| Adler32 |
Computes Adler32 checksum for a stream of data. An Adler32
checksum is not as reliable as a CRC32 checksum, but a lot faster to
compute.
The specification for Adler32 may be found in RFC 1950.
ZLIB Compressed Data Format Specification version 3.3)
From that document:
"ADLER32 (Adler-32 checksum)
This contains a checksum value of the uncompressed data
(excluding any dictionary data) computed according to Adler-32
algorithm. This algorithm is a 32-bit extension and improvement
of the Fletcher algorithm, used in the ITU-T X.224 / ISO 8073
standard.
Adler-32 is composed of two sums accumulated per byte: s1 is
the sum of all bytes, s2 is the sum of all s1 values. Both sums
are done modulo 65521. s1 is initialized to 1, s2 to zero. The
Adler-32 checksum is stored as s2*65536 + s1 in most-
significant-byte first (network) order."
"8.2. The Adler-32 algorithm
The Adler-32 algorithm is much faster than the CRC32 algorithm yet
still provides an extremely low probability of undetected errors.
The modulo on unsigned long accumulators can be delayed for 5552
bytes, so the modulo operation time is negligible. If the bytes
are a, b, c, the second sum is 3a + 2b + c + 3, and so is position
and order sensitive, unlike the first sum, which is just a
checksum. That 65521 is prime is important to avoid a possible
large class of two-byte errors that leave the check unchanged.
(The Fletcher checksum uses 255, which is not prime and which also
makes the Fletcher check insensitive to single byte changes 0 -
255.)
The sum s1 is initialized to 1 instead of zero to make the length
of the sequence part of s2, so that the length does not have to be
checked separately. (Any sequence of zeroes has a Fletcher
checksum of zero.)"
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| Crc32 |
Generate a table for a byte-wise 32-bit CRC calculation on the polynomial:
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.
Polynomials over GF(2) are represented in binary, one bit per coefficient,
with the lowest powers in the most significant bit. Then adding polynomials
is just exclusive-or, and multiplying a polynomial by x is a right shift by
one. If we call the above polynomial p, and represent a byte as the
polynomial q, also with the lowest power in the most significant bit (so the
byte 0xb1 is the polynomial x^7+x^3+x+1), then the CRC is (q*x^32) mod p,
where a mod b means the remainder after dividing a by b.
This calculation is done using the shift-register method of multiplying and
taking the remainder. The register is initialized to zero, and for each
incoming bit, x^32 is added mod p to the register if the bit is a one (where
x^32 mod p is p+x^32 = x^26+...+1), and the register is multiplied mod p by
x (which is shifting right by one and adding x^32 mod p if the bit shifted
out is a one). We start with the highest power (least significant bit) of
q and repeat for all eight bits of q.
The table is simply the CRC of all possible eight bit values. This is all
the information needed to generate CRC's on data a byte at a time for all
combinations of CRC register values and incoming bytes.
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