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-\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{pgfmathlog}
-
-\parindent=0pt
-
-
-\author{Christian Feuers\"anger}
-\title{Test cases for pgfmathlog.sty}
-
-\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}}
-
-\begin{document}
-\maketitle
-
-\def\vgl#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\normalize#1{%
- \begingroup
- \message{NORMALISING #1...}%
- \sciparse#1\to\M\powten\E
- \sciparsenumber{#1}\S\MM\EE
- \[ #1 \mapsto \M \cdot 10^{\E}\quad \bigl( = \MM\cdot 10^{\EE}\quad [S=\S]\, \bigr) \]
- \endgroup
-}
-
-\def\pretty#1{%
- \message{Pretty-printing #1...}%
- \[ #1 \mapsto \prettyprintnumber{#1} \]
-}
-
-
-
-%--------------------------------------------------
-% \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{logarithms, compared with PGF arithmetics}
-
-\vgl{0.1}{-2.30259}
-\vgl{0.12}{-2.12026}
-\vgl{0.2}{-1.60944}
-\vgl{0.3}{-1.20397}
-\vgl{0.4}{-0.916291}
-\vgl{0.5}{-0.693147}
-\vgl{0.6}{-0.510826}
-\vgl{0.7}{-0.356675}
-\vgl{0.75}{-0.287682}
-\vgl{0.8}{-0.223144}
-\vgl{0.823}{-0.194799}
-\vgl{0.9}{-0.105361}
-\vgl{0.96}{-0.040822}
-\vgl{1.2}{0.182322}
-\vgl{1.5}{0.405465}
-\vgl{1.6}{0.470004}
-\vgl{9.0}{2.1972245773}
-\vgl{9.2}{2.2192034}
-\vgl{9.3}{2.23001440}
-\vgl{9.7}{2.27212588}
-\vgl{10.0}{2.302585092}
-\vgl{100.0}{4.605170185}
-\vgl{1351.0}{7.208600337}
-\vgl{9752.0}{9.185227671}
-\vgl{9600.0}{9.169518377}
-
-\vskip1cm
-\vgl{0.000142}{-8.8596835}
-\vgl{0.0054124}{-5.219062661}
-\vgl{0.000912697124}{-6.9991064}
-
-\vskip1cm
-\vgl{8.31160034e-02}{-2.48751801563782}%
-\vgl{2.54685628e-02}{-3.67031041875206}%
-\vgl{7.40715288e-03}{-4.90530914022879}%
-\vgl{2.10192154e-03}{-6.16490333357987}%
-\vgl{5.87352989e-04}{-7.43988457474844}%
-\vgl{1.62269942e-04}{-8.72624930084187}%
-\vgl{4.44248889e-05}{-10.0217106847708}%
-\vgl{1.20714122e-05}{-11.3246705288704}%
-\vgl{3.26101452e-06}{-12.6334722085451}%
-
-\vskip1cm
-\vgl{5}{1.6094379124341}%
-\vgl{17}{2.83321334405622}%
-\vgl{39}{3.66356164612965}%
-\vgl{49}{3.89182029811063}%
-\vgl{129}{4.85981240436167}%
-\vgl{321}{5.77144112313002}%
-\vgl{769}{6.64509096950564}%
-\vgl{1793}{7.49164547360513}%
-\vgl{4097}{8.31801027754687}%
-\vgl{9217}{9.12880488399366}%
-
-
-\testsection{Conversion to normalised floating point numbers basis 10}
-\normalize{123.41251}%
-\normalize{1023.52}
-\normalize{123412.51}%
-\normalize{12341251.0}%
-\tracingmacros=2\tracingcommands=2
-\normalize{-12341251.0}%
-\tracingmacros=0\tracingcommands=0
-\normalize{1.2341251}%
-\normalize{8.02410024}
-\normalize{8.024100}
-\normalize{0001234.3100}
-\normalize{0001234.00001}
-\normalize{0001000.00001}
-\normalize{0001000.00001000}
-\normalize{0.12341251}%
-\normalize{0.0012341251}%
-\normalize{0.00000012341251}%
-\normalize{-0.00000012341251}%
-\normalize{10}
-\normalize{100}
-\normalize{99999}
-\normalize{999.000}
-
-\normalize{8.31160034e-02}%
