diff options
author | Karl Berry <karl@freefriends.org> | 2010-12-16 23:58:18 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2010-12-16 23:58:18 +0000 |
commit | d4578705f135c332f8be53e89baf508a8bd4e13e (patch) | |
tree | 8851426aee39718e45a9d554a460a755d28c2421 | |
parent | f565a84e02adcdb964437eb46e1f5c3a6554ddc2 (diff) |
xlop 0.23 (17dec10)
git-svn-id: svn://tug.org/texlive/trunk@20769 c570f23f-e606-0410-a88d-b1316a301751
-rw-r--r-- | Master/texmf-dist/doc/generic/xlop/LISEZ.MOI | 8 | ||||
-rw-r--r-- | Master/texmf-dist/doc/generic/xlop/READ.ME (renamed from Master/texmf-dist/doc/generic/xlop/README) | 6 | ||||
-rw-r--r-- | Master/texmf-dist/doc/generic/xlop/XLOP03 | 35 | ||||
-rw-r--r-- | Master/texmf-dist/doc/generic/xlop/fr-user.pdf | bin | 283832 -> 0 bytes | |||
-rw-r--r-- | Master/texmf-dist/doc/generic/xlop/history.txt | 7 | ||||
-rw-r--r-- | Master/texmf-dist/doc/generic/xlop/xlop-doc-fr.pdf | bin | 0 -> 336088 bytes | |||
-rw-r--r-- | Master/texmf-dist/doc/generic/xlop/xlop-doc-fr.tex (renamed from Master/texmf-dist/doc/generic/xlop/fr-user.tex) | 277 | ||||
-rw-r--r-- | Master/texmf-dist/doc/generic/xlop/xlop-doc.pdf | bin | 0 -> 317393 bytes | |||
-rw-r--r-- | Master/texmf-dist/doc/generic/xlop/xlop-doc.tex | 2271 | ||||
-rw-r--r-- | Master/texmf-dist/source/generic/xlop/manual.sty | 7 | ||||
-rw-r--r-- | Master/texmf-dist/tex/generic/xlop/xlop.sty | 2 | ||||
-rw-r--r-- | Master/texmf-dist/tex/generic/xlop/xlop.tex | 1896 |
12 files changed, 3442 insertions, 1067 deletions
diff --git a/Master/texmf-dist/doc/generic/xlop/LISEZ.MOI b/Master/texmf-dist/doc/generic/xlop/LISEZ.MOI index 01be2e2d666..ae96e144eac 100644 --- a/Master/texmf-dist/doc/generic/xlop/LISEZ.MOI +++ b/Master/texmf-dist/doc/generic/xlop/LISEZ.MOI @@ -31,12 +31,14 @@ Installation ------------ L'extension étant prévue pour pouvoir fonctionner aussi bien sous TeX que sous LaTeX, les recommandations de la TDS indiquent que l'endroit -le plus correct pour placer ces fichiers (xlop.tex et xlop.sty) est : -[texmf]/tex/generic/xlop/. +le plus correct pour placer le fichier xlop.tex est + [texmf]/tex/generic/xlop/ +et celui pour placer le fichier xlop.sty est + [texmf]/tex/latex/xlop/ Il reste les fichiers de documentation (LISEZ.MOI, README, history.txt, manual.sty et fr-user.*). Leur place normale devrait -être [texmf]/doc/generic/xlop/. +être [texmf]/doc/xlop/. Il reste à rafraichir la base en lançant la commande texhash (ou mktexlsr, ou ...) et tout devrait être opérationnel. diff --git a/Master/texmf-dist/doc/generic/xlop/README b/Master/texmf-dist/doc/generic/xlop/READ.ME index c87c71c828a..83b40a26c55 100644 --- a/Master/texmf-dist/doc/generic/xlop/README +++ b/Master/texmf-dist/doc/generic/xlop/READ.ME @@ -26,8 +26,10 @@ Distribution consists of files: Installation ------------ xlop can be used under TeX or LaTeX. Thus, TDS recommendations are -that the best place to put files (xlop.tex and xlop.sty) is -[texmf]/tex/generic/xlop/. +that the best place to put the file xlop.tex is + [texmf]/tex/generic/xlop/ +and that the best place to put xlop xlop.sty is + [texmf]/tex/latex/xlop/ For documentation files (README, history.txt, manual.sty, and fr-user.*), best place should be [texmf]/doc/generic/xlop/. diff --git a/Master/texmf-dist/doc/generic/xlop/XLOP03 b/Master/texmf-dist/doc/generic/xlop/XLOP03 deleted file mode 100644 index b742723029a..00000000000 --- a/Master/texmf-dist/doc/generic/xlop/XLOP03 +++ /dev/null @@ -1,35 +0,0 @@ -xlop is still under construction. In fact, xlop 0.2 is just a beta -release; xlop 0.3 will provide: - - * Full redefinition about internal number representation (faster - and less memory space). - * Some macros improved (\opprint, \opdisplay, \opput, ...). - * New parameters (format=normal/sci/eng, carrymul, - hyphen (multiline for very long numbers), fine division and - multiplication control, ...) - * Calculation on basis 2 to 36 - e.g. \opadd[style=text]{"2"11010}{"2"10010} will display - 11010 + 10010 = 101100 - * Support language (languages defined in babel, oldrussian, and - babylon) e.g. \div[displayintermediary=all]{33}{2} displays - - language= french english - - 33 | 2 16.5 - -2 |--- ______ - --- | 16,5 2 ) 33 - 13 | 20 - -12 | -- - ---- | 13 - 10 | 12 - -10 | ---- - --- | 1.0 - 0 | 1.0 - --- - 0 - Language define decimal separator, thousand separator, type of - displayed multiplication, type of displayed division (Author knows - 3 types of multiplications and 2 types of divisions) . - * High level functions (exp, log, sin, asin, sinh, argsin, (idem - for cos, tan, and cot), sqrt, root). - * last but not least, english documentation! diff --git a/Master/texmf-dist/doc/generic/xlop/fr-user.pdf b/Master/texmf-dist/doc/generic/xlop/fr-user.pdf Binary files differdeleted file mode 100644 index 4e30e3edc6c..00000000000 --- a/Master/texmf-dist/doc/generic/xlop/fr-user.pdf +++ /dev/null diff --git a/Master/texmf-dist/doc/generic/xlop/history.txt b/Master/texmf-dist/doc/generic/xlop/history.txt index 97ef8d73097..19a54ce28b9 100644 --- a/Master/texmf-dist/doc/generic/xlop/history.txt +++ b/Master/texmf-dist/doc/generic/xlop/history.txt @@ -50,6 +50,11 @@ Correction d'un bogue sur la division 4 janvier 2006 version 0.22 ------------- +-------------- Correction d'un bogue sur l'affichage de la multiplication posée +16 décembre 2010 version 0.23 +--------------- + Correction d'un bogue sur la division + Ajout de \opexport + Manuel en anglais diff --git a/Master/texmf-dist/doc/generic/xlop/xlop-doc-fr.pdf b/Master/texmf-dist/doc/generic/xlop/xlop-doc-fr.pdf Binary files differnew file mode 100644 index 00000000000..b24c2aaca8c --- /dev/null +++ b/Master/texmf-dist/doc/generic/xlop/xlop-doc-fr.pdf diff --git a/Master/texmf-dist/doc/generic/xlop/fr-user.tex b/Master/texmf-dist/doc/generic/xlop/xlop-doc-fr.tex index 9a8a37be4fc..4dfffa85b5e 100644 --- a/Master/texmf-dist/doc/generic/xlop/fr-user.tex +++ b/Master/texmf-dist/doc/generic/xlop/xlop-doc-fr.tex @@ -1,6 +1,7 @@ \documentclass[12pt]{report} \usepackage{manual} \usepackage[frenchb]{babel} +\usepackage[autolanguage]{numprint} \fvset{label=source}% français \begin{document} @@ -163,10 +164,10 @@ pouvoir réaliser des calculs complexes sous forme infixe : \`A quelques exceptions près qui seront étudiées en temps voulu, les macros de \package{xlop} peuvent éventuellement avoir un argument optionnel entre crochets pour modifier localement la valeur des -paramètres de fonctionnement, les autres arguments (obligatoires) -étant des nombres. Les deux sections de ce chapitre décrivent en -détail ce qu'est un nombre pour \package{xlop} et comment se servir -de ses paramètres. +paramètres de fonctionnement, les autres arguments (qui sont +obligatoires) étant presque toujours des nombres. Les deux sections de +ce chapitre décrivent en détail ce qu'est un nombre pour +\package{xlop} et comment se servir des paramètres. \section{Au début était le nombre} \label{sec:Au début etait le nombre} @@ -177,15 +178,15 @@ pencher sur la particularité de \package{xlop} qui est de pouvoir manipuler des nombres de taille quelconque. \index{nombre!taille}Pour être tout à fait précis, la taille théorique -maximum d'un nombre est de $2^{31}-1$ chiffres. En pratique, cette -limite ne pourra pas être atteinte pour deux raisons essentielles. La -première est qu'une multiplication avec deux opérandes ayant $2^{25}$ -chiffres demanderait plus de $7\,000$ années de calcul sur -l'ordinateur de l'auteur ! La seconde est beaucoup plus restrictive -car elle est liée aux limites de taille des piles de \TeX{}. Voici un -tableau indiquant une compilation sous \TeX{} avec une multiplication -de deux opérandes de même taille sur une machine Linux, pentium~II~600 -et 256~Mo de RAM : +maximum d'un nombre est de $2^{31}-1$ chiffres\index{nombre!limite}. +En pratique, cette limite ne pourra pas être atteinte pour deux +raisons essentielles. La première est qu'une multiplication avec deux +opérandes ayant $2^{25}$ chiffres demanderait plus de $7\,000$ années +de calcul sur l'ordinateur de l'auteur ! La seconde est beaucoup plus +restrictive car elle est liée aux limites de taille des piles de +\TeX{}. Voici un tableau indiquant une compilation sous \TeX{} avec +une multiplication de deux opérandes de même taille sur une machine +Linux, pentium~II~600 et 256~Mo de RAM : \begin{center} \begin{tabular}{|l|*{6}{c|}} \hline @@ -194,21 +195,19 @@ et 256~Mo de RAM : \end{tabular} \end{center} Le \og crash \fg{} indiqué dans le tableau est dû au débordement de la -table de hachage (hash table). -\index{hash table}% +table de hachage (hash table). \index{hash table}% \index{depassement de capacite@dépassement de capacité}% Sous \LaTeX{}, la limite avant crash sera plus réduite. D'autre part, ces tests ont été effectués sur un fichier minimum : avec un document source classique, cette limite sera un peu plus basse. Une autre limite qui risque d'être atteinte relativement rapidement est la -taille du spouleur (spool size). -\index{spool size}% +taille du spouleur (spool size). \index{spool size}% Pour composer ce document qui contient un grand nombre d'appel aux macros de \package{xlop}, l'auteur a augmenté la taille du spouleur -à~$250\,000$ ($125\,000$ s'étant révélé insuffisante) en éditant la -ligne \verb+pool_size+ du fichier \file{texmf.cnf}. De même, la table -de hachage a dû être augmentée en stipulant la valeur \texttt{1000} au -niveau de la ligne \verb+hash_extra+ du fichier \file{texmf.cnf}. +de~$125\,000$ à~$250\,000$ en éditant la ligne \verb+pool_size+ du +fichier \file{texmf.cnf}. De même, la table de hachage a dû être +augmentée en stipulant la valeur \texttt{1000} au niveau de la ligne +\verb+hash_extra+ du fichier \file{texmf.cnf}. \subsection{Syntaxe} \label{subsec:Syntaxe} @@ -226,6 +225,7 @@ explications plus humaines suivront : \*sep* \\ \sameline \textnormal{et} \*chiffre* \end{syntaxBNF} +\index{syntaxe BNF}\index{BNF}\index{grammaire BNF} Le symbole \texttt{caractère} désigne presque n'importe quel caractère accepté par \TeX{}. Les seules exceptions sont les caractères \verb+%+, @@ -241,16 +241,18 @@ contrainte comme le montre le code suivant : \opadd*{2}{2}{a/b_{^c}!&$} \opprint{\prefix_{^c}!&$} \end{SideBySideExample} -On notera en particulier que \verb+a/b_{^c}!&$+ et -\verb+\prefix_{^c}!&$+ représentent exactement le même nom, si -\verb+\prefix+ a la définition adéquate évidemment. Cette possibilité -d'obtenir un nom en utilisant des macros peut sembler inutile mais il -n'en est rien. On peut ainsi réaliser des boucles avec des noms tels -que \verb+r1+, \verb+r2+, \ldots, \verb+r<n>+ en utilisant le code -\verb+r\the\cpt+ comme nom où \verb+cpt+ est un compteur (au sens -\TeX{}, le mécanisme des compteurs avec \LaTeX{} empêche d'être aussi -flexible). Nous verrons un exemple d'utilisation de cette forme à la -section~\ref{sec:Creation d'operations complexes} +\index{nom de nombre}% +On notera que \verb+a/b_{^c}!&$+ et \verb+\prefix_{^c}!&$+ +représentent très exactement le même nom, si \verb+\prefix+ a la +définition adéquate évidemment. Cette possibilité d'obtenir un nom en +utilisant des macros peut sembler inutile mais il n'en est rien. On +peut ainsi réaliser des boucles\index{boucle} avec des noms tels que +\verb+r1+, \verb+r2+, \ldots, \verb+r<n>+ en utilisant le code +\verb+r\the\cpt+ comme nom où \verb+cpt+ est un compteur au sens +\TeX{}. Le mécanisme des compteurs avec \LaTeX{} donne un code un peu +plus long avec \verb+r\number\value{cpt}+ où \verb+cpt+ est maintenant +un compteur au sens \LaTeX. Nous verrons un exemple d'utilisation de +cette forme à la section~\ref{sec:Creation d'operations complexes} page~\pageref{sec:Creation d'operations complexes}. \index{nombre!valide}En pratique, que signifient toutes ces règles ? @@ -284,9 +286,10 @@ maintenant.\opset{decimalsepsymbol={,}} \subsection{Symboles} \label{subsecSymboles} -Le paramètre \parameter{afterperiodsymbol} indique le symbole qui -suit l'écriture d'un quotient en ligne lors d'une division avec -recherche de période. Sa valeur par défaut est \verb+$\ldots$+ +Le paramètre \parameter{afterperiodsymbol} indique le symbole qui suit +l'écriture d'un quotient en ligne lors d'une division avec recherche +de période\index{division!période}. Sa valeur par défaut est +\verb+$\ldots$+ Le paramètre \parameter{equalsymbol} indique le symbole utilisé pour l'égalité. Sa valeur par défaut est \verb+$=$+. En réalité, le @@ -345,10 +348,10 @@ l'opération et nous y reviendrons lors de la présentation des différentes opérations. Le paramètre \parameter{style} indique si l'opération doit être posée -(valeur \verb+display+ qui est la valeur par défaut) ou bien être -affichée en ligne (valeur \verb+text+). On reviendra sur ce paramètre -lors de la présentation de la division car les possibilités sont alors -un peu plus nombreuses. +(avec la valeur \verb+display+ qui est la valeur par défaut) ou bien +être affichée en ligne (valeur \verb+text+). On reviendra sur ce +paramètre lors de la présentation de la division car les possibilités +sont alors un peu plus nombreuses. \begin{SideBySideExample} \opadd[style=text]{45}{172} \end{SideBySideExample} @@ -393,12 +396,12 @@ possibles sont : Dans les opérations posées, les chiffres sont placés dans des boîtes de dimensions fixées. La largeur est donnée par le paramètre \parameter{columnwidth} et la hauteur par le paramètre -\parameter{lineheight}. La valeur par défaut de \texttt{lineheight} -est \verb+\baselineskip+ ce qui fait que les lignes des opérations -seront espacées, par défaut, comme les lignes d'un paragraphe. La -valeur par défaut de \texttt{columnwidth} est de \texttt{2ex} car la -largeur \og normale \fg{} des chiffres aurait donné des résultats peu -lisibles. +\parameter{lineheight}. La valeur par défaut du paramètre +\texttt{lineheight} est \verb+\baselineskip+ ce qui fait que les +lignes des opérations seront espacées, par défaut, comme les lignes +d'un paragraphe. La valeur par défaut de \texttt{columnwidth} est de +\texttt{2ex} car la largeur \og normale \fg{} des chiffres aurait +donné des résultats peu lisibles. \begin{SideBySideExample} \opadd[columnwidth=0.5em] {45.89}{127.5} @@ -407,7 +410,7 @@ Ce piètre résultat est dû en partie au fait que la virgule est placé dans une boîte dont la largeur est contrôlée par le paramètre \parameter{decimalsepwidth} dont la valeur par défaut est nulle. Un essai d'amélioration peut être effectué en donnant à ce paramètre la -largeur \fg{} normale \og d'une virgule. +largeur \og{} normale \fg d'une virgule. \begin{SideBySideExample} \opadd[columnwidth=0.5em, decimalsepwidth=0.27778em] @@ -433,8 +436,8 @@ publiques uniquement pour pouvoir les lire, pas pour les modifier. Les deux paramètres suivants permettent de spécifier les largeurs des traits horizontaux et verticaux tracés par \package{xlop}. Il s'agit -des paramètres \parameter{hrulewidth} et \parameter{vrulewidth} dont -la valeur par défaut est \texttt{0.4pt}. +des deux paramètres \parameter{hrulewidth} et \parameter{vrulewidth} +dont la valeur par défaut est \texttt{0.4pt}. Ces traits sont composés sans perturber la grille, c'est-à-dire sans ajouter d'espace vertical. Ainsi, avec des valeurs importantes pour @@ -517,6 +520,7 @@ On peut également utiliser une macro à un paramètre comme style. resultstyle.2=\hole] {45.89}{127.5} \end{SideBySideExample} +\index{operation@opération!à trou}% Lorsque le style est une macro, le chiffre constitue le dernier argument de cette macro. Voici un exemple plus compliqué et utilisant l'extension \package{pst-node} de la suite \package{pstricks} : @@ -624,8 +628,8 @@ dans l'affichage posé. \section{Soustraction} \label{sec:soustraction} La soustraction est gérée par la macro \macro{opsub}. La soustraction, -lorsqu'elle est posée n'affiche que des nombres positifs. Cela va -avoir pour conséquence d'affficher une addition lorsqu'une des +lorsqu'elle est posée, n'affiche que des nombres positifs. Par +conséquence cette macro va afficher une addition lorsqu'une des opérandes est négative. \begin{SideBySideExample} \opsub{-245}{72} @@ -650,9 +654,9 @@ Bien entendu, l'opération en ligne donnera le résultat exact. Outre les paramètres généraux vus à la section~\ref{sec:Parametres de - xlop}, \verb+\opsub+ est sensible aux paramètres -\texttt{carrysub}, \texttt{lastcarry}, \texttt{offsetcarry}, -\texttt{deletezero} et \texttt{behaviorsub}. + xlop}, \verb+\opsub+ est sensible à \texttt{carrysub}, +\texttt{lastcarry}, \texttt{offsetcarry}, \texttt{deletezero} et +\texttt{behaviorsub}. Le paramètre \parameter{carrysub} est un paramètre booléen qui indique si les retenues doivent être ou non présentes. Sa valeur @@ -724,7 +728,6 @@ et l'opération ne sera pas effectuée. \section{Multiplication} \label{sec:Multiplication} La multiplication est gérée par la macro \macro{opmul}. - Nous présenterons les paramètres \texttt{hfactor}, \texttt{displayintermediary}, \texttt{shiftintermediarysymbol}, \texttt{displayshiftintermediary} et finalement \texttt{deletezero}, @@ -855,7 +858,7 @@ puisqu'il n'y a même plus d'approximation ! Une division non euclidienne peut également s'arrêter sur la détection de la survenue d'une période. Pour cela, il suffit de donner la valeur -\texttt{true} au paramètre \parameter{period}. +\texttt{true} au paramètre \parameter{period}\index{division!période}. \begin{SideBySideExample} \opdiv[period]{100}{3} \end{SideBySideExample} @@ -1071,7 +1074,7 @@ un style particulier aux chiffres individuels. \end{SideBySideExample} Les macros \macro{oplput} et \macro{oprput} permettent de placer un -objet à un emplacement déterminé. La syntaxe de ces deux commandes ne +objet à un emplacement déterminé. La syntaxe de ces commandes ne suit pas celle des autres macros de \package{xlop} puisque l'emplacement est indiqué sous forme de coordonnées entre parenthèses. Les coordonnées utilisent \macro{opcolumnwidth} et @@ -1108,6 +1111,27 @@ les traits verticaux. On rappelle que les paramètres \oplput(1,0){T}\oplput(2,0){W}\oplput(3,0){O} \end{CenterExample} +La macro \macro{opexport}\refstepcounter{stuff}\label{macro-opexport} +permet d'exporter un nombre dans une macro. Il s'agit d'un ajout de la +version 0.23 qui est très utile pour faire dialoguer \package{xlop} +avec le monde extérieur. Le premier argument est un nombre au sens +\package{xlop}, c'est-à-dire soit un nombre écrit directement avec des +chiffres, soit un nom de variable. Le nombre sera écrit sous une forme +directement compréhensible par \TeX{} dans le deuxième argument qui +doit donc être un nom de macro. On notera cependant que le séparateur +décimal sera celui désigné par \parameter{decimalsepsymbol} débarrassé +de ses éventuelles accolades. +\begin{SideBySideExample} + \opmul*{5}{3.141592654}{C} + \opexport{C}{\fivepi} + \texttt{\meaning\fivepi} +\end{SideBySideExample} + +On peut se servir de cette macro, par exemple, pour afficher des +nombres calculés par \package{xlop} dans un tableau avec un alignement +décimal ou encore pour initialiser un compteur ou une longueur (ne pas +oublier l'unité dans ce dernier cas). + \section{Chiffres d'un nombre} \label{sec:Chiffres d'un nombre} Les macros \macro{opwidth}, \macro{opintegerwidth} et @@ -1138,9 +1162,11 @@ du nombre passé en argument. \end{SideBySideExample} Les macros \macro{integer} et \macro{opdecimal} donnent respectivement -la partie entière et la partie décimale d'un nombre. Le premier -argument est le nombre à traiter et le second est la variable qui -contiendra le résultat. +la partie entière et la partie décimale d'un nombre. +\index{nombre!partie entière}\index{partie entière}% +\index{nombre!partie décimale}\index{partie décimale}% +Le premier argument est le nombre à traiter et le second est la +variable qui contiendra le résultat. \begin{SideBySideExample} \opcopy{-37.69911}{a}% \opinteger{a}{ia}% @@ -1190,7 +1216,7 @@ Pour des raisons techniques, \package{xlop} donne des définitions globales aux six tests précédents. Ceux-ci ne seront donc pas protégés par les groupes. Comme ces tests sont utilisés par un grand nombre de macros de \package{xlop}, une conséquence pratique est qu'il faut -\textbf{toujours} réaliser les tests \verb+\ifop...+ immédiatement +\emph{toujours} réaliser les tests \verb+\ifop...+ immédiatement après le \macro{opcmp}, ou, du moins, avant toute autre utilisation de macros de \package{xlop} sous peine de bogues éventuels difficiles à comprendre ! @@ -1227,16 +1253,18 @@ Les macros qui nous restent à voir proviennent soit de commandes utilisées de façon interne et qu'il aurait été dommage de ne pas rendre publiques, soit de demandes d'utilisateurs. -Les macros utilisées de façon interne sont \macro{opgcd} qui donne le -pgcd de deux nombres et \macro{opdivperiod} qui donne la longueur de +Les macros utilisées de façon interne sont \macro{opgcd}\index{pgcd} +qui donne le pgcd de deux nombres et +\macro{opdivperiod}\index{division!période} qui donne la longueur de la période d'un quotient de deux nombres. Pour des raisons d'efficacité, ces macros n'utilisent pas les nombres de \package{xlop} mais des nombres directement accessibles à \TeX{}. Cela a pour conséquence que les nombres passés en paramètres dans les deux -premiers arguments ne devront pas excéder \texttt{2147483647} pour -\macro{opgcd} et \texttt{214748364} pour \macro{opdivperiod}. Un -message d'avertissement rappellera à l'ordre en cas de dépassement. Le -résultat sera stocké dans la variable indiqué en troisième paramètre. +premiers arguments ne devront pas dépasser la valeur +\texttt{2147483647} pour \macro{opgcd} et \texttt{214748364} pour +\macro{opdivperiod}. Un message d'avertissement rappellera à l'ordre +en cas de dépassement. Le résultat sera stocké dans la variable +indiqué en troisième paramètre. Il y aura également quelques vérifications sur les deux premiers paramètres. Un pgcd ne peut pas avoir d'argument nul et le calcul de @@ -1262,16 +1290,16 @@ trouve : de longueur $\opprint{p}$. \end{SideBySideExample} -Les macros \macro{opcastingoutnines} et \macro{opcastingoutelevens} -vont permettre de composer des preuves par neuf et par onze. -L'extension \package{xlop} ne propose pas directement ces compositions -puisqu'elles nécessitent des traits en diagonal et donc le recours à -d'autres extensions. En réalité, la macro \macro{opcastingoutnines} va -faire la somme modulo~9 des chiffres du premier argument et stockera -le résultat dans le second argument tandis que la macro -\macro{opcastingoutelevens} fera la somme des chiffres de rangs -impairs, la somme des chiffres de rangs pairs puis la différence -modulo~11 de ces deux sommes. +Les macros \macro{opcastingoutnines}\index{preuve!par neuf} et +\macro{opcastingoutelevens}\index{preuve!par onze} vont permettre de +composer des preuves par neuf et par onze. L'extension \package{xlop} +ne propose pas directement ces compositions puisqu'elles nécessitent +des traits en diagonal et donc le recours à d'autres extensions. En +réalité, la macro \macro{opcastingoutnines} va faire la somme modulo~9 +des chiffres du premier argument et stockera le résultat dans le +second argument tandis que la macro \macro{opcastingoutelevens} fera +la somme des chiffres de rangs impairs, la somme des chiffres de rangs +pairs puis la différence modulo~11 de ces deux sommes. \begin{SideBySideExample} \newcommand\castingoutnines[3]{% \opcastingoutnines{#1}{cna}% @@ -1299,16 +1327,15 @@ Les deux macros suivantes sont très simples. Il s'agit de sauvegarde dans la variable indiquée par le second argument et de \macro{opabs} qui réalise la même chose mais avec la valeur absolue. -La macro \macro{oppower} permet de calculer des puissances entières de -nombres. Cette macro demande trois paramètres, le troisième paramètre -étant la variable recevant le résultat du premier paramètre à la -puissance le deuxième paramètre. Le deuxième paramètre doit être un -nombre entier. Lorsque le premier argument est nul, si le deuxième -paramètre est nul, le résultat sera~1, s'il est strictement positif, -le résultat sera nul et s'il est strictement négatif il y aura une -erreur et aucun résultat ne sera fourni. Il n'y a aucune limitation -sur le premier paramètre ce qui peut entraîner quelques problèmes. Par -exemple : +La macro \macro{oppower} calcule des puissances entières. Cette macro +demande trois paramètres, le troisième paramètre étant la variable +recevant le résultat du premier paramètre à la puissance le deuxième +paramètre. Le deuxième paramètre doit être un nombre entier. Lorsque +le premier argument est nul, si le deuxième paramètre est nul, le +résultat sera~1, s'il est strictement positif, le résultat sera nul et +s'il est strictement négatif il y aura une erreur et aucun résultat ne +sera fourni. Il n'y a aucune limitation sur le premier paramètre ce +qui peut entraîner quelques problèmes. Par exemple : \begin{CenterExample}[xrightmargin=0pt] \opcopy{0.8}{a}\opcopy{-17}{n}% \oppower{a}{n}{r}% @@ -1322,7 +1349,7 @@ Avec $0{,}7$ au lieu de $0{,}8$, le problème aurait été encore pire : $\opprint{a}^{\opprint{n}}$ a \opprint{dr} chiffres apr\`es la virgule. \end{CenterExample} -Tout cela est dû au fait que lorsque l'exposant est négatif, +Cela est dû au fait que lorsque l'exposant est négatif, \package{xlop} calcule \emph{d'abord} l'inverse du nombre pour \emph{ensuite} calculer la puissance avec l'opposé de l'exposant. Si on avait laissé $-17$ au lieu de $-8$ dans l'exemple précédent, les @@ -1426,6 +1453,7 @@ de ces trois macros. \end{tabular} \end{center} +\index{expression complexe|(} La dernière macro qui nous reste à voir est \macro{opexpr} qui permet de réaliser le calcul d'une expression complexe. Cette macro demande deux paramètres : le premier est l'expression à calculer donnée sous @@ -1471,9 +1499,9 @@ correspondantes (la fonction \texttt{xxx} faisant appel à la macro \texttt{round}, le nombre \texttt{i} indique le rang sur lequel doit se faire l'arrondi. -La macro \macro{opexpr} accepte un argument optionnel puisqu'elle peut +La macro \macro{opexpr} accepte un argument optionnel car elle peut réaliser des divisions et que ces divisions doivent pouvoir être -contrôlées via les paramètres \parameter{maxdivstep}, +contrôlées \emph{via} les paramètres \parameter{maxdivstep}, \parameter{safedivstep} et \parameter{period}. Notre premier exemple est assez basique : \begin{CenterExample}[xrightmargin=0pt] @@ -1493,6 +1521,7 @@ macro : (\try)))))}{r} La fraction continue de base $u_n=2$ vaut \opprint{r} au rang~5. \end{CenterExample} +\index{expression complexe|)} \appendix \chapter{Aide-mémoire} @@ -1500,8 +1529,11 @@ macro : \section{Temps de compilation} \label{sec:Temps de compilation} Les temps de compilation ont été mesurés sur une machine à processeur -Pentium~II~600\,MHz ayant 256\,Mo de RAM et tournant sous linux -(Debian woody). Le principe a été de faire un fichier TeX{} minimum +Pentium~II~600\,MHz ayant 256\,Mo de RAM et tournant sous Linux +(Debian woody)\footnote{En réalité, ces mesures ont été effectuées en + 2004 lors de la sortie de la version 0.2. L'auteur étant fainéant, + il n'a pas repris ces tests avec son matériel actuel (bien plus + performant) !