在C/C++中计算32位CRC查找表

Question

我想计算一个32位CRC查找表。我尝试的一种方法是使用此网站中的以下代码：

#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;
}

我尝试的另一种方法是使用我从这个 StackOverflow 问题中找到的以下代码，并且可以从此处下载代码在名为 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;
}

这是基于此链接的正确决赛桌：

// 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);

但是，这是我的两个程序的输出（我对输出进行了比较，它们的输出是相同的），并且它是不正确：

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

位反转。请注意，表条目为

array[0x80]

（0x80 是 0x01 反转）

= 0xEDB88320

，即

0x04C11DB7

反转。

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Flash和RAM（嵌入式软件）不够，可以使用此功能：

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;
}

但是CRC计算需要更多时间。

Answer 3

表格生成：

template <typename T, size_t max_size>
consteval std::array<T, max_size> genCRCTable(T magic_number) noexcept
{
    return [&](){
        std::array<T, max_size> crc_table;

        for(T index {}; auto&& elem : crc_table)
        {
            T remainder { index };
            for (int bit{}; bit < 8; ++bit)
                remainder = (remainder >> 1) ^ (remainder & 1 ? magic_number : 0);

            elem = remainder;
            ++index;
        }
        return crc_table;
    }();
}

表格打印：

template <typename T, size_t max_size>
void printCRCTable(const std::array<T, max_size>& crc_table) noexcept
{
    constexpr size_t tsize { sizeof(T) };
    constexpr size_t width { tsize * 2 };
    constexpr size_t max_count_elem_in_line { 16 / tsize };

    for(size_t i{}; auto&& elem : crc_table)
    {
        std::cout << std::setfill('0') << std::hex;
        std::cout << std::setw(width) << (tsize == 1 ? static_cast<int>(elem) : elem) << ((++i % max_count_elem_in_line)  == 0 ? "\n" : " ");
    }

    std::cout << "\n";
}

主要测试uint32_t：

int main()
{
    using crc_type = uint32_t;
    constexpr size_t table_size { 64 };
    constexpr size_t magic_number { 0xEDB88320 };
    auto crc_table { genCRCTable<crc_type , table_size >( magic_number ) };
    
    printCRCTable(crc_table);
}

//------------------------------------------------------------ ---------

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

//------------------------------------------------------------ ----------

主要测试uint16_t：

int main()
{
    using crc_type = uint16_t;
    constexpr size_t table_size { 64 };
    constexpr size_t magic_number { 0xEDB8 };
    auto crc_table { genCRCTable<crc_type , table_size >( magic_number ) };
    
    printCRCTable(crc_table);
}

//------------------------------------------------------------

0000 51de a3bc f262 9c09 cdd7 3fb5 6e6b
e363 b2bd 40df 1101 7f6a 2eb4 dcd6 8d08
1db7 4c69 be0b efd5 81be d060 2202 73dc
fed4 af0a 5d68 0cb6 62dd 3303 c161 90bf
3b6e 6ab0 98d2 c90c a767 f6b9 04db 5505
d80d 89d3 7bb1 2a6f 4404 15da e7b8 b666
26d9 7707 8565 d4bb bad0 eb0e 196c 48b2
c5ba 9464 6606 37d8 59b3 086d fa0f abd1

//------------------------------------------------------------ -

主要测试uint8_t：

int main()
{
    using crc_type = uint8_t;
    constexpr size_t table_size { 64 };
    constexpr size_t magic_number { 0xED };
    auto crc_table { genCRCTable<crc_type , table_size >( magic_number ) };
    
    printCRCTable(crc_table);
}

//------------------------------------------------------------

00 05 0a 0f 14 11 1e 1b 28 2d 22 27 3c 39 36 33
50 55 5a 5f 44 41 4e 4b 78 7d 72 77 6c 69 66 63
a0 a5 aa af b4 b1 be bb 88 8d 82 87 9c 99 96 93
f0 f5 fa ff e4 e1 ee eb d8 dd d2 d7 cc c9 c6 c3