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pito · (This post was last modified: 06-07-2014 01:23 PM by pito.)

(06-06-2014 10:55 PM)Paul Dale Wrote: Alpha padded the result with semi-random digits just like I asked for.
- Pauli

In Wolfram Alpha:

Code:

With 120 digits of "precision" (use "xxx`ndigits"):

cos(1.57079632679489661923132169163975144`120)

2.098584699687552910487472296153908203143104499314017412671058533991074041716259​78775626172739947883181185207919839... × 10^-36

With 120 digits of "accuracy" (use "xxx``ndigits"):

cos(1.57079632679489661923132169163975144``120)

2.098584699687552910487472296153908203143104499314017412671058533991074041716259​78775626172739947883181185207919839... × 10^-36

And the quick test from the top of this thread:

Code:

1.0000001`120 ^ (2`120 ^ 27`120)

674530.4707410845593826891780297468128444441434103420317423773278390177617568356​46924185036948314117161449392236580649487...

Paul Dale · (This post was last modified: 06-07-2014 12:20 PM by Paul Dale.)

(06-07-2014 11:56 AM)pito Wrote: In Wolfram Alpha:

Code:

With 120 digits of "precision": cos(1.57079632679489661923132169163975144`120) 2.09858469968755291048747229615390820314310449931401741267105853399107404171625978775626172739947883181185207919839... × 10^-36 ...

Ahh, the problem seems to be the decimal point limiting the number of significant digits. Adding zeros would increase the number of digits used and hence the correct result.

Expressing the decimal number as a rational yields the result we're looking for:

Code:

cos(157079632679489661923132169163975144/1e35)

- Pauli

pito · (This post was last modified: 06-07-2014 05:59 PM by pito.)

(06-07-2014 12:20 PM)Paul Dale Wrote: ..
Ahh, the problem seems to be the decimal point limiting the number of significant digits. Adding zeros would increase the number of digits used and hence the correct result.

Expressing the decimal number as a rational yields the result we're looking for:

We make Mr. Wolfram unhappy when not utilizing his recommendations.. Smile

We have to explicitly request an N digits precision with any number/constant and calculus (in Mathematica as well in Alfa), otherwise "machine precision" will be used instead.

So for example we want calculate with 666 digits precision:

Code:

 2.989 * sin ( 22.12 / 7.1 - 0.0023 )

It has to be entered into Alfa as:

Code:

 2.989`666 * sin ( 22.12`666 / 7.1`666 - 0.0023`666 )

In Mathematica (works in Alfa too]:

Code:

 N[2.989`666 * Sin ( 22.12`666 / 7.1`666 - 0.0023`666), 666 ]

Gerson W. Barbosa · 06-08-2014, 02:10 AM

(06-03-2014 10:06 PM)Massimo Gnerucci Wrote:
(06-03-2014 09:39 PM)Gerson W. Barbosa Wrote: Our university library had a subscription to Scientific American and lots of issues then. That's one of the few articles I still have a copy of. I hope they still have them. It might be cheaper to go there and scan the articles I am interested in than paying SciAm $7,99 each :-)

Gerson.

I've got all "Le Scienze" issues from 1968 to 2008 on 2 DVDs, unfortunately not all sections are present, only main articles.
However I found complete text online.

This way is better, though...

I know. That's why I've suggested "DECIMAL-POINT IS COMMA" :-)

https://www.google.com.br/webhp?sourceid...%2C0561%22

pito · (This post was last modified: 06-08-2014 01:54 PM by pito.)

(06-02-2014 10:37 PM)pito Wrote: A friend of mine has advised me today there is following quick precision test when testing better calculators in the shop:

Take 1.0000001 and do x^2 27times..

UPDATE:
Basic precision:

Code:

