如何获得 CRC64 分布式计算（使用其线性属性）？
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【中文标题】如何获得 CRC64 分布式计算（使用其线性属性）？【英文标题】：How to get CRC64 distributed calculation (use its linearity property)? 【发布时间】：2013-12-31 23:43:12 【问题描述】：我需要对存储在分布式 FS 上的相当大的文件进行哈希处理。我能够以比整个文件更好的性能处理文件的某些部分，因此我希望能够计算部分的哈希值，然后对其求和。
我正在考虑将 CRC64 作为散列算法，但我不知道如何使用其理论上的“线性函数”属性，因此我可以对部分文件进行 CRC 求和。有什么推荐吗？我在这里错过了什么？
附加说明为什么我在看CRC64：
CRC32 实现(zlib)，它包括对部分CRC 求和的方法，但我想要更广泛的东西。 8 个字节对我来说看起来不错。
我知道 CRC 非常快。我想从中获利，因为文件可能非常大（最多几 Gb）。
【问题讨论】：
【参考方案1】：认为这通常足以编写和提供：
/* 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
madler@alumni.caltech.edu
*/
/* 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;
【讨论】：
多项式为什么要反转？那是因为表格的生成方式吗？还是根本没有具体原因？ 您可以定义特定的 CRC 是否被反转。这个被定义为反转，所以你必须以这种方式生成它。历史上反转的 CRC 更为常见，因为它们在软件中的按位实现和按字节实现更简单一些，因此速度也更快。 你能创建一个 CRC 函数来支持任何 CRC 多项式，而不管长度如何？我不确定它是否可能，我想我只是不明白它是如何运作的。 如果你可以限制长度，那么可以。见我的crcany code。【参考方案2】：好的，我对此的贡献。移植到 Java。
如果不做不安全的事情，我无法从 8 字节块中获胜，因此我删除了块计算。 我坚持使用 ECMA 多项式 - ISO 对我来说看起来太透明了。 当然在最终版本中我会将测试代码移到 JUnit 下。代码如下：
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);
【讨论】：
保留前后反转。没有它们，一串零的 CRC 始终为零，与长度无关。有了它们，零的 CRC 不为零，它取决于有多少个零。 你应该热爱数学。 谢谢，经过进一步调查，我得出了同样的结论。 很好，很高兴你现在喜欢数学。 为了将来参考，这里有东西：github.com/MrBuddyCasino/crc-64以上是关于如何获得 CRC64 分布式计算（使用其线性属性）？的主要内容，如果未能解决你的问题，请参考以下文章