c - 反转 CRC32(a)

Question

我正在尝试将我在本文档中阅读的内容付诸实践: https://sar.informatik.hu-berlin.de/research/publications/SAR-PR-2006-05/SAR-PR-2006-05_.pdf

我正在使用 Normal Polynimal = 0x04C11DB7 的 CRC32。我建表和反转表。 CRC的表应该是对的，不知道反表对不对。下面您将找到生成表格并尝试将 crc 强制到固定位置的代码。

你能给我一些建议吗？我哪里做错了？

#define CRCPOLY  0x04C11DB7
#define CRCPOLYR  0xEDB88320
#define INITXOR  0xFFFFFFFF
#define FINALXOR 0xFFFFFFFF


static uint32_t crc_table[256];
static uint32_t crc_revtable[256];

void make_crc_table()
{
    for (uint32_t byte = 0; byte <= 0xFF; byte++ )
    {
        uint32_t crc = (byte << 24);

        for (uint8_t bit = 0; bit < 8; bit++ )
        {
            if (crc & 0x80000000)
            {
                crc = (crc << 1) ^ CRCPOLY;
            }
            else
            {
                crc = (crc << 1);
            }
        }

        crc_table[ byte ] = crc;
    }
}

void make_crc_revtable()
{
    for (uint32_t byte = 0; byte < 256; byte++)
    {
        uint32_t crc = byte;

        for (uint8_t bit = 0; bit < 8; bit++)
        {
            if ((crc & 1) != 0)
            {
                crc = (crc >> 1) ^ CRCPOLYR;
            }
            else
            {
                crc >>= 1;
            }
        }

        crc_revtable[byte] = crc;
    }
}


int crc32(uint8_t *buffer, size_t length)
{
    uint32_t crcreg = INITXOR;

    for (size_t i = 0; i < length; ++i) {
        crcreg = crc_table[ (buffer[i]  ^ (crcreg >> 24)) & 0xFF ] ^ (crcreg << 8);
    }

    return crcreg ^ FINALXOR;
}

void fix_crc_pos(uint8_t *buffer, int length, uint32_t tcrcreg, int fix_pos)
{
    int i;

    // make sure fix_pos is within 0..(length-1)
    fix_pos = ((fix_pos % length) + length) % length;

    // calculate crc register at position fix_pos; this is essentially crc32()
    uint32_t crcreg = INITXOR;
    for (i = 0; i < fix_pos; ++i) {
        crcreg = crc_table[ (buffer[i] ^ (crcreg >> 24)) & 0xFF ] ^ (crcreg << 8);
    }

    // inject crcreg as content
    for (i = 0; i < 4; ++i) {
        buffer[fix_pos + i] = (crcreg >> i * 8) & 0xFF;
    }

    // calculate crc backwards to fix_pos, beginning at the end
    tcrcreg ^= FINALXOR;
    for (i = length - 1; i >= fix_pos; --i) {
        tcrcreg = crc_revtable[tcrcreg & 0xFF] ^ buffer[i] ^ (tcrcreg >> 8);
    }

    // inject new content
    for (i = 0; i < 4; ++i) {
        buffer[fix_pos + i] = (tcrcreg >> i * 8) & 0xFF;
    }
}


int main()
{
    make_crc_table();
    make_crc_revtable();

    // Check valid CRC32(a)
    char crc32_check_txt[] = "123456789";
    uint32_t  crc32_check = 0xFC891918;

    uint32_t crc = crc32((uint8_t*)crc32_check_txt, std::strlen(crc32_check_txt));

    if(crc != crc32_check)
        return -1;


    // Change 1 byte and restore the previus CRC
    crc32_check_txt[0] = '4';

    fix_crc_pos((uint8_t*)crc32_check_txt, std::strlen(crc32_check_txt), crc32_check, 4);


    // Verify CRC32
    crc = crc32((uint8_t*)crc32_check_txt, std::strlen(crc32_check_txt));

    if(crc != crc32_check)
        return -1;

    return 0;
}

表格:

CRCa Table
0x00000000, 0x04c11db7, 0x09823b6e, 0x0d4326d9, 0x130476dc, 0x17c56b6b, 0x1a864db2, 0x1e475005,
0x2608edb8, 0x22c9f00f, 0x2f8ad6d6, 0x2b4bcb61, 0x350c9b64, 0x31cd86d3, 0x3c8ea00a, 0x384fbdbd,
0x4c11db70, 0x48d0c6c7, 0x4593e01e, 0x4152fda9, 0x5f15adac, 0x5bd4b01b, 0x569796c2, 0x52568b75,
0x6a1936c8, 0x6ed82b7f, 0x639b0da6, 0x675a1011, 0x791d4014, 0x7ddc5da3, 0x709f7b7a, 0x745e66cd,
0x9823b6e0, 0x9ce2ab57, 0x91a18d8e, 0x95609039, 0x8b27c03c, 0x8fe6dd8b, 0x82a5fb52, 0x8664e6e5,
0xbe2b5b58, 0xbaea46ef, 0xb7a96036, 0xb3687d81, 0xad2f2d84, 0xa9ee3033, 0xa4ad16ea, 0xa06c0b5d,
0xd4326d90, 0xd0f37027, 0xddb056fe, 0xd9714b49, 0xc7361b4c, 0xc3f706fb, 0xceb42022, 0xca753d95,
0xf23a8028, 0xf6fb9d9f, 0xfbb8bb46, 0xff79a6f1, 0xe13ef6f4, 0xe5ffeb43, 0xe8bccd9a, 0xec7dd02d,
0x34867077, 0x30476dc0, 0x3d044b19, 0x39c556ae, 0x278206ab, 0x23431b1c, 0x2e003dc5, 0x2ac12072,
0x128e9dcf, 0x164f8078, 0x1b0ca6a1, 0x1fcdbb16, 0x018aeb13, 0x054bf6a4, 0x0808d07d, 0x0cc9cdca,
0x7897ab07, 0x7c56b6b0, 0x71159069, 0x75d48dde, 0x6b93dddb, 0x6f52c06c, 0x6211e6b5, 0x66d0fb02,
0x5e9f46bf, 0x5a5e5b08, 0x571d7dd1, 0x53dc6066, 0x4d9b3063, 0x495a2dd4, 0x44190b0d, 0x40d816ba,
0xaca5c697, 0xa864db20, 0xa527fdf9, 0xa1e6e04e, 0xbfa1b04b, 0xbb60adfc, 0xb6238b25, 0xb2e29692,
0x8aad2b2f, 0x8e6c3698, 0x832f1041, 0x87ee0df6, 0x99a95df3, 0x9d684044, 0x902b669d, 0x94ea7b2a,
0xe0b41de7, 0xe4750050, 0xe9362689, 0xedf73b3e, 0xf3b06b3b, 0xf771768c, 0xfa325055, 0xfef34de2,
0xc6bcf05f, 0xc27dede8, 0xcf3ecb31, 0xcbffd686, 0xd5b88683, 0xd1799b34, 0xdc3abded, 0xd8fba05a,
0x690ce0ee, 0x6dcdfd59, 0x608edb80, 0x644fc637, 0x7a089632, 0x7ec98b85, 0x738aad5c, 0x774bb0eb,
0x4f040d56, 0x4bc510e1, 0x46863638, 0x42472b8f, 0x5c007b8a, 0x58c1663d, 0x558240e4, 0x51435d53,
0x251d3b9e, 0x21dc2629, 0x2c9f00f0, 0x285e1d47, 0x36194d42, 0x32d850f5, 0x3f9b762c, 0x3b5a6b9b,
0x0315d626, 0x07d4cb91, 0x0a97ed48, 0x0e56f0ff, 0x1011a0fa, 0x14d0bd4d, 0x19939b94, 0x1d528623,
0xf12f560e, 0xf5ee4bb9, 0xf8ad6d60, 0xfc6c70d7, 0xe22b20d2, 0xe6ea3d65, 0xeba91bbc, 0xef68060b,
0xd727bbb6, 0xd3e6a601, 0xdea580d8, 0xda649d6f, 0xc423cd6a, 0xc0e2d0dd, 0xcda1f604, 0xc960ebb3,
0xbd3e8d7e, 0xb9ff90c9, 0xb4bcb610, 0xb07daba7, 0xae3afba2, 0xaafbe615, 0xa7b8c0cc, 0xa379dd7b,
0x9b3660c6, 0x9ff77d71, 0x92b45ba8, 0x9675461f, 0x8832161a, 0x8cf30bad, 0x81b02d74, 0x857130c3,
0x5d8a9099, 0x594b8d2e, 0x5408abf7, 0x50c9b640, 0x4e8ee645, 0x4a4ffbf2, 0x470cdd2b, 0x43cdc09c,
0x7b827d21, 0x7f436096, 0x7200464f, 0x76c15bf8, 0x68860bfd, 0x6c47164a, 0x61043093, 0x65c52d24,
0x119b4be9, 0x155a565e, 0x18197087, 0x1cd86d30, 0x029f3d35, 0x065e2082, 0x0b1d065b, 0x0fdc1bec,
0x3793a651, 0x3352bbe6, 0x3e119d3f, 0x3ad08088, 0x2497d08d, 0x2056cd3a, 0x2d15ebe3, 0x29d4f654,
0xc5a92679, 0xc1683bce, 0xcc2b1d17, 0xc8ea00a0, 0xd6ad50a5, 0xd26c4d12, 0xdf2f6bcb, 0xdbee767c,
0xe3a1cbc1, 0xe760d676, 0xea23f0af, 0xeee2ed18, 0xf0a5bd1d, 0xf464a0aa, 0xf9278673, 0xfde69bc4,
0x89b8fd09, 0x8d79e0be, 0x803ac667, 0x84fbdbd0, 0x9abc8bd5, 0x9e7d9662, 0x933eb0bb, 0x97ffad0c,
0xafb010b1, 0xab710d06, 0xa6322bdf, 0xa2f33668, 0xbcb4666d, 0xb8757bda, 0xb5365d03, 0xb1f740b4,

