How to get CRC64 distributed calculation (use its

Question

I need hash over pretty large files which is stored on distributed FS. I'm able to process parts of file with much more better performance than whole file so I'd like to be able to calculate hash over parts and then sum it.

I'm thinking about CRC64 as hashing algorithm but I have no clue how to use its theoretical 'linear function' property so I can sum CRC over parts of file. Any recommendation? Anything I missed here?

Additional notes why I'm looking at CRC64:

• I can control file blocks but because of application nature they need to have different size (up to 1 byte, no any fixed blocks are possible).
• I know about CRC32 implementation (zlib) which includes way to sum CRC over parts but I'd like something more wider. 8 bytes look nice for me.
• I know CRC is pretty fast. I'd like to get profit from this as file can be really huge (up to few Gb).

Answer 1

Decided that this was generally useful enough to write and make available:

/* crc64.c -- compute CRC-64
 * Copyright (C) 2013 Mark Adler
 * Version 1.4  16 Dec 2013  Mark Adler
 */

/*
  This software is provided 'as-is', without any express or implied
  warranty.  In no event will the author be held liable for any damages
  arising from the use of this software.

  Permission is granted to anyone to use this software for any purpose,
  including commercial applications, and to alter it and redistribute it
  freely, subject to the following restrictions:

  1. The origin of this software must not be misrepresented; you must not
     claim that you wrote the original software. If you use this software
     in a product, an acknowledgment in the product documentation would be
     appreciated but is not required.
  2. Altered source versions must be plainly marked as such, and must not be
     misrepresented as being the original software.
  3. This notice may not be removed or altered from any source distribution.

  Mark Adler
  [e-mail]
 */

/* Compute CRC-64 in the manner of xz, using the ECMA-182 polynomial,
   bit-reversed, with one's complement pre and post processing.  Provide a
   means to combine separately computed CRC-64's. */

/* Version history:
   1.0  13 Dec 2013  First version
   1.1  13 Dec 2013  Fix comments in test code
   1.2  14 Dec 2013  Determine endianess at run time
   1.3  15 Dec 2013  Add eight-byte processing for big endian as well
                     Make use of the pthread library optional
   1.4  16 Dec 2013  Make once variable volatile for limited thread protection
 */

#include <stdio.h>
#include <inttypes.h>
#include <assert.h>

/* The include of pthread.h below can be commented out in order to not use the
   pthread library for table initialization.  In that case, the initialization
   will not be thread-safe.  That's fine, so long as it can be assured that
   there is only one thread using crc64(). */
#include <pthread.h>            /* link with -lpthread */

/* 64-bit CRC polynomial with these coefficients, but reversed:
    64, 62, 57, 55, 54, 53, 52, 47, 46, 45, 40, 39, 38, 37, 35, 33, 32,
    31, 29, 27, 24, 23, 22, 21, 19, 17, 13, 12, 10, 9, 7, 4, 1, 0 */
#define POLY UINT64_C(0xc96c5795d7870f42)

/* Tables for CRC calculation -- filled in by initialization functions that are
   called once.  These could be replaced by constant tables generated in the
   same way.  There are two tables, one for each endianess.  Since these are
   static, i.e. local, one should be compiled out of existence if the compiler
   can evaluate the endianess check in crc64() at compile time. */
static uint64_t crc64_little_table[8][256];
static uint64_t crc64_big_table[8][256];

/* Fill in the CRC-64 constants table. */
static void crc64_init(uint64_t table[][256])
{
    unsigned n, k;
    uint64_t crc;

    /* generate CRC-64's for all single byte sequences */
    for (n = 0; n < 256; n++) {
        crc = n;
        for (k = 0; k < 8; k++)
            crc = crc & 1 ? POLY ^ (crc >> 1) : crc >> 1;
        table[0][n] = crc;
    }

    /* generate CRC-64's for those followed by 1 to 7 zeros */
    for (n = 0; n < 256; n++) {
        crc = table[0][n];
        for (k = 1; k < 8; k++) {
            crc = table[0][crc & 0xff] ^ (crc >> 8);
            table[k][n] = crc;
        }
    }
}

/* This function is called once to initialize the CRC-64 table for use on a
   little-endian architecture. */
static void crc64_little_init(void)
{
    crc64_init(crc64_little_table);
}

/* Reverse the bytes in a 64-bit word. */
static inline uint64_t rev8(uint64_t a)
{
    uint64_t m;

    m = UINT64_C(0xff00ff00ff00ff);
    a = ((a >> 8) & m) | (a & m) << 8;
    m = UINT64_C(0xffff0000ffff);
    a = ((a >> 16) & m) | (a & m) << 16;
    return a >> 32 | a << 32;
}

