在C/C++中计算32位CRC查找表

Question

我想计算一个32位的CRC查找表.我尝试过的一种方法是使用本网站中的以下代码

#include <iostream>
#include <stdint.h>

void make_crc_table()
{
    unsigned long POLYNOMIAL = 0x04c11db7;
    unsigned long WIDTH = 8 * sizeof(unsigned long);
    unsigned long TOPBIT = 1 << (WIDTH - 1);
    unsigned long crcTable[256];
    unsigned long remainder;
    // Compute the remainder of each possible dividend
    for (int dividend = 0; dividend < 256; ++dividend)
    {
        // Start with the dividend followed by zeros
        remainder = dividend << (WIDTH - 8);

        // Perform modulo-2 division, a bit at a time
        for (unsigned long bit = 8; bit > 0; --bit)
        {
            // Try to divide the current data bit
            if (remainder & TOPBIT)
            {
                remainder = (remainder << 1) ^ POLYNOMIAL;
            }
            else
            {
                remainder = (remainder << 1);
            }
        }
        crcTable[dividend] = remainder;
    }

    // Print the CRC table
    for (int i = 0; i < 256; i++)
    {
        if (i % 4 == 0)
        {
            std::cout <<"\n";
        }
        std::cout << std::hex << crcTable[i];
        std::cout << ", ";
    }
}

int main()
{
    make_crc_table();
    return 0;
}

我尝试过的另一种方法是使用我从这个StackOverflow问题中找到的以下代码，这些代码可以下载在这里，在一个名为CRC Calculator.zip的文件中

#include <iostream>
#include <stdint.h>

#define POLYNOMIAL      0x04C11DB7
uint32_t A_crcLookupTable[256] = {0};
#define WIDTH    (8 * sizeof(uint32_t))
#define TOPBIT   (((uint32_t)1) << (WIDTH - 1))

#define FP_reflect_DATA(_DATO)                      (_DATO)
#define FP_reflect_CRCTableValue(_CRCTableValue)    (_CRCTableValue)

uint32_t F_CRC_ObtenValorDeTabla(uint8_t VP_Pos_Tabla)
{
    uint32_t VP_CRCTableValue = 0;
    uint8_t VP_Pos_bit = 0;

    VP_CRCTableValue = ((uint32_t) FP_reflect_DATA(VP_Pos_Tabla)) << (WIDTH - 8);

    for (VP_Pos_bit = 0; VP_Pos_bit < 8; VP_Pos_bit++)
    {
        if (VP_CRCTableValue & TOPBIT)
        {
            VP_CRCTableValue = (VP_CRCTableValue << 1) ^ POLYNOMIAL;
        }
        else
        {
            VP_CRCTableValue = (VP_CRCTableValue << 1);
        }
    }
    return (FP_reflect_CRCTableValue(VP_CRCTableValue));
}

void F_CRC_InicializaTabla(void)
{
    uint16_t VP_Pos_Array = 0;

    for (VP_Pos_Array = 0; VP_Pos_Array < 256; VP_Pos_Array++)
    {
        A_crcLookupTable[VP_Pos_Array] = F_CRC_ObtenValorDeTabla((uint8_t)(VP_Pos_Array &0xFF));

    }

}


void make_crc_table()
{
    F_CRC_InicializaTabla();

    // Print the CRC table
    for (int i = 0; i < 256; i++)
    {
        if (i % 4 == 0)
        {
            std::cout <<"\n";
        }
        std::cout << std::hex << A_crcLookupTable[i];
        std::cout << ", ";
    }
}

int main()
{
    make_crc_table();
    return 0;
}

下面是正确的最终表应该是什么，基于此链接

// The constants here are for the CRC-32 generator 
// polynomial, as defined in the Microsoft 
// Systems Journal, March 1995, pp. 107-108
CONST
  table: ARRAY[0..255] OF DWORD =
 ($00000000, $77073096, $EE0E612C, $990951BA,
  $076DC419, $706AF48F, $E963A535, $9E6495A3,
  $0EDB8832, $79DCB8A4, $E0D5E91E, $97D2D988,
  $09B64C2B, $7EB17CBD, $E7B82D07, $90BF1D91,
  $1DB71064, $6AB020F2, $F3B97148, $84BE41DE,
  $1ADAD47D, $6DDDE4EB, $F4D4B551, $83D385C7,
  $136C9856, $646BA8C0, $FD62F97A, $8A65C9EC,
  $14015C4F, $63066CD9, $FA0F3D63, $8D080DF5,
  $3B6E20C8, $4C69105E, $D56041E4, $A2677172,
  $3C03E4D1, $4B04D447, $D20D85FD, $A50AB56B,
  $35B5A8FA, $42B2986C, $DBBBC9D6, $ACBCF940,
  $32D86CE3, $45DF5C75, $DCD60DCF, $ABD13D59,
  $26D930AC, $51DE003A, $C8D75180, $BFD06116,
  $21B4F4B5, $56B3C423, $CFBA9599, $B8BDA50F,
  $2802B89E, $5F058808, $C60CD9B2, $B10BE924,
  $2F6F7C87, $58684C11, $C1611DAB, $B6662D3D,

  $76DC4190, $01DB7106, $98D220BC, $EFD5102A,
  $71B18589, $06B6B51F, $9FBFE4A5, $E8B8D433,
  $7807C9A2, $0F00F934, $9609A88E, $E10E9818,
  $7F6A0DBB, $086D3D2D, $91646C97, $E6635C01,
  $6B6B51F4, $1C6C6162, $856530D8, $F262004E,
  $6C0695ED, $1B01A57B, $8208F4C1, $F50FC457,
  $65B0D9C6, $12B7E950, $8BBEB8EA, $FCB9887C,
  $62DD1DDF, $15DA2D49, $8CD37CF3, $FBD44C65,
  $4DB26158, $3AB551CE, $A3BC0074, $D4BB30E2,
  $4ADFA541, $3DD895D7, $A4D1C46D, $D3D6F4FB,
  $4369E96A, $346ED9FC, $AD678846, $DA60B8D0,
  $44042D73, $33031DE5, $AA0A4C5F, $DD0D7CC9,
  $5005713C, $270241AA, $BE0B1010, $C90C2086,
  $5768B525, $206F85B3, $B966D409, $CE61E49F,
  $5EDEF90E, $29D9C998, $B0D09822, $C7D7A8B4,
  $59B33D17, $2EB40D81, $B7BD5C3B, $C0BA6CAD,

  $EDB88320, $9ABFB3B6, $03B6E20C, $74B1D29A,
  $EAD54739, $9DD277AF, $04DB2615, $73DC1683,
  $E3630B12, $94643B84, $0D6D6A3E, $7A6A5AA8,
  $E40ECF0B, $9309FF9D, $0A00AE27, $7D079EB1,
  $F00F9344, $8708A3D2, $1E01F268, $6906C2FE,
  $F762575D, $806567CB, $196C3671, $6E6B06E7,
  $FED41B76, $89D32BE0, $10DA7A5A, $67DD4ACC,
  $F9B9DF6F, $8EBEEFF9, $17B7BE43, $60B08ED5,
  $D6D6A3E8, $A1D1937E, $38D8C2C4, $4FDFF252,
  $D1BB67F1, $A6BC5767, $3FB506DD, $48B2364B,
  $D80D2BDA, $AF0A1B4C, $36034AF6, $41047A60,
  $DF60EFC3, $A867DF55, $316E8EEF, $4669BE79,
  $CB61B38C, $BC66831A, $256FD2A0, $5268E236,
  $CC0C7795, $BB0B4703, $220216B9, $5505262F,
  $C5BA3BBE, $B2BD0B28, $2BB45A92, $5CB36A04,
  $C2D7FFA7, $B5D0CF31, $2CD99E8B, $5BDEAE1D,

  $9B64C2B0, $EC63F226, $756AA39C, $026D930A,
  $9C0906A9, $EB0E363F, $72076785, $05005713,
  $95BF4A82, $E2B87A14, $7BB12BAE, $0CB61B38,
  $92D28E9B, $E5D5BE0D, $7CDCEFB7, $0BDBDF21,
  $86D3D2D4, $F1D4E242, $68DDB3F8, $1FDA836E,
  $81BE16CD, $F6B9265B, $6FB077E1, $18B74777,
  $88085AE6, $FF0F6A70, $66063BCA, $11010B5C,
  $8F659EFF, $F862AE69, $616BFFD3, $166CCF45,
  $A00AE278, $D70DD2EE, $4E048354, $3903B3C2,
  $A7672661, $D06016F7, $4969474D, $3E6E77DB,
  $AED16A4A, $D9D65ADC, $40DF0B66, $37D83BF0,
  $A9BCAE53, $DEBB9EC5, $47B2CF7F, $30B5FFE9,
  $BDBDF21C, $CABAC28A, $53B39330, $24B4A3A6,
  $BAD03605, $CDD70693, $54DE5729, $23D967BF,
  $B3667A2E, $C4614AB8, $5D681B02, $2A6F2B94,
  $B40BBE37, $C30C8EA1, $5A05DF1B, $2D02EF8D);

然而，这就是我从两个程序中输出的内容(我对输出进行了区分，这两个程序的输出是相同的)，而且这是错误的

0, 4c11db7, 9823b6e, d4326d9, 
130476dc, 17c56b6b, 1a864db2, 1e475005, 
2608edb8, 22c9f00f, 2f8ad6d6, 2b4bcb61, 
350c9b64, 31cd86d3, 3c8ea00a, 384fbdbd, 
4c11db70, 48d0c6c7, 4593e01e, 4152fda9, 
5f15adac, 5bd4b01b, 569796c2, 52568b75, 
6a1936c8, 6ed82b7f, 639b0da6, 675a1011, 
791d4014, 7ddc5da3, 709f7b7a, 745e66cd, 
9823b6e0, 9ce2ab57, 91a18d8e, 95609039, 
8b27c03c, 8fe6dd8b, 82a5fb52, 8664e6e5, 
be2b5b58, baea46ef, b7a96036, b3687d81, 
ad2f2d84, a9ee3033, a4ad16ea, a06c0b5d, 
d4326d90, d0f37027, ddb056fe, d9714b49, 
c7361b4c, c3f706fb, ceb42022, ca753d95, 
f23a8028, f6fb9d9f, fbb8bb46, ff79a6f1, 
e13ef6f4, e5ffeb43, e8bccd9a, ec7dd02d, 
34867077, 30476dc0, 3d044b19, 39c556ae, 
278206ab, 23431b1c, 2e003dc5, 2ac12072, 
128e9dcf, 164f8078, 1b0ca6a1, 1fcdbb16, 
18aeb13, 54bf6a4, 808d07d, cc9cdca, 
7897ab07, 7c56b6b0, 71159069, 75d48dde, 
6b93dddb, 6f52c06c, 6211e6b5, 66d0fb02, 
5e9f46bf, 5a5e5b08, 571d7dd1, 53dc6066, 
4d9b3063, 495a2dd4, 44190b0d, 40d816ba, 
aca5c697, a864db20, a527fdf9, a1e6e04e, 
bfa1b04b, bb60adfc, b6238b25, b2e29692, 
8aad2b2f, 8e6c3698, 832f1041, 87ee0df6, 
99a95df3, 9d684044, 902b669d, 94ea7b2a, 
e0b41de7, e4750050, e9362689, edf73b3e, 
f3b06b3b, f771768c, fa325055, fef34de2, 
c6bcf05f, c27dede8, cf3ecb31, cbffd686, 
d5b88683, d1799b34, dc3abded, d8fba05a, 
690ce0ee, 6dcdfd59, 608edb80, 644fc637, 
7a089632, 7ec98b85, 738aad5c, 774bb0eb, 
4f040d56, 4bc510e1, 46863638, 42472b8f, 
5c007b8a, 58c1663d, 558240e4, 51435d53, 
251d3b9e, 21dc2629, 2c9f00f0, 285e1d47, 
36194d42, 32d850f5, 3f9b762c, 3b5a6b9b, 
315d626, 7d4cb91, a97ed48, e56f0ff, 
1011a0fa, 14d0bd4d, 19939b94, 1d528623, 
f12f560e, f5ee4bb9, f8ad6d60, fc6c70d7, 
e22b20d2, e6ea3d65, eba91bbc, ef68060b, 
d727bbb6, d3e6a601, dea580d8, da649d6f, 
c423cd6a, c0e2d0dd, cda1f604, c960ebb3, 
bd3e8d7e, b9ff90c9, b4bcb610, b07daba7, 
ae3afba2, aafbe615, a7b8c0cc, a379dd7b, 
9b3660c6, 9ff77d71, 92b45ba8, 9675461f, 
8832161a, 8cf30bad, 81b02d74, 857130c3, 
5d8a9099, 594b8d2e, 5408abf7, 50c9b640, 
4e8ee645, 4a4ffbf2, 470cdd2b, 43cdc09c, 
7b827d21, 7f436096, 7200464f, 76c15bf8, 
68860bfd, 6c47164a, 61043093, 65c52d24, 
119b4be9, 155a565e, 18197087, 1cd86d30, 
29f3d35, 65e2082, b1d065b, fdc1bec, 
3793a651, 3352bbe6, 3e119d3f, 3ad08088, 
2497d08d, 2056cd3a, 2d15ebe3, 29d4f654, 
c5a92679, c1683bce, cc2b1d17, c8ea00a0, 
d6ad50a5, d26c4d12, df2f6bcb, dbee767c, 
e3a1cbc1, e760d676, ea23f0af, eee2ed18, 
f0a5bd1d, f464a0aa, f9278673, fde69bc4, 
89b8fd09, 8d79e0be, 803ac667, 84fbdbd0, 
9abc8bd5, 9e7d9662, 933eb0bb, 97ffad0c, 
afb010b1, ab710d06, a6322bdf, a2f33668, 
bcb4666d, b8757bda, b5365d03, b1f740b4,

Answer 1

这些比特被反转了。请注意，array[0x80] (0x80为0x01反向)的表条目是= 0xEDB88320，而0x04C11DB7则相反。

示例代码：

#include <iostream>
#include <iomanip>

void make_crc_table(unsigned long crcTable[]) {
    unsigned long POLYNOMIAL = 0xEDB88320;
    unsigned long remainder;
    unsigned char b = 0;
    do {
        // Start with the data byte
        remainder = b;
        for (unsigned long bit = 8; bit > 0; --bit) {
            if (remainder & 1)
                remainder = (remainder >> 1) ^ POLYNOMIAL;
            else
                remainder = (remainder >> 1);
        }
        crcTable[(size_t)b] = remainder;
    } while(0 != ++b);
}

unsigned long gen_crc(unsigned char *p, size_t n, unsigned long crcTable[]) {
    unsigned long crc = 0xfffffffful;
    size_t i;
    for(i = 0; i < n; i++)
        crc = crcTable[*p++ ^ (crc&0xff)] ^ (crc>>8);
    return(~crc);
}

int main() {
    unsigned long crcTable[256];
    make_crc_table(crcTable);
    // Print the CRC table
    for (size_t i = 0; i < 256; i++) {
        std::cout << std::setfill('0') << std::setw(8) << std::hex << crcTable[i];
        if (i % 4 == 3)
            std::cout << std::endl;
        else
            std::cout << ", ";
    }
    return 0;
}

Answer 2

如果没有足够的Flash和RAM (嵌入式软件)，可以使用以下功能：

uint32_t CRC32_function(uint8_t *buf, uint32_t len){

    uint32_t val, crc;
    uint8_t i;

    crc = 0xFFFFFFFF;
    while(len--){
        val=(crc^*buf++)&0xFF;
        for(i=0; i<8; i++){
            val = val & 1 ? (val>>1)^0xEDB88320 : val>>1;
        }
        crc = val^crc>>8;
    }
    return crc^0xFFFFFFFF;
}

但CRC计算需要更多的时间。