NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Review of the Longhand Haversine Sight Reduction method
From: Gary LaPook
Date: 2015 Jun 27, 18:25 +0000
From: Hanno Ix <NoReply_HannoIx@fer3.com>
To: garylapook@pacbell.net
Sent: Saturday, June 27, 2015 9:41 AM
Subject: [NavList] Re: Review of the Longhand Haversine Sight Reduction method
H
From: Gary LaPook
Date: 2015 Jun 27, 18:25 +0000
I read those.
"I only show finding the 4 leading digits of the product which is what I need for CelNav. There is a way, not described here, to continue the patterns so as to yield the full result. The www has examples of the full procedure.
Stopping a multiplication will cause a truncation, not a rounding, of the product. That truncation causes a systematic positive error, and I have made a simulation that shows that error's mean as being very close to 6 units of the 5th digit to the right. That's what one would expect. It can be included in the scheme as a carry 6, shown in red, into the 4th column. Also according to this simulation, most truncation errors are 6 +-1.5. Good enough for me.
This method reduced my multiplication error rate drastically to the point of becoming actually useful. Before I just could never trust my results. The orderly record keeping of even the smallest details make the process easy to check. Others don't need all that, they barely make any errors. I wish I did!
H"
My question is if the butterfly algorithm is valid then it should produce a completely accurate answer and you only end up computing a partial answer. I also looked on the internet for an explanation and couldn't find one. How about showing us the complete computation.
gl
From: Hanno Ix <NoReply_HannoIx@fer3.com>
To: garylapook@pacbell.net
Sent: Saturday, June 27, 2015 9:41 AM
Subject: [NavList] Re: Review of the Longhand Haversine Sight Reduction method
Gary,
would you mind re-reading my posting, particularly the last 2 or 3 paragraphs?On Sat, Jun 27, 2015 at 6:01 AM, Gary LaPook <NoReply_LaPook@fer3.com> wrote:
I followed your mulitplication on your form:But it appears that you only got the right answer (truncated) by adding a "fudge factor" of "6." Without that you would not have gotten the correct answer. You said it is a "carry," a carry from where? If this method of multiplication is good then why doesn't it produce the correct answer of 12196860 that could be rounded off if needed. Where are the rest of the digits in the multiplication result?gl
