CRC校验总结

事实上网上很多CRC校验算法，在接收端进行CRC校验时，余数不为零。这往往是因为CRC校验算法本身是有问题的，但不妨碍我们进行校验。接收端可以对需要校验的字段带入CRC校验算法，计算得到校验值，并与发送数据中的校验值进行比较，如果两者相等，则数据接收正确。

CRC校验算法的代码呈现形式往往有两种：计算法和查表法。查表法是在计算法的基础上将其中部分固定的计算过程的结果写成表格，通过查表方式可以加快计算的速度。

以下为8位CRC的一种C代码实现形式（计算法）：

该校验算法使用的注意事项为发送方的len为待校验字段的长度，接收方的len为待校验字段+校验码的长度。这样接收方计算的校验码应该为0。

特征多项式 x8 + x4 + x3 + x2 + 1    0x11D

uint8 CheckSum_CAN(uint8 *ptr,uint8 len)
{
    uint8 i;
    uint8 crc = 0x00;//跟上面原理讲的一样,校验码的位数比多项式少一位；这里有两种变体，一种是赋值全0（0x00），一种是赋值全1（0xFF）。两种最后得到的校验码正好取反，所以这里赋值全1时，最后会有一个取反的操作。

    uint8 POLY = 0x1D;//这里会把最高位去掉，最高位都是1，根据实际情况修改

    while(len--)
    {
        crc ^= *ptr++;//一个8位一个8位的计算CRC，进行迭代
    
        for(i = 8;i > 0;i--)
        {
            if(crc & 0x80)//如果最高位是1，进行异或
            {
                crc = ( crc << 1) ^ POLY;//多项式的最高位是1，如果crc的最高位也是1，异或结果就是0，前面POLY上最高位省掉    了，所以这里直接移位了
            }
            else//如果最高位不是1的话，直接移位，直到最高位是1，才进行异或
            {
                crc = (crc << 1);
            }
        }
    }

    //如果前面的crc初始定义时赋值的时全1，这里要对crc进行取反。
    return crc;
}

以下为8位CRC校验算法计算法和查表法形式，可以对比来看：

计算法代码形式：

static byte CRC8(byte *u8_data,byte u8_len)
{
    byte i, j;
    byte u8_crc8;
    byte u8_poly;

    u8_crc8 = 0xFF;
    u8_poly = 0x1D;

    for (i = 0; i < u8_len; i++)
    {
        u8_crc8 ^= u8_data[i];

        for (j = 0; j < 8; j++)
        {
            if (u8_crc8 & 0x80)
            {
                u8_crc8 = (u8_crc8 << 1) ^ u8_poly;
            }
            else
            {
                u8_crc8 <<= 1;
            }
        }
    }    
    u8_crc8 ^= (byte)0xFF;
    return u8_crc8;
}



查表法代码形式：

//多项式x^8+x^4+x^3+x^2+1
unsigned char crc8_poly1D (const unsigned char * p_data)
{
    unsigned char crc = 0xFF, i;
    for (i = 7; i > 0; --i)
    {
        // Every byte is xored with table value ‘addressed’ on the basis of its own value
        crc = crctable [crc ^ p_data [i]];
    } 
    return (~ crc); // final NOT
}

CRC计算法形式中以下移位处理的代码对于每一个8位数（共256个）都有一个固定的结果，将这些结果提前计算出来，写成table表。
for (j = 0; j < 8; j++)
{
    if (u8_crc8 & 0x80)
    {
       u8_crc8 = (u8_crc8 << 1) ^ u8_poly;
    }
    else
    {
       u8_crc8 <<= 1;
    }
}

