LMS*_*LMS 26 c++ crc32 polynomial-math
所以我的设计结合了CRC32C校验和,以确保数据没有被损坏.我决定使用CRC32C,因为如果运行软件的计算机支持SSE 4.2,我可以同时拥有软件版本和硬件加速版本.
我将使用英特尔的开发人员手册(第2A卷),它似乎提供了该crc32指令背后的算法.但是,我运气不好.英特尔的开发人员指南说明如下:
BIT_REFLECT32: DEST[31-0] = SRC[0-31]
MOD2: Remainder from Polynomial division modulus 2
TEMP1[31-0] <- BIT_REFLECT(SRC[31-0])
TEMP2[31-0] <- BIT_REFLECT(DEST[31-0])
TEMP3[63-0] <- TEMP1[31-0] << 32
TEMP4[63-0] <- TEMP2[31-0] << 32
TEMP5[63-0] <- TEMP3[63-0] XOR TEMP4[63-0]
TEMP6[31-0] <- TEMP5[63-0] MOD2 0x11EDC6F41
DEST[31-0] <- BIT_REFLECT(TEMP6[31-0])
现在,据我所知,我已经完成了TEMP6正确开始的所有事情,但我想我可能要么误解多项式除法,要么错误地实现它.如果我的理解是正确的,那么1 / 1 mod 2 = 1,0 / 1 mod 2 = 0两个除零都是未定义的.
我不明白的是64位和33位操作数的二进制除法是如何工作的.如果SRC是0x00000000,并且DEST是0xFFFFFFFF,TEMP5[63-32]将所有设置位,而TEMP5[31-0]将全部取消设置位.
如果我要使用来自TEMP5分子的位,那么将有30个除以零,因为多项式11EDC6F41只有33位长(因此将其转换为64位无符号整数会使前30位未设置),因此分母未设置为30位.
但是,如果我使用多项式作为分子,则底部的32位TEMP5未设置,导致除以零,结果的前30位将为零,因为分子的前30位将是零,如0 / 1 mod 2 = 0.
我误解了这是如何工作的吗？只是简单地遗漏了什么 或者英特尔在其文档中遗漏了一些关键步骤？
我之所以使用英特尔开发人员指南看似他们使用的算法是因为他们使用了33位多项式,我想让输出相同,这在我使用32位多项式时没有发生1EDC6F41(显示下面).
uint32_t poly = 0x1EDC6F41, sres, crcTable[256], data = 0x00000000;
for (n = 0; n < 256; n++) {
sres = n;
for (k = 0; k < 8; k++)
sres = (sres & 1) == 1 ? poly ^ (sres >> 1) : (sres >> 1);
crcTable[n] = sres;
}
sres = 0xFFFFFFFF;
for (n = 0; n < 4; n++) {
sres = crcTable[(sres ^ data) & 0xFF] ^ (sres >> 8);
}
上面的代码产生4138093821输出,crc32操作码2346497208使用输入产生0x00000000.
对不起,如果这些内容写得不好或难以理解,对我来说已经很晚了.
Mar*_*ler 66
以下是CRC-32C的软件和硬件版本.软件版本经过优化,一次可处理8个字节.硬件版本经过优化,可crc32q在单个内核上有效并行运行三条指令,因为该指令的吞吐量为一个周期,但延迟为三个周期.
