= IPAddress IPAddress is a Ruby library designed to make the use of IPv4 and IPv6 addresses simple, powerful and enjoyable. It provides a complete set of methods to handle IP addresses for any need, from simple scripting to full network design. IPAddress is written with a full OO interface, and its code is easy to read, maintain and extend. The documentation is full of examples, to let you start being productive immediately. This document provides a brief introduction to the library and examples of typical usage. == Requirements * Ruby 1.9.3 or later Please refer to {Travis CI}[https://travis-ci.org/ipaddress2-gem/ipaddress2] for Build Tests on specific versions of Ruby. {Build Status}[https://travis-ci.org/ipaddress2-gem/ipaddress2] {}[https://codeclimate.com/github/ipaddress2-gem/ipaddress2] If you want to contribute, please refer to {Contributing.md}[https://github.com/ipaddress2-gem/ipaddress2/blob/master/CONTRIBUTING.md]. == Installation Install the library using rubygems $ gem install ipaddress_2 You can then use it in your programs: require 'ipaddress_2' == Documentation The code is fully documented with RDoc. You can generate the documentation with Rake: ipaddress$ rake rdoc The latest documentation can be found online at {this address}[http://www.rubydoc.info/gems/ipaddress_2/0.9.0] == IPv4 Class `IPAddress::IPv4` is used to handle IPv4 type addresses. IPAddress is similar to other IP Addresses libraries, like Ruby's own IPAddr. However it works slightly different, as we will see. === Create a new IPv4 address The usual way to express an IP Address is using its dotted decimal form, such as `172.16.10.1`, and a prefix, such as `24`, separated by a slash. 172.16.10.1/24 To create a new IPv4 object, you can use IPv4 own class ip = IPAddress::IPv4.new "172.16.10.1/24" or, in a easier way, using the IPAddress parse method ip = IPAddress.parse "172.16.10.1/24" which accepts and parses any kind of IP (uint32, IPv4, IPV6 and IPv4 IPv6 Mapped addresses). If you like syntactic sugar, you can use the wrapper method `IPAddress()`, which is built around `IPAddress::parse`: ip = IPAddress "172.16.10.1/24" You can specify an IPv4 address in any of two ways: IPAddress "172.16.10.1/24" IPAddress "172.16.10.1/255.255.255.0" In this example, prefix `/24` and netmask `255.255.255.0` are the same and you have the flexibility to use either one of them. If you don't explicitly specify the prefix (or the subnet mask), IPAddress thinks you're dealing with host addresses and not with networks. Therefore, the default prefix will be `/32`, or `255.255.255.255`. For example: # let's declare an host address host = IPAddress::IPv4.new "10.1.1.1" puts host.to_string #=> "10.1.1.1/32" The new created object has prefix `/32`, which is the same as we created the following: host = IPAddress::IPv4.new "10.1.1.1/32" You can also pass a `uint32` to obtain an `IPAddress::IPv4` object: # Create host object ip = IPAddress 167837953 puts ip.to_string #=> "10.1.1.1/32" === Handling the IPv4 address Once created, you can obtain the attributes for an IPv4 object: ip = IPAddress("172.16.10.1/24") ip.address #=> "172.16.10.1" ip.prefix #=> 24 In case you need to retrieve the netmask in IPv4 format, you can use the `IPv4#netmask` method: ip.netmask #=> "255.255.255.0" A special attribute, `IPv4#octets`, is available to get the four decimal octets from the IP address: ip.octets #=> [172,16,10,1] Shortcut method `IPv4#[]`, provides access to a given octet whithin the range: ip[1] #=> 16 If you need to print out the IPv4 address in a canonical form, you can use `IPv4#to_string`: ip.to_string #=> "172.16.10.l/24" === Changing netmask You can set a new prefix (netmask) after creating an IPv4 object. For example: ip.prefix = 25 ip.to_string #=> "172.16.10.l/25" If you need to use a netmask in IPv4 format, you can achive so by using the `IPv4#netmask=` method: ip.netmask = "255.255.255.252" ip.to_string #=> "172.16.10.1/30" === Working with networks, broadcasts and addresses Some very important topics in dealing with IP addresses are the concepts of +network+ and +broadcast+, as well as the addresses included in a range. When you specify an IPv4 address such as `172.16.10.1/24`, you are actually handling two different information: * The IP address itself, "172.16.10.1" * The subnet mask which indicates the network The network number is the IP which has