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What calculator do you use ?

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saturation:
Yes, it affects only the generation of FX that look like the FX260.  Here is a 'family' photo spanning 30 years.

Once in the VPAM or graphing Casios, that error is not there.

The left is the FX-100 that I used in college in the late 1970s.  The lower right is the credit card FX-98, which is nearly identical to the 100 except its 8 digits, and thus, rounds out the same error.  Finally on the right is the modern Fx-260.





--- Quote from: baljemmett on April 23, 2012, 04:52:49 pm ---
--- Quote from: saturation on April 23, 2012, 03:54:58 pm ---For example, for financial transactions try this simple mortgage table:

200000 (1 + 0.06/360)^(360*30)

Casio scientifics have a small rounding issue, as seen in the FX260 and other models, it returns 1209747.95.

The right answer is 1209748.04, which can be done with higher precision calculators or better rounding.

--- End quote ---

Interesting -- the Casios have obviously gone backwards sometime since the mid-80s/early-90s, then!  Just tried that on my fx-7000GB and got 1209748.042; doing it in Fix2 mode also gives 1209748.04.

--- End quote ---

amspire:

--- Quote from: slateraptor on April 23, 2012, 01:38:17 pm ---
--- Quote from: ejeffrey on April 23, 2012, 01:13:55 pm ---So financial calculations must be done either with integers (representing cents), or decimal (BCD) representations.

--- End quote ---

Learn something new everyday. I suppose that would explain the BCD-encoded registers in older HP CPU architectures.

Are there any handheld calculators that actually use double-precision floats?

EDIT: Evidently, a few Sharp querty handhelds fit the bill...doesn't seem to be many without diving into the user-space realm.

--- End quote ---
As far as I know, all HP calculators use BCD binary internally. The modern calculators using ARM processors(or whatever they use) are running emulators of the older HP calculator processor chips which are all based around BCD registers.

Richard.

baljemmett:

--- Quote from: saturation on April 23, 2012, 11:07:50 pm ---Yes, it affects only the generation of FX that look like the FX260.  Here is a 'family' photo spanning 30 years.

Once in the VPAM or graphing Casios, that error is not there.

--- End quote ---

Yes, I just grabbed my other two and tried the same thing; the fx-6300G (early-90s 'baby graphic', newer than the one I tried at work) gives exactly the rounding error you mentioned, 1209747.95, whereas the CFX-9850G (mid-90s colour 'power graphic') gives the correct (to displayed resolution) 1209748.037.

I wish I knew where the 'just a normal scientific calculator' fx-85M and fx-85V models I remember using as a kiddie had got to, would be interesting to try it on them too...

I guess it goes to show how valuable it can be to characterise your tools, to work out what level of precision you can depend upon!

HLA-27b:
Casio fx-5800P displays 1209748.037
SpeedCrunch which I use instead of windows calculator displays 1209748.037229630210239761

SpeedCrunch is highly recommended btw.

saturation:
Yes, since all calculators have to round in the end, the more digits or bits it uses to represent a digit, the less likely the rounding error will appear.   Of course, some algorithms are worse than others depending on how they round and what they round. 

I recall some calculator-nuts did benchmark testing using formulas designed to 'expose' these types of errors, see here and enjoy!

http://www.rskey.org/~mwsebastian/miscprj/forensics.htm

http://voidware.com/calcs/torturetest.htm




--- Quote from: HAL-42b on April 23, 2012, 11:51:55 pm ---Casio fx-5800P displays 1209748.037
SpeedCrunch which I use instead of windows calculator displays 1209748.037229630210239761

SpeedCrunch is highly recommended btw.

--- End quote ---

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