}. Le principe a été de faire un fichier TeX{} minimum dont le schéma général est donné par : \begin{verbatim} \input xlop @@ -1613,6 +1645,7 @@ paramètres. Cela dit, le tableau permet d'avoir quand même une idée de ce à quoi il faut s'attendre. \index{compilation (temps de)|)}\index{temps de calcul|)} +\clearpage \section{Liste des macros} \label{sec:Liste des macros} \noindent\index{macros!table des|(}% @@ -1674,6 +1707,8 @@ ce à quoi il faut s'attendre. \verb+\opdivperiod{T1}{T2}{N}+ & Calcule la longueur de la période de la division de \verb+T1+ par \verb+T2+ et place le résultat dans \verb+N+. \\\hline + \verb+\opexport[P]{n}\cmd+ & + Copie le nombre \verb+n+ dans la macro \verb+\cmd+. \\\hline \verb+\opexpr[P]{F}{N}+ & \'Évalue la formule \texttt{F} est place le résultat final dans le nombre \texttt{N}. \\\hline @@ -1772,10 +1807,11 @@ Dans ce tableau, les paramètres : \item \texttt{T} et \texttt{Ti} (où \texttt{i} représente un indice) indiquent que le paramètre doit être un nombre donné sous forme décimale ou sous forme d'un nom de variable mais ne devant pas - excéder la taille des nombres directement acceptables par \TeX{} (en - l'occurrence $-2147483648 \le \mathtt{T} \le 2147483647$). + excéder la taille des nombres directement acceptables par \TeX{} + ($-2147483648 \le \mathtt{T} \le 2147483647$ en l'occurrence). \end{itemize} +\newpage \section{Liste des paramètres} \label{sec:Liste des parametres} \index{parametres@paramètres!table des|(}% @@ -2007,15 +2043,15 @@ nombre correspondant à cette longueur avec l'unité \texttt{sp}. \dimen0=#1\relax \count255=\dimen0 \opcopy{\the\count255}{#2}} - \getsize{1pt}{r}$1\,\mathrm{pt} = \opprint{r}\,\mathrm{sp}$\quad - \getsize{1pc}{r}$1\,\mathrm{pc} = \opprint{r}\,\mathrm{sp}$\quad - \getsize{1in}{r}$1\,\mathrm{in} = \opprint{r}\,\mathrm{sp}$\quad - \getsize{1bp}{r}$1\,\mathrm{bp} = \opprint{r}\,\mathrm{sp}$\quad - \getsize{1cm}{r}$1\,\mathrm{cm} = \opprint{r}\,\mathrm{sp}$\quad - \getsize{1mm}{r}$1\,\mathrm{mm} = \opprint{r}\,\mathrm{sp}$\quad - \getsize{1dd}{r}$1\,\mathrm{dd} = \opprint{r}\,\mathrm{sp}$\quad - \getsize{1cc}{r}$1\,\mathrm{cc} = \opprint{r}\,\mathrm{sp}$\quad - \getsize{1sp}{r}$1\,\mathrm{sp} = \opprint{r}\,\mathrm{sp}$\quad + \getsize{1pt}{r}$1\,\mathrm{pt}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1pc}{r}$1\,\mathrm{pc}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1in}{r}$1\,\mathrm{in}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1bp}{r}$1\,\mathrm{bp}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1cm}{r}$1\,\mathrm{cm}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1mm}{r}$1\,\mathrm{mm}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1dd}{r}$1\,\mathrm{dd}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1cc}{r}$1\,\mathrm{cc}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1sp}{r}$1\,\mathrm{sp}=\opprint{r}\,\mathrm{sp}$\quad \end{CenterExample} N'oubliez cependant pas que le but principal de \package{xlop} est d'\emph{afficher} automatiquement les opérations. @@ -2053,7 +2089,7 @@ L'utilisation des macros de \package{xlop} associées au mécanisme de boucle de \TeX{} permet de créer des opérations à volonté. Nous ne donnerons que deux exemples. Le premier est la décomposition d'un nombre en facteurs premiers, le second est un calcul général de -fraction continue.\index{nombre!premier}% +fraction continue.\index{nombre!premier}\index{boucle|(}% \index{decomposition@décomposition en nombres premiers} \begin{Verbatim}[xrightmargin=0pt] \newcount\primeindex @@ -2227,11 +2263,12 @@ la macro pour protéger les modifications de paramètres de \`A ce propos, on notera également qu'un paramètre vide n'est pas accepté. C'est tout à fait volontaire, l'auteur de l'extension pensant qu'un utilisateur tapant des crochets sans rien mettre à l'intérieur -est sans doute en train de commettre une erreur. Pour palier à cette +est sans doute en train de commettre une erreur. Pour pallier à cette impossibilité de transmettre un paramètre vide \index{parametre@paramètre!vide}% il existe le paramètre particulier \parameter{nil} qui a exactement ce rôle. +\index{boucle|)} On notera enfin l'astuce \verb+{\setbox2=\box2}+ qui permet d'obtenir un registre de boîte vide et les manipulations finales @@ -2269,9 +2306,9 @@ carrées de~2 et~3. \opcopy{result}{#2}% } \endgroup - \continuedfraction{1,1,1,1,1,1,1,1,1,1}{r}\opprint{r}\quad - \continuedfraction{1,2,2,2,2,2,2,2,2,2}{r}\opprint{r}\quad - \continuedfraction{1,1,2,1,2,1,2,1,2,1}{r}\opprint{r} + \continuedfraction{1,1,1,1,1,1,1,1,1,1,1,1}{r}\opprint{r}\quad + \continuedfraction{1,2,2,2,2,2,2,2,2,2,2,2}{r}\opprint{r}\quad + \continuedfraction{1,1,2,1,2,1,2,1,2,1,2,1}{r}\opprint{r} \end{CenterExample} \makeatother Une fois n'est pas coutume, nous avons fait appel à des commandes @@ -2310,9 +2347,16 @@ de \LaTeX{} ou bien en indiquant un code de catégorie égal à~11 \makeatother \end{SideBySideExample} +On notera que cette façon de faire ne fonctionne plus forcément +lorsque le séparateur décimal est entre accolade car la macro +\verb+\opprint{var}+ contiendra ces accolades. Dans ce cas, le plus +simple est de passer par la macro \macro{opexport} décrite à la +page~\pageref{macro-opexport}. + \chapter{Versions futures} \label{chap:Versions futures} -L'extension \package{xlop} en est à sa version~0.2 qui est +L'extension \package{xlop} en est à sa version~0.23 qui n'est qu'une +version déboguée de la version~0.2 qui est elle même essentiellement une version corrigée de la version~0.1 (première version publique). La prochaine version sera la~0.3 dont la version \og stable \fg{} sera alors la version~0.4. @@ -2325,7 +2369,9 @@ arrêté mais il y a déjà plusieurs points prévus : \item ajout de fonctions de haut niveau avec les racines (\macro{oproot} pour les racines quelconques et \macro{opsqrt} pour la racine carrée), exponentielle, logarithme, fonctions - trigonométriques (directes, inverses, hyperboliques) ; + trigonométriques (directes, inverses, hyperboliques) en passant par + l'extension \package{xfp} qui est une version déboguée (par + l'auteur) de l'extension \package{fp} ; \item ajout d'une macro permettant de réaliser une écriture formatée, c'est-à-dire une écriture d'un nombre où les longueurs des parties entière et décimale seront indiquées (si ces longueurs ne sont pas @@ -2347,17 +2393,8 @@ arrêté mais il y a déjà plusieurs points prévus : \item manuel en anglais. \end{itemize} -Pour le premier point, seules la division anglo-saxonne, la -multiplication dite russe et la multiplication dite babylonienne sont -en cours d'étude, l'auteur ne connaissant pas les habitudes des autres -pays en la matière. Si vous connaissez d'autres façons de poser les -opérations à part celles présentées dans ce manuel, la division -anglo-saxonne, la multiplication russe (double colonne avec des -divisions par deux sur une colonne et des multiplications par deux sur -l'autre) et la multiplication babylonienne (ou vénitienne qui consiste -à faire une grande grille de multiplication à un chiffre et à effectuer -les sommes finales en diagonale), l'auteur vous sera éternellement -reconnaissant de le contacter à l'adresse : +Pour toute demande ou rapport de bogue, l'auteur vous sera +éternellement reconnaissant de le contacter à l'adresse : \begin{verbatim} Jean-Come.Charpentier@wanadoo.fr \end{verbatim} @@ -2366,7 +2403,7 @@ en plaçant le mot \og \texttt{xlop} \fg{} dans le sujet du message. Il serait souhaitable d'avoir un manuel du hacker qui expliquerait en détail le code source. Cet outil pourrait être tout à fait bénéfique pour que chacun puisse apporter plus facilement des améliorations au -code. Malheureusement, le code actuel fait plus de~\nombre{3900} +code. Malheureusement, le code actuel fait plus de~\nombre{4000} lignes et le travail nécessaire risque d'être trop important. Éventuellement, il pourra y avoir un manuel du hacker expliquant les spécifications générales du code sans entrer dans trop de détails diff --git a/Master/texmf-dist/doc/generic/xlop/xlop-doc.pdf b/Master/texmf-dist/doc/generic/xlop/xlop-doc.pdf Binary files differnew file mode 100644 index 00000000000..0d3bbaa5900 --- /dev/null +++ b/Master/texmf-dist/doc/generic/xlop/xlop-doc.pdf diff --git a/Master/texmf-dist/doc/generic/xlop/xlop-doc.tex b/Master/texmf-dist/doc/generic/xlop/xlop-doc.tex new file mode 100644 index 00000000000..17ec50a0516 --- /dev/null +++ b/Master/texmf-dist/doc/generic/xlop/xlop-doc.tex @@ -0,0 +1,2271 @@ +\documentclass[12pt]{report} +\usepackage{manual} +\usepackage[english]{babel} +\usepackage[autolanguage]{numprint} +\usepackage{dcolumn} + +\newcommand*\boi{\textbackslash} +\newcommand*\at{@} +\fvset{label=source}% english + +\renewcommand\parameter[1]{\texttt{#1}\index{#1@\texttt{#1}}% + \index{parameter!\texttt{#1}}} + +\begin{document} +\begin{titlepage} + \null\par\vfill + \begin{center} + \begin{minipage}{0.75\linewidth} + \hrule width\linewidth height2pt depth0pt + \hrule width0pt height3pt depth0pt + \hrule width\linewidth height1pt depth0pt + \hrule width0pt height18pt depth0pt + \begin{center} + \Huge\bfseries XLOP v \fileversion\par\vskip18pt + User Manual + \end{center} + \hrule width0pt height6pt depth0pt + \hrule width\linewidth height1pt depth0pt + \hrule width0pt height3pt depth0pt + \hrule width\linewidth height2pt depth0pt + \end{minipage} + \end{center} + \vfill + \begin{center} + Jean-Côme Charpentier\\ + \today + \end{center} + \vfill\null\par +\end{titlepage} +\newpage +\pagenumbering{roman} +\tableofcontents +\newpage +\pagenumbering{arabic} + +\chapter{Overview} +\label{chap:Présentation} +The \package{xlop} package is intended to make automatic arithmetic +operation on arbitrary sized numbers and to display result either on +display mode or inline mode. Here is a first exemple for an overview +of the syntax: +\begin{SideBySideExample} + \opadd{45,05}{78,4} +\end{SideBySideExample} +We comment this first example in order to give an idea about how use +\package{xlop}. +Addition is displayed ``like in school'': this is the default +displaying. We have an alignment on dots (operand's dot and result's +dot), operator symbol is put on the left and it is vertically centered +between the operands, and the decimal separator is a dot even though we +have specified operands with comma. Finally, note that there is a +carry above the first operand. + +Alignment on dot is obligatory. The other points above are deal with +options. Many macros accept an optional argument which controls some +aspects of displaying or computing operation. For that, we use a +``keyval-like'' syntax: we specify a sequence of parameter's +modifications through an affectation's comma separated sequence. One +affectation has one of the two possible syntax below: +\begin{verbatim} + <parameter>=<value> + <parameter> +\end{verbatim} +the second one is a shorthand for: +\begin{verbatim} + <parameter>=true +\end{verbatim} +In this affectation sequence, we can put space(s) after comma. But +don't put space around the equal sign nor before comma: if you put +space(s) here, that means that parameter name or value has a space. + +So, if you want a comma as decimal separator , an operator symbol side +by side with the second operand, and no carry, you have just to say: +\begin{SideBySideExample} + \opadd[decimalsepsymbol={,}, + voperator=bottom, + carryadd=false]{45.05}{78.4} +\end{SideBySideExample} +Note the trick which consists to put the comma between braces in the +decimal separator symbol definition. In fact, if you say: +\begin{Verbatim}[xrightmargin=0pt] + \opadd[decimalsepsymbol=,,voperator=bottom, + carryadd=false]{45.05}{78.4} +\end{Verbatim} +\package{xlop} drives mad! It don't understand what is this sort of +list! + +Another important point, though it is less apparent, is that the +figures are put in very precise places. Each figure is put in a box of +fixed width and fixed height (user can change these values), decimal +separator is put in a null-width box (by default), and the lines have +a regular interspace (with or without horizontal rule). This allows +exact spacing and to place what we want where we want. +\begin{SideBySideExample} + \psset{xunit=\opcolumnwidth, + yunit=\oplineheight} + \opadd{45.05}{78.4} + \oplput(1.5,3){carry} + \psline{->}(1,3.15)(-3.25,3.15) +\end{SideBySideExample} +This example uses package +\package{pstricks}\index{pstricks@\package{pstricks}} + +We have said that \package{xlop} package is able to deal with +arbitrary sized numbers. We come again about this subject and, for +now, we just give an example which shows what is possible. Don't look +at the code, some explanations will be given later in this manual, for +now just admire the result! +\begin{CenterExample}[xrightmargin=0pt] + \opdiv[style=text,period]{1}{49} +\end{CenterExample} + +The package \package{xlop} provides some other features. It is +possible to manipulate numbers through variables. These variables can +be created with an assignation or as a computation result. You can +also manipulate the figures individually: +\begin{SideBySideExample} + \opadd*{45.05}{78.4}{r}% + The first figure after dot of + $45.05+78.4$ is + \opgetdecimaldigit{r}{1}{d}% + $\opprint{d}$. +\end{SideBySideExample} +you can make tests: +\begin{SideBySideExample} + \opadd*{45.05}{78.4}{r}% + The sum $45.05+78.4$ is + \opcmp{r}{100}% + \ifopgt greater than + \else\ifoplt less than + \else equal to + \fi\fi + $100$. +\end{SideBySideExample} +you can use some operations and some functions: +\begin{SideBySideExample} + gcd of $182$ and $442$ is + \opgcd{182}{442}{d}$\opprint{d}$ +\end{SideBySideExample} +you can compute complex expression in infix form: +\begin{SideBySideExample} + \opexpr{(2+3^2)/(gcd(22,33))}{r}% + $$\frac{2+3^2}{\gcd(22,33)} = + \opprint{r}$$ +\end{SideBySideExample} + +\chapter{\package{xlop} Instructions} +Except some macros which will be examined later, the \package{xlop}'s +macros can have an optional argument between squared braces in order +to localy modify parameter's values. The other arguments (mandatory) +are (nearly) always numbers. The two sections of this chapter describe +in details what is a number for \package{xlop} and how use parameters. + +\section{In the Beginning Was the Number} +\label{sec:Au début etait le nombre} +\subsection{Size} +\label{subsec:Taille} +Before we see the general syntax of number, we examin the very +particular \package{xlop} feature: the ability to deal with arbitrary +sized number. + +\index{number!size}To be precise, the theoric maximum size of a number +is $2^{31}-1$ digits\index{number!limit}. In practice, this limit +can't be reached for two essential reasons. The first one is that a +multiplication with two numbers with $2^{25}$~digits needs more than +$7\,000$ years to be performed on the author computer! The second one +is more restrictive because it is linked to \TeX{} stack size limits. +Here is a table showing a \TeX{} compilation for a multiplication with +two operands of same size, on a linux computer, pentium~II~600 and +256~Mb RAM:\footnote{In fact it was the author computer in 2004. The + actual author computer is \emph{more} powerfull but the author is + lazy, and he have not remake the tests!} +\begin{center} + \begin{tabular}{|l|*{6}{c|}} + \hline + number of digits & 100 & 200 & 300 & 400 & 425 & 450 \\\hline + compilation time (s) & 2 & 8 & 18 & 32 & 36 & crash \\\hline + \end{tabular} +\end{center} +The ``crash'' in the table is due to an overstack for hash table. +\index{hash table}% +\index{overflow}% +On \LaTeX{}, the limit before crash will be reduced. These tests are +made on a minimal file. With a typical document, this limit will be +reduced too. The spool size is another limit quickly reached. +\index{spool size}% +To typeset this document which contain many calls to the +\package{xlop} macros, the author has grown up the spool size +to~$250000$ ($125\,000$ was insufficient) editing the line +\verb+pool_size+ in the \file{texmf.cnf} file. Also, the author has +grown up the hash table to~\texttt{1000} in the line +\verb+hash_extra+. + +\subsection{Syntax} +\label{subsec:Syntaxe} +Now we present the syntax using the BNF grammar. There will be human +explanations later: +\begin{syntaxBNF} + \*number* & \{\*sign*\}\*positive* \alt \*name* \\ + \*sign* & + \alt - \\ + \*positive* & \*integer* \alt \*sep*\*integer* \alt \\ + \sameline \*integer*\*sep* \alt \*integer*\*sep*\*integer* \\ + \*sep* & . \alt , \\ + \*integer* & \*digit*\{\*digit*\} \\ + \*name* & \*start*\{character\} \\ + \*start* & character \textnormal{except } \*sign*\textnormal{,} + \*sep* \\ + \sameline \textnormal{, and } \*digit* +\end{syntaxBNF} +\index{syntax!BNF}\index{BNF grammar} + +The \texttt{character} symbol means nearly any character accepted by +\TeX{}. The exceptions are characters \verb+%+ and \verb+#+ which are +completely prohibited. In fact, the use of active characters is +risked. For instance, on \LaTeX{}, the \verb+~+ definition prohibits the +use of it inside a variable name. In the other hand, the \verb+\ +is +always the escape char, that is, the variable name will be the name +\emph{after} all is expanded. There isn't any other restraint as the +following code show it: +\begin{SideBySideExample} + \newcommand\prefix{a/b} + \opadd*{2}{2}{a/b_{^c}!&$} + \opprint{\prefix_{^c}!&$} +\end{SideBySideExample} +\index{number!name}% +Note particullary that \verb+a/b_{^c}!&$+ and \verb+\prefix_{^c}!&$+ +produce exactly the same name\ldots{} obviously if \verb+\prefix+ have +the right definition! This possibility to have a name using macro +could seem useless but it is not true. For instance, you can realize +loops\index{loop} with names as \verb+r1+, \verb+r2+, \ldots, +\verb+r<n>+ using the code \verb+r\the\cpt+ as variable name, where +\verb+cpt+ is a counter in the \TeX{} meaning. With \LaTeX{}, the code +is more verbose with \verb+r\number\value{cpt}+ where \verb+cpt+ is +now a \LaTeX{} counter. We will see an example using this syntax in +the section~\ref{sec:Creation d'operations complexes} +page~\pageref{sec:Creation d'operations complexes}. + +\index{number!valid}In practice, what does it mean all these rules? +First, they means that a number writes in a decimal form can be +preceded by any sequence of plus or minus signs. Obviously, if there +is a odd number of minus signs, the number will be negative. Next, a +decimal number admits only one decimal separator symbol which can +be a dot or a comma, this one can be put anywhere in the +number. Finally, a number is write in basis~10. Be carefull: these +rules mean that \verb+-a+ is not valid. + +The package uses some private names and it is safe to not begin a +variable name with the character \texttt{@}. + +\section{\package{xlop} Parameters} +\label{sec:Parametres de xlop} +\index{parameter!syntax|(} +Parameter assignments are local to the macro when they are indicated +in the optional argument. To make global a parameter assignment, you +have to use the \macro{opset} macro. For example: +\begin{Verbatim}[xrightmargin=0pt] + \opset{decimalsepsymbol={,}} +\end{Verbatim} +give the comma as decimal separator symbol for the whole document, at +least, until another redefinition with \verb+\opset+. + +\subsection{Symbols} +\label{subsecSymboles} +The \parameter{afterperiodsymbol} parameter indicates the symbol that +follows a quotient in line in a division with period +search\index{division!period}. Its default value is \verb+$\ldots$+ + +The \parameter{equalsymbol} parameter indicates the symbol used for +equality. Its default value is \verb+$=$+. In fact, this parameter is +defined with: +\begin{Verbatim}[xrightmargin=0pt] + \opset{equalsymbol={$=$}} +\end{Verbatim} +that is, with braces in order to protect the equal sign. Without +theses braces, there will be a compilation error. You have to process +like that when there is an equal sign or a comma in the +value.\index{parameter!with ``='' or ``,''\quad} + +The parameter \parameter{approxsymbol} indicates the symbol used for +approximations. Its default value is \verb+$\approx$+. + +The parameter \parameter{decimalsepsymbol} indicates the symbol used +for the decimal separator. Its default value is a dot. + +Parameters \parameter{addsymbol}, \parameter{subsymbol}, +\parameter{mulsymbol}, and \parameter{divsymbol} indicate the symbols +used for the four arithmetic operations. The default value are +\verb!$+$!, \verb!$-$!, \verb!$\times$! et \verb!$\div$! respectively. + +\subsection{General Displaying} +\label{subsec:Presentation generale} +The \parameter{voperation} parameter indicates the way a dispayed +operation is put with respect to the baseline. The possible values are +\verb+top+, \verb+center+, and \verb+bottom+, the latter one is the +default value. +\begin{SideBySideExample} + top\quad + \opadd[voperation=top]{45}{172}\par + center\quad + \opadd[voperation=center]{45}{172}\par + bottom\quad + \opadd[voperation=bottom]{45}{172} +\end{SideBySideExample} + +The \parameter{voperator} parameter indicates how the operator symbol +is put with repect to operands. The possible values are \verb+top+, +\verb+center+ (default value), and \verb+bottom+. +\begin{SideBySideExample} + top\quad + \opadd[voperator=top]{45}{172}\par + center\quad + \opadd[voperator=center]{45}{172}\par + bottom\quad + \opadd[voperator=bottom]{45}{172} +\end{SideBySideExample} + +The \parameter{deletezero} parameter indicates if some numbers in +operation should be displayed with or whithout non-significant +zeros. Exact rôle of this parameter depends of the actual +operation. We will see that when we will study the different +operations. + +The \parameter{style} parameter indicates the way an operation is +displayed: display with \verb+display+ value (default value) or inline +with \verb+text+ value. We will see when we will study division +because there is many possibilities with this operation. +\begin{SideBySideExample} + \opadd[style=text]{45}{172} +\end{SideBySideExample} +In inline operations, \package{xlop} takes care to not typeset the +formula in mathematic mode in a direct way. This allow to specify what +you want as in the next example, and it is also for that that you have +to specify the classical values of symbols between mathematic +delimiters. +\begin{SideBySideExample} + \opadd[addsymbol=plus, + equalsymbol=equal, + style=text]{42}{172} +\end{SideBySideExample} +Meanwhile, \package{xlop} introduces exactly the same penalities and +the same spaces as for a mathematic formula. + +The \parameter{parenthesisnegative} parameter indicates how to typeset +negative numbers in inline operations. The possible values are: +\begin{itemize} +\item \texttt{none} which typesets negative numbers without + parenthesis; +\item \texttt{all} which typesets negative numbers with parenthesis; +\item \texttt{last} which typesets negative numbers with parenthesis + but the first one. +\end{itemize} +\begin{SideBySideExample} + \opadd[style=text, + parenthesisnegative=none] + {-12}{-23}\par + \opadd[style=text, + parenthesisnegative=all] + {-12}{-23}\par + \opadd[style=text, + parenthesisnegative=last] + {-12}{-23} +\end{SideBySideExample} + +\subsection{Dimensions} +\label{subsec:Dimensions} +In displayed operations, figures are put in fixed size boxes. The +width is given by the \parameter{lineheight} parameter and the height +is given by the \parameter{lineheight} parameter. The default value of +\texttt{lineheight} is \verb+\baselineskip+ that is, interline space +in operation is the same (by default) as in the normal text. The +default value for \texttt{columnwidth} is \texttt{2ex} because the +``normal'' width of figures would give bad results. +\begin{SideBySideExample} + \opadd[columnwidth=0.5em] + {45.89}{127.5} +\end{SideBySideExample} +One reason for this bad result is that the decimal separator is put in +a box which width is controlled by the \parameter{decimalsepwidth} +parameter and the default value of this parameter is null. You can +improve this presentation giving a ``normal'' width to the dot. +\begin{SideBySideExample} + \opadd[columnwidth=0.5em, + decimalsepwidth=0.27778em] + {45.89}{127.5} +\end{SideBySideExample} +It is better but give a positive width to the box that contain the +decimal separator is risked. It will be more difficult to place +extern object and it is counter against the idea to have a fixed +grid. You should avoid this in normal time. + +The \parameter{columnwidth} and \parameter{lineheight} parameters +correspond to the only dimensions that \package{xlop} provides as +public one, that is, +\verb+\opcolumnwidth+\index{opcolumnwidth@\texttt{$\backslash$opcolumnwidth}} +and +\verb+\oplineheight+\index{oplineheight@\texttt{$\backslash$oplineheight}} +respectively. It is dangerous to directly modify these dimensions +since a modification in a ``normal'' way doesn't only change the +dimension value. Package \package{xlop} make these dimensions public +only for reading, not for writting. + +The two next parameters allow to specify width of horizontal and +vertical rules stroked by \package{xlop}. We have +\parameter{hrulewidth} and \parameter{vrulewidth} parameters. The +default values are both \texttt{0.4pt}. + +These rules are typeset with no change on grid. That is, with no space +added. Therefore, with great values for thickness, the rules could +run over numbers. +\begin{SideBySideExample} + \opadd[hrulewidth=8pt]{42}{172} +\end{SideBySideExample} + +There is also a paramater which allows to control the horizontal shift +of decimal separator. It is the \parameter{decimalsepoffset} paramater +with a default value of~\texttt{-0.35}. This value indicates a length +with the unit \verb+\opcolumnwidth+. We will see an example at +section~\ref{sec:Division} page~\pageref{sec:Division}. + +\subsection{Figure's Styles} +\label{subsec:Styles des chiffres} +The \package{xlop} package provides five types of numbers and +associates five style paramaters: +\begin{itemize} +\item operands with \parameter{operandstyle}; +\item result with \parameter{resultstyle}; +\item remainders with \parameter{remainderstyle}; +\item intermediary numbers with \parameter{intermediarystyle}; +\item carries with \parameter{carrystyle}. +\end{itemize} +\begin{SideBySideExample} + \opadd[operandstyle=\blue, + resultstyle=\red, + carrystyle=\scriptsize\green] + {45.89}{127.5} +\end{SideBySideExample} +Keep in mind that, in this manual, we use +\package{pstricks}\index{pstricks} package. + +\index{parameter!index|(}% +In fact, the management of these styles is even more powerfull since +you can distingish different number of a same class. In one operation, +you have several operands, and, possibly several remainders and +several intermediary numbers. You can access to the style of these +numbers adding an index to the matching style. +\begin{SideBySideExample} + \opadd[operandstyle=\blue, + operandstyle.1=\lightgray, + resultstyle=\red, + carrystyle=\scriptsize\green] + {45.89}{127.5} +\end{SideBySideExample} +In this example, we indicate that the first operand must be typesetted +with the \verb+\lightgray+ style. We don't indicate anything for the +second operand, so it takes the basic style for its class. (Then with +\verb+\blue+ style.) + +This mechanism is even more powerfull since you can write two level +index for operands, carries, and intermediary numbers (one level for +result and carry) in order to access to each style figure of these +numbers. To simplify index, a positive index indicates the rank of a +figure in the integer part (right to left order, index~1 is for the +unit figure) and a negative index indicates the rank of a figure in +the decimal part (left to right order, $-1$ is for the tenth figure). +\begin{SideBySideExample} + \opadd[operandstyle.1.1=\white, + operandstyle.1.