all zeroes in the host portion. In our example, because the prefix is 24, we identify our network number to have the last 8 (32-24) bits all zeroes. Thus, IP address `172.16.10.1/24` belongs to network `172.16.10.0/24`. This is very important because, for instance, IP `172.16.10.1/16` is very different to the previous one, belonging to the very different network `172.16.0.0/16`. ==== Networks With IPAddress it's very easy to calculate the network for an IP address: ip = IPAddress "172.16.10.1/24" net = ip.network #=> # net.to_string #=> "172.16.10.0/24" Method IPv4#network creates a new IPv4 object from the network number, calculated after the original object. We want to outline here that the network address is a perfect legitimate IPv4 address, which just happen to have all zeroes in the host portion. You can use method `IPv4#network?` to check whether an IP address is a network or not: ip1 = IPAddress "172.16.10.1/24" ip2 = IPAddress "172.16.10.4/30" ip1.network? #=> false ip2.network? #=> true ==== Broadcast The broadcast address is the contrary than the network number: where the network number has all zeroes in the host portion, the broadcast address has all one's. For example, ip `172.16.10.1/24` has broadcast `172.16.10.255/24`, where ip `172.16.10.1/16` has broadcast `172.16.255.255/16`. Method `IPv4#broadcast` has the same behavior as is `#network` counterpart: it creates a new IPv4 object to handle the broadcast address: ip = IPAddress "172.16.10.1/24" bcast = ip.broadcast #=> # bcast.to_string #=> "172.16.10.255/24" ==== Addresses, ranges and iterators So we see that the netmask essentially specifies a range for IP addresses that are included in a network: all the addresses between the network number and the broadcast. IPAddress has many methods to iterate between those addresses. Let's start with `IPv4#each`, which iterates over all addresses in a range ip = IPAddress "172.16.10.1/24" ip.each do |addr| puts addr end It is important to note that it doesn't matter if the original IP is a host IP or a network number (or a broadcast address): the #each method only considers the range that the original IP specifies. If you only want to iterate over hosts IP, use the `IPv4#each_host` method: ip = IPAddress "172.16.10.1/24" ip.each_host do |host| puts host end Methods `IPv4#first` and `IPv4#last` return a new object containing respectively the first and the last host address in the range ip = IPAddress "172.16.10.100/24" ip.first.to_string #=> "172.16.10.1/24" ip.last.to_string #=> "172.16.10.254/24" Checking if an address is loopback is easy with the `IPv4#loopback?` method: ip = IPAddress "127.0.0.1" ip.loopback? #=> true Checking if an address is in the multicast range can be done using the `IPv4#multicast?` method: ip = IPAddress "224.0.0.1/32" ip.multicast? #=> true The ability to generate a range also exists by using the `IPv4#to()` method. This allows you to create a subnet agnostic range based off a fixed amount. ip = IPAddress "172.16.10.100/24" ip.to('172.16.10.110') #=> ["172.16.10.100", ..., "172.16.10.110"] === IP special formats The IPAddress library provides a complete set of methods to access an IPv4 address in special formats, such as binary, 32 bits unsigned int, data and hexadecimal. Let's take the following IPv4 as an example: ip = IPAddress "172.16.10.1/24" ip.address #=> "172.16.10.1" The first thing to highlight here is that all these conversion methods only take into consideration the address portion of an IPv4 object and not the prefix (netmask). So, to express the address in binary format, use the `IPv4#bits` method: ip.bits #=> "10101100000100000000101000000001" To calculate the 32 bits unsigned int format of the ip address, use the `IPv4#to_u32` method ip.to_u32 #=> 2886732289 This method is the equivalent of the Unix call `pton()`, expressing an IP address in the so called +network byte order+ notation. However, if you want to transmit your IP over a network socket, you might need to transform it in data format using the `IPv4#data` method: ip.data #=> "\254\020\n\001" Also, you can transform an IPv4 address into a format which is suitable to use in IPv4-IPv6 mapped addresses: ip.to_ipv6 #=> "ac10:0a01" Finally, much like `IPv4#to_ipv6` you can use to `IPv4#to_h` method to return a non-semicolon delineated string (useful with pcap/byte level usage): ip.to_h #=> "ac100a01" === Classful