Re: Why no 'Floor for fixed point types

["Robert I. Eachus" <rieachus@comcast.net>]

Nick Roberts wrote:

> For a fixed point type Tf -- assuming it has a delta which is less than 
> 1 -- you can write:
> 
>    Scale: constant := 1/Tf'Small;
> 
>    type Ti is range Tf'First*Scale .. Tf'Last*Scale;
> 
>    function Scaled_Floor (X: in Tf) return Ti is
>    begin
>       return Ti(X*Scale) - Ti(X*Scale) mod Ti(Scale);
>    end;
> 
> The basic idea is that with fixed point types, a 'floor' function will 
> inevitably need to be scaled, and the integer type it returns needs to 
> be customised to the fixed point type (its range and delta) and the 
> chosen scale. I've shown a scale of 1/Tf'Small, but the chances are that 
> the scale you will require in a certain situation will be different (it 
> might be unity).

Ignore this.  To quote RM 3.5.9(8): "The set of values of a fixed point 
type comprise the integral multiples of a number called the small of the 
type."  So the effect of all the code above can be better accomplished by:

   function Mantissa(X: in Tf) return Ti is
   begin return Ti(X/Tf'Small); end Mantissa;

-- Technically you could use the constant named Scale above, but there
-- are some potential rounding issues.  Writing it this way allows the
-- compiler to convert the division to a multiplication that gives the
-- same result, if it can.

-- Of course, any decent compiler should be able to recognize this
-- special case and do nothing.  If your compiler doesn't recognize this
-- you could rewrite Mantissa as an instance of Unchecked_Conversion.



-- 
                                                     Robert I. Eachus

"Quality is the Buddha. Quality is scientific reality. Quality is the 
goal of Art. It remains to work these concepts into a practical, 
down-to-earth context, and for this there is nothing more practical or 
down-to-earth than what I have been talking about all along...the repair 
of an old motorcycle."  -- from Zen and the Art of Motorcycle 
Maintenance by Robert Pirsig