Re: pi seems not to be a constant

On Sun, Oct 18, 2015 at 8:57 PM, Don Cohen
<[email protected]> wrote:
> Pierpaolo Bernardi writes:
>  > On Sun, Oct 18, 2015 at 8:02 PM, Don Cohen
>  > <[email protected]> wrote:
>  > > Pierpaolo Bernardi writes:
>  >
>  > >  > At the cost of every computation involving pi and long floats
>  > >  > returning wrong answers!
>  > >
>  > > Why do you think they're wrong?
>  >
>  > They would be wrong if PI had not the required long float precision.
>
> Wrong in what sense?

PI is required to be the best long float approximation to pi. If it
wasn't then it would be wrong.

Also, PI is required to be a constant variable. It isn't and so it's
wrong.  But i  think this "wrong" is a very small price to pay in
exchange for having adjustable precision long floats.

>  (setf (EXT:LONG-FLOAT-DIGITS) 128)
>  (setf s2 (sqrt 2l0))
>  (setf (EXT:LONG-FLOAT-DIGITS) 64)
>  (* 2 s2)
> Is this now wrong because s2 was computed with higher precision?
> If this is what I intended then I think it's right.

In this case you are using a Clisp extension and you are getting what
Clisp promises to deliver. So it is right.

>  > PI not being a constant is a much more benign non conformity. Surely
>  > you can work around it?
>
> I think you could use ext:pi for the cases where you want it to
> change.

The problem then is the value of CL:PI.  What do you propose it should be?

> In fact, it occurs to me that it would make more sense to use
> (pi &optional precision) to compute pi (values could still be cached),
> and allow special binding of *ext:long-float-digits* to control
> default precision.

The problem of what should be the value of CL:PI remains.

> BTW, it now occurs to be that things like MOST-POSITIVE-LONG-FLOAT
> have to be reinterpreted compared to other lisp implementations:
> (setf (EXT:MOST-POSITIVE-LONG-FLOAT)
> (setf (EXT:LONG-FLOAT-DIGITS) 64)
> (> mp128 MOST-POSITIVE-LONG-FLOAT)
> =>
> T
>
> It would make sense to me to treat these other "constants" in the same
> way I now propose to treat pi.

If you use EXT:LONG-FLOAT-DIGITS then you are outside of portable CL,
and you should take into account your uses of this function in your
coding.

If you don't use EXT:LONG-FLOAT-DIGITS then the only non-confomance is
that some things that should be constant variables are variables
instead (but they won't in fact vary).

------------------------------------------------------------------------------
_______________________________________________
clisp-list mailing list
[email protected]
https://lists.sourceforge.net/lists/listinfo/clisp-list