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@ -51,17 +51,18 @@ sfuid_decode(string, &result);
## How does this work? ## How does this work?
It's basically a kind of MCG (multiplicative congruential generator) but instead of the last entry in the series beeing the factor I used the current ID. That means the result is not as random because the distance between consecutive ID is basically constant. The reason I did this is to save computation time (also 128 bit won't be enough for numbers that size). It's basically a kind of MCG (multiplicative congruential generator) but instead of the last entry in the series being the parameter I used the current ID. That means the result is not as random because the distance between consecutive ID is basically constant. The reason I did this is to save computation time (exponentiation would work, but 128 bit won't be enough for numbers that size).
So the formular to get a specific ID is: So the formular to get a specific ID is:
s(i) := p\*i mod m
![s(i) := p\*i mod m](https://raw.githubusercontent.com/overflowerror/null/master/projects/libsfuid/formular.gif?token=AEuWLXTFaZj0xp6HvvskmihKWeIQcRIdks5cR6sxwA%3D%3D) The condition for p and m is that their GCD is 1. I chose m to be a power of 2 so it's prime factors are only 2s. For p I chose a prime that is about 25 % of m. For that I hardcoded a list of possible primes candidates into the program.
The condition for p and m is that their GCD is 1. I chose m to be a power of 2 so it's prime factors are only 2. For p I chose a prime that is about 25 % of m. For that I hardcoded a list of possible primes candidated into the program. To make it more efficient the program calculates m to be the greatest power of 2 that fits in the output space.
For example: Let the character set be "0-9" (10 characters) and the length of the result is 4, the output space would be 10^4. The biggest power of 2 in that space is 2^13. That's m. The p would be 2039 (about 25 % of m).
To make it most efficient the program calculates m to be the greatest power of 2 that fits in the output space. (Note to myself: Maybe just using a big Mersenne prime (like 2^61-1) would also work. That would maximize the useable output space efficiency, because it's guaranteed that x^y with y > 1 is not a prime, thus m can be size of the output space.)
For example: Let's our character set is "0-9" (10 characters) and the length of the result is 4, the output space would be 10^4. The biggest power of 2 in that space is 2^13. That's our m. The p would be 2039 (about 25 % of m).
(Note to myself: Maybe just using a big Mersenne prime (like 2^61-1) would also work. That would maximize the output space efficiency, because it's guaranteed that x^y with y > 1 is not a prime.)
The result of the MCG is then converted into the string by treating it as a number with the length of the charset as its basis. The result of the MCG is then converted into the string by treating it as a number with the length of the charset as its basis.
As for the decoding we have to solve the congruence equation x == p * i (mod m) for i. We can do that by multiplying x the multiplicative inverse of p and m.