.\" 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.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\"    notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\"    notice, this list of conditions and the following disclaimer in the
.\"    documentation and/or other materials provided with the distribution.
.\" 3. All advertising materials mentioning features or use of this software
.\"    must display the following acknowledgement:
.\"	This product includes software developed by the University of
.\"	California, Berkeley and its contributors.
.\" 4. Neither the name of the University nor the names of its contributors
.\"    may be used to endorse or promote products derived from this software
.\"    without specific prior written permission.
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.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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.\"
.\"	@(#)cksum.1	5.5 (Berkeley) 6/27/91
.\"
.Dd June 27, 1991
.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 (or the standard input by default).
These fields are a checksum
.Tn CRC ,
the total number of bytes in the file and
the file name.
.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 of the file are considered to be the coefficients of a mod 2
polynomial M(x) of degree
.Ar n Ns \-1 .
.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.
During the division, each time the intermediate remainder is zero, it
is changed to the next value from a predefined sequence of
32-bit integers before completing the division.
This sequence is long and complex -- see the source code for more
information.
.Pp
The coefficients of R(x) are considered to be a 32-bit sequence.
.Ed
.Pp
The calculation used is identical to that given in pseudo-code in
the
.Tn ACM
article referenced below.
.Pp
The
.Nm cksum
utility exits 0 on success, and >0 if an error occurs.
.Sh SEE ALSO
.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 .