CRCa Rev Table
0x00000000, 0x77073096, 0xee0e612c, 0x990951ba, 0x076dc419, 0x706af48f, 0xe963a535, 0x9e6495a3,
0x0edb8832, 0x79dcb8a4, 0xe0d5e91e, 0x97d2d988, 0x09b64c2b, 0x7eb17cbd, 0xe7b82d07, 0x90bf1d91,
0x1db71064, 0x6ab020f2, 0xf3b97148, 0x84be41de, 0x1adad47d, 0x6ddde4eb, 0xf4d4b551, 0x83d385c7,
0x136c9856, 0x646ba8c0, 0xfd62f97a, 0x8a65c9ec, 0x14015c4f, 0x63066cd9, 0xfa0f3d63, 0x8d080df5,
0x3b6e20c8, 0x4c69105e, 0xd56041e4, 0xa2677172, 0x3c03e4d1, 0x4b04d447, 0xd20d85fd, 0xa50ab56b,
0x35b5a8fa, 0x42b2986c, 0xdbbbc9d6, 0xacbcf940, 0x32d86ce3, 0x45df5c75, 0xdcd60dcf, 0xabd13d59,
0x26d930ac, 0x51de003a, 0xc8d75180, 0xbfd06116, 0x21b4f4b5, 0x56b3c423, 0xcfba9599, 0xb8bda50f,
0x2802b89e, 0x5f058808, 0xc60cd9b2, 0xb10be924, 0x2f6f7c87, 0x58684c11, 0xc1611dab, 0xb6662d3d,
0x76dc4190, 0x01db7106, 0x98d220bc, 0xefd5102a, 0x71b18589, 0x06b6b51f, 0x9fbfe4a5, 0xe8b8d433,
0x7807c9a2, 0x0f00f934, 0x9609a88e, 0xe10e9818, 0x7f6a0dbb, 0x086d3d2d, 0x91646c97, 0xe6635c01,
0x6b6b51f4, 0x1c6c6162, 0x856530d8, 0xf262004e, 0x6c0695ed, 0x1b01a57b, 0x8208f4c1, 0xf50fc457,
0x65b0d9c6, 0x12b7e950, 0x8bbeb8ea, 0xfcb9887c, 0x62dd1ddf, 0x15da2d49, 0x8cd37cf3, 0xfbd44c65,
0x4db26158, 0x3ab551ce, 0xa3bc0074, 0xd4bb30e2, 0x4adfa541, 0x3dd895d7, 0xa4d1c46d, 0xd3d6f4fb,
0x4369e96a, 0x346ed9fc, 0xad678846, 0xda60b8d0, 0x44042d73, 0x33031de5, 0xaa0a4c5f, 0xdd0d7cc9,
0x5005713c, 0x270241aa, 0xbe0b1010, 0xc90c2086, 0x5768b525, 0x206f85b3, 0xb966d409, 0xce61e49f,
0x5edef90e, 0x29d9c998, 0xb0d09822, 0xc7d7a8b4, 0x59b33d17, 0x2eb40d81, 0xb7bd5c3b, 0xc0ba6cad,
0xedb88320, 0x9abfb3b6, 0x03b6e20c, 0x74b1d29a, 0xead54739, 0x9dd277af, 0x04db2615, 0x73dc1683,
0xe3630b12, 0x94643b84, 0x0d6d6a3e, 0x7a6a5aa8, 0xe40ecf0b, 0x9309ff9d, 0x0a00ae27, 0x7d079eb1,
0xf00f9344, 0x8708a3d2, 0x1e01f268, 0x6906c2fe, 0xf762575d, 0x806567cb, 0x196c3671, 0x6e6b06e7,
0xfed41b76, 0x89d32be0, 0x10da7a5a, 0x67dd4acc, 0xf9b9df6f, 0x8ebeeff9, 0x17b7be43, 0x60b08ed5,
0xd6d6a3e8, 0xa1d1937e, 0x38d8c2c4, 0x4fdff252, 0xd1bb67f1, 0xa6bc5767, 0x3fb506dd, 0x48b2364b,
0xd80d2bda, 0xaf0a1b4c, 0x36034af6, 0x41047a60, 0xdf60efc3, 0xa867df55, 0x316e8eef, 0x4669be79,
0xcb61b38c, 0xbc66831a, 0x256fd2a0, 0x5268e236, 0xcc0c7795, 0xbb0b4703, 0x220216b9, 0x5505262f,
0xc5ba3bbe, 0xb2bd0b28, 0x2bb45a92, 0x5cb36a04, 0xc2d7ffa7, 0xb5d0cf31, 0x2cd99e8b, 0x5bdeae1d,
0x9b64c2b0, 0xec63f226, 0x756aa39c, 0x026d930a, 0x9c0906a9, 0xeb0e363f, 0x72076785, 0x05005713,
0x95bf4a82, 0xe2b87a14, 0x7bb12bae, 0x0cb61b38, 0x92d28e9b, 0xe5d5be0d, 0x7cdcefb7, 0x0bdbdf21,
0x86d3d2d4, 0xf1d4e242, 0x68ddb3f8, 0x1fda836e, 0x81be16cd, 0xf6b9265b, 0x6fb077e1, 0x18b74777,
0x88085ae6, 0xff0f6a70, 0x66063bca, 0x11010b5c, 0x8f659eff, 0xf862ae69, 0x616bffd3, 0x166ccf45,
0xa00ae278, 0xd70dd2ee, 0x4e048354, 0x3903b3c2, 0xa7672661, 0xd06016f7, 0x4969474d, 0x3e6e77db,
0xaed16a4a, 0xd9d65adc, 0x40df0b66, 0x37d83bf0, 0xa9bcae53, 0xdebb9ec5, 0x47b2cf7f, 0x30b5ffe9,
0xbdbdf21c, 0xcabac28a, 0x53b39330, 0x24b4a3a6, 0xbad03605, 0xcdd70693, 0x54de5729, 0x23d967bf,
0xb3667a2e, 0xc4614ab8, 0x5d681b02, 0x2a6f2b94, 0xb40bbe37, 0xc30c8ea1, 0x5a05df1b, 0x2d02ef8d,

