ComposingNormalizer and DecomposingNormalizer currently provide methods is_normalized(), is_normalized_utf8(), and is_normalized_utf16(). If the return value is false and the application then decides to normalize, the normalization-related data structure lookups are done twice for the (potential) already-normalized prefix.

ComposingNormalizer and DecomposingNormalizer should provide methods is_normalized_up_to(), is_normalized_utf8_up_to(), and is_normalized_utf16_up_to() that return usize such that the return value is the largest possible (but no larger than the length of input) with which the following assert passes:

fn test_is_normalized_up_to(input: &str) {
  // set up normalizer `norm`
  let up_to = norm.is_normalized_up_to(input)`
  let (head, tail) = input.split_at(up_to);
  let mut normalized = String::from(head);
  let _ = norm.normalize_to(tail, &mut normalized);
  assert!(norm.is_normalized(&normalized));
}

Then this should become a valid alternative implementation of is_normalized():

pub fn is_normalized(&self, text: &str) -> bool {
    self.is_normalized_up_to(text) == text.len()
}

Gecko use case: https://searchfox.org/mozilla-central/rev/e94bcd536a2a4caad0597d1b2d624342e6a389c4/intl/components/src/String.h#132

(Note that ICU4X deliberately doesn't implement quick check, which Gecko currently uses for the prefix computation.)