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1  %$Header: /home/dashley/cvsrep/e3ft_gpl01/e3ft_gpl01/dtaipubs/esrgubka/c_dcm0/c_dcm0.tex,v 1.13 2001/08/18 18:37:56 dtashley Exp $  %$Header$
2    
3  \chapter{\cdcmzerolongtitle{}}  \chapter{\cdcmzerolongtitle{}}
4    
5  \label{cdcm0}  \label{cdcm0}
6    
7    
8  `''---From A Chinese Restaurant  `''---From A Chinese Restaurant
9           Fortune Cookie, 01/26/01           Fortune Cookie, 01/26/01
10    
11  \beginchapterquote{``Simplicity of character is the natural result  \beginchapterquote{``Simplicity of character is the natural result
12                     of profound thought.''}                     of profound thought.''}
13                     {From A Chinese Restaurant fortune cookie, 01/26/01}                     {From A Chinese Restaurant fortune cookie, 01/26/01}
14    
15  \section{Introduction}  \section{Introduction}
16  %Section Tag: INT0  %Section Tag: INT0
17  \label{cdcm0:sint0}  \label{cdcm0:sint0}
18    
19  \emph{The Iju Tool Set} includes a number of DOS console-mode utilities.  \emph{The Iju Tool Set} includes a number of DOS console-mode utilities.
20  Although these utilities present a humble interface (text-only input and output),  Although these utilities present a humble interface (text-only input and output),
21  some are very powerful.  Because the internal architecture of the  some are very powerful.  Because the internal architecture of the
22  \index{Microsoft \emph{Windows}@Microsoft Windows}\emph{Windows} family of  \index{Microsoft \emph{Windows}@Microsoft Windows}\emph{Windows} family of
23  operating systems has changed over the years so that DOS console-mode  operating systems has changed over the years so that DOS console-mode
24  applications now use the Win32 memory model, these applications can now  applications now use the Win32 memory model, these applications can now
25  allocate at least hundreds of megabytes of memory and are generally unfettered  allocate at least hundreds of megabytes of memory and are generally unfettered
26  in their operation.  Despite the humble interface, console-mode applications  in their operation.  Despite the humble interface, console-mode applications
27  can now be very powerful indeed.  can now be very powerful indeed.
28    
29  Many of these utilities are very similar to---and sometimes use the  Many of these utilities are very similar to---and sometimes use the
30  same software components as---Tcl/Tk extensions that perform the same  same software components as---Tcl/Tk extensions that perform the same
31  functions.  functions.
32    
33  The first part of this chapter describes command-line option formats which  The first part of this chapter describes command-line option formats which
34  are common across more than one utility.  The second part of the chapter describes  are common across more than one utility.  The second part of the chapter describes
35  each of the utilities in detail.  each of the utilities in detail.
36    
37    
38  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
39  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
40  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
41    
42  \subsection{Notational Conventions}  \subsection{Notational Conventions}
43  %Subsection tag: NCO0  %Subsection tag: NCO0
44  \label{ctin0:sccl0:snco0}  \label{ctin0:sccl0:snco0}
45    
46  We use the angle brackets (`\texttt{<}' and `\texttt{>}') to denote a  We use the angle brackets (`\texttt{<}' and `\texttt{>}') to denote a
47  parameter which must occur and be completed with the information  parameter which must occur and be completed with the information
48  indicated.  For example, we would use \texttt{<winfname>} to indicate  indicated.  For example, we would use \texttt{<winfname>} to indicate
49  that the name of a file must be provided in a format acceptable to  that the name of a file must be provided in a format acceptable to
50  Windows.  Windows.
51    
52  We use the square brackets (`\texttt{[}' and `\texttt{]}') to denote  We use the square brackets (`\texttt{[}' and `\texttt{]}') to denote
53  an optional parameter.  Square brackets may be nested arbitrarily  an optional parameter.  Square brackets may be nested arbitrarily
54  deep---for example, `\texttt{[lastname [firstname]]}' would  deep---for example, `\texttt{[lastname [firstname]]}' would
55  indicate that both first name and last name may be omitted, but  indicate that both first name and last name may be omitted, but
56  the first name may not occur alone without the last name.  the first name may not occur alone without the last name.
57    
58  In all cases, the parameter types described in Section  In all cases, the parameter types described in Section
59  \ctinzeroxrefhyphen{}\ref{ctin0:sccl0}  \ctinzeroxrefhyphen{}\ref{ctin0:sccl0}
60  are used.  are used.
61    
62  In some cases it may be necessary to distinguish between the  In some cases it may be necessary to distinguish between the
63  \emph{name} of a parameter and the \emph{type} of the parameter.  \emph{name} of a parameter and the \emph{type} of the parameter.
64  For example, two parameters may both be of type \texttt{uint32}  For example, two parameters may both be of type \texttt{uint32}
65  but may serve different functions---one may be, for example,  but may serve different functions---one may be, for example,
66  a dividend and the other a divisor.  In these cases we use  a dividend and the other a divisor.  In these cases we use
67  the underscore character (`\texttt{\_}') to separate  the underscore character (`\texttt{\_}') to separate
68  the name and the type.  For example, in such a case we may  the name and the type.  For example, in such a case we may
69  use a description such as \texttt{divisor\_uint32}.  use a description such as \texttt{divisor\_uint32}.
70    
71  \subsection{The \texttt{-help} Option}  \subsection{The \texttt{-help} Option}
72  %Subsection tag: hel0  %Subsection tag: hel0
73  \label{cdcm0:sccl0:shel0}  \label{cdcm0:sccl0:shel0}
74    
75  \index{help@\texttt{-help}}  \index{help@\texttt{-help}}
76  \index{-help@\texttt{-help}}  \index{-help@\texttt{-help}}
77  The command-line option \texttt{-help} (which must be used alone with no  The command-line option \texttt{-help} (which must be used alone with no
78  other parameters) will cause a full set of help information to be written  other parameters) will cause a full set of help information to be written
79  to the standard output stream.  to the standard output stream.
80    
81  Any command line which is not recognized (i.e. that contains no parameters or is  Any command line which is not recognized (i.e. that contains no parameters or is
82  otherwise invalid) will cause a message to be displayed to the effect that  otherwise invalid) will cause a message to be displayed to the effect that
83  the utility may be re-run with the \texttt{-help} parameter to obtain help  the utility may be re-run with the \texttt{-help} parameter to obtain help
84  information.  information.
85    
86  \subsection{The \texttt{-verbose} And \texttt{-debug} Options}  \subsection{The \texttt{-verbose} And \texttt{-debug} Options}
87  %Subsection tag: ver0  %Subsection tag: ver0
88  \label{cdcm0:sccl0:sver0}  \label{cdcm0:sccl0:sver0}
89    
90  \index{verbose@\texttt{-verbose}}  \index{verbose@\texttt{-verbose}}
91  \index{-verbose@\texttt{-verbose}}  \index{-verbose@\texttt{-verbose}}
92  \index{debug@\texttt{-debug}}  \index{debug@\texttt{-debug}}
93  \index{-debug@\texttt{-debug}}  \index{-debug@\texttt{-debug}}
94  The command-line option \texttt{-verbose} will cause intermediate results and other  The command-line option \texttt{-verbose} will cause intermediate results and other
95  useful information to be written to the standard output as the utility runs.  useful information to be written to the standard output as the utility runs.
96  Because it is very often  Because it is very often
97  used, the \texttt{-verbose} option  used, the \texttt{-verbose} option
98  can always be abbreviated \texttt{-v}.  can always be abbreviated \texttt{-v}.
99  For utilities which perform arithmetic, these intermediate results may be useful  For utilities which perform arithmetic, these intermediate results may be useful
100  in verifying hand calculations or for other purposes.  in verifying hand calculations or for other purposes.
101    
102  The \texttt{-debug} option will cause debugging information to be written to  The \texttt{-debug} option will cause debugging information to be written to
103  the standard output.  Because the \texttt{-debug} option is very rarely used,  the standard output.  Because the \texttt{-debug} option is very rarely used,
104  it does not have an abbreviated form.  The debugging information consists of  it does not have an abbreviated form.  The debugging information consists of
105  information that may be useful in diagnosing the internal problem if a utility  information that may be useful in diagnosing the internal problem if a utility
106  ever is found to contain a software defect.  ever is found to contain a software defect.
107    
108  The \texttt{-verbose} and \texttt{-debug} options are potentially orthogonal.  The \texttt{-verbose} and \texttt{-debug} options are potentially orthogonal.
109  The information output enabled by the \texttt{-verbose} option may be different  The information output enabled by the \texttt{-verbose} option may be different
110  than the information output enabled by the \texttt{-debug} option.  The options  than the information output enabled by the \texttt{-debug} option.  The options
111  may be used together.  may be used together.
112    
113  \subsection{The \texttt{-noformat} Option}  \subsection{The \texttt{-noformat} Option}
114  %Subsection tag: nfo0  %Subsection tag: nfo0
115  \label{cdcm0:sccl0:snfo0}  \label{cdcm0:sccl0:snfo0}
116    
117  \index{noformat@\texttt{-noformat}}  \index{noformat@\texttt{-noformat}}
118  \index{-noformat@\texttt{-noformat}}  \index{-noformat@\texttt{-noformat}}
119  The command-line option \texttt{-noformat} will cause formatting of the output to be  The command-line option \texttt{-noformat} will cause formatting of the output to be
120  suppressed.  Because it is very often used, this option can always be abbreviated  suppressed.  Because it is very often used, this option can always be abbreviated
121  \texttt{-nf}.  \texttt{-nf}.
122    
123  Normally, each command will format the output to be very aesthetic and  Normally, each command will format the output to be very aesthetic and
124  human-readable.  This involves adding commas and comments and splitting  human-readable.  This involves adding commas and comments and splitting
125  long integers across multiple lines.  However, when piping data from one  long integers across multiple lines.  However, when piping data from one
126  utility to another or spawning these utilities from a script or other program,  utility to another or spawning these utilities from a script or other program,
127  it may be desirable to suppress all but the output data.  it may be desirable to suppress all but the output data.
128    
129  The \texttt{-verbose} and \texttt{-debug} options override (i.e. cancel)  The \texttt{-verbose} and \texttt{-debug} options override (i.e. cancel)
130  the \texttt{-noformat} option.  The \texttt{-noformat} option will not be  the \texttt{-noformat} option.  The \texttt{-noformat} option will not be
131  honored if it appears on the same command line as the  honored if it appears on the same command line as the
132  \texttt{-verbose} option or the \texttt{-debug} option.  \texttt{-verbose} option or the \texttt{-debug} option.
