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
