Re: [gentoo-user] OT: Mapping random numbers (PRNG)

Canek Peláez Valdés <caneko@×××××.com> [14-06-06 17:36]:
> On Thu, Jun 5, 2014 at 9:56 PM,  <meino.cramer@×××.de> wrote:
> > Hi,
> >
> > I am experimenting with the C code of the ISAAC pseudo random number generator
> > (http://burtleburtle.net/bob/rand/isaacafa.html).
> >
> > Currently the implementation creates (on my embedded linux) 32 bit
> > hexadecimal output.
>
> So it's a 32 bit integer.
>
> > From this I want to create random numbers in the range of [a-Za-z0-9]
> > *without violating randomness* and (if possible) without throwing
> > away bits of the output.
>
> You mean *characters* int the range [A-Za-z0-9]?
>
> > How can I do this mathemtically (in concern of the quality of output)
> > correct?
>
> The easiest thing to do would be:
>
> -------------------------------------------------------------------------------
> #include <time.h>
> #include <stdio.h>
> #include <stdlib.h>
>
> #define N (26+26+10)
>
> static char S[] = { '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' };
>
> int
> next_character()
> {
>         // Use the correct call for ISAAC instead of rand()
>         unsigned int idx = rand() % N;
>         return S[idx];
> }
>
> int
> main(int argc, char* argv[])
> {
>         // Use the correct call for initializing the ISAAC seed
>         srand((unsigned int)time(NULL));
>         for (int i = 0; i < 20; i++) // --std=c99
>                 printf("%c\n", next_character());
>         return 0;
> }
> -------------------------------------------------------------------------------
>
> If the ISAAC RNG has a good distribution, then the next_character()
> function will give a good distribution among the set [A-Za-z0-9].
>
> Unless I missunderstood what you meant with "create random numbers in
> the range of [a-Za-z0-9]".
>
> Regards.
> --
> Canek Peláez Valdés
> Profesor de asignatura, Facultad de Ciencias
> Universidad Nacional Autónoma de México
>

Hi,

Thank you very much for the input! :)

I have a question about the algorithm:
Suppose rand() has an equal distribution of numbers and furthermore
one has a count of 2^32 random numbers listed in numerical sort
order.
In this list each number would appear (nearly) with the same count: 1

To get an better imagination of that...suppose the rand() would only 
return numbers in the range of 1...12 and the alphabet has only 8
characters (as 2^32 is not devideable by 62)

rand():
1 2 3 4 5 6 7 8 9 10 11 12

rand()%N : rand()%7
1 2 3 4 5 6 7 0 1  2  3  4  

or in other words: An even distribution of numbers of rand() 
would result in a unevenly distributed sequence of characters...or?
This would break the quality of ISAACs output.

I am sure I did something wrong here...but where is the logic trap?


Thank you very much for any help in advance!
Best regards,
mcc