Re: Question for the folks who designed Ada95

[Samuel Mize <smize@imagin.net>]

Corey Ashford <yeroca@rocketmail.com> wrote:
> 
> About modular types.
...
> Why didn't Ada95 make a shift operator a first-class
> operator on modular types.
...
> The problem with the interfaces package shift
> operators is that they have fixed types.  So it's
> difficult to write code for types whose size can vary.
...
> Any thoughts as to why the shift operator wasn't given
> a better treatment?

I'm not one of "the folks who designed Ada95" but I have a guess.

I expect it was because shifting is usually a low-level thing to do,
which comes up in interfaces to the machine.  So, the concern was to
make it available for the types that have direct machine support on a
given architecture.  Nobody cared about other moduluses (modulii?).

Also, bear in mind that modular types don't have to have a power-of-2
modulus.  Consider a mod 5 type.  If its value before shifting is
three, its lowest four bits are:

  0011

Shift left 1, and its bits are:

  0110

which is 6, which is out of range for the type.  Should we get a
constraint error, or should it saturate to 5, or should it wrap to 6
mod 5 (0001)?  The last makes the most sense, in terms of modular
numbers, and would do what you want for a power-of-two modulus.  But
it destroys the meaning of shifting.

Any of the above adds complexity -- you're no longer doing an
efficient shift operation, but shifting and checking constraints.  Of
course, you could expect a compiler to elide all this in the case of a
power-of-two modulus.  But you can't test for that, so you can't make
it a requirement.  It's reasonable behavior to expect, but so is
implementing division by a constant power of two as a simple shift.


> Or am I all wet, and there's really a good way to do shifts?

For a non-hardware-supported power-of-two-modulus unsigned type, you
will need to do a shift, then mask the result down under your modulus.
You can do this with a type from Interfaces that has more bits than
your type.  For instance:

  with Interfaces; use Interfaces;
  ...
  type My_Type is mod 2 ** 30;
  My_Var: My_Type;
  ...
  My_Var := My_Type (Shift_Left (Unsigned_32 (My_Var), 3) mod 2 ** 30);

The conversion to Unsigned_32 should take no cycles, it's implicit
in reading the value into a register to work on it.

The mod 2**30 has to be done anyway, as I described above, since the
machine doesn't directly support a mod 2**30 type (or it would be in
Interfaces).  I'd expect a mod operation using a static power of two
to be implemented as a simple bit-mask operation.

I wouldn't expect the conversion to My_Type to do a range check, since
the compiler can tell statically that the value can't be out of range.
If you're extremely exercised about CPU time you'll be compiling with
range-checks off anyway.

So this should be as efficient as possible.

Best,
Sam Mize

-- 
Samuel Mize -- smize@imagin.net (home email) -- Team Ada
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