Table of Contents
*****************

Numdiff User Manual
1 Copying
2 Acknowledgments
3 Overview
  3.1 Output format
4 Installing
5 Invoking
6 Tools
7 Warnings
Appendix A GNU Free Documentation License
Index


Numdiff User Manual
*******************

_"und der eignen Kraft vertrauend steigt ein frei Geschlecht empor"_


This manual describes how to install and use Numdiff, a program which
compares putatively similar files line by line and field by field,
ignoring small numeric differences or/and different numeric formats.

   Copyright (C) 2005-2007  Ivano Primi  <ivprimi(at)libero(dot)it>

     Permission is granted to copy, distribute and/or modify this
     document under the terms of the GNU Free Documentation License,
     Version 1.2 or any later version published by the Free Software
     Foundation; with no Invariant Sections, with the Front-Cover Texts
     being "Numdiff User Manual, version 5.0", and with no Back-Cover
     Texts. A copy of the license is included in *Note GNU Free
     Documentation License::.

1 Copying
*********

Numdiff (also written numdiff) is free software; you can redistribute
it and/or modify it under the terms of the GNU General Public License
as published by the Free Software Foundation; either version 2 of the
License, or (at your option) any later version.

   Numdiff is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

   You should have received a copy of the GNU General Public License
along with the program; if not, write to the Free Software Foundation,
Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA .

2 Acknowledgments
*****************

I want to thank Mr. Norman Clerman <norm(dot)opcon(at)fuse(dot)net> for
several suggestions he gave me to improve the readability and the
effectiveness of the output produced by Numdiff.  Moreover, he pointed
out the need to implement a filter to resynchronize the lines between
two files in case of addition or deletion of one or more lines.  I have
to give him credit for the urge to prepare the version 4.x of Numdiff.

   Moreover, I want to thank my friend Mariapia Palombaro since she
removed some errors while reviewing the first version of this document.

3 Overview
**********

Computer users often find occasion to ask how two files differ.
Perhaps one file is a newer version of the other file.  Or maybe the
two files started out as identical copies but were changed by different
people.

   There are several ways to think about the differences between two
files.  One way to think of the differences is as a series of lines
that were deleted from, inserted in, or changed in one file to produce
the other file.  The well-known `diff' program compares two files line
by line, finds groups of lines that differ, and reports each group of
differing lines.  Without particular options, the `diff' program
considers any change in the amount or in the type of the characters as a
relevant difference. However, trough some command line options it also
provides ways to suppress certain kinds of differences that are not
important to the user.  For instance, `diff' provides ways to ignore
differences in the amount of white space between words or lines, or
differences in alphabetic case.

   Another way to think of the differences is as a series of words that
were deleted from, inserted in, or changed in one file to produce the
other file.  Here "word" refers to a sequence of non white-space
characters delimited by a couple of white-spaces, one before and the
other one after the word.

   The less known `wdiff' program by Franc,ois Pinard
<pinard@iro.umontreal.ca> compares words in two files and reports the
differences.

   At last, one can think of the differences between two files as a
sequence of pairs of bytes that can be either identical or different.
The `cmp' program reports the differences between two files byte by
byte, instead of line by line or word by word.  As a result, it is
often more useful than `diff' or `wdiff' for comparing binary files.

   However, none of these approaches turns out to be good when you want
to compare a couple of text files composed partially or entirely by
numerical fields.  Indeed, when you compare a couple of such files,
what you want to obtain usually is a list of the numerical fields in
the second file which *numerically* differ from the corresponding
fields in the first file.  But, as you probably knows, a same number
can be written using different notations and programs like `diff' or
`wdiff' can not recognize whether a difference between two numeric
fields is only due to the notation or is actually a difference of
numerical values.

   For instance, 11.23   and   11.2300000 are the same number but
represented in different ways.  While, if you are interested in
numerical values, it is obvious that the difference in the
representation is not meaningful and then it should be ignored, however
`diff' and `wdiff' consider the previous one as a relevant difference
and there is no way for you to tell these programs to ignore it !

   Another example of this type is given by 98765.4321  and
9.87654321E04 where the difference is only due to the use of the
scientific notation in place of the common notation.

   Moreover, depending on your country you could stick to different
conventions in writing numbers.  For instance, the amount "three
hundred millions and fifty-two thousands of dollars and forty-six cents"
is usually written by an Italian accountant as 300.052.000,46$ while an
American accountant would write 300,052,000.46$.  Of course,
300.052.000,46$  and  300,052,000.46$ represent the same amount of
money but `diff' and `wdiff' would report a difference, which probably
is not what you would in a similar case.

   At last, sometimes you could want to ignore even differences in
numerical values as long as they do not overcome a certain threshold.
In other words, you could desire to suppress all "small" numerical
differences too.

   For instance, it could happen that you want to ignore all numerical
differences whose absolute value is not greater than 0.0001. If this is
the case, then the numerical fields 33  and  33.00009 must be
considered equal, while 33  and  33.00011 must be reported as different.

   However, `diff' and `wdiff' can not be used to ignore "small"
numerical differences, since they do not even know what a numerical
difference is.

   What I have been saying till now explains why I decided to implement
a new program with the capability to "appropriately" compare files
containing numerical fields.  In writing this program I was inspired by
`ndiff', a GPL'ed software by Nelson H. Baabe of the Salt Lake City
University. The author of `ndiff' had the same good reasons as me to
write `ndiff'. Actually `ndiff' is a good tool and I used it for a
while. But I did not completely like the way it works and so `numdiff'
was born.  Although `ndiff' inspired `numdiff', they are completely
different from the viewpoint of the source code: `numdiff' has been
entirely written from scratch.

   `numdiff' can be used to compare putatively similar files line by
line and field by field, ignoring small numeric differences or/and
different numeric formats.  `numdiff' takes two mandatory arguments,
the paths of the two files to compare, and, after splitting them into
lines and the lines into fields according to a given list of field
delimiters, it compares every field of every line of the first file with
the field of the second file at the same position (here position refers
both to the line number and to the  location within the line).  If the
compared fields are both legal numerical values, then `numdiff'
performs a numerical comparison between them, else it performs a
literal comparison, that is to say the usual byte by byte comparison.
In case of literal comparison, two fields are regarded as equal if they
are formed by the same sequence of characters.  In case of numerical
comparison and without specific command line options, two fields are
regarded as equal if their numerical difference is zero.  Be careful !
If you do not explicitly specify a list of field delimiters by the
option `-s', then `numdiff' takes as field delimiters the characters
newline (`\n', ASCII code 0x0A), horizontal tabulation (`\t', ASCII
code 0x09), and blank (` ', ASCII code 0x20).

   For instance, if the file `list1' contains the data

accident        123     23Joshua          34.55           +3+4i	        water
dog       -3455.321     cat             2.345678e-9     .0005-6.23e2i

and file `list2' contains the data


Accident        123     23456          34.5500         +3.0001+4i
dog       -3455.320098  Cat     +2.345678e-9            -6.23e2i    $$$
A new line

then the output of the command `numdiff list1 list2' will be:

     ----------------
     ##1       #:1   <== accident
                     ==> Accident
                                                          @
     ##1       #:3   <== 23Joshua
                     ==> 23456
                                                          @
     ##1       #:5   <== +3+4i
                     ==> +3.0001+4i
      Absolute error = 1.0000000000e-4, Relative error = 2.0000000000e-5
     ##1       #>6   <== water
                     ==>
      Line 1 in file "list2" is shorter!
     ----------------
     ##2       #:2   <== -3455.321
                     ==> -3455.320098
      Absolute error = 9.0200000000e-4, Relative error = 2.6104672633e-7
     ##2       #:3   <== cat
                     ==> Cat
                                                          @
     ##2       #:5   <== .0005-6.23e2i
                     ==> -6.23e2i
      Absolute error = 5.0000000000e-4, Relative error = 8.0256821830e-7
     ##2       #>6   <==
                     ==> $$$
      Line 2 in file "list1" is shorter!
     ----------------
     ##3       #>1   <==
                     ==> A new line
      Line 3 in file "list1" is shorter!
     ----------------
     ##4       <==
               ==>


     +++  File "list1" differs from file "list2"

   At the same time `numdiff' will print the following error message on
stderr:
     ***  End of file "list1" reached
          Likely the files "list1" and "list2" do not have the same number of lines !

   I have to remark that `numdiff' can recognize complex numbers,
provided that they are written in the form a+bi or a-bi with no extra
characters between the values a, b and the sign + or - (actually the
symbol i used to represent the imaginary unit can be changed by a
suitable command line option, but we shall see it in *Note Invoking::).
If you do not know what complex numbers are, do not worry !  In this
case probably you will never manage files containing complex numbers
and so you can happily continue to ignore them. :) Even if the output
of `numdiff' is self-explanatory, in the next section I will explain in
details all you have to know about it.

3.1 Output format
=================

Let us go back to the previous example.  If the files `list1' and
`list2' contain the data

accident        123     23Joshua          34.55           +3+4i	        water
dog       -3455.321     cat             2.345678e-9     .0005-6.23e2i

and


Accident        123     23456          34.5500         +3.0001+4i
dog       -3455.320098  Cat     +2.345678e-9            -6.23e2i    $$$
A new line

respectively, then the output of the command `numdiff list1 list2' will
be:

     ----------------
     ##1       #:1   <== accident
                     ==> Accident
                                                          @
     ##1       #:3   <== 23Joshua
                     ==> 23456
                                                          @
     ##1       #:5   <== +3+4i
                     ==> +3.0001+4i
      Absolute error = 1.0000000000e-4, Relative error = 2.0000000000e-5
     ##1       #>6   <== water
                     ==>
      Line 1 in file "list2" is shorter!
     ----------------
     ##2       #:2   <== -3455.321
                     ==> -3455.320098
      Absolute error = 9.0200000000e-4, Relative error = 2.6104672633e-7
     ##2       #:3   <== cat
                     ==> Cat
                                                          @
     ##2       #:5   <== .0005-6.23e2i
                     ==> -6.23e2i
      Absolute error = 5.0000000000e-4, Relative error = 8.0256821830e-7
     ##2       #>6   <==
                     ==> $$$
      Line 2 in file "list1" is shorter!
     ----------------
     ##3       #>1   <==
                     ==> A new line
      Line 3 in file "list1" is shorter!
     ----------------
     ##4       <==
               ==>


     +++  File "list1" differs from file "list2"

   `numdiff' prints a report on the standard output for every field of
the first file which differs from the corresponding field of the second
one.

