apnum (13feb16)

git-svn-id: svn://tug.org/texlive/trunk@39710 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 73 insertions, 54 deletions

diff --git a/Master/texmf-dist/tex/generic/apnum/apnum.tex b/Master/texmf-dist/tex/generic/apnum/apnum.tex
index e3a7bb53161..4c2e885904f 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, 2015       Petr Olsak
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% 2014, 2015, 2016       Petr Olsak
 
 % See the documentation apnum.pdf or apnum.d for more information
 
-\def\apVERSION{1.5 <Jan 2016>}
+\def\apVERSION{1.6 <Feb 2016>}
 \message{The Arbitrary Precision Numbers, \apVERSION}
 
 %%%%%%%%%%%% Internal registers, sec. 2.1 in apnum.pdf
@@ -20,13 +20,15 @@
 \newcount\apE
 \newcount\apTOT   \apTOT=0
 \newcount\apFRAC  \apFRAC=20
+\newcount\apEX    \apEX=10
 
 \apnumZ=\catcode`\@ \catcode`\@=12
 
 %%%%%%%%%%%% Evaluation of the expression, sec. 2.2 in apnum.pdf
 
-\def\evaldef{\relax \apEVALa}
-\def\apEVALa#1#2{\begingroup \apnumA=0 \apnumE=1 \apEVALb#2\limits \tmpb \apEND \let#1=\OUT}
+\def\evaldef{\relax \apEVALa{\apEadd\OUT}}
+\def\evalmdef{\relax \apEVALa{}}
+\def\apEVALa#1#2#3{\begingroup \apnumA=0 \apnumE=1 \apEVALb#3\limits \tmpb \apEND #1\let#2=\OUT}
 \def\apEVALb{\def\tmpa{}\apEVALc}
 \def\apEVALc#1{%
    \ifx+#1\apEVALd \apEVALc \fi
@@ -111,7 +113,7 @@
 %%%%%%%%%%%% Preparation of the parameter, sec. 2.3 in apnum.pdf
 
 \def\apPPa#1#2{\expandafter\apPPb#2@#1}
-\def\apPPb{\def\tmpc{}\apSIGN=1 \apE=0 \apXfalse \expandafter\expandafter\expandafter\apPPc}
+\def\apPPb{\def\tmpc{}\apSIGN=1 \apE=0 \expandafter\expandafter\expandafter\apPPc}
 \def\apPPc#1{%
    \ifx+#1\apPPd \fi
    \ifx-#1\apSIGN=-\apSIGN \apPPd \fi
@@ -119,8 +121,8 @@
    \apPPg#1%
 }
 \def\apPPd#1\apPPg#2{\fi\expandafter\expandafter\expandafter\apPPc}
-\def\apPPe#1\apPPg#2#3@{\fi\apXtrue 
-   \begingroup#3% execution of the parameter in the group
+\def\apPPe#1\apPPg#2#3@{\fi 
+   \begingroup\apE=0 #3% execution of the parameter in the group
    \edef\tmpb{\apE=\the\apE\relax\noexpand\apPPf\OUT@}\expandafter\endgroup\tmpb
 }
 \def\apPPf#1{\ifx-#1\apSIGN=-\apSIGN \expandafter\apPPg\else\expandafter\apPPg\expandafter#1\fi}
@@ -133,7 +135,7 @@
    \expandafter\apPPi\tmpc
 }
 \def\apPPh#1\apPPi\tmpc{\fi\apPPg}
-\def\apPPi{\ifapX \expandafter\apPPj \else \expandafter\apPPk \fi}
+\def\apPPi{\ifnum\apE=0 \expandafter\apPPk \else \expandafter\apPPj \fi}
 \def\apPPj#1@#2{\def#2{#1}}
 \def\apPPk#1@#2{\ifx@#1@\apSIGN=0 \def#2{0}\else \apPPl#1E@#2\fi}
 \def\apPPl#1E#2@#3{%
@@ -702,7 +704,7 @@
 %%%%%%%%%%%% Function-like macros, sec. 2.10 in apnum.pdf
 