-\normalize{2.54685628e-02}%
-\normalize{7.40715288e-03}%
-\normalize{2.10192154e-03}%
-\normalize{5.87352989e-04}%
-\normalize{-1.62269942e-04}%
-\normalize{4.44248889e-05}%
-\normalize{1.20714122e-05}%
-\normalize{3.26101452e-06}%
-\normalize{3261.01452e-06}%
-\normalize{0.000326101452e-06}%
-
-\message{SPECIAL CASE 0}%
-\normalize{0}
-\normalize{-0}
-\normalize{-0.000}
-\normalize{+0.000}
-\normalize{+0}
-\normalize{-1}
-\normalize{1.0e1}
-\tracingmacros=2\tracingcommands=2
-\normalize{1e1}
-\tracingmacros=0\tracingcommands=0
-\normalize{1141}
-\normalize{-53e-5}
-
-\testsection{Test for prettyprinter}
-\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{-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{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}
-}
-
-\testsubsection{STD format}
-\pgfkeys{/numbers/std}
-\prettytest
-
-{
-\testsubsection{FIXED format}
-\testsubsubsection{with period}
-\pgfkeys{/numbers/fixed,/numbers/use period}
-\prettytest
-
-\testsubsubsection{with comma}
-\pgfkeys{/numbers/fixed,/numbers/use comma}
-\prettytest
-}
-
-{
-\testsubsection{FIXED ZEROFILL format}
-\testsubsubsection{with period}
-\pgfkeys{/numbers/fixed zerofill,/numbers/use period}
-\prettytest
-
-\testsubsubsection{with comma}
-\pgfkeys{/numbers/fixed zerofill,/numbers/use comma}
-\prettytest
-}
-
-{
-\testsubsection{sci format}
-\testsubsubsection{with period}
-\pgfkeys{/numbers/sci,/numbers/use period}
-\prettytest
-
-\testsubsubsection{with comma}
-\pgfkeys{/numbers/sci,/numbers/use comma}
-\prettytest
-
-%\testsubsection{may skip mantisse}
-%\pgfkeys{/numbers/sci may skip mantisse=true}
-%\prettytest
-
-}{
-\testsubsection{sci format zerofill}
-\testsubsubsection{with period}
-\pgfkeys{/numbers/sci zerofill,/numbers/use period}
-\prettytest
-
-\testsubsubsection{with comma}
-\pgfkeys{/numbers/sci zerofill,/numbers/use comma}
-\prettytest
-
-\testsubsubsection{e-style}
-\pgfkeys{/numbers/sci e}
-\prettytest
-
-\testsubsubsection{subscript-style}
-\pgfkeys{/numbers/sci subscript}
-\prettytest
-
-\testsubsubsection{subscript-style + period + no zero fill}
-\pgfkeys{/numbers/sci subscript,/numbers/use period,/numbers/sci}
-\prettytest
-
-\testsubsubsection{subscript-style precision 4}
-\pgfkeys{/numbers/sci subscript,/numbers/precision=4}
-\prettytest
-}
-
-\testsubsection{int trunc format}
-\pgfkeys{/numbers/int trunc}
-\prettytest
-
-\testsubsection{int detect format}
-\pgfkeys{/numbers/int detect}
-\prettytest
-}
-\onecolumn
-
-\testsection{testing scimathlessthan}
-\def\testsci#1#2{%
- \sciparsenumber{#1}\S\M\E
- \sciparsenumber{#2}\SS\MM\EE
- \message{checking #1 <= #2; [\S] \M * 10^\E <= [\SS] \MM * 10^\EE}%
- \scimathlessthan\S\M\E\and\SS\MM\EE
- \ifscimathlessthan
- \def\result{<}%
- \else
- \def\result{\ge}%
- \fi
- \[ \text{scimathlessthan: } \bigl( [\S]\, \M \cdot 10^{\E} \bigr)\; = #1 \result #2\; \bigl( = [\SS]\, \MM \cdot 10^{\EE} \big). \]
-}%
-
-\testsci{4}{5}
