Hmm. I get the same results both ways: 

P:\test>findstr # LR-nearFactor.pl
#!/usr/bin/perl
#    my $sqrt = sqrt( $N );
    my $end = $#factor;
        return $f ; #< $sqrt ? $f : undef;
            splice(@subset, $#subset - 1, 1);
            splice(@subset, $#subset - 1, 2, $pos);

P:\test>LR-nearFactor.pl 24777695232
11
1
P:\test>findstr # LR-nearFactor.pl
#!/usr/bin/perl
    my $end = $#factor;
            splice(@subset, $#subset - 1, 1);
            splice(@subset, $#subset - 1, 2, $pos);

P:\test>LR-nearFactor.pl 24777695232
11
1

[download]

Which version of Parei do you have? I have 

====================
    Name: Math-Pari
 Version: 2.010603
  Author: Ilya Zakharevich (cpan@ilyaz.org)
   Title: Math-Pari
Abstract: Perl interface to PARI.
InstDate:  21:18:09 2005
Location: http://ppm.ActiveState.com/cgibin/PPM/ppmserver-5.8-windows.
+pl?urn:/PPMServer
Available Platforms:
       1. MSWin32-x86-multi-thread-5.8
====================

[download]

It's kind of hard to see how using the built in sqrt function would influence factorint()> but have you tried moving the call to sqrt after the call to factorint()?

Anyway, trying to get beyond that, I picked a few ideas from tall_man's code (which is definitely the benchmark in this thread) and modified your code to read as: 

#!/usr/bin/perl
use strict;
use warnings;
use Math::Pari qw/:int factorint sqrtint PARImat/;

my $N = '1' . '0' x $ARGV[0] . '1';

print "Result for $N is ", nearest_sqrt(  $N );

sub prime_factors {
    my $N = shift;
    my %p_fact = PARImat( factorint( $N ) ) =~ /(\d+)/g;
    return map { ($_) x $p_fact{$_} } sort { $a <=> $b } keys %p_fact;
}

sub nearest_sqrt {
    my $N = shift;
    my $sqrt = sqrtint( $N );
    my @factor = prime_factors( $N );
....

[download]

As I understand it, ':int', makes all integers in the program Pari compatible?. And using sqrtint() ought to bypass any imcompatibilities.

The fudge with $ARGV[ 0 ] at the top allows me to test the code on some really big numbers without having to type out all the digits--I applied the same hack to tall_man's code, and then ran a few tests.

The following is the results from a few carefully chosen (particularly hard) examples timing both programs.

Going by the time your program takes in comparison to tall_man's, you appear to be doing a similar amount of work, but your code is returning -1, which I do not understand? 

P:\test>timethis TM-nearFactor.pl 55   & timethis LR-nearFactor.pl 55

TimeThis :  Command Line :  TM-nearFactor.pl 55
TimeThis :    Start Time :  Sat Feb 26 14:38:33 2005

Result for 100000000000000000000000000000000000000000000000000000001 i
+s 7376575663406069736503138401

TimeThis :  Command Line :  TM-nearFactor.pl 55
TimeThis :    Start Time :  Sat Feb 26 14:38:33 2005
TimeThis :      End Time :  Sat Feb 26 14:38:36 2005
TimeThis :  Elapsed Time :  00:00:03.281

TimeThis :  Command Line :  LR-nearFactor.pl 55
TimeThis :    Start Time :  Sat Feb 26 14:38:37 2005

Result for 100000000000000000000000000000000000000000000000000000001 i
+s -1
TimeThis :  Command Line :  LR-nearFactor.pl 55
TimeThis :    Start Time :  Sat Feb 26 14:38:37 2005
TimeThis :      End Time :  Sat Feb 26 14:38:40 2005
TimeThis :  Elapsed Time :  00:00:03.265

P:\test>timethis TM-nearFactor.pl 58   & timethis LR-nearFactor.pl 58

TimeThis :  Command Line :  TM-nearFactor.pl 58
TimeThis :    Start Time :  Sat Feb 26 14:38:50 2005

Result for 10000000000000000000000000000000000000000000000000000000000
+1 is 22665854592333022426775023

TimeThis :  Command Line :  TM-nearFactor.pl 58
TimeThis :    Start Time :  Sat Feb 26 14:38:50 2005
TimeThis :      End Time :  Sat Feb 26 14:39:07 2005
TimeThis :  Elapsed Time :  00:00:17.578

TimeThis :  Command Line :  LR-nearFactor.pl 58
TimeThis :    Start Time :  Sat Feb 26 14:39:07 2005

Result for 10000000000000000000000000000000000000000000000000000000000
+1 is -1
TimeThis :  Command Line :  LR-nearFactor.pl 58
TimeThis :    Start Time :  Sat Feb 26 14:39:07 2005
TimeThis :      End Time :  Sat Feb 26 14:39:25 2005
TimeThis :  Elapsed Time :  00:00:17.578

[download]

The timings of these two particularly difficult runs, going by how long tall_man'code takes relative to most other runs like: 

P:\test>timethis TM-nearFactor.pl 57   & timethis LR-nearFactor.pl 57

TimeThis :  Command Line :  TM-nearFactor.pl 57
TimeThis :    Start Time :  Sat Feb 26 14:38:49 2005

Result for 10000000000000000000000000000000000000000000000000000000001
+ is 846610559160061

TimeThis :  Command Line :  TM-nearFactor.pl 57
TimeThis :    Start Time :  Sat Feb 26 14:38:49 2005
TimeThis :      End Time :  Sat Feb 26 14:38:50 2005
TimeThis :  Elapsed Time :  00:00:00.140

TimeThis :  Command Line :  LR-nearFactor.pl 57
TimeThis :    Start Time :  Sat Feb 26 14:38:50 2005

Result for 10000000000000000000000000000000000000000000000000000000001
+ is -1
TimeThis :  Command Line :  LR-nearFactor.pl 57
TimeThis :    Start Time :  Sat Feb 26 14:38:50 2005
TimeThis :      End Time :  Sat Feb 26 14:38:50 2005
TimeThis :  Elapsed Time :  00:00:00.109

[download]

which despite being nearly as big a number, is solved in under a 1/5th of a second rather than 17+ seconds above. The very close similarity in timing between your code and tall_man's suggests that you are probably doing a very similar amount of work and possibly arriving at the same result, but for some reason, failing to display it?.

Maybe a rounding error somewhere. I tried to follow this through--but as you know your code better than I, you might find the solution more quickly.

Either way, your determination of the appropriate sequence of tests and short-ciruiting is very impressive. I congratulate you++ :).

Examine what is said, not who speaks.
Silence betokens consent.
Love the truth but pardon error.

In reply to Re^9: OT: Finding Factor Closest To Square Root by BrowserUk
in thread OT: Finding Factor Closest To Square Root by QM

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!
  • 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, details, 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, summary, 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.