Henry Rich wrote:
>
> I'm not following this thread closely, but Algorithm M in section
> 3.4.1 of TAOCP is a very fast way of generating
> normal deviates. It can be modified to support generating
> them in batches.
>
> Knuth says (p. 113 of my 1969 edition) "a general-purpose
> subroutine based on Algorithm M will be a valuable part of
> any subroutine library".
>
> Henry Rich
>
Presumably it is about the code that avoids sin and cos of
the Box-Mueller code by picking a random point within the unit
circle and then doing a transformation involving only ln
and square root.
It can be done like this:
F=:(1-~2*(?,?)@0:)^:(1<:+&*:/)^:_
Nrnd=:({.,)(*([:%:@([EMAIL PROTECTED]:@^. % ])+&*:/))@F"0@($1:)@>[EMAIL
PROTECTED]:
F picks the point, Nrnd does the rest. There is doubling of
computation of +&*:/ for every found point.
The following mathematically equivalent routine done via
complex numbers is a bit faster:
ReIm=:9 11&o.
G=:(1j1-~2*(?j.?)@0:)^:(1<:|)^:_
Nrnd1=:({.,)(((%:@[EMAIL PROTECTED] % ])@| * ReIm)"[EMAIL
PROTECTED]"0@($1:))@>[EMAIL PROTECTED]:
but both are much slower than other tacit routines from this thread.
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