On Monday, 17 December, 2018 12:27, Jay Kreibich <j...@kreibi.ch> wrote:
>> On Dec 17, 2018, at 1:12 PM, Keith Medcalf <kmedc...@dessus.com> wrote: >> The "nearest" representation of 211496.26 is >> 211496.26000000000931323. The two representable IEEE-754 double >> precision floating point numbers bounding 211496.26 are: >> 211496.26000000000931323 >> 211496.2599999999802094 >> The difference between 211496.25999999992 (which is itself a >> truncated representation -- the actual stored value should presumably >> be 211496.25999999992200173) and 211496.26000000000931323 is >> 8.73114913702011e-11, or 3 ULP. >> Applying half-even rounding at the second "decimal place" to >> 211496.25999999992 (which when multiplied by 100 is >> 21149625.9999999925494194 which half-even rounds to 21149626.0 which >> when divided by 100 is 211496.26000000000931323 or exactly the >> "nearest representable IEEE-754 double precision floating point >> number" to 211496.26 > Which brings up an important point…. When saying "double-precision > floating point is accurate to within 15 decimal digits” it does NOT > mean floating point can perfectly represent any number up to 15 > digits long, it means that the delta between intent and > representation is 15 digits smaller than the largest represented > digit. In this case, the delta is 10 digits under the radix point, > plus another 5 or 6 digits from the other side of the radix point. > In short, the problem _is_ storage… or at least representation. And > that’s before calculations muck everything up further. Which is why: sqlite> create table x(x); sqlite> insert into x values(1.0); sqlite> insert into x values(1.0e100); sqlite> insert into x values(1.0); sqlite> insert into x values(-1.0e100); sqlite> select sum(x) from x; 0.0 but sqlite> select sum(x) from (select x from x order by abs(x) desc); 2.0 --- The fact that there's a Highway to Hell but only a Stairway to Heaven says a lot about anticipated traffic volume. _______________________________________________ sqlite-users mailing list sqlite-users@mailinglists.sqlite.org http://mailinglists.sqlite.org/cgi-bin/mailman/listinfo/sqlite-users
