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authorKarl Berry <karl@freefriends.org>2013-07-17 22:13:10 +0000
committerKarl Berry <karl@freefriends.org>2013-07-17 22:13:10 +0000
commiteec0a21648f82e9f409ed8151e1bc83f34bfec79 (patch)
treedd59250c0f9496a72010ad5b1097e0199888f06f /Master/texmf-dist/tex
parentd9add100de8f268f2b408533a41cc5624ef1ee7a (diff)
minifp (17jul13)
git-svn-id: svn://tug.org/texlive/trunk@31221 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/tex')
-rw-r--r--Master/texmf-dist/tex/generic/minifp/mfpextra.tex416
-rw-r--r--Master/texmf-dist/tex/generic/minifp/minifp.sty268
2 files changed, 339 insertions, 345 deletions
diff --git a/Master/texmf-dist/tex/generic/minifp/mfpextra.tex b/Master/texmf-dist/tex/generic/minifp/mfpextra.tex
index 2e9a6d88bf0..9d65d0ff1aa 100644
--- a/Master/texmf-dist/tex/generic/minifp/mfpextra.tex
+++ b/Master/texmf-dist/tex/generic/minifp/mfpextra.tex
@@ -21,6 +21,26 @@
%% is Daniel H. Luecking. The Base Interpreters associated
%% with minifp are plain TeX and LaTeX.
%%
+\expandafter\ifx\csname MFP@xfinish\endcsname\relax
+\else \expandafter\endinput\fi
+\expandafter\edef\csname MFP@xfinish\endcsname{%
+ \catcode64=\the\catcode64 \space
+ \catcode46=\the\catcode46 \space
+ \catcode60=\the\catcode60 \space
+ \catcode62=\the\catcode62 \space}%
+\catcode64=11 % @
+\catcode46=12 % . (period)
+\catcode60=12 % <
+\catcode62=12 % >
+\ifx\MFP@Rextra\UndEfInEd \input minifp.sty \fi
+\ifx\MFP@Rextra\@empty
+\else
+ \immediate\write16{mfpextra.tex: already loaded.^^J}%
+ \MFP@xfinish
+ \expandafter\endinput
+\fi
+\immediate\write16{%
+ mfpextra.tex: extra operations for the MiniFP package.^^J}%
\def\MFP@Rextra{%
\def\Rcos {\MFP@stack@Unary\MFP@Rcos }%
\def\Rsin {\MFP@stack@Unary\MFP@Rsin }%
@@ -51,104 +71,110 @@
\def\LogOfZeroFrac{\MaxRealFrac}%
\def\MFP@expoverflow@err{%
\MFP@errmsg{Power too large}%
- {The power you tried to calcualate is too large for %
+ {The power you tried to calculate is too large for %
8 digits. If you continue, ^^Jthe value assigned will be %
\MaxRealInt.\MaxRealFrac.}}%
-\def\MFP@sqrtofneg@err{%
- \MFP@errmsg{square root of a negative number}%
- {You tried to take the square root of a negative value. What %
- were you thinking? If you continue, zero will be returned.}}%
\def\MFP@badpower@err{%
\MFP@errmsg{negative power of zero}%
