Beefy Boxes and Bandwidth Generously Provided by pair Networks
Don't ask to ask, just ask

comment on

( #3333=superdoc: print w/replies, xml ) Need Help??
Here is a variation of that one that deals with log factorials, so it needs only regular arithmetic. It uses the gammln recently posted here by ewijaya.

It is extremely fast, solving 1..99 in about 2 seconds. (There may be roundoff error issues. I have not checked all the answers.)

Update: I added an independent confirmation with Math::Pari for every number I insert in the queue. They all come out correct. With checking added, the solution to 1..99 takes a minute and 23 seconds. The hardest to get is 92, which passes through 12985 factorial.

#!/usr/bin/perl use strict; use Inline qw(C); use Math::Pari qw(ifact sqrtint PARI); my $max = shift || 10; my @try; my $maxlog = log(1024*1024); my $log2 = log(2.0); my $biggest = 0; # deal with '1' explicitly my %seen = (1 => 's'); my $waiting = $max - 1; print "1 => s\n"; insert(3, ''); my $m; while (@try) { my $n = shift @try; $biggest = $n if $n > $biggest; my $s = 'f' . $seen{$n}; #$n->bfac; # $n = ($n)! my $logfact = gammln($n + 1.0); if ($logfact > $maxlog) { while ($logfact > $maxlog) { $logfact /= 2.0; $s = "s$s"; } # truncate the square root. $m = int(exp($logfact)); } else { # round a straight gamma log. $m = int(exp($logfact) + .5); } while (!defined $seen{$m}) { insert($m, $s); $m = int(sqrt($m)); $s = "s$s"; } } sub insert { my($n, $s) = @_; if ($s ne "") { my $check_n = confirm($s); if ($check_n != $n) { print "$n did not confirm correctly -- expression gave $check_ +n\n"; } } if ($n <= $max) { print "$n => $s\n"; if (--$waiting == 0) { print "biggest tried was $biggest\n"; exit 0; } } $seen{$n} = $s; my($min, $max) = (0, scalar @try); while ($min + 1 < $max) { my $new = ($min + $max) >> 1; if ($try[$new] > $n) { $max = $new; } else { $min = $new; } } ++$min if $min < @try && $try[$min] < $n; splice @try, $min, 0, $n; } sub confirm { my $s = shift; my @ops = reverse split //,$s; my $val = PARI 3; foreach my $op (@ops) { if ($op eq "f") { #print "doing $val factorial\n"; $val = ifact($val); } else { $val = sqrtint($val); #print "doing sqrt\n"; } } #"final result is $val\n"; return $val; } __END__ __C__ double gammln(double xx) { double x,y, tmp,ser; static double cof[6] = {76.18009172947146, -86.50532032941677, 24.01409824083091, -1.231739572450155, 0.12086509738661e-2, -0.5395239384953e-5}; int j; y = x = xx; tmp= x+5.5; tmp -= (x+0.5)*log(tmp); ser=1.000000000190015; for (j=0;j<=5;j++) ser += cof[j]/++y; return -tmp+log(2.5066282746310005*ser/x); }

In reply to Re^2: Challenge: Chasing Knuth's Conjecture by tall_man
in thread Challenge: Chasing Knuth's Conjecture by kvale

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!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • 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
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            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?

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

    How do I use this? | Other CB clients
    Other Users?
    Others pondering the Monastery: (10)
    As of 2019-11-15 12:47 GMT
    Find Nodes?
      Voting Booth?
      Strict and warnings: which comes first?

      Results (83 votes). Check out past polls.