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The forensics algorithm for the 10s - Printable Version

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The forensics algorithm for the 10s - Palmer O. Hanson, Jr. - 01-19-2010

I had a good weekend for collecting by finding a Pickett N-500S in very good condition for two dollars, a old paper reactance slide rule by Shure for a dollar, and a HP-10s for three dollars.

I ran Mike Sebastian's forensic algorithm on the 10s. The answer is 9.000000002124 . The eight zeroes after the decimal point makes the result better than any other HP machine listed at Mike's site. Am I doing something incorrectly or is the 10s really that good?


Re: The forensics algorithm for the 10s - Gerson W. Barbosa - 01-19-2010

Quote:
The answer is 9.000000002124 . The eight zeroes after the decimal point makes the result better than any other HP machine listed at Mike's site.

The HP-30S, also listed at the site, returns 9.000000000, for which Rodger Rosenbaum has provided an explanation:

http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv015.cgi?read=85973

Edited: 19 Jan 2010, 10:48 p.m.


Re: The forensics algorithm for the 10s --> 30b - Katie Wasserman - 01-19-2010

The 30b comes in at 8.99999864267, the same as the Pioneers (20S, 32S, etc.).

-Katie




Re: The forensics algorithm for the 10s - Palmer O. Hanson, Jr. - 01-20-2010

The end of Rodger's dissertation states:

Quote:
So finally, this is why the HP30S gets exactly 9.00000000000000000 when running the calculator forensics test. To see the real error, one should subtract the input argument of the test from the final result. That is, do:


arcsin(arcos(arctan(tan(cos(sin(9))))))-9


On the HP30S, the result is 0, leading one to believe that the HP30S is *really* accurate. But redo the test as:


arcsin(arcos(arctan(tan(cos(sin(9.1))))))-9.1


to foil its rounding near integers and see a result: 4.833288903E-11


Not all that great for a calculator that can do 24 digit calculations, eh?


I did the Rodger's 9.1 version of the forensics algorithm on my 10s and received 9.100000002602 . Does that suggest that the 10s isn't doing any of the funny arithmetic that Rodger was writing about?


Re: The forensics algorithm for the 10s - Gerson W. Barbosa - 01-20-2010

Quote:
Does that suggest that the 10s isn't doing any of the funny arithmetic that Rodger was writing about?

Yes, apparently the 10s isn't doing any trick to make it look more accurate than it really is, otherwise it would return 9.00000000000 in the original test. Assuming the algorithms are correct, it is possible internal calculations are carried out with 15 or 16 digits internally. On classic 12-digit HP calculators intermediate results are rounded to the number of digits of the display, so the forensic results will be a bit away from 9, even though the algorithms are flawless:

http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv016.cgi?read=103151

It looks like HP is back to its original philosopy (see Katie's result for the 30b below).