Re: Using localprec to add guard word(s)

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Thu, Jan 21, 2016 at 02:22:01AM -0500, Charles Greathouse wrote:
> I have what I imagine is a common use case for localprec(): I have a
> calculation which is likely to need additional precision so it can return a
> result at the current precision. My inclination was to write
> 
> foo()=localprec(default(realprecision)+9); ...
> 
> but I realized that default(realprecision) is really the wrong thing, as it
> could be higher or lower than the current precision, as indeed ??localprec
> states. Is there a good way to do this?

You can use precision(1.) instead of default(realprecision).

However in practice consider whether you have some inexact input x: in
which case you should use the precision of x instead.

Consider this function, which return x modulo Pi:
rpi(x)=
{
  my(q=floor(x/Pi));
  my(nprec=bitprecision(1.)+logint(q,2));
  localbitprec(nprec);
  x-Pi*q
}
? rpi(10^22)
%20 = 2.1214152610307062651444413979983384289
which is correct.
However, if x is intended to be a t_REAL, then

rpi(x)=
{
  my(q=floor(x/Pi));
  my(nprec=bitprecision(x)+logint(q,2));
  localbitprec(nprec);
  x-Pi*q
}
is better since the precision of x can be larger than the default
precision.

Cheers,
Bill.