in reply to Re^2: Small Perl 6 discoveries II, Rats
in thread [Perl6] Small discoveries I, __DATA__

If you want arbitrary precision rational arithmetic, you can use a FatRat

I didn't know about FatRats (yes, I know very little about perl6) - so I had a bit of a play (on rakudo-star-2017.07) and encountered confusing results: 
> my $x = 1.111111111111111111111.FatRat; my $y = 1.111111111111111111
+111.Rat; $x - $y
0
> $x == $y
True
> say $x
1.111111111111111111111
> say $y
1.11111111111111111604544
>

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On the bases that $x-$y==0 and $x==$y one is led to believe that $x and $y are exactly equivalent.
Yet, say() presents us with different values.

Are the 2 rationals equivalent ?
If so, then why does say() output different values ?
If not, then why do both $x-$y==0 and $x==$y evaluate as "True" ?

Interestingly, 1.11111111111111111604544 is the value of the double 1.1111111111111111 (16 decimal places) rounded to 23 decimals: 
C:\>perl -le "printf '%.22e\n', 1.1111111111111111;"
1.1111111111111111604544e+000\n

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Perhaps this ties in with: 
> my $x = 1.111111111111111111111.FatRat; my $y = 1.1111111111111111.N
+um; $x - $y
0
> $x == $y
True

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How does one coerce perl6 into displaying the actual numerator and denominator of these rationals ?

Cheers,
Rob

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Re^4: Small Perl 6 discoveries II, Rats
by Anonymous Monk on Oct 20, 2017 at 15:02 UTC
    How does one coerce perl6 into displaying the actual numerator and denominator of these rationals?
    $x.nude

    That would make sense if the numerator and denominator were $x.nu and $x.de, but they're not. You have to type out $x.numerator and $x.denominator. I thought we were trying to make Perl6 safe for 10-year-old girls, but I guess someone just couldn't pass up an opportunity for a crude joke.

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      $x.nude

      That enables me to see that 1.111111111111111111111.FatRat and 1.111111111111111111111.Rat have equivalent rational values: 
      > my $x = 1.111111111111111111111.Rat; $x.nude
(1111111111111111111111 1000000000000000000000)
> my $y = 1.111111111111111111111.FatRat; $y.nude
(1111111111111111111111 1000000000000000000000)

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      and that $x (the Rat) gets handled in a way that I don't really expect: 
      > my $r1 = $x * 0.3
0.333333333333333
> $r1 = $x * 0.3.Rat
0.333333333333333
> $r1 = $x * 0.3.Num
0.333333333333333
> $r1 = $x * 3e-1
0.333333333333333
> $r1 = $x * 0.3.FatRat
0.3333333333333333333333

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      though the last result is as I expected.
      Compare those outputs with: 
      > my $r2 = $y * 0.3
0.3333333333333333333333
> my $r2 = $y * 0.3.Rat
0.3333333333333333333333
> my $r2 = $y * 0.3.Num
0.333333333333333
> my $r2 = $y * 3e-1
0.333333333333333
> my $r2 = $y * 0.3.FatRat
0.3333333333333333333333

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      which is more in keeping with my expectations.

      I'm sure it all makes sense if you know how to look at it from the appropriate angle.

      Cheers,
      Rob
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[d/l]
[select]
        From docs.perl6.org/type/Rat (anons can't post full urls):
        To prevent the numerator and denominator from becoming pathologically large, the denominator is limited to 64 bit storage. On overflow of the denominator a Num (floating-point number) is returned instead.
        However, Rat values generated from decimal notation can violate the 64-bit limit.

        You can use $x.WHAT to find $x's type if you get tired of guessing based on the number of decimal places displayed.

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