From 22536bb2b5257046d271b1eaa11b4a275d5ec041 Mon Sep 17 00:00:00 2001
From: Karl Berry <karl@freefriends.org>
Date: Sat, 5 Jan 2019 22:40:38 +0000
Subject: pgf (5jan19)

git-svn-id: svn://tug.org/texlive/trunk@49607 c570f23f-e606-0410-a88d-b1316a301751
---
 .../text-en/pgfmanual-en-library-fixedpoint.tex    | 195 +++++++++------------
 1 file changed, 82 insertions(+), 113 deletions(-)

(limited to 'Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-library-fixedpoint.tex')

diff --git a/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-library-fixedpoint.tex b/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-library-fixedpoint.tex
index 1be2d41e7b8..238d0c16ad2 100644
--- a/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-library-fixedpoint.tex
+++ b/Master/texmf-dist/doc/generic/pgf/text-en/pgfmanual-en-library-fixedpoint.tex
@@ -11,109 +11,81 @@
 \section{Fixed Point Arithmetic Library}
 
 \begin{pgflibrary}{fixedpointarithmetic}
-  This library provides an interface to the \LaTeX{} package
-  |fp| for fixed point arithmetic. 	In addition to loading this
-  library you must ensure |fp| is loaded, otherwise errors
-  will occur.
+    This library provides an interface to the \LaTeX{} package |fp| for fixed
+    point arithmetic. In addition to loading this library you must ensure |fp|
+    is loaded, otherwise errors will occur.
 \end{pgflibrary}
 
-\subsection{Overview}
 
-  Whilst the mathematical engine that comes with \pgfname{} is
-  reasonably fast and flexible when it comes to parsing, the accuracy
-  tends to be fairly low, particularly for expressions involving many
-  operations chained together. In addition the range of values that
-  can be computed is very small: $\pm16383.99999$.
-	Conversely, the |fp| package has a reasonably high accuracy, and
-	can	perform computations over a wide range of
-	values (approximately $\pm9.999\times10^{17}$), but is comparatively
-	slow and not very
-	flexible, particularly regarding parsing.
-
-  This library enables the combination of the two: the flexible parser
-  of the \pgfname{} mathematical engine with the evaluation accuracy
-  of |fp|. There are, however, a number of important points to
-  bear in mind:
+\subsection{Overview}
 
+Whilst the mathematical engine that comes with \pgfname{} is reasonably fast
+and flexible when it comes to parsing, the accuracy tends to be fairly low,
+particularly for expressions involving many operations chained together. In
+addition the range of values that can be computed is very small:
+$\pm16383.99999$. Conversely, the |fp| package has a reasonably high accuracy,
+and can perform computations over a wide range of values (approximately
+$\pm9.999\times10^{17}$), but is comparatively slow and not very flexible,
+particularly regarding parsing.
+
+This library enables the combination of the two: the flexible parser of the
+\pgfname{} mathematical engine with the evaluation accuracy of |fp|. There are,
+however, a number of important points to bear in mind:
+%
 \begin{itemize}
-	
-  \item
-
-  Whilst |fp| supports very large numbers, \pgfname{} and
-  \tikzname{} do not. It is possible to calculate the result of
-  |2^20| or |1.2e10+3.4e10|, but it is not possible to use these
-  results in pictures directly without some ``extra work''.
-
-  \item
-
-  The \pgfname{} mathematical engine will still be used to evaluate
-  lengths, such as |10pt| or |3em|, so it is not possible for an
-  length to exceed the range of values supported by
-  \TeX-dimensions ($\pm16383.99999$pt), even though the resulting
-  expression is within the range of |fp|. So, for example, one can
-  calculate |3cm*10000|, but not |3*10000cm|.
-
-  \item
-
-  Not all of the functions listed in Section~\ref{pgfmath-syntax},
-  have been mapped onto |fp| equivalents. Of those that have been,
-  it is not guaranteed that functions will perform in the same way as
-  they do in \pgfname. Reference should be made to the documentation
-  for |fp|.
-
-  \item
-
-  In \pgfname, trigonometric functions such as |sin| and |cos| assume
-  arguments are in degrees, and functions such as |asin| and |acos|
-  return results in degrees. Although |fp| uses radians for such
-  functions, \pgfname{} automatically converts arguments from degrees
-  to radians, and converts results from radians to degrees, to ensure
-  everything ``works properly''.
-
-  \item
-
-  The overall speed will actually be slower than using
-  \pgfname{} mathematical engine. The calculating power of |fp|
-  comes at the cost of an increased processing time.
-
-
+    \item Whilst |fp| supports very large numbers, \pgfname{} and \tikzname{}
+        do not. It is possible to calculate the result of |2^20| or
+        |1.2e10+3.4e10|, but it is not possible to use these results in
+        pictures directly without some ``extra work''.
+    \item The \pgfname{} mathematical engine will still be used to evaluate
+        lengths, such as |10pt| or |3em|, so it is not possible for an length
+        to exceed the range of values supported by \TeX-dimensions
+        ($\pm16383.99999$pt), even though the resulting expression is within
+        the range of |fp|. So, for example, one can calculate |3cm*10000|, but
+        not |3*10000cm|.
+    \item Not all of the functions listed in Section~\ref{pgfmath-syntax}, have
+        been mapped onto |fp| equivalents. Of those that have been, it is not
+        guaranteed that functions will perform in the same way as they do in
+        \pgfname. Reference should be made to the documentation for |fp|.
+    \item In \pgfname, trigonometric functions such as |sin| and |cos| assume
+        arguments are in degrees, and functions such as |asin| and |acos|
+        return results in degrees. Although |fp| uses radians for such
+        functions, \pgfname{} automatically converts arguments from degrees to
+        radians, and converts results from radians to degrees, to ensure
+        everything ``works properly''.
+    \item The overall speed will actually be slower than using \pgfname{}
+        mathematical engine. The calculating power of |fp| comes at the cost of
+        an increased processing time.
 \end{itemize}
 
