On Sun, Oct 31, 2021 at 6:51 PM ToddAndMargo via perl6-users <
perl6-us...@perl.org> wrote:
> >> How do I get more digits out of sqrt?
>
> On 10/31/21 17:50, Kevin Pye wrote:
> > You don't.
> >
> > sqrt is a function which acts on 64-bit floating point numbers, and
> there's no more meaningful digits available. If you need more precision
> you're on your own.
>
> Dang! I was hoping ther was some thing like UInt.
>
Fortunately, it's easy.
Wikipedia describes the following recurrence formula for approximating the
square root of 2 from an initial guess a₀:
aₙ₊₁ = (aₙ / 2 + 1 / aₙ)
So just iterate this sequence until successive terms become close enough
for you, using the unlimited precision FatRat type, for example:
(2.FatRat, { $_ / 2 + 1 / $_ } ... (* - *).abs < 1e-100).tail
This gives the root to a precision of one in a googol.
