Re: [Rd] Weakness in Knuth-TAOCP RNG (fwd) (PR#1336)

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From: Prof Brian D Ripley (ripley@stats.ox.ac.uk)
Date: Sun 03 Mar 2002 - 20:28:04 EST


Message-id: <Pine.GSO.4.44.0203030923530.27666-100000@auk.stats>

It's not that simple. This is an new generator, incompatible with
the old one.

I am sure the `weakness' does not arise in reasonable R usage, but I was
amazed that Knuth was unaware of the problem (which I regard as
well-known): but then he is a theoretician.

I will have to add this as a separate generator, since we really, really
can't re-define random number generators and so make work unreproducible.

On Sun, 3 Mar 2002 schutz@wehi.edu.au wrote:

> Prof Brian D Ripley wrote:
>
> >Attachments don't really work with R-bugs. To save us trying to unpick
> >this manually, could you re-send it as the body of a message to R-bugs
> >in reply to this one, or quoting (PR#1336) in the subject, please?
>
> Sorry about that (Pine sometimes modify lines of the body without warning,
> so I preferred using an attachment). Here is the patch for src/main/RNG.c.
>
> Frédéric
> ---
> >> Don Knuth recently updated its RNG, following the discovery of a
> >> weakness in the seed initialisation (see
> >> http://Sunburn.Stanford.EDU/~knuth/news02.html), so I believe that the
> >> corresponding code in R should be updated as well. If it may be usefull,
> >> I attach a patch to do the change.
> >>
> >> Notes:
> >>
> >> - only a few lines of code have really changed, but the order of the
> >> functions has changed in Knuth's original code, so the patch is
> >> longer than it should really be;
> >> - Despite Knuth's request that no change should be made to the code,
> >> the present R code (1.5.0-devel and previous) contains a change (the
> >> line "long ran_x[KK];" is commented, and ran_x is defined elsewhere
> >> in the program). The patch contains the _same_ change; I let you
> >> decide if this is acceptable in regard to Knuth's request.
>
> --- RNG.c.old Fri Mar 1 08:42:45 2002
> +++ RNG.c Fri Mar 1 14:26:08 2002
> @@ -543,6 +543,7 @@
> #define ran_x dummy
>
> /* =================== Knuth TAOCP ========================== */
> +/* From http://www-cs-faculty.Stanford.EDU/~knuth/programs/rng.c */
>
> /* Please do NOT alter this part of the code */
>
> @@ -551,15 +552,17 @@
> * It is explained in Seminumerical Algorithms, 3rd edition, Section 3.6
> * (or in the errata to the 2nd edition --- see
> * http://www-cs-faculty.stanford.edu/~knuth/taocp.html
> - * in the changes to pages 171 and following of Volume 2). */
> + * in the changes to Volume 2 on pages 171 and following). */
> +
> +/* N.B. The MODIFICATIONS introduced in the 9th printing (2002) are
> + included here; there's no backwards compatibility with the original. */
>
> /* If you find any bugs, please report them immediately to
> * taocp@cs.stanford.edu
> * (and you will be rewarded if the bug is genuine). Thanks! */
>
> /************ see the book for explanations and caveats! *******************/
> -
> -/* the old C calling conventions are used here, for reasons of portability */
> +/************ in particular, you need two's complement arithmetic **********/
>
> #define KK 100 /* the long lag */
> #define LL 37 /* the short lag */
> @@ -568,10 +571,13 @@
>
> /*long ran_x[KK]; */ /* the generator state */
>
> -/* void ran_array(long aa[],int n) */
