Re: Truncating a fixed-point value

[Gene <gene.ressler@gmail.com>]

On Jul 9, 11:13 pm, Gene <gene.ress...@gmail.com> wrote:
> On Jul 9, 7:21 pm, Adam Beneschan <a...@irvine.com> wrote:
>
>
>
>
>
> > On Jul 9, 1:34 pm, Simon Wright <si...@pushface.org> wrote:
>
> > > Adam Beneschan <a...@irvine.com> writes:
> > > > I must be suffering from an embarrassing mental block, because I'm
> > > > sure there's a simple solution, but I can't see what it is.
>
> > > > I have a value X of a fixed-point type, X >= 0.0, and I need to
> > > > compute Floor(X) as an Integer.  'Truncation and 'Floor aren't defined
> > > > for fixed-point types; the type conversion Integer(X) rounds; and
> > > > Integer(X-0.5) fails if X=0.0.
>
> > > > How do others do this?  Or do I have to resort to an IF statement (or
> > > > conditional expression in Ada 2012) to handle the different cases?
>
> > > Looks as though Integer(X+0.5)-1 might do the trick ..
>
> > Yes, it looks like it, as long as X >= 0.0 and 0.5 is a model number
> > of the fixed-point type (I think I'm using the right term).  Those
> > conditions do hold for the code I need it for.  It isn't useful for
> > negative numbers---it yields -2 if X=-1.0, which is not useful whether
> > you want a truncation or a floor operation---but I did stipulate
> > nonnegative X in my original question.
>
> >                          -- Adam
>
> Shouldn't there be a way to convert a fixed point type to a
> corresponding modular or integer type with one integer value per
> floating point value, use rem to compute a floor, and convert back?- Hide quoted text -

I'll try to answer my own question.  Here is an attempt that works for
a variety of fixed point types.  I'm no expert on fixed point. Perhaps
I've embedded some non-portable assumptions. With optimizations turned
up and range checks off, the Floor function inlines as the 3 (x86)
instructions you'd expect (subtract, "and" with mask, add) using GPL
2007.

with Ada.Text_IO; use Ada.Text_IO;

procedure FPF is

  type FP is delta 0.125 range -10.0 .. 50.0;

  function Floor(X : FP) return FP is
    Delta_Inv : constant := 1.0 / FP'Delta;
    type Bits is mod 2 ** 32;
    type FP_Bits is delta 1.0 range 0.0 .. (FP'Last - FP'First) *
Delta_Inv;
    Ordinal : constant Bits := Bits((X - FP'First) * Delta_Inv) and
not(Bits(Delta_Inv) - 1);
  begin
    return FP'Base(FP_Bits(Ordinal) * FP'Delta) + FP'First;
  end;

  X : FP := FP'First;
begin
  loop
    Put_Line(FP'Image(X) & " -> " & FP'Image(Floor(X)));
    exit when X = FP'Last;
    X := X + FP'Delta;
  end loop;
end;