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\input texinfo   @c -*-texinfo-*-
@c %**start of header
@setfilename numdiff.info
@settitle Numdiff Manual 5.9
@afourpaper
@c %**end of header

@dircategory Text creation and manipulation
@direntry
* Numdiff: (numdiff).  Comparing files containing numeric fields (and not only)
@end direntry

@copying

@emph{``...und der eignen Kraft vertrauend steigt ein frei Geschlecht empor!''}
@sp 2

@noindent
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 @copyright{} 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017  Ivano Primi  @email{ivprimi(at)libero(dot)it}

@quotation
Permission is granted to copy, distribute and/or modify this
document under the terms of the GNU Free Documentation License, Version
1.3 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 @ref{GNU Free Documentation License}.
@end quotation
@end copying

@titlepage
@title Numdiff User Manual, version 5.9
@page
@vskip 0pt plus 1filll
@insertcopying
@end titlepage

@c Output the table of the contents at the beginning.
@contents

@ifnottex
@node Top, Copying, (dir), (dir)
@top Numdiff User Manual

@insertcopying
@end ifnottex

@menu
* Copying::                     Numdiff Copying Conditions (GPL)
* Acknowledgments::             Acknowledgments
* Overview::                    Introduction to numdiff
* Installing::                  How to install numdiff
* Invoking numdiff::            How to use numdiff     
* ndselect::                    (numdiff) ndselect. Selecting lines and fields
* Invoking ndselect::           How to use ndselect
* Filtering::                   How to use the filter of numdiff      
* Warnings::                    Various recommendations
* GNU Free Documentation License::  The license covering this document  
* Index::                       Complete index
@end menu


@node Copying, Acknowledgments, Top, Top
@chapter Copying

@cindex Copying Conditions
@cindex License
@cindex GNU General Public License
@cindex GPL

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 3 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 this program.  If not, see @uref{http://www.gnu.org/licenses/}.

@node Acknowledgments, Overview, Copying, Top
@chapter Acknowledgments

@cindex Acknowledgments
@cindex Thanks

I want to thank Mr. Norman Clerman @email{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.
He also 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
versions 4.x and 5.x of Numdiff.

Moreover, I want to thank my friends Mariapia Palombaro,
since she removed some errors while
reviewing the first version of this document, and
Paolo Caramanica, who suggested me to add more
information to the output of the option @option{-S}. 

@node Overview, Installing, Acknowledgments, Top
@chapter Overview

@cindex Introduction
@cindex Usage of numdiff
@cindex Purposes
@cindex How to use numdiff

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 look at the differences between two
files.  One way consists in looking at the series of lines
that were deleted from, inserted in, or changed in one file to produce
the other file.  
The well-known @command{diff} program compares two files line by line, 
finds groups of lines that differ, and reports each group of differing lines.
Without particular options, when comparing lines 
the @command{diff} program considers any
change in the amount or in the type of the characters as a
difference. However, trough some command line options
the user can suppress the output of certain kinds of
differences that are not important to him.
For instance, @command{diff} provides options to ignore differences
in the amount of white space between words or lines, or
differences in alphabetic case.

Another way to look at the differences between two files consists
in considering the 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 @command{wdiff} program by Fran@,{c}ois Pinard  
@email{pinard(at)iro(dot)umontreal(dot)ca}
compares words in two files and reports the differences.

Finally, one can regard the differences between two files as a
sequence of pairs of differing bytes.
The @command{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 @command{diff} or @command{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.
In such a case what you want to obtain usually is a list of the numerical fields
in the second file which @strong{numerically} differ
from the corresponding fields in the first file. 
But, while a number can be written using different notations, 
programs like @command{diff} or @command{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.
If you are interested in the numerical values, 
the difference in the representation is not meaningful
and then should be ignored. However, @command{diff} and @command{wdiff}
always consider the previous one as an actual difference: 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.
Here the difference is only due to the use
of the scientific notation in place of the ordinary decimal notation.

In addition, depending on your country you could stick
to different conventions in writing numbers.
For example, 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
@command{diff} and @command{wdiff} would report a difference,
which probably is not what you want in such a case.

Lastly, sometimes you could wish to ignore even
differences in numerical values as long as they do not
exceed a certain threshold. In other words,
you could desire to suppress the report of all ``small''
numerical differences.

For example, 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
should be considered equal, while 33  and  33.00011
should be reported as different.

However, @command{diff} and @command{wdiff} can not be used
to ignore small numerical differences, since they
do not even know what a numerical difference is.

These are the reasons 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 @command{ndiff},
a GPL'ed software by Nelson H. Baabe of the Salt Lake
City University. @command{ndiff} is actually a good tool,
and I used it for a while. But I did not
completely like the way it works, and so @command{numdiff} was conceived.
Although @command{ndiff} inspired @command{numdiff}, they are completely
different from the viewpoint of the source code:
@command{numdiff} has been entirely written from scratch
with the addition of code coming from GNU bc, GNU diff
and GNUlib.
In addition, the last versions of Numdiff offer much more
features than @command{ndiff} does.

@command{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.
@command{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 corresponding field of the second file.
What @emph{corresponding} here exactly means
depends on the options passed to the program on
the command line. With no options, corresponding
means the field of the second file at the same position,
where position refers both to the line number and to the
location within the line.
If the compared fields are both legal numerical values,
then @command{numdiff} performs a numerical comparison
between them, otherwise it performs a literal comparison,
i.e. 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.
Mind that, if you do not explicitly 
specify a list of field delimiters by means of the option @option{-s}
or @option{-D}, @command{numdiff} takes as field delimiters
the characters newline (@samp{\n}, ASCII code 0x0A),
horizontal tabulation (@samp{\t}, ASCII code 0x09),
and blank (@samp{ }, ASCII code 0x20).

For example, if the file @file{list1} contains the data
@verbatim
accident        123     23Joshua          34.55           +3+4i	        water
dog       -3455.321     cat             2.345678e-9     .0005-6.23e2i

@end verbatim

@noindent
and file @file{list2} contains the data

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

@end verbatim

@noindent
then the output of the command @samp{numdiff list1 list2} will be:

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


+++  File "list1" differs from file "list2"
@end example

At the same time @command{numdiff} will print the following error message
on stderr:
@example
***  End of file "list1" reached while trying to read line 4.
     File "list2" has more lines than file "list1",
     line 4 is the last one read from file "list2"
@end example

It is worth remarking that @command{numdiff} can recognize complex numbers,
provided that they are written in the form @math{a+bi} or
@math{a-bi} with no extra characters between the values @math{a}, @math{b} and
the sign @math{+} or @math{-} (the symbol @math{i},
used to represent the imaginary unit, can be changed by a suitable
command line option, @pxref{Invoking numdiff}).
Do not worry if you do not know what complex numbers are:
probably you will never manage files containing complex numbers,
thus you can live happily without them. :)

We consider now an example which shows how Numdiff can
resynchronize the lines between two files in case of addition or deletion 
of one or more lines.
The versions of Numdiff prior to 5 did 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 @command{numdiff} version 4.x does @strong{not} show only the one line difference:
once the files are out of synchronization @command{numdiff} 4.x reports
every line as different.
Since version 5 it is possible in such cases to activate a filter which handles
additions and deletions of lines. 
There are several options ruling how the filter
actually works, and I will give later a detailed explanation
on how to use them to obtain each time the wished result.
The simplest way to activate the filter consists in
using the option @option{-z @@}.
If @file{bill1} and @file{bill2} are given by
@verbatim
 Month          Expenses
-------------------------
 Jan09          $  233.56
 Feb09          $  850.77
 Mar09          $   12.55
 Apr09          $  524.00
 May09          $   78.25
 Jun09          $  230.00
 Jul09          $  443.10
 Aug09          $   67.65
 Sep09          $   10.00
 Oct09          $  201.45
 Nov09          $  110.00
 Dec09          $  200.27
-------------------------
Total           $ 2961.60
@end verbatim

@noindent
and

@verbatim
 Month          Expenses
 Jan09          $  234.00
 Mar09          $   13.00
 May09          $   78.25
 Jul09          $  443.10
 Sep09          $   10.00
 Nov09          $  110.00
 Jan10          $  200.00
-------------------------

Total           $ 1088.35   
@end verbatim

@noindent
respectively, then the differences between the two files are:
@itemize
@item the insertion of the separator @verb{|-------------------------|}
in @file{bill1} before the list of the months,
@item the deletion in @file{bill2} of the lines
related to the expenses for the months February,
April, June, August, October, December, 
@item small changes in @file{bill2} to the expenses
of the months January 2009 and March,
@item the presence in @file{bill2} of an entry for January 2010
just before the separator @verb{|-------------------------|},
@item the addition of an empty line to @file{bill2} after the separator
@verb{|-------------------------|},
@item and the different values for the total sum of the expenses.
@end itemize

The output of the command @samp{numdiff -z @@ -V bill1 bill2}
(I have added here the option @option{-V} to let Numdiff show
 which couples of lines it is comparing each time) 
shows exactly the expected differences:
@anchor{command}
@example

----------------
##2       <== -------------------------
          ==>

----------------
##3       <==  Jan09          $  233.56
##2       ==>  Jan09          $  234.00

##3       #:3   <== 233.56
##2       #:3   ==> 234.00
@@ Absolute error = 4.4000000000e-1, Relative error = 1.8838842268e-3
----------------
##4       <==  Feb09          $  850.77
          ==>

----------------
##5       <==  Mar09          $   12.55
##3       ==>  Mar09          $   13.00

##5       #:3   <== 12.55
##3       #:3   ==> 13.00
@@ Absolute error = 4.5000000000e-1, Relative error = 3.5856573705e-2
----------------
##6       <==  Apr09          $  524.00
          ==>

----------------
##8       <==  Jun09          $  230.00
          ==>

----------------
##10      <==  Aug09          $   67.65
          ==>

----------------
##12      <==  Oct09          $  201.45
          ==>

----------------
##14      <==  Dec09          $  200.27
##8       ==>  Jan10          $  200.00

##14      #:1   <== Dec09
##8       #:1   ==> Jan10
@@                                                     @@@@
##14      #:3   <== 200.27
##8       #:3   ==> 200.00
@@ Absolute error = 2.7000000000e-1, Relative error = 1.3500000000e-3
----------------
          <==
##10      ==> 

----------------
##16      <== Total           $ 2961.60
##11      ==> Total           $ 1088.35

##16      #:3   <== 2961.60
##11      #:3   ==> 1088.35
@@ Absolute error = 1.8732500000e+3, Relative error = 1.7211834428e+0

+++  File "bill1" differs from file "bill2"

@end example
Looking at the displayed report we see that:
@itemize
@item the second line of file @file{bill1}, i.e.
the one containing the separator, has no
correspondance, or, if you prefer, has been deleted 
from file @file{bill2}.
@item The lines related to the months January
and March 2009 have been slightly modified in
@file{bill2}, namely the values of the expenses
are slightly different. Notice that the line 
with the expenses for January 2009 is the third one
in file @file{bill1} and the second one in file
@file{bill2}. This information
is printed by Numdiff in the form
@example
##3       <==  Jan09          $  233.56
##2       ==>  Jan09          $  234.00
@end example
Analogously,
@example
##5       <==  Mar09          $   12.55
##3       ==>  Mar09          $   13.00
@end example 
says that the line for March is
the fifth one in @file{bill1} and the third
one in @file{bill2}. 
@item The line related to
the total amount of the expenses
appears also differently in the two files,
since the amount of the expenses is different.
Notice that this line is the 16th one
in file @file{bill1} and the 11th one in file
@file{bill2}.
@item The lines related to the months February,
April, June, August and October, i.e. the lines
no. 4, 6, 8, 10, and 12 of @file{bill1}, are not present
in @file{bill2}. 
@item The line of @file{bill1} with the expenses for December 2009
is replaced in @file{bill2} by the line containing
the value of the expenses for January 2010.
@item The tenth line of @file{bill2}, i.e. the empty line
after the separator, is not present in @file{bill1}.
With respect to @file{bill1} this line represents then an addition.
@end itemize

If you compare @file{bill1} and @file{bill2}
without using the option @option{-z @@}, the result is completely
misleading. This is the output of @samp{numdiff -V bill1 bill2}:
@example

----------------
##2       <== -------------------------
##2       ==>  Jan09          $  234.00

##2       #:1   <== -------------------------
##2       #:1   ==> Jan09
@@                                                     @@@@
##2             <==
##2       #>2   ==> $  234.00
@@ Line 2 in file "bill1" is shorter than expected!
----------------
##3       <==  Jan09          $  233.56
##3       ==>  Mar09          $   13.00

##3       #:1   <== Jan09
##3       #:1   ==> Mar09
@@                                                     @@@@
##3       #:3   <== 233.56
##3       #:3   ==> 13.00
@@ Absolute error = 2.2056000000e+2, Relative error = 1.6966153846e+1
----------------
##4       <==  Feb09          $  850.77
##4       ==>  May09          $   78.25

##4       #:1   <== Feb09
##4       #:1   ==> May09
@@                                                     @@@@
##4       #:3   <== 850.77
##4       #:3   ==> 78.25
@@ Absolute error = 7.7252000000e+2, Relative error = 9.8724600639e+0
----------------
##5       <==  Mar09          $   12.55
##5       ==>  Jul09          $  443.10

##5       #:1   <== Mar09
##5       #:1   ==> Jul09
@@                                                     @@@@
##5       #:3   <== 12.55
##5       #:3   ==> 443.10
@@ Absolute error = 4.3055000000e+2, Relative error = 3.4306772908e+1
----------------
##6       <==  Apr09          $  524.00
##6       ==>  Sep09          $   10.00

##6       #:1   <== Apr09
##6       #:1   ==> Sep09
@@                                                     @@@@
##6       #:3   <== 524.00
##6       #:3   ==> 10.00
@@ Absolute error = 5.1400000000e+2, Relative error = 5.1400000000e+1
----------------
##7       <==  May09          $   78.25
##7       ==>  Nov09          $  110.00

##7       #:1   <== May09
##7       #:1   ==> Nov09
@@                                                     @@@@
##7       #:3   <== 78.25
##7       #:3   ==> 110.00
@@ Absolute error = 3.1750000000e+1, Relative error = 4.0575079872e-1
----------------
##8       <==  Jun09          $  230.00
##8       ==>  Jan10          $  200.00

##8       #:1   <== Jun09
##8       #:1   ==> Jan10
@@                                                     @@@@
##8       #:3   <== 230.00
##8       #:3   ==> 200.00
@@ Absolute error = 3.0000000000e+1, Relative error = 1.5000000000e-1
----------------
##9       <==  Jul09          $  443.10
##9       ==> -------------------------

##9       #:1   <== Jul09
##9       #:1   ==> -------------------------
@@                                                     @@@@
##9       #>2   <== $  443.10
##9             ==>
@@ Line 9 in file "bill2" is shorter than expected!
----------------
##10      <==  Aug09          $   67.65
##10      ==> 

##10      #>1   <== Aug09          $   67.65
##10            ==>
@@ Line 10 in file "bill2" is shorter than expected!
----------------
##11      <==  Sep09          $   10.00
##11      ==> Total           $ 1088.35

##11      #:1   <== Sep09
##11      #:1   ==> Total
@@                                                     @@@@
##11      #:3   <== 10.00
##11      #:3   ==> 1088.35
@@ Absolute error = 1.0783500000e+3, Relative error = 1.0783500000e+2
----------------
##12      <==  Oct09          $  201.45
          ==>


***  End of file "bill2" reached while trying to read line 12.
     File "bill1" has more lines than file "bill2",
     line 12 is the last one read from file "bill1"


+++  File "bill1" differs from file "bill2"
@end example
Numdiff compares now the first, second, third line of @file{bill1}
with the first, second, third line of @file{bill2}, and so on.
But probably this is not what you want in such a case: what
is reasonable here is to compare entries related to the same
month and not lines having the same location, i.e. the
same line number.

Numdiff offers also an option to run just the filter
and see how it resynchronizes the two given files
without performing any comparison of corresponding lines.
The output of @samp{numdiff -z @@ -f bill1 bill2} is
@example
 Month          Expenses          Month          Expenses
-------------------------     <
 Jan09          $  233.56         Jan09          $  234.00
 Feb09          $  850.77     <
 Mar09          $   12.55         Mar09          $   13.00
 Apr09          $  524.00     <
 May09          $   78.25         May09          $   78.25
 Jun09          $  230.00     <
 Jul09          $  443.10         Jul09          $  443.10
 Aug09          $   67.65     <
 Sep09          $   10.00         Sep09          $   10.00
 Oct09          $  201.45     <
 Nov09          $  110.00         Nov09          $  110.00
 Dec09          $  200.27     |   Jan10          $  200.00
-------------------------        -------------------------
                              >
Total           $ 2961.60        Total           $ 1088.35


+++  File "bill1" differs from file "bill2"
@end example

@noindent
and shows that the filter is doing its job in the right way,
associating the lines according to the month
and not to the line number.
Running just the filter is extremely useful in all
situations when you are not sure if the filter is working as
you wish.
You have indeed to instruct the filter in the right way to let
it work correctly, and this requires the use of different
options depending on the structure of the files to compare.
Since guessing the right options can be sometimes
tricky, running just the filter and see the result is
the best way to be certain that you are setting up
everything correctly. 
Later, @pxref{Filtering}, I will explain in detail 
@itemize
@item what the filter 
does behind the scenes to understand
if and how it has to resynchronize the files to compare,
@item and how the related options affect the action
of the filter.
@end itemize

By the way, it is even possible to use @option{-f}
without any other additional option for the filter, like
in @samp{numdiff -f bill1 bill2}, but the result is more or less
the same you would obtain by performing a byte-by-byte comparison
with removal of the field delimiters.

The option @option{-f} can be followed by an argument in the form
of an integer number whose meaning will be explained 
later, @pxref{Use of the option -f}.

Even if the output of @command{numdiff} is supposed to be self-explanatory,
in the next section I will explain in details all you should know about it.

@menu
* Output format::         How numdiff prints its reports on stdout
* Overview mode::         An alternative way to print listings of differences
* Filter output::         How the built-in filter prints its report 
* Raw output::            A compact output format suitable for automated parsing
@end menu

@node Output format, Overview mode, , Overview
@section Output format

@cindex Output format (numdiff)
@cindex Format of the reports

Let us go back to our first example.
If the files @file{list1} and @file{list2} contain the data
@verbatim
accident        123     23Joshua          34.55           +3+4i	        water
dog       -3455.321     cat             2.345678e-9     .0005-6.23e2i

@end verbatim

@noindent
and

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

@end verbatim

@noindent
respectively, then the output of the command @samp{numdiff list1 list2}
will be:

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


+++  File "list1" differs from file "list2"
@end example

@command{numdiff} prints a report on the standard output
for every field of the first file which
differs from the corresponding field of the second file.

