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diff --git a/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-math-numberprinting.tex b/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-math-numberprinting.tex new file mode 100644 index 00000000000..9deedd2e504 --- /dev/null +++ b/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-math-numberprinting.tex @@ -0,0 +1,528 @@ +\section{Number Printing} + +\label{pgfmath-numberprinting}% + +{\emph{An extension by Christian Feuers\"anger}} + +\medskip +\noindent +\pgfname\ supports number printing in different styles and rounds to arbitrary precision. + +\begin{command}{\pgfmathprintnumber\marg{x}} +Generates pretty-printed output for the (real) number \marg{x}. The input number \marg{x} is parsed using |\pgfmathfloatparsenumber| which allows arbitrary precision. + +Numbers are typeset in math mode using the current set of number printing options, see below. Optional arguments can also be provided using |\pgfmathprintnumber[|\meta{options}|]|\marg{x}. +\end{command} + +\begin{command}{\pgfmathprintnumberto\marg{x}\marg{\textbackslash macro}} + Returns the resulting number into \marg{\textbackslash macro} instead of typesetting it directly. +\end{command} + +\begin{key}{/pgf/number format/fixed} +Configures |\pgfmathprintnumber| to round the number to a fixed number of digits after the period, discarding any trailing zeros. + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,fixed,precision=2} +\pgfmathprintnumber{4.568}\hspace{1em} +\pgfmathprintnumber{5e-04}\hspace{1em} +\pgfmathprintnumber{0.1}\hspace{1em} +\pgfmathprintnumber{24415.98123}\hspace{1em} +\pgfmathprintnumber{123456.12345} +\end{codeexample} + +See section~\ref{sec:number:styles} for how to change the appearance. +\end{key} + +\begin{key}{/pgf/number format/fixed zerofill=\marg{boolean} (default true)} +Enables or disables zero filling for any number drawn in fixed point format. + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,fixed,fixed zerofill,precision=2} +\pgfmathprintnumber{4.568}\hspace{1em} +\pgfmathprintnumber{5e-04}\hspace{1em} +\pgfmathprintnumber{0.1}\hspace{1em} +\pgfmathprintnumber{24415.98123}\hspace{1em} +\pgfmathprintnumber{123456.12345} +\end{codeexample} +This key affects numbers drawn with |fixed| or |std| styles (the latter only if no scientific format is chosen). +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,std,fixed zerofill,precision=2} +\pgfmathprintnumber{4.568}\hspace{1em} +\pgfmathprintnumber{5e-05}\hspace{1em} +\pgfmathprintnumber{1}\hspace{1em} +\pgfmathprintnumber{123456.12345} +\end{codeexample} + +See section~\ref{sec:number:styles} for how to change the appearance. +\end{key} + +\begin{key}{/pgf/number format/sci} +Configures |\pgfmathprintnumber| to display numbers in scientific format, that means sign, mantissa and exponent (basis~$10$). The mantissa is rounded to the desired |precision| (or |sci precision|, see below). + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,sci,precision=2} +\pgfmathprintnumber{4.568}\hspace{1em} +\pgfmathprintnumber{5e-04}\hspace{1em} +\pgfmathprintnumber{0.1}\hspace{1em} +\pgfmathprintnumber{24415.98123}\hspace{1em} +\pgfmathprintnumber{123456.12345} +\end{codeexample} + +See section~\ref{sec:number:styles} for how to change the exponential display style. +\end{key} + +\begin{key}{/pgf/number format/sci zerofill=\marg{boolean} (default true)} +Enables or disables zero filling for any number drawn in scientific format. + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,sci,sci zerofill,precision=2} +\pgfmathprintnumber{4.568}\hspace{1em} +\pgfmathprintnumber{5e-04}\hspace{1em} +\pgfmathprintnumber{0.1}\hspace{1em} +\pgfmathprintnumber{24415.98123}\hspace{1em} +\pgfmathprintnumber{123456.12345} +\end{codeexample} +As with |fixed zerofill|, this option does only affect numbers drawn in |sci| format (or |std| if the scientific format is chosen). + +See section~\ref{sec:number:styles} for how to change the exponential display style. +\end{key} + +\begin{stylekey}{/pgf/number format/zerofill=\marg{boolean} (default true)} + Sets both, |fixed zerofill| and |sci zerofill| at once. +\end{stylekey} + +\begin{keylist}{/pgf/number format/std,% + /pgf/number format/std=\meta{lower e}, + /pgf/number format/std=\meta{lower e}:\meta{upper e}} +Configures |\pgfmathprintnumber| to