assert_eq!(Sat(2067187500000000).cycle(), 1);
    assert_eq!(Sat(2067187500000000 + 1).cycle(), 1);
  }

  #[test]
  fn third() {
    assert_eq!(Sat(0).third(), 0);
    assert_eq!(Sat(50 * COIN_VALUE - 1).third(), 4999999999);
    assert_eq!(Sat(50 * COIN_VALUE).third(), 0);
    assert_eq!(Sat(50 * COIN_VALUE + 1).third(), 1);
  }

  #[test]
  fn percentile() {
    assert_eq!(Sat(0).percentile(), "0%");
    assert_eq!(Sat(Sat::LAST.n() / 2).percentile(), "49.99999999999998%");
    assert_eq!(Sat::LAST.percentile(), "100%");
  }

  #[test]
  fn from_percentile() {
    "-1%".parse::<Sat>().unwrap_err();
    "101%".parse::<Sat>().unwrap_err();
  }

  #[test]
  fn percentile_round_trip() {
    #[track_caller]
    fn case(n: u64) {
      let expected = Sat(n);
      let actual = expected.percentile().parse::<Sat>().unwrap();
      assert_eq!(expected, actual);
    }

    for n in 0..1024 {
      case(n);
      case(Sat::LAST.n() / 2 + n);
      case(Sat::LAST.n() - n);
      case(Sat::LAST.n() / (n + 1));
    }