Re: Signed integer to modular type conversion

[Mark Johnson <mark_h_johnson@raytheon.com>]

Adam Beneschan wrote:
> 
> I have two integer values.  One is in the range 0 .. 2**32-1, and the
> other is in the range -2**31 .. 2**31-1.  I want to find the
> mathematical sum of these two integers.  Let's assume that I expect
> the result to be in the range 0..2**32-1, and am not worried about
> what happens if it isn't.
> 
>     type ModType is mod 2**32;
>     X : ModType;
>     Y : Integer;
>     Z : ModType;
> 
> I want to compute Z := X + Y, but of course I can't write this.
Why not? You can if you define the "+" operator for the right parameter
as integer and the left as your ModType (and the associative version as
well...). I will also assume I have the unary plus operator
(Unchecked_Conversion) as previously described....
  function "+"(Left: Integer; Right:ModType) return ModType is
    Temp : ModType := +Left; -- convert to ModType
  begin
    return Temp+Right;
  end "+";
Which converts the left operator to ModType and uses modular add to get
the result. Let's try some examples...
  1+2000 is 2001
  -1+2000 is 1999
The modular arithmetic should do the "right thing" for the unsigned
addition.
  --Mark