 \def\ABS#1{\relax        % mandatory \relax for "function-like" macros
-   \evaldef\OUT{#1}%     % evaluation of the input parameter
+   \evalmdef\OUT{#1}%    % evaluation of the input parameter
    \ifnum\apSIGN<0       % if (input < 0)
       \apSIGN=1          %   sign = 1 
       \apREMfirst\OUT    %   remove first "minus" from OUT
@@ -710,33 +712,33 @@
 }
 \def\SGN#1{\relax \evaldef\OUT{#1}\edef\OUT{\the\apSIGN}\apE=0 }
 \def\iDIV#1#2{\relax \apINIT               % calculation in group
-   \evaldef\apAparam{#1}\apEadd\apAparam
-   \evaldef\apBparam{#2}\apEadd\apBparam   % evaluation of the parameters
+   \evalmdef\apAparam{#1}\apEnum\apAparam
+   \evalmdef\apBparam{#2}\apEnum\apAparam      % evaluation of the parameters
    \apTOT=0 \apFRAC=0 \apDIV\apAparam\apBparam % integer division
    \apEND                                  % end of group
 }
 \def\iMOD#1#2{\relax \apINIT               % calculation in group
-   \evaldef\apAparam{#1}\apEadd\apAparam
-   \evaldef\apBparam{#2}\apEadd\apBparam   % evaluation of the parameters
+   \evalmdef\apAparam{#1}\apEnum\apAparam
+   \evalmdef\apBparam{#2}\apEnum\apBparam  % evaluation of the parameters
    \apTOT=0 \apFRAC=0 \apDIV\apAparam\apBparam % integer division
    \let\OUT=\XOUT                          % remainder is the output
    \apEND                                  % end of group
 }
-\def\iFLOOR#1{\relax \evaldef\OUT{#1}\apEnum\OUT \apROUND\OUT0%
+\def\iFLOOR#1{\relax \evalmdef\OUT{#1}\apEnum\OUT \apROUND\OUT0%
    \ifnum\apSIGN<0 \ifx\XOUT\empty \else \apPLUS\OUT{-1}\fi\fi
    \def\tmp{0}\ifx\tmp\OUT \apSIGN=0 \fi
 }
 \def\iFRAC#1{\relax 
-   \evaldef\OUT{#1}\apEnum\OUT \apROUND\OUT0% % preparing the parameter
-   \ifx\XOUT\empty \def\OUT{0}\apSIGN=0       % empty fraction part means zero
+   \evalmdef\OUT{#1}\apEnum\OUT \apROUND\OUT0% % preparing the parameter
+   \ifx\XOUT\empty \def\OUT{0}\apSIGN=0        % empty fraction part means zero
    \else \ifnum\apSIGN<0 
-            \edef\XOUT{-.\XOUT}\apPLUS1\XOUT  % OUT = 1 - .\XOUT
-         \else \edef\OUT{.\XOUT}\apSIGN=1     % else OUT = .\XOUT 
+            \edef\XOUT{-.\XOUT}\apPLUS1\XOUT   % OUT = 1 - .\XOUT
+         \else \edef\OUT{.\XOUT}\apSIGN=1      % else OUT = .\XOUT 
    \fi   \fi
 }
 
