// returns 0 for identical, 1 for completely different
static <A> double chiSquared_histogramsWithSum1(Map<A, Double> map1, Map<A, Double> map2) {
  if (empty(map1) || empty(map2)) ret Double.NaN;
  double sum = 0;
  for (A key : joinSets(keys(map1), keys(map2))) {
    double mi = or0(map1.get(key));
    double ni = or0(map2.get(key));
    double item = sqr(ni-mi)/(mi+ni);
    ifdef chiSquared_histogramsWithSum1_debug
      printVars_str(+key, +mi, +ni, +item);
    endifdef
    sum += item;
  }
  ret sum/2;
}