class Ed25519EncodedFieldElement implements Serializable {

  public Ed25519EncodedFieldElement modQ() {
    // s0, ..., s22 have 21 bits, s23 has 29 bits
    long s0 = 0x1FFFFF & threeBytesToLong(this.values, 0);
    long s1 = 0x1FFFFF & (fourBytesToLong(this.values, 2) >> 5);
    long s2 = 0x1FFFFF & (threeBytesToLong(this.values, 5) >> 2);
    long s3 = 0x1FFFFF & (fourBytesToLong(this.values, 7) >> 7);
    long s4 = 0x1FFFFF & (fourBytesToLong(this.values, 10) >> 4);
    long s5 = 0x1FFFFF & (threeBytesToLong(this.values, 13) >> 1);
    long s6 = 0x1FFFFF & (fourBytesToLong(this.values, 15) >> 6);
    long s7 = 0x1FFFFF & (threeBytesToLong(this.values, 18) >> 3);
    long s8 = 0x1FFFFF & threeBytesToLong(this.values, 21);
    long s9 = 0x1FFFFF & (fourBytesToLong(this.values, 23) >> 5);
    long s10 = 0x1FFFFF & (threeBytesToLong(this.values, 26) >> 2);
    long s11 = 0x1FFFFF & (fourBytesToLong(this.values, 28) >> 7);
    long s12 = 0x1FFFFF & (fourBytesToLong(this.values, 31) >> 4);
    long s13 = 0x1FFFFF & (threeBytesToLong(this.values, 34) >> 1);
    long s14 = 0x1FFFFF & (fourBytesToLong(this.values, 36) >> 6);
    long s15 = 0x1FFFFF & (threeBytesToLong(this.values, 39) >> 3);
    long s16 = 0x1FFFFF & threeBytesToLong(this.values, 42);
    long s17 = 0x1FFFFF & (fourBytesToLong(this.values, 44) >> 5);
    final long s18 = 0x1FFFFF & (threeBytesToLong(this.values, 47) >> 2);
    final long s19 = 0x1FFFFF & (fourBytesToLong(this.values, 49) >> 7);
    final long s20 = 0x1FFFFF & (fourBytesToLong(this.values, 52) >> 4);
    final long s21 = 0x1FFFFF & (threeBytesToLong(this.values, 55) >> 1);
    final long s22 = 0x1FFFFF & (fourBytesToLong(this.values, 57) >> 6);
    final long s23 = (fourBytesToLong(this.values, 60) >> 3);
    long carry0;
    long carry1;
    long carry2;
    long carry3;
    long carry4;
    long carry5;
    long carry6;
    long carry7;
    long carry8;
    long carry9;
    long carry10;
    long carry11;
    final long carry12;
    final long carry13;
    final long carry14;
    final long carry15;
    final long carry16;

    /**
     * Lots of magic numbers :) To understand what's going on below, note that
     *
     * <p>(1) q = 2^252 + q0 where q0 = 27742317777372353535851937790883648493. (2) s11 is the
     * coefficient of 2^(11*21), s23 is the coefficient of 2^(^23*21) and 2^252 = 2^((23-11) * 21)).
     * (3) 2^252 congruent -q0 modulo q. (4) -q0 = 666643 * 2^0 + 470296 * 2^21 + 654183 * 2^(2*21)
     * - 997805 * 2^(3*21) + 136657 * 2^(4*21) - 683901 * 2^(5*21)
     *
     * <p>Thus s23 * 2^(23*11) = s23 * 2^(12*21) * 2^(11*21) = s3 * 2^252 * 2^(11*21) congruent s23
     * * (666643 * 2^0 + 470296 * 2^21 + 654183 * 2^(2*21) - 997805 * 2^(3*21) + 136657 * 2^(4*21) -
     * 683901 * 2^(5*21)) * 2^(11*21) modulo q = s23 * (666643 * 2^(11*21) + 470296 * 2^(12*21) +
     * 654183 * 2^(13*21) - 997805 * 2^(14*21) + 136657 * 2^(15*21) - 683901 * 2^(16*21)).
     *
     * <p>The same procedure is then applied for s22,...,s18.
     */
    s11 += s23 * 666643;
    s12 += s23 * 470296;
    s13 += s23 * 654183;
    s14 -= s23 * 997805;
    s15 += s23 * 136657;
    s16 -= s23 * 683901;

    s10 += s22 * 666643;
    s11 += s22 * 470296;
    s12 += s22 * 654183;
    s13 -= s22 * 997805;
    s14 += s22 * 136657;
    s15 -= s22 * 683901;

    s9 += s21 * 666643;
    s10 += s21 * 470296;
    s11 += s21 * 654183;
    s12 -= s21 * 997805;
    s13 += s21 * 136657;
    s14 -= s21 * 683901;

    s8 += s20 * 666643;
    s9 += s20 * 470296;
    s10 += s20 * 654183;
    s11 -= s20 * 997805;
    s12 += s20 * 136657;
    s13 -= s20 * 683901;

    s7 += s19 * 666643;
    s8 += s19 * 470296;
    s9 += s19 * 654183;
    s10 -= s19 * 997805;
    s11 += s19 * 136657;
    s12 -= s19 * 683901;

    s6 += s18 * 666643;
    s7 += s18 * 470296;
    s8 += s18 * 654183;
    s9 -= s18 * 997805;
    s10 += s18 * 136657;
    s11 -= s18 * 683901;

