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CKSUM(1)		  BSD General Commands Manual		      CKSUM(1)

     cksum, sum	-- display file	checksums and block counts

     cksum [-o 1 | 2 | 3] [file	...]
     sum [file ...]

     The cksum utility writes to the standard output three whitespace sepa-
     rated fields for each input file.	These fields are a checksum CRC, the
     total number of octets in the file	and the	file name.  If no file name is
     specified,	the standard input is used and no file name is written.

     The sum utility is	identical to the cksum utility,	except that it de-
     faults to using historic algorithm	1, as described	below.	It is provided
     for compatibility only.

     The options are as	follows:

     -o	     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 System V UNIX 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

	     Algorithm 2 is the	algorithm used by historic AT&T	System V UNIX
	     systems as	the default sum(1) algorithm.  This is a 32-bit	check-
	     sum, 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	check-
     ing in the	networking standard ISO/IEC 8802-3:1989.  The CRC checksum en-
     coding 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 signif-
	   icant 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.

     The cksum and sum utilities exit 0	on success, and	>0 if an error occurs.


     The default calculation is	identical to that given	in pseudo-code in the
     following ACM article.

     Dilip V. Sarwate, "Computation of Cyclic Redundancy Checks	Via Table
     Lookup", Communications of	the ACM, August	1988.

     The cksum utility is expected to conform to IEEE Std 1003.2-1992

     The cksum utility appeared	in 4.4BSD.

BSD				April 28, 1995				   BSD


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