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big_endian_table[0] := 0 crc := 0x8000 // Assuming a 16-bit polynomial i := 1 do { if crc and 0x8000 { crc := (crc leftShift 1) xor 0x1021 // The CRC polynomial} else { crc := crc leftShift 1 } // crc is the value of big_endian_table[i]; let j iterate over the already-initialized entries for j from 0 to i−1 { big_endian_table[i + j] := crc ...
The ITU-T G.hn standard also uses CRC-32C to detect errors in the payload (although it uses CRC-16-CCITT for PHY headers). CRC-32C computation is implemented in hardware as an operation ( CRC32 ) of SSE4.2 instruction set, first introduced in Intel processors' Nehalem microarchitecture.
When the data word is divided into 8-bit blocks, as in the example above, two 8-bit sums result and are combined into a 16-bit Fletcher checksum. Usually, the second sum will be multiplied by 256 and added to the simple checksum, effectively stacking the sums side-by-side in a 16-bit word with the simple checksum at the least significant end.
BSD checksum (Unix) 16 bits sum with circular rotation SYSV checksum (Unix) 16 bits sum with circular rotation sum8 8 bits sum Internet Checksum: 16 bits sum (ones' complement) sum24 24 bits sum sum32 32 bits sum fletcher-4: 4 bits sum fletcher-8: 8 bits sum fletcher-16: 16 bits sum fletcher-32: 32 bits sum Adler-32: 32 bits sum xor8: 8 bits ...
The checksum algorithms most used in practice, such as Fletcher's checksum, Adler-32, and cyclic redundancy checks (CRCs), address these weaknesses by considering not only the value of each word but also its position in the sequence. This feature generally increases the cost of computing the checksum.
The cyclic redundancy check (CRC) is a check of the remainder after division in the ring of polynomials over GF(2) (the finite field of integers modulo 2). That is, the set of polynomials where each coefficient is either zero or one, and arithmetic operations wrap around.
By far the most popular FCS algorithm is a cyclic redundancy check (CRC), used in Ethernet and other IEEE 802 protocols with 32 bits, in X.25 with 16 or 32 bits, in HDLC with 16 or 32 bits, in Frame Relay with 16 bits, [3] in Point-to-Point Protocol (PPP) with 16 or 32 bits, and in other data link layer protocols.
cksum is a command in Unix and Unix-like operating systems that generates a checksum value for a file or stream of data. The cksum command reads each file given in its arguments, or standard input if no arguments are provided, and outputs the file's 32-bit cyclic redundancy check (CRC) checksum and byte count. [1]