Re: On writing negative zero - with or without sign

jvorbrueggen@xxxxxxxxxxxxxxx writes:

I am unfamiliar with the concept of interval arithmetic.

In all seriousness: If you are using floating-point arithmetic at all, not
knowing interval arithmetic is a serious gap in education.

I disagree.

The English
Wikipedia only has a short section in a larger article on intervals, but
points you to the corresponding German article that even has a nice worked
example. As a motivation, it uses measurement error of physical properties,
but of course the intrinsic properties of floating-point numbers apply in just
the same way.

For that I use propagation of error techniques. Sounds like a different
path to the same end result, hence my disagreement above.

Doesn't sound like interval arithmetic is necessarily going to provide
what a physical scientist needs. Consider the following simplified
example. Suppose you want to know the distance from A to C, but what
you have are measurements of the distance from A to B, and from B to C.
Suppose the positions of A and C are extremely well known, but the
position of B is very poorly known. Your measurement of the distance
from A to B will have a large uncertainty associated with it. Ditto for
your measurement of the distance from B to C. Computationally, the
distance from A to C is simply the sum of the distances between A and B,
and between B and C. You might erroneously propagate the error using

dz**2 = dx**2 + dy**2

for the case

z = x + y

the error being due to the fact that x and y are anticorrelated. How is
interval arithmetic going to know that?

.

Relevant Pages

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