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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
index c3afcc8b234..9cd4a9a6dd6 100644
--- 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
@@ -1,32 +1,33 @@
-\section{Number Printing}
-\label{pgfmath-numberprinting}%
+\section{Number Printing}
+\label{pgfmath-numberprinting}
-{\emph{An extension by Christian Feuers\"anger}}
+{\emph{An extension by Christian Feuersänger}}
\medskip
\noindent
-\pgfname\ supports number printing in different styles and rounds to arbitrary precision.
+\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.
+ 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}.
+ 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.
+ 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.
-
+ 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}
@@ -36,14 +37,13 @@
\pgfmathprintnumber{123456.12345}
\end{codeexample}
- See section~\ref{sec:number:styles} for how to change the
- appearance.
+ 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.
-
+ 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}
@@ -52,8 +52,10 @@
\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).
+ %
+ 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}
@@ -62,16 +64,14 @@
\pgfmathprintnumber{123456.12345}
\end{codeexample}
- See section~\ref{sec:number:styles} for how to change the
- appearance.
+ 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).
-
+ 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}
@@ -81,14 +81,13 @@
\pgfmathprintnumber{123456.12345}
\end{codeexample}
-See section~\ref{sec:number:styles} for how to change the exponential
-display style.
+ 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.
-
+ 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}
@@ -97,26 +96,28 @@ display style.
\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).
+ %
+ 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.
+ 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.
+ 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.
-
+ /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}
@@ -125,22 +126,26 @@ display style.
\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.
+ %
+ 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.
+ 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:}
- This key addresses different use-cases.
-
- \paragraph{First use-case:} provide a unified format for a
- \emph{sequence} of numbers. Consider the following test:
+ 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}
@@ -149,24 +154,26 @@ display style.
\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.
-
+ %
+ \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|.
-
+ %
+ \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}
@@ -174,81 +181,87 @@ display style.
\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:
+ \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:
+ %
+ \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.
+ %
+ \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.
+
+ 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.
+ A style which configures how the |relative| method finally displays its
+ results.
- The initial configuration is
+ 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).
+ 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).
+ 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}.
+ 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.
+ 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:
+ 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}
@@ -259,35 +272,33 @@ display style.
\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}
+ 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.
-\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.
+ 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}
@@ -296,27 +307,29 @@ display style.
\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.
+ 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.
+ 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|.
+ 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).
+ 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}
@@ -325,11 +338,12 @@ display style.
\pgfmathprintnumber{24415.98123}\hspace{1em}
\pgfmathprintnumber{123456.12345}
\end{codeexample}
+ %
\end{key}
\begin{key}{/pgf/number format/frac}
- Displays numbers as fractionals.
-
+ Displays numbers as fractionals.
+ %
\begin{codeexample}[width=3cm]
\pgfkeys{/pgf/number format/frac}
\pgfmathprintnumber{0.333333333333333}\hspace{1em}
@@ -348,13 +362,14 @@ display style.
\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 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{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}
@@ -363,11 +378,13 @@ display style.
\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.
+ \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}
@@ -376,237 +393,260 @@ display style.
\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/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.
+ 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.
+ 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).
+ 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.
+ 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.
+ %
+ 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}
+ read comma as period,
+ use comma}
\pgfmathprintnumber{1234,56}
\end{codeexample}
+ %
\end{key}
+
\subsection{Changing display styles}%
-\label{sec:number: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.
+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).
+ 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|.
+ 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|.
+ 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).
-
+ 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={}}
+ 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={}}
+ 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={.}}
+ 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={,}}
+ 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={{{,}}}}
+ fixed,
+ fixed zerofill,
+ precision=2,
+ set thousands separator={{{,}}}}
\pgfmathprintnumber{1234567890}
\end{codeexample}
- The last example employs commas and disables the default
- comma-spacing.
+ %
+ 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|.
+ 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|.
+ 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.
+ 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.
+ 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,
- }
+ 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,
- }
+ 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 $1e4 = 10000$.
+ 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}
+ 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}
+ 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}
+ 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).
+ %
+ \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.
-
+ 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.
-
+ 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.
+ 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.}
+ 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}
+ 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.
+ Enables or disables the display of plus signs for non-negative numbers.
+ %
\begin{codeexample}[]
\pgfkeys{/pgf/number format/showpos}
\pgfmathprintnumber{12.345}
@@ -621,190 +661,214 @@ display style generates proper \TeX-code.
\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}.
+ 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.
-
+ 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|'.
+ 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.
-
+ 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}'.
-
+ 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.
-
+ 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.
-
+ 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}
-
+ 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}}}}
+ /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.
+ %
+ 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.
+ 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.
+ 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.
+ 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.
+ 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!
+ 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}
+ 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.
+ 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}
+ /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.
+ %
+ 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.
+ 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 $1.00$.
+% \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%
+% #1{\cdot}#2%
% }%
% \def\myfixedpointstyle#1{%
-% \pgfutilensuremath{%
-% \ifpgfmathfloatroundhasperiod
-% \expandafter\myfixedpointstyleimpl#1\relax
-% \else
-% #1%
-% \fi
-% }%
+% \pgfutilensuremath{%
+% \ifpgfmathfloatroundhasperiod
+% \expandafter\myfixedpointstyleimpl#1\relax
+% \else
+% #1%
+% \fi
+% }%
% }
% \pgfkeys{/my own fixed point style/.code={%
-% \let\pgfmathprintnumber@fixed@style=\myfixedpointstyle}
+% \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.
+% 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:
+% \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'
+% % 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},
+% \let\pgfmathfloatrounddisplaystyle=\myscistyle},
% }%
% \end{lstlisting}
% \end{enumerate}