/* This function is called once to initialize the CRC-64 table for use on a
   big-endian architecture. */
static void crc64_big_init(void)
{
    unsigned k, n;

    crc64_init(crc64_big_table);
    for (k = 0; k < 8; k++)
        for (n = 0; n < 256; n++)
            crc64_big_table[k][n] = rev8(crc64_big_table[k][n]);
}

/* Run the init() function exactly once.  If pthread.h is not included, then
   this macro will use a simple static state variable for the purpose, which is
   not thread-safe.  The init function must be of the type void init(void). */
#ifdef PTHREAD_ONCE_INIT
#  define ONCE(init) \
    do { \
        static pthread_once_t once = PTHREAD_ONCE_INIT; \
        pthread_once(&once, init); \
    } while (0)
#else
#  define ONCE(init) \
    do { \
        static volatile int once = 1; \
        if (once) { \
            if (once++ == 1) { \
                init(); \
                once = 0; \
            } \
            else \
                while (once) \
                    ; \
        } \
    } while (0)
#endif

/* Calculate a CRC-64 eight bytes at a time on a little-endian architecture. */
static inline uint64_t crc64_little(uint64_t crc, void *buf, size_t len)
{
    unsigned char *next = buf;

    ONCE(crc64_little_init);
    crc = ~crc;
    while (len && ((uintptr_t)next & 7) != 0) {
        crc = crc64_little_table[0][(crc ^ *next++) & 0xff] ^ (crc >> 8);
        len--;
    }
    while (len >= 8) {
        crc ^= *(uint64_t *)next;
        crc = crc64_little_table[7][crc & 0xff] ^
              crc64_little_table[6][(crc >> 8) & 0xff] ^
              crc64_little_table[5][(crc >> 16) & 0xff] ^
              crc64_little_table[4][(crc >> 24) & 0xff] ^
              crc64_little_table[3][(crc >> 32) & 0xff] ^
              crc64_little_table[2][(crc >> 40) & 0xff] ^
              crc64_little_table[1][(crc >> 48) & 0xff] ^
              crc64_little_table[0][crc >> 56];
        next += 8;
        len -= 8;
    }
    while (len) {
        crc = crc64_little_table[0][(crc ^ *next++) & 0xff] ^ (crc >> 8);
        len--;
    }
    return ~crc;
}

/* Calculate a CRC-64 eight bytes at a time on a big-endian architecture. */
static inline uint64_t crc64_big(uint64_t crc, void *buf, size_t len)
{
    unsigned char *next = buf;

    ONCE(crc64_big_init);
    crc = ~rev8(crc);
    while (len && ((uintptr_t)next & 7) != 0) {
        crc = crc64_big_table[0][(crc >> 56) ^ *next++] ^ (crc << 8);
        len--;
    }
    while (len >= 8) {
        crc ^= *(uint64_t *)next;
        crc = crc64_big_table[0][crc & 0xff] ^
              crc64_big_table[1][(crc >> 8) & 0xff] ^
              crc64_big_table[2][(crc >> 16) & 0xff] ^
              crc64_big_table[3][(crc >> 24) & 0xff] ^
              crc64_big_table[4][(crc >> 32) & 0xff] ^
              crc64_big_table[5][(crc >> 40) & 0xff] ^
              crc64_big_table[6][(crc >> 48) & 0xff] ^
              crc64_big_table[7][crc >> 56];
        next += 8;
        len -= 8;
    }
    while (len) {
        crc = crc64_big_table[0][(crc >> 56) ^ *next++] ^ (crc << 8);
        len--;
    }
    return ~rev8(crc);
}

/* Return the CRC-64 of buf[0..len-1] with initial crc, processing eight bytes
   at a time.  This selects one of two routines depending on the endianess of
   the architecture.  A good optimizing compiler will determine the endianess
   at compile time if it can, and get rid of the unused code and table.  If the
   endianess can be changed at run time, then this code will handle that as
   well, initializing and using two tables, if called upon to do so. */
uint64_t crc64(uint64_t crc, void *buf, size_t len)
{
    uint64_t n = 1;

    return *(char *)&n ? crc64_little(crc, buf, len) :
                         crc64_big(crc, buf, len);
}

#define GF2_DIM 64      /* dimension of GF(2) vectors (length of CRC) */

static uint64_t gf2_matrix_times(uint64_t *mat, uint64_t vec)
{
    uint64_t sum;

    sum = 0;
    while (vec) {
        if (vec & 1)
            sum ^= *mat;
        vec >>= 1;
        mat++;
    }
    return sum;
}

static void gf2_matrix_square(uint64_t *square, uint64_t *mat)
{
    unsigned n;

    for (n = 0; n < GF2_DIM; n++)
        square[n] = gf2_matrix_times(mat, mat[n]);
}

