Sorry, i replied to wrong Scott Hess... mine was meant to be a reply to his message... " Internally, they are base-2 scientific notation, so asking for more significant digits in the base-10 representation won't help - base-10 fractional numbers cannot always be represented precisely in base-2, ALSO base-2 fractional numbers cannot always be represented precisely in base-10". Sorry for my error. Il 23/ott/2015 19:18, "Scott Robison" <scott at casaderobison.com> ha scritto:
On Fri, Oct 23, 2015 at 10:45 AM, Alessandro Marzocchi < alessandro.marzocchi at gmail.com> wrote: > Scott.... actually all base2 fractions are rapresentable as base10 > fractions... 10 is divisable by 2. > As for Richard.... try to think about this... computer does 2 base > calculations as we usually do calculation in base 10. But the same would > happend to us when talking about different bases.. > Let's say we want to add 3 times 20 minutes (expressed in decimal of hours > up to 6th digit). 0h20' is 0.333333 hours . If you multiply that for 3 you > get 0.999999.. not 1 as you expect. The > Yes, they are. What did I write that leads you to believe I don't understand that? Or are you addressing a different Scott (as there are three in this conversation)? I'm not upset or angry or demanding satisfaction, just trying to understand where my commentary went wrong and if I need to correct anything for the record. When I say floating point calculations are "inexact" what I mean is "potentially inexact" because conversion from decimal in source code to binary floating point in memory is potentially inexact, the arithmetic performed will potentially involve rounding of some form, and the final conversion back from binary floating point to decimal representation for humans can only work with what is left over after those previous potential approximations. > Il 23/ott/2015 18:31, "Scott Robison" <scott at casaderobison.com> ha > scritto: > > > On Fri, Oct 23, 2015 at 9:34 AM, Rousselot, Richard A < > > Richard.A.Rousselot at centurylink.com> wrote: > > > > > Scott, > > > > > > I agree with everything you said but... To me if a program/CPU > evaluates > > > something internally, then when it reports the result it should be the > > > result as it sees it. It shouldn't report something different. > > > > > > > This is true to an extent, and there are ways to display something "more > > exact". But the library programmers wrote code to format floating point > > numbers in a way that is appropriate for display to humans. Knowing that > > floating point calculations are inexact, they round values after a > certain > > number of decimal places, as most applications expect to see something > like > > "25" not "24.9999999999999995" (numbers made up). > > > > > > > > > > So using your analogy, I ask a English speaking person a two > interrelated > > > questions, they translate the questions to Japanese in their head, then > > > answers one question in Japanese and another in English. I say pick a > > > language and stick with it. Either answer my question all in English > or > > > all in Japanese don't mix it. > > > > > > I think we are getting to hung up on the details of what is going on > > > internally. The real question is why don't the two results, which are > > > coming from the same program, agree? (i.e. return 22.99999999999999 > not > > > 23.0) > > > > > > Richard > > > > > > -----Original Message----- > > > From: sqlite-users-bounces at mailinglists.sqlite.org [mailto: > > > sqlite-users-bounces at mailinglists.sqlite.org] On Behalf Of Scott Hess > > > Sent: Friday, October 23, 2015 10:05 AM > > > To: General Discussion of SQLite Database > > > Subject: Re: [sqlite] Simple Math Question > > > > > > On Fri, Oct 23, 2015 at 7:39 AM, Dominique Devienne < > ddevienne at gmail.com > > > > > > wrote: > > > > > > > On Fri, Oct 23, 2015 at 4:16 PM, Rousselot, Richard A < > > > > Richard.A.Rousselot at centurylink.com> wrote: > > > > > So I decided to output 1000 digits, because why not? So now I am > > > > > more perplexed with all these digits showing it is working the > > > > > opposite of > > > > how I > > > > > expected it. Why is the second set of equations evaluating to a > > "yes" > > > > when > > > > > it is the only one that is obviously NOT equal to the expression??? > > > > > > > > Indeed, that's puzzling :) > > > > > > > > > Just to be clear, though, how floating-point numbers work is breaking > > your > > > expectations because your expectations are wrong when applied to > > > floating-point numbers. Internally, they are base-2 scientific > notation, > > > so asking for more significant digits in the base-10 representation > won't > > > help - base-10 fractional numbers cannot always be represented > precisely > > in > > > base-2, ALSO base-2 fractional numbers cannot always be represented > > > precisely in base-10, so it's like a game of telephone where you can > end > > up > > > slightly removed from where you started out, even though it seems like > > it's > > > a simple round trip. Since each individual digit cannot be represented > > > perfectly, it doesn't matter how many digits of precision you ask for, > > > you'll always be able to find cases where it doesn't line up like you > > > expect. > > > > > > Think of it this way: Find an English sentence, and find an English to > > > Japanese translator. Translate each individual word of the sentence > from > > > English to Japanese, then concatenate the results together. Then > > translate > > > the entire original sentence to Japanese. The results will almost > never > > be > > > the same. Then do the same process translating the Japanese back to > > > English. Again, the two routes will provide different results, _and_ > > both > > > of those results will almost certainly not match the original English > > > sentence. This isn't a reflection of the translator's abilities at > all. > > > > > > I'm not saying the computer is always right, just that the computer is > > > following a very strict recipe with reproducible results. I don't mean > > > reproducible like your three examples make logical sense to you, the > > user, > > > I mean reproducible like my Intel box gives the same results as my AMD > > box > > > as my ARM box. If you want to be able to deal with fractional decimal > > > values with high fidelity, you either need to arrange for base-10 > > > representation (slow, because computers have to simulate it), or you > have > > > to do your math in shifted fashion (fast, but can be error prone). > > > > > > -scott > > > _______________________________________________ > > > sqlite-users mailing list > > > sqlite-users at mailinglists.sqlite.org > > > http://mailinglists.sqlite.org/cgi-bin/mailman/listinfo/sqlite-users > > > This communication is the property of CenturyLink and may contain > > > confidential or privileged information. Unauthorized use of this > > > communication is strictly prohibited and may be unlawful. If you have > > > received this communication in error, please immediately notify the > > sender > > > by reply e-mail and destroy all copies of the communication and any > > > attachments. > > > _______________________________________________ > > > sqlite-users mailing list > > > sqlite-users at mailinglists.sqlite.org > > > http://mailinglists.sqlite.org/cgi-bin/mailman/listinfo/sqlite-users > > > > > > > > > > > -- > > Scott Robison > > _______________________________________________ > > sqlite-users mailing list > > sqlite-users at mailinglists.sqlite.org > > http://mailinglists.sqlite.org/cgi-bin/mailman/listinfo/sqlite-users > > > _______________________________________________ > sqlite-users mailing list > sqlite-users at mailinglists.sqlite.org > http://mailinglists.sqlite.org/cgi-bin/mailman/listinfo/sqlite-users > -- Scott Robison _______________________________________________ sqlite-users mailing list sqlite-users at mailinglists.sqlite.org http://mailinglists.sqlite.org/cgi-bin/mailman/listinfo/sqlite-users
