如何将表驱动的 CRC 实现转换为按位实现

您首先需要 CRC 多项式，您可以在此类表的第二个条目或第 128 个条目中找到该多项式，具体取决于 CRC 的位顺序。 或者在这种情况下，您可以在评论中找到它，0x17531 . x之后的1是多项式的第一项，它简单地定义了CRC的长度。 它在计算中删除。 您可以在表的第二个条目中找到0x7531。

此例程（在 C 中）仅使用多项式生成上表：

void make_crc_table(unsigned poly, unsigned *table)
{
    unsigned n, k, crc;
    for (n = 0; n < 256; n++) {
        crc = n << 8;
        for (k = 0; k < 8; k++)
            crc = crc & 0x8000 ? (crc << 1) ^ poly : crc << 1;
        table[n] = crc & 0xffff;
    }
}

这样称呼它：make_crc_table(0x7531, table)其中table是一个由 256 个无符号整数组成的数组。

按位 CRC 例程看起来大致相同：

unsigned epobit(unsigned char *buf, unsigned len, unsigned poly)
{
    unsigned n, k, crc = 0;
    for (n = len; n > 0; n--) {
        crc ^= (*buf++ << 8);
        for (k = 0; k < 8; k++)
            crc = crc & 0x8000 ? (crc << 1) ^ poly : crc << 1;
    }
    return crc & 0xffff;
}

对于一个工具，请查看pycrc，它有一个用于任何任意CRC的代码生成器。

有关 CRC 计算的说明，请参阅 CRC 错误检测算法的无痛指南。

// Bitise and tablewise CRC-16 can be compared by following source code with polynomial 0x17531 !
// CRC.cpp : 
//
#include "stdafx.h"
#include "CRC.h"
#include "afx.h"
#include <conio.h>
#ifdef _DEBUG
#define new DEBUG_NEW
#endif