This report indicates first the locations
of the fields, namely the numbers
of the lines where the fields appear and
their positions within the line. The position in the line 
is ``1'' for the first field of a line, ``2''
for the second field, ``3'' for 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 @command{numdiff} shows in what the difference consists.
For example,
@example
##1       #:1   <== accident
##1       #:1   ==> Accident
@@                                                     @@@@
@end example

@noindent
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 be then canceled
by removing ``accident'' from the first file
and inserting ``Accident'' in place of it.
The arrows ``<=='' and ``==>'' try to
visualize this idea.
Analogously,
@example
##2       #:2   <== -3455.321
##2       #:2   ==> -3455.320098
@@ Absolute error = 9.0200000000e-4, Relative error = 2.6104672633e-7
@end example

@noindent
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, @command{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 @emph{n1} is the value appearing in the first
file and @emph{n2} is the value in the second file,
then the absolute error is given by the formula @emph{A=|n1-n2|},
while the relative error @emph{R} is given by:

@itemize
@item @emph{R = 0} if @emph{n1} and @emph{n2} are equal,
@item @emph{Inf} (infinity) if @emph{n2} differs from @emph{n1} and
at least one of them is zero,
@item @emph{R = A/ min(|n1|, |n2|)} if @emph{n1} and @emph{n2} are
both non zero and @emph{n2} differs from @emph{n1}. @emph{min(|n1|, |n2|)}
denotes the minimum between the absolute value of @emph{n1}
and the absolute value of @emph{n2}.
@end itemize

@noindent
With these definitions of absolute
and relative error it turns out that @emph{A(n2, n1) = A(n1, n2)} and
@emph{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.
Since version 5 it is actually possible to let Numdiff
compute the relative error always with respect to the value
from the first file or always with respect to the value
from the second file, instead of using the preceding formula.
This can be done through the option @option{-F}, 
@pxref{Alternative formulas for the computation of the relative difference}.

If at least one of the compared fields is not numerical, then the output line
reporting absolute and relative errors is replaced by
the separator:
@verbatim
@                                                     @@
@end verbatim

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.
If this is the case, @command{numdiff} reports this difference
by telling that a certain line (identified by its
line number) appears to be shorter than expected,
just as in
@example
##1       #>6   <== water
##1             ==>
@@ Line 1 in file "list2" is shorter than expected!
@end example

or in
@example
##3             <==
##3       #>1   ==> A new line
@@ Line 3 in file "list1" is shorter than expected!
@end example

In addition, @command{numdiff} shows
the @i{tail} of the longer line, using the notation ``#>@math{n}''
to indicate the number @math{n} of the first field of the longer line
for which there is no corresponding field in the shorter line.
For example,
@example
##1       #>6   <== water
##1             ==>
@@ Line 1 in file "list2" is shorter than expected!
@end example

@noindent
means that none of the fields of the first line starting from the sixth one
has a corresponding field in the second file (@file{list2}).
In this context, the symbol @verb{|<<*>>|} (if 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 @emph{newline} character. 

It can also happen that one of the two
files to compare has less lines than the other one.
In this case, if no special option is passed to the program,
@command{numdiff} prints the number of the first
line which appears in only one of the two files and
a message on the standard error telling in which of the two files
the end has been prematurely reached:
@example
***  End of file "list1" reached while trying to read line 4.
     File "list2" has more lines than file "list1",
     line 4 is the last one read from file "list2"
@end example

Unless the option @option{-q} is used (@pxref{Invoking numdiff}),
@command{numdiff} prints to the 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:
@example
+++  File "list1" differs from file "list2"
@end example

@node Overview mode, Filter output, Output format, Overview
@section Overview mode

@cindex Overview mode of numdiff
@cindex Side-by-side report (numdiff)

Since version 5.6 an alternative way to display the differences
between two files is available, which can be activated 
through the option @option{-O}. 
If this option is present on the command line, @command{numdiff}
prints a side-by-side report instead of the usual one.

For example, if @file{sheet1} contains the text
@verbatim
A    1    1
B    2    4
C    3    9
D    4   16
E    5   25
F    6   36
G    7   49
H    8   64
I    9   81
J   10  100
@end verbatim

@noindent
and @file{sheet2} the following lines

@verbatim
A    1      1
B    2      4
C    3.3    9.03
D    4     16
E    5.5   25.05
F    6.6   36
G    7.7   49.49
H    8     64
I    9.9   81.09
@end verbatim

@noindent
then @samp{numdiff -O sheet1 sheet2} prints this report
@example
A    1    1                            A    1      1
B    2    4                            B    2      4
C    3    9                         :!:C    3.3    9.03
D    4   16                            D    4     16
E    5   25                         :!:E    5.5   25.05
F    6   36                         :!:F    6.6   36
G    7   49                         :!:G    7.7   49.49
H    8   64                            H    8     64
I    9   81                         :!:I    9.9   81.09
J   10  100                         :<:

***  End of file "sheet2" reached while trying to read line 10.
     File "sheet1" has more lines than file "sheet2",
     line 10 is the last one read from file "sheet1"


+++  File "sheet1" differs from file "sheet2"
@end example

On the left side you can see the lines coming from the file
specified as first on the command line, i.e. @file{sheet1},
on the right side the lines from the second file of the command line,
in this case @file{sheet2}. In the middle there is a @i{gutter}
which contains one of these markers:
@table @samp
@item white spaces
The corresponding lines are in common.  That is, either the lines
are identical, or the difference is ignored because of one of the
options @option{-s}, @option{-D}, @option{-I}, @option{-X}, @option{-a}, 
@option{-r}, @option{-P}, or @option{-N}. 

@item :!:
The corresponding lines have at least one field which differs.

@item :<:
The files differ and only the first file contains the line.

@item :>:
The files differ and only the second file contains the line.
@end table

In the case of @file{sheet1} and @file{sheet2} a message
is printed after the report saying that the end of the second file 
has been prematurely reached. The two files do not have indeed
the same number of lines and the filter has not been activated. 

The option @option{-O} can take an optional argument, which
allows to set the width of the output and eventually to suppress
common lines, @pxref{Invoking numdiff}. 
The default value for the width of the side-by-side report
is 130. No wonder then that the command @samp{numdiff -O40 sheet1 sheet2}
displays a report with shorter lines:
@example
A    1    1           A    1      1
B    2    4           B    2      4
C    3    9       :!: C    3.3    9.03
D    4   16           D    4     16
E    5   25       :!: E    5.5   25.05
F    6   36       :!: F    6.6   36
G    7   49       :!: G    7.7   49.49
H    8   64           H    8     64
I    9   81       :!: I    9.9   81.09
J   10  100       :<:

***  End of file "sheet2" reached while trying to read line 10.
     File "sheet1" has more lines than file "sheet2",
     line 10 is the last one read from file "sheet1"


+++  File "sheet1" differs from file "sheet2"
@end example 

A negative argument makes that only the differences are listed in
the side-by-side report, as shown by
the output of the command @samp{numdiff -O40 sheet1 sheet2}:
@example
C    3    9       :!: C    3.3    9.03
E    5   25       :!: E    5.5   25.05
F    6   36       :!: F    6.6   36
G    7   49       :!: G    7.7   49.49
I    9   81       :!: I    9.9   81.09
J   10  100       :<:

***  End of file "sheet2" reached while trying to read line 10.
     File "sheet1" has more lines than file "sheet2",
     line 10 is the last one read from file "sheet1"


+++  File "sheet1" differs from file "sheet2"
@end example

If you set the width of the report to a too small value, it can happen
that some or even all lines from the compared files appear truncated as
in the output of @samp{numdiff -O24 sheet1 sheet2}:
@example
A    1         A    1  
B    2         B    2  
C    3    :!:  C    3.3
D    4         D    4  
E    5    :!:  E    5.5
F    6    :!:  F    6.6
G    7    :!:  G    7.7
H    8         H    8  
I    9    :!:  I    9.9
J   10    :<:

***  End of file "sheet2" reached while trying to read line 10.
     File "sheet1" has more lines than file "sheet2",
     line 10 is the last one read from file "sheet1"


+++  File "sheet1" differs from file "sheet2"
@end example

If you set the width of the report to a very small value, Numdiff
ignores it and uses the default value, i.e. 130.

Notice that the numeric argument must immediately follow the option @option{-O},
intermediate spaces are not allowed. This
is also the case for the optional argument of @option{-f}, while
the options of Numdiff which require a mandatory argument permit
the presence of intermediate spaces between them and the argument.

The option @option{-O} can be used together with any other option of
Numdiff except for @option{-f}, @option{-q}, @option{-U}, @option{-E},
@option{-V} and @option{-b}. When @option{-O} is in use, @option{-U}, 
@option{-E}, @option{-V} and @option{-b} are ignored. If @option{-q}
is present on the command line together with @option{-O}, then
@option{-O} is ignored. Finally, if both @option{-f} and @option{-O}
are present, then the behavior depends on the order: the option which
appears first on the command line is the one which matters. 

Therefore, the command @samp{numdiff -O40 -f sheet1 sheet2}
displays the same report as @samp{numdiff -O40 sheet1 sheet2},
while the output of @samp{numdiff -f -O40 sheet1 sheet2} is
given by
@example
A    1    1                            A    1      1
B    2    4                            B    2      4
C    3    9                          | C    3.3    9.03
D    4   16                            D    4     16
E    5   25                          | E    5.5   25.05
F    6   36                          | F    6.6   36
G    7   49                          | G    7.7   49.49
H    8   64                            H    8     64
I    9   81                          | I    9.9   81.09
J   10  100                          <


+++  File "sheet1" differs from file "sheet2"
@end example 

@noindent
and coincides then with the output of @samp{numdiff -f sheet1 sheet2}.

The option @option{-O} can be used together with the filter to cope
with the addition/deletion of lines.
If the file @file{sheet3} contains the text
@verbatim
A    1      1
C    3.3    9.03
E    5.5   25.05
G    7.7   49.49
I    9.9   81.09
J    10   100.00
K    0      0.02
@end verbatim

@noindent
then @samp{numdiff -O40 sheet1 sheet3} prints a wrong report,
as in the example with files @file{bill1} and @file{bill2}:
@example
A    1    1           A    1      1
B    2    4     :!:   C    3.3    9.03
C    3    9     :!:   E    5.5   25.05
D    4   16     :!:   G    7.7   49.49
E    5   25     :!:   I    9.9   81.09
F    6   36     :!:   J    10   100.00
G    7   49     :!:   K    0      0.02
H    8   64     :<:

***  End of file "sheet3" reached while trying to read line 8.
     File "sheet1" has more lines than file "sheet3",
     line 8 is the last one read from file "sheet1"


+++  File "sheet1" differs from file "sheet3"
@end example

On the other hand, the presence of @option{-z @@} makes Numdiff
always compare fields of corresponding lines, as shown by
the output of the command @samp{numdiff -O40 -z @@ sheet1 sheet3}:
@example
A    1    1           A    1      1
B    2    4     :<:
C    3    9     :!:   C    3.3    9.03
D    4   16     :<:
E    5   25     :!:   E    5.5   25.05
F    6   36     :<:
G    7   49     :!:   G    7.7   49.49
H    8   64     :<:
I    9   81     :!:   I    9.9   81.09
J   10  100           J    10   100.00
                :>:   K    0      0.02

+++  File "sheet1" differs from file "sheet3"
@end example

Side-by-side format is easy to read, but it has limitations.  
It generates much wider output than usual, and truncates
lines that are too long to fit.  Also, it relies on lining up output
quite heavily, so its output looks particularly bad if you
use varying width fonts, nonstandard tab stops, or nonprinting
characters.
 
@node Filter output, Raw output, Overview mode, Overview
@section Output of the filter

@cindex Filter output (numdiff)

The output produced just by running the filter (option @option{-f}) is
a side-by-side difference listing of the compared files
like the one displayed by GNU sdiff. 
The files are listed in two columns with a gutter between them.  The
gutter contains one of the following markers:
@table @samp
@item white space
The corresponding lines are in common.  That is, either the lines
are identical, or the difference is ignored because of one of the
options @option{-s}, @option{-D}, @option{-I}, @option{-X}, 
@option{-z}, or @option{-Z}. 

@item |
The corresponding lines differ, and they are either both complete
or both incomplete.

@item <
@itemx (
The files differ and only the first file contains the line.

@item >
@itemx )
The files differ and only the second file contains the line.

@item \
The corresponding lines differ, and only the first line is
incomplete.

@item /
The corresponding lines differ, and only the second line is
incomplete.
@end table

An input line is incomplete if its last character is not a newline.
This can happen only if the line is the last one of its file.
When an output line of the side by side difference listing
represents two differing lines, one might be incomplete
while the other is not.  In this case the gutter is marked 
@samp{\} if the line from the first file is incomplete, @samp{/} 
if the line from the second file is it.

Like @option{-O}, the option @option{-f} can take an optional argument which
allows to set the width of the output and eventually to suppress
common lines, @pxref{Invoking numdiff} and @ref{Use of the option -f}.

More generally, the user can always make @command{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, @pxref{Invoking numdiff}.

@node Raw output, , Filter output, Overview
@section Raw output

@cindex Raw output format

Since version 5.9 Numdiff can report the results of the
comparison of two files in a particularly compact format,
which can be easily parsed by other programs.
This @emph{raw} format is chosen by Numdiff whenever
the user requests it through the command line option @option{--raw}.
Below you can see an example of raw output in the case
of the comparison of the files @file{list1} and @file{list2}
from section @ref{Output format}:
@example
1:1:1:1:*:*:accident ==> Accident
1:1:3:3:*:*:23Joshua ==> 23456
1:1:5:5:1.0000000000e-4:2.0000000000e-5:+3+4i ==> +3.0001+4i
1:1:6:*:water
2:2:2:2:9.0200000000e-4:2.6104672633e-7:-3455.321 ==> -3455.320098
2:2:3:3:*:*:cat ==> Cat
2:2:5:5:5.0000000000e-4:8.0256821830e-7:.0005-6.23e2i ==> -6.23e2i
2:2:*:6:$$$
3:3:*:1:A new line
*:4

+++  File "list1" differs from file "list2"
@end example

The raw format is not at all convenient for humans.
It has been provided only for being used by the forthcoming
graphic user interface of Numdiff (yes, Numdiff will have
a GUI sometime in the future!).

@node Installing, Invoking numdiff, Overview, Top
@chapter Installing

@cindex Install
@cindex Compile
@cindex Build

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 @option{-o} to write its output to a specified file,
the option @option{-D} for macros predefinition,
the option @option{-l} to search for a specified library,
and the options @option{-I} and @option{-L}
to add a given directory to the search path for include and
library files respectively.

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

Numdiff has been successfully compiled and tested on:

@itemize
@item Slackware@registeredsymbol{} GNU/Linux 10.2 with the version 3.3.6 of the GNU C Compiler (GCC),
@item Slackware GNU/Linux 11 with GCC 3.4.6,
@item Slackware GNU/Linux 12.2 with GCC 4.2.4, 
@item Slackware GNU/Linux 13 with GCC 4.3.3, 
@item Debian@registeredsymbol{} GNU/Linux 4.0 with GCC 4.1.2 20061115 (prerelease) (Debian 4.1.1-21),
@item Debian GNU/Linux 6.0.3 with GCC 4.4.5 (Debian 4.4.5-8),
@item Debian GNU/Linux 7.1 with GCC 4.7.2 (Debian 4.7.2-5),
@item Debian GNU/Linux 8.6 with GCC 4.9.2 (Debian 4.9.2-10),
@item SunOS@registeredsymbol{} 5.8 with GCC 2.95.3, and
@item SunOS 5.10 (i386) with the version 5.9 of the Sun C compiler.
@end itemize

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

@noindent
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
@samp{make} you will have to type and run
@example
        make install-nls
@end example

By default, @samp{make install} will install all the files in
@file{/usr/local/bin}, @file{/usr/local/info} etc.  You can specify
an installation prefix other than @file{/usr/local} using the
option @option{--prefix} in the @command{configure} step,
for instance @samp{--prefix=$HOME}:
@example
        ./configure --prefix=$HOME
@end example 

@noindent
For better control, you can use the options
@option{--bindir}, @option{--infodir}, and so on.
Type @samp{./configure --help} to obtain
the complete list of all available options.

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

Once Numdiff has been installed you can remove all files 
related to Numdiff by a simple @samp{make uninstall}.
If you have also installed the localization files trough
@samp{make install-nls}, use @samp{make uninstall-nls} in place
of @samp{make uninstall} to remove them too.

Between the options accepted by @command{configure}
there are @option{--enable-debug}, @option{--enable-optimization}, 
@option{--enable-nls} and @option{--enable-gmp}.

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

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

The option @option{--enable-nls} turns on Natural Language Support.
You do not need to use it explicitly since Natural
Language Support is enabled by default.
To disable it, use @option{--disable-nls}.
Disabling Natural Language Support is suggested whenever
you want to install Numdiff on a system where the GNU gettext library
is not present. In this case
the installation of Numdiff can be accomplished, for example, through
@example
        ./configure --disable-nls
        make
        make install
@end example

@noindent
Since version 5.2.0 Numdiff uses to perform all computations
the GNU Multiple Precision Arithmetic Library
(also called GNU MP or GMP), if this library is available 
at build-time.
The old internal support for multiple precision arithmetic
is a fall-back in case GNU MP is absent.
However, it is possible to use the internal support for 
multiple precision arithmetic even if GNU MP is available:
it is sufficient to pass the option @option{--enable-gmp=no}
or @option{--disable-gmp} to the  configure  script
before building the program, like in
@example
        ./configure --disable-gmp
        make
        make install
@end example

@noindent
Enabling the old internal support for multiple precision arithmetic
is deprecated, @pxref{with GNU MP is better}.
The latest version of GNU MP is available at
@uref{http://ftp.gnu.org/gnu/gmp/}. See the GNU MP web page
at @uref{http://gmplib.org/} for up-to-date information on GNU MP.

