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/*
* Experimental data distribution table generator
* Taken from the uncopyrighted NISTnet code (public domain).
*
* Read in a series of "random" data values, either
* experimentally or generated from some probability distribution.
* From this, create the inverse distribution table used to approximate
* the distribution.
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <malloc.h>
#include <string.h>
#include <sys/types.h>
#include <sys/stat.h>
double *
readdoubles(FILE *fp, int *number)
{
struct stat info;
double *x;
int limit;
int n=0, i;
fstat(fileno(fp), &info);
if (info.st_size > 0) {
limit = 2*info.st_size/sizeof(double); /* @@ approximate */
} else {
limit = 10000;
}
x = calloc(limit, sizeof(double));
if (!x) {
perror("double alloc");
exit(3);
}
for (i=0; i<limit; ++i){
fscanf(fp, "%lf", &x[i]);
if (feof(fp))
break;
++n;
}
*number = n;
return x;
}
void
arraystats(double *x, int limit, double *mu, double *sigma, double *rho)
{
int n=0, i;
double sumsquare=0.0, sum=0.0, top=0.0;
double sigma2=0.0;
for (i=0; i<limit; ++i){
sumsquare += x[i]*x[i];
sum += x[i];
++n;
}
*mu = sum/(double)n;
*sigma = sqrt((sumsquare - (double)n*(*mu)*(*mu))/(double)(n-1));
for (i=1; i < n; ++i){
top += ((double)x[i]- *mu)*((double)x[i-1]- *mu);
sigma2 += ((double)x[i-1] - *mu)*((double)x[i-1] - *mu);
}
*rho = top/sigma2;
}
/* Create a (normalized) distribution table from a set of observed
* values. The table is fixed to run from (as it happens) -4 to +4,
* with granularity .00002.
*/
#define TABLESIZE 16384/4
#define TABLEFACTOR 8192
#ifndef MINSHORT
#define MINSHORT -32768
#define MAXSHORT 32767
#endif
/* Since entries in the inverse are scaled by TABLEFACTOR, and can't be bigger
* than MAXSHORT, we don't bother looking at a larger domain than this:
*/
#define DISTTABLEDOMAIN ((MAXSHORT/TABLEFACTOR)+1)
#define DISTTABLEGRANULARITY 50000
#define DISTTABLESIZE (DISTTABLEDOMAIN*DISTTABLEGRANULARITY*2)
static int *
makedist(double *x, int limit, double mu, double sigma)
{
int *table;
int i, index, first=DISTTABLESIZE, last=0;
double input;
table = calloc(DISTTABLESIZE, sizeof(int));
if (!table) {
perror("table alloc");
exit(3);
}
for (i=0; i < limit; ++i) {
/* Normalize value */
input = (x[i]-mu)/sigma;
index = (int)rint((input+DISTTABLEDOMAIN)*DISTTABLEGRANULARITY);
if (index < 0) index = 0;
if (index >= DISTTABLESIZE) index = DISTTABLESIZE-1;
++table[index];
if (index > last)
last = index +1;
if (index < first)
first = index;
}
return table;
}
/* replace an array by its cumulative distribution */
static void
cumulativedist(int *table, int limit, int *total)
{
int accum=0;
while (--limit >= 0) {
accum += *table;
*table++ = accum;
}
*total = accum;
}
static short *
inverttable(int *table, int inversesize, int tablesize, int cumulative)
{
int i, inverseindex, inversevalue;
short *inverse;
double findex, fvalue;
inverse = (short *)malloc(inversesize*sizeof(short));
for (i=0; i < inversesize; ++i) {
inverse[i] = MINSHORT;
}
for (i=0; i < tablesize; ++i) {
findex = ((double)i/(double)DISTTABLEGRANULARITY) - DISTTABLEDOMAIN;
fvalue = (double)table[i]/(double)cumulative;
inverseindex = (int)rint(fvalue*inversesize);
inversevalue = (int)rint(findex*TABLEFACTOR);
if (inversevalue <= MINSHORT) inversevalue = MINSHORT+1;
if (inversevalue > MAXSHORT) inversevalue = MAXSHORT;
inverse[inverseindex] = inversevalue;
}
return inverse;
}
/* Run simple linear interpolation over the table to fill in missing entries */
static void
interpolatetable(short *table, int limit)
{
int i, j, last, lasti = -1;
last = MINSHORT;
for (i=0; i < limit; ++i) {
if (table[i] == MINSHORT) {
for (j=i; j < limit; ++j)
if (table[j] != MINSHORT)
break;
if (j < limit) {
table[i] = last + (i-lasti)*(table[j]-last)/(j-lasti);
} else {
table[i] = last + (i-lasti)*(MAXSHORT-last)/(limit-lasti);
}
} else {
last = table[i];
lasti = i;
}
}
}
static void
printtable(const short *table, int limit)
{
int i;
printf("# This is the distribution table for the experimental distribution.\n");
for (i=0 ; i < limit; ++i) {
printf("%d%c", table[i],
(i % 8) == 7 ? '\n' : ' ');
}
}
int
main(int argc, char **argv)
{
FILE *fp;
double *x;
double mu, sigma, rho;
int limit;
int *table;
short *inverse;
int total;
if (argc > 1) {
if (!(fp = fopen(argv[1], "r"))) {
perror(argv[1]);
exit(1);
}
} else {
fp = stdin;
}
x = readdoubles(fp, &limit);
if (limit <= 0) {
fprintf(stderr, "Nothing much read!\n");
exit(2);
}
arraystats(x, limit, &mu, &sigma, &rho);
#ifdef DEBUG
fprintf(stderr, "%d values, mu %10.4f, sigma %10.4f, rho %10.4f\n",
limit, mu, sigma, rho);
#endif
table = makedist(x, limit, mu, sigma);
free((void *) x);
cumulativedist(table, DISTTABLESIZE, &total);
inverse = inverttable(table, TABLESIZE, DISTTABLESIZE, total);
interpolatetable(inverse, TABLESIZE);
printtable(inverse, TABLESIZE);
return 0;
}
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