Re: new PRNG's

[Dirk Laurie <dirk.laurie@...>]

2018-05-08 23:53 GMT+02:00 Hartmut Henkel <hartmut_henkel@gmx.de>:
> On Tue, 8 May 2018, Rodrigo Azevedo wrote:
>
>> Just an update of a real-world application. I'm working on a
>> scientific stochastic code that "can" use the default PRNG of luajit
>> and lua-5.4.0-work1 (don't worry!). Compared to luajit,
>> lua-5.4.0-work1 exhibits a higher convergence rate, which is a symptom
>> of a (maybe) better PRNG. Moreover,  luajit is "only" 60% faster (no
>> I/O bound) than lua-5.4.0-work1, which makes me think about forgetting
>> luajit forever.
>
> Just a remark, if good convergence rate is needed, e. g. for Monte Carlo
> simulation or integration, Halton or Sobol "low-discrepancy" sequences
> may perform better than PRNG and can be used as drop-in replacements. E.
> g.,
>
> local halton = function (index, base)
> -- from en.wikipedia.org/wiki/Halton_sequence
>   local result = 0
>   local f = 1
>   local i = index
>   while i > 0 do
>     f = f / base
>     result = result + f * (i % base)
>     i = math.floor(i / base)
>   end
>   return result
> end

For integration, lattice methods (which superficially look like linear
congruential PRNGs but are designed to run over a complete cycle of
relatively small period) are worth a try.