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/* This program by D E Knuth is in the public domain and freely copyable.
* 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 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. */
/* This version also adopts Brendan McKay's suggestion to
accommodate naive users who forget to call ranf_start(seed). */
/* If you find any bugs, please report them immediately to
* [email protected]
* (and you will be rewarded if the bug is genuine). Thanks! */
/************ see the book for explanations and caveats! *******************/
/************ in particular, you need two's complement arithmetic **********/
#define KK 100 /* the long lag */
#define LL 37 /* the short lag */
#define mod_sum(x,y) (((x)+(y))-(int)((x)+(y))) /* (x+y) mod 1.0 */
double ran_u[KK]; /* the generator state */
#ifdef __STDC__
void ranf_array(double aa[], int n)
#else
void ranf_array(aa,n) /* put n new random fractions in aa */
double *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_u[j];
for (;j<n;j++) aa[j]=mod_sum(aa[j-KK],aa[j-LL]);
for (i=0;i<LL;i++,j++) ran_u[i]=mod_sum(aa[j-KK],aa[j-LL]);
for (;i<KK;i++,j++) ran_u[i]=mod_sum(aa[j-KK],ran_u[i-LL]);
}
/* the following routines are adapted from exercise 3.6--15 */
/* after calling ranf_start, get new randoms by, e.g., "x=ranf_arr_next()" */
#define QUALITY 1009 /* recommended quality level for high-res use */
double ranf_arr_buf[QUALITY];
double ranf_arr_dummy=-1.0, ranf_arr_started=-1.0;
double *ranf_arr_ptr=&ranf_arr_dummy; /* the next random fraction, or -1 */
#define TT 70 /* guaranteed separation between streams */
#define is_odd(s) ((s)&1)
#ifdef __STDC__
void ranf_start(long seed)
#else
void ranf_start(seed) /* do this before using ranf_array */
long seed; /* selector for different streams */
#endif
{
register int t,s,j;
double u[KK+KK-1];
double ulp=(1.0/(1L<<30))/(1L<<22); /* 2 to the -52 */
double ss=2.0*ulp*((seed&0x3fffffff)+2);
for (j=0;j<KK;j++) {
u[j]=ss; /* bootstrap the buffer */
ss+=ss; if (ss>=1.0) ss-=1.0-2*ulp; /* cyclic shift of 51 bits */
}
u[1]+=ulp; /* make u[1] (and only u[1]) "odd" */
for (s=seed&0x3fffffff,t=TT-1; t; ) {
for (j=KK-1;j>0;j--)
u[j+j]=u[j],u[j+j-1]=0.0; /* "square" */
for (j=KK+KK-2;j>=KK;j--) {
u[j-(KK-LL)]=mod_sum(u[j-(KK-LL)],u[j]);
u[j-KK]=mod_sum(u[j-KK],u[j]);
}
if (is_odd(s)) { /* "multiply by z" */
for (j=KK;j>0;j--) u[j]=u[j-1];
u[0]=u[KK]; /* shift the buffer cyclically */
u[LL]=mod_sum(u[LL],u[KK]);
}
if (s) s>>=1; else t--;
}
for (j=0;j<LL;j++) ran_u[j+KK-LL]=u[j];
for (;j<KK;j++) ran_u[j-LL]=u[j];
for (j=0;j<10;j++) ranf_array(u,KK+KK-1); /* warm things up */
ranf_arr_ptr=&ranf_arr_started;
}
#define ranf_arr_next() (*ranf_arr_ptr>=0? *ranf_arr_ptr++: ranf_arr_cycle())
double ranf_arr_cycle()
{
if (ranf_arr_ptr==&ranf_arr_dummy)
ranf_start(314159L); /* the user forgot to initialize */
ranf_array(ranf_arr_buf,QUALITY);
ranf_arr_buf[KK]=-1;
ranf_arr_ptr=ranf_arr_buf+1;
return ranf_arr_buf[0];
}
#include <stdio.h>
int main()
{
register int m; double a[2009]; /* a rudimentary test */
ranf_start(310952);
for (m=0;m<2009;m++) ranf_array(a,1009);
printf("%.20f\n", ran_u[0]); /* 0.36410514377569680455 */
/* beware of buggy printf routines that do not give full accuracy here! */
ranf_start(310952);
for (m=0;m<1009;m++) ranf_array(a,2009);
printf("%.20f\n", ran_u[0]); /* 0.36410514377569680455 */
return 0;
}
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