[R] simple questions about R

Francisco Cribari cribari at de.ufpe.br
Wed Nov 4 19:36:24 CET 1998

Bill Simpson wrote:

> Marsaglia's multiply-with-carry generator is very easy to implement--he
> has posted some C code to newsgroups--and seems to test out OK. I wonder
> if it would make sense to use one of his generators instead.

I am reproducing Marsaglia's message to sci.stat.math below. (I am
not suggesting that this one should be the RNG in R. I am just
reproducing his message.) This RNG has been implemented into the
latest version of the Ox matrix programming language (along w/ two
other RNGs of different periods). I would tend to suggest to use

#define UNI (znew+wnew)*2.32830643708e-10

instead of what is used below. (This is the way that Ox implemented

Regards, FC.

----------------------- Marsaglia's message -----------------------------

I have often been asked to suggest random number generators
 for use in C.  Many good ones are available through the net,
 but they often require  complicated code and various
 ways to use or initialize through calls to subroutines.
 The following suggestion has these properties:
      Seems to pass all tests of randomness put to it.

      Has much much longer period, >2^60, than most
      system generators, <2^32,  and versions can be
      combined to get periods > 2^90, 2^120, etc.

      Exploits the feature of C that provides segments
      of in-line code through #define statements.  Thus
      random integers or reals can be put directly into
      expressions, avoiding the cost of calls to subroutines.

      Uses what I view as the most promising new method
      for random number generation: multiply-with-carry.

 Here is what you do: keep the following six lines of code
 somwhere in your files.

    #define znew  ((z=36969*(z&65535)+(z>>16))<<16)
    #define wnew  ((w=18000*(w&65535)+(w>>16))&65535)
    #define IUNI  (znew+wnew)
    #define UNI   (znew+wnew)*2.328306e-10
    static unsigned long z=362436069, w=521288629;
    void setseed(unsigned long i1,unsigned long i2){z=i1; w=i2;}

 Whenever you need random integers or random reals in your
 C program, just insert those six lines at (near?) the beginning
 of the program. In every expression where you want a random real
 in [0,1) use UNI, or use IUNI for a random 32-bit integer.
 No need to mess with ranf() or ranf(lastI), etc, with their
 requisite overheads.  Choices for replacing the two multipliers
 36969 and 18000 are given below.  Thus you can tailor your own
 in-line multiply-with-carry random number generator.

 This section is expressed as a C comment, in case you want to
 keep it filed with your essential six lines:
    /* Use of IUNI in an expression will produce a 32-bit unsigned
     random integer, while UNI will produce a random real in [0,1).
     The static variables z and w can be reassigned to i1 and i2
     by setseed(i1,i2);
    You may replace the two constants 36969 and 18000 by any
    pair of distinct constants from this list:
    18000 18030 18273 18513 18879 19074 19098 19164 19215 19584
    19599 19950 20088 20508 20544 20664 20814 20970 21153 21243
    21423 21723 21954 22125 22188 22293 22860 22938 22965 22974
    23109 23124 23163 23208 23508 23520 23553 23658 23865 24114
    24219 24660 24699 24864 24948 25023 25308 25443 26004 26088
    26154 26550 26679 26838 27183 27258 27753 27795 27810 27834
    27960 28320 28380 28689 28710 28794 28854 28959 28980 29013
    29379 29889 30135 30345 30459 30714 30903 30963 31059 31083
    (or any other 16-bit constants k for which both k*2^16-1
    and k*2^15-1 are prime)*/

 I don't program in C, so the above comes from looking in manuals,
 (the mathematics, of course, is my own and I am pretty sure of it,
 and pretty sure of the randomness through my Diehard battery,
 available in
           The Marsaglia Random Number CDROM
           The Diehard Battery of Tests of Randomness
 at    http://www.cs.hku.hk
 or    http://www.stat.fsu.edu
 Theory behind multiply-with-carry is in the file mwc1.ps
 in the postscript directory of the CDROM).

 I welcome suggestions if I have misinterpreted C conventions or
 standards.  But interest in random number generators seems great
 enough to risk cluttering up the news group with yet another dumb post.

George Marsaglia geo at stat.fsu.edu

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