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authorNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
committerNorbert Preining <norbert@preining.info>2019-09-02 13:46:59 +0900
commite0c6872cf40896c7be36b11dcc744620f10adf1d (patch)
tree60335e10d2f4354b0674ec22d7b53f0f8abee672 /graphics/pgf/base/source/pgfmathtestsuite.tex
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+% FIXME: this class is MESSY.
+%
+% rewrite with proper assertions ... it goes back to a time where I
+% merely wanted to inspect the results!
+%
+% --> see 'assertEquals' in this file
+%
+\documentclass[a4paper]{article}
+
+\usepackage[intlimits]{amsmath}
+\usepackage{amssymb}
+\usepackage{amsfonts}
+\usepackage{ifpdf}
+
+\ifpdf
+ \usepackage{hyperref}
+\else
+ \def\pgfsysdriver{pgfsys-dvipdfm.def}
+ \usepackage[dvipdfm]{hyperref}
+\fi
+\usepackage{tikz}
+\usepackage{fp}
+
+\makeatletter
+\pgfutil@ifundefined{pgfmathdeclarefunction}{
+ % load pgfplots with its pgf 2.00 compatibility code:
+ \usepackage{pgfplots}
+}{
+ \usepgflibrary{fpu}
+}
+\makeatother
+
+\pgfmathfloatcreate{1}{5.0}{-4}
+\let\THRESH=\pgfmathresult
+
+
+\parindent=0pt
+
+
+\author{Christian Feuers\"anger}
+\title{Test cases for pgffloatmath.code.tex}
+
+\def\testsection#1{\message{---------- STARTING TEST SECTION '#1'}\section{#1}}
+\def\testsubsection#1{\message{-------STARTING TEST SUBSECTION '#1'}\subsection{#1}}
+\def\testsubsubsection#1{\message{------STARTING TEST SUBSUBSECTION '#1'}\subsubsection{#1}}
+
+
+\def\compare#1#2{%
+ \begingroup
+ \message{COMPUTING LOG(#1)}%
+ \pgfmathlog{#1}%
+ \let\actual=\pgfmathresult
+ \def\expected{#2}%
+ \pgfmathsubtract\actual\expected%
+ \let\abserr=\pgfmathresult
+ \pgfmathdivide\abserr\expected
+ \let\relerr=\pgfmathresult
+ \noindent
+ log(#1)\hfill=
+ \expected;\hfill%
+ actual=\actual;\hfill%
+ abserr=\abserr;\hfill%
+ relerr=\relerr;\hfill%
+ \endgroup
+ \par
+}%
+%--------------------------------------------------
+% \def\showlowlevelfloat#1#2e#3\relax{%
+% \ensuremath{[#1] \cdot #2 \cdot 10^{#3}}%
+% }%
+%--------------------------------------------------
+\long\def\showlowlevelfloatmacro#1{#1}
+
+\long\def\showlowlevelfloatmacrolong#1{%
+ #1 is decomposed into
+
+ {%
+ \gdef\testerror{}%
+ \pgfmathfloattoregisters{#1}{\count0 }{\dimen0 }{\count1 }%
+ pgfmathfloattoregisters: flags \the\count0; M=\the\dimen0; E=\the\count1
+ \ifx\testerror\empty
+ \else
+ \par (caught \texttt{\testerror})%
+ \fi
+ }%
+
+ {%
+ \gdef\testerror{}%
+ pgfmathfloattoregisterstok: \pgfmathfloattoregisterstok{#1}{\count0 }{\toks0 }{\count1 }%
+ flags \the\count0; M=\the\toks0; E=\the\count1
+ \ifx\testerror\empty
+ \else
+ \par (caught \texttt{\testerror})%
+ \fi
+ }%
+
+ {%
+ \gdef\testerror{}%
+ pgfmathfloatgetflags \pgfmathfloatgetflags{#1}{\count0 }
+ flags \the\count0;
+ \ifx\testerror\empty
+ \else
+ \par (caught \texttt{\testerror})%
+ \fi
+ }%
+
+ \medskip
+ %\expandafter\showlowlevelfloat#1\relax
+}%
+
+\def\showsinglenumberparsing#1{%
+%\tracingmacros=2\tracingcommands=2
+ \begingroup
+ \message{PARSING NUMBER #1...}%
+ \gdef\testerror{}%
+ \pgfmathfloatparsenumber{#1}%
+ \let\resultasfloat=\pgfmathresult
+ \pgfmathfloattofixed\resultasfloat
+ \let\resultasfixed=\pgfmathresult
+ \[ #1 \mapsto \resultasfloat = \showlowlevelfloatmacro\resultasfloat \mapsto \resultasfixed
+ \]
+ \ifx\testerror\empty
+ \else
+ \par (caught \texttt{\testerror})%
+ \fi
+ \endgroup
+%\tracingmacros=0\tracingcommands=0
+}
+
+\def\pretty#1{%
+ \message{Pretty-printing #1...}%
+ \pgfmathprintnumberto{#1}\result
+ {\pgfkeys{/pgf/number format/showpos}\pgfmathprintnumberto{#1}\resultpos\global\let\resultpos=\resultpos}%
+ \[ #1 \mapsto \pgfmathprintnumber{#1} [=\resultpos] \]
+ \message{#1 mapsto \meaning\result}%
+}
+
+\begin{document}
+\maketitle
+
+
+%--------------------------------------------------
+% \showit{2.8128}
+% log(12)=\pgfmathlog{1.2}\pgfmathadd{\pgfmathresult}{2.30258}\pgfmathresult\par
+% \showit{1.2}
+% \showit{4.0}
+% log(1200)=\pgfmathlog{1.2}\pgfmathadd{\pgfmathresult}{6.9077}\pgfmathresult\par
+% log(6.241e-7)=\pgfmathlog{6.241}\pgfmathadd{\pgfmathresult}{-16.11809}\pgfmathresult\par
+%--------------------------------------------------
+
+\testsection{Conversion to normalised floating point numbers basis 10}
+\showsinglenumberparsing{123.41251}%
+\showsinglenumberparsing{1023.52}
+\showsinglenumberparsing{123412.51}%
+\showsinglenumberparsing{12341251.0}%
+\showsinglenumberparsing{-12341251.0}%
+\showsinglenumberparsing{1.2341251}%
+\showsinglenumberparsing{8.02410024}
+\showsinglenumberparsing{8.024100}
+\showsinglenumberparsing{0001234.3100}
+\showsinglenumberparsing{0001234.00001}
+\showsinglenumberparsing{0001000.00001}
+\showsinglenumberparsing{0001000.00001000}
+\showsinglenumberparsing{0.12341251}%
+\showsinglenumberparsing{0.0012341251}%
+\showsinglenumberparsing{0.00000012341251}%
+\showsinglenumberparsing{-0.00000012341251}%
+\showsinglenumberparsing{10}
+\showsinglenumberparsing{100.351}
+\showsinglenumberparsing{100.35100}
