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%D In order to support rotation over arbitrary angles, we need a sine
%D and cosine calculator. For this purpose we borrow a few macros by
%D David Carlisle (his trig package). Because local variables are
%D used, I patched the macros a bit. Also, I used a few different names
%D for variabels and macros and use existing auxiliary macros.
\unprotect
% compare: \number 0.5 \number -0.5 \number 1.5 \number -1.5
%
% so we need:
\def\realnumber#1{\withoutpt\the\dimexpr#1\s!pt\relax} % brrr
\chardef \@iv = 4
\chardef \@xc = 90 % was \nin@ty
\chardef \@clxx = 180
\chardef \@lxxi = 71
\mathchardef \@mmmmlxviii = 4068
\mathchardef \@xvi@k = 16384
\chardef \tr@coeffz = 72
\chardef \tr@coefb = 42
\mathchardef \tr@coefc = 840
\mathchardef \tr@coefd = 5040
\def\tg@series
{\!!dimena\@lxxi\!!dimena
\divide\!!dimena\@mmmmlxviii
\edef\!!stringa{\withoutpt\the\!!dimena}%
\!!dimena\!!stringa\!!dimena
\edef\!!stringb{\withoutpt\the\!!dimena}%
\divide\!!dimena\tr@coeffz
\advance\!!dimena\minusone\onepoint
\!!dimena\!!stringb\!!dimena
\advance\!!dimena \tr@coefb\onepoint
\!!dimena\!!stringb\!!dimena
\advance\!!dimena -\tr@coefc\onepoint
\!!dimena\!!stringb\!!dimena
\advance\!!dimena \tr@coefd\onepoint
\!!dimena\!!stringa\!!dimena
\divide\!!dimena \tr@coefd}
\def\tg@reduce#1#2%
{\!!dimena#1#2\@xc\onepoint
\advance\!!dimena#2-\@clxx\onepoint
\!!dimena-\!!dimena
\tg@@sin}
\def\tg@@sin
{\ifdim\tg@reduce>+\else\ifdim\tg@reduce<-\else
\tg@series
\fi\fi}
%D Calculating a sine is a two step process: first a value is
%D calculated, and afterwards it can be used. This saves redundant
%D calculations.
\def\calculatesin#1%
{{\expandafter\ifx\csname sin \realnumber{#1}\endcsname\relax
\!!dimena#1\onepoint
\tg@@sin
\expandafter\xdef\csname sin \realnumber{#1}\endcsname{\withoutpt\the\!!dimena}%
\fi}}
\def\calculatecos#1%
{{\expandafter\ifx\csname cos \realnumber{#1}\endcsname\relax
\!!dimena\@xc\onepoint
\advance\!!dimena-#1\onepoint
\tg@@sin
\expandafter\xdef\csname cos \realnumber{#1}\endcsname{\withoutpt\the\!!dimena}%
\fi}}
\def\calculatetan#1%
{{\expandafter\ifx\csname tan \realnumber{#1}\endcsname\relax
\calculatesin{#1}%
\calculatecos{#1}%
\!!dimena\calculatedcos{#1}\onepoint
\divide\!!dimena\@iv
\!!dimenb\calculatedsin{#1}\onepoint
\!!dimenb\@xvi@k\!!dimenb
\divide\!!dimenb\!!dimena
\expandafter\xdef\csname tan \realnumber{#1}\endcsname{\withoutpt\the\!!dimenb}%
\fi}}
%D The results are accessed with:
\def\calculatedsin#1{\csname sin \realnumber{#1}\endcsname}
\def\calculatedcos#1{\csname cos \realnumber{#1}\endcsname}
\def\calculatedtan#1{\csname tan \realnumber{#1}\endcsname}
%D A more save implementation would be:
\def\calculatedsin#1{\executeifdefined{sin \realnumber{#1}}\!!zerocount}
\def\calculatedcos#1{\executeifdefined{cos \realnumber{#1}}\!!plusone }
\def\calculatedtan#1{\executeifdefined{tan \realnumber{#1}}\!!zerocount}
%D A few values are predefined, although, on todays systems there
%D is no real reason for that. I've added the 270 ones and changed
%D the -90 tan. Also, I prefer text (\type {\!!..} instead of
%D counters \type {\..}.
\expandafter\let\csname sin \realnumber{ 0}\endcsname\!!zerocount
\expandafter\let\csname cos \realnumber{ 0}\endcsname\!!plusone
\expandafter\let\csname sin \realnumber{ 90}\endcsname\!!plusone
\expandafter\let\csname cos \realnumber{ 90}\endcsname\!!zerocount
\expandafter\let\csname sin \realnumber{180}\endcsname\!!zerocount
\expandafter\let\csname cos \realnumber{180}\endcsname\!!minusone
\expandafter\let\csname sin \realnumber{270}\endcsname\!!minusone
\expandafter\let\csname cos \realnumber{270}\endcsname\!!zerocount
\expandafter\let\csname sin \realnumber{-90}\endcsname\!!minusone
\expandafter\let\csname cos \realnumber{-90}\endcsname\!!zerocount
\expandafter\def\csname tan \realnumber{ 90}\endcsname{\writestatus\m!systems{infinite tan +90}}
\expandafter\def\csname tan \realnumber{-90}\endcsname{\writestatus\m!systems{infinite tan -90}}
%D Usage: \type {\calculatesin{10}} and \type {\calculatedsin{10}}
\protect \endinput
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