   First this report indicates the location of the field, that is to
say the number of the line where the field appears and its position
within the line (this is "1" if it is the first field of its line, "2"
if it is the second field of the line, "3" if it is the third one and
so on. Fields are numerated starting from the left hand of the line and
proceeding towards the right hand).  For each report the line number is
introduced  by the symbol "##", while the field number by "#:".  Then
`numdiff' shows in what the difference consists.  For instance,
     ##1       #:1   <== accident
                     ==> Accident
                                                          @

   means that the first field of the first line is "accident" in the
first file, while in the second file it appears as "Accident".  This
difference could then be canceled by removing "accident" from the first
file and inserting "Accident" in place of it.  The arrows "<==" and
"==>" try to visualize this idea.  Analogously,
     ##2       #:2   <== -3455.321
                     ==> -3455.320098
      Absolute error = 9.0200000000e-4, Relative error = 2.6104672633e-7

   means that the second field of the second line is "-3455.321" in the
first file and "-3455.320098" in the second one.  Since the contents of
the field are numerical in both files, `numdiff' also prints the
absolute and relative errors.

   The absolute error (or absolute difference) is given by the absolute
value of the difference between the values appearing in the two files.

   The relative error (or relative difference) is actually defined in a
more complicated way.  If "n1" is the value appearing in the first file
and "n2" is the value in the second file, then the absolute error is
given by the formula "A=|n1-n2|", while the relative error "R" is given
by:

   * "R = 0" if "n1" and "n2" are equal,

   * "Inf" (infinity) if "n2" differs from "n1" and at least one of
     them is zero,

   * "R = A/ min(|n1|, |n2|)" if "n1" and "n2" are both non zero and
     "n2" differs from "n1". "min(|n1|, |n2|)" denotes the minimum
     between the absolute value of "n1" and the absolute value of "n2".
   I have to remark that, with these definitions of absolute and
relative error it turns out that A(n2, n1) = A(n1, n2) and R(n2, n1) =
R(n1, n2). In other words, the absolute/relative error does not change
if you only change the order of the compared values.

   If the contents of a field are, in at least one of the compared
files, non-numerical, then the output line reporting absolute and
relative errors is replaced by the separator:

@                                                     @@

   It can happen that a line in one of the two files to compare contains
more fields than the corresponding line of the other file.  When this
is the case, `numdiff' reports this difference by telling that a
certain line (identified by its line number) appears to be shorter in
one of the two files, just as in
     ##1       #>6   <== water
                     ==>
      Line 1 in file "list2" is shorter!

   or in
     ##3       #>1   <==
                     ==> A new line
      Line 3 in file "list1" is shorter!

   When this is the case, `numdiff' also shows the tail of the line as
it appears in one of the compared files. Moreover, it uses the notation
"#>n" to indicate the number n of the first field in the longer line
for which there is no corresponding field in the shorter line.  For
instance,
     ##1       #>6   <== water
                     ==>
      Line 1 in file "list2" is shorter!

   means that all the fields of the first line starting from the sixth
one are empty in the second file (`list2').  In this context, the
symbol <<*>> (when it appears) is used to denote the End-Of-File, i.e.
a line or the tail of a line which is located at the end of the
corresponding file and does not have a terminating *newline* character.

   It can also happen that one of the two files to compare has less
lines than the other one.  In this case `numdiff' prints the number of
the first line which compares in only one of the two files.  Moreover,
it prints on the standard error a message telling in which of the two
files the end has been prematurely reached:
     ***  End of file "list1" reached
          Likely the files "list1" and "list2" do not have the same number of lines !

   At last, `numdiff' prints on standard output a message reporting the
final status of the comparison.  This message says either the two files
are equal or they are different, just as in the example we are
considering:
     +++  File "list1" differs from file "list2"

   I have to remark that the user can make `numdiff' avoid to print,
partially or totally, the messages that it would otherwise send to
standard output.  This can be achieved by some suitable command line
options, see *Note Invoking::.

4 Installing
************

To successfully compile, build and install Numdiff some tools are
required. The first one is an ANSI C compiler.  This compiler should at
least accept the option `-o' in order to place its output in a
specified file.  Numdiff has been successfully compiled and tested on
Slackware GNU/Linux 10.2 with the version 3.3.6 of the GNU C Compiler
(GCC), on Slackware GNU/Linux 11 with GCC 3.4.6, on Debian GNU/Linux
4.0 with GCC 4.1.2 20061115 (prerelease) (Debian 4.1.1-21; the
installation on Debian required however a tricky modification of the
standard procedure, see below for more details), and on SunOS 5.8 with
the version 2.95.3 of the same compiler.

   Moreover, you need a POSIX implementation of the `make' utility (I
used both GNU make and smake by Joerg Schilling to compile Numdiff) and
a POSIX implementation of the commands `rm' and `find'.  At last, you
need a proper installation of GNU Texinfo (in order to install the info
documentation) and a shell sh-compatible.

   Configuration, building and installation of Numdiff can be performed
through the standard three steps:
             ./configure
             make
             make install

If you want to install Numdiff on Debian GNU/Linux, you may have to
manually correct the Makefile before doing `make install': if you find
the line

	INSTINFO=

then you have to add ginstall-info at the end of this line to correctly
define the variable `INSTINFO'

	INSTINFO=ginstall-info

If you leave enabled the Natural Language Support and you also want to
install the localization files (at the moment only the italian
localization is supplied), then, after `make', you will have to type
and run
             make install-nls

   By default, `make install' will install all the files in
`/usr/local/bin', `/usr/local/info' etc.  You can specify an
installation prefix other than `/usr/local' using the option `--prefix'
in the `configure' step, for instance `--prefix=$HOME':
             ./configure --prefix=$HOME

For better control, you can use the options `--bindir', `--infodir',
and so on.  Type `./configure --help' to obtain the complete list of
all the available options.

   Anyway, the documentation files, including a full User Manual
available in several formats (HTML, PDF and plain ASCII text), will
always be put in `DOCDIR/numdiff', where DOCDIR is the path specified
by the option `--docdir' or, if this option has not been given to
`configure', `PREFIX/local/doc'.  Here PREFIX is the installation
prefix specified by the option `--prefix' or the default `/usr/local'.

   Once Numdiff has been installed you can remove all the files
previously installed by a simple `make uninstall'.  If you have also
installed the localization files trough `make install-nls', then, in
order to remove also these ones, use `make uninstall-nls' in place of
`make uninstall'.

   Between the options accepted by `configure' there are
`--enable-debug', `--enable-optimization', and `--enable-nls'.

   The option `--enable-debug' turns on debugging when compiling the
source code. This is obtained by passing to the compiler the `-g'
option, but you can change this default debugging flag (which could not
even be recognized by your compiler) by setting the environment
variable `DBGFLAGS' before calling `configure'.

   The option `--enable-optimization' turns on basic optimization when
compiling the source code. This is obtained by passing to the compiler
the `-O' option, but you can change this default flag (which could not
even be recognized by your compiler) by setting the environment
variable `OPTFLAGS' before calling `configure'.

   The option `--enable-nls' turns on Natural Language Support.  But
you do not need to use it explicitly, since Natural Language Support is
enabled by default.  However, you can disable it by using
`--disable-nls'.

5 Invoking
**********

*SYNOPSIS*

        numdiff -h|v
   or
        numdiff [-a maxerr][-r maxerr][-2][-P][-N][-s ifs][-b][-V][-q][-D][-E]
        [-I][-S][-# prec][-d c1c2][-t c1c2][-g n1n2][-p c1c2][-n c1c2][-e c1c2]
        [-i c1c2][-F f1-f2][-L l1-l2][-l path][-o path] FILE1 FILE2

where FILE1 and FILE2 are the names of the two files to compare.

   In the first case `numdiff' prints a short help (actually not so
short) or/and version number, Copyright, NO-Warranty disclaimer and
some information about the way it was built.  In the second case
`numdiff' compares the files specified by the two (mandatory) arguments
following the list of the options.  The complete path of a file should
be given, a directory name is not accepted.  Moreover, the two
arguments cannot refer to the same file but one of them can be "-",
which refers to stdin.

