POSIX 1003.2, D11.2 modified the CRC! Bring up to date.

[unix-history] / usr / src / usr.bin / cksum / cksum.1

.\" Copyright (c) 1991, 1991 The Regents of the University of California.
.\" All rights reserved.
.\"
.\" This code is derived from software contributed to Berkeley by
.\" the Institute of Electrical and Electronics Engineers, Inc.
.\"
.\" %sccs.include.redist.roff%
.\"
.\"	@(#)cksum.1	5.6 (Berkeley) %G%
.\"
.Dd 
.Dt CKSUM 1
.Os
.Sh NAME
.Nm cksum
.Nd display file checksums and block counts
.Sh SYNOPSIS
.Nm cksum
.Op Fl o Op \&1 \&| \&2
.Op Ar file ...
.Sh DESCRIPTION
The
.Nm cksum
utility writes to standard output three whitespace separated fields for each
input file.
These fields are a checksum
.Tn 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.
.Pp
The options are as follows:
.Bl -tag -width indent
.It Fl o
Use historic algorithms instead of the (superior) default one.
.Pp
Algorithm 1 is the algorithm used by historic
.Bx
systems as the 
.Xr sum 1
algorithm and by historic
.At V
systems as the
.Xr sum
algorithm when using the
.Fl r
option.
This is a 16-bit checksum, with a right rotation before each addition;
overflow is discarded.
.Pp
Algorithm 2 is the algorithm used by historic
.At V
systems as the
default
.Xr sum
algorithm.
This is a 32-bit checksum, and is defined as follows:
.Bd -unfilled -offset indent
s = sum of all bytes;
r = s % 2^16 + (s % 2^32) / 2^16;
cksum = (r % 2^16) + r / 2^16;
.Ed
.Pp
Both algorithm 1 and 2 write to 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.
.El
.Pp
The default
.Tn CRC
used is based on the polynomial used for
.Tn CRC
error checking
in the networking standard
.St -iso8802-3
The
.Tn CRC
checksum encoding is defined by the generating polynomial:
.Pp
.Bd -unfilled -offset indent
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
.Ed
.Pp
Mathematically, the
.Tn CRC
value corresponding to a given file is defined by
the following procedure:
.Bd -filled -offset indent
The
.Ar n
bits to be evaluated are considered to be the coefficients of a mod 2
polynomial M(x) of degree
.Ar n Ns \-1 .
These
.Ar 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.
.Pp
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.
.Pp
The coefficients of R(x) are considered to be a 32-bit sequence.
.Pp
The bit sequence is complemented and the result is the CRC.
.Ed
.Pp
The
.Nm cksum
utility exits 0 on success, and >0 if an error occurs.
.Sh SEE ALSO
The default calculation is identical to that given in pseudo-code
in the following
.Tn ACM
article.
.Rs
.%T "Computation of Cyclic Redundancy Checks Via Table Lookup"
.%A Dilip V. Sarwate
.%J "Communications of the \\*(tNACM\\*(sP"
.%D "August 1988"
.Re
.Sh STANDARDS
.Nm Cksum
is expected to conform to
.St -p1003.2 .
.Sh HISTORY
The
.Nm cksum
utility is
.Ud .