 \def\FAC#1{\relax \apINIT             % "function-like" in the group, FAC = factorial
-   \evaldef\OUT{#1}\apEnum\OUT       % preparing the parameter
+   \evalmdef\OUT{#1}\apEnum\OUT       % preparing the parameter
    \localcounts \N;%                  % local \newcount
    \ifnum\apSIGN<0 \apERR{\string\FAC: argument {\OUT} cannot be negative}\apRETURN\fi
    \let\tmp=\OUT \apROUND\tmp0%       % test, if parameter is integer
@@ -748,8 +750,8 @@
    \apEND                             % end of group
 }
 \def\BINOM#1#2{\relax \apINIT         % BINOM = {#1 \choose #2} ... 
-   \evaldef\apAparam{#1}\apEnum\apAparam
-   \evaldef\apBparam{#2}\apEnum\apBparam % preparation of the parameters  
+   \evalmdef\apAparam{#1}\apEnum\apAparam
+   \evalmdef\apBparam{#2}\apEnum\apBparam % preparation of the parameters  
    \localcounts \A \B \C ;%           % local \newcounts
    \let\OUT=\apBparam \apROUND\OUT0%  % test if B is integer
    \ifx\XOUT\empty\else\apERR{\string\BINOM: second arg. {\apBparam} must be integer}\apRETURN\fi
@@ -775,7 +777,7 @@
    \apEND
 }
 \def\SQRT#1{\relax \apINIT           % OUT = SQRT(#1) ...
-   \evaldef\A{#1}%                   % parameter preparation
+   \evalmdef\A{#1}%                  % parameter preparation
    \localcounts \M \E ;%             % local counters
    \E=\apE \apE=0
    \ifnum\apSIGN=0 \apRETURN\fi      % SQRT(0) = 0 (OUT is set to 0 by previous \evaldef)  
@@ -819,39 +821,53 @@
    \edef\OUT{\expandafter\apNOPT\the\dimen0}%  OUT = dimen0
 }
 \def\EXP#1{\relax\apINIT                         % OUT = EXP(#1) ...
-   \evaldef\OUT{#1}\apEnum\OUT                  % OUT = #1
+   \evalmdef\OUT{#1}\apEnum\OUT                  % OUT = #1
    \localcounts \N \K ;%
    \ifnum\apSIGN=0 \def\OUT{1}\apSIGN=1 \apRETURN \fi
-   \edef\digits{\the\apFRAC}\advance\apFRAC by3
+   \edef\digits{\the\apFRAC}\advance\apFRAC by4
    \edef\signX{\the\apSIGN}%
    \ifnum\apSIGN<0 \apSIGN=1 \apREMfirst\OUT \fi % remove "minus" sign
-   \K=0 \N=0                                     % K = 0, N = 0
+   \def\testBig ##1##2##3\relax##4{\ifx##1.\apXfalse \else
+      \ifx##2.\ifnum##1<4 \apXfalse \else \apXtrue \fi \else \apXtrue 
+      \fi \fi \ifapX}%
+   \expandafter\testBig \OUT.\relax 
+   \iftrue \apEXPb \else \apEXPa \fi   % OUT = e^OUT
+   \ifnum\signX<0 \K=-\apE \apDIV 1\OUT \apE=\K \fi % if (signX < 0)  OUT = 1 / OUT
+   \apSIGN=1                 % EXP is always positive
+   \apEND
+}
+\def\apEXPa{%
    \def\testDot ##1##2\relax##3{\ifx##1.}%
-   \loop \expandafter \testDot\OUT \relax        % loop if (OUT >= 1)
-         \iftrue \else                           %         OUT = OUT/2
-            \apDIV\OUT{2}%                       %         K++
-            \advance\K by1                       %         repeat
-            \repeat                              % now: #1 = 2^K * OUT, OUT < 1
