本文以CRC8实际代码为例启发各位读者，如何编写一个CRC的校验算法。让各位读者直接跳过繁琐的原理说明阶段，快速应用到工程当中。
一、例程介绍
CRC的校验有很多很多种，掌握以下思路，写任何一个CRC的源生代码都应该没有问题。
本文使用的示范代码为本人编写，算法为CRC-8-MAXIM,多项式为X^8+X^5+X^4+1,即0x31
初始值为0xFF，结果异或值0x00,输入数据和输出数据均不反转。
1.多项式计算的方法
有很多人不知道这个0x31是怎么来的，这里为大家计算一下展开的话就是
1*x^8+0*x^7+0*x^6+1*x^5+1*x^4+0*x^3+0*x^2+0*x^1+1*x^0 对应二进制1 0011 0001 即0x131
CRC8校验取低字节，那么多项式的值就是0x31了
1.反转解释
意思就是将低位变高位，再进行计算
例如：0001 1100 0010 1001 反转后得到的就是 0011 1000 1001 0100
二、代码示例
1.计算法
#include <stdio.h>
unsigned char CRC8_MAXIM(unsigned char *dat,unsigned int len){
unsigned char crc_value=0xFF,j; //初始值为0xff，也有很多初始值为0x00的，此处可修改
unsigned int i;
for(i=0;i<len;i++){
crc_value ^= *dat++;
for(j=0;j<8;j++){
if(crc_value&0x80){
crc_value=(crc_value<<1)^0x31;//其余的CRC校验算法修改该多项式的值即可
}else{
crc_value=(crc_value<<1);
}
}
}
return crc_value;
}
/*使用示例*/
int main(void)
{
unsigned char buff[2]={0xbe,0xef};
printf("crc=%X\n", CRC8_MAXIM(buff,2));
return 0;
}
2.查表法
查表法的原理就是把已经计算出来的值放入一个数组内，这里教大家一个小技巧，用代码写代码，255个值总不能自己去一个个算出来手敲吧。
调用刚刚的计算法函数，编写如下代码，然后在一个C在线编译工具打印出来即可
int main(void)
{
unsigned int k=256; //因为本示例代码的初始值是0xff,所以这里要注意，表格要倒序
//如果初始值是0x00，那表格应该换成正序的
unsigned char buff[2]={0xbe,0xef};
printf("unsigned char CRC8_MAXIM_TABLE[256]={ \n");
while(k--){ /*初始化为0x00时应替换为 for(k=0;k<255;k++)*/
printf("0x%.2x,",CRC8_MAXIM(&k,1));
if(k%8==0){
printf("\n");
}
}
printf("}; \n");
return 0;
}
打印出来的数组如下：
unsigned char CRC8_MAXIM_TABLE[256]={
0x00,0x31,0x62,0x53,0xc4,0xf5,0xa6,0x97,
0xb9,0x88,0xdb,0xea,0x7d,0x4c,0x1f,0x2e,
0x43,0x72,0x21,0x10,0x87,0xb6,0xe5,0xd4,
0xfa,0xcb,0x98,0xa9,0x3e,0x0f,0x5c,0x6d,
0x86,0xb7,0xe4,0xd5,0x42,0x73,0x20,0x11,
0x3f,0x0e,0x5d,0x6c,0xfb,0xca,0x99,0xa8,
0xc5,0xf4,0xa7,0x96,0x01,0x30,0x63,0x52,
0x7c,0x4d,0x1e,0x2f,0xb8,0x89,0xda,0xeb,
0x3d,0x0c,0x5f,0x6e,0xf9,0xc8,0x9b,0xaa,
0x84,0xb5,0xe6,0xd7,0x40,0x71,0x22,0x13,
0x7e,0x4f,0x1c,0x2d,0xba,0x8b,0xd8,0xe9,
0xc7,0xf6,0xa5,0x94,0x03,0x32,0x61,0x50,
0xbb,0x8a,0xd9,0xe8,0x7f,0x4e,0x1d,0x2c,
0x02,0x33,0x60,0x51,0xc6,0xf7,0xa4,0x95,
0xf8,0xc9,0x9a,0xab,0x3c,0x0d,0x5e,0x6f,
0x41,0x70,0x23,0x12,0x85,0xb4,0xe7,0xd6,
0x7a,0x4b,0x18,0x29,0xbe,0x8f,0xdc,0xed,
0xc3,0xf2,0xa1,0x90,0x07,0x36,0x65,0x54,
0x39,0x08,0x5b,0x6a,0xfd,0xcc,0x9f,0xae,
0x80,0xb1,0xe2,0xd3,0x44,0x75,0x26,0x17,
0xfc,0xcd,0x9e,0xaf,0x38,0x09,0x5a,0x6b,
0x45,0x74,0x27,0x16,0x81,0xb0,0xe3,0xd2,
0xbf,0x8e,0xdd,0xec,0x7b,0x4a,0x19,0x28,
0x06,0x37,0x64,0x55,0xc2,0xf3,0xa0,0x91,
0x47,0x76,0x25,0x14,0x83,0xb2,0xe1,0xd0,
0xfe,0xcf,0x9c,0xad,0x3a,0x0b,0x58,0x69,
0x04,0x35,0x66,0x57,0xc0,0xf1,0xa2,0x93,
0xbd,0x8c,0xdf,0xee,0x79,0x48,0x1b,0x2a,
0xc1,0xf0,0xa3,0x92,0x05,0x34,0x67,0x56,
0x78,0x49,0x1a,0x2b,0xbc,0x8d,0xde,0xef,
0x82,0xb3,0xe0,0xd1,0x46,0x77,0x24,0x15,
0x3b,0x0a,0x59,0x68,0xff,0xce,0x9d,0xac
};
现在就可以开始用查表法进行计算了，代码如下：
#include <stdio.h>
unsigned char crc8_maxim(unsigned char *puchMsg, unsigned int usDataLen)
{
unsigned char uchCRC = 0xFF ;
unsigned int i=0;
while (usDataLen--) /* 传输消息缓冲区 */
// for(i=0;i<usDataLen;i++)
{
uchCRC = CRC8_MAXIM_TABLE[uchCRC^*puchMsg++];
}
return uchCRC ;
}
/*使用示例*/
int main(void)
{
unsigned char cs[2]={0xbe,0xef};
printf("crc=%x\n",crc8_maxim(&cs[0],2));
return 0;
}
总结
CRC的计算法和查表法各有各的优点，查表法的时间复杂度要低，占用内存空间较大，适合于大的数据段计算，计算法会比较耗时，占用空间很小，数据越长所需要的时间就越长，适合于小的数据段计算。