Mike Sebastian's Calculator Forensics

[Joerg Woerner]

Hi Folks,

There is still room for improvement - THIS $15.95 calculator checked out with 18 (!) digits of resolution and reported an unparalleled result of:

9.00000000000072767

Yes, TWELVE ZEROES behind the decimal point.

Cheers,

Joerg

[John B. Smitherman]

Wow! Does it glow in the dark? ;-)

John

[Joerg Woerner]

No, but in the US you'll see only this bright lime green. In UK they have wonderful teal and pink versions, too. All made of recycled photocopiers and anti-bacterial keyboards ;-))

Regards,
Joerg

[Frank Boehm (Germany)]

when doing your time travel calculations and including the expansion of the universe with appropriate accuracy to not miss the bus.
Otherwise this might only be useful to calculate the total worldwide debt :)
(Btw. the Sanyo ICC-804D had 16 digit precision back in 1971 - but no nifty functions besides 4 basic operations and on/off)

[Marcus von Cube, Germany]

Hi Jörg,

can you let it calculate tan 89.999999 degrees? There is a recent discussion about trig precision near discontinuities which revealed some astonishing results.

[Joerg Woerner]

tan (89.999999) = 57295779.51... like my TI-36X on the desk, too.

Rgeards,
Joerg

[Marcus von Cube, Germany]

Thanks Jörg! What do you get if you subtract the integer part?

[Joerg Woerner]

57295779.5130823151 on the Canon and

57295779.5132 on the TI-36X

Joerg

[Marcus von Cube, Germany]

The Canon is extremely accurate. The result is correctly rounded to the last digit. (The last digit should be a 0 and the following a 5. Taking rounding into account, the result is perfect.)

[Paul Dale]

The 34s only gets 10 zeros after the decimal:

        9.000000000029361

This is, however, the correctly rounded result for devices with sixteen digits. I.e. each operation correctly rounded its answer.

Pauli

[Marcus von Cube, Germany]

Pauli, that's the point. The forensics is not meant to highlight the accuracy of a certain calculator but to identify identical algorithms and/or calculator chips.

[Walter B]

Quote:

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The forensics is not meant to highlight the accuracy of a certain calculator but to identify identical algorithms and/or calculator chips.

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True for this level of precision we're talking about here. In general, however, the forensics sheds some light on the reliability of calculation results. Think of error propagation in iterative computations ...

[Gerson W. Barbosa]

Paul,

The WP-34s displays 9.00000000003, that is, the internal result is rounded to the number of digits of the display. HP used to round the result and truncate it to the number of digits in the display at the end of each operation. Thus, the HP-42S displays 8.99999864267. HP's method makes sense because the results of the operations are coherent to the actual figures of the operands the user has access to (by examining their mantissas, for instance).

I assume the 34s is a 16-digit device, but the calculations are carried out with extra guard digits, otherwise it wouldn't achieve the correct rounded 16-digit result we see. Another reason to get the WP-34s as soon it's available :-)

Correct result for various numbers of digits in this old thread.

Regards,

Gerson.

[Marcus von Cube, Germany]

Gerson, wp34s *is* on the agenda. :)

[Paul Dale]

Try subtracting 9 from that result :-)

Yes, the 34s is a 16 digit device. Registers are IEEE 854 64 bit packed decimals. As you guessed, internal calculations are in higher precision using unpacked decimal numbers.

I could round to the display size (12 digits) easily enough. For a variety of reason I didn't.

- Pauli

Edited: 10 Mar 2011, 1:34 a.m.

[Gerson W. Barbosa]

Quote:

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Try subtracting 9 from that result :-)

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Not necessary. I just pressed 'F' to see the full stack to 16 digits.

Quote:

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I could round to the display size (12 digits) easily enough. For a variety of reason I didn't.

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I'm glad you didn't.

Regards,

Gerson.