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

["Jeffrey R. Carter" <spam@spam.com>]

Justin Gombos wrote:

> Question for the language lawyers-
> 
> Suppose you have the type:
> 
> type Sine_Type is digits 6 range -1.0..1.0;

You need to remember the distinction between a type and a subtype. The name in a
type declaration is the first-named subtype. Your declaration is equivalent to

type Sine_Type'Base is digits X;

subtype Sine_Type is Sine_Type'Base range -1.0 .. 1.0;

where X >= 6. Sine_Type'Base is an unconstrained floating-point type that makes 
sense for your hardware.

> Oversized : Sine_Type := Sine_Type'Last + Sine_Type'Small;

This is odd; 'Small is defined only for fixed-point types (ARM K). Maybe this is 
compiler specific. You should probably use 'Model_Small.

Anyway, since 'Small gives 2.58494E-26 and you probably have 6 digits of 
accuracy, 1.0 + 'Small = 1.0. Remember that "+" is defined for the base type.

> Well_Oversized : constant Float := Float(Sine_Type'Last) +
>                                    Float(Sine_Type'Small * 500000.0);

Similarly here, 5.0E5 * 2.58494E-26 ~ 1.3E-20, and 1.0 + 1.3E-20 = 1.0 with 6 
digits of accuracy.

> -- I was expecting this to report a model number close to 1.0, not
> 3.40282E+38. -- 
 > Ada.Text_IO.Put ("Safe_Last is " &
>                  Float'Image(Sine_Type'Safe_Last));

For a subtype S of a floating-point type T, S'Safe_Last "Yields the upper bound
of the safe range of T." (ARM G.2.2). In your case, T is Sine_Type'Base, and its
upper bound is much larger than 1.0.

> Oversized := Sine_Type(Well_Oversized);

Since Well_Oversized is 1.0, there's no problem here. Even if you had a floating 
point type with enough digits to represent 1.0 + 1.3E-20 as different from 1.0, 
the conversion to Sine_Type'Base would result in a value of 1.0.

-- 
Jeff Carter
"You cheesy lot of second-hand electric donkey-bottom biters."
Monty Python & the Holy Grail
14