133    
134    
135  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
136  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
137  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
138  \section{Invocation Of The Utilities}  \section{Invocation Of The Utilities}
139  %Section tag: INV0  %Section tag: INV0
140    
141  The most common way to invoke any of these command-line utilities is  The most common way to invoke any of these command-line utilities is
142  to open a console box (in Windows), and then to run these utilities  to open a console box (in Windows), and then to run these utilities
143  from the command line or from a batch file.  from the command line or from a batch file.
144    
145  These utilities could also be run from a Tcl/Tk script, or spawned from  These utilities could also be run from a Tcl/Tk script, or spawned from
146  a Windows application.  a Windows application.
147    
148  These utilities do not write to the standard error stream (only to the  These utilities do not write to the standard error stream (only to the
149  standard output), so output can always be redirected.  standard output), so output can always be redirected.
150    
151  These utilities will generate a return code of 0 if no errors are detected, or  These utilities will generate a return code of 0 if no errors are detected, or
152  a return code of 4 if any errors are detected.  a return code of 4 if any errors are detected.
153    
154    
155  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
156  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
157  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
158  \section{File CRC And Hash Function Utilities}  \section{File CRC And Hash Function Utilities}
159  %Section tag: CHF0  %Section tag: CHF0
160  \label{cdcm0:schf0}  \label{cdcm0:schf0}
161    
162    
163  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
164  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
165  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
166  \subsection{The \emph{crc32} Utility}  \subsection{The \emph{crc32} Utility}
167  %Subection tag: CRC0  %Subection tag: CRC0
168  \label{cdcm0:schf0:scrc0}  \label{cdcm0:schf0:scrc0}
169    
170  \index{crc32@\emph{crc32}}  \index{crc32@\emph{crc32}}
171  \begin{dosutilcommandname}{crc32}%  \begin{dosutilcommandname}{crc32}%
172  calculates the CRC-32 and file size (in bytes) of a file.  calculates the CRC-32 and file size (in bytes) of a file.
173  The CRC-32 is written to the standard output in hexadecimal  The CRC-32 is written to the standard output in hexadecimal
174  notation, and the file size is written to the standard output  notation, and the file size is written to the standard output
175  in decimal notation with commas.  in decimal notation with commas.
176  \end{dosutilcommandname}  \end{dosutilcommandname}
177    
178  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
179  \dosutilcommandsynopsisline{crc32}{winfname [$<$options$>$]}  \dosutilcommandsynopsisline{crc32}{winfname [$<$options$>$]}
180  \dosutilcommandsynopsisline{crc32}{-help}  \dosutilcommandsynopsisline{crc32}{-help}
181  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
182    
183  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
184  The \emph{crc32} utility calculates the CRC-32 and length of a file.  The \emph{crc32} utility calculates the CRC-32 and length of a file.
185  This utility relies on C-language code obtained from a web page  This utility relies on C-language code obtained from a web page
186  maintained by \index{Ellingson, Richard A.}Richard A. Ellingson  maintained by \index{Ellingson, Richard A.}Richard A. Ellingson
187  \cite{bibref:w:ellingsoncrc32pages}.  \cite{bibref:w:ellingsoncrc32pages}.
188  The utility was checked against the values calculated by  The utility was checked against the values calculated by
189  \index{WinZip@\emph{WinZip}}\emph{WinZip}  \index{WinZip@\emph{WinZip}}\emph{WinZip}
190  \cite{bibref:s:winzip}.  \cite{bibref:s:winzip}.
191  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
192    
193  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
194  \begin{scriptsize}  \begin{scriptsize}
195  \begin{verbatim}  \begin{verbatim}
196  C:\>crc32 t1.bin  C:\>crc32 t1.bin
197  0x9567CF44 (116,785,153)  0x9567CF44 (116,785,153)
198    
199  C:\>crc32 t1.bin -noformat  C:\>crc32 t1.bin -noformat
200  9567CF44  9567CF44
201  116785153  116785153
202  \end{verbatim}  \end{verbatim}
203  \end{scriptsize}  \end{scriptsize}
204  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
205    
206  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
207  See also the \emph{crc32} Tcl extension,  See also the \emph{crc32} Tcl extension,
208  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:scrc0:scrc0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:scrc0:scrc0}.
209  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
210    
211    
212  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
213  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
214  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
215  \section{Arbitrary-Length Integer Utilities}  \section{Arbitrary-Length Integer Utilities}
216  %Section tag: ALI0  %Section tag: ALI0
217  \label{cdcm0:sali0}  \label{cdcm0:sali0}
218    
219    
220  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
221  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
222  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
223  \subsection{The \emph{intadd} Utility}  \subsection{The \emph{intadd} Utility}
224  %Subection tag: ADD0  %Subection tag: ADD0
225  \label{cdcm0:sali0:sadd0}  \label{cdcm0:sali0:sadd0}
226    
227  \index{intadd@\emph{intadd}}  \index{intadd@\emph{intadd}}
228  \begin{dosutilcommandname}{intadd}%  \begin{dosutilcommandname}{intadd}%
229  adds two integers.  (Mnemonic:  \emph{int}eger  adds two integers.  (Mnemonic:  \emph{int}eger
230  \emph{add}ition.)  \emph{add}ition.)
231  \end{dosutilcommandname}  \end{dosutilcommandname}
232    
233  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
234  \dosutilcommandsynopsisline{intadd}{sint sint [$<$options$>$]}  \dosutilcommandsynopsisline{intadd}{sint sint [$<$options$>$]}
235  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
236    
237  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
238  The \emph{intadd} utility calculates the sum of two integers.  The \emph{intadd} utility calculates the sum of two integers.
239  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
240    
241  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
242  \begin{scriptsize}  \begin{scriptsize}
243  \begin{verbatim}  \begin{verbatim}
244  C:\>intadd 1e20 4912471263493214  C:\>intadd 1e20 4912471263493214
245  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
246                  arg1:           100,000,000,000,000,000,000   (     21 digits)                  arg1:           100,000,000,000,000,000,000   (     21 digits)
247  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
248                  arg2:                 4,912,471,263,493,214   (     16 digits)                  arg2:                 4,912,471,263,493,214   (     16 digits)
249  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
250           arg1 + arg2:           100,004,912,471,263,493,214   (     21 digits)           arg1 + arg2:           100,004,912,471,263,493,214   (     21 digits)
251  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
252  \end{verbatim}  \end{verbatim}
253  \end{scriptsize}  \end{scriptsize}
254  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
255    
256  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
257  See also the \emph{arbint intadd} Tcl extension,  See also the \emph{arbint intadd} Tcl extension,
258  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:sadd0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:sadd0}.
259  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
260    
261    
262  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
263  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
264  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
265  \subsection{The \emph{intsub} Utility}  \subsection{The \emph{intsub} Utility}
266  %Subection tag: SUB0  %Subection tag: SUB0
267  \label{cdcm0:sali0:ssub0}  \label{cdcm0:sali0:ssub0}
268    
269  \index{intsub@\emph{intsub}}  \index{intsub@\emph{intsub}}
270  \begin{dosutilcommandname}{intsub}%  \begin{dosutilcommandname}{intsub}%
271  subtracts two integers.  (Mnemonic:  \emph{int}eger  subtracts two integers.  (Mnemonic:  \emph{int}eger
272  \emph{sub}traction.)  \emph{sub}traction.)
273  \end{dosutilcommandname}  \end{dosutilcommandname}
274    
275  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
276  \dosutilcommandsynopsisline{intsub}{sint sint [$<$options$>$]}  \dosutilcommandsynopsisline{intsub}{sint sint [$<$options$>$]}
277  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
278    
279  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
280  The \emph{intsub} utility calculates the difference of two integers.  The \emph{intsub} utility calculates the difference of two integers.
281  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
282    
283  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
284  \begin{scriptsize}  \begin{scriptsize}
285  \begin{verbatim}  \begin{verbatim}
286  C:\>intsub 1e110 99  C:\>intsub 1e110 99
287  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
288                  arg1:                                   100,  (    111 digits)                  arg1:                                   100,  (    111 digits)
289                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
290                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
291                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
292                          000,000,000,000,000,000,000,000,000                          000,000,000,000,000,000,000,000,000
293  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
294                  arg2:                                    99   (      2 digits)                  arg2:                                    99   (      2 digits)
295  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
296           arg1 - arg2:                                    99,  (    110 digits)           arg1 - arg2:                                    99,  (    110 digits)
297                          999,999,999,999,999,999,999,999,999,                          999,999,999,999,999,999,999,999,999,
298                          999,999,999,999,999,999,999,999,999,                          999,999,999,999,999,999,999,999,999,
299                          999,999,999,999,999,999,999,999,999,                          999,999,999,999,999,999,999,999,999,
300                          999,999,999,999,999,999,999,999,901                          999,999,999,999,999,999,999,999,901
301  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
302    
303  C:\>intsub 1e110 99 -nf  C:\>intsub 1e110 99 -nf
304  10000000000000000000000000000000000000000000000000000000000000000000000000000000  10000000000000000000000000000000000000000000000000000000000000000000000000000000
305  0000000000000000000000000000000  0000000000000000000000000000000
306  99  99
307  99999999999999999999999999999999999999999999999999999999999999999999999999999999  99999999999999999999999999999999999999999999999999999999999999999999999999999999
308  999999999999999999999999999901  999999999999999999999999999901
309  \end{verbatim}  \end{verbatim}
310  \end{scriptsize}  \end{scriptsize}
311  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
312    
313  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
314  See also the \emph{arbint intsub} Tcl extension,  See also the \emph{arbint intsub} Tcl extension,
315  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:ssub0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:ssub0}.
316  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
317    
318    
319  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
320  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
321  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
322  \subsection{The \emph{intmul} Utility}  \subsection{The \emph{intmul} Utility}
323  %Subsection tag: MUL0  %Subsection tag: MUL0
324  \label{cdcm0:sali0:smul0}  \label{cdcm0:sali0:smul0}
325    
326  \index{intmul@\emph{intmul}}  \index{intmul@\emph{intmul}}
327  \begin{dosutilcommandname}{intmul}%  \begin{dosutilcommandname}{intmul}%
328  calculates the product of  calculates the product of
329  two integers.  (Mnemonic:  \emph{int}eger  two integers.  (Mnemonic:  \emph{int}eger
330  \emph{mul}tiplication.)  \emph{mul}tiplication.)
