// Use a seed so that the test is deterministic:
    Random r = new Random(0L);
    for (int i = 0; i < 1000000; i++) {
      long dividend = r.nextLong();
      long divisor = r.nextLong();
      // Test that the Euclidean property is preserved:
      assertThat(
              dividend
                  - (divisor * UnsignedLongs.divide(dividend, divisor)
                      + UnsignedLongs.remainder(dividend, divisor)))

    // Use a seed so that the test is deterministic:
    Random r = new Random(0L);
    for (int i = 0; i < 1000000; i++) {
      int dividend = r.nextInt();
      int divisor = r.nextInt();
      // Test that the Euclidean property is preserved:
      assertThat(
              dividend
                  - (divisor * UnsignedInts.divide(dividend, divisor)
                      + UnsignedInts.remainder(dividend, divisor)))

    // Use a seed so that the test is deterministic:
    Random r = new Random(0L);
    for (int i = 0; i < 1000000; i++) {
      long dividend = r.nextLong();
      long divisor = r.nextLong();
      // Test that the Euclidean property is preserved:
      assertThat(
              dividend
                  - (divisor * UnsignedLongs.divide(dividend, divisor)
                      + UnsignedLongs.remainder(dividend, divisor)))

    // Use a seed so that the test is deterministic:
    Random r = new Random(0L);
    for (int i = 0; i < 1000000; i++) {
      int dividend = r.nextInt();
      int divisor = r.nextInt();
      // Test that the Euclidean property is preserved:
      assertThat(
              dividend
                  - (divisor * UnsignedInts.divide(dividend, divisor)
                      + UnsignedInts.remainder(dividend, divisor)))

    } else if (b == 0) {
      return a; // similar logic
    }
    /*
     * Uses the binary GCD algorithm; see http://en.wikipedia.org/wiki/Binary_GCD_algorithm. This is
     * >40% faster than the Euclidean algorithm in benchmarks.
     */
    int aTwos = Integer.numberOfTrailingZeros(a);
    a >>= aTwos; // divide out all 2s
    int bTwos = Integer.numberOfTrailingZeros(b);
    b >>= bTwos; // divide out all 2s

    } else if (b == 0) {
      return a; // similar logic
    }
    /*
     * Uses the binary GCD algorithm; see http://en.wikipedia.org/wiki/Binary_GCD_algorithm. This is
     * >60% faster than the Euclidean algorithm in benchmarks.
     */
    int aTwos = Long.numberOfTrailingZeros(a);
    a >>= aTwos; // divide out all 2s
    int bTwos = Long.numberOfTrailingZeros(b);
    b >>= bTwos; // divide out all 2s