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+% proflycee-tools-arithm.tex
+% Copyright 2023 Cédric Pierquet
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+% http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+
+%%------ConversionsBases
+%dec->bin avec blocs de 4 chiffres
+\setKVdefault[CONVDECBIN]{%
+ AffBase=true
+}
+\NewDocumentCommand\ConversionDecBin{ s O{} m }{%
+ \useKVdefault[CONVDECBIN]
+ \setKV[CONVDECBIN]{#2}% on paramètres les nouvelles clés et on les simplifie
+ \def\resbrut{\xintDecToBin{#3}}
+ \StrLen{\resbrut}[\nbchiffres]
+ \def\nbgrp{\fpeval{4*ceil(\nbchiffres/4,0)}}
+ \IfBooleanTF{#1}
+ {\num{#3}\ifboolKV[CONVDECBIN]{AffBase}{_{10}}{}=\num[digit-group-size=4]{\resbrut}\ifboolKV[CONVDECBIN]{AffBase}{_{2}}{}}
+ {\num{#3}\ifboolKV[CONVDECBIN]{AffBase}{_{10}}{}=\num[digit-group-size=4,minimum-integer-digits=\nbgrp]{\resbrut}\ifboolKV[CONVDECBIN]{AffBase}{_{2}}{}}
+}
+
+\setKVdefault[CONVBINHEX]{%
+ %trait=0.5pt,%
+ AffBase=true,%
+ Details=true
+}
+%bourrage de 0 avant
+\ExplSyntaxOn
+\NewExpandableDocumentCommand{\PLstrzeros}{m}
+{
+ \int_compare:nT { #1 > 0 }
+ {
+ 0 \prg_replicate:nn { #1 - 1 } { 0 }
+ }
+}
+\ExplSyntaxOff
+
+
+%la conversion complète
+\newcommand\ConversionBinHex[2][]{%
+ \useKVdefault[CONVBINHEX]
+ \setKV[CONVBINHEX]{#1}% on paramètres les nouvelles clés et on les simplifie
+ \def\chbrut{#2}
+ \StrLen{\chbrut}[\nbchiffres] %nb de chiffres du binaire
+ \xdef\nbgrp{\fpeval{4*ceil(\nbchiffres/4,0)}} %nb de chiffres avec blocs de 4
+ \xdef\nbblocs{\fpeval{\nbgrp/4}} %nb de blocs
+ %on rajoute des zeros si besoin := OK
+ \xdef\resinter{\chbrut}
+ \num[digit-group-size=4]{\chbrut}\ifboolKV[CONVBINHEX]{AffBase}{_{2}}{}=
+ \ifboolKV[CONVBINHEX]{Details}{%
+ \ifnum\nbchiffres<\nbgrp
+ \xdef\nbz{\inteval{\nbgrp-\nbchiffres}}
+ \xdef\resinter{\PLstrzeros{\nbz}\chbrut}
+ \num[digit-group-size=4,minimum-integer-digits=\nbgrp]{\resinter}=
+ \fi
+ %découpage par blocs et conversion en hexa := OK
+ \newcount\cpt
+ \cpt0
+ \loop\ifnum \cpt<\nbblocs
+ \def\iinit{\fpeval{4*\cpt+1}}%
+ \def\ifinal{\fpeval{4*(\cpt+1)}}%
+ \StrMid{\resinter}{\iinit}{\ifinal}[\blocinter]%