/*****************************************************************
Begin of CRC Lookup Table
*****************************************************************/
unsigned char crctable [256] = {
0x00, 0x1D, 0x3A, 0x27, 0x74, 0x69, 0x4E, 0x53,
0xE8, 0xF5, 0xD2, 0xCF, 0x9C, 0x81, 0xA6, 0xBB,
0xCD, 0xD0, 0xF7, 0xEA, 0xB9, 0xA4, 0x83, 0x9E,
0x25, 0x38, 0x1F, 0x02, 0x51, 0x4C, 0x6B, 0x76,
0x87, 0x9A, 0xBD, 0xA0, 0xF3, 0xEE, 0xC9, 0xD4,
0x6F, 0x72, 0x55, 0x48, 0x1B, 0x06, 0x21, 0x3C,
0x4A, 0x57, 0x70, 0x6D, 0x3E, 0x23, 0x04, 0x19,
0xA2, 0xBF, 0x98, 0x85, 0xD6, 0xCB, 0xEC, 0xF1,
0x13, 0x0E, 0x29, 0x34, 0x67, 0x7A, 0x5D, 0x40,
0xFB, 0xE6, 0xC1, 0xDC, 0x8F, 0x92, 0xB5, 0xA8,
0xDE, 0xC3, 0xE4, 0xF9, 0xAA, 0xB7, 0x90, 0x8D,
0x36, 0x2B, 0x0C, 0x11, 0x42, 0x5F, 0x78, 0x65,
0x94, 0x89, 0xAE, 0xB3, 0xE0, 0xFD, 0xDA, 0xC7,
0x7C, 0x61, 0x46, 0x5B, 0x08, 0x15, 0x32, 0x2F,
0x59, 0x44, 0x63, 0x7E, 0x2D, 0x30, 0x17, 0x0A,
0xB1, 0xAC, 0x8B, 0x96, 0xC5, 0xD8, 0xFF, 0xE2,
0x26, 0x3B, 0x1C, 0x01, 0x52, 0x4F, 0x68, 0x75,
0xCE, 0xD3, 0xF4, 0xE9, 0xBA, 0xA7, 0x80, 0x9D,
0xEB, 0xF6, 0xD1, 0xCC, 0x9F, 0x82, 0xA5, 0xB8,
0x03, 0x1E, 0x39, 0x24, 0x77, 0x6A, 0x4D, 0x50,
0xA1, 0xBC, 0x9B, 0x86, 0xD5, 0xC8, 0xEF, 0xF2,
0x49, 0x54, 0x73, 0x6E, 0x3D, 0x20, 0x07, 0x1A,
0x6C, 0x71, 0x56, 0x4B, 0x18, 0x05, 0x22, 0x3F,
0x84, 0x99, 0xBE, 0xA3, 0xF0, 0xED, 0xCA, 0xD7,
0x35, 0x28, 0x0F, 0x12, 0x41, 0x5C, 0x7B, 0x66,
0xDD, 0xC0, 0xE7, 0xFA, 0xA9, 0xB4, 0x93, 0x8E,
0xF8, 0xE5, 0xC2, 0xDF, 0x8C, 0x91, 0xB6, 0xAB,
0x10, 0x0D, 0x2A, 0x37, 0x64, 0x79, 0x5E, 0x43,
0xB2, 0xAF, 0x88, 0x95, 0xC6, 0xDB, 0xFC, 0xE1,
0x5A, 0x47, 0x60, 0x7D, 0x2E, 0x33, 0x14, 0x09,
0x7F, 0x62, 0x45, 0x58, 0x0B, 0x16, 0x31, 0x2C,
0x97, 0x8A, 0xAD, 0xB0, 0xE3, 0xFE, 0xD9, 0xC4};

以下为CRC16查表法的代码形式：

UINT16 GetCRC16(UINT8 *pSource, UINT16 len)
{
    UINT16 i;
    UINT16 result =0;
    for (i=0; i <len; i++)
    {
        result = (result << 8) ^ CRC16Table[(result >> 8) ^ (UINT8)*pSource++];
    }
    return result;
}

