Re: digits of a float

["Ruud H.G. van Tol" <rvtol@isolution.nl>]

On 2024-12-15 12:31, Bill Allombert wrote:
> On Sat, Dec 14, 2024 at 12:07:29PM +0100, Ruud H.G. van Tol wrote:
> > How to properly isolate a digit of a float?
> >
> > Example:
> >
> > ? my(n=19437); localprec(n+2); Pi *10^(n-1) \1 %10
> > %4 = 7
> >
> > ? my(n=19437); localprec(n+3); Pi *10^(n-1) \1 %10
> > %5 = 6
> >
> > That type of code depends on the number of 9-digits in the decimal expansion
> > of the value.
> >
> > See also https://oeis.org/A000796, which uses localprec(n*6\5+29).
> >
> > What clean ways are there?
> This is difficult. One need to round toward 0 instead of rounding to nearest
> as usual.
>
> In this instance the number end by 574699992... which is (correctly) rounded to nearest
> by PARI to 5747.....
>
> I wrote this, which increase the accuracy until there is no more ambiguity.
> {
>    my(n=19437,z);
>    for(m=n+1,oo,
>      localprec(m+1);
>      z = round(Pi *10^m)/10^m;
>      if(abs(z-Pi)>10^-(m+1),break));
>    z*10^(n-1)\1%10
> }
>
> but this need to be checked more carefully

Yes, I have used something similar. Also for non-Pi-cases.


Bigger steps are feasible:

? my(r=List(), p=0); for(i=1, 10, localprec(p+1); listput(~r, 
p=precision(.))); Vec(r)
% [19, 38, 57, 77, 96, 115, 134, 154, 173, 192]


Specifically for Pi, I noticed that 4*atan(1) has a higher precision 
than default:
? localprec(1); [ precision(.), precision(Pi), precision(4*atan(1)) ]
% [19, 19, 38]


The "precision" mentioned in the printf-docs is yet another type of 
precision:
? localprec(1); my(v=1-10^-40); strprintf("%s | %s | %.*f", 
precision(.), 1.-v, 28, v*1.)
% "19 | 0.E-18 | 0.9999999999999999999731564544"

-- Ruud