-\testsci{0}{2}
-\testsci{91751123}{241924}
-\testsci{-1}{-1}
-\testsci{-1231}{0}
-\testsci{10}{-5}
-\testsci{0}{0}
-\testsci{-0}{-0}
-\testsci{0}{14}
-\testsci{114812}{-123124123}
-\testsci{114812}{1241231451}
-\testsci{-141285}{29}
-\testsci{-141285}{0}
-\testsci{-141285}{-50}
-\testsci{-141285}{-12498149012}
-
-\testsection{Sci to fixed test}
-\def\testscitofixed#1{%
- \sciparsenumber{#1}\S\M\E
-%\tracingmacros=2\tracingcommands=2
- \message{converting #1 = [\S] \M * 10^\E\ to fixed point}%
- \scitofixed\S\M\E\result
- \message{-> \result}%
-%\tracingmacros=0\tracingcommands=0
- \[ \bigl( [\S]\, \M \cdot 10^{\E} \bigr)\; = #1 \mapsto \result \]
-}%
-\testscitofixed{0}
-\testscitofixed{5}
-\testscitofixed{5.520241}
-\testscitofixed{124.10241}
-\testscitofixed{-121.248}
-\testscitofixed{-12e-5}
-\testscitofixed{412e3}
-\testscitofixed{0.0001}
-\testscitofixed{0.0}
-\testscitofixed{-0.012125}
-\testscitofixed{1.2e-1}
-\testscitofixed{1.2e-2}
-\testscitofixed{1.2e4}
-\testscitofixed{1.2345e4}
-\testscitofixed{1.234567e4}
-\testscitofixed{1.51234e0}
-\testscitofixed{15}
-\testscitofixed{-20}
-
-\testsection{Testing scimathmax and scimathmin}
-\def\testscimathminmax#1#2{%
- \sciparsenumber{#1}\S\M\E
- \sciparsenumber{#2}\SS\MM\EE
-%\tracingmacros=2\tracingcommands=2
- \message{computing min/max #1 and #2}%
- \scimathmin\S\M\E\and\SS\MM\EE\to\SSS\MMM\EEE
- \scitofixed\SSS\MMM\EEE\result
- \[ \min\{#1,#2\} = \min\{ [\S]\, \M \cdot 10^{\E}, [\SS]\, \MM\cdot 10^{\EE}\} \; = [\SSS]\; \MMM\cdot10^{\EEE} = \result \]
- %
- \scimathmax\S\M\E\and\SS\MM\EE\to\SSS\MMM\EEE
- \scitofixed\SSS\MMM\EEE\result
- \[ \max\{#1,#2\} = \max\{ [\S]\, \M \cdot 10^{\E}, [\SS]\, \MM\cdot 10^{\EE}\} \; = [\SSS]\; \MMM\cdot10^{\EEE} = \result \]
-}%
-\testscimathminmax{42}{56}
-\testscimathminmax{-4122}{1256}
-\testscimathminmax{1e12}{5.235412e24}
-\testscimathminmax{-12}{-145}
-
-\testsection{Testing scimathshift}
-\def\testscimathshift#1#2{%
- \sciparsenumber{#1}\S\M\E
- \message{computing mathshift #1 by #2}%
- \let\SS=\S\let\MM=\M\let\EE=\E
- \scimathshift\S\M\E{#2}%
- \scitofixed\S\M\E\result
- \[ #1 \cdot 10^{#2} = [\SS]\, \MM \cdot 10^{\EE} \cdot 10^{#2} = [\S]\, \M \cdot 10^{\E} = \result \]
-}%
-\testscimathshift{4}{1}
-\testscimathshift{4}{2}
-\testscimathshift{4}{-1}
-\testscimathshift{4}{-2}
-\testscimathshift{0}{-2}
-\testscimathshift{1.1415130}{-2}
-\testscimathshift{1.1415130}{5}
-
-\testsection{Testing name floating point data structure}
-\let\SS=\empty
-\let\MM=\empty
-\let\EE=\empty
-\def\testsciDS#1#2{%
- \sciparsenumber{#1}\S\M\E
- \message{assigning #1=(\S,\M,\E) to single-name-macro ... }%
- \scisetcomponents{#2}\S\M\E
- \scigetcomponents{#2}\SS\MM\EE
- \message{result: (\SS,\MM,\EE)}%
- \edef\expandedtest{{\noexpand #2}{\S}{\M}{\E}}%
- \message{now with raw-numbers to single-name-macro ... }%
- \expandafter\scisetcomponents\expandedtest
- \scigetcomponents{#2}\SSS\MMM\EEE
