[ODE] What is the ODE approach to denormals?

[GARY VANSICKLE]

> Ah, but those aren't what we actually want.

Wha-huh?  According to one (admittedly rather old and crusty but AFAIK still
valid) source:

"static T 
min ();
Returns the minimum finite value. For floating point types with
denormalization, min() must return the minimum normalized value."

"minimum normalized value", that's exactly what we want, isn't it?

> Especially for the denormal-
> if-you-square-it number. For numerical precision reasons, using
> <float>::min and taking sqrt() of it won't cut it.

Well <float>::min() will give you a number with an exponent of 0, so isn't
the same mantissa with an exponent of -1 the
(almost-)denormal-if-you-square-it number we seek?  Assuming a
numeric_limits::radix of 2 of course.

> And, in addition,
> because I'm a little bit superstitious magic epsilons, I prefer for these
> epsilons to be slightly bigger than the absolutely minimum representable
> number.
> 

I prefer that my magic epsilons contain as little magic as possible ;-).

> Anyway, there are zillions of places where ODE compares "> 0" where it
> should compare "> some_epsilon" -- identifying all of them is the hard
> part. Figuring out the value of the epsilon is just a matter of
> preference. (degrees or radians in XML, anyone? :-)
> 

Gotta disagree with you there.  Say the instance in question works fine with
the minimum non-denormal.  Nothing says the next "> 0", even if it should be
an epsilon, would work with the same value.  That would have to be evaluated
on a case-by-case basis.