Calculator Display Display-INT Note ======================================================================= W.Alfa (Ref) 674530.470741 .4707410845 The reference ----------------------------------------------------------------------- Citizen SRP-325G 674530.4707411 ? basic precision, web source Citizen SRP-400G 674530.4707411 ? basic precision, web source Canon X Mk I Pro 674530.4707 .4707399243 Casio CPad300Plus 674530.4706 web source WP-34s 674530.47054 .4705396874 WP-31s 674530.47054 .4705396874 Canon F-715SG 674530.4702 .470205499 Olympia LCD-8110 674530.4702 .470205499 Ti-80 674530.318 .3180426 TI-83 Plus Silver 674529.4131 web source Ti-89 674529.413051 .41305068 TI-92 Plus 674529.413051 web source Casio fx-9860 674529.1121 web source Casio FX-6910AG 674529.1097 web source Sharp EL-W506X 674523.3747 .3747398 SR-52 674520.6053 web source TI-59 674520.6053 web source HP-50g 674514.86877 .86877 HP-35s 674514.86877 .86877 HP-39GII 674514.86877 web source HP Prime 674514.86877 web source HP-49g 674514.86877 web source HP-30b 674514.86877 web source Sigma GC 500 674512.576 .576 Casio FX-602p 674494.0561 web source HP-25 674494.05 .0561 Anitech SC100 674492.7511 .75112 Casio fx-3650P 674475.4416 web source Casio FX-702p 674475.3961 web source Casio fx-991MS 674472.4416 .441611 TI-57 674432.82 web source Truly SC106A 674294.1172 .1172 Casio FX-502p 674185.8477 web source

I've updated the list with calculators we've tested in situ (thanks Martin!) and found from available sources (web).

walter b · (This post was last modified: 06-08-2014 02:45 PM by walter b.)

(06-08-2014 12:44 PM)pito Wrote: Take 1.0000001 and do x^2 27times..

UPDATE:
Basic precision:

Code:

Calculator Display Display-INT ================================================= W.Alfa (Ref) 674530.470741 .4707410845 ------------------------------------------------- Canon X Mk I Pro 674530.4707 .4707399243 WP-34s 674530.47054 .4705396874 WP-31s 674530.47054 .4705396874

WP 34S and WP 31S share the same SW in that matter so it's no wonder they both return the same single precision result. After DBLON, however, the WP 34S displays 674530.470741 with a fractional part (FP) of 0.470741084559 Smile

And looking at its full precision via < and >, we see it is 0.4707410845593826891847277722). Anybody selling more, FWIW?

d:-)

P.S.: Wolfram alpha returns 674 530.470 741 084 559 382 689 178... at it's machine precision. If I counted correctly, that's a deviation of 10[super]-26[/super], FWIW.

pito · (This post was last modified: 06-08-2014 02:23 PM by pito.)

(06-08-2014 01:57 PM)walter b Wrote: Anybody selling more, FWIW?
d:-)

I've updated the table (a continuous update).. Smile

PS: maybe you have to rethink your marketing approach when "selling" your calculator..
I would set the Double as the default setting and sell it as the "standard precision".. Smile

walter b · 06-08-2014, 03:00 PM

(06-08-2014 02:07 PM)pito Wrote: ... maybe you have to rethink your marketing approach when "selling" your calculator..
I would set the Double as the default setting and sell it as the "standard precision".. :)

First of all you should quote Wolfram's result correctly.

And second: Your suggestions faintly reminds me on frequency meter ads in US-American electronic magazines I saw in the Eighties of last century, where some devices were shamelessly advertized as ppm or ppb meters just because they displayed the appropriate number of digits. No, what we're "selling" are real world calculators for real world problems - and IMHO even our single precision implemented covers most of them. Just compare the precision of physical constants (published e.g. by NIST) and you will know where the real world ends so far.

d:-/

walter b · 06-08-2014, 05:28 PM

(06-07-2014 04:44 PM)pito Wrote: We have to explicitly request an N digits precision with any number/constant and calculus (in Mathematica as well in Alfa), otherwise "machine precision" will be used instead.

So for example we want calculate with 666 digits precision:

Code:

2.989 * sin ( 22.12 / 7.1 - 0.0023 )

It has to be entered into Alfa as:

Code:

2.989`666 * sin ( 22.12`666 / 7.1`666 - 0.0023`666 )

In Mathematica (works in Alfa too]:

Code:

N[2.989`666 * Sin ( 22.12`666 / 7.1`666 - 0.0023`666), 666 ]

Hmmh, I went through all that and entered
(...((1.0000001`34)^2`34) ... )^2`34
into Alfa but it returned >34 digits nevertheless. What did I miss?

d:-?

Paul Dale · 06-08-2014, 10:46 PM

(06-08-2014 02:07 PM)pito Wrote: I would set the Double as the default setting and sell it as the "standard precision"..

This is not going to happen, single precision is solid and reliable and for the most part correctly rounded -- I don't currently know of any cases where it isn't but there will be some situations where the rounding goes the wrong way.

In double precision, this simply isn't true. The results of some functions aren't even accurate to all returned digits.

A calculator must be trustworthy first and foremost. Returning a wrong answer simply isn't acceptable. Double precision doesn't meet this.

Double precision was exposed to users primarily so that they could implement accurate keystroke programs for single precision.

- Pauli