Information on calculator Random Number Generators from PPC Journal articles

[Dieter]

(11-13-2016 10:46 PM)I Wrote:  According to my results the ^5 version is not better than the ^3 version, as far as Chi² and autocorrelation are concerned. I may be wrong, but just to be sure...

I did another test of the (x+pi)^5 generator and got a somewhat interesting result.
The test was done in Excel VBA, simulating the 41's 10-digit precision with this code:

Code:

    x = Round(r + 3.141592654, 9)
    r = x ^ 5
    d = 9 - Int(Log(r) * lge)  ' remaining digits right of the decimal point, lge = 0,43429...
    r = Round(r - Int(r), d)

And here are the results from 10 runs of 1000 random numbers each:

Code:

 Chi² =   10,40     33,44     33,44     33,44     33,44     33,44     33,44     33,44     33,44     33,44
---------------------------------------------------------------------------------------------------------
0,0..0,1:   106       104       104       104       104       104       104       104       104       104
0,1..0,2:   118       130       130       130       130       130       130       130       130       130
0,2..0,3:   106       120       120       120       120       120       120       120       120       120
0,3..0,4:    87        76        76        76        76        76        76        76        76        76
0,4..0,5:   106        98        98        98        98        98        98        98        98        98
0,5..0,6:    83        72        72        72        72        72        72        72        72        72
0,6..0,7:    98       110       110       110       110       110       110       110       110       110
0,7..0,8:   104       104       104       104       104       104       104       104       104       104
0,8..0,9:    89       108       108       108       108       108       108       108       108       108
0,9..1,0:   103        78        78        78        78        78        78        78        78        78

After the first run (starting with r=0,12345) and Chi²=10,4 all subsequent runs with 1000 numbers yielded the same results. I assume this is due to a rather short period. This behaviour occurs with different seeds.

Now, we have learned that the autocorrelation of the ^5 generator is a bit better than with the ^3 version. But there seems to be another property that makes the ^5 generator ..."not the first choice". Gene and Namir, what do you think?

BTW I could not find something similar with the (x+pi)^3 generator.
At least not yet. ;-)

Dieter