a standard algorithm. It chooses either |fixed| or |sci|, depending on the order of magnitude. Let $n=s \cdot m \cdot 10^e$ be the input number and $p$ the current precision. If $-p/2 \le e \le 4$, the number is displayed using |fixed| format. Otherwise, it is displayed using |sci| format. + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,std,precision=2} +\pgfmathprintnumber{4.568}\hspace{1em} +\pgfmathprintnumber{5e-04}\hspace{1em} +\pgfmathprintnumber{0.1}\hspace{1em} +\pgfmathprintnumber{24415.98123}\hspace{1em} +\pgfmathprintnumber{123456.12345} +\end{codeexample} +The parameters can be customized using the optional integer argument(s): if $\text{\meta{lower e}} \le e \le \text{\meta{upper e}}$, the number is displayed in |fixed| format, otherwise in |sci| format. Note that \meta{lower e} should be negative for useful results. The precision used for scientific format can be adjusted with |sci precision| if necessary. + +\end{keylist} + +\begin{key}{/pgf/number format/int detect} +Configures |\pgfmathprintnumber| to detect integers automatically. If the input number is an integer, no period is displayed at all. If not, the scientific format is chosen. + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,int detect,precision=2} +\pgfmathprintnumber{15}\hspace{1em} +\pgfmathprintnumber{20}\hspace{1em} +\pgfmathprintnumber{20.4}\hspace{1em} +\pgfmathprintnumber{0.01}\hspace{1em} +\pgfmathprintnumber{0} +\end{codeexample} +\end{key} + +\begin{command}{\pgfmathifisint\marg{number constant}\marg{true code}\marg{false code}} + A command which does the same check as |int detect|, but it invokes \meta{true code} if the \meta{number constant} actually is an integer and the \meta{false code} if not. + + As a side--effect, |\pgfretval| will contain the parsed number, either in integer format or as parsed floating point number. + + + The argument \meta{number constant} will be parsed with |\pgfmathfloatparsenumber|. +\begin{codeexample}[] +15 \pgfmathifisint{15}{is an int: \pgfretval.}{is no int}\hspace{1em} +15.5 \pgfmathifisint{15.5}{is an int: \pgfretval.}{is no int} +\end{codeexample} +\end{command} + +\begin{key}{/pgf/number format/int trunc} +Truncates every number to integers (discards any digit after the period). + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,int trunc} +\pgfmathprintnumber{4.568}\hspace{1em} +\pgfmathprintnumber{5e-04}\hspace{1em} +\pgfmathprintnumber{0.1}\hspace{1em} +\pgfmathprintnumber{24415.98123}\hspace{1em} +\pgfmathprintnumber{123456.12345} +\end{codeexample} +\end{key} + +\begin{key}{/pgf/number format/frac} +Displays numbers as fractionals. + +\begin{codeexample}[width=3cm] +\pgfkeys{/pgf/number format/frac} +\pgfmathprintnumber{0.333333333333333}\hspace{1em} +\pgfmathprintnumber{0.5}\hspace{1em} +\pgfmathprintnumber{2.133333333333325e-01}\hspace{1em} +\pgfmathprintnumber{0.12}\hspace{1em} +\pgfmathprintnumber{2.666666666666646e-02}\hspace{1em} +\pgfmathprintnumber{-1.333333333333334e-02}\hspace{1em} +\pgfmathprintnumber{7.200000000000000e-01}\hspace{1em} +\pgfmathprintnumber{6.666666666666667e-02}\hspace{1em} +\pgfmathprintnumber{1.333333333333333e-01}\hspace{1em} +\pgfmathprintnumber{-1.333333333333333e-02}\hspace{1em} +\pgfmathprintnumber{3.3333333}\hspace{1em} +\pgfmathprintnumber{1.2345}\hspace{1em} +\pgfmathprintnumber{1}\hspace{1em} +\pgfmathprintnumber{-6} +\end{codeexample} + +\begin{key}{/pgf/number format/frac TeX=\marg{\textbackslash macro} (initially \texttt{\textbackslash frac})} + Allows to use a different implementation for |\frac| inside of the |frac| display type. +\end{key} +\begin{key}{/pgf/number format/frac denom=\meta{int} (initially empty)} + Allows to provide a custom denominator for |frac|. +\begin{codeexample}[width=3cm] +\pgfkeys{/pgf/number format/.cd,frac, frac denom=10} +\pgfmathprintnumber{0.1}\hspace{1em} +\pgfmathprintnumber{0.5}\hspace{1em} +\pgfmathprintnumber{1.2}\hspace{1em} +\pgfmathprintnumber{-0.6}\hspace{1em} +\pgfmathprintnumber{-1.4}\hspace{1em} +\end{codeexample} +\end{key} +\begin{key}{/pgf/number format/frac whole=\mchoice{true,false} (initially true)} + Configures whether complete integer parts shall be placed in front of the fractional part. In this case, the fractional part will be less then $1$. Use |frac whole=false| to avoid whole number parts. +\begin{codeexample}[width=3cm] +\pgfkeys{/pgf/number