Thank you very much, Fernando, I'll try that as soon as I get back home.
Cheers,
Laurent.
Le ven. 19 avr. 2019 à 16:00, Fernando Santagata <nando.santag...@gmail.com>
a écrit :
> This one works fine:
>
> sub plouffe (Int $k) {
> my $result = 1.FatRat * (1 / 16 ** $k).FatRat * ((4 / (8 * $k +
> 1)).FatRat - (2 / (8 * $k + 4)).FatRat - (1 / (8 * $k + 5)).FatRat - (1 /
> (8 * $k + 6)).FatRat );
> }
>
> say (plouffe $_).WHAT for ^20
>
> I guess that until a certain point all the terms not specifically cast to
> FatRat are of type Rat. After reaching the maximum possible Rat they're
> converted to Num and FatRat * Num = Num.
>
> On Fri, Apr 19, 2019 at 3:37 PM Laurent Rosenfeld via perl6-users <
> perl6-us...@perl.org> wrote:
>
>> Hello,
>>
>> in the context of the Perl Weekly Challenge, I was trying to use one of
>> Franco-Canadian mathematician Simon Plouffe's formulas to compute the
>> digits of pi.
>>
>> For this, I have written the following subroutine:
>>
>> sub plouffe (Int $k) {
>> my $result = (1 / 16 ** $k) * ( (4 / (8 * $k + 1)) - (2 / (8 * $k
>> + 4)) - (1 / (8 * $k + 5)) - (1 / (8 * $k + 6) ) );
>> }
>>
>> With this, it should be possible to compute the pi decimals with
>> something like this:
>>
>> > my $k = [+] (plouffe $_ for 0..15)
>> 3.141592653589793129614170564041344859
>> >
>>
>> That doesn't work properly, however as the digitss are wrong after a
>> certain rank (16th). The reason seems to be that, after a while, rationals
>> are converted to floats and precision is lost:
>>
>> > say (plouffe $_).WHAT for 0..15;
>> (Rat)
>> (Rat)
>> (Rat)
>> (Rat)
>> (Rat)
>> (Rat)
>> (Rat)
>> (Rat)
>> (Rat)
>> (Rat)
>> (Rat)
>> (Num)
>> (Num)
>> (Num)
>> (Num)
>> (Num)
>> >
>>
>> So, for an input value of 11 or more, the plouffe subroutine returns a
>> Num.
>>
>> So I decided to try with FatRat:
>>
>> sub plouffe (Int $k) {
>> my $result = 1.FatRat * (1 / 16 ** $k) * ( (4 / (8 * $k + 1)) - (2
>> / (8 * $k + 4)) - (1 / (8 * $k + 5)) - (1 / (8 * $k + 6) ) );
>> }
>>
>> It is a bit better, but I am again falling back to Num when the
>> subroutine input value reaches 17 or above:
>>
>> > say (plouffe $_).WHAT for 0..20;
>> (FatRat)
>> (FatRat)
>> (FatRat)
>> (FatRat)
>> (FatRat)
>> (FatRat)
>> (FatRat)
>> (FatRat)
>> (FatRat)
>> (FatRat)
>> (FatRat)
>> (FatRat)
>> (FatRat)
>> (FatRat)
>> (FatRat)
>> (FatRat)
>> (Num)
>> (Num)
>> (Num)
>> (Num)
>> (Num)
>>
>> Has anyone an idea why we are not keeping FatRat values all the way? Or,
>> is there a better way to guarantee that we continue to use FatRat's?
>>
>> Note that I have found other ways of computing many pi digits, but the
>> one described above would be much simpler and much more elegant, if only it
>> worked OK. So my question is really not how to compute pi's digits, but
>> more this: why are the above computations falling from FatRat to Num after
>> a while, and is there something to do to keep FatRat calculation all the
>> way?
>>
>> Thanks to anyone who would be able to shed light on this.
>>
>>
>>
>>
>>
>>
>>
>>
>>
>
> --
> Fernando Santagata
>
