| 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.)" |
| 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. |