Le 11 mai 09 à 22:09, Colin Holgate a écrit :
On May 11, 2009, at 3:40 PM, Jan Schenkel wrote:
Scott Raney - the original developer of Metacard, the underlying
engine for Revolution - opted for the better speed of CPU-native
numbers, instead of the byte arithmetic algorithm as implemented in
HyperCard
While that is interesting, HyperCard also has the same math issue.
So does Javascript (I know that's not like Java, but you might think
that its math was on the same lines):
on mouseUp
set the numberformat to "#.0000000000000000"
answer 283.67-150.00-133.67
end mouseUp
shows an answer of .0000000000000284. This:
<html><script type="text/javascript">alert(283.67-150.00-133.67)</
script></html>
alerts an answer of 2.842170943040401e-14. So it seems like everyone
gets it wrong!
For completeness, I tried Java too:
println((283.67-150.00)-133.67);
shows as 1.5258789E-5, so Java is off on its own level of error.
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my two cents:
if you want arbitrary precision, work with rational numbers (i.e.,
fractions of integers). All operations only require a finite number of
bytes to be exact. If you want to represent functions, try to use
rational operations. For instance, a Lagrange interpolation over a set
of rational knots (for instance, linear interpolation between two
points with rational coordinates) are solved by a linear systems with
rational coefficients, and yields a rational value at rational points;
therefore, the computations yield exact results (in fractional form).
If I remember well, this line of thought was followed by Wolfram in
the implementations of Mathematica that I have come to see.
On the other hand, "numerical packages" like Matlab rely on floating
point arithmetic; the advantage is that the number of bytes required
to represent a number is fixed once for all (it does not grow
dynamically). It is well suited to multiplication, but fails miserably
on summation when the numbers do not have a "similar" magnitude.
"Infinity is long, especially towards the end"
Woody Allen (?)
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