331  \end{dosutilcommandname}  \end{dosutilcommandname}
332    
333  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
334  \dosutilcommandsynopsisline{intmul}{sint sint [$<$options$>$]}  \dosutilcommandsynopsisline{intmul}{sint sint [$<$options$>$]}
335  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
336    
337  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
338  The \emph{intmul} utility calculates product of two  The \emph{intmul} utility calculates product of two
339  integers.  integers.
340  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
341    
342    
343  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
344  \begin{scriptsize}  \begin{scriptsize}
345  \begin{verbatim}  \begin{verbatim}
346  C:\>intmul -916439216486321439672164132964 4321846.2864e28  C:\>intmul -916439216486321439672164132964 4321846.2864e28
347  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
348                  arg1: -                                 916,  (     30 digits)                  arg1: -                                 916,  (     30 digits)
349                          439,216,486,321,439,672,164,132,964                          439,216,486,321,439,672,164,132,964
350  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
351                  arg2:                            43,218,462,  (     35 digits)                  arg2:                            43,218,462,  (     35 digits)
352                          864,000,000,000,000,000,000,000,000                          864,000,000,000,000,000,000,000,000
353  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
354           arg1 * arg2: -                      39,607,094,244,  (     65 digits)           arg1 * arg2: -                      39,607,094,244,  (     65 digits)
355                          827,339,704,438,441,915,017,392,248,                          827,339,704,438,441,915,017,392,248,
356                          896,000,000,000,000,000,000,000,000                          896,000,000,000,000,000,000,000,000
357  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
358    
359  C:\>intmul -916439216486321439672164132964 4321846.2864e28 -nf  C:\>intmul -916439216486321439672164132964 4321846.2864e28 -nf
360  -916439216486321439672164132964  -916439216486321439672164132964
361  43218462864000000000000000000000000  43218462864000000000000000000000000
362  -39607094244827339704438441915017392248896000000000000000000000000  -39607094244827339704438441915017392248896000000000000000000000000
363  \end{verbatim}  \end{verbatim}
364  \end{scriptsize}  \end{scriptsize}
365  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
366    
367  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
368  See also the \emph{arbint intmul} Tcl extension,  See also the \emph{arbint intmul} Tcl extension,
369  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:smul0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:smul0}.
370  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
371    
372  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
373  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
374  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
375  \subsection{The \emph{intdiv} Utility}  \subsection{The \emph{intdiv} Utility}
376  %Subsection tag: DIV0  %Subsection tag: DIV0
377  \label{cdcm0:sali0:sdiv0}  \label{cdcm0:sali0:sdiv0}
378    
379  \index{intdiv@\emph{intdiv}}  \index{intdiv@\emph{intdiv}}
380  \begin{dosutilcommandname}{intdiv}%  \begin{dosutilcommandname}{intdiv}%
381  calculates the integer quotient (i.e. without remainder) of  calculates the integer quotient (i.e. without remainder) of
382  two integers.  two integers.
383  (Mnemonic:  \emph{int}eger  (Mnemonic:  \emph{int}eger
384  \emph{div}ision.)  \emph{div}ision.)
385  \end{dosutilcommandname}  \end{dosutilcommandname}
386    
387  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
388  \dosutilcommandsynopsisline{intdiv}{sint sint [$<$options$>$]}  \dosutilcommandsynopsisline{intdiv}{sint sint [$<$options$>$]}
389  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
390    
391  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
392  The \emph{intdiv} utility calculates the integer quotient  The \emph{intdiv} utility calculates the integer quotient
393  of two integers.  The mapping that is made is  of two integers.  The mapping that is made is
394  more precisely described in  more precisely described in
395  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:sdiv0} in the  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:sdiv0} in the
396  description of the \emph{arbint intdiv} Tcl extension.  description of the \emph{arbint intdiv} Tcl extension.
397  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
398    
399  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
400  \begin{scriptsize}  \begin{scriptsize}
401  \begin{verbatim}  \begin{verbatim}
402  C:\>intdiv 296491826436721 91843682163  C:\>intdiv 296491826436721 91843682163
403  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
404                  arg1:                   296,491,826,436,721   (     15 digits)                  arg1:                   296,491,826,436,721   (     15 digits)
405  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
406                  arg2:                        91,843,682,163   (     11 digits)                  arg2:                        91,843,682,163   (     11 digits)
407  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
408           arg1 / arg2:                                 3,228   (      4 digits)           arg1 / arg2:                                 3,228   (      4 digits)
409  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
410    
411  C:\>intdiv 296491826436721 91843682163 -nf  C:\>intdiv 296491826436721 91843682163 -nf
412  296491826436721  296491826436721
413  91843682163  91843682163
414  3228  3228
415  \end{verbatim}  \end{verbatim}
416  \end{scriptsize}  \end{scriptsize}
417  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
418    
419  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
420  See also the \emph{arbint intdiv} Tcl extension,  See also the \emph{arbint intdiv} Tcl extension,
421  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:sdiv0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:sdiv0}.
422  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
423    
424    
425  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
426  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
427  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
428  \subsection{The \emph{intmod} Utility}  \subsection{The \emph{intmod} Utility}
429  %Subsection tag: MOD0  %Subsection tag: MOD0
430  \label{cdcm0:sali0:smod0}  \label{cdcm0:sali0:smod0}
431    
432  \index{intmod@\emph{intmod}}  \index{intmod@\emph{intmod}}
433  \begin{dosutilcommandname}{intmod}%  \begin{dosutilcommandname}{intmod}%
434  calculates the integer modulo (i.e. remainder of division) of  calculates the integer modulo (i.e. remainder of division) of
435  two integers.  two integers.
436  (Mnemonic:  \emph{int}eger  (Mnemonic:  \emph{int}eger
437  \emph{mod}ulo.)  \emph{mod}ulo.)
438  \end{dosutilcommandname}  \end{dosutilcommandname}
439    
440  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
441  \dosutilcommandsynopsisline{intmod}{sint sint [$<$options$>$]}  \dosutilcommandsynopsisline{intmod}{sint sint [$<$options$>$]}
442  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
443    
444  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
445  The \emph{intmod} utility calculates the integer modulo  The \emph{intmod} utility calculates the integer modulo
446  of two integers.  The mapping that is made is  of two integers.  The mapping that is made is
447  more precisely described in  more precisely described in
448  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:smod0} in the  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:smod0} in the
449  description of the \emph{arbint intmod} Tcl extension.  description of the \emph{arbint intmod} Tcl extension.
450  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
451    
452  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
453  \begin{scriptsize}  \begin{scriptsize}
454  \begin{verbatim}  \begin{verbatim}
455  C:\>intmod 2836549213654 15432154  C:\>intmod 2836549213654 15432154
456  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
457                  arg1:                     2,836,549,213,654   (     13 digits)                  arg1:                     2,836,549,213,654   (     13 digits)
458  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
459                  arg2:                            15,432,154   (      8 digits)                  arg2:                            15,432,154   (      8 digits)
460  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
461           arg1 % arg2:                            11,283,376   (      8 digits)           arg1 % arg2:                            11,283,376   (      8 digits)
462  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
463    
464  C:\>intmod 2836549213654 0  C:\>intmod 2836549213654 0
465  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
466                  arg1:                     2,836,549,213,654   (     13 digits)                  arg1:                     2,836,549,213,654   (     13 digits)
467  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
468                  arg2:                                     0   (      1 digit )                  arg2:                                     0   (      1 digit )
469  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
470           arg1 % arg2:                GMP_INTS_EF_INTOVF_POS           arg1 % arg2:                GMP_INTS_EF_INTOVF_POS
471  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
472    
473  C:\>intmod 2836549213654 0 -nf  C:\>intmod 2836549213654 0 -nf
474  2836549213654  2836549213654
475  0  0
476  GMP_INTS_EF_INTOVF_POS  GMP_INTS_EF_INTOVF_POS
477  \end{verbatim}  \end{verbatim}
478  \end{scriptsize}  \end{scriptsize}
479  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
480    
481  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
482  See also the \emph{arbint intmod} Tcl extension,  See also the \emph{arbint intmod} Tcl extension,
483  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:smod0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:smod0}.
484  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
485    
486    
487  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
488  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
489  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
490  \subsection{The \emph{intgcd} Utility}  \subsection{The \emph{intgcd} Utility}
491  %Subsection tag: GCD0  %Subsection tag: GCD0
492  \label{cdcm0:sali0:sgcd0}  \label{cdcm0:sali0:sgcd0}
493    
494  \index{intgcd@\emph{intgcd}}  \index{intgcd@\emph{intgcd}}
495  \begin{dosutilcommandname}{intgcd}%  \begin{dosutilcommandname}{intgcd}%
496  calculates the g.c.d. of two arbitrary integers using  calculates the g.c.d. of two arbitrary integers using
497  Euclid's algorithm.  (Mnemonic:  \emph{int}eger  Euclid's algorithm.  (Mnemonic:  \emph{int}eger
498  \emph{g}reatest \emph{c}ommon \emph{d}ivisor.)  \emph{g}reatest \emph{c}ommon \emph{d}ivisor.)
499  \end{dosutilcommandname}  \end{dosutilcommandname}
500    
501  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
502  \dosutilcommandsynopsisline{intgcd}{sint\_1 sint\_2 [$<$options$>$]}  \dosutilcommandsynopsisline{intgcd}{sint\_1 sint\_2 [$<$options$>$]}
503  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
504    
505  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
506  The \emph{intgcd} utility calculates the g.c.d. of two  The \emph{intgcd} utility calculates the g.c.d. of two
507  integers.  integers.
508    
509  If either or both integers are 0, the result will be 1.  If either or both integers are 0, the result will be 1.
510  If either or both integers are negative, the absolute  If either or both integers are negative, the absolute
511  value of the negative argument(s) will be used in the  value of the negative argument(s) will be used in the
512  calculation of the g.c.d.  calculation of the g.c.d.
513    
514  The algorithm employed is the  The algorithm employed is the
515  \emph{Modern Euclidian Algorithm} as  \emph{Modern Euclidian Algorithm} as
516  described in \cite{bibref:b:knuthclassic2ndedvol2}, p. 337.  described in \cite{bibref:b:knuthclassic2ndedvol2}, p. 337.
517  Although faster algorithms for computer  Although faster algorithms for computer
518  implementation do exist, this is the simplest  implementation do exist, this is the simplest
519  and most direct algorithm.  and most direct algorithm.
