F04 if are using "J1"
Subroutine:
"J0" or "J1" or "J2" - cf "Julian & Gregorian Calendar for the HP-41"
| 01 LBL "DT-HLS"
02 XEQ "J0" 03 4 04 * 05 7452317 06 + 07 STO 00 08 948 09 * 10 STO Y 11 111980 12 MOD 13 - 14 STO 01 15 1 16 STO 02 |
17 CLX
18 115421 19 STO 03 20 MOD 21 3441 22 X<>Y 23 X<=Y? 24 X=0? 25 DSE 02 26 CLX 27 RCL 00 28 1422 29 * 30 STO Y 31 5599 32 STO 00 |
33 MOD
34 - 35 RCL 00 36 / 37 FIX 0 38 RND 39 30 40 MOD 41 1 42 ST+ Y 43 % 44 RCL 02 45 + 46 10 47 / 48 RCL 01 |
49 ENTER^
50 CHS 51 RCL 03 52 MOD 53 + 54 RCL 03 55 ST+ 01 56 / 57 12 58 ST* 03 59 MOD 60 + 61 1 62 ST+ Y 63 % 64 RCL 01 |
65 ENTER^
66 CHS 67 RCL 03 68 MOD 69 + 70 RCL 03 71 / 72 1 73 - 74 + 75 FIX 5 76 END |
( 129 bytes / SIZE 004 )
| STACK | INPUT | OUTPUT |
| X | YYYY.MNDDGr/Ju | yyyy.mmbddHLS |
where b is a boolean:
b = 1 indicates a leap month
b = 0 indicates a regular month
Examples:
-3101.0218 XEQ "DT-HLS" >>>>
0.01001
1976.0101
R/S >>>>
5076.10129
here, we have a leap month
1976.0103
R/S >>>>
5076.10001
1979.0716
R/S >>>>
5080.04022
2009.1225
R/S >>>>
5110.10009
Notes:
-A leap-month precedes the regular month of the same name.
-Months have 29 or 30 civil days.
-Sometimes, there are lost days: one day is skipped!
-For instance, 2000.0220 gives 5100.12015
whereas 2000.0221
gives 5100.12017
-Thus, 5100.12016 is lost!
-There will be no roundoff-error for Gregorian dates < 4118.0315
Reverse conversion:
Formula: Given a date yyyy.mmbdd in the old Hindu solar calendar,
Number of days since 2000/01/01
= CEIL [ -1863080.25 + lny + m' B + (d-1) B/30 ]
where
lny = lunar-new-year = B + p - p mod B with p = (12y-1) A/12
m' = m-1 if { the month is
not leap ( b = 0 ) and ceil [ ( B - p mod B ) / ( A/12 - B ) ] <=
m }
m' = m otherwise
Again, we apply these formulae with
One sidereal year = A = 346263/948 = 365.256329...
days
One Lunar month = B = 27995/948 = 29.53059072...
