The Museum of HP Calculators
The Museum of HP Calculators
This program is Copyright © 2007 by Jean-Marc Baillard and is used here by permission.
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.
1°) Date >>> Number of days since 2000/01/01 0h
a) Program#1
b) Program#2
c) Program#3 - Gregorian Calendar only
- ( Time Module required )
2°) Number of days since 2000/01/01 0h >>> Date
a) Program#1
b) Program#2
c) Program#3 - Gregorian Calendar only
- ( Time Module required )
3°) Date <> Day of the Year
a) Program#1
b) Program#2 ( Time Module required
)
4°) Tropical Year
Notes:
-Programs 1°) a) & 2°) a) were previously listed in "Phases
of the Moon for the HP-41"
-The "B.C." years are counted astronomically:
year 0 = 1 B.C.
year -1 = 2 B.C. ...etc...
-All the dates are expressed in YMD format.
1°) Date >>> Number of days since 2000/01/01 0h
a) Program#1
-This program computes the number of days since 2000/01/01 0h
( i-e the Julian Day number minus 2451544.5 )
in X-register and the day of the week in T-register.
-Registers Y and Z are saved.
-The Gregorian calendar reform is taken into account: The day following
1582/10/04 is 1582/10/15
-"J0" ( and "DT" - cf 2°)a) ) are valid at least since 4713 B.C.
up to ... the next calendar reform!
-Synthetic registers M, N, O, P can be replaced by R00, R01, R02, R03.
Data Registers: /
Flags: /
Subroutines: /
01 LBL "J0"
02 STO O
03 ENTER^
04 INT
05 STO N
06 -
07 ABS
08 E2
09 *
10 ENTER^
11 INT
12 STO M
13 -
14 E2
15 *
16 X<> M
17 3
18 +
19 6
20 X>Y?
21 DSE N
22 LBL 00
23 X<=Y?
24 CHS
25 +
26 4
27 +
28 30.6
29 *
30 INT
31 730550
32 -
33 ST+ M
34 CLX
35 RCL N
36 487
37 *
38 X<0?
39 DSE X
40 LBL 00
41 .75
42 *
43 INT
44 ST+ M
45 CLX
46 RCL O
47 1582.1015
48 -
49 X<0?
50 GTO 01
51 X<> N
52 E2
53 /
54 INT
55 25
56 %
57 INT
58 -
59 2
60 -
61 ST- M
62 LBL 01
63 CLX
64 RCL M
65 1
66 -
67 7
68 MOD
69 INT
70 STO T
71 X<> O
72 SIGN
73 X<> M
74 CLA
75 END
( 123 Bytes / SIZE 000 )
| STACK | INPUTS | OUTPUTS |
| T | / | dow |
| Z | Z | Z |
| Y | Y | Y |
| X | YYYY.MNDDdd | N |
| L | / | YYYY.MNDDdd |
( dow = day of week = 0 for Sunday, 1 for Monday, ... , 6 for Saturday )
-N= the number of days between a date YYYY.MMDDdd and 2000/01/01 at 0h = the Julian Day number minus 2451544.5
Examples:
April 4th 2134 at 6h AM 2134.040425 XEQ "J0" >>> N = 49036.25 RDN RDN dow = 0 = Sunday
1234.0428 R/S >>> N = -279651 RDN RDN dow = 5 = Friday
-4123.0707 R/S >>>
N = -2236225 RDN RDN dow = 1 = Monday
b) Program#2
-The following program is only a variant of a routine listed in the
PPC ROM user's manual.