    /** Time to reduce the coefficient in order not to get an overflow. */
    carry6 = (s6 + (1 << 20)) >> 21;
    s7 += carry6;
    s6 -= carry6 << 21;
    carry8 = (s8 + (1 << 20)) >> 21;
    s9 += carry8;
    s8 -= carry8 << 21;
    carry10 = (s10 + (1 << 20)) >> 21;
    s11 += carry10;
    s10 -= carry10 << 21;
    carry12 = (s12 + (1 << 20)) >> 21;
    s13 += carry12;
    s12 -= carry12 << 21;
    carry14 = (s14 + (1 << 20)) >> 21;
    s15 += carry14;
    s14 -= carry14 << 21;
    carry16 = (s16 + (1 << 20)) >> 21;
    s17 += carry16;
    s16 -= carry16 << 21;

    carry7 = (s7 + (1 << 20)) >> 21;
    s8 += carry7;
    s7 -= carry7 << 21;
    carry9 = (s9 + (1 << 20)) >> 21;
    s10 += carry9;
    s9 -= carry9 << 21;
    carry11 = (s11 + (1 << 20)) >> 21;
    s12 += carry11;
    s11 -= carry11 << 21;
    carry13 = (s13 + (1 << 20)) >> 21;
    s14 += carry13;
    s13 -= carry13 << 21;
    carry15 = (s15 + (1 << 20)) >> 21;
    s16 += carry15;
    s15 -= carry15 << 21;

    /** Continue with above procedure. */
    s5 += s17 * 666643;
    s6 += s17 * 470296;
    s7 += s17 * 654183;
    s8 -= s17 * 997805;
    s9 += s17 * 136657;
    s10 -= s17 * 683901;

    s4 += s16 * 666643;
    s5 += s16 * 470296;
    s6 += s16 * 654183;
    s7 -= s16 * 997805;
    s8 += s16 * 136657;
    s9 -= s16 * 683901;

    s3 += s15 * 666643;
    s4 += s15 * 470296;
    s5 += s15 * 654183;
    s6 -= s15 * 997805;
    s7 += s15 * 136657;
    s8 -= s15 * 683901;

    s2 += s14 * 666643;
    s3 += s14 * 470296;
    s4 += s14 * 654183;
    s5 -= s14 * 997805;
    s6 += s14 * 136657;
    s7 -= s14 * 683901;

    s1 += s13 * 666643;
    s2 += s13 * 470296;
    s3 += s13 * 654183;
    s4 -= s13 * 997805;
    s5 += s13 * 136657;
    s6 -= s13 * 683901;

    s0 += s12 * 666643;
    s1 += s12 * 470296;
    s2 += s12 * 654183;
    s3 -= s12 * 997805;
    s4 += s12 * 136657;
    s5 -= s12 * 683901;
    s12 = 0;

    /** Reduce coefficients again. */
    carry0 = (s0 + (1 << 20)) >> 21;
    s1 += carry0;
    s0 -= carry0 << 21;
    carry2 = (s2 + (1 << 20)) >> 21;
    s3 += carry2;
    s2 -= carry2 << 21;
    carry4 = (s4 + (1 << 20)) >> 21;
    s5 += carry4;
    s4 -= carry4 << 21;
    carry6 = (s6 + (1 << 20)) >> 21;
    s7 += carry6;
    s6 -= carry6 << 21;
    carry8 = (s8 + (1 << 20)) >> 21;
    s9 += carry8;
    s8 -= carry8 << 21;
    carry10 = (s10 + (1 << 20)) >> 21;
    s11 += carry10;
    s10 -= carry10 << 21;

    carry1 = (s1 + (1 << 20)) >> 21;
    s2 += carry1;
    s1 -= carry1 << 21;
    carry3 = (s3 + (1 << 20)) >> 21;
    s4 += carry3;
    s3 -= carry3 << 21;
    carry5 = (s5 + (1 << 20)) >> 21;
    s6 += carry5;
    s5 -= carry5 << 21;
    carry7 = (s7 + (1 << 20)) >> 21;
    s8 += carry7;
    s7 -= carry7 << 21;
    carry9 = (s9 + (1 << 20)) >> 21;
    s10 += carry9;
    s9 -= carry9 << 21;
    carry11 = (s11 + (1 << 20)) >> 21;
    s12 += carry11;
    s11 -= carry11 << 21;