+\showsinglenumberparsing{100.35100234}
+\showsinglenumberparsing{100.0035100234}
+\showsinglenumberparsing{100}
+\showsinglenumberparsing{99999}
+\showsinglenumberparsing{999.000}
+
+%\tracingmacros=2 \tracingcommands=2
+\showsinglenumberparsing{8.31160034e-02}%
+\showsinglenumberparsing{2.54685628e-02}%
+\showsinglenumberparsing{7.40715288e-03}%
+\showsinglenumberparsing{2.10192154e-03}%
+\showsinglenumberparsing{5.87352989e-04}%
+\showsinglenumberparsing{-1.62269942e-04}%
+\showsinglenumberparsing{4.44248889e-05}%
+\showsinglenumberparsing{1.20714122e-05}%
+\showsinglenumberparsing{3.26101452e-06}%
+\showsinglenumberparsing{3261.01452e-06}%
+\showsinglenumberparsing{0.000326101452e-06}%
+\showsinglenumberparsing{1.2345e-12}%
+\showsinglenumberparsing{1.2345e+12}%
+
+\message{SPECIAL CASE 0}%
+\showsinglenumberparsing{0}
+\showsinglenumberparsing{-0}
+\showsinglenumberparsing{-0.000}
+\showsinglenumberparsing{+0.000}
+\showsinglenumberparsing{+0}
+\showsinglenumberparsing{-1}
+\showsinglenumberparsing{1.0e1}
+\showsinglenumberparsing{1e1}
+\showsinglenumberparsing{1141}
+\showsinglenumberparsing{-53e-5}
+
+\testsubsection{Error handling}
+{
+ \pgfkeys{
+ /pgf/fpu/handlers/empty number/.code 2 args={%
+ \gdef\testerror{handlers/empty number=\{#1\}\{#2\}}%
+ },
+ /pgf/fpu/handlers/invalid number/.code 2 args={%
+ \gdef\testerror{handlers/invalid number=\{#1\}\{#2\}}%
+ },
+ /pgf/fpu/handlers/wrong lowlevel format/.code 2 args={%
+ \gdef\testerror{handlers/wrong lowlevel format=\{#1\}\{#2\}}%
+ },
+ }
+ \showsinglenumberparsing{-53e-5 not terminated}
+ %\showsinglenumberparsing{-53e-}
+ \showsinglenumberparsing{}
+ \showsinglenumberparsing{ ASDZ@414e12}
+
+ This one has trailing spaces and should work:
+ \showsinglenumberparsing{10 }
+
+ This one has leading spaces and should work:
+ \showsinglenumberparsing{ 10}
+
+ \testsubsection{Error handling of decompose routines}
+
+ \pgfmathfloatparsenumber{100}
+ \showlowlevelfloatmacrolong{\pgfmathresult}
+
+ \showlowlevelfloatmacrolong{132}
+
+ \showlowlevelfloatmacrolong{Z}
+}
+
+\testsection{logarithms, compared with PGF arithmetics}
+
+\compare{0.1}{-2.30259}
+\compare{0.12}{-2.12026}
+\compare{0.2}{-1.60944}
+\compare{0.3}{-1.20397}
+\compare{0.4}{-0.916291}
+\compare{0.5}{-0.693147}
+\compare{0.6}{-0.510826}
+\compare{0.7}{-0.356675}
+\compare{0.75}{-0.287682}
+\compare{0.8}{-0.223144}
+\compare{0.823}{-0.194799}
+\compare{0.9}{-0.105361}
+\compare{0.96}{-0.040822}
+\compare{1.2}{0.182322}
+\compare{1.5}{0.405465}
+\compare{1.6}{0.470004}
+\compare{9.0}{2.1972245773}
+\compare{9.2}{2.2192034}
+\compare{9.3}{2.23001440}
+\compare{9.7}{2.27212588}
+\compare{10.0}{2.302585092}
+\compare{100.0}{4.605170185}
+\compare{1351.0}{7.208600337}
+\compare{9752.0}{9.185227671}
+\compare{9600.0}{9.169518377}
+
+\vskip1cm
+\compare{0.000142}{-8.8596835}
+\compare{0.0054124}{-5.219062661}
+\compare{0.000912697124}{-6.9991064}
+
+\vskip1cm
+\compare{8.31160034e-02}{-2.48751801563782}%
+\compare{2.54685628e-02}{-3.67031041875206}%
+\compare{7.40715288e-03}{-4.90530914022879}%
+\compare{2.10192154e-03}{-6.16490333357987}%
+\compare{5.87352989e-04}{-7.43988457474844}%
+\compare{1.62269942e-04}{-8.72624930084187}%
+\compare{4.44248889e-05}{-10.0217106847708}%
+\compare{1.20714122e-05}{-11.3246705288704}%
+\compare{3.26101452e-06}{-12.6334722085451}%
+
+\vskip1cm
+\compare{5}{1.6094379124341}%
+\compare{17}{2.83321334405622}%
+\compare{39}{3.66356164612965}%
+\compare{49}{3.89182029811063}%
+\compare{129}{4.85981240436167}%
+\compare{321}{5.77144112313002}%
+\compare{769}{6.64509096950564}%
+\compare{1793}{7.49164547360513}%
+\compare{4097}{8.31801027754687}%
+\compare{9217}{9.12880488399366}%
+
+
+\testsection{Test for prettyprinter}
+%\tracingmacros=2\tracingcommands=2
+\message{PRETTY PRINTING}
+{
+\twocolumn
+\def\prettytest{%
+ \pretty{1}
+ \pretty{1.0}
+ \pretty{-1.02311}
+ \pretty{-11241.02311}
+ \pretty{-11241}
+ \pretty{8124.99999}
+ \pretty{8124.849999}
+ \pretty{8124.843333}
+ \pretty{8.82}
+ \pretty{8.5}
+ \pretty{9.}
+ \pretty{5.9}
+ \pretty{-0.00001}
+ \pretty{-1.00001}
+ \pretty{-0.559}
+ \pretty{-0.554}
+ \pretty{-0.00000141}
+ \pretty{1.234e10}
+ \pretty{123456781}
+ \pretty{1234}
+ \pretty{8}
+ \pretty{-9.995}
+ \pretty{-0.015}
+ \pretty{-0.1}
+ \pretty{-0.15}
+ \pretty{0.15}
+ \pretty{-0}
+ \pretty{0}
+ \pretty{9.00}
+ \pretty{200.01}
+ \pretty{200.0000}
+ \pretty{1.5e-7}
+ \pretty{0.00035}
+ \pretty{0.00005}
+ \pretty{nan}
+ \pretty{inf}
+ \pretty{-inf}
+ \pretty{10}
+ \pretty{100}
+ \pretty{200}
+ \pretty{500}
+ \pretty{1000}
+ \pretty{30000}
+ \pretty{600000}
+ \pretty{1000000}
+ \pretty{30000000}
+ \pretty{600000000}
+ \pretty{1000000000}
+ \pretty{-10}
+ \pretty{-100}
+ \pretty{-200}
+ \pretty{-500}
+ \pretty{-1000}
+ \pretty{-30000}
+ \pretty{-600000}
+ \pretty{-1000000}
+ \pretty{-30000000}
+ \pretty{-600000000}
+ \pretty{-1000000000}
+}
+
+\testsubsection{STD format}
+\pgfqkeys{/pgf/number format}{std}
+\prettytest
+
+{
+\testsubsubsection{precision 0}