networks IPAddress allows you to create and manipulate objects using the old and deprecated (but apparently still popular) classful networks concept. Classful networks and addresses don't have a prefix: their subnet mask is univocally identified by their address, and therefore divided in classes. As per RFC 791, these classes are: * Class A, from 0.0.0.0 to 127.255.255.255 * Class B, from 128.0.0.0 to 191.255.255.255 * Class C, from 192.0.0.0 to 255.255.255.255 Since classful networks here are only considered to calculate the default prefix number, classes D and E are not considered. To create a classful IP and prefix from an IP address, use the IPv4::parse_classful method: # classful ip ip = IPAddress::IPv4::parse_classful "10.1.1.1" ip.prefix #=> 8 The method automatically created a new IPv4 object and assigned it the correct prefix. You can easily check which CLASSFUL network an IPv4 object belongs: ip = IPAddress("10.0.0.1/24") ip.a? #=> true ip = IPAddress("172.16.10.1/24") ip.b? #=> true ip = IPAddress("192.168.1.1/30") ip.c? #=> true Remember that these methods are only checking the address portion of an IP, and are independent from its prefix, as classful networks have no concept of prefix. For more information on CLASSFUL networks visit the {Wikipedia page}[http://en.wikipedia.org/wiki/Classful_network] === Network design with IPAddress IPAddress includes a lot of useful methods to manipulate IPv4 and IPv6 networks and do some basic network design. ==== Subnetting The process of subnetting is the division of a network into smaller (in terms of hosts capacity) networks, called subnets, so that they all share a common root, which is the starting network. For example, if you have network "172.16.10.0/24", we can subnet it into 4 smaller subnets. The new prefix will be /26, because 4 is 2^2 and therefore we add 2 bits to the network prefix (24+2=26). Subnetting is easy with IPAddress. You actually have two options: * IPv4#subnet: specify a new prefix * IPv4#split: tell IPAddress how many subnets you want to create. Let's examine `IPv4#subnet` first. Say you have network "172.16.10.0/24" and you want to subnet it into /26 networks. With IPAddress it's very easy: network = IPAddress "172.16.10.0/24" subnets = network.subnet(26) subnets.map{|i| i.to_string} #=> ["172.16.10.0/26", "172.16.10.64/26", "172.16.10.128/26", "172.16.10.192/26"] As you can see, an Array has been created, containing 4 new IPv4 objects representing the new subnets. Another way to create subnets is to tell IPAddress how many subnets you'd like to have, and letting the library calculate the new prefix for you. Let's see how it works, using `IPv4#split` method. Say you want 4 new subnets: network = IPAddress("172.16.10.0/24") subnets = network.split(4) subnets.map{|i| i.to_string} #=> ["172.16.10.0/26", "172.16.10.64/26", "172.16.10.128/26", "172.16.10.192/26"] Hey, that's the same result as before! This actually makes sense, as the two operations are complementary. When you use `IPv4#subnet` with the new prefix, IPAddress will always create a number of subnets that is a power of two. This is equivalent to use IPv4#split with a power of 2. Where `IPv4#split` really shines is with the so called "uneven subnetting". You are not limited to split a network into a power-of-two numbers of subnets: IPAddress lets you create any number of subnets, and it will try to organize the new created network in the best possible way, making an efficient allocation of the space. An example here is worth a thousand words. Let's use the same network as the previous examples: network = IPAddress("172.16.10.0/24") How do we split this network into 3 subnets? Very easy: subnets = network.split(3) subnets.map{|i| i.to_string} #=> ["172.16.10.0/26", "172.16.10.64/26", "172.16.10.128/25"] As you can see, IPAddress tried to perform a good allocation by filling up all the address space from the original network. There is no point in splitting a network into 3 subnets like `172.16.10.0/26`, `172.16.10.64/26` and `172.16.10.128/26`, as you would end up having `172.16.10.192/26` wasted (plus, I suppose I wouldn't need a Ruby library to perform un-efficient IP allocation, as I do that myself very well ;) ). We can go even further and split into 11 subnets: network.split(11) #=> ["172.16.10.0/28", "172.16.10.16/28", "172.16.10.32/28", "172.16.10.48/28", "172.16.10.64/28", "172.16.10.80/28", "172.16.10.96/28", "172.16.10.112/28", "172.16.10.128/27", "172.16.10.160/27", "172.16.10.192/26"] As you can see, most of the networks are `/28`, with a few `/27` and one `/26` to fill up the remaining space. ==== Summarization Summarization (or aggregation) is the process when two or more networks are taken together to check if a supernet, including all and only these networks, exists. If it exists then this supernet is called the summarized (or aggregated) network. It is very important to understand that summarization can only occur if there are no holes in the aggregated network, or, in other words, if the given networks fill completely the address space of the supernet. So the two rules are: 1) The aggregate network must contain +all+ the IP addresses of the original networks; 2) The aggregate network must contain +only+ the IP addresses of the original networks; A few examples will help clarify the above. Let's consider for instance the following two networks: ip1 = IPAddress("172.16.10.0/24") ip2 = IPAddress("172.16.11.0/24") These two networks can be expressed using only one IP address network if we change the prefix. Let Ruby do the work: IPAddress::IPv4::summarize(ip1,ip2).map(&:to_string) #=> "172.16.10.0/23" We note how the network `172.16.10.0/23` includes all the addresses specified in the above networks, and (more important) includes ONLY those addresses. If we summarized +ip1+ and +ip2+ with the following network: "172.16.0.0/16" we would have satisfied rule #1 above, but not rule #2. So "172.16.0.0/16" is not an aggregate network for +ip1+ and +ip2+. If it's not possible to compute a single aggregated network for all the original networks, the method returns an array with all the aggregate networks found. For example, the following four networks can be aggregated in a single `/22`: ip1 = IPAddress("10.0.0.1/24") ip2 = IPAddress("10.0.1.1/24") ip3 = IPAddress("10.0.2.1/24") ip4 = IPAddress("10.0.3.1/24") IPAddress::IPv4::summarize(ip1,ip2,ip3,ip4).map{|i| i.to_string} #=> ["10.0.0.0/22"] But the following networks can't be summarized in a single network: ip1 = IPAddress("10.0.1.1/24") ip2 = IPAddress("10.0.2.1/24") ip3 = IPAddress("10.0.3.1/24") ip4 = IPAddress("10.0.4.1/24") IPAddress::IPv4::summarize(ip1,ip2,ip3,ip4).map{|i| i.to_string} #=> ["10.0.1.0/24","10.0.2.0/23","10.0.4.0/24"] In this case, the two summarizables networks have been aggregated into a single `/23`, while the other two networks have been left untouched. ==== Supernetting Supernetting is a different operation than aggregation, as it only works on a single network and returns a new single IPv4 object, representing the supernet. Supernetting is similar to subnetting, except that you getting as a result a network with a smaller prefix (bigger host space). For example, given the network ip = IPAddress("172.16.10.0/24") you can supernet it with a new /23 prefix ip.supernet(23).to_string #=> "172.16.10.0/23" However if you supernet it with a `/22` prefix, the network address will change: ip.supernet(22).to_string #=> "172.16.8.0/22" This is because `172.16.10.0/22` is not a network anymore, but an host address. == IPv6 IPAddress is not only fantastic for IPv4 addresses, it's also great to handle IPv6 addresses family! Let's discover together how to use it in our projects. === IPv6 addresses IPv6 addresses are 128 bits long, in contrast with IPv4 addresses which are only 32 bits long. An IPv6 address is generally written as eight groups of four hexadecimal digits, each group representing 16 bits or two octet. For example, the following is a valid IPv6 address: 2001:0db8:0000:0000:0008:0800:200c:417a Letters in an IPv6 address are usually written downcase, as per RFC. You can create a new IPv6 object using uppercase letters, but they will be converted. ==== Compression Since IPv6 addresses are very long to write, there are some simplifications and compressions that you can use to shorten them. * Leading zeroes: all the leading zeroes within a group can be omitted: "0008" would become "8" * A string of consecutive zeroes can be replaced by the string "::". This can be only applied once. Using compression, the IPv6 address written above can be shorten into the following, equivalent, address 2001:db8::8:800:200c:417a This short version is often used in human representation. ==== Network Mask As we used