// 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 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;

        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;

      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;

      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]);

        }
      }
    }
  }

  public void testRemainder() {
    for (long a : UNSIGNED_INTS) {
      for (long b : UNSIGNED_INTS) {
        try {
          assertThat(UnsignedInts.remainder((int) a, (int) b)).isEqualTo((int) (a % b));
          assertThat(b).isNotEqualTo(0);
        } catch (ArithmeticException e) {
          assertThat(b).isEqualTo(0);
        }
      }
    }
  }

   *
   * @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 {

        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);
        }
      }
    }
  }