days
Data Registers: R00-R05: temp
Flag:
F04 if are using "D1"
Subroutine:
"DT" or "D1" or "D2" - cf "Julian & Gregorian Calendar for the HP-41"
| 01 LBL "HLS-DT"
02 INT 03 STO 00 04 LASTX 05 FRC 06 E2 07 STO 03 08 * 09 INT 10 STO 01 11 LASTX 12 FRC 13 10 14 * 15 INT 16 STO 02 17 LASTX 18 FRC |
19 ST* 03
20 RCL 00 21 12 22 * 23 1 24 - 25 115421 26 * 27 STO 04 28 111980 29 STO 05 30 STO Z 31 MOD 32 - 33 ST+ 04 34 RCL 02 35 X#0? 36 GTO 00 |
37 RCL 01
38 RCL Z 39 ENTER^ 40 CHS 41 3441 42 ST* T 43 MOD 44 + 45 X<=Y? 46 ISG 01 47 LBL 00 48 RCL 01 49 1 50 - 51 RCL 05 52 ST* 03 53 ST- 03 54 * |
55 RCL 04
56 + 57 948 58 - 59 STO Y 60 LASTX 61 4 62 * 63 STO 01 64 MOD 65 STO 02 66 - 67 RCL 01 68 / 69 RCL 02 70 30 71 ST* 01 72 * |
73 RCL 03
74 + 75 ENTER^ 76 CHS 77 RCL 01 78 MOD 79 + 80 RCL 01 81 / 82 + 83 1863079 84 - 85 XEQ "DT" 86 END |
( 136 bytes / SIZE 006 )
| STACK | INPUT | OUTPUT |
| X | YYYY.MMbDDHLS | yyyy.mnddGr/Ju |
where b is a boolean:
b = 1 indicates a leap
month
b = 0 indicates a regular
month
Examples:
0.01001
XEQ "HLS-DT" >>>> -3101.0218
5076.10129
R/S
>>>> 1976.0101
5080.04022
R/S
>>>> 1979.0716
5110.10009
R/S
>>>> 2009.1225
b) "New-Old" Hindu Luni-Solar
( program #2 )
-This variant employs:
1 sidereal year = 365.256363
days
1 lunar month = 29.53058886
days
Data Registers: R00-R06: temp
Flag:
F04 if are using "J1"
Subroutine:
"J0" or "J1" or "J2" - cf "Julian & Gregorian Calendar for the HP-41"
| 01 LBL "DT-HLS"
02 XEQ "J0" 03 1863079 04 + 05 STO 01 06 4 07 1/X 08 STO 02 09 + 10 STO 00 11 29.53058886 12 STO 03 13 MOD 14 ST- 02 15 SIGN 16 STO 04 17 365.256363 18 STO 05 |
19 12
20 / 21 STO 06 22 RCL 03 23 - 24 RCL 01 25 RCL 06 26 MOD 27 RCL 02 28 ST+ 01 29 LASTX 30 MOD 31 + 32 RCL 06 33 MOD 34 X#0? 35 X>Y? 36 DSE 04 |
37 CLX
38 RCL 00 39 30 40 * 41 STO Y 42 RCL 03 43 MOD 44 - 45 RCL 03 46 / 47 FIX 0 48 RND 49 30 50 MOD 51 1 52 ST+ Y 53 % 54 RCL 04 |
55 +
56 10 57 / 58 RCL 01 59 ENTER^ 60 CHS 61 RCL 06 62 ST+ 01 63 MOD 64 + 65 RCL 06 66 / 67 RND 68 12 69 MOD 70 + 71 1 72 ST+ Y |
73 %
74 RCL 01 75 ENTER^ 76 CHS 77 RCL 05 78 MOD 79 + 80 RCL 05 81 / 82 RND 83 1 84 - 85 + 86 FIX 5 87 END |
( 140 bytes / SIZE 007 )
| STACK | INPUT | OUTPUT |
| X | YYYY.MNDDGr/Ju | yyyy.mmbddHLS |
where b is a boolean:
b = 1 indicates a leap month
b = 0 indicates a regular
month
Examples:
-3101.0218 XEQ "DT-HLS" >>>>
0.01001
1979.0716
R/S >>>>
5080.04022
2000.0503
R/S >>>>
5101.02130 a leap
month
2000.0504
R/S >>>>
5101.02001
2009.1225
R/S >>>>
5110.10009
Notes:
-The values of the sidereal year y ( line 17 ) and the lunar month m
( line 11 ) may be changed provided 1000000 y and 100000000 m
are integers and multiples of 3 - otherwise, roundoff-errors
would be possible.
