I would like to generate a short, unique ID without having to check for collisions.
I currently do something like this, but the ID I currently generate is random and che
You could probably generate a MD5 hash of the current datetime/random number and truncate it to the length you need (5-8 characters) and store it as the id field.
If you are using storing this information in a database, you don't need to use a for loop to do the collision check, but you could just do a select statement - something like
SELECT count(1) c FROM Table WHERE id = :id
where :id would be the newly generated id. If c is greater than 0 then you know it already exists.
EDIT
This may may not be the best way to go about it. But I'll give it a shot, so I guess what you need is someway of converting a numbers into a unique short string and that is not in sequence.
I guess as you said, base64 encoding already does the number to short string conversion. To avoid the sequence problem you could have some mapping between your auto-generated id's to some "random" value (unique mapping). Then you can base64 encode this unique value.
You could generate this mapping as follows. Have a temporary table store values from 1 - 10,000,000. Sort it in random order and store it into you Map table.
INSERT INTO MappingTable (mappedId) SELECT values FROM TemporaryTable ORDER BY RAND()
Where MappingTable would have the 2 fields id (your auto-generated id would look up against this) and mappedId (which is what you would generate the base64 encoding for).
As you get closer to 10,000,000 you could rerun the above code again and change the values in the temporary table with 10,000,001-20,000,000 or something like that.
This blog post has something close to what you are after.
http://kevin.vanzonneveld.net/techblog/article/create_short_ids_with_php_like_youtube_or_tinyurl/
An MD5 of an incrementing number should be fine, but I worry that if you're truncating your MD5 (which is normally 128 bits) down to 5-8 characters, you will almost certainly be damaging it's capability to act as a unique signature...
If you cannot use an auto increment field, and want an absolutely unique value, use UUID. If you decide to use anything else (besides auto increment), you would be silly to NOT check for collisions.
You'll need something that's correct by construction, i.e. a permutation function: this is a function that does a one-to-one, reversible mapping of one integer (your sequential counter) to another. Some examples (any combination of these should also work):
Example: this function will convert 0, 1, 2, 3, 5, .. into 13, 4, 12, 7, 15, .. for numbers up to 15:
$i=($input+97) & 0xf;
$result=((($i&0x1) << 3) + (($i&0xe) >> 1)) ^ 0x5;
EDIT
An easier way would to use a linear congruential generator (LCG, which is usually used for generating random numbers), which is defined by a formula of the form:
X_n+1 = (a * X_n + c) mod m
For good values of a, c and m, the sequence of X_0, X_1 .. X_m-1 will contain all numbers between 0 and m-1 exactly once. Now you can start from a linearly increasing index, and use the next value in the LCG sequence as your "secret" key.
EDIT2
Implementation: You can design your own LCG parameters, but if you get it wrong it won't cover the full range (and thus have duplicates) so I'll use a published and tried set of parameters here from this paper:
a = 16807, c = 0, m = 2147483647
This gives you a range of 2**31. With pack() you can get the resulting integer as a string, base64_encode() makes it a readable string (of up to 6 significant characters, 6 bits per byte) so this could be your function:
substr(base64_encode(pack("l", (16807 * $index) % 2147483647)), 0, 6)
you can use a bitwise XOR to scramble some of the bits:
select thefield ^ 377 from thetable;
+-----+---------+
| a | a ^ 377 |
+-----+---------+
| 154 | 483 |
| 152 | 481 |
| 69 | 316 |
| 35 | 346 |
| 72 | 305 |
| 139 | 498 |
| 96 | 281 |
| 31 | 358 |
| 11 | 370 |
| 127 | 262 |
+-----+---------+