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