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
SUBROUTINE RANDU(X,IY,YFL)
IY = IX*899
if (IY) 5,6,6
5 IY=IY+32767+1
6 YFL=IY
YFL=YFL/32767.
RETURN
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
_______________________________________________
time-nuts mailing list -- [email protected] -- To unsubscribe send an
email to [email protected]
To unsubscribe, go to and follow the instructions there.
