apnum (4jan15)

git-svn-id: svn://tug.org/texlive/trunk@35958 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 65 insertions, 74 deletions

diff --git a/Master/texmf-dist/tex/generic/apnum/apnum.tex b/Master/texmf-dist/tex/generic/apnum/apnum.tex
index cb891d55bcc..28f1dea9557 100644
--- a/Master/texmf-dist/tex/generic/apnum/apnum.tex
+++ b/Master/texmf-dist/tex/generic/apnum/apnum.tex
@@ -1,10 +1,10 @@
 % Arbitrary precision numbers
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% 2014             Petr Olsak
+% 2014, 2015       Petr Olsak
 
 % See the documentation apnum.pdf or apnum.d for more information
 
-\def\apnumversion{1.0 <Nov. 2014>}
+\def\apnumversion{1.1 <Jan. 2015>}
 \message{The Arbitrary Precision Numbers, \apnumversion}
 
 %%%%%%%%%%%% Internal registers:
@@ -55,17 +55,17 @@
    \apTESTdigit#1\iftrue 
       \ifx E#1\let\tmpb=\tmpa \expandafter\apEVALd\expandafter\apEVALk
       \else \edef\tmpb{\tmpa#1}\expandafter\apEVALd\expandafter\apEVALn\fi\fi
-   \edef\tmpb{\tmpa\noexpand#1}\futurelet\next\apEVALg
+   \edef\tmpb{\tmpa\noexpand#1}\futurelet\apNext\apEVALg
 }
-\def\apEVALd#1\fi#2\next\apEVALg{\fi#1}
+\def\apEVALd#1\fi#2\apNext\apEVALg{\fi#1}
 \def\apEVALe{%
    \ifx\tmpa\empty \else \ifnum\tmpa1<0 \def\tmpb{-1}\apEVALp \MUL 4\fi\fi
    \advance\apnumA by4
    \apEVALb
 }
 \def\apEVALf#1#2{\expandafter\def\expandafter\tmpb\expandafter{\tmpa#1#2}\apEVALo}
-\def\apEVALg{\ifx\next \bgroup \expandafter\apEVALh \else \expandafter\apEVALo \fi}
-\def\apEVALh#1{\expandafter\def\expandafter\tmpb\expandafter{\tmpb{#1}}\futurelet\next\apEVALg}
+\def\apEVALg{\ifx\apNext \bgroup \expandafter\apEVALh \else \expandafter\apEVALo \fi}
+\def\apEVALh#1{\expandafter\def\expandafter\tmpb\expandafter{\tmpb{#1}}\futurelet\apNext\apEVALg}
 \def\apEVALk{\afterassignment\apEVALm\apE=}
 \def\apEVALm{\edef\tmpb{\tmpb E\the\apE}\apEVALo}
 \def\apEVALn#1{\apTESTdigit#1%
@@ -73,22 +73,22 @@
            \else\edef\tmpb{\tmpb#1}\expandafter\expandafter\expandafter\apEVALn\fi
    \else \expandafter\apEVALo\expandafter#1\fi
 }
-\def\apEVALo#1{\let\next=\apEVALb
+\def\apEVALo#1{\let\apNext=\apEVALb
    \ifx+#1\apEVALp \apEPLUS 1\fi
    \ifx-#1\apEVALp \apEMINUS 1\fi
    \ifx*#1\apEVALp \apEMUL 2\fi
    \ifx/#1\apEVALp \apEDIV 2\fi
    \ifx^#1\apEVALp \apEPOW 3\fi
-   \ifx)#1\advance\apnumA by-4 \let\next=\apEVALo \let\tmpa=\relax
+   \ifx)#1\advance\apnumA by-4 \let\apNext=\apEVALo \let\tmpa=\relax
       \ifnum\apnumA<0 \apEVALerror{many brackets ")"}\fi
    \fi
    \ifx\end#1%
       \ifnum\apnumA>0 \apEVALerror{missing bracket ")"}% 
       \else \apEVALp\END 0\fi
-      \let\next=\relax
+      \let\apNext=\relax
    \fi
