[time-nuts] Re: Simple simulation model for an OCXO?

[Lux, Jim]

On 5/2/22 7:03 PM, Magnus Danielson via time-nuts wrote:
> Hi Jim,
>
> Thanks for the corrections. Was way to tired to get the uniform and 
> normal distributions right.
>
> rand() is then by classical UNIX tradition is generated as a unsigned 
> integer divided by the suitable (32th) power of two, so the maximum 
> value will not be there, and this is why a small bias is introduced, 
> since 0 can be reached but not 1.

I'll bet it's "pre-Unix" -

System/360 Scientific Subroutine Package Programmer's Manual, Version 
III, DOI: 10.3247/SL2Soft08.001 says 1968 version, but I'm pretty sure 
the SSP is older (it is Version 3 after all)

I used it on an IBM 1130 as a mere youth in 1969

http://media.ibm1130.org/1130-106-ocr.pdf


 Â Â Â  SUBROUTINE RANDU(X,IY,YFL)
 Â Â Â  IY = IX*899
 Â Â Â  if (IY) 5,6,6
5Â Â  IY=IY+32767+1
6Â Â  YFL=IY
 Â Â Â  YFL=YFL/32767.
 Â Â Â  RETURN
 Â Â Â  END


GAUSS does normal distribution, with this comment:

Y approaches a true normal distribution asympototically as K approaches 
infinity. For this subroutine, K was chosen as 12 to reduce execution time.

It also helps that the variance of a uniform distribution is 1/12, so 
summing 12 numbers produces a distribution with a variance of 1.


But it's older than that.. I found a reference to it in some 
documentation for 7090 from 1961.  Since Unix wasn't even a name until 
1970...


>
> In practice the bias is small, but care is taken never the less.

Yes, that's a clever technique.

And the less said about the actual "randomness" of generators from that 
era, the better.


>
> Cheers,
> Magnus