Discussion: CMWC with lag PRNG

[David Roberts]

Re my last snippet if we use two loops we get some interesting results.

For example:

For i = 0 To 255
  a(i) += p
  p += [COLOR="Red"]3[/COLOR] ' Any prime number except 2
Next

For i = 0 To 255
  a(i) += p
  p += [COLOR="Red"]5[/COLOR] ' Any prime number except 2
Next

With 3 followed by 5 we get 0,0,0,0,0,0,0,0,8,8,8,8,8,8,8,8, ..., 248,248,248,248,248,248,248,248

With 3 followed by 9 we get 0,0,0,0,4,4,4,4, ..., 252,252,252,252

With 3 followed by 7 we get 0,0,2,2, ..., 254,254

as we do with 5 followed by 9 and 3 followed by 3.

There is a theorem lurking about here.

Gleason's theorem sounds good to me except it hasn't been formalized yet.

[John Gleason]

I think even Gleason's conjecture would be way pushing it.

[Arthur Gomide]

Hi David,

I get a random greater than one with your double-precision routine CMWCFD. Is it normal?

[David Roberts]

Hi Arthur

Is it normal?

No it is not - it is impossible. With a 12 bit right shift we get a sign bit of zero and all the 11 exponent bits as zero so we must have [0,1).

The bit map shows -155697.8

We cannot get that with 'Global RandomDouble As Double' but we could get that with 'Global RandomDouble As Single'.

I have just generated 10 billion and they were all in [0,1); although we only need one to upset the apple cart.

[Arthur Gomide]

Hi David,

You're right. My fault!

Nice work!