520  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
521    
522  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
523  \begin{scriptsize}  \begin{scriptsize}
524  \begin{verbatim}  \begin{verbatim}
525  C:\>intgcd 8326413249250 12935482154386850  C:\>intgcd 8326413249250 12935482154386850
526  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
527                  arg1:                     8,326,413,249,250   (     13 digits)                  arg1:                     8,326,413,249,250   (     13 digits)
528  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
529                  arg2:                12,935,482,154,386,850   (     17 digits)                  arg2:                12,935,482,154,386,850   (     17 digits)
530  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
531       gcd(arg1, arg2):                                    50   (      2 digits)       gcd(arg1, arg2):                                    50   (      2 digits)
532  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
533    
534  C:\>intgcd 8326413249250 12935482154386850 -nf  C:\>intgcd 8326413249250 12935482154386850 -nf
535  8326413249250  8326413249250
536  12935482154386850  12935482154386850
537  50  50
538  \end{verbatim}  \end{verbatim}
539  \end{scriptsize}  \end{scriptsize}
540  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
541    
542  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
543  See also the \emph{arbint intgcd} Tcl extension,  See also the \emph{arbint intgcd} Tcl extension,
544  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:sgcd0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:sgcd0}.
545  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
546    
547  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
548  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
549  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
550  \subsection{The \emph{intlcm} Utility}  \subsection{The \emph{intlcm} Utility}
551  %Subsection tag: LCM0  %Subsection tag: LCM0
552  \label{cdcm0:sali0:slcm0}  \label{cdcm0:sali0:slcm0}
553    
554  \index{intlcm@\emph{intlcm}}  \index{intlcm@\emph{intlcm}}
555  \begin{dosutilcommandname}{intlcm}%  \begin{dosutilcommandname}{intlcm}%
556  calculates the l.c.m. (least common multiple)  calculates the l.c.m. (least common multiple)
557  of two integers.  (Mnemonic:  \emph{int}eger  of two integers.  (Mnemonic:  \emph{int}eger
558  \emph{l}east \emph{c}ommon \emph{m}ultiple.)  \emph{l}east \emph{c}ommon \emph{m}ultiple.)
559  \end{dosutilcommandname}  \end{dosutilcommandname}
560    
561  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
562  \dosutilcommandsynopsisline{intlcm}{sint\_1 sint\_2 [$<$options$>$]}  \dosutilcommandsynopsisline{intlcm}{sint\_1 sint\_2 [$<$options$>$]}
563  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
564    
565  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
566  The \emph{intlcm} utility calculates the l.c.m. of two  The \emph{intlcm} utility calculates the l.c.m. of two
567  integers.  integers.
568    
569  The mapping from arguments to output and the details  The mapping from arguments to output and the details
570  of how the l.c.m. is calculated are described  of how the l.c.m. is calculated are described
571  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:slcm0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:slcm0}.
572  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
573    
574  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
575  \begin{scriptsize}  \begin{scriptsize}
576  \begin{verbatim}  \begin{verbatim}
577  C:\>intlcm 12 69  C:\>intlcm 12 69
578  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
579                  arg1:                                    12   (      2 digits)                  arg1:                                    12   (      2 digits)
580  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
581                  arg2:                                    69   (      2 digits)                  arg2:                                    69   (      2 digits)
582  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
583       lcm(arg1, arg2):                                   276   (      3 digits)       lcm(arg1, arg2):                                   276   (      3 digits)
584  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
585  \end{verbatim}  \end{verbatim}
586  \end{scriptsize}  \end{scriptsize}
587  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
588    
589  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
590  See also the \emph{arbint intlcm} Tcl extension,  See also the \emph{arbint intlcm} Tcl extension,
591  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:slcm0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:slcm0}.
592  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
593    
594    
595  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
596  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
597  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
598  \subsection{The \emph{intexp} Utility}  \subsection{The \emph{intexp} Utility}
599  %Subsection tag: IXP0  %Subsection tag: IXP0
600  \label{cdcm0:sali0:sixp0}  \label{cdcm0:sali0:sixp0}
601    
602  \index{intexp@\emph{intexp}}  \index{intexp@\emph{intexp}}
603  \begin{dosutilcommandname}{intexp}%  \begin{dosutilcommandname}{intexp}%
604  exponentiates a signed integer to a non-negative integer  exponentiates a signed integer to a non-negative integer
605  power.  (Mnemonic:  \emph{int}eger  power.  (Mnemonic:  \emph{int}eger
606  \emph{exp}onent.)  \emph{exp}onent.)
607  \end{dosutilcommandname}  \end{dosutilcommandname}
608    
609  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
610  \dosutilcommandsynopsisline{intexp}{sint\_base uint32\_exponent [$<$options$>$]}  \dosutilcommandsynopsisline{intexp}{sint\_base uint32\_exponent [$<$options$>$]}
611  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
612    
613  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
614  The \emph{intexp} utility exponentiates an integer to a non-negative  The \emph{intexp} utility exponentiates an integer to a non-negative
615  integer power.  For convenience and simplicity, $0^0$ produces 1,  integer power.  For convenience and simplicity, $0^0$ produces 1,
616  which is inconsistent with the mathematical definition; but all other  which is inconsistent with the mathematical definition; but all other
617  exponentiations are as expected.  The mapping is more precisely described  exponentiations are as expected.  The mapping is more precisely described
618  with the \emph{arbint intexp} Tcl extension in  with the \emph{arbint intexp} Tcl extension in
619  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:sixp0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:sixp0}.
620  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
621    
622  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
623  \begin{scriptsize}  \begin{scriptsize}
624  \begin{verbatim}  \begin{verbatim}
625  C:\>intexp -22 41  C:\>intexp -22 41
626  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
627                  base: -                                  22   (      2 digits)                  base: -                                  22   (      2 digits)
628  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
629              exponent:                                    41   (      2 digits)              exponent:                                    41   (      2 digits)
630  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
631      base ** exponent: -                                  10,  (     56 digits)      base ** exponent: -                                  10,  (     56 digits)
632                          947,877,107,572,929,152,919,737,180,                          947,877,107,572,929,152,919,737,180,
633                          202,022,857,988,400,441,953,615,872                          202,022,857,988,400,441,953,615,872
634  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
635    
636  C:\>intexp -22 41 -nf  C:\>intexp -22 41 -nf
637  -22  -22
638  41  41
639  -10947877107572929152919737180202022857988400441953615872  -10947877107572929152919737180202022857988400441953615872
640  \end{verbatim}  \end{verbatim}
641  \end{scriptsize}  \end{scriptsize}
642  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
643    
644  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
645  See also the \emph{arbint intexp} Tcl extension,  See also the \emph{arbint intexp} Tcl extension,
646  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:sixp0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:sixp0}.
647  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
648    
649  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
650  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
651  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
652  \subsection{The \emph{intfac} Utility}  \subsection{The \emph{intfac} Utility}
653  %Subsection tag: IFC0  %Subsection tag: IFC0
654  \label{cdcm0:sali0:sifc0}  \label{cdcm0:sali0:sifc0}
655    
656  \index{intfac@\emph{intfac}}  \index{intfac@\emph{intfac}}
657  \begin{dosutilcommandname}{intfac}%  \begin{dosutilcommandname}{intfac}%
658  calculates the \index{factorial function}factorial of a non-negative  calculates the \index{factorial function}factorial of a non-negative
659  integer.  (Mnemonic:  \emph{int}eger  integer.  (Mnemonic:  \emph{int}eger
660  \emph{fac}torial.)  \emph{fac}torial.)
661  \end{dosutilcommandname}  \end{dosutilcommandname}
662    
663  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
664  \dosutilcommandsynopsisline{intfac}{uint32 [$<$options$>$]}  \dosutilcommandsynopsisline{intfac}{uint32 [$<$options$>$]}
665  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
666    
667  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
668  The \emph{intfac} utility calculates the factorial of  The \emph{intfac} utility calculates the factorial of
669  a non-negative integer.  0! is defined to be 1.  a non-negative integer.  0! is defined to be 1.
670    
671  This utility is useful for calculating the factorial of  This utility is useful for calculating the factorial of
672  integers where the result would be quite large (larger than  integers where the result would be quite large (larger than
673  could be displayed on a pocket calculator, for example).  could be displayed on a pocket calculator, for example).
674  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
675    
676  \begin{dosutilcommandremarks}  \begin{dosutilcommandremarks}
677  At the present time (07/2001, Version 1.04), the \emph{intfac} utility  At the present time (07/2001, Version 1.04), the \emph{intfac} utility
678  is constrained by the division operations required to convert from the  is constrained by the division operations required to convert from the
679  binary internal integer format to a base-10 ASCII representation.  binary internal integer format to a base-10 ASCII representation.
680  The \emph{intfac} utility will not calculate factorials of over about  The \emph{intfac} utility will not calculate factorials of over about
681  1,000 decimal digits without a fair delay.  In the future, algorithmic  1,000 decimal digits without a fair delay.  In the future, algorithmic
682  improvements may raise this limit.  improvements may raise this limit.
683  \end{dosutilcommandremarks}  \end{dosutilcommandremarks}
684    
685  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
686  \begin{scriptsize}  \begin{scriptsize}
687  \begin{verbatim}  \begin{verbatim}
688  C:\>intfac 47  C:\>intfac 47
689  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
690                   arg:                                    47   (      2 digits)                   arg:                                    47   (      2 digits)
691  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
692                  arg!:                               258,623,  (     60 digits)                  arg!:                               258,623,  (     60 digits)
693                          241,511,168,180,642,964,355,153,611,                          241,511,168,180,642,964,355,153,611,
694                          979,969,197,632,389,120,000,000,000                          979,969,197,632,389,120,000,000,000
695  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
696    
697  C:\>intfac 47 -noformat  C:\>intfac 47 -noformat
698  47  47
699  258623241511168180642964355153611979969197632389120000000000  258623241511168180642964355153611979969197632389120000000000
700  \end{verbatim}  \end{verbatim}
701  \end{scriptsize}  \end{scriptsize}
702  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
703    
704  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
705  See also the \emph{arbint intfac} Tcl extension,  See also the \emph{arbint intfac} Tcl extension,
706  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:sfac0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:sarb0:sfac0}.
