Closed. This question needs to be more focused. It is not currently accepting answers.
Closed 1 year ago.
Locked. This question and its answers are locked because the question is off-topic but has historical significance. It is not currently accepting new answers or interactions.
I want to create a URL shortener service where you can write a long URL into an input field and the service shortens the URL to "http://www.example.org/abcdef".
Instead of "abcdef" there can be any other string with six characters containing a-z, A-Z and 0-9. That makes 56~57 billion possible strings.
My approach:
I have a database table with three columns:
id, integer, auto-increment
long, string, the long URL the user entered
short, string, the shortened URL (or just the six characters)
I would then insert the long URL into the table. Then I would select the auto-increment value for "id" and build a hash of it. This hash should then be inserted as "short". But what sort of hash should I build? Hash algorithms like MD5 create too long strings. I don't use these algorithms, I think. A self-built algorithm will work, too.
My idea:
For "http://www.google.de/" I get the auto-increment id 239472. Then I do the following steps:
short = '';
if divisible by 2, add "a"+the result to short
if divisible by 3, add "b"+the result to short
... until I have divisors for a-z and A-Z.
That could be repeated until the number isn't divisible any more. Do you think this is a good approach? Do you have a better idea?
Due to the ongoing interest in this topic, I've published an efficient solution to GitHub, with implementations for JavaScript, PHP, Python and Java. Add your solutions if you like :)
I would continue your "convert number to string" approach. However, you will realize that your proposed algorithm fails if your ID is a prime and greater than 52.
Theoretical background
You need a Bijective Function f. This is necessary so that you can find a inverse function g('abc') = 123 for your f(123) = 'abc' function. This means:
There must be no x1, x2 (with x1 ≠ x2) that will make f(x1) = f(x2),
and for every y you must be able to find an x so that f(x) = y.
How to convert the ID to a shortened URL
Think of an alphabet we want to use. In your case, that's [a-zA-Z0-9]. It contains 62 letters.
Take an auto-generated, unique numerical key (the auto-incremented id of a MySQL table for example).
For this example, I will use 12510 (125 with a base of 10).
Now you have to convert 12510 to X62 (base 62).
12510 = 2×621 + 1×620 = [2,1]
This requires the use of integer division and modulo. A pseudo-code example:
digits = []
while num > 0
remainder = modulo(num, 62)
digits.push(remainder)
num = divide(num, 62)
digits = digits.reverse
Now map the indices 2 and 1 to your alphabet. This is how your mapping (with an array for example) could look like:
0 → a
1 → b
...
25 → z
...
52 → 0
61 → 9
With 2 → c and 1 → b, you will receive cb62 as the shortened URL.
http://shor.ty/cb
How to resolve a shortened URL to the initial ID
The reverse is even easier. You just do a reverse lookup in your alphabet.
e9a62 will be resolved to "4th, 61st, and 0th letter in the alphabet".
e9a62 = [4,61,0] = 4×622 + 61×621 + 0×620 = 1915810
Now find your database-record with WHERE id = 19158 and do the redirect.
Example implementations (provided by commenters)
C++
Python
Ruby
Haskell
C#
CoffeeScript
Perl
Why would you want to use a hash?
You can just use a simple translation of your auto-increment value to an alphanumeric value. You can do that easily by using some base conversion. Say you character space (A-Z, a-z, 0-9, etc.) has 62 characters, convert the id to a base-40 number and use the characters as the digits.
public class UrlShortener {
private static final String ALPHABET = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789";
private static final int BASE = ALPHABET.length();
public static String encode(int num) {
StringBuilder sb = new StringBuilder();
while ( num > 0 ) {
sb.append( ALPHABET.charAt( num % BASE ) );
num /= BASE;
}
return sb.reverse().toString();
}
public static int decode(String str) {
int num = 0;
for ( int i = 0; i < str.length(); i++ )
num = num * BASE + ALPHABET.indexOf(str.charAt(i));
return num;
}
}
Not an answer to your question, but I wouldn't use case-sensitive shortened URLs. They are hard to remember, usually unreadable (many fonts render 1 and l, 0 and O and other characters very very similar that they are near impossible to tell the difference) and downright error prone. Try to use lower or upper case only.