*OPTIONS*

   * `-a maxerr' Specify the maximum absolute error permitted before
     that two numerical values are regarded as different (The default
     value is zero)

   * `-r maxerr' Specify the maximum relative error permitted before
     that two numerical values are regarded as different (The default
     value is zero)

   * `-2' Order that two numerical values are regarded as equal only if
     both absolute and relative error do not exceed the corresponding
     tolerance threshold (The default behavior is considering equal two
     numerical values if at least one between absolute and relative
     error does not exceed the corresponding tolerance threshold, or
     zero if no tolerance threshold has been specified)

   * `-P' Ignore all differences due to numeric fields of the second
     file that are less than the corresponding numeric fields in the
     first file (consider only positive errors)

   * `-N' Ignore all differences due to numeric fields of the second
     file that are greater than the corresponding numeric fields in the
     first file (consider only negative errors)

   * `-E' While printing the differences between the two compared files
     show only the numerical ones

   * `-D' While printing the differences between the two compared files
     neglect all the numerical ones

   * `-I' Ignore changes in case while doing literal comparisons

   * `-s ifs' Specify the set of characters to use to split the input
     lines into fields (The default set of characters is white space,
     tab and newline)

   * `-b'        Suppress all messages concerning the differences
     discovered in the structures of the two files

   * `-V'        For every line differing in at least one field print
     an header to show how this line appears in the two compared files

   * `-q'        Suppress all the standard output of the program

   * `-S'        Add some statistics to the standard output

   * `-# prec'   Specify the number of digits in the significands used
     in multiple-precision arithmetic

   * `-d c1c2'   Specify the characters representing the decimal point
     in the two files to compare

   * `-t c1c2'   Specify the characters representing the thousands
     separator in the two files to compare

   * `-g n1n2'   Specify the number of digits forming each group of
     thousands in the two files to compare

   * `-p c1c2'   Specify the (optional) prefixes for positive values
     used in the two files to compare

   * `-n c1c2'   Specify the prefixes for negative values used in the
     two files to compare

   * `-e c1c2'   Specify the exponent letters used in the two files to
     compare

   * `-i c1c2'   Specify the characters representing the imaginary unit
     in the two files to compare

   * `-F f1-f2'  Select the fields that have to be compared (The
     default behavior is comparing all the fields)

   * `-L l1-l2'  Select the lines whose fields have to be compared (The
     default behavior is comparing all the fields in all the lines)

   * `-l path'   Redirect warning and error messages from stderr to the
     indicated file

   * `-o path'   Redirect output from stdout to the indicated file

   * `-h'        Show help message and predefined settings

   * `-v'        Show version number, Copyright and NO-Warranty

*DIAGNOSTICS*

   The exit status is 1 if the two given files differ, 0 if they are
equal, -1 (255) in case of error.

*DEFAULT NUMERIC FORMAT (for both files to compare):*

   Decimal point = `.'

   Thousands separator = `,'

   Number of digits in each thousands group = 3

   Positive sign = `+'

   Negative sign = `-'

   Prefix for decimal exponent = `e'

   Symbol used to denote the imaginary unit = `i'

*SOME EXPLANATIONS*

   The options `-D', `-E', `-b' and `-q' are used to hide part of the
standard output of the program according to some rule.

   The option `-D' triggers the "dummy mode". In this mode `numdiff'
does not print the numerical differences. A numerical difference occurs
when a given field turns out to be of numerical type in both files to
compare, but it has in the second file a value differing from the one
contained in the first file.  The "dummy mode" is so called since when
it is active, `numdiff' does not perform the job for which I created it.

   The option `-E' triggers the "essential mode". In this mode
`numdiff' only prints the numerical differences between the two files
and, if there are some, the differences in the structure, which occur
either when a line of text comes out to be formed by a different number
of fields in the two files to compare or when the two files have a
different number of lines.

   The option `-b' triggers the "brief mode". In this mode `numdiff'
does not print the differences in the structure of the two files, i.e.
the ones consisting in a different number of fields on a line, or in a
different number of lines in the two files.

   Finally, the option `-q' triggers the "quiet mode". When in this
mode `numdiff' does not print anything on the standard output. The
"quiet mode" is useful if you only want to know whether a couple of
files are equal or not.  This information can be obtained by looking at
the exit status of the program.

   The option `-V' triggers the "verbose mode". In this mode `numdiff'
produces a richer report by printing an header for every line differing
in at least one field in order to show how this line appears in the two
compared files.  For instance, if the files `data1' and `data2' contain
the data

12      33
22      44.5
0.008   1.002
221.12  -34.56  water
2101.21 boats

and


12      33
22.3      44.5
0.008   1.202
221.12  -34.56
2101.21 boats   dogs

respectively, then the command `numdiff -V data1 data2' will print the
following output:
     ----------------
     ##2       <== 22      44.5
               ==> 22.3      44.5

     ##2       #:1   <== 22
                     ==> 22.3
      Absolute error = 3.0000000000e-1, Relative error = 1.3636363636e-2
     ----------------
     ##3       <== 0.008   1.002
               ==> 0.008   1.202

     ##3       #:2   <== 1.002
                     ==> 1.202
      Absolute error = 2.0000000000e-1, Relative error = 1.9960079840e-1
     ----------------
     ##4       <== 221.12  -34.56  water
               ==> 221.12  -34.56

     ##4       #>3   <== water
                     ==>
      Line 4 in file "data2" is shorter!
     ----------------
     ##5       <== 2101.21 boats
               ==> 2101.21 boats   dogs

     ##5       #>3   <==
                     ==> dogs
      Line 5 in file "data1" is shorter!

     +++  File "data1" differs from file "data2"

   You must care that the options `-b' and `-V' will be overridden if
`-q' is also set.

   Moreover, the amount of additional information printed by the option
`-V' is trivially influenced by the options eventually set between the
ones altering the way `numdiff' performs the comparisons between fields
(for instance `-a', `-r', `-2', `-N', `-P', `-D', `-E', `-I', `-F').
In the headers printed by `numdiff' when in "verbose mode" can also
appear the symbol <<*>>. This symbol, if present, is always located at
the end of a line to mean that the line is at the end of the
corresponding file and does not have a terminating *newline* character.

   The option `-S' adds to the standard output of `numdiff' the
following information:
   * the largest absolute error in the set of relevant numerical
     differences and the corresponding relative error, and

   * the largest relative error in the set of relevant numerical
     differences together with the corresponding absolute error.
   For relevant numerical differences I mean those ones appearing in
the output of `numdiff' when the options `-D' and `-q' are not used.
The information printed by the option `-S' is not removed when this
option is used together with `-q'.

   The options `-a', `-r', `-2', `-P' and `-N' affect the way `numdiff'
performs the comparisons between numerical values.  Without any of
these options, `numdiff' considers two numerical fields as equal when
their difference is zero.

   The option `-a' can be used to specify that two numerical fields
must be considered equal as long as their absolute difference does not
exceed a given threshold, which is supplied by the argument following
the `-a' option.

   The option `-r' can be used to specify that two numerical fields
must be considered equal as long as their relative difference does not
exceed a given threshold, which is supplied by the argument following
the `-r' option.

   The option `-2' is only meaningful when both `-a' and `-r' are
present on the command line.  If the user specifies a non-zero
tolerance threshold for both absolute and relative error by using both
`-a' and `-r', `numdiff' adopts this behavior: it considers equal two
numerical fields as long as at least one between absolute and relative
error does not exceed the corresponding threshold.  With the option
`-2' `numdiff' regards two numerical values as equal only if both
absolute and relative error do not exceed the threshold of tolerance.
For instance, if FILE1 contains the unique line

100

and FILE2 the line

100.00012

then the output of the command `numdiff FILE1 FILE2' will be

     ----------------
     ##1       #:1   <== 100
                     ==> 100.00012
     @ Absolute error = 1.2000000000e-4, Relative error = 1.2000000000e-6

     +++  File "FILE1" differs from file "FILE2"

the output of the commands `numdiff -a 1.0e-4 FILE1 FILE2' and `numdiff
-r 1.0e-6 FILE1 FILE2' will be the same, while `numdiff -a 1.0e-4 -r
1.3e-6 FILE1 FILE2' and `numdiff -a 1.3e-4 -r 1.0e-6 FILE1 FILE2' will
print the message

     +++  Files "FILE1" and "FILE2" are equal

since the actual relative error is 1.2e-6 < 1.3e-6, the actual absolute
error is 1.2e-4 < 1.3e-4, and it is sufficient that one of them does
not exceed the tolerance specified on the command line to make
`numdiff' consider equal the two compared values.  However, the commands
`numdiff -a 1.0e-4 -r 1.3e-6 -2 FILE1 FILE2' and `numdiff -a 1.3e-4 -r
1.0e-6 -2 FILE1 FILE2' will print the message

     ----------------
     ##1       #:1   <== 100
                     ==> 100.00012
     @ Absolute error = 1.2000000000e-4, Relative error = 1.2000000000e-6

     +++  File "FILE1" differs from file "FILE2"

since the option `-2' makes `numdiff' regard two values as equal only
if both absolute and relative difference do not exceed the
corresponding threshold of tolerance.

   The option `-P' makes `numdiff' consider two values equal whenever
the second one, i.e. the one coming from the file specified as last on
the command line, is less or equal than the first one, which is the
value coming from the file specified as first on the command line.  If
the values to compare are complex numbers, saying that the second one
is less or equal than the first one means that both real and imaginary
part of the second one are not greater than the real part and,
respectively, the imaginary part of the first one.

   Finally, the option `-N' makes `numdiff' consider two values equal
whenever the second one, i.e. the one coming from the file specified as
last on the command line, is greater or equal than the first one, which
is the value coming from the file specified as first on the command
line.  If the values to compare are complex numbers, saying that the
second one is greater or equal than the first one means that both real
and imaginary part of the second one are not less than the real part
and, respectively, the imaginary part of the first one.

   The options `-I', `-l', `-o', `-h' and `-v' do not require further
explanations.  The options `-l' and `-o' are only supplied for the
users of some poorly designed operating systems (like MSDog or
MSWindoze), whose default shell does not allow the redirection of
standard error and standard output.  The option `-I' has no effect on
the outcome of numerical comparisons.

   Several things must be told about the option `-s'.  First, it will
be better if you will always quote the set of the delimiters, just as
in the next examples:

     numdiff -s ' \t\n,;:.' FILE1 FILE2
     numdiff -s ' \t\n\r\f\v"\:;' FILE1 FILE2
     numdiff -s `` \t\n''' FILE1 FILE2

I recommend you actually to always use the single quote character (')
to enclose the list of the delimiters, since in this way you will
prevent any substitution or handling of characters by the shell.