CWinApp theApp;
using namespace std;
#define BUFLENGTH (0x100000*1)  //0x100000=1MB
void makeCRC16Table();
void crc16update(unsigned short &crc0, const void *data, int length);
void crc16updateBitwise(unsigned short &crc0, const void *data, int length);
static byte crc8Table[256];
static unsigned short crc16Table[256];
static unsigned long crc32Table[256];
int _tmain(int argc, TCHAR* argv[], TCHAR* envp[])
{
    int nRetCode = 0;
    unsigned char crc8=0x00;
    unsigned short crc16=0x0000;
    unsigned long crc32=0x00000000;
    byte *dataBuf = new byte[BUFLENGTH];
    if(dataBuf==0)
    {
        cout<<"Not enough memory allocation to dataBuf[] !";
        while(!_kbhit());
        return nRetCode;
    }
    for(int i=0; i<BUFLENGTH; i++)
        dataBuf[i]=i+1;
    makeCRC16Table();
    crc16=0x00;
    crc16update(crc16, dataBuf, BUFLENGTH);
    crc16=0x00;
    crc16updateBitwise(crc16, dataBuf, BUFLENGTH);
    delete[] dataBuf;
    while(!_kbhit());
    }
    return nRetCode;
}
void makeCRC16Table()
{
    /* generate a table for a byte-wise 16-bit CRC caculation on the polynomial ;
      */
    CString soutputfile=_T("crc16Table.txt");
    CString soutputbuffer;
    CStdioFile fileTarget( soutputfile, CFile::modeCreate | CFile::modeWrite );
    int i,j;
    unsigned long poly, cc;
    /* terms of polynomial defining this crc (except x^16) */
    //static const byte pp[]={0,5,12};
    static const byte pp[]={0,2,15};
    /* make exclusive-or pattern from polynomial 0x1021 */
    poly=0;
    //for(i=0; i<sizeof(pp)/sizeof(byte); i++) 
    //  poly|=1<<pp[i];
    poly=0x7531;
    //poly=0x1021;
    //poly=0x8005;
    for(i=0; i<256; i++) {
        cc=i<<8; 
        for(j=0; j<8; j++) {
            cc=(cc&0x8000)?(poly^(cc<<1)):(cc<<1);  //MSB first transmission
        }
        crc16Table[i]=cc&0xffff;
        soutputbuffer.Format("%3d:%04Xn", i, crc16Table[i]);
        fileTarget.WriteString(soutputbuffer);
    }
    fileTarget.Close();
    //ShellExecute(NULL, NULL, soutputfile, NULL, NULL, SW_SHOWNORMAL);
}
void crc16update(unsigned short &crc0, const void *data, int length)
{
    CString soutputfile=_T("crc16.txt");
    cout<<"n"<<soutputfile<<"n";
    CString soutputbuffer, soutputbufferTotal;
    CStdioFile fileTarget( soutputfile, CFile::modeCreate | CFile::modeWrite );
    int percentage=0, ntemp;
    unsigned short crc,crc1;
    const unsigned char *buf=(const unsigned char *)data;
    int i=0, j;
    crc=crc0;
    while(i<length) 
    {
        ntemp=i/(length/100);
        if(ntemp!=percentage)
        {
            soutputbuffer.Format("%d%% ", percentage );
            cout<<soutputbuffer;
            percentage=ntemp;
            if(ntemp<0)
                int nn=0;
        }
        crc1=crc;
        j = ((crc >> 8) ^ buf[i]) & 0xff;
        crc = (crc << 8) ^ crc16Table[j];
        soutputbuffer.Format("%d:%02X:%04X>%04Xn", i, buf[i], crc1, crc );
        fileTarget.WriteString(soutputbuffer);
        i++;
    }
    soutputbuffer.Format("n%04X>%04X", crc1, crc );
    cout<<soutputbuffer;
    crc0=crc;
    fileTarget.Close();
    //ShellExecute(NULL, NULL, soutputfile, NULL, NULL, SW_SHOWNORMAL);
}
void crc16updateBitwise(unsigned short &crc0, const void *data, int length)
{
    CString soutputfile=_T("crc16BW.txt");
    cout<<"n"<<soutputfile<<"n";
    CString soutputbuffer;
    CStdioFile fileTarget( soutputfile, CFile::modeCreate | CFile::modeWrite );
    static const byte BitTable[]={0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80};
    int percentage=0, ntemp;
    unsigned long poly;
    /* terms of polynomial defining this crc (except x^16) */
    //static const byte pp[]={0,5,12};//CCITT
    static const byte pp[]={0,2,15};//GENERAL
    /* make exclusive-or pattern from polynomial 0x1021 */
    int i;
    poly=0;
    //for(i=0; i<sizeof(pp)/sizeof(byte); i++) 
    //  poly|=1<<pp[i];
    //poly=0x8005;
    poly=0x7531;
    unsigned short crc,crc1;
    const unsigned char *buf=(const unsigned char *)data;
    byte a,b,c;
    crc=crc0;
    i=0;
    while(i<length) 
    {
        ntemp=i/(length/100);
        if(ntemp!=percentage)
        {
            soutputbuffer.Format("%d%% ", percentage );
            cout<<soutputbuffer;
            percentage=ntemp;
        }
        crc1=crc;
        for(int j=0; j<8; j++) {
            a=(crc&0x8000)?1:0;//x^16
            b=(buf[i]&BitTable[7-j])?1:0;////MSB first transmission 
            c=a^b;
            crc=(c?(poly^(crc<<1)):(crc<<1))&0xffff;
        }
        soutputbuffer.Format("%d:%02X:%04X>%04Xn", i, buf[i], crc1&0xffff, crc&0xffff );
        fileTarget.WriteString(soutputbuffer);
        i++;
    }
    soutputbuffer.Format("n%04X>%04X", crc1&0xffff, crc&0xffff );
    cout<<soutputbuffer;
    crc0=crc;
    fileTarget.Close();
    //ShellExecute(NULL, NULL, soutputfile, NULL, NULL, SW_SHOWNORMAL);
}