Answer 1

我修复了问题中的代码。一个问题是 CRC 注入(inject)以相反的顺序存储字节。我展开了注入(inject)代码的循环以使顺序清晰。生成反向 CRC 表的代码使用正常的 CRC。将 CRC xor 的缓冲区数据反转为 CRC 的最高有效字节的代码。

#include <iostream>

#define CRCPOLY  0x04C11DB7
#define INITXOR  0xFFFFFFFF
#define FINALXOR 0xFFFFFFFF

static uint32_t crc_table[256];
static uint32_t crc_revtable[256];

void make_crc_table()
{
    for (uint32_t byte = 0; byte <= 0xFF; byte++ )
    {
        uint32_t crc = (byte << 24);
        for (uint8_t bit = 0; bit < 8; bit++ )
        {
            if (crc & 0x80000000)
                crc = (crc << 1) ^ CRCPOLY;
            else
                crc = (crc << 1);
        }
        crc_table[ byte ] = crc;
    }
}

void make_crc_revtable()
{
    for (uint32_t byte = 0; byte < 256; byte++)
    {
        uint32_t crc = byte;
        for (uint8_t bit = 0; bit < 8; bit++)
        {
            if ((crc & 1) != 0)
                crc = (crc >> 1) ^ (CRCPOLY >> 1) ^ 0x80000000u;
            else
                crc >>= 1;
        }
        crc_revtable[byte] = crc;
    }
}


int crc32(uint8_t *buffer, size_t length)
{
    uint32_t crcreg = INITXOR;
    for (size_t i = 0; i < length; ++i) {
        crcreg = crc_table[ (buffer[i]  ^ (crcreg >> 24)) & 0xFF ] ^ (crcreg << 8);
    }
    return crcreg ^ FINALXOR;
}

void fix_crc_pos(uint8_t *buffer, int length, uint32_t tcrcreg, int fix_pos)
{
    int i;

