title: Calculate a 32-bit CRC lookup table in C/C++
body: <p>I want to calculate a 32-bit CRC lookup table. One way I tried is by using the following code from <a href="http://www.barrgroup.com/Embedded-Systems/How-To/CRC-Calculation-C-Code" rel="noreferrer">this website</a>:</p>
  
  <pre><code>#include &lt;iostream&gt;
  #include &lt;stdint.h&gt;
  
  void make_crc_table()
  {
      unsigned long POLYNOMIAL = 0x04c11db7;
      unsigned long WIDTH = 8 * sizeof(unsigned long);
      unsigned long TOPBIT = 1 &lt;&lt; (WIDTH - 1);
      unsigned long crcTable[256];
      unsigned long remainder;
      // Compute the remainder of each possible dividend
      for (int dividend = 0; dividend &lt; 256; ++dividend)
      {
          // Start with the dividend followed by zeros
          remainder = dividend &lt;&lt; (WIDTH - 8);
  
          // Perform modulo-2 division, a bit at a time
          for (unsigned long bit = 8; bit &gt; 0; --bit)
          {
              // Try to divide the current data bit
              if (remainder &amp; TOPBIT)
              {
                  remainder = (remainder &lt;&lt; 1) ^ POLYNOMIAL;
              }
              else
              {
                  remainder = (remainder &lt;&lt; 1);
              }
          }
          crcTable[dividend] = remainder;
      }
  
      // Print the CRC table
      for (int i = 0; i &lt; 256; i++)
      {
          if (i % 4 == 0)
          {
              std::cout &lt;&lt;"\n";
          }
          std::cout &lt;&lt; std::hex &lt;&lt; crcTable[i];
          std::cout &lt;&lt; ", ";
      }
  }
  
  int main()
  {
      make_crc_table();
      return 0;
  }
  </code></pre>
  
  <p>Another way I tried is by using the following code that I found from <a href="https://stackoverflow.com/questions/22693578/crc-16-ccitt-with-lookup-table">this StackOverflow question</a>, and the code can be downloaded <a href="http://sourceforge.net/projects/crccalculator/files/CRC/" rel="noreferrer">from here in a file called CRC Calculator.zip</a></p>
  
  <pre><code>#include &lt;iostream&gt;
  #include &lt;stdint.h&gt;
  
  #define POLYNOMIAL      0x04C11DB7
  uint32_t A_crcLookupTable[256] = {0};
  #define WIDTH    (8 * sizeof(uint32_t))
  #define TOPBIT   (((uint32_t)1) &lt;&lt; (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)) &lt;&lt; (WIDTH - 8);
  
      for (VP_Pos_bit = 0; VP_Pos_bit &lt; 8; VP_Pos_bit++)
      {
          if (VP_CRCTableValue &amp; TOPBIT)
          {
              VP_CRCTableValue = (VP_CRCTableValue &lt;&lt; 1) ^ POLYNOMIAL;
          }
          else
          {
              VP_CRCTableValue = (VP_CRCTableValue &lt;&lt; 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 &lt; 256; VP_Pos_Array++)
      {
          A_crcLookupTable[VP_Pos_Array] = F_CRC_ObtenValorDeTabla((uint8_t)(VP_Pos_Array &amp;0xFF));
  
      }
  
  }
  
  
  void make_crc_table()
  {
      F_CRC_InicializaTabla();
  
      // Print the CRC table
      for (int i = 0; i &lt; 256; i++)
      {
          if (i % 4 == 0)
          {
              std::cout &lt;&lt;"\n";
          }
          std::cout &lt;&lt; std::hex &lt;&lt; A_crcLookupTable[i];
          std::cout &lt;&lt; ", ";
      }
  }
  
  int main()
  {
      make_crc_table();
      return 0;
  }
  </code></pre>
  
  <p>Here is what the <strong>correct</strong> final table should be, based on <a href="http://www.efg2.com/Lab/Mathematics/CRC.htm" rel="noreferrer">this link</a>:</p>
  
  <pre><code>// 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);
  </code></pre>
  
  <p>However, this is what my output is from both programs (I diffed the output, and it's the same for both of them), and it's <strong>incorrect</strong>:</p>
  
  <pre><code>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,
  </code></pre>