> +#ifdef __STDC__
> +void ran_array(long aa[],int n)
> +#else
> void ran_array(aa,n) /* put n new random numbers in aa */
> long *aa; /* destination */
> int n; /* array length (must be at least KK) */
> +#endif
> {
> register int i,j;
> for (j=0;j<KK;j++) aa[j]=ran_x[j];
> @@ -580,57 +586,57 @@
> for (;i<KK;i++,j++) ran_x[i]=mod_diff(aa[j-KK],ran_x[i-LL]);
> }
>
> +/* the following routines are from exercise 3.6--15 */
> +/* after calling ran_start, get new randoms by, e.g., "x=ran_arr_next()" */
> +
> +#define QUALITY 1009 /* recommended quality level for high-res use */
> +long ran_arr_buf[QUALITY];
> +long ran_arr_sentinel=-1;
> +long *ran_arr_ptr=&ran_arr_sentinel; /* the next random number, or -1 */
> +
> +#define ran_arr_next() (*ran_arr_ptr>=0? *ran_arr_ptr++: ran_arr_cycle())
> +long ran_arr_cycle()
> +{
> + ran_array(ran_arr_buf,QUALITY);
> + ran_arr_buf[100]=-1;
> + ran_arr_ptr=ran_arr_buf+1;
> + return ran_arr_buf[0];
> +}
> +
> #define TT 70 /* guaranteed separation between streams */
> #define is_odd(x) ((x)&1) /* units bit of x */
> -#define evenize(x) ((x)&(MM-2)) /* make x even */
>
> -/* void ran_start(long seed) */
> +#ifdef __STDC__
> +void ran_start(long seed)
> +#else
> void ran_start(seed) /* do this before using ran_array */
> long seed; /* selector for different streams */
> +#endif
> {
> register int t,j;
> long x[KK+KK-1]; /* the preparation buffer */
> - register long ss=evenize(seed+2);
> + register long ss=(seed+2)&(MM-2);
> for (j=0;j<KK;j++) {
> x[j]=ss; /* bootstrap the buffer */
> ss<<=1; if (ss>=MM) ss-=MM-2; /* cyclic shift 29 bits */
> }
> - for (;j<KK+KK-1;j++) x[j]=0;
> x[1]++; /* make x[1] (and only x[1]) odd */
> - ss=seed&(MM-1);
> - t=TT-1; while (t) {
> - for (j=KK-1;j>0;j--) x[j+j]=x[j]; /* "square" */
> - for (j=KK+KK-2;j>KK-LL;j-=2) x[KK+KK-1-j]=evenize(x[j]);
> - for (j=KK+KK-2;j>=KK;j--) if(is_odd(x[j])) {
> - x[j-(KK-LL)]=mod_diff(x[j-(KK-LL)],x[j]);
> + for (ss=seed&(MM-1),t=TT-1; t; ) {
> + for (j=KK-1;j>0;j--) x[j+j]=x[j], x[j+j-1]=0; /* "square" */
> + for (j=KK+KK-2;j>=KK;j--)
> + x[j-(KK-LL)]=mod_diff(x[j-(KK-LL)],x[j]),
> x[j-KK]=mod_diff(x[j-KK],x[j]);
> - }
> if (is_odd(ss)) { /* "multiply by z" */
> for (j=KK;j>0;j--) x[j]=x[j-1];
> x[0]=x[KK]; /* shift the buffer cyclically */
> - if (is_odd(x[KK])) x[LL]=mod_diff(x[LL],x[KK]);
> + x[LL]=mod_diff(x[LL],x[KK]);
> }
> if (ss) ss>>=1; else t--;
> }
> for (j=0;j<LL;j++) ran_x[j+KK-LL]=x[j];
> for (;j<KK;j++) ran_x[j-LL]=x[j];
> -}
> -
> -/* the following routines are from exercise 3.6--15 */
> -/* after calling ran_start, get new randoms by, e.g., "x=ran_arr_next()" */
> -
> -#define QUALITY 1009 /* recommended quality level for high-res use */
> -long ran_arr_buf[QUALITY];
> -long ran_arr_sentinel=-1;
> -long *ran_arr_ptr=&ran_arr_sentinel; /* the next random number, or -1 */
> -
> -#define ran_arr_next() (*ran_arr_ptr>=0? *ran_arr_ptr++: ran_arr_cycle())
> -long ran_arr_cycle()
> -{
> - ran_array(ran_arr_buf,QUALITY);
> - ran_arr_buf[100]=-1;
> - ran_arr_ptr=ran_arr_buf+1;
> - return ran_arr_buf[0];
> + for (j=0;j<10;j++) ran_array(x,KK+KK-1); /* warm things up */
> + ran_arr_ptr=&ran_arr_sentinel;
> }
>
> /* ===================== end of Knuth's code ====================== */
>
>
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-- 
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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