a curious little number encoder

joe.pl

#!/usr/bin/perl

use common::sense;
use Math::BigInt;

my $orig = $ARGV[0] ? Math::BigInt->new(shift) : Math::BigInt->new(1 . (0 x 3000)) + 7;
my $res  = blog_reduce($orig);

print stringify_series( $res ), "\n";

sub stringify_series {
    my ($base, $logf, $delta) = @{$_[0]};

    my $ret = "$base";
       $ret .= "^"   . (ref($logf)  eq "ARRAY" ? "(" . stringify_series($logf)  . ")" : $logf);
       $ret .= " + " . (ref($delta) eq "ARRAY" ? "(" . stringify_series($delta) . ")" : $delta) if $delta;

    return $ret;
}

sub blog_reduce {
    my $arg = shift;
    my $logf  = $arg->copy->blog(10);
    my $delta = $arg - Math::BigInt->new(10)->bpow($logf);

    $logf  = blog_reduce( $logf  ) if $logf  > 99;
    $delta = blog_reduce( $delta ) if $delta > 99;

    return [10, $logf, $delta];
}