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