On 24 May 2019, at 19:53, Warren Young <war...@etr-usa.com> wrote: > > On May 24, 2019, at 7:10 AM, Jose Isaias Cabrera <jic...@outlook.com> wrote: >> >> Dr. Richard Hipp, on Friday, May 24, 2019 08:44 AM, wrote... >>>> Dr. Hipp, how many more scenarios, where round gives the wrong answer, >>>> exist? Thanks. >>> >>> Consider these two queries: >>> >>> SELECT round(3.255,2); >>> SELECT round(3.2549999999999998,2); >>> >>> Do you expect them to give different answers? >> >> 3.26 >> 3.25 > > Go read this: https://www.floating-point-gui.de/ > > Then install this extension: > > https://chiselapp.com/user/lifepillar/repository/sqlite3decimal/index
sqlite3decimal’s author here: be warned that the extension is still in development. In particular, it’s far from being optimized and the syntax is cumbersome. But the computations should give correct results wrt to decimal arithmetic (and you may choose the rounding algorithm)! I am currently working on different projects that are consuming all my time, but I plan to bring the extension to production level. Eventually :) Knowing that there is a need out there for this type of calculations is a strongly motivating factor. > Having done both, you’ll know why SQLite does what it does, and will have a > solution for the problem where it matters. > > And it doesn’t always matter! Anything dealing in real-world measurements, > for example, generally doesn’t need more than 9 decimal digits of precision, > depending on the measuring instrument, which is more than covered by an > IEEE-754 double. Measurement instruments are not absolutely precise: they > have inherent inaccuracies, and electronic instruments have drift and other > characteristics that can prevent them from giving the same answer given the > same task. > > Since the measurement itself cannot be more precise than an IEEE-754 double, > any “error” in an answer computed from it is down in the noise floor of the > measurement. That is to say, two measurements taken back-to-back might give > the same or greater error. > > This is no accident. IEEE-754 was designed by people working in the physical > sciences, and they knew all of this when they designed it. It is what it was > designed *for*. > > What IEEE-754 was *not* designed for was discrete math, such as monetary > matters on scales smaller than a national economy. That is correct as far as IEEE 754-1985 is concerned. But the latest revision (IEEE 754-2008) standardises floating-point decimal arithmetic, too. So, “IEEE 754” does not imply binary floating-point any longer. It is better to be explicit whether you are talking about “binary” or “decimal” IEEE 754, nowadays. Re the different DBMSs’ specifications, PostgreSQL’s does the right thing, IMO. Unfortunately, SQLite does not have exact numeric types, so the choice is either to implement round() on binary floating-point numbers or not to implement round() at all. Life. _______________________________________________ sqlite-users mailing list sqlite-users@mailinglists.sqlite.org http://mailinglists.sqlite.org/cgi-bin/mailman/listinfo/sqlite-users