    s0 += s12 * 666643;
    s1 += s12 * 470296;
    s2 += s12 * 654183;
    s3 -= s12 * 997805;
    s4 += s12 * 136657;
    s5 -= s12 * 683901;
    s12 = 0;

    carry0 = s0 >> 21;
    s1 += carry0;
    s0 -= carry0 << 21;
    carry1 = s1 >> 21;
    s2 += carry1;
    s1 -= carry1 << 21;
    carry2 = s2 >> 21;
    s3 += carry2;
    s2 -= carry2 << 21;
    carry3 = s3 >> 21;
    s4 += carry3;
    s3 -= carry3 << 21;
    carry4 = s4 >> 21;
    s5 += carry4;
    s4 -= carry4 << 21;
    carry5 = s5 >> 21;
    s6 += carry5;
    s5 -= carry5 << 21;
    carry6 = s6 >> 21;
    s7 += carry6;
    s6 -= carry6 << 21;
    carry7 = s7 >> 21;
    s8 += carry7;
    s7 -= carry7 << 21;
    carry8 = s8 >> 21;
    s9 += carry8;
    s8 -= carry8 << 21;
    carry9 = s9 >> 21;
    s10 += carry9;
    s9 -= carry9 << 21;
    carry10 = s10 >> 21;
    s11 += carry10;
    s10 -= carry10 << 21;
    carry11 = s11 >> 21;
    s12 += carry11;
    s11 -= carry11 << 21;

    s0 += s12 * 666643;
    s1 += s12 * 470296;
    s2 += s12 * 654183;
    s3 -= s12 * 997805;
    s4 += s12 * 136657;
    s5 -= s12 * 683901;

    carry0 = s0 >> 21;
    s1 += carry0;
    s0 -= carry0 << 21;
    carry1 = s1 >> 21;
    s2 += carry1;
    s1 -= carry1 << 21;
    carry2 = s2 >> 21;
    s3 += carry2;
    s2 -= carry2 << 21;
    carry3 = s3 >> 21;
    s4 += carry3;
    s3 -= carry3 << 21;
    carry4 = s4 >> 21;
    s5 += carry4;
    s4 -= carry4 << 21;
    carry5 = s5 >> 21;
    s6 += carry5;
    s5 -= carry5 << 21;
    carry6 = s6 >> 21;
    s7 += carry6;
    s6 -= carry6 << 21;
    carry7 = s7 >> 21;
    s8 += carry7;
    s7 -= carry7 << 21;
    carry8 = s8 >> 21;
    s9 += carry8;
    s8 -= carry8 << 21;
    carry9 = s9 >> 21;
    s10 += carry9;
    s9 -= carry9 << 21;
    carry10 = s10 >> 21;
    s11 += carry10;
    s10 -= carry10 << 21;

    // s0, ..., s11 got 21 bits each.
    final byte[] result = new byte[32];
    result[0] = (byte) (s0);
    result[1] = (byte) (s0 >> 8);
    result[2] = (byte) ((s0 >> 16) | (s1 << 5));
    result[3] = (byte) (s1 >> 3);
    result[4] = (byte) (s1 >> 11);
    result[5] = (byte) ((s1 >> 19) | (s2 << 2));
    result[6] = (byte) (s2 >> 6);
    result[7] = (byte) ((s2 >> 14) | (s3 << 7));
    result[8] = (byte) (s3 >> 1);
    result[9] = (byte) (s3 >> 9);
    result[10] = (byte) ((s3 >> 17) | (s4 << 4));
    result[11] = (byte) (s4 >> 4);
    result[12] = (byte) (s4 >> 12);
    result[13] = (byte) ((s4 >> 20) | (s5 << 1));
    result[14] = (byte) (s5 >> 7);
    result[15] = (byte) ((s5 >> 15) | (s6 << 6));
    result[16] = (byte) (s6 >> 2);
    result[17] = (byte) (s6 >> 10);
    result[18] = (byte) ((s6 >> 18) | (s7 << 3));
    result[19] = (byte) (s7 >> 5);
    result[20] = (byte) (s7 >> 13);
    result[21] = (byte) (s8);
    result[22] = (byte) (s8 >> 8);
    result[23] = (byte) ((s8 >> 16) | (s9 << 5));
    result[24] = (byte) (s9 >> 3);
    result[25] = (byte) (s9 >> 11);
    result[26] = (byte) ((s9 >> 19) | (s10 << 2));
    result[27] = (byte) (s10 >> 6);
    result[28] = (byte) ((s10 >> 14) | (s11 << 7));
    result[29] = (byte) (s11 >> 1);
    result[30] = (byte) (s11 >> 9);
    result[31] = (byte) (s11 >> 17);

    return new Ed25519EncodedFieldElement(result);
  }

  public  Ed25519EncodedFieldElement(final byte[] values);

}