The main sense I am getting from this, is that Perl is all about the storage.

bignum still appears to store the value as an IV though. and converting a number into a rat is the same problem only stepped up to a relationship between Rationals and Naturals, the Natural numbers now being a subset of Rationals rather than a subset of Integers.

#use bignum;
=head1 output
 
    SV = PVAV(0x6fb404) at 0x6fa59c
        REFCNT = 1
        FLAGS = ()
        ARRAY = 0x2ce1c64
        FILL = 1
        MAX = 3
        ARYLEN = 0x0
        FLAGS = (REAL)
        Elt No. 0
        SV = IV(0x25bfd30) at 0x25bfd34
          REFCNT = 1
          FLAGS = (IOK,pIOK)
          IV = 4967296
        Elt No. 1
        SV = IV(0x6fa578) at 0x6fa57c
          REFCNT = 1
          FLAGS = (IOK,pIOK)
          IV = 429
=cut
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Interestingly when I was hacking MvT attempting to use hashkeys to represent natural numbers i kept getting (FAKE) flags, maybe there's something in that. Also storing bitfields as hashkeys has unexpected results.

bignum still appears to store the value as an IV though.

No, they're objects*. See the output of perl -Mbignum -MDevel::Peek -e 'my $x=1; Dump($x)' or perl -Mbignum -MData::Dump -e 'my $x=1; dd($x)'.

It would seem that some kind of overloading solution may be the way to go, let Perl handle the storage, but overload the operations with XSUBS that do type checking/coercion. Or even straight up Inlining C.

Well, again, if you don't tell us what for, we can't really comment.

* Update: I guess you maybe mean internally? The point is, how they're stored internally is abstracted and encapsulated in an object, and you shouldn't worry about it. bignum will allow you to work with numbers of any size and any precision without any loss due to the usual floating-point imprecisions, overflows, etc.

for the greater understanding and enoblement of homus erectus.

That and, well one reason may be to help with the documentation on the Rat() function in Perl 6. By understanding what Perl is doing with numbers at the level of the Naturals we can possibly figure out how to convert the Rationals into Reals and update the Docs accordingly.

Well that and just sanity in general.

The main sense I am getting from this, is that Perl is all about the storage.

My sense is that Perl is all about the DWIM. What I haven't seen so far (and apologies if I've missed it) is where your problem lies. Here's a simple example:

#!/usr/bin/env perl 
use strict;
use warnings;

use Test::More tests => 1;

my $x = 3;
my $y = 2;
is $x + $y, 5, 'Yes, your integers behave exactly as expected';
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What else do you expect to happen?

well, and this may a little bit controversial, but...

#!perl 
use strict;
use warnings;

use Test::More tests => 1;

my $x = 5;
my $y = 3;
is $x / $y, undef, 'Yes, your integers behave exactly as expected';

=head1 output

1..1
not ok 1 - yes your integers behave as expected
#   Failed test 'yes your integers behave as expected'
#   at -e line 1.
#          got: '1.66666666666667'
#     expected: undef
# Looks like you failed 1 test of 1.

=cut
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