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-rw-r--r--Master/texmf-dist/tex/generic/pgf/libraries/pgflibraryfpu.code.tex212
1 files changed, 180 insertions, 32 deletions
diff --git a/Master/texmf-dist/tex/generic/pgf/libraries/pgflibraryfpu.code.tex b/Master/texmf-dist/tex/generic/pgf/libraries/pgflibraryfpu.code.tex
index dbaf9847cd1..00ce27705f8 100644
--- a/Master/texmf-dist/tex/generic/pgf/libraries/pgflibraryfpu.code.tex
+++ b/Master/texmf-dist/tex/generic/pgf/libraries/pgflibraryfpu.code.tex
@@ -157,24 +157,13 @@
\expandafter\let\expandafter#1\csname pgfmathfloat@backup@\string#1\endcsname%
}%
}
-\def\pgfmathfloat@prepareuninstallcmd@csname#1{%
- % and store backup information (globally - I don't want to do that
- % all the time when the FPU is used!):
- {%
- \globaldefs=1
- \pgfutil@namelet{pgfmathfloat@backup@#1}{#1}%
- \expandafter\gdef\expandafter\pgfmathfloat@uninstall\expandafter{\pgfmathfloat@uninstall
- \pgfutil@namelet{#1}{pgfmathfloat@backup@#1}%
- }%
- }%
-}
\def\pgfmathfloat@install#1=#2{%
\pgfmathfloat@prepareuninstallcmd{#1}%
\let#1=#2%
}
\def\pgfmathfloat@install@csname#1#2{%
- \pgfmathfloat@prepareuninstallcmd@csname{#1}%
+ \expandafter\pgfmathfloat@prepareuninstallcmd\csname #1\endcsname%
\pgfutil@namelet{#1}{#2}%
}
\def\pgfmathfloat@install@unimplemented#1{%
@@ -213,8 +202,11 @@
\pgfmathfloat@install\pgfmathmultiply@=\pgfmathfloatmultiply@%
\pgfmathfloat@install\pgfmathdivide@=\pgfmathfloatdivide@%
\pgfmathfloat@install\pgfmathabs@=\pgfmathfloatabs@%
+ \pgfmathfloat@install\pgfmathsign@=\pgfmathfloatsign@%
\pgfmathfloat@install\pgfmathround@=\pgfmathfloatround@%
\pgfmathfloat@install\pgfmathfloor@=\pgfmathfloatfloor@%
+ \pgfmathfloat@install\pgfmathceil@=\pgfmathfloatceil@
+ \pgfmathfloat@install\pgfmathint@=\pgfmathfloatint@
\pgfmathfloat@install\pgfmathmod@=\pgfmathfloatmod@%
\pgfmathfloat@install\pgfmathmax@=\pgfmathfloatmax@%
\pgfmathfloat@install\pgfmathmin@=\pgfmathfloatmin@%
@@ -268,13 +260,12 @@
\pgfmathfloat@install\pgfmathcosh@=\pgfmathfloatcosh@
\pgfmathfloat@install\pgfmathsinh@=\pgfmathfloatsinh@
\pgfmathfloat@install\pgfmathtanh@=\pgfmathfloattanh@
- \pgfmathfloat@install@unimplemented{ceil}%
+ \expandafter\pgfmathfloat@install\csname pgfmathatan2@\endcsname=\pgfmathfloatatantwo@
\pgfmathfloat@install@unimplemented{frac}%
\pgfmathfloat@install@unimplemented{random}%
\pgfmathfloat@install@unimplemented{setseed}%
\pgfmathfloat@install@unimplemented{Mod}%
\pgfmathfloat@install@unimplemented{real}%
-% \pgfmathfloat@install@unimplemented{atan2}%
% \pgfmathfloat@install@unimplemented{height}%
%
%
@@ -308,6 +299,21 @@
\pgfmathfloat@install\pgfmath@parse@exponent=\pgfmathfloat@parse@float@or@exponent
%
\pgfmathfloat@install\pgfmathparse=\pgfmathfloatparse%
+ %\pgfmathfloat@install\pgfmathparse@trynumber@token=\pgfmathfloat@parse@trynumber@token
+ \pgfmathfloat@install\pgfmathparse@expression@is@number=\pgfmathfloat@parse@expression@is@number
+}%
+
+% This here might bring speed improvements... if implemented
+% correctly.
+% However, this heuristics might fail in cases like "1+1" vs "1e+1" ...