`numdiff' recognizes and interprets the following sequences of
characters within the argument passed to the option `-s':

   * `\f'     form feed

   * `\n'     newline

   * `\r'     carriage return

   * `\t'     horizontal tab

   * `\v'     vertical tab

since these characters are often used as delimiters in files containing
numerical data and they could not be included directly in the set of
delimiters.  Then, by passing the string ` \t\n,;:.' as argument for
the option `-s', one tells `numdiff' use as field delimiters the
characters *blank*, *horizontal tab*, *newline*, *comma*, *semicolon*,
*colon* and *dot*.  Passing ` \t\n' as argument to the option `-s' is
the same as not using at all the option `-s', since *blank*,
*horizontal tab* and *newline* are the default field delimiters.  In
the list of field delimiters the character *backslash* (`\') is always
treated in a special way.  If followed by `f', `n', `r', `t' and `v' it
is combined with the subsequent character and interpreted in the way we
have just seen.  Otherwise, the *backslash* is coupled with the
following character and then removed. In particular, if you want to
specify the *backslash* itself as field delimiter, you have to put *two
backslashes* (`\\') in the list of delimiters.  Therefore, the
delimiters specified by the command line

     numdiff -s' \t\n\\\"' FILE1 FILE2

are *blank*, *horizontal tab*, *newline*, *backslash* and *double
quote* since `\\' and `\"' are interpreted by `numdiff' as `\' and `"'.

   Even if I have recommended to enclose the set of delimiters in
single quotes, there are cases in which you will be constrained to use
the double quote character (`"') to enclose the set of field
delimiters, just as in one of the previous examples.  However you must
take into account that in this case the shell could make some
substitutions on the command line before executing `numdiff'.  For
instance, if your shell is GNU bash, then (citing the man page of GNU
bash)

     Enclosing characters in double quotes preserves the literal value
     of all characters within the quotes, with the exception of `$',
     ``', and `\'.  The characters `$' and ``' retain their special
     meaning within double quotes.  The backslash retains its special
     meaning only when followed by one of the following characters:
     `$', ``', `"', `\', or *<newline>*.  A double quote may be quoted
     within double quotes by preceding it with a backslash ....  The
     special parameters * and @ have special meaning when in double
     quotes ...

Therefore, if the set of delimiters is formed by ` ', `\t', `\n', `\'
and `"' and you decide to enclose them in double quotes, then the
`numdiff' command line should be

     numdiff -s'' \t\n\\\\\"'' FILE1 FILE2

and not

     numdiff -s'' \t\n\\\"'' FILE1 FILE2

Indeed, in this last case the shell would replace the string

   ` \t\n\\\"'

with

   ` \t\n\"'

and then `numdiff' would take ` ', `\t', `\n' and `"' as field
delimiters.

   A last advice about the use of the option `-s'.  I recommend you to
always put *newline* (on Unix(C) and Unix-like operating systems, like
GNU(C)) and *carriage return* (on MSDog/MSWindoze) in the set of field
delimiters.  Otherwise, these characters would be included in all the
fields staying at the end of a line and this would cause some
undesirable effects. For instance, a number put at the end of a line
would not be considered as a numerical field by `numdiff', since
`numdiff' would consider the final *newline* as part of the field which
then would be qualified as non-numerical.  Maybe in the future I will
modify `numdiff' in order to remove the mandatory specification of
*newline* as field delimiter.

   The option `-#' lets the user specify the number of digits in the
significands used in multiple-precision arithmetic.  The default value
is 35, the largest admissible value is 180.  Take into account that an
higher precision makes the execution of `numdiff' slower. This is
particularly true when the files to compare contain a lot of numerical
fields.  Moreover, you have to care that `numdiff' can truncate the
value of a numerical field if it has too much digits with respect to
the current precision. To be precise, denoted by P the current value of
the precision:
   * If the number is written in common notation, then `numdiff' will
     consider, in addition to all the digits of the integer part, only
     the first P digits of the fractional part.

   * If the value is written in scientific notation, then `numdiff'
     will only consider the first P digits of the fractional part of
     the mantissa.

The options `-d', `-t', `-g', `-p', `-n', `-e' and `-i' can be used to
instruct `numdiff' about the numeric formats used in the files which it
is going to compare.  The two files to compare do not have to adopt the
same numeric format, and then `numdiff' allows to specify different
numeric formats for them.  Indeed each of the options `-d', `-t', `-g',
`-p', `-n', `-e' and `-i' can have as argument one or two characters
(one or two digits if the option is `-g'). In the first case, the
argument refers to both files to compare, in the second one the first
character is for the file specified as first on the command line, the
second character is for the file specified as last one on the command
line.  For instance, the option `-d' can be used to tell `numdiff'
which character(s) is(are) used to mean the decimal point in the two
files to compare.  If you give the command `numdiff -d_ FILE1 FILE2',
then `numdiff' will understand that both in FILE1 and FILE2 the
character *underscore* (`_') is used in place of the default one (`.')
to indicate the position of the decimal point in the numerical values.
But if the command is `numdiff -d_: FILE1 FILE2', then `numdiff' will
understand that the decimal point is indicated by the character
*underscore* in FILE1, and by *colon* (`:') in FILE2.

   Naturally, if you omit to use one of the options `-d', `-t', `-g',
`-p', `-n', `-e' and `-i', then the corresponding attribute will take
its default value, see *Note Default Numeric Format::.

   You must be really careful when you use one or more of these options.
First, not all characters can be passed to them as arguments.  For
instance, the arguments of the option `-g' must be digits.  The
arguments of the options `-d' and `-t' must be punctuation marks (the
punctuation marks are all the characters of the ASCII set for which the
standard C function `ispunct' returns a non zero value), those ones of
the options `-p', `-n', `-e' and `-i' must be graphical characters but
digits (graphical characters are all the characters of the ASCII set
for which the standard C function `isgraph' returns a non zero value).

   Moreover, it is not possible to set the decimal point, the thousands
separator, the positive sign, the negative sign, the prefix for decimal
exponent and the symbol of the imaginary unit so that, for a same file,
two or more of these characters come out to be equal.  This rule also
applies when you miss to explicitly set one of the previous arguments
through the appropriate option.  For instance, the command `numdiff
-d,. FILE1 FILE2' will make `numdiff' abnormally terminate after
printing the error message:

     The numeric format specified for the first file is illegal,
     the following symbols should be all different
     while two or more of them are actually equal:

     Decimal point = `,'
     Thousands separator = `,'
     Positive sign = `+'
     Negative sign = `-'
     Prefix for decimal exponent = `e'
     Symbol used to denote the imaginary unit = `i'

Indeed, through the option `-d' we have told to `numdiff' that in the
first file the decimal point is indicated by the character *comma*, but
at the same time we have not modified the character in use to separate
the groups of thousands, which has remained the default one, i.e.
*comma*, for both files to compare.  In this way, we have implicitly
told to `numdiff' that in FILE1 the character *comma* represents both
decimal point and thousands separator. Since this is not reasonable,
`numdiff' refuses to work.  To avoid this problem it would be
sufficient to explicitly notify to `numdiff' the thousands separator
through the option `-t': `numdiff -d,. -t., FILE1 FILE2'.  Of course,
here we are supposing that the decimal point and the thousands
separator are represented in FILE1 by *comma* and *dot* respectively, in
FILE2 by *dot* and *comma*.  I strongly suggest you that in writing a
file you avoid the use of the same symbol to mean two different things
(like would be using *comma* for both decimal point and thousands
separator): it would be dummy, would not it ?  :)

   At last, it is possible (but it is stupid) to use as argument for
the options `-d', `-t', `-g', `-p', `-n', `-e' and `-i' one of the
characters used to separate the fields in the files to compare.  In a
such case `numdiff' does not complain but you have to consider that
first it uses the set of field delimiters in order to split the files
into fields and then it takes into account the numeric formats
specified for the two files when it has to distinguish between
numerical and non-numerical fields.  However, it should never happen to
specify as argument for one of the options `-d', `-t', `-g', `-p',
`-n', `-e' and `-i' a character which is also used as field delimiter:
again, in writing a file you should avoid (and people usually avoid it)
to use the same symbol to mean two different things.

   The options `-L' and `-F' can be used to restrict the comparison
between files to a certain range of lines or to a certain group of
fields.  Without these options `numdiff' compares all the fields of all
the lines.

   With the option `-L' the user can make `numdiff' restrict the
comparison to a certain line or to a certain range of lines.  For
instance `numdiff -L 5 FILE1 FILE2' will make `numdiff' compare only
the fields in the fifth line of FILE1 with the corresponding fields in
the fifth line of FILE2.

   Similarly `numdiff -L 5-10 FILE1 FILE2' will make `numdiff' compare
only the fields which are contained in the lines from 5 to 10.

   As you can see, you can specify a range of lines by using the
notation `N1-N2', where N1 and N2 are the line numbers of the first and
of the last line in the range of lines that you want to compare.

   If you use two or more times the option `-L' with different
specifications, then `numdiff' will only consider the last
specification.  Therefore `numdiff -L 5-10 -L 6 -L 10-20 FILE1 FILE2'
will make `numdiff' compare the fields in the lines from 10 to 20.

   With the option `-F' the user can make `numdiff' restrict the
comparison to a certain field or to a certain group of fields.  For
instance `numdiff -F 3 FILE1 FILE2' will make `numdiff' compare only
the third field of each line of FILE1 with the third field of the
corresponding line of FILE2.

   Similarly `numdiff -F 3-7 FILE1 FILE2' will make `numdiff' compare,
for every line in FILE1 and FILE2, only the fields from the third one
to the seventh one (both included).

   As you can see, you can specify a range of fields by using the
notation `N1-N2', where N1 and N2 are the field numbers of the first
and of the last field in the range of fields that you want to compare.

   Remember that the fields of a line are numerated starting from the
left hand of the line and proceeding towards the right hand.

