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Re: Multiply With Carry random generators

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Albert van der Horst albert@spenarnc.xs4all.nl wrote:

> Looking into random number generators lately, mhx mentioned the
> diehard program.
> This was written by Marsaglia and with his linux version of the program
> he distributes a file mwcp.ps explaining the Multiply With Carry random
> generators.
> 
> They are simple enough to be typed in by heart whenever you need one,
> yet they have respectable periods of 2^64 for 32-bits and 2^128 for
> 64 bits. Where Marsaglia promotes them they must be pretty good.
> The nice thing are the constants. They are small enough to remember.
> The multipliers are from wikipedia.
> Like the congruentual generators they are simpler in Forth than in other
> languages, especially given the double precision wordsets.
> 
...some [untested] code snipped...

It turns out that both Fortran and C encounter some complexities in 
getting 64-bit randoms from MWC algorithms.  It's certainly simple in 
Forth; you do just what I posted years ago with suitable choices for 
64-bit systems, which I didn't cover way back then.

For possible convenience I'm including a loadable file.  If you really 
want 64-bit randoms on a smaller system, just run separate generators for 
pieces of the value you need.

regards   cgm

\ 64-bit pseudo-random number generators 
\ Charles G. Montgomery   Nov2012  

DEFER rand	\ set to choice of generators

HEX

\  multiply-with-carry (George Marsaglia)
400000000000001 Constant rmult    \ 2^58+1

2VARIABLE rloc
3456123456123456 4567890987654321 rloc 2!   \ Marsaglia's values
: mwc  ( -- u ) rloc 2@ rmult UM* ROT 0 D+ OVER rloc 2! ;

' mwc is rand

\ recommended rmult values for other cell sizes
\ 32 bits: 7A3FFD4B 7549D83B  70DCB7DC  6A364C22  62AFDC7A
\ 16 bits: 65E8 61BF 62DC 6594 6363 5E9B
\  8 bits: 65FF 56FF 68FF 317F
\ periods ~2^29 for 16 bits, ~2^58 for 32 bits, ~2^121 for 64 bits


\  linear congruential multiplier (with Marsaglia's constants)
   
19BAFFBED CONSTANT rgen    12D687 CONSTANT rplus 

VARIABLE rseed   12345678 rseed !
: lcm  ( -- u )  rseed @ rgen um* drop rplus + dup rseed ! ;
\ ====end of file========

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Multiply With Carry random generators albert@spenarnc.xs4all.nl (Albert van der Horst) - 2013-11-25 01:44 +0000
  Re: Multiply With Carry random generators mhx@iae.nl - 2013-11-25 10:40 -0800
  Re: Multiply With Carry random generators C G Montgomery <cgm@physics.utoledo.edu> - 2013-11-25 13:46 -0500

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