CRC算法是在通訊領(lǐng)域廣泛采用的校驗(yàn)算法。原理我就不說了，這里說一下簡單的程序實(shí)現(xiàn)。以下均采用CRC多項(xiàng)式為0x1021即：
g(x) = x16+x12+x5+x0;CRC的基本原理就不說了，那個(gè)搜一下就有了。
??? ?? 最基本的算法應(yīng)該是按位計(jì)算了，這個(gè)方法可以適用于所有長度的數(shù)據(jù)校驗(yàn)，最為靈活，但由于是按位計(jì)算，其效率并不是最優(yōu)，只適用于對(duì)速度不敏感的場合。基本的算法如下：
unsigned short do_crc_16(unsigned char *message, unsigned int len)
{
??? int i, j;
??? unsigned short crc_reg = 0;
??? unsigned short current;
???????
??? for (i = 0; i < len; i++)
??? {
??????? current = message[i] << 8;
??????? for (j = 0; j < 8; j++)
??????? {
??????????? if ((short)(crc_reg ^ current) < 0)
??????????????? crc_reg = (crc_reg << 1) ^ 0x1021;
??????????? else
??????????????? crc_reg <<= 1;
??????????? current <<= 1;???????????
??????? }
??? }
??? return crc_reg;
}
以是方法可以計(jì)算出任意長度數(shù)據(jù)的校驗(yàn)。但速度慢。下面介紹一種按字節(jié)計(jì)算的方法：
按字節(jié)校驗(yàn)是每次計(jì)算8位數(shù)據(jù)，多是基于查表的算法，首先要準(zhǔn)備一個(gè)表，一共256項(xiàng)。
unsigned int crc_ta[256]={?????????????? /* CRC余式表 */
??? 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
? };
unsigned short do_crc_table(unsigned char *ptr,int len)
{
??? unsigned short int crc;
?? unsigned char da;
??? crc=0;
?? while(len--!=0)?
??? {
?? ??? da=(unsigned short)crc>>8;??? /* 以8位二進(jìn)制數(shù)的形式暫存CRC的高8位 */
??? ??? crc<<=8;????????????? /* 左移8位，相當(dāng)于CRC的低8位乘以? */
??? ??? crc^=crc_ta[da^*ptr];?? /* 高8位和當(dāng)前字節(jié)相加后再查表求CRC ，再加上以前的CRC */
??? ??? ptr++;
? ??? }
?? return(crc);
}
以上算法實(shí)現(xiàn)了按字節(jié)進(jìn)行計(jì)算校驗(yàn)值。在使用的時(shí)候，把計(jì)算出來的校驗(yàn)值放在最后兩個(gè)字節(jié)里，將其發(fā)送出去，接收端對(duì)所有的數(shù)據(jù)進(jìn)行相同的校驗(yàn)，如校驗(yàn)值為0我們則認(rèn)為其數(shù)據(jù)沒有出錯(cuò)。這個(gè)是按高位到低位的發(fā)送順序時(shí)使用的校驗(yàn)方法。
在實(shí)際應(yīng)用中，還有一種按低位到高位的發(fā)送方法，這樣 ，就要進(jìn)行反相的校驗(yàn)，但如果把數(shù)據(jù)反相，顯然加大計(jì)算量，故可以使用相應(yīng)的查表算法來進(jìn)行計(jì)算。只是計(jì)算方法與表不太一樣，其實(shí)現(xiàn)算法如下：
unsigned short?crc16_ccitt_table[256] =
{
??? 0x0000, 0x1189, 0x2312, 0x329b, 0x4624, 0x57ad, 0x6536, 0x74bf,
??? 0x8c48, 0x9dc1, 0xaf5a, 0xbed3, 0xca6c, 0xdbe5, 0xe97e, 0xf8f7,
??? 0x1081, 0x0108, 0x3393, 0x221a, 0x56a5, 0x472c, 0x75b7, 0x643e,
??? 0x9cc9, 0x8d40, 0xbfdb, 0xae52, 0xdaed, 0xcb64, 0xf9ff, 0xe876,
??? 0x2102, 0x308b, 0x0210, 0x1399, 0x6726, 0x76af, 0x4434, 0x55bd,
??? 0xad4a, 0xbcc3, 0x8e58, 0x9fd1, 0xeb6e, 0xfae7, 0xc87c, 0xd9f5,
??? 0x3183, 0x200a, 0x1291, 0x0318, 0x77a7, 0x662e, 0x54b5, 0x453c,
??? 0xbdcb, 0xac42, 0x9ed9, 0x8f50, 0xfbef, 0xea66, 0xd8fd, 0xc974,
??? 0x4204, 0x538d, 0x6116, 0x709f, 0x0420, 0x15a9, 0x2732, 0x36bb,
??? 0xce4c, 0xdfc5, 0xed5e, 0xfcd7, 0x8868, 0x99e1, 0xab7a, 0xbaf3,
??? 0x5285, 0x430c, 0x7197, 0x601e, 0x14a1, 0x0528, 0x37b3, 0x263a,
??? 0xdecd, 0xcf44, 0xfddf, 0xec56, 0x98e9, 0x8960, 0xbbfb, 0xaa72,
??? 0x6306, 0x728f, 0x4014, 0x519d, 0x2522, 0x34ab, 0x0630, 0x17b9,
??? 0xef4e, 0xfec7, 0xcc5c, 0xddd5, 0xa96a, 0xb8e3, 0x8a78, 0x9bf1,
??? 0x7387, 0x620e, 0x5095, 0x411c, 0x35a3, 0x242a, 0x16b1, 0x0738,
??? 0xffcf, 0xee46, 0xdcdd, 0xcd54, 0xb9eb, 0xa862, 0x9af9, 0x8b70,
??? 0x8408, 0x9581, 0xa71a, 0xb693, 0xc22c, 0xd3a5, 0xe13e, 0xf0b7,
??? 0x0840, 0x19c9, 0x2b52, 0x3adb, 0x4e64, 0x5fed, 0x6d76, 0x7cff,
??? 0x9489, 0x8500, 0xb79b, 0xa612, 0xd2ad, 0xc324, 0xf1bf, 0xe036,
??? 0x18c1, 0x0948, 0x3bd3, 0x2a5a, 0x5ee5, 0x4f6c, 0x7df7, 0x6c7e,
??? 0xa50a, 0xb483, 0x8618, 0x9791, 0xe32e, 0xf2a7, 0xc03c, 0xd1b5,
??? 0x2942, 0x38cb, 0x0a50, 0x1bd9, 0x6f66, 0x7eef, 0x4c74, 0x5dfd,
??? 0xb58b, 0xa402, 0x9699, 0x8710, 0xf3af, 0xe226, 0xd0bd, 0xc134,
??? 0x39c3, 0x284a, 0x1ad1, 0x0b58, 0x7fe7, 0x6e6e, 0x5cf5, 0x4d7c,
??? 0xc60c, 0xd785, 0xe51e, 0xf497, 0x8028, 0x91a1, 0xa33a, 0xb2b3,
??? 0x4a44, 0x5bcd, 0x6956, 0x78df, 0x0c60, 0x1de9, 0x2f72, 0x3efb,
??? 0xd68d, 0xc704, 0xf59f, 0xe416, 0x90a9, 0x8120, 0xb3bb, 0xa232,
??? 0x5ac5, 0x4b4c, 0x79d7, 0x685e, 0x1ce1, 0x0d68, 0x3ff3, 0x2e7a,
??? 0xe70e, 0xf687, 0xc41c, 0xd595, 0xa12a, 0xb0a3, 0x8238, 0x93b1,
??? 0x6b46, 0x7acf, 0x4854, 0x59dd, 0x2d62, 0x3ceb, 0x0e70, 0x1ff9,
??? 0xf78f, 0xe606, 0xd49d, 0xc514, 0xb1ab, 0xa022, 0x92b9, 0x8330,
??? 0x7bc7, 0x6a4e, 0x58d5, 0x495c, 0x3de3, 0x2c6a, 0x1ef1, 0x0f78,
};
unsigned short do_crc_table_1(unsigned char *pData,int nLength)
{
??? unsigned short fcs = 0xffff;??? // 初始化
???
??? while(nLength>0)
??? {
??????? fcs = (fcs >> 8) ^?crc16_ccitt_table[(fcs ^ *pData) & 0xff];
??????? nLength--;
??????? pData++;
??? }
???
??? return ~fcs;??? // 取反
}
檢驗(yàn)的時(shí)候，只要用以下方法就可以

