"James Tursa" wrote in message <email@example.com>...
> False. 9 has an exact IEEE double representation. 0.09 does not ... the closest is: > > 0.0899999999999999966693309261245303787291049957275390625 > > > More generally, most integers do not have an exact representation in this format. > > False. All of the integers in the range of your particular problem can be represented exactly in IEEE double. All integers from 0 up to 2^53 have exact IEEE double representations.
OK. I got it (after some embarrassment). The IEEE 754 format description on Wikipedia was a bit confusing - all those negative powers of 2! It really boils down to - if a number can be represented as a sum of powers of 2, then it has an exact representation - so all integers (within some range) will have an exact representation.
Nevertheless, it does appear that exact calculations even with integers has to be thought through on a case by case basis.
> > So, does Matlab treat small integers in a special way? > > No. They are treated just like all other IEEE double numbers. > > > James Tursa