+
 \subsection{Using Fixed Point Arithmetic in PGF and \tikzname}
 
-  The following key is provided to use |fp| in \pgfname{}
-  and \tikzname:
+The following key is provided to use |fp| in \pgfname{} and \tikzname:
 
 \begin{key}{/pgf/fixed point arithmetic=\meta{options}}
 \keyalias{tikz}
-
-  This key will set the key path to |/pgf/fixed point|, and
-  execute \meta{options}. Then it will install the necessary
-  commands so that the \pgfname{} parser will use |fp| to perform
-  calculations.
-  The best way to use this key is as an argument to a scope or
-  picture. This means that |fp| does not always have to be used,
-  and \pgfname{} can use its own mathematical engine at other times,
-  which can lead to a significant reduction in the time for a document
-  to compile.
-
+    This key will set the key path to |/pgf/fixed point|, and execute
+    \meta{options}. Then it will install the necessary commands so that the
+    \pgfname{} parser will use |fp| to perform calculations. The best way to
+    use this key is as an argument to a scope or picture. This means that |fp|
+    does not always have to be used, and \pgfname{} can use its own
+    mathematical engine at other times, which can lead to a significant
+    reduction in the time for a document to compile.
 \end{key}
 
-  Currently there are only a few keys key supported for \meta{options}:
+Currently there are only a few keys key supported for \meta{options}:
 
 \begin{key}{/pgf/fixed point/scale results=\meta{factor}}
-
-	As noted above, |fp| can process a far greater range of numbers
-	than \pgfname{} and \tikzname{}. In order to use results from
-	|fp| in a |{pgfpicture}| or a |{tikzpicture}| they need to be
-	scaled. When this key is used \pgfname{} will scale results
-	of any evaluation by \meta{factor}. However, as it is not
-	desirable for every part of every expression to be scaled,
-	scaling will only take place if a special prefix |*| is used.
-	If |*| is used at the beginning of an expression the evaluation
-	of the expression will evaluated and then multiplied by
-	\meta{factor}.
-
+    As noted above, |fp| can process a far greater range of numbers than
+    \pgfname{} and \tikzname{}. In order to use results from |fp| in a
+    |{pgfpicture}| or a |{tikzpicture}| they need to be scaled. When this key
+    is used \pgfname{} will scale results of any evaluation by \meta{factor}.
+    However, as it is not desirable for every part of every expression to be
+    scaled, scaling will only take place if a special prefix |*| is used. If
+    |*| is used at the beginning of an expression the evaluation of the
+    expression will evaluated and then multiplied by \meta{factor}.
+    %
 \begin{codeexample}[]
 \begin{tikzpicture}[fixed point arithmetic={scale results=10^-6}]
 \draw [help lines] grid (3,2);
@@ -122,30 +94,27 @@
 \end{tikzpicture}
 \end{codeexample}
 
-  A special case of scaling involves plots of data containing
-  large numbers from files.
-  It is possible to ``pre-process'' a file, typically using the
-  application that generates the data, to either precede
-  the relevant column with |*| or to perform the scaling as part
-  of the calculation process. However, it may be desirable for
-  the data in a plot to appear in a table as well, so, two files would
-  be required, one pre-processed for plotting, and one not. This
-  extra work may be undesirable so the following keys are provided:
-
-\begin{key}{/pgf/fixed point/scale file plot x=\meta{factor}}
-  This key will scale the first column of data read from
-  a file before it is plotted. It is independent of the
-  |scale results| key.
-\end{key}
-
-\begin{key}{/pgf/fixed point/scale file plot y=\meta{factor}}
-  This key will scale the second column of data read from
-  a file before it is plotted.
-\end{key}
-
-\begin{key}{/pgf/fixed point/scale file plot z=\meta{factor}}
-  This key will scale the third column of data read from
-  a file before it is plotted.
-\end{key}
-
+    A special case of scaling involves plots of data containing large numbers
+    from files. It is possible to ``pre-process'' a file, typically using the
+    application that generates the data, to either precede the relevant column
+    with |*| or to perform the scaling as part of the calculation process.
+    However, it may be desirable for the data in a plot to appear in a table as
+    well, so, two files would be required, one pre-processed for plotting, and
+    one not. This extra work may be undesirable so the following keys are
+    provided:
+
+    \begin{key}{/pgf/fixed point/scale file plot x=\meta{factor}}
+        This key will scale the first column of data read from a file before it
+        is plotted. It is independent of the |scale results| key.
+    \end{key}
+
+    \begin{key}{/pgf/fixed point/scale file plot y=\meta{factor}}
+        This key will scale the second column of data read from a file before
+        it is plotted.
+    \end{key}
+
+    \begin{key}{/pgf/fixed point/scale file plot z=\meta{factor}}
+        This key will scale the third column of data read from a file before it
+        is plotted.
+    \end{key}
 \end{key}
-- 
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