Self-describing numbers

You are encouraged to solve this task according to the task description, using any language you may know.
There are several so-called "self-describing" or "self-descriptive" integers.

An integer is said to be "self-describing" if it has the property that, when digit positions are labeled 0 to N-1, the digit in each position is equal to the number of times that that digit appears in the number.

For example,   2020   is a four-digit self describing number:

   position   0   has value   2   and there are two 0s in the number;
   position   1   has value   0   and there are no 1s in the number;
   position   2   has value   2   and there are two 2s;
   position   3   has value   0   and there are zero 3s.


Self-describing numbers < 100.000.000  are:     1210,   2020,   21200,   3211000,   42101000.



Task Description
 Write a function/routine/method/... that will check whether a given positive integer is self-describing.
 As an optional stretch goal - generate and display the set of self-describing numbers.


Related tasks

   Fours is the number of letters in the ...
   Look-and-say sequence
   Number names
   Self-referential sequence
   Spelling of ordinal numbers


#include <stdio.h>
 
inline int self_desc(unsigned long long xx)
{
	register unsigned int d, x;
	unsigned char cnt[10] = {0}, dig[10] = {0};
 
	for (d = 0; xx > ~0U; xx /= 10)
		cnt[ dig[d++] = xx % 10 ]++;
 
	for (x = xx; x; x /= 10)
		cnt[ dig[d++] = x % 10 ]++;
 
	while(d-- && dig[x++] == cnt[d]);
 
	return d == -1;
}
 
int main()
{
	int i;
	for (i = 1; i < 100000000; i++) /* don't handle 0 */
		if (self_desc(i)) printf("%d\n", i);
 
	return 0;
}