texlive[43006] Master: trigonometry (21jan17)
commits+karl at tug.org
commits+karl at tug.org
Sat Jan 21 23:40:40 CET 2017
Revision: 43006
http://tug.org/svn/texlive?view=revision&revision=43006
Author: karl
Date: 2017-01-21 23:40:40 +0100 (Sat, 21 Jan 2017)
Log Message:
-----------
trigonometry (21jan17)
Modified Paths:
--------------
trunk/Master/tlpkg/bin/tlpkg-ctan-check
trunk/Master/tlpkg/libexec/ctan2tds
trunk/Master/tlpkg/tlpsrc/collection-genericextra.tlpsrc
Added Paths:
-----------
trunk/Master/texmf-dist/doc/generic/trigonometry/
trunk/Master/texmf-dist/doc/generic/trigonometry/README.txt
trunk/Master/texmf-dist/tex/generic/trigonometry/
trunk/Master/texmf-dist/tex/generic/trigonometry/trigonometry.tex
trunk/Master/tlpkg/tlpsrc/trigonometry.tlpsrc
Added: trunk/Master/texmf-dist/doc/generic/trigonometry/README.txt
===================================================================
--- trunk/Master/texmf-dist/doc/generic/trigonometry/README.txt (rev 0)
+++ trunk/Master/texmf-dist/doc/generic/trigonometry/README.txt 2017-01-21 22:40:40 UTC (rev 43006)
@@ -0,0 +1,3 @@
+The file "Trigonometry.tex" is released under the Knuthian Licence, the current CTAN entry for which reads along the following lines (amendments to grammar and spelling made in the following text) --
+
+"This software is copyright and you are explicitly granted a licence which allows you, the “user” of the software, to copy, distribute and/or modify the software, provided only that if you modify and then re-distribute the software it must be with a different name to that of the original software."
\ No newline at end of file
Added: trunk/Master/texmf-dist/tex/generic/trigonometry/trigonometry.tex
===================================================================
--- trunk/Master/texmf-dist/tex/generic/trigonometry/trigonometry.tex (rev 0)
+++ trunk/Master/texmf-dist/tex/generic/trigonometry/trigonometry.tex 2017-01-21 22:40:40 UTC (rev 43006)
@@ -0,0 +1,206 @@
+%= = = = = = = = = = = = = T R I G O N O M E T R Y . T E X = = = = = = = = =
+
+%%% Trigonometry.TeX: (as published in TeXhax Digest, September 1989)
+%%% Philip Taylor, Royal Holloway and Bedford New College, University of London
+
+%%% Routines to calculate the sine of an angle expressed in radians.
+%%% So far as I can tell, the results are accurate to four places
+%%% of decimals, for arguments in the range -pi/2 .. pi/2, except
+%%% for `ridiculously small' arguments, which cannot be accurately represented.
+
+%%% The routines for cosine and tangent are left to the reader ...
+
+%%% After a call to \Sin (<angle>), the result is available for typesetting
+%%% or boxing, and may also be extracted from the control-sequence \sine.
+
+%%% Grouping is used to hide most things, but the following csnames are
+%%% globally defined:
+
+%%% \nodimen, \n at dimen, \product, \sine, \term, \t at rm, \Term
+
+\newif \ifdebug %%% turn me on to see TeX hard at work ...
