x /= commonDivisor;
    denominator /= commonDivisor;
    // We know gcd(x, denominator) = 1, and x * numerator / denominator is exact,
    // so denominator must be a divisor of numerator.
    return x * (numerator / denominator);
  }

  /*
   * binomial(biggestBinomials[k], k) fits in a long, but not binomial(biggestBinomials[k] + 1, k).
   */
  static final int[] biggestBinomials = {
    Integer.MAX_VALUE,

    x /= commonDivisor;
    denominator /= commonDivisor;
    // We know gcd(x, denominator) = 1, and x * numerator / denominator is exact,
    // so denominator must be a divisor of numerator.
    return x * (numerator / denominator);
  }

  /*
   * binomial(biggestBinomials[k], k) fits in a long, but not binomial(biggestBinomials[k] + 1, k).
   */
  static final int[] biggestBinomials = {
    Integer.MAX_VALUE,

   * quantities.
   *
   * <p><b>Java 8+ users:</b> use {@link Integer#divideUnsigned(int, int)} instead.
   *
   * @param dividend the dividend (numerator)
   * @param divisor the divisor (denominator)
   * @throws ArithmeticException if divisor is 0
   */
  public static int divide(int dividend, int divisor) {
    return (int) (toLong(dividend) / toLong(divisor));
  }

  /**

   * quantities.
   *
   * <p><b>Java 8+ users:</b> use {@link Integer#divideUnsigned(int, int)} instead.
   *
   * @param dividend the dividend (numerator)
   * @param divisor the divisor (denominator)
   * @throws ArithmeticException if divisor is 0
   */
  public static int divide(int dividend, int divisor) {
    return (int) (toLong(dividend) / toLong(divisor));
  }

  /**

// shardSize returns the shard size for a given block size and data blocks.
func shardSize(blockSize, dataBlocks int) (sz int) {
	if dataBlocks == 0 {
		// do nothing on invalid input
		return
	}
	// Make denominator positive
	if dataBlocks < 0 {
		blockSize = -blockSize
		dataBlocks = -dataBlocks
	}
	sz = blockSize / dataBlocks
	if blockSize > 0 && blockSize%dataBlocks != 0 {
		sz++
	}
	return
}

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