The cksum command calculates and writes to standard output a cyclic redundancy check (CRC) for each input file, and also writes to standard output the number of octets in each file.
For each file processed successfully, cksum will write in the following format:
"%u %d %s\n" <checksum>, <# of octets>, <path name>
If no file operand was specified, the path name and its leading space will be omitted.
The CRC used is based on the polynomial used for CRC error checking in the referenced Ethernet standard.
The encoding for the CRC checksum is defined by the generating polynomial:
G(x) = x32 + x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x + 1
Mathematically, the CRC value corresponding to a given file is defined by the following procedure:
- The n bits to be evaluated are considered to be the coefficients of a mod 2 polynomial M(x) of degree n-1. These n bits are the bits from the file, with the most significant bit being the most significant bit of the first octet of
the file and the last bit being the least significant bit of the last octet, padded with zero bits (if necessary) to achieve an integral number of octets, followed by one or more octets representing the
length of the file as a binary value, least significant octet first. The smallest number of octets capable of representing this integer is used.
-
M(x) is multiplied by x 32 (that is, shifted
left 32 bits) and divided by G(x) using mod 2 division, producing a remainder R(x) of degree <=
31.
- The coefficients of R(x) are considered to be a 32-bit sequence.
- The bit sequence is complemented and the result is the CRC.
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