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st.ata.util.FPGenerator Maven / Gradle / Ivy

package st.ata.util;

import java.util.Hashtable;

/**

 This class provides methods that construct fingerprints of strings
of bytes via operations in GF[2^d] for 0 < d <= 64.
GF[2^d] is represented as the set of polynomials of degree
d with coefficients in Z(2), modulo an irreducible
polynomial P of degree d.  The representation of
polynomials is as an unsigned binary number in which the least
significant exponent is kept in the most significant bit.

 Let S be a string of bytes and g(S) the string obtained by
taking the byte 0x01 followed by eight 0x00
bytes followed by S.  Let f(S) be the polynomial
associated to the string S viewed as a polynomial with
coefficients in the field Z(2).  The fingerprint of S is simply
the value f(g(S)) modulo P.  Because polynomials are
represented with the least significant coefficient in the most
significant bit, fingerprints of degree d are stored in the
d most significant bits of a long word.

 Fingerprints can be used as a probably unique id for the input
string.  More precisely, if P is chosen at random among
irreducible polynomials of degree d, then the probability that
any two strings A and B have the same fingerprint is
less than max(|A|,|B|)/2^(d+1) where |A| is the length
of A in bits.

 The routines named extend[8] and fp[8]
return reduced results, while extend_[byte/char/int/long]
do not.  An unreduced result is a number that is equal (mod
polynomial to the desired fingerprint but may have
degree degree or higher.  The method reduce
reduces such a result to a polynomial of degree less than
degree.  Obtaining reduced results takes longer than
obtaining unreduced results; thus, when fingerprinting long strings,
it's better to obtain irreduced results inside the fingerprinting loop
and use reduce to reduce to a fingerprint after the loop.

*/
// Tested by: TestFPGenerator
public final class FPGenerator {

    /** Return a fingerprint generator.  The fingerprints generated
        will have degree degree and will be generated by
        polynomial.  If a generator based on
        polynomial has already been created, it will be
        returned.  Requires that polynomial is an
        irreducible polynomial of degree degree (the
        array polynomials contains some irreducible
        polynomials). */
    public static FPGenerator make(long polynomial, int degree) {
        Long l = new Long(polynomial);
        FPGenerator fpgen = (FPGenerator) generators.get(l);
        if (fpgen == null) {
            fpgen = new FPGenerator(polynomial, degree);
            generators.put(l, fpgen);
        }
        return fpgen;
    }
    private static final Hashtable generators = new Hashtable(10);

    private static final long zero = 0;
    private static final long one = 0x8000000000000000L;


    /** Return a value equal (mod polynomial) to
        fp and of degree less than degree. */
    public long reduce(long fp) {
        int N = (8 - degree/8);
        long local = (N == 8 ? 0 : fp & (-1L << 8*N));
        long temp = zero;
        for (int i = 0; i < N; i++) {
            temp ^= ByteModTable[8+i][((int)fp) & 0xff];
            fp >>>= 8;
        };
        return local ^ temp;
    }

    /** Extends f with lower eight bits of v
        without full reduction.  In other words, returns a
        polynomial that is equal (mod polynomial) to the
        desired fingerprint but may be of higher degree than the
        desired fingerprint. */
    public long extend_byte(long f, int v) {
        f ^= (0xff & v);
        int i = (int)f;
        long result = (f>>>8);
        result ^= ByteModTable[7][i & 0xff];
        return result;
    }

    /** Extends f with lower sixteen bits of v.
        Does not reduce. */
    public long extend_char(long f, int v) {
        f ^= (0xffff & v);
        int i = (int)f;
        long result = (f>>>16);
        result ^= ByteModTable[6][i & 0xff]; i >>>= 8;
        result ^= ByteModTable[7][i & 0xff];
        return result;
    }

    /** Extends f with (all bits of) v.
        Does not reduce. */
    public long extend_int(long f, int v) {
        f ^= (0xffffffffL & v);
        int i = (int)f;
        long result = (f>>>32);
        result ^= ByteModTable[4][i & 0xff]; i >>>= 8;
        result ^= ByteModTable[5][i & 0xff]; i >>>= 8;
        result ^= ByteModTable[6][i & 0xff]; i >>>= 8;
        result ^= ByteModTable[7][i & 0xff];
        return result;
    }