to do with IPv4 addresses, an IPv6 address can be written using the prefix notation to specify the subnet mask: 2001:db8::8:800:200c:417a/64 The /64 part means that the first 64 bits of the address are representing the network portion, and the last 64 bits are the host portion. === Using IPAddress with IPv6 addresses All the IPv6 representations we've just seen are perfectly fine when you want to create a new IPv6 address: ip6 = IPAddress "2001:0db8:0000:0000:0008:0800:200C:417A" ip6 = IPAddress "2001:db8:0:0:8:800:200C:417A" ip6 = IPAddress "2001:db8:8:800:200C:417A" All three are giving out the same IPv6 object. The default subnet mask for an IPv6 is 128, as IPv6 addresses don't have classes like IPv4 addresses. If you want a different mask, you can go ahead and explicit it: ip6 = IPAddress "2001:db8::8:800:200c:417a/64" Access the address portion and the prefix by using the respective methods: ip6 = IPAddress "2001:db8::8:800:200c:417a/64" ip6.address #=> "2001:0db8:0000:0000:0008:0800:200c:417a" ip6.prefix #=> 64 A compressed version of the IPv6 address can be obtained with the `IPv6#compressed` method: ip6 = IPAddress "2001:0db8:0000:0000:0008:200c:417a:00ab/64" ip6.compressed #=> "2001:db8::8:800:200c:417a" === Handling the IPv6 address Accessing the groups that form an IPv6 address is very easy with the `IPv6#groups` method: ip6 = IPAddress "2001:db8::8:800:200c:417a/64" ip6.groups #=> [8193, 3512, 0, 0, 8, 2048, 8204, 16762] As with IPv4 addresses, each individual group can be accessed using the `IPv6#[]` shortcut method: ip6[0] #=> 8193 ip6[1] #=> 3512 ip6[2] #=> 0 ip6[3] #=> 0 Note that each 16 bits group is expressed in its decimal form. You can also obtain the groups into hexadecimal format using the `IPv6#hexs` method: ip6.hexs #=> => ["2001", "0db8", "0000", "0000", "0008", "0800", "200c", "417a"] A few other methods are available to transform an IPv6 address into decimal representation, with `IPv6.to_i` ip6.to_i #=> 42540766411282592856906245548098208122 or to hexadecimal representation ip6.to_hex #=> "20010db80000000000080800200c417a" To print out an IPv6 address in human readable form, use the `IPv6#to_s`, `IPv6#to_string` and `IPv6#to_string_uncompressed` methods ip6 = IPAddress "2001:db8::8:800:200c:417a/64" ip6.to_string #=> "2001:db8::8:800:200c:417a/96" ip6.to_string_uncompressed #=> "2001:0db8:0000:0000:0008:0800:200c:417a/96" As you can see, `IPv6.to_string` prints out the compressed form, while `IPv6.to_string_uncompressed` uses the expanded version. ==== Compressing and uncompressing If you have a string representing an IPv6 address, you can easily compress it and uncompress it using the two class methods IPv6::expand and IPv6::compress. For example, let's say you have the following uncompressed IPv6 address: ip6str = "2001:0DB8:0000:CD30:0000:0000:0000:0000" Here is the compressed version: IPAddress::IPv6.compress ip6str #=> "2001:db8:0:cd30::" The other way works as well: ip6str = "2001:db8:0:cd30::" IPAddress::IPv6.expand ip6str #=> "2001:0DB8:0000:CD30:0000:0000:0000:0000" These methods can be used when you don't want to create a new object just for expanding or compressing an address (although a new object is actually created internally). === New IPv6 address from other formats You can create a new IPv6 address from different formats than just a string representing the colon-hex groups. For instance, if you have a data stream, you can use `IPv6::parse_data`, like in the following example: data = " \001\r\270\000\000\000\000\000\b\b\000 \fAz" ip6 = IPAddress::IPv6::parse_data data ip6.prefix = 64 ip6.to_string #=> "2001:db8::8:800:200c:417a/64" A new IPv6 address can also be created from an unsigned 128 bits integer: u128 = 42540766411282592856906245548098208122 ip6 = IPAddress::IPv6::parse_u128 u128 ip6.prefix = 64 ip6.to_string #=>"2001:db8::8:800:200c:417a/64" Finally, a new IPv6 address can be created from an hex string: hex = "20010db80000000000080800200c417a" ip6 = IPAddress::IPv6::parse_hex hex ip6.prefix = 64 ip6.to_string #=> "2001:db8::8:800:200c:417a/64" === Special IPv6 addresses Some IPv6 have a special meaning and are expressed in a special form, quite different than an usual IPv6 address. IPAddress has built-in support for unspecified, loopback and mapped IPv6 addresses. ==== Unspecified address The address with all zero bits is called the +unspecified+ address (corresponding to `0.0.0.0` in IPv4). It should be something like this: 0000:0000:0000:0000:0000:0000:0000:0000 but, with the use of compression, it is usually written as just two colons: :: or, specifying the netmask: ::/128 With IPAddress, create a new unspecified IPv6 address using its own subclass: ip = IPAddress::IPv6::Unspecified.new ip.to_string #=> "::/128" You can easily check if an IPv6 object is an unspecified address by using the IPv6#unspecified? method ip.unspecified? #=> true An unspecified IPv6 address can also be created with the wrapper method, like we've seen before ip = IPAddress "::" ip.unspecified? #=> true This address must never be assigned to an interface and is to be used only in software before the application has learned its host's source address appropriate for a pending connection. Routers must not forward packets with the unspecified address. ==== Loopback address The loopback address is a unicast localhost address. If an application in a host sends packets to this address, the IPv6 stack will loop these packets back on the same virtual interface. Loopback addresses are expressed in the following form: ::1 or, with their appropriate prefix, ::1/128 As for the unspecified addresses, IPv6 loopbacks can be created with IPAddress calling their own class: ip = IPAddress::IPv6::Loopback.new ip.to_string #=> "::1/128" or by using the wrapper: ip = IPAddress "::1" ip.to_string #=> "::1/128" Checking if an address is loopback is easy with the `IPv6#loopback?` method: ip.loopback? #=> true The IPv6 loopback address corresponds to `127.0.0.1` in IPv4. ==== Mapped address It is usually identified as a IPv4 mapped IPv6 address, a particular IPv6 address which aids the transition from IPv4 to IPv6. The structure of the address is ::ffff:w.y.x.z where `w.x.y.z` is a normal IPv4 address. For example, the following is a mapped IPv6 address: ::ffff:192.168.100.1 IPAddress is very powerful in handling mapped IPv6 addresses, as the IPv4 portion is stored internally as a normal IPv4 object. Let's have a look at some examples. To create a new mapped address, just use the class builder itself ip6 = IPAddress::IPv6::Mapped.new "::ffff:172.16.10.1/128" or just use the wrapper method ip6 = IPAddress "::ffff:172.16.10.1/128" Let's check it's really a mapped address: ip6.mapped? #=> true ip6.to_string #=> "::ffff:172.16.10.1/128" Now with the `#ipv4` attribute, we can easily access the IPv4 portion of the mapped IPv6 address: ip6.ipv4.address #=> "172.16.10.1" Internally, the IPv4 address is stored as two 16 bits groups. Therefore all the usual methods for an IPv6 address are working perfectly fine: ip6.to_hex #=> "00000000000000000000ffffac100a01" ip6.address #=> "0000:0000:0000:0000:0000:ffff:ac10:0a01" A mapped IPv6 can also be created just by specify the address in the following format: ip6 = IPAddress "::172.16.10.1" That is, two colons and the IPv4 address. However, as by RFC, the `ffff` group will be automatically added at the beginning ip6.to_string => "::ffff:172.16.10.1/128" making it a mapped IPv6 compatible address. == Why not using IPAddr? IPAddr is the IP addresses library that comes with Ruby standard lib. We found this library, although very well written, not very suitable for all our needs, and not very flexible. Some quick examples of things you can't do with IPAddr: * store both the address and the prefix information * quickly find the broadcast address of a network * iterate over hosts * perform subnetting or network aggregation Many methods and procedures are so old that they have been declared deprecated by the IETF, and some others have bugs in their implementation. Moreover, IPAddress is more robust and is already around 50% faster than IPAddr, in addition to provide an organic API with logical separation and OO structure. We hope that IPAddress will address all these issues and meet all your needs in network programming. == Thanks to Thanks to Luca Russo (vargolo) and Simone Carletti (weppos) for all the support and technical review. Thanks to Marco Beri, Bryan T. Richardson, Nicolas Fevrier, jdpace, Daniele Alessandri, jrdioko, Ghislain Charrier, Pawel Krzesniak, Mark Sullivan, Leif Gensert, Erik Ahlström, Peter Vandenberk and Steve Rawlinson for their support, feedback and bug reports. == Copyright Copyright (c) 2009-2015 Marco Ceresa and Mike Mackintosh. See LICENSE for details.