Overengineered fizzbuzz in C

fizzbuzz.c

#include <stdio.h>
#include <string.h>

#define BUFLEN 9

int main() {
  char buf[BUFLEN];

  FILE *stream = fmemopen(&buf, BUFLEN, "w");
  if (stream == NULL) {
    perror("couldn't open stream");
    return 1;
  }

  setbuf(stream, NULL);

  for (unsigned short i = 1; i <= 100; i++) {
    bzero(&buf, BUFLEN);
    rewind(stream);

    if (i % 3 == 0) fputs("Fizz", stream);
    if (i % 5 == 0) fputs("Buzz", stream);
    if (!*buf)      fprintf(stream, "%hu", i);

    puts(buf);
  }
}