Also, try to have a format where you mix the numbers and characters in a predefined form. There are studies that show that people tend to remember one form better than others (think phone numbers, where the numbers are grouped in a specific form). Try something like num-char-char-num-char-char. I know this will lower the combinations, especially if you don't have upper and lower case, but it would be more usable and therefore useful.
My approach: Take the Database ID, then Base36 Encode it. I would NOT use both Upper AND Lowercase letters, because that makes transmitting those URLs over the telephone a nightmare, but you could of course easily extend the function to be a base 62 en/decoder.
Here is my PHP 5 class.
<?php
class Bijective
{
public $dictionary = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789";
public function __construct()
{
$this->dictionary = str_split($this->dictionary);
}
public function encode($i)
{
if ($i == 0)
return $this->dictionary[0];
$result = '';
$base = count($this->dictionary);
while ($i > 0)
{
$result[] = $this->dictionary[($i % $base)];
$i = floor($i / $base);
}
$result = array_reverse($result);
return join("", $result);
}
public function decode($input)
{
$i = 0;
$base = count($this->dictionary);
$input = str_split($input);
foreach($input as $char)
{
$pos = array_search($char, $this->dictionary);
$i = $i * $base + $pos;
}
return $i;
}
}
A Node.js and MongoDB solution
Since we know the format that MongoDB uses to create a new ObjectId with 12 bytes.
a 4-byte value representing the seconds since the Unix epoch,
a 3-byte machine identifier,
a 2-byte process id
a 3-byte counter (in your machine), starting with a random value.
Example (I choose a random sequence)
a1b2c3d4e5f6g7h8i9j1k2l3
a1b2c3d4 represents the seconds since the Unix epoch,
4e5f6g7 represents machine identifier,
h8i9 represents process id
j1k2l3 represents the counter, starting with a random value.
Since the counter will be unique if we are storing the data in the same machine we can get it with no doubts that it will be duplicate.
So the short URL will be the counter and here is a code snippet assuming that your server is running properly.
const mongoose = require('mongoose');
const Schema = mongoose.Schema;
// Create a schema
const shortUrl = new Schema({
long_url: { type: String, required: true },
short_url: { type: String, required: true, unique: true },
});
const ShortUrl = mongoose.model('ShortUrl', shortUrl);
// The user can request to get a short URL by providing a long URL using a form
app.post('/shorten', function(req ,res){
// Create a new shortUrl */
// The submit form has an input with longURL as its name attribute.
const longUrl = req.body["longURL"];
const newUrl = ShortUrl({
long_url : longUrl,
short_url : "",
});
const shortUrl = newUrl._id.toString().slice(-6);
newUrl.short_url = shortUrl;
console.log(newUrl);
newUrl.save(function(err){
console.log("the new URL is added");
})
});
I keep incrementing an integer sequence per domain in the database and use Hashids to encode the integer into a URL path.
static hashids = Hashids(salt = "my app rocks", minSize = 6)
I ran a script to see how long it takes until it exhausts the character length. For six characters it can do 164,916,224 links and then goes up to seven characters. Bitly uses seven characters. Under five characters looks weird to me.
Hashids can decode the URL path back to a integer but a simpler solution is to use the entire short link sho.rt/ka8ds3 as a primary key.
Here is the full concept:
function addDomain(domain) {
table("domains").insert("domain", domain, "seq", 0)
}
function addURL(domain, longURL) {
seq = table("domains").where("domain = ?", domain).increment("seq")
shortURL = domain + "/" + hashids.encode(seq)
table("links").insert("short", shortURL, "long", longURL)
return shortURL
}
// GET /:hashcode
function handleRequest(req, res) {
shortURL = req.host + "/" + req.param("hashcode")
longURL = table("links").where("short = ?", shortURL).get("long")
res.redirect(301, longURL)
}
C# version:
public class UrlShortener
{
private static String ALPHABET = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789";
private static int BASE = 62;
public static String encode(int num)
{
StringBuilder sb = new StringBuilder();
while ( num > 0 )
{
sb.Append( ALPHABET[( num % BASE )] );
num /= BASE;
}
StringBuilder builder = new StringBuilder();
for (int i = sb.Length - 1; i >= 0; i--)
{
builder.Append(sb[i]);
}
return builder.ToString();
}
public static int decode(String str)
{
int num = 0;
for ( int i = 0, len = str.Length; i < len; i++ )
{
num = num * BASE + ALPHABET.IndexOf( str[(i)] );
}
return num;
}
}
You could hash the entire URL, but if you just want to shorten the id, do as marcel suggested. I wrote this Python implementation:
https://gist.github.com/778542
Take a look at https://hashids.org/ it is open source and in many languages.