@node Invoking numdiff, ndselect, Installing, Top
@chapter Invoking numdiff

@cindex Invoking numdiff
@cindex Options, command line (numdiff)
@cindex Command line options for numdiff
@cindex Synopsis (numdiff)
@cindex Diagnostics (numdiff)
@cindex Predefined settings of numdiff

@strong{SYNOPSIS}

@example
   numdiff -h|--help|-v|--version
@end example
or
@example
   numdiff [-s @var{IFS}][-D @var{DELIMS}][-a @var{THRVAL}[:@var{RANGE}|:@var{RANGE1}:@var{RANGE2}]]
   [-r @var{THRVAL}[:@var{RANGE}|:@var{RANGE1}:@var{RANGE2}]][-2][-F @var{NUM}][-# @var{NUM}][-P][-N][-I]
   [-c @var{CURRNAME}][-d @var{C1C2}][-t @var{C1C2}][-g @var{N1N2}][-p @var{C1C2}][-n @var{C1C2}][-e @var{C1C2}]
   [-i @var{C1C2}][-X 1:@var{RANGE}][-X 2:@var{RANGE}][-E][-U][-b][-V][-O[@var{NUM}]][--raw][-q][-S]
   [-z 1:@var{RANGE}][-z 2:@var{RANGE}][-Z 1:@var{RANGE}][-Z 2:@var{RANGE}][-m][-H][-f[@var{NUM}]]
   [-T][-B][-l @var{PATH}][-o @var{PATH}] @var{FILE1} @var{FILE2}
@end example

@noindent
where @var{FILE1} and @var{FILE2} are the names of the two files to compare
and @var{RANGE}, @var{RANGE1} and @var{RANGE2} stay for a positive integer
value or for a range of integer values, like @samp{1-}, @samp{3-5} or @samp{-7}.

In the first case @command{numdiff} prints a short help
(not so short actually :)) or/and version number, Copyright, License notice,
NO-Warranty disclaimer, and some information about the way it was built.
In the second case @command{numdiff} compares the files specified by
the two mandatory arguments which follow the list of the options.
The complete paths of the files should be given,
a directory name is not accepted.
In addition, the two arguments cannot refer to the same file
but one of them can be @verb{|-|}, which refers to stdin.

@noindent
@strong{OPTIONS}

@table @option
@item -s, --separators=@var{IFS}
Specify the set of characters to use as delimiters
while splitting the input lines into fields
(The default set of delimiters is space, tab and newline).
If @var{IFS} is prefixed with @samp{1:} or @samp{2:}, use the given delimiter set
only for the lines from the first or the second file respectively

@item -D, --delimiters=@var{DELIMS}
Specify the set of strings to use as delimiters
while splitting the input lines into fields
(The default set of delimiters is space, tab and newline).
If @var{DELIMS} is prefixed with @samp{1:} or @samp{2:}, use the given delimiter set
only for the lines from the first or the second file respectively

@item -a, --absolute-tolerance=@var{THRVAL}[:@var{RANGE}|:@var{RANGE1}:@var{RANGE2}]
Set to @var{THRVAL} the maximum absolute difference permitted
before two numeric fields are regarded as different (The default value is zero).
If a @var{RANGE} is given, use the specified
threshold only when comparing fields whose indexes lie in @var{RANGE}.
If both @var{RANGE1} and @var{RANGE2} are given and have the same length,
then use the specified threshold when comparing a field of @var{FILE1}
lying in @var{RANGE1} with the corresponding field of @var{FILE2} in @var{RANGE2}

@item -r, --relative-tolerance=@var{THRVAL}[:@var{RANGE}|:@var{RANGE1}:@var{RANGE2}]
Set to @var{THRVAL} the maximum relative difference permitted
before two numeric fields are regarded as different (The default value is zero).
If a @var{RANGE} is given, use the specified
threshold only when comparing fields whose indexes lie in @var{RANGE}.
If both @var{RANGE1} and @var{RANGE2} are given and have the same length,
then use the specified threshold when comparing a field of @var{FILE1}
lying in @var{RANGE1} with the corresponding field of @var{FILE2} in @var{RANGE2}

@item -2, --strict 
Consider two numerical values as equal only if
both absolute and relative difference do not exceed
the respective tolerance threshold

@item -F, --formula=@var{NUM}
Use the formula indicated by @var{NUM} to compute the relative errors.
If @var{NUM} is 0 use the classic formula.
If @var{NUM} is 1 compute the relative errors by considering
the values in @var{FILE1} as sample values.
If @var{NUM} is 2 compute the relative errors by considering
the values in @var{FILE2} as sample values.

@item -#, --digits=@var{NUM}
Set to @var{NUM} the number of digits in the significands
used in multiple precision arithmetic

@item -P, --positive-differences
Ignore all differences due to numeric fields of the second file that
are less than the corresponding numeric fields in the first file

@item -N, --negative-differences
Ignore all differences due to numeric fields of the second file that
are greater than the corresponding numeric fields in the first file

@item -I, --ignore-case
Ignore changes in case while doing literal comparisons

@item -c, --currency=@var{CURRNAME}
Set to @var{CURRNAME} the currency name for the two files to compare.
@var{CURRNAME} must be prefixed with @samp{1:} or @samp{2:} to specify the
currency name only for the first or the second file

@item -d, --decimal-point=@var{C1C2}
Specify the characters representing the decimal point
in the two files to compare

@item -t, --thousands-separator=@var{C1C2}
Specify the characters representing the thousands separator
in the two files to compare

@item -g, --group-length=@var{N1N2}
Specify the number of digits forming each group of thousands
in the two files to compare

@item -p, --plus-prefix=@var{C1C2}
Specify the (optional) prefixes for positive values
used in the two files to compare

@item -n, --minus-prefix=@var{C1C2}
Specify the prefixes for negative values
used in the two files to compare

@item -e, --exponent-letter=@var{C1C2}
Specify the exponent letters
used in the two files to compare

@item -i, --imaginary-unit=@var{C1C2}
Specify the characters representing the imaginary unit
in the two files to compare

@item -X, --exclude=1:@var{RANGE}
Select the fields of the first file that have to be ignored

@item -X, --exclude=2:@var{RANGE}
Select the fields of the second file that have to be ignored

@item -E, --essential
While printing the differences between the two compared files
show only the numerical ones

@item -U, --dummy
While printing the differences between the two compared files
neglect all the numerical ones (dummy mode)

@item -b, --brief
Suppress all messages concerning the differences discovered
in the structures of the two files

@item -V, --verbose
For every couple of lines which differ in at least one field print an header
to show how these lines appear in the two compared files

@item -O, --overview[=@var{NUM}]
Display a side by side difference listing of the two files
showing which lines are present only in one file, which
lines are present in both files but with one or more differing fields,
and which lines are identical.
If @var{NUM} is zero or is not specified, output at most 130 columns per line.
If @var{NUM} is a positive number, output at most @var{NUM} columns per line.
If @var{NUM} is a negative number, do not output common lines
and display at most -@var{NUM} columns per line.

@item --raw
Display the differences between the two compared files
in raw format (not very convenient for humans)

@item -q, --quiet, --silent
Suppress all the standard output

@item -S, --statistics
Add some statistics to the standard output

@item -z, --blur-if-numerical=1:@var{RANGE}
Select the fields of the first file that have to be
blurred during the synchronization procedure
only if they turn out to be numeric

@item -z, --blur-if-numerical=2:@var{RANGE}
Select the fields of the second file that have to be
blurred during the synchronization procedure
only if they turn out to be numeric

@item -Z, --blur-unconditionally=1:@var{RANGE}
Select the fields of the first file that have to be
unconditionally blurred during the synchronization procedure

@item -Z, --blur-unconditionally=2:@var{RANGE}
Select the fields of the second file that have to be
unconditionally blurred during the synchronization procedure

@item -m, --minimal
During synchronization try hard to find a smaller set of changes

@item -H, --speed-large-files
During synchronization assume large files and
many scattered small changes

@item -f, --test-filter[=@var{NUM}]
Run only the filter and then show the results of its
attempt to synchronize the two files.
If @var{NUM} is zero or is not specified, output at most 130 columns per line.
If @var{NUM} is a positive number, output at most
@var{NUM} columns per line.
If @var{NUM} is a negative number, do not output common lines
and display at most -@var{NUM} columns per line.

@item -T, --expand-tabs
Expand tabs to spaces in output while displaying the results of the
synchronization procedure (meaningful only together with option @option{-O}
or @option{-f})

@item -B, --binary
Treat both files as binary files (only meaningful under Doz/Windoz)

@item -l, --warnings-to=@var{PATH}
Redirect warning and error messages from stderr to the indicated file

@item -o, --output=@var{PATH}
Redirect output from stdout to the indicated file

@item -h, --help
Show help message and predefined settings

@item -v, --version
Show version number, Copyright, Distribution Terms and NO-Warranty
@end table

@noindent
@strong{DIAGNOSTICS}

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

@noindent
@strong{DEFAULT NUMERIC FORMAT (for both files to compare):}
@anchor{Default Numeric Format}

Currency name = ""
@sp 1
Decimal point = `.'
@sp 1
Thousands separator = `,'
@sp 1
Number of digits in each thousands group = 3
@sp 1
Leading positive sign = `+'
@sp 1
Leading negative sign = `-'
@sp 1
Prefix for decimal exponent = `e'
@sp 1
Symbol used to denote the imaginary unit = `i'

@noindent
@strong{SOME EXPLANATIONS}

The options @option{-U}, @option{-E}, @option{-b}, and
@option{-q} are used to hide part of the standard output of the program
according to certain rules.

The option @option{-U} triggers the @i{dummy mode}. In this mode
@command{numdiff} does not print the numerical differences. A numerical
difference occurs whenever the compared fields turn out to be both of numerical
type, but the field from the second file has a value
which differs from the one of the field from the first file.
The @i{dummy mode} is so called since in this mode
@command{numdiff} does not perform the job for which I created it.

The option @option{-E} triggers the @i{essential mode}. In this mode
@command{numdiff} only prints the numerical differences between the
files and, if there are some, the differences in the
structure. The latter ones occur either when one of
the files contains a line for which there is no
corresponding line in the other file, or
when the comparison of corresponding lines shows
that one of them contains a field for which there exists no
corresponding field in the other line. 
If you are not running any filter or cutting out any
fields through the option @option{-X}, then 
the differences in the structure simply consist either
in a different number of lines in the
two files, or in a different number of fields on a line.

The option @option{-b} triggers the @i{brief mode}. In this mode
@command{numdiff} does not print the differences in
the structure of the two files (see above for an explanation
about what differences in the structure are).

The option @option{-q} triggers the @i{quiet mode}.
In this mode @command{numdiff} does not print anything on the
standard output. The @i{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 @option{-O} activates the @i{overview mode},
which makes @command{numdiff} print a side-by-side report
in the form described in section @ref{Overview mode}.
The optional numeric argument after @option{-O} must immediately
follow, intermediate spaces are not allowed. 
The option @option{-O} can be used together with any other option 
of Numdiff except for @option{-f}, @option{-q}, @option{-U}, @option{-E},
@option{-V}, @option{-b}, and @option{--raw}. 
Whenever @option{-O} is in use, @option{-U}, @option{-E},
@option{-V} and @option{-b} are ignored. 
If @option{--raw} or @option{-q} is present on the command line together
with @option{-O}, then @option{-O} is ignored. 
Finally, if both @option{-f} and @option{-O} are
present, the behavior of Numdiff will depend on their order: 
the option which appears first on the command line is the
one which matters.

The option @option{-V} triggers the @i{verbose mode}. In this
mode @command{numdiff} produces a richer report by printing an header
whenever the compared lines differ. The header shows
how and where these lines appear in the compared files.
For instance, if the files @file{data1} and @file{data2} contain the data
@verbatim
12      33
22      44.5
0.008   1.002
221.12  -34.56  water
2101.21 boats
@end verbatim

@noindent
and

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

@noindent
respectively, then the command @samp{numdiff -V data1 data2}
will print the following output:
@example
----------------
##2       <== 22      44.5
##2       ==> 22.3      44.5

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

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

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

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

+++  File "data1" differs from file "data2"
@end example

Mind that the options @option{-b} and @option{-V}
will be overridden if @option{-q} is also set.

The amount of additional information printed by @option{-V} is 
trivially influenced by the options that alter 
the way @command{numdiff} performs the comparisons between fields
(for instance @option{-a}, @option{-r}, @option{-2}, @option{-N},
@option{-P}, @option{-U}, @option{-E}, @option{-I}, @option{-X}). 

In the headers printed by @command{numdiff} in ``verbose mode''
the symbol @verb{|<<*>>|} can appear. 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 @strong{newline} character. 

The option @option{-S} adds to the standard output of @command{numdiff}
a statistical report with the following information:
@itemize
@item the number of numeric comparisons the program has done (this quantity,
like the successive ones, is influenced by the options @option{-P} and
@option{-N}) and the number of those ones whose outcome
is a major @footnote{By major numerical differences and major errors
I mean those ones listed in the output of @command{numdiff} if none
of the options @option{-U}, @option{-f}, @option{-O}, and @option{-q} is used.}
numerical difference.
@item the largest absolute error in the set of major numerical differences
together with the corresponding relative error, and the positions of its
first occurrences in the compared files, 
@item the largest relative error in the set of major numerical differences
together with the corresponding absolute error, and the positions of its
first occurrences in the compared files, 
@item the sum and the arithmetic mean of all absolute errors,
@item the sum and the arithmetic mean of the major absolute errors,
@item the square root of the sum of the squares of all absolute errors,
@item the square root of the sum of the squares of the major absolute errors,
@item the quadratic mean of all absolute errors, and
@item the quadratic mean of the major absolute errors.
@end itemize
The information printed by @option{-S} is not
removed if this option is used together with @option{-q},
and is not influenced by the option @option{--raw}.

The options @option{-a}, @option{-r}, @option{-2},
@option{-P} and @option{-N} affect the way @command{numdiff}
performs the comparisons between numerical values.
Without any of these options, @command{numdiff} considers two
numerical fields as equal if their difference is zero.

The option @option{-a} can be used to make
two numerical fields be considered equal as long
as their absolute difference does not exceed a certain threshold,
which is specified by the argument that follows the @option{-a} option.
This argument can take several forms. The basic form consists of a
single numerical value, the extended form adds the
specification of one or two ranges of integer values.

Independently of the form of the argument, if the absolute
difference between two fields does not exceed the given threshold value, 
the fields are considered equal;
otherwise, @command{numdiff} prints the difference in its report,
unless some other option, for example @option{-P} or @option{-N}, 
makes the difference be neglected.
If nothing else follows the threshold value, the rule just explained applies
to all comparisons between numerical fields.
To see this in practice, if the file
@file{many_columns1} contains the text
@verbatim
A	1	 1.2	  1	 0.1	  11.0         1.0e-1
B	2        2.4      4      0.4      24.0         1.0e-2
C	3        3.6      9      0.9      39.0         1.0e-3
D	4	 4.8     16      1.6     416.0         1.0e-4
@end verbatim

@noindent
and the contents of the file @file{many_columns2} are given by

@verbatim
A	1.1	1.08	 1.01	 0.1	 11.011        -1.0e-1
B	2.2     2.16     4.04    0.4     24.024        -1.0e-2
C	3.3     3.24     9.09    0.9     39.039        -1.0e-3
D	4.4	4.32    16.16    1.6    416.039        -1.0e-4
@end verbatim

@noindent
then the output of the command @samp{numdiff -a 0.5 many_columns1 many_columns2}
will be
@example

+++  Files "many_columns1" and "many_columns2" are equal
@end example

@noindent
The highest absolute difference between a field from 
@file{many_columns1} and the corresponding field from @file{many_columns2}
is given indeed by  |4.32 - 4.8| = |-0.48| = 0.48, and then all
numeric differences between the two files remain below the
threshold value 0.5.

On the other hand, the command @samp{numdiff -a 0.35 many_columns1 many_columns2} 
prints the report
@example
----------------
##3       #:3   <== 3.6
##3       #:3   ==> 3.24
@ Absolute error = 3.6000000000e-1, Relative error = 1.1111111111e-1
----------------
##4       #:2   <== 4
##4       #:2   ==> 4.4
@ Absolute error = 4.0000000000e-1, Relative error = 1.0000000000e-1
##4       #:3   <== 4.8
##4       #:3   ==> 4.32
@ Absolute error = 4.8000000000e-1, Relative error = 1.1111111111e-1

+++  File "many_columns1" differs from file "many_columns2"
@end example

@noindent
since the absolute differences |3.24-3.6| = |-0.36| = 0.36,
|4.4-4| = |0.4| = 0.4, and |4.32 - 4.8| = 0.48 exceed
the value 0.35, while the other differences are below this threshold.