+\pgfqkeys{/pgf/number format}{precision=0}
+\prettytest
+}
+
+{
+\testsubsection{FIXED format}
+\testsubsubsection{with period}
+\pgfqkeys{/pgf/number format}{fixed,use period}
+\prettytest
+
+{
+\testsubsubsection{precision 0}
+\pgfqkeys{/pgf/number format}{precision=0}
+\prettytest
+}
+{
+\testsubsubsection{skip 0.=true}
+\pgfqkeys{/pgf/number format}{skip 0.=true}
+\prettytest
+}
+
+{
+\testsubsubsection{1000 sep; min exponent for 1000 sep=4}
+\pgfqkeys{/pgf/number format}{1000 sep=',min exponent for 1000 sep=4}
+\prettytest
+}
+
+\testsubsubsection{with comma}
+\pgfqkeys{/pgf/number format}{fixed,use comma}
+\prettytest
+}
+
+
+{
+\testsubsection{FIXED ZEROFILL format}
+\testsubsubsection{with period}
+\pgfqkeys{/pgf/number format}{fixed,fixed zerofill,use period}
+\prettytest
+
+{
+\testsubsubsection{precision 0}
+\pgfqkeys{/pgf/number format}{precision=0}
+\prettytest
+}
+
+\testsubsubsection{with comma}
+\pgfqkeys{/pgf/number format}{fixed,fixed zerofill,use comma}
+%\tracingmacros=2\tracingcommands=2
+\prettytest
+%\tracingmacros=0\tracingcommands=0
+}
+
+{
+\testsubsection{sci format}
+\testsubsubsection{with period}
+\pgfqkeys{/pgf/number format}{sci,use period}
+\prettytest
+
+{
+\testsubsubsection{precision 0}
+\pgfqkeys{/pgf/number format}{precision=0}
+\prettytest
+}
+
+\testsubsubsection{with comma}
+\pgfqkeys{/pgf/number format}{sci,use comma}
+\prettytest
+
+%\testsubsection{may skip mantisse}
+%\pgfqkeys{/pgf/number format}{sci may skip mantisse=true}
+%\prettytest
+
+}{
+\testsubsection{sci format zerofill}
+\testsubsubsection{with period}
+\pgfqkeys{/pgf/number format}{sci,sci zerofill,use period}
+\prettytest
+
+\testsubsubsection{with comma}
+\pgfqkeys{/pgf/number format}{sci,sci zerofill,use comma}
+\prettytest
+
+\testsubsubsection{e-style}
+\pgfqkeys{/pgf/number format}{sci e}
+\prettytest
+
+\testsubsubsection{subscript-style}
+\pgfqkeys{/pgf/number format}{sci subscript}
+\prettytest
+
+\testsubsubsection{subscript-style + period + no zero fill}
+\pgfqkeys{/pgf/number format}{sci subscript,use period,sci}
+\prettytest
+
+\testsubsubsection{subscript-style precision 4}
+\pgfqkeys{/pgf/number format}{sci subscript,precision=4}
+\prettytest
+}
+
+\testsubsection{int trunc format}
+\pgfqkeys{/pgf/number format}{int trunc}
+\prettytest
+
+\testsubsection{int detect format}
+\pgfqkeys{/pgf/number format}{int detect}
+\prettytest
+
+\testsubsection{frac}
+\pgfqkeys{/pgf/number format}{frac}
+\pretty{0.333333333333333}
+\pretty{0.5}
+\pretty{2.133333333333325e-01}%
+\pretty{0.12}
+\pretty{2.666666666666646e-02}%
+\pretty{-1.333333333333334e-02}%
+\pretty{7.200000000000000e-01}%
+\pretty{6.666666666666667e-02}%
+\pretty{1.333333333333333e-01}%
+\pretty{-1.333333333333333e-02}%
+\pretty{8.533333333333298e-01}
+\pretty{8.533333e-01}
+}
+\onecolumn
+
+\testsection{Pretty printing using the relative style}
+{
+\long\def\TESTIT#1#2{%
+ \gdef\temptable{\begin{tabular}}%
+ \gdef\header{l}%
+ \def\n{\noexpand\n}%
+ \foreach \number in {#2} {%
+ \xdef\header{\header c}%
+ }%
+ \toks0=\expandafter{\temptable}%
+ \xdef\temptable{\the\toks0 {\header}\n}%
+ %
+ \toks0=\expandafter{\temptable}%
+ \toks1={}%
+ \xdef\temptable{\the\toks0 \the\toks1}%
+ \foreach \number in {#2} {%
+ \toks0=\expandafter{\temptable}%
+ \toks1=\expandafter{\number}%
+ \xdef\temptable{\the\toks0 & \noexpand\texttt{\the\toks1}}%
+ }%
+ \toks0=\expandafter{\temptable}%
+ \xdef\temptable{\the\toks0 \noexpand\\\n}%
+ %
+ \toks0=\expandafter{\temptable}%
+ \toks1={With actual config:}%
+ \xdef\temptable{\the\toks0 \the\toks1}%
+ \foreach \number in {#2} {%
+ \toks0=\expandafter{\temptable}%
+ \toks1=\expandafter{\number}%
+ \xdef\temptable{\the\toks0 & \noexpand\pgfmathprintnumber{\the\toks1}}%
+ }%
+ \toks0=\expandafter{\temptable}%
+ \xdef\temptable{\the\toks0 \noexpand\\\n}%
+ %
+ \foreach \relativeto in {#1} {%
+ \toks0=\expandafter{\temptable}%
+ \xdef\temptable{\the\toks0 Relative to $10^{\relativeto}$:}%
+ \foreach \number in {#2} {%
+ \toks0=\expandafter{\temptable}%
+ \toks1=\expandafter{\number}%
+ \xdef\temptable{\the\toks0 & \noexpand\pgfmathprintnumber[relative={\relativeto}]{\the\toks1}}%
+ }%
+ \toks0=\expandafter{\temptable}%
+ \xdef\temptable{\the\toks0 \noexpand\\\n}%
+ }%
+ %
+ %
+ \toks0=\expandafter{\temptable}%
+ \toks1={\end{tabular}\n}%
+ \xdef\temptable{\the\toks0 \the\toks1}%
+ %
+ \def\n{^^J}%
+%\message{TEMP-TABLE: \n\meaning\temptable\n}%
+ %
+ \let\n=\relax
+ \noindent
+ \temptable
+}%
+%\tracingmacros=2 \tracingcommands=2
+
+\TESTIT{1,3}{1e-16,0,15,17,20}
+
+\TESTIT{0,1,3,4,5,6,7,8,9}{-100.123456,1e-16,1431,2000.1234,123456789.1234}
+
+
+
+\TESTIT{-4,-3,-2,-1,0,1,2,3}{0.0001,0.00012678,0.00013678,0.00016678,1.23,2.345,123.4,1234.5}
+
+{
+\subsection*{every relative/.style={sci}}
+\pgfkeys{/pgf/number format/every relative/.style={sci}}
+\TESTIT{-4,-3,-2,-1,0,1,2,3}{0.0001,0.00012678,0.00013678,0.00016678,1.23,2.345,123.4,1234.5}
+}
+
+\TESTIT{-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9}{-123.123456,123.1234565}