/* crc32c.c -- compute CRC-32C using the Intel crc32 instruction
* Copyright (C) 2013 Mark Adler
* Version 1.1 1 Aug 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
*/
/* Use hardware CRC instruction on Intel SSE 4.2 processors. This computes a
CRC-32C, *not* the CRC-32 used by Ethernet and zip, gzip, etc. A software
version is provided as a fall-back, as well as for speed comparisons. */
/* Version history:
1.0 10 Feb 2013 First version
1.1 1 Aug 2013 Correct comments on why three crc instructions in parallel
*/
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <unistd.h>
#include <pthread.h>
/* CRC-32C (iSCSI) polynomial in reversed bit order. */
#define POLY 0x82f63b78
/* Table for a quadword-at-a-time software crc. */
static pthread_once_t crc32c_once_sw = PTHREAD_ONCE_INIT;
static uint32_t crc32c_table[8][256];
/* Construct table for software CRC-32C calculation. */
static void crc32c_init_sw(void)
{
uint32_t n, crc, k;
for (n = 0; n < 256; n++) {
crc = n;
crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
crc32c_table[0][n] = crc;
}
for (n = 0; n < 256; n++) {
crc = crc32c_table[0][n];
for (k = 1; k < 8; k++) {
crc = crc32c_table[0][crc & 0xff] ^ (crc >> 8);
crc32c_table[k][n] = crc;
}
}
}
/* Table-driven software version as a fall-back. This is about 15 times slower
than using the hardware instructions. This assumes little-endian integers,
as is the case on Intel processors that the assembler code here is for. */
static uint32_t crc32c_sw(uint32_t crci, const void *buf, size_t len)
{
const unsigned char *next = buf;
uint64_t crc;
pthread_once(&crc32c_once_sw, crc32c_init_sw);
crc = crci ^ 0xffffffff;
while (len && ((uintptr_t)next & 7) != 0) {
crc = crc32c_table[0][(crc ^ *next++) & 0xff] ^ (crc >> 8);
len--;
}
while (len >= 8) {
crc ^= *(uint64_t *)next;
crc = crc32c_table[7][crc & 0xff] ^
crc32c_table[6][(crc >> 8) & 0xff] ^
crc32c_table[5][(crc >> 16) & 0xff] ^
crc32c_table[4][(crc >> 24) & 0xff] ^
crc32c_table[3][(crc >> 32) & 0xff] ^
crc32c_table[2][(crc >> 40) & 0xff] ^
crc32c_table[1][(crc >> 48) & 0xff] ^
crc32c_table[0][crc >> 56];
next += 8;
len -= 8;
}
while (len) {
crc = crc32c_table[0][(crc ^ *next++) & 0xff] ^ (crc >> 8);
len--;
}
return (uint32_t)crc ^ 0xffffffff;
}
/* Multiply a matrix times a vector over the Galois field of two elements,
GF(2). Each element is a bit in an unsigned integer. mat must have at
least as many entries as the power of two for most significant one bit in
vec. */
static inline uint32_t gf2_matrix_times(uint32_t *mat, uint32_t vec)
{
uint32_t sum;
sum = 0;
while (vec) {
if (vec & 1)
sum ^= *mat;
vec >>= 1;
mat++;
}
return sum;
}
/* Multiply a matrix by itself over GF(2). Both mat and square must have 32
rows. */
static inline void gf2_matrix_square(uint32_t *square, uint32_t *mat)
{
int n;
for (n = 0; n < 32; n++)
square[n] = gf2_matrix_times(mat, mat[n]);
}
/* Construct an operator to apply len zeros to a crc. len must be a power of
two. If len is not a power of two, then the result is the same as for the
largest power of two less than len. The result for len == 0 is the same as
for len == 1. A version of this routine could be easily written for any
len, but that is not needed for this application. */
static void crc32c_zeros_op(uint32_t *even, size_t len)
{
int n;
uint32_t row;
uint32_t odd[32]; /* odd-power-of-two zeros operator */
/* put operator for one zero bit in odd */
odd[0] = POLY; /* CRC-32C polynomial */
row = 1;
for (n = 1; n < 32; 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);
/* first square will put the operator for one zero byte (eight zero bits),
in even -- next square puts operator for two zero bytes in odd, and so
on, until len has been rotated down to zero */
do {
gf2_matrix_square(even, odd);
len >>= 1;
if (len == 0)
return;
gf2_matrix_square(odd, even);
len >>= 1;
} while (len);
/* answer ended up in odd -- copy to even */
for (n = 0; n < 32; n++)
even[n] = odd[n];
}
/* Take a length and build four lookup tables for applying the zeros operator
for that length, byte-by-byte on the operand. */
static void crc32c_zeros(uint32_t zeros[][256], size_t len)
{
uint32_t n;
uint32_t op[32];
crc32c_zeros_op(op, len);
for (n = 0; n < 256; n++) {
zeros[0][n] = gf2_matrix_times(op, n);
zeros[1][n] = gf2_matrix_times(op, n << 8);
zeros[2][n] = gf2_matrix_times(op, n << 16);
zeros[3][n] = gf2_matrix_times(op, n << 24);
}
}
/* Apply the zeros operator table to crc. */
static inline uint32_t crc32c_shift(uint32_t zeros[][256], uint32_t crc)
{
