* primitive utilities</a>.
 *
 * @author Louis Wasserman
 * @author Brian Milch
 * @author Colin Evans
 * @since 10.0
 */
@GwtCompatible
@ElementTypesAreNonnullByDefault
public final class UnsignedLongs {
  private UnsignedLongs() {}

  public static final long MAX_VALUE = -1L; // Equivalent to 2^64 - 1

  /**
   * A (self-inverse) bijection which converts the ordering on unsigned longs to the ordering on

    assertThat(UnsignedLongs.divide(0xfffffffffffffffeL, 5)).isEqualTo(3689348814741910322L);
  }

  public void testRemainder() {
    assertThat(UnsignedLongs.remainder(14, 5)).isEqualTo(4);
    assertThat(UnsignedLongs.remainder(0, 50)).isEqualTo(0);
    assertThat(UnsignedLongs.remainder(0xfffffffffffffffeL, 0xfffffffffffffffdL)).isEqualTo(1);

    assertThat(UnsignedLongs.divide(0xfffffffffffffffeL, 5)).isEqualTo(3689348814741910322L);
  }

  public void testRemainder() {
    assertThat(UnsignedLongs.remainder(14, 5)).isEqualTo(4);
    assertThat(UnsignedLongs.remainder(0, 50)).isEqualTo(0);
    assertThat(UnsignedLongs.remainder(0xfffffffffffffffeL, 0xfffffffffffffffdL)).isEqualTo(1);

  void setUp() {
    for (int i = 0; i < ARRAY_SIZE; i++) {
      longs[i] = random();
      divisors[i] = randomDivisor(longs[i]);
      decimalStrings[i] = UnsignedLongs.toString(longs[i]);
      binaryStrings[i] = UnsignedLongs.toString(longs[i], 2);
      hexStrings[i] = UnsignedLongs.toString(longs[i], 16);
      prefixedHexStrings[i] = "0x" + hexStrings[i];
    }
  }

  @Benchmark
  long divide(int reps) {
    long tmp = 0;

   * @since 14.0
   */
  public UnsignedLong dividedBy(UnsignedLong val) {
    return fromLongBits(UnsignedLongs.divide(value, checkNotNull(val).value));
  }

  /**
   * Returns this modulo {@code val}.
   *
   * @since 14.0
   */
  public UnsignedLong mod(UnsignedLong val) {
    return fromLongBits(UnsignedLongs.remainder(value, checkNotNull(val).value));
  }

  void setUp() {
    for (int i = 0; i < ARRAY_SIZE; i++) {
      longs[i] = random();
      divisors[i] = randomDivisor(longs[i]);
      decimalStrings[i] = UnsignedLongs.toString(longs[i]);
      binaryStrings[i] = UnsignedLongs.toString(longs[i], 2);
      hexStrings[i] = UnsignedLongs.toString(longs[i], 16);
      prefixedHexStrings[i] = "0x" + hexStrings[i];
    }
  }

  @Benchmark
  long divide(int reps) {
    long tmp = 0;

    TEST_BIG_INTEGERS = testBigIntegersBuilder.build();
  }

  public void testAsUnsignedAndLongValueAreInverses() {
    for (long value : TEST_LONGS) {
      assertWithMessage(UnsignedLongs.toString(value))
          .that(UnsignedLong.fromLongBits(value).longValue())
          .isEqualTo(value);
    }
  }

  public void testAsUnsignedBigIntegerValue() {
    for (long value : TEST_LONGS) {

    TEST_BIG_INTEGERS = testBigIntegersBuilder.build();
  }

  public void testAsUnsignedAndLongValueAreInverses() {
    for (long value : TEST_LONGS) {
      assertWithMessage(UnsignedLongs.toString(value))
          .that(UnsignedLong.fromLongBits(value).longValue())
          .isEqualTo(value);
    }
  }

  public void testAsUnsignedBigIntegerValue() {
    for (long value : TEST_LONGS) {

 *   <li>{@link Doubles}
 *   <li>{@link Floats}
 *   <li>{@link Ints}
 *       <ul>
 *         <li>{@link UnsignedInts}
 *       </ul>
 *   <li>{@link Longs}
 *       <ul>
 *         <li>{@link UnsignedLongs}
 *       </ul>
 *   <li>{@link Shorts}
 * </ul>
 *
 * <h3>General static utilities</h3>
 *
 * <ul>
 *   <li>{@link Primitives}
 * </ul>
 */
@ParametersAreNonnullByDefault
@CheckReturnValue

        if (result < 0) {
          result = UnsignedLongs.remainder(result, m);
        }
        // result < 2^63 again
        result += aLo * bHi; // aLo * bHi < 2^63, result < 2^64
        result = times2ToThe32Mod(result, m); // result < m < 2^63
        return plusMod(result, UnsignedLongs.remainder(aLo * bLo /* < 2^64 */, m), m);
      }

      @Override