int IsCrc16Good(unsigned char* pData, int nLength)
{
??? unsigned short fcs = 0xffff;??? // 初始化
???
??? while(nLength>0)
??? {
??????? fcs = (fcs >> 8) ^??crc16_ccitt_table[(fcs ^ *pData) & 0xff];
??????? nLength--;
??????? pData++;
??? }
???
? //? return ();? // 0xf0b8是CRC-ITU的"Magic Value"
??? if(fcs == 0xf0b8)
??? ??? return 1;
??? else
??? ??? return -1;
}
返回1則數(shù)據(jù)無誤，否則數(shù)據(jù)錯(cuò)誤。
其表的生成方法也比較簡單，對(duì)于前一種查表方法，其生成表的算法可以由按位生成算法來計(jì)算得到，對(duì)0～255的字節(jié)進(jìn)行CRC校驗(yàn)，得到的校驗(yàn)值分別做為表的相應(yīng)項(xiàng)。
對(duì)于后一種查表方法，其碼表可以由以下方法計(jì)算得到，
void?crc16_ccitt()
{
??? unsigned char index = 0;
??? unsigned short to_xor;
??? int i;

??? printf("unsigned short?crc16_ccitt_table[256] =/n{");
??? while (1)
??? {
??????? if (!(index % 8))
??????????? printf("/n");
???????
??????? to_xor = index;??????
??????? for (i = 0; i < 8; i++)
??????? {
??????????? if (to_xor & 0x0001)
??????????????? to_xor = (to_xor >>1) ^ 0x8408;
??????????? else
??????????????? to_xor >>= 1;??????????
??????? }???????????
??????? printf("0x%04x", to_xor);
???????
??????? if (index == 255)
??????? {
??????????? printf("/n");
??????????? break;
??????? }
??????? else
??????? {
??????????? printf(", ");
??????????? index++;
??????? }
??? }
??? printf("};");
??? //return 0;
}
這樣，對(duì)CRC算法算是有一個(gè)新的認(rèn)識(shí)了，至少是分清了對(duì)于同一個(gè)多項(xiàng)式，為什么會(huì)有不同的計(jì)算方法。弄清后，就會(huì)明白在什么場合用什么樣的算法。

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