    \ifx\tmpa\relax \else \apEVALerror{unknown operator "\string#1"}\fi
-   \apnumE=0 \next
+   \apnumE=0 \apNext
 }
 \def\apEVALp#1#2{%
    \apnumB=#2 \advance\apnumB by\apnumA
@@ -112,7 +112,7 @@
    \fi\fi
 }
 \def\apEVALerror#1{\message{\noexpand\evaldef ERROR: #1.}%
-   \def\tmpb{\def\OUT{??}}\def\next##1\end{}%
+   \def\tmpb{\def\OUT{??}}\def\apNext##1\end{}%
 }
 \def\apTESTdigit#1#2{%
    \ifx E#1\apXtrue \else
@@ -166,12 +166,12 @@
 }
 \def\apPPs#1#2#3{\def\tmpc{#3}\expandafter\apPPt\expandafter#1#2.@#2}
 \def\apPPt#1#2{%
-   \ifx-#2\apnumG=-1 \def\next{#1}%
-   \else \ifx0#2\apnumG=0 \def\next{\apPPu#1}\else \apnumG=1 \def\next{#1#2}\fi\fi 
-   \next
+   \ifx-#2\apnumG=-1 \def\apNext{#1}%
+   \else \ifx0#2\apnumG=0 \def\apNext{\apPPu#1}\else \apnumG=1 \def\apNext{#1#2}\fi\fi 
+   \apNext
 }
 \def\apPPu#1#2.@#3{\ifx@#2@\apnumG=0 \ifx#1\apROUNDa\def\XOUT{}\fi
-   \else\def\next{\apPPt#1#2.@#3}\expandafter\next\fi
+   \else\def\apNext{\apPPt#1#2.@#3}\expandafter\apNext\fi
 }
 \def\apEVALone#1#2{\evaldef\OUT{#2}\ifnum\apSIGN<0 \expandafter\apNOminus\OUT@\OUT\fi #1}
 \def\apEVALtwo#1#2#3{%
@@ -201,8 +201,8 @@
    \else \apnumC=-\apnumC    \apPLUSb \tmpa\apnumE \tmpb\apnumF \apnumA
    \fi
    \ifnum\apnumG=0 \def\OUT{0}\apSIGN=0 \apE=0 \else
-      \ifnum\apSIGN=0 \apSIGN=\apnumG \let\next=\apPLUSm \else \let\next=\apPLUSp \fi
-      \apnumX=0 \edef\OUT{\expandafter}\expandafter \next \OUT@% second pass
+      \ifnum\apSIGN=0 \apSIGN=\apnumG \let\apNext=\apPLUSm \else \let\apNext=\apPLUSp \fi
+      \apnumX=0 \edef\OUT{\expandafter}\expandafter \apNext \OUT@% second pass
       \ifnum\apnumD<1 % result in the form .000123
          \apnumZ=-\apnumD
          \def\tmpa{.}%
@@ -215,11 +215,11 @@
 \def\apPLUSb#1#2#3#4#5{%
    \edef\tmpd{\ifcase#4\or{}{}{}\or{}{}\or{}\fi#3}%
    \edef\tmpc{\ifcase#2\or{}{}{}\or{}{}\or{}\fi}%
-   \let\next=\apPLUSc \apnumD=#5\advance\apnumD by4 \apnumG=0 \apnumZ=0 \def\OUT{}%
+   \let\apNext=\apPLUSc \apnumD=#5\advance\apnumD by4 \apnumG=0 \apnumZ=0 \def\OUT{}%
    \expandafter\expandafter\expandafter\apPLUSc\expandafter\tmpc#1\apNL\apNL\apNL\apNL@%
 }
 \def\apPLUSc#1#2#3#4{\apnumY=\apPLUSxA#1#2#3#4\relax 
-   \ifx\apNL#4\let\next=\apPLUSd\fi 
+   \ifx\apNL#4\let\apNext=\apPLUSd\fi 
    \ifx\apNL#1\relax \ifx\tmpd\empty \expandafter\expandafter\expandafter\apPLUSf \fi\fi
    \apPLUSe
 }
@@ -230,7 +230,7 @@
    \ifnum\apnumZ=0 \apPLUSh \fi
    \edef\OUT{{\the\apnumY}\OUT}% 
    \advance\apnumD by-4
-   \next
+   \apNext
 }
 \def\apPLUSf#1@{}
 \def\apPLUSg{\let\tmpc=\apPLUSxA \let\apPLUSxA=\apPLUSxB \let\apPLUSxB=\tmpc}
@@ -371,7 +371,7 @@
             \edef\OUT{\ifnum\apSIGN<0-\fi}%
             \ifnum\apnumD<0 \edef\OUT{\OUT.}\apnumZ=-\apnumD \apADDzeros\OUT \fi
