The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.stat.math

Replies: 10   Last Post: Oct 9, 1997 4:10 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
George Marsaglia

Posts: 363
Registered: 12/7/04
Posted: Sep 29, 1997 7:41 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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)*4.656613e-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
Theory behind multiply-with-carry is in the file
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

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.