in reply to Re: 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: 
> say 1.111111111111111111111.FatRat
1.111111111111111111111

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Re^3: Small Perl 6 discoveries II, Rats
by syphilis (Archbishop) on Oct 20, 2017 at 04:12 UTC
    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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      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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Re^3: Small Perl 6 discoveries II, Rats
by Anonymous Monk on Oct 19, 2017 at 15:52 UTC
    If the Rat class isn't any more accurate than a Num, but it's much slower, then what purpose does it serve?
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      Well -- I'd say it is more accurate (though not more precise) -- it can accurately represent rational numbers, so you can do rational arithmetic without rounding errors. e.g. 
      > .3.Num - .2.Num - .1.Num == 0
False
> .3 - .2 - .1 == 0
True

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[d/l]
        The reason this digression started is because it can't accurately represent rational numbers. Except for trivial examples, I suppose.
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