             \apnumE=1 \apnumZ=0
-            \let\next=\apDIVg \next % <--- the main calculation loop is here
+            \let\apNext=\apDIVg \apNext % <--- the main calculation loop is here
             \ifnum\apnumD>0 \apnumZ=\apnumD \apADDzeros\OUT \fi 
             \ifnum\apnumE=0 \def\XOUT{0}\else % extracting remainder from \XOUT
                \edef\XOUT{\expandafter}\expandafter\apDIVv\XOUT
@@ -383,8 +383,8 @@
 \def\apDIVcomp#1#2{%
    \expandafter\def\expandafter\tmpc\expandafter{#1\apNL\apNL\apNL\apNL\apNL\apNL\apNL\apNL@}%
    \expandafter\def\expandafter\tmpd\expandafter{#2\apNL\apNL\apNL\apNL\apNL\apNL\apNL\apNL@}%
-   \def\next{\expandafter\expandafter\expandafter\apDIVcompA\expandafter\tmpc\tmpd}%
-   \apXtrue \next
+   \def\apNext{\expandafter\expandafter\expandafter\apDIVcompA\expandafter\tmpc\tmpd}%
+   \apXtrue \apNext
 }
 \def\apDIVcompA#1#2#3#4#5#6#7#8#9@{%
    \ifx#8\apNL \def\tmpc{0000000\apNL@}\else\def\tmpc{#9@}\fi
@@ -392,28 +392,29 @@
    \apDIVcompB
 }
 \def\apDIVcompB#1#2#3#4#5#6#7#8#9@{%
-   \ifnum\apnumX<#1#2#3#4#5#6#7#8 \let\next=\relax \apXfalse \else
-   \ifnum\apnumX>#1#2#3#4#5#6#7#8 \let\next=\relax \apXtrue
+   \ifnum\apnumX<#1#2#3#4#5#6#7#8 \let\apNext=\relax \apXfalse \else
+   \ifnum\apnumX>#1#2#3#4#5#6#7#8 \let\apNext=\relax \apXtrue
    \fi\fi
-   \ifx\next\relax\else 
-      \ifx#8\apNL \def\tmpd{0000000\apNL@}\ifx\tmpc\tmpd\let\next=\relax\fi \else\def\tmpd{#9@}\fi
+   \ifx\apNext\relax\else 
+      \ifx#8\apNL \def\tmpd{0000000\apNL@}\ifx\tmpc\tmpd\let\apNext=\relax\fi 
+      \else\def\tmpd{#9@}\fi
    \fi
-   \next
+   \apNext
 }
 \def\apDIVg{%
    \ifx\tmpb\empty
-      \ifx\tmpa\empty  \def\next{\apDIVi!}\let\nexti=\apDIVi
-      \else \def\next{\expandafter\apDIVh\tmpa\apNL\apNL\apNL\apNL!}\let\nexti=\apDIVh
+      \ifx\tmpa\empty  \def\apNext{\apDIVi!}\let\apNexti=\apDIVi
+      \else \def\apNext{\expandafter\apDIVh\tmpa\apNL\apNL\apNL\apNL!}\let\apNexti=\apDIVh
    \fi\fi
-   \ifx\next\apDIVg
+   \ifx\apNext\apDIVg
       \apIVread\tmpa \apnumA=\apnumX
       \apIVread\tmpb
       \edef\XOUT{{\the\apnumX}{\the\apnumA}\XOUT}%
    \fi
-   \next
+   \apNext
 }
 \def\apDIVh#1#2#3#4{\apnumZ=#1#2#3#4
-   \ifx\apNL#4\let\nexti=\apDIVi\fi
+   \ifx\apNL#4\let\apNexti=\apDIVi\fi
    \apDIVi
 }
 \def\apDIVi{%
@@ -422,7 +423,7 @@
       \expandafter\apDIVp\XOUT
       \advance\apnumC by-4  
       \apnumZ=0
-      \expandafter\nexti
+      \expandafter\apNexti
    \else 
       \expandafter\apDIVj
    \fi
@@ -432,7 +433,7 @@
    \apnumA=\apDIVxA \divide\apnumA by\apDIVxB
    \def\apOUTl{}\apnumO=1 \apnumL=0
    \apnumX=0 \apnumB=0 \apnumE=0 
-   \let\next=\apDIVq \next 0\apnumZ
