Use historic algorithms instead of the (superior) default one.
Algorithm 1 is the algorithm used by historic BSD systems as the sum(1) algorithm and by historic AT&T V systems as the sum(1) algorithm when using the -r option. This is a 16-bit checksum, with a right rotation before each addition; overflow is discarded.
Algorithm 2 is the algorithm used by historic AT&T V systems as the default sum(1) algorithm. This is a 32-bit checksum, and is defined as follows:
s = sum of all bytes; r = s % 2^16 + (s % 2^32) / 2^16; cksum = (r % 2^16) + r / 2^16;
Algorithm 3 is what is commonly called the 32bit CRC algorithm. This is a 32-bit checksum.
Both algorithm 1 and 2 write to the standard output the same fields as the default algorithm except that the size of the file in bytes is replaced with the size of the file in blocks. For historic reasons, the block size is 1024 for algorithm 1 and 512 for algorithm 2. Partial blocks are rounded up.
The default CRC used is based on the polynomial used for CRC error checking in the networking standard -iso8802-3. The CRC checksum encoding is defined by the generating polynomial:
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
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, with 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 are used.
M(x) is multiplied by x^32 (i.e., 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.
.Ex -std cksum sum
The default calculation is identical to that given in pseudo-code in the following ACM article.
.Rs Computation of Cyclic Redundancy Checks Via Table Lookup
The cksum utility is expected to conform to -p1003.2-92.
The cksum utility appeared in BSD 4.4 .