"Campbell, Greg" <greg(dot)campbell(at)us(dot)michelin(dot)com> writes:
I've disassociated floats and exactness, that is floating point
representations and exact matches do not seem to go together.
The issue is that "float" types actually means fractions encoded in
base 2 for efficiency reasons. Almost every time you go back and forth
between base 2 and base 10 you have to round, there is no exact
mapping between those two spaces.
For instance you can not write 1/3 (one third) in base 10 whereas you
can in base 3 using just a couple of digits (it's just "0.1")
The idea was made more profound when I started looking into the
multitude of options in representing a float in 16, 32 or 64
bits. There are so many different ways to allocate bits for the
number, and bits for the exponent, leading to radically different
precisions.
Actually on today's hardware I thought it was hard to find anything
else than IEEE754 32 and 64 bits floats, standardized across all
platforms, and 32 bits values being a subset of 64 bits. So that does
not look like "many different ways" to me. Could you detail?
Between a value
on the server and a value on the client a difference out in the 15th
decimal place hardly seems surprising.
Whether conversions and roundings happen on the server on or the
client does not seem to change the problem much IMHO.
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