+   \let\apNext=\apDIVq \apNext 0\apnumZ
 }
 \def\apDIVq#1#2#3{% B A B
    \advance\apnumO by-1 \ifnum\apnumO=0 \apOUTx \fi
@@ -446,15 +447,15 @@
    \expandafter
       \edef\csname apOUT:\apOUTn\endcsname{\csname apOUT:\apOUTn\endcsname{#3}{\the\apnumB}}%
    \ifnum\apnumE<\apnumB \apnumE=\apnumB \fi
-   \ifx@#3\let\next=\apDIVr \fi
-   \next{#3}%
+   \ifx@#3\let\apNext=\apDIVr \fi
+   \apNext{#3}%
 }
 \def\apDIVr#1#2{%
    \ifnum\apnumX=#2  % the calculated Digit is OK, we save it
       \edef\XOUT{\expandafter\apOUTs\apOUTl.,}%
       \edef\tmpa{\ifnum\apnumF=4 \expandafter\apIVwrite\else \expandafter\the\fi\apnumA}%
       \ifnum\apnumD<\apnumF \ifnum\apnumD>-1 \apDIVt \fi\fi %adding dot
-      \ifx\nexti\apDIVh \apnumE=1 \fi
+      \ifx\apNexti\apDIVh \apnumE=1 \fi
       \ifnum\apnumE=0 \apDIVu % removing zeros
             \advance\apnumD by-\apNUMdigits\tmpa \relax
       \else \advance\apnumD by-\apnumF \apnumF=4 \fi
@@ -463,9 +464,9 @@
    \else  % we need do correction and run the remainder calculation again
       \advance\apnumA by-1 \apnumX=0 \apnumB=0 \apnumE=0
       \def\apOUTl{}\apnumO=1 \apnumL=0
-      \def\next{\let\next=\apDIVq
-      \expandafter\next\expandafter0\expandafter\apnumZ\XOUT}%
-      \expandafter\next
+      \def\apNext{\let\apNext=\apDIVq
+      \expandafter\apNext\expandafter0\expandafter\apnumZ\XOUT}%
+      \expandafter\apNext
    \fi
 }
 \def\apDIVt{\edef\tmpa{\apIVdot\apnumD\tmpa}\edef\tmpa{\tmpa}}
@@ -499,11 +500,8 @@
          \edef\tmpc{\ifcase\apnumA\or{}{}{}\or{}{}\or{}\fi}\def\OUT{}%
          \expandafter\expandafter\expandafter \apMULb \expandafter \tmpc \tmpa @@@@%
          \edef\OUT{*.\OUT}%    \OUT := \tmpa in interleaved format
-         \let\tmpd=\tmpa \def\tmpa{}%
-         \expandafter\expandafter\expandafter \apMULc \expandafter \tmpc \tmpd @@@@%
-         \def\tmpc{*.1*}\apnumE=10
-         \edef\tmpb{\apREV\tmpb}%
-         \expandafter\apPOWb\tmpb@%  do multiplications
+         \def\tmpc{*.1*}%
+         \apnumE=\tmpb\relax \apPOWb
          \expandafter\apPOWg \tmpc % \OUT := \tmpc in human raedable form
          \ifnum\apnumD=0 \ifnum \apSIGN<0 \edef\OUT{-\OUT}\fi
          \else \def\tmpc{-\apnumD}\apnumG=\apSIGN \expandafter\apROLLa\OUT.@\OUT\fi
@@ -511,26 +509,17 @@
          \relax
    \fi\fi
 }
-\def\apPOWb#1{%
-   \ifx@#1\else
-      \ifnum\apnumE<10 
-         \expandafter\apPOWc\ifcase\apnumE
-            ppmp.\or ppmp.\or pmp.\or mmp.\or mp.\or p.\or mmmm.\or mmm.\or mm.\or m.\or .\fi         
-         \def\tmpb{}\expandafter\apPOWd\OUT \let\tmpa=\tmpb
-      \fi
-      \apnumE=#1
-      \ifnum\apnumE=0 \else
-         \expandafter\apPOWc\ifcase\apnumE