format/.cd,frac, frac whole=false} +\pgfmathprintnumber{20.1}\hspace{1em} +\pgfmathprintnumber{5.5}\hspace{1em} +\pgfmathprintnumber{1.2}\hspace{1em} +\pgfmathprintnumber{-5.6}\hspace{1em} +\pgfmathprintnumber{-1.4}\hspace{1em} +\end{codeexample} +\end{key} +\begin{key}{/pgf/number format/frac shift=\marg{integer} (initially 4)} + In case you experience problems because of stability problems, try experimenting with a different |frac shift|. + Higher shift values $k$ yield higher sensitivity to inaccurate data or inaccurate arithmetics. + + Technically, the following happens. If $r < 1$ is the fractional part of the mantissa, then a scale $i = 1/r \cdot 10^k$ is computed where $k$ is the shift; fractional parts of $i$ are neglected. The value $1/r$ is computed internally, its error is amplified. + + If you still experience stability problems, use |\usepackage{fp}| in your preamble. The |frac| style will then automatically employ the higher absolute precision of |fp| for the computation of $1/r$. +\end{key} +\end{key} + +\begin{key}{/pgf/number format/precision=\marg{number}} +Sets the desired rounding precision for any display operation. For scientific format, this affects the mantissa. +\end{key} + +\begin{key}{/pgf/number format/sci precision=\meta{number or empty} (initially empty)} + Sets the desired rounding precision only for |sci| styles. + + Use |sci precision={}| to restore the initial configuration (which uses the argument provided to |precision| for all number styles). +\end{key} + +\subsection{Changing display styles}% +\label{sec:number:styles}% +You can change the way how numbers are displayed. For example, if you use the `\texttt{fixed}' style, the input number is rounded to the desired precision and the current fixed point display style is used to typeset the number. The same is applied to any other format: first, rounding routines are used to get the correct digits, afterwards a display style generates proper \TeX-code. + +\begin{key}{/pgf/number format/set decimal separator=\marg{text}} +Assigns \marg{text} as decimal separator for any fixed point numbers (including the mantissa in sci format). + +Use |\pgfkeysgetvalue{/pgf/number format/set decimal separator}\value| to get the current separator into |\value|. +\end{key} + +\begin{stylekey}{/pgf/number format/dec sep=\marg{text}} + Just another name for |set decimal separator|. +\end{stylekey} + +\begin{key}{/pgf/number format/set thousands separator=\marg{text}} +Assigns \marg{text} as thousands separator for any fixed point numbers (including the mantissa in sci format). + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd, + fixed, + fixed zerofill, + precision=2, + set thousands separator={}} +\pgfmathprintnumber{1234.56} +\end{codeexample} +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd, + fixed, + fixed zerofill, + precision=2, + set thousands separator={}} +\pgfmathprintnumber{1234567890} +\end{codeexample} + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd, + fixed, + fixed zerofill, + precision=2, + set thousands separator={.}} +\pgfmathprintnumber{1234567890} +\end{codeexample} +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd, + fixed, + fixed zerofill, + precision=2, + set thousands separator={,}} +\pgfmathprintnumber{1234567890} +\end{codeexample} +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd, + fixed, + fixed zerofill, + precision=2, + set thousands separator={{{,}}}} +\pgfmathprintnumber{1234567890} +\end{codeexample} +The last example employs commas and disables the default comma-spacing. + +Use |\pgfkeysgetvalue{/pgf/number format/set thousands separator}\value| to get the current separator into |\value|. +\end{key} + +\begin{stylekey}{/pgf/number format/1000 sep=\marg{text}} + Just another name for |set thousands separator|. +\end{stylekey} + +\begin{key}{/pgf/number format/min exponent for 1000 sep=\marg{number} (initially 0)} + Defines the smallest exponent in scientific notation which is required to draw thousand separators. The exponent is the number of digits minus one, so $\meta{number}=4$ will use thousand separators starting with $1e4 = 10000$. +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd, + int detect, + 1000 sep={\,}, + min exponent for 1000 sep=0} +\pgfmathprintnumber{5000}; \pgfmathprintnumber{1000000} +\end{codeexample} + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd, + int detect, + 1000 sep={\,}, + min exponent for 1000 sep=4} +\pgfmathprintnumber{1000}; \pgfmathprintnumber{5000} +\end{codeexample} +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd, + int detect, + 1000 sep={\,}, + min exponent for 1000 sep=4} +\pgfmathprintnumber{10000}; \pgfmathprintnumber{1000000} +\end{codeexample} +\noindent A value of |0| disables this feature (negative values are ignored). +\end{key} + +\begin{key}{/pgf/number format/use period} +A predefined style which installs periods `\texttt{.