From: Yannick Duchêne (Hibou57) on
Le Mon, 09 Aug 2010 19:59:45 +0200, <tmoran(a)acm.org> a écrit:
> They are also subject to the possible error
> of failing to write the "mod" part, whereas with modular types the
> compiler has the responsibility to remember to do the mod operation.
DRY principle in action
From: Robert A Duff on
"Yannick Duch�ne (Hibou57)" <yannick_duchene(a)yahoo.fr> writes:

> Le Mon, 09 Aug 2010 19:59:45 +0200, <tmoran(a)acm.org> a �crit:
>> They are also subject to the possible error
>> of failing to write the "mod" part, whereas with modular types the
>> compiler has the responsibility to remember to do the mod operation.
> DRY principle in action

It's a good point. But you can get DRY without an implicit-mod type.
For example, for a circular buffer, you can write a Next_Index
function that does the explicit "mod", so you don't scatter "mod"
ops all over the code. You don't need modular types for that.
And you don't want any "*"-with-implicit-mod operator for the index.
Nor do you want "xor" on the index.

- Bob
From: Robert A Duff on
"Yannick Duch�ne (Hibou57)" <yannick_duchene(a)yahoo.fr> writes:

> Le Mon, 09 Aug 2010 15:28:02 +0200, Robert A Duff
> <bobduff(a)shell01.theworld.com> a �crit:
>>> Hmmm... Hash coded tables?
>>
>> Signed integers work fine for that. Except when you need
>> that one extra bit -- that's the problem.
>
> All of the hash functions I have seen so far use modular types. Do you
> known ones computing on integers ?

Modular types are integer types in Ada terms. So that should be
"...computing on SIGNED integers". Sorry for nitpicking. ;-)

Well, all the ones I wrote in Ada 83, or Pascal, or... used
signed integers.

But I concede the point -- modular types are appropriate for
hash functions.

- Bob
From: Jacob Sparre Andersen on
Robert A Duff wrote:
> Jeffrey Carter <spam.jrcarter.not(a)spam.not.acm.org> writes:

>> type T is range 0 .. 2 ** N - 1;
>> for T'Size use N;

> Yes. And T'Size = N by default in Ada >= 95, so I would write:
>
> pragma Assert(T'Size = N);
>
> instead of the Size clause.

But don't you loose the compile time error in case the compiler
cannot make T'Size = N?

Jacob
--
PNG: Pretty Nice Graphics
From: Phil Clayton on
On Aug 8, 9:51 pm, Robert A Duff <bobd...(a)shell01.TheWorld.com> wrote:

> P.S. Can anybody recall the definition of "not" on modular
> types, when the modulus is not a power of 2, without
> looking it up?  Hint: It makes no sense.  The only feature
> that's worse than "modular types" is "modular types with a
> non-power-of-2 modulus".  ;-)

I have the identity

not X + 1 = -X

ingrained on my brain because I wrote too much in assembly language!
I haven't checked (honest!) but I'm sure Ada just uses this identity
to define "not" for modular types, i.e.

not X = -X - 1 (rhs wraps around)

In my view, this is still useful when the modulus is not a power of
two, it's just that "not" is a terrible name for the operation.

Only yesterday, I was working in another language with arrays starting
at index 0 and needed the elements in reverse: the required effect was
achieved by subscripting from the end rather than the start. Had I
been working in Ada with an array indexed by a modular type, the
effect of reversing the elements could have been achieved by replacing

A(I)

with

A(not I)

which I think that is nicer than

A(-I - 1)

provided people have the intuitive understanding that "not" is
effectively an operator that reverses the elements of a modular type.
In the other language I was using, I effectively had to write

A(A'Length - I - 1)

(not valid Ada, of course.)

Perhaps "reverse" would be a better name for the operator "not" when
the modulus is not a power of two?

Phil