+ {\underbracket{\blocinter}_{\xintBinToHex{\blocinter}}\,}
+ \advance\cpt by 1
+ \repeat
+ \!=
+ }%
+ {}
+ \xintBinToHex{\chbrut}\ifboolKV[CONVBINHEX]{AffBase}{_{16}}{}
+}
+
+%hexa/bin->dec avec écriture polynomiale
+\defKV[CONVTODEC]{%
+ BaseDep=\def\basedepart{#1}
+}
+\setKVdefault[CONVTODEC]{%
+ BaseDep=2,%
+ AffBase=true,%
+ Details=true,%
+ Zeros=true
+}
+
+\ExplSyntaxOn
+\newcommand\convertbasetobasedix[2]{%
+ \int_from_base:nn {#1}{#2}
+}
+\ExplSyntaxOff
+
+\newcommand\ConversionVersDec[2][]{%
+ \useKVdefault[CONVTODEC]
+ \setKV[CONVTODEC]{#1}% on paramètres les nouvelles clés et on les simplifie
+ \def\nbdepart{#2}
+ \StrLen{\nbdepart}[\nbchiffres]
+ \StrChar{\nbdepart}{1}[\chiffre]
+ %si on est en base 16
+ \xintifboolexpr{\basedepart == 16}%
+ {%
+ \nbdepart\ifboolKV[CONVTODEC]{AffBase}{_{\basedepart}}{} =
+ \ifboolKV[CONVTODEC]{Details}{%
+ \xintHexToDec{\chiffre}\times\basedepart^{\inteval{\nbchiffres-1}}%
+ \newcount\cpt
+ \cpt2
+ \loop\ifnum \cpt<\inteval{\nbchiffres+1}
+ \def\puiss{\inteval{\nbchiffres-\cpt}}
+ \StrChar{\nbdepart}{\cpt}[\chiffre]
+ \ifboolKV[CONVTODEC]{Zeros}%
+ {%
+ +\xintHexToDec{\chiffre}\times\basedepart^{\puiss}%
+ }
+ {
+ \ifnum\xintHexToDec{\chiffre} > 0
+ +\xintHexToDec{\chiffre}\times\basedepart^{\puiss}%
+ \fi
+ }
+ \advance\cpt by 1
+ \repeat
+ =
+ }
+ {}
+ \num{\xintHexToDec{\nbdepart}}\ifboolKV[CONVTODEC]{AffBase}{_{10}}{}
+ }%
+ {}
+ \xintifboolexpr{\basedepart == 2}%
+ {%
+ \num[digit-group-size=4]{\nbdepart}\ifboolKV[CONVTODEC]{AffBase}{_{\basedepart}}{} =
+ \ifboolKV[CONVTODEC]{Details}{%
+ \chiffre\times\basedepart^{\inteval{\nbchiffres-1}}%
+ \newcount\cpt
+ \cpt2
+ \loop\ifnum \cpt<\inteval{\nbchiffres+1}
+ \def\puiss{\inteval{\nbchiffres-\cpt}}
+ \StrChar{\nbdepart}{\cpt}[\chiffre]
+ \ifboolKV[CONVTODEC]{Zeros}%
+ {%
+ +\chiffre\times\basedepart^{\puiss}%
+ }
+ {
+ \ifnum\chiffre > 0
+ +\chiffre\times\basedepart^{\puiss}%
+ \fi
+ }
+ \advance\cpt by 1
+ \repeat
+ =
+ }
+ {}
+ \num{\xintBinToDec{\nbdepart}}\ifboolKV[CONVTODEC]{AffBase}{_{10}}{}
+ }%
+ {}%
+}
+
+\newcommand\ConversionBaseDix[3][]{%1=options,%2=nb,%3=basedep ??