If you want that the specified threshold value applies
only when comparing some particular fields, you
have to use the extended form for the argument of @option{-a}.
This means that after the threshold value one
or two ranges of integer numbers must follow, each
preceded by a colon (`:').
If you specify only one range of numbers after
the threshold value, @command{numdiff} uses the
given threshold only when comparing fields whose positions lie 
in the specified range.
Remember that the positions of the fields on a line
are numbered starting from the left hand of the line
and proceeding towards the right hand.
For example, @samp{-a 0.01:2-5} sets the threshold value
to 0.01 only for the comparisons between numerical fields
which occupy on their lines a position between the second and the fifth one inclusive.
For the other comparisons the threshold value is left unchanged;
in particular, it is equal to zero if it has not been explicitly set.
If the files @file{many_columns1} and @file{many_columns2} are the same as before,
then the command @samp{numdiff -a 0.5:3-6 many_columns1 many_columns2} will
display the following report
@example
----------------
##1       #:2   <== 1
##1       #:2   ==> 1.1
@ Absolute error = 1.0000000000e-1, Relative error = 1.0000000000e-1
##1       #:7   <== 1.0e-1
##1       #:7   ==> -1.0e-1
@ Absolute error = 2.0000000000e-1, Relative error = 2.0000000000e+0
----------------
##2       #:2   <== 2
##2       #:2   ==> 2.2
@ Absolute error = 2.0000000000e-1, Relative error = 1.0000000000e-1
##2       #:7   <== 1.0e-2
##2       #:7   ==> -1.0e-2
@ Absolute error = 2.0000000000e-2, Relative error = 2.0000000000e+0
----------------
##3       #:2   <== 3
##3       #:2   ==> 3.3
@ Absolute error = 3.0000000000e-1, Relative error = 1.0000000000e-1
##3       #:7   <== 1.0e-3
##3       #:7   ==> -1.0e-3
@ Absolute error = 2.0000000000e-3, Relative error = 2.0000000000e+0
----------------
##4       #:2   <== 4
##4       #:2   ==> 4.4
@ Absolute error = 4.0000000000e-1, Relative error = 1.0000000000e-1
##4       #:7   <== 1.0e-4
##4       #:7   ==> -1.0e-4
@ Absolute error = 2.0000000000e-4, Relative error = 2.0000000000e+0

+++  File "many_columns1" differs from file "many_columns2"
@end example

@noindent
since the threshold value 0.5 applies now only when comparing
fields in third, fourth, fifth and sixth position, while for the other
comparisons the threshold value is the default one, i.e. zero.
If you want to specify a non null threshold also for the fields
in second and seventh position, you can do it by using the option
@option{-a} more times. The command
@samp{numdiff -a 0.5:3-6 -a 0.25:2 -a 4e-3:7 many_columns1 many_columns2}
sets the threshold value to 0.25 for the comparisons between the
fields in second position, and to 4e-3 for the comparisons of the
fields in seventh position. No wonder then, that the command
prints exactly this report:
@example
----------------
##1       #:7   <== 1.0e-1
##1       #:7   ==> -1.0e-1
@ Absolute error = 2.0000000000e-1, Relative error = 2.0000000000e+0
----------------
##2       #:7   <== 1.0e-2
##2       #:7   ==> -1.0e-2
@ Absolute error = 2.0000000000e-2, Relative error = 2.0000000000e+0
----------------
##3       #:2   <== 3
##3       #:2   ==> 3.3
@ Absolute error = 3.0000000000e-1, Relative error = 1.0000000000e-1
----------------
##4       #:2   <== 4
##4       #:2   ==> 4.4
@ Absolute error = 4.0000000000e-1, Relative error = 1.0000000000e-1

+++  File "many_columns1" differs from file "many_columns2"
@end example

@noindent
Observe that @verb{|:2|} and @verb{|:7|} are abbreviations
of @verb{|:2-2|} and @verb{|:7-7|}, respectively.
It is even possible to use range expressions like
@samp{@var{m}-} or @samp{-@var{n}}. 
The first expression means all fields starting from
the @var{m}th one (inclusive) till to the end of line,
the second selects all fields from the first one
till to the @var{n}th one, both inclusive.
 
If you specify two ranges of numbers after
the threshold value and they have the same length
(the length of a range is the difference between its maximum and its minimum), 
@command{numdiff} uses the given threshold when 
comparing a field of the first file
lying in the first range with the corresponding field 
of the second file from the second range.
For example, @samp{-a 1e-4:3-5:4-6} sets the threshold value
to 0.0001 only for the numerical comparisons of the third,
fourth, and fifth field of each line from the first file
with the fourth, fifth and sixth field respectively
of the corresponding line from the second file.
For the other comparisons the threshold value is left unchanged
and is in particular equal to zero if it has not been
explicitly set. This way to restrict the application of
a threshold value is useful in conjunction with the
option @option{-X}, which makes @command{numdiff} ignore one
or more fields from one of the compared files.

The file @file{many_columns3}:
@verbatim
A    I	1.1	1.08	 1.01	 0.1	 11.011        -1.0e-1
B   II	2.2     2.16     4.04    0.4     24.024        -1.0e-2
C  III	3.3     3.24     9.09    0.9     39.039        -1.0e-3
D   IV	4.4	4.32    16.16    1.6    416.039        -1.0e-4
@end verbatim

@noindent
has one column more than the file @file{many_columns1}, namely
the second one. When comparing @file{many_columns1} with
@file{many_columns3} it is natural then to ignore the second
column of the second file. This can be achieved by passing
the argument 2:2 to the option @option{-X} (for a full
description of the use of this option,
@pxref{Restriction of the comparison to particular fields}).
Ignoring the second field of each line of @file{many_columns3}
implies that the fields in the third column of this file
are compared with the corresponding fields of the second
column of @file{many_columns1}, the fields in the fourth column
of @file{many_columns3} are compared with the ones in the third
column of @file{many_columns1}, and so on.
Therefore, if you want to set a threshold value only for the
comparisons between some particular fields you have to consider 
that @samp{-X 2:2} makes @command{numdiff} compare the
first, second, third, fourth, fifth, sixth, and seventh field
of each line of @file{many_columns1} with the first, third, fourth,
fifth, sixth, seventh, and eighth field respectively of
the corresponding line of  @file{many_columns3}.
Therefore, the command @samp{numdiff -X 2:2 -a 0.5:3-6 many_columns1 many_columns3}
will use 0.5 as threshold value only when comparing 
the third, fourth, and fifth field of a line from 
@file{many_columns1} with the fourth,
fifth, and sixth field respectively of the corresponding line
of @file{many_columns3}.
This explains why the report of @samp{numdiff -X 2:2 -a 0.5:3-6 many_columns1 many_columns3}
@example
----------------
##1       #:2   <== 1
##1       #:3   ==> 1.1
@ Absolute error = 1.0000000000e-1, Relative error = 1.0000000000e-1
##1       #:6   <== 11.0
##1       #:7   ==> 11.011
@ Absolute error = 1.1000000000e-2, Relative error = 1.0000000000e-3
##1       #:7   <== 1.0e-1
##1       #:8   ==> -1.0e-1
@ Absolute error = 2.0000000000e-1, Relative error = 2.0000000000e+0
----------------
##2       #:2   <== 2
##2       #:3   ==> 2.2
@ Absolute error = 2.0000000000e-1, Relative error = 1.0000000000e-1
##2       #:6   <== 24.0
##2       #:7   ==> 24.024
@ Absolute error = 2.4000000000e-2, Relative error = 1.0000000000e-3
##2       #:7   <== 1.0e-2
##2       #:8   ==> -1.0e-2
@ Absolute error = 2.0000000000e-2, Relative error = 2.0000000000e+0
----------------
##3       #:2   <== 3
##3       #:3   ==> 3.3
@ Absolute error = 3.0000000000e-1, Relative error = 1.0000000000e-1
##3       #:6   <== 39.0
##3       #:7   ==> 39.039
@ Absolute error = 3.9000000000e-2, Relative error = 1.0000000000e-3
##3       #:7   <== 1.0e-3
##3       #:8   ==> -1.0e-3
@ Absolute error = 2.0000000000e-3, Relative error = 2.0000000000e+0
----------------
##4       #:2   <== 4
##4       #:3   ==> 4.4
@ Absolute error = 4.0000000000e-1, Relative error = 1.0000000000e-1
##4       #:6   <== 416.0
##4       #:7   ==> 416.039
@ Absolute error = 3.9000000000e-2, Relative error = 9.3750000000e-5
##4       #:7   <== 1.0e-4
##4       #:8   ==> -1.0e-4
@ Absolute error = 2.0000000000e-4, Relative error = 2.0000000000e+0

+++  File "many_columns1" differs from file "many_columns3"
@end example

@noindent
does not show the same difference listing of the command
@samp{numdiff -a 0.5:3-6 many_columns1 many_columns2}.

If what you want is to obtain the same difference listing
of @samp{numdiff -a 0.5:3-6 many_columns1 many_columns2}, then
the right command is @samp{numdiff -X 2:2 -a 0.5:3-6:4-7 many_columns1 many_columns3}.
The report printed by this last command is indeed
@example
----------------
##1       #:2   <== 1
##1       #:3   ==> 1.1
@ Absolute error = 1.0000000000e-1, Relative error = 1.0000000000e-1
##1       #:7   <== 1.0e-1
##1       #:8   ==> -1.0e-1
@ Absolute error = 2.0000000000e-1, Relative error = 2.0000000000e+0
----------------
##2       #:2   <== 2
##2       #:3   ==> 2.2
@ Absolute error = 2.0000000000e-1, Relative error = 1.0000000000e-1
##2       #:7   <== 1.0e-2
##2       #:8   ==> -1.0e-2
@ Absolute error = 2.0000000000e-2, Relative error = 2.0000000000e+0
----------------
##3       #:2   <== 3
##3       #:3   ==> 3.3
@ Absolute error = 3.0000000000e-1, Relative error = 1.0000000000e-1
##3       #:7   <== 1.0e-3
##3       #:8   ==> -1.0e-3
@ Absolute error = 2.0000000000e-3, Relative error = 2.0000000000e+0
----------------
##4       #:2   <== 4
##4       #:3   ==> 4.4
@ Absolute error = 4.0000000000e-1, Relative error = 1.0000000000e-1
##4       #:7   <== 1.0e-4
##4       #:8   ==> -1.0e-4
@ Absolute error = 2.0000000000e-4, Relative error = 2.0000000000e+0

+++  File "many_columns1" differs from file "many_columns3"
@end example

@noindent
and up to the positions of the fields from @file{many_columns3}
coincides with the one of @samp{numdiff -a 0.5:3-6 many_columns1 many_columns2}.

The option @option{-a} can appear more times on the command line.
In case of conflicts, the last setting is the one
which matters.
If you look at the report of the command 
@samp{numdiff -a 0.5:3-6 -a 0.08:4 many_columns1 many_columns2}
@example
----------------
##1       #:2   <== 1
##1       #:2   ==> 1.1
@ Absolute error = 1.0000000000e-1, Relative error = 1.0000000000e-1
##1       #:7   <== 1.0e-1
##1       #:7   ==> -1.0e-1
@ Absolute error = 2.0000000000e-1, Relative error = 2.0000000000e+0
----------------
##2       #:2   <== 2
##2       #:2   ==> 2.2
@ Absolute error = 2.0000000000e-1, Relative error = 1.0000000000e-1
##2       #:7   <== 1.0e-2
##2       #:7   ==> -1.0e-2
@ Absolute error = 2.0000000000e-2, Relative error = 2.0000000000e+0
----------------
##3       #:2   <== 3
##3       #:2   ==> 3.3
@ Absolute error = 3.0000000000e-1, Relative error = 1.0000000000e-1
##3       #:4   <== 9
##3       #:4   ==> 9.09
@ Absolute error = 9.0000000000e-2, Relative error = 1.0000000000e-2
##3       #:7   <== 1.0e-3
##3       #:7   ==> -1.0e-3
@ Absolute error = 2.0000000000e-3, Relative error = 2.0000000000e+0
----------------
##4       #:2   <== 4
##4       #:2   ==> 4.4
@ Absolute error = 4.0000000000e-1, Relative error = 1.0000000000e-1
##4       #:4   <== 16
##4       #:4   ==> 16.16
@ Absolute error = 1.6000000000e-1, Relative error = 1.0000000000e-2
##4       #:7   <== 1.0e-4
##4       #:7   ==> -1.0e-4
@ Absolute error = 2.0000000000e-4, Relative error = 2.0000000000e+0

+++  File "many_columns1" differs from file "many_columns2"
@end example

@noindent
you see that 0.08 and not 0.5 is taken as threshold value
for the comparison of the fields in fourth position.

Finally, if @option{-a} is not present on the command line,
then the default threshold value of zero applies to all comparisons
of numerical fields and any non null absolute difference
is considered as significant, unless some other option, 
for example @option{-P} or @option{-N}, makes @command{numdiff} ignore it.

The option @option{-r} can be used to make two numerical fields 
be considered equal as long as their relative difference does 
not exceed a certain threshold, which is specified by the argument
that follows the @option{-r} option.
As for the option @option{-a}, the argument of @option{-r}
can have several forms. These forms are the same accepted by
@option{-a} and have the same meanings, but the threshold value
applies to the relative difference, not to the absolute one.

The relative difference is normally defined in this way.
If @emph{n1} is a value from the file 
specified as first on the command line and @emph{n2} 
is the corresponding value from the second file,
then the absolute difference is given by the formula @emph{A=|n1-n2|}.
The relative difference @emph{R} is given by:

@itemize
@item @emph{R = 0} if @emph{n1} and @emph{n2} are equal,
@item @emph{Inf} (infinity) if @emph{n2} differs from @emph{n1} and
at least one of them is zero,
@item @emph{R = A/ min(|n1|, |n2|)} if @emph{n1} and @emph{n2} are
both non zero and @emph{n2} differs from @emph{n1}. @emph{min(|n1|, |n2|)}
denotes the minimum between the absolute value of @emph{n1}
and the absolute value of @emph{n2}.
@end itemize

@noindent
With this definition of relative difference it turns out that 
@emph{R(n2, n1) = R(n1, n2)}: the relative difference
does not change if you only change the ordering of the compared files
on the command line.

@anchor{Alternative formulas for the computation of the relative difference}
There are cases when this default definition of
relative error makes no sense. This can happen for instance
when one of the files is a sample file containing a list of expected data,
which could have been computed theoretically or come from experiments in a laboratory.
In this case it is more natural to define the relative difference
as the ratio between the absolute difference and the absolute
value of the number coming from the sample file.
If you use the option @option{-F} together with the argument 1
(or 2), then Numdiff always compute 
the relative difference as the ratio between the absolute difference and the absolute
value of the number from the first file (the second file, respectively).
More precisely, with @samp{-F 1} 
the relative difference @emph{R} is computed according to
these rules:
@itemize
@item @emph{R = 0} if @emph{n1} and @emph{n2} are equal,
@item @emph{Inf} (infinity) if @emph{n2} differs from @emph{n1} and
@emph{n1} is zero,
@item @emph{R = |n1-n2|/ |n1|} if @emph{n1} is not zero 
and @emph{n2} differs from @emph{n1}. 
@end itemize

@noindent
With @samp{-F 2} the rules become:
@itemize
@item @emph{R = 0} if @emph{n1} and @emph{n2} are equal,
@item @emph{Inf} (infinity) if @emph{n2} differs from @emph{n1} and
@emph{n2} is zero,
@item @emph{R = |n1-n2|/ |n2|} if @emph{n2} is not zero 
and @emph{n2} differs from @emph{n1}. 
@end itemize

@noindent
With the last two sets of rules it is not anymore true
that @emph{R(n2, n1) = R(n1, n2)}: the relative difference
changes, in the general case, together with the ordering of the files
on the command line.
As a simple example, suppose that @var{file1} and @var{file2} contain
@verbatim
1    9.9  0.5  440
@end verbatim

@noindent
and
@verbatim
1.2  8    0.51 400 
@end verbatim

@noindent
respectively. Then
@samp{numdiff @var{file1} @var{file2}} displays
@example
----------------
##1       #:1   <== 1
##1       #:1   ==> 1.2
@ Absolute error = 2.0000000000e-1, Relative error = 2.0000000000e-1
##1       #:2   <== 9.9
##1       #:2   ==> 8
@ Absolute error = 1.9000000000e+0, Relative error = 2.3750000000e-1
##1       #:3   <== 0.5
##1       #:3   ==> 0.51
@ Absolute error = 1.0000000000e-2, Relative error = 2.0000000000e-2
##1       #:4   <== 440
##1       #:4   ==> 400
@ Absolute error = 4.0000000000e+1, Relative error = 1.0000000000e-1

+++  File "file1" differs from file "file2"
@end example

@noindent
@samp{numdiff -F 1 @var{file1} @var{file2}}
prints
@example
----------------
##1       #:1   <== 1
##1       #:1   ==> 1.2
@ Absolute error = 2.0000000000e-1, Relative error = 2.0000000000e-1
##1       #:2   <== 9.9
##1       #:2   ==> 8
@ Absolute error = 1.9000000000e+0, Relative error = 1.9191919192e-1
##1       #:3   <== 0.5
##1       #:3   ==> 0.51
@ Absolute error = 1.0000000000e-2, Relative error = 2.0000000000e-2
##1       #:4   <== 440
##1       #:4   ==> 400
@ Absolute error = 4.0000000000e+1, Relative error = 9.0909090909e-2

+++  File "file1" differs from file "file2"
@end example

@noindent
the output of
@samp{numdiff -F 2 @var{file1} @var{file2}} is
@example
----------------
##1       #:1   <== 1
##1       #:1   ==> 1.2
@ Absolute error = 2.0000000000e-1, Relative error = 1.6666666667e-1
##1       #:2   <== 9.9
##1       #:2   ==> 8
@ Absolute error = 1.9000000000e+0, Relative error = 2.3750000000e-1
##1       #:3   <== 0.5
##1       #:3   ==> 0.51
@ Absolute error = 1.0000000000e-2, Relative error = 1.9607843137e-2
##1       #:4   <== 440
##1       #:4   ==> 400
@ Absolute error = 4.0000000000e+1, Relative error = 1.0000000000e-1

+++  File "file1" differs from file "file2"
@end example

@noindent
@samp{numdiff -F 1 -r 0.195 @var{file1} @var{file2}}
displays
@example
----------------
##1       #:1   <== 1
##1       #:1   ==> 1.2
@ Absolute error = 2.0000000000e-1, Relative error = 2.0000000000e-1

+++  File "file1" differs from file "file2"
@end example

@noindent
and finally, 
@samp{numdiff -F 2 -r 0.195 @var{file1} @var{file2}}
displays
@example
----------------
##1       #:2   <== 9.9
##1       #:2   ==> 8
@ Absolute error = 1.9000000000e+0, Relative error = 2.3750000000e-1

+++  File "file1" differs from file "file2"
@end example

@noindent

The option @option{-2} is only meaningful when the user 
specifies a non-zero tolerance threshold for both
absolute and relative difference. Without this option
@command{numdiff} considers two numerical fields equal 
as long as at least one between
absolute and relative difference does not exceed the
corresponding threshold.
With the option @option{-2} @command{numdiff} regards two numerical
fields as equal only if both absolute and relative difference do not exceed the
thresholds of tolerance specified for those fields.
For example, if @var{file1} contains the unique line
@verbatim
100
@end verbatim

@noindent
and @var{file2} the line
@verbatim
100.00012
@end verbatim

@noindent
then the output of the command @samp{numdiff @var{file1} @var{file2}}
will be

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

+++  File "@var{file1}" differs from file "@var{file2}"
@end example

@noindent
The output of the commands
@samp{numdiff -a 1.0e-4 @var{file1} @var{file2}} and
@samp{numdiff -r 1.0e-6 @var{file1} @var{file2}}
will be the same as above, but
@samp{numdiff -a 1.0e-4 -r 1.3e-6 @var{file1} @var{file2}} and
@samp{numdiff -a 1.3e-4 -r 1.0e-6 @var{file1} @var{file2}}
will print the message
@example

+++  Files "@var{file1}" and "@var{file2}" are equal
@end example

@noindent
since the relative difference is 1.2e-6 < 1.3e-6,
the absolute difference is 1.2e-4 < 1.3e-4, and
it is sufficient that one of them does not exceed
its tolerance threshold.

