Re: digits(n,-4)

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

On Sun, Oct 15, 2023 at 12:46:48PM +0200, Ruud H.G. van Tol wrote:
> 
> On 2023-10-14 20:34, Bill Allombert wrote:
> > On Sat, Oct 14, 2023 at 07:24:35PM +0200, Ruud H.G. van Tol wrote:
> > > ? fromdigits( [1,3,0], -4 )
> > > % 4
> > Note that we do need to know that the set of digits is here.
> > 
> > > ? my(n=4, v=[]); while( n=divrem(n,-4), v=concat(n[2],v); n=n[1] ); v
> > > % [1, 3, 0]
> > > 
> > > Is there a better way to do this?
> > I would start with use digits(n,16) and split the digits.
> 
> Thanks, am still chewing on that.

I offer the following which should handle all cases and has the benefit of being
asymptotically fast.

? negdigits(-41,-4)
%1 = [1,2,3,3]
? negdigits(41,-4)
%2 = [3,2,1]

Cheers,
Bill.

negdigits(n,b)=
{
  my(B=abs(b));
  my(V=digits(abs(n),B));
  if (b > 0, return(V));
  my(carry=0);
  if(n<0,V=-V);
  for(i=0,#V-1,
    my(u=V[#V-i]*(-1)^i+carry);
    if (u<0,u+=B;carry=1,
        u>=B,u-=B;carry=-1,
        carry=0);
    V[#V-i]=u);
  if (carry>0, concat(carry,V),carry<0,concat([1,carry+B],V),V);
}