A quick precision test

06072014, 11:56 AM
(This post was last modified: 06072014 01:23 PM by pito.)
Post: #61




RE: A quick precision test
(06062014 10:55 PM)Paul Dale Wrote: Alpha padded the result with semirandom digits just like I asked for. In Wolfram Alpha: Code: With 120 digits of "precision" (use "xxx`ndigits"): And the quick test from the top of this thread: Code:


06072014, 12:20 PM
(This post was last modified: 06072014 12:20 PM by Paul Dale.)
Post: #62




RE: A quick precision test
(06072014 11:56 AM)pito Wrote: In Wolfram Alpha: 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 

06072014, 04:44 PM
(This post was last modified: 06072014 05:59 PM by pito.)
Post: #63




RE: A quick precision test
(06072014 12:20 PM)Paul Dale Wrote: .. We make Mr. Wolfram unhappy when not utilizing his recommendations.. 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 ] 

06082014, 02:10 AM
Post: #64




RE: A quick precision test
(06032014 10:06 PM)Massimo Gnerucci Wrote:(06032014 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 :) I know. That's why I've suggested "DECIMALPOINT IS COMMA" :) https://www.google.com.br/webhp?sourceid...%2C0561%22 

06082014, 12:44 PM
(This post was last modified: 06082014 01:54 PM by pito.)
Post: #65




RE: A quick precision test
(06022014 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:I've updated the list with calculators we've tested in situ (thanks Martin!) and found from available sources (web). 

06082014, 01:57 PM
(This post was last modified: 06082014 02:45 PM by walter b.)
Post: #66




RE: A quick precision test
(06082014 12:44 PM)pito Wrote: Take 1.0000001 and do x^2 27times.. 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 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. 

06082014, 02:07 PM
(This post was last modified: 06082014 02:23 PM by pito.)
Post: #67




RE: A quick precision test  
06082014, 03:00 PM
Post: #68




RE: A quick precision test
(06082014 02:07 PM)pito Wrote: ... maybe you have to rethink your marketing approach when "selling" your calculator.. First of all you should quote Wolfram's result correctly. And second: Your suggestions faintly reminds me on frequency meter ads in USAmerican 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:/ 

06082014, 05:28 PM
Post: #69




RE: A quick precision test
(06072014 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. 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:? 

06082014, 10:46 PM
Post: #70




RE: A quick precision test
(06082014 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 

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