On Mon, Nov 1, 2021 at 2:35 PM ToddAndMargo via perl6-users <
perl6-us...@perl.org> wrote:
> On 10/31/21 19:39, Sean McAfee wrote:
>
> > (2.FatRat, { $_ / 2 + 1 / $_ } ... (* - *).abs < 1e-100).tail
>
> 1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641572735013846230912297024924836055850737212644121497099935831413222665927505592755799950501152782060571
>
>
> Awesome!
>
Note that what you have there is a 200-decimal-digit (around 658-bit)
precision representation of the square root of 2 - which is quite different
to the (53-bit precision) Real sqrt(2).
If you obtained a 200-decimal-digit representation of that original Real,
you'd end up with:
1.4142135623730951454746218587388284504413604736328125
That has, of course, significantly fewer digits than 200 - the reason being
that the missing (147) additional digits are all zeros.
That is, 1.4142135623730951454746218587388284504413604736328125 is an exact
decimal representation of the actual precise value held by the Real sqrt(2).
>From that it can be established that the exact rational representation of
the Real sqrt(2) is 6369051672525773/4503599627370496.
I don't know how all of that could be done in raku.
In perl:
C:\>perl -le "printf '%.200g', sqrt 2;"
1.4142135623730951454746218587388284504413604736328125
C:\>perl -MMath::BigRat -le "print
Math::BigRat->new(Math::BigFloat->new('1.4142135623730951454746218587388284504413604736328125'));"
6369051672525773/4503599627370496
Anyway ... this is probably not all that relevant ... especially if you
were actually just seeking a higher-precision calculation of sqrt(2) than
the Real provides.
Cheers,
Rob