+{
+\subsection*{precision=4}
+\pgfkeys{/pgf/number format/precision=4}
+\TESTIT{-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9}{-123.123456,123.1234565}
+}
+}
+
+\begingroup
+\testsection{testing pgfmathfloatadd}
+\def\testfloataddnonsymmetric#1#2{%
+ \pgfmathfloatparsenumber{#1}%
+ \let\first=\pgfmathresult
+ \pgfmathfloatparsenumber{#2}%
+ \let\second=\pgfmathresult
+ \message{computing #1 + #2; \first + \second}%
+ \pgfmathfloatadd\first\second
+ \let\result=\pgfmathresult
+ \pgfmathfloattofixed\result
+ \let\resultfixed=\pgfmathresult
+ \[ \text{pgfmathfloatadd: } \showlowlevelfloatmacro\first + \showlowlevelfloatmacro\second = \showlowlevelfloatmacro\result \; \bigl( #1 + #2 = \resultfixed \bigr). \]
+}%
+\def\testfloatadd#1#2{%
+ \testfloataddnonsymmetric{#1}{#2}%
+ \testfloataddnonsymmetric{#2}{#1}%
+}%
+
+\testfloatadd{1}{100}
+\testfloatadd{100}{100}
+\testfloatadd{1}{2}
+\testfloatadd{1}{0}
+\testfloatadd{9.999999}{0}
+\testfloatadd{9.9999}{0.0001}
+\testfloatadd{9.9999e-5}{0.0001e-5}
+\testfloatadd{1e6}{1e5}
+\testfloatadd{1e6}{1e3}
+\testfloatadd{1e6}{1}
+\testfloatadd{1e6}{0.1}
+
+\testfloatadd{1}{-100}
+\testfloatadd{100}{-100}
+\testfloatadd{1}{-2}
+\testfloatadd{1e6}{-1e5}
+\testfloatadd{1e6}{-1e3}
+\testfloatadd{1e6}{-1}
+\testfloatadd{1e6}{-0.1}
+
+\testfloatadd{1e-3}{0}
+
+\testfloatadd{inf}{0}
+\testfloatadd{inf}{5}
+\testfloatadd{nan}{5}
+\testfloatadd{0}{0}
+\testfloatadd{-inf}{inf}
+\testfloatadd{-inf}{40}
+\endgroup
+
+\begingroup
+\testsection{testing pgfmathfloatmultiplyfixed}
+\def\testfloatmultiplyfixed#1#2{%
+ \pgfmathfloatparsenumber{#1}%
+ \let\first=\pgfmathresult
+ \pgfmathfloatparsenumber{#2}%
+ \pgfmathfloattofixed\pgfmathresult
+ \let\second=\pgfmathresult
+ \message{computing #1 * #2; \first * \second}%
+ \pgfmathfloatmultiplyfixed\first\second
+ \let\result=\pgfmathresult
+ \pgfmathfloattofixed\result
+ \let\resultfixed=\pgfmathresult
+ \[ \text{pgfmathfloatmultiplyfixed: } \showlowlevelfloatmacro\first \cdot \second = \showlowlevelfloatmacro\result \; \bigl( #1 \cdot #2 = \resultfixed \bigr). \]
+}%
+
+\testfloatmultiplyfixed{1}{100}
+\testfloatmultiplyfixed{100}{100}
+\testfloatmultiplyfixed{1}{2}
+\testfloatmultiplyfixed{5}{2}
+\testfloatmultiplyfixed{5e4}{10}
+\testfloatmultiplyfixed{1}{0}
+\testfloatmultiplyfixed{9.999999}{0}
+\testfloatmultiplyfixed{9.9999}{0.0001}
+\testfloatmultiplyfixed{9.9999e-5}{0.001}
+\testfloatmultiplyfixed{1e6}{4}
+\testfloatmultiplyfixed{1e6}{100}
+\testfloatmultiplyfixed{1e6}{1}
+\testfloatmultiplyfixed{1e6}{0.1}
+
+\testfloatmultiplyfixed{1}{-100}
+\testfloatmultiplyfixed{100}{-100}
+\testfloatmultiplyfixed{1}{-2}
+\testfloatmultiplyfixed{1e6}{-9}
+\testfloatmultiplyfixed{1e6}{-100}
+\testfloatmultiplyfixed{1e6}{-1}
+\testfloatmultiplyfixed{1e6}{-0.1}
+
+\testfloatmultiplyfixed{1e-3}{0}
+
+\testfloatmultiplyfixed{inf}{0}
+\testfloatmultiplyfixed{inf}{5}
+\testfloatmultiplyfixed{nan}{5}
+\testfloatmultiplyfixed{0}{0}
+\testfloatmultiplyfixed{-inf}{40}
+\endgroup
+
+
+\testsection{testing pgfmathfloatlessthan}
+\def\testfloatlessthan#1#2{%
+ \pgfmathfloatparsenumber{#1}%
+ \let\first=\pgfmathresult
+ \pgfmathfloatparsenumber{#2}%
+ \let\second=\pgfmathresult
+ \message{checking #1 <= #2; \first <= \second}%
+ \pgfmathfloatlessthan\first\second
+ \ifpgfmathfloatcomparison
+ \def\result{<}%
+ \else
+ \def\result{\ge}%
+ \fi
+ \[ \text{pgfmathfloatlessthan: } \bigl( \showlowlevelfloatmacro\first \bigr)\; = #1 \result #2\; \bigl( = \showlowlevelfloatmacro\second \big). \]
+}%
+
+\testfloatlessthan{4}{5}
+\testfloatlessthan{0}{2}
+\testfloatlessthan{91751123}{241924}
+\testfloatlessthan{-1}{-1}
+\testfloatlessthan{-1231}{0}
+\testfloatlessthan{10}{-5}
+\testfloatlessthan{0}{0}
+\testfloatlessthan{-0}{-0}
+\testfloatlessthan{0}{14}
+\testfloatlessthan{114812}{-123124123}
+\testfloatlessthan{114812}{1241231451}
+\testfloatlessthan{-141285}{29}
+\testfloatlessthan{-141285}{0}
+\testfloatlessthan{-141285}{-50}
+\testfloatlessthan{-141285}{-12498149012}
+
+\testsection{float to fixed test}
+\def\testpgfmathfloattofixed#1{%
+ \pgfmathfloatparsenumber{#1}%
+%\tracingmacros=2\tracingcommands=2
+ \let\argument=\pgfmathresult
+ \message{converting #1 = \argument\ to fixed point}%
+ \pgfmathfloattofixed\argument
+ \let\result=\pgfmathresult
+ \message{-> \result}%
+%\tracingmacros=0\tracingcommands=0
+ \[ \bigl( \showlowlevelfloatmacro\argument \bigr)\; = #1 \mapsto \result \]
+}%
+\testpgfmathfloattofixed{0}
+\testpgfmathfloattofixed{5}
+\testpgfmathfloattofixed{5.520241}
+\testpgfmathfloattofixed{124.10241}
+\testpgfmathfloattofixed{-121.248}
+\testpgfmathfloattofixed{-12e-5}
+\testpgfmathfloattofixed{412e3}
+\testpgfmathfloattofixed{0.0001}
+\testpgfmathfloattofixed{0.0}
+\testpgfmathfloattofixed{-0.012125}
+\testpgfmathfloattofixed{1.2e-1}
+\testpgfmathfloattofixed{1.2e-2}
+\testpgfmathfloattofixed{1.2e4}
+\testpgfmathfloattofixed{1.2345e4}
+\testpgfmathfloattofixed{1.234567e4}
+\testpgfmathfloattofixed{1.51234e0}
