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From: Ludovic Brenta <ludovic@ludovic-brenta.org>
Newsgroups: comp.lang.ada
Subject: Re: Question about ordinary fixed point types.
Date: Mon, 16 Aug 2010 03:03:59 -0700 (PDT)
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Date: 2010-08-16T03:03:59-07:00
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Jeffrey Carter wrote on comp.lang.ada:
> Consider this example, which I 1st encountered in 1984:
>
> with Ada.Text_IO;
>
> procedure Fixed_Test is
> =A0 =A0 type Money is delta 0.01 range -100.0 .. 100.0;
>
> =A0 =A0 Cent : constant Money :=3D Money'Delta;
>
> =A0 =A0 Change : Money :=3D 0.0;
> begin -- Fixed_Test
> =A0 =A0 Sum : for I in 1 .. 5 loop
> =A0 =A0 =A0 =A0Change :=3D Change + Cent;
> =A0 =A0 end loop Sum;
>
> =A0 =A0 Ada.Text_IO.Put_Line (Item =3D> Money'Image (Change) );
> end Fixed_Test;
>
> Typically, the 'Small will be 2#0.000_000_1#, and the program will output=
 0.04.
> The program adds the machine number closest to 'Delta (which is 'Small) e=
ach
> time, not 'Delta, so there's no "snapping" taking place, except in the
> conversion of 0.01 to a machine number of type Money.

Money is quite special; this is an area where approximation of a one
cent to a power of two is not acceptable. Ada has decimal fixed-point
types for this purpose.

More generally, Ada allows the programmer to specify the 'Small with
an attribute definition clause, so theoretically the exact solution to
Peter's problem would be:

Epsilon : constant :=3D Ada.Numerics.Pi / 2 ** 15;
type Angle is delta Epsilon range -Ada.Numerics.Pi .. Ada.Numerics.Pi;
for Angle'Small use Epsilon;

This would, in theory, create the desired mapping from the integer
range [-2**15 .. 2**15] to the real range [-Pi .. Pi] without wasting
any machine numbers.

However and unfortunately, ARM 3.5.9(21) allows an implementation to
reject any 'Small that is not a power of two (and, in particular,
decimal fixed-point types). I'm not sure whether GNAT supports
arbitrary Smalls; from the doc, it seems that it actually rounds them
down to a power of two no smaller than 2**(-63).

--
Ludovic Brenta.