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A quick precision test
06-07-2014, 11:56 AM (This post was last modified: 06-07-2014 01:23 PM by pito.)
Post: #61
RE: A quick precision test
(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...
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06-07-2014, 12:20 PM (This post was last modified: 06-07-2014 12:20 PM by Paul Dale.)
Post: #62
RE: A quick precision test
(06-07-2014 11:56 AM)pito Wrote:  In Wolfram Alpha:

Code:
With 120 digits of "precision":

cos(1.57079632679489661923132169163975144`120)

2.098584699687552910487472296153908203143104499314017412671058533991074041716259​78775626172739947883181185207919839... × 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
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06-07-2014, 04:44 PM (This post was last modified: 06-07-2014 05:59 PM by pito.)
Post: #63
RE: A quick precision test
(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 ]
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06-08-2014, 02:10 AM
Post: #64
RE: A quick precision test
(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
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06-08-2014, 12:44 PM (This post was last modified: 06-08-2014 01:54 PM by pito.)
Post: #65
RE: A quick precision test
(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).
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06-08-2014, 01:57 PM (This post was last modified: 06-08-2014 02:45 PM by walter b.)
Post: #66
RE: A quick precision test
(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.
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06-08-2014, 02:07 PM (This post was last modified: 06-08-2014 02:23 PM by pito.)
Post: #67
RE: A quick precision test
(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
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06-08-2014, 03:00 PM
Post: #68
RE: A quick precision test
(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:-/
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06-08-2014, 05:28 PM
Post: #69
RE: A quick precision test
(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:-?
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06-08-2014, 10:46 PM
Post: #70
RE: A quick precision test
(06-08-2014 02:07 PM)pito Wrote:  I would set the Double as the default setting and sell it as the "standard precision".. Smile

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
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