Their page outlines some of the pitfalls of other approaches.
If you don't want re-invent the wheel ... http://lilurl.sourceforge.net/
// simple approach
$original_id = 56789;
$shortened_id = base_convert($original_id, 10, 36);
$un_shortened_id = base_convert($shortened_id, 36, 10);
alphabet = map(chr, range(97,123)+range(65,91)) + map(str,range(0,10))
def lookup(k, a=alphabet):
if type(k) == int:
return a[k]
elif type(k) == str:
return a.index(k)
def encode(i, a=alphabet):
'''Takes an integer and returns it in the given base with mappings for upper/lower case letters and numbers 0-9.'''
try:
i = int(i)
except Exception:
raise TypeError("Input must be an integer.")
def incode(i=i, p=1, a=a):
# Here to protect p.
if i <= 61:
return lookup(i)
else:
pval = pow(62,p)
nval = i/pval
remainder = i % pval
if nval <= 61:
return lookup(nval) + incode(i % pval)
else:
return incode(i, p+1)
return incode()
def decode(s, a=alphabet):
'''Takes a base 62 string in our alphabet and returns it in base10.'''
try:
s = str(s)
except Exception:
raise TypeError("Input must be a string.")
return sum([lookup(i) * pow(62,p) for p,i in enumerate(list(reversed(s)))])a
Here's my version for whomever needs it.
Why not just translate your id to a string? You just need a function that maps a digit between, say, 0 and 61 to a single letter (upper/lower case) or digit. Then apply this to create, say, 4-letter codes, and you've got 14.7 million URLs covered.
Here is a decent URL encoding function for PHP...
// From http://snipplr.com/view/22246/base62-encode--decode/
private function base_encode($val, $base=62, $chars='0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ') {
$str = '';
do {
$i = fmod($val, $base);
$str = $chars[$i] . $str;
$val = ($val - $i) / $base;
} while($val > 0);
return $str;
}
Don't know if anyone will find this useful - it is more of a 'hack n slash' method, yet is simple and works nicely if you want only specific chars.
$dictionary = "abcdfghjklmnpqrstvwxyz23456789";
$dictionary = str_split($dictionary);
// Encode
$str_id = '';
$base = count($dictionary);
while($id > 0) {
$rem = $id % $base;
$id = ($id - $rem) / $base;
$str_id .= $dictionary[$rem];
}
// Decode
$id_ar = str_split($str_id);
$id = 0;
for($i = count($id_ar); $i > 0; $i--) {
$id += array_search($id_ar[$i-1], $dictionary) * pow($base, $i - 1);
}
Did you omit O, 0, and i on purpose?
I just created a PHP class based on Ryan's solution.
<?php
$shorty = new App_Shorty();
echo 'ID: ' . 1000;
echo '<br/> Short link: ' . $shorty->encode(1000);
echo '<br/> Decoded Short Link: ' . $shorty->decode($shorty->encode(1000));
/**
* A nice shorting class based on Ryan Charmley's suggestion see the link on Stack Overflow below.
* #author Svetoslav Marinov (Slavi) | http://WebWeb.ca
* #see http://stackoverflow.com/questions/742013/how-to-code-a-url-shortener/10386945#10386945
*/
class App_Shorty {
/**
* Explicitly omitted: i, o, 1, 0 because they are confusing. Also use only lowercase ... as
* dictating this over the phone might be tough.
* #var string
*/
private $dictionary = "abcdfghjklmnpqrstvwxyz23456789";
private $dictionary_array = array();
public function __construct() {
$this->dictionary_array = str_split($this->dictionary);
}
/**
* Gets ID and converts it into a string.