-2=\white, + operandstyle.2.3=\white, + resultstyle.2=\white, + deletezero=false] + {045.89}{127.50} +\end{SideBySideExample} +You can also use a macro with one parameter as a style. +\begin{SideBySideExample} + \newcommand\hole[1]{$\bullet$} + \opadd[operandstyle.1.1=\hole, + operandstyle.1.-2=\hole, + operandstyle.2.3=\hole, + resultstyle.2=\hole] + {45.89}{127.5} +\end{SideBySideExample} +\index{operation!with hole}% +When the style is a macro with argument, this one is the figure. Here +is a more complicated example using \package{pst-node} package of the +\package{pstricks} bundle: +\begin{SideBySideExample} + \newcommand\OPoval[3]{% + \dimen1=#2\opcolumnwidth + \ovalnode{#1} + {\kern\dimen1 #3\kern\dimen1}} + \opadd[voperation=top, + operandstyle.1.1=\OPoval{A}{0}, + operandstyle.2.2=\OPoval{C}{0.8}] + {45}{172}\qquad + \begin{minipage}[t]{2cm} + \pnode(0,0.2em){B}\ figure + \ncarc{->}{A}{B}\par + \pnode(0,0.2em){D}\ number + \ncarc{<-}{D}{C} + \end{minipage} +\end{SideBySideExample} +As for figures, the decimal separator take account to number style. To +access individually to the decimal separator style, you have to use +\texttt{d} index, numeric indexes are for figures. +\begin{SideBySideExample} + \newcommand\hole[1]{\texttt{\_}} + \opmul[intermediarystyle=\hole, + resultstyle=\hole, + resultstyle.d=\white]{2.46}{35.7} +\end{SideBySideExample} +\index{parameter!index|)}% +\index{parameter!syntax|)} + +\chapter{Arithmetic Operations} +\label{chap:Opérations arithmétiques} +\section{Addition} +\label{sec:Addition} +Addition is deal by the \macro{opadd} macro. When it is in display +mode, it display only nonnegative numbers. Then, it displays a +substraction when one of the operands is nonpositive.% +\index{number!nonpositive in displayed operation} +\begin{SideBySideExample} + \opadd{-245}{72} +\end{SideBySideExample} +In a general manner, the principle is to display the operation that +allows to find the result as you make it ``by hand''. On the contrary, +the inline mode shows always an addition since we can now write +nonpositive numbers. +\begin{SideBySideExample} + \opadd[style=text]{-245}{72} +\end{SideBySideExample} +In addition to the general parameters discussed in the +section~\ref{sec:Parametres de xlop}, the macro \verb+\opadd+ uses +parameters \texttt{carryadd}, \texttt{lastcarry}, and +\texttt{deletezero}. + +The \parameter{carryadd} parameter is a boolean +parameter\index{parameter!boolean}, that is, it accepts only the +values \texttt{true} and \texttt{false}. By habit, when you don't +specify the value and the equal sign, that is like assignment +\texttt{=true}. This parameter indicates if the carries must be showed +or not. Its default value is \texttt{true}. + +The \parameter{lastcarry} parameter is also a boolean parameter. It +indicates if a carry without matching digit for the two operands must +be showed or not. Its default value is \texttt{false}. Take care to +the exact rôle of this parameter. For instance, if the second operand +in the following example is~15307, the last carry would be showed for +any value of the \texttt{lastcarry} parameter since there is a +matching digit in the second operand. +\begin{SideBySideExample} + \opadd{4825}{5307} +\end{SideBySideExample} +\begin{SideBySideExample} + \opadd[carryadd=false]{4825}{5307} +\end{SideBySideExample} +\begin{SideBySideExample} + \opadd[lastcarry]{4825}{5307} +\end{SideBySideExample} + +The \parameter{deletezero} parameter is also a boolean parameter. It +indicates if non-significant zeros must be deleted or not. Its default +value is \texttt{true}. When this parameter is \texttt{false}, the +operands and the result have the same number of digits. For that, +\package{xlop} package adds non-significant zeros. Also, the +non-significant zeros of operands are not removed. +\begin{SideBySideExample} + \opadd{012.3427}{5.2773}\par + \opadd[deletezero=false] + {012.3427}{5.2773} +\end{SideBySideExample} + +This parameter has exactly the same rôle for inline mode than for +displayed mode. +\begin{SideBySideExample} + \opadd[style=text]{02.8}{1.2}\par + \opadd[style=text, + deletezero=false]{02.8}{1.2}\par +\end{SideBySideExample} + +\section{Substraction} +\label{sec:soustraction} +Substraction is made by \macro{opsub} macro. In displayed mode, the +substraction shows only nonnegative numbers. For that, it shows an +addition when one operand is nonpositive. +\begin{SideBySideExample} + \opsub{-245}{72} +\end{SideBySideExample} +In a general way, the principle is to display the operation which +allow to find the result as you make it ``by hand''. On the contrary, +inline mode shows always a substraction since you can now write +nonpositive numbers. +\begin{SideBySideExample} + \opsub[style=text]{-245}{72} +\end{SideBySideExample} +This principle apply also when the first operand is less than the +second one (positive case). In this case, we have an operand +inversion. +\begin{SideBySideExample} + \opsub{1.2}{2.45} +\end{SideBySideExample} +Of course, inline operation gives an exact result. +\begin{SideBySideExample} + \opsub[style=text]{1.2}{2.45} +\end{SideBySideExample} + +In addition to general parameters we have seen at +section~\ref{sec:Parametres de xlop}, \verb+\opsub+ takes account of +\texttt{carrysub}, \texttt{lastcarry}, \texttt{offsetcarry}, +\texttt{deletezero}, and \texttt{behaviorsub} parameters. + +The \parameter{carrysub} parameter is a boolean one which indicates if +carries must be present or not. Its default value is \texttt{false}. +(Remember that the default value of \texttt{carryadd} parameter is +\texttt{true}.) +\begin{SideBySideExample} + \opsub[carrysub]{1234}{567} +\end{SideBySideExample} + +In the last example, you can see that there is no carry above the last +digit of 1234. This is quite common (at least in France). If you want +display this last carry, you have to use the \parameter{lastcarry} +parameter. This parameter does not have the same behavior in +substraction and in addition since here, the last carry is not +displayed when the second operand does not have correspondent +digit. (For addition, last carry is not displayed when \emph{all} the +operands do not have correspondent digit.) +\begin{SideBySideExample} + \opsub[carrysub,lastcarry]{1234}{567} +\end{SideBySideExample} +Note that, in this case, it is better to set the +\parameter{deletezero} parameter to \texttt{false} in order to have a +nicer result. +\begin{SideBySideExample} + \opsub[carrysub, + lastcarry, + deletezero=false]{1234}{567} +\end{SideBySideExample} + +Perhaps it seems to you that showing carries for substraction is a bit +more dense. You can enlarge the figure box with the +\parameter{opcolumnwidth} parameter. You can also indicate the carry +horizontal shift using the \parameter{offsetcarry} parameter. Its +default value is \texttt{-0.35}. +\begin{SideBySideExample} + \opsub[carrysub, + lastcarry, + deletezero=false]{12.34}{5.67} + + \bigskip + \opsub[carrysub, + lastcarry, + columnwidth=2.5ex, + offsetcarry=-0.4, + decimalsepoffset=-3pt, + deletezero=false]{12.34}{5.67} +\end{SideBySideExample} + +It is possible that a substraction with two positive numbers and with +the first one less than the second one signs an user error. In this +case, and only in this case, the \parameter{behaviorsub} parameter +allows a call to order. The three possible values are: +\begin{itemize} +\item \texttt{silent} which is the default value and which gives the + result; +\item \texttt{warning} which gives also the result but shows the + warning message: +\begin{Verbatim}[xrightmargin=0pt,frame=none] + xlop warning. Substraction with first operand less than second one + See documentation for further information. +\end{Verbatim} +\item \texttt{error} which shows the error message: +\begin{Verbatim}[xrightmargin=0pt,frame=none] + xlop error. See documentation for further information. + Type H <return> for immediate help. + ! Substraction with first operand less than second one. +\end{Verbatim} + and the operation is not performed. +\end{itemize} + +\section{Multiplication} +\label{sec:Multiplication} +The multiplication is under the control of the \macro{opmul} macro. + +The parameters we will see below are \texttt{hfactor}, +\texttt{displayintermediary}, \texttt{shiftintermediarysymbol}, and +\texttt{deletezero}. We studied the other parameters in +section~\ref{sec:Parametres de xlop}. + +The \parameter{shiftintermediarysymbol} parameter indicates what is +the symbol used for showing the shifting of intermediary numbers +(default value is \verb+$\cdot$+). The +\parameter{displayshiftintermediary} parameter can take value +\texttt{shift} (default value) which shows this symbol only for +shifting greater than one level, value \texttt{all} which shows this +symbol for all the shiftings, and the value \texttt{none} which means +that this symbol will be never showed. +\begin{CenterExample}[xrightmargin=0pt] + \opmul[displayshiftintermediary=shift]{453}{1001205}\qquad + \opmul[displayshiftintermediary=all]{453}{1001205}\qquad + \opmul[displayshiftintermediary=none]{453}{1001205} +\end{CenterExample} + +In fact, null intermediary numbers are not display because of the +default value \texttt{none} of the \parameter{displayintermediary} +parameter. The value \texttt{all} shows all the intermediary numbers, +even null intermediary numbers. +\begin{SideBySideExample} + \opmul[displayintermediary=all] + {453}{1001205} +\end{SideBySideExample} +Note that null intermediary numbers are displayed with the same width +than the first factor width. + +The \parameter{displayintermediary} parameter accepts the value +\texttt{nonzero} which means the same than the \texttt{none} value +except when second factor has only one digit. +\begin{CenterExample}[xrightmargin=0pt] + \opmul{3.14159}{4}\qquad + \opmul[displayintermediary=nonzero]{3.14159}{4} +\end{CenterExample} + +The \parameter{hfactor} parameter indicates how align operands. The +default value, \texttt{right}, gives a raggedleft alignment. The +\texttt{decimal} value gives an alignment on dot. +\begin{CenterExample}[xrightmargin=0pt] + \opmul{3.1416}{12.8}\qquad\opmul[hfactor=decimal]{3.1416}{12.8} +\end{CenterExample} + +For displayed multiplication, the \parameter{deletezero} parameter is +only for operands. The result keeps its non-significant zeros since +there are necessary in order to make a correct dot shifting when we +work ``by hand''. +\begin{CenterExample}[xrightmargin=0pt] + \opmul[deletezero=false]{01.44}{25}\qquad + \opmul{01.44}{25} +\end{CenterExample} +In the other hand, this parameter has its usual behaviour in inline +multiplication. +\begin{CenterExample}[xrightmargin=0pt] + \opmul[deletezero=false,style=text]{01.44}{25}\qquad + \opmul[style=text]{01.44}{25} +\end{CenterExample} + +\section{Division} +\label{sec:Division} +The \package{xlop} package deals with ``normal'' division via +\macro{opdiv} macro and with euclidean division via \macro{opidiv} +macro. Division is a very complex operation so it is not strange that +there are many parameters to control it. + +Pay attention that the \package{xlop} package v. 0.23 is unable to +deal with ``english'' division. In this package version, the division +is the ``french'' one, which is more or less used as it in some other +countries. The \package{xlop} package v. 0.3 will allow ``enlish'' +division (and many more feautures). + +\subsection{End Control} +\label{subsec:Controle de l'arret} +In the following text, term \emph{step} means the set of process which +allow to get one digit for the quotient. This number of steps is (not +only) under the control of \parameter{maxdivstep}, +\parameter{safedivstep}, and \parameter{period} parameters. It is only +partially true because a classical division will stop automatically +when a remainder will be zero, whatever the values of these three +parameters and a euclidean division will stop with an integer quotient +without attention for these three parameters. +\begin{SideBySideExample} + \opdiv{25}{7} +\end{SideBySideExample} +\begin{SideBySideExample} + \opidiv{25}{7} +\end{SideBySideExample} +The first example stops because of the value of \parameter{maxdivstep} +which is 10 by default. Pay attention that the maximum step number +could cause strange result when it is too small. +\begin{SideBySideExample} + \opdiv[maxdivstep=2]{1248}{3} +\end{SideBySideExample} +Clearly, the last result is false. In the other hand, \package{xlop} +package did what we have ask, that is, obtain two digits (maximum) for +the quotient. + +The inline mode differ with zero remainder or not and with the type of +division (classical or euclidean). +\begin{SideBySideExample} + \opdiv[style=text]{3.14}{2}\par + \opdiv[style=text]{3.14}{3}\par + \opidiv[style=text]{314}{2}\par + \opidiv[style=text]{314}{3} +\end{SideBySideExample} +Note the use of \parameter{equalsymbol} or \parameter{approxsymbol} +parameter according to the case. Note also that \package{xlop} +displays results with floor, not with round. We will see how obtain a +round in section~\ref{sec:Operations evoluees}. + +For inline mode of \verb+\opdiv+, \package{xlop} take account of +\parameter{maxdivstep}. It means that we can obtain results very false +with too small values of this parametrer and, unlike with display mode +division, inline mode don't allow to understand what is wrong. +\begin{SideBySideExample} + \opdiv[maxdivstep=2,style=text] + {1248}{3} +\end{SideBySideExample} +In addition, if the last remainder is zero, we obtain a must: +\begin{SideBySideExample} + \opdiv[maxdivstep=1,style=text] + {1208}{3} +\end{SideBySideExample} +because there is no approximation at all! + +A classical division can stop with period detection. For that, you +have just to give the value \texttt{true} for the \parameter{period} +parameter\index{division!period}. +\begin{SideBySideExample} + \opdiv[period]{100}{3} +\end{SideBySideExample} + +To avoid comparizons between each remainder with all previous +remainder, \package{xlop} calculates immediatly the period +length. That allows to process only one comparizon for each step, then +to have a much more efficient process.\footnote{Thanks to Olivier + Viennet about mathematic precisions that allows to implement these + calculations.} Unfortunately, these calculations are made with +numbers that are directly accesible to \TeX{}. As consequence, you +can't use operand with absolute value greater than +$\left\lfloor\frac{2^{31}-1}{10}\right\rfloor = 214748364$. + +In order to avoid too long calculations, \package{xlop} don't process +beyond the value of \parameter{safedivstep} parameter in division with +period. Its default value is~50. However, \package{xlop} package show +this problem. For example, if you ask for such a division with the +code: +\begin{Verbatim}[xrightmargin=0pt,frame=none] + \opdiv[period]{1}{289} +\end{Verbatim} +you obtain the warning message: +\begin{Verbatim}[xrightmargin=0pt,frame=none] + xlop warning. Period of division is too big (272 > safedivstep). + Division will stop before reach it. + See documentation for further information. +\end{Verbatim} +which indicates that this division period is~272 and that it can be +achieved because of the \texttt{safedivstep} value. + +The inline mode for division with period have some particularities. +\begin{SideBySideExample} + \opdiv[period,style=text]{150}{7} +\end{SideBySideExample} +We obtain an equality rather than an approximation, there is a rule +under the period, and there is ellipsis after the period. All these +components can be configured. The equality symbol is given +by the \parameter{equalsymbol} parameter (default value is +\verb+{$=$}+). The rule thickness is given by +the \parameter{hrulewidth} parameter (default value is +\texttt{0.4pt}). The vertical offset of this rule is given +by \parameter{vruleperiod} parameter (default value is \texttt{-0.2}) +which indicates a vertical offset taking \verb+\oplineheight+ as +unit. The ellipsis are given by the +parameter \parameter{afterperiodsymbol} (default value +\verb+$\ldots$+). +\begin{SideBySideExample} + \opdiv[period,style=text, + equalsymbol=$\approx$, + hrulewidth=0.2pt, + vruleperiod=0.7, + afterperiodsymbol=] + {150}{7} +\end{SideBySideExample} + +\subsection{Other Features} +\label{subsec:Elements supplementaires} +Displayed divisions can include successive substractions which allow +remainder calculations. For \package{xlop}, the numbers which are +substracted are intermediary numbers, so the different ways to +represent substractions use \parameter{displayintermediary} parameter +see for multiplication. The default value, valeur \texttt{none}, don't +display any substraction; the value \texttt{all} displays all the +substractions, and the value \texttt{nonzero} displays substractions +with non-zero numbers +\begin{CenterExample}[xrightmargin=0pt] + \opdiv[displayintermediary=none,voperation=top] + {251}{25}\quad + \opdiv[displayintermediary=nonzero,voperation=top] + {251}{25}\quad + \opdiv[displayintermediary=all,voperation=top] + {251}{25} +\end{CenterExample} + +When we write a display division, we can draw a ``bridge'' over the +part of dividend which is taken in count for the first step of +calculation. The \package{xlop} package allow to draw this symbol +thanks to the boolean parameter \parameter{dividendbridge} (default +value is \texttt{false}). +\begin{SideBySideExample} + \opdiv[dividendbridge]{1254}{30} +\end{SideBySideExample} + +\subsection{Non Integer Numbers and Negative Numbers} +\label{subsec:Nombres non entiers et negatifs} +The \parameter{shiftdecimalsep} parameter governs non integer operands +aspect/ Its default value is \texttt{both} which indicates that +decimal separator is shifted in order to obtain integer divisor and +integer dividend. The value \texttt{divisor} indicates that there is +the shifting that allows an integer divisor. The value \texttt{none} +indicates that there isn't any shifting. +\begin{CenterExample}[xrightmargin=0pt] + \opdiv[shiftdecimalsep=both]{3.456}{25.6}\quad + \opdiv[shiftdecimalsep=divisor]{3.456}{25.6}\quad + \opdiv[shiftdecimalsep=none]{3.456}{25.6} +\end{CenterExample} + +Parameter \parameter{strikedecimalsepsymbol} gives the symbol used +to show the old place of decimal separator when this one is +shifted. The default value is empty, that is, there isn't any +symbol. This explain why you don't see anything on previous examples. +\begin{CenterExample}[xrightmargin=0pt] + \opset{strikedecimalsepsymbol={\rlap{,}\rule[-1pt]{3pt}{0.4pt}}} + \opdiv[shiftdecimalsep=both]{3.456}{25.6}\quad + \opdiv[shiftdecimalsep=divisor]{3.456}{25.6}\quad + \opdiv[shiftdecimalsep=none]{3.456}{25.6} +\end{CenterExample} + +When there is a non empty symbol for the striked decimal separator, it +is possible to have non-significant zeros in operands. +\begin{SideBySideExample} + \opdiv[shiftdecimalsep=divisor, + strikedecimalsepsymbol=% + \hspace{-3pt}\tiny$\times$] + {0.03456}{2.56} +\end{SideBySideExample} + +We have already seen that \macro{opidiv} macro gives integer +quotient. This is true even with non integer operands. It is somewhere +strange to perform an euclidian division with non integer operands. The +\macro{opidiv} macro will be strict about the +presentation. Parameters \parameter{maxdivstep}, \parameter{safedivstep}, +and \parameter{period} haven't any effect, as +for \parameter{shiftdecimalsep} parameter since operands are changed +to integer ones. +\begin{SideBySideExample} + \opidiv[strikedecimalsepsymbol=% + \hspace{-3pt}\tiny$\times$] + {34.57}{7} +\end{SideBySideExample} + +When operands are negative, the inline \macro{opidiv} numbers is +different from the displayed \macro{opidiv} ones. Remainder will be +between zero (include) and absolute value of divisor (exclude). +\begin{SideBySideExample} + \opdiv[style=text]{124}{7}\par + \opidiv[style=text]{124}{7}\par + \opidiv[style=text]{124}{-7}\par + \opidiv[style=text]{-124}{7}\par + \opidiv[style=text]{-124}{-7} +\end{SideBySideExample} + +This condition for remainder is valid even with non integer divisor. +\begin{SideBySideExample} + \opidiv[style=text]{1.24}{0.7}\par + \opidiv[style=text]{1.24}{-0.7}\par + \opidiv[style=text]{-1.24}{0.7}\par + \opidiv[style=text]{-1.24}{-0.7} +\end{SideBySideExample} + +\chapter{Other Commands} +\label{chap:Autres commandes} +\section{Starred Macros} +\label{sec:Macros etoilees} +The five macros seen in previous chapter have a starred version. These +starred macros perform the calculation and don't display +anything. Result is record in a variable given as argument. + +Since these commands don't display anything, parameters don't make +sens and aren't allowed for \macro{opadd*}, \macro{opsub*}, +\macro{opmul*}, and \macro{opidiv*}. In the other hand, +parameters \parameter{maxdivestep}, \parameter{safedivstep}, +and \parameter{period} influence calculations, then \macro{opdiv*} +macro accepts an optional argument to take account of them. +\begin{SideBySideExample} + \opmul*{2}{2}{a}% + \opmul*{a}{a}{a}\opmul*{a}{a}{a}% + \opadd[style=text]{a}{1} +\end{SideBySideExample} +For macros \macro{opdiv} and \macro{opidiv}, there are two extra +arguments to record quotient and final remainder. +\begin{SideBySideExample} + \opdiv*[maxdivstep=1]{-88}{16}{q}{r}% + \opmul*{q}{16}{bq}% + \opmul[style=text]{16}{q}\par + \opadd[style=text]{bq}{r} +\end{SideBySideExample} + +\section{Input-Output} +\label{sec:Entree-sorties} +The \macro{opcopy} macro copies its first argument into its second +one. Then, the first argument is a number write in decimal form or +\emph{via} a variable, whereas the second one is a variable name. + +The \macro{opprint} macro displays its argument. The following example +uses the counter \macro{time} which indicates numbers of minutes since +midnight. +\begin{SideBySideExample} + \opidiv*{\the\time}{60}{h}{m}% + It is \opprint{h}~hours + \opprint{m}~minutes +\end{SideBySideExample} +We will see at section~\ref{sec:Comparaisons} how to improve this +example with tests. + +The \macro{opdisplay} macro also displays a number but here, each +figure is in a box. The width of this box is given +by \parameter{columnwidth} and the height of this box is given +by \parameter{lineheight}. Style is specified by the first +argument. This macro accepts an optional argument in order to give a +specific style for individual figures. +\begin{SideBySideExample} + \opdisplay[resultstyle.1=\bfseries, + resultstyle.