return zeros[0][crc & 0xff] ^ zeros[1][(crc >> 8) & 0xff] ^
zeros[2][(crc >> 16) & 0xff] ^ zeros[3][crc >> 24];
}
/* Block sizes for three-way parallel crc computation. LONG and SHORT must
both be powers of two. The associated string constants must be set
accordingly, for use in constructing the assembler instructions. */
#define LONG 8192
#define LONGx1 "8192"
#define LONGx2 "16384"
#define SHORT 256
#define SHORTx1 "256"
#define SHORTx2 "512"
/* Tables for hardware crc that shift a crc by LONG and SHORT zeros. */
static pthread_once_t crc32c_once_hw = PTHREAD_ONCE_INIT;
static uint32_t crc32c_long[4][256];
static uint32_t crc32c_short[4][256];
/* Initialize tables for shifting crcs. */
static void crc32c_init_hw(void)
{
crc32c_zeros(crc32c_long, LONG);
crc32c_zeros(crc32c_short, SHORT);
}
/* Compute CRC-32C using the Intel hardware instruction. */
static uint32_t crc32c_hw(uint32_t crc, const void *buf, size_t len)
{
const unsigned char *next = buf;
const unsigned char *end;
uint64_t crc0, crc1, crc2; /* need to be 64 bits for crc32q */
/* populate shift tables the first time through */
pthread_once(&crc32c_once_hw, crc32c_init_hw);
/* pre-process the crc */
crc0 = crc ^ 0xffffffff;
/* compute the crc for up to seven leading bytes to bring the data pointer
to an eight-byte boundary */
while (len && ((uintptr_t)next & 7) != 0) {
__asm__("crc32b\t" "(%1), %0"
: "=r"(crc0)
: "r"(next), "0"(crc0));
next++;
len--;
}
/* compute the crc on sets of LONG*3 bytes, executing three independent crc
instructions, each on LONG bytes -- this is optimized for the Nehalem,
Westmere, Sandy Bridge, and Ivy Bridge architectures, which have a
throughput of one crc per cycle, but a latency of three cycles */
while (len >= LONG*3) {
crc1 = 0;
crc2 = 0;
end = next + LONG;
do {
__asm__("crc32q\t" "(%3), %0\n\t"
"crc32q\t" LONGx1 "(%3), %1\n\t"
"crc32q\t" LONGx2 "(%3), %2"
: "=r"(crc0), "=r"(crc1), "=r"(crc2)
: "r"(next), "0"(crc0), "1"(crc1), "2"(crc2));
next += 8;
} while (next < end);
crc0 = crc32c_shift(crc32c_long, crc0) ^ crc1;
crc0 = crc32c_shift(crc32c_long, crc0) ^ crc2;
next += LONG*2;
len -= LONG*3;
}
/* do the same thing, but now on SHORT*3 blocks for the remaining data less
than a LONG*3 block */
while (len >= SHORT*3) {
crc1 = 0;
crc2 = 0;
end = next + SHORT;
do {
__asm__("crc32q\t" "(%3), %0\n\t"
"crc32q\t" SHORTx1 "(%3), %1\n\t"
"crc32q\t" SHORTx2 "(%3), %2"
: "=r"(crc0), "=r"(crc1), "=r"(crc2)
: "r"(next), "0"(crc0), "1"(crc1), "2"(crc2));
next += 8;
} while (next < end);
crc0 = crc32c_shift(crc32c_short, crc0) ^ crc1;
crc0 = crc32c_shift(crc32c_short, crc0) ^ crc2;
next += SHORT*2;
len -= SHORT*3;
}
/* compute the crc on the remaining eight-byte units less than a SHORT*3
block */
end = next + (len - (len & 7));
while (next < end) {
__asm__("crc32q\t" "(%1), %0"
: "=r"(crc0)
: "r"(next), "0"(crc0));
next += 8;
}
len &= 7;
/* compute the crc for up to seven trailing bytes */
while (len) {
__asm__("crc32b\t" "(%1), %0"
: "=r"(crc0)
: "r"(next), "0"(crc0));
next++;
len--;
}
/* return a post-processed crc */
return (uint32_t)crc0 ^ 0xffffffff;
}
/* Check for SSE 4.2. SSE 4.2 was first supported in Nehalem processors
introduced in November, 2008. This does not check for the existence of the
cpuid instruction itself, which was introduced on the 486SL in 1992, so this
will fail on earlier x86 processors. cpuid works on all Pentium and later
processors. */
#define SSE42(have) \
do { \
uint32_t eax, ecx; \
eax = 1; \
__asm__("cpuid" \
: "=c"(ecx) \
: "a"(eax) \
: "%ebx", "%edx"); \
(have) = (ecx >> 20) & 1; \
} while (0)
/* Compute a CRC-32C. If the crc32 instruction is available, use the hardware
version. Otherwise, use the software version. */
uint32_t crc32c(uint32_t crc, const void *buf, size_t len)
{
int sse42;
SSE42(sse42);
return sse42 ? crc32c_hw(crc, buf, len) : crc32c_sw(crc, buf, len);
}
#ifdef TEST
#define SIZE (262144*3)
#define CHUNK SIZE
int main(int argc, char **argv)
{
char *buf;
ssize_t got;
size_t off, n;
uint32_t crc;
(void)argv;
crc = 0;
buf = malloc(SIZE);
if (buf == NULL) {
fputs("out of memory", stderr);
return 1;
}
while ((got = read(0, buf, SIZE)) > 0) {
off = 0;
do {
n = (size_t)got - off;
if (n > CHUNK)
n = CHUNK;
crc = argc > 1 ? crc32c_sw(crc, buf + off, n) :
crc32c(crc, buf + off, n);
off += n;
} while (off < (size_t)got);
}
free(buf);
if (got == -1) {
fputs("read error\n", stderr);
return 1;
}
printf("%08x\n", crc);
return 0;
}
#endif /* TEST */
Rob*_*žan 13
Mark Adler的答案是正确和完整的,但那些寻求快速简便地将CRC-32C集成到其应用程序中的人可能会发现调整代码有点困难,特别是如果他们使用的是Windows和.NET.
