一、CRC-16 MAXIM-DOW演算法簡介

別名：CRC-16/MAXIM。

---

二、CRC-16/MAXIM-DOW演算法基本資訊

CRC演算法名稱	CRC-16/MAXIM-DOW
多項式公式	x16 + x15 + x2 + 1
寬度width	16
多項式poly	0x8005
初始值init	0x0000
輸入反轉refin	true
輸出反轉refout	true
輸出結果異或值xorout	0xFFFF
check	0x44C2
residue	0xB001

---

三、CRC-16/MAXIM-DOW演算法的C語言實現

1、查表法計算CRC-16/MAXIM-DOW

/* CRC餘式表 */
const unsigned int crc_table[256] = {
    0x0000, 0xc0c1, 0xc181, 0x0140, 0xc301, 0x03c0, 0x0280, 0xc241,
    0xc601, 0x06c0, 0x0780, 0xc741, 0x0500, 0xc5c1, 0xc481, 0x0440,
    0xcc01, 0x0cc0, 0x0d80, 0xcd41, 0x0f00, 0xcfc1, 0xce81, 0x0e40,
    0x0a00, 0xcac1, 0xcb81, 0x0b40, 0xc901, 0x09c0, 0x0880, 0xc841,
    0xd801, 0x18c0, 0x1980, 0xd941, 0x1b00, 0xdbc1, 0xda81, 0x1a40,
    0x1e00, 0xdec1, 0xdf81, 0x1f40, 0xdd01, 0x1dc0, 0x1c80, 0xdc41,
    0x1400, 0xd4c1, 0xd581, 0x1540, 0xd701, 0x17c0, 0x1680, 0xd641,
    0xd201, 0x12c0, 0x1380, 0xd341, 0x1100, 0xd1c1, 0xd081, 0x1040,
    0xf001, 0x30c0, 0x3180, 0xf141, 0x3300, 0xf3c1, 0xf281, 0x3240,
    0x3600, 0xf6c1, 0xf781, 0x3740, 0xf501, 0x35c0, 0x3480, 0xf441,
    0x3c00, 0xfcc1, 0xfd81, 0x3d40, 0xff01, 0x3fc0, 0x3e80, 0xfe41,
    0xfa01, 0x3ac0, 0x3b80, 0xfb41, 0x3900, 0xf9c1, 0xf881, 0x3840,
    0x2800, 0xe8c1, 0xe981, 0x2940, 0xeb01, 0x2bc0, 0x2a80, 0xea41,
    0xee01, 0x2ec0, 0x2f80, 0xef41, 0x2d00, 0xedc1, 0xec81, 0x2c40,
    0xe401, 0x24c0, 0x2580, 0xe541, 0x2700, 0xe7c1, 0xe681, 0x2640,
    0x2200, 0xe2c1, 0xe381, 0x2340, 0xe101, 0x21c0, 0x2080, 0xe041,
    0xa001, 0x60c0, 0x6180, 0xa141, 0x6300, 0xa3c1, 0xa281, 0x6240,
    0x6600, 0xa6c1, 0xa781, 0x6740, 0xa501, 0x65c0, 0x6480, 0xa441,
    0x6c00, 0xacc1, 0xad81, 0x6d40, 0xaf01, 0x6fc0, 0x6e80, 0xae41,
    0xaa01, 0x6ac0, 0x6b80, 0xab41, 0x6900, 0xa9c1, 0xa881, 0x6840,
    0x7800, 0xb8c1, 0xb981, 0x7940, 0xbb01, 0x7bc0, 0x7a80, 0xba41,
    0xbe01, 0x7ec0, 0x7f80, 0xbf41, 0x7d00, 0xbdc1, 0xbc81, 0x7c40,
    0xb401, 0x74c0, 0x7580, 0xb541, 0x7700, 0xb7c1, 0xb681, 0x7640,
    0x7200, 0xb2c1, 0xb381, 0x7340, 0xb101, 0x71c0, 0x7080, 0xb041,
    0x5000, 0x90c1, 0x9181, 0x5140, 0x9301, 0x53c0, 0x5280, 0x9241,
    0x9601, 0x56c0, 0x5780, 0x9741, 0x5500, 0x95c1, 0x9481, 0x5440,
    0x9c01, 0x5cc0, 0x5d80, 0x9d41, 0x5f00, 0x9fc1, 0x9e81, 0x5e40,
    0x5a00, 0x9ac1, 0x9b81, 0x5b40, 0x9901, 0x59c0, 0x5880, 0x9841,
    0x8801, 0x48c0, 0x4980, 0x8941, 0x4b00, 0x8bc1, 0x8a81, 0x4a40,
    0x4e00, 0x8ec1, 0x8f81, 0x4f40, 0x8d01, 0x4dc0, 0x4c80, 0x8c41,
    0x4400, 0x84c1, 0x8581, 0x4540, 0x8701, 0x47c0, 0x4680, 0x8641,
    0x8201, 0x42c0, 0x4380, 0x8341, 0x4100, 0x81c1, 0x8081, 0x4040,
};