-2=\bfseries] + {resultstyle}{129.192} +\end{SideBySideExample} +Macros \macro{oplput} and \macro{oprput} allow to put anything +anywhere. The syntax of both of them is different from the other ones +of \package{xlop} since the place is indicated with coordinates +between parenthesis. The coordinates use \macro{opcolumnwidth} and +\macro{oplineheight} as units. Then user is able to build his own +``operations''. +\begin{SideBySideExample} + \psset{xunit=\opcolumnwidth, + yunit=\oplineheight}% + \psgrid[subgriddiv=1,gridlabels=7pt, + griddots=5](0,1)(10,-2) + \oplput(2,0){Hello} + \oprput(8,-1){world!} + $\bullet$ +\end{SideBySideExample} +On example above, note that these macros don't move the reference +point. As a precaution, they kill the trailing space and then, there +is no need to protect the end of line with a \verb+%+. + +Macros \macro{ophline} and \macro{opvline} complete the previous ones +to give all the tools the user needs to build its own operations. +\macro{ophline} allows to draw a horizontal rule; its length is given +by the parameter after coordinates. \macro{opvline} does the same for +vertical rules. Remember that parameters \parameter{hrulewidth} +and \parameter{vrulewidth} indicate the thickness of these rules. +\begin{CenterExample}[xrightmargin=0pt] + \par\vspace{2\oplineheight} + \oplput(1,2){O}\oplput(2,2){N}\oplput(3,2){E} + \oplput(0,1.5){$+$} + \oplput(1,1){O}\oplput(2,1){N}\oplput(3,1){E} + \ophline(0,0.8){4} + \oplput(1,0){T}\oplput(2,0){W}\oplput(3,0){O} +\end{CenterExample} + +Macro \macro{opexport}\refstepcounter{stuff}\label{macro-opexport} +allow to export a number in a macro. It's an extra to version~0.23 +which is very usefull to exchange datas between \package{xlop} and the +outside world. The first argument is a number in the \package{xlop} +sense, that is, either a number write with figures, or a variable +name. The number is translated in a form directly acceptable for +\TeX{} and hold in the second argument which should be a macro +name. However, note that decimal separator will be the one specified +by \parameter{decimalsepsymbol} (without its possible braces). +\begin{SideBySideExample} + \opmul*{5}{3.141592654}{F} + \opexport{F}{\fivepi} + \texttt{\meaning\fivepi} +\end{SideBySideExample} +We can use this macro to typeset numbers calculated by \package{xlop} +in an array with a decimal alignment, or to initialize a counter or a +length (don't forget the unit in the last case). + +\section{Figures of Numbers} +\label{sec:Chiffres d'un nombre} +Macros \macro{opwidth}, \macro{opintegerwidth}, and +\macro{opdecimalwidth} indicate number of digits of the whole number, +of its integer part, of its decimal part respectively. The first +argument is the examined number and the second one indicates the +variable where result will be record. +\begin{SideBySideExample} + \opcopy{123456.1234}{a}% + \opwidth{a}{na}% + \opintegerwidth{a}{ia}% + \opdecimalwidth{a}{da}% + \opprint{a} is written with + \opprint{na} figures (\opprint{ia} in + the integer part and \opprint{da} in + the decimal part). +\end{SideBySideExample} + +Macro \macro{opunzero} delete all the non-significant +zeros\index{non-significant zero} of the number passed as argument. +\begin{SideBySideExample} + \opcopy{00150.00250}{a}% + Before : \opprint{a}\par + \opunzero{a}% + After : \opprint{a} +\end{SideBySideExample} + +Macros \macro{integer} and \macro{opdecimal} give the integer part and +the decimal part of a number respectively. +\index{number!integer part}\index{integer part}% +\index{number!decimal part}\index{decimal part}% +First argument is the number to process, and the second one is the +variable name which hold the result. +\begin{SideBySideExample} + \opcopy{-37.69911}{a}% + \opinteger{a}{ia}% + \opdecimal{a}{da}% + Integer part: \opprint{ia}\par + Decimal part: \opprint{da} +\end{SideBySideExample} + +Six macros allow to write or read a figure of a number. You can read +or read a figure according to its place in the whole number, or in the +integer part, or in the decimal part. Figures for whole number and for +decimal part are numbered from right to left, figures for integer part +are numbered from left to right. For instance, with the number +1234.56789, the second figure is 8, the second figure of the integer +part is 3, and the second figure of the decimal part is 6. It is now +easy to guess the rôle of the six next macros: +\begin{itemize} +\item \parameter{opgetdigit} ; +\item \parameter{opsetdigit} ; +\item \parameter{opgetintegerdigit} ; +\item \parameter{opsetintegerdigit} ; +\item \parameter{opgetdecimaldigit} ; +\item \parameter{opsetdecimaldigit} ; +\end{itemize} +Syntax is the same for these macros. The first argument is the +processed number (reading or writting), the second one is the index of +te figure, and the third one is the variable name which hold the +result (figure read or changed number). If index is out of the range, +the reading macros give \texttt{0} as result and writing macros +extend the number in order to reach this index (for that, zero will be +created in new slots). + +\section{Comparisons} +\label{sec:Comparaisons} +When you want complex macros, often you need to realize tests. For +that, \package{xlop} gives the macro \macro{opcmp}. The two +arguments are numbers and this macro setup the tests \macro{ifopgt}, +\macro{ifopge}, \macro{ifople}, \macro{ifoplt}, \macro{ifopeq}, and +\macro{ifopneq} to indicate that first operand is greater, greater or +equal, less or equal, less, equal, or different to the second operand +respectively. + +For technical reasons, \package{xlop} give global definitions for the +six tests above. Then, they are not protected by groups. Since these +tests are used by many \package{xlop} macros, you must \emph{always} +use tests \verb+\ifop...+ immediately after \macro{opcmp}, or, at +least, before any use of a \package{xlop} macro. Otherwise, there will +be bugs hard to fix! + +Let's resume the hour display macro see at +section~\ref{sec:Entree-sorties}. But now, we check if argument is +between 0 (include) and 1440 (exclude), then we process tests in order +to know if ``hour'' is plural or not, as for ``minute''. + +\begin{CenterExample}[xrightmargin=0pt] + \newcommand\hour[1]{% + \opcmp{#1}{0}\ifopge + \opcmp{#1}{1440}\ifoplt + \opidiv*{#1}{60}{h}{m}% + \opprint{h} hour% + \opcmp{h}{1}\ifopgt + s% + \fi + \opcmp{m}{0}\ifopneq + \space\opprint{m} minute% + \opcmp{m}{1}\ifopgt + s% + \fi + \fi + \fi\fi + } + \hour{60} -- \hour{1080} -- \hour{1081} -- \hour{1082} +\end{CenterExample} + +\section{Advanced Operations} +\label{sec:Operations evoluees} +The macros left to be examined are either internal macros and which it +will be a shame to keep private , or macro asked for users. + +Internal macros are \macro{opgcd}\index{gcd} which gives gcd of two +numbers and macro \macro{opdivperiod}\index{division!period} which +gives the period length of quotient of two numbers. For efficiency +reason, these macros don't use \package{xlop} number, they rather use +numbers directly understand by \TeX{}. There are two consequences: the +numbers can't be greater than \texttt{2147483647} for \macro{opgcd}; +it can't be greater than \texttt{214748364} for +\macro{opdivperiod}. A warning is displayed for an overflow. Result is +put in the third parameter. + +There is also some checks on the two first parameters: a gcd mustn't +have null argument; length of period can't be processed with null +quotient. Futhermore, if an argument is a non integer number, only the +integer part will be take account. +\begin{SideBySideExample} + \opcopy{5376}{a}% + \opcopy{2304}{b}% + \opgcd{a}{b}{gcd(ab)}% + $\gcd(\opprint{a},\opprint{b}) = + \opprint{gcd(ab)}$ +\end{SideBySideExample} +You can play and find long period of divisions. Without going into +mathematical details, square of prime numbers are good choices. For +instance with $257^2=66049$ you obtain: +\begin{SideBySideExample} + \opdivperiod{1}{66049}{p}% + $\frac{1}{66049}$ have a period + of length $\opprint{p}$. +\end{SideBySideExample} + +With macros \macro{opcastingoutnines}\index{casting out of nines} and +\macro{opcastingoutelevens}\index{casting out of elevens} you can +build casting out of nines and casting out of elevens. \package{xlop} +don't typeset directly these ``operations'' since they need diagonal +rules, and then, need some particular packages. In fact, macro +\macro{opcastingoutnines} calculates the sum modulo~9 of first +argument digits and put the result in second argument. Macro +\macro{opcastingoutelevens} calculates the sum modulo~11 of the even +rank digits of first argument, calculates the sum moldulo~11 of the +odd rank digits of first argument, and calculates the difference of +these two sums. +\begin{SideBySideExample} + \newcommand\castingoutnines[3]{% + \opcastingoutnines{#1}{cna}% + \opcastingoutnines{#2}{cnb}% + \opmul*{cna}{cnb}{cna*cnb} + \opcastingoutnines{cna*cnb}{cna*cnb}% + \opcastingoutnines{#3}{cn(a*b)}% + \begin{pspicture}(-3.5ex,-3.5ex)% + (3.5ex,3.5ex) + \psline(-3.5ex,-3.5ex)(3.5ex,3.5ex) + \psline(-3.5ex,3.5ex)(3.5ex,-3.5ex) + \rput(-2.75ex,0){\opprint{cna}} + \rput(2.75ex,0){\opprint{cnb}} + \rput(0,2.75ex){\opprint{cna*cnb}} + \rput(0,-2.75ex){\opprint{cn(a*b)}} + \end{pspicture} + } + \castingoutnines{157}{317}{49669} +\end{SideBySideExample} +In passing, this example shows that $157\times317\neq49669$! The right +operation is \opmul[style=text]{157}{317}. + +The two next macros are very simple. We have \macro{opneg} which +calculates the opposite of its first argument and store it in the +variable indicated by the second argument. We have also \macro{opabs} +which does the same with absolute value. + +Macro \macro{oppower} calculates integer powers of numbers. This macro +has three parameters. The third one store the first argument to the +power of the second argument. When the first argument is zero: if the +second argument is zero, result is~1; if the second argument is +positive, result is~0; if the second argument is negative, there is an +error. There isn't any limitation on first parameter. This leads to +some problems, for instance: +\begin{CenterExample}[xrightmargin=0pt] + \opcopy{0.8}{a}\opcopy{-17}{n}% + \oppower{a}{n}{r}% + $\opprint{a}^{\opprint{n}} = \opprint{r}$ +\end{CenterExample} +With $0.7$ rather than $0.8$, problem is worse: +\begin{CenterExample}[xrightmargin=0pt] + \opcopy{0.7}{a}\opcopy{-8}{n}% + \oppower{a}{n}{r}% + \opdecimalwidth{r}{dr} + $\opprint{a}^{\opprint{n}}$ has \opprint{dr} + figures after dot. +\end{CenterExample} +In fact, when exponent is negative, \emph{first} \package{xlop} +calulates inverse of the number and \emph{after that}, it calculates +the power with opposite of the exponent. In this example, if we had +left $-17$ rather than $-8$, then there will be a capacity overflow +capacity of \TeX{}. + +Three macros allow a control about precision. They allow to +approximate a number giving the rank of the approximation. There are +\macro{opfloor}, \macro{opceil}, and \macro{opround}. They need three +parameters which are (in order): start number, rank of approximation, +variable name to store the result. + +Rank is an integer value giving number of digits after decimal +separator which must be present. If this rank is negative, +approximation will be done before the decimal separator. If rank +is positive and indicates more digits than decimal part has, then +zeros will be added. If rank is negative and indicates more digits +than integer part has, then approximation will be locked in order to +give the first digit of the number at least. + +Here is a summary table which allow to understand how these macros +work. +\begin{center} + \opcopy{3838.3838}{a} + \begin{tabular}{|r|l|l|l|} + \hline + \multicolumn{4}{|c|}{\textbf{\texttt{\textbackslash + op\ldots{}\{3838.3838\}\{n\}\{r\}}}}\\\hline + \multicolumn{1}{|c|}{\textbf{\texttt{n}}} & + \multicolumn{1}{c|}{\textbf{\texttt{floor}}} & + \multicolumn{1}{c|}{\textbf{\texttt{ceil}}} & + \multicolumn{1}{c|}{\textbf{\texttt{round}}} \\\hline + \opcopy{6}{n}$\opprint{n}$ & + \opfloor{a}{n}{r}$\opprint{r}$ & + \opceil{a}{n}{r}$\opprint{r}$ & + \opround{a}{n}{r}$\opprint{r}$ \\ + \opcopy{4}{n}$\opprint{n}$ & + \opfloor{a}{n}{r}$\opprint{r}$ & + \opceil{a}{n}{r}$\opprint{r}$ & + \opround{a}{n}{r}$\opprint{r}$ \\ + \opcopy{3}{n}$\opprint{n}$ & + \opfloor{a}{n}{r}$\opprint{r}$ & + \opceil{a}{n}{r}$\opprint{r}$ & + \opround{a}{n}{r}$\opprint{r}$ \\ + \opcopy{0}{n}$\opprint{n}$ & + \opfloor{a}{n}{r}$\opprint{r}$ & + \opceil{a}{n}{r}$\opprint{r}$ & + \opround{a}{n}{r}$\opprint{r}$ \\ + \opcopy{-1}{n}$\opprint{n}$ & + \opfloor{a}{n}{r}$\opprint{r}$ & + \opceil{a}{n}{r}$\opprint{r}$ & + \opround{a}{n}{r}$\opprint{r}$ \\ + \opcopy{-2}{n}$\opprint{n}$ & + \opfloor{a}{n}{r}$\opprint{r}$ & + \opceil{a}{n}{r}$\opprint{r}$ & + \opround{a}{n}{r}$\opprint{r}$ \\ + \opcopy{-6}{n}$\opprint{n}$ & + \opfloor{a}{n}{r}$\opprint{r}$ & + \opceil{a}{n}{r}$\opprint{r}$ & + \opround{a}{n}{r}$\opprint{r}$ \\\hline + \end{tabular} + \opcopy{-3838.3838}{a} + \begin{tabular}{|r|l|l|l|} + \hline + \multicolumn{4}{|c|}{\textbf{\texttt{\textbackslash + op\ldots{}\{-3838.3838\}\{n\}\{r\}}}}\\\hline + \multicolumn{1}{|c|}{\textbf{\texttt{n}}} & + \multicolumn{1}{c|}{\textbf{\texttt{floor}}} & + \multicolumn{1}{c|}{\textbf{\texttt{ceil}}} & + \multicolumn{1}{c|}{\textbf{\texttt{round}}} \\\hline + \opcopy{6}{n}$\opprint{n}$ & + \opfloor{a}{n}{r}$\opprint{r}$ & + \opceil{a}{n}{r}$\opprint{r}$ & + \opround{a}{n}{r}$\opprint{r}$ \\ + \opcopy{4}{n}$\opprint{n}$ & + \opfloor{a}{n}{r}$\opprint{r}$ & + \opceil{a}{n}{r}$\opprint{r}$ & + \opround{a}{n}{r}$\opprint{r}$ \\ + \opcopy{3}{n}$\opprint{n}$ & + \opfloor{a}{n}{r}$\opprint{r}$ & + \opceil{a}{n}{r}$\opprint{r}$ & + \opround{a}{n}{r}$\opprint{r}$ \\ + \opcopy{0}{n}$\opprint{n}$ & + \opfloor{a}{n}{r}$\opprint{r}$ & + \opceil{a}{n}{r}$\opprint{r}$ & + \opround{a}{n}{r}$\opprint{r}$ \\ + \opcopy{-1}{n}$\opprint{n}$ & + \opfloor{a}{n}{r}$\opprint{r}$ & + \opceil{a}{n}{r}$\opprint{r}$ & + \opround{a}{n}{r}$\opprint{r}$ \\ + \opcopy{-2}{n}$\opprint{n}$ & + \opfloor{a}{n}{r}$\opprint{r}$ & + \opceil{a}{n}{r}$\opprint{r}$ & + \opround{a}{n}{r}$\opprint{r}$ \\ + \opcopy{-6}{n}$\opprint{n}$ & + \opfloor{a}{n}{r}$\opprint{r}$ & + \opceil{a}{n}{r}$\opprint{r}$ & + \opround{a}{n}{r}$\opprint{r}$ \\\hline + \end{tabular} +\end{center} + +\index{complex expression|(} +The very last macro we have to study is \macro{opexpr}. It calculates +a complex expression. This macro needs two parameters: the first one +is the expression in infix form (the natural one for human), the +second one is the variable name where the result is stored. + +Initially, expression must have been polish one (for instance, +notation used on old HP calculator, or PostScript language), but +another work with Christophe Jorssen has given the actual form for +expression in \package{xlop}, more pleasant for users. + +Formulas accept usual arithmetic operators \texttt{+}, \texttt{-}, +\texttt{*}, and \texttt{/}. They accept also \texttt{:} operator for +euclidian division, and \verb+^+ for power. The \texttt{-} operator +has both rôle of substraction and unary operator for opposite. The +\texttt{+} has also these rôles, here the unary operator do\dots{} +nothing! Operands are written in decimal form or \emph{via} variable +name. However, \macro{opexpr} introduces a restriction about variable +name since variable names must be different to function names +recognized by \macro{opexpr}. Accessible functions are: +\begin{itemize} +\item \texttt{abs(a)} ; +\item \texttt{ceil(a,i)} ; +\item \texttt{decimal(a)} ; +\item \texttt{floor(a,i)} ; +\item \texttt{gcd(a,b)} ; +\item \texttt{integer(a)} ; +\item \texttt{mod(a,b)} gives result of \texttt{a} modulo + \texttt{b} ; +\item \texttt{rest(a,b)} gives remainder of \texttt{a} divide by + \texttt{b} (difference between remainider and modulo is the same as + between non euclidian division and euclidian division); +\item \texttt{round(a,i)}. +\end{itemize} +where functions that aren't listed above ask the matching macros. +(function \texttt{xxx} calls macro \verb+\opxxx+) For functions +\texttt{ceil}, \texttt{floor}, and \texttt{round}, the number +\texttt{i} indicates rank for approximation. + +Macro \macro{opexpr} accept optional argument since it can realize +division which can be controlled +by \parameter{maxdivstep},\parameter{safedivstep}, +and \parameter{period} parameters. Our first example is quite basic: +\begin{CenterExample}[xrightmargin=0pt] + \opexpr{3--gcd(15*17,25*27)*2}{r}% + $3--\gcd(15\times17,25\times27)\times2 = \opprint{r}$ +\end{CenterExample} + +Here is another example that shows that datas can come from a macro: +\begin{CenterExample}[xrightmargin=0pt] + \newcommand\try{2}% + \opexpr{\try+1/ + (\try+1/ + (\try+1/ + (\try+1/ + (\try+1/ + (\try)))))}{r} + Continued fraction of base $u_n=2$ equal \opprint{r} at rank~5. +\end{CenterExample} +\index{complex expression|)} + +\appendix +\chapter{Short Summary} +\label{chap:Aide-mémoire} +\section{Compilation times} +\label{sec:Temps de compilation} +Compilation times was measured on a computer with +processor Pentium II 600\,MHz, RAM 256\,MB, on linux system (Debian +woody).\footnote{In fact, these measures was done in 2004, when the + 0.2 version was released. Author is somewhere lasy and he doesn't + measure with his new computer (more efficient)!}. The principle is +to do a minimal file \texttt{.tex}. The general canvas is: +\begin{verbatim} + \input xlop + \count255=0 + \loop + \ifnum\count255<1000 + <operation to test> + \advance\count255 by1 + \repeat + \bye +\end{verbatim} +Compilation time with \verb+<operation to test>+ empty was substract +from the others test. Only the user time was take account. Results are +given in millisecond and should be read with great precautions. + +\index{compilation time|(}\index{time (calculation)|(}% +Next table gives operation times in milliseconds. Operands used had +decimal notation but some trails with variable has shown that times +was very closed. + +First line indicates the numbers of digits for both operands. +Operands were build like this: +\begin{itemize} +\item $\mathrm{A} = 1$ et $\mathrm{B} = 9$ for one digit; +\item $\mathrm{A} = 12$ et $\mathrm{B} = 98$ for two digits; +\item $\mathrm{A} = 123$ et $\mathrm{B} = 987$ for three digits; +\item $\mathrm{A} = 12345$ et $\mathrm{B} = 98765$ for five digits; +\item $\mathrm{A} = 1234567890$ et $\mathrm{B} = 9876543210$ for ten + digits; +\item $\mathrm{A} = 12345678901234567890$ et $\mathrm{B} = + 98765432109876543210$ for twenty digits; +\end{itemize} +Here is results, some comments follow: + +\bigskip\noindent\hbox to\linewidth{\hss + \begin{tabular}{|r|*{6}{l|}} + \cline{2-7} + \multicolumn{1}{l|}{} & + \multicolumn{1}{c|}{1} & + \multicolumn{1}{c|}{2} & + \multicolumn{1}{c|}{3} & + \multicolumn{1}{c|}{5} & + \multicolumn{1}{c|}{10} & + \multicolumn{1}{c|}{20} \\\hline + \verb+\opadd*{A}{B}{r}+ & + 1.1 & 1.4 & 1.6 & 2.1 & 3.3 & 5.8 \\\cline{2-7} + \verb+\opadd*{B}{A}{r}+ & + 1.1 & 1.4 & 1.6 & 2.1 & 3.3 & 5.8 \\\hline + \verb+\opsub*{A}{B}{r}+ & + 1.7 & 2.1 & 2.4 & 3.0 & 4.8 & 8.3 \\\cline{2-7} + \verb+\opsub*{B}{A}{r}+ & + 1.5 & 1.7 & 2.0 & 2.6 & 4.0 & 7.0 \\\hline + \verb+\opmul*{A}{B}{r}+ & + 4.6 & 6.3 & 8.2 & 12.8 & 29.9 & 87.0 \\\cline{2-7} + \verb+\opmul*{B}{A}{r}+ & + 5.0 & 6.6 & 8.5 & 13.2 & 30.3 & 87.8 \\\hline + \verb+\opdiv*{A}{B}{q}{r}+ & + 46.4 & 53.8 & 53.8 & 64.3 & 85.8 & 124.7 \\\cline{2-7} + \verb+\opdiv*{B}{A}{q}{r}+ & + 12.4 & 48.9 & 55.7 & 58.6 & 72.8 & 111.0 \\\hline + \verb+\opdiv*[maxdivstep=5]{A}{B}{q}{r}+ & + 26.8 & 30.0 & 32.6 & 37.6 & 49.5 & 73.5 \\\cline{2-7} + \verb+\opdiv*[maxdivstep=5]{B}{A}{q}{r}+ & + 12.4 & 29.1 & 32.6 & 35.2 & 43.3 & 67.9 \\\hline + \verb+\opidiv*{A}{B}{q}{r}+ & + 10.8 & 12.2 & 13.5 & 16.0 & 22.3 & 35.5 \\\cline{2-7} + \verb+\opidiv*{B}{A}{q}{r}+ & + 11.6 & 13.0 & 14.2 & 16.6 & 23.0 & 36.7 \\\hline + \verb+\opidiv*{A}{2}{q}{r}+ & + 10.7 & 12.0 & 15.3 & 22.3 & 42.9 & 83.0 \\\hline + \end{tabular} + \hss +} +\par\bigskip +It is normal that inversion of operands don't have sensible influence +for addition. Then, it could be strange that there is influence for +substraction. In fact, when the second operand is bigger than the +second one, there is additional process (double inversion, operation +on the sign of the result). + +It is normal that division time is greater than the multiplication +one. It could be abnormal that division seems catch up! In fact, the +multiplication complexity grows quickly with the operand length. In +the other hand, division complexity is stopped +by \parameter{maxdivstep} parameter. It is clear on example where +there is only five steps. + +Some results seems odd. For instance \verb+\opdiv*{9}{1}{q}{r}+ is +very fast. These is due to the one digit quotient. +\verb+\opdiv*{123}{987}{q}{r}+, even more odd, is rather fast. Here, +explanation is quite subtle: this is due to many zeros in the +quotient. + +When operands have comparable length, euclidian division is much +faster than non euclidian one. This is because quotient has few +digits (only one for all the numbers \texttt{A} and \texttt{B}). The +last line of the table is more relevant for this operation time. + +All these remarks are written to put the emphasis on the difficulty to +evaluate the compilation time: it depends on too many parameters. On +the other hand, this table give a pretty good idea of what can be +expected. +\index{compilation time|)}\index{time (calculation)|)}% + +\newpage +\section{Macros List} +\label{sec:Liste des macros} +\index{macros!table of|(}% +\noindent\begin{longtable}{|l|p{6.3cm}|} + \hline + \multicolumn{1}{|c|}{\textbf{Macro}} & + \multicolumn{1}{c|}{\textbf{Description}} \\\hline\hline + \endfirsthead + \hline + \multicolumn{1}{|c|}{\textbf{Macro}} & + \multicolumn{1}{c|}{\textbf{Description}} \\\hline\hline + \endhead + \hline + \multicolumn{2}{|c|}{$\ldots$ to be continued $\ldots$}\\ + \hline + \endfoot + \hline + \endlastfoot + \verb+\opabs{n}{N}+ & + \verb+N+ stores the absolute value of \verb+n+. \\\hline + \verb+\opadd[P]{n1}{n2}+ & + Displays result of \verb-n1+n2-. \\\hline + \verb+\opadd*{n1}{n2}{N}+ & + Calcules \verb-n1+n2- and put result in \verb+N+. \\\hline + \verb+\opcastingoutelevens{n}{N}+ & + Calcules difference (modulo 11) of sum of rank odd digits and sum of + rank even digits of \verb+n+ and put the result in \verb+N+.