* #param int $id
*/
public function encode($id) {
$str_id = '';
$base = count($this->dictionary_array);
while ($id > 0) {
$rem = $id % $base;
$id = ($id - $rem) / $base;
$str_id .= $this->dictionary_array[$rem];
}
return $str_id;
}
/**
* Converts /abc into an integer ID
* #param string
* #return int $id
*/
public function decode($str_id) {
$id = 0;
$id_ar = str_split($str_id);
$base = count($this->dictionary_array);
for ($i = count($id_ar); $i > 0; $i--) {
$id += array_search($id_ar[$i - 1], $this->dictionary_array) * pow($base, $i - 1);
}
return $id;
}
}
?>
public class TinyUrl {
private final String characterMap = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789";
private final int charBase = characterMap.length();
public String covertToCharacter(int num){
StringBuilder sb = new StringBuilder();
while (num > 0){
sb.append(characterMap.charAt(num % charBase));
num /= charBase;
}
return sb.reverse().toString();
}
public int covertToInteger(String str){
int num = 0;
for(int i = 0 ; i< str.length(); i++)
num += characterMap.indexOf(str.charAt(i)) * Math.pow(charBase , (str.length() - (i + 1)));
return num;
}
}
class TinyUrlTest{
public static void main(String[] args) {
TinyUrl tinyUrl = new TinyUrl();
int num = 122312215;
String url = tinyUrl.covertToCharacter(num);
System.out.println("Tiny url: " + url);
System.out.println("Id: " + tinyUrl.covertToInteger(url));
}
}
This is what I use:
# Generate a [0-9a-zA-Z] string
ALPHABET = map(str,range(0, 10)) + map(chr, range(97, 123) + range(65, 91))
def encode_id(id_number, alphabet=ALPHABET):
"""Convert an integer to a string."""
if id_number == 0:
return alphabet[0]
alphabet_len = len(alphabet) # Cache
result = ''
while id_number > 0:
id_number, mod = divmod(id_number, alphabet_len)
result = alphabet[mod] + result
return result
def decode_id(id_string, alphabet=ALPHABET):
"""Convert a string to an integer."""
alphabet_len = len(alphabet) # Cache
return sum([alphabet.index(char) * pow(alphabet_len, power) for power, char in enumerate(reversed(id_string))])
It's very fast and can take long integers.
For a similar project, to get a new key, I make a wrapper function around a random string generator that calls the generator until I get a string that hasn't already been used in my hashtable. This method will slow down once your name space starts to get full, but as you have said, even with only 6 characters, you have plenty of namespace to work with.
I have a variant of the problem, in that I store web pages from many different authors and need to prevent discovery of pages by guesswork. So my short URLs add a couple of extra digits to the Base-62 string for the page number. These extra digits are generated from information in the page record itself and they ensure that only 1 in 3844 URLs are valid (assuming 2-digit Base-62). You can see an outline description at http://mgscan.com/MBWL.