+%\def\pgfmathfloat@parse@trynumber@token{numericfpu}
+%\pgfmath@tokens@make{numericfpu}{eE+-Y.0123456789}
+
+\def\pgfmathfloat@parse@expression@is@number{%
+ \pgfmathfloatparsenumber{\pgfmath@expression}%
+ \pgfmath@smuggleone\pgfmathresult%
+ \endgroup
+ \ignorespaces
}%
\def\pgfmathfloat@defineadapter@for@pgf@two@null@null@ONEARG#1{%
@@ -993,7 +999,7 @@
\if#2+%
\pgfmathfloatifflags{#1}{1}{#3}{#4}%
\else
- \pgfmathfloatgetflagstomacro#1\pgfmathfloat@loc@TMPa
+ \pgfmathfloatgetflagstomacro{#1}\pgfmathfloat@loc@TMPa
\if#2u%
\ifnum\pgfmathfloat@loc@TMPa>2
#3\relax
@@ -1424,8 +1430,24 @@
}%
\def\pgfmathfloatint@@loop@gobble#1\pgfmathfloat@EOI{}%
\let\pgfmathfloatint=\pgfmathfloatint@
-\let\pgfmathfloatfloor=\pgfmathfloatint
-\let\pgfmathfloatfloor@=\pgfmathfloatint@
+
+\def\pgfmathfloatfloor#1{%
+ \edef\pgfmathfloat@loc@TMPa{#1}%
+ \pgfmathfloatcreate{2}{5.0}{-1}% -0.5
+ \let\pgfmathfloat@loc@TMPb=\pgfmathresult
+ \pgfmathfloatadd@{\pgfmathfloat@loc@TMPa}{\pgfmathfloat@loc@TMPb}%
+ \expandafter\pgfmathfloatround@\expandafter{\pgfmathresult}%
+}
+\let\pgfmathfloatfloor@=\pgfmathfloatfloor
+
+\def\pgfmathfloatceil#1{%
+ \edef\pgfmathfloat@loc@TMPa{#1}%
+ \pgfmathfloatcreate{1}{5.0}{-1}% +0.5
+ \let\pgfmathfloat@loc@TMPb=\pgfmathresult
+ \pgfmathfloatadd@{\pgfmathfloat@loc@TMPa}{\pgfmathfloat@loc@TMPb}%
+ \expandafter\pgfmathfloatround@\expandafter{\pgfmathresult}%
+}
+\let\pgfmathfloatceil@=\pgfmathfloatceil
\def\pgfmathfloat@notimplemented#1{%
\pgfmath@error{Sorry, the operation '#1' has not yet been implemented in the floating point unit :-(}{}%
@@ -1476,7 +1498,34 @@
\pgfmath@smuggleone\pgfmathresult
\endgroup
}%
-\let\pgfmathfloatabs=\pgfmathfloatabs@
+%
+% Defines \pgfmathresult to be sign(#1)
+\def\pgfmathfloatsign@#1{%
+ \begingroup
+ \expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
+ \ifcase\pgfmathfloat@a@S
+ % 0:
+ \pgfmathfloatcreate{0}{0.0}{0}%
+ \or
+ % +: ok, is positive.
+ \pgfmathfloatcreate{1}{1.0}{0}%
+ \or
+ % -:
+ \pgfmathfloatcreate{2}{1.0}{0}%
+ \or
+ % nan: do nothing.
+ \pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}%
+ \or
+ % +infty:.
+ \pgfmathfloatcreate{1}{1.0}{0}%
+ \or
+ % -infty:
+ \pgfmathfloatcreate{2}{1.0}{0}%
+ \fi
+ \pgfmath@smuggleone\pgfmathresult
+ \endgroup
+}%
+\let\pgfmathfloatsign=\pgfmathfloatsign@
% Computes the absolute error |#1 - #2| into \pgfmathresult.
\def\pgfmathfloatabserror@#1#2{%
@@ -1494,8 +1543,8 @@
\let\pgfmathresult=\pgfmathfloat@subtract
}{%
\pgfmathfloatdivide@{\pgfmathfloat@subtract}{#2}%
- \pgfmathfloatabs@{\pgfmathresult}%
}%
+ \pgfmathfloatabs@{\pgfmathresult}%
}%
\let\pgfmathfloatrelerror=\pgfmathfloatrelerror@
@@ -1567,14 +1616,27 @@
%
% #1 is a one-argument macro which assigns \pgfmathresult.
