Re: Types with physical dimension

[eachus@spectre.mitre.org (Robert I. Eachus)]

In article <SAL714.94Oct3133110@rs710.gsfc.nasa.gov> sal714@rs710.gsfc.nasa.gov (Stephen A. Leake) writes:

 > I run robots with Ada, so I deal with real dimensions all the time.
 > Very early on, I started to write a package that enforced
 > dimensionality; I defined METERS, METERS_PER_SECOND, etc. I quickly
 > discovered that even simple equations need up to cubic dimensions,
 > in all combinations of length, mass and time.  Defining all these
 > types and the associated operators was far too time-consuming to be
 > worth it. So now I rely on code reviews and careful testing.

 > The moral; strong typing is nice, but is no substitute for careful design
 > and thorough testing.

  Paul Hilfinger did a nice paper on using discriminants to check
dimensionality.   I don't have the paper in front of me but it works
something like this:

   type Measure(Length,Mass,Time: Integer) is record
     Value: Float;
   end record;

   subtype Meters is Measure(1,0,0);
   subtype Kilograms is Measure(0,1,0);
   subtype Time is Measure(0,0,1);
   ...etc.

   Now you can define all the standard arithmetic operations on type
Measure so that they keep the discriminants correct:

   function "*"(L,R: Measure) return Measure is
   begin
     return(L.Length+R.Length,L.Mass+R.Mass,L.Time+R.Time,L.Value*R.Value);
   end "*";

   function "+"(L,R: Measure) return Measure is
   begin
     if L.Length /= R.Length or L.Mass /= R.Mass or L.Time /= R.Time
     then raise Constraint_Error; end if;
     return L.Value+R.Value;
   end "+";

     In theory, if you use pragma INLINE, a good compiler should never
store the discriminants and eliminate all the discriminant related
code at compile time.  In practice, when I used this technique, I had
two versions of the specification of the types package, one with the
discriminants and one which said "type Measure is Float;" and kept all
the subtype declarations.  I used the full package during unit test,
and the streamlined package thereafter.

     The only problem I had was with square roots.  I thought about
changing the package to double all the dimensional values, so length
would be (2,0,0), but I never did.

--

					Robert I. Eachus

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