+   \K=0 \N=0                                  % K = 0, N = 0
+   \loop \expandafter \testDot\OUT \relax     % loop if (OUT >= 1)
+      \iftrue \else                           %         OUT = OUT/2
+         \apDIV\OUT{2}%                       %         K++
+         \advance\K by1                       %         repeat
+         \repeat                              % oriOUT = 2^K * OUT, OUT < 1
    \advance\apFRAC by\K                          
-   \def\S{1}\def\Sn{1}\N=0 \let\X=\OUT           % S = 1, Sn = 1, N = 0, X = OUT
-   \loop \advance\N by1                          % loop N++
-         \do\Sn=\apDIV{\apMUL\Sn\X}{\the\N};%    %      Sn = Sn * X / N
-         \apTAYLOR\iftrue \repeat                %      S = S + Sn (... Taylor)
+   \def\S{1}\def\Sn{1}\N=0 \let\X=\OUT        % S = 1, Sn = 1, N = 0, X = OUT
+   \loop \advance\N by1                       % loop N++
+      \do\Sn=\apDIV{\apMUL\Sn\X}{\the\N};%    %      Sn = Sn * X / N
+      \apTAYLOR\iftrue \repeat                %      S = S + Sn (... Taylor)
    \N=0
-   \loop \ifnum\N < \K                           % loop if (N < K)
-         \apPOW\OUT{2}\apROUND\OUT\apFRAC        %      OUT = OUT^2
-         \advance\N by1 \repeat                  %      N++
-   \ifnum\signX<0 \apDIV 1\OUT \fi               % if (signX < 0)  OUT = 1 / OUT
-   \apROUND\OUT\digits \apSIGN=1                 % EXP is always positive
-   \apEND
+   \loop \ifnum\N < \K                        % loop if (N < K)
+      \apPOW\OUT{2}%                          %      OUT = OUT^2
+      \advance\N by1 \repeat                  %      N++
+   \apFRAC=\digits\relax  \apROUND\OUT\apFRAC
 }
 \def\apTAYLOR#1{\ifnum\apSIGN=0 \let\OUT=\S \else \apPLUS\S\Sn \let\S=\OUT }
-
-\def\LN#1{\relax \apINIT          % OUT = LN(#1) ...
-   \evaldef\X{#1}%                   % X = #1
+\def\apEXPb{%
+   \let\X=\OUT \apLNtenexec  \apDIV\X\apLNten  \let\D=\OUT
+   \apROUND\D{0}%             % D = floor( X/ln(X) )
+   \ifnum\D<\apEX  \advance\apFRAC by\D \relax \apLNtenexec \fi
+   \EXP{\X-\D*\apLNten}%      % mantissa = EXP(X-D*LN(10))
+   \ifnum\D<\apEX  \apROLL\OUT\D \apE=0 \else \apE=\D \relax \fi
+   \apFRAC=\digits  \apROUND\OUT\apFRAC  % OUT = mantissa * 10^D
+}
+\def\LN#1{\relax \apINIT             % OUT = LN(#1) ...
+   \evalmdef\X{#1}%                  % X = #1
    \localcounts \M \N \E;%
    \E=\apE
-   \def\round{\apROUND\OUT\apFRAC}%
    \edef\digits{\the\apFRAC}\advance\apFRAC by4
    \ifnum\apSIGN>0 \else \apERR{\string\LN: argument {\X} is out of range}\apRETURN\fi
    \apDIG\OUT\relax \M=\apnumD       % find M: X = mantissa * 10^M
@@ -880,10 +896,10 @@
    \apDIV{\apPLUS{\A}{-1}}{\apPLUS{\A}{1}}%  % OUT = (A-1) / (A+1)     
    \ifnum\apSIGN=0 \def\OUT{0}\else          % ln 1 = 0 else:
       \let\Sn=\OUT \let\Kn=\OUT \let\S=\OUT  %    Sn = OUT, Kn = OUT, S = OUT