+\testpgfmathfloattofixed{15}
+\testpgfmathfloattofixed{-20}
+
+\testsection{Testing pgfmathfloatmin and pgfmathfloatmax}
+\def\testfloatminmax#1#2{%
+ \pgfmathfloatparsenumber{#1}%
+ \let\first=\pgfmathresult
+ \pgfmathfloatparsenumber{#2}%
+ \let\second=\pgfmathresult
+%\tracingmacros=2\tracingcommands=2
+ \message{computing min/max #1 and #2}%
+ \pgfmathfloatmin\first\second
+ \let\result=\pgfmathresult
+ \pgfmathfloattofixed\result
+ \[ \min\{#1,#2\} = \min\{ \showlowlevelfloatmacro\first, \showlowlevelfloatmacro\second \} \; = \showlowlevelfloatmacro\result = \pgfmathresult \]
+ %
+ \pgfmathfloatmax\first\second
+ \let\result=\pgfmathresult
+ \pgfmathfloattofixed\result
+ \[ \max\{#1,#2\} = \max\{ \showlowlevelfloatmacro\first, \showlowlevelfloatmacro\second \} \; = \showlowlevelfloatmacro\result = \pgfmathresult \]
+}%
+\testfloatminmax{42}{56}
+\testfloatminmax{-4122}{1256}
+\testfloatminmax{1e12}{5.235412e24}
+\testfloatminmax{-12}{-145}
+
+\testsection{Testing pgfmathfloatshift}
+\def\pgfmathfloatshifttest#1#2{%
+ \pgfmathfloatparsenumber{#1}%
+ \let\argument=\pgfmathresult
+ \message{computing mathshift #1 by #2}%
+ \pgfmathfloatshift\argument{#2}%
+ \let\result=\pgfmathresult
+ \pgfmathfloattofixed\result
+ \[ #1 \cdot 10^{#2} = \showlowlevelfloatmacro\argument \cdot 10^{#2} = \showlowlevelfloatmacro\result = \pgfmathresult \]
+}%
+\pgfmathfloatshifttest{4}{1}
+\pgfmathfloatshifttest{4}{2}
+\pgfmathfloatshifttest{4}{-1}
+\pgfmathfloatshifttest{4}{-2}
+\pgfmathfloatshifttest{0}{-2}
+\pgfmathfloatshifttest{1.1415130}{-2}
+\pgfmathfloatshifttest{1.1415130}{5}
+
+\testsection{Testing pgfmathfloatmultiply}
+\begingroup
+\def\pgfmathfloatmultiplytest#1#2{%
+ \pgfmathfloatparsenumber{#1}%
+ \let\argumenta=\pgfmathresult
+ \pgfmathfloatparsenumber{#2}%
+ \let\argumentb=\pgfmathresult
+ \message{computing mathmultiply #1 by #2}%
+ \pgfmathfloatmultiply\argumenta\argumentb%
+ \let\result=\pgfmathresult
+ \pgfmathfloattofixed\result
+ \[ #1 \cdot #2 = \showlowlevelfloatmacro\result = \pgfmathresult \]
+}%
+\def\tests{%
+ \pgfmathfloatmultiplytest{4}{1}
+ \pgfmathfloatmultiplytest{4}{2}
+ \pgfmathfloatmultiplytest{4}{-1}
+ \pgfmathfloatmultiplytest{4}{-2}
+ \pgfmathfloatmultiplytest{0}{-2}
+ \pgfmathfloatmultiplytest{1.1415130}{-2}
+ \pgfmathfloatmultiplytest{1.1415130}{5}
+ \pgfmathfloatmultiplytest{10}{10}
+ \pgfmathfloatmultiplytest{100}{100}
+ \pgfmathfloatmultiplytest{9999999}{9999999}
+ gnuplot for $\cdot$: $99999980000001.0$
+ \pgfmathfloatmultiplytest{-10}{10}
+ \pgfmathfloatmultiplytest{-90}{3}
+ \pgfmathfloatmultiplytest{-90}{-3}
+ \pgfmathfloatmultiplytest{-inf}{nan}
+ \pgfmathfloatmultiplytest{-inf}{+inf}
+ \pgfmathfloatmultiplytest{1}{0}
+ \pgfmathfloatmultiplytest{1}{0}
+ \pgfmathfloatmultiplytest{1}{-0}
+ \pgfmathfloatmultiplytest{3.14159265358979}{2}
+}%
+\tests
+
+\testsection{Testing pgfmathfloatdivide}
+
+\def\pgfmathfloatmultiplytest#1#2{%
+ \pgfmathfloatparsenumber{#1}%
+ \let\argumenta=\pgfmathresult
+ \pgfmathfloatparsenumber{#2}%
+ \let\argumentb=\pgfmathresult
+ \message{computing mathdivide #1 by #2}%
+ \pgfmathfloatdivide\argumenta\argumentb%
+ \let\result=\pgfmathresult
+ \pgfmathfloattofixed\result
+ \[ #1 / #2 = \showlowlevelfloatmacro\result = \pgfmathresult \]
+}%
+\tests
+
+% #1/#2 expected #3
+\def\pgfmathfloattest#1#2#3{%
+ \pgfmathfloatparsenumber{#1}%
+ \let\argumenta=\pgfmathresult
+ \pgfmathfloatparsenumber{#2}%
+ \let\argumentb=\pgfmathresult
+ \pgfmathfloatparsenumber{#3}%
+ \let\reference=\pgfmathresult
+ \message{computing (#1/#2)}%
+ \pgfmathfloatdivide\argumenta\argumentb%
+ \let\resultfloat=\pgfmathresult
+ \pgfmathfloattosci\pgfmathresult
+ \let\result=\pgfmathresult
+ \pgfmathfloatrelerror\resultfloat\reference
+ \pgfmathfloattosci\pgfmathresult
+ \[ #1/#2 = \result\quad (\text{error/r to }#3 = \pgfmathprintnumber\pgfmathresult)\]
+}%
+\pgfmathfloattest{83407811.0}{166815640.0}{0.499999946048224}
+\endgroup
+
+
+{
+\testsection{Testing pgfmathfloatsqrt}
+% #1 : number
+% #2 : the reference, sqrt (#1)
+\def\pgfmathfloatsqrttest#1#2{%
+ \pgfmathfloatparsenumber{#1}%
+ \let\argumenta=\pgfmathresult
+ \pgfmathfloatparsenumber{#2}%
+ \let\reference=\pgfmathresult
+ \message{computing sqrt(#1)}%
+ \pgfmathfloatsqrt\argumenta%
+ \let\resultfloat=\pgfmathresult
+ \pgfmathfloattosci\pgfmathresult
+ \let\result=\pgfmathresult
+ \pgfmathfloatrelerror\resultfloat\reference
+ \pgfmathfloattosci\pgfmathresult
+ \[ \sqrt{#1} = \result\quad (\text{rel. error } \pgfmathresult)\]
+}%
+\def\tests{%
+ \pgfmathfloatsqrttest{0}{0}
+ \pgfmathfloatsqrttest{1}{1}
+ \pgfmathfloatsqrttest{2}{1.414213562373}
+ \pgfmathfloatsqrttest{4}{2}
+ \pgfmathfloatsqrttest{16}{4}
+ \pgfmathfloatsqrttest{10}{3.162277660168}
+ \pgfmathfloatsqrttest{1000000}{1000}
+ \pgfmathfloatsqrttest{123456789}{1.111111106055556e+04}
+}%
+\tests
+}
+
+{
+\testsection{Testing pgfmathfloatint}
+% #1 : number
+\def\pgfmathfloatinttest#1{%
+ \pgfmathfloatparsenumber{#1}%
+ \let\argumenta=\pgfmathresult
+ \message{computing int(#1)}%