Very good answer, I have created a Golang implementation of the bjf:
package bjf
import (
"math"
"strings"
"strconv"
)
const alphabet = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
func Encode(num string) string {
n, _ := strconv.ParseUint(num, 10, 64)
t := make([]byte, 0)
/* Special case */
if n == 0 {
return string(alphabet[0])
}
/* Map */
for n > 0 {
r := n % uint64(len(alphabet))
t = append(t, alphabet[r])
n = n / uint64(len(alphabet))
}
/* Reverse */
for i, j := 0, len(t) - 1; i < j; i, j = i + 1, j - 1 {
t[i], t[j] = t[j], t[i]
}
return string(t)
}
func Decode(token string) int {
r := int(0)
p := float64(len(token)) - 1
for i := 0; i < len(token); i++ {
r += strings.Index(alphabet, string(token[i])) * int(math.Pow(float64(len(alphabet)), p))
p--
}
return r
}
Hosted at github: https://github.com/xor-gate/go-bjf
Implementation in Scala:
class Encoder(alphabet: String) extends (Long => String) {
val Base = alphabet.size
override def apply(number: Long) = {
def encode(current: Long): List[Int] = {
if (current == 0) Nil
else (current % Base).toInt :: encode(current / Base)
}
encode(number).reverse
.map(current => alphabet.charAt(current)).mkString
}
}
class Decoder(alphabet: String) extends (String => Long) {
val Base = alphabet.size
override def apply(string: String) = {
def decode(current: Long, encodedPart: String): Long = {
if (encodedPart.size == 0) current
else decode(current * Base + alphabet.indexOf(encodedPart.head),encodedPart.tail)
}
decode(0,string)
}
}
Test example with Scala test:
import org.scalatest.{FlatSpec, Matchers}
class DecoderAndEncoderTest extends FlatSpec with Matchers {
val Alphabet = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
"A number with base 10" should "be correctly encoded into base 62 string" in {
val encoder = new Encoder(Alphabet)
encoder(127) should be ("cd")
encoder(543513414) should be ("KWGPy")
}
"A base 62 string" should "be correctly decoded into a number with base 10" in {
val decoder = new Decoder(Alphabet)
decoder("cd") should be (127)
decoder("KWGPy") should be (543513414)
}
}
Function based in Xeoncross Class
function shortly($input){
$dictionary = ['a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z','A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z','0','1','2','3','4','5','6','7','8','9'];
if($input===0)
return $dictionary[0];
$base = count($dictionary);
if(is_numeric($input)){
$result = [];
while($input > 0){
$result[] = $dictionary[($input % $base)];
$input = floor($input / $base);
}
return join("", array_reverse($result));
}
$i = 0;
$input = str_split($input);
foreach($input as $char){
$pos = array_search($char, $dictionary);
$i = $i * $base + $pos;
}
return $i;
}
Here is a Node.js implementation that is likely to bit.ly. generate a highly random seven-character string.
It uses Node.js crypto to generate a highly random 25 charset rather than randomly selecting seven characters.
var crypto = require("crypto");
exports.shortURL = new function () {
this.getShortURL = function () {
var sURL = '',
_rand = crypto.randomBytes(25).toString('hex'),
_base = _rand.length;
for (var i = 0; i < 7; i++)
sURL += _rand.charAt(Math.floor(Math.random() * _rand.length));
return sURL;
};
}
My Python 3 version
base_list = list("0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ")
base = len(base_list)
def encode(num: int):
result = []
if num == 0:
result.append(base_list[0])
while num > 0:
result.append(base_list[num % base])
num //= base
print("".join(reversed(result)))
def decode(code: str):
num = 0
code_list = list(code)
for index, code in enumerate(reversed(code_list)):
num += base_list.index(code) * base ** index
print(num)
if __name__ == '__main__':
encode(341413134141)
decode("60FoItT")
For a quality Node.js / JavaScript solution, see the id-shortener module, which is thoroughly tested and has been used in production for months.
It provides an efficient id / URL shortener backed by pluggable storage defaulting to Redis, and you can even customize your short id character set and whether or not shortening is idempotent. This is an important distinction that not all URL shorteners take into account.
In relation to other answers here, this module implements the Marcel Jackwerth's excellent accepted answer above.
The core of the solution is provided by the following Redis Lua snippet:
local sequence = redis.call('incr', KEYS[1])
local chars = '0123456789ABCDEFGHJKLMNPQRSTUVWXYZ_abcdefghijkmnopqrstuvwxyz'
local remaining = sequence
local slug = ''
while (remaining > 0) do
local d = (remaining % 60)
local character = string.sub(chars, d + 1, d + 1)
slug = character .. slug
remaining = (remaining - d) / 60
end
redis.call('hset', KEYS[2], slug, ARGV[1])
return slug
Why not just generate a random string and append it to the base URL? This is a very simplified version of doing this in C#.
static string chars = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ1234567890";
static string baseUrl = "https://google.com/";
private static string RandomString(int length)
{
char[] s = new char[length];
Random rnd = new Random();
for (int x = 0; x < length; x++)
{
s[x] = chars[rnd.Next(chars.Length)];
}
Thread.Sleep(10);
return new String(s);
}
Then just add the append the random string to the baseURL:
string tinyURL = baseUrl + RandomString(5);
Remember this is a very simplified version of doing this and it's possible the RandomString method could create duplicate strings. In production you would want to take in account for duplicate strings to ensure you will always have a unique URL. I have some code that takes account for duplicate strings by querying a database table I could share if anyone is interested.