// CRC16校验
//X16 + X12 + X5 + 1（1021）

const UINT16 CRC16Table[256] = {
0x0000,0x1021,0x2042,0x3063,0x4084,0x50a5,0x60c6,0x70e7,
0x8108,0x9129,0xa14a,0xb16b,0xc18c,0xd1ad,0xe1ce,0xf1ef,
0x1231,0x0210,0x3273,0x2252,0x52b5,0x4294,0x72f7,0x62d6,
0x9339,0x8318,0xb37b,0xa35a,0xd3bd,0xc39c,0xf3ff,0xe3de,
0x2462,0x3443,0x0420,0x1401,0x64e6,0x74c7,0x44a4,0x5485,
0xa56a,0xb54b,0x8528,0x9509,0xe5ee,0xf5cf,0xc5ac,0xd58d,
0x3653,0x2672,0x1611,0x0630,0x76d7,0x66f6,0x5695,0x46b4,
0xb75b,0xa77a,0x9719,0x8738,0xf7df,0xe7fe,0xd79d,0xc7bc,
0x48c4,0x58e5,0x6886,0x78a7,0x0840,0x1861,0x2802,0x3823,
0xc9cc,0xd9ed,0xe98e,0xf9af,0x8948,0x9969,0xa90a,0xb92b,
0x5af5,0x4ad4,0x7ab7,0x6a96,0x1a71,0x0a50,0x3a33,0x2a12,
0xdbfd,0xcbdc,0xfbbf,0xeb9e,0x9b79,0x8b58,0xbb3b,0xab1a,
0x6ca6,0x7c87,0x4ce4,0x5cc5,0x2c22,0x3c03,0x0c60,0x1c41,
0xedae,0xfd8f,0xcdec,0xddcd,0xad2a,0xbd0b,0x8d68,0x9d49,
0x7e97,0x6eb6,0x5ed5,0x4ef4,0x3e13,0x2e32,0x1e51,0x0e70,
0xff9f,0xefbe,0xdfdd,0xcffc,0xbf1b,0xaf3a,0x9f59,0x8f78,
0x9188,0x81a9,0xb1ca,0xa1eb,0xd10c,0xc12d,0xf14e,0xe16f,
0x1080,0x00a1,0x30c2,0x20e3,0x5004,0x4025,0x7046,0x6067,
0x83b9,0x9398,0xa3fb,0xb3da,0xc33d,0xd31c,0xe37f,0xf35e,
0x02b1,0x1290,0x22f3,0x32d2,0x4235,0x5214,0x6277,0x7256,
0xb5ea,0xa5cb,0x95a8,0x8589,0xf56e,0xe54f,0xd52c,0xc50d,
0x34e2,0x24c3,0x14a0,0x0481,0x7466,0x6447,0x5424,0x4405,
0xa7db,0xb7fa,0x8799,0x97b8,0xe75f,0xf77e,0xc71d,0xd73c,
0x26d3,0x36f2,0x0691,0x16b0,0x6657,0x7676,0x4615,0x5634,
0xd94c,0xc96d,0xf90e,0xe92f,0x99c8,0x89e9,0xb98a,0xa9ab,
0x5844,0x4865,0x7806,0x6827,0x18c0,0x08e1,0x3882,0x28a3,
0xcb7d,0xdb5c,0xeb3f,0xfb1e,0x8bf9,0x9bd8,0xabbb,0xbb9a,
0x4a75,0x5a54,0x6a37,0x7a16,0x0af1,0x1ad0,0x2ab3,0x3a92,
0xfd2e,0xed0f,0xdd6c,0xcd4d,0xbdaa,0xad8b,0x9de8,0x8dc9,
0x7c26,0x6c07,0x5c64,0x4c45,0x3ca2,0x2c83,0x1ce0,0x0cc1,
0xef1f,0xff3e,0xcf5d,0xdf7c,0xaf9b,0xbfba,0x8fd9,0x9ff8,
0x6e17,0x7e36,0x4e55,0x5e74,0x2e93,0x3eb2,0x0ed1,0x1ef0
};

以下为CRC32的查表法代码形式：

static uint32_t crc32(uint8_t *buf, uint32_t size)
{
	uint32_t i, crc;
	crc = 0xFFFFFFFF;
	for (i = 0; i < size; i++)
		crc = crc32tab[(crc ^ buf[i]) & 0xff] ^ (crc >> 8);
	return crc ^ 0xFFFFFFFF;
}

const uint32_t crc32tab[256] = {
0x0, 0x77073096, 0xEE0E612C, 0x990951BA,
0x76DC419, 0x706AF48F, 0xE963A535, 0x9E6495A3,
0xEDB8832, 0x79DCB8A4, 0xE0D5E91E, 0x97D2D988,
0x9B64C2B, 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, 0x1DB7106, 0x98D220BC, 0xEFD5102A,
0x71B18589, 0x6B6B51F, 0x9FBFE4A5, 0xE8B8D433,
0x7807C9A2, 0xF00F934, 0x9609A88E, 0xE10E9818,
0x7F6A0DBB, 0x86D3D2D, 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, 0x3B6E20C, 0x74B1D29A,
0xEAD54739, 0x9DD277AF, 0x4DB2615, 0x73DC1683,
0xE3630B12, 0x94643B84, 0xD6D6A3E, 0x7A6A5AA8,
0xE40ECF0B, 0x9309FF9D, 0xA00AE27, 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, 0x26D930A,
0x9C0906A9, 0xEB0E363F, 0x72076785, 0x5005713,
0x95BF4A82, 0xE2B87A14, 0x7BB12BAE, 0xCB61B38,
0x92D28E9B, 0xE5D5BE0D, 0x7CDCEFB7, 0xBDBDF21,
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
};