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In the part of the basic Sarwate algorithm where the previous CRC value is shifted by the size of the table lookup, the previous CRC value is shifted away entirely (what remains is all zero), so the XOR can be eliminated from the critical path. The resultant slice-by-n inner loop consists of: XOR the current CRC with the next n bytes of the ...
These n bits are the remainder of the division step, and will also be the value of the CRC function (unless the chosen CRC specification calls for some postprocessing). The validity of a received message can easily be verified by performing the above calculation again, this time with the check value added instead of zeroes.
By definition, the smallest value of such that a polynomial divides + is the polynomial's order or exponent. The polynomials with the largest order are called primitive polynomials , and for polynomials of degree n {\displaystyle n} with binary coefficients, have order 2 n − 1 {\displaystyle 2^{n}-1} .
XOR/table Paul Hsieh's SuperFastHash [1] 32 bits Buzhash: variable XOR/table Fowler–Noll–Vo hash function (FNV Hash) 32, 64, 128, 256, 512, or 1024 bits xor/product or product/XOR Jenkins hash function: 32 or 64 bits XOR/addition Bernstein's hash djb2 [2] 32 or 64 bits shift/add or mult/add or shift/add/xor or mult/xor PJW hash / Elf Hash ...
This is the modular sum of the values taken by the simple checksum as each block of the data word is added to it. The modulus used is the same. So, for each block of the data word, taken in sequence, the block's value is added to the first sum and the new value of the first sum is then added to the second sum.
The frame check sequence (FCS) is a 16-bit CRC-CCITT or a 32-bit CRC-32 computed over the Address, Control, and Information fields. It provides a means by which the receiver can detect errors that may have been induced during the transmission of the frame, such as lost bits, flipped bits, and extraneous bits.
Depending on the values being precomputed, precomputation with interpolation can also be used to shrink the lookup table size while maintaining accuracy. While often effective, employing a lookup table may nevertheless result in a severe penalty if the computation that the LUT replaces is relatively simple.
CRC: Cyclic redundancy check Link and other layers 24 References here. CRC-16-CCITT: Cyclic redundancy check (X.25, HDLC) Link layers Reference on CRC page. CRT: Cathode Ray Tube Television set, Computer Monitor Cathode ray tube: CSMA/CA: Carrier sense multiple access / collision avoidance Wireless IEEE Std 802.11 Downloads: CSMA/CD