   By using two or more times the option `-F' you can extend the
comparison to a group of fields formed by more ranges and/or single
fields.  For instance `numdiff -F 5-10 -F 6 -F 12-20 -F 4 FILE1 FILE2'
will make `numdiff' compare the fourth field, the fields from the 5th
one to the 10th one and the fields from the 12th one to the 20th one of
every line.  Care the difference with respect to the option `-L',
since, as I told above, if you use two or more times the option `-L'
only the last specification will be considered by `numdiff'.

   Moreover, take into account that the largest field number that you
can use while writing a specification for the option `-F' is 32768.

   Of course, you can use the options `-F' and `-L' together. In this
way you can restrict the comparison to a certain group of fields within
a certain range of lines.

   If you use the option `-F' and/or the option `-L' the exit status of
`numdiff' will reflect the outcome of the restricted comparison.  For
instance, the exit status of `numdiff -L 1-7 FILE1 FILE2' will be 1
only if `numdiff' will have found a difference in the first seven lines
of FILE1 and FILE2.  If the two files differ only in the lines after
the seventh one, then `numdiff' will end with a zero exit status.

6 Tools
*******

Together with the version 5.x of Numdiff are shipped a couple of useful
tools, `ndselect' and `ndfilter'.  These tools are provided because
Numdiff lacks the capability to resynchronize the lines between two
files in case of addition or deletion of one or more lines. When I
wrote down the first stable version of Numdiff, I wanted just to create
a program able to perform numerical comparisons between files having
the same structure, i.e. same number of lines and, on each line, same
number and type of fields.  Then I added the capability to restrict the
comparison to a given range of lines (through the option `-L') or to
some specific fields (through the option `-F').  However, even with
these additions, Numdiff is not able to deal with some important issues
related to the comparison between files.

   The first tool shipped with Numdiff is `ndselect'. I decided to
create this utility in order to deal with a situation that comes out
often in Numerical Analysis. Here I present a very simple example of
such a situation. Let us suppose that file LIST1 contains the values of
the square root, rounded to the 20th decimal digit, for all the integer
numbers between 10 and 20:

12       3.46410161513775458705
13       3.60555127546398929312
14       3.74165738677394138558
15       3.87298334620741688518
16       4
17       4.12310562561766054982
18       4.24264068711928514641
19       4.35889894354067355224
20       4.47213595499957939282
21       4.58257569495584000659
22       4.69041575982342955457
23       4.7958315233127195416
24       4.89897948556635619639

while LIST2 contains _suitable_ approximations of the square root only
for the numbers between 12 and 21 which are multiple of 3:


12       3.46410162002945508100
15       3.87298387096774193548
18       4.24264705882352941176
21       4.58260869565217391304

These approximations could have been obtained for instance by using the
famous Heron's algorithm, which, given an approximation `a' for the
square root of a number `x', computes a better approximation by the
formula `a := 0.5 * (x/a + a)'.  What we want now is to understand how
good are the approximations contained in file LIST2 using `numdiff'. Of
course, we cannot execute directly the command `numdiff LIST1 LIST2',
since in this way we would compare the approximations provided for the
square roots of 15, 18, and 21 with the square roots of 13, 14, and 15
respectively. To make the comparison in the right way, one could open
LIST1 in a text editor and remove from it all the non interesting lines
till to leave only the ones related to the numbers 12, 15, 18, and 21.
But this approach is practicable because we have to remove few lines,
and one can easily figure out how boring and inefficient would be to
manually remove hundreds or thousands of lines from a file in order to
compare it with another one.

   An expert GNU/Linux(C) user would suggest that it is possible to
make this removal automatic by the well known utilities `head' and
`sed', in this particular case `head -n 10 LIST1 | sed -n -e '1~3 p' >
LIST1' A quick explanation for the ones who do not know how to use
`head' and `sed': the previous command extracts from LIST1 the first 10
lines, namely the ones containing the square roots of the numbers from
12 to 21, then it picks every third line starting from the first one
between the extracted lines, in order to select only the ones related
to 12, 15, 18, and 21. Finally, these lines are printed on the file
LIST1, which then looks like:

12       3.46410161513775458705
15       3.87298334620741688518
18       4.24264068711928514641
21       4.58257569495584000659

   Once obtained LIST1, we can perform with `numdiff' the comparison
between the values we are interested in: `numdiff LIST1 LIST2' .
Unfortunately, this trick only works if you have installed the GNU
version of `sed', which, as far as I know, is the only one to provide
the extension FIRST~STEP to specify line addresses.  That is way I
decided to implement `ndselect', which allows to obtain the same result
as before with the simpler command: `ndselect -b 1 -e 10 -s 3 LIST1 >
LIST1'

   The meaning of the arguments passed to the options `-b', `-e', and
`-s' is the following: we are telling `ndselect' to print every third
line of file LIST1 (the option `-s' specifies the step), starting from
the first one (the option `-b' specifies the begin) and ending within
the tenth one possibly inclusive (the option `-e' specifies the end).
Because of the presence of the redirection operator `>', the previous
command sends to the file LIST1 what `ndselect' would print on the
screen (standard output).

   Using `ndselect' is very simple and elegant, other than extremely
useful in the situations just outlined. A complete description of its
use follows.

*SYNOPSIS*

        ndselect -h|v
   or
        ndselect [-b FIRST][-e LAST][-s STEP][-l path][-o path] [FILE]

where FILE is the name of the file to scan.

   In the first case `ndselect' prints a short help or/and version
number, Copyright and NO-Warranty disclaimer.  In the second case
`ndselect' prints on the standard output every STEPth line of FILE
starting with line FIRST and ending within line LAST.  The complete
path of FILE should be given, a directory name is not accepted.  If no
input file is specified, the program reads from the standard input.

*OPTIONS*

   * `-b FIRST' Specify the first line to print (The default behavior
     is to start with line number 1)

   * `-e LAST'  Specify the last line that can be printed (The default
     behavior is to arrive till to the end of the file)

   * `-s STEP'  Specify the step to use when selecting the lines to
     print (The default value for the step is 1)

   * `-l path'  Redirect warning and error messages from stderr to the
     indicated file

   * `-o path'  Redirect output from stdout to the indicated file

   * `-h'       Show this help message

   * `-v'       Show version number, Copyright and NO-Warranty

Passing 0 as argument to the option `-e' is equivalent to omit this
option and leave enabled the default behavior (which consists in
scanning till to the end of the file).

*DIAGNOSTICS*

   The exit status is 0 in case of normal termination, -1 (255) in case
of error.

   Numdiff does not work well if one of the two files to compare
contains in the middle some lines more or less than the other one.  For
instance, if you have one file that is 1000 lines long that you are
comparing to a second file 1001 lines long, and except for that one
extra line, located, let us say, at line 500, the files are identical,
then `numdiff' will *not* show only the one line difference: once the
files are out of synchronization `numdiff' reports every line as
different. Although the ultimate solution would be adding to Numdiff
the capabilities of the `diff' command, since I do not have time to do
that for the moment, I decided to supply a tool, called `ndfilter',
which can turn out useful in similar cases.  A simple example will
explain how to employ `ndfilter'.  Let us suppose that FILE1 and FILE2
have the following contents,

file1:

 Day            Expenses
-------------------------
  1             $  233.56
  2             $  850.77
  3             $   12.55
  4             $  524.00
  5             $   78.25
 10             $  230.00
 11             $  443.10
 12             $   67.65
 13             $   10.00
 14             $  201.45
 15             $  110.00
-------------------------
Total           $ 2761.33

and


file2:

 Day            Expenses
  1             $  233.56
  2             $  850.77
  3             $   12.55
  4             $  524.00
  5             $   78.25
  6             $  432.90
  7             $   60.88
  8             $  759.00
  9             $  322.54
 10             $  230.00
 11             $  443.10
 12             $   67.65
 13             $   10.00
 14             $  201.45
-------------------------
Total           $ 4226.65

The differences between FILE1 and FILE2 are given by
   * the insertion of the separator ------------------------- in FILE1
     before the list of the days,

   * the insertion in FILE2 of the lines related to the expenses for
     the days 6,7,8, and 9,

   * the addition in FILE1 of the entry for the day 15, and

   * the different values for the total sum of the expenses.