/* Return the CRC-64 of two sequential blocks, where crc1 is the CRC-64 of the
   first block, crc2 is the CRC-64 of the second block, and len2 is the length
   of the second block. */
uint64_t crc64_combine(uint64_t crc1, uint64_t crc2, uintmax_t len2)
{
    unsigned n;
    uint64_t row;
    uint64_t even[GF2_DIM];     /* even-power-of-two zeros operator */
    uint64_t odd[GF2_DIM];      /* odd-power-of-two zeros operator */

    /* degenerate case */
    if (len2 == 0)
        return crc1;

    /* put operator for one zero bit in odd */
    odd[0] = POLY;              /* CRC-64 polynomial */
    row = 1;
    for (n = 1; n < GF2_DIM; n++) {
        odd[n] = row;
        row <<= 1;
    }

    /* put operator for two zero bits in even */
    gf2_matrix_square(even, odd);

    /* put operator for four zero bits in odd */
    gf2_matrix_square(odd, even);

    /* apply len2 zeros to crc1 (first square will put the operator for one
       zero byte, eight zero bits, in even) */
    do {
        /* apply zeros operator for this bit of len2 */
        gf2_matrix_square(even, odd);
        if (len2 & 1)
            crc1 = gf2_matrix_times(even, crc1);
        len2 >>= 1;

        /* if no more bits set, then done */
        if (len2 == 0)
            break;

        /* another iteration of the loop with odd and even swapped */
        gf2_matrix_square(odd, even);
        if (len2 & 1)
            crc1 = gf2_matrix_times(odd, crc1);
        len2 >>= 1;

        /* if no more bits set, then done */
    } while (len2 != 0);

    /* return combined crc */
    crc1 ^= crc2;
    return crc1;
}

/* Test crc64() on vector[0..len-1] which should have CRC-64 crc.  Also test
   crc64_combine() on vector[] split in two. */
static void crc64_test(void *vector, size_t len, uint64_t crc)
{
    uint64_t crc1, crc2;

    /* test crc64() */
    crc1 = crc64(0, vector, len);
    if (crc1 ^ crc)
        printf("mismatch: %" PRIx64 ", should be %" PRIx64 "\n", crc1, crc);

    /* test crc64_combine() */
    crc1 = crc64(0, vector, (len + 1) >> 1);
    crc2 = crc64(0, vector + ((len + 1) >> 1), len >> 1);
    crc1 = crc64_combine(crc1, crc2, len >> 1);
    if (crc1 ^ crc)
        printf("mismatch: %" PRIx64 ", should be %" PRIx64 "\n", crc1, crc);
}

/* Test vectors. */
#define TEST1 "123456789"
#define TESTLEN1 9
#define TESTCRC1 UINT64_C(0x995dc9bbdf1939fa)
#define TEST2 "This is a test of the emergency broadcast system."
#define TESTLEN2 49
#define TESTCRC2 UINT64_C(0x27db187fc15bbc72)

int main(void)
{
    crc64_test(TEST1, TESTLEN1, TESTCRC1);
    crc64_test(TEST2, TESTLEN2, TESTCRC2);
    return 0;
}

Answer 2

OK, my contribution to this. Ported to Java.

• I cannot win from 8-byte blocks without doing unsafe thing so I removed block calculation.
• I stay with ECMA polynom - ISO one looks too transparent as for me.
• Of course in final version I will move test code under JUnit.

So here is code:

package com.test;

import java.util.Arrays;

/**
 * CRC-64 implementation with ability to combine checksums calculated over different blocks of data.
 **/
public class CRC64 {

    private final static long POLY = (long) 0xc96c5795d7870f42L; // ECMA-182

    /* CRC64 calculation table. */
    private final static long[] table;

    /* Current CRC value. */
    private long value;

    static {
        table = new long[256];

        for (int n = 0; n < 256; n++) {
            long crc = n;
            for (int k = 0; k < 8; k++) {
                if ((crc & 1) == 1) {
                    crc = (crc >>> 1) ^ POLY;
                } else {
                    crc = (crc >>> 1);
                }
            }
            table[n] = crc;
        }
    }

    public CRC64() {
        this.value = 0;
    }

    public CRC64(long value) {
        this.value = value;
    }

    public CRC64(byte [] b, int len) {
        this.value = 0;
        update(b, len);
    }

    /**
     * Construct new CRC64 instance from byte array.
     **/
    public static CRC64 fromBytes(byte [] b) {
        long l = 0;
        for (int i = 0; i < 4; i++) {
            l <<= 8;
            l ^= (long) b[i] & 0xFF;
        }
        return new CRC64(l);
    }

    /**
     * Get 8 byte representation of current CRC64 value.
     **/
    public byte[] getBytes() {
        byte [] b = new byte[8];
        for (int i = 0; i < 8; i++) {
            b[7 - i] = (byte) (this.value >>> (i * 8));
        }
        return b;
    }