\def\pgfmathfloatTRIG@#1#2{%
- \expandafter\ifx\csname pgfmathfloatTRIG@NUM\endcsname\relax%
- % Lazy evaluation:
- \pgfmathfloatcreate{1}{3.6}{2}%
- \global\let\pgfmathfloatTRIG@NUM=\pgfmathresult
- \pgfmathfloatcreate{1}{2.77777777777778}{-3}%
- \global\let\pgfmathfloatTRIG@NUM@INV=\pgfmathresult
+ \if0\pgfmath@trig@format@choice
+ % trig format=deg
+ \expandafter\ifx\csname pgfmathfloatTRIG@NUM\endcsname\relax%
+ % Lazy evaluation:
+ \pgfmathfloatcreate{1}{3.6}{2}%
+ \global\let\pgfmathfloatTRIG@NUM=\pgfmathresult
+ \pgfmathfloatcreate{1}{2.77777777777778}{-3}%
+ \global\let\pgfmathfloatTRIG@NUM@INV=\pgfmathresult
+ \fi
+ \pgfmathfloatmodknowsinverse@{#2}{\pgfmathfloatTRIG@NUM}{\pgfmathfloatTRIG@NUM@INV}%
+ \else
+ % trig format=rad
+ \expandafter\ifx\csname pgfmathfloatTRIG@rad@NUM\endcsname\relax%
+ % Lazy evaluation:
+ \pgfmathfloatcreate{1}{6.28318530717959}{0}%
+ \global\let\pgfmathfloatTRIG@rad@NUM=\pgfmathresult
+ \pgfmathfloatcreate{1}{1.59154943091895}{-1}%
+ \global\let\pgfmathfloatTRIG@rad@NUM@INV=\pgfmathresult
+ \fi
+ \pgfmathfloatmodknowsinverse@{#2}{\pgfmathfloatTRIG@rad@NUM}{\pgfmathfloatTRIG@rad@NUM@INV}%
\fi
- \pgfmathfloatmodknowsinverse@{#2}{\pgfmathfloatTRIG@NUM}{\pgfmathfloatTRIG@NUM@INV}%
\pgfmathfloattofixed@{\pgfmathresult}%
\expandafter#1\expandafter{\pgfmathresult}%
\pgfmathfloatparsenumber{\pgfmathresult}%
@@ -1618,11 +1680,19 @@
\fi
\pgfmathfloatgreaterthan@{#1}{\pgfmathfloatatan@TMP}%
\ifpgfmathfloatcomparison
- \pgfmathfloatcreate{1}{9.0}{1}%
+ \pgfmathiftrigonometricusesdeg{%
+ \pgfmathfloatcreate{1}{9.0}{1}%
+ }{%
+ \pgfmathfloatcreate{1}{1.570796326794}{0}%
+ }%
\else
\pgfmathfloatlessthan{#1}{\pgfmathfloatatan@TMPB}%
\ifpgfmathfloatcomparison
- \pgfmathfloatcreate{2}{9.0}{1}%
+ \pgfmathiftrigonometricusesdeg{%
+ \pgfmathfloatcreate{2}{9.0}{1}%
+ }{%
+ \pgfmathfloatcreate{2}{1.570796326794}{0}%
+ }%
\else
\pgfmathfloattofixed@{#1}%
\expandafter\pgfmath@basic@atan@\expandafter{\pgfmathresult}%
@@ -1634,6 +1704,76 @@
}%
\let\pgfmathfloatatan=\pgfmathfloatatan@
+\def\pgfmathfloatatantwo#1#2{%
+ % Note: first parameter is y (!), second is x (!)
+ \begingroup%
+ \let\pgfmath@trig@format@choice@@=\pgfmath@trig@format@choice
+ \def\pgfmath@trig@format@choice{0}%
+ %
+ \expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
+ \expandafter\pgfmathfloat@decompose#2\relax\pgfmathfloat@b@S\pgfmathfloat@b@M\pgfmathfloat@b@E
+ \ifnum\pgfmathfloat@a@S=0
+ % ok, #1 = 0. Substitute by 1e-16 such that the next \ifnum catches it:
+ \pgfmathfloat@a@E=-16 %
+ \fi
+ %
+ \ifnum\pgfmathfloat@a@E<-3 %
+ \ifnum\pgfmathfloat@b@S=2 %
+ % #2 < 0
+ \pgfmathfloatcreate{1}{1.8}{2}% +180
+ \else
+ \ifnum\pgfmathfloat@b@S=1 %
+ % #2 >0
+ \pgfmathfloatcreate{0}{0.0}{0}%
+ \else
+ % + or - 90, just use the sign of #1:
+ \pgfmathfloatcreate{\the\pgfmathfloat@a@S}{9.0}{1}%
+ \fi
+ \fi
+ \else%
+ \pgfmathfloatabs@{#1}\let\pgfmath@tempa\pgfmathresult%