我创建了一个库,使用硬件或软件方法实现CRC-32C,具体取决于可用的硬件.它可以作为C++和.NET的NuGet包使用.它当然是开源的.
除了上面包含Mark Adler的代码之外,我还找到了一种简单的方法来将软件回退的吞吐量提高50%.在我的计算机上,该库现在在软件中达到2 GB/s,在硬件中达到20 GB/s.对于那些好奇的人,这里是优化的软件实现:
static uint32_t append_table(uint32_t crci, buffer input, size_t length)
{
buffer next = input;
#ifdef _M_X64
uint64_t crc;
#else
uint32_t crc;
#endif
crc = crci ^ 0xffffffff;
#ifdef _M_X64
while (length && ((uintptr_t)next & 7) != 0)
{
crc = table[0][(crc ^ *next++) & 0xff] ^ (crc >> 8);
--length;
}
while (length >= 16)
{
crc ^= *(uint64_t *)next;
uint64_t high = *(uint64_t *)(next + 8);
crc = table[15][crc & 0xff]
^ table[14][(crc >> 8) & 0xff]
^ table[13][(crc >> 16) & 0xff]
^ table[12][(crc >> 24) & 0xff]
^ table[11][(crc >> 32) & 0xff]
^ table[10][(crc >> 40) & 0xff]
^ table[9][(crc >> 48) & 0xff]
^ table[8][crc >> 56]
^ table[7][high & 0xff]
^ table[6][(high >> 8) & 0xff]
^ table[5][(high >> 16) & 0xff]
^ table[4][(high >> 24) & 0xff]
^ table[3][(high >> 32) & 0xff]
^ table[2][(high >> 40) & 0xff]
^ table[1][(high >> 48) & 0xff]
^ table[0][high >> 56];
next += 16;
length -= 16;
}
#else
while (length && ((uintptr_t)next & 3) != 0)
{
crc = table[0][(crc ^ *next++) & 0xff] ^ (crc >> 8);
--length;
}
while (length >= 12)
{
crc ^= *(uint32_t *)next;
uint32_t high = *(uint32_t *)(next + 4);
uint32_t high2 = *(uint32_t *)(next + 8);
crc = table[11][crc & 0xff]
^ table[10][(crc >> 8) & 0xff]
^ table[9][(crc >> 16) & 0xff]
^ table[8][crc >> 24]
^ table[7][high & 0xff]
^ table[6][(high >> 8) & 0xff]
^ table[5][(high >> 16) & 0xff]
^ table[4][high >> 24]
^ table[3][high2 & 0xff]
^ table[2][(high2 >> 8) & 0xff]
^ table[1][(high2 >> 16) & 0xff]
^ table[0][high2 >> 24];
next += 12;
length -= 12;
}
#endif
while (length)
{
crc = table[0][(crc ^ *next++) & 0xff] ^ (crc >> 8);
--length;
}
return (uint32_t)crc ^ 0xffffffff;
}
正如你所看到的,它只是一次压缩更大的块.它需要更大的查找表,但它仍然是缓存友好的.该表以相同的方式生成,仅包含更多行.
我探讨的另一件事是使用PCLMULQDQ指令在AMD处理器上获得硬件加速.我已经设法将针对zlib(也可在GitHub上提供)的英特尔CRC补丁移植到CRC-32C多项式除了魔法常数0x9db42487.如果有人能够破译那个,请告诉我.在superaw7对reddit的出色解释之后,我已经移植了难以捉摸的0x9db42487常量,我只需要找一些时间进行润色和测试.
小智 5
我在这里比较了各种算法：https：//github.com/htot/crc32c
最快的算法来自Intel的crc_iscsi_v_pcl.asm汇编代码（可在Linux内核中以修改形式获得），并使用了此项目中包含的C包装器（crcintelasm.cc）。
为了能够在32位平台上首先运行此代码，已尽可能将其移植到C（crc32intelc），需要进行少量的内联汇编。代码的某些部分取决于位，crc32q在32位上不可用，而movq都不可用，它们与32位平台的备用代码一起放在宏（crc32intel.h）中。