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From: "Nick Roberts" <nickroberts@adaos.worldonline.co.uk>
Newsgroups: comp.lang.ada
Subject: Re: Dimensionality Checking (Ada 20XX)
Date: Sun, 9 Dec 2001 22:58:11 -0000
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Some details.

Fixed point types and objects would have the attribute Unit, of type
Ada.Units.Unit_Type. A 'unit' (a value of this type) has two (notional or
actual) components: its 'dimensionality', of type Ada.Units.Dimensionality,
obtainable by the function Dim; and its 'scaling', of type universal_real,
obtainable by the function Scaling.

The types Ada.Units.Unit_Type and Ada.Units.Dimensionality would be 'static'
subtypes: a constant of such a subtype whose initial value is static, is
itself static.

The Ada.Units package would include (in addition to what I said in my
previous post):


   function "*" (Left: Unit_Type; Right: universal_integer) return
Unit_Type;
   function "*" (Left: universal_integer; Right: Unit_Type) return
Unit_Type;
   function "/" (Left: Unit_Type; Right: universal_integer) return
Unit_Type;
   function "/" (Left: universal_integer; Right: Unit_Type) return
Unit_Type;

   function "**" (Left: Unit_Type; Right: universal_integer) return
Unit_Type;

   function Scaling (The_Unit: in Unit_Type) return universal_real;

   type Dimensionality is private;

   function Dim (The_Unit: in Unit_Type) return Dimensionality;


For the (explicit) conversion between two unit-specific (fixed point) types,
their dimensionalities must be the same. Conversion between a unit-specific
and a non-unit-specific type entails no dimensionality check.

The value of Scaling(T'Unit) for any non-unit-specific fixed point type T is
always 1.0.

For the value conversion:


   T1(X)


where X is of type T2, where T1 and T2 are both fixed point, the value of
the result would be the value of X*Scaling(T1'Unit)/Scaling(T2'Unit).

For the view conversion (an actual parameter):


   T1(X)


where X is of type T2, where T1 and T2 are both fixed point, the value
passed in (to the subprogram being called) would be the value of
X*Scaling(T1'Unit)/Scaling(T2'Unit), and the value passed out (back into X)
would be the value of X*Scaling(T2'Unit)/Scaling(T1'Unit).


There would be the following extra rules for the predefined multiplication
and division operations. For multiplication:


   function "*"(Left:  in universal_fixed;
                Right: in universal_fixed) return universal_fixed;


the value of the result is the value of
(Left*Scaling(Left'Unit))*(Right*Scaling(Right'Unit)), and, if the expected
type is unit-specific, it must have the same dimensions as
Dim(Left'Unit*Right'Unit).

For division:


   function "/"(Left:  in universal_fixed;
                Right: in universal_fixed) return universal_fixed;



the value of the result is the value of
(Left*Scaling(Left'Unit))/(Right*Scaling(Right'Unit)), and, if the expected
type is unit-specific, it must have the same dimensions as
Dim(Left'Unit/Right'Unit).


For predefined exponentiation of any fixed point type T1, the function
declaration becomes:


   function "**"(Left:  in T1;
                 Right: in Integer'Base) return T2;



the value of the result is the value of (Left*Scaling(Left'Unit))**Right,
and, if the type T1 is unit-specific, T2 is an anonymous fixed point type
which is the same as T1 except that it has the dimensions of
Left'Dimensionality**Right (otherwise T2 is identical to T1).

In all other cases the semantics are as in Ada 95.

--
Best wishes,
Nick Roberts