Le 18/09/2017 à 20:54, Samuel Gougeon a écrit :
Now comes the issue:
In (A), the relative difference 1/2^53 is too small (< %eps) to be
recorded and to change the number. OK.
Since 1 / (2^53 +2) is even smaller than 1 / (2^53), it should nor
make a difference. Yet, it does:
--> (2^53 + 2^1) + 1 == (2^53 + 2^1)
ans =
F
How is this possible ??!
Hi all,
no issue here but simply the round to even rule. Every real number
should be approximated by the nearest floating point number but in
case of
a number exactly between 2 successive floats the one with an even end
digit win. You can see this rule as a mean to approximate those
ambiguous cases,
one in two down and one in two up, but has more subtle features in it
such
(it is explained in Knuth I).
OK that2^53 + 2^1 is exactly represented
(it is a double float number). When computing :
x = (2^53 + 2^1) + 1
it is not a float but is exactly at the same distance between the two
floats :
2^53 + 2^1 and 2^53 + 2^2 but this last one ends with a even digit (0)
so :
fl( (2^53 + 2^1) + 1) = 2^53 + 2^2
hth
Bruno
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