    /** Extends f with v.
        Does not reduce. */
    public long extend_long(long f, long v) {
        f ^= v;
        long result = ByteModTable[0][(int)(f & 0xff)]; f >>>= 8;
        result ^= ByteModTable[1][(int)(f & 0xff)]; f >>>= 8;
        result ^= ByteModTable[2][(int)(f & 0xff)]; f >>>= 8;
        result ^= ByteModTable[3][(int)(f & 0xff)]; f >>>= 8;
        result ^= ByteModTable[4][(int)(f & 0xff)]; f >>>= 8;
        result ^= ByteModTable[5][(int)(f & 0xff)]; f >>>= 8;
        result ^= ByteModTable[6][(int)(f & 0xff)]; f >>>= 8;
        result ^= ByteModTable[7][(int)(f & 0xff)];
        return result;
    }


    /** Compute fingerprint of "n" bytes of "buf" starting from
        "buf[start]".  Requires "[start, start+n)" is in bounds. */
    public long fp(byte[] buf, int start, int n) {
        return extend(empty, buf, start, n);
    }

    /** Compute fingerprint of (all bits of) "n" characters of "buf"
        starting from "buf[i]".  Requires "[i, i+n)" is in bounds. */
    public long fp(char[] buf, int start, int n) {
        return extend(empty, buf, start, n);
    }

// COMMENTED OUT TO REMOVE Dependency on st.ata.util.Text
//    /** Compute fingerprint of (all bits of) t */
//    public long fp(Text t) {
//        return extend(empty, t);
//    }
    /** Compute fingerprint of (all bits of) the characters of "s". */
    public long fp(CharSequence s) {
        return extend(empty, s);
    }

    /** Compute fingerprint of (all bits of) "n" characters of "buf"
        starting from "buf[i]".  Requires "[i, i+n)" is in bounds. */
    public long fp(int[] buf, int start, int n) {
        return extend(empty, buf, start, n);
    }

    /** Compute fingerprint of (all bits of) "n" characters of "buf"
        starting from "buf[i]".  Requires "[i, i+n)" is in bounds. */
    public long fp(long[] buf, int start, int n) {
        return extend(empty, buf, start, n);
    }

    /** Compute fingerprint of the lower eight bits of the characters
        of "s". */
    public long fp8(String s) {
        return extend8(empty, s);
    }

    /** Compute fingerprint of the lower eight bits of "n" characters
        of "buf" starting from "buf[i]".  Requires "[i, i+n)" is in
        bounds. */
    public long fp8(char[] buf, int start, int n) {
        return extend8(empty, buf, start, n);
    }


    /** Extends fingerprint f by adding the low eight
        bits of "b". */
    public long extend(long f, byte v) {
        return reduce(extend_byte(f, v));
    }

    /** Extends fingerprint f by adding (all bits of)
        "v". */
    public long extend(long f, char v) {
        return reduce(extend_char(f, v));
    }

    /** Extends fingerprint f by adding (all bits of)
        "v". */
    public long extend(long f, int v) {
        return reduce(extend_int(f, v));
    }

    /** Extends fingerprint f by adding (all bits of)
        "v". */
    public long extend(long f, long v) {
        return reduce(extend_long(f, v));
    }

    /** Extends fingerprint f by adding "n" bytes of
        "buf" starting from "buf[start]".
        Result is reduced.
        Requires "[i, i+n)" is in bounds. */
    public long extend(long f, byte[] buf, int start, int n) {
        for (int i = 0; i < n; i++) {
            f = extend_byte(f, buf[start+i]);
        }
        return reduce(f);
    }

    /** Extends fingerprint f by adding (all bits of) "n"
        characters of "buf" starting from "buf[i]".
        Result is reduced.
        Requires "[i, i+n)" is in bounds. */
    public long extend(long f, char[] buf, int start, int n) {
        for (int i = 0; i < n; i++) {
            f = extend_char(f, buf[start+i]);
        }
        return reduce(f);
    }

    /** Extends fingerprint f by adding (all bits of)
        the characters of "s".
        Result is reduced. */
    public long extend(long f, CharSequence s) {
        int n = s.length();
        for (int i = 0; i < n; i++) {
            int v = (int) s.charAt(i);
            f = extend_char(f, v);
        }
        return reduce(f);
    }

//  COMMENTED OUT TO REMOVE Dependency on st.ata.util.Text
//    /** Extends fingerprint f by adding (all bits of)
//     *  t */
//    public long extend(long f, Text t) {
//        return extend(f, t.buf, t.start, t.length());
//    }


    /** Extends fingerprint f by adding (all bits of) "n"
        characters of "buf" starting from "buf[i]".
        Result is reduced.
        Requires "[i, i+n)" is in bounds. */
    public long extend(long f, int[] buf, int start, int n) {
        for (int i = 0; i < n; i++) {
            f = extend_int(f, buf[start+i]);
        }
        return reduce(f);
    }

