Beefy Boxes and Bandwidth Generously Provided by pair Networks
Your skill will accomplish
what the force of many cannot
 
PerlMonks  

Comment on

( #3333=superdoc: print w/ replies, xml ) Need Help??

Ever since I've read about them, I've been fascinated by spigot algorithms for producing digits of pi.

The basic idea for those algorithms is that most "interesting" transcendental numbers (like pi, e, ln(2)) have a pretty simple representation if the base is allowed (in a regular pattern) for each digit. Then the task of computing the first $N first digits is just that of a base conversion. And the fascinating part is that you can work with integers only-

To stay a bit on topic, I've ported this C implementation of a spigot algorithm for pi to Perl 6:

sub pi-spigot(Int $digits) { my $len = 1 + floor 10 * $digits / 3; my @a = 2 xx $len; my Int $nines = 0; my Int $predigit = 0; join '', gather for 1 .. ($digits + 1) -> $j { my Int $q = 0; loop (my int $i = $len; $i > 0; $i = $i - 1) { my int $x = 10 * @a[$i - 1] + $q * $i; @a[$i - 1] = $x % ( 2 * $i - 1); $q = $x div (2 * $i - 1); } @a[0] = $q % 10; $q div= 10; if $q == 9 { ++$nines; } elsif $q == 10 { take $predigit + 1, 0 xx $nines; $nines = 0; $predigit = 0; } else { take $predigit; $predigit = $q; take 9 xx $nines; $nines = 0; } } } multi MAIN($n = 100) { say pi-spigot($n.Int); } multi MAIN('test') { use Test; plan 1; is pi-spigot(100), '03141592653589793238462643383279502884197169399375105820974944 +59230781640628620899862803482534211706', 'it works'; }

Since Rakudo is still pretty slow for this kind of stuff, I've traded a bit of readabilty for speed by using a native int in the inner loop, which means that Rakudo can inline most operators, but means I have to write $i = $i - 1 instead of $i-- (because native ints are value types, and you cannot (yet?) pass them as writable values to routines, so the -- operator cannot work on them).


In reply to Re: Computing pi to multiple precision by moritz
in thread Computing pi to multiple precision by ambrus

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post; it's "PerlMonks-approved HTML":



  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • Outside of code tags, you may need to use entities for some characters:
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.
  • Log In?
    Username:
    Password:

    What's my password?
    Create A New User
    Chatterbox?
    and the web crawler heard nothing...

    How do I use this? | Other CB clients
    Other Users?
    Others chanting in the Monastery: (13)
    As of 2014-12-19 16:55 GMT
    Sections?
    Information?
    Find Nodes?
    Leftovers?
      Voting Booth?

      Is guessing a good strategy for surviving in the IT business?





      Results (90 votes), past polls