707  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
708    
709    
710  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
711  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
712  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
713  \section{Rational Number Arithmetic Utilities}  \section{Rational Number Arithmetic Utilities}
714  %Section tag: RNU0  %Section tag: RNU0
715  \label{cdcm0:srnu0}  \label{cdcm0:srnu0}
716    
717    
718  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
719  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
720  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
721  \subsection{The \emph{rnadd} Utility}  \subsection{The \emph{rnadd} Utility}
722  %Subsection tag: RNA0  %Subsection tag: RNA0
723  \label{cdcm0:srnu0:srna0}  \label{cdcm0:srnu0:srna0}
724    
725  \index{rnadd@\emph{rnadd}}  \index{rnadd@\emph{rnadd}}
726  \begin{dosutilcommandname}{rnadd}%  \begin{dosutilcommandname}{rnadd}%
727  adds two rational numbers to produce a normalized rational result.    adds two rational numbers to produce a normalized rational result.  
728  (Mnemonic:  \emph{r}ational \emph{n}umber  (Mnemonic:  \emph{r}ational \emph{n}umber
729  \emph{add}ition.)  \emph{add}ition.)
730  \end{dosutilcommandname}  \end{dosutilcommandname}
731    
732  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
733  \dosutilcommandsynopsisline{rnadd}{srn srn [$<$options$>$]}  \dosutilcommandsynopsisline{rnadd}{srn srn [$<$options$>$]}
734  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
735    
736  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
737  The \emph{rnadd} utility calculates the sum of two arbitrary  The \emph{rnadd} utility calculates the sum of two arbitrary
738  rational numbers.  rational numbers.
739  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
740    
741  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
742  \begin{scriptsize}  \begin{scriptsize}
743  \begin{verbatim}  \begin{verbatim}
744  C:\>rnadd 3.29 42/67  C:\>rnadd 3.29 42/67
745  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
746              arg1_num:                                   329   (      3 digits)              arg1_num:                                   329   (      3 digits)
747  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
748              arg1_den:                                   100   (      3 digits)              arg1_den:                                   100   (      3 digits)
749  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
750              arg2_num:                                    42   (      2 digits)              arg2_num:                                    42   (      2 digits)
751  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
752              arg2_den:                                    67   (      2 digits)              arg2_den:                                    67   (      2 digits)
753  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
754            result_num:                                26,243   (      5 digits)            result_num:                                26,243   (      5 digits)
755  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
756            result_den:                                 6,700   (      4 digits)            result_den:                                 6,700   (      4 digits)
757  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
758  \end{verbatim}  \end{verbatim}
759  \end{scriptsize}  \end{scriptsize}
760  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
761    
762  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
763  See also the \emph{arbint rnadd} Tcl extension,  See also the \emph{arbint rnadd} Tcl extension,
764  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:srne0:srad0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:srne0:srad0}.
765  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
766    
767    
768  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
769  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
770  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
771  \subsection{The \emph{rnsub} Utility}  \subsection{The \emph{rnsub} Utility}
772  %Subsection tag: RSB0  %Subsection tag: RSB0
773  \label{cdcm0:srnu0:srsb0}  \label{cdcm0:srnu0:srsb0}
774    
775  \index{rnsub@\emph{rnsub}}  \index{rnsub@\emph{rnsub}}
776  \begin{dosutilcommandname}{rnsub}%  \begin{dosutilcommandname}{rnsub}%
777  subtracts two rational numbers to produce a normalized rational result.    subtracts two rational numbers to produce a normalized rational result.  
778  (Mnemonic:  \emph{r}ational \emph{n}umber  (Mnemonic:  \emph{r}ational \emph{n}umber
779  \emph{sub}traction.)  \emph{sub}traction.)
780  \end{dosutilcommandname}  \end{dosutilcommandname}
781    
782  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
783  \dosutilcommandsynopsisline{rnsub}{srn srn [$<$options$>$]}  \dosutilcommandsynopsisline{rnsub}{srn srn [$<$options$>$]}
784  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
785    
786  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
787  The \emph{rnsub} utility calculates the difference of two arbitrary  The \emph{rnsub} utility calculates the difference of two arbitrary
788  rational numbers.  The second argument is subtracted from the first,  rational numbers.  The second argument is subtracted from the first,
789  i.e. $arg_2 - arg_1$ is calculated.  i.e. $arg_2 - arg_1$ is calculated.
790  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
791    
792  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
793  \begin{scriptsize}  \begin{scriptsize}
794  \begin{verbatim}  \begin{verbatim}
795  C:\>rnsub 3.29 42/67  C:\>rnsub 3.29 42/67
796  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
797              arg1_num:                                   329   (      3 digits)              arg1_num:                                   329   (      3 digits)
798  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
799              arg1_den:                                   100   (      3 digits)              arg1_den:                                   100   (      3 digits)
800  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
801              arg2_num:                                    42   (      2 digits)              arg2_num:                                    42   (      2 digits)
802  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
803              arg2_den:                                    67   (      2 digits)              arg2_den:                                    67   (      2 digits)
804  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
805            result_num:                                17,843   (      5 digits)            result_num:                                17,843   (      5 digits)
806  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
807            result_den:                                 6,700   (      4 digits)            result_den:                                 6,700   (      4 digits)
808  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
809  \end{verbatim}  \end{verbatim}
810  \end{scriptsize}  \end{scriptsize}
811  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
812    
813  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
814  See also the \emph{arbint rnsub} Tcl extension,  See also the \emph{arbint rnsub} Tcl extension,
815  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:srne0:srsb0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:srne0:srsb0}.
816  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
817    
818    
819  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
820  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
821  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
822  \subsection{The \emph{rnmul} Utility}  \subsection{The \emph{rnmul} Utility}
823  %Subsection tag: RMU0  %Subsection tag: RMU0
824  \label{cdcm0:srnu0:srmu0}  \label{cdcm0:srnu0:srmu0}
825    
826  \index{rnmul@\emph{rnmul}}  \index{rnmul@\emph{rnmul}}
827  \begin{dosutilcommandname}{rnmul}%  \begin{dosutilcommandname}{rnmul}%
828  calculates the product of two rational numbers.  calculates the product of two rational numbers.
829  (Mnemonic:  \emph{r}ational  (Mnemonic:  \emph{r}ational
830  \emph{n}umber \emph{mul}tiplication.)  \emph{n}umber \emph{mul}tiplication.)
831  \end{dosutilcommandname}  \end{dosutilcommandname}
832    
833  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
834  \dosutilcommandsynopsisline{rnmul}{srn srn [$<$options$>$]}  \dosutilcommandsynopsisline{rnmul}{srn srn [$<$options$>$]}
835  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
836    
837  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
838  The \emph{rnmul} utility calculates the product  The \emph{rnmul} utility calculates the product
839  of two rational numbers.  of two rational numbers.
840  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
841    
842  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
843  \begin{scriptsize}  \begin{scriptsize}
844  \begin{verbatim}  \begin{verbatim}
845  E:\>rnmul 3.14 64/207  E:\>rnmul 3.14 64/207
846  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
847              arg1_num:                                   314   (      3 digits)              arg1_num:                                   314   (      3 digits)
848  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
849              arg1_den:                                   100   (      3 digits)              arg1_den:                                   100   (      3 digits)
850  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
851              arg2_num:                                    64   (      2 digits)              arg2_num:                                    64   (      2 digits)
852  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
853              arg2_den:                                   207   (      3 digits)              arg2_den:                                   207   (      3 digits)
854  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
855            result_num:                                 5,024   (      4 digits)            result_num:                                 5,024   (      4 digits)
856  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
857            result_den:                                 5,175   (      4 digits)            result_den:                                 5,175   (      4 digits)
858  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
859  \end{verbatim}  \end{verbatim}
860  \end{scriptsize}  \end{scriptsize}
861  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
862    
863  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
864  See also the \emph{arbint rnmul} Tcl extension,  See also the \emph{arbint rnmul} Tcl extension,
865  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:srne0:srmu0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:srne0:srmu0}.
866  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
867    
868    
869  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
870  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
871  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
872  \subsection{The \emph{rndiv} Utility}  \subsection{The \emph{rndiv} Utility}
873  %Subsection tag: RDV0  %Subsection tag: RDV0
874  \label{cdcm0:srnu0:srdv0}  \label{cdcm0:srnu0:srdv0}
875    
876  \index{rndiv@\emph{rndiv}}  \index{rndiv@\emph{rndiv}}
877  \begin{dosutilcommandname}{rndiv}%  \begin{dosutilcommandname}{rndiv}%
878  calculates the quotient of two rational numbers.  calculates the quotient of two rational numbers.
879  (Mnemonic:  \emph{r}ational  (Mnemonic:  \emph{r}ational
880  \emph{n}umber \emph{div}ision.)  \emph{n}umber \emph{div}ision.)
881  \end{dosutilcommandname}  \end{dosutilcommandname}
882    
883  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
884  \dosutilcommandsynopsisline{rndiv}{srn srn [$<$options$>$]}  \dosutilcommandsynopsisline{rndiv}{srn srn [$<$options$>$]}
885  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
886    
887  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
888  The \emph{rnmul} utility calculates the quotient  The \emph{rnmul} utility calculates the quotient
889  of two rational numbers.  The first argument is divided  of two rational numbers.  The first argument is divided
890  by the second; i.e. the quotient $arg_1 / arg_2$ is calculated.  by the second; i.e. the quotient $arg_1 / arg_2$ is calculated.
891  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
892    
893  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
894  \begin{scriptsize}  \begin{scriptsize}
895  \begin{verbatim}  \begin{verbatim}
896  E:\>rndiv 3.14 34/291  E:\>rndiv 3.14 34/291
897  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
898              arg1_num:                                   314   (      3 digits)              arg1_num:                                   314   (      3 digits)
899  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
900              arg1_den:                                   100   (      3 digits)              arg1_den:                                   100   (      3 digits)
901  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
902              arg2_num:                                    34   (      2 digits)              arg2_num:                                    34   (      2 digits)
903  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
904              arg2_den:                                   291   (      3 digits)              arg2_den:                                   291   (      3 digits)
905  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
906            result_num:                                45,687   (      5 digits)            result_num:                                45,687   (      5 digits)
907  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
908            result_den:                                 1,700   (      4 digits)            result_den:                                 1,700   (      4 digits)
909  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
910  \end{verbatim}  \end{verbatim}
911  \end{scriptsize}  \end{scriptsize}
912  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
913    
914  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
915  See also the \emph{arbint rndiv} Tcl extension,  See also the \emph{arbint rndiv} Tcl extension,
916  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:srne0:srdv0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:srne0:srdv0}.