+ \pgfmathfloatint\argumenta%
+ \pgfmathfloattosci\pgfmathresult
+ \let\result=\pgfmathresult
+ \[ int(#1) = \result \]
+ %
+ \pgfmathfloatparsenumber{-#1}%
+ \let\argumenta=\pgfmathresult
+ \message{computing int(-#1)}%
+ \pgfmathfloatint\argumenta%
+ \pgfmathfloattosci\pgfmathresult
+ \let\result=\pgfmathresult
+ \[ int(-#1) = \result \]
+}%
+\def\tests{%
+ \pgfmathfloatinttest{1.23}
+ \pgfmathfloatinttest{12.34}
+ \pgfmathfloatinttest{123.4}
+ \pgfmathfloatinttest{1234.}
+ \pgfmathfloatinttest{1234.1}
+ \pgfmathfloatinttest{1e-2}
+ \pgfmathfloatinttest{0}
+ \pgfmathfloatinttest{3.456789e4}
+ \pgfmathfloatinttest{3.456789e10}
+}%
+\tests
+}
+
+{
+\testsection{Testing pgfmathfloatexp}
+% #1 : number
+% #2 : the reference, sqrt (#1)
+\def\pgfmathfloattest#1#2{%
+ \pgfmathfloatparsenumber{#1}%
+ \let\argumenta=\pgfmathresult
+ \pgfmathfloatparsenumber{#2}%
+ \let\reference=\pgfmathresult
+ \message{computing (#1)}%
+ \pgfmathfloatexp\argumenta%
+ \let\resultfloat=\pgfmathresult
+ \pgfmathfloattosci\pgfmathresult
+ \let\result=\pgfmathresult
+ \pgfmathfloatrelerror\resultfloat\reference
+ \pgfmathfloattosci\pgfmathresult
+ \[ \exp(#1) = \result\quad (\text{error/r to }#2 = \pgfmathresult)\]
+}%
+%\tracingmacros=2\tracingcommands=2
+ \pgfmathfloattest{-700}{9.85967654375977e-305}
+ \pgfmathfloattest{-1.0000000e+02}{3.7200760e-44}
+ \pgfmathfloattest{-9.5918367e+01}{2.2038516e-42}
+ \pgfmathfloattest{-9.1836735e+01}{1.3056083e-40}
+ \pgfmathfloattest{-8.7755102e+01}{7.7346991e-39}
+ \pgfmathfloattest{-8.3673469e+01}{4.5821992e-37}
+ \pgfmathfloattest{-7.9591837e+01}{2.7145916e-35}
+ \pgfmathfloattest{-7.5510204e+01}{1.6081814e-33}
+ \pgfmathfloattest{-7.1428571e+01}{9.5272065e-32}
+ \pgfmathfloattest{-6.7346939e+01}{5.6441184e-30}
+ \pgfmathfloattest{-6.3265306e+01}{3.3436950e-28}
+ \pgfmathfloattest{-5.9183673e+01}{1.9808756e-26}
+ \pgfmathfloattest{-5.5102041e+01}{1.1735125e-24}
+ \pgfmathfloattest{-5.1020408e+01}{6.9521362e-23}
+ \pgfmathfloattest{-4.6938776e+01}{4.1185924e-21}
+ \pgfmathfloattest{-4.2857143e+01}{2.4399411e-19}
+ \pgfmathfloattest{-3.8775510e+01}{1.4454727e-17}
+ \pgfmathfloattest{-3.4693878e+01}{8.5632855e-16}
+ \pgfmathfloattest{-3.0612245e+01}{5.0730713e-14}
+ \pgfmathfloattest{-2.6530612e+01}{3.0053946e-12}
+ \pgfmathfloattest{-2.2448980e+01}{1.7804593e-10}
+ \pgfmathfloattest{-1.8367347e+01}{1.0547817e-08}
+ \pgfmathfloattest{-1.4285714e+01}{6.2487495e-07}
+ \pgfmathfloattest{-1.0204082e+01}{3.7018912e-05}
+ \pgfmathfloattest{-6.1224490e+00}{2.1930786e-03}
+ \pgfmathfloattest{-2.0408163e+00}{1.2992261e-01}
+ \pgfmathfloattest{2.0408163e+00}{7.6968898e+00}
+ \pgfmathfloattest{6.1224490e+00}{4.5598001e+02}
+ \pgfmathfloattest{1.0204082e+01}{2.7013219e+04}
+ \pgfmathfloattest{1.4285714e+01}{1.6003202e+06}
+ \pgfmathfloattest{1.8367347e+01}{9.4806349e+07}
+ \pgfmathfloattest{2.2448980e+01}{5.6165284e+09}
+ \pgfmathfloattest{2.6530612e+01}{3.3273501e+11}
+ \pgfmathfloattest{3.0612245e+01}{1.9711925e+13}
+ \pgfmathfloattest{3.4693878e+01}{1.1677761e+15}
+ \pgfmathfloattest{3.8775510e+01}{6.9181522e+16}
+ \pgfmathfloattest{4.2857143e+01}{4.0984595e+18}
+ \pgfmathfloattest{4.6938776e+01}{2.4280140e+20}
+ \pgfmathfloattest{5.1020408e+01}{1.4384068e+22}
+ \pgfmathfloattest{5.5102041e+01}{8.5214258e+23}
+ \pgfmathfloattest{5.9183673e+01}{5.0482727e+25}
+ \pgfmathfloattest{6.3265306e+01}{2.9907034e+27}
+ \pgfmathfloattest{6.7346939e+01}{1.7717559e+29}
+ \pgfmathfloattest{7.1428571e+01}{1.0496256e+31}
+ \pgfmathfloattest{7.5510204e+01}{6.2182039e+32}
+ \pgfmathfloattest{7.9591837e+01}{3.6837954e+34}
+ \pgfmathfloattest{8.3673469e+01}{2.1823582e+36}
+ \pgfmathfloattest{8.7755102e+01}{1.2928751e+38}
+ \pgfmathfloattest{9.1836735e+01}{7.6592653e+39}
+ \pgfmathfloattest{9.5918367e+01}{4.5375106e+41}
+ \pgfmathfloattest{1.0000000e+02}{2.6881171e+43}
+ \pgfmathfloattest{700}{1.014232054735e+304}
+}
+
+{
+\testsection{Testing pgfmathfloatmod}
+% #1 : operand 1
+% #2 : operand 2
+% #3 : the reference, #1 mod #2
+\def\pgfmathfloattest#1#2#3{%
+ \pgfmathfloatparsenumber{#1}%
+ \let\argumenta=\pgfmathresult
+ \pgfmathfloatparsenumber{#2}%
+ \let\argumentb=\pgfmathresult
+ \pgfmathfloatparsenumber{#3}%
+ \let\reference=\pgfmathresult
+ \message{computing #1 mod #2}%
+ \pgfmathfloatmod\argumenta\argumentb%
+ \let\resultfloat=\pgfmathresult
+ \pgfmathfloattosci\pgfmathresult
+ \let\result=\pgfmathresult
+ \pgfmathfloatrelerror\resultfloat\reference
+ \pgfmathfloattosci\pgfmathresult
+ \[ #1\text{ mod }#2 = \result\quad (\text{error/r to }#3 = \pgfmathresult)\]
+}%
+%\tracingmacros=2\tracingcommands=2
+ \pgfmathfloattest{4}{3}{1}
+ \pgfmathfloattest{10}{10}{0}
+ \pgfmathfloattest{20}{6}{2}
+ \pgfmathfloattest{-100}{30}{-10}
+ \pgfmathfloattest{10.5}{5}{0.5}
+ \pgfmathfloattest{300.63}{360}{300.63}
+ \pgfmathfloattest{-20}{30}{-20}
+}
+
+{
+\testsection{Testing Trigonometric functions}
+% #1 : operator
+% #2 : operand
+% #3 : the reference, #2(#1)
+\def\pgfmathfloattest#1#2#3{%
+ \pgfmathfloatparsenumber{#2}%
