}
        boolean dividesEvenly = (p % q) == 0;
        try {
          assertEquals(p + "/" + q, p, IntMath.divide(p, q, UNNECESSARY) * q);
          assertTrue(p + "/" + q + " not expected to divide evenly", dividesEvenly);
        } catch (ArithmeticException e) {
          assertFalse(p + "/" + q + " expected to divide evenly", dividesEvenly);
        }
      }
    }
  }

  public void testZeroDivIsAlwaysZero() {

          long expected =
              new BigDecimal(valueOf(p)).divide(new BigDecimal(valueOf(q)), 0, mode).longValue();
          long actual = LongMath.divide(p, q, mode);
          if (expected != actual) {
            failFormat("expected divide(%s, %s, %s) = %s; got %s", p, q, mode, expected, actual);
          }
        }
      }
    }
  }

  @GwtIncompatible // TODO

    new RoundToDoubleTester(BigDecimal.ZERO).setExpectation(0.0, values()).test();
  }

  public void testRoundToDouble_oneThird() {
    new RoundToDoubleTester(
            BigDecimal.ONE.divide(BigDecimal.valueOf(3), new MathContext(50, HALF_EVEN)))
        .roundUnnecessaryShouldThrow()
        .setExpectation(0.33333333333333337, UP, CEILING)

        }
        boolean dividesEvenly = (p % q) == 0;
        try {
          assertEquals(p + "/" + q, p, IntMath.divide(p, q, UNNECESSARY) * q);
          assertTrue(p + "/" + q + " not expected to divide evenly", dividesEvenly);
        } catch (ArithmeticException e) {
          assertFalse(p + "/" + q + " expected to divide evenly", dividesEvenly);
        }
      }
    }
  }

  public void testZeroDivIsAlwaysZero() {

       */
      sqrt0 = sqrtApproxWithDoubles(x.shiftRight(shift)).shiftLeft(shift >> 1);
    }
    BigInteger sqrt1 = sqrt0.add(x.divide(sqrt0)).shiftRight(1);
    if (sqrt0.equals(sqrt1)) {
      return sqrt0;
    }
    do {
      sqrt0 = sqrt1;
      sqrt1 = sqrt0.add(x.divide(sqrt0)).shiftRight(1);
    } while (sqrt1.compareTo(sqrt0) < 0);
    return sqrt0;
  }

  @GwtIncompatible // TODO

  public static long divide(long dividend, long divisor) {
    if (divisor < 0) { // i.e., divisor >= 2^63:
      if (compare(dividend, divisor) < 0) {
        return 0; // dividend < divisor
      } else {
        return 1; // dividend >= divisor
      }
    }

    // Optimization - use signed division if dividend < 2^63
    if (dividend >= 0) {
      return dividend / divisor;
    }

    /*

    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)))
          .isEqualTo(0);
    }
  }

    // ceil(199*index/2).
    if (index % 2 == 0) {
      int position = IntMath.divide(199 * index, 2, UNNECESSARY);
      return PSEUDORANDOM_DATASET_SORTED.get(position);
    } else {
      int positionFloor = IntMath.divide(199 * index, 2, FLOOR);
      int positionCeil = IntMath.divide(199 * index, 2, CEILING);
      double lowerValue = PSEUDORANDOM_DATASET_SORTED.get(positionFloor);

    a >>= aTwos; // divide out all 2s
    int bTwos = Long.numberOfTrailingZeros(b);
    b >>= bTwos; // divide out all 2s
    while (a != b) { // both a, b are odd
      // The key to the binary GCD algorithm is as follows:
      // Both a and b are odd. Assume a > b; then gcd(a - b, b) = gcd(a, b).
      // But in gcd(a - b, b), a - b is even and b is odd, so we can divide out powers of two.

    a >>= aTwos; // divide out all 2s
    int bTwos = Long.numberOfTrailingZeros(b);
    b >>= bTwos; // divide out all 2s
    while (a != b) { // both a, b are odd
      // The key to the binary GCD algorithm is as follows:
      // Both a and b are odd. Assume a > b; then gcd(a - b, b) = gcd(a, b).
      // But in gcd(a - b, b), a - b is even and b is odd, so we can divide out powers of two.