cksum [-o 1 | 2] [file ...]
sum [-r] [file ...]
The cksum(1) utility writes to the standard output three, white-space separated fields for each input file:
These fields contain a checksum (crc), the total number of octets in the file (#_octets) and the file name. If no file name is specified, the standard input is used and no file name is written.
crc #_octets file_name
The sum(1) utility writes to the standard output three, white-space separated fields for each input file:
crc #_blocks file_name
These fields contain a checksum (-crc), the total number of 512-byte blocks in the file (#_blocks), and the file name.
s = sum of all bytes;
r = s % 2^16 + (s % 2^32) / 2^16;
cksum = (r % 2^16) + r / 2^16;
Without the -r option, the sum(1) command is equivalent to:
cksum -o 1
cskum -o 2
The default Cyclical Redundancy Checking (CRC) used is based on the polynomial used for CRC error checking in the networking standard ISO 8802-3:1989. The CRC checksum encoding is defined by the generating polynomial:
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. 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.
G(x) = 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
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.