On the other hand, the commands
@samp{numdiff -a 1.0e-4 -r 1.3e-6 -2 @var{file1} @var{file2}} and
@samp{numdiff -a 1.3e-4 -r 1.0e-6 -2 @var{file1} @var{file2}}
will both print the message

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

+++  File "@var{file1}" differs from file "@var{file2}"
@end example

@noindent
since the option @option{-2} makes @command{numdiff} regard two values
as equal only if both absolute and relative difference do not exceed
the respective threshold of tolerance.

The option @option{-P} makes @command{numdiff} consider two values equal
whenever the second one, i.e. the value 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 value are
not greater than real and imaginary part of the first value, respectively. 

Finally, the option @option{-N} makes @command{numdiff} consider two values equal
whenever the second one, i.e. the value 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 value are
not less than real and imaginary part of the first value, respectively. 

The options @option{-B}, @option{-I}, @option{-l}, @option{-o}, @option{-h}, and
@option{-v} do not require further explanations.
The options @option{-l} and @option{-o} are only supplied
for the users of poorly designed operating systems, 
whose default shell does not allow the redirection of 
standard error and standard output.
The option @option{-I} has no effect on the outcome
of numerical comparisons but affects the action of
the filter, @pxref{Filtering}.

The option @option{-s} requires as argument a set of characters,
which will be taken as field delimiters.
It is better to quote the set of the delimiters, 
just as in the next examples:

@example
numdiff -s ' \t\n,;:.' @var{file1} @var{file2}
numdiff -s ' \t\n\r\f\v"\:;' @var{file1} @var{file2}
numdiff -s `` \t\n''' @var{file1} @var{file2}
@end example

@noindent
If you want to include in the set of delimiters also
some special characters, e.g. the @strong{blank}, then
you must quote it.
I recommend you to always use the single quote character 
(@verb{|'|}) to enclose the list of the delimiters, 
since in this way you will prevent
any substitution or handling of characters by the shell.

@noindent
@command{numdiff} recognizes and interprets
the following sequences of characters within the argument
passed to the option @option{-s}:

@itemize
@item @samp{\a}     alert (bell),
@item @samp{\b}     backspace,
@item @samp{\f}     form feed,
@item @samp{\n}     newline,
@item @samp{\r}     carriage return,
@item @samp{\s}     blank,
@item @samp{\t}     horizontal tab,
@item @samp{\v}     vertical tab,
@item @samp{\\}     backslash,
@item @samp{\@var{nnn}}   the eight-bit character whose value is the octal value @var{nnn} (one to three digits),
@item @samp{\x@var{HH}}   the eight-bit character whose value is the hexadecimal value @var{HH} (one or two digits). 
@end itemize

@noindent
Thus, by passing the string @samp{ \t\n,;:.} as argument
for the option @option{-s} one tells @command{numdiff} to use
as field delimiters the characters @strong{blank}, 
@strong{horizontal tab}, @strong{newline}, @strong{comma},
@strong{semicolon}, @strong{colon}, and @strong{dot}.
Passing @samp{ \t\n} as argument to the option @option{-s}
is the same as not using at all the option @option{-s}, since
@strong{blank}, @strong{horizontal tab}, and @strong{newline}
are the default field delimiters.

In the list of field delimiters the character @strong{backslash}
(@samp{\}) is always treated in a special way.
If it forms, combined with the subsequent character(s), one
of the escape sequences listed above, then it is
considered to be an escape character, and the whole escape sequence is 
decoded as shown above. Otherwise, the @strong{backslash} is just ignored. 

Therefore, the delimiters specified by the command line

@example
numdiff -s' \t\n\\\"' @var{file1} @var{file2}
@end example

@noindent
are @strong{blank}, @strong{horizontal tab}, @strong{newline},
@strong{backslash} and @strong{double quote}, since
@samp{\\} and @samp{\"} are interpreted by @command{numdiff}
as @samp{\} and @samp{"}.

Even if I have recommended to enclose the set of
delimiters in single quotes, there are 
cases in which you will be forced to use
the double quote character (@samp{"}) to enclose
the set of field delimiters, e.g. if the single
quote character is used itself as field delimiter, like
in one of the precedent examples.
However, you must take into account that in this case
the shell could make some substitutions on the command line
before executing @command{numdiff}.
For instance, if your shell is GNU bash, then (citing the man page of
GNU bash)
@quotation
Enclosing characters in double quotes preserves the literal value of 
all characters within the quotes, with the exception of @samp{$}, 
@samp{`}, and @samp{\}. 
The characters @samp{$} and @samp{`} retain their special 
meaning within double quotes. 
The backslash retains its special meaning only when followed by one of 
the following characters: @samp{$}, @samp{`}, @samp{"}, 
@samp{\}, or @strong{<newline>}. 
A double quote may be quoted within double quotes by preceding 
it with a backslash @enddots{}
The special parameters * and @@ have special meaning when in double quotes
@dots{}
@end quotation

@noindent
Therefore, if the set of delimiters is formed by @samp{ }, @samp{\t},
@samp{\n}, @samp{\} and @samp{"}, and you decide to enclose them
in double quotes, the @command{numdiff} command line should be

@example
numdiff -s'' \t\n\\\\\"'' @var{file1} @var{file2}
@end example

@noindent
and not

@example
numdiff -s'' \t\n\\\"'' @var{file1} @var{file2}
@end example

@noindent
In the latter case the shell would indeed replace the string

@samp{ \t\n\\\"} 

@noindent
by

@samp{ \t\n\"} 

@noindent
and then @command{numdiff} would take @samp{ }, @samp{\t}, @samp{\n} 
and @samp{"} as field delimiters.

@command{numdiff} requires the presence of the @strong{newline}
in the set of characters passed to @option{-s}. The absence
of the @strong{newline} in the set of delimiters causes the issue
of a warning message and the termination of the program.

If you run Numdiff with the option @option{-B} (@option{--binary})
on files created under MSDog/MSWindoze, then you should
put the @strong{carriage return} in the set of field delimiters.
Otherwise, this character would be included in all the fields
which stay 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 regarded as a numerical field
by @command{numdiff}, since @command{numdiff} would consider
the final @strong{carriage return} as part of the field, and
this one would be then qualified as non-numerical.

You can specify different delimiters for the two files to compare
by putting the prefix @samp{1:} or @samp{2:} in front of the
set of characters passed to @option{-s}.
If the argument of @option{-s} begins with @samp{1:}, the
characters after this prefix are used as field delimiters
only for the file passed as first on the command line.
Analogously, if the prefix is @samp{2:}, then the
characters after it are used as field delimiters only
for the file specified as second on the command line.
You can also provide an explicit set of
delimiters for just one of the files to compare,
in which case @command{numdiff} uses the default field
delimiters @strong{blank}, @strong{tab} and @strong{newline}
for the other file.
Therefore, with
@samp{numdiff -s '1:: \n' @var{file1} @var{file2}} 
the program will take @strong{colon}, @strong{blank}
and @strong{newline} as delimiters for @var{file1},
and @strong{blank}, @strong{tab} and
@strong{newline} as delimiters for @var{file2}.
The recommendations about quoting the set of delimiters
are valid also in presence of a prefix.

Starting from version 5.8 @command{numdiff} allows to specify
whole strings as field delimiters instead of single characters.
To this purpose the option @option{-D} is provided.
Assume that file @file{register1} and file @file{register2} contain
@verbatim
--A:    +1.0---
--B:    -2.0---
--C:    +3.0---
--D:    -4.0---
--E:    +5.0---
--F:    -6.0---
@end verbatim

@noindent
and
@verbatim
--a:    +1.1---
--b:    -2.2---
--c:    +3.3---
--d:    -4.4---
--e:    +5.5---
--f:    -6.6---
@end verbatim

@noindent
respectively. Assume in addition, you would like that the dashes
at the begin and at the end of every line are treated as delimiters and then
neglected during the line by line comparison. To obtain this you cannot just
specify the character @verb{|-|} (minus) as delimiter via the option 
@option{-s}: if you do it, the negative numbers appearing in the
two files will be treated as positive, since the minus sign will be regarded
as a delimiter. By means of the option @option{-D} you can tell @command{numdiff}
to consider the strings @verb{|--|} and @verb{|---|} as field delimiters,
but not the single character @verb{|-|}.
To see this in practice, look at the output of the command 
@samp{numdiff -D ': -- --- \s \n' register1 register2}:
@example
----------------
##1       #:1   <== A
##1       #:1   ==> a
@                                                     @@
##1       #:2   <== +1.0
##1       #:2   ==> +1.1
@ Absolute error = 1.0000000000e-1, Relative error = 1.0000000000e-1
----------------
##2       #:1   <== B
##2       #:1   ==> b
@                                                     @@
##2       #:2   <== -2.0
##2       #:2   ==> -2.2
@ Absolute error = 2.0000000000e-1, Relative error = 1.0000000000e-1
----------------
##3       #:1   <== C
##3       #:1   ==> c
@                                                     @@
##3       #:2   <== +3.0
##3       #:2   ==> +3.3
@ Absolute error = 3.0000000000e-1, Relative error = 1.0000000000e-1
----------------
##4       #:1   <== D
##4       #:1   ==> d
@                                                     @@
##4       #:2   <== -4.0
##4       #:2   ==> -4.4
@ Absolute error = 4.0000000000e-1, Relative error = 1.0000000000e-1
----------------
##5       #:1   <== E
##5       #:1   ==> e
@                                                     @@
##5       #:2   <== +5.0
##5       #:2   ==> +5.5
@ Absolute error = 5.0000000000e-1, Relative error = 1.0000000000e-1
----------------
##6       #:1   <== F
##6       #:1   ==> f
@                                                     @@
##6       #:2   <== -6.0
##6       #:2   ==> -6.6
@ Absolute error = 6.0000000000e-1, Relative error = 1.0000000000e-1

+++  File "register1" differs from file "register2"
@end example

@noindent
The argument @samp{-D ': -- --- \s \n'} instructs @command{numdiff} to
regard every occurrence of a colon (@verb{|:|}), of a blank (@verb{|\s|}),
of a newline (@verb{|\n|}), as well as every occurrence of the strings
@verb{|--|} and @verb{|---|} as field delimiters. The minus sign in
front of the negative numbers is then properly handled.

In general the argument to the option @option{-D} is a blank
separated sequence of one or more strings each of which contains
no blank. 
Thus, the general form of the argument to the option @option{-D} is
@example
@var{string1} @var{string2} ... @var{stringN}
@end example

@noindent
where @var{string1}, @var{string2}, and so on are sequences of one or
more characters (strings) containing no blank.

Mind that at least one of these strings must be @samp{\n}.
In addition, if a string contains the newline character, this
must be the only one: strings like @samp{#\n}, @samp{%%\n}, or
@samp{\s\n} are not allowed (entering such a string makes
the program terminate after issuing a warning message).

Since the blank character has a special meaning for the shell, if
the argument of @option{-D} is formed by two or more strings
it should be quoted either with a single (@samp{'}) 
or with a double quote (@samp{"}). 
Quoting is also adviced if one of the strings passed to @option{-D}
contains a character (or a sequence of characters)
having a special meaning for the shell.

For the usage of single and double quoting to delimit 
the argument of @option{-D} the same warnings and recommendations 
apply as for the argument of @option{-s}. 

If you want to set as delimiter a string which contains one or more blanks,
then you have to make use of the escape sequence @option{\s}, 
like in the example above: within the argument of @option{-D} the blank
character is always interpreted as a separator of adjacent delimiters.

More generally, when writing the argument of @option{-D} 
the same escape sequences are allowed as for the argument of @option{-s}.
This turns out to be particularly useful whenever a multibyte character
is used as delimiter in (one of) the files to compare.
As example consider the comparison between @file{ledger1}:
@example
             In                            Out

Jan      1200.00@euro{}                1000.00@euro{}
Feb       800.40@euro{}                 650.00@euro{}
Mar      1620.50@euro{}                1500.00@euro{}
Apr       760.00@euro{}                 900.00@euro{}

Total    4380.90@euro{}                4050.00@euro{}

Difference: +330.90@euro{}
@end example

@noindent
and @file{ledger2}:
@example
             In                            Out

Jan      1100.00@euro{}                1000.00@euro{}
Feb       800.40@euro{}                 750.00@euro{}
Mar      1620.50@euro{}                1700.00@euro{}
Apr       750.00@euro{}                 900.00@euro{}

Total    4270.90@euro{}                4350.00@euro{}

Difference: -79.10@euro{}
@end example

Since the Euro symbol is attached to all values, 
@command{numdiff} cannot compare them in the proper way 
if it is run with the default field delimiters, as
the output of the command @samp{numdiff ledger1 ledger2} shows:
@example
----------------
##3       #:2   <== 1200.00@euro{}
##3       #:2   ==> 1100.00@euro{}
@                                                     @@
----------------
##4       #:3   <== 650.00@euro{}
##4       #:3   ==> 750.00@euro{}
@                                                     @@
----------------
##5       #:3   <== 1500.00@euro{}
##5       #:3   ==> 1700.00@euro{}
@                                                     @@
----------------
##6       #:2   <== 760.00@euro{}
##6       #:2   ==> 750.00@euro{}
@                                                     @@
----------------
##8       #:2   <== 4380.90@euro{}
##8       #:2   ==> 4270.90@euro{}
@                                                     @@
##8       #:3   <== 4050.00@euro{}
##8       #:3   ==> 4350.00@euro{}
@                                                     @@
----------------
##10      #:2   <== +330.90@euro{}
##10      #:2   ==> -79.10@euro{}
@                                                     @@

+++  File "ledger1" differs from file "ledger2"
@end example

@noindent
The trick to perform the comparison in the proper way consists
in specifying the @euro{} symbol as field delimiter, in addition
to blank, horizontal tabulation and newline.
If @file{ledger1} and @file{ledger2} are encoded in UTF-8,
this can be done by using the option @option{-D} with the argument
@samp{\xE2\x82\xAC \s \t \n}, since the hexadecimal representation
of @euro{} in UTF8 is given by the byte sequence 0xE2 0x82 0xAC.
On my PC the output of the command 
@samp{numdiff -D '\xE2\x82\xAC \s \t \n' ledger1 ledger2}
shows that with such a choice of the delimiters @command{numdiff} performs
indeed a numerical comparison of the values contained in the two files:
@example
----------------
##3       #:2   <== 1200.00
##3       #:2   ==> 1100.00
@ Absolute error = 1.0000000000e+2, Relative error = 9.0909090909e-2
----------------
##4       #:3   <== 650.00
##4       #:3   ==> 750.00
@ Absolute error = 1.0000000000e+2, Relative error = 1.5384615385e-1
----------------
##5       #:3   <== 1500.00
##5       #:3   ==> 1700.00
@ Absolute error = 2.0000000000e+2, Relative error = 1.3333333333e-1
----------------
##6       #:2   <== 760.00
##6       #:2   ==> 750.00
@ Absolute error = 1.0000000000e+1, Relative error = 1.3333333333e-2
----------------
##8       #:2   <== 4380.90
##8       #:2   ==> 4270.90
@ Absolute error = 1.1000000000e+2, Relative error = 2.5755695521e-2
##8       #:3   <== 4050.00
##8       #:3   ==> 4350.00
@ Absolute error = 3.0000000000e+2, Relative error = 7.4074074074e-2
----------------
##10      #:2   <== +330.90
##10      #:2   ==> -79.10
@ Absolute error = 4.1000000000e+2, Relative error = 5.1833122630e+0

+++  File "ledger1" differs from file "ledger2"
@end example

If @file{ledger1} and @file{ledger2} had been saved using
a multi-byte encoding different from UTF-8, then the sequence
of bytes which corresponds to @euro{} in this other encoding should have been
passed to @option{-D}.

As for @option{-s}, with @option{-D} you can specify different delimiters 
for the two files to compare by means of the prefixes @samp{1:} and @samp{2:},
like in @samp{numdiff -D '1:\t \n' -D '2: -- \s \n' first_file second_file}.
The recommendations about quoting the set of delimiters
are valid also in presence of a prefix.
Mind that, if you provide an explicit set of delimiters for just one of the 
files to compare, @command{numdiff} uses the default field
delimiters @strong{blank}, @strong{tab} and @strong{newline}
for the other file.

If you run Numdiff with the option @option{-B} (@option{--binary})
on files created under MSDog/MSWindoze, you should 
always include the character @samp{\r} in the set of field delimiters.

The option @option{-s} and @option{-D} can appear more than once
on the command line. In case of conflicts, @command{numdiff}
assumes as set of delimiters for a given file the one
specified last on the command line.

By means of the option @option{-#} the user can set the number of digits 
in the significands used in multiple precision arithmetic.
The default value is 35, the largest admissible value is 180.
If @command{numdiff} has been linked against the 
GNU Multiple Precision Arithmetic Library (also called GNU MP), 
then the precision it uses is typically higher
than the specified one. On my machine the actual value
of the precision is 20 if the user requests a value between 0 and 20,
30 if the user specifies a precision between 21 and 30,
40 for a user-specified value between 31 and 40, and so on.
Anyway, the actual precision is never less than
the one requested by the user.

