On 20-ott-10, at 23:28, Don wrote:
Fawzi Mohamed wrote:
On 20-ott-10, at 20:53, Don wrote:
Andrei Alexandrescu wrote:
On 10/20/10 10:52 CDT, Don wrote:
I don't think it's possible to have a sensible default for
absolute
tolerance, because you never know what scale is important. You
can do a
default for relative tolerance, because floating point numbers
work that
way (eg, you can say they're equal if they differ in only the
last 4
bits, or if half of the mantissa bits are equal).
I would even think that the acceptable relative error is almost
always
known at compile time, but the absolute error may not be.
I wonder if it could work to set either number, if zero, to the
smallest normalized value. Then proceed with the feqrel
algorithm. Would that work?
Andrei
feqrel actually treats zero fairly. There are exactly as many
possible values almost equal to zero, as there are near any other
number.
So in terms of the floating point number representation, the
behaviour is perfect.
Thinking out loud here...
I think that you use absolute error to deal with the difference
between the computer's representation, and the real world. You're
almost pretending that they are fixed point numbers.
Pretty much any real-world data set has a characteristic
magnitude, and anything which is more than (say) 10^^50 times
smaller than the average is probably equivalent to zero.
The thing is two fold, from one thing, yes numbers 10^^50 smaller
are not important, but the real problem is another, you will
probably add and subtract numbers of magnitude x, on this operation
the *absolute* error is x*epsilon.
Note that the error is relative to the magnitude of the operands,
not of the result, it is really an absolute error.
You have just lost precision.
BTW -- I haven't yet worked out if we are disagreeing with each
other, or not.
eheh I think we both know the problems, and it is just the matter of
the kind of tests we do more often.
feqrel is a very important primitive, and it should be available, that
is what should have been used by Lars.
I happen to test often things where the result is a postion, an energy
difference,... and in those cases I have a magnitude, and so
implicitly also an absolute error.
In any case all this discussion was useful, as it made me improve my
code by making the magnitude an explicit argument.
Fawzi
