RNGs cannot be parallelized without modification, as the effectiveness of the randomness representation ceases if the sequences are related.

Previous discussions have been found from

But can we use some alternative solutions?

Consider some ancient algorithms that are probably not in use nowadays(most written from the book Numerical Analysis by T. Sauer)

```
# rng
#random number generators
#Computers are not capable of generating true random numbers
#but can generate sequences with statistical randomness
# 1 Julia's implemented solution
rand(100)
# LCP psuedo solutions
function rng_Park_Miller1998(n;x1=3)
x=zeros(n)
x[1] = x1
u = zeros(n)
for i in 2:n
x[i] =mod(16807*x[i-1],2147483647)#7^5 \ 2^31-1 31th mason prime
end
u = x./2147483647
return u
end
# implemented in Matlab 4 1990
rng_Park_Miller1998(100;x1=3)
function rng_randu(n;x1=3)
x = zeros(n)
x[1]=x1
for i in 2:n
x[i] = mod(65539*x[i-1],2147483648)
end
u = x./2147483648
return u
end
rng_randu(100)
# iterative psudo solutions
function rng_LMap(n;x1=.4)
x = zeros(n)
x[1] = x1
for i in 2:n
x[i]=1-2*x[i-1]^2
end
return((x./2) .+.5)
end
rng_LMap(100)
# self - avoiding solutio
function rng_Halton(n;x1 = 3)
b = zeros(Int(ceil(log(n)/log(x1))))
u = zeros(n)
for j in 1:n
i = 1
b[1] = b[1]+1
while b[i]>(x1-1+eps())
b[i]=0
i=i+1
b[i]=b[i]+1
end
u[j]=0
for k=1:length(b)
u[j] = u[j]+b[k]*Float64(x1)^(-k);
end
end
return u
end
rng_Halton(100)
```

It seems not hard if a random seq can be generated with a ārootā, so that if we pre-calculate some of the terms as starting values for each thread, then they may end up independent. Is this mistakenļ¼

BTW the code is from my repository