$x overloads stringification, stringifying as "27". The new method presumably does something like:

sub new {
  my ($class, $value) = @_;
  bless { value => $value } => "$class";
}
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Thus you end up with a reference blessed into package "27".

Generally speaking, constructors are designed to be called as class methods not object methods.

Agreed. However, here is the first part of new:

sub new 
  {
  # create a new BigInt object from a string or another BigInt object.
+ 
  # see hash keys documented at top

  # the argument could be an object, so avoid ||, && etc on it, this w
+ould
  # cause costly overloaded code to be called. The only allowed ops ar
+e
  # ref() and defined.

  my ($class,$wanted,$a,$p,$r) = @_;
 
  # avoid numify-calls by not using || on $wanted!
  return $class->bzero($a,$p) if !defined $wanted;    # default to 0
  return $class->copy($wanted,$a,$p,$r)
   if ref($wanted) && $wanted->isa($class);        # MBI or subclass

  $class->import() if $IMPORT == 0;        # make require work
  
  my $self = bless {}, $class;
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If it gets to the last line, and $class == 27, then $class must have been changed somewhere?

And generally speaking, if I want a new object from an existing object, shouldn't the existing object be able to create one for me? Or do I have to go around doing this?

my $y = {ref $x}->new();
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(or whatever the syntax is for that)

-QM
--
Quantum Mechanics: The dreams stuff is made of

$class is the same as $x (i.e. the bigint 27) the whole way through new, and bless implicitly stringifies its second argument (like print implicitly stringifies its arguments).

ref($x)->new(48) should do what you want. Another reasonably common idiom is:

my $new = (ref($existing) // $existing)->new(...)
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This allows $existing to be either an existing object or a class name.

perl -E'sub Monkey::do{say$_,for@_,do{($monkey=[caller(0)]->[3])=~s{::}{ }and$monkey}}"Monkey say"->Monkey::do'

I also think this is strange. There is no checking for ref($class). I guess something like ...

    if ( ref($class) ){
        my $t = $wanted; 
        $t =~ s/^[+-]//;

        return bless {
            sign => $class->{sign},
            value => $CALC->_new($t),
        }, ref($class);
    }

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should be in new constructor, doesn't it?