// get a rounded ratio and a remainder which can be expressed as ints, without risk of
        // overflow:
        int quotient = (int) LongMath.divide(numerator, scale, RoundingMode.DOWN);
        int remainder = (int) (numerator - (long) quotient * scale);
        quotients[i] = quotient;
        remainders[i] = remainder;
        requiredSelections[requiredSelectionsCount] = quotient;

      int positionFloor = (int) LongMath.divide(numerator, scale, RoundingMode.DOWN);
      int remainder = (int) (numerator - positionFloor * scale);
      if (remainder == 0) {
        return dataset[positionFloor];
      } else {
        double positionFrac = (double) remainder / scale;
        return dataset[positionFloor]
            + positionFrac * (dataset[positionFloor + 1] - dataset[positionFloor]);

      int positionFloor = (int) LongMath.divide(numerator, scale, RoundingMode.DOWN);
      int remainder = (int) (numerator - positionFloor * scale);
      if (remainder == 0) {
        return dataset[positionFloor];
      } else {
        double positionFrac = (double) remainder / scale;
        return dataset[positionFloor]
            + positionFrac * (dataset[positionFloor + 1] - dataset[positionFloor]);

    }

    // returns the minimum x such as x >= a && (x % b) == 0
    private static int ceilToMultiple(int a, int b) {
      int remainder = a % b;
      return remainder == 0 ? a : a + b - remainder;
    }

    void assertBytes(byte[] expected) {
      byte[] got = out.toByteArray();
      for (int i = 0; i < expected.length; i++) {
        assertEquals(expected[i], got[i]);

        assertEquals("test query", queryContext.getQueryString());
        assertEquals("url", queryContext.getDefaultField());
    }

    // Test constructor with allinurl prefix and empty remainder
    @Test
    public void test_constructor_allinurlPrefixEmptyRemainder() {
        queryContext = new QueryContext("allinurl:", false);
        assertEquals("*", queryContext.getQueryString());

   *
   * @param dividend the dividend (numerator)
   * @param divisor the divisor (denominator)
   * @throws ArithmeticException if divisor is 0
   * @since 11.0
   */
  public static long remainder(long dividend, long divisor) {
    if (divisor < 0) { // i.e., divisor >= 2^63:
      if (compare(dividend, divisor) < 0) {
        return dividend; // dividend < divisor
      } else {

    )

    @Throws(IOException::class)
    fun nextPart(): Part? {
      check(!closed) { "closed" }

      if (noMoreParts) return null

      // Read a boundary, skipping the remainder of the preceding part as necessary.
      if (partCount == 0 && source.rangeEquals(0L, dashDashBoundary)) {
        // This is the first part. Consume "--" followed by the boundary.

        if (b != 0) {
          UnsignedLong aUnsigned = UnsignedLong.fromLongBits(a);
          UnsignedLong bUnsigned = UnsignedLong.fromLongBits(b);
          long expected =
              aUnsigned.bigIntegerValue().remainder(bUnsigned.bigIntegerValue()).longValue();
          UnsignedLong unsignedRem = aUnsigned.mod(bUnsigned);
          assertThat(unsignedRem.longValue()).isEqualTo(expected);
        }
      }
    }
  }

}

// parsePAXRecord parses the input PAX record string into a key-value pair.
// If parsing is successful, it will slice off the currently read record and
// return the remainder as r.
func parsePAXRecord(s string) (k, v, r string, err error) {
	// The size field ends at the first space.
	nStr, rest, ok := strings.Cut(s, " ")
	if !ok {
		return "", "", s, ErrHeader
	}

        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