@noindent
Take into account that an higher precision makes the
execution of @command{numdiff} slower. This is particularly
true if @command{numdiff} is not using the computational routines
from the GNU MP library and the files to compare contain a lot of numerical fields.
In addition, mind that @command{numdiff} truncates
the value of a numerical field if it has @i{too much} digits with respect
to the current precision. To be precise, denoted by
@var{P} the current value of the precision, the following
rules apply.
@itemize
@item If @command{numdiff} has been built with
its own internal support for multiple precision arithmetic, then
@itemize
@item if a number is written in ordinary decimal notation, @command{numdiff}
will consider, in addition to all digits of the integer part, only
the first @var{P} digits of the fractional part;
@item if a value is written in scientific notation, then @command{numdiff}
will only consider the first @var{P} digits of the fractional part
of the mantissa.
@end itemize
@item If @command{numdiff} uses the routines from the GNU MP library
to perform its computations, the value of a numerical
field is first translated into scientific notation and then 
only the first @var{P} digits of the fractional part
of the mantissa are considered.
@end itemize

@noindent
You can find out whether your local version of @command{numdiff}
is relying on GNU MP or not by executing the command @samp{numdiff -v}.
If @command{numdiff} uses GNU MP, then this command will display
the following message or similar (possibly translated
into your mother language) among other information:
@example
The software has been linked against
the GNU Multiple Precision Arithmetic Library,
version number 4.2.4.
@end example

@noindent
If @command{numdiff} does not rely on GNU MP, then
the displayed message will be (up to translation into
your mother language)
@example
The software has been built with
its own internal support for multiple precision arithmetic.
@end example

@noindent
By means of the option @option{-c} the user can qualify
a string as a symbol or name for a currency. 
The string passed as argument to this option is ignored
whenever it appears immediately before the first digit of a number.
In particular, the presence of this string does not prevent a
field from being considered of numeric type. By prefixing
the argument of @option{-c} with @samp{1:} or @samp{2:}
it is possible to set the currency name/symbol only
for one of the compared files, or to specify different
currency names for the two files.
As example we consider the files @file{money1}:
@verbatim
	Profits			Expenses

	+$430.10		-$300.50
	+$750.20		-$550.02
	+$876.24		-$720.00

Totals  $2056.54               -$1570.52
@end verbatim

@noindent
and @file{money2}:
@verbatim
	Profits			Expenses

	USD430.10		-USD300.50
	USD750.20		-USD550.02
	USD876.24		-USD720.15
	
Totals    2056.54                 -1570.67
@end verbatim
To properly compare them, we have to tell @command{numdiff}
that @samp{$} and @samp{USD} are the currency symbols for
@file{money1} and @file{money2}, respectively.
This can be achieved by @samp{-c 1:$} and @samp{-c 2:USD}.
The output of the command @samp{numdiff -c 1:$ -c 2:USD money1 money2} is
@example
----------------
##5       #:2   <== -$720.00
##5       #:2   ==> -USD720.15
@ Absolute error = 1.5000000000e-1, Relative error = 2.0833333333e-4
----------------
##7       #:3   <== -$1570.52
##7       #:3   ==> -1570.67
@ Absolute error = 1.5000000000e-1, Relative error = 9.5509767466e-5

+++  File "money1" differs from file "money2"
@end example

@noindent
as it is reasonable to expect. 

The argument of @option{-c} may also be
a multi-byte string, in particular a multi-byte string encoded in UTF-8. 
If your locale uses UTF-8 as encoding, you can write the argument directly
in this form. For instance, you can write @samp{-c @euro{}}
to specify as currency name the Euro symbol.
If your locale does not use UTF-8 as encoding, or UTF-8 is not
supported by your terminal, you may still write an
UTF-8 encoded string as a multi-byte string by specifying each single byte
of every (multi-byte) character.
To this purpose you can use the same octal and hexadecimal escape sequences
recognized by the options @option{-s} and @option{-D}, but then the argument
of @option{-c} has to be quoted to avoid the interpretation of the hexadecimal
escape sequences by the shell.

For example, if the files to compare are encoded in UTF-8,
you can set @euro{} as currency name by
adding @samp{-c '\xE2\x82\xAC'} to the command line of
@command{numdiff}, since the hexadecimal representation
of @euro{} in UTF-8 is given by the sequence of bytes
0xE2 0x82 0xAC.

To see this in practice, if @file{euro1} contains the text
@example
	Profits			       Expenses

	+@euro{}430.10		      -@euro{}300.50
	+@euro{}750.20		      -@euro{}550.02
	+@euro{}876.24		      -@euro{}720.00
@end example

@noindent
and @file{euro2} the text
@example
	Profits			       Expenses

	+@euro{}430.10		      -@euro{}300.00
	+@euro{}750.20		      -@euro{}550.02
	+@euro{}876.00		      -@euro{}720.00
@end example

@noindent
then the report of @samp{numdiff -c '\xE2\x82\xAC' euro1 euro2} is
@example
----------------
##3       #:2   <== -@euro{}300.50
##3       #:2   ==> -@euro{}300.00
@ Absolute error = 5.0000000000e-1, Relative error = 1.6666666667e-3
----------------
##5       #:1   <== +@euro{}876.24
##5       #:1   ==> +@euro{}876.00
@ Absolute error = 2.4000000000e-1, Relative error = 2.7397260274e-4

+++  File "euro1" differs from file "euro2"
@end example

Please consider that @option{-c}
is only provided to let @command{numdiff} regard
a field as numeric also in presence of a currency name
immediately before its first digit: @command{numdiff}
does not know anything about currencies and can not perform any
kind of conversion between them. 
In addition, mind that the number after the currency name
can be written in any format, not only in financial notation.
@command{numdiff} can even cope with the currency name
when it appears in a complex number. For example,
with @samp{-c EUR} @command{numdiff} considers
@verb{|+EUR12-EUR0.24i|} and @verb{|+12-0.24i|}
as equal.

The options @option{-d}, @option{-t}, @option{-g}, 
@option{-p}, @option{-n}, @option{-e} and @option{-i} can be used
to instruct @command{numdiff} about the numeric formats used in the
files which it is going to compare.
Since the two files to compare do not have to adopt the same numeric format,
@command{numdiff} allows to specify different numeric formats for them.
Each of the options @option{-d}, @option{-t}, @option{-g}, 
@option{-p}, @option{-n}, @option{-e}, and @option{-i}
can have as argument one or two (single-byte) characters, in particular 
one or two digits if the option is @option{-g}. In the first case
the argument refers to both files to compare, in the second case
the first character is for the file specified
first on the command line, the second character for
the file specified last.
For instance, the option @option{-d} can be used to
tell @command{numdiff} which character(s) is(are) 
used to indicate the decimal point in the two files to compare. 
If you give the command
@samp{numdiff -d_ @var{file1} @var{file2}},
then @command{numdiff} will understand that both in @var{file1} and in @var{file2}
the character @strong{underscore} (@samp{_}) is used in place
of the default one (@samp{.}) to indicate
the position of the decimal point in the numerical values.
But if the command is
@samp{numdiff -d_: @var{file1} @var{file2}},
then @command{numdiff} will understand that the decimal point
is indicated by the character @strong{underscore} in @var{file1},
and by @strong{colon} (@samp{:}) in @var{file2}.

If you omit to use one of the options
@option{-d}, @option{-t}, @option{-g}, 
@option{-p}, @option{-n}, @option{-e}, and @option{-i}, then the corresponding
attribute will take its default value, @pxref{Default Numeric Format}. 

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

It is not possible to set the decimal point, the thousands separator,
the positive sign, the negative sign, the
prefix for decimal exponent or the
symbol of the imaginary unit in such a way that, for a same file,
two or more of these characters come out to be equal.
This rule also applies if you miss/omit to explicitly select
a symbol through the appropriate option.
For instance, the command
@samp{numdiff -d,. @var{file1} @var{file2}}
will make @command{numdiff} abnormally terminate after printing
the error message:

@example
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 = `,'
Leading positive sign = `+'
Leading negative sign = `-'
Prefix for decimal exponent = `e'
Symbol used to denote the imaginary unit = `i'
@end example

@noindent
With the option @option{-d} we have told @command{numdiff}
that in the first file the decimal point is indicated by the character
@strong{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. @strong{comma}, for both files to compare.
In this way we have implicitly told that in
@var{file1} the character @strong{comma} represents both decimal point
and thousands separator. Since this is not reasonable, @command{numdiff}
refuses to work.
To avoid this problem it would be sufficient to
set explicitly the thousands separator
by means of the option @option{-t}:
@samp{numdiff -d,. -t., @var{file1} @var{file2}}.
Of course, we assume here that the decimal point
and the thousands separator are represented in @var{file1}
by @strong{comma} and @strong{dot} respectively, in
@var{file2} by @strong{dot} and @strong{comma}.

I strongly suggest you, whenever you write a file, to 
avoid using the same symbol for two different things (like would be using
@strong{comma} for both decimal point and thousands
separator), it is nonsense.

At last, it is possible (but silly) to specify
as argument for the options @option{-d}, @option{-t}, @option{-g}, 
@option{-p}, @option{-n}, @option{-e}, or @option{-i}
one of the characters used as delimiters in the files to compare.
@command{numdiff} does not complain, but you have
to consider that the program first uses the set of field delimiters
to split the files into fields and only afterwards, when it has to distinguish
between numerical and non-numerical fields, it takes
into account the numeric formats specified for the two files.
To prevent conflicts, you should then avoid to specify as argument for
the options @option{-d}, @option{-t}, @option{-g}, 
@option{-p}, @option{-n}, @option{-e}, or @option{-i} a character
which is also used as field delimiter. 
As a general rule, in writing a file you should avoid using the same symbol
to mean two different things.
What we have said also explains why the argument
of the option @option{-c} should never contain field delimiters.

@anchor{Restriction of the comparison to particular fields}
The option @option{-X} can be used
to restrict the comparison between files to a certain
group of fields.
@anchor{Use of the option -X}
This option requires as argument a range of positive integer values
or eventually just one positive integer number. The argument indicates
the position(s) of the fields that @command{numdiff} has to ignore.
Remember that the fields of a line are numerated starting 
from the left hand of the line
and proceeding towards the right hand.

The argument passed to @option{-X} can start with a prefix,
which must be either @samp{1:} or @samp{2:}.
@samp{1:} refers to the file passed as first on the command line,
@samp{2:} to the file specified as second.
With the prefix @samp{1:} only the fields of the first file
corresponding to the specified position(s) are ignored.  
Similarly, you have to use the prefix @samp{2:}
if you want to ignore only fields from the second file.

The option @option{-X} can appear more times on the command line,
in which case @command{numdiff} will ignore all fields
located in the positions so specified.
Some examples can clarify the use of ranges and prefixes.
If the file @file{List1} contains the data
@verbatim
* a  1    1     1     1
* b  2    2     2     2
* c  3    3     3     3
* d  4    4     4     4
* e  5    5     5     5
@end verbatim

@noindent
and @file{List2} the data
@verbatim
     1    1.1  1.01   A  1.001  1.0001
     2    2.2  2.02   B  2.002  2.0002
     3    3.3  3.03   C  3.003  3.0003
     4    4.4  4.04   D  4.004  4.0004
     5    5.5  5.05   E  5.005  5.0005
@end verbatim

@noindent
then the output of @samp{numdiff -X 1:1-2 -X 2:4 -X 1:6 -X 2:5-6 List1 List2} is
@example
----------------
##1       #:4   <== 1
##1       #:2   ==> 1.1
@@ Absolute error = 1.0000000000e-1, Relative error = 1.0000000000e-1
##1       #:5   <== 1
##1       #:3   ==> 1.01
@@ Absolute error = 1.0000000000e-2, Relative error = 1.0000000000e-2
----------------
##2       #:4   <== 2
##2       #:2   ==> 2.2
@@ Absolute error = 2.0000000000e-1, Relative error = 1.0000000000e-1
##2       #:5   <== 2
##2       #:3   ==> 2.02
@@ Absolute error = 2.0000000000e-2, Relative error = 1.0000000000e-2
----------------
##3       #:4   <== 3
##3       #:2   ==> 3.3
@@ Absolute error = 3.0000000000e-1, Relative error = 1.0000000000e-1
##3       #:5   <== 3
##3       #:3   ==> 3.03
@@ Absolute error = 3.0000000000e-2, Relative error = 1.0000000000e-2
----------------
##4       #:4   <== 4
##4       #:2   ==> 4.4
@@ Absolute error = 4.0000000000e-1, Relative error = 1.0000000000e-1
##4       #:5   <== 4
##4       #:3   ==> 4.04
@@ Absolute error = 4.0000000000e-2, Relative error = 1.0000000000e-2
----------------
##5       #:4   <== 5
##5       #:2   ==> 5.5
@@ Absolute error = 5.0000000000e-1, Relative error = 1.0000000000e-1
##5       #:5   <== 5
##5       #:3   ==> 5.05
@@ Absolute error = 5.0000000000e-2, Relative error = 1.0000000000e-2

+++  File "List1" differs from file "List2"
@end example

@noindent
Numdiff cuts off from @file{List1} the fields in the positions 1, 2 and 6
and from @file{List2} the fields in the positions 4, 5 and 6.
In this way it compares the third, fourth and fifth field 
of every line of
@file{List1} with the first, second and third field respectively
of the corresponding line of @file{List2}.
An equivalent form of the command
@samp{numdiff -X 1:1-2 -X 2:4 -X 1:6 -X 2:5-6 List1 List2}
is given by
@samp{numdiff -X 1:1-2 -X 2:4-5 -X 6 List1 List2} :
since the sixth field is cut off from both files, we can
refer to it without a prefix.

As you can see, you can specify a range of fields
by using the notation @samp{@var{m}-@var{n}},
where @var{m} and @var{n} are the field numbers
of the first and of the last field in the range.
It is even possible to use range expressions like
@samp{@var{m}-} or @samp{-@var{n}}. The first
expression corresponds to all fields starting from
the @var{m}th one (inclusive) till to the end of line,
the second selects all fields from the first one
till to the @var{n}th one (inclusive).
Therefore the command
@samp{numdiff -X 1:1-2 -X 2:4 -X 1:6 -X 2:5-6 List1 List2}
is equivalent to
@samp{numdiff -X 1:-2 -X 2:4 -X 1:6 -X 2:5- List1 List2}
and to
@samp{numdiff -X 1:-2 -X 1:6 -X 2:4- List1 List2}.

Mind that, while writing a specification for the option @option{-X},
the largest field number you can use is 32768.

If you employ the option @option{-X} the exit status of @command{numdiff} 
reflects the outcome of the restricted comparison.
For instance, the exit status of @samp{numdiff -X 8- @var{file1} @var{file2}}
is 1 only if @command{numdiff} has found a difference
in the first seven fields of @var{file1} and @var{file2}.
If the two files differ only in the fields after the seventh one,
then @command{numdiff} ends with a zero exit status.

Going back to the example with @file{List1} and @file{List2},
the output of
@samp{numdiff -X 1:1-2 -X 1:4- -X 2:2- List1 List2} is
@example

+++  Files "List1" and "List2" are equal
@end example

@noindent
since every field of @file{List1} at position 3 is equal
to the first field in the corresponding line of @file{List2}.
The exit code returned by the program to the shell is in this case zero.

The options @option{-z}, @option{-Z}, @option{-m}, @option{-H},
@option{-f}, and @option{-T} influence the action of the filter  
and their use is then described later, @ref{Filtering}.
Care that @option{-z} and @option{-Z} need both an argument in the same
form required by @option{-X}.

Since version 5 Numdiff accepts also long options to conform to
the GNU standards. For example, now it is possible to use
@samp{--separators='\n\t %'} or @samp{--separators '\n\t %'} 
instead of using @samp{-s '\n\t %'}.

The long options, which start all with two dashes,
are listed at the beginning of this chapter, each one near to
the corresponding short option.

The argument of a long option may or may not be preceded
by the @verb{|=|} sign. The only exceptions are the options
@option{--test-filter} and @option{--overview},
for which the presence of the @verb{|=|} before the argument is mandatory.
Thus, @samp{--test-filter=60} is correct while
@samp{--test-filter 60} is not accepted.

@node ndselect, Invoking ndselect, Invoking numdiff, Top
@chapter Selecting lines and fields for the comparison

@cindex ndselect (introduction to its use)
@cindex Tools

Together with the version 5.x of Numdiff is shipped the program @command{ndselect}.
Originally, 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 @file{list1}
contains the values of the square root, rounded to the 20th decimal digit,
for all integer numbers between 12 and 24:
@verbatim
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
@end verbatim

@noindent
File @var{list2} contains @emph{suitable} approximations of the square root 
only for the numbers between 12 and 21 which are multiple of 3:

@verbatim
12       3.46410162002945508100
15       3.87298387096774193548
18       4.24264705882352941176
21       4.58260869565217391304
@end verbatim

@noindent
These approximations could have been obtained
by using the famous Heron's algorithm: given an approximation
@code{a} for the square root of a number @code{x}, a better
approximation is computed by using the formula @code{a := 0.5 * (x/a + a)}.
What we want now is to understand by means of @command{numdiff} 
how good the approximations contained in file @var{list2} are.
Unfortunately, we cannot execute directly the command
@samp{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 @file{list1} in a text editor and remove from this file
all lines but the ones related to the numbers 12, 15, 18, and 21. 
This approach is practicable since we have to remove only a few lines:
one can easily figure out how boring and inefficient would be to manually
remove hundreds or thousands of lines from a file.

An expert GNU user would suggest that it is
possible to automate this removal by using the well known utilities
@command{head} and @command{sed}, in this particular case
@samp{head -n 10 list1 | sed -n -e '1~3 p' > List1}.
A quick explanation for the ones who do not know how to use @command{head}
and @command{sed}: the previous command extracts from
@file{list1} the first 10 lines, namely the lines containing the square roots 
of the numbers from 12 to 21, then picks every third line starting
from the first one to select only the lines related to 12, 15, 18, and 21.
Finally, these lines are printed to the file @file{List1},
which then looks like:
@verbatim
12       3.46410161513775458705
15       3.87298334620741688518
18       4.24264068711928514641
21       4.58257569495584000659
@end verbatim 

Once obtained @file{List1}, we can perform the comparison between 
the values we are interested in by means of @samp{numdiff List1 list2} .
Unfortunately, this trick only works if you have installed the GNU version
of @command{sed} which, as far as I know, is the only one
providing the extension @var{first~step} to specify line addresses.
This is why I decided to implement @command{ndselect}, which allows to
obtain the same result as above with the simpler command
@samp{ndselect -b 1 -e 10 -s 3 list1 > List1}. 

The meaning of the arguments passed to the options @option{-b},
@option{-e}, and @option{-s} is the following: we tell
@command{ndselect} to print every third line of file @file{list1}
(the option @option{-s} specifies the step)
starting from the first one (the option @option{-b} specifies the beginning) 
and ending within the tenth one possibly inclusive 
(the option @option{-e} specifies the end). 
Because of the presence of the redirection operator @code{>},
the previous command sends to the file @file{List1} 
what @command{ndselect} would print to the screen (standard output).