//查表法計算crc
unsigned short do_crc_table(unsigned char *ptr, int len)
{
    unsigned short crc = 0x0000;
    
    while(len--) 
    {
        crc = (crc >> 8) ^ crc_table[(crc ^ *ptr++) & 0xff];
    }
    
    crc ^= 0xffff;
    
    return (crc);
}

2、直接計演算法計算CRC-16/MAXIM-DOW

//直接計演算法計算crc
unsigned short do_crc(unsigned char *ptr, int len)
{
    unsigned int i;
    unsigned short crc = 0x0000;
    
    while(len--)
    {
        crc ^= *ptr++;
        for (i = 0; i < 8; ++i)
        {
            if (crc & 1)
                crc = (crc >> 1) ^ 0xA001;
            else
                crc = (crc >> 1);
        }
    }
    
    return ~crc;
}

3、測試程式

//測試資料
unsigned char test_buff[]={
    0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
    0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 
    0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17,
    0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 
    0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27,
    0x28, 0x29, 0x2a, 0x2b, 0x2c, 0x2d, 0x2e, 0x2f, 
    0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x37,
    0x38, 0x39, 0x3a, 0x3b, 0x3c, 0x3d, 0x3e, 0x3f, 
    0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47,
    0x48, 0x49, 0x4a, 0x4b, 0x4c, 0x4d, 0x4e, 0x4f, 
    0x50, 0x51, 0x52, 0x53, 0x54, 0x55, 0x56, 0x57,
    0x58, 0x59, 0x5a, 0x5b, 0x5c, 0x5d, 0x5e, 0x5f, 
    0x60, 0x61, 0x62, 0x63, 0x64, 0x65, 0x66, 0x67,
    0x68, 0x69, 0x6a, 0x6b, 0x6c, 0x6d, 0x6e, 0x6f, 
    0x70, 0x71, 0x72, 0x73, 0x74, 0x75, 0x76, 0x77,
    0x78, 0x79, 0x7a, 0x7b, 0x7c, 0x7d, 0x7e, 0x7f, 
    0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87,
    0x88, 0x89, 0x8a, 0x8b, 0x8c, 0x8d, 0x8e, 0x8f, 
    0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97,
    0x98, 0x99, 0x9a, 0x9b, 0x9c, 0x9d, 0x9e, 0x9f, 
    0xa0, 0xa1, 0xa2, 0xa3, 0xa4, 0xa5, 0xa6, 0xa7,
    0xa8, 0xa9, 0xaa, 0xab, 0xac, 0xad, 0xae, 0xaf, 
    0xb0, 0xb1, 0xb2, 0xb3, 0xb4, 0xb5, 0xb6, 0xb7,
    0xb8, 0xb9, 0xba, 0xbb, 0xbc, 0xbd, 0xbe, 0xbf, 
    0xc0, 0xc1, 0xc2, 0xc3, 0xc4, 0xc5, 0xc6, 0xc7,
    0xc8, 0xc9, 0xca, 0xcb, 0xcc, 0xcd, 0xce, 0xcf, 
    0xd0, 0xd1, 0xd2, 0xd3, 0xd4, 0xd5, 0xd6, 0xd7,
    0xd8, 0xd9, 0xda, 0xdb, 0xdc, 0xdd, 0xde, 0xdf, 
    0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7,
    0xe8, 0xe9, 0xea, 0xeb, 0xec, 0xed, 0xee, 0xef, 
    0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6, 0xf7,
    0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff
};

int main(int argc, char* argv[])
{
    unsigned short crc;

    //查表法
    crc = do_crc_table(test_buff, sizeof(test_buff));
    printf("CRC-16/MAXIM-DOW : 0x%x\n", crc);

    //直接計演算法
    crc = do_crc(test_buff, sizeof(test_buff));
    printf("CRC-16/MAXIM-DOW : 0x%x\n", crc);

    return 0;
}

測試結果

CRC-16/MAXIM-DOW : 0x452c
CRC-16/MAXIM-DOW : 0x452c

---

[參考資料]

CRC RevEng