917  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
918    
919    
920  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
921  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
922  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
923  \subsection{The \emph{rndeq} Utility}  \subsection{The \emph{rndeq} Utility}
924  %Subsection tag: RNQ0  %Subsection tag: RNQ0
925  \label{cdcm0:srnu0:srnq0}  \label{cdcm0:srnu0:srnq0}
926    
927  \index{rndeq@\emph{rndeq}}  \index{rndeq@\emph{rndeq}}
928  \begin{dosutilcommandname}{rndeq}%  \begin{dosutilcommandname}{rndeq}%
929  calculates the decimal equivalent of a rational number.  calculates the decimal equivalent of a rational number.
930  (Mnemonic:  \emph{r}ational \emph{n}umber  (Mnemonic:  \emph{r}ational \emph{n}umber
931  \emph{d}ecimal \emph{eq}uivalent.)  \emph{d}ecimal \emph{eq}uivalent.)
932  \end{dosutilcommandname}  \end{dosutilcommandname}
933    
934  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
935  \dosutilcommandsynopsisline{rndeq}{srn [$<$options$>$]}  \dosutilcommandsynopsisline{rndeq}{srn [$<$options$>$]}
936  \dosutilcommandsynopsisline{rndeq}{srn uint [$<$options$>$]}  \dosutilcommandsynopsisline{rndeq}{srn uint [$<$options$>$]}
937  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
938    
939  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
940  The \emph{rndeq} utility calculates the decimal equivalent  The \emph{rndeq} utility calculates the decimal equivalent
941  of a rational number using a large integer  of a rational number using a large integer
942  algorithm.  algorithm.
943    
944  Let $a/b$ be a rational number that we wish to express  Let $a/b$ be a rational number that we wish to express
945  as a decimal number, let $N$ be an integral power  as a decimal number, let $N$ be an integral power
946  of 10, and let $x$ be an integer chosen so that $x/N$  of 10, and let $x$ be an integer chosen so that $x/N$
947  is an approximation to $a/b$.  is an approximation to $a/b$.
948    
949  If we choose  If we choose
950    
951  \begin{equation}  \begin{equation}
952  \label{eq:cdcm0:sali0:srnq0:01}  \label{eq:cdcm0:sali0:srnq0:01}
953  x = sgn \left( {\frac{a}{b}} \right)  x = sgn \left( {\frac{a}{b}} \right)
954  \left\lfloor {\left| \frac{a}{b} \right| N} \right\rfloor ,  \left\lfloor {\left| \frac{a}{b} \right| N} \right\rfloor ,
955  \end{equation}  \end{equation}
956    
957  it can be shown that  it can be shown that
958    
959  \begin{equation}  \begin{equation}
960  \label{eq:cdcm0:sali0:srnq0:02}  \label{eq:cdcm0:sali0:srnq0:02}
961  \left| {\frac{a}{b}} \right| - \frac{1}{N}  \left| {\frac{a}{b}} \right| - \frac{1}{N}
962  <  <
963  \frac{\left\lfloor {\left| {\frac{a}{b}} \right| N} \right\rfloor}{N}  \frac{\left\lfloor {\left| {\frac{a}{b}} \right| N} \right\rfloor}{N}
964  \leq  \leq
965  \left|{\frac{a}{b}}\right|.  \left|{\frac{a}{b}}\right|.
966  \end{equation}  \end{equation}
967    
968  In other words, the result if $x$ is chosen as specified in  In other words, the result if $x$ is chosen as specified in
969  (\ref{eq:cdcm0:sali0:srnq0:01}), $x/N$ will be at or up to one numerator  (\ref{eq:cdcm0:sali0:srnq0:01}), $x/N$ will be at or up to one numerator
970  count less in magnitude than $a/b$.  Stated differently,  count less in magnitude than $a/b$.  Stated differently,
971  $x/N$ is ``truncated down'' in magnitude.  $x/N$ is ``truncated down'' in magnitude.
972    
973  The \emph{rndeq} utility performs the mapping implied by  The \emph{rndeq} utility performs the mapping implied by
974  (\ref{eq:cdcm0:sali0:srnq0:01}) and  (\ref{eq:cdcm0:sali0:srnq0:01}) and
975  (\ref{eq:cdcm0:sali0:srnq0:02}), by default using  (\ref{eq:cdcm0:sali0:srnq0:02}), by default using
976  $N=10^{108}$.  The value of $N=10^{108}$ was chosen  $N=10^{108}$.  The value of $N=10^{108}$ was chosen
977  because it produces an attractive display format at  because it produces an attractive display format at
978  27 digits per line, and also places the imaginary decimal  27 digits per line, and also places the imaginary decimal
979  point between lines so it is easier to interpret the output of  point between lines so it is easier to interpret the output of
980  this utility.  An example is interpreted in the sample invocations  this utility.  An example is interpreted in the sample invocations
981  below.  below.
982    
983  This utility will accept an optional second parameter, which  This utility will accept an optional second parameter, which
984  is a value of $N$ to override the default of $10^{108}$.  This  is a value of $N$ to override the default of $10^{108}$.  This
985  optional second parameter can be used to provide more decimal places,  optional second parameter can be used to provide more decimal places,
986  or to provide a different type of mapping.\footnote{Please be aware that integers  or to provide a different type of mapping.\footnote{Please be aware that integers
987  may be specified using scientific notation.  For example, to effectively double  may be specified using scientific notation.  For example, to effectively double
988  the number of decimal places displayed by \texttt{rndeq} in the  the number of decimal places displayed by \texttt{rndeq} in the
989  invocation example below, one might enter the command line  invocation example below, one might enter the command line
990  \texttt{rndeq 5345/319 1e216}.  We would regret it if this fact were unknown  \texttt{rndeq 5345/319 1e216}.  We would regret it if this fact were unknown
991  and some desperate user were to enter the digit ``1'' followed by  and some desperate user were to enter the digit ``1'' followed by
992  216 zeros!}  216 zeros!}
993    
994  It is not required that the second parameter, if supplied, be a power of  It is not required that the second parameter, if supplied, be a power of
995  10---the mappings described by the equations above will be carried  10---the mappings described by the equations above will be carried
996  out with \emph{any} supplied denominator.    out with \emph{any} supplied denominator.  
997  However, it is not intuitively obvious how this utility would be  However, it is not intuitively obvious how this utility would be
998  useful with a denominator that is not a power of 10.  useful with a denominator that is not a power of 10.
999  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
1000    
1001  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
1002  \begin{scriptsize}  \begin{scriptsize}
1003  \begin{verbatim}  \begin{verbatim}
1004  C:\>rndeq 5345/319  C:\>rndeq 5345/319
1005  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1006               arg_num:                                 5,345   (      4 digits)               arg_num:                                 5,345   (      4 digits)
1007  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1008               arg_den:                                   319   (      3 digits)               arg_den:                                   319   (      3 digits)
1009  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1010               dap_num:                                    16,  (    110 digits)               dap_num:                                    16,  (    110 digits)
1011                          755,485,893,416,927,899,686,520,376,                          755,485,893,416,927,899,686,520,376,
1012                          175,548,589,341,692,789,968,652,037,                          175,548,589,341,692,789,968,652,037,
1013                          617,554,858,934,169,278,996,865,203,                          617,554,858,934,169,278,996,865,203,
1014                          761,755,485,893,416,927,899,686,520                          761,755,485,893,416,927,899,686,520
1015  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1016               dap_den:                                     1,  (    109 digits)               dap_den:                                     1,  (    109 digits)
1017                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1018                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1019                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1020                          000,000,000,000,000,000,000,000,000                          000,000,000,000,000,000,000,000,000
1021  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1022  \end{verbatim}  \end{verbatim}
1023  \end{scriptsize}  \end{scriptsize}
1024    
1025  It can be seen from the sample invocation above that  It can be seen from the sample invocation above that
1026  5345/319$\approx$16.755---note how the imaginary decimal point is placed  5345/319$\approx$16.755---note how the imaginary decimal point is placed
1027  between lines of \texttt{dap\_num}.  It can also be seen that the  between lines of \texttt{dap\_num}.  It can also be seen that the
1028  decimal representation repeats, i.e.  decimal representation repeats, i.e.
1029    
1030  \begin{equation}  \begin{equation}
1031  \frac{5345}{319} = 16.\overline{7554858934169278996865203761}.  \frac{5345}{319} = 16.\overline{7554858934169278996865203761}.
1032  \end{equation}  \end{equation}
1033  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
1034    
1035    
1036  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1037  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1038  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1039  \subsection{The \emph{rnred} Utility}  \subsection{The \emph{rnred} Utility}
1040  %Subsection tag: RNR0  %Subsection tag: RNR0
1041  \label{cdcm0:srnu0:srnr0}  \label{cdcm0:srnu0:srnr0}
1042    
1043  \index{rnred@\emph{rnred}}  \index{rnred@\emph{rnred}}
1044  \begin{dosutilcommandname}{rnred}%  \begin{dosutilcommandname}{rnred}%
1045  reduces a rational number to lowest terms and normalizes it.  reduces a rational number to lowest terms and normalizes it.
1046  (Mnemonic:  \emph{r}ational  (Mnemonic:  \emph{r}ational
1047  \emph{n}umber \emph{red}uce and normalize.)  \emph{n}umber \emph{red}uce and normalize.)
1048  \end{dosutilcommandname}  \end{dosutilcommandname}
1049    
1050  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
1051  \dosutilcommandsynopsisline{rnred}{srn [$<$options$>$]}  \dosutilcommandsynopsisline{rnred}{srn [$<$options$>$]}
1052  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
1053    
1054  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
1055  The \emph{rnred} reduces a rational number to its lowest terms  The \emph{rnred} reduces a rational number to its lowest terms
1056  and normalizes it.  This process is the same process  and normalizes it.  This process is the same process
1057  described in the description of the \emph{arbint rnred} Tcl  described in the description of the \emph{arbint rnred} Tcl
1058  extension, Section \cxtnzeroxrefhyphen{}\ref{cxtn0:srne0:srnr0}.  extension, Section \cxtnzeroxrefhyphen{}\ref{cxtn0:srne0:srnr0}.
1059  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
1060    
1061  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
1062  \begin{scriptsize}  \begin{scriptsize}
1063  \begin{verbatim}  \begin{verbatim}
1064  C:\>rnred 422.414  C:\>rnred 422.414
1065  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1066             numerator:                               211,207   (      6 digits)             numerator:                               211,207   (      6 digits)
1067  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1068           denominator:                                   500   (      3 digits)           denominator:                                   500   (      3 digits)
1069  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1070    
1071  C:\>rnred 422.414 -nf  C:\>rnred 422.414 -nf
1072  211207  211207
1073  500  500
1074  \end{verbatim}  \end{verbatim}
1075  \end{scriptsize}  \end{scriptsize}
1076  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
1077    
1078  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
1079  See also the \emph{arbint rnred} Tcl extension,  See also the \emph{arbint rnred} Tcl extension,
1080  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:srne0:srnr0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:srne0:srnr0}.