-Y-register is saved in Y Z T
-Synthetic register M may be replaced by any standard register ( like
R00 )
Data Registers: /
Flag: F04
Set flag F04 for the Julian Calendar
Clear flag F04 for the Gregorian Calendar
Subroutines: /
01 LBL "J1"
02 ENTER^
03 INT
04 ST- Y
05 X<>Y
06 E2
07 *
08 ENTER^
09 INT
10 STO M
11 -
12 E2
13 *
14 X<> M
15 1
16 E^X
17 -
18 12
19 /
20 +
21 INT
22 ST- M
23 LASTX
24 367
25 *
26 INT
27 ST+ M
28 SIGN
29 FS? 04
30 ISG X
31 %
32 INT
33 .75
34 ST* Z
35 *
36 X<>Y
37 ST- M
38 CLX
39 X<> M
40 INT
41 X<>Y
42 -
43 INT
44 730434
45 -
46 END
( 75 bytes / SIZE 000 )
| STACK | INPUTS | OUTPUTS |
| T | / | Y |
| Z | / | Y |
| Y | Y | Y |
| X | YYYY.MNDD | N |
Examples:
CF 04 2134.0404 XEQ "J1" >>>
N = 49036
SF 04 1234.0428 R/S
>>> N = -279651
Notes:
-Here, the days cannot have decimals
-You can choose the Julian Calendar after 1582/10/15
and you can choose the Gregorian Calendar before 1582/10/04
-This program only works since 0000/03/01 ( March 1st Year 0 )
-However, it will work for all dates - including negative years - if you have programmed a FLOOR function in M-Code:
>>> Replace lines 43-40-32-26-21 by FLOOR add CLX after line 27 and add ABS after line 05
-If you don't have a FLOOR function, replace it by
RCL X 1 MOD - ( lines 43-40-32-26 )
replace line 23 by R^ and replace line 22 by
ENTER^ STO Z 1 MOD -
-The day of the week may be computed by ( N-1) MOD 7
c) Program#3 - Gregorian Calendar
only - TIME Module required
-The functions of the TIME Module work for dates between 1582/10/15
and 4320/09/10
-"J2" overcomes these limitations and it is shorter than "J0" &
"J1"
Data Registers: /
Flags: /
Subroutines: /
01 LBL "J2"
02 MDY
03 ENTER^
04 FRC
05 STO N
06 -
07 RCL X
08 400
09 MOD
10 STO M
11 -
12 2 E3
13 ST+ M
14 -
15 365.2425
16 *
17 X<> M
18 E6
19 /
20 RCL N
21 ABS
22 E2
23 *
24 +
25 1.012
26 X<>Y
27 DDAYS
28 RCL M
29 +
30 DMY
this line is only useful if you live in a DMY country
31 CLA
32 END
( 66 bytes / SIZE 000 )
| STACK | INPUTS | OUTPUTS |
| T | / | Y |
| Z | / | Y |
| Y | Y | Y |
| X | YYYY.MNDD | N |
Examples:
10234.0704 XEQ "J2" >>> N = 3007591
2134.0404 R/S
>>> N = 49036
1234.0428 R/S
>>> N = -279658
-4123.0707 R/S
>>> N = -2236192
2°) Number of days since 2000/01/01 0h >>> Date
-These 3 programs are the inverses of "J0" "J1" "J2"
a) Program#1
Data Registers: /
Flags: /
Subroutines: /
01 LBL "DT"
02 STO O
03 2453069
04 +
05 ENTER^
06 FRC
07 STO M
08 -
09 STO N
10 2300685
11 -
12 X<0?
13 GTO 01
14 4
15 *
16 1727779
17 +
18 146097
19 /
20 INT
21 ST+ N
22 4
23 /
24 INT
25 ST- N
26 ISG N
27 LBL 01
28 CLX
29 RCL N
30 122.1
31 -
32 365.25
33 STO P
34 /
35 INT
36 ST* P
37 RCL P
38 INT
39 ST- N
40 CLX
41 4715
42 -
43 X<> N
44 ST+ M
45 30.61
46 STO P
47 /
48 INT
49 ST* P
50 RCL P
51 INT
52 ST- M
53 CLX
54 13
55 X<Y?
56 X=0?
57 SIGN
58 -
59 E2
60 ST/ M
61 LOG
62 X<Y?
63 DSE N
64 CLX
65 X<> M
66 +
67 E2
68 /
69 RCL N
70 SIGN
71 *
72 RCL N
73 +
74 RCL O
75 SIGN
76 RDN
77 CLA
78 END
( 151 bytes / SIZE 000 )
| STACK | INPUTS | OUTPUTS |
| Z | Z | Z |
| Y | Y | Y |
| X | N | YYYY.MNDDdd |
| L | / | N |
Examples:
N = 49036.25 XEQ "DT"
>>> 2134.040425
N = -279651
R/S >>> 1234.0428
N = -2236225
R/S >>> -4123.0707
b) Program#2
-Like "J1", this program is also a variant of a routine listed in the
PPC ROM user's manual.
-Y-register is saved in Y Z T
-Synthetic register M may be replaced by any standard register ( like
R00 )
Data Registers: /
Flag: F04
Set flag F04 for the Julian Calendar
Clear flag F04 for the Gregorian Calendar
Subroutines: /
01 LBL "D1"
02 730425.8
03 +
04 RCL X
05 36524.25
06 /
07 INT
08 25
09 %
10 INT
11 -
12 2
13 FS? 04
14 X<>Y
15 RDN
16 +
17 RCL X
18 365.25
19 ST/ Y
20 X<>Y
21 INT
22 STO M
23 *
24 INT
25 -
26 .3
27 -
28 RCL X
29 30.6
30 ST/ Y
31 X<>Y
32 INT
33 *
34 ST- Y
35 ISG Y
36 X<> L
37 3
38 -
39 6
40 X<Y?
41 ISG M
42 CHS
43 -
44 X<>Y
45 INT
46 E2
47 /
48 +
49 E2
50 /
51 0
52 X<> M
53 +
54 END
( 99 bytes / SIZE 000 )
| STACK | INPUTS | OUTPUTS |
| T | / | Y |
| Z | / | Y |
| Y | Y | Y |
| X | N | YYYY.MNDD |
Examples:
CF 04 N = 49036 XEQ "D1"
>>> 2134.0404
SF 04 N = -279651 R/S
>>> 1234.0428
Notes:
-N must be an integer.