-For example, if you replace line 11 by 29.53058181 and line
17 by 365.258682, you get a calendar that is very close to the traditional
old hindu lunisolar
( though probably not exactly the same )
-An example of "lost day" is 5100.12009:
2000.0213 ( Gregorian ) >>>> 5100.12008
is followed by
2000.0214 ( Gregorian ) >>>> 5100.12010
Reverse conversion:
Data Registers: R00-R06: temp
Flag:
F04 if are using "D1"
Subroutine:
"DT" or "D1" or "D2" - cf "Julian & Gregorian Calendar for the HP-41"
| 01 LBL "HLS-DT"
02 INT 03 STO 00 04 LASTX 05 FRC 06 E2 07 STO 03 08 * 09 INT 10 STO 01 11 LASTX 12 FRC 13 10 14 * 15 INT 16 STO 02 17 LASTX 18 FRC 19 ST* 03 20 365.256363 21 STO 06 22 INT 23 RCL 00 24 * 25 30 |
26 -
27 STO 04 28 RCL 00 29 RCL 06 30 FRC 31 * 32 INT 33 ST+ 04 34 LASTX 35 FRC 36 RCL 06 37 12 38 / 39 STO 00 40 FRC 41 - 42 STO Y 43 29.53058886 44 STO 06 45 MOD 46 RCL 04 47 LASTX 48 MOD 49 + 50 RCL 06 |
51 STO Z
52 MOD 53 - 54 + 55 STO 05 56 LASTX 57 ENTER^ 58 CHS 59 RCL 00 60 RCL 06 61 - 62 STO 00 63 MOD 64 + 65 RCL 00 66 / 67 FIX 0 68 RND 69 1 70 ST- 03 71 RCL 02 72 - 73 RCL 01 74 * 75 X<Y? |
76 DSE 01
77 CLX 78 RCL 01 79 RCL 06 80 INT 81 * 82 ST+ 04 83 RCL 01 84 RCL 06 85 FRC 86 * 87 4 88 1/X 89 - 90 RCL 03 91 RCL 03 92 10 93 MOD 94 STO 03 95 - 96 RCL 06 97 30 98 / 99 ST* 03 100 * |
101 +
102 RCL 05 103 + 104 INT 105 ST+ 04 106 LASTX 107 FRC 108 RCL 03 109 + 110 ENTER^ 111 CHS 112 1 113 MOD 114 + 115 RCL 04 116 + 117 1863079 118 - 119 XEQ "DT" 120 FIX 4 121 END |
( 177 bytes / SIZE 007 )
| STACK | INPUT | OUTPUT |
| X | YYYY.MMbDDHLS | yyyy.mnddGr/Ju |
where b is a boolean:
b = 1 indicates a leap
month
b = 0 indicates a regular
month
Examples:
0.01001
XEQ "HLS-DT" >>>> -3101.0218
5080.04022
R/S
>>>> 1979.0716
5101.02130
R/S
>>>> 2000.0503
5101.02001
R/S
>>>> 2000.0504
5110.10009
R/S
>>>> 2009.1225
Notes:
-Like in the previous routine, line 20 may be replaced by another value
y provided 106 y is an integer and a multiple of 3
and line 43 by another value m provided 108
m is also an integer and a multiple of 3.
-Try for instance 365.258682 and 29.53058181 to get -
almost
- the traditional old Lunisolar Hindu Calendar.
c) "New-Old" Hindu Luni-Solar
( program #3 )
-The star Spica ( alpha Virginis ) is often regarded as a fixed star
in Hindu astrology.
-Since Spica has a proper motion of about -27.5 arcseconds
per millenium in longitude with respect to J2000.0,
the value of the mean sidereal year 365.256363 days could
be replaced by something like 365.2563554 days for the year 2000
-The following program uses 2 rational numbers for the mean sidereal year and the mean Lunar month:
A = 172401 / 472 ~ 365.2563559
days
B = 27995 / 948 ~
29.53059072 days
-Unlike the values of A and B that are used in the routine listed in
§2-a) the denominators are different.
