Re: Non-static constant propagation in

Re: Non-static constant propagation in

[Michael Hunter]

firth@sei.cmu.edu (Robert Firth) writes:
>In article <20600032@inmet> stt@inmet.inmet.com writes:
>
>>In ARM 4.10:4, it states:
>>   . . . Furthermore, if a universal expression is a static expression,
>>then the evaluation must be exact.
>>
>>Let's hope they don't try to define "SQRT" on universal reals ! ;-*
>
>The sentence quoted was perpetrated by one of the Neoplatonists on
>the language design team.  The point of the joke, of course, is that
>in Ada all 'universal' expressions yield only rational results, and
>so may indeed be computed exactly.

I'm missing something here....no matter how hard to try to compute the square
root of 2....you ain't gonna get it exactly...I don't care if you are doing
your arithmatic with rational immediate results!!  The sqare root of 2 doesn't
exist in the rationals!!!!  (go check with your college abstract algebra book
or if you want overkill check out galois theory!)  Now you can computer the
root of 2 to maximum percision of the hardware percisely...that is a different
matter...!

                                        Michael

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Re: Non-static constant propagation in

[Michael Hunter]

stt@inmet.inmet.com writes:
>
>As Robert Firth said, the point of my joke about SQRT on universals
>was exactly that the result is not always a rational number.
Someone on the net said that I insulted you with my comment that the square
root of two is not rational.  I apologize if I did.

                                        Michael

Mike Hunter - Box's and CPU's from HELL: iapx80[012]86, PR1ME 50 Series, 1750a
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Non-static constant propagation in optimizing Ada compilers

[Joe Orost]

Ada compilers must be able to compute arithmetic expressions exactly.  It
says so in the language definition.  Should an optimizing compiler use this
"infinite precision" arithmetic when it is performing non-static constant
propagation?  What do you think?   For example:

   function example return float is
      f : float := 1.000000000000000000000000001;
      i : integer;
   begin
      i := integer(f);
      return f - float(i);
   end example;

If an optimizing compiler used "infinite precision" arithmetic,
it could replace the program with:

   function example return float is
   begin
      return 0.000000000000000000000000001;
   end example;

The other alternative is for the compiler to use the arithmetic of the
target machine to perform the calculations (possibly requiring emulation
if host /= target).  In this case, the function would return 0.0, which is
the answer you would get from a non-optimizing compiler.

Other similar problems occur when an optimizing compiler register allocates
floating point values, especially on a 68881/68882 where the registers hold
much more precision than single precision memory locations, which again will
cause different results than in a non-optimizing compiler.  I hear that they
are fixing this problem in the 68040.

Re: Non-static constant propagation in

[stt]

An Ada expression is always allowed to evaluate to a result more
accurate than that required by the type.
This can be due either to compile-time infinite
precision calculation, or by simply using greater
precision at run-time.
The only absolute requirement for accuracy has to do
with operations where both operands are model numbers.
See ARM 4.5.7.

S. Tucker Taft
Intermetrics, Inc.
Cambridge, MA  02138

Re: Non-static constant propagation in

[stt]

With regard to accuracy of compile-time calculations...

In ARM 4.10:4, it states:
   . . . Furthermore, if a universal expression is a static expression,
then the evaluation must be exact.

Let's hope they don't try to define "SQRT" on universal reals ! ;-*

S. Tucker Taft
Intermetrics, Inc.
Cambridge, MA  02138

Re: Non-static constant propagation in

[Robert Firth]

In article <20600032@inmet> stt@inmet.inmet.com writes:

>In ARM 4.10:4, it states:
>   . . . Furthermore, if a universal expression is a static expression,
>then the evaluation must be exact.
>
>Let's hope they don't try to define "SQRT" on universal reals ! ;-*

The sentence quoted was perpetrated by one of the Neoplatonists on
the language design team.  The point of the joke, of course, is that
in Ada all 'universal' expressions yield only rational results, and
so may indeed be computed exactly.

Re: Non-static constant propagation in

[stt]

As Robert Firth said, the point of my joke about SQRT on universals
was exactly that the result is not always a rational number.
The definition of Ada does not currently include any operations on universal
reals which produce irrational results.  If we were to add SQRT,
then the cited wording would have to change.  I have no expectation
that SQRT will be added to the set of operations defined on
universal reals, by the way...

S. Tucker Taft
Intermetrics, Inc.
Cambridge, MA  02138

P.S. I wouldn't rule out some clever implementation which could
represent all algebraic numbers "exactly", but it would clearly
have to be more complicated than simply a pair of universal
integers as is used for rationals
(probably a tree structure of some sort, requiring symbolic
evaluation, etc).
-T