+ \useKVdefault[CONVTODEC]
+ \setKV[CONVTODEC]{#1}% on paramètres les nouvelles clés et on les simplifie
+ \def\NBdepart{#2}
+ \def\basedepart{#3}
+ \StrLen{\NBdepart}[\nbchiffres]
+ \StrChar{\NBdepart}{1}[\chiffre]
+ \NBdepart\ifboolKV[CONVTODEC]{AffBase}{_{\basedepart}}{} =
+ \ifboolKV[CONVTODEC]{Details}{%
+ \xintHexToDec{\chiffre}\times\basedepart^{\inteval{\nbchiffres-1}}%
+ \newcount\cpt
+ \cpt2
+ \loop\ifnum \cpt<\inteval{\nbchiffres+1}
+ \def\puiss{\inteval{\nbchiffres-\cpt}}
+ \StrChar{\NBdepart}{\cpt}[\chiffre]
+ \ifboolKV[CONVTODEC]{Zeros}%
+ {%
+ +\xintHexToDec{\chiffre}\times\basedepart^{\puiss}%
+ }
+ {
+ \ifnum\xintHexToDec{\chiffre} > 0
+ +\xintHexToDec{\chiffre}\times\basedepart^{\puiss}%
+ \fi
+ }
+ \advance\cpt by 1
+ \repeat
+ =
+ }%
+ {}%
+ \num{\convertbasetobasedix{#2}{#3}}\ifboolKV[CONVTODEC]{AffBase}{_{10}}{}%
+}
+
+%%------CONVFROMDEC
+\newcommand\PLnoeud[2]{\tikz[remember picture,baseline=(#1.base)]\node[shape=rectangle,inner sep=0pt](#1){#2};}
+\ExplSyntaxOn
+\newcommand\convertbasedixtobase[2]{%
+ \int_to_Base:nn {#1}{#2}
+}
+\ExplSyntaxOff
+
+\defKV[convfromten]{%
+ Couleur=\def\PLConvCouleur{#1},%
+ DecalH=\def\PLConvDecalH{#1},%
+ DecalV=\def\PLConvDecalV{#1},%
+ Noeud=\def\PLConvNoeud{#1}
+}
+
+\setKVdefault[convfromten]{%
+ Couleur=red,%
+ DecalH=2pt,%
+ DecalV=3pt,%
+ Rect=true,%
+ Noeud=EEE,%
+ CouleurRes=false
+}
+
+\newcommand\ConversionDepuisBaseDix[3][]{%
+ \useKVdefault[convfromten]%
+ \setKV[convfromten]{#1}%
+ \xdef\ValRes{\xintDecToHex{#2}}%
+ \xdef\ValA{#2}\xdef\ValB{#3}%
+ \xdef\ValTMP{#2}%
+ \xdef\ValMU{\inteval{#3-1}}%
+ \ensuremath{%
+ \left\lbrace\begin{array}{@{\,}r@{\;=\;}l@{\;+\;}r}
+ %1ere division
+ \xdef\ValQ{\fpeval{trunc(\ValTMP/#3,0)}}\xdef\ValR{\fpeval{\ValTMP-#3*\ValQ}}
+ \num{\ValTMP}\uppercase{&}\num{\ValB}\times\num{\ValQ}\uppercase{&}\PLnoeud{\PLConvNoeud1}{\num{\ValR}}%
+ \xdef\ValTMP{\ValQ}%
+ \whiledo {\ValTMP > \ValMU}%
+ {%
+ \xdef\ValQ{\fpeval{trunc(\ValTMP/#3,0)}}\xdef\ValR{\fpeval{\ValTMP-#3*\ValQ}}%
+ \\ \num{\ValTMP}\uppercase{&}\num{\ValB}\times\num{\ValQ}\uppercase{&}\num{\ValR}
+ \xdef\ValTMP{\ValQ}%
+ }
+ %dernière
+ \xdef\ValQ{\fpeval{trunc(\ValTMP/#3,0)}}\xdef\ValR{\fpeval{\ValTMP-#3*\ValQ}}%
+ \\ \num{\ValTMP}\uppercase{&}\num{\ValB}\times\num{\ValQ}\uppercase{&}\PLnoeud{\PLConvNoeud2}{\num{\ValR}}
+ \end{array} \right| \Rightarrow \num{#2}_{10}=\ifboolKV[convfromten]{CouleurRes}{\mathcolor{\PLConvCouleur}{\convertbasedixtobase{#2}{#3}_{#3}}}{\convertbasedixtobase{#2}{#3}_{#3}}}%
+ \ifboolKV[convfromten]{Rect}%
+ {%
