LMS - 1 year ago 138

C++ Question

So I have a design which incorporates CRC32C checksums to ensure data hasn't been damaged. I decided to use CRC32C because I can have both a software version and a hardware-accelerated version if the computer the software runs on supports SSE 4.2

I'm going by Intel's developer manual (vol 2A), which seems to provide the algorithm behind the

`crc32`

`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])

Now, as far as I can tell, I've done everything up to the line starting

`TEMP6`

`1 / 1 mod 2 = 1`

`0 / 1 mod 2 = 0`

What I don't understand is how binary division with 64-bit and 33-bit operands will work. If

`SRC`

`0x00000000`

`DEST`

`0xFFFFFFFF`

`TEMP5[63-32]`

`TEMP5[31-0]`

If I was to use the bits from

`TEMP5`

`11EDC6F41`

However, if I was to use the polynomial as the numerator, the bottom 32 bits of

`TEMP5`

`0 / 1 mod 2 = 0`

Am I misunderstanding how this works? Just plain missing something? Or has Intel left out some crucial step in their documentation?

The reason I went to Intel's developer guide for what appeared to be the algorithm they used is because they used a 33-bit polynomial, and I wanted to make outputs identical, which didn't happen when I used the 32-bit polynomial

`1EDC6F41`

`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);

}

The above code produces

`4138093821`

`crc32`

`2346497208`

`0x00000000`

Sorry if this is badly written or incomprehensible in places, it is rather late for me.

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Answer Source

Here are both software and hardware versions of CRC-32C. The software version is optimized to process eight bytes at a time. The hardware version is optimized to run three `crc32q`

instructions effectively in parallel on a single core, since the throughput of that instruction is one cycle, but the latency is three cycles.

```
/* 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 */
```

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