-So, the calculation is a little more complicated, all the more that
the results are correct until gregorian year 25778
Data Registers: R00-R03: temp
Flag:
F04 if are using "J1"
Subroutine:
"J0" or "J1" or "J2" - cf "Julian & Gregorian Calendar for the HP-41"
| 01 LBL "DT-HLS"
02 XEQ "J0" 03 4 04 * 05 7452317 06 + 07 STO 00 08 237 09 * 10 STO Y 11 27995 12 MOD 13 - 14 STO 01 15 1 16 STO 02 17 CLX |
18 13619679
19 STO 03 20 MOD 21 472 22 * 23 RCL 03 24 MOD 25 406039 26 X<>Y 27 X#0? 28 X>Y? 29 DSE 02 30 CLX 31 RCL 00 32 1422 33 * 34 STO Y |
35 5599
36 STO 00 37 MOD 38 - 39 RCL 00 40 / 41 FIX 0 42 RND 43 30 44 MOD 45 1 46 ST+ Y 47 % 48 RCL 02 49 + 50 10 51 / |
52 RCL 01
53 472 54 * 55 ENTER^ 56 STO 01 57 CHS 58 RCL 03 59 MOD 60 + 61 RCL 03 62 ST+ 01 63 / 64 RND 65 12 66 ST* 03 67 MOD 68 + |
69 1
70 ST+ Y 71 % 72 RCL 01 73 ENTER^ 74 CHS 75 RCL 03 76 MOD 77 + 78 RCL 03 79 / 80 RND 81 1 82 - 83 + 84 FIX 5 85 END |
( 145 bytes / SIZE 004 )
| STACK | INPUT | OUTPUT |
| X | YYYY.MNDDGr/Ju | yyyy.mmbddHLS |
where b is a boolean:
b = 1 indicates a leap
month
b = 0 indicates a regular
month
Examples:
-3101.0218 XEQ "DT-HLS" >>>>
0.01001
1979.0716
R/S >>>>
5080.04022
2000.0428
R/S >>>>
5101.02125 ( leap-month )
2009.1225
R/S >>>>
5110.10009
21428.1212
R/S >>>>
24529.01012
Reverse conversion:
Data Registers: R00-R06: temp
Flag:
F04 if are using "D1"
Subroutine:
"DT" or "D1" or "D2" - cf "Julian & Gregorian Calendar for the HP-41"
| 01 LBL "HLS-DT"
02 INT 03 STO 00 04 LASTX 05 FRC 06 E2 07 STO 03 08 * 09 INT 10 STO 01 11 LASTX 12 FRC 13 10 14 * 15 INT 16 STO 02 17 LASTX 18 FRC |
19 ST* 03
20 RCL 00 21 406039 22 STO 04 23 * 24 13213640 25 STO 05 26 STO 06 27 MOD 28 12 29 * 30 RCL 04 31 - 32 RCL 05 33 MOD 34 ST- 05 35 RCL 02 36 X#0? |
37 GTO 00
38 RCL 01 39 RCL 05 40 ENTER^ 41 CHS 42 RCL 04 43 ST* T 44 MOD 45 + 46 X<=Y? 47 ISG 01 48 LBL 00 49 RCL 00 50 344124 51 * 52 RCL 01 53 RCL 06 54 3 |
55 *
56 ST* Y 57 - 58 + 59 RCL 03 60 RCL 06 61 10 62 / 63 ST* Y 64 - 65 + 66 RCL 05 67 3 68 * 69 + 70 41194629 71 - 72 ENTER^ |
73 CHS
74 1342368 75 STO 01 76 MOD 77 + 78 RCL 01 79 / 80 RCL 00 81 365 82 * 83 + 84 1863079 85 - 86 XEQ "DT" 87 END |
( 150 bytes / SIZE 007 )
| STACK | INPUT | OUTPUT |
| X | YYYY.MMbDDHLS | yyyy.mnddGr/Ju |
where b is a boolean:
b = 1 indicates a leap
month
b = 0 indicates a regular
month
Examples:
0.01001
XEQ "HLS-DT" >>>> -3101.0218
5080.04022
R/S
>>>> 1979.0716
5101.02125
R/S
>>>> 2000.0428
5110.10009
R/S
>>>> 2009.1225
24529.01012
R/S
>>>> 21428.1212
Notes:
-Of course, these "new-old" calendars are somewhat artificial:
they have never been - and will be probably never - used.
-Other values can be used for the mean sidereal year and / or the mean
lunar month
( cf "Sidereal Year, Tropical Year & Lunar Month for the
HP-41" )
Interesting Formulae
-The following formulae have been used in the routines listed above:
(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
Reference:
[1] Nachum Dershowitz & Edward M. Reingold - "Calendrical
Calculations" - Cambridge University Press - ISBN 978-0-521-70238-6