   However, if you compare directly FILE1 and FILE2 using `numdiff',
then the result will be completely misleading:
     ----------------
     ##1       #:1   <== file1:
                     ==> file2:
                                                          @
     ----------------
     ##4       #:1   <== -------------------------
                     ==> 1
                                                          @
     ##4       #>2   <==
                     ==> $  233.56
      Line 4 in file "file1" is shorter!
     ----------------
     ##5       #:1   <== 1
                     ==> 2
      Absolute error = 1.0000000000e+0, Relative error = 1.0000000000e+0
     ##5       #:3   <== 233.56
                     ==> 850.77
      Absolute error = 6.1721000000e+2, Relative error = 2.6426185991e+0
     ----------------
     ##6       #:1   <== 2
                     ==> 3
      Absolute error = 1.0000000000e+0, Relative error = 5.0000000000e-1
     ##6       #:3   <== 850.77
                     ==> 12.55
      Absolute error = 8.3822000000e+2, Relative error = 6.6790438247e+1
     ----------------
     ##7       #:1   <== 3
                     ==> 4
      Absolute error = 1.0000000000e+0, Relative error = 3.3333333333e-1
     ##7       #:3   <== 12.55
                     ==> 524.00
      Absolute error = 5.1145000000e+2, Relative error = 4.0752988048e+1
     ----------------
     ##8       #:1   <== 4
                     ==> 5
      Absolute error = 1.0000000000e+0, Relative error = 2.5000000000e-1
     ##8       #:3   <== 524.00
                     ==> 78.25
      Absolute error = 4.4575000000e+2, Relative error = 5.6964856230e+0
     ----------------
     ##9       #:1   <== 5
                     ==> 6
      Absolute error = 1.0000000000e+0, Relative error = 2.0000000000e-1
     ##9       #:3   <== 78.25
                     ==> 432.90
      Absolute error = 3.5465000000e+2, Relative error = 4.5322683706e+0
     ----------------
     ##10      #:1   <== 10
                     ==> 7
      Absolute error = 3.0000000000e+0, Relative error = 4.2857142857e-1
     ##10      #:3   <== 230.00
                     ==> 60.88
      Absolute error = 1.6912000000e+2, Relative error = 2.7779237845e+0
     ----------------
     ##11      #:1   <== 11
                     ==> 8
      Absolute error = 3.0000000000e+0, Relative error = 3.7500000000e-1
     ##11      #:3   <== 443.10
                     ==> 759.00
      Absolute error = 3.1590000000e+2, Relative error = 7.1293161814e-1
     ----------------
     ##12      #:1   <== 12
                     ==> 9
      Absolute error = 3.0000000000e+0, Relative error = 3.3333333333e-1
     ##12      #:3   <== 67.65
                     ==> 322.54
      Absolute error = 2.5489000000e+2, Relative error = 3.7677753141e+0
     ----------------
     ##13      #:1   <== 13
                     ==> 10
      Absolute error = 3.0000000000e+0, Relative error = 3.0000000000e-1
     ##13      #:3   <== 10.00
                     ==> 230.00
      Absolute error = 2.2000000000e+2, Relative error = 2.2000000000e+1
     ----------------
     ##14      #:1   <== 14
                     ==> 11
      Absolute error = 3.0000000000e+0, Relative error = 2.7272727273e-1
     ##14      #:3   <== 201.45
                     ==> 443.10
      Absolute error = 2.4165000000e+2, Relative error = 1.1995532390e+0
     ----------------
     ##15      #:1   <== 15
                     ==> 12
      Absolute error = 3.0000000000e+0, Relative error = 2.5000000000e-1
     ##15      #:3   <== 110.00
                     ==> 67.65
      Absolute error = 4.2350000000e+1, Relative error = 6.2601626016e-1
     ----------------
     ##16      #:1   <== -------------------------
                     ==> 13
                                                          @
     ##16      #>2   <==
                     ==> $   10.00
      Line 16 in file "file1" is shorter!
     ----------------
     ##17      #:1   <== Total
                     ==> 14
                                                          @
     ##17      #:3   <== 2761.33
                     ==> 201.45
      Absolute error = 2.5598800000e+3, Relative error = 1.2707272276e+1
     ----------------
     ##18      <==
               ==> -------------------------


     ***  End of file "file1" reached
          Likely the files "file1" and "file2" do not have the same number of lines !

     +++  File "file1" differs from file "file2"

   The reason for that is the inability of `numdiff' to deal correctly
with the insertion and the deletion of one or more lines in the files
being compared.  `ndfilter' can be very useful in similar situations.
It takes two mandatory arguments, the names of the files to compare,
and, after comparing the given files by recalling the standard Unix(C)
utility `sdiff', it uses the results of this comparison to create a new
couple of files. Each of these new files is identical to the
corresponding original, except for the eventual addition of one or more
empty lines.  Namely, the command `ndfilter FILE1 FILE2' will create
two new files in the current working directory named respectively
`FILE1.new' and `FILE2.new'. The file `FILE1.new' is identical to FILE1
with the eventual exception of one or more empty lines, which are
exactly put to compensate the presence of lines in FILE2 which do not
have a correspondence in FILE1.  Analogously, `FILE2.new' is identical
to FILE2 if we except the empty lines that could have been inserted to
compensate the presence in FILE1 of lines not having a correspondence
in FILE2.

   To be more precise, `ndfilter' uses the output of the command `sdiff
FILE1 FILE2' to establish if and which lines were deleted from,
inserted in, or changed in one file to produce the other file. Then
`ndfilter' knows for every line of FILE1 and FILE2 if it is present
only in FILE1, or only in FILE2, or in both files maybe with some
changes. The files `FILE1.new' and `FILE2.new' are created using this
information according to the following rules. `ndfilter' reads line by
line the output of `sdiff FILE1 FILE2' and if a line is marked as
present both in FILE1 and in FILE2, then it is copied both in
`FILE1.new' and in `FILE2.new'. If there are changes between the
_version_ in FILE1 and the one in FILE2, then `ndfilter' prints on
`FILE1.new' the version coming from FILE1 and on `FILE2.new' the one
coming from FILE2.  If a line is present in FILE1 but has no
correspondence in FILE2, then `ndfilter' adds this line to `FILE1.new'
and at the same time puts an empty line in `FILE2.new'.  On the other
hand, if a line turns out to be present only in FILE2, then `ndfilter'
adds this line to `FILE2.new' and an empty line to `FILE1.new'.

   The new files created by `ndfilter' have the same number of lines
and through the addition of empty lines they are often correctly
synchronized to be compared by `numdiff'.

   If FILE1 and FILE2 are the same shown above, then the output of
`sdiff FILE1 FILE2' is (I used GNU sdiff from GNU diffutils 2.8.1 to
obtain it)

file1:				      |	file2:

 Day            Expenses		 Day            Expenses
-------------------------	      <
  1             $  233.56		  1             $  233.56
  2             $  850.77		  2             $  850.77
  3             $   12.55		  3             $   12.55
  4             $  524.00		  4             $  524.00
  5             $   78.25		  5             $   78.25
				      >	  6             $  432.90
				      >	  7             $   60.88
				      >	  8             $  759.00
				      >	  9             $  322.54
 10             $  230.00		 10             $  230.00
 11             $  443.10		 11             $  443.10
 12             $   67.65		 12             $   67.65
 13             $   10.00		 13             $   10.00
 14             $  201.45		 14             $  201.45
 15             $  110.00	      <
-------------------------		-------------------------
Total           $ 2761.33	      |	Total           $ 4226.65

   The special symbols <, >, and | in the _gutter_ column are used to
mark the lines which are present only in FILE1, or only in FILE2, or in
both files but with changes.  When no symbol is present, then the
corresponding line appears with no changes both in FILE1 and in FILE2.
According to the output of `sdiff FILE1 FILE2', the files `FILE1.new'
and `FILE2.new' created by `ndfilter FILE1 FILE2' have the following
contents (side by side view):

file1:                         #    file2:
                               #
 Day            Expenses       #     Day            Expenses
-------------------------      #
  1             $  233.56      #      1             $  233.56
  2             $  850.77      #      2             $  850.77
  3             $   12.55      #      3             $   12.55
  4             $  524.00      #      4             $  524.00
  5             $   78.25      #      5             $   78.25
                               #      6             $  432.90
                               #      7             $   60.88
                               #      8             $  759.00
                               #      9             $  322.54
 10             $  230.00      #     10             $  230.00
 11             $  443.10      #     11             $  443.10
 12             $   67.65      #     12             $   67.65
 13             $   10.00      #     13             $   10.00
 14             $  201.45      #     14             $  201.45
 15             $  110.00      #
-------------------------      #    -------------------------
Total           $ 2761.33      #    Total           $ 4226.65

   Now, if we perform the comparison of the _synchronized_ files
`FILE1.new' and `FILE2.new' instead of the original ones, we obtain the
right result. The output of `numdiff FILE1.new FILE2.new' is indeed
     ----------------
     ##1       #:1   <== file1:
                     ==> file2:
                                                          @
     ----------------
     ##4       #>1   <== -------------------------
                     ==>
      Line 4 in file "/home/ivano/file2.new" is shorter!
     ----------------
     ##10      #>1   <==
                     ==> 6             $  432.90
      Line 10 in file "/home/ivano/file1.new" is shorter!
     ----------------
     ##11      #>1   <==
                     ==> 7             $   60.88
      Line 11 in file "/home/ivano/file1.new" is shorter!
     ----------------
     ##12      #>1   <==
                     ==> 8             $  759.00
      Line 12 in file "/home/ivano/file1.new" is shorter!
     ----------------
     ##13      #>1   <==
                     ==> 9             $  322.54
      Line 13 in file "/home/ivano/file1.new" is shorter!
     ----------------
     ##19      #>1   <== 15             $  110.00
                     ==>
      Line 19 in file "/home/ivano/file2.new" is shorter!
     ----------------
     ##21      #:3   <== 2761.33
                     ==> 4226.65
      Absolute error = 1.4653200000e+3, Relative error = 5.3065732817e-1

     +++  File "/home/ivano/file1.new" differs from file "/home/ivano/file2.new"

   Unfortunately, `ndfilter' is currently implemented so that it gets
easily confused. As we have seen above, `ndfilter' relies on the
`sdiff' utility to work, but `sdiff' does not know anything about
numerical differences: whenever `sdiff' compares a couple of files, it
performs a literal comparison. Therefore, when `sdiff' has to establish
if a line was deleted from, inserted in, or changed in one of the two
files, it decides according to the results of a literal comparison,
which is not in line with the way `numdiff' compares the files.  To
work right, `ndfilter' should use the numerical comparison whenever it
is appropriate.

   For instance, if we suppose that FILE1 and FILE2 have the following
contents

file1:

 Day            Expenses
-------------------------
  1             $  233.56
  2             $  850.77
  3             $   12.55
  4             $  524.00
  5             $   78.25
 10             $  230.05
 11             $  443.10
 12             $   67.65
 13             $   10.00
 14             $  201.45
 15             $  110.00
-------------------------
Total           $ 2761.38

and


file2:

 Day            Expenses
  1             $  233.54
  2             $  850.80
  3             $   12.65
  4             $  524.00
  5             $   78.25
  6             $  432.90
  7             $   60.88
  8             $  759.00
  9             $  322.54
 10             $  230.00
 11             $  443.10
 12             $   67.65
 13             $   10.00
 14             $  201.45
-------------------------
Total           $ 4226.76

then the differences between FILE1 and FILE2 are given by
   * the insertion of the separator ------------------------- in FILE1
     before the list of the days,

   * the slightly different values for the expenses related to the days
     1, 2, and 3,

   * the insertion in FILE2 of the lines related to the expenses for
     the days 6,7,8, and 9,

   * the slightly different values for the expenses of the day 10,

   * the addition in FILE1 of the entry for the day 15, and

   * the different values for the total sum of the expenses.