+
+\def \term #1{{x^{#1} \over #1!}}
+The power series expansion for $\sin$ is:
+$$ \sin x = x - \term3 + \term5 - \term7 + \cdots$$
+\indent and for $\cos$ is:
+$$ \cos x = 1 - \term2 + \term4 - \term6 + \cdots$$
+
+\let \then = \relax
+\chardef \letter = 11
+\chardef \other = 12
+\def \radian {pt }
+\let \radians = \radian
+\let \dimensionlessunit = \radian
+\let \dimensionlessunits = \dimensionlessunit
+\def \internalunit {sp }
+\let \internalunits = \internalunit
+\newif \ifstillconverging
+\def \Message #1{\ifdebug \then \message {#1} \fi}
+
+{ %%% Things that need abnormal catcodes %%%
+ \catcode `\@ = \letter
+ \gdef \nodimen {\expandafter \n at dimen \the \dimen}
+ \gdef \term #1 #2 #3%
+ {\edef \t@ {\the #1}%%% freeze parameter 1 (count, by value)
+ \edef \t@@ {\expandafter \n at dimen \the #2\radian}%
+ %%% freeze parameter 2 (dimen, by value)
+ \t at rm {\t@} {\t@@} {#3}%
+ }
+ \gdef \t at rm #1 #2 #3%
+ {{%
+ \count 0 = 0
+ \dimen 0 = 1 \dimensionlessunit
+ \dimen 2 = #2\relax
+ \Message {Calculating term #1 of \nodimen 2}%
+ \loop
+ \ifnum \count 0 < #1
+ \then \advance \count 0 by 1
+ \Message {Iteration \the \count 0 \space}%
+ \Multiply \dimen 0 by {\dimen 2}%
+ \Message {After multiplication, term = \nodimen 0}%
+ \Divide \dimen 0 by {\count 0}%
+ \Message {After division, term = \nodimen 0}%
+ \repeat
+ \Message {Final value for term #1 of
+ \nodimen 2 \space is \nodimen 0}%
+ \xdef \Term {#3 = \nodimen 0 \radians}%
+ \aftergroup \Term
+ }}
+ \catcode `\p = \other
+ \catcode `\t = \other
+ \gdef \n at dimen #1pt{#1} %%% throw away the ``pt''
+}
+
+\def \Divide #1by #2{\divide #1 by #2} %%% just a synonym
+
+\def \Multiply #1by #2%%% allows division of a dimen by a dimen
+ {{%%% should really freeze parameter 2 (dimen, passed by value)
+ \count 0 = #1\relax
+ \count 2 = #2\relax
+ \count 4 = 65536
+ \Message {Before scaling, count 0 = \the \count 0 \space and
+ count 2 = \the \count 2}%
+ \ifnum \count 0 > 32767 %%% do our best to avoid overflow
+ \then \divide \count 0 by 4
+ \divide \count 4 by 4
+ \else \ifnum \count 0 < -32767
+ \then \divide \count 0 by 4
+ \divide \count 4 by 4
+ \else
+ \fi
+ \fi
+ \ifnum \count 2 > 32767 %%% while retaining reasonable accuracy
+ \then \divide \count 2 by 4
+ \divide \count 4 by 4
+ \else \ifnum \count 2 < -32767
+ \then \divide \count 2 by 4
+ \divide \count 4 by 4
+ \else
+ \fi
+ \fi
+ \multiply \count 0 by \count 2
+ \divide \count 0 by \count 4
+ \xdef \product {#1 = \the \count 0 \internalunits}%
+ \aftergroup \product
+ }}
+
+\def \Sin (#1)%
+ {{%
+ \dimen 0 = #1 \radian
+ \dimen 2 = 3.1415926535897963 \radian %%% a well-known constant
+ \divide \dimen 2 by 2 %%% we only deal with -pi/2 : pi/2
+ \ifdim \dimen 0 > \dimen 2
+ \then \message {Sin: argument (\nodimen 0) too large
+ --- use range reduction}%
+ \xdef \sine {<undefined>}%
+ \else \ifdim \dimen 0 < - \dimen 2
+ \then \message {Sin: argument (\nodimen 0) too large
+ --- use range reduction}%
+ \xdef \sine {<undefined>}%
+ \else \Message {Sin: calculating Sin of \nodimen 0}%
+ \count 0 = 1 %%% see power-series expansion for sine
+ \dimen 2 = 1 \radian %%% ditto
+ \dimen 4 = 0 \radian %%% ditto
+ \loop
+ \ifnum \dimen 2 = 0 %%% then we've done
+ \then \stillconvergingfalse
+ \else \stillconvergingtrue
+ \fi