Since version 5.6 @command{ndselect} can also be used to select
particular fields of a file.
Instead of printing all fields of every line, you may want to print
indeed only the fields at particular positions.
To do this you can employ the option @option{-F} to
indicate the position of the first field to print,
the option @option{-L} to indicate the position of the last field that
can be printed, the option @option{-I} to set the increment
when selecting the fields. In addition, the option @option{-S}
can be used to specify a set of field delimiters different from the
default one (which consists of @strong{blank}, @strong{tab} and 
@strong{newline}). As for @command{numdiff}, the field
delimiters are used to split the input lines into fields.

The option @option{-S} of @command{ndselect}
recognizes and accepts the same escape sequences of
@command{numdiff} options @option{-s}, @option{-D}, and @option{-c}.

As example consider the selection of the even fields between
the second and the sixth one inclusive from the file
@file{many_many_columns}, whose contents are shown here:
@verbatim
A |   I | 1.1 |   1.08  |   1.01  |  0.1  |   11.011    |    -1.0e-1  
B |  II | 2.2 |   2.16  |   4.04  |  0.4  |   24.024    |    -1.0e-2  
C | III | 3.3 |   3.24  |   9.09  |  0.9  |   39.039    |    -1.0e-3  
D |  IV | 4.4 |   4.32  |  16.16  |  1.6  |  416.039    |    -1.0e-4  
E |   V | 5.5 |   5.40  |  25.25  |  2.5  |  525.416    |    -1.0e-5  
F |   # |  #  |    #    |    #    |   #   |     #       |      #
@end verbatim

@noindent
This selection can be accomplished by means of the command
@samp{ndselect -S '| \t\n' -F 2 -L 6 -I 2 many_many_columns}, whose
output shows only the selected fields:
@example
I | 1.08  |   0.1
II | 2.16  |   0.4
III | 3.24  |   0.9
IV | 4.32  |  1.6
V | 5.40  |  2.5
# |  #    |    #
@end example

@noindent
Of course, you can also select particular fields of particular lines,
as shown by the output of the command
@samp{ndselect -S '| \t\n' -b 1 -e 5 -s 3 -F 2 -L 6 -I 2 many_many_columns}:
@example
I | 1.08  |   0.1
IV | 4.32  |  1.6
@end example

By default, @command{ndselect} reuses the delimiters found in the input
lines while writing the selected fields to the standard output.
You can specify a custom separator by means of the option @option{-O}.
This one recognizes and accepts the same escape sequences of
@command{numdiff} options @option{-s}, @option{-D}, and @option{-c}.
For example,
@samp{ndselect -S '| \t\n' -b 1 -e 5 -s 3 -F 2 -L 6 -I 2 -O '\t\t' many_many_columns}
puts two horizontal tabulations after every printed field:
@verbatim
I		1.08		0.1		
IV		4.32		1.6		
@end verbatim

Even if the implementation of a filter in @command{numdiff} and the addition
of the option @option{-X} have made @command{ndselect} much less useful than
in the past, this tool can still be used to handle some special cases.
In addition, it can be used as a filter for other programs than @command{numdiff}.
The complete synopsis of @command{ndselect} can be found in the
next chapter. 

@node Invoking ndselect, Filtering, ndselect, Top
@chapter Invoking ndselect

@cindex Invoking ndselect
@cindex Options, command line (ndselect)
@cindex Command line options for ndselect
@cindex Synopsis (ndselect)
@cindex Diagnostics (ndselect)

@noindent
@strong{SYNOPSIS}

@example
   ndselect -h|--help|-v|--version 
@end example
or
@example
   ndselect [-b @var{N}][-e @var{N}][-s @var{N}][-F @var{N}][-L @var{N}][-I @var{N}][-S @var{IFS}][-D @var{DELIMS}]
   [-O @var{OSEP}][-x][-l @var{PATH}][-o @var{PATH}][@var{FILE}]
@end example

@noindent
where @var{FILE} is the name of the file to read from.

In the first case @command{ndselect} prints a 
short help or/and version number, Copyright, License notice, 
and NO-Warranty disclaimer.
In the second case @command{ndselect} prints to the standard output 
a subset of lines and fields from @var{FILE}.
The complete path of @var{FILE} should be given,
a directory name is not accepted.
If no input file is specified, the program reads from the standard input.

@noindent
@strong{OPTIONS}

@table @option
@item -b, --beginning, --start=@var{N}
Set to @var{N} the number of the first line to print
(The default behavior is to start with line number 1)

@item -e, --end=@var{N}
Set to @var{N} the number of the last line that can be printed
(The default behavior is to arrive till to the end of the file)

@item -s, --step=@var{N}
Set to @var{N} the increment to use when selecting the lines to print
(The default value for the increment is 1)

@item -F, --first-field=@var{N}
Set to @var{N} the number of the first field to print
(The default behavior is to start with field number 1)

@item -L, --last-field=@var{N}
Set to @var{N} the number of the last field that can be printed
(The default behavior is to arrive till to the end of every line)

@item -I, --increment=@var{N}
Set to @var{N} the increment to use when selecting the fields to print
(The default value for the increment is 1)

@item -S, --separators=@var{IFS}
Specify the set of characters to use as delimiters
while splitting the input lines into fields
(The default set of delimiters is space, tab and newline)

@item -D, --delimiters=@var{DELIMS}
Specify the set of strings to use as delimiters
while splitting the input lines into fields
(The default set of delimiters is space, tab and newline)

@item -O, --output-separator=@var{OSEP}
Specify the string to use as separator
while writing the selected fields to the standard output
(The default behavior consists in reusing the delimiters found in the input lines)

@item -x, --omit-empty-lines
Do not print empty lines

@item -l, --warnings-to=@var{PATH}
Redirect warning and error messages from stderr 
to the indicated file

@item -o, --output=@var{PATH}
Redirect output from stdout to the indicated file

@item -h, --help
Show this help message

@item -v, --version
Show version number, Copyright, Distribution Terms and NO-Warranty
@end table

@noindent
Passing 0 as argument to the option @option{-L} or to @option{-e} 
is equivalent to omit this option and leave enabled the default behavior
(which consists in scanning till to the end of the line and of
the file, respectively). 

@noindent
@strong{DIAGNOSTICS}

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

@noindent
As @command{numdiff} does, since version 5 also @command{ndselect}
accepts long options. Thus, instead of @samp{ndselect -b 1 -e 10 -s 3 list1 > List1}
you can write @samp{ndselect --start=1 --end=10 --step=3 list1 > List1}.

The usage of the option @option{-D} is the same as for @command{numdiff}.
The option @option{-S} corresponds to the option @option{-s} of @command{numdiff}.

@node Filtering, Warnings, Invoking ndselect, Top
@chapter Using the filter of numdiff

@cindex Filter

Since version 5 you can activate a filter
when launching @command{numdiff} to make the program appropriately compare
the given files even if they do not have the same structure.
Recalling the example of chapter 6,
if you run the command @command{numdiff -z 2- -V list1 list2}
you obtain the following result:
@example

----------------
##1       <== 12       3.46410161513775458705
##1       ==> 12       3.46410162002945508100

##1       #:2   <== 3.46410161513775458705
##1       #:2   ==> 3.46410162002945508100
@ Absolute error = 4.8917004940e-9, Relative error = 1.4121122985e-9
----------------
##2       <== 13       3.60555127546398929312
          ==>

----------------
##3       <== 14       3.74165738677394138558
          ==>

----------------
##4       <== 15       3.87298334620741688518
##2       ==> 15       3.87298387096774193548

##4       #:2   <== 3.87298334620741688518
##2       #:2   ==> 3.87298387096774193548
@ Absolute error = 5.2476032505e-7, Relative error = 1.3549253331e-7
----------------
##5       <== 16       4
          ==>

----------------
##6       <== 17       4.12310562561766054982
          ==>

----------------
##7       <== 18       4.24264068711928514641
##3       ==> 18       4.24264705882352941176

##7       #:2   <== 4.24264068711928514641
##3       #:2   ==> 4.24264705882352941176
@ Absolute error = 6.3717042443e-6, Relative error = 1.5018250929e-6
----------------
##8       <== 19       4.35889894354067355224
          ==>

----------------
##9       <== 20       4.47213595499957939282
          ==>

----------------
##10      <== 21       4.58257569495584000659
##4       ==> 21       4.58260869565217391304

##10      #:2   <== 4.58257569495584000659
##4       #:2   ==> 4.58260869565217391304
@ Absolute error = 3.3000696334e-5, Relative error = 7.2013423303e-6
----------------
##11      <== 22       4.69041575982342955457
          ==>

----------------
##12      <== 23       4.7958315233127195416
          ==>

----------------
##13      <== 24       4.89897948556635619639
          ==>


+++  File "list1" differs from file "list2"
@end example

Numdiff has recognized that the lines of @file{list1}
with the square roots for the numbers
13, 14, 16, 17, 19, 20, 22, 23, and 24
have been deleted from @file{list2}.
The numerical comparison has been done by coupling each line of @file{list2}
with the line of @file{list1} which displays the square root for the same
integer value. The output obtained running
the filter of Numdiff via @command{numdiff -f -z 2- list1 list2}
confirms this:
@example
12       3.46410161513775458705         12       3.46410162002945508100
13       3.60555127546398929312      <
14       3.74165738677394138558      <
15       3.87298334620741688518         15       3.87298387096774193548
16       4                           <
17       4.12310562561766054982      <
18       4.24264068711928514641         18       4.24264705882352941176
19       4.35889894354067355224      <
20       4.47213595499957939282      <
21       4.58257569495584000659         21       4.58260869565217391304
22       4.69041575982342955457      <
23       4.7958315233127195416       <
24       4.89897948556635619639      <


+++  File "list1" differs from file "list2"
@end example

If you compare the command
@command{numdiff -z 2- -V list1 list2} with the one
used for the files @file{bill1} and
@file{bill2}, @pxref{command},  you surely notice that the filter
has been invoked in different ways, first
with @option{-z @@} and then with @option{-z 2-}.

The @i{synchronization} procedure used by the filter
is based on @i{blurring} and byte-by-byte comparison.
The options @option{-z} and @option{-Z} are used
to select which fields from which file have to
be blurred. They take both an argument in the
same form requested by @option{-X}, @pxref{Use of the option -X},
but accept additionally the special value @samp{@@}
as abbreviation for the range of fields @samp{1-}.
Thus, the specifications @samp{1:@@}, @samp{2:@@} and @samp{@@}
are used to mean all fields of the first file,
of the second one or of both, respectively.   

Employing @option{-z} and @option{-Z} in the right way
is extremely important to let the filter work as desired.
For instance, @command{numdiff -f -z @@ list1 list2}
matches the lines of @file{list1} and @file{list2}
in the same wrong way
@example
12       3.46410161513775458705         12       3.46410162002945508100
13       3.60555127546398929312         15       3.87298387096774193548
14       3.74165738677394138558         18       4.24264705882352941176
15       3.87298334620741688518         21       4.58260869565217391304
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      <


+++  File "list1" differs from file "list2"
@end example

@noindent
as Numdiff would do without employing the filter.

It is essential then to understand what @i{blurring a field} means
and how the filter uses blurring to match the lines
of the files to compare.

After reading the files the filter removes from each of them
(from their images in the memory, actually) 
all the fields selected by the option
@option{-X}, then it replaces each of the fields that
have to be blurred by a special character.
This special character is the same for both files
and it is so chosen that it cannot appear in
the text. Blurring a field means to replace
it by this sort of @i{place card}.

After doing this, the filter converts all remaining numerical
fields to a standard format and then compares
the files byte by byte neglecting the field delimiters.
This comparison is just used to establish which
lines of the first file are not present in the second,
which lines of the second file are missing in the first one,
and how to match the remaining lines to create
a one-to-one correspondence.

Only at this point @command{numdiff} inspects each couple of corresponding lines,
splits the two lines into the constituent fields, and
neglecting those ones eventually specified through the option @option{-X}
compares corresponding fields as it is supposed to do, performing
a numerical comparison whenever the fields are both legal numerical values.

Blurring the right fields is essential to appropriately match the lines
from the two files before doing any numerical comparison.
Without blurring, the numerical fields could prevent the filter of 
@command{numdiff} from an appropriate matching of the lines
by creating confusion with their (maybe small) numeric differences.

Blurring can be of two types, conditional or unconditional. 
The blurring is conditional if it has to be performed only for fields 
which turn out to be legal numerical values.
The arguments of the option @option{-z} indicate which
fields of which file have to be blurred @strong{under the condition that 
they are recognized as numeric fields}. Non-numeric fields
are left by @option{-z} untouched (no blurring occurs for them).
Then @samp{-z 1:5-7} makes the filter blur the 5th, 6th and 7th field of each
line of the first file whenever they are recognized as numeric.

By means of the option @option{-Z} you can specify which
fields have to be unconditionally blurred, i.e.
independently of their type, numeric or not.
For example, @samp{-Z 2:3-4} activates the blurring of the 3th and 4th field of each
line of the second file.

Going back to the comparison of the files @file{list1} and @file{list2},
the option @samp{-z 2-} of the command @samp{numdiff -z 2- -V list1 list2}
makes the filter transform the (memory copies of the)
two files as
@example
12       @bullet{}
13       @bullet{}
14       @bullet{}
15       @bullet{}
16       @bullet{}
17       @bullet{}
18       @bullet{}
19       @bullet{}
20       @bullet{}
21       @bullet{}
22       @bullet{}
23       @bullet{}
24       @bullet{}
@end example

@noindent
and

@example
12       @bullet{}
15       @bullet{}
18       @bullet{}
21       @bullet{}
@end example

@noindent
respectively. Here @bullet{} denotes the special
symbol used by the filter in the blurring procedure, even if this
symbol is not actually a bullet.
Since in this example space, tab and newline are
used as field delimiters, the byte-by-byte comparison between
the transformed files produces the same result displayed by the command 
@samp{sdiff -W} when applied to them:

@example
12       @bullet{}                        12       @bullet{}
13       @bullet{}                     <
14       @bullet{}                     <
15       @bullet{}                        15       @bullet{}
16       @bullet{}                     <
17       @bullet{}                     <
18       @bullet{}                        18       @bullet{}
19       @bullet{}                     <
20       @bullet{}                     <
21       @bullet{}                        21       @bullet{}
22       @bullet{}                     <
23       @bullet{}                     <
24       @bullet{}                     <
@end example

@noindent
If you put the blurred fields back you obtain exactly the output
of @samp{numdiff -f -z 2- list1 list2}, i.e. the outcome of the filtering:

@example
12       3.46410161513775458705           12       3.46410162002945508100
13       3.60555127546398929312        <
14       3.74165738677394138558        <
15       3.87298334620741688518           15       3.87298387096774193548
16       4                             <
17       4.12310562561766054982        <
18       4.24264068711928514641           18       4.24264705882352941176
19       4.35889894354067355224        <
20       4.47213595499957939282        <
21       4.58257569495584000659           21       4.58260869565217391304
22       4.69041575982342955457        <
23       4.7958315233127195416         <
24       4.89897948556635619639        <


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

@end example

@noindent
Since the second field is a numerical value in all lines
of @file{list1} and @file{list2}, using the option @option{-Z}
instead of @option{-z} makes no difference in this case. 
The output of @samp{numdiff -f -Z 2- list1 list2} is then the
same of @samp{numdiff -f -z 2- list1 list2}.

After this explanation you should also understand why 
@samp{numdiff -f -z @@ list1 list2} gives a wrong result.
Since also the first field is always a numerical value,
the option @samp{-z @@} makes the filter transform the two
given files as
@example
@bullet{}       @bullet{}
@bullet{}       @bullet{}
@bullet{}       @bullet{}
@bullet{}       @bullet{}
@bullet{}       @bullet{}
@bullet{}       @bullet{}
@bullet{}       @bullet{}
@bullet{}       @bullet{}
@bullet{}       @bullet{}
@bullet{}       @bullet{}
@bullet{}       @bullet{}
@bullet{}       @bullet{}
@bullet{}       @bullet{}
@end example

@noindent
and

@example
@bullet{}       @bullet{}
@bullet{}       @bullet{}
@bullet{}       @bullet{}
@bullet{}       @bullet{}
@end example

@noindent
respectively, making then impossible to match the lines in a reasonable way.
 
We consider now a typical situation
in which it is better to use @option{-Z} in place of @option{-z}.
If file @file{Table1} contains
@verbatim
-6 	 2.449490
-5 	 2.236068
-4 	 2.000000
-3 	 1.732051
-2 	 1.414214
-1       1.000000
0        0
- - - - - - - - -
1 	 1.000000
2 	 1.414214
3 	 1.732051
4 	 2.000000
- - - - - - - - -
5 	 2.236068
6 	 2.449490
7 	 2.645751
- - - - - - - - -
8 	 2.828427
9 	 3.000000
10 	 3.162278
11 	 3.316625
12 	 3.464102
- - - - - - - - -
- - - - - - - - -
13 	 3.605551
14 	 3.741657
@end verbatim

@noindent
and @file{Table2} contains

@verbatim
-6       Not_defined
-4       Not_defined
-2       Not_defined
 0       0.000000
 2 	 1.414216
 4 	 2.000000
 6 	 2.449494
 8 	 2.828469
 10 	 3.162278
 12 	 3.464102
 14 	 3.741658
********************END
@end verbatim

@noindent
then the output of @samp{numdiff -z 1:2 -Z 2:2 -f Table1 Table2} is
@example
-6       2.449490               -6       Not_defined
-5       2.236068            <
-4       2.000000               -4       Not_defined
-3       1.732051            <
-2       1.414214               -2       Not_defined
-1       1.000000            <
0        0                       0       0.000000
- - - - - - - - -            <
1        1.000000            <
2        1.414214                2       1.414216
3        1.732051            <
4        2.000000                4       2.000000
- - - - - - - - -            <
5        2.236068            <
6        2.449490                6       2.449494
7        2.645751            <
- - - - - - - - -            <
8        2.828427                8       2.828469
9        3.000000            <
10       3.162278                10      3.162278
11       3.316625            <
12       3.464102                12      3.464102
- - - - - - - - -            <
- - - - - - - - -            <
13       3.605551            <
14       3.741657                14      3.741658
                             >  ********************END


+++  File "Table1" differs from file "Table2"
@end example

@noindent
which is exactly what is expected.
On the other hand the command @samp{numdiff -z 2 -f Table1 Table2} displays
@example
-6       2.449490            |  -6       Not_defined
-5       2.236068            |  -4       Not_defined
-4       2.000000            |  -2       Not_defined
-3       1.732051            <
-2       1.414214            <
-1       1.000000            <
0        0                       0       0.000000
- - - - - - - - -            <
1        1.000000            <
2        1.414214                2       1.414216
3        1.732051            <
4        2.000000                4       2.000000
- - - - - - - - -            <
5        2.236068            <
6        2.449490                6       2.449494
7        2.645751            <
- - - - - - - - -            <
8        2.828427                8       2.828469
9        3.000000            <
10       3.162278                10      3.162278
11       3.316625            <
12       3.464102                12      3.464102
- - - - - - - - -            <
- - - - - - - - -            <
13       3.605551            <
14       3.741657                14      3.741658
                             >  ********************END


+++  File "Table1" differs from file "Table2"
@end example

@noindent
which is partially wrong.