This is my initial thoughts, and more thinking can be done, or some simulation can be made to see if it works well or any improvement is needed:
My answer is to remember the long URL in the database, and use the ID 0 to 9999999999999999 (or however large the number is needed).
But the ID 0 to 9999999999999999 can be an issue, because
it can be shorter if we use hexadecimal, or even base62 or base64. (base64 just like YouTube using A-Z a-z 0-9 _ and -)
if it increases from 0 to 9999999999999999 uniformly, then hackers can visit them in that order and know what URLs people are sending each other, so it can be a privacy issue
We can do this:
have one server allocate 0 to 999 to one server, Server A, so now Server A has 1000 of such IDs. So if there are 20 or 200 servers constantly wanting new IDs, it doesn't have to keep asking for each new ID, but rather asking once for 1000 IDs
for the ID 1, for example, reverse the bits. So 000...00000001 becomes 10000...000, so that when converted to base64, it will be non-uniformly increasing IDs each time.
use XOR to flip the bits for the final IDs. For example, XOR with 0xD5AA96...2373 (like a secret key), and the some bits will be flipped. (whenever the secret key has the 1 bit on, it will flip the bit of the ID). This will make the IDs even harder to guess and appear more random
Following this scheme, the single server that allocates the IDs can form the IDs, and so can the 20 or 200 servers requesting the allocation of IDs. The allocating server has to use a lock / semaphore to prevent two requesting servers from getting the same batch (or if it is accepting one connection at a time, this already solves the problem). So we don't want the line (queue) to be too long for waiting to get an allocation. So that's why allocating 1000 or 10000 at a time can solve the issue.
I have a long "binary string" like the output of PHPs pack function.
How can I convert this value to base62 (0-9a-zA-Z)?
The built in maths functions overflow with such long inputs, and BCmath doesn't have a base_convert function, or anything that specific. I would also need a matching "pack base62" function.
I think there is a misunderstanding behind this question. Base conversion and encoding/decoding are different. The output of base64_encode(...) is not a large base64-number. It's a series of discrete base64 values, corresponding to the compression function. That is why BC Math does not work, because BC Math is concerned with single large numbers, not strings that are in reality groups of small numbers that represent binary data.
Here's an example to illustrate the difference:
base64_encode(1234) = "MTIzNA=="
base64_convert(1234) = "TS" //if the base64_convert function existed
base64 encoding breaks the input up into groups of 3 bytes (3*8 = 24 bits), then converts each sub-segment of 6 bits (2^6 = 64, hence "base64") to the corresponding base64 character (values are "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/", where A = 0, / = 63).
In our example, base64_encode() treats "1234" as a string of 4 characters, not an integer (because base64_encode() does not operate on integers). Therefore it outputs "MTIzNA==", because (in US-ASCII/UTF-8/ISO-8859-1) "1234" is 00110001 00110010 00110011 00110100 in binary. This gets broken into 001100 (12 in decimal, character "M") 010011 (19 in decimal, character "T") 001000 ("I") 110011 ("z") 001101 ("N") 00. Since the last group isn't complete, it gets padded with 0's and the value is 000000 ("A"). Because everything is done by groups of 3 input characters, there are 2 groups: "123" and "4". The last group is padded with ='s to make it 3 chars long, so the whole output becomes "MTIzNA==".
converting to base64, on the other hand, takes a single integer value and converts it into a single base64 value. For our example, 1234 (decimal) is "TS" (base64), if we use the same string of base64 values as above. Working backward, and left-to-right: T = 19 (column 1), S = 18 (column 0), so (19 * 64^1) + (18 * 64^0) = 19 * 64 + 18 = 1234 (decimal). The same number can be represented as "4D2" in hexadecimal (base16): (4 * 16^2) + (D * 16^1) + (2 * 16^0) = (4 * 256) + (13 * 16) + (2 * 1) = 1234 (decimal).
