CRC16浅析

CRC即循环冗余校验码（Cyclic Redundancy Check），是数据通信领域中最常用的一种查错校验码。额，原理/理论方面请自行搜索。

1，为什么多项式的最高项可以不写？

例：CRC-16/xmodem的多项式为：x16+x12+x5+1。即多项式为0x11021，但一般记为0x1021。下面以求0x03的crc为例，手动算出crc。

0x03的多项式为 K(x) = x+1;而G(x) = x16+x12+x5+1,用最高项x16*K(x)=x17+x16,用其除（模2除法）以G(x)求余。

 0011 0000  0000  0000  0000

     10 0010  0000  0100  001 

     01 0010  0000  0100  0010

       1 0001  0000  0010  0001 
       0 0011  0000  0110  0011

得crc为0x3063。由于多项式的最高位的1总是与被除数的最高位1异或得0，所以只要将信息位左移一位，再与去掉最高项的多项式异或即可（crc = (crc << 1) ^poly;）。

2，为什么有的要将多项式0x8005反转，写成0xA001?

由于CRC模型有很多，不只体现在多项式的不同，还有输入值，输出值的操作上，对其进行反转等。例如CRC16_CCITT，就要对其输入，输出值进行反转。如果要对其进行反转，势必会加重其运算效率。所以为了提高效率，可以把多项式反转一下。例如：0x8005 -> 0xA001，然后对信息位从最低位开始右移异或即可。

#include<stdio.h>
#include<stdbool.h>

typedef unsigned short u16;

const u16 crc16_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
};

unsigned char char_invert(unsigned char ch)
{
char i;
unsigned char invert = 0;

for (i = 0; i < 8; i++) {
if (ch & 0x1)
invert |= 0x01 << (7-i);
ch >>= 1;
}

return invert;
}

u16 short_invert(u16 sh)
{
char i;
u16 invert = 0;

for (i = 0; i < 16; i++) {
if (sh & 0x1)
invert |= 0x01 << (15-i);
sh >>= 1;
}

return invert;
}

u16 crc16(u16 crc, u16 poly, bool input_invert,
bool output_invert, u16 output_xor, unsigned char *buf, u16 len)
{
unsigned char i;

while (len--) {
if (input_invert)
crc ^= (char_invert((*buf++)) << 8);
else
crc ^= ((*buf++) << 8);

for (i = 0; i < 8; i++) {
if (crc & 0x8000)
crc = (crc << 1) ^poly;
else
crc <<= 1;
}

}

if (output_invert)
return short_invert(crc)^output_xor;
return crc^output_xor;
}

u16 crc16_ibm(unsigned char *buf, u16 len)
{
return crc16(0x0, 0x8005, true, true, 0x0,buf, len);
}

u16 crc16_modbus(unsigned char *buf, u16 len)
{
return crc16(0xffff, 0x8005, true, true, 0x0, buf, len);
}

u16 crc16_ccitt(unsigned char *buf, u16 len)
{
return crc16(0x0, 0x1021, true, true, 0x0, buf, len);
}

u16 crc16_xmodem(unsigned char *buf, u16 len)
{
return crc16(0x0, 0x1021, false, false, 0x0, buf, len);
}

u16 crc16_x25(unsigned char *buf, u16 len)
{
return crc16(0xffff, 0x1021, true, true, 0xffff, buf, len);
}

static u16 crc16_byte(u16 crc, const unsigned char data)
{
return (crc >> 8) ^ crc16_table[(crc ^ data) & 0xff];
}

u16 crc16_tab(u16 crc, unsigned char const *buffer, size_t len)
{
while (len--)
crc = crc16_byte(crc, *buffer++);
return crc;
}

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