+ \pgfmathfloatabs@{#2}\let\pgfmath@tempb\pgfmathresult%
+ \pgfmathfloatgreaterthan@{\pgfmath@tempa}{\pgfmath@tempb}%
+ \ifpgfmathfloatcomparison
+ \pgfmathfloatdivide@{#2}{\pgfmath@tempa}%
+ \expandafter\pgfmathfloatatan@\expandafter{\pgfmathresult}%
+ \let\pgfmath@tempa=\pgfmathresult
+ \pgfmathfloatcreate{1}{9.0}{1}%
+ \let\pgfmath@tempb=\pgfmathresult
+ \pgfmathfloatsubtract@{\pgfmath@tempb}{\pgfmath@tempa}%
+ \else%
+ \pgfmathfloatdivide@{\pgfmath@tempa}{#2}%
+ \expandafter\pgfmathfloatatan@\expandafter{\pgfmathresult}%
+ \expandafter\pgfmathfloatifflags\expandafter{\pgfmathresult}{2}{%
+ \let\pgfmath@tempa=\pgfmathresult
+ \pgfmathfloatcreate{1}{1.8}{2}%
+ \let\pgfmath@tempb=\pgfmathresult
+ \pgfmathfloatadd@{\pgfmath@tempa}{\pgfmath@tempb}%
+ }{}%
+ \fi%
+ %
+ \pgfmathfloatifflags{#1}{-}{%
+ % #1 < 0:
+ \pgfmathfloatmultiplyfixed@{\pgfmathresult}{-1}%
+ }{}%
+ \fi%
+ \if1\pgfmath@trig@format@choice@@
+ % trig format=rad
+ \pgfmathfloat@scale@deg@to@rad\pgfmathresult
+ \fi
+ \pgfmath@smuggleone\pgfmathresult%
+ \endgroup%
+}%
+\let\pgfmathfloatatantwo@=\pgfmathfloatatantwo
+\expandafter\let\csname pgfmathfloatatan2\endcsname=\pgfmathfloatatantwo
+\expandafter\let\csname pgfmathfloatatan2@\endcsname=\pgfmathfloatatantwo@
+
+\def\pgfmathfloat@scale@deg@to@rad#1{%
+ \edef\pgfmathfloat@loc@TMPb{#1}%
+ \pgfmathfloatcreate{1}{1.74532925199433}{-2}% = pi / 180
+ \pgfmathfloatmultiply@{\pgfmathresult}{\pgfmathfloat@loc@TMPb}%
+}%
+
\def\pgfmathfloatsec@#1{\pgfmathfloatTRIG@\pgfmath@basic@cos@{#1}\pgfmathfloatreciprocal@{\pgfmathresult}}
\let\pgfmathfloatsec=\pgfmathfloatsec@
\def\pgfmathfloatcosec@#1{\pgfmathfloatTRIG@\pgfmath@basic@sin@{#1}\pgfmathfloatreciprocal@{\pgfmathresult}}
@@ -1664,16 +1804,24 @@
\expandafter\def\csname pgfmathfloatlog10@\endcsname#1{%
\pgfmathfloatln@{#1}%
- \let\pgfmathfloat@log@ten=\pgfmathresult
+ \let\pgfmathfloat@log@e=\pgfmathresult
\pgfmathfloatcreate{1}{4.34294481903252}{-1}% 1/ln(10)
- \pgfmathfloatmultiply@{\pgfmathresult}{\pgfmathfloat@log@ten}%
+ \pgfmathfloatmultiply@{\pgfmathresult}{\pgfmathfloat@log@e}%
}%
+\pgfutil@namelet{pgfmathfloatlog10}{pgfmathfloatlog10@}%
+
\expandafter\def\csname pgfmathfloatlog2@\endcsname#1{%
\pgfmathfloatln@{#1}%
- \let\pgfmathfloat@log@two=\pgfmathresult
+ \let\pgfmathfloat@log@e=\pgfmathresult
\pgfmathfloatcreate{1}{1.44269504088896}{0}% 1/ln(2)
- \pgfmathfloatmultiply@{\pgfmathresult}{\pgfmathfloat@log@two}%
+ \pgfmathfloatmultiply@{\pgfmathresult}{\pgfmathfloat@log@e}%
}%
+\pgfutil@namelet{pgfmathfloatlog2}{pgfmathfloatlog2@}%
+
+\expandafter\let\expandafter\pgfmathfloatlogtwo\csname pgfmathfloatlog2\endcsname
+\expandafter\let\expandafter\pgfmathfloatlogtwo@\csname pgfmathfloatlog2@\endcsname
+\expandafter\let\expandafter\pgfmathfloatlogten\csname pgfmathfloatlog10\endcsname
+\expandafter\let\expandafter\pgfmathfloatlogten@\csname pgfmathfloatlog10@\endcsname
% Computes log(x) into \pgfmathresult.
%