これだからPerlは…

result

zsh % carton exec perl tmp.pl
$VAR1 = {
          '1.79769313486232e+308' => '1.79769313486232e+308'
        };
$VAR2 = {
          '1.79769313486232e+308' => 'inf'
        };
zsh % bundle exec ruby tmp.rb
{1.7976931348623157e+308=>1.7976931348623157e+308}
{"1.7976931348623157e+308"=>1.7976931348623157e+308}

tmp.pl

#! /bin/perl

use strict;
use warnings;
use utf8;
use JSON::XS;
use Data::Dumper;

my $json = JSON::XS->new->utf8->allow_nonref;
my $val  = unpack "d", "\xFF\xFF\xFF\xFF\xFF\xFF\xEF\x7F";
my $hash = +{ $val => $val };
my $str  = $json->encode($hash);
my $data = $json->decode($str);
print Data::Dumper::Dumper($hash, $data);

tmp.rb

#! /bin/ruby

require 'json'

val  = "\xFF\xFF\xFF\xFF\xFF\xFF\xEF\x7F".unpack('d').first
hash = { val => val }
str  = JSON.dump(hash)
data = JSON.parse(str);
p hash, data