Precision
02-13-2022, 10:39 AM (This post was last modified: 02-13-2022 02:04 PM by kuenze.)
Post: #1
 kuenze Junior Member Posts: 8 Joined: Nov 2019
Precision
Programming some Astro formulas in HPPL I found some precision issues; if one can get higher precision data types, please let me know.
The textbook I am working with shows the following result for the expression mentioned later: M= 350 °.1010164

with the HP Prime I get:
M=(357.52772+35999.05034*0.139780971+0.04106667845*14.39333329) mod360

M= 350°.10101799

Help is greatly appreciated, greetings Kuenze
02-13-2022, 03:25 PM
Post: #2
 thenozone Member Posts: 61 Joined: Mar 2017
RE: Precision
wolfram alpha shows the digits after the decimal as .1010179931242506005
02-13-2022, 04:24 PM
Post: #3
 StephenG1CMZ Senior Member Posts: 1,036 Joined: May 2015
RE: Precision
There is an extended precision program in the library that might help.

Stephen Lewkowicz (G1CMZ)
https://my.numworks.com/python/steveg1cmz
02-13-2022, 05:09 PM (This post was last modified: 02-13-2022 05:25 PM by C.Ret.)
Post: #4
 C.Ret Member Posts: 257 Joined: Dec 2013
RE: Precision
(02-13-2022 10:39 AM)kuenze Wrote:  The textbook I am working with shows the following result for the expression mentioned later: M= 350 °.1010164
with the HP Prime I get:
M=(357.52772+35999.05034*0.139780971+0.04106667845*14.39333329) mod360
M= 350°.10101799

Your notation is illegal, you may have express M as dd.ddddddd° or dd°mm'ss.sss"
I am not sure I correctly interpret your strange notation !?

The result you get completely agree the inputs you give.
At least, you can manage to better use the internal precision of the HP Prime by extracting the fractional parts of the arguments with FP().

[attachment=10363]

This way you may indirectly get M = 350.10101799004° or 350°06'03.66476"
But nothing closer to the textbook result 350°.1010164 (aka 350.1010164° or 350°06'03.65904" )
Note that if THIS is the notation used in your textbook, please close it and go buying a better one.

Are you sure you are using the exact inputs from the book (with the same exactly full precision ?). Ins't any rounding or hidden decimals in the printed values in the book ?

Another question, is it of a great importance that you get an error in the range of 5/10³ of a second ?
I am really curious the name and the price of the astrological instrument you are currently planning to use ?
02-13-2022, 09:19 PM
Post: #5
 kuenze Junior Member Posts: 8 Joined: Nov 2019
RE: Precision
Dear C.Ret,

i am working with Meeus, Astronomical Algorithms German Edition 1992. the Author mentions the "old astronomical praxis" to write 28°.5793 for 28.5793 degrees. (Meeus 1992, p.13)
The other Textbook with the problematic calculations is K.A. Zischka:Astronavigation.Springer 2018. There are lots of errata in this book, the example I use(d) makes only sense when you change the date (JJJJ/MM/DD/HH/MinMin/SS) of the calculation from 2013/12/24/14/25/36 to 2013/12/24/14/23/36.
The Text also confuses "l" and "1" in print.
I guess you are right in that I should not continue to work with this book. Funny, Springer charges some 140 Euros for the book...
How precise does my program need to be?
Meeus writes about mistakes that cumulate and I don't know if some terms will generate a result further off then .25´.
i want to get the data and the algorithm for sight reductions for Maritime navigation, and most textbooks on that agree that a precision of about 0.2´is all you need.

Your notation is illegal, you may have express M as dd.ddddddd° or dd°mm'ss.sss"
I am not sure I correctly interpret your strange notation !?

The result you get completely agree the inputs you give.
At least, you can manage to better use the internal precision of the HP Prime by extracting the fractional parts of the arguments with FP().

This way you may indirectly get M = 350.10101799004° or 350°06'03.66476"
But nothing closer to the textbook result 350°.1010164 (aka 350.1010164° or 350°06'03.65904" )
Note that if THIS is the notation used in your textbook, please close it and go buying a better one.

Are you sure you are using the exact inputs from the book (with the same exactly full precision ?). Ins't any rounding or hidden decimals in the printed values in the book ?

Another question, is it of a great importance that you get an error in the range of 5/10³ of a second ?
I am really curious the name and the price of the astrological instrument you are currently planning to use ?
[/quote]
02-13-2022, 09:28 PM
Post: #6
 kuenze Junior Member Posts: 8 Joined: Nov 2019
RE: Precision
here is the page 296/97 from Zischka. greetings Kuenze
the typo in Step 7 and Step 11 is a real challenge.

Attached File(s)
02-13-2022, 09:32 PM
Post: #7
 kuenze Junior Member Posts: 8 Joined: Nov 2019
RE: Precision
Wonderful that the prime ist beating the Springer Text book! Thanks, Kuenze

(02-13-2022 03:25 PM)thenozone Wrote:  wolfram alpha shows the digits after the decimal as .1010179931242506005

Attached File(s)