// 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;

        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

      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 j = i & ARRAY_MASK;
      tmp += UnsignedLongs.divide(longs[j], divisors[j]);
    }
    return tmp;
  }

  @Benchmark
  long remainder(int reps) {
    long tmp = 0;
    for (int i = 0; i < reps; i++) {
      int j = i & ARRAY_MASK;
      tmp += UnsignedLongs.remainder(longs[j], divisors[j]);
    }
    return tmp;
  }

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

    assertThat(UnsignedLongs.remainder(14, 5)).isEqualTo(4);
    assertThat(UnsignedLongs.remainder(0, 50)).isEqualTo(0);
    assertThat(UnsignedLongs.remainder(0xfffffffffffffffeL, 0xfffffffffffffffdL)).isEqualTo(1);
    assertThat(UnsignedLongs.remainder(0xfffffffffffffffdL, 0xfffffffffffffffeL))
        .isEqualTo(0xfffffffffffffffdL);
    assertThat(UnsignedLongs.remainder(0xfffffffffffffffeL, 65535)).isEqualTo(65534L);

        if (length == 0) {
            return "";
        }
        final StringBuilder buffer = new StringBuilder((int) Math.ceil(length / 3d) * 4);
        final int remainder = length % 3;
        length -= remainder;
        int block;
        int i = 0;
        while (i < length) {
            block = (bytes[i++] & 0xff) << 16 | (bytes[i++] & 0xff) << 8 | bytes[i++] & 0xff;

            sb.setLength(0);
            String[] words = S_FILTER.split(line);
            for (String word : words) {
                if (sb.length() >= remainder - word.length() - (!sb.isEmpty() ? 1 : 0)) {
                    repeat(sb, ' ', remainder - sb.length());
                    result.add(BOX_CHAR + " " + sb + " " + BOX_CHAR);
                    sb.setLength(0);
                }
                if (!sb.isEmpty()) {

      int j = i & ARRAY_MASK;
      tmp += UnsignedLongs.divide(longs[j], divisors[j]);
    }
    return tmp;
  }

  @Benchmark
  long remainder(int reps) {
    long tmp = 0;
    for (int i = 0; i < reps; i++) {
      int j = i & ARRAY_MASK;
      tmp += UnsignedLongs.remainder(longs[j], divisors[j]);
    }
    return tmp;
  }

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

    assertThat(UnsignedLongs.remainder(14, 5)).isEqualTo(4);
    assertThat(UnsignedLongs.remainder(0, 50)).isEqualTo(0);
    assertThat(UnsignedLongs.remainder(0xfffffffffffffffeL, 0xfffffffffffffffdL)).isEqualTo(1);
    assertThat(UnsignedLongs.remainder(0xfffffffffffffffdL, 0xfffffffffffffffeL))
        .isEqualTo(0xfffffffffffffffdL);
    assertThat(UnsignedLongs.remainder(0xfffffffffffffffeL, 65535)).isEqualTo(65534L);

      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]);