\\\hline + \verb+\opcastingoutnines{n}{N}+. & + Calcules sum modulo 9 of digits of \verb+n+ and put result in + \verb+N+. \\\hline + \verb+\opceil{n}{T}{N}+ & + Places in \verb+N+ the approximation (ceiling) of \verb+n+ to rank + \verb+T+. \\\hline + \verb+\opcmp{n1}{n2}+ & + Compares numbers \verb+n1+ and \verb+n2+ and setup the tests + \verb+\ifopeq+, \verb+\ifopneq+, \verb+\ifopgt+, \verb+\ifopge+, + \verb+\ifople+ et \verb+\ifoplt+. \\\hline + \verb+\opcopy{n}{N}+ & + Copy number \verb+n+ in \verb+N+. \\\hline + \verb+\opdecimal{n}{N}+ & + Copy decimal part (positive integer number) of \verb+n+ in + \verb+N+. \\\hline + \verb+\opdecimalwidth{n}{N}+ & + \verb+N+ stores the width of decimal part of number \verb+n+. + \\\hline + \verb+\opdisplay[P]{S}{n}+ & + Display number \verb+n+ width style \verb+S+ puting each figure in a + box which have a width of \verb+\opcolumnwidth+ and a height of + \verb+\oplineheight+. \\\hline + \verb+\opdiv[P]{n1}{n2}+ & + Display result of n1/n2. \\\hline + \verb+\opdiv*[P]{n1}{n2}{N1}{N2}+ & + Calculates \verb+n1/n2+, put the quotient in \verb+N1+ and the + remainder in \verb+N2+. \\\hline + \verb+\opdivperiod{T1}{T2}{N}+ & + Calculates length of period of \verb+T1+ divide by \verb+T2+ and put + the result in \verb+N+. \\\hline + \verb+\opexport[P]{n}\cmd+ & + Copy number \verb+n+ in macro \verb+\cmd+. \\\hline + \verb+\opexpr[P]{F}{N}+ & + Evaluates formula \texttt{F} and put the final result in + \texttt{N}. \\\hline + \verb+\opfloor{n}{T}{N}+ & + Put in \verb+N+ the apprimation (floor) of \verb+n+ at rank + \verb+T+. \\\hline + \verb+\opgcd{T1}{T2}{N}+ & + Calculates gcd of \verb+T1+ and \verb+T2+ and put result in + \verb+N+. \\\hline + \verb+\opgetdecimaldigit{n}{T}{N}+ & + Build the number \verb+N+ with the only digit in slot + \verb+T+ of decimal part of \verb+n+. \\\hline + \verb+\opgetdigit{n}{T}{N}+ & + Build the number \verb+N+ with the only digit in slot + \verb+T+ of number \verb+n+. \\\hline + \verb+\opgetintegerdigit{n}{T}{N}+ & + Build the number \verb+N+ width the only digit in slot + \verb+T+ of integer part of \verb+n+. \\\hline + \verb+\ophline(T1,T2){T3}+ & + Draw a horizontal rule of length \verb+T3+, of thickness + \verb+hrulewidth+, and which begin at \verb+(T1,T2)+ in relation to + reference point. \\\hline + \verb+\opidiv[P]{n1}{n2}+ & + Display the result of \verb+n1/n2+. (euclidian division, that is, + with integer division) \\\hline + \verb+\opidiv*{n1}{n2}{N1}{N2}+ & + Calculates \verb+n1/n2+ (euclidian division), put quotient + (integer) in \verb+N1+ and remainder (between 0 (include) and + \verb+|n2|+ (exclude)) in \verb+N2+. \\\hline + \verb+\opinteger{n}{N}+ & + Copy integer part (positive integer number) of \verb+n+ + in \verb+N+. \\\hline + \verb+\opintegerwidth{n}{N}+ & + Number \verb+N+ stores the width of integer part of number \verb+n+. + \\\hline + \verb+\oplput(T1,T2){<object>}+ & + Put \verb+<object>+ to the right of the point with coordinates + \verb+(T1,T2)+ in relation to reference point. \\\hline + \verb+\opmul[P]{n1}{n2}+ & + Display result of \verb+n1*n2+. \\\hline + \verb+\opmul*{n1}{n2}{N}+ & + Calculates \verb+n1*n2+ and put the result in \verb+N+. \\\hline + \verb+\opneg{n}{N}+ & + Number \verb+N+ stores opposite of \verb+n+. \\\hline + \verb+\oppower{n}{T}{N}+ & + Calculates \verb+n+ to the power of \verb+T+ and put the result in + \verb+N+. \\\hline + \verb+\opprint{n}+ & + Display number \verb+n+ in a direct way. \\\hline + \verb+\opround{n}{T}{N}+ & + Put in \verb+N+ the approximation of \verb+n+ at rank \verb+T+. + \\\hline + \verb+\oprput(T1,T2){<object>}+ & + Put \verb+<object>+ to the left of the point with coordinates + \verb+(T1,T2)+ in relation to reference point. \\\hline + \verb+\opset{L}+ & + Allocates globally \package{xlop} parameters given in the list + \verb+L+. \\\hline + \verb+\opsetdecimaldigit{n}{T}{N}+ & + Modify the digit of rank \verb+T+ in decimal part of \verb+N+ in + order to have the value \verb+n+ for this digit. \\\hline + \verb+\opsetdigit{n}{T}{N}+ & + Modify the digit of rank \verb+T+ of \verb+N+ in + order to have the value \verb+n+ for this digit. \\\hline + \verb+\opsetintegerdigit{n}{T}{N}+ & + Modify the digit of rank \verb+T+ in integer part of \verb+N+ in + order to have the value \verb+n+ for this digit. \\\hline + \verb+\opsub[P]{n1}{n2}+ & + Display result of \verb+n1-n2+. \\\hline + \verb+\opsub*{n1}{n2}{N}+ & + Calculates \verb+n1-n2+ and put the result in \verb+N+. \\\hline + \verb+\opunzero{N}+ & + Delete non-significant zeros of \verb+N+. \\\hline + \verb+\opvline(T1,T2){T3}+ & + Draw a vertical ruleof length \verb+T3+, of thickness + \verb+hrulewidth+ and which begin at \verb+(T1,T2)+ in relation to + reference point. \\\hline + \verb+\opwidth{n}{N}+ & + Number \verb+N+ stores number of digits of number \verb+n+. \\\hline +\end{longtable}\index{macros!table of|)} + +In this table, parameters: +\begin{itemize} +\item \texttt{n} and \texttt{ni} (where \texttt{i} is an index) + indicate that parameter must be a number given in decimal form or a + variable name; +\item \texttt{N} and \texttt{Ni} (where \texttt{i} is an index) + indicate that parameter must be a number given in decimal form or a + variable name; +\item \texttt{[P]} indicates that the macro accept an optional + parameter which allow to modify parameter of \package{xlop}; +\item \texttt{T} and \texttt{Ti} (where \texttt{i} is an index) + indicate that parameter must be a number given in decimal form or a + variable name but must be less than numbers acceptable by \TeX{}, + that is, $-2147483648 \le \mathtt{T} \le 2147483647$. +\end{itemize} + +\section{Parameter list} +\label{sec:Liste des parametres} +\index{parameter@parameter!table of|(}% +\begingroup +\advance\hoffset by-1.75cm \advance\linewidth by1.75cm +\begin{longtable}{|l|l|p{7cm}|} + \hline + \multicolumn{1}{|c|}{\textbf{Parameter}} & + \multicolumn{1}{c|}{\textbf{Default}} & + \multicolumn{1}{c|}{\textbf{Signification}} \\\hline\hline + \endfirsthead + \hline + \multicolumn{1}{|c|}{\textbf{Parameter}} & + \multicolumn{1}{c|}{\textbf{Default}} & + \multicolumn{1}{c|}{\textbf{Signification}} \\\hline\hline + \endhead + \hline + \multicolumn{3}{|c|}{$\ldots$ to be continued $\ldots$}\\ + \hline + \endfoot + \hline + \endlastfoot + \verb+afterperiodsymbol+ & + \verb+$\ldots$+ & + Symbol used after a period of a division. \\\hline + \verb+approxsymbol+ & + \verb+$\approx$+ & + Symbol used as approximation relation in inline operations. \\\hline + \verb+equalsymbol+ & + \verb+{$=$}+ & + Symbol used as equality relation in inline operations. \\\hline + \verb+addsymbol+ & + \verb-$+$- & + Symbol used as addition operator. \\\hline + \verb+subsymbol+ & + \verb+$-$+ & + Symbol used as substraction operator. \\\hline + \verb+mulsymbol+ & + \verb+$\times$+ & + Symbol used as multiplication operator. \\\hline + \verb+divsymbol+ & + \verb+$\div$+ & + Symbol used as multiplication operator for inline + operations. \\\hline + \verb+decimalsepsymbol+ & + \verb+.+ & + Symbol used as decimal separator. \\\hline + \verb+strikedecimalsepsymbol+ & + & + Symbol used as decimal separator moved in dividend and divisor for + display division. \\\hline + \verb+shiftintermediarysymbol+ & + \verb+$\cdot$+ & + Symbol used to show intermediary numbers shifting for display + multiplication. \\\hline + \verb+displayshiftintermediary+ & + \verb+shift+ & + Indicates that the shifting character for multiplications will be + displayed only for additional shifting (value \verb+shift+), for + all the shifting (value \verb+all+), or never (value + \verb+none+). \\\hline + \verb+voperation+ & + \verb+bottom+ & + Vertical alignement for displayed operation. The value \verb+bottom+ + indicates that the bottom of operation will be aligned with + baseline. The value \verb+top+ indicates that the top of operation + will be aligned with baseline. The value \verb+center+ indicates + that operation will be verticaly centred with baseline. \\\hline + \verb+voperator+ & + \verb+center+ & + Vertical alignement for operators in displayed operations. The value + \verb+top+ put operator at the level of first operand. The value + \verb+bottom+ put operator at the level of second operand. The value + \verb+center+ put operator between operands. \\\hline + \verb+hfactor+ & + \verb+decimal+ & + Sort of operands alignement for displayed operation. The value + \verb+decimal+ indicates an alignement on decimal separator. The + value \verb+right+ indicates a flushright alignement. \\\hline + \verb+vruleperiod+ & + \verb+-0.2+ & + Vertical position of rule which indicates period of quotient for + inline division. \\\hline + \verb+dividendbridge+ & + \verb+false+ & + Indicates if there is a ``bridge'' above dividend. \\\hline + \verb+shiftdecimalsep+ & + \verb+both+ & + Indicates how shift decimal separator into operands for a displayed + division. The value \verb+both+ indicates that shifting are made on + both divisor and dividend in order to make integer numbers. The + value \verb+divisor+ indicates that the shifting must give an + integer divisor. The value \verb+none+ indicates that there is no + shifting. \\\hline + \verb+maxdivstep+ & + \verb+10+ & + Maximal number of steps in division. \\\hline + \verb+safedivstep+ & + \verb+50+ & + Maximal number of steps in division when there is a period to + reach. \\\hline + \verb+period+ & + \verb+false+ & + Indicates if division must be stoped when a whole period is + reached. \\\hline + \verb+deletezero+ & + \verb+true+ & + Indicates that non-significant zeros are displayed (\verb+false+) or + deleted (\verb+true+). \\\hline + \verb+carryadd+ & + \verb+true+ & + Indicates that carries are displayed (\verb+true+) for displayed + additions. \\\hline + \verb+carrysub+ & + \verb+false+ & + Indicates that carries are displayed (\verb+true+) for displayed + substractions. \\\hline + \verb+offsetcarry+ & + \verb+-0.35+ & + Horizontal offset for carries into displayed substractions. \\\hline + \verb+style+ & + \verb+display+ & + Indicates tha operation are inline (\verb+text+) or displayed + (\verb+display+). \\\hline + \verb+displayintermediary+ & + \verb+nonzero+ & + Indicates that all intermediary results are displayed (\verb+all+), + only non null ones are displayed (\verb+nonzero+), or any + intermediary result isn't displayed into displayed multiplications + and divisions. \\\hline + \verb+lastcarry+ & + \verb+false+ & + Indicates that carry with no figure just below it must be displayed + (\verb+true+), or not (\verb+false+). \\\hline + \verb+parenthesisnegative+ & + \verb+none+ & + Behavior to display negative numbers in inline operations. The value + \verb+none+ displays them without parenthesis. The value \verb+all+ + displays them always with parenthesis. The value \verb+last+ display + parenthesis except for first operand of an expression. \\\hline + \verb+columnwidth+ & + \verb+2ex+ & + With of box for one figure. \\\hline + \verb+lineheight+ & + \verb+\baselineskip+ & + Height of box for one figure. \\\hline + \verb+decimalsepwidth+ & + \verb+0pt+ & + Width of box that hold the decimal separator. \\\hline + \verb+decimalsepoffset+ & + \verb+0pt+ & + Horizontal offset for decimal separator. \\\hline + \verb+hrulewidth+ & + \verb+0.4pt+ & + Thickness of horizontal rules. \\\hline + \verb+vrulewidth+ & + \verb+0.4pt+ & + Thickness of vertical rules. \\\hline + \verb+behaviorsub+ & + \verb+silent+ & + \package{xlop} behavior for an ``impossible'' substraction, that is, + a substraction with two positive operands, the second greater + than the first one. The value \verb+silent+ does operation swapping + the two operands in a slient way. With the value \verb+warning+, + there are also a swapping but \package{xlop} gives a warning. The + value \verb+error+ display an error message and operation isn't + processed. \\\hline + \verb+country+ & + \verb+french+ & + Indicates the displayed operation behavior depending of + contry. Package \package{xlop} put forward only \verb+french+, + \verb+american+, and \verb+russian+ but these different ways to + display operations aren't encoded in version 0.23. \\\hline + \verb+operandstyle+ & + & + Style for operands. \\\hline + \verb+resultstyle+ & + & + Style for results. \\\hline + \verb+remainderstyle+ & + & + Style for remainders. \\\hline + \verb+intermediarystyle+ & + & + Style for intermediary results (intermediary numbers in + multiplication and number to substract in division when successive + substractions are displayed). \\\hline + \verb+carrystyle+ & + \verb+\scriptsize+ & + Style for carries. The default value when compilation are made + without \LaTeX{} is \verb+\sevenrm+. \\\hline +\end{longtable}\index{parameter@parameter!table of|)} +\endgroup + +\chapter{Tricks} +\label{chap:Trucs et astuces} +\section{\package{xlop} vs. \package{calc} and \package{fp}} +You could believe that \package{xlop} can replace package such +\package{calc}\index{package!calc}\index{calc} and +\package{fp}\index{package!fp}\index{fp}. In fact, that is not so +simple. Obviously \package{xlop} can do complex calculations, on arbitrary +long numbers but, unlike \package{calc}, it don't allow to process +directly dimensions. Comparison with \package{fp} is somewhere more +realistic but remember that \package{xlop} can make memory usage too +high. + +If you want to process calculations on length\index{length}, you can use +that a dimen register allocation to a counter gives a number which +correspond to this length with unit \texttt{sp}. +\begin{CenterExample}[xrightmargin=0pt] + \newcommand\getsize[2]{% + \dimen0=#1\relax + \count255=\dimen0 + \opcopy{\the\count255}{#2}} + \getsize{1pt}{r}$1\,\mathrm{pt}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1pc}{r}$1\,\mathrm{pc}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1in}{r}$1\,\mathrm{in}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1bp}{r}$1\,\mathrm{bp}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1cm}{r}$1\,\mathrm{cm}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1mm}{r}$1\,\mathrm{mm}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1dd}{r}$1\,\mathrm{dd}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1cc}{r}$1\,\mathrm{cc}=\opprint{r}\,\mathrm{sp}$\quad + \getsize{1sp}{r}$1\,\mathrm{sp}=\opprint{r}\,\mathrm{sp}$\quad +\end{CenterExample} +However, don't forget that the \package{xlop} main goal is to +\emph{display} operations. + +With this \macro{getsize} macro, it is possible to realise +calculations on length. +\begin{SideBySideExample} + \newcommand\getsize[2]{% + \dimen0=#1\relax + \count255=\dimen0 + \opcopy{\the\count255}{#2}} + \getsize{1cm}{u}% + \getsize{\textwidth}{w}% + \getsize{\textheight}{h}% + \opexpr{w*h/u^2}{S}% + \opround{S}{2}{S}% + Surface of spread is + \opprint{S}\,$\mathrm{cm}^2$ +\end{SideBySideExample} + +\section{Complex Operations} +\label{sec:Creation d'operations complexes} +Use of \package{xlop} macros with loop of \TeX{} allow to create +operations as you want. Here, we give only two examples. The first one +can express a number as a product of prime factors, the second one is +a general calculation for continued +fraction.\index{number!prime}\index{loop|(}% +\index{product of prime factors} +\begin{Verbatim}[xrightmargin=0pt] + \newcount\primeindex + \newcount\tryindex + \newif\ifprime + \newif\ifagain + \newcommand\getprime[1]{% + \opcopy{2}{P0}% + \opcopy{3}{P1}% + \opcopy{5}{try} + \primeindex=2 + \loop + \ifnum\primeindex<#1\relax + \testprimality + \ifprime + \opcopy{try}{P\the\primeindex}% + \advance\primeindex by1 + \fi + \opadd*{try}{2}{try}% + \ifnum\primeindex<#1\relax + \testprimality + \ifprime + \opcopy{try}{P\the\primeindex}% + \advance\primeindex by1 + \fi + \opadd*{try}{4}{try}% + \fi + \repeat + } + \newcommand\testprimality{% + \begingroup + \againtrue + \global\primetrue + \tryindex=0 + \loop + \opidiv*{try}{P\the\tryindex}{q}{r}% + \opcmp{r}{0}% + \ifopeq \global\primefalse \againfalse \fi + \opcmp{q}{P\the\tryindex}% + \ifoplt \againfalse \fi + \advance\tryindex by1 + \ifagain + \repeat + \endgroup + } +\end{Verbatim} +\newcount\primeindex +\newcount\tryindex +\newif\ifprime +\newif\ifagain +\newcommand\getprime[1]{% + \opcopy{2}{P0}% + \opcopy{3}{P1}% + \opcopy{5}{try} + \primeindex=2 + \loop + \ifnum\primeindex<#1\relax + \testprimality + \ifprime + \opcopy{try}{P\the\primeindex}% + \advance\primeindex by1 + \fi + \opadd*{try}{2}{try}% + \ifnum\primeindex<#1\relax + \testprimality + \ifprime + \opcopy{try}{P\the\primeindex}% + \advance\primeindex by1 + \fi + \opadd*{try}{4}{try}% + \fi + \repeat +} +\newcommand\testprimality{% + \begingroup + \againtrue + \global\primetrue + \tryindex=0 + \loop + \opidiv*{try}{P\the\tryindex}{q}{r}% + \opcmp{r}{0}% + \ifopeq \global\primefalse \againfalse \fi + \opcmp{q}{P\the\tryindex}% + \ifoplt \againfalse \fi + \advance\tryindex by1 + \ifagain + \repeat + \endgroup +} + +With this code, we can create a prime numbers list (here the 20~first +ones). +\begin{SideBySideExample} + \getprime{20}% + \opprint{P0}, \opprint{P1}, \ldots, + \opprint{P9}, \ldots \opprint{P19}. +\end{SideBySideExample} + +Note that this code is very bad: it is very slow and don't give +anything against native \TeX{} operations. It is only a educational +example. Note also that the tricks to put loop into loop with macro +\verb+\testprimality+ inside a group. \package{xlop} operations give +global results.\index{global allocation} + +Once you have your prime numbers ``table'', you can use it to +write a number as product of prime number. +\begin{CenterExample}[xrightmargin=0pt] + \newcommand\primedecomp[2][nil]{% + \begingroup + \opset{#1}% + \opcopy{#2}{NbtoDecompose}% + \opabs{NbtoDecompose}{NbtoDecompose}% + \opinteger{NbtoDecompose}{NbtoDecompose}% + \opcmp{NbtoDecompose}{0}% + \ifopeq + I refuse to factorize zero. + \else + \setbox1=\hbox{\opdisplay{operandstyle.1}% + {NbtoDecompose}}% + {\setbox2=\box2{}}% + \count255=1 + \primeindex=0 + \loop + \opcmp{NbtoDecompose}{1}\ifopneq + \opidiv*{NbtoDecompose}{P\the\primeindex}{q}{r}% + \opcmp{0}{r}\ifopeq + \ifvoid2 + \setbox2=\hbox{% + \opdisplay{intermediarystyle.\the\count255}% + {P\the\primeindex}}% + \else + \setbox2=\vtop{% + \hbox{\box2} + \hbox{% + \opdisplay{intermediarystyle.\the\count255}% + {P\the\primeindex}}} + \fi + \opcopy{q}{NbtoDecompose}% + \advance\count255 by1 + \setbox1=\vtop{% + \hbox{\box1} + \hbox{% + \opdisplay{operandstyle.\the\count255}% + {NbtoDecompose}} + }% + \else + \advance\primeindex by1 + \fi + \repeat + \hbox{\box1 + \kern0.5\opcolumnwidth + \opvline(0,0.75){\the\count255.25} + \kern0.5\opcolumnwidth + \box2}% + \fi + \endgroup + } + + \getprime{20}% + \primedecomp[operandstyle.2=\red, + intermediarystyle.2=\red]{252} +\end{CenterExample} +Note the use of group for the whole macro in order to protect +\package{xlop} parameter modifications.% +\index{parameter!local modification} Note also that void parameter +aren't allowed. It's not a bug, it's a feature. Author thinks that a +user who write brackets without anything between these brackets is +going to make a mistake. To obviate this +prohibition\index{parameter!void}, there is the particular +parameter \parameter{nil} which has exactly this rôle. +\index{loop|)} + +Finally, note the trick \verb+{\setbox2=\box2}+ to obtain a void box +register, and final manipulations to show the vertical rule in a +easy-to-read way. + +The second example allow to calculates a continued fraction like: +\def\dfrac#1#2{\frac{\displaystyle #1}{\displaystyle #2}} +\[a_0+\dfrac{1}{a_1+\dfrac{1}{a_2+\dfrac{1}{a_3+\cdots}}}\] +giving the sequence $a_0,a_1,a_2,a_3,\ldots$ to the macro. This +example gives fractions corresponding to gold number, and square root +for~2 and~3. +\makeatletter +\begin{CenterExample}[xrightmargin=0pt] + \begingroup + \long\gdef\continuedfraction#1#2{% + \let\@mirror\relax + \@for\op@Nb:=#1\do + {% + \ifx\@mirror\relax + \edef\@mirror{\op@Nb}% + \else + \edef\@mirror{\op@Nb,\@mirror}% + \fi + }% + \let\Op@result\relax + \@for\op@Nb:=\@mirror\do + {% + \ifx\Op@result\relax + \opcopy{\op@Nb}{result}% + \else + \opexpr{\op@Nb+1/result}{result}% + \fi + }% + \opcopy{result}{#2}% + } + \endgroup + \continuedfraction{1,1,1,1,1,1,1,1,1,1,1,1}{r}\opprint{r}\quad + \continuedfraction{1,2,2,2,2,2,2,2,2,2,2,2}{r}\opprint{r}\quad + \continuedfraction{1,1,2,1,2,1,2,1,2,1,2,1}{r}\opprint{r} +\end{CenterExample} +\makeatother +It does no harm just this once, we use \LaTeX{} commands for the +loop. + +\section{Direct Access to Number} +\label{sec:Acces direct aux nombres} +When a number is saved in a \package{xlop} variable, it is possible to +process with it in many different ways. However, in certain +situations, you would creat you own macro or use external macro giving +such numbers as parameter. + +Giving directly \verb+\opprint{var}+ is ineffective since this macro +is a complex a gives side effect. It is necessary to access directly +to this number. When a variable hold a number, \package{xlop} creates +a macro +\texttt{$\backslash$Op@var}\index{Opvar@\texttt{\boi {Op\at var}}} +which contain this number. Note the uppercase ``O'' and the lowercase +``p''. The at sign is here to do this definition a private one, that +is, you have to enclose it with \macro{makeatletter} and +\macro{makeatother} to access it (or \macro{catcode @=11} in \TeX). +\begin{SideBySideExample} + \opcopy{1234}{a}\opcopy{56}{b}% + \opmul*{a}{b}{r}% + \makeatletter + \newcolumntype{.}{D{.}{.}{-1}} + \begin{tabular}{l.} + & \Op@a \\ + $\times$ & \Op@b \\ + $=$ & \Op@r + \end{tabular} + \makeatother +\end{SideBySideExample} + +Note that this way of doing don't work when decimal separator is +between braces since macro \verb+\opprint{var}+ contain such +braces. In this case, the simplest is to use \macro{opexport} macro +(see page~\pageref{macro-opexport}). + +\chapter{Future Versions} +\label{chap:Versions futures} +Version of \package{xlop} package is~0.23 which is only a debuging +version of version~0.2, which is itself a correcting version of +version~0.1 (first public release). The next release will be +version~0.3 and its ``stable'' version will be version~0.4. + +The features of version~0.3 aren't definitively fixed but there are +some points planned: +\begin{itemize} +\item international version for posées; +\item opérations from 2 to 36~basis; +\item additional high level functions with roots (\macro{oproot} for + any roots and \macro{opsqrt} for square root), exponential function, + logarithm, trigonometric functions (direct, inverse, hyperbolic); +\item macro to have a formated writing, that is, write a number where + length of decimal part and integer part are given (if these widths + are not the ones of the number, there will be overflow or filling); + this macro was present in version~0.1 and allow to display numbers + decimal aligned, right aligned, or left aligned; +\item macro for addition with more than two operands; +\item parameter for scientific or engineer notation; +\item macro to allow to write a multi-line number and/or with thousand + separator; +\item carries for multiplications; +\item make public the successive remainders of a division; +\item negative values of \parameter{maxdivstep} and + \parameter{safedivstep} parameters will take acount of decimal digit + of quotient. +\end{itemize} + +For all requests or bug report, the author will be grateful to you to +contact him at: +\begin{verbatim} + Jean-Come.Charpentier@wanadoo.fr +\end{verbatim} +placing the word ``xlop'' in the subject in order to help my spam killer. + +It would be nice to have a hacker manual which explain in details the +source. This tool could be usefull in order to improve +\package{xlop}. Unfortunately, the current code has more +than~4000~lines and the work to do that may well be too long. + +%\printindex +\chapter{Index} +\label{chap:index} +\begin{multicols}{2} +\makeatletter +\parindent \z@\relax +\parskip \z@ \@plus.3\p@\relax +\let\item\@idxitem +\makeatother +\renewenvironment{theindex}{}{}% +\input\jobname.ind +\end{multicols} +\end{document} diff --git a/Master/texmf-dist/source/generic/xlop/manual.sty b/Master/texmf-dist/source/generic/xlop/manual.sty index a186256b849..1047dd3766d 100644 --- a/Master/texmf-dist/source/generic/xlop/manual.sty +++ b/Master/texmf-dist/source/generic/xlop/manual.sty @@ -1,12 +1,16 @@ \usepackage[T1]{fontenc} \usepackage[latin1]{inputenc} -\usepackage{lmodern} +\usepackage{fourier} +\usepackage[scaled]{helvet} +\usepackage[scaled]{luximono} \usepackage{makeidx} \usepackage{longtable} \usepackage{multicol} \usepackage{pst-node} \usepackage{fvrb-ex} \usepackage{geometry} +\usepackage{hyperref} +\usepackage{microtype} \usepackage{xlop} \fvset{xrightmargin=5cm,frame=single,fontsize=\small} @@ -38,4 +42,5 @@ \newcommand\bull{\vrule width3pt height4pt depth-1pt} +\newcounter{stuff} \makeindex diff --git a/Master/texmf-dist/tex/generic/xlop/xlop.sty b/Master/texmf-dist/tex/generic/xlop/xlop.sty index 8c672c8d15e..65de248f1f0 100644 --- a/Master/texmf-dist/tex/generic/xlop/xlop.sty +++ b/Master/texmf-dist/tex/generic/xlop/xlop.sty @@ -1,3 +1,3 @@ -\ProvidesPackage{xlop}[2006/01/04 package wrapper for xlop.tex] +\ProvidesPackage{xlop}[2009/12/02 package wrapper for xlop.tex] \input xlop.tex \endinput diff --git a/Master/texmf-dist/tex/generic/xlop/xlop.tex b/Master/texmf-dist/tex/generic/xlop/xlop.tex index dea98da45d0..004adf7c8f1 100644 --- a/Master/texmf-dist/tex/generic/xlop/xlop.tex +++ b/Master/texmf-dist/tex/generic/xlop/xlop.tex @@ -1,5 +1,5 @@ -\def\fileversion{0.22} -\def\filedate{2006/01/04} +\def\fileversion{0.23} +\def\filedate{2009/12/02} %% %% xlop.tex: %% eXtra Large OPeration macros for Generic TeX. @@ -21,12 +21,13 @@ \let\xlopLoaded\endinput \edef\opAtCode{\the\catcode`\@} \catcode`\@=11\relax -\newcount\count@z -\newcount\count@i -\newcount\count@ii -\newcount\count@iii -\newcount\count@iv -\newcount\count@v +\newcount\op@count@z +\newcount\op@count@i +\newcount\op@count@ii +\newcount\op@count@iii +\newcount\op@count@iv +\newcount\op@count@v +\newcount\op@count@vi \newtoks\op@currentstyle \expandafter\ifx\csname @latexerr\endcsname\relax \long\def\@ifundefined#1#2#3{% @@ -97,17 +98,17 @@ #1^^J\@spaces See documentation for further information.^^J}% \endgroup } -\let\@nil\relax +\let\op@nil\relax \def\opset#1{% - \Pop@set#1,\@nil + \Pop@set#1,\op@nil \ifop@error\op@errorwrite\fi \ignorespaces } \def\Pop@set#1,{% - \Pop@@set#1==\@nil - \@ifnextchar\@nil{\@gobble}{\Pop@set}% + \Pop@@set#1==\op@nil + \@ifnextchar\op@nil{\@gobble}{\Pop@set}% } -\def\Pop@@set#1=#2=#3\@nil{% +\def\Pop@@set#1=#2=#3\op@nil{% \@ifundefined{pOP@#1}% {\Pop@@@set#1.={#2}} {\@nameuse{pOP@#1}{#2}}% @@ -469,19 +470,19 @@ \opset{carrystyle=\scriptsize} \fi -\count@z=`\0 \edef\op@numbegin{\the\count@z} -\count@z=`\9 \edef\op@numend{\the\count@z} -\count@z=`\+ \edef\op@plus{\the\count@z} -\count@z=`\- \edef\op@minus{\the\count@z} -\count@z=`\* \edef\op@multiply{\the\count@z} -\count@z=`\/ \edef\op@divide{\the\count@z} -\count@z=`\: \edef\op@idivide{\the\count@z} -\count@z=`\^ \edef\op@pow{\the\count@z} -\count@z=`\. \edef\op@dot{\the\count@z} -\count@z=`\, \edef\op@comma{\the\count@z} -\count@z=`\( \edef\op@lparenthesis{\the\count@z} -\count@z=`\) \edef\op@rparenthesis{\the\count@z} -\count@z=`\ \edef\op@space{\the\count@z} +\op@count@z=`\0 \edef\op@numbegin{\the\op@count@z} +\op@count@z=`\9 \edef\op@numend{\the\op@count@z} +\op@count@z=`\+ \edef\op@plus{\the\op@count@z} +\op@count@z=`\- \edef\op@minus{\the\op@count@z} +\op@count@z=`\* \edef\op@multiply{\the\op@count@z} +\op@count@z=`\/ \edef\op@divide{\the\op@count@z} +\op@count@z=`\: \edef\op@idivide{\the\op@count@z} +\op@count@z=`\^ \edef\op@pow{\the\op@count@z} +\op@count@z=`\. \edef\op@dot{\the\op@count@z} +\op@count@z=`\, \edef\op@comma{\the\op@count@z} +\op@count@z=`\( \edef\op@lparenthesis{\the\op@count@z} +\op@count@z=`\) \edef\op@rparenthesis{\the\op@count@z} +\op@count@z=`\ \edef\op@space{\the\op@count@z} \newcount\op@parenthesis \newcount\op@token \newcount\op@stack @@ -518,17 +519,17 @@ \op@isplusfalse \op@isminusfalse \op@isdecimalsepfalse - \count@z=`#1\relax - \ifnum\count@z=\op@plus\relax + \op@count@z=`#1\relax + \ifnum\op@count@z=\op@plus\relax \op@isplustrue - \else\ifnum\count@z=\op@minus\relax + \else\ifnum\op@count@z=\op@minus\relax \op@isminustrue - \else\ifnum\count@z=\op@dot\relax + \else\ifnum\op@count@z=\op@dot\relax \op@isdecimalseptrue - \else\ifnum\count@z=\op@comma\relax + \else\ifnum\op@count@z=\op@comma\relax \op@isdecimalseptrue - \else\ifnum\count@z<\op@numbegin\relax - \else\ifnum\count@z>\op@numend\relax + \else\ifnum\op@count@z<\op@numbegin\relax + \else\ifnum\op@count@z>\op@numend\relax \else \op@isdigittrue \fi\fi\fi\fi\fi\fi @@ -536,7 +537,7 @@ \def\op@split#1#2{% \begingroup \edef\op@arg{#1}% - \expandafter\op@readnumber\op@arg\@nil + \expandafter\op@readnumber\op@arg\op@nil \ifop@error \op@error{Number name `#1' is undefined}% {See documentation about number name}% @@ -545,30 +546,30 @@ \else \edef\op@name{#2}% \op@length - \count@i=\@nameuse{OP@\op@name @w}\relax + \op@count@i=\@nameuse{OP@\op@name @w}\relax \edef\op@arg{\op@arg.