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Re: how do I turn a real into and array of Integers?

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From:
sisyphus
Date:
November 1, 2021 08:53
Subject:
Re: how do I turn a real into and array of Integers?
Message ID:
CADZSBj3938-DjpTWJmzUg_Hy1H0r5qXY-Fq3nY8DypnHae=JVw@mail.gmail.com
On Mon, Nov 1, 2021 at 2:35 PM ToddAndMargo via perl6-users <
perl6-users@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

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