-            \or .\or p.\or pm.\or pp.\or ppm.\or pmp.\or pmpm.\or ppp.\or pppm.\fi
-         \def\tmpb{}\expandafter\apPOWd\OUT
-         \let\tmpd=\OUT \let\OUT=\tmpc
-         \expandafter\apMULd \tmpb@\expandafter\apPOWn\OUT@% 
-         \let\tmpc=\OUT \let\OUT=\tmpd
-      \fi
-      \expandafter\apPOWb
+\def\apPOWb{%
+   \ifodd\apnumE   \def\tmpb{}\expandafter\apPOWd\OUT
+                   \let\tmpd=\OUT \let\OUT=\tmpc
+                   \expandafter\apMULd \tmpb@\expandafter\apPOWn\OUT@% 
+                   \let\tmpc=\OUT \let\OUT=\tmpd
    \fi
-}
-\def\apPOWc#1{\ifx.#1\else \csname apPOW#1\endcsname \expandafter\apPOWc\fi}
+   \divide\apnumE by2
+   \ifnum\apnumE>0 \expandafter\apPOWt\OUT \expandafter\apPOWn\OUT@%
+                   \expandafter\apPOWb
+   \fi
+}                 
 \def\apPOWd#1#2{% \apPOWd <spec format> => \tmpb (in simple reverse format)
    \ifx*#1\expandafter\apPOWd \else
       \edef\tmpb{\tmpb{#1}}%
@@ -542,8 +531,6 @@
 \def\apPOWh#1#2{\apnumA=#1 
    \ifx*#2\edef\OUT{\the\apnumA\OUT}\else \edef\OUT{\apIVwrite\apnumA\OUT}\expandafter\apPOWh\fi
 }
-\def\apPOWm{\expandafter\apMULd\tmpa@\expandafter\apPOWn\OUT@}
-\def\apPOWp{\expandafter\apPOWt\OUT \expandafter\apPOWn\OUT@}
 \def\apPOWn#1{\def\OUT{*}\apPOWna}
 \def\apPOWna#1{\ifx*#1\expandafter\apPOWnn\else \edef\OUT{\OUT0{#1}}\expandafter\apPOWna\fi}
 \def\apPOWnn#1#2{\ifx*#1\edef\OUT{\OUT*}\else\edef\OUT{\OUT0{#1}}\expandafter\apPOWnn\fi}
@@ -608,13 +595,13 @@
    \else \expandafter\apROUNDb
    \fi
 }
-\def\apROUNDb#1.{\edef\tmpc{#1}\apnumX=0 \def\tmpd{}\let\next=\apROUNDc \next}
-\def\apROUNDc#1{\ifx@#1\def\next{\apROUNDd.@}%
+\def\apROUNDb#1.{\edef\tmpc{#1}\apnumX=0 \def\tmpd{}\let\apNext=\apROUNDc \apNext}
+\def\apROUNDc#1{\ifx@#1\def\apNext{\apROUNDd.@}%
    \else \advance\apnumD by-1 
-         \ifnum\apnumD<0 \def\next{\apROUNDd#1}%
+         \ifnum\apnumD<0 \def\apNext{\apROUNDd#1}%
          \else \ifx.#1\else \advance\apnumX by#1 \edef\tmpd{\tmpd#1}\fi
          \fi
-   \fi \next
+   \fi \apNext
 }
 \def\apROUNDd#1.@#2{\def\XOUT{#1}%
    \ifnum\apnumX=0 \def\tmpd{}\fi
@@ -667,9 +654,9 @@
    \else \expandafter\apDIGc \expandafter#1\fi
 }
 \def\apDIGc#1.{\def\tmpd{#1}%
-   \ifx\tmpc\empty \let\next=\apDIGe
-   \else \def\next{\expandafter\apDIGd\tmpd@}%
-   \fi \next
+   \ifx\tmpc\empty \let\apNext=\apDIGe
+   \else \def\apNext{\expandafter\apDIGd\tmpd@}%
+   \fi \apNext
 }
 \def\apDIGd#1{\ifx@#1\expandafter\apDIGe \else \tmpc \expandafter\apDIGd \fi}
 \def\apDIGe#1@#2{%
@@ -728,3 +715,7 @@
 \catcode`\@=\apnumZ
 \endinput
 
+1.0 <Nov. 2014> - First version released
+1.1 <Jan. 2015> 
+    - POW implemented more simple (by base 2 of exponent)
+    - \next renamed in order to avoid name conflict