    /** Extends fingerprint f by adding (all bits of) "n"
        characters of "buf" starting from "buf[i]".
        Result is reduced.
        Requires "[i, i+n)" is in bounds. */
    public long extend(long f, long[] buf, int start, int n) {
        for (int i = 0; i < n; i++) {
            f = extend_long(f, buf[start+i]);
        }
        return reduce(f);
    }

    /** Extends fingerprint f by adding the lower eight
        bits of the characters of "s".
        Result is reduced. */
    public long extend8(long f, String s) {
        int n = s.length();
        for (int i = 0; i < n; i++) {
            int x = (int) s.charAt(i);
            f = extend_byte(f, x);
        }
        return reduce(f);
    }

    /** Extends fingerprint f by adding the lower eight
        bits of "n" characters of "buf" starting from "buf[i]".
        Result is reduced.
        Requires "[i, i+n)" is in bounds. */
    public long extend8(long f, char[] buf, int start, int n) {
        for (int i = 0; i < n; i++) {
            f = extend_byte(f, buf[start+i]);
        }
        return reduce(f);
    }


    /** Fingerprint of the empty string of bytes. */
    public final long empty;

    /** The number of bits in fingerprints generated by
        this. */
    public final int degree;

    /** The polynomial used by this to generate
        fingerprints. */
    public long polynomial;

    /** Result of reducing certain polynomials.  Specifically, if
        f(S) is bit string S interpreted as
        a polynomial, f(ByteModTable[i][j]) equals
        mod(x^(127 - 8*i) * f(j), P). */
    private long[][] ByteModTable;

    /** Create a fingerprint generator.  The fingerprints generated
        will have degree degree and will be generated by
        polynomial.  Requires that
        polynomial is an irreducible polynomial of degree
        degree (the array polynomials
        contains some irreducible polynomials). */
    private FPGenerator(long polynomial, int degree) {
        this.degree = degree;
        this.polynomial = polynomial;
        ByteModTable = new long[16][256];

        long[] PowerTable = new long[128];

        long x_to_the_i = one;
        long x_to_the_degree_minus_one = (one >>> (degree-1));
        for (int i = 0; i < 128; i++) {
            // Invariants:
            //   x_to_the_i = mod(x^i, polynomial)
            //   forall 0 <= j < i, PowerTable[i] = mod(x^i, polynomial)
            PowerTable[i] = x_to_the_i;
            boolean overflow = ((x_to_the_i & x_to_the_degree_minus_one) != 0);
            x_to_the_i >>>= 1;
            if (overflow) {
                x_to_the_i ^= polynomial;
            }
        }
        this.empty = PowerTable[64];