}' as decimal separators and commas `\texttt{,}' as thousands separators. This style is the default. + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,fixed,precision=2,use period} +\pgfmathprintnumber{12.3456} +\end{codeexample} +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,fixed,precision=2,use period} +\pgfmathprintnumber{1234.56} +\end{codeexample} +\end{key} + +\begin{key}{/pgf/number format/use comma} +A predefined style which installs commas `\texttt{,}' as decimal separators and periods `\texttt{.}' as thousands separators. + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,fixed,precision=2,use comma} +\pgfmathprintnumber{12.3456} +\end{codeexample} +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,fixed,precision=2,use comma} +\pgfmathprintnumber{1234.56} +\end{codeexample} +\end{key} + +\begin{key}{/pgf/number format/skip 0.=\marg{boolean} (initially false)} + Configures whether numbers like $0.1$ shall be typeset as $.1$ or not. +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd, + fixed, + fixed zerofill,precision=2, + skip 0.} +\pgfmathprintnumber{0.56} +\end{codeexample} +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd, + fixed, + fixed zerofill,precision=2, + skip 0.=false} +\pgfmathprintnumber{0.56} +\end{codeexample} +\end{key} + +\begin{key}{/pgf/number format/showpos=\marg{boolean} (initially false)} + Enables or disables display of plus signs for non-negative numbers. +\begin{codeexample}[] +\pgfkeys{/pgf/number format/showpos} +\pgfmathprintnumber{12.345} +\end{codeexample} + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/showpos=false} +\pgfmathprintnumber{12.345} +\end{codeexample} + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,showpos,sci} +\pgfmathprintnumber{12.345} +\end{codeexample} +\end{key} + +\begin{stylekey}{/pgf/number format/print sign=\marg{boolean}} + A style which is simply an alias for |showpos=|\marg{boolean}. +\end{stylekey} + +\begin{key}{/pgf/number format/sci 10e} +Uses $m \cdot 10^e$ for any number displayed in scientific format. + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,sci,sci 10e} +\pgfmathprintnumber{12.345} +\end{codeexample} +\end{key} + +\begin{key}{/pgf/number format/sci 10\textasciicircum e} +The same as `|sci 10e|'. +\end{key} + +\begin{key}{/pgf/number format/sci e} +Uses the `$1e{+}0$' format which is generated by common scientific tools for any number displayed in scientific format. + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,sci,sci e} +\pgfmathprintnumber{12.345} +\end{codeexample} +\end{key} + +\begin{key}{/pgf/number format/sci E} +The same with an uppercase `\texttt{E}'. + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,sci,sci E} +\pgfmathprintnumber{12.345} +\end{codeexample} +\end{key} + +\begin{key}{/pgf/number format/sci subscript} +Typesets the exponent as subscript for any number displayed in scientific format. This style requires very few space. + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,sci,sci subscript} +\pgfmathprintnumber{12.345} +\end{codeexample} +\end{key} + +\begin{key}{/pgf/number format/sci superscript} +Typesets the exponent as superscript for any number displayed in scientific format. This style requires very few space. + +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,sci,sci superscript} +\pgfmathprintnumber{12.345} +\end{codeexample} +\end{key} + +\begin{key}{/pgf/number format/sci generic=\marg{keys}} +Allows to define an own number style for the scientific format. Here, \meta{keys} can be one of the following choices (omit the long key prefix): + +\begin{key}{/pgf/number format/sci generic/mantissa sep=\marg{text} (initially empty)} + Provides the separator between a mantissa and the exponent. It might be |\cdot|, for example, +\end{key} +\begin{key}{/pgf/number