The C++ standard does not say anything about the usability of the values
returned by the numeric_limits classess. In particular, there is no
requirement that the expressions:

1./numeric_limits<double>.min()
1./numeric_limits<double>.max()
1.f/numeric_limits<float>.min()
1.f/numeric_limits<float>.max()

have meaninful values.  This, perhaps, should be addressed in a future
version of the standard.



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David Sachs wrote:
>
> The C++ standard does not say anything about the usability of the values
> returned by the numeric_limits classess. In particular, there is no
> requirement that the expressions:
>
> 1./numeric_limits<double>.min()
> 1./numeric_limits<double>.max()
> 1.f/numeric_limits<float>.min()
> 1.f/numeric_limits<float>.max()
>
> have meaninful values.  This, perhaps, should be addressed in a future
> version of the standard.

The standard is deliberately written to not mandate the representation
of floating point numbers, in order to give implementors the freedom to
implement C++ on unusualy platforms. What would you have the standard
say, that won't unduly constrain the implementation? Consider

 T product = numeric_limits<T>.min() * numeric_limits<T>.max();

If product > 1.0, then T(1.0)/numeric_limits<T>.max() can underflow,
though it may be denormalized if
numeric_limits<T>.has_denorm!=denorm_absent.

If product < 1.0, then T(1.0)/numeric_limits<T>.min() can overflow,
though it should be numeric_limits<T>.infinity() if
numeric_limits<T>.has_infinity is true.

I'm not certain, but I don't think it's possible for anything remotely
similar to ISO/IEC floating point, to have product==1.0, so you have to
have either one problem, or the other.

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