   In this case the output of `sdiff FILE1 FILE2' is (when using
`sdiff' from GNU diffutils 2.8.1)

file1:				      |	file2:

 Day            Expenses		 Day            Expenses
-------------------------	      |	  1             $  233.54
  1             $  233.56	      |	  2             $  850.80
  2             $  850.77	      |	  3             $   12.65
  3             $   12.55	      <
  4             $  524.00		  4             $  524.00
  5             $   78.25		  5             $   78.25
 10             $  230.05	      |	  6             $  432.90
				      >	  7             $   60.88
				      >	  8             $  759.00
				      >	  9             $  322.54
				      >	 10             $  230.00
 11             $  443.10		 11             $  443.10
 12             $   67.65		 12             $   67.65
 13             $   10.00		 13             $   10.00
 14             $  201.45		 14             $  201.45
 15             $  110.00	      <
-------------------------		-------------------------
Total           $ 2761.38	      |	Total           $ 4226.76

and it is easy to deduce that `ndfilter' will fail in resynchronizing
the files.  The files `FILE1.new' and `FILE2.new' created by `ndfilter
FILE1 FILE2' are actually (side by side view):

file1:                        #     file2:
                              #
 Day            Expenses      #     Day            Expenses
-------------------------     #     1             $  233.54
  1             $  233.56     #     2             $  850.80
  2             $  850.77     #     3             $   12.65
  3             $   12.55     #
  4             $  524.00     #     4             $  524.00
  5             $   78.25     #     5             $   78.25
 10             $  230.05     #     6             $  432.90
                              #     7             $   60.88
                              #     8             $  759.00
                              #     9             $  322.54
                              #    10             $  230.00
 11             $  443.10     #    11             $  443.10
 12             $   67.65     #    12             $   67.65
 13             $   10.00     #    13             $   10.00
 14             $  201.45     #    14             $  201.45
 15             $  110.00     #
-------------------------     #   -------------------------
Total           $ 2761.38     #   Total           $ 4226.76

and the output of `numdiff FILE1.new FILE2.new' will be then completely
misleading.

   Until a new improved version of `ndfilter' will be made available, I
strongly recommend to inspect the files created by `ndfilter' before
comparing them with `numdiff'. At the moment it is quite likely that
`ndfilter' does not manage to perform a correct resynchronization.

   When you have a couple of files which need to be resynchronized to
be correctly compared by `numdiff', try to do that cleverly using
`ndselect' and `grep' before turning to `ndfilter'.

*SYNOPSIS*

     ndfilter -h|v
   or
     ndfilter [-s suffix][-e "opts"][-p col][-t tabwd][-n][-d][-l path][-o path]
     FILE1 FILE2

where FILE1 and FILE2 are the names of the files to compare. The
complete paths of the files should be given, a directory name is not
accepted. These paths cannot refer to the same file.

   In the first case `ndfilter' prints a short help or/and version
number, Copyright and NO-Warranty disclaimer.  In the second case
`ndfilter' compares the given files by recalling `sdiff', and use the
results of this comparison to create a new couple of files which
_should_ be correctly synchronized for a later comparison through
`numdiff'.

*OPTIONS*

   * `-s suffix' Specify the suffix to add to the old name when
     creating each of the two new files (The default suffix is ".new")

   * `-e "opts"' Specify the options to put on the command line when
     calling `sdiff' (The default behavior is executing `sdiff' with no
     options)

   * `-p col'    Specify the column number of the gutter in the `sdiff'
     output (The default value is the one for GNU sdiff, i.e. 62)

   * `-t tabwd'  Specify the width of the tabulations in the `sdiff'
     output (The default value is 8)

   * `-n'        Print the line number at the head of each line when
     writing the two new files

   * `-d'        Print debug information on stderr

   * `-l path'   Redirect warning and error messages from stderr to the
     indicated file

   * `-o path'   Redirect output from stdout to the indicated file

   * `-h'        Show this help message

   * `-v'        Show version number, Copyright and NO-Warranty

The option `-s' never accepts an empty suffix ("") as argument.

   The option `-e' is particularly useful to ignore case differences.
In this case, just use the option `-e' with the string ```-I''' as
argument: `ndfilter -e "-I" FILE1 FILE2' .  Look at the man page of the
`sdiff' utility to know which options are supported by the version of
`sdiff' installed on your system.

   The options `-p' and `-t' are useful to cope with the differences in
the output of the different versions of `sdiff'.  Not all the versions
of `sdiff' place the gutter in the same column, for instance the
`sdiff' utility included in the GNU diffutils package (version 2.8.1)
puts the gutter in the column number 62, while the `sdiff' utility
included in SunOS(R) 5.10 puts the gutter in the column 64 (if I well
remember :) ).  The option `-p' can be used to notify to `ndfilter' the
position of the gutter in the `sdiff' output, if it differs from the
default value (which is the one for GNU `sdiff', namely 62).  If
`ndfilter' ends abnormally with an error message sounding like ''Error
occurred while creating the new files'', then you probably omitted to
specify the right value for the column position of the gutter.

   The option `-t' is only useful if the `sdiff' utility does not
expand automatically the tabulations present in the files when printing
its output. Normally, the default value for the width of a tabulation
(namely 8) is the right one.  Otherwise, you can change it with the
option `-t'.

   The option `-d' is only used for debugging by the author of
`ndfilter', so you should never use it.

   The options `-l' and `-o' have the same use as for `numdiff' and
`ndselect'.

   If the option `-n' is set, then, whenever `ndfilter' copies a line
from one of the two original files in the new corresponding one, it
adds at the head the line number referring to the original position of
the line. It is only useful if you want to keep trace of the positions
of the lines in the original files.

*DIAGNOSTICS*

   Exit status: 0 in case of normal termination, -1 (255) in case of
error.

7 Warnings
**********

   * After reading a numerical field, Numdiff can truncate its value if
     this number has too much digits with respect to the current
     precision. To be precise, denoted by P the current value of the
     precision:

     If the number is written in common notation, then `numdiff' will
     consider, in addition to all the digits of the integer part, only
     the first P digits of the fractional part.

     If the value is written in scientific notation, then `numdiff'
     will only consider the first P digits of the fractional part of
     the mantissa.

     By current value of the precision I mean the integer value
     specified by the option `-#', or the default one (35) when this
     option is not in use.

   * At the moment Numdiff can only manage text files with an 8-bit
     encoding (ASCII and ISO 8859-* text files).  Sooner or later
     Numdiff might support UTF-8 encoding.

   * This manual describes the version 5.x of Numdiff.  The versions
     preceding 4.0.0 (i.e. 3.0.2 and below) used a slightly different
     format for the output. Some changes were then introduced in order
     to make the output more consistent.  These changes included a
     better use of the separator ----------------, the use of the
     symbol <<*>> to mark the last line of a file when it does not have
     a terminating *newline* character, and the way Numdiff signals
     that a line has in one of the two files less fields than in the
     other file.  While before these reports had the following format
          Line 1 in file "list2" is shorter:
          <== water
          ==>

     the current format is given by
          ##1       #>6   <== water
                          ==>
           Line 1 in file "list2" is shorter!

     Moreover, the versions of Numdiff preceding 4.0.0 did not provide
     the "verbose mode" with the related option `-V'.  Finally, in the
     passage from the version 3.0.2 to the 4.0.0 one a minor bug
     related to the handling of the last line of a file has been
     corrected.

   * Bug reports have to be sent to the address
     <ivprimi(at)libero(dot)it> . Please, put Numdiff in the subject
     and indicate the version of Numdiff you are using, the version of
     the operating system you are running and, if you know it, the
     version of the compiler used to build Numdiff.

Appendix A GNU Free Documentation License
*****************************************


		GNU Free Documentation License
		  Version 1.2, November 2002


 Copyright (C) 2000,2001,2002  Free Software Foundation, Inc.
     51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
 Everyone is permitted to copy and distribute verbatim copies
 of this license document, but changing it is not allowed.


0. PREAMBLE

The purpose of this License is to make a manual, textbook, or other
functional and useful document "free" in the sense of freedom: to
assure everyone the effective freedom to copy and redistribute it,
with or without modifying it, either commercially or noncommercially.
Secondarily, this License preserves for the author and publisher a way
to get credit for their work, while not being considered responsible
for modifications made by others.

This License is a kind of "copyleft", which means that derivative
works of the document must themselves be free in the same sense.  It
complements the GNU General Public License, which is a copyleft
license designed for free software.

We have designed this License in order to use it for manuals for free
software, because free software needs free documentation: a free
program should come with manuals providing the same freedoms that the
software does.  But this License is not limited to software manuals;
it can be used for any textual work, regardless of subject matter or
whether it is published as a printed book.  We recommend this License
principally for works whose purpose is instruction or reference.


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2. VERBATIM COPYING

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If the required texts for either cover are too voluminous to fit
legibly, you should put the first ones listed (as many as fit
reasonably) on the actual cover, and continue the rest onto adjacent
pages.

If you publish or distribute Opaque copies of the Document numbering
more than 100, you must either include a machine-readable Transparent
copy along with each Opaque copy, or state in or with each Opaque copy
a computer-network location from which the general network-using
public has access to download using public-standard network protocols
a complete Transparent copy of the Document, free of added material.
If you use the latter option, you must take reasonably prudent steps,
when you begin distribution of Opaque copies in quantity, to ensure
that this Transparent copy will remain thus accessible at the stated
location until at least one year after the last time you distribute an
Opaque copy (directly or through your agents or retailers) of that
edition to the public.

It is requested, but not required, that you contact the authors of the
Document well before redistributing any large number of copies, to give
them a chance to provide you with an updated version of the Document.


