To use Perl's built in sort, requires that you supply an array for sorting. As you are storing your data in a single string, you would (at minimum) need to supply an array of integers, 1 .. NO_OF_RECORDS, from which you could use your EPOCH and BYTE offset formulas to substr the string for the comparisons.

However, given the small size of your data elements, 8 bytes, and the size of an SV*, even an integer one, there would be no memory savings inherent in this. So, rather than concatenating all your epoch/offset pairs into a single string, you'd be better to simply build a normal array of the pack'd pairs. The memory requirement for this will be less than an array of integers PLUS the big string.

If you reverse the ordering of the pairings so that the binary encoded epoch comes first and the offset second, then a simple (alphanumeric) sort applied to the array will sort the data by epoch with the offset acting as a tiebreak for equal datetimes.

As default alpha sort is the fastest built in sort, and using the array would avoid repeated substring of the data, it will be much faster also.

Update: Added modifed code.

Update2: Switched 'V's to 'N's commensurate with Tye's comment below.

This should be equivalent to your original code but using an array ratehr than the big string. As you can see, the sort becomes simplicity itself.

#!/usr/bin/perl -w
use strict;
use Date::Calc qw(Mktime Today_and_Now Delta_DHMS);

my @starttime = Today_and_Now;

open (BIGLOG, "< E:/biglog.log") || die "Cannot open log\n";

my @index;

while (<BIGLOG>){
    my $offset = tell BIGLOG;
    my $epoch = ( /^\s*#/ or /^\s\n/ or $_ !~ /^\s*\d/ ) ? 0 
        : Mktime( unpack 'A4xA2xA2xA2xA2xA2', $_  );
    push @index, pack 'NN', $epoch, $offset;
}

my @endindex = Today_and_Now;
print "\nIndexed ". @index ." Lines in ";
printf "%02d Days, %02d Hours, %02d Minutes, %02d Seconds", 
    Delta_DHMS( @starttime, @endindex );

@index = sort @index;

my @endtime = Today_and_Now;

print "\nTotal runtime:\t\t";
printf "%02d Days, %02d Hours, %02d Minutes, %02d Seconds\n", 
    Delta_DHMS( @starttime, @endtime );

close BIGLOG;
exit;

sub readline_n{ 
    my( $fh, $line) = @_; 
    seek $fh, unpack( 'x[N]N', $line ), 0;
    scalar <$fh> 
}
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