1081  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
1082    
1083    
1084  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1085  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1086  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1087  \section[Number Theory, CF, And Approximation Utilities]  \section[Number Theory, CF, And Approximation Utilities]
1088          {Number Theory, Continued Fraction, And Best Rational Approximation          {Number Theory, Continued Fraction, And Best Rational Approximation
1089           Utilities}           Utilities}
1090  %Section tag: nth0  %Section tag: nth0
1091  \label{cdcm0:snth0}  \label{cdcm0:snth0}
1092    
1093    
1094  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1095  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1096  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1097  \subsection{The \emph{cfratnum} Utility}  \subsection{The \emph{cfratnum} Utility}
1098  %Subsection tag: CFR0  %Subsection tag: CFR0
1099  \label{cdcm0:snth0:scfr0}  \label{cdcm0:snth0:scfr0}
1100    
1101  \index{cfratnum@\emph{cfratnum}}  \index{cfratnum@\emph{cfratnum}}
1102  \begin{dosutilcommandname}{cfratnum}%  \begin{dosutilcommandname}{cfratnum}%
1103  calculates the continued fraction partial quotients and convergents  calculates the continued fraction partial quotients and convergents
1104  of a non-negative rational number.  (Mnemonic:  \emph{c}ontinued  of a non-negative rational number.  (Mnemonic:  \emph{c}ontinued
1105  \emph{f}raction partial quotients and convergents of  \emph{f}raction partial quotients and convergents of
1106  a \emph{rat}ional \emph{num}ber.)  a \emph{rat}ional \emph{num}ber.)
1107  \end{dosutilcommandname}  \end{dosutilcommandname}
1108    
1109  \begin{dosutilcommandsynopsis}  \begin{dosutilcommandsynopsis}
1110  \dosutilcommandsynopsisline{cfratnum}{urn [$<$options$>$]}  \dosutilcommandsynopsisline{cfratnum}{urn [$<$options$>$]}
1111  \end{dosutilcommandsynopsis}  \end{dosutilcommandsynopsis}
1112    
1113  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
1114  The \emph{cfratnum} utility calculates the continued fraction  The \emph{cfratnum} utility calculates the continued fraction
1115  partial quotients and convergents of a non-negative rational number.  partial quotients and convergents of a non-negative rational number.
1116  This information can be useful in a variety of contexts, including  This information can be useful in a variety of contexts, including
1117  finding best rational approximations.  finding best rational approximations.
1118    
1119  Additionally, this DOS utility provides a decimal approximation  Additionally, this DOS utility provides a decimal approximation
1120  of each convergent, using a denominator of  of each convergent, using a denominator of
1121  $10^{108}$ (see the description of the \emph{rndeq} utility, Section  $10^{108}$ (see the description of the \emph{rndeq} utility, Section
1122  \ref{cdcm0:srnu0:srnq0}).  \ref{cdcm0:srnu0:srnq0}).
1123  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
1124    
1125  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
1126  \begin{scriptsize}  \begin{scriptsize}
1127  \begin{verbatim}  \begin{verbatim}
1128  C:\>cfratnum 3.14  C:\>cfratnum 3.14
1129  ******************************************************************************  ******************************************************************************
1130  *******************   Continued Fraction Representation    *******************  *******************   Continued Fraction Representation    *******************
1131  ******************************************************************************  ******************************************************************************
1132       Input Numerator:                                   314   (      3 digits)       Input Numerator:                                   314   (      3 digits)
1133  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1134     Input Denominator:                                   100   (      3 digits)     Input Denominator:                                   100   (      3 digits)
1135  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1136           dividend(0):                                   314   (      3 digits)           dividend(0):                                   314   (      3 digits)
1137  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1138            divisor(0):                                   100   (      3 digits)            divisor(0):                                   100   (      3 digits)
1139  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1140                  a(0):                                     3   (      1 digit )                  a(0):                                     3   (      1 digit )
1141  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1142                  p(0):                                     3   (      1 digit )                  p(0):                                     3   (      1 digit )
1143  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1144                  q(0):                                     1   (      1 digit )                  q(0):                                     1   (      1 digit )
1145  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1146              dap_h(0):                                     3,  (    109 digits)              dap_h(0):                                     3,  (    109 digits)
1147                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1148                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1149                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1150                          000,000,000,000,000,000,000,000,000                          000,000,000,000,000,000,000,000,000
1151  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1152              dap_k(0):                                     1,  (    109 digits)              dap_k(0):                                     1,  (    109 digits)
1153                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1154                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1155                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1156                          000,000,000,000,000,000,000,000,000                          000,000,000,000,000,000,000,000,000
1157  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1158           dividend(1):                                   100   (      3 digits)           dividend(1):                                   100   (      3 digits)
1159  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1160            divisor(1):                                    14   (      2 digits)            divisor(1):                                    14   (      2 digits)
1161  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1162                  a(1):                                     7   (      1 digit )                  a(1):                                     7   (      1 digit )
1163  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1164                  p(1):                                    22   (      2 digits)                  p(1):                                    22   (      2 digits)
1165  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1166                  q(1):                                     7   (      1 digit )                  q(1):                                     7   (      1 digit )
1167  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1168              dap_h(1):                                     3,  (    109 digits)              dap_h(1):                                     3,  (    109 digits)
1169                          142,857,142,857,142,857,142,857,142,                          142,857,142,857,142,857,142,857,142,
1170                          857,142,857,142,857,142,857,142,857,                          857,142,857,142,857,142,857,142,857,
1171                          142,857,142,857,142,857,142,857,142,                          142,857,142,857,142,857,142,857,142,
1172                          857,142,857,142,857,142,857,142,857                          857,142,857,142,857,142,857,142,857
1173  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1174              dap_k(1):                                     1,  (    109 digits)              dap_k(1):                                     1,  (    109 digits)
1175                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1176                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1177                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1178                          000,000,000,000,000,000,000,000,000                          000,000,000,000,000,000,000,000,000
1179  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1180           dividend(2):                                    14   (      2 digits)           dividend(2):                                    14   (      2 digits)
1181  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1182            divisor(2):                                     2   (      1 digit )            divisor(2):                                     2   (      1 digit )
1183  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1184                  a(2):                                     7   (      1 digit )                  a(2):                                     7   (      1 digit )
1185  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1186                  p(2):                                   157   (      3 digits)                  p(2):                                   157   (      3 digits)
1187  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1188                  q(2):                                    50   (      2 digits)                  q(2):                                    50   (      2 digits)
1189  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1190              dap_h(2):                                     3,  (    109 digits)              dap_h(2):                                     3,  (    109 digits)
1191                          140,000,000,000,000,000,000,000,000,                          140,000,000,000,000,000,000,000,000,
1192                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1193                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1194                          000,000,000,000,000,000,000,000,000                          000,000,000,000,000,000,000,000,000
1195  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1196              dap_k(2):                                     1,  (    109 digits)              dap_k(2):                                     1,  (    109 digits)
1197                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1198                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1199                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1200                          000,000,000,000,000,000,000,000,000                          000,000,000,000,000,000,000,000,000
1201  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1202  \end{verbatim}  \end{verbatim}
1203  \end{scriptsize}  \end{scriptsize}
1204    
1205  Note in the sample invocation above that each convergent  Note in the sample invocation above that each convergent
1206  also includes a decimal approximation.  For example,  also includes a decimal approximation.  For example,
1207  in the invocation above, it can be seen that  in the invocation above, it can be seen that
1208  22/7 $\approx$ 3.142857142857 \ldots{}.  22/7 $\approx$ 3.142857142857 \ldots{}.
1209    
1210  Note also that at each round of calculation of partial  Note also that at each round of calculation of partial
1211  quotients and convergents, the remainder is not shown because  quotients and convergents, the remainder is not shown because
1212  it becomes the divisor of the next round, and so it would be  it becomes the divisor of the next round, and so it would be
1213  redundant to show it.  Note also that the final non-zero remainder  redundant to show it.  Note also that the final non-zero remainder
1214  (which is the g.c.d. of the numerator and denominator)  (which is the g.c.d. of the numerator and denominator)
1215  appears as the final divisor.  In the sample  appears as the final divisor.  In the sample
1216  invocation above, it can be seen that the g.c.d. of  invocation above, it can be seen that the g.c.d. of
1217  314 and 100 is the integer labeled as  314 and 100 is the integer labeled as
1218  \texttt{divisor(2)}, which has the value of 2.  \texttt{divisor(2)}, which has the value of 2.
1219  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
1220    
1221  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
1222  See also the \emph{arbint cfratnum} Tcl extension,  See also the \emph{arbint cfratnum} Tcl extension,
1223  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:snth0:scfr0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:snth0:scfr0}.
1224  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
1225    
1226    
1227  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1228  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1229  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1230  \subsection{The \emph{cfbrapab} Utility}  \subsection{The \emph{cfbrapab} Utility}
1231  %Subsection tag: BRA0  %Subsection tag: BRA0
1232  \label{cdcm0:snth0:sbra0}  \label{cdcm0:snth0:sbra0}
1233    
1234  \index{cfbrapab@\emph{cfbrapab}}  \index{cfbrapab@\emph{cfbrapab}}
1235  \begin{dosutilcommandname}{cfbrapab}%  \begin{dosutilcommandname}{cfbrapab}%
1236  calculates the best rational approximation to a  calculates the best rational approximation to a
1237  rational  rational
1238  number in the Farey series of order  number in the Farey series of order
1239  $k_{MAX}$, or in a rectangular region of the integer lattice  $k_{MAX}$, or in a rectangular region of the integer lattice
1240  defined by $k \leq k_{MAX}$ and $h \leq h_{MAX}$.  defined by $k \leq k_{MAX}$ and $h \leq h_{MAX}$.
1241  (Mnemonic:  \emph{c}ontinued  (Mnemonic:  \emph{c}ontinued
1242  \emph{f}raction \emph{b}est \emph{r}ational \emph{ap}proximation  \emph{f}raction \emph{b}est \emph{r}ational \emph{ap}proximation
1243  in $F_{a, \overline{b}}$.)  in $F_{a, \overline{b}}$.)