format/sci generic/exponent=\marg{text} (initially empty)} + Provides text to format the exponent. The actual exponent is available as argument |#1| (see below). +\end{key} + +\begin{codeexample}[] +\pgfkeys{ + /pgf/number format/.cd, + sci, + sci generic={mantissa sep=\times,exponent={10^{#1}}}} +\pgfmathprintnumber{12.345}; +\pgfmathprintnumber{0.00012345} +\end{codeexample} + The \meta{keys} can depend on three parameters, namely on |#1| which is the exponent, |#2| containing the flags entity of the floating point number and |#3| is the (unprocessed and unformatted) mantissa. + + Note that |sci generic| is \emph{not} suitable to modify the appearance of fixed point numbers, nor can it be used to format the mantissa (which is typeset like fixed point numbers). Use |dec sep|, |1000 sep| and |print sign| to customize the mantissa. +\end{key} + + +\begin{key}{/pgf/number format/@dec sep mark=\marg{text}} + Will be placed right before the place where a decimal separator belongs to. However, \marg{text} will be inserted even if there is no decimal separator. It is intended as place-holder for auxiliary routines to find alignment positions. + + This key should never be used to change the decimal separator! Use |dec sep| instead. +\end{key} + +\begin{key}{/pgf/number format/@sci exponent mark=\marg{text}} + Will be placed right before exponents in scientific notation. It is intended as place-holder for auxiliary routines to find alignment positions. + + This key should never be used to change the exponent! +\end{key} + +\begin{key}{/pgf/number format/assume math mode=\marg{boolean} (default true)} + Set this to |true| if you don't want any checks for math mode. The initial setting checks whether math mode is active using |\pgfutilensuremath| for each final number. + + Use |assume math mode=true| if you know that math mode is active. In that case, the final number is typeset as-is, no further checking is performed. +\end{key} + + +\begin{stylekey}{/pgf/number format/verbatim} + A style which configures the number printer to produce verbatim text output, i.e.\ it doesn't contain \TeX\ macros. +\begin{codeexample}[] +\pgfkeys{ + /pgf/fpu, + /pgf/number format/.cd, + sci, + verbatim} +\pgfmathprintnumber{12.345}; +\pgfmathprintnumber{0.00012345}; +\pgfmathparse{exp(15)} +\pgfmathprintnumber{\pgfmathresult} +\end{codeexample} + The style resets |1000 sep|, |dec sep|, |print sign|, |skip 0.| and sets |assume math mode|. Furthermore, it installs a |sci generic| format for verbatim output of scientific numbers. + + However, it will still respect |precision|, |fixed zerofill|, |sci zerofill| and the overall styles |fixed|, |sci|, |int detect| (and their variants). It might be useful if you intent to write output files. +\end{stylekey} +%-------------------------------------------------- +% \subsubsection{Defining own display styles} +% You can define own display styles, although this may require some insight into \TeX-programming. Here are two examples: +% \begin{enumerate} +% \item A new fixed point display style: The following code defines a new style named `\texttt{my own fixed point style}' which uses $1{\cdot}00$ instead of $1.00$. +% \begin{lstlisting} +% \def\myfixedpointstyleimpl#1.#2\relax{% +% #1{\cdot}#2% +% }% +% \def\myfixedpointstyle#1{% +% \pgfutilensuremath{% +% \ifpgfmathfloatroundhasperiod +% \expandafter\myfixedpointstyleimpl#1\relax +% \else +% #1% +% \fi +% }% +% } +% \pgfkeys{/my own fixed point style/.code={% +% \let\pgfmathprintnumber@fixed@style=\myfixedpointstyle} +% }% +% \end{lstlisting} +% You only need to overwrite the macro \lstinline!\pgfmathprintnumber@fixed@style!. This macro takes one argument (the result of any numerical computations). The \TeX-boolean \lstinline!\ifpgfmathfloatroundhasperiod! is true if and only if the input number contains a period. +% +% \item An example for a new scientific display style: +% \begin{lstlisting} +% % #1: +% % 0 == '0' (the number is +- 0.0), +% % 1 == '+', +% % 2 == '-', +% % 3 == 'not a number' +% % 4 == '+ infinity' +% % 5 == '- infinity' +% % #2: the mantissa +% % #3: the exponent +% \def\myscistyle#1#2e#3\relax{% +% ... +% } +% \pgfkeys{/my own sci style/.code={% +% \let\pgfmathfloatrounddisplaystyle=\myscistyle}, +% }% +% \end{lstlisting} +% \end{enumerate} +%-------------------------------------------------- |