Notice that in @file{Table1} you find (truncated to the sixth decimal digit)
the square roots of the absolute values of the integer numbers
between -6 and 20, plus some randomly added lines.
The file @file{Table2} contains approximations (obtained by Newton's method)
of the square roots of the even numbers between -6 and 20. 
Since the (real) square root is not defined for
negative numbers, the values corresponding to -6, -4 and -2
are replaced by @verb{|Not_defined|}.

Since @verb{|Not_defined|} is not a numeric value,
during the execution of the last command the filter
transforms @file{Table1} in this way
@example
-6       @bullet{}
-5       @bullet{}
-4       @bullet{}
-3       @bullet{}
-2       @bullet{}
-1       @bullet{}
0        @bullet{}
- - - - - - - - -
1        @bullet{}
2        @bullet{}
3        @bullet{}
4        @bullet{}
- - - - - - - - -
5        @bullet{}
6        @bullet{}
7        @bullet{}
- - - - - - - - -
8        @bullet{}
9        @bullet{}
10       @bullet{}
11       @bullet{}
12       @bullet{}
- - - - - - - - -
- - - - - - - - -
13       @bullet{}
14       @bullet{}
@end example

@noindent
and @file{Table2} in this other way

@example
-6       Not_defined
-4       Not_defined
-2       Not_defined
 0       @bullet{}
 2       @bullet{}
 4       @bullet{}
 6       @bullet{}
 8       @bullet{}
 10      @bullet{}
 12      @bullet{}
 14      @bullet{}
********************END
@end example

@noindent
Unfortunately the first three lines are enough to
confuse the synchronization procedure of the filter, which is based on
a byte-by-byte comparison with exclusion of the field
delimiters, as explained before.

You can check that this is definitely the case by
looking at the output of the command
@samp{sdiff -W} on the transformed files, 
which is
@example
-6       @bullet{}           |  -6       Not_defined
-5       @bullet{}           |  -4       Not_defined
-4       @bullet{}           |  -2       Not_defined
-3       @bullet{}           <
-2       @bullet{}           <
-1       @bullet{}           <
0        @bullet{}               0       @bullet{}
- - - - - - - - -    <
1        @bullet{}           <
2        @bullet{}               2       @bullet{}
3        @bullet{}           <
4        @bullet{}               4       @bullet{}
- - - - - - - - -    <
5        @bullet{}           <
6        @bullet{}               6       @bullet{}
7        @bullet{}           <
- - - - - - - - -    <
8        @bullet{}               8       @bullet{}
9        @bullet{}           <
10       @bullet{}               10      @bullet{}
11       @bullet{}           <
12       @bullet{}               12      @bullet{}
- - - - - - - - -    <
- - - - - - - - -    <
13       @bullet{}           <
14       @bullet{}               14      @bullet{}
                     >  ********************END
@end example

If we give the command @samp{numdiff -z 1:2 -Z 2:2 -f Table1 Table2}
instead of @samp{numdiff -z 2 -f Table1 Table2}, 
the second field of the lines of @file{Table2} is always
blurred. The filter transforms then
@file{Table2} into
@example
-6       @bullet{}
-4       @bullet{}
-2       @bullet{}
 0       @bullet{}
 2       @bullet{}
 4       @bullet{}
 6       @bullet{}
 8       @bullet{}
 10      @bullet{}
 12      @bullet{}
 14      @bullet{}
********************END
@end example

@noindent
and @i{re-synchronizes} the files @file{Table1} and @file{Table2} 
in the right way.

Using the unconditional blurring is suggested in all cases
when a certain field, which you want to include
in the comparison (use @option{-X} to completely
neglect one or more fields), is of numeric type
in almost all lines of (one of) the given
files. This can be for instance the case when in some
lines the contents of the field are given by
a special numeric value, like @verb{|Infinity|}, @verb{|Inf|}, 
@verb{|+Inf|} or @verb{|-Inf|},
or by @verb{|NaN|}, abbreviation for @i{Not a Number}.

Concerning the numeric fields which are not blurred,
it is worth remarking that the filter is not confused by differences in the
numeric format. Before the byte-by-byte comparison,
numeric values are converted indeed to a standard format. 
To offer an example of this, let us suppose that @file{short1} contains a list
of numbers with their logarithms
@verbatim
0.001          -3
0.01           -2
0.1            -1
1               0
1000            3
1000000         6
1000000000      9
@end verbatim

@noindent
and @file{short2} the same list of numbers and logarithms, but
with differences in the numeric format:
@verbatim
******************
0.0010000       -3
.0100           -2
0000.10         -1
1.               0
1,000.000        3
1,000,000.       6
1,000,000,000    9
@end verbatim

@noindent
Then @samp{numdiff -f -z 2- short1 short2} displays
@example
                             >  ******************
0.001          -3               0.0010000       -3
0.01           -2               .0100           -2
0.1            -1               0000.10         -1
1               0               1.               0
1000            3               1,000.000        3
1000000         6               1,000,000.       6
1000000000      9               1,000,000,000    9


+++  File "short1" differs from file "short2"
@end example

@noindent
showing that the filter has matched 
the lines in the right way.

The filter can even handle the case
when the same numerical value is written in
decimal notation in one file and in scientific
notation in the other one.
If the files @file{decimal} and @file{scientific} contain
@verbatim
.001           -3
.01            -2
.1             -1
* * * * * * * * *
1               0
1000            3
1000000         6
1000000000      9
@end verbatim

@noindent
and
@verbatim
*****************
1.0e-3         -3
1.0e-2         -2
1.0e-1         -1
1.0e0           0
1.0e3           3
1.0e6           6
1.0e9           9
*****************
@end verbatim

@noindent
respectively, then @samp{numdiff -f -z 2- decimal scientific} prints
@example
                             >  *****************
.001           -3               1.0e-3         -3
.01            -2               1.0e-2         -2
.1             -1               1.0e-1         -1
* * * * * * * * *            < 
1               0               1.0e0           0
1000            3               1.0e3           3
1000000         6               1.0e6           6
1000000000      9               1.0e9           9
                             >  *****************


+++  File "decimal" differs from file "scientific"
@end example

@noindent
proving that the filter does not get confused.

No problems arise also in the case when for the same field
the scientific notation is used in both files.
If the files @file{sc1} and @file{sc2} contain
@verbatim
  1.E-3          -3
  1.00E-2        -2
  1.0E-1         -1
  1.0000E0        0
001.0E3           3
+01.000E6         6
  1.0E+09         9
  1.0E+10        10
* * * * * * * * * *
@end verbatim

@noindent
and
@verbatim
*****************
 1.0e-003      -3
 1.0e-2        -2
 1.0e-1        -1
 1.0e0          0
+1.0e3          3
 1.0e+6         6
 1.0e9          9
@end verbatim

@noindent
respectively, then @samp{numdiff -f -z 2- sc1 sc2}
correctly displays
@example
                             >  *****************
  1.E-3          -3              1.0e-003      -3
  1.00E-2        -2              1.0e-2        -2
  1.0E-1         -1              1.0e-1        -1
  1.0000E0        0              1.0e0          0
001.0E3           3             +1.0e3          3
+01.000E6         6              1.0e+6         6
  1.0E+09         9              1.0e9          9
  1.0E+10        10          <
* * * * * * * * * *          <


+++  File "sc1" differs from file "sc2"
@end example

@noindent

The filter can even handle an improper use
of the scientific notation, meaning for example that 
it can recognize @samp{123.456E+2}
and @samp{1.23456E+4} as equal.

We can see this in the case of the files @file{Scnot1}:
@verbatim
-------------------------
1.2E0             *     1
2.45E-1           *     2
-3.678E-2         *     3
@end verbatim

@noindent
and @file{Scnot2}:
@verbatim
12E-1             *     1
245E-3            *     2
-0.003678E+1      *     3
@end verbatim

@noindent
@samp{numdiff -f -z 3- Scnot1 Scnot2}
displays the report:
@example
-------------------------    <
1.2E0             *     1       12E-1             *     1
2.45E-1           *     2       245E-3            *     2
-3.678E-2         *     3       -0.003678E+1      *     3


+++  File "Scnot1" differs from file "Scnot2"
@end example

@noindent
which is exactly what you would expect in such a case.
Also pretty hard cases do not confuse the filter.
If @file{Scnot1} is given by
@verbatim
 1.2000e0         *     1
02.4500e-1        *     2
-003.678E-2       *     3
@end verbatim

@noindent
and @file{Scnot2} is the same file as before, the output of
the command @samp{numdiff -f -z 3- Scnot1 Scnot2} is still right:
@example
 1.2000e0         *     1       12E-1             *     1
02.4500e-1        *     2       245E-3            *     2
-003.678E-2       *     3       -0.003678E+1      *     3


+++  Files "Scnot1" and "Scnot2" have the same structure
@end example

In all examples above the option @option{-f} is used with no argument.
@anchor{Use of the option -f}

However, @option{-f} accepts an optional argument, which can be used to control
how @option{-f} displays its output.
If you provide an argument, care not to leave any space
between the option and the argument:
@samp{-f60} is correct while @samp{-f 60}
makes Numdiff terminate after printing an error message.

If the argument is a positive number @var{NUM}, then
the side-by-side output produced by @option{-f}
will be @var{NUM} columns wide. The default value
for the width of the output is 130, which can fit onto a
traditional printer line, and is the one used
when @option{-f} has no argument, or the supplied argument is zero.
In other words, @samp{-f} and @samp{-f0} are just easier to remind
versions of @samp{-f130}. 

A negative argument has the same effect as the positive argument 
with the same absolute value, but it causes in addition the removal of
common lines from the output. 
For example, the command @samp{numdiff -z 1:2 -Z 2:2 -f-130 Table1 Table2}
displays the following text
@example
-5       2.236068            <
-3       1.732051            <
-1       1.000000            <
- - - - - - - - -            <
1        1.000000            <
3        1.732051            <
- - - - - - - - -            <
5        2.236068            <
7        2.645751            <
- - - - - - - - -            <
9        3.000000            <
11       3.316625            <
- - - - - - - - -            <
- - - - - - - - -            <
13       3.605551            <
                             >  ********************END


+++  File "Table1" differs from file "Table2"
@end example

In conjunction with the option @option{-f} or @option{-O} you can use
@option{-T} to expand tabs to spaces in the produced output. 
This is useful to preserve the  alignment of tabs in the input files,
if it is thrown off by the presence of the gutter.

The options @option{-H} and @option{-m} affect the
performance of the filter of Numdiff.
But performance has more than one dimension and  
these options improve one aspect of performance at
the cost of another, or they improve performance in some cases while
hurting it in others.

The re-synchronization of the two compared files made by the filter always
comes up with a near-minimal set of deletions/insertions of lines, that
usually is good enough for practical purposes.  
If the filter displays a large set of line deletions/insertions, you
might want it to use a modified algorithm that sometimes produces a
smaller set of differences.  The @option{-m} option does this;
however, it can also cause the filter to run more slowly than usual, 
so it is not the default behavior.

If the files you are comparing are large and have small groups of
changes scattered throughout them, you can use the
@option{-H} option to make a different modification to the
algorithm employed by the filter. If the input files have a constant small
density of changes, where change means here deletion/insertion of lines,
this option speeds up the comparison without
changing the output or in the worst case introducing minor modifications.

@node Warnings, Index, Filtering, Top
@chapter Warnings

@cindex Warnings
@cindex Notes
@cindex Caveats

@itemize
@item Bug reports have to be sent to the address
@email{ivprimi(at)libero(dot)it} . Please, put Numdiff
in the subject and indicate the version of the operating system you
are running (in particular, do not forget to specify if
it is a 32- or a 64-bit system), and, if you know it, 
the version of the compiler used to build Numdiff. 
Please write also whether your version
of Numdiff uses the GNU MP library or not.
Before writing an email be sure to run the latest
stable version of Numdiff, I do not provide
support for older versions.

@item Numdiff does not accept numbers in scientific notation
whose exponents lie outside the range -1073741824, @dots{}, +1073741824.
If such a number is found in any of the files to compare,
the execution of the program is stopped
after printing a suitable error message on stderr.
Under the assumption that the numeric format in use is the default one,
with "1.0001e-2147483640" the displayed error messages is
@example
numdiff: A number with a too small exponent has been found,
namely "1.0001e-2147483640".
Exponents smaller than -1073741824 are not accepted,
the execution of the program ends now
@end example

@item @anchor{with GNU MP is better}
If Numdiff has been built with its own internal support 
for multiple precision arithmetic instead of being linked
against the GNU MP Library,
then performance degradation and memory exhaustion can already make 
impossible to handle exponents of magnitude @math{10^6 = 1000000}.
This is what I obtained on my laptop, equipped with a dual core processor @@1.50 GHz
and with 1GB of RAM, when I tried to compare
the numbers 1.101e1000000000 and 1.0e1000000000:
@example
numdiff: Insufficient memory for new allocation,
the execution of the program ends now
@end example
In addition, you can overload the processor with numbers
whose exponents lie outside the range -1000000, @dots{}, 1000000.
But at least on my machine, everything works fine and quick enough
as long as exponent and size of the mantissa of the numbers
are in the range -1000, @dots{}, 1000.
Be careful and remember that Numdiff is distributed 
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Consider also that, if you have numeric data with exponents
outside the range -300, @dots{}, 300, probably there is something
wrong with your data: either you are using the wrong scale,
or you should replace very small numbers, like 1e-100, by zero,
or it is quite likely that the machine/program/algorithm which
produced these data is not working right.

@item If Numdiff has been linked against the 
GNU Multiple Precision Arithmetic Library (also called GNU MP), 
then the precision it uses is typically higher
than the specified one. On my machine the actual value
of the precision is 20 if the user gives a value between 0 and 20,
30 if the user specifies a precision between 21 and 30,
40 for a user-specified value between 31 and 40, and so on.
Anyway, the actual precision is never less than
the one required by the user.

@item After reading a numeric field, Numdiff truncates its value
if this number has @i{too much} digits with respect
to the current precision. 
To be precise, denoted by
@var{P} the current value of the precision, the following
rules apply.

If @command{numdiff} has been built with
its own internal support for multiple precision arithmetic, then
@itemize
@item if the number is written in ordinary decimal notation, @command{numdiff}
will consider, in addition to all digits of the integer part, only
the first @var{P} digits of the fractional part;
@item if the value is written in scientific notation, then @command{numdiff}
will only consider the first @var{P} digits of the fractional part
of the mantissa.
@end itemize

If @command{numdiff} uses the GNU MP library
to perform its computations, the value of a numeric
field is first translated into scientific notation and then 
only the first @var{P} digits of the fractional part
of the mantissa are considered.

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

@item You can find out whether your local version of @command{numdiff}
is relying on GNU MP or not by executing the command @samp{numdiff -v}.
If @command{numdiff} uses GNU MP, then this command will display
the following message or similar (possibly translated
into your mother language) among other information:
@example
The software has been linked against
the GNU Multiple Precision Arithmetic Library,
version number 4.2.4.
@end example

@noindent
If @command{numdiff} does not rely on GNU MP, then
the displayed message will be (up to translation into
your mother language)
@example
The software has been built with
its own internal support for multiple precision arithmetic.
@end example

@item Numdiff can only be used on text files:
the program terminates after printing a suitable error message
if one of the files to compare turns out to be a binary file.
To detect if a file is binary or not, @command{numdiff} checks
for the presence of null bytes (0x00) in the file.

@item If you are not including the so called white-space characters
(usually @samp{ }, @samp{\t}, @samp{\f}, @samp{\v} and @samp{\r})
in the set of field delimiters, then a real and an imaginary number
which are separated just by white-spaces can be coupled together
and considered as a whole complex number.
For example, if you are using only @strong{colon} (@samp{:}) and
@strong{newline} as field delimiters and Numdiff finds a line
like that
@verbatim
::::3.0-5.6e-356i::::-12.9   +4.34i::::-12.9    4.34i::::New York::::
@end verbatim

@noindent
then it will consider this line as formed by four fields, the first two
are numeric and given by the complex numbers @i{3.0-5.6e-356i} and
@i{-12.9+4.34i}, the last two ones are the strings @verb{|New York|}
and @verb{|-12.9    4.34i|}.
I still do not know if I will modify this in the next version
of Numdiff, so that the program recognizes only @verb{|3.0-5.6e-356i|}
as numeric field and treats @verb{|-12.9   +4.34i|} as non-numeric
due to the presence of spaces in the middle.
@verb{|-12.9    4.34i|} is already considered as non-numeric
due to the absence of a leading sign in the imaginary value.

@item We have seen that one of the two files passed to @command{numdiff}
can be @verb{|-|}, which refers to stdin (standard input). In this way one of
the two files to compare can be the output produced by another
command, like in @samp{cat file2 | numdiff -a 1.0e-3 file1 -}.
However, if you activate the filter by means of the options @option{-z} or/and
@option{-Z}, Numdiff can not work with the standard input unless you
use also the option @option{-f}. Therefore, the command
@samp{cat file2 | numdiff -a 1.0e-3 -z @@ file1 -}
displays only the error message
@verbatim
numdiff: -: Illegal seek
@end verbatim
(or maybe the translation of this message in the language
 you are using on your computer)
but @samp{cat file2 | numdiff -a 1.0e-3 -z @@ -f file1 -}
works as expected.

@item This manual describes the version 5.9 of Numdiff.
Prior 5.x versions did not recognize all the options that are
currently accepted, versions 4.0.0 and 3.x used even a
different format for the output. 
@end itemize

@node GNU Free Documentation License,  ,  , Top
@appendix GNU Free Documentation License

@cindex GNU Free Documentation License
@cindex GNU FDL
@cindex FDL

@include fdl.texi

@node Index,  , Warnings, Top
@unnumbered Index

@printindex cp

@bye