1244  \end{dosutilcommandname}  \end{dosutilcommandname}
1245    
1246  \begin{dosutilcommanddescription}  \begin{dosutilcommanddescription}
1247  Except for display format,  Except for display format,
1248  this utility behaves the same way and  this utility behaves the same way and
1249  accepts the same options as the \emph{arbint cfbrapab}  accepts the same options as the \emph{arbint cfbrapab}
1250  Tcl extension, described in Section \cxtnzeroxrefhyphen{}\ref{cxtn0:snth0:sbra0}.  Tcl extension, described in Section \cxtnzeroxrefhyphen{}\ref{cxtn0:snth0:sbra0}.
1251  Please see the documentation of this Tcl extension, which also applies  Please see the documentation of this Tcl extension, which also applies
1252  to this DOS command-line utility.  to this DOS command-line utility.
1253  \end{dosutilcommanddescription}  \end{dosutilcommanddescription}
1254    
1255    
1256  \begin{dosutilcommandsampleinvocations}  \begin{dosutilcommandsampleinvocations}
1257  \begin{scriptsize}  \begin{scriptsize}
1258  \begin{verbatim}  \begin{verbatim}
1259  C:\swprojs\cfbrapab\Release>cfbrapab 1.6093 255 255  C:\swprojs\cfbrapab\Release>cfbrapab 1.6093 255 255
1260  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1261  MAJOR MODE:  Finding closest rational number(s) under the constraints.  MAJOR MODE:  Finding closest rational number(s) under the constraints.
1262  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1263     RI_IN   Numerator:                                16,093   (      5 digits)     RI_IN   Numerator:                                16,093   (      5 digits)
1264  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1265     RI_IN Denominator:                                10,000   (      5 digits)     RI_IN Denominator:                                10,000   (      5 digits)
1266  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1267                 K_MAX:                                   255   (      3 digits)                 K_MAX:                                   255   (      3 digits)
1268  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1269                 H_MAX:                                   255   (      3 digits)                 H_MAX:                                   255   (      3 digits)
1270  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1271        approx_num(-1):                                   243   (      3 digits)        approx_num(-1):                                   243   (      3 digits)
1272  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1273        approx_den(-1):                                   151   (      3 digits)        approx_den(-1):                                   151   (      3 digits)
1274  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1275           dap_num(-1):                                     1,  (    109 digits)           dap_num(-1):                                     1,  (    109 digits)
1276                          609,271,523,178,807,947,019,867,549,                          609,271,523,178,807,947,019,867,549,
1277                          668,874,172,185,430,463,576,158,940,                          668,874,172,185,430,463,576,158,940,
1278                          397,350,993,377,483,443,708,609,271,                          397,350,993,377,483,443,708,609,271,
1279                          523,178,807,947,019,867,549,668,874                          523,178,807,947,019,867,549,668,874
1280  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1281           dap_den(-1):                                     1,  (    109 digits)           dap_den(-1):                                     1,  (    109 digits)
1282                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1283                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1284                          000,000,000,000,000,000,000,000,000,                          000,000,000,000,000,000,000,000,000,
1285                          000,000,000,000,000,000,000,000,000                          000,000,000,000,000,000,000,000,000
1286  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1287         error_num(-1): -                                  43   (      2 digits)         error_num(-1): -                                  43   (      2 digits)
1288  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1289         error_den(-1):                             1,510,000   (      7 digits)         error_den(-1):                             1,510,000   (      7 digits)
1290  ------------------------------------------------------------------------------  ------------------------------------------------------------------------------
1291  \end{verbatim}  \end{verbatim}
1292  \end{scriptsize}  \end{scriptsize}
1293    
1294  Note in the sample invocation above that the  Note in the sample invocation above that the
1295  decimal equivalent of the approximation is also provided.  decimal equivalent of the approximation is also provided.
1296  Note also that the different parameters of this utility produce  Note also that the different parameters of this utility produce
1297  different output formats which are not documented here, for  different output formats which are not documented here, for
1298  brevity.  For example, using the \texttt{-pred} or \texttt{-succ}  brevity.  For example, using the \texttt{-pred} or \texttt{-succ}
1299  options does not produce decimal approximation information, because  options does not produce decimal approximation information, because
1300  these options are not normally used for approximation---such  these options are not normally used for approximation---such
1301  behaviors are inconsequential and not documented.  behaviors are inconsequential and not documented.
1302  \end{dosutilcommandsampleinvocations}  \end{dosutilcommandsampleinvocations}
1303    
1304    
1305  \begin{dosutilcommandseealso}  \begin{dosutilcommandseealso}
1306  This extension uses the continued fraction  This extension uses the continued fraction
1307  algorithms presented in Chapter \ccfrzeroxrefhyphen{}\ref{ccfr0}.  algorithms presented in Chapter \ccfrzeroxrefhyphen{}\ref{ccfr0}.
1308  See also the \emph{arbint cfbrapab} Tcl extension,  See also the \emph{arbint cfbrapab} Tcl extension,
1309  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:snth0:sbra0}.  Section \cxtnzeroxrefhyphen{}\ref{cxtn0:snth0:sbra0}.
1310  \end{dosutilcommandseealso}  \end{dosutilcommandseealso}
1311    
1312    
1313  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1314  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1315  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1316  \section{Authors And Acknowledgements}  \section{Authors And Acknowledgements}
1317  %Section tag: ACK0  %Section tag: ACK0
1318    
1319    
1320  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1321  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1322  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1323  \section{Exercises}  \section{Exercises}
1324  %Section tag: EXE0  %Section tag: EXE0
1325    
1326    
1327    
1328  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1329    
1330  \noindent\begin{figure}[!b]  \noindent\begin{figure}[!b]
1331  \noindent\rule[-0.25in]{\textwidth}{1pt}  \noindent\rule[-0.25in]{\textwidth}{1pt}
1332  \begin{tiny}  \begin{tiny}
1333  \begin{verbatim}  \begin{verbatim}
1334  $RCSfile: c_dcm0.tex,v $  $RCSfile: c_dcm0.tex,v $
1335  $Source: /home/dashley/cvsrep/e3ft_gpl01/e3ft_gpl01/dtaipubs/esrgubka/c_dcm0/c_dcm0.tex,v $  $Source: /home/dashley/cvsrep/e3ft_gpl01/e3ft_gpl01/dtaipubs/esrgubka/c_dcm0/c_dcm0.tex,v $
1336  $Revision: 1.13 $  $Revision: 1.13 $
1337  $Author: dtashley $  $Author: dtashley $
1338  $Date: 2001/08/18 18:37:56 $  $Date: 2001/08/18 18:37:56 $
1339  \end{verbatim}  \end{verbatim}
1340  \end{tiny}  \end{tiny}
1341  \noindent\rule[0.25in]{\textwidth}{1pt}  \noindent\rule[0.25in]{\textwidth}{1pt}
1342  \end{figure}  \end{figure}
1343    
1344  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1345  % $Log: c_dcm0.tex,v $  % $Log: c_dcm0.tex,v $
1346  % Revision 1.13  2001/08/18 18:37:56  dtashley  % Revision 1.13  2001/08/18 18:37:56  dtashley
1347  % Preparation for v1.05 release.  % Preparation for v1.05 release.
1348  %  %
1349  % Revision 1.12  2001/08/16 19:53:27  dtashley  % Revision 1.12  2001/08/16 19:53:27  dtashley
1350  % Beginning to prepare for v1.05 release.  % Beginning to prepare for v1.05 release.
1351  %  %
1352  % Revision 1.11  2001/08/12 10:15:33  dtashley  % Revision 1.11  2001/08/12 10:15:33  dtashley
1353  % Safety check-in.  Substantial progress.  % Safety check-in.  Substantial progress.
1354  %  %
1355  % Revision 1.10  2001/08/10 00:56:07  dtashley  % Revision 1.10  2001/08/10 00:56:07  dtashley
1356  % Completion of basic rational number arithmetic utilities and extensions.  % Completion of basic rational number arithmetic utilities and extensions.
1357  %  %
1358  % Revision 1.9  2001/08/08 02:25:03  dtashley  % Revision 1.9  2001/08/08 02:25:03  dtashley
1359  % Completion of RNRED utility and ARBINT RNRED Tcl extension.  % Completion of RNRED utility and ARBINT RNRED Tcl extension.
1360  %  %
1361  % Revision 1.8  2001/08/07 10:46:44  dtashley  % Revision 1.8  2001/08/07 10:46:44  dtashley
1362  % Completion of CFRATNUM Tcl extension and DOS command-line utility.  % Completion of CFRATNUM Tcl extension and DOS command-line utility.
1363  %  %
1364  % Revision 1.7  2001/08/01 03:37:39  dtashley  % Revision 1.7  2001/08/01 03:37:39  dtashley
1365  % Finished most primitive integer operations, both as Tcl extensions and  % Finished most primitive integer operations, both as Tcl extensions and
1366  % as DOS command-line utilities, such as addition, subtraction,  % as DOS command-line utilities, such as addition, subtraction,
1367  % multiplication, division, and modulo.  % multiplication, division, and modulo.
1368  %  %
1369  % Revision 1.6  2001/07/30 02:54:17  dtashley  % Revision 1.6  2001/07/30 02:54:17  dtashley
1370  % INTFAC extension and command-line utility finished.  % INTFAC extension and command-line utility finished.
1371  %  %
1372  % Revision 1.5  2001/07/23 21:40:43  dtashley  % Revision 1.5  2001/07/23 21:40:43  dtashley
1373  % Hopefully final changes to the section about convergents as best  % Hopefully final changes to the section about convergents as best
1374  % approximations.  Tool documentation changes.  % approximations.  Tool documentation changes.
1375  %  %
1376  % Revision 1.4  2001/07/23 06:50:44  dtashley  % Revision 1.4  2001/07/23 06:50:44  dtashley
1377  % Completion of INTFAC command and documentation.  % Completion of INTFAC command and documentation.
1378  %  %
1379  % Revision 1.3  2001/07/23 03:30:20  dtashley  % Revision 1.3  2001/07/23 03:30:20  dtashley
1380  % Edits.  % Edits.
1381  %  %
1382  % Revision 1.2  2001/07/13 06:57:50  dtashley  % Revision 1.2  2001/07/13 06:57:50  dtashley
1383  % Safety check-in.  % Safety check-in.
1384  %  %
1385  % Revision 1.1  2001/07/11 20:10:30  dtashley  % Revision 1.1  2001/07/11 20:10:30  dtashley
1386  % Chapter on DOS console-mode utilities added.  % Chapter on DOS console-mode utilities added.
1387  %  %
1388  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1389  %End of file C_DCM0.TEX  %End of file C_DCM0.TEX
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