+ \ifstillconverging %%% then calculate next term
+ \then \term {\count 0} {\dimen 0} {\dimen 2}%
+ \advance \count 0 by 2
+ \count 2 = \count 0
+ \divide \count 2 by 2
+ \ifodd \count 2 %%% signs alternate
+ \then \advance \dimen 4 by \dimen 2
+ \else \advance \dimen 4 by -\dimen 2
+ \fi
+ \repeat
+ \xdef \sine {\nodimen 4}%
+ \fi
+ \fi
+ \aftergroup \sine
+ }}
+
+%%% What follows is just a demonstration of the \Sin function
+
+$$
+\def \rule {\noalign {\hrule}}
+\def \SIN (#1){&&\Sin (#1)&\cr\noalign{\message {The sine of #1 is \sine}}}
+\mathcode `\- = 32768 %%% just a bodge to improve alignment
+\let \minus = -
+\begingroup
+\catcode `\- = \active
+\gdef -{\llap{\minus}}
+\endgroup
+\vbox {\offinterlineskip
+\halign
+{\vrule #& \qquad \hfil $#$ & \vrule # & \qquad $#$ \hfil & \vrule # \strut \cr
+ \rule
+ &\omit {\hfil $x$ \hfil} && \omit {\hfil $\sin x$ \hfil} & \cr
+ \rule
+ \SIN (-1.6)
+ \SIN (-1.5)
+ \SIN (-1.4)
+ \SIN (-1.3)
+ \SIN (-1.2)
+ \SIN (-1.1)
+ \SIN (-1.0)
+ \SIN (-0.9)
+ \SIN (-0.8)
+ \SIN (-0.7)
+ \SIN (-0.6)
+ \SIN (-0.5)
+ \SIN (-0.4)
+ \SIN (-0.3)
+ \SIN (-0.2)
+ \SIN (-0.1)
+ \SIN (-0.01)
+ \SIN (-0.001)
+ \SIN (-0.0001)
+ \SIN (0)
+ \SIN (0.0001)
+ \SIN (0.001)
+ \SIN (0.01)
+ \SIN (0.1)
+ \SIN (0.2)
+ \SIN (0.3)
+ \SIN (0.4)
+ \SIN (0.5)
+ \SIN (0.6)
+ \SIN (0.7)
+ \SIN (0.8)
+ \SIN (0.9)
+ \SIN (1.0)
+ \SIN (1.1)
+ \SIN (1.2)
+ \SIN (1.3)
+ \SIN (1.4)
+ \SIN (1.5)
+ \SIN (1.6)
+ \rule}
+}
+$$
+\end
+
Modified: trunk/Master/tlpkg/bin/tlpkg-ctan-check
===================================================================
--- trunk/Master/tlpkg/bin/tlpkg-ctan-check 2017-01-21 22:38:41 UTC (rev 43005)
+++ trunk/Master/tlpkg/bin/tlpkg-ctan-check 2017-01-21 22:40:40 UTC (rev 43006)
@@ -608,7 +608,8 @@
translation-filecontents-de translation-moreverb-de
translation-natbib-fr translation-tabbing-fr
translations
- tree-dvips treetex trfsigns trimspaces trivfloat trsym truncate
+ tree-dvips treetex trfsigns
+ trigonometry trimspaces trivfloat trsym truncate
tsemlines
tucv tudscr tufte-latex tugboat tugboat-plain
tui turabian turabian-formatting turkmen turnstile turnthepage
Modified: trunk/Master/tlpkg/libexec/ctan2tds
===================================================================
--- trunk/Master/tlpkg/libexec/ctan2tds 2017-01-21 22:38:41 UTC (rev 43005)
+++ trunk/Master/tlpkg/libexec/ctan2tds 2017-01-21 22:40:40 UTC (rev 43006)
@@ -1812,6 +1812,7 @@
'translation-europecv-de', 'NULL', # doc
'translation-tabbing-fr', 'NULL', # doc
'treetex', '(treetex|l_pic|classes)\.tex',
+ 'trigonometry','\.tex',
'truncate', '^..[^s].*\.sty', # not miscdoc.sty
'tudscr', 'DDC.*|TUD.*|' . $standardtex,
'tugboat-plain','\.cmn|' . $standardtex,
Modified: trunk/Master/tlpkg/tlpsrc/collection-genericextra.tlpsrc
===================================================================
--- trunk/Master/tlpkg/tlpsrc/collection-genericextra.tlpsrc 2017-01-21 22:38:41 UTC (rev 43005)
+++ trunk/Master/tlpkg/tlpsrc/collection-genericextra.tlpsrc 2017-01-21 22:40:40 UTC (rev 43006)
@@ -51,6 +51,7 @@
depend tabto-generic
depend termmenu
depend tracklang
+depend trigonometry
depend texapi
depend upca
depend xlop
Added: trunk/Master/tlpkg/tlpsrc/trigonometry.tlpsrc
===================================================================
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