The most accurate scientific calculator??

[zeno333]

If one includes calculators that run on a Smartphone as a pocket calculator, the most accurate scientific calculator I know about is the "Champ Pro" for Android. It does the square root of 2 to 117 decimal places, and can display all digits. Is there another more accurate scientific out there I do not know about??

[Joe Horn]

(11-28-2018 12:04 PM)zeno333 Wrote:  If one includes calculators that run on a Smartphone as a pocket calculator, the most accurate scientific calculator I know about is the "Champ Pro" for Android. It does the square root of 2 to 117 decimal places, and can display all digits. Is there another more accurate scientific out there I do not know about??

The HP 50g with the LongFloat library installed can be set to do almost all calculations (including square roots) to any desired number of significant digits, up to 9999.

[Garth Wilson]

Does the accuracy match the precision though, particularly in functions that are calculated by polynomials with tweaked coefficients to take the place of infinite series?

[Joe Horn]

(11-28-2018 07:52 PM)Garth Wilson Wrote:  Does the accuracy match the precision though, particularly in functions that are calculated by polynomials with tweaked coefficients to take the place of infinite series?

If you are referring to the LongFloat library for the HP 50g, its documentation says that "All results is [sic] calculated within +/- 1 in last digit." The only exception seems to be its FGAMMA function which is "only guaranteed to 32 digits" regardless of the current DIGITS setting.

[Jim Horn]

There was a posting some time back to an article about an Android app with essentially unlimited precision. When used, it would let the user scroll the display to show more digits of its calculation, while computing more digits as needed. I downloaded and tried it - very interesting! Unfortunately, the phone I had died and I've not found the reference with the Forum's search feature.

[cdmackay]

(11-29-2018 04:36 AM)Jim Horn Wrote:  There was a posting some time back to an article about an Android app with essentially unlimited precision. When used, it would let the user scroll the display to show more digits of its calculation, while computing more digits as needed. I downloaded and tried it - very interesting! Unfortunately, the phone I had died and I've not found the reference with the Forum's search feature.

Google search for "android calculator arbitrary precision" produces lots of possibilities, hopefully it is one of those?

[John Keith]

(11-29-2018 04:36 AM)Jim Horn Wrote:  There was a posting some time back to an article about an Android app with essentially unlimited precision. When used, it would let the user scroll the display to show more digits of its calculation, while computing more digits as needed. I downloaded and tried it - very interesting! Unfortunately, the phone I had died and I've not found the reference with the Forum's search feature.

Possibly Pari/GP? But Pari has a command line interface, not what most would consider a "calculator".

[Jim Horn]

The continuously variable precision scientific calculator I read about (and have) is the Google android calculator from their Play Store. Now, to try to find the technical article on its development which was a fascinating one...

[Jim Horn]

Oh, here it is: The article, "Small-Data Computing: Correct Calculator Arithmetic" is at:
https://cacm.acm.org/magazines/2017/8/21...g/fulltext

Enjoy!

[Albert Chan]

Thanks for the article

Quote:It is still possible for previously displayed digits to change as we are scrolling.
But we always compute a number of digits more than we actually need, so this is exceedingly unlikely.

Since our goal is an error of strictly less than one in the last displayed digit,
we will never, for example, display an answer of exactly 2 as 1.9999999999.
That would involve an error of exactly one in the last place, which is too much for us.

From the description, precision is great, but not good enough for title "most accurate"

I believe the winner goes to spigot
All outputted digits are guaranteed correct

If precision is not supplied, it will run forever (until memory are exhausted)

[Sukiari]

If you’re talking about calculators with “stock” firmware the WP-34s and the DM-42 both use Intel’s decimal128 library, making them the most accurate calculators in the floating point domain. With integers the 50G wins, with its built in arbitrary length integer math.

[Paul Dale]

(12-04-2018 08:44 AM)Sukiari Wrote:  If you’re talking about calculators with “stock” firmware the WP-34s and the DM-42 both use Intel’s decimal128 library, making them the most accurate calculators in the floating point domain.

The WP 34S does not use Intel's library. It uses the decNumber library for the basic operations and everything else is implemented on top of this. I'm aware of a couple of instances where the 34S rounds correctly whereas Intel's library is off by one in the last digit. I'm not aware of the reverse (yet).


Pauli

[Sukiari]

(12-04-2018 09:34 AM)Paul Dale Wrote:  

(12-04-2018 08:44 AM)Sukiari Wrote:  If you’re talking about calculators with “stock” firmware the WP-34s and the DM-42 both use Intel’s decimal128 library, making them the most accurate calculators in the floating point domain.

The WP 34S does not use Intel's library. It uses the decNumber library for the basic operations and everything else is implemented on top of this. I'm aware of a couple of instances where the 34S rounds correctly whereas Intel's library is off by one in the last digit. I'm not aware of the reverse (yet).


Pauli

Thanks for the information and your kind work. I purchased a hard copy manual and enjoy it as well.