Unlike encoding, which takes a string of characters and changes it, base conversion does not alter the actual number, just changes its presentation. The hexadecimal (base16) "FF" is the same number as decimal (base10) "255", which is the same number as "11111111" in binary (base2). Think of it like currency exchange, if the exchange rate never changed: $1 USD has the same value as £0.79 GBP (exchange rate as of today, but pretend it never changes).
In computing, integers are typically operated on as binary values (because it's easy to build 1-bit arithmetic units and then stack them together to make 32-bit/etc. arithmetic units). To do something as simple as "255 + 255" (decimal), the computer needs to first convert the numbers to binary ("11111111" + "11111111") and then perform the operation in the Arithmetic Logic Unit (ALU).
Almost all other uses of bases are purely for the convenience of humans (presentational) - computers display their internal value 11111111 (binary) as 255 (decimal) because humans are trained to operate on decimal numbers. The function base64_convert() doesn't exist as part of the standard PHP repertoire because it's not often useful to anyone: not many humans read base64 numbers natively. By contrast, binary 1's and 0's are sometimes useful for programmers (we can use them like on/off switches!), and hexadecimal is convenient for humans editing binary data because an entire 8-bit byte can be represented unambiguously as 00 through FF, without wasting too much space.
You may ask, "if base conversion is just for presentation, why does BC Math exist?" That's a fair question, and also exactly why I said "almost" purely for presentation: typical computers are limited to 32-bit or 64-bit wide numbers, which are usually plenty big enough. Sometimes you need to operate on really, really big numbers (RSA moduli for example), which don't fit in those registers. BC Math solves this problem by acting as an abstraction layer: it converts huge numbers into long strings of text. When it's time to do some operation, BC Math painstakingly breaks the long strings of text up into small chunks which the computer can handle. It's much, much slower than native operations, but it can handle arbitrary-sized numbers.
Here is a function base_conv() that can convert between completely arbitrary bases, expressed as arrays of strings; Each array element represents a single "digit" in that base, thus also allowing multi-character values (it is your responsibility to avoid ambiguity).
function base_conv($val, &$baseTo, &$baseFrom)
{
return base_arr_to_str(base_conv_arr(base_str_to_arr((string) $val, $baseFrom), count($baseTo), count($baseFrom)), $baseTo);
}
function base_conv_arr($val, $baseToDigits, $baseFromDigits)
{
$valCount = count($val);
$result = array();
do
{
$divide = 0;
$newlen = 0;
for ($i = 0; $i < $valCount; ++$i)
{
$divide = $divide * $baseFromDigits + $val[$i];
if ($divide >= $baseToDigits)
{
$val[$newlen ++] = (int) ($divide / $baseToDigits);
$divide = $divide % $baseToDigits;
}
else if ($newlen > 0)
{
$val[$newlen ++] = 0;
}
}
$valCount = $newlen;
array_unshift($result, $divide);
}
while ($newlen != 0);
return $result;
}
function base_arr_to_str($arr, &$base)
{
$str = '';
foreach ($arr as $digit)
{
$str .= $base[$digit];
}
return $str;
}
function base_str_to_arr($str, &$base)
{
$arr = array();
while ($str === '0' || !empty($str))
{
foreach ($base as $index => $digit)
{
if (mb_substr($str, 0, $digitLen = mb_strlen($digit)) === $digit)
{
$arr[] = $index;
$str = mb_substr($str, $digitLen);
continue 2;
}
}
throw new Exception();
}
return $arr;
}
Examples:
$baseDec = str_split('0123456789');
$baseHex = str_split('0123456789abcdef');
echo base_conv(255, $baseHex, $baseDec); // ff
echo base_conv('ff', $baseDec, $baseHex); // 255
// multi-character base:
$baseHelloworld = array('hello ', 'world ');
echo base_conv(37, $baseHelloworld, $baseDec); // world hello hello world hello world
echo base_conv('world hello hello world hello world ', $baseDec, $baseHelloworld); // 37
// ambiguous base:
// don't do this! base_str_to_arr() won't know how to decode e.g. '11111'
// (well it does, but the result might not be what you'd expect;
// It matches digits sequentially so '11111' would be array(0, 0, 1)
// here (matched as '11', '11', '1' since they come first in the array))
$baseAmbiguous = array('11', '1', '111');