- CRC算法简单说明
crc算法通常用在对数据传输完成后，对数据的完整性进行校验.
在一个p位二进制数据序列之后附加一个r位二进制校检码，构成一个总长为p+r的二进制序列。附加在数据序列之后的这个校检码与p位二进制序列之间存在一个特定的关系，如果因干扰等原因使得数据序列中的一些位发生错误，这种特性的关系就会破坏。因此，可以通过检查该关系，实现对接收到的数据正确性的检验。
摘自:https://blog.csdn.net/u010190210/article/details/80707698
- 按字节运算的CRC( CRC-16-CCITT CRC多项式为x16+x12+x5+1)（1021<—>8408)
uint16_t CRC(vector<uint8_t> input)
{
uint16_t crc = 0xffff;
uint8_t indata;
for(auto i=input.begin();i!=input.end();i++){
indata = *i;
for(int j=0;j<8;j++){
if( (crc^indata)&0xfe ){
crc = crc>>1;
crc = crc ^ 0x8408;
}else{
crc = crc>>1;
}
indata >>= 1;
}
}
return crc;
}
该算法的时间的轮次为 8*n (假设有n个数据需要进行CRC)
uint16_t crcboxs[]={
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};
uint16_t CRC_BOX(uint8_t *input,int len)
{
uint16_t crc = 0xffff;
uint8_t indata;
for(int i=0;i<len;i++){
indata = input[i];
crc = (crc>>8)^ crcboxs[(crc^indata)&0xff];
}
return crc;
}
那么它的这个表咋来的呢。
我们不讨论原理,我们只看代码.
uint16_t CRC(uint8_t *input,int len)
{
uint16_t crc = 0xffff;
uint8_t indata;
for(int i=0;i<len;i++){
indata = input[i];
#if 0
for(int j=0;j<8;j++){
if( (crc^indata)&0xfe ){
crc = crc>>1;
crc = crc ^ 0x8408;
}else{
crc = crc>>1;
}
indata >>= 1;
}
#else
crc = (crc>>8)^ crcboxs[(crc^indata)&0xff];
#endif
}
return crc;
}
在宏#if #else #endif中包裹的代码是等效的
也就是
crc= (crc>>8)^ crcboxs[(crc^indata)&0xff]
等价于
for(int j=0;j<8;j++){
if( (crc^indata)&0xfe ){
crc = crc>>1;
crc = crc ^ 0x8408;
}else{
crc = crc>>1;
}
indata >>= 1;
}
我们观察for循环的代码
发觉 可以确定输入为 crc和indata（8bit） 输出为crc(8bit)
由于循环次数为8,也就是2^8 一共256种输入对应256种输出
并且,映射关系为一一对应.
那么我们可以预先把这堆映射提前计算出来.
计算代码为
void creatCrcBox(uint16_t *crcBox)
{
uint16_t crc;
uint8_t indata;
for(int i=0;i<0x100;i++){
indata = i;
crc = 0x0000;
for(int j=0;j<8;j++){
if( (crc^indata) & 0x01 ){
crc = crc>>1;
crc = crc ^ 0x8408;
}else{
crc = crc>>1;
}
indata >>= 1;
}
crcBox[i] = crc;
}
}
crcBox[0x100]就是我们需要的映射表
也就是crcboxs[]
在
crc = (crc>>8)^ crcboxs[(crc^indata)&0xff];
中,crc^indata就是256中输入,由于我们仅仅用到8bit,所以剩余的8bit需要移位
也就是说在我们已知crc多项式后,我们可以利用void creatCrcBox(uint16_t *crcBox)这个函数,获取所有crc的查表法,用到的数据表
crc查表法的总轮次为N,明显少于8N,单片机表示hold得住
老板笑眯眯的说,下次给你一个更慢的单片机.原先的百元机变成十元机,十元机变成N元机,N元机变成几毛钱的单片机。加油打工人
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