Re: When floating point result intervals span the boundary - what value is selected?

["Jeff Carter" <jcgoogle@earthlink.net>]

Justin Gombos wrote:
>
> I repeated the experiment adding Sine_Type'Model_Small instead.  If
> Sine_Type'Last is the highest possible model number in the set, how is
> it possible to add Sine_Type'Model_Small to that without throwing a
> constraint error?  While I expect the "+" operation to complete
> because it's working with Sine_Type'Base, I expect the assignment of
> that result to Oversized to fail.  It must be converted back to a
> model number prior to storage, and the resulting model number is out
> of range.

In Ada, exceptions are raised. Please do not use "throw" when
discussing Ada exceptions.

No. Floating-point operations only deal with a fixed number of bits in
the mantissa. This gives at least the decimal number of digits given in
the type declaration. When you add 2 numbers with different exponents,
the smaller one is scaled to have the same exponent as the larger one
before adding. When a small number like 1.0E-20 is scaled to match a
much larger number like 1.0, the smaller number becomes zero. Thus, the
result of the addition is 1.0.

> What exactly is going on in this case?  The calculations must produce
> a result that is greater than 1.0, at least initially.

No, they don't.

> I know I'm missing something here, because I expect the following two
> lines to have the exact same result:
>
>    Oversized : Sine_Type := Sine_Type'Last + Sine_Type'Model_Number;
>    Oversized : Sine_Type := Sine_Type'Succ(Sine_Type'Last);
>
> The first line runs without error, and the second line throws a
> constraint error.

The first line adds zero to 1.0, giving 1.0, as described above. The
second line yields the next model number of the base type > 1.0. This
number exists, but is not in the range of the subtype, so
Constraint_Error is raised.

--
Jeff Carter
jrcarter commercial-at adm [period | full stop] org