+ \IfSubStr{\PLConvDecalH}{/}%
+ {\StrCut{\PLConvDecalH}{/}{\PLConvDecalHg}{\PLConvDecalHd}}%
+ {\def\PLConvDecalHg{\PLConvDecalH}\def\PLConvDecalHd{\PLConvDecalH}}%
+ \begin{tikzpicture}
+ \draw[overlay,rounded corners=4pt,\PLConvCouleur,thick] ($(\PLConvNoeud1.north west)+(-\PLConvDecalHg,\PLConvDecalV)$) rectangle ($(\PLConvNoeud2.south east)+(\PLConvDecalHd,-\PLConvDecalV)$) ;
+ \draw[overlay,rounded corners=4pt,\PLConvCouleur,thick,->,>=latex] ($(\PLConvNoeud2.east)+(\PLConvDecalHd,0)$)--++(0,{0.75\baselineskip}) ;
+ \end{tikzpicture}%
+ }{}%
+}
+
+%%------PRESPGCD
+\DeclareMathOperator{\PLpgcd}{PGCD}
+\defKV[prespgcd]{%
+ Couleur=\def\PLPGCDCouleur{#1},%
+ DecalRect=\def\PLPGCDDecal{#1},%
+ Noeud=\def\PLPGCDNoeud{#1}
+}
+
+\setKVdefault[prespgcd]{%
+ Couleur=red,%
+ DecalRect=2pt,%
+ Rectangle=true,%
+ Noeud=FFF,%
+ CouleurResultat=false,%
+ AfficheConclusion=true,%
+ AfficheDelimiteurs=true
+}
+
+\newcommand\PresentationPGCD[3][]{%
+ \useKVdefault[prespgcd]%
+ \setKV[prespgcd]{#1}%
+ \xdef\respgcd{\xinteval{gcd(#2,#3)}}
+ \xdef\ValA{#2}\xdef\ValB{#3}%on stocke les valeurs du départ
+ \ensuremath{%
+ \ifboolKV[prespgcd]{AfficheDelimiteurs}%
+ {\left\lbrace}%
+ {}%
+ \begin{array}{@{\,}r@{\;=\;}l@{\;+\;}r}
+ %1ère division
+ \xdef\ValQ{\fpeval{trunc(\ValA/\ValB,0)}}\xdef\ValR{\fpeval{\ValA-\ValB*\ValQ}}
+ \num{\ValA}\uppercase{&}\num{\ValB}\times\num{\ValQ}\uppercase{&}%
+ \xintifboolexpr{\ValR == \respgcd}%
+ {\PLnoeud{\PLPGCDNoeud1}{\num{\ValR}}}%noeud si c'est le pgcd
+ {\num{\ValR}}%
+ \xdef\ValA{\ValB}\xdef\ValB{\ValR}%nouvelles valeurs
+ \whiledo {\ValR > 0}%
+ {%
+ \xdef\ValQ{\fpeval{trunc(\ValA/\ValB,0)}}\xdef\ValR{\fpeval{\ValA-\ValB*\ValQ}}%
+ \\%
+ \num{\ValA}\uppercase{&}\num{\ValB}\times\num{\ValQ}\uppercase{&}%
+ \xintifboolexpr{\ValR == \respgcd}%
+ {\PLnoeud{\PLPGCDNoeud1}{\num{\ValR}}}%noeud si c'est le pgcd
+ {\num{\ValR}}%
+ \xdef\ValA{\ValB}\xdef\ValB{\ValR}%nouvelles valeurs
+ }%
+ \end{array}%
+ \ifboolKV[prespgcd]{AfficheDelimiteurs}%
+ {\right|}%
+ {}%
+ \ifboolKV[prespgcd]{AfficheConclusion}%
+ {%
+ \Rightarrow \PLpgcd\left(\num{#2};\num{#3}\right)=\ifboolKV[prespgcd]{CouleurResultat}{\mathcolor{\PLPGCDCouleur}{\num{\respgcd}}}{\num{\respgcd}}%
+ }%
+ {}%
+ }%
+ \ifboolKV[prespgcd]{Rectangle}%
+ {%
+ \begin{tikzpicture}
+ \draw[overlay,rounded corners=4pt,\PLPGCDCouleur,thick] ($(\PLPGCDNoeud1.north west)+(-\PLPGCDDecal,\PLPGCDDecal)$) rectangle ($(\PLPGCDNoeud1.south east)+(\PLPGCDDecal,-\PLPGCDDecal)$) ;
+ \end{tikzpicture}%
+ }{}%
+}
+
+\endinput \ No newline at end of file