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author | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
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committer | Norbert Preining <norbert@preining.info> | 2019-09-02 13:46:59 +0900 |
commit | e0c6872cf40896c7be36b11dcc744620f10adf1d (patch) | |
tree | 60335e10d2f4354b0674ec22d7b53f0f8abee672 /graphics/pgf/base/doc/text-en/pgfmanual-en-math-numberprinting.tex |
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diff --git a/graphics/pgf/base/doc/text-en/pgfmanual-en-math-numberprinting.tex b/graphics/pgf/base/doc/text-en/pgfmanual-en-math-numberprinting.tex new file mode 100644 index 0000000000..9cd4a9a6dd --- /dev/null +++ b/graphics/pgf/base/doc/text-en/pgfmanual-en-math-numberprinting.tex @@ -0,0 +1,875 @@ + +\section{Number Printing} +\label{pgfmath-numberprinting} + +{\emph{An extension by Christian Feuersänger}} + +\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 \meta{x}. The input + number \meta{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}|]|\meta{x}. +\end{command} + +\begin{command}{\pgfmathprintnumberto\marg{x}\marg{macro}} + Returns the resulting number into \meta{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 the scientific format can be adjusted with |sci precision| if + necessary. +\end{keylist} + +\begin{keylist}{/pgf/number format/relative*=\meta{exponent base 10}} + Configures |\pgfmathprintnumber| to format numbers relative to an order of + magnitude, $10^r$, where $r$ is an integer number. + + This key addresses different use-cases. + + \paragraph{First use-case:} + + provide a unified format for a \emph{sequence} of numbers. Consider the + following test: + % +\begin{codeexample}[] +\pgfkeys{/pgf/number format/relative*={1}} +\pgfmathprintnumber{6.42e-16}\hspace{1em} +\pgfmathprintnumber{1.2}\hspace{1em} +\pgfmathprintnumber{6}\hspace{1em} +\pgfmathprintnumber{20.6}\hspace{1em} +\pgfmathprintnumber{87} +\end{codeexample} + % + \noindent With any other style, the |6.42e-16| would have been formatted as + an isolated number. Here, it is rounded to |0| because when viewed relative + to $10^1$ (the exponent $1$ is the argument for |relative|), it has no + significant digits. + % +\begin{codeexample}[] +\pgfkeys{/pgf/number format/relative*={2}} +\pgfmathprintnumber{123.345}\hspace{1em} +\pgfmathprintnumber{0.0012}\hspace{1em} +\pgfmathprintnumber{0.0014}\hspace{1em} +\end{codeexample} + % + \noindent The example above applies the initial |precision=2| to |123.345| + -- relative to $100$. Two significant digits of |123.345| relative to $100$ + are |123|. Note that the ``$2$ significant digits of |123.345|'' translates + to ``round |1.2345| to $2$ digits'', which would yield |1.2300|. Similarly, + the other two numbers are |0| compared to $100$ using the given + |precision|. + % +\begin{codeexample}[] +\pgfkeys{/pgf/number format/relative*={-3}} +\pgfmathprintnumber{123.345}\hspace{1em} +\pgfmathprintnumber{0.0012}\hspace{1em} +\pgfmathprintnumber{0.0014}\hspace{1em} +\end{codeexample} + + \paragraph{Second use-case:} + + improve rounding in the presence of \emph{inaccurate} numbers. Let us + suppose that some limited-precision arithmetics resulted in the result + |123456999| (like the |fpu| of \pgfname). You know that its precision is + about five or six significant digits. And you want to provide a fixed point + output. In this case, the trailing digits |....999| are a numerical + artifact due to the limited precision. Use |relative*=3,precision=0| to + eliminate the artifacts: + % +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,relative*={3},precision=0} +\pgfmathprintnumber{123456999}\hspace{1em} +\pgfmathprintnumber{123456999.12} +\end{codeexample} + % + \noindent Here, |precision=0| means that we inspect |123456.999| and round + that number to $0$ digits. Finally, we move the period back to its initial + position. Adding |relative style=fixed| results in fixed point output + format: + % +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,relative*={3},precision=0,relative style=fixed} +\pgfmathprintnumber{123456999}\hspace{1em} +\pgfmathprintnumber{123456999.12} +\end{codeexample} + % + \noindent Note that there is another alternative for this use-case which is + discussed later: the |fixed relative| style. + % +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,fixed relative,precision=6} +\pgfmathprintnumber{123456999}\hspace{1em} +\pgfmathprintnumber{123456999.12} +\end{codeexample} + + You might wonder why there is an asterisk in the key's name. The short + answer is: there is also a \declareandlabel{/pgf/number format/relative} + number printer which does unexpected things. The key |relative*| repairs + this. Existing code will still use the old behavior. + + Technically, the key works as follows: as already explained above, + |relative*=3| key applied to |123456999.12| moves the period by three + positions and analyzes |123456.99912|. Mathematically speaking, we are + given a number $x = \pm m \cdot 10^e$ and we attempt to apply + |relative*=|$r$. The method then rounds $x / 10^r$ to |precision| digits. + Afterwards, it multiplies the result by $10^r$ and typesets it. +\end{keylist} + +\begin{stylekey}{/pgf/number format/every relative} + A style which configures how the |relative| method finally displays its + results. + + The initial configuration is + % +\begin{codeexample}[code only] +\pgfkeys{/pgf/number format/every relative/.style=std} +\end{codeexample} + + Note that rounding is turned off when the resulting style is being + evaluated (since |relative| already rounded the number). + + Although supported, I discourage from using |fixed zerofill| or + |sci zerofill| in this context -- it may lead to a suggestion of higher + precision than is actually used (because |fixed zerofill| might simply add + |.00| although there was a different information before |relative| rounded + the result). +\end{stylekey} + +\begin{key}{/pgf/number format/relative style=\marg{options}} + The same as |every relative/.append style=|\marg{options}. +\end{key} + +\begin{keylist}{/pgf/number format/fixed relative} + Configures |\pgfmathprintnumber| to format numbers in a similar way to the + |fixed| style, but the |precision| is interpreted relatively to the + number's exponent. + + The motivation is to get the same rounding effect as for |sci|, but to + display the number in the |fixed| style: + % +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd,fixed relative,precision=3} +\pgfmathprintnumber{1000.0123}\hspace{1em} +\pgfmathprintnumber{100.0567}\hspace{1em} +\pgfmathprintnumber{0.000010003452}\hspace{1em} +\pgfmathprintnumber{0.010073452}\hspace{1em} +\pgfmathprintnumber{1.23567}\hspace{1em} +\pgfmathprintnumber{1003.75}\hspace{1em} +\pgfmathprintnumber{1006.75}\hspace{1em} +\end{codeexample} + + The effect of |fixed relative| is that the number is rounded to + \emph{exactly} the first \meta{precision} non-zero digits, no matter how + many leading zeros the number might have. + + Use |fixed relative| if you want |fixed| and if you know that only the + first $n$ digits are correct. Use |sci| if you need a scientific display + style and only the first $n$ digits are correct. + + Note that |fixed relative| ignores the |fixed zerofill| flag. + + See also the |relative*| key. Note that the |relative=|\marg{exponent} key + explicitly moves the period to some designated position before it attempts + to round the number. Afterwards, it ``rounds from the right'', i.e.\ it + rounds to that explicitly chosen digit position. In contrast to that, + |fixed relative| ``rounds from the left'': it takes the \emph{first} + non-zero digit, temporarily places the period after this digit, and rounds + that number. The rounding style |fixed| leaves the period where it is, and + rounds everything behind that digit. The |sci| style is similar to |fixed + relative|. +\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} + +\begin{key}{/pgf/number format/read comma as period=\mchoice{true,false} (initially false)} + This is one of the few keys which allows to customize the number parser. If + this switch is turned on, a comma is read just as a period. + % +\begin{codeexample}[] +\pgfkeys{/pgf/number format/read comma as period} +\pgfmathprintnumber{1234,56} +\end{codeexample} + % + This is typically undesired as it can cause side-effects with math parsing + instructions. However, it is supported to format input numbers or input + tables. Consider |use comma| to typeset the result with a comma as well. + % +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd, + read comma as period, + use comma} +\pgfmathprintnumber{1234,56} +\end{codeexample} + % +\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/1000 sep in fractionals=\marg{boolean} (initially false)} + Configures whether the fractional part should also be grouped into groups + of three digits. + + The value |true| will active the |1000 sep| for both, integer and + fractional parts. The value |false| will active |1000 sep| only for the + integer part. + % +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd, + fixed, + precision=999, + set thousands separator={\,}, + 1000 sep in fractionals, + } +\pgfmathprintnumber{1234.1234567} +\end{codeexample} + % +\begin{codeexample}[] +\pgfkeys{/pgf/number format/.cd, + fixed,fixed zerofill, + precision=9, + set thousands separator={\,}, + 1000 sep in fractionals, + } +\pgfmathprintnumber{1234.1234567} +\end{codeexample} + % +\end{key} + +\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 the 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 little 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 little 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/retain unit mantissa=\mchoice{true,false} (initially true)} + Allows to omit a unit mantissa. + % +\begin{codeexample}[] +\pgfkeys{ + /pgf/number format/.cd, + sci, retain unit mantissa=false} +\pgfmathprintnumber{10.5}; +\pgfmathprintnumber{10}; +\pgfmathprintnumber{1010}; +\pgfmathprintnumber[precision=1]{-1010}; +\end{codeexample} + % + The feature is applied after rounding to the desired precision: if the + remaining mantissa is equal to~$1$, it will be omitted. It applies to all + styles involving the scientific format (including |std|). +\end{key} + +\begin{key}{/pgf/number format/\protect\atmarktext 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/\protect\atmarktext 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 intend 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} +%-------------------------------------------------- |