Calculator Forensics results

General discussion about calculators, SwissMicros or otherwise
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HPMike
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Calculator Forensics results

Post by HPMike »

There is a website https://www.rskey.org/~mwsebastian/misc ... ensics.htm that describes an algorithm intended to help identify the underlying calculator processor that is being used in a particular calculator brand and model. Often times the chip set from a particular manufacturer was the basis for many different calculator brands. For example, the Texas Mostek RPN chipset was used in the APF Mark 55, Omron 12SR, Privileg SR54CC, Corvus 500 and Sanyo CZ2901. When running the algorithm, all calculators using the same chipset produce the same numeric result. The evaluation algorithm is as follows:

arcsin (arccos (arctan (tan (cos (sin (9)))))) with the calculator set to degrees mode.

The exact result is 9, but the vast number of calculators produce a different result due to peculiarities in the function algorithms and number of digits of accuracy. In the case of the Texas Mostek based calculators, the result is 8.99999614252. So, how do the SwissMicros calculators compare against their HP counterparts ? Well, the DM15 and DM41X are both faithful reproductions of the HP-15C and HP-41C, so not surprisingly they all produce the same result, which is 9.000417403. However, the DM42 which is based not on the HP42S, but instead on the Free42 emulator, yields 9.00000000000, whereas the HP42S produces 8.99999864267. This suggests, that the math algorithms used in the Free42 emulator and carried over to the DM42 are a bit more precise than the original HP42S. No doubt Thomas Okken can explain this in more detail. Perhaps the SwissMicros claim that the DM42 is the most precise calculator on the worldwide market is not hyperbole.
DM15L, S/N 00548. DM42, SN: 00159. DM41X, SN: 00973.
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Walter
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Re: Calculator Forensics results

Post by Walter »

AFAIK Free42 calculates with 34 digits which is a bit more than what the HP-42 uses. This is a simple explanation for different results in that test.
DM42 SN: 00041 β
WP 43S running on this device

HP-35, HP-45, ..., HP-35S, WP 34S, WP 31S, DM16L
bernouilli
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Re: Calculator Forensics results

Post by bernouilli »

Free42 works with about 34 significant digits. If you substrat 9 to the forensic result, you get something like 6e-29, which is very small, due to the high precision.
Some others calculators have an extended precision like the sharp pc1475 (20 digits) or the wp34s (32 digits?).
DM15L - DM42 - DM41x
Thomas Okken
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Re: Calculator Forensics results

Post by Thomas Okken »

Note that even though it works with 34 digits, Free42 will only display up to 12 digits, like the HP-42S. You can see the contents of the X register at full precision using SHOW, i.e. [Shift] [.]. SHOW will show the full precision for 2 seconds before reverting to the normal display, but you can see it longer by holding down the [.] key.
HPMike
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Re: Calculator Forensics results

Post by HPMike »

So the result with Free42 is 8.999999999999999999999999999937534. Amazing !
DM15L, S/N 00548. DM42, SN: 00159. DM41X, SN: 00973.
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Walter
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Re: Calculator Forensics results

Post by Walter »

HPMike wrote:
Tue Dec 01, 2020 2:28 am
So the result with Free42 is 8.999999999999999999999999999937534. Amazing !
As amazing as WP34S since 2011 and WP43S... 8-)

EDIT: Sorry, I forgot a deviation of 1e-34 (sic!). The WP34S produces the correctly rounded result ...37535 as well as the WP43S. Merci to Over_score for reminding me.
Last edited by Walter on Tue Dec 01, 2020 9:46 pm, edited 2 times in total.
DM42 SN: 00041 β
WP 43S running on this device

HP-35, HP-45, ..., HP-35S, WP 34S, WP 31S, DM16L
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Over_score
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Re: Calculator Forensics results

Post by Over_score »

WP43S returns 8.999 999 999 999 999 999 999 999 999 937 535 and this result is correctly rounded
The result of free42 is not!
The correctly rounded intermediate calculations are:
sin(9) = 0.1564344650402308690101053194671669
cos(0.1564344650402308690101053194671669) = 0.9999962727428850241175162050113502
tan(0.9999962727428850241175162050113502) = 0.01745499985548866079139414092834847
arctan(0.01745499985548866079139414092834847) = 0.9999962727428850241175162050113503
arccos(0.9999962727428850241175162050113503) = 0.1564344650402308690101053194660901
arcsin(0.1564344650402308690101053194660901) = 8.999999999999999999999999999937535
DM42 (SN 00284 & 03835), DM15L, HP41CV, HP42S, HP35s, WP34S, HP Prime
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