}% \let\next\op@@split \fi - \expandafter\next\op@arg\@nil + \expandafter\next\op@arg\op@nil \endgroup } -\def\op@@split#1#2\@nil{% - \ifnum\count@i>0 +\def\op@@split#1#2\op@nil{% + \ifnum\op@count@i>0 \edef\op@argi{#1}% \edef\op@argii{#2}% \let\next\op@@split \expandafter\op@testchar\op@argi \ifop@isdigit - \@namexdef{OP@\op@name @\the\count@i}{\op@argi}% - \advance\count@i by -1 + \@namexdef{OP@\op@name @\the\op@count@i}{\op@argi}% + \advance\op@count@i by -1 \fi \else \let\next\relax \let\op@argii\relax \fi - \expandafter\next\op@argii\@nil + \expandafter\next\op@argii\op@nil } -\def\op@readnumber#1#2\@nil{% +\def\op@readnumber#1#2\op@nil{% \op@testchar{#1}% \ifop@isdigit \else \ifop@isplus \else @@ -581,25 +582,25 @@ } \def\op@length{% \begingroup - \expandafter\op@@length\op@arg\@nil - \ifnum\count@i=0 - \count@i=1 + \expandafter\op@@length\op@arg\op@nil + \ifnum\op@count@i=0 + \op@count@i=1 \xdef\op@arg{0\op@arg}% \fi - \@namexdef{OP@\op@name @i}{\the\count@i}% - \@namexdef{OP@\op@name @d}{\the\count@ii}% - \advance\count@i by \count@ii - \@namexdef{OP@\op@name @w}{\the\count@i}% + \@namexdef{OP@\op@name @i}{\the\op@count@i}% + \@namexdef{OP@\op@name @d}{\the\op@count@ii}% + \advance\op@count@i by \op@count@ii + \@namexdef{OP@\op@name @w}{\the\op@count@i}% \endgroup } -\def\op@@length#1#2\@nil{% +\def\op@@length#1#2\op@nil{% \edef\op@argi{#1}% \edef\op@argii{#2}% \expandafter\op@testchar\op@argi \ifop@isdigit \@namexdef{OP@\op@name @s}{0}% - \count@i=1 - \count@ii=0 + \op@count@i=1 + \op@count@ii=0 \ifx\empty\op@argii \let\next\relax \let\op@argii\relax @@ -614,8 +615,8 @@ \let\next\op@length@after@sign \else \ifop@isdecimalsep \@namexdef{OP@\op@name @s}{0}% - \count@i=0 - \count@ii=0 + \op@count@i=0 + \op@count@ii=0 \let\next\op@length@after@decimalsep \else \op@error{\op@argi\op@argii\space isn't a valid number}% @@ -629,14 +630,14 @@ \let\next\relax \let\op@argii\relax \fi - \expandafter\next\op@argii\@nil + \expandafter\next\op@argii\op@nil } -\def\op@length@after@digit#1#2\@nil{% +\def\op@length@after@digit#1#2\op@nil{% \edef\op@argi{#1}% \edef\op@argii{#2}% \expandafter\op@testchar\op@argi \ifop@isdigit - \advance\count@i by 1 + \advance\op@count@i by 1 \let\next\op@length@after@digit \else \ifop@isdecimalsep \let\next\op@length@after@decimalsep @@ -650,9 +651,9 @@ \ifx\empty\op@argii \let\next\relax \fi - \expandafter\next\op@argii\@nil + \expandafter\next\op@argii\op@nil } -\def\op@length@after@sign#1#2\@nil{% +\def\op@length@after@sign#1#2\op@nil{% \edef\op@argi{#1}% \edef\op@argii{#2}% \expandafter\op@testchar\op@argi @@ -671,27 +672,27 @@ {See documentation for syntax of valid number}% \let\next\relax \else - \count@i=0 - \count@ii=0 + \op@count@i=0 + \op@count@ii=0 \let\next\op@length@after@decimalsep \fi \else \ifop@isdigit - \count@i=1 - \count@ii=0 + \op@count@i=1 + \op@count@ii=0 \ifx\empty\op@argii \let\next\relax \else \let\next\op@length@after@digit \fi \fi\fi\fi\fi - \expandafter\next\op@argii\@nil + \expandafter\next\op@argii\op@nil } -\def\op@length@after@decimalsep#1#2\@nil{% +\def\op@length@after@decimalsep#1#2\op@nil{% \edef\op@argi{#1}% \edef\op@argii{#2}% \expandafter\op@testchar\op@argi \ifop@isdigit - \advance\count@ii by 1 + \advance\op@count@ii by 1 \let\next\op@length@after@decimalsep \else \op@error{#1#2 not allowed here. \space I forget it}% @@ -704,7 +705,7 @@ \let\next\relax \let\op@argii\relax \fi - \expandafter\next\op@argii\@nil + \expandafter\next\op@argii\op@nil } \def\op@unsplit#1#2{% \begingroup @@ -714,22 +715,22 @@ \else \def\op@macroname{}% \fi - \count@z=\@nameuse{OP@\op@name @i}\relax - \count@i=\@nameuse{OP@\op@name @w}\relax + \op@count@z=\@nameuse{OP@\op@name @i}\relax + \op@count@i=\@nameuse{OP@\op@name @w}\relax \loop - \ifnum\count@z>0 + \ifnum\op@count@z>0 \edef\op@macroname{\op@macroname - \@nameuse{OP@\op@name @\the\count@i}}% - \advance\count@z by-1 - \advance\count@i by-1 + \@nameuse{OP@\op@name @\the\op@count@i}}% + \advance\op@count@z by-1 + \advance\op@count@i by-1 \repeat - \ifnum\count@i>0 + \ifnum\op@count@i>0 \edef\op@macroname{\op@macroname\op@decimalsepsymbol}% \loop - \ifnum\count@i>0 + \ifnum\op@count@i>0 \edef\op@macroname{\op@macroname - \@nameuse{OP@\op@name @\the\count@i}}% - \advance\count@i by-1 + \@nameuse{OP@\op@name @\the\op@count@i}}% + \advance\op@count@i by-1 \repeat \fi \@namexdef{Op@#2}{\op@macroname}% @@ -762,55 +763,55 @@ \begingroup \edef\op@name{#4}% \dimen0=\opcolumnwidth - \count@z=#1% - \advance\count@z by-\@nameuse{OP@\op@name @i}\relax - \multiply\dimen0 by\count@z + \op@count@z=#1% + \advance\op@count@z by-\@nameuse{OP@\op@name @i}\relax + \multiply\dimen0 by\op@count@z \global\setbox0=\hbox{% \op@strut\vrule width\dimen0 height\z@ depth\z@}% - \count@z=\@nameuse{OP@\op@name @i}\relax - \count@i=\@nameuse{OP@\op@name @w}\relax + \op@count@z=\@nameuse{OP@\op@name @i}\relax + \op@count@i=\@nameuse{OP@\op@name @w}\relax \loop - \ifnum\count@z>0 - \op@setstyle{#3.\the\count@z}% + \ifnum\op@count@z>0 + \op@setstyle{#3.\the\op@count@z}% \global\setbox0=\hbox{\box0 \hbox to\opcolumnwidth{\hss\the\op@currentstyle - {\@nameuse{OP@\op@name @\the\count@i}}\hss}}% - \advance\count@z by-1 - \advance\count@i by-1 + {\@nameuse{OP@\op@name @\the\op@count@i}}\hss}}% + \advance\op@count@z by-1 + \advance\op@count@i by-1 \repeat - \ifnum\count@i>0 + \ifnum\op@count@i>0 \op@setstyle{#3.d}% \global\setbox0=\hbox{\box0 \hbox to\op@decimalsepwidth{\hss \vrule width\op@decimalsepoffset height\z@ depth\z@ \the\op@currentstyle\op@decimalsepsymbol \hss}}% - \count@z=-1 + \op@count@z=-1 \loop - \ifnum\count@i>0 - \op@setstyle{#3.\the\count@z}% + \ifnum\op@count@i>0 + \op@setstyle{#3.\the\op@count@z}% \global\setbox0=\hbox{\box0 \hbox to\opcolumnwidth{\hss\the\op@currentstyle - {\@nameuse{OP@\op@name @\the\count@i}}\hss}}% - \advance\count@z by-1 - \advance\count@i by-1 + {\@nameuse{OP@\op@name @\the\op@count@i}}\hss}}% + \advance\op@count@z by-1 + \advance\op@count@i by-1 \repeat \fi \dimen0=\opcolumnwidth - \count@z=#2\relax - \advance\count@z by-\@nameuse{OP@\op@name @d}\relax - \multiply\dimen0 by\count@z + \op@count@z=#2\relax + \advance\op@count@z by-\@nameuse{OP@\op@name @d}\relax + \multiply\dimen0 by\op@count@z \global\setbox0=\hbox{\box0 \vrule width\dimen0 height\z@ depth\z@}% \endgroup } \def\op@setstyle#1{% \edef\op@arg{#1}% - \expandafter\op@@setstyle\op@arg..\@nil + \expandafter\op@@setstyle\op@arg..\op@nil } -\def\op@@setstyle#1.#2.#3\@nil{% +\def\op@@setstyle#1.#2.#3\op@nil{% \edef\op@styleroot{#1}% \edef\op@styleindex{#2}% - \op@setstylesubindex#3.\@nil + \op@setstylesubindex#3.\op@nil \ifx\empty\op@stylesubindex \@ifundefined{op@\op@styleroot.\op@styleindex}% {\op@currentstyle={\@nameuse{op@\op@styleroot.0}}}% @@ -825,7 +826,7 @@ {\@nameuse{op@\op@styleroot.\op@styleindex.\op@stylesubindex}}}% \fi } -\def\op@setstylesubindex#1.#2\@nil{\def\op@stylesubindex{#1}} +\def\op@setstylesubindex#1.#2\op@nil{\def\op@stylesubindex{#1}} \def\opdisplay{\@ifnextchar[{\op@displaypar}{\op@displaypar[nil]}} \def\op@displaypar[#1]#2#3{% \begingroup @@ -853,46 +854,78 @@ } \def\op@format#1#2#3{% \begingroup - \count@iii=#1\relax - \count@iv=#2\relax - \count@z=\count@iv - \advance\count@z by-\@nameuse{OP@#3@d}\relax - \ifnum\count@z>0 - \count@i=\@nameuse{OP@#3@w}\relax - \advance\count@z by\count@i\relax + \op@count@iii=#1\relax + \op@count@iv=#2\relax + \op@count@z=\op@count@iv + \advance\op@count@z by-\@nameuse{OP@#3@d}\relax + \ifnum\op@count@z>0 + \op@count@i=\@nameuse{OP@#3@w}\relax + \advance\op@count@z by\op@count@i\relax \loop - \@namexdef{OP@#3@\the\count@z}{\@nameuse{OP@#3@\the\count@i}}% - \advance\count@i by-1 - \advance\count@z by-1\relax - \ifnum\count@i>0 + \@namexdef{OP@#3@\the\op@count@z}{\@nameuse{OP@#3@\the\op@count@i}}% + \advance\op@count@i by-1 + \advance\op@count@z by-1\relax + \ifnum\op@count@i>0 \repeat \loop - \@namexdef{OP@#3@\the\count@z}{0}% - \advance\count@z by-1\relax - \ifnum\count@z>0 + \@namexdef{OP@#3@\the\op@count@z}{0}% + \advance\op@count@z by-1\relax + \ifnum\op@count@z>0 \repeat - \@namexdef{OP@#3@d}{\the\count@iv}% - \count@i=\@nameuse{OP@#3@i}% - \advance\count@i by\count@iv\relax - \@namexdef{OP@#3@w}{\the\count@i}% - \fi - \count@z=\count@iii - \advance\count@z by-\@nameuse{OP@#3@i}\relax - \ifnum\count@z>0 - \count@i=\@nameuse{OP@#3@w}\relax + \@namexdef{OP@#3@d}{\the\op@count@iv}% + \op@count@i=\@nameuse{OP@#3@i}% + \advance\op@count@i by\op@count@iv\relax + \@namexdef{OP@#3@w}{\the\op@count@i}% + \fi + \op@count@z=\op@count@iii + \advance\op@count@z by-\@nameuse{OP@#3@i}\relax + \ifnum\op@count@z>0 + \op@count@i=\@nameuse{OP@#3@w}\relax \loop - \advance\count@i by1 - \@namexdef{OP@#3@\the\count@i}{0}% - \advance\count@z by-1\relax - \ifnum\count@z>0 + \advance\op@count@i by1 + \@namexdef{OP@#3@\the\op@count@i}{0}% + \advance\op@count@z by-1\relax + \ifnum\op@count@z>0 \repeat - \@namexdef{OP@#3@i}{\the\count@iii}% + \@namexdef{OP@#3@i}{\the\op@count@iii}% \fi - \count@i=\@nameuse{OP@#3@i}\relax - \advance\count@i by\@nameuse{OP@#3@d}\relax - \@namexdef{OP@#3@w}{\the\count@i}% + \op@count@i=\@nameuse{OP@#3@i}\relax + \advance\op@count@i by\@nameuse{OP@#3@d}\relax + \@namexdef{OP@#3@w}{\the\op@count@i}% \endgroup } +% add 0.23 +\def\opexport{\@ifnextchar[{\op@export}{\op@export[nil]}} +\def\op@export[#1]#2#3{% + \begingroup + \def\op@@export{}% + \opset{#1}% + \expandafter\def\expandafter\op@decimalsepsymbol\op@decimalsepsymbol + \op@split{#2}{tmp}% + \ifop@error + \op@errorwrite + \else + \op@count@vi=0 + \loop + \ifnum\op@count@vi<\OP@tmp@d + \advance\op@count@vi by1 + \xdef\op@@export{\@nameuse{OP@tmp@\the\op@count@vi}\op@@export}% + \repeat + \ifnum\OP@tmp@d>0 + \xdef\op@@export{\op@decimalsepsymbol\op@@export}% + \op@count@i=0 + \loop + \ifnum\op@count@i<\OP@tmp@i + \advance\op@count@vi by1 + \advance\op@count@i by1 + \xdef\op@@export{\@nameuse{OP@tmp@\the\op@count@vi}\op@@export}% + \repeat + \fi + \fi + \endgroup + \edef#3{\op@@export}% +} +% end add 0.23 \def\opunzero#1{% \op@split{#1}{uzr}% \ifop@error @@ -904,47 +937,47 @@ } \def\op@unzero#1{% \begingroup - \count@z=\@nameuse{OP@#1@i}\relax - \count@i=\@nameuse{OP@#1@w}\relax - \count@ii=\@nameuse{OP@#1@i}\relax + \op@count@z=\@nameuse{OP@#1@i}\relax + \op@count@i=\@nameuse{OP@#1@w}\relax + \op@count@ii=\@nameuse{OP@#1@i}\relax \loop - \ifnum\count@z>1\relax - \ifnum\@nameuse{OP@#1@\the\count@i}=0\relax - \advance\count@ii by-1 + \ifnum\op@count@z>1\relax + \ifnum\@nameuse{OP@#1@\the\op@count@i}=0\relax + \advance\op@count@ii by-1 \else - \count@z=0 + \op@count@z=0 \fi - \advance\count@z by-1 - \advance\count@i by-1 + \advance\op@count@z by-1 + \advance\op@count@i by-1 \repeat - \@namexdef{OP@#1@i}{\the\count@ii}% - \count@z=\@nameuse{OP@#1@d}\relax - \count@i=1\relax - \count@ii=0\relax + \@namexdef{OP@#1@i}{\the\op@count@ii}% + \op@count@z=\@nameuse{OP@#1@d}\relax + \op@count@i=1\relax + \op@count@ii=0\relax \loop - \ifnum\count@z>0\relax - \ifnum\@nameuse{OP@#1@\the\count@i}=0\relax - \advance\count@ii by1 - \advance\count@z by-1 - \advance\count@i by1 + \ifnum\op@count@z>0\relax + \ifnum\@nameuse{OP@#1@\the\op@count@i}=0\relax + \advance\op@count@ii by1 + \advance\op@count@z by-1 + \advance\op@count@i by1 \else - \count@z=0 + \op@count@z=0 \fi \repeat - \ifnum\count@ii>0\relax - \count@z=1\relax - \count@i=\@nameuse{OP@#1@w}\relax - \count2=\count@ii - \advance\count@ii by1 + \ifnum\op@count@ii>0\relax + \op@count@z=1\relax + \op@count@i=\@nameuse{OP@#1@w}\relax + \count@=\op@count@ii + \advance\op@count@ii by1 \loop - \@namexdef{OP@#1@\the\count@z}{\@nameuse{OP@#1@\the\count@ii}}% - \ifnum\count@ii<\count@i - \advance\count@z by1 - \advance\count@ii by1 + \@namexdef{OP@#1@\the\op@count@z}{\@nameuse{OP@#1@\the\op@count@ii}}% + \ifnum\op@count@ii<\op@count@i + \advance\op@count@z by1 + \advance\op@count@ii by1 \repeat - \count@ii=\@nameuse{OP@#1@d}% - \advance\count@ii by-\count2 - \@namexdef{OP@#1@d}{\the\count@ii}% + \op@count@ii=\@nameuse{OP@#1@d}% + \advance\op@count@ii by-\count@ + \@namexdef{OP@#1@d}{\the\op@count@ii}% \fi \ifnum\@nameuse{OP@#1@i}=1\relax \ifnum\@nameuse{OP@#1@d}=0\relax @@ -953,9 +986,9 @@ \fi \fi \fi - \count@i=\@nameuse{OP@#1@i}\relax - \advance\count@i by\@nameuse{OP@#1@d}\relax - \@namexdef{OP@#1@w}{\the\count@i}% + \op@count@i=\@nameuse{OP@#1@i}\relax + \advance\op@count@i by\@nameuse{OP@#1@d}\relax + \@namexdef{OP@#1@w}{\the\op@count@i}% \endgroup } \def\opcopy#1#2{% @@ -972,11 +1005,11 @@ \@namexdef{OP@#2@i}{\@nameuse{OP@#1@i}}% \@namexdef{OP@#2@d}{\@nameuse{OP@#1@d}}% \@namexdef{OP@#2@s}{\@nameuse{OP@#1@s}}% - \count@z=\@nameuse{OP@#2@w}\relax + \op@count@z=\@nameuse{OP@#2@w}\relax \loop - \ifnum\count@z>0 - \@namexdef{OP@#2@\the\count@z}{\@nameuse{OP@#1@\the\count@z}}% - \advance\count@z by-1 + \ifnum\op@count@z>0 + \@namexdef{OP@#2@\the\op@count@z}{\@nameuse{OP@#1@\the\op@count@z}}% + \advance\op@count@z by-1 \repeat \endgroup } @@ -1020,25 +1053,25 @@ \global\opneqtrue \else \op@againtrue - \count@i=\OP@ca@w\relax - \count@ii=\OP@cb@w\relax + \op@count@i=\OP@ca@w\relax + \op@count@ii=\OP@cb@w\relax \loop \ifop@again - \ifnum\@nameuse{OP@ca@\the\count@i}> - \@nameuse{OP@cb@\the\count@ii}\relax + \ifnum\@nameuse{OP@ca@\the\op@count@i}> + \@nameuse{OP@cb@\the\op@count@ii}\relax \op@againfalse \global\opgttrue \global\opgetrue \global\opneqtrue - \else \ifnum\@nameuse{OP@ca@\the\count@i}< - \@nameuse{OP@cb@\the\count@ii}\relax + \else \ifnum\@nameuse{OP@ca@\the\op@count@i}< + \@nameuse{OP@cb@\the\op@count@ii}\relax \op@againfalse \global\oplttrue \global\opletrue \global\opneqtrue - \else \ifnum\count@i=1\relax + \else \ifnum\op@count@i=1\relax \op@againfalse - \ifnum\count@ii=1\relax + \ifnum\op@count@ii=1\relax \global\opeqtrue \global\opgetrue \global\opletrue @@ -1047,14 +1080,14 @@ \global\opletrue \global\opneqtrue \fi - \else \ifnum\count@ii=1\relax + \else \ifnum\op@count@ii=1\relax \op@againfalse \global\opgttrue \global\opgetrue \global\opneqtrue \fi\fi\fi\fi - \advance\count@i by-1 - \advance\count@ii by-1 + \advance\op@count@i by-1 + \advance\op@count@ii by-1 \repeat \fi\fi \ifnum\OP@ca@s=1\relax @@ -1221,56 +1254,56 @@ \def\op@add#1#2#3{% \begingroup \global\op@carryfalse - \count@i=\op@max{\@nameuse{OP@#1@i}}{\@nameuse{OP@#2@i}}% - \count@ii=\op@max{\@nameuse{OP@#1@d}}{\@nameuse{OP@#2@d}}% - \op@format{\the\count@i}{\the\count@ii}{#1}% - \op@format{\the\count@i}{\the\count@ii}{#2}% - \@namexdef{OP@#3@i}{\the\count@i}% - \@namexdef{OP@#3@d}{\the\count@ii}% + \op@count@i=\op@max{\@nameuse{OP@#1@i}}{\@nameuse{OP@#2@i}}% + \op@count@ii=\op@max{\@nameuse{OP@#1@d}}{\@nameuse{OP@#2@d}}% + \op@format{\the\op@count@i}{\the\op@count@ii}{#1}% + \op@format{\the\op@count@i}{\the\op@count@ii}{#2}% + \@namexdef{OP@#3@i}{\the\op@count@i}% + \@namexdef{OP@#3@d}{\the\op@count@ii}% \@namexdef{OP@#3@s}{0}% \xdef\OP@carry@s{0}% \xdef\OP@carry@d{0}% - \advance\count@i by\count@ii - \@namexdef{OP@#3@w}{\the\count@i}% - \xdef\OP@carry@i{\the\count@i}% - \xdef\OP@carry@w{\the\count@i}% - \count@ii=1 + \advance\op@count@i by\op@count@ii + \@namexdef{OP@#3@w}{\the\op@count@i}% + \xdef\OP@carry@i{\the\op@count@i}% + \xdef\OP@carry@w{\the\op@count@i}% + \op@count@ii=1 \def\op@carry{0}% \@namexdef{OP@carry@1}{ }% \loop - \count@z=\@nameuse{OP@#1@\the\count@ii}% - \advance\count@z by\@nameuse{OP@#2@\the\count@ii}% - \advance\count@z by\op@carry\relax - \ifnum\count@z>9 - \advance\count@z by-10 + \op@count@z=\@nameuse{OP@#1@\the\op@count@ii}% + \advance\op@count@z by\@nameuse{OP@#2@\the\op@count@ii}% + \advance\op@count@z by\op@carry\relax + \ifnum\op@count@z>9 + \advance\op@count@z by-10 \def\op@carry{1}% \global\op@carrytrue \else \def\op@carry{0}% \fi - \@namexdef{OP@#3@\the\count@ii}{\the\count@z}% - \ifnum\count@ii<\count@i - \advance\count@ii by1\relax + \@namexdef{OP@#3@\the\op@count@ii}{\the\op@count@z}% + \ifnum\op@count@ii<\op@count@i + \advance\op@count@ii by1\relax \ifnum\op@carry=0 - \@namexdef{OP@carry@\the\count@ii}{ }% + \@namexdef{OP@carry@\the\op@count@ii}{ }% \else - \@namexdef{OP@carry@\the\count@ii}{1}% + \@namexdef{OP@carry@\the\op@count@ii}{1}% \global\op@carrytrue \fi \repeat \ifnum\op@carry=1 - \advance\count@i by1 - \@namexdef{OP@#3@w}{\the\count@i}% - \@namexdef{OP@#3@\the\count@i}{1}% + \advance\op@count@i by1 + \@namexdef{OP@#3@w}{\the\op@count@i}% + \@namexdef{OP@#3@\the\op@count@i}{1}% \ifop@lastcarry - \@namexdef{OP@carry@w}{\the\count@i}% - \@namexdef{OP@carry@i}{\the\count@i}% - \@namexdef{OP@carry@\the\count@i}{1}% + \@namexdef{OP@carry@w}{\the\op@count@i}% + \@namexdef{OP@carry@i}{\the\op@count@i}% + \@namexdef{OP@carry@\the\op@count@i}{1}% \global\op@carrytrue \fi - \count@i=\@nameuse{OP@#3@i}\relax - \advance\count@i by1 - \@namexdef{OP@#3@i}{\the\count@i}% + \op@count@i=\@nameuse{OP@#3@i}\relax + \advance\op@count@i by1 + \@namexdef{OP@#3@i}{\the\op@count@i}% \fi \endgroup } @@ -1376,45 +1409,45 @@ \def\op@sub#1#2#3{% \begingroup \global\op@carryfalse - \count@i=\op@max{\@nameuse{OP@#1@i}}{\@nameuse{OP@#2@i}}\relax - \count@ii=\op@max{\@nameuse{OP@#1@d}}{\@nameuse{OP@#2@d}}\relax - \count@iii=\@nameuse{OP@#2@w}\relax - \advance\count@iii by1 - \op@format{\the\count@i}{\the\count@ii}{#1}% - \op@format{\the\count@i}{\the\count@ii}{#2}% - \@namexdef{OP@#3@i}{\the\count@i}% - \@namexdef{OP@#3@d}{\the\count@ii}% + \op@count@i=\op@max{\@nameuse{OP@#1@i}}{\@nameuse{OP@#2@i}}\relax + \op@count@ii=\op@max{\@nameuse{OP@#1@d}}{\@nameuse{OP@#2@d}}\relax + \op@count@iii=\@nameuse{OP@#2@w}\relax + \advance\op@count@iii by1 + \op@format{\the\op@count@i}{\the\op@count@ii}{#1}% + \op@format{\the\op@count@i}{\the\op@count@ii}{#2}% + \@namexdef{OP@#3@i}{\the\op@count@i}% + \@namexdef{OP@#3@d}{\the\op@count@ii}% \@namexdef{OP@#3@s}{0}% \xdef\OP@carry@s{0}% \xdef\OP@carry@d{0}% - \advance\count@i by\count@ii - \@namexdef{OP@#3@w}{\the\count@i}% - \xdef\OP@carry@i{\the\count@i}% - \xdef\OP@carry@w{\the\count@i}% - \count@ii=1 + \advance\op@count@i by\op@count@ii + \@namexdef{OP@#3@w}{\the\op@count@i}% + \xdef\OP@carry@i{\the\op@count@i}% + \xdef\OP@carry@w{\the\op@count@i}% + \op@count@ii=1 \def\op@carry{0}% \@namexdef{OP@carry@1}{ }% \loop - \count@z=\@nameuse{OP@#1@\the\count@ii}% - \advance\count@z by-\@nameuse{OP@#2@\the\count@ii}% - \advance\count@z by-\op@carry\relax - \ifnum\count@z<0 - \advance\count@z by10 + \op@count@z=\@nameuse{OP@#1@\the\op@count@ii}% + \advance\op@count@z by-\@nameuse{OP@#2@\the\op@count@ii}% + \advance\op@count@z by-\op@carry\relax + \ifnum\op@count@z<0 + \advance\op@count@z by10 \def\op@carry{1}% \else \def\op@carry{0}% \fi - \@namexdef{OP@#3@\the\count@ii}{\the\count@z}% - \ifnum\count@ii<\count@i - \advance\count@ii by1\relax - \@namexdef{OP@carry@\the\count@ii}{ }% + \@namexdef{OP@#3@\the\op@count@ii}{\the\op@count@z}% + \ifnum\op@count@ii<\op@count@i + \advance\op@count@ii by1\relax + \@namexdef{OP@carry@\the\op@count@ii}{ }% \ifnum\op@carry=0 \else \ifop@lastcarry - \@namexdef{OP@carry@\the\count@ii}{1}% + \@namexdef{OP@carry@\the\op@count@ii}{1}% \global\op@carrytrue \else - \ifnum\count@ii<\count@iii\relax - \@namexdef{OP@carry@\the\count@ii}{1}% + \ifnum\op@count@ii<\op@count@iii\relax + \@namexdef{OP@carry@\the\op@count@ii}{1}% \global\op@carrytrue \fi \fi @@ -1434,14 +1467,14 @@ \op@format{\OP@a@i}{\OP@b@d}{a}% \fi \fi - \count@i=\op@max{\OP@a@i}{\OP@b@i}% - \count@i=\op@max{\the\count@i}{\OP@r@i}% - \advance\count@i by1 - \count@ii=\op@max{\OP@a@d}{\OP@b@d}% - \count@ii=\op@max{\the\count@ii}{\OP@r@d}% - \count@z=\count@i - \advance\count@z by\count@ii - \setbox1=\hbox to\count@z\opcolumnwidth{% + \op@count@i=\op@max{\OP@a@i}{\OP@b@i}% + \op@count@i=\op@max{\the\op@count@i}{\OP@r@i}% + \advance\op@count@i by1 + \op@count@ii=\op@max{\OP@a@d}{\OP@b@d}% + \op@count@ii=\op@max{\the\op@count@ii}{\OP@r@d}% + \op@count@z=\op@count@i + \advance\op@count@z by\op@count@ii + \setbox1=\hbox to\op@count@z\opcolumnwidth{% \ifx\op@voperator\op@string@top \oplput(0,2){\op@realsymbol}% \else\ifx\op@voperator\op@string@bottom @@ -1449,16 +1482,16 @@ \else \oplput(0,1.5){\op@realsymbol}% \fi\fi - \ophline(0,0.75){\the\count@z}% + \ophline(0,0.75){\the\op@count@z}% \ifnum\OP@r@d>0\relax - \oplput(\the\count@z,0.75){% + \oplput(\the\op@count@z,0.75){% \vrule width\op@decimalsepwidth depth0.5\op@hrulewidth height0.5\op@hrulewidth} \fi \ifx\op@realsymbol\op@subsymbol \ifop@carrysub \ifop@carry - \op@makebox{\the\count@z}{0}{carrystyle}{carry}% + \op@makebox{\the\op@count@z}{0}{carrystyle}{carry}% \oplput(\op@offsetcarry,2){\kern\opcolumnwidth\copy0}% \oplput(\op@offsetcarry,1){\box0}% \fi @@ -1468,16 +1501,16 @@ \ifx\op@realsymbol\op@addsymbol \ifop@carryadd \ifop@carry - \op@makebox{\the\count@z}{0}{carrystyle}{carry}% + \op@makebox{\the\op@count@z}{0}{carrystyle}{carry}% \hbox{\box0}% \fi \fi \fi - \op@makebox{\the\count@i}{\the\count@ii}{operandstyle.1}{a}% + \op@makebox{\the\op@count@i}{\the\op@count@ii}{operandstyle.1}{a}% \hbox{\box0}% - \op@makebox{\the\count@i}{\the\count@ii}{operandstyle.2}{b}% + \op@makebox{\the\op@count@i}{\the\op@count@ii}{operandstyle.2}{b}% \hbox{\box0}% - \op@makebox{\the\count@i}{\the\count@ii}{resultstyle}{r}% + \op@makebox{\the\op@count@i}{\the\op@count@ii}{resultstyle}{r}% \hbox{\box0}% }% }% @@ -1562,31 +1595,31 @@ \expandafter\if\csname OP@b@\OP@b@w\endcsname0 \ifnum\OP@r@i>1 \expandafter\if\csname OP@r@\OP@r@w\endcsname0 - \count@i=\OP@r@w - \advance\count@i\m@ne - \edef\OP@r@w{\the\count@i}% - \count@i=\OP@r@i - \advance\count@i\m@ne - \edef\OP@r@i{\the\count@i}% + \op@count@i=\OP@r@w + \advance\op@count@i\m@ne + \edef\OP@r@w{\the\op@count@i}% + \op@count@i=\OP@r@i + \advance\op@count@i\m@ne + \edef\OP@r@i{\the\op@count@i}% \fi\fi\fi\fi \setbox1=\hbox to\OP@r@w\opcolumnwidth{% \vbox{% \ifx\op@hfactor\op@string@right - \count@i=\OP@r@w - \advance\count@i by-\OP@a@d - \op@makebox{\the\count@i}{\OP@a@d}{operandstyle.1}{a}% + \op@count@i=\OP@r@w + \advance\op@count@i by-\OP@a@d + \op@makebox{\the\op@count@i}{\OP@a@d}{operandstyle.1}{a}% \hbox{\box0}% - \count@i=\OP@r@w - \advance\count@i by-\OP@b@d - \op@makebox{\the\count@i}{\OP@b@d}{operandstyle.2}{b}% + \op@count@i=\OP@r@w + \advance\op@count@i by-\OP@b@d + \op@makebox{\the\op@count@i}{\OP@b@d}{operandstyle.2}{b}% \hbox{\box0}% \else - \count@i=\OP@r@w - \count@ii=\op@max{\OP@a@d}{\OP@b@d}% - \advance\count@i by-\count@ii - \op@makebox{\the\count@i}{\the\count@ii}{operandstyle.1}{a}% + \op@count@i=\OP@r@w + \op@count@ii=\op@max{\OP@a@d}{\OP@b@d}% + \advance\op@count@i by-\op@count@ii + \op@makebox{\the\op@count@i}{\the\op@count@ii}{operandstyle.1}{a}% \hbox{\box0}% - \op@makebox{\the\count@i}{\the\count@ii}{operandstyle.2}{b}% + \op@makebox{\the\op@count@i}{\the\op@count@ii}{operandstyle.2}{b}% \hbox{\box0}% \fi \op@againtrue @@ -1595,31 +1628,31 @@ \op@againfalse \fi \fi - \global\count@z=0\relax + \global\op@count@z=0\relax \ifop@again - \count@ii=0\relax + \op@count@ii=0\relax \setbox2=\hbox{}% \loop - \ifnum\count@ii<\OP@b@w - \advance\count@ii by1 - \count@iii=\@nameuse{OP@b@\the\count@ii}% - \count@iv=\OP@r@w - \advance\count@iv by-\count@ii - \advance\count@iv by1 - \op@makebox{\the\count@iv}{0}% - {intermediarystyle.\the\count@ii}{T\the\count@iii}% + \ifnum\op@count@ii<\OP@b@w + \advance\op@count@ii by1 + \op@count@iii=\@nameuse{OP@b@\the\op@count@ii}% + \op@count@iv=\OP@r@w + \advance\op@count@iv by-\op@count@ii + \advance\op@count@iv by1 + \op@makebox{\the\op@count@iv}{0}% + {intermediarystyle.