1  /* Not copyrighted 1990 Mark Adler */
       2  
       3  #include <config.h>
       4  #include <stdio.h>
       5  
       6  int
       7  main ()
       8  /*
       9    Generate a table for a byte-wise 32-bit CRC calculation on the polynomial:
      10    x^32+x^26+x^23+x^22+x^16+x^12+x^11+x^10+x^8+x^7+x^5+x^4+x^2+x+1.
      11  
      12    Polynomials over GF(2) are represented in binary, one bit per coefficient,
      13    with the lowest powers in the most significant bit.  Then adding polynomials
      14    is just exclusive-or, and multiplying a polynomial by x is a right shift by
      15    one.  If we call the above polynomial p, and represent a byte as the
      16    polynomial q, also with the lowest power in the most significant bit (so the
      17    byte 0xb1 is the polynomial x^7+x^3+x+1), then the CRC is (q*x^32) mod p,
      18    where a mod b means the remainder after dividing a by b.
      19  
      20    This calculation is done using the shift-register method of multiplying and
      21    taking the remainder.  The register is initialized to zero, and for each
      22    incoming bit, x^32 is added mod p to the register if the bit is a one (where
      23    x^32 mod p is p+x^32 = x^26+...+1), and the register is multiplied mod p by
      24    x (which is shifting right by one and adding x^32 mod p if the bit shifted
      25    out is a one).  We start with the highest power (least significant bit) of
      26    q and repeat for all eight bits of q.
      27  
      28    The table is simply the CRC of all possible eight bit values.  This is all
      29    the information needed to generate CRC's on data a byte at a time for all
      30    combinations of CRC register values and incoming bytes.  The table is
      31    written to stdout as 256 long hexadecimal values in C language format.
      32  */
      33  {
      34    unsigned long c;      /* crc shift register */
      35    unsigned long e;      /* polynomial exclusive-or pattern */
      36    int i;                /* counter for all possible eight bit values */
      37    int k;                /* byte being shifted into crc apparatus */
      38  
      39    /* terms of polynomial defining this crc (except x^32): */
      40    static int p[] = {0,1,2,4,5,7,8,10,11,12,16,22,23,26};
      41  
      42    /* Make exclusive-or pattern from polynomial (0xedb88320) */
      43    e = 0;
      44    for (i = 0; i < sizeof(p)/sizeof(int); i++)
      45      e |= 1L << (31 - p[i]);
      46  
      47    /* Compute and print table of CRC's, five per line */
      48    printf("  0x00000000L");
      49    for (i = 1; i < 256; i++)
      50    {
      51      c = i;
      52      /* The idea to initialize the register with the byte instead of
      53       * zero was stolen from Haruhiko Okumura's ar002
      54       */
      55      for (k = 8; k; k--)
      56        c = c & 1 ? (c >> 1) ^ e : c >> 1;
      57      printf(i % 5 ? ", 0x%08lxL" : ",\n  0x%08lxL", c);
      58    }
      59    putchar('\n');
      60    return 0;
      61  }