- \message{result: (\SSS,\MMM,\EEE)}%
- \scitofixed\SS\MM\EE\result
- \scitofixed\SSS\MMM\EEE\resultX
- \[ #1 = [\S]\, \M \cdot 10^{\E}\text{ re-extracted }\to[\SS]\, \MM \cdot 10^{\EE} = \result\; [ \text{again: }\resultX ] \]
-}%
-\testsciDS{141.241}\test
-\testsciDS{141.241}{test}
-\testsciDS{141.241}{341}
-\def\test{eins zwei drei}
-\testsciDS{141.241}\test
-
-
-\scitofixed{1}{1.0}{2}\result\result
-
-\testsection{Testing fixedpointround}
-\def\testfpround#1#2{%
-\tracingmacros=2\tracingcommands=2
- \message{computing fixedpointround(#1):}%
- \def\sciroundprecision{#2}%
- \fixedpointround{#1}\result
- \fixedpointroundzerofill{#1}\resultz
- \message{fixedpointround(#1) -> \result; (\resultz)}%
- \[ \text{rnd }#1 \text{ to }#2 \to \result\; (\resultz) \]
-\tracingmacros=0\tracingcommands=0
-}%
-\[ \text{rnd }x \text{ to PREC} \to \text{no trailing zeros }\; (\text{trailing zeros}) \]
-\testfpround{1.0000}{2}
-\testfpround{-1.0000}{2}
-\testfpround{+1.0000}{2}
-\testfpround{1.003}{2}
-\testfpround{-1.003}{2}
-\testfpround{1.123}{2}
-\testfpround{1.12300012}{5}
-\testfpround{-9.995}{2}
-\testfpround{-0.995}{2}
-\testfpround{-9.95}{1}
-\testfpround{-0.95}{1}
-\testfpround{9}{2}
-\testfpround{1341}{2}
-\testfpround{0.996}{2}
-\testfpround{19999.9996}{2}
-\testfpround{-19999.9996}{2}
-\testfpround{+19999.9996}{2}
-\testfpround{9999.9996}{2}
-\testfpround{0.0004982}{3}
-\testfpround{0.0004982}{4}
-\testfpround{0.0004982}{5}
-\testfpround{0.0004982}{6}
-\testfpround{0.0004982}{7}
-\testfpround{0.0004982}{8}
-\testfpround{0.0004982}{9}
-
-\testsection{Testing sciround}
-\def\testsciround#1#2{%
-\tracingmacros=2\tracingcommands=2
- \message{computing sciround(#1):}%
- \sciparsenumber{#1}\S\M\E
- \def\sciroundprecision{#2}%
- \sciround\S\M\E\to\rS\rM\rE
- % DOESN'T WORK BECAUSE PERIOD IS MISSING:
-% \scitofixed\rS\rM\rE\result
- \sciroundzerofill\S\M\E\to\rrS\rrM\rrE
- \scitofixed\rrS\rrM\rrE\resultz
- \message{#1: round([\S] \M \cdot 10^{\E}) to #2 -> [\rS] \rM * 10^{\rM}; ([\rrS] \rrM * 10^{\rrE})}%
- \[ #1:
- \text{rnd}([\S] \M \cdot 10^{\E})
- \text{ to } #2
- \to
- [\rS] \rM \cdot 10^{\rE} %= \result
- \quad
- ([\rrS] \rrM \cdot 10^{\rrE} = \resultz)
- \]
-\tracingmacros=0\tracingcommands=0
-}%
-\[ \text{rnd }x \text{ to PREC} \to \text{no trailing zeros }\; (\text{trailing zeros}) \]
-\testsciround{1.0000}{2}
-\testsciround{-1.0000}{2}
-\testsciround{+1.0000}{2}
-\testsciround{1.003}{2}
-\testsciround{-1.003}{2}
-\testsciround{1.123}{2}
-\testsciround{1.12300012}{5}
-\testsciround{9}{2}
-\testsciround{1341}{2}
-\testsciround{0.996}{2}
-\testsciround{19999.9996}{2}
-\testsciround{-19999.9996}{2}
-\testsciround{+19999.9996}{2}
-\testsciround{9999.9996}{2}
-\testsciround{0.0004982}{3}
-\testsciround{0.0004982}{4}
-\testsciround{0.0004982}{5}
-\testsciround{0.0004982}{6}
-\testsciround{0.0004982}{7}
-\testsciround{0.0004982}{8}
-\testsciround{0.0004982}{9}
-\end{document}