    // make sure fix_pos is within 0..(length-1)
    fix_pos = ((fix_pos % length) + length) % length;

    // calculate crc register at position fix_pos; this is essentially crc32()
    uint32_t crcreg = INITXOR;
    for (i = 0; i < fix_pos; ++i) {
        crcreg = crc_table[(buffer[i]^(crcreg>>24))&0xff]^(crcreg<<8);
    }

    // inject crcreg as content
    buffer[fix_pos + 0] = (crcreg >> 24) & 0xFF;
    buffer[fix_pos + 1] = (crcreg >> 16) & 0xFF;
    buffer[fix_pos + 2] = (crcreg >>  8) & 0xFF;
    buffer[fix_pos + 3] = (crcreg >>  0) & 0xFF;

    // calculate crc backwards to fix_pos, beginning at the end
    tcrcreg ^= FINALXOR;
    for (i = length - 1; i >= fix_pos; --i) {
        tcrcreg = crc_revtable[tcrcreg&0xff]^(tcrcreg>>8)^(((uint32_t)buffer[i])<<24);
    }

    // inject new content
    buffer[fix_pos + 0] = (tcrcreg >> 24) & 0xFF;
    buffer[fix_pos + 1] = (tcrcreg >> 16) & 0xFF;
    buffer[fix_pos + 2] = (tcrcreg >>  8) & 0xFF;
    buffer[fix_pos + 3] = (tcrcreg >>  0) & 0xFF;
}

int main()
{
    make_crc_table();
    make_crc_revtable();

    // Check valid CRC32(a)
    char crc32_check_txt[] = "123456789";
    uint32_t  crc32_check = 0xFC891918;

    uint32_t crc = crc32((uint8_t*)crc32_check_txt, std::strlen(crc32_check_txt));

    if(crc != crc32_check){
        std::cout << "error on forward crc\n";
        return 0;
    }

    // Change 1 byte and restore the previus CRC
    crc32_check_txt[0] = '4';

    fix_crc_pos((uint8_t*)crc32_check_txt, (int) std::strlen(crc32_check_txt), crc32_check, 4);

    // Verify CRC32
    crc = crc32((uint8_t*)crc32_check_txt, std::strlen(crc32_check_txt));

    if(crc != crc32_check){
        std::cout << "error on backward crc\n";
        return 0;
    }

    return 0;
}

---

这是另一种方法。要向后循环 CRC，您可以将 CRC 乘以 1/pow(2，要向后循环的位数)== CRC * pow(2，-1-(要向后循环的位数)% CRC_POLY。

#include <iostream>

#define CRCPOLY  0x04C11DB7
#define INITXOR  0xFFFFFFFF
#define FINALXOR 0xFFFFFFFF

static uint32_t crc_table[256];

void make_crc_table()
{
    for (uint32_t byte = 0; byte <= 0xFF; byte++ )
    {
        uint32_t crc = (byte << 24);

        for (uint8_t bit = 0; bit < 8; bit++ )
        {
            if (crc & 0x80000000)
            {
                crc = (crc << 1) ^ CRCPOLY;
            }
            else
            {
                crc = (crc << 1);
            }
        }

        crc_table[ byte ] = crc;
    }
}

int crc32(uint8_t *buffer, size_t length)
{
    uint32_t crcreg = INITXOR;

    for (size_t i = 0; i < length; ++i) {
        crcreg = crc_table[ (buffer[i]  ^ (crcreg >> 24)) & 0xFF ] ^ (crcreg << 8);
    }

    return crcreg ^ FINALXOR;
}

// carryless multiply modulo crc polynomial
uint32_t MpyModCrc(uint32_t a, uint32_t b) // (a*b)%crc
{
uint32_t pd = 0;
uint32_t i;
    for(i = 0; i < 32; i++){
        pd = (pd<<1)^((0-(pd>>31))&0x04c11db7u);
        pd ^= (0-(b>>31))&a;
        b <<= 1;
    }
    return pd;
}