        for (int i = 0; i < 16; i++) {
            // Invariant: forall 0 <= i' < i, forall 0 <= j' < 256,
            //   ByteModTable[i'][j'] = mod(x^(127 - 8*i') * f(j'), polynomial)
            for (int j = 0; j < 256; j++) {
                // Invariant: forall 0 <= i' < i, forall 0 <= j' < j,
                //   ByteModTable[i'][j'] = mod(x^(degree+i')*f(j'),polynomial)
                long v = zero;
                for (int k = 0; k < 8; k++) {
                    // Invariant:
                    //   v = mod(x^(degree+i) * f(j & ((1<d between 1 and 64 (inclusive),
        polynomials[d][i] is an irreducible polynomial of
        degree d.  There are at least two irreducible
        polynomials for each degree. */
    public static final long polynomials[][] = {
        null,
        {0xC000000000000000L, 0xC000000000000000L},
        {0xE000000000000000L, 0xE000000000000000L},
        {0xD000000000000000L, 0xB000000000000000L},
        {0xF800000000000000L, 0xF800000000000000L},
        {0xEC00000000000000L, 0xBC00000000000000L},
        {0xDA00000000000000L, 0xB600000000000000L},
        {0xE500000000000000L, 0xE500000000000000L},
        {0x9680000000000000L, 0xD480000000000000L},
        {0x80C0000000000000L, 0x8840000000000000L},
        {0xB0A0000000000000L, 0xE9A0000000000000L},
        {0xD9F0000000000000L, 0xC9B0000000000000L},
        {0xE758000000000000L, 0xDE98000000000000L},
        {0xE42C000000000000L, 0x94E4000000000000L},
        {0xD4CE000000000000L, 0xB892000000000000L},
        {0xE2AB000000000000L, 0x9E39000000000000L},
        {0xCCE4800000000000L, 0x9783800000000000L},
        {0xD8F8C00000000000L, 0xA9CDC00000000000L},
        {0x9A28200000000000L, 0xFD79E00000000000L},
        {0xC782500000000000L, 0x96CD300000000000L},
        {0xBEE6880000000000L, 0xE902C80000000000L},
        {0x86D7E40000000000L, 0xF066340000000000L},
        {0x9888060000000000L, 0x910ABE0000000000L},
        {0xFF30E30000000000L, 0xB27EFB0000000000L},
        {0x8E375B8000000000L, 0xA03D948000000000L},
        {0xD1415C4000000000L, 0xF5357CC000000000L},
        {0x91A916E000000000L, 0xB6CE66E000000000L},
        {0xE6D2FC5000000000L, 0xD55882B000000000L},
        {0x9A3BA0B800000000L, 0xFBD654E800000000L},
        {0xAEA5D2E400000000L, 0xF0E533AC00000000L},
        {0xDA88B7BE00000000L, 0xAA3AAEDE00000000L},
        {0xBA75BB4300000000L, 0xF5A811C500000000L},
        {0x9B6C9A2F80000000L, 0x9603CCED80000000L},
        {0xFABB538840000000L, 0xE2747090C0000000L},
        {0x8358898EA0000000L, 0x8C698D3D20000000L},
        {0xDA8ABD5BF0000000L, 0xF6DF3A0AF0000000L},
        {0xB090C3F758000000L, 0xD3B4D3D298000000L},
        {0xAD9882F5BC000000L, 0x88DA4FB544000000L},
        {0xC3C366272A000000L, 0xDCCF2A2262000000L},
        {0x9BC0224A97000000L, 0xAF5D96F273000000L},
        {0x8643FFF621800000L, 0x8E390C6EDC800000L},
        {0xE45C01919BC00000L, 0xCBB34C8945C00000L},
        {0x80D8141BC2E00000L, 0x886AFC3912200000L},
        {0xF605807C26500000L, 0xA3B92D28F6300000L},
        {0xCE9A2CFC76280000L, 0x98400C1921280000L},
        {0xF61894904C040000L, 0xC8BE6DBCEC8C0000L},
        {0xE3A44C104D160000L, 0xCA84A59443760000L},
        {0xC7E84953A11B0000L, 0xD9D4F6AA02CB0000L},
        {0xC26CDD1C9A358000L, 0x8BE8478434328000L},
        {0xAE125DBEB198C000L, 0xFCC5DBFD5AAAC000L},
        {0x86DE52A079A6A000L, 0xC5F16BD883816000L},
        {0xDF82486AAFE37000L, 0xA293EC735692D000L},
        {0xE91ABA275C272800L, 0xD686192874E3C800L},
        {0x963D0960DAB3FC00L, 0xBA9DE62072621400L},
        {0xA2188C4E8A46CE00L, 0xD31F75BCB4977E00L},
        {0xC43A416020A6CB00L, 0x99F57FECA12B3900L},
        {0xA4F72EF82A58AE80L, 0xCECE4391B81DA380L},
        {0xB39F119264BC0940L, 0x80A277D20DABB9C0L},
        {0xFD6616C0CBFA0B20L, 0xED16E64117DC11A0L},
        {0xFFA8BC44327B5390L, 0xEDFB13DB3B66C210L},
        {0xCAE8EB99E73AB548L, 0xC86135B6EA2F0B98L},
        {0xBA49BADCDD19B16CL, 0x8F1944AFB18564C4L},
        {0xECFC86D765EABBEEL, 0x9190E1C46CC13702L},
        {0xE1F8D6B3195D6D97L, 0xDF70267FF5E4C979L},
        {0xD74307D3FD3382DBL, 0x9999B3FFDC769B48L}
    };

    /** The standard 64-bit fingerprint generator using
        polynomials[0][64]. */
    public static final FPGenerator std64 = make(polynomials[64][0], 64);

    /** A standard 32-bit fingerprint generator using
        polynomials[0][32]. */
    public static final FPGenerator std32 = make(polynomials[32][0], 32);
    
    // Below added by St.Ack on 09/30/2004.
    /** A standard 40-bit fingerprint generator using
        polynomials[0][40]. */
    public static final FPGenerator std40 = make(polynomials[40][0], 40);
    /** A standard 24-bit fingerprint generator using
        polynomials[0][24]. */
    public static final FPGenerator std24 = make(polynomials[24][0], 24);
}