Number of Days After January 1
03-11-2019, 02:25 AM
Post: #1
 Eddie W. Shore Senior Member Posts: 1,383 Joined: Dec 2013
Number of Days After January 1
Introduction

The program DATENO calculates the number of days from January 1. The program prompts whether we are working in a leap year or not.

With D = Day and M = Month, the days between January 1 and any other date within the calendar year is:

If M = 1 and M = 2 Then
DATE# = int(30.6 * M + 368.8) + D - 400

Otherwise,
DATE# = int(30.6 * M + 1.6) +D - 35 (non-leap year)
DATE# = int(30.6 * M + 1.6) + D - 34 (leap year)

HP 41C/DM 41L Program: DATENO

(^T: beginning of an alpha string)

Code:
01 LBL^T DATENO
02 ^T MONTH
03 PROMPT
04 STO 01
05 ^T DAY?
06 PROMPT
07 STO 02
08 ^T LEAP? N=0,L=1
09 PROMPT
10 STO 03
11 RCL 01
12 3
13 X<=Y?
14 GTO 00
15 30.6
16 RCL 01
17 *
18 368.8
19 +
20 INT
21 RCL 02
22 +
23 400
24 -
25 GTO 01
26 LBL 00
27 RCL 01
28 30.6
29 *
30 1.6
31 +
32 INT
33 RCL 02
34 +
35 35
36 -
37 RCL 03
38 +
39 LBL 01
40 STO 04
41 END

Examples

Days between January 1 and February 16 (M = 2, D = 16): 46

Days between January 1 and October 1 (M = 10, D = 1):
(Non-leap year): 273
(Leap year): 274

03-11-2019, 06:53 PM (This post was last modified: 03-11-2019 07:00 PM by Dieter.)
Post: #2
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: Number of Days After January 1
(03-11-2019 02:25 AM)Eddie W. Shore Wrote:  The program DATENO calculates the number of days from January 1.

Maybe you should add 1 to the result to get the more common "day of year", i.e. 1 January = day 1 and 31 December = day 365.

(03-11-2019 02:25 AM)Eddie W. Shore Wrote:  If M = 1 and M = 2 Then
DATE# = int(30.6 * M + 368.8) + D - 400

What about 31*M + D -32 ?-)

Anyway, here is my attempt at a day-of-year program. I have derived the formulas myself, so beware. ;-) Please try it and report any errors you find.

Code:
01 LBL "DOY"
02 4
03 MOD
04 X≠0?
05 SIGN
06 CHS
07 STO T
08 RDN
09 30,6
10 *
11 31,3
12 -
13 50
14 X>Y?
15 GTO 01
16 RDN
17 INT
18 +
19 +
20 GTO 02
21 LBL 01
22 RDN
23 1,2
24 +
25 INT
26 +
27 LBL 02
28 END

Usage:
day [ENTER] month [ENTER] year XEQ "DOY"

If you prefer month, day, year instead simply insert an X<>Y command between line 08 and 09.

The program automatically checks for leap years, this works for all dates between 1 January 1901 and 28 February 2100.

Example:
1 [ENTER] 10 [ENTER] 1999 XEQ"DOY" => 274
1 [ENTER] 10 [ENTER] 2000 XEQ"DOY" => 275

Dieter
03-11-2019, 08:30 PM
Post: #3
 Thomas Klemm Senior Member Posts: 1,804 Joined: Dec 2013
Number of Days After March 1st
(03-11-2019 02:25 AM)Eddie W. Shore Wrote:  The program DATENO calculates the number of days from January 1.

Somewhat related is the following program from the article Sunrise and Sunset.

Here it is adapted for the HP-42S:
Code:
00 { 30-Byte Prgm }
01 IP
02 12
03 LASTX
04 FP
05 100
06 ×
07 3
08 -
09 X<0?
10 +
11 30.6
12 ×
13 0.5
14 +
15 IP
16 R↑
17 +
18 END

Examples:

1.03 R/S
1

28.02 R/S
365

29.02 R/S
366

This avoids having to deal with leap years.

Cheers
Thomas
03-14-2019, 07:20 PM
Post: #4
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: Number of Days After January 1
(03-11-2019 02:25 AM)Eddie W. Shore Wrote:  If M = 1 and M = 2 Then
DATE# = int(30.6 * M + 368.8) + D - 400

Otherwise,
DATE# = int(30.6 * M + 1.6) +D - 35 (non-leap year)
DATE# = int(30.6 * M + 1.6) + D - 34 (leap year)

Eddie, you can simplify these formulas significantly.
Since D and 400 are positive integers...

int(30.6 * M + 368.8) + D - 400
= int(30.6 * M + 368.8 + D - 400)
= int(30.6 * M + D - 31.2)

Or here (D=1 or 2) simply

= int(30.6 * M + D - 31)

The two other formulas can be simplified the same way.
Or they can be derived from the Jan/Feb formula.

With L=0 (common year) or 1 (leap year):

days = 30.6 * M + D - 31
if M >= 3 then days = days - 2.3 + L
return int(days)

Note: according to your formulas the final 2.3 would be 2.4, but subtracting only 2.3 leaves a fractional part between 0.1 and 0.9 so that roundoff problems are avoided (e.g. in non-decimal environments) that may lead to cases like int(242.9999999....) for 1 September.

Here is a version of your HP-41C program that implements this idea.

Code:
01 LBL "DAYD"
02 "MONTH↑DAY ?"
03 PROMPT
04 RCL Y
05 30.6
06 *
07 +
08 31
09 -
10 X<>Y
11 3
12 X>y?
13 GTO 01
14 2.3
15 ST- T
16 R↑
17 "LEAP YR 0/1?"
18 PROMPT
19 +
20 STO Z
21 LBL 01
22 RCL Z
23 INT
24 END

XEQ "DAYD"
MONTH↑DAY ?
10 [ENTER] 1 [R/S]
LEAP YR 0/1?
0 [R/S]

=> 273

Note that the program only prompts for a leap year input if this is required, i.e. for months between March and December.

Dieter
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