-      \apPOW\OUT{2}\round \let\XX=\OUT       %    XX = OUT^2
+      \apPOW\OUT{2}\apROUND\OUT\apFRAC \let\XX=\OUT  %    XX = OUT^2
       \N=1                                   %    N = 1
       \loop \advance\N by2                   %    loop N = N + 2
-            \do\Kn=\apMUL\Kn\XX\round;%      %         Kn = Kn * XX
+            \do\Kn=\apMUL\Kn\XX\apROUND\OUT\apFRAC;%   Kn = Kn * XX
             \do\Sn=\apDIV\Kn{\the\N};%       %         Sn = Kn / N
             \apTAYLOR\iftrue \repeat         %         S = S + Sn (Taylor)
       \apMUL\S{2}%                           %    OUT = 2 * OUT
@@ -965,7 +981,7 @@
 \def\COS{\relax \let\apSINCOSx=\apCOSx \apSINCOSa}
 \def\apSINCOSa#1{\apINIT
    \advance\apFRAC by3
-   \evaldef\X{#1}\apEnum\X
+   \evalmdef\X{#1}\apEnum\X
    \def\signK{1}\apSINCOSo\apCOSx
    \ifnum\apSIGN<0 \apREMfirst\X \def\sign{-}\else\def\sign{+}\fi
    \ifx\apSINCOSx\apCOSx \def\sign{+}\fi
@@ -1013,7 +1029,7 @@
 \def\apSINCOSo#1{\ifnum\apSIGN=0 \ifx#1\SCgo \apSIGN=\signK \let\OUT=\signK \fi \apRETURN\fi}
 \def\TAN#1{\relax \apINIT
    \advance\apFRAC by3
-   \evaldef\X{#1}\apEnum\X
+   \evalmdef\X{#1}\apEnum\X
    \advance\apFRAC by-3
    \do\denom=\COS\X;%
    \ifnum\apSIGN=0 \apERR{\string\TAN: argument {\X} is out of range}\apRETURN\fi
@@ -1023,7 +1039,7 @@
 }
 \def\ATAN#1{\relax \apINIT
    \advance\apFRAC by3
-   \evaldef\X{#1}\apEnum
+   \evalmdef\X{#1}\apEnum\X
    \ifnum\apSIGN=0 \def\OUT{0}\apRETURN\fi 
    \ifnum\apSIGN<0 \def\sign{-}\apREMfirst\X \else\def\sign{}\fi
    \let\tmp=\X \apDIG\tmp\relax
@@ -1053,7 +1069,7 @@
       \apTAYLOR \iftrue \repeat
 }
 \def\ASIN#1{\relax \apINIT 
-   \evaldef\X{#1}\apEnum\X \edef\sign{\the\apSIGN}%
+   \evalmdef\X{#1}\apEnum\X \edef\sign{\the\apSIGN}%
    \apPLUS 1{-\apPOW\X2}%  OUT = 1 - X^2
    \ifnum\apSIGN<0 \apERR{\string\ASIN: argument {\X} is out of range}\apRETURN\fi
    \do\sqrt=\SQRT\OUT;%    sqrt = SRQT {1 - X^1}
@@ -1138,7 +1154,7 @@
 \let\SIGN=\apSIGN \let\ROUND=\apROUND \let\NORM=\apNORM \let\ROLL=\apROLL
 
 \ifx\documentclass\undefined \else % please, don't remove this message
-\message{SORRY, you are using LaTeX. I don't recommend this. Petr Olsak}\fi
+\message{WARNING: the author of apnum package recommends: Never use LaTeX.}\fi
 \catcode`\@=\apnumZ
 \endinput
 
@@ -1167,8 +1183,11 @@
     - \ATAN, \ASIN, \ACOS added
     - \SIN, \COS, \TAN added
     - \apTOT=0 by default
-1.4a  \end -> \limits, internal change in \ebvaldef because LaTeX redefines \end
+1.4a  \end -> \limits, internal change in \evaldef because LaTeX redefines \end
 1.4b  \apSINCOS: \ifx\OUT eq 0 added after \apROUND (bug fixed).
-1.5 <Jan 2015>
+1.5 <Jan 2016>
     - \iROUND replaced by \iFLOOR, \iFRAC corrected (for negative numbers)
     - \eprint introduced
+1.6 <Feb 2016>
+    - \evalmdef introduced
+    - \EXP for arg>=4 rewritten, \apEX register introduced