-You can choose the Julian Calendar after 1582/10/15
and you can choose the Gregorian Calendar before 1582/10/04
-This program only works since 0000/03/01 ( March 1st Year 0 ) [ i-e N >= -730425 in the Gregorian Calendar , N >= -730427 in the Julian Calendar ]
-But if you have a FLOOR function, "D1" will work for all dates if you
add RCL M SIGN *
after line 50
LBL 00
X<Y? X=0? after line 41
replace lines 24-21-10-07 by FLOOR
-Otherwise, replace lines 15 to 24 by X<> M + RCL
X 365.25 / RCL X 1 MOD -
STO M 365.25 * RCL X 1 MOD -
replace lines 10 and 07 by RCL X 1 MOD -
and replace line 04 by STO M
c) Program#3 - Gregorian Calendar
only - TIME Module required
Data Registers: /
Flags: /
Subroutines: /
01 LBL "D2"
02 MDY
03 RCL X
04 146097
05 MOD
06 STO M
07 ST- Y
08 X<> L
09 /
10 400
11 *
12 X<> M
13 1.012
14 X<>Y
15 DATE+
16 E2
17 *
18 ENTER^
19 FRC
20 ST- Y
21 E4
22 ST/ Z
23 *
24 0
25 X<> M
26 +
27 STO Z
28 SIGN
29 *
30 +
31 DMY
only if you live in a DMY country
32 END
( 64 bytes / SIZE 000 )
| STACK | INPUTS | OUTPUTS |
| T | / | Y |
| Z | / | Y |
| Y | Y | Y |
| X | N | YYYY.MNDD |
Examples:
1000000 XEQ "D2" >>>
4737.1128
-1000000 R/S
>>> -738.0203
3°) Date <> Day
of the Year
a) Program#1
Data Registers: /
Flags: F04 & F00
Set flag F04 for the Julian Calendar
F00 is cleared for a common year
Clear flag F04 for the Gregorian Calendar
F00 is set for a leap year
Subroutines: /
01 LBL "DOY"
02 FRC
03 LASTX
04 INT
05 XEQ 00
06 RDN
07 ABS
08 E2
09 *
10 FRC
11 LASTX
12 INT
13 RCL X
14 XEQ 02
15 X<>Y
16 E2
17 *
18 +
19 30
20 -
21 RTN
22 LBL "YN-D"
23 X<>Y
24 STO M
25 XEQ 00
26 CLX
27 32
28 RCL Y
29 X<Y?
30 ST- Z
31 RCL Z
32 2
33 FS? 00
34 SIGN
35 +
36 9
37 *
38 275
39 /
40 .98
41 +
42 INT
43 RCL M
44 SIGN
45 %
46 ST+ M
47 RDN
48 ENTER^
49 XEQ 02
50 30
51 -
52 -
53 E4
54 /
55 RCL M
56 SIGN
57 *
58 0
59 X<> M
60 +
61 RTN
62 LBL 00
63 CF 00
64 1
65 %
66 FRC
67 FC? 04
68 X#0?
69 GTO 01
70 X<> L
71 INT
72 4
73 MOD
74 ST+ Y
75 LBL 01
76 CLX
77 4
78 MOD
79 X=0?
80 SF 00
81 RTN
82 LBL 02
83 275
84 *
85 9
86 ST+ Z
87 /
88 INT
89 X<>Y
90 12
91 /
92 INT
93 FC? 00
94 ST+ X
95 -
96 END
( 151 bytes / SIZE 000 )
1- Date >>> Day of the Year
| STACK | INPUTS | OUTPUTS |
| X | YYYY.MNDD | DOY |
Example:
CF 04 ( Gregorian Calendar ) 2134.0707
XEQ "DOY" >>>> doy = 188 Flag F00 is clear:
2134 is a common year
SF 04 ( Julian Calendar )
1248.0707 XEQ "DOY" >>>> doy = 189
Flag F00 is set: 1248 is a leap year
2-Day of the Year >>> Date
| STACK | INPUTS | OUTPUTS |
| Y | YYYY | N |
| X | N | YYYY.MNDD |
Example:
CF 04 ( Gregorian Calendar ) 2134 ENTER^
188 XEQ "YN-D" >>> Date = 2134.0707
Flag F00 is clear: 2134 is a common year
SF 04 ( Julian Calendar )
1248 ENTER^ 189 XEQ "YN-D" >>> Date = 1248.0707
Flag F00 is set: 1248 is a leap year
Notes:
-This program works for positive and negative years,
but it doesn't work in 1582 between October 15th and December
31st ( subtract 10 to DOY )
-LBL 00 ( lines 62 to 81 ) determines whether a given year is
a common year ( F00 is cleared ) or a leap year ( F00 is set )
-These lines may constitute a separate subroutine.
