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Re: How to avoid wrong answers in simple arithmetic expressions.
Posted:
Jan 20, 2013 3:49 AM
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"James Tursa" wrote in message <kdfc0c$v7$1@newscl01ah.mathworks.com>...
> False. 9 has an exact IEEE double representation. 0.09 does not ... the closest is:
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> 0.0899999999999999966693309261245303787291049957275390625
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> > More generally, most integers do not have an exact representation in this format.
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> 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.
Best Regards.
> > So, does Matlab treat small integers in a special way?
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> No. They are treated just like all other IEEE double numbers.
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>
> James Tursa
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