    /**
     * Get long representation of current CRC64 value.
     **/
    public long getValue() {
        return this.value;
    }

    /**
     * Update CRC64 with new byte block.
     **/
    public void update(byte [] b, int len) {

        int idx = 0;
        this.value = ~this.value;
        while (len > 0) {
            this.value = table[((int) (this.value ^ b[idx])) & 0xff] ^ (this.value >>> 8);
            idx++;
            len--;
        }
        this.value = ~this.value;
    }

    private static final int GF2_DIM = 64; /* dimension of GF(2) vectors (length of CRC) */

    private static long gf2MatrixTimes(long [] mat, long vec)
    {
        long sum = 0;
        int idx = 0;
        while (vec != 0) {
            if ((vec & 1) == 1)
                sum ^= mat[idx];
            vec >>>= 1;
            idx++;
        }
        return sum;
    }

    private static void gf2MatrixSquare(long [] square, long [] mat)
    {
        for (int n = 0; n < GF2_DIM; n++)
            square[n] = gf2MatrixTimes(mat, mat[n]);
    }

    /*
     * Return the CRC-64 of two sequential blocks, where summ1 is the CRC-64 of the
     * first block, summ2 is the CRC-64 of the second block, and len2 is the length
     * of the second block.
     */
    static public CRC64 combine(CRC64 summ1, CRC64 summ2, long len2)
    {
        // degenerate case.
        if (len2 == 0)
            return new CRC64(summ1.getValue());

        int n;
        long row;
        long [] even = new long[GF2_DIM]; // even-power-of-two zeros operator
        long [] odd  = new long[GF2_DIM];  // odd-power-of-two zeros operator

        // put operator for one zero bit in odd
        odd[0] = POLY;      // CRC-64 polynomial

        row = 1;
        for (n = 1; n < GF2_DIM; n++) {
            odd[n] = row;
            row <<= 1;
        }

        // put operator for two zero bits in even
        gf2MatrixSquare(even, odd);

        // put operator for four zero bits in odd
        gf2MatrixSquare(odd, even);

        // apply len2 zeros to crc1 (first square will put the operator for one
        // zero byte, eight zero bits, in even)
        long crc1 = summ1.getValue();
        long crc2 = summ2.getValue();
        do {
            // apply zeros operator for this bit of len2
            gf2MatrixSquare(even, odd);
            if ((len2 & 1) == 1)
                crc1 = gf2MatrixTimes(even, crc1);
            len2 >>>= 1;

            // if no more bits set, then done
            if (len2 == 0)
                break;

            // another iteration of the loop with odd and even swapped
            gf2MatrixSquare(odd, even);
            if ((len2 & 1) == 1)
                crc1 = gf2MatrixTimes(odd, crc1);
            len2 >>>= 1;

            // if no more bits set, then done
        } while (len2 != 0);

        // return combined crc.
        crc1 ^= crc2;
        return new CRC64(crc1);
    }

    private static void test(byte [] b, int len, long crcValue) throws Exception {

        /* Test CRC64 default calculation. */
        CRC64 crc = new CRC64(b, len);
        if (crc.getValue() != crcValue) {
            throw new Exception("mismatch: " + String.format("%016x", crc.getValue())
                + " should be " + String.format("%016x", crcValue));
        }

        /* test combine() */
        CRC64 crc1 = new CRC64(b, (len + 1) >>> 1);
        CRC64 crc2 = new CRC64(Arrays.copyOfRange(b, (len + 1) >>> 1, b.length), len >>> 1);
        crc = CRC64.combine(crc1, crc2, len >>> 1);

        if (crc.getValue() != crcValue) {
            throw new Exception("mismatch: " + String.format("%016x", crc.getValue())
                + " should be " + String.format("%016x", crcValue));
        }
    }

    public static void main(String [] args) throws Exception {

        final byte[] TEST1 = "123456789".getBytes();
        final int    TESTLEN1 = 9;
        final long   TESTCRC1 = 0x995dc9bbdf1939faL; // ECMA.
        test(TEST1, TESTLEN1, TESTCRC1);

        final byte[] TEST2 = "This is a test of the emergency broadcast system.".getBytes();
        final int    TESTLEN2 = 49;
        final long   TESTCRC2 = 0x27db187fc15bbc72L; // ECMA.
        test(TEST2, TESTLEN2, TESTCRC2);

        final byte[] TEST3 = "IHATEMATH".getBytes();
        final int    TESTLEN3 = 9;
        final long   TESTCRC3 = 0x3920e0f66b6ee0c8L; // ECMA.
        test(TEST3, TESTLEN3, TESTCRC3);
    }
}