+ \let\argumenta=\pgfmathresult
+ \pgfmathfloatparsenumber{#3}%
+ \let\reference=\pgfmathresult
+ \message{computing \string#1(#2)}%
+ #1\argumenta%
+ \let\resultfloat=\pgfmathresult
+ \pgfmathfloattosci\pgfmathresult
+ \let\result=\pgfmathresult
+ \pgfmathfloatrelerror\resultfloat\reference
+ \pgfmathfloattosci\pgfmathresult
+ \[ \string#1(#2) = \result\quad (\text{error/r to }#3 = \pgfmathresult)\]
+}%
+%\tracingmacros=2\tracingcommands=2
+\testsubsection{SIN}
+ \pgfmathfloattest\pgfmathfloatsin{-7.2000000e+02}{4.8985872e-16}
+ \pgfmathfloattest\pgfmathfloatsin{-6.5454545e+02}{9.0963200e-01}
+ \pgfmathfloattest\pgfmathfloatsin{-5.8909091e+02}{7.5574957e-01}
+ \pgfmathfloattest\pgfmathfloatsin{-5.2363636e+02}{-2.8173256e-01}
+ \pgfmathfloattest\pgfmathfloatsin{-4.5818182e+02}{-9.8982144e-01}
+ \pgfmathfloattest\pgfmathfloatsin{-3.9272727e+02}{-5.4064082e-01}
+ \pgfmathfloattest\pgfmathfloatsin{-3.2727273e+02}{5.4064082e-01}
+ \pgfmathfloattest\pgfmathfloatsin{-2.6181818e+02}{9.8982144e-01}
+ \pgfmathfloattest\pgfmathfloatsin{-1.9636364e+02}{2.8173256e-01}
+ \pgfmathfloattest\pgfmathfloatsin{-1.3090909e+02}{-7.5574957e-01}
+ \pgfmathfloattest\pgfmathfloatsin{-6.5454545e+01}{-9.0963200e-01}
+ \pgfmathfloattest\pgfmathfloatsin{0.0000000e+00}{0.0000000e+00}
+ \pgfmathfloattest\pgfmathfloatsin{6.5454545e+01}{9.0963200e-01}
+ \pgfmathfloattest\pgfmathfloatsin{1.3090909e+02}{7.5574957e-01}
+ \pgfmathfloattest\pgfmathfloatsin{1.9636364e+02}{-2.8173256e-01}
+ \pgfmathfloattest\pgfmathfloatsin{2.6181818e+02}{-9.8982144e-01}
+ \pgfmathfloattest\pgfmathfloatsin{3.2727273e+02}{-5.4064082e-01}
+ \pgfmathfloattest\pgfmathfloatsin{3.9272727e+02}{5.4064082e-01}
+ \pgfmathfloattest\pgfmathfloatsin{4.5818182e+02}{9.8982144e-01}
+ \pgfmathfloattest\pgfmathfloatsin{5.2363636e+02}{2.8173256e-01}
+ \pgfmathfloattest\pgfmathfloatsin{5.8909091e+02}{-7.5574957e-01}
+ \pgfmathfloattest\pgfmathfloatsin{6.5454545e+02}{-9.0963200e-01}
+ \pgfmathfloattest\pgfmathfloatsin{7.2000000e+02}{-4.8985872e-16}
+
+
+
+\testsubsection{COS}
+ \pgfmathfloattest\pgfmathfloatcos{-7.2000000e+02}{1.0000000e+00}
+ \pgfmathfloattest\pgfmathfloatcos{-6.5454545e+02}{4.1541501e-01}
+ \pgfmathfloattest\pgfmathfloatcos{-5.8909091e+02}{-6.5486073e-01}
+ \pgfmathfloattest\pgfmathfloatcos{-5.2363636e+02}{-9.5949297e-01}
+ \pgfmathfloattest\pgfmathfloatcos{-4.5818182e+02}{-1.4231484e-01}
+ \pgfmathfloattest\pgfmathfloatcos{-3.9272727e+02}{8.4125353e-01}
+ \pgfmathfloattest\pgfmathfloatcos{-3.2727273e+02}{8.4125353e-01}
+ \pgfmathfloattest\pgfmathfloatcos{-2.6181818e+02}{-1.4231484e-01}
+ \pgfmathfloattest\pgfmathfloatcos{-1.9636364e+02}{-9.5949297e-01}
+ \pgfmathfloattest\pgfmathfloatcos{-1.3090909e+02}{-6.5486073e-01}
+ \pgfmathfloattest\pgfmathfloatcos{-6.5454545e+01}{4.1541501e-01}
+ \pgfmathfloattest\pgfmathfloatcos{0.0000000e+00}{1.0000000e+00}
+ \pgfmathfloattest\pgfmathfloatcos{6.5454545e+01}{4.1541501e-01}
+ \pgfmathfloattest\pgfmathfloatcos{1.3090909e+02}{-6.5486073e-01}
+ \pgfmathfloattest\pgfmathfloatcos{1.9636364e+02}{-9.5949297e-01}
+ \pgfmathfloattest\pgfmathfloatcos{2.6181818e+02}{-1.4231484e-01}
+ \pgfmathfloattest\pgfmathfloatcos{3.2727273e+02}{8.4125353e-01}
+ \pgfmathfloattest\pgfmathfloatcos{3.9272727e+02}{8.4125353e-01}
+ \pgfmathfloattest\pgfmathfloatcos{4.5818182e+02}{-1.4231484e-01}
+ \pgfmathfloattest\pgfmathfloatcos{5.2363636e+02}{-9.5949297e-01}
+ \pgfmathfloattest\pgfmathfloatcos{5.8909091e+02}{-6.5486073e-01}
+ \pgfmathfloattest\pgfmathfloatcos{6.5454545e+02}{4.1541501e-01}
+ \pgfmathfloattest\pgfmathfloatcos{7.2000000e+02}{1.0000000e+00}
+
+
+\testsubsection{TAN}
+ \pgfmathfloattest\pgfmathfloattan{-7.2000000e+02}{4.8985872e-16}
+ \pgfmathfloattest\pgfmathfloattan{-6.5454545e+02}{2.1896946e+00}
+ \pgfmathfloattest\pgfmathfloattan{-5.8909091e+02}{-1.1540615e+00}
+ \pgfmathfloattest\pgfmathfloattan{-5.2363636e+02}{2.9362649e-01}
+ \pgfmathfloattest\pgfmathfloattan{-4.5818182e+02}{6.9551528e+00}
+ \pgfmathfloattest\pgfmathfloattan{-3.9272727e+02}{-6.4266098e-01}
+ \pgfmathfloattest\pgfmathfloattan{-3.2727273e+02}{6.4266098e-01}
+ \pgfmathfloattest\pgfmathfloattan{-2.6181818e+02}{-6.9551528e+00}
+ \pgfmathfloattest\pgfmathfloattan{-1.9636364e+02}{-2.9362649e-01}
+ \pgfmathfloattest\pgfmathfloattan{-1.3090909e+02}{1.1540615e+00}
+ \pgfmathfloattest\pgfmathfloattan{-6.5454545e+01}{-2.1896946e+00}
+ \pgfmathfloattest\pgfmathfloattan{0.0000000e+00}{0.0000000e+00}
+ \pgfmathfloattest\pgfmathfloattan{6.5454545e+01}{2.1896946e+00}
+ \pgfmathfloattest\pgfmathfloattan{1.3090909e+02}{-1.1540615e+00}
+ \pgfmathfloattest\pgfmathfloattan{1.9636364e+02}{2.9362649e-01}
+ \pgfmathfloattest\pgfmathfloattan{2.6181818e+02}{6.9551528e+00}
+ \pgfmathfloattest\pgfmathfloattan{3.2727273e+02}{-6.4266098e-01}
+ \pgfmathfloattest\pgfmathfloattan{3.9272727e+02}{6.4266098e-01}
+ \pgfmathfloattest\pgfmathfloattan{4.5818182e+02}{-6.9551528e+00}
+ \pgfmathfloattest\pgfmathfloattan{5.2363636e+02}{-2.9362649e-01}
+ \pgfmathfloattest\pgfmathfloattan{5.8909091e+02}{1.1540615e+00}