// exponentiate by repeated squaring modulo crc
uint32_t PowModCrc(uint32_t p)          // pow(2,p)%crc
{
uint32_t prd = 0x1u;                    // current product
uint32_t sqr = 0x2u;                    // current square
    while(p){
        if(p&1)
            prd = MpyModCrc(prd, sqr);
        sqr = MpyModCrc(sqr, sqr);
        p >>= 1;
    }
    return prd;
}

void fix_crc_pos(uint8_t *buffer, int length, uint32_t tcrcreg, int fix_pos)
{
uint32_t crc;                                   // crc
uint32_t par;                                   // parities
uint32_t pmr;                                   // 1/pow(2, number of bits to cycle backwards)
size_t i;

    for(i = 0; i < 4; i++)                      // zero out data to be replaced
        buffer[fix_pos+i] = 0;
    pmr = PowModCrc(-1-((length-fix_pos)*8));   // pmr = 1/pow(2, number of bits to cycle backwards)
    crc = crc32(buffer, length);                // generate crc
    crc ^= tcrcreg;                             // adjust crc
    par = MpyModCrc(crc, pmr);                  // par = (crc*pmr)%crc
    buffer[fix_pos+0] = (uint8_t)(par>>24);     // store parities
    buffer[fix_pos+1] = (uint8_t)(par>>16);
    buffer[fix_pos+2] = (uint8_t)(par>> 8);
    buffer[fix_pos+3] = (uint8_t)(par>> 0);
}

int main()
{
    make_crc_table();

    // Check valid CRC32(a)
    char crc32_check_txt[] = "123456789";
    uint32_t  crc32_check = 0xFC891918;

    uint32_t crc = crc32((uint8_t*)crc32_check_txt, std::strlen(crc32_check_txt));

    if(crc != crc32_check){
        std::cout << "error on forward crc\n";
        return 0;
    }

    // Change 1 byte and restore the previus CRC
    crc32_check_txt[0] = 'x';

    fix_crc_pos((uint8_t*)crc32_check_txt, (int) std::strlen(crc32_check_txt), crc32_check, 4);

    // Verify CRC32
    crc = crc32((uint8_t*)crc32_check_txt, std::strlen(crc32_check_txt));

    if(crc != crc32_check){
        std::cout << "error on backward crc\n";
        return 0;
    }

    return 0;
}

---

使用 Visual Studio 内部函数 (PCLMULQDQ) 进行无进位乘法的示例。由于没有无借位除法，因此使用多项式的倒数(由 GenMPoly() 生成)，并进行乘法运算，结果商在 XMM 寄存器的高 64 位中，在下面的代码中为 mt。 m128i_u64[1]，评论为 t[1]。

因此序列是无进位的，两个 32 位值 p = a · b 相乘，得到 63 位结果(没有进位，所以只有 63 位乘积)。乘以 poly 的倒数得到商 t = p/POLY。乘以 poly 得到截断的乘积 t = t*POLY。然后乘积模 poly = p ^ t。

#define POLY  (0x104c11db7ull)
#define POLYM ( 0x04c11db7u)

static __m128i poly;                    /* poly */
static __m128i invpoly;                 /* 2^64 / POLY */

void GenMPoly(void)                     /* generate __m12i8 poly info */
{
uint64_t N = 0x100000000ull;
uint64_t Q = 0;
    for(size_t i = 0; i < 33; i++){
        Q <<= 1;
        if(N&0x100000000ull){
            Q |= 1;
            N ^= POLY;
        }
        N <<= 1;
    }
    poly.m128i_u64[0] = POLY;
    invpoly.m128i_u64[0] = Q;
}
// ...
// carryless multiply modulo crc
uint32_t MpyModCrc(uint32_t a, uint32_t b) // (a*b)%crc
{
__m128i ma, mb, mp, mt;
    ma.m128i_u64[0] = a;
    mb.m128i_u64[0] = b;
    mp = _mm_clmulepi64_si128(ma, mb, 0x00);      // p[0] = a*b
    mt = _mm_clmulepi64_si128(mp, invpoly, 0x00); // t[1] = (p[0]*((2^64)/POLY))>>64
    mt = _mm_clmulepi64_si128(mt, poly, 0x01);    // t[0] = t[1]*POLY
    return mp.m128i_u32[0] ^ mt.m128i_u32[0];     // ret =  p[0] ^ t[0]
}
// ...
int main()
{
    GenMPoly();
// ...