Re: experimental localprec() feature

[Karim Belabas <Karim.Belabas@math.u-bordeaux.fr>]

* Loïc Grenié [2014-10-09 22:41]:
> 2014-10-09 17:37 GMT+02:00 Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>:
>> I have created an experimental git branch bill-localprec that adds a command
>> localprec() which allow to set the real precision locally:
>>
>> Consider the function:
>> f(s)=Pi^s
>> and
>> s=precision(1.,100)
>>
>> Pi is computed using the current precision.
>> If we want the resut to be correct to the precision of s,
>> we could do
>>
>> g(s)=
>> { my(prec=default(realprecision));
>>   default(realprecision,precision(s));
>>   my(r=Pi^s);
>>   default(realprecision,prec);
>>   r;
>> }
>>
>> which is rather cumbersome. Using localprec() it is sufficient to say:
>>
>> g(s)=localprec(precision(s));Pi^s
>>
>> Also it is safer since the value of realprecision is restored even if an
>> error occurs.
> 
>      Nice! Thanks! That's something that I have dreamed for a long time.

BTW, some precisions:

1) as Bill's original save/restore example suggests, it is really a
'localprec' with the semantics of 'local' (dynamic scoping); not a
'myprec' with the semantics of 'my' (lexical scoping). I.e.

  \p38
  g()=Pi;
  f()=localprec(100);g(s);

Then f() does compute Pi with 100 decimals, even though the call to 'Pi' 
itself occurs outside of the body of f. Note that

  \p38
  g=Pi;
  f()=localprec(100);g;

returns a result with 38 decimals of accuracy since g in that case is a
constant that was previously computed and not a function evaluated when f() is
called, while localprec is in effect.

2) 'realprecision' itself is unaffected by localprec settings

  ? localprec(100);default(realprecision);
  %1 = 38

Conversely, changing 'realprecision' from within a localprec() scope
is a local no-op. The new accuracy is overriden by localprec settings
in that scope:

  ? \p100
  ? localprec(57); default(realprecision,38); precision(Pi)
  %2 = 57

It does become the new default precision, of course

  ? default(realprecision)
  %3 = 38

Thus one should no longer change default(realprecision,) in new scripts: it
will interact with localprec() in confusing ways. This changes for the better:
'realprecision' becomes a true global "default" corresponding to user's
preferences in a given context.

Cheers,

    K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 69 50
351, cours de la Liberation    http://www.math.u-bordeaux1.fr/~kbelabas/
F-33405 Talence (France)       http://pari.math.u-bordeaux1.fr/  [PARI/GP]
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