+ \pgfmathfloattest\pgfmathfloattan{6.5454545e+02}{-2.1896946e+00}
+ \pgfmathfloattest\pgfmathfloattan{7.2000000e+02}{-4.8985872e-16}
+
+
+
+}
+
+{
+ % #1 : expression
+ % #2 : the reference
+ \def\assertEquals#1#2{%
+ \pgfmathfloatparsenumber{#2}%
+ \let\reference=\pgfmathresult
+ \message{parsing expression #1...}%
+ \pgfmathparse{#1}%
+ \pgfmathfloatparsenumber{\pgfmathresult}%
+ \let\argumenta=\pgfmathresult
+ \let\resultfloat=\pgfmathresult
+ \pgfmathfloattosci\pgfmathresult
+ \let\result=\pgfmathresult
+ \pgfmathfloatrelerror\resultfloat\reference
+ \let\actualerror=\pgfmathresult
+ \pgfmathfloatgreaterthan{\pgfmathresult}{\THRESH}%
+ \ifpgfmathfloatcomparison
+ \begingroup
+ \pgfkeys{/pgf/fpu=false}%
+ \pgfmathparse{#1}%
+ \global\let\actualBasic=\pgfmathresult
+ \endgroup
+ \PackageError{pgf-fpu}{Got error: expected #1=#2, but was \result\space (error \actualerror; basic level returns \actualBasic)}{}%
+ \fi
+ \pgfmathfloattosci\actualerror
+ \[ #1 = \result \quad[= \resultfloat] \quad (\text{error/r to }#2 = \pgfmathresult)\]
+ }%
+ \def\mathparserTestCases{%
+ \assertEquals{1+1}{2}
+ \assertEquals{1234567*4}{4938268}
+ \assertEquals{exp(200)}{7.22597376812575e+86}
+ \assertEquals{rad(360)}{6.28318530717959}
+ \assertEquals{rad(180)}{3.14159265358979}
+ \assertEquals{deg(2*pi)}{360}
+ \assertEquals{deg(pi)}{180}
+ \assertEquals{ln(1)}{0}
+ \assertEquals{round(1.5)}{2}
+ \assertEquals{round(-1.5)}{-2}
+ \assertEquals{- (1.5)}{-1.5}
+ \assertEquals{(1e4 - 1e3) * 1e5}{900000000.0}
+ \assertEquals{4^2}{16}
+ \assertEquals{4^3}{64}
+ \assertEquals{4^-3}{0.015625}
+ \assertEquals{4^-6}{0.000244140625}
+ \assertEquals{111^4}{151807041}
+ \assertEquals{8^10}{1073741824}
+ \assertEquals{3^1.5}{5.19615242270663}
+ \assertEquals{16^5.5}{4194304}
+ \assertEquals{15^-0.25}{0.508132748154615}
+ \assertEquals{sec(45)}{1.4142136e+00}
+ \assertEquals{cot(30)}{1.7320508e+00}
+ \assertEquals{asin(7.0710678e-01)}{45}
+ \assertEquals{acos(8.6602540e-01)}{30}
+ \assertEquals{atan(5.7735027e-01)}{30}
+ \assertEquals{atan(16000)}{89.9964}
+ \assertEquals{atan(1e6)}{8.9999943e+01}
+ \assertEquals{atan(-1e6)}{-8.9999943e+01}
+ \assertEquals{-12^2}{-144}%
+ \assertEquals{0-12^2}{-144}%
+ \assertEquals{-(12)^2}{-144}%
+ \assertEquals{exp(-12^2)}{2.8946e-63}%
+ \assertEquals{round(98.8)}{99}%
+ \assertEquals{-pi}{-3.14159265358979}%
+ \assertEquals{2*(-pi)}{-6.28318530717959}%
+ \assertEquals{2*(-3)}{-6}%
+ \assertEquals{veclen(1,1)}{1.414213562373095}%
+ \assertEquals{veclen(1e5,6e5)}{6.082762530298220e+05}%
+ \assertEquals{cosh(5)}{74.20994852478784}%
+ \assertEquals{sinh(0.6)}{0.636653582148241}%
+ \assertEquals{tanh(0.6)}{0.537049566998035}%
+
+ {\pgfkeys{/pgf/trig format=rad}
+ \assertEquals{atan2(4,5)}{0.674740942223553}%
+ \assertEquals{atan2(-4,5)}{-0.674740942223553}%
+ \assertEquals{atan2(4,-5)}{2.46685171136624}%
+ \assertEquals{atan2(-4,-5)}{-2.46685171136624}%
+ %
+ \assertEquals{atan2(5,4)}{0.89605538457134}%
+ \assertEquals{atan2(-5,4)}{-0.89605538457134}%
+ \assertEquals{atan2(5,-4)}{2.24553726901845}%
+ \assertEquals{atan2(-5,-4)}{-2.24553726901845}%
+ %
+ \assertEquals{atan2(4e-5,5)}{0}%
+ \assertEquals{atan2(4e-5,-5)}{3.1415126535899}%
+ }
+ % \assertEquals{ceil(1.5)}{2}
+ }
+
+
+ {
+ \testsection{Testing the FPU library (and math parser)}
+ \pgfkeys{/pgf/fpu}
+ %\tracingmacros=2\tracingcommands=2
+ \mathparserTestCases
+ }
+
+ {
+ \def\mathparserTestCases{%
+ \assertEquals{sin(90)}{1.0}%
+ \assertEquals{cos(90)}{0.0}%
+ \assertEquals{tan(45)}{1.0}%
+ \assertEquals{sec(45)}{1.41429}%
+ \assertEquals{cosec(30)}{2.0}%
+ \assertEquals{cot(15)}{3.73215}%
+ \assertEquals{asin(0.7071)}{44.99945}%
+ \assertEquals{acos(0.5)}{60}%
+ \assertEquals{atan(1)}{45}%
+ \assertEquals{atan(16001)}{90}%
+ \assertEquals{atan(-16001)}{-90}%
+ %\assertEquals{atan2(-4,3)}{-53.13011}%
+ }%
+ \testsection{Testing trig format=deg, basic layer (selected examples)}
+ %\tracingmacros=2\tracingcommands=2
+ \mathparserTestCases
+
+ \testsection{Testing trig format=deg, FPU (selected examples)}
+ \pgfkeys{/pgf/fpu}
+ \mathparserTestCases
+ }
+
+ {
+ \pgfkeys{/pgf/trig format=rad}
+ \def\mathparserTestCases{%
+ \assertEquals{sin(pi/2)}{1.0}%
+ \assertEquals{cos(pi/2)}{0.0}%
+ \assertEquals{tan(pi/4)}{1.0}%
+ \assertEquals{sec(pi/4)}{1.41429}%
+ \assertEquals{cosec(rad(30))}{2.0}%
+ \assertEquals{cot(rad(15))}{3.73215}%
+ \assertEquals{asin(0.7071)}{0.785388564086562}% 44.99945}%
+ \assertEquals{acos(0.5)}{1.0471975511966}%
+ \assertEquals{atan(1)}{0.785398163397448}%45}%
+ \assertEquals{atan(16001)}{1.570796326794}%
+ \assertEquals{atan(-16001)}{-1.570796326794}%
+ %\assertEquals{atan2(-4,3)}{-53.13011}%
+ }%
+ \testsection{Testing trig format=rad, basic layer (selected examples)}
+ %\tracingmacros=2\tracingcommands=2
+ \mathparserTestCases
+
+ \testsection{Testing trig format=rad, FPU (selected examples)}
+ \pgfkeys{/pgf/fpu}
+ \mathparserTestCases
+ }
+}
+\end{document}
generated by cgit v1.2.3 (git 2.39.1) at 2024-11-15 18:24:12 +0000