b) Program#2 - TIME Module
required
-Here is a shorter version if you have a TIME Module
Data Registers: /
Flags: F04 & F00
Set flag F04 for the Julian Calendar
F00 is cleared for a common year
Clear flag F04 for the Gregorian Calendar
F00 is set for a leap year
Subroutines: /
01 LBL "DOY"
02 FRC
03 LASTX
04 INT
05 XEQ 00
06 RDN
07 ABS
08 E2
09 *
10 XEQ 02
11 +
12 1.01
13 LASTX
14 +
15 X<>Y
16 DDAYS
17 1
18 +
19 DMY
if DMY is your favorite format
20 RTN
21 LBL "YN-D"
22 X<>Y
23 STO M
24 XEQ 00
25 SIGN
26 -
27 XEQ 02
28 1.01
29 +
30 X<>Y
31 DATE+
32 E2
33 *
34 INT
35 E4
36 /
37 RCL M
38 SIGN
39 *
40 0
41 X<> M
42 +
43 DMY
if DMY is your favorite format
44 RTN
45 LBL 00
46 MDY
47 CF 00
48 1
49 %
50 FRC
51 FC? 04
52 X#0?
53 GTO 01
54 X<> L
55 INT
56 4
57 MOD
58 ST+ Y
59 LBL 01
60 CLX
61 4
62 MOD
63 X=0?
64 SF 00
65 RTN
66 LBL 02
67 2001
68 FS? 00
69 DSE X
70 E6
71 /
72 END
( 124 bytes / SIZE 000 )
1- Date >>> Day of the Year
| STACK | INPUTS | OUTPUTS |
| X | YYYY.MNDD | DOY |
Example:
CF 04 ( Gregorian Calendar ) 2134.0707
XEQ "DOY" >>>> doy = 188 Flag F00 is clear:
2134 is a common year
SF 04 ( Julian Calendar )
1248.0707 XEQ "DOY" >>>> doy = 189
Flag F00 is set: 1248 is a leap year
2-Day of the Year >>> Date
| STACK | INPUTS | OUTPUTS |
| Y | YYYY | / |
| X | N | YYYY.MNDD |
Example:
CF 04 ( Gregorian Calendar ) 2134 ENTER^
188 XEQ "YN-D" >>> Date = 2134.0707
Flag F00 is clear: 2134 is a common year
SF 04 ( Julian Calendar )
1248 ENTER^ 189 XEQ "YN-D" >>> Date = 1248.0707
Flag F00 is set: 1248 is a leap year
Notes:
-This program works for positive and negative years,
but it doesn't work in 1582 between October 15th and December
31st ( subtract 10 to DOY )
-LBL 00 ( lines 45 to 65 ) determines whether a given year is
a common year ( F00 is cleared ) or a leap year ( F00 is set )
4°) Tropical Year
-A Julian Year has 365.25 days and a Gregorian Year has 365.2425
days
-Actually, the tropical year slowly varies with time
-This short routine ( based on the VSOP 87 theory ) calculates
the number of days of a mean tropical year.
01 LBL "TY"
02 2 E3
03 -
04 ENTER^
05 STO Z
06 3 E17
07 /
08 4 E13
09 1/X
10 -
11 *
12 26144 E-13
13 -
14 *
15 6 E-7
16 +
17 *
18 .60643
19 +
20 *
21 3600076975
22 +
23 13149 E8
24 X<>Y
25 /
26 END
( 73 bytes / SIZE 000 )
| STACK | INPUTS | OUTPUTS |
| X | YYYY | number of days |
Examples:
-4000 XEQ "TY" >>> 365.242506
days
-2000
R/S
365.242420 days
0
R/S
365.242311 days
2000
R/S
365.242190 days
4000
R/S
365.242069 days
6000
R/S
365.241961 days
-So the Gregorian Calendar would have been perfect in the year
3841 B.C.
References:
Jean Meeus , "Astronomical Algorithms" - Willmann-Bell - ISBN
0-943396-35-2
PPC ROM user's manual
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