\the\op@count@ii}{T\the\op@count@iii}% \ifx\op@displayintermediary\op@string@all \hbox{\box0\copy2}% - \global\advance\count@z by1 + \global\advance\op@count@z by1 \else - \ifnum\the\count@iii=0 + \ifnum\the\op@count@iii=0 \ifx\op@displayshiftintermediary\op@string@shift \setbox2=\hbox{\box2\hbox to\opcolumnwidth{% \hss\op@shiftintermediarysymbol\hss}}% \fi \else \hbox{\box0\copy2}% - \global\advance\count@z by1 + \global\advance\op@count@z by1 \ifx\op@displayshiftintermediary\op@string@shift \setbox2=\hbox{}% \fi @@ -1634,46 +1667,46 @@ \op@makebox{\OP@r@i}{\OP@r@d}{resultstyle}{r}% \hbox{\box0}% }% - \count@i=\OP@r@w - \ophline(-\the\count@i,0.75){\the\count@i}% + \op@count@i=\OP@r@w + \ophline(-\the\op@count@i,0.75){\the\op@count@i}% \ifnum\OP@r@d>0\relax - \oprput(-\the\count@i,0.75){% + \oprput(-\the\op@count@i,0.75){% \vrule width\op@decimalsepwidth depth0.5\op@hrulewidth height0.5\op@hrulewidth} \fi \ifx\op@hfactor\op@string@right - \count@i=\op@max{\OP@a@w}{\OP@b@w}% + \op@count@i=\op@max{\OP@a@w}{\OP@b@w}% \else - \count@i=\op@max{\OP@a@d}{\OP@b@d}% - \advance\count@i by\op@max{\OP@a@i}{\OP@b@i}% + \op@count@i=\op@max{\OP@a@d}{\OP@b@d}% + \advance\op@count@i by\op@max{\OP@a@i}{\OP@b@i}% \fi - \advance\count@i by1\relax - \ophline(-\the\count@i,\the\count@z.75){\the\count@i}% + \advance\op@count@i by1\relax + \ophline(-\the\op@count@i,\the\op@count@z.75){\the\op@count@i}% \ifx\op@voperator\op@string@top - \advance\count@z by2 - \oplput(-\the\count@i,\the\count@z){\op@mulsymbol}% - \advance\count@z by-2 + \advance\op@count@z by2 + \oplput(-\the\op@count@i,\the\op@count@z){\op@mulsymbol}% + \advance\op@count@z by-2 \else\ifx\op@voperator\op@string@bottom - \advance\count@z by1 - \oplput(-\the\count@i,\the\count@z){\op@mulsymbol}% - \advance\count@z by-1 + \advance\op@count@z by1 + \oplput(-\the\op@count@i,\the\op@count@z){\op@mulsymbol}% + \advance\op@count@z by-1 \else - \advance\count@z by1 - \oplput(-\the\count@i,\the\count@z.5){\op@mulsymbol}% - \advance\count@z by-1 + \advance\op@count@z by1 + \oplput(-\the\op@count@i,\the\op@count@z.5){\op@mulsymbol}% + \advance\op@count@z by-1 \fi\fi }% \leavevmode \ifx\op@voperation\op@string@center - \advance\count@z by3 + \advance\op@count@z by3 \dimen0=\oplineheight - \multiply\dimen0 by\count@z + \multiply\dimen0 by\op@count@z \dimen0=0.5\dimen0 \lower\dimen0\box1 \else\ifx\op@voperation\op@string@top - \advance\count@z by2 + \advance\op@count@z by2 \dimen0=\oplineheight - \multiply\dimen0 by\count@z + \multiply\dimen0 by\op@count@z \lower\dimen0\box1 \else \box1 @@ -1684,33 +1717,33 @@ \def\op@mul#1#2#3{% \begingroup \op@multable{#1}% - \count@z=\@nameuse{OP@#2@w}\relax + \op@count@z=\@nameuse{OP@#2@w}\relax \op@copy{zero}{mr}% \loop - \count@iii=\@nameuse{OP@#2@\the\count@z}% - \advance\count@z by-1 - \op@copy{T\the\count@iii}{rr}% - \op@lshift{\the\count@z}{rr}% + \op@count@iii=\@nameuse{OP@#2@\the\op@count@z}% + \advance\op@count@z by-1 + \op@copy{T\the\op@count@iii}{rr}% + \op@lshift{\the\op@count@z}{rr}% \op@add{rr}{mr}{mr}% - \ifnum\count@z>0 + \ifnum\op@count@z>0 \repeat - \count@z=\@nameuse{OP@#1@d}% - \advance\count@z by\@nameuse{OP@#2@d}% - \xdef\OP@mr@d{\the\count@z}% - \count@i=\OP@mr@w - \advance\count@i by-\count@z - \ifnum\count@i>0\relax - \xdef\OP@mr@i{\the\count@i}% + \op@count@z=\@nameuse{OP@#1@d}% + \advance\op@count@z by\@nameuse{OP@#2@d}% + \xdef\OP@mr@d{\the\op@count@z}% + \op@count@i=\OP@mr@w + \advance\op@count@i by-\op@count@z + \ifnum\op@count@i>0\relax + \xdef\OP@mr@i{\the\op@count@i}% \else \xdef\OP@mr@i{1}% - \count@z=\@nameuse{OP@mr@d}% - \advance\count@z by1 - \count@i=\@nameuse{OP@mr@w}% - \@namexdef{OP@mr@w}{\the\count@z}% + \op@count@z=\@nameuse{OP@mr@d}% + \advance\op@count@z by1 + \op@count@i=\@nameuse{OP@mr@w}% + \@namexdef{OP@mr@w}{\the\op@count@z}% \loop - \ifnum\count@i<\count@z - \advance\count@i by1 - \@namexdef{OP@mr@\the\count@i}{0}% + \ifnum\op@count@i<\op@count@z + \advance\op@count@i by1 + \@namexdef{OP@mr@\the\op@count@i}{0}% \repeat \fi \op@copy{mr}{#3}% @@ -1721,6 +1754,7 @@ \@namexdef{OP@T1@i}{\@nameuse{OP@T1@w}}% \@namexdef{OP@T1@d}{0}% \@namexdef{OP@T1@s}{0}% + \op@unzero{T1}% \op@add{T1}{T1}{T2}% \op@add{T1}{T2}{T3}% \op@add{T1}{T3}{T4}% @@ -1729,46 +1763,45 @@ \op@add{T1}{T6}{T7}% \op@add{T1}{T7}{T8}% \op@add{T1}{T8}{T9}% - \op@unzero{T1}% \op@format{\@nameuse{OP@T1@i}}{\@nameuse{OP@T1@d}}{T0}% } \def\op@lshift#1#2{% \begingroup - \count@i=#1\relax - \count@z=\@nameuse{OP@#2@w}\relax - \advance\count@i by\count@z - \@namexdef{OP@#2@w}{\the\count@i}% - \@namexdef{OP@#2@i}{\the\count@i}% + \op@count@i=#1\relax + \op@count@z=\@nameuse{OP@#2@w}\relax + \advance\op@count@i by\op@count@z + \@namexdef{OP@#2@w}{\the\op@count@i}% + \@namexdef{OP@#2@i}{\the\op@count@i}% \loop - \ifnum\count@z>0 - \@namexdef{OP@#2@\the\count@i}{\@nameuse{OP@#2@\the\count@z}}% - \advance\count@z by-1 - \advance\count@i by-1 + \ifnum\op@count@z>0 + \@namexdef{OP@#2@\the\op@count@i}{\@nameuse{OP@#2@\the\op@count@z}}% + \advance\op@count@z by-1 + \advance\op@count@i by-1 \repeat \loop - \ifnum\count@i>0 - \@namexdef{OP@#2@\the\count@i}{0}% - \advance\count@i by-1 + \ifnum\op@count@i>0 + \@namexdef{OP@#2@\the\op@count@i}{0}% + \advance\op@count@i by-1 \repeat \endgroup } \def\op@rshift#1#2{% \begingroup - \count@i=#1\relax - \count@z=\@nameuse{OP@#2@w}\relax - \advance\count@z by-\count@i - \ifnum\count@z>0 - \@namexdef{OP@#2@w}{\the\count@z}% - \@namexdef{OP@#2@i}{\the\count@z}% + \op@count@i=#1\relax + \op@count@z=\@nameuse{OP@#2@w}\relax + \advance\op@count@z by-\op@count@i + \ifnum\op@count@z>0 + \@namexdef{OP@#2@w}{\the\op@count@z}% + \@namexdef{OP@#2@i}{\the\op@count@z}% \@namexdef{OP@#2@d}{0}% \@namexdef{OP@#2@s}{0}% - \advance\count@i by1\relax - \count@ii=1 + \advance\op@count@i by1\relax + \op@count@ii=1 \loop - \@namexdef{OP@#2@\the\count@ii}{\@nameuse{OP@#2@\the\count@i}}% - \advance\count@i by1 - \ifnum\count@ii<\count@z - \advance\count@ii by1 + \@namexdef{OP@#2@\the\op@count@ii}{\@nameuse{OP@#2@\the\op@count@i}}% + \advance\op@count@i by1 + \ifnum\op@count@ii<\op@count@z + \advance\op@count@ii by1 \repeat \else \op@copy{zero}{#2}% @@ -1782,6 +1815,16 @@ \opset{#1} \op@split{#2}{a}% \op@split{#3}{b}% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% Ajout du 20/11/2006 %%% +%%% Sur indication de Cristophe Poulain %%% + \op@cmp{b}{zero}% + \ifopeq + \op@error{divisor must be nonzero}% + {You have to learn some math}% + \fi +%%% Fin ajout %%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \ifop@error \op@errorwrite \else @@ -1825,6 +1868,16 @@ \opset{#1}% \op@split{#2}{a}% \op@split{#3}{b}% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% Ajout du 20/11/2006 %%% +%%% Sur indication de Cristophe Poulain %%% + \op@cmp{b}{zero}% + \ifopeq + \op@error{divisor must be nonzero}% + {You have to learn some math}% + \fi +%%% Fin ajout %%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \ifop@error \op@errorwrite \else @@ -1862,35 +1915,35 @@ \op@unzero{b}% \ifx\op@shiftdecimalsep\op@string@none \def\op@shift{0}% - \count@v=\OP@a@d - \advance\count@v by-\OP@b@d\relax - \ifnum\count@v>0 - \op@divpowerten{qq}{\the\count@v}% + \op@count@v=\OP@a@d + \advance\op@count@v by-\OP@b@d\relax + \ifnum\op@count@v>0 + \op@divpowerten{qq}{\the\op@count@v}% \else - \count@v=-\count@v - \op@mulpowerten{qq}{\the\count@v}% + \op@count@v=-\op@count@v + \op@mulpowerten{qq}{\the\op@count@v}% \fi \else\ifx\op@shiftdecimalsep\op@string@divisor \edef\op@shift{\OP@a@d}% - \count@v=\OP@a@d - \advance\count@v by-\OP@b@d\relax - \ifnum\count@v>0 - \op@divpowerten{qq}{\the\count@v}% + \op@count@v=\OP@a@d + \advance\op@count@v by-\OP@b@d\relax + \ifnum\op@count@v>0 + \op@divpowerten{qq}{\the\op@count@v}% \else - \count@v=-\count@v - \op@mulpowerten{qq}{\the\count@v}% + \op@count@v=-\op@count@v + \op@mulpowerten{qq}{\the\op@count@v}% \fi \edef\op@shift{\OP@b@d}% \op@split{#2}{a}% \ifx\op@strikedecimalsepsymbol\empty \op@unzero{a}% \else - \count@z=\OP@a@w + \op@count@z=\OP@a@w \fi \op@mulpowerten{a}{\OP@b@d}% \ifx\op@strikedecimalsepsymbol\empty\else - \advance\count@z by-\OP@a@d - \op@format{\the\count@z}{\OP@a@d}{a}% + \advance\op@count@z by-\OP@a@d + \op@format{\the\op@count@z}{\OP@a@d}{a}% \fi \xdef\OP@b@i{\OP@b@w}% \xdef\OP@b@d{0}% @@ -1903,16 +1956,16 @@ \op@unzero{a}% \op@unzero{b}% \else - \count@z=\OP@a@w - \count@i=\OP@b@w + \op@count@z=\OP@a@w + \op@count@i=\OP@b@w \fi \op@mulpowerten{a}{\op@shift}% \op@mulpowerten{b}{\op@shift}% \ifx\op@strikedecimalsepsymbol\empty\else - \advance\count@z by-\OP@a@d - \op@format{\the\count@z}{\OP@a@d}{a}% - \advance\count@i by-\OP@b@d - \op@format{\the\count@i}{\OP@b@d}{b}% + \advance\op@count@z by-\OP@a@d + \op@format{\the\op@count@z}{\OP@a@d}{a}% + \advance\op@count@i by-\OP@b@d + \op@format{\the\op@count@i}{\OP@b@d}{b}% \fi \fi\fi \ifx\op@country\op@string@french @@ -1999,6 +2052,16 @@ \begingroup \op@split{#1}{a}% \op@split{#2}{b}% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% Ajout du 20/11/2006 %%% +%%% Sur indication de Cristophe Poulain %%% + \op@cmp{b}{zero}% + \ifopeq + \op@error{divisor must be nonzero}% + {You have to learn some math}% + \fi +%%% Fin ajout %%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \ifop@error \op@errorwrite \else @@ -2041,6 +2104,16 @@ \let\op@shiftdecimalsep\op@string@both \op@split{#2}{a}% \op@split{#3}{b}% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% Ajout du 20/11/2006 %%% +%%% Sur indication de Cristophe Poulain %%% + \op@cmp{b}{zero}% + \ifopeq + \op@error{divisor must be nonzero}% + {You have to learn some math}% + \fi +%%% Fin ajout %%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \ifop@error \op@errorwrite \else @@ -2062,16 +2135,16 @@ \op@copy{q}{qq}% \edef\op@shift{\op@max{\OP@a@d}{\OP@b@d}}% \ifx\op@strikedecimalsepsymbol\empty\else - \count@z=\OP@a@w - \count@i=\OP@b@w + \op@count@z=\OP@a@w + \op@count@i=\OP@b@w \fi \op@mulpowerten{a}{\op@shift}% \op@mulpowerten{b}{\op@shift}% \ifx\op@strikedecimalsepsymbol\empty\else - \advance\count@z by-\OP@a@d - \op@format{\the\count@z}{\OP@a@d}{a}% - \advance\count@i by-\OP@b@d - \op@format{\the\count@i}{\OP@b@d}{b}% + \advance\op@count@z by-\OP@a@d + \op@format{\the\op@count@z}{\OP@a@d}{a}% + \advance\op@count@i by-\OP@b@d + \op@format{\the\op@count@i}{\OP@b@d}{b}% \fi \ifx\op@country\op@string@french \op@divdisplayone @@ -2162,23 +2235,23 @@ } \def\op@divdisplayone{% \begingroup - \count@z=\z@\relax - \count@i=\OP@a@w + \op@count@z=\z@\relax + \op@count@i=\OP@a@w \loop - \ifnum\@nameuse{OP@a@\the\count@i}=0 - \advance\count@i by-1 - \advance\count@z by1 + \ifnum\@nameuse{OP@a@\the\op@count@i}=0 + \advance\op@count@i by-1 + \advance\op@count@z by1 \repeat - \count@i=\op@firstlength - \advance\count@i by\count@z - \xdef\op@firstlength{\the\count@i}% + \op@count@i=\op@firstlength + \advance\op@count@i by\op@count@z + \xdef\op@firstlength{\the\op@count@i}% \setbox2=\vbox{% - \count@i=\op@firstlength - \advance\count@i by1 + \op@count@i=\op@firstlength + \advance\op@count@i by1 \hbox{% \ifx\op@displayintermediary\op@string@none\else \kern\opcolumnwidth - \advance\count@i by1 + \advance\op@count@i by1 \fi \ifop@dividendbridge \vrule width0pt depth0pt height\oplineheight @@ -2188,19 +2261,19 @@ \fi \op@display{operandstyle.1}{a}% \ifnum\op@shift=0\relax\else - \count@v=\op@shift - \advance\count@v by\OP@a@d - \oplput(-\the\count@v,0){\op@strikedecimalsepsymbol}% + \op@count@v=\op@shift + \advance\op@count@v by\OP@a@d + \oplput(-\the\op@count@v,0){\op@strikedecimalsepsymbol}% \fi }% - \count@z=\OP@q@w - \count@ii=1\relax + \op@count@z=\OP@q@w + \op@count@ii=1\relax \ifx\op@displayintermediary\op@string@none - \advance\count@i by-1\relax + \advance\op@count@i by-1\relax \else - \count@iv=\@nameuse{OP@q@\the\count@z}\relax - \count@iii=\count@i - \advance\count@iii by-\@nameuse{OP@T\the\count@iv @w}% + \op@count@iv=\@nameuse{OP@q@\the\op@count@z}\relax + \op@count@iii=\op@count@i + \advance\op@count@iii by-\@nameuse{OP@T\the\op@count@iv @w}% \hbox{% \ifx\op@voperator\op@string@center \oplput(0,0.5){\op@subsymbol}% @@ -2210,31 +2283,31 @@ \oplput(0,0){\op@subsymbol}% \fi\fi \ophline(1,-0.25){\op@firstlength}% - \advance\count@ii by1 - \kern\count@iii\opcolumnwidth + \advance\op@count@ii by1 + \kern\op@count@iii\opcolumnwidth \op@display{intermediarystyle.1}% - {T\the\count@iv}% + {T\the\op@count@iv}% }% \fi {\global\setbox4=\hbox{}\setbox4=\box4}% \loop - \advance\count@z by-1 - \advance\count@i by1\relax - \ifnum\count@z>0\relax - \count@iv=\@nameuse{OP@q@\the\count@z}\relax - \ifnum\count@iv=0 + \advance\op@count@z by-1 + \advance\op@count@i by1\relax + \ifnum\op@count@z>0\relax + \op@count@iv=\@nameuse{OP@q@\the\op@count@z}\relax + \ifnum\op@count@iv=0 \ifx\op@displayintermediary\op@string@all - \count@v=\count@i - \advance\count@v by-\@nameuse{OP@R\the\count@ii @w}% + \op@count@v=\op@count@i + \advance\op@count@v by-\@nameuse{OP@R\the\op@count@ii @w}% \hbox{% - \kern\count@v\opcolumnwidth - \op@display{remainderstyle.\the\count@ii}% - {R\the\count@ii}% + \kern\op@count@v\opcolumnwidth + \op@display{remainderstyle.\the\op@count@ii}% + {R\the\op@count@ii}% }% - \count@iii=\count@i - \advance\count@iii by-\@nameuse{OP@T\the\count@iv @w}% + \op@count@iii=\op@count@i + \advance\op@count@iii by-\@nameuse{OP@T\the\op@count@iv @w}% \hbox{% - \kern\count@v\opcolumnwidth + \kern\op@count@v\opcolumnwidth \ifx\op@voperator\op@string@center \oplput(-1,0.5){\op@subsymbol}% \else\ifx\op@voperator\op@string@top @@ -2242,39 +2315,39 @@ \else \oplput(-1,0){\op@subsymbol}% \fi\fi - \ophline(0,-0.25){\@nameuse{OP@R\the\count@ii @w}}% - \kern-\count@v\opcolumnwidth - \kern\count@iii\opcolumnwidth - \op@display{intermediarystyle.\the\count@ii}% - {T\the\count@iv}% + \ophline(0,-0.25){\@nameuse{OP@R\the\op@count@ii @w}}% + \kern-\op@count@v\opcolumnwidth + \kern\op@count@iii\opcolumnwidth + \op@display{intermediarystyle.\the\op@count@ii}% + {T\the\op@count@iv}% }% \else - \ifnum\@nameuse{OP@R\the\count@ii @w}=2 - \ifnum\@nameuse{OP@R\the\count@ii @2}=0 - \op@makebox{1}{0}{remainderstyle.\the\count@ii.1}{zero}% + \ifnum\@nameuse{OP@R\the\op@count@ii @w}=2 + \ifnum\@nameuse{OP@R\the\op@count@ii @2}=0 + \op@makebox{1}{0}{remainderstyle.\the\op@count@ii.1}{zero}% \setbox4=\hbox to\opcolumnwidth{\hss\box0\hss}% \fi \fi \fi - \advance\count@ii by1\relax + \advance\op@count@ii by1\relax \else - \count@v=\count@i - \advance\count@v by-\@nameuse{OP@R\the\count@ii @w}% + \op@count@v=\op@count@i + \advance\op@count@v by-\@nameuse{OP@R\the\op@count@ii @w}% \ifvoid4\relax\else - \advance\count@v by-1 + \advance\op@count@v by-1 \fi \hbox{% - \kern\count@v\opcolumnwidth\copy4 - \op@display{remainderstyle.\the\count@ii}% - {R\the\count@ii}% + \kern\op@count@v\opcolumnwidth\copy4 + \op@display{remainderstyle.\the\op@count@ii}% + {R\the\op@count@ii}% }% - \advance\count@ii by1\relax + \advance\op@count@ii by1\relax \ifx\op@displayintermediary\op@string@none \else - \count@iii=\count@i - \advance\count@iii by-\@nameuse{OP@T\the\count@iv @w}% + \op@count@iii=\op@count@i + \advance\op@count@iii by-\@nameuse{OP@T\the\op@count@iv @w}% \hbox{% - \kern\count@v\opcolumnwidth + \kern\op@count@v\opcolumnwidth \ifx\op@voperator\op@string@center \oplput(-1,0.5){\op@subsymbol}% \else\ifx\op@voperator\op@string@top @@ -2282,40 +2355,40 @@ \else \oplput(-1,0){\op@subsymbol}% \fi\fi - \advance\count@ii by-1 + \advance\op@count@ii by-1 \ifvoid4\relax - \ophline(0,-0.25){\@nameuse{OP@R\the\count@ii @w}}% + \ophline(0,-0.25){\@nameuse{OP@R\the\op@count@ii @w}}% \else - \ophline(0,-0.25){\@nameuse{OP@T\the\count@iv @w}}% - \ophline(\@nameuse{OP@T\the\count@iv @w},-0.25){1}% + \ophline(0,-0.25){\@nameuse{OP@T\the\op@count@iv @w}}% + \ophline(\@nameuse{OP@T\the\op@count@iv @w},-0.25){1}% {\setbox4=\box4}% \fi - \advance\count@ii by1 - \kern-\count@v\opcolumnwidth - \kern\count@iii\opcolumnwidth - \op@display{intermediarystyle.\the\count@ii}% - {T\the\count@iv}% + \advance\op@count@ii by1 + \kern-\op@count@v\opcolumnwidth + \kern\op@count@iii\opcolumnwidth + \op@display{intermediarystyle.\the\op@count@ii}% + {T\the\op@count@iv}% }% \fi \fi \repeat - \advance\count@i by-1 - \count@iii=\count@i - \advance\count@iii by-\@nameuse{OP@R\the\count@ii @w}% + \advance\op@count@i by-1 + \op@count@iii=\op@count@i + \advance\op@count@iii by-\@nameuse{OP@R\the\op@count@ii @w}% \hbox{% - \kern\count@iii\opcolumnwidth - \op@display{remainderstyle.\the\count@ii}% - {R\the\count@ii}% + \kern\op@count@iii\opcolumnwidth + \op@display{remainderstyle.\the\op@count@ii}% + {R\the\op@count@ii}% }% }% \setbox3=\vbox{% - \count@v=\op@max{\OP@qq@w}{\OP@b@w} - \hbox{\ophline(-0.5,-0.25){\the\count@v.5}% + \op@count@v=\op@max{\OP@qq@w}{\OP@b@w} + \hbox{\ophline(-0.5,-0.25){\the\op@count@v.5}% \op@display{operandstyle.2}{b}% \ifnum\op@shift=0\relax\else - \count@v=\op@shift - \advance\count@v by\OP@b@d - \oplput(-\the\count@v,0){\op@strikedecimalsepsymbol}% + \op@count@v=\op@shift + \advance\op@count@v by\OP@b@d + \oplput(-\the\op@count@v,0){\op@strikedecimalsepsymbol}% \fi} \hbox{\op@display{resultstyle}{qq}} }% @@ -2357,10 +2430,14 @@ \def\op@divmode{#1}% \op@copy{#2}{da}% \op@copy{#3}{db}% - \count@iv=0 - \count@iii=\op@max{\OP@da@d}{\OP@db@d}\relax - \op@powten{da}{\the\count@iii}% - \op@powten{db}{\the\count@iii}% + \op@count@iv=0 + \op@count@iii=\op@max{\OP@da@d}{\OP@db@d}\relax + \op@powten{da}{\the\op@count@iii}% + \op@powten{db}{\the\op@count@iii}% +% add 0.23 + \op@unzero{da}% + \op@unzero{db}% +% end 0.23 \ifnum\op@divmode=1 \op@cmp{da}{maxinteger}% \ifopgt @@ -2387,29 +2464,29 @@ \fi\fi \fi \op@multable{db}% + \op@copy{da}{R}% \op@cmp{da}{db}% \ifople - \op@copy{da}{R}% - \count@i=\OP@da@w + \op@count@i=\OP@da@w \else \xdef\OP@R@d{0}% \xdef\OP@R@s{0}% - \count@i=\@nameuse{OP@db@w}% - \op@leftdividend{\the\count@i}% + \op@count@i=\@nameuse{OP@db@w}% + \op@leftdividend{\the\op@count@i}% \op@cmp{R}{db}% \ifoplt - \ifnum\OP@da@w>\count@i - \advance\count@i by1 - \op@leftdividend{\the\count@i}% + \ifnum\OP@da@w>\op@count@i + \advance\op@count@i by1 + \op@leftdividend{\the\op@count@i}% \fi \fi \fi - \xdef\op@firstlength{\the\count@i}% - \count@i=-\count@i - \advance\count@i by\OP@da@w + \xdef\op@firstlength{\the\op@count@i}% + \op@count@i=-\op@count@i + \advance\op@count@i by\OP@da@w \op@copy{R}{R0}% \op@copy{zero}{dq}% - \count@ii=0 + \op@count@ii=0 \op@againtrue \loop \ifop@again @@ -2419,96 +2496,96 @@ \op@sub{R}{T\op@k}{dr}% \op@unzero{T\op@k}% \op@multen{dr}% - \ifnum\count@i>0 - \@namexdef{OP@dr@1}{\@nameuse{OP@da@\the\count@i}}% + \ifnum\op@count@i>0 + \@namexdef{OP@dr@1}{\@nameuse{OP@da@\the\op@count@i}}% \fi - \advance\count@i by-1\relax + \advance\op@count@i by-1\relax \op@unzero{dr}% \ifnum\OP@dr@w=1 \xdef\OP@dr@w{2}% \xdef\OP@dr@i{2}% \@namexdef{OP@dr@2}{0}% \fi - \advance\count@ii by1\relax - \op@copy{dr}{R\the\count@ii}% + \advance\op@count@ii by1\relax + \op@copy{dr}{R\the\op@count@ii}% \op@copy{dr}{R}% \ifcase\op@divmode\relax - \ifnum\count@ii<\op@maxdivstep\relax\else + \ifnum\op@count@ii<\op@maxdivstep\relax\else \op@againfalse \fi - \ifnum\count@i<0\relax% + \ifnum\op@count@i<0\relax% \op@cmp{zero}{R}% \ifopeq \op@againfalse \fi \fi \or - \ifnum\count@ii<\op@safedivstep\relax\else + \ifnum\op@count@ii<\op@safedivstep\relax\else \op@againfalse \fi - \ifnum\count@i<-\op@lengthperiod\relax - \count@iv=\count@ii - \advance\count@iv by-\op@lengthperiod - \op@cmp{R\the\count@iv}{R\the\count@ii}% + \ifnum\op@count@i<-\op@lengthperiod\relax + \op@count@iv=\op@count@ii + \advance\op@count@iv by-\op@lengthperiod + \op@cmp{R\the\op@count@iv}{R\the\op@count@ii}% \ifopeq \op@againfalse \fi \fi \or - \ifnum\count@i=-1 + \ifnum\op@count@i=-1 \op@againfalse \fi \fi \repeat \op@copy{zero}{T0}% - \advance\count@i by1\relax - \ifnum\count@i<0 - \xdef\OP@dq@d{-\the\count@i}% - \count@z=\OP@dq@w - \advance\count@z by\count@i - \xdef\OP@dq@i{\the\count@z}% + \advance\op@count@i by1\relax + \ifnum\op@count@i<0 + \xdef\OP@dq@d{-\the\op@count@i}% + \op@count@z=\OP@dq@w + \advance\op@count@z by\op@count@i + \xdef\OP@dq@i{\the\op@count@z}% \fi \op@unzero{dq}% \op@copy{dq}{#4}% \op@unzero{dr}% \op@copy{dr}{R}% \op@rshift{1}{dr}% - \op@copy{dr}{R\the\count@ii}% - \count@i=\count@iii - \advance\count@i by1 - \advance\count@i by\OP@dq@d\relax - \count@ii=\count@i - \advance\count@ii by\OP@R@w - \op@format{\the\count@ii}{0}{R}% - \count@z=\OP@R@w - \advance\count@z by-\count@i - \xdef\OP@R@i{\the\count@z}% - \xdef\OP@R@d{\the\count@i}% + \op@copy{dr}{R\the\op@count@ii}% + \op@count@i=\op@count@iii + \advance\op@count@i by1 + \advance\op@count@i by\OP@dq@d\relax + \op@count@ii=\op@count@i + \advance\op@count@ii by\OP@R@w + \op@format{\the\op@count@ii}{0}{R}% + \op@count@z=\OP@R@w + \advance\op@count@z by-\op@count@i + \xdef\OP@R@i{\the\op@count@z}% + \xdef\OP@R@d{\the\op@count@i}% \op@unzero{R}% \op@copy{R}{#5}% \endgroup } \def\op@powten#1#2{% \begingroup - \count@z=#2\relax - \advance\count@z by-\@nameuse{OP@#1@d}% + \op@count@z=#2\relax + \advance\op@count@z by-\@nameuse{OP@#1@d}% \@namexdef{OP@#1@d}{0}% - \count@i=\@nameuse{OP@#1@w}% - \advance\count@i by\count@z - \@namexdef{OP@#1@w}{\the\count@i}% - \@namexdef{OP@#1@i}{\the\count@i}% - \count@ii=\count@i - \advance\count@ii by-\count@z + \op@count@i=\@nameuse{OP@#1@w}% + \advance\op@count@i by\op@count@z + \@namexdef{OP@#1@w}{\the\op@count@i}% + \@namexdef{OP@#1@i}{\the\op@count@i}% + \op@count@ii=\op@count@i + \advance\op@count@ii by-\op@count@z \loop - \ifnum\count@ii>0 - \@namexdef{OP@#1@\the\count@i}{\@nameuse{OP@#1@\the\count@ii}}% - \advance\count@i by-1 - \advance\count@ii by-1 + \ifnum\op@count@ii>0 + \@namexdef{OP@#1@\the\op@count@i}{\@nameuse{OP@#1@\the\op@count@ii}}% + \advance\op@count@i by-1 + \advance\op@count@ii by-1 \repeat \loop - \ifnum\count@i>0 - \@namexdef{OP@#1@\the\count@i}{0}% - \advance\count@i by-1 + \ifnum\op@count@i>0 + \@namexdef{OP@#1@\the\op@count@i}{0}% + \advance\op@count@i by-1 \repeat \endgroup } @@ -2558,15 +2635,15 @@ } \def\op@divperiod#1#2#3{% \begingroup - \count@i=#1\relax - \count@ii=#2\relax - \ifnum\count@ii=0\relax + \op@count@i=#1\relax + \op@count@ii=#2\relax + \ifnum\op@count@ii=0\relax \@namexdef{#3}{1}% \else - \op@gcd{\the\count@i}{\the\count@ii}{op@tmp}% - \count@iii=\op@tmp - \divide\count@ii by\count@iii - \op@twofiveQ{\the\count@ii}{op@tmp}% + \op@gcd{\the\op@count@i}{\the\op@count@ii}{op@tmp}% + \op@count@iii=\op@tmp + \divide\op@count@ii by\op@count@iii + \op@twofiveQ{\the\op@count@ii}{op@tmp}% \op@order{\op@tmp}{op@tmp}% \@namexdef{#3}{\op@tmp}% \fi @@ -2616,83 +2693,83 @@ } \def\op@gcd#1#2#3{% \begingroup - \count@i=#1\relax - \count@ii=#2\relax + \op@count@i=#1\relax + \op@count@ii=#2\relax \loop - \count@iii=\count@i - \divide\count@iii by\count@ii - \multiply\count@iii by\count@ii - \advance\count@i by-\count@iii - \count@iii=\count@i\relax - \count@i=\count@ii\relax - \count@ii=\count@iii - \ifnum\count@ii>0 + \op@count@iii=\op@count@i + \divide\op@count@iii by\op@count@ii + \multiply\op@count@iii by\op@count@ii + \advance\op@count@i by-\op@count@iii + \op@count@iii=\op@count@i\relax + \op@count@i=\op@count@ii\relax + \op@count@ii=\op@count@iii + \ifnum\op@count@ii>0 \repeat - \@namexdef{#3}{\the\count@i}% + \@namexdef{#3}{\the\op@count@i}% \endgroup } \def\op@twofiveQ#1#2{% \begingroup - \count@i=#1\relax + \op@count@i=#1\relax \loop - \count@ii=\count@i - \divide\count@ii by2 - \multiply\count@ii by2 - \ifnum\count@ii=\count@i - \divide\count@i by2 + \op@count@ii=\op@count@i + \divide\op@count@ii by2 + \multiply\op@count@ii by2 + \ifnum\op@count@ii=\op@count@i + \divide\op@count@i by2 \repeat \loop - \count@ii=\count@i - \divide\count@ii by5 - \multiply\count@ii by5 - \ifnum\count@ii=\count@i - \divide\count@i by5 + \op@count@ii=\op@count@i + \divide\op@count@ii by5 + \multiply\op@count@ii by5 + \ifnum\op@count@ii=\op@count@i + \divide\op@count@i by5 \repeat - \@namexdef{#2}{\the\count@i}% + \@namexdef{#2}{\the\op@count@i}% \endgroup } \def\op@order#1#2{% \begingroup - \count@i=1\relax - \count@ii=0 + \op@count@i=1\relax + \op@count@ii=0 \loop - \multiply\count@i by10 - \count@iii=\count@i - \divide\count@iii by#1\relax - \multiply\count@iii by#1\relax - \advance\count@i by-\count@iii - \advance\count@ii by1 - \ifnum\count@i>1 + \multiply\op@count@i by10 + \op@count@iii=\op@count@i + \divide\op@count@iii by#1\relax + \multiply\op@count@iii by#1\relax + \advance\op@count@i by-\op@count@iii + \advance\op@count@ii by1 + \ifnum\op@count@i>1 \repeat - \@namexdef{#2}{\the\count@ii} + \@namexdef{#2}{\the\op@count@ii} \endgroup } \def\op@leftdividend#1{% \begingroup - \count@z=#1\relax - \count@i=\OP@da@w - \xdef\OP@R@w{\the\count@z}% - \xdef\OP@R@i{\the\count@z}% + \op@count@z=#1\relax + \op@count@i=\OP@da@w + \xdef\OP@R@w{\the\op@count@z}% + \xdef\OP@R@i{\the\op@count@z}% \loop - \@namexdef{OP@R@\the\count@z}{\@nameuse{OP@da@\the\count@i}}% - \advance\count@i by-1 - \advance\count@z by-1 - \ifnum\count@z>0 + \@namexdef{OP@R@\the\op@count@z}{\@nameuse{OP@da@\the\op@count@i}}% + \advance\op@count@i by-1 + \advance\op@count@z by-1 + \ifnum\op@count@z>0 \repeat \endgroup } \def\op@multen#1{% \begingroup - \count@z=\@nameuse{OP@#1@w}\relax - \count@i=\count@z - \advance\count@i by1 - \@namexdef{OP@#1@w}{\the\count@i}% - \@namexdef{OP@#1@i}{\the\count@i}% + \op@count@z=\@nameuse{OP@#1@w}\relax + \op@count@i=\op@count@z + \advance\op@count@i by1 + \@namexdef{OP@#1@w}{\the\op@count@i}% + \@namexdef{OP@#1@i}{\the\op@count@i}% \loop - \ifnum\count@z>0 - \@namexdef{OP@#1@\the\count@i}{\@nameuse{OP@#1@\the\count@z}}% - \advance\count@z by-1 - \advance\count@i by-1 + \ifnum\op@count@z>0 + \@namexdef{OP@#1@\the\op@count@i}{\@nameuse{OP@#1@\the\op@count@z}}% + \advance\op@count@z by-1 + \advance\op@count@i by-1 \repeat \@namexdef{OP@#1@1}{0}% \endgroup @@ -2700,32 +2777,32 @@ \def\op@mulpowerten#1#2{% \begingroup \ifnum\@nameuse{OP@#1@d}<#2\relax - \count@z=#2\relax - \advance\count@z by-\@nameuse{OP@#1@d}\relax - \count@ii=\@nameuse{OP@#1@w}% - \count@i=\@nameuse{OP@#1@w}% - \advance\count@i by\count@z - \@namexdef{OP@#1@w}{\the\count@i}% - \@namexdef{OP@#1@i}{\the\count@i}% + \op@count@z=#2\relax + \advance\op@count@z by-\@nameuse{OP@#1@d}\relax + \op@count@ii=\@nameuse{OP@#1@w}% + \op@count@i=\@nameuse{OP@#1@w}% + \advance\op@count@i by\op@count@z + \@namexdef{OP@#1@w}{\the\op@count@i}% + \@namexdef{OP@#1@i}{\the\op@count@i}% \@namexdef{OP@#1@d}{0}% \loop - \ifnum\count@ii>0 - \@namexdef{OP@#1@\the\count@i}{\@nameuse{OP@#1@\the\count@ii}}% - \advance\count@i by-1 - \advance\count@ii by-1 + \ifnum\op@count@ii>0 + \@namexdef{OP@#1@\the\op@count@i}{\@nameuse{OP@#1@\the\op@count@ii}}% + \advance\op@count@i by-1 + \advance\op@count@ii by-1 \repeat \loop - \ifnum\count@z>0 - \@namexdef{OP@#1@\the\count@z}{0}% - \advance\count@z by-1\relax + \ifnum\op@count@z>0 + \@namexdef{OP@#1@\the\op@count@z}{0}% + \advance\op@count@z by-1\relax \repeat \else - \count@z=\@nameuse{OP@#1@d}\relax - \advance\count@z by-#2\relax - \@namexdef{OP@#1@d}{\the\count@z}% - \count@z=\@nameuse{OP@#1@i}\relax - \advance\count@z by#2\relax - \@namexdef{OP@#1@i}{\the\count@z}% + \op@count@z=\@nameuse{OP@#1@d}\relax + \advance\op@count@z by-#2\relax + \@namexdef{OP@#1@d}{\the\op@count@z}% + \op@count@z=\@nameuse{OP@#1@i}\relax + \advance\op@count@z by#2\relax + \@namexdef{OP@#1@i}{\the\op@count@z}% \fi \op@unzero{#1}% \endgroup @@ -2733,25 +2810,25 @@ \def\op@divpowerten#1#2{% \begingroup \ifnum\@nameuse{OP@#1@i}>#2\relax - \count@z=\@nameuse{OP@#1@d}\relax - \advance\count@z by#2\relax - \@namexdef{OP@#1@d}{\the\count@z}% - \count@z=\@nameuse{OP@#1@i}\relax - \advance\count@z by-#2\relax - \@namexdef{OP@#1@i}{\the\count@z}% + \op@count@z=\@nameuse{OP@#1@d}\relax + \advance\op@count@z by#2\relax + \@namexdef{OP@#1@d}{\the\op@count@z}% + \op@count@z=\@nameuse{OP@#1@i}\relax + \advance\op@count@z by-#2\relax + \@namexdef{OP@#1@i}{\the\op@count@z}% \else - \count@z=\@nameuse{OP@#1@d}\relax - \advance\count@z by#2\relax - \@namexdef{OP@#1@d}{\the\count@z}% + \op@count@z=\@nameuse{OP@#1@d}\relax + \advance\op@count@z by#2\relax + \@namexdef{OP@#1@d}{\the\op@count@z}% \@namexdef{OP@#1@i}{1}% - \advance\count@z by1\relax - \count@i=\@nameuse{OP@#1@w}% - \@namexdef{OP@#1@w}{\the\count@z}% - \advance\count@z by1 + \advance\op@count@z by1\relax + \op@count@i=\@nameuse{OP@#1@w}% + \@namexdef{OP@#1@w}{\the\op@count@z}% + \advance\op@count@z by1 \loop - \ifnum\count@i<\count@z - \advance\count@i by1 - \@namexdef{OP@#1@\the\count@i}{0}% + \ifnum\op@count@i<\op@count@z + \advance\op@count@i by1 + \@namexdef{OP@#1@\the\op@count@i}{0}% \repeat \fi \op@unzero{#1}% @@ -2823,17 +2900,17 @@ \def\op@integer#1#2{% \begingroup \op@unzero{#1}% - \count@z=\@nameuse{OP@#1@d}\relax - \ifnum\count@z>0\relax - \count@i=0 + \op@count@z=\@nameuse{OP@#1@d}\relax + \ifnum\op@count@z>0\relax + \op@count@i=0 \loop - \ifnum\count@z<\@nameuse{OP@#1@w}% - \advance\count@z by1\relax - \advance\count@i by1\relax - \@namexdef{OP@#2@\the\count@i}{\@nameuse{OP@#1@\the\count@z}}% + \ifnum\op@count@z<\@nameuse{OP@#1@w}% + \advance\op@count@z by1\relax + \advance\op@count@i by1\relax + \@namexdef{OP@#2@\the\op@count@i}{\@nameuse{OP@#1@\the\op@count@z}}% \repeat - \@namexdef{OP@#2@w}{\the\count@i}% - \@namexdef{OP@#2@i}{\the\count@i}% + \@namexdef{OP@#2@w}{\the\op@count@i}% + \@namexdef{OP@#2@i}{\the\op@count@i}% \@namexdef{OP@#2@d}{0}% \else \op@copy{#1}{#2}% @@ -2888,17 +2965,17 @@ \op@unsplit{b}{@b}% \@namexdef{OP@a@#2}{\Op@@b}% \ifnum\OP@a@w<#2\relax - \count@z=\OP@a@w\relax - \advance\count@z by1\relax + \op@count@z=\OP@a@w\relax + \advance\op@count@z by1\relax \loop - \ifnum\count@z<#2\relax - \@namexdef{OP@a@\the\count@z}{0}% - \advance\count@z by1 + \ifnum\op@count@z<#2\relax + \@namexdef{OP@a@\the\op@count@z}{0}% + \advance\op@count@z by1 \repeat \xdef\OP@a@w{#2}% - \count@z=#2\relax - \advance\count@z by-\OP@a@d - \xdef\OP@a@i{\the\count@z}% + \op@count@z=#2\relax + \advance\op@count@z by-\OP@a@d + \xdef\OP@a@i{\the\op@count@z}% \fi \op@unsplit{a}{#1}% \fi @@ -2910,10 +2987,10 @@ \ifop@error \op@errorwrite \else - \count@z=\OP@a@d - \advance\count@z by#2\relax - \ifnum\OP@a@w>\count@z\relax - \@namexdef{Op@#3}{\@nameuse{OP@a@\the\count@z}}% + \op@count@z=\OP@a@d + \advance\op@count@z by#2\relax + \ifnum\OP@a@w>\op@count@z\relax + \@namexdef{Op@#3}{\@nameuse{OP@a@\the\op@count@z}}% \else \@namexdef{Op@#3}{0}% \fi @@ -2928,20 +3005,20 @@ \op@errorwrite \else \op@unsplit{b}{@b}% - \count@z=\OP@a@d - \advance\count@z by#2\relax - \@namexdef{OP@a@\the\count@z}{\Op@@b}% - \ifnum\OP@a@w>\count@z\relax\else - \count@i=\OP@a@w - \xdef\OP@a@w{\the\count@z}% - \advance\count@i by1 + \op@count@z=\OP@a@d + \advance\op@count@z by#2\relax + \@namexdef{OP@a@\the\op@count@z}{\Op@@b}% + \ifnum\OP@a@w>\op@count@z\relax\else + \op@count@i=\OP@a@w + \xdef\OP@a@w{\the\op@count@z}% + \advance\op@count@i by1 \loop - \ifnum\count@i<\count@z - \@namexdef{OP@a@\the\count@i}{0}% - \advance\count@i by1 + \ifnum\op@count@i<\op@count@z + \@namexdef{OP@a@\the\op@count@i}{0}% + \advance\op@count@i by1 \repeat - \advance\count@z by-\OP@a@d - \xdef\OP@a@i{\the\count@z}% + \advance\op@count@z by-\OP@a@d + \xdef\OP@a@i{\the\op@count@z}% \fi \op@unsplit{a}{#1}% \fi @@ -2956,10 +3033,10 @@ \ifnum\OP@a@d<#2\relax \@namexdef{Op@#3}{0}% \else - \count@z=\OP@a@d - \advance\count@z by-#2\relax - \advance\count@z by1 - \@namexdef{Op@#3}{\@nameuse{OP@a@\the\count@z}}% + \op@count@z=\OP@a@d + \advance\op@count@z by-#2\relax + \advance\op@count@z by1 + \@namexdef{Op@#3}{\@nameuse{OP@a@\the\op@count@z}}% \fi \fi \endgroup @@ -2973,31 +3050,42 @@ \else \op@unsplit{b}{@b}% \ifnum\OP@a@d<\Op@@b\relax - \count@z=\Op@@b - \advance\count@z by-\OP@a@d - \advance\count@z by1\relax - \count@i=\OP@a@w - \advance\count@i by\count@z\relax - \count@z=\OP@a@w - \xdef\OP@a@w{\the\count@i}% + \op@count@z=\Op@@b + \advance\op@count@z by-\OP@a@d +%%% [2006/10/06] Bug find by Dave Jarvis. +% \advance\op@count@z by1\relax +%%% end bug fixing + \op@count@i=\OP@a@w + \advance\op@count@i by\op@count@z\relax + \op@count@z=\OP@a@w + \xdef\OP@a@w{\the\op@count@i}% \xdef\OP@a@d{\Op@@b}% \loop - \ifnum\count@z>0 - \@namexdef{OP@a@\the\count@i}{\@nameuse{OP@a@\the\count@z}}% - \advance\count@z by-1 - \advance\count@i by-1 + \ifnum\op@count@z>0 + \@namexdef{OP@a@\the\op@count@i}{\@nameuse{OP@a@\the\op@count@z}}% + \advance\op@count@z by-1 + \advance\op@count@i by-1 \repeat \loop - \ifnum\count@i>1 - \@namexdef{OP@a@\the\count@i}{0}% - \advance\count@i by-1 + \ifnum\op@count@i>1 + \@namexdef{OP@a@\the\op@count@i}{0}% + \advance\op@count@i by-1 \repeat - \@namexdef{OP@a@1}{\Op@@b}% +%%% [2006/10/06] Bug find by Dave Jarvis. +% \@namexdef{OP@a@1}{\Op@@b}% + \@namexdef{OP@a@1}{#2}% +%%% end bug fixing \else - \count@z=\OP@a@d - \advance\count@z by-#2\relax - \advance\count@z by1 - \@namexdef{OP@a@\the\count@z}{\Op@@b}% + \op@count@z=\OP@a@d +%%% [2006/10/06] Bug find by Dave Jarvis. +% \advance\op@count@z by-#2\relax + \advance\op@count@z by-\Op@@b\relax +%%% end bug fixing + \advance\op@count@z by1 +%%% [2006/10/06] Bug find by Dave Jarvis. +% \@namexdef{OP@a@\the\op@count@z}{\Op@@b}% + \@namexdef{OP@a@\the\op@count@z}{#2}% +%%% end bug fixing \fi \op@unsplit{a}{#1}% \fi @@ -3009,17 +3097,17 @@ \ifop@error \op@errorwrite \else - \count@z=\OP@a@w\relax - \count@i=0\relax + \op@count@z=\OP@a@w\relax + \op@count@i=0\relax \loop - \ifnum\count@z>0 - \advance\count@i by\@nameuse{OP@a@\the\count@z}\relax - \ifnum\count@i>8 - \advance\count@i by-9 + \ifnum\op@count@z>0 + \advance\op@count@i by\@nameuse{OP@a@\the\op@count@z}\relax + \ifnum\op@count@i>8 + \advance\op@count@i by-9 \fi - \advance\count@z by-1 + \advance\op@count@z by-1 \repeat - \opcopy{\the\count@i}{#2}% + \opcopy{\the\op@count@i}{#2}% \fi \endgroup } @@ -3029,28 +3117,28 @@ \ifop@error \op@errorwrite \else - \count@ii=\OP@a@w - \advance\count@ii by1\relax - \count@i=0\relax - \count@z=-1\relax + \op@count@ii=\OP@a@w + \advance\op@count@ii by1\relax + \op@count@i=0\relax + \op@count@z=-1\relax \loop - \advance\count@z by2\relax - \ifnum\count@z<\count@ii - \advance\count@i by\@nameuse{OP@a@\the\count@z}\relax - \ifnum\count@i>10 - \advance\count@i by-11 + \advance\op@count@z by2\relax + \ifnum\op@count@z<\op@count@ii + \advance\op@count@i by\@nameuse{OP@a@\the\op@count@z}\relax + \ifnum\op@count@i>10 + \advance\op@count@i by-11 \fi \repeat - \count@z=0\relax + \op@count@z=0\relax \loop - \advance\count@z by2\relax - \ifnum\count@z<\count@ii - \advance\count@i by-\@nameuse{OP@a@\the\count@z}\relax - \ifnum\count@i<0 - \advance\count@i by11 + \advance\op@count@z by2\relax + \ifnum\op@count@z<\op@count@ii + \advance\op@count@i by-\@nameuse{OP@a@\the\op@count@z}\relax + \ifnum\op@count@i<0 + \advance\op@count@i by11 \fi \repeat - \opcopy{\the\count@i}{#2}% + \opcopy{\the\op@count@i}{#2}% \fi \endgroup } @@ -3075,9 +3163,9 @@ \op@againtrue \fi\fi\fi \ifop@again - \count@z=1 - \advance\count@z by-\@nameuse{OP@#2@s}\relax - \@namexdef{OP@#2@s}{\the\count@z}% + \op@count@z=1 + \advance\op@count@z by-\@nameuse{OP@#2@s}\relax + \@namexdef{OP@#2@s}{\the\op@count@z}% \fi \endgroup } @@ -3126,30 +3214,30 @@ \op@error{Exponent is too big (>1073741824)}% {Sorry}% \else - \count@z=0 + \op@count@z=0 \@namexdef{Op@@e0}{1}% \xdef\Op@@tmp{1}% \@namexdef{Op@@p0}{\Op@@a}% \@namexdef{Op@@ptmp}{\@nameuse{Op@@p0}}% \loop - \ifnum\@nameuse{Op@@e\the\count@z}<\Op@@b + \ifnum\@nameuse{Op@@e\the\op@count@z}<\Op@@b \opadd*{@tmp}{@tmp}{@@tmp}% \opmul*{@ptmp}{@ptmp}{@@ptmp}% - \advance\count@z by1 + \advance\op@count@z by1 \xdef\Op@@tmp{\Op@@@tmp}% \xdef\Op@@ptmp{\Op@@@ptmp}% - \@namexdef{Op@@e\the\count@z}{\Op@@@tmp}% - \@namexdef{Op@@p\the\count@z}{\Op@@@ptmp}% + \@namexdef{Op@@e\the\op@count@z}{\Op@@@tmp}% + \@namexdef{Op@@p\the\op@count@z}{\Op@@@ptmp}% \repeat \opcopy{1}{@r}% \loop \ifnum\Op@@b>0\relax - \ifnum\Op@@b<\@nameuse{Op@@e\the\count@z}\relax + \ifnum\Op@@b<\@nameuse{Op@@e\the\op@count@z}\relax \else - \opmul*{@r}{@p\the\count@z}{@r}% - \opsub*{@b}{@e\the\count@z}{@b}% + \opmul*{@r}{@p\the\op@count@z}{@r}% + \opsub*{@b}{@e\the\op@count@z}{@b}% \fi - \advance\count@z by-1 + \advance\op@count@z by-1 \repeat \opcopy{@r}{#3}% \fi @@ -3187,9 +3275,9 @@ \opneg{@rb}{@rb}% \ifnum\Op@@rb<\@nameuse{OP@ra@i}\relax \else - \count@z=\@nameuse{OP@ra@i}% - \advance\count@z by-1 - \xdef\Op@@rb{\the\count@z}% + \op@count@z=\@nameuse{OP@ra@i}% + \advance\op@count@z by-1 + \xdef\Op@@rb{\the\op@count@z}% \fi \opneg{@rb}{@rb}% \fi @@ -3226,56 +3314,56 @@ \begingroup \op@unsplit{#2}{@fb}% \op@unzero{#1}% - \count@z=\Op@@fb\relax - \ifnum\count@z<0 - \count@z=-\count@z - \ifnum\count@z<\@nameuse{OP@#1@i}\relax\else - \count@z=\@nameuse{OP@#1@i}% - \advance\count@z by-1 + \op@count@z=\Op@@fb\relax + \ifnum\op@count@z<0 + \op@count@z=-\op@count@z + \ifnum\op@count@z<\@nameuse{OP@#1@i}\relax\else + \op@count@z=\@nameuse{OP@#1@i}% + \advance\op@count@z by-1 \fi \op@integer{#1}{#1}% \loop - \ifnum\count@z>0 - \@namexdef{OP@#1@\the\count@z}{0}% - \advance\count@z by-1\relax + \ifnum\op@count@z>0 + \@namexdef{OP@#1@\the\op@count@z}{0}% + \advance\op@count@z by-1\relax \repeat \else - \ifnum\count@z>\@nameuse{OP@#1@d}% - \advance\count@z by-\@nameuse{OP@#1@d}% - \count@i=\@nameuse{OP@#1@d}% - \advance\count@i by\count@z - \@namexdef{OP@#1@d}{\the\count@i}% - \count@i=\@nameuse{OP@#1@w}\relax - \count@ii=\count@i - \advance\count@ii by\count@z - \@namexdef{OP@#1@w}{\the\count@ii}% + \ifnum\op@count@z>\@nameuse{OP@#1@d}% + \advance\op@count@z by-\@nameuse{OP@#1@d}% + \op@count@i=\@nameuse{OP@#1@d}% + \advance\op@count@i by\op@count@z + \@namexdef{OP@#1@d}{\the\op@count@i}% + \op@count@i=\@nameuse{OP@#1@w}\relax + \op@count@ii=\op@count@i + \advance\op@count@ii by\op@count@z + \@namexdef{OP@#1@w}{\the\op@count@ii}% \loop - \ifnum\count@i>0 - \@namexdef{OP@#1@\the\count@ii}{\@nameuse{OP@#1@\the\count@i}}% - \advance\count@i by-1 - \advance\count@ii by-1 + \ifnum\op@count@i>0 + \@namexdef{OP@#1@\the\op@count@ii}{\@nameuse{OP@#1@\the\op@count@i}}% + \advance\op@count@i by-1 + \advance\op@count@ii by-1 \repeat \loop - \ifnum\count@ii>0 - \@namexdef{OP@#1@\the\count@ii}{0}% - \advance\count@ii by-1 + \ifnum\op@count@ii>0 + \@namexdef{OP@#1@\the\op@count@ii}{0}% + \advance\op@count@ii by-1 \repeat \else - \advance\count@z by-\@nameuse{OP@#1@d}\relax - \count@z=-\count@z\relax - \count@i=\@nameuse{OP@#1@w}\relax - \count@ii=\count@i\relax - \advance\count@i by-\count@z - \@namexdef{OP@#1@w}{\the\count@i}\relax - \count@i=\@nameuse{OP@#1@d}\relax - \advance\count@i by-\count@z - \@namexdef{OP@#1@d}{\the\count@i}% - \count@i=0\relax + \advance\op@count@z by-\@nameuse{OP@#1@d}\relax + \op@count@z=-\op@count@z\relax + \op@count@i=\@nameuse{OP@#1@w}\relax + \op@count@ii=\op@count@i\relax + \advance\op@count@i by-\op@count@z + \@namexdef{OP@#1@w}{\the\op@count@i}\relax + \op@count@i=\@nameuse{OP@#1@d}\relax + \advance\op@count@i by-\op@count@z + \@namexdef{OP@#1@d}{\the\op@count@i}% + \op@count@i=0\relax \loop - \ifnum\count@z<\count@ii - \advance\count@z by1\relax - \advance\count@i by1 - \@namexdef{OP@#1@\the\count@i}{\@nameuse{OP@#1@\the\count@z}}% + \ifnum\op@count@z<\op@count@ii + \advance\op@count@z by1\relax + \advance\op@count@i by1 + \@namexdef{OP@#1@\the\op@count@i}{\@nameuse{OP@#1@\the\op@count@z}}% \repeat \fi \fi @@ -3285,10 +3373,10 @@ \op@unsplit{#1}{@Ca}% \op@unsplit{#2}{@Cb}% \op@unzero{#1}% - \count@z=\Op@@Cb\relax - \ifnum\count@z>0\relax - \ifnum\count@z<\@nameuse{OP@#1@d}\relax - \oppower{0.1}{\the\count@z}{@Cr}% + \op@count@z=\Op@@Cb\relax + \ifnum\op@count@z>0\relax + \ifnum\op@count@z<\@nameuse{OP@#1@d}\relax + \oppower{0.1}{\the\op@count@z}{@Cr}% \opadd*{@Ca}{@Cr}{@Ca}% \op@split{@Ca}{#1}% \op@split{@Cb}{#2}% @@ -3300,13 +3388,13 @@ \fi \else \opneg{@Cb}{@Cb}% - \count@z=-\count@z\relax - \ifnum\count@z<\@nameuse{OP@#1@i}\relax - \oppower{10}{\the\count@z}{@Cr}% + \op@count@z=-\op@count@z\relax + \ifnum\op@count@z<\@nameuse{OP@#1@i}\relax + \oppower{10}{\the\op@count@z}{@Cr}% \else - \count@z=\@nameuse{OP@#1@i}% - \advance\count@z by-1 - \oppower{10}{\the\count@z}{@Cr}% + \op@count@z=\@nameuse{OP@#1@i}% + \advance\op@count@z by-1 + \oppower{10}{\the\op@count@z}{@Cr}% \fi \opadd*{@Ca}{@Cr}{@Ca}% \opneg{@Cb}{@Cb}% @@ -3387,8 +3475,8 @@ \catcode`\ =12 \op@scan@@line } -\def\op@scan@@line#1{\op@scan@@@line#1\@nil\endgroup} -\def\op@scan@@@line#1#2\@nil{% +\def\op@scan@@line#1{\op@scan@@@line#1\op@nil\endgroup} +\def\op@scan@@@line#1#2\op@nil{% \op@testch@r{#1}% \ifop@isdigit \global\op@in@signfalse @@ -3482,293 +3570,293 @@ \else \let\next\op@scan@@@line \fi - \expandafter\next\@tempa\@nil + \expandafter\next\@tempa\op@nil } \def\op@search@subexpr#1#2{% \begingroup - \count@i=#1\relax - \count@v=#2\relax - \ifnum\count@i=\count@v + \op@count@i=#1\relax + \op@count@v=#2\relax + \ifnum\op@count@i=\op@count@v \op@token@use{#1}% \else - \count@iii=\count@v - \count@iv=\count@i - \advance\count@iv by-1 - \count@ii=0 + \op@count@iii=\op@count@v + \op@count@iv=\op@count@i + \advance\op@count@iv by-1 + \op@count@ii=0 \loop - \ifnum\count@iii>\count@iv - \expandafter\ifx\csname OP@token\the\count@iii\endcsname + \ifnum\op@count@iii>\op@count@iv + \expandafter\ifx\csname OP@token\the\op@count@iii\endcsname \op@string@rpar\relax \advance\op@parenthesis by1 \fi - \expandafter\ifx\csname OP@token\the\count@iii\endcsname + \expandafter\ifx\csname OP@token\the\op@count@iii\endcsname \op@string@lpar\relax \advance\op@parenthesis by-1 \fi - \expandafter\ifx\csname OP@token\the\count@iii\endcsname + \expandafter\ifx\csname OP@token\the\op@count@iii\endcsname \op@string@comma\relax \ifnum\op@parenthesis=0 - \count@ii=\count@iii\relax - \count@iii=0 + \op@count@ii=\op@count@iii\relax + \op@count@iii=0 \fi \fi - \advance\count@iii by-1 + \advance\op@count@iii by-1 \repeat - \ifnum\count@ii=0\relax + \ifnum\op@count@ii=0\relax \ifnum\op@parenthesis=0 - \op@search@term{\the\count@i}{\the\count@v}% + \op@search@term{\the\op@count@i}{\the\op@count@v}% \else \op@error{Unbalanced parenthesis in expression}% {Error between tokens #1 and #2}% \fi \else - \advance\count@ii by-1 - \op@search@subexpr{\the\count@i}{\the\count@ii}% - \advance\count@ii by2 - \op@search@subexpr{\the\count@ii}{\the\count@v}% + \advance\op@count@ii by-1 + \op@search@subexpr{\the\op@count@i}{\the\op@count@ii}% + \advance\op@count@ii by2 + \op@search@subexpr{\the\op@count@ii}{\the\op@count@v}% \fi \fi \endgroup } \def\op@search@term#1#2{% \begingroup - \count@i=#1\relax - \count@v=#2\relax - \ifnum\count@i=\count@v + \op@count@i=#1\relax + \op@count@v=#2\relax + \ifnum\op@count@i=\op@count@v \op@token@use{#1}% \else - \count@iii=\count@v - \count@iv=\count@i - \advance\count@iv by-1 - \count@ii=0\relax + \op@count@iii=\op@count@v + \op@count@iv=\op@count@i + \advance\op@count@iv by-1 + \op@count@ii=0\relax \loop - \ifnum\count@iii>\count@iv\relax - \expandafter\ifx\csname OP@token\the\count@iii\endcsname + \ifnum\op@count@iii>\op@count@iv\relax + \expandafter\ifx\csname OP@token\the\op@count@iii\endcsname \op@string@rpar\relax \advance\op@parenthesis by1 \fi - \expandafter\ifx\csname OP@token\the\count@iii\endcsname + \expandafter\ifx\csname OP@token\the\op@count@iii\endcsname \op@string@lpar\relax \advance\op@parenthesis by-1 \fi - \expandafter\ifx\csname OP@token\the\count@iii\endcsname + \expandafter\ifx\csname OP@token\the\op@count@iii\endcsname \op@string@add\relax \ifnum\op@parenthesis=0 - \count@ii=\count@iii\relax - \count@iii=0 + \op@count@ii=\op@count@iii\relax + \op@count@iii=0 \fi \fi - \expandafter\ifx\csname OP@token\the\count@iii\endcsname + \expandafter\ifx\csname OP@token\the\op@count@iii\endcsname \op@string@sub\relax \ifnum\op@parenthesis=0 - \count@ii=\count@iii\relax - \count@iii=0 + \op@count@ii=\op@count@iii\relax + \op@count@iii=0 \fi \fi - \advance\count@iii by-1 + \advance\op@count@iii by-1 \repeat - \ifnum\count@ii=0\relax + \ifnum\op@count@ii=0\relax \ifnum\op@parenthesis=0 - \op@search@factor{\the\count@i}{\the\count@v}% + \op@search@factor{\the\op@count@i}{\the\op@count@v}% \else \op@error{Unbalanced parenthesis in expression}% {Error between tokens #1 and #2}% \fi \else - \advance\count@ii by-1 - \op@search@term{\the\count@i}{\the\count@ii}% - \advance\count@ii by2 - \op@search@term{\the\count@ii}{\the\count@v}% - \advance\count@ii by-1 - \op@token@use{\the\count@ii}% + \advance\op@count@ii by-1 + \op@search@term{\the\op@count@i}{\the\op@count@ii}% + \advance\op@count@ii by2 + \op@search@term{\the\op@count@ii}{\the\op@count@v}% + \advance\op@count@ii by-1 + \op@token@use{\the\op@count@ii}% \fi \fi \endgroup } \def\op@search@factor#1#2{% \begingroup - \count@i=#1\relax - \count@v=#2\relax - \ifnum\count@i=\count@v + \op@count@i=#1\relax + \op@count@v=#2\relax + \ifnum\op@count@i=\op@count@v \op@token@use{#1}% \else - \count@iii=\count@v - \count@iv=\count@i - \advance\count@iv by-1 - \count@ii=0 + \op@count@iii=\op@count@v + \op@count@iv=\op@count@i + \advance\op@count@iv by-1 + \op@count@ii=0 \loop - \ifnum\count@iii>\count@iv - \expandafter\ifx\csname OP@token\the\count@iii\endcsname + \ifnum\op@count@iii>\op@count@iv + \expandafter\ifx\csname OP@token\the\op@count@iii\endcsname \op@string@rpar\relax \advance\op@parenthesis by1 \fi - \expandafter\ifx\csname OP@token\the\count@iii\endcsname + \expandafter\ifx\csname OP@token\the\op@count@iii\endcsname \op@string@lpar\relax \advance\op@parenthesis by-1 \fi - \expandafter\ifx\csname OP@token\the\count@iii\endcsname + \expandafter\ifx\csname OP@token\the\op@count@iii\endcsname \op@string@mul\relax \ifnum\op@parenthesis=0 - \count@ii=\count@iii\relax - \count@iii=0 + \op@count@ii=\op@count@iii\relax + \op@count@iii=0 \fi \fi - \expandafter\ifx\csname OP@token\the\count@iii\endcsname + \expandafter\ifx\csname OP@token\the\op@count@iii\endcsname \op@string@div\relax \ifnum\op@parenthesis=0 - \count@ii=\count@iii\relax - \count@iii=0 + \op@count@ii=\op@count@iii\relax + \op@count@iii=0 \fi \fi - \expandafter\ifx\csname OP@token\the\count@iii\endcsname + \expandafter\ifx\csname OP@token\the\op@count@iii\endcsname \op@string@idiv\relax \ifnum\op@parenthesis=0 - \count@ii=\count@iii\relax - \count@iii=0 + \op@count@ii=\op@count@iii\relax + \op@count@iii=0 \fi \fi - \advance\count@iii by-1 + \advance\op@count@iii by-1 \repeat - \ifnum\count@ii=0\relax + \ifnum\op@count@ii=0\relax \ifnum\op@parenthesis=0 - \op@search@power{\the\count@i}{\the\count@v}% + \op@search@power{\the\op@count@i}{\the\op@count@v}% \else \op@error{Unbalanced parenthesis in expression}% {Error between tokens #1 and #2}% \fi \else - \advance\count@ii by-1 - \op@search@factor{\the\count@i}{\the\count@ii}% - \advance\count@ii by2 - \op@search@factor{\the\count@ii}{\the\count@v}% - \advance\count@ii by-1 - \op@token@use{\the\count@ii}% + \advance\op@count@ii by-1 + \op@search@factor{\the\op@count@i}{\the\op@count@ii}% + \advance\op@count@ii by2 + \op@search@factor{\the\op@count@ii}{\the\op@count@v}% + \advance\op@count@ii by-1 + \op@token@use{\the\op@count@ii}% \fi \fi \endgroup } \def\op@search@power#1#2{% \begingroup - \count@i=#1\relax - \count@v=#2\relax - \ifnum\count@i=\count@v + \op@count@i=#1\relax + \op@count@v=#2\relax + \ifnum\op@count@i=\op@count@v \op@token@use{#1}% \else - \count@iii=\count@v - \count@iv=\count@i - \advance\count@iv by-1 - \count@ii=0 + \op@count@iii=\op@count@v + \op@count@iv=\op@count@i + \advance\op@count@iv by-1 + \op@count@ii=0 \loop - \ifnum\count@iii>\count@iv - \expandafter\ifx\csname OP@token\the\count@iii\endcsname + \ifnum\op@count@iii>\op@count@iv + \expandafter\ifx\csname OP@token\the\op@count@iii\endcsname \op@string@rpar\relax \advance\op@parenthesis by1 \fi - \expandafter\ifx\csname OP@token\the\count@iii\endcsname + \expandafter\ifx\csname OP@token\the\op@count@iii\endcsname \op@string@lpar\relax \advance\op@parenthesis by-1 \fi - \expandafter\ifx\csname OP@token\the\count@iii\endcsname + \expandafter\ifx\csname OP@token\the\op@count@iii\endcsname \op@string@power\relax \ifnum\op@parenthesis=0 - \count@ii=\count@iii\relax - \count@iii=0 + \op@count@ii=\op@count@iii\relax + \op@count@iii=0 \fi \fi - \advance\count@iii by-1 + \advance\op@count@iii by-1 \repeat - \ifnum\count@ii=0\relax + \ifnum\op@count@ii=0\relax \ifnum\op@parenthesis=0 - \op@search@primary{\the\count@i}{\the\count@v}% + \op@search@primary{\the\op@count@i}{\the\op@count@v}% \else \op@error{Unbalanced parenthesis in expression}% {Error between tokens #1 and #2}% \fi \else - \advance\count@ii by-1 - \op@search@power{\the\count@i}{\the\count@ii}% - \advance\count@ii by2 - \op@search@power{\the\count@ii}{\the\count@v}% - \advance\count@ii by-1 - \op@token@use{\the\count@ii}% + \advance\op@count@ii by-1 + \op@search@power{\the\op@count@i}{\the\op@count@ii}% + \advance\op@count@ii by2 + \op@search@power{\the\op@count@ii}{\the\op@count@v}% + \advance\op@count@ii by-1 + \op@token@use{\the\op@count@ii}% \fi \fi \endgroup } \def\op@search@primary#1#2{% \begingroup - \count@i=#1\relax - \count@v=#2\relax - \ifnum\count@i=\count@v + \op@count@i=#1\relax + \op@count@v=#2\relax + \ifnum\op@count@i=\op@count@v \op@token@use{#1}% \else \expandafter\ifx\csname OP@token#1\endcsname\op@string@abs - \advance\count@i by1 - \op@search@primary{\the\count@i}{\the\count@v}% - \advance\count@i by-1 - \op@token@use{\the\count@i}% + \advance\op@count@i by1 + \op@search@primary{\the\op@count@i}{\the\op@count@v}% + \advance\op@count@i by-1 + \op@token@use{\the\op@count@i}% \fi \expandafter\ifx\csname OP@token#1\endcsname\op@string@ceil - \advance\count@i by1 - \op@search@primary{\the\count@i}{\the\count@v}% - \advance\count@i by-1 - \op@token@use{\the\count@i}% + \advance\op@count@i by1 + \op@search@primary{\the\op@count@i}{\the\op@count@v}% + \advance\op@count@i by-1 + \op@token@use{\the\op@count@i}% \fi \expandafter\ifx\csname OP@token#1\endcsname\op@string@decimal - \advance\count@i by1 - \op@search@primary{\the\count@i}{\the\count@v}% - \advance\count@i by-1 - \op@token@use{\the\count@i}% + \advance\op@count@i by1 + \op@search@primary{\the\op@count@i}{\the\op@count@v}% + \advance\op@count@i by-1 + \op@token@use{\the\op@count@i}% \fi \expandafter\ifx\csname OP@token#1\endcsname\op@string@floor - \advance\count@i by1 - \op@search@primary{\the\count@i}{\the\count@v}% - \advance\count@i by-1 - \op@token@use{\the\count@i}% + \advance\op@count@i by1 + \op@search@primary{\the\op@count@i}{\the\op@count@v}% + \advance\op@count@i by-1 + \op@token@use{\the\op@count@i}% \fi \expandafter\ifx\csname OP@token#1\endcsname\op@string@integer - \advance\count@i by1 - \op@search@primary{\the\count@i}{\the\count@v}% - \advance\count@i by-1 - \op@token@use{\the\count@i}% + \advance\op@count@i by1 + \op@search@primary{\the\op@count@i}{\the\op@count@v}% + \advance\op@count@i by-1 + \op@token@use{\the\op@count@i}% \fi \expandafter\ifx\csname OP@token#1\endcsname\op@string@gcd - \advance\count@i by1 - \op@search@primary{\the\count@i}{\the\count@v}% - \advance\count@i by-1 - \op@token@use{\the\count@i}% + \advance\op@count@i by1 + \op@search@primary{\the\op@count@i}{\the\op@count@v}% + \advance\op@count@i by-1 + \op@token@use{\the\op@count@i}% \fi \expandafter\ifx\csname OP@token#1\endcsname\op@string@mod - \advance\count@i by1 - \op@search@primary{\the\count@i}{\the\count@v}% - \advance\count@i by-1 - \op@token@use{\the\count@i}% + \advance\op@count@i by1 + \op@search@primary{\the\op@count@i}{\the\op@count@v}% + \advance\op@count@i by-1 + \op@token@use{\the\op@count@i}% \fi \expandafter\ifx\csname OP@token#1\endcsname\op@string@neg - \advance\count@i by1 - \op@search@primary{\the\count@i}{\the\count@v}% - \advance\count@i by-1 - \op@token@use{\the\count@i}% + \advance\op@count@i by1 + \op@search@primary{\the\op@count@i}{\the\op@count@v}% + \advance\op@count@i by-1 + \op@token@use{\the\op@count@i}% \fi \expandafter\ifx\csname OP@token#1\endcsname\op@string@rest - \advance\count@i by1 - \op@search@primary{\the\count@i}{\the\count@v}% - \advance\count@i by-1 - \op@token@use{\the\count@i}% + \advance\op@count@i by1 + \op@search@primary{\the\op@count@i}{\the\op@count@v}% + \advance\op@count@i by-1 + \op@token@use{\the\op@count@i}% \fi \expandafter\ifx\csname OP@token#1\endcsname\op@string@round - \advance\count@i by1 - \op@search@primary{\the\count@i}{\the\count@v}% - \advance\count@i by-1 - \op@token@use{\the\count@i}% + \advance\op@count@i by1 + \op@search@primary{\the\op@count@i}{\the\op@count@v}% + \advance\op@count@i by-1 + \op@token@use{\the\op@count@i}% \fi \expandafter\ifx\csname OP@token#1\endcsname \op@string@lpar\relax \expandafter\ifx\csname OP@token#2\endcsname \op@string@rpar\relax - \advance\count@i by1 - \advance\count@v by-1 - \op@search@subexpr{\the\count@i}{\the\count@v}% + \advance\op@count@i by1 + \advance\op@count@v by-1 + \op@search@subexpr{\the\op@count@i}{\the\op@count@v}% \else \op@error{Garbage after parenthesis}% {Error between tokens #1 and #2}% @@ -3905,32 +3993,32 @@ \op@isrparenthesisfalse \op@isspacefalse \op@isotherfalse - \count255=`#1\relax - \ifnum\count255=\op@plus \relax + \count@=`#1\relax + \ifnum\count@=\op@plus \relax \op@isplustrue - \else \ifnum\count255=\op@minus \relax + \else \ifnum\count@=\op@minus \relax \op@isminustrue - \else \ifnum\count255=\op@multiply \relax + \else \ifnum\count@=\op@multiply \relax \op@ismultiplytrue - \else \ifnum\count255=\op@divide \relax + \else \ifnum\count@=\op@divide \relax \op@isdividetrue - \else \ifnum\count255=\op@idivide \relax + \else \ifnum\count@=\op@idivide \relax \op@isidividetrue - \else \ifnum\count255=\op@pow \relax + \else \ifnum\count@=\op@pow \relax \op@ispowertrue - \else \ifnum\count255=\op@dot \relax + \else \ifnum\count@=\op@dot \relax \op@isdottrue - \else \ifnum\count255=\op@comma \relax + \else \ifnum\count@=\op@comma \relax \op@iscommatrue - \else \ifnum\count255=\op@lparenthesis \relax + \else \ifnum\count@=\op@lparenthesis \relax \op@islparenthesistrue - \else \ifnum\count255=\op@rparenthesis \relax + \else \ifnum\count@=\op@rparenthesis \relax \op@isrparenthesistrue - \else \ifnum\count255=\op@space \relax + \else \ifnum\count@=\op@space \relax \op@isspacetrue - \else \ifnum\count255<\op@numbegin \relax + \else \ifnum\count@<\op@numbegin \relax \op@isothertrue - \else \ifnum\count255>\op@numend \relax + \else \ifnum\count@>\op@numend \relax \op@isothertrue \else \op@isdigittrue \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi |