Re: Lua 5.4 random number generator

[Albert Chan <albertmcchan@...>]

On Mar 26, 2018, at 3:43 PM, Coda Highland <chighland@gmail.com> wrote:
>> On Mon, Mar 26, 2018 at 12:01 PM, albertmcchan <albertmcchan@yahoo.com> wrote:
>> function last128()
>>  for i=1,128 do io.write(math.random(0) & 1) end
>> end
>> 
>> If what you are saying is true, period of last128() is also 2^128 - 1, all unique.
>> 
>> Each last128() map 1-to-1 to 2^128 - 1 internal states.
>> 
>> one last128() pattern will never occurs. (all zeroes ?)
> 
> Not "all unique" because the output of the PRNG isn't 128 bits -- by
> the pigeonhole principle, some of the function outputs will be
> duplicated along the way, but importantly the SEQUENCE of those
> outputs will NOT be repeated.

I did not say output of the PRNG (only 64 bits) is all unique.
I said returns of last128() are all unique, with period 2^128 - 1

Using pigeonhole principle, 2^128-1 last128() are ALL unique