4. MODIFICATIONS

You may copy and distribute a Modified Version of the Document under
the conditions of sections 2 and 3 above, provided that you release
the Modified Version under precisely this License, with the Modified
Version filling the role of the Document, thus licensing distribution
and modification of the Modified Version to whoever possesses a copy
of it.  In addition, you must do these things in the Modified Version:

A. Use in the Title Page (and on the covers, if any) a title distinct
   from that of the Document, and from those of previous versions
   (which should, if there were any, be listed in the History section
   of the Document).  You may use the same title as a previous version
   if the original publisher of that version gives permission.
B. List on the Title Page, as authors, one or more persons or entities
   responsible for authorship of the modifications in the Modified
   Version, together with at least five of the principal authors of the
   Document (all of its principal authors, if it has fewer than five),
   unless they release you from this requirement.
C. State on the Title page the name of the publisher of the
   Modified Version, as the publisher.
D. Preserve all the copyright notices of the Document.
E. Add an appropriate copyright notice for your modifications
   adjacent to the other copyright notices.
F. Include, immediately after the copyright notices, a license notice
   giving the public permission to use the Modified Version under the
   terms of this License, in the form shown in the Addendum below.
G. Preserve in that license notice the full lists of Invariant Sections
   and required Cover Texts given in the Document's license notice.
H. Include an unaltered copy of this License.
I. Preserve the section Entitled "History", Preserve its Title, and add
   to it an item stating at least the title, year, new authors, and
   publisher of the Modified Version as given on the Title Page.  If
   there is no section Entitled "History" in the Document, create one
   stating the title, year, authors, and publisher of the Document as
   given on its Title Page, then add an item describing the Modified
   Version as stated in the previous sentence.
J. Preserve the network location, if any, given in the Document for
   public access to a Transparent copy of the Document, and likewise
   the network locations given in the Document for previous versions
   it was based on.  These may be placed in the "History" section.
   You may omit a network location for a work that was published at
   least four years before the Document itself, or if the original
   publisher of the version it refers to gives permission.
K. For any section Entitled "Acknowledgements" or "Dedications",
   Preserve the Title of the section, and preserve in the section all
   the substance and tone of each of the contributor acknowledgements
   and/or dedications given therein.
L. Preserve all the Invariant Sections of the Document,
   unaltered in their text and in their titles.  Section numbers
   or the equivalent are not considered part of the section titles.
M. Delete any section Entitled "Endorsements".  Such a section
   may not be included in the Modified Version.
N. Do not retitle any existing section to be Entitled "Endorsements"
   or to conflict in title with any Invariant Section.
O. Preserve any Warranty Disclaimers.

If the Modified Version includes new front-matter sections or
appendices that qualify as Secondary Sections and contain no material
copied from the Document, you may at your option designate some or all
of these sections as invariant.  To do this, add their titles to the
list of Invariant Sections in the Modified Version's license notice.
These titles must be distinct from any other section titles.

You may add a section Entitled "Endorsements", provided it contains
nothing but endorsements of your Modified Version by various
parties--for example, statements of peer review or that the text has
been approved by an organization as the authoritative definition of a
standard.

You may add a passage of up to five words as a Front-Cover Text, and a
passage of up to 25 words as a Back-Cover Text, to the end of the list
of Cover Texts in the Modified Version.  Only one passage of
Front-Cover Text and one of Back-Cover Text may be added by (or
through arrangements made by) any one entity.  If the Document already
includes a cover text for the same cover, previously added by you or
by arrangement made by the same entity you are acting on behalf of,
you may not add another; but you may replace the old one, on explicit
permission from the previous publisher that added the old one.

The author(s) and publisher(s) of the Document do not by this License
give permission to use their names for publicity for or to assert or
imply endorsement of any Modified Version.


5. COMBINING DOCUMENTS

You may combine the Document with other documents released under this
License, under the terms defined in section 4 above for modified
versions, provided that you include in the combination all of the
Invariant Sections of all of the original documents, unmodified, and
list them all as Invariant Sections of your combined work in its
license notice, and that you preserve all their Warranty Disclaimers.

The combined work need only contain one copy of this License, and
multiple identical Invariant Sections may be replaced with a single
copy.  If there are multiple Invariant Sections with the same name but
different contents, make the title of each such section unique by
adding at the end of it, in parentheses, the name of the original
author or publisher of that section if known, or else a unique number.
Make the same adjustment to the section titles in the list of
Invariant Sections in the license notice of the combined work.

In the combination, you must combine any sections Entitled "History"
in the various original documents, forming one section Entitled
"History"; likewise combine any sections Entitled "Acknowledgements",
and any sections Entitled "Dedications".  You must delete all sections
Entitled "Endorsements".


6. COLLECTIONS OF DOCUMENTS

You may make a collection consisting of the Document and other documents
released under this License, and replace the individual copies of this
License in the various documents with a single copy that is included in
the collection, provided that you follow the rules of this License for
verbatim copying of each of the documents in all other respects.

You may extract a single document from such a collection, and distribute
it individually under this License, provided you insert a copy of this
License into the extracted document, and follow this License in all
other respects regarding verbatim copying of that document.


7. AGGREGATION WITH INDEPENDENT WORKS

A compilation of the Document or its derivatives with other separate
and independent documents or works, in or on a volume of a storage or
distribution medium, is called an "aggregate" if the copyright
resulting from the compilation is not used to limit the legal rights
of the compilation's users beyond what the individual works permit.
When the Document is included in an aggregate, this License does not
apply to the other works in the aggregate which are not themselves
derivative works of the Document.

If the Cover Text requirement of section 3 is applicable to these
copies of the Document, then if the Document is less than one half of
the entire aggregate, the Document's Cover Texts may be placed on
covers that bracket the Document within the aggregate, or the
electronic equivalent of covers if the Document is in electronic form.
Otherwise they must appear on printed covers that bracket the whole
aggregate.


8. TRANSLATION

Translation is considered a kind of modification, so you may
distribute translations of the Document under the terms of section 4.
Replacing Invariant Sections with translations requires special
permission from their copyright holders, but you may include
translations of some or all Invariant Sections in addition to the
original versions of these Invariant Sections.  You may include a
translation of this License, and all the license notices in the
Document, and any Warranty Disclaimers, provided that you also include
the original English version of this License and the original versions
of those notices and disclaimers.  In case of a disagreement between
the translation and the original version of this License or a notice
or disclaimer, the original version will prevail.

If a section in the Document is Entitled "Acknowledgements",
"Dedications", or "History", the requirement (section 4) to Preserve
its Title (section 1) will typically require changing the actual
title.


9. TERMINATION

You may not copy, modify, sublicense, or distribute the Document except
as expressly provided for under this License.  Any other attempt to
copy, modify, sublicense or distribute the Document is void, and will
automatically terminate your rights under this License.  However,
parties who have received copies, or rights, from you under this
License will not have their licenses terminated so long as such
parties remain in full compliance.


10. FUTURE REVISIONS OF THIS LICENSE

The Free Software Foundation may publish new, revised versions
of the GNU Free Documentation License from time to time.  Such new
versions will be similar in spirit to the present version, but may
differ in detail to address new problems or concerns.  See
http://www.gnu.org/copyleft/.

Each version of the License is given a distinguishing version number.
If the Document specifies that a particular numbered version of this
License "or any later version" applies to it, you have the option of
following the terms and conditions either of that specified version or
of any later version that has been published (not as a draft) by the
Free Software Foundation.  If the Document does not specify a version
number of this License, you may choose any version ever published (not
as a draft) by the Free Software Foundation.


ADDENDUM: How to use this License for your documents

To use this License in a document you have written, include a copy of
the License in the document and put the following copyright and
license notices just after the title page:

    Copyright (c)  YEAR  YOUR NAME.
    Permission is granted to copy, distribute and/or modify this document
    under the terms of the GNU Free Documentation License, Version 1.2
    or any later version published by the Free Software Foundation;
    with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
    A copy of the license is included in the section entitled "GNU
    Free Documentation License".

If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts,
replace the "with...Texts." line with this:

    with the Invariant Sections being LIST THEIR TITLES, with the
    Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST.

If you have Invariant Sections without Cover Texts, or some other
combination of the three, merge those two alternatives to suit the
situation.

If your document contains nontrivial examples of program code, we
recommend releasing these examples in parallel under your choice of
free software license, such as the GNU General Public License,
to permit their use in free software.

Index
*****

Acknowledgments:                               See 2.        (line   57)
Build:                                         See 4.        (line  412)
Caveats:                                       See 7.        (line 1771)
Command line options:                          See 5.        (line  498)
Compile:                                       See 4.        (line  412)
Copying Conditions:                            See 1.        (line   40)
Diagnostics:                                   See 5.        (line  498)
FDL:                                           See Appendix A.
                                                             (line 1825)
Format of the reports:                         See 3.1.      (line  250)
GNU FDL:                                       See Appendix A.
                                                             (line 1825)
GNU Free Documentation License:                See Appendix A.
                                                             (line 1825)
GNU General Public License:                    See 1.        (line   40)
GPL:                                           See 1.        (line   40)
How to use it:                                 See 3.        (line   70)
Install:                                       See 4.        (line  412)
Invoking:                                      See 5.        (line  498)
License:                                       See 1.        (line   40)
ndfilter:                                      See 6.        (line 1088)
ndselect:                                      See 6.        (line 1088)
Notes:                                         See 7.        (line 1771)
Options, command line:                         See 5.        (line  498)
Output format:                                 See 3.1.      (line  250)
Overview:                                      See 3.        (line   70)
Predefined settings:                           See 5.        (line  498)
Purposes:                                      See 3.        (line   70)
Synopsis:                                      See 5.        (line  498)
Thanks:                                        See 2.        (line   57)
Tools:                                         See 6.        (line 1088)
Usage:                                         See 3.        (line   70)
Warnings:                                      See 7.        (line 1771)