{You tried to take a negative power of zero. What were you
thinking? If you ^^Jcontinue, the value assigned will be %
\xOverZeroInt.\xOverZeroFrac.}}%
+\def\MFPshowreg #1{%
+\ifMFPdebug
+\begingroup
+ \edef\theregister{%
+ #1 = \expandafter \MFP@Sign
+ \csname MFP@#1@Sgn\endcsname %
+ \csname MFP@#1@Int\endcsname.%
+ \csname MFP@#1@Frc\endcsname}%
+ \show\theregister
+\endgroup
+\fi}%
\def\MFP@Rcopyz#1{\MFP@Rload {#1}\MFP@z@Sgn\MFP@z@Int\MFP@z@Frc}%
\def\MFP@Rcopyzx{\MFP@Rcopyz x}%
\def\MFP@Rcopyzy{\MFP@Rcopyz y}%
-\def\MFP@Rdeg{%
- \MFP@Rcopy xt\MFP@Rload y1{57}{29577951}\MFP@Rmul
- \MFP@Rcopyz s\MFP@Rcopy tx\MFP@Rload y10{30823209}\MFP@Rmul
- \MFP@tempa\MFP@z@Int\relax
- \ifnum\MFP@z@Frc<50000000 \else \advance\MFP@tempa 1 \fi
- \MFP@Rload x{\ifnum\MFP@tempa>0 \MFP@z@Sgn\else0\fi}0\MFP@tempa
- \MFP@Rcopy sy\MFP@Radd}%
-\def\MFP@Rrad{%
- \MFP@Rcopy xt\MFP@Rload y10{0174 5329}\MFP@Rmul
- \MFP@Rcopyz s\MFP@Rcopy tx\MFP@Rload y10{25199433}\MFP@Rmul
- \MFP@tempa\MFP@z@Int\relax
- \ifnum\MFP@z@Frc<50000000 \else \advance\MFP@tempa 1 \fi
- \MFP@Rload x{\ifnum\MFP@tempa>0 \MFP@z@Sgn\else0\fi}0\MFP@tempa
- \MFP@Rcopy sy\MFP@Radd}%
-\def\MFP@Rcos{%
- \MFP@Rcopy xy\MFP@Rload x1{90}0\MFP@Rsub
- \MFP@Rcopyzx\MFP@Rsin}%
-\def\MFP@Rsin{%
- \ifnum \MFP@x@Sgn=0 % return 0
+\def\MFP@DPmul#1#2#3{%
+ \ifnum\MFP@x@Sgn=0
\MFP@Rzero
\else
- \MFP@tempa\MFP@x@Int\relax
- \MFP@reduce@angle
- \ifnum \MFP@tempa<180
- \edef\MFP@sin@Sgn{\MFP@x@Sgn}%
- \else
- \edef\MFP@sin@Sgn{\number-\MFP@x@Sgn}%
- \advance \MFP@tempa-180
+ \MFP@Rcopy xv%
+ \MFP@Rload y1{#1}{#2}\MFP@Rmul
+ \edef\MFP@w@Und{\MFP@z@Und}%
+ \ifnum\MFP@z@Frc@iii>4999
+ \MFP@tempa\MFP@z@Frc \advance\MFP@tempa-1
+ \edef\MFP@z@Frc{\number\MFP@tempa}%
+ \makeMFP@eightdigits\MFP@z@Frc
\fi
- \MFP@tempb\MFP@x@Frc\relax
- \ifnum\MFP@tempa>0
- \MFP@@Rsin
- \else\ifnum\MFP@tempb>0
- \MFP@@Rsin
+ \MFP@Rcopyz w%
+ \MFP@Rcopy vx\MFP@Rload y10{#3}\MFP@Rmul
+ \MFP@Rcopyzx\MFP@Rload y\MFP@v@Sgn 0{\MFP@w@Und}\MFP@Radd
+ \MFP@tempa\MFP@z@Int\relax
+ \ifnum\MFP@z@Frc<50000000 \else \advance\MFP@tempa 1 \fi
+ \ifnum\MFP@tempa<\MFP@ttteight\relax
+ \MFP@Rload x{\ifnum\MFP@tempa>0 \MFP@z@Sgn\else0\fi}0\MFP@tempa
\else
- \MFP@Rzero
- \fi\fi
+ \MFP@Rload x\MFP@z@Sgn10%
+ \fi
+ \MFP@Rcopy wy\MFP@Radd
\fi}%
+\def\MFP@Rdeg{\MFP@DPmul{57}{29577951}{30823209}}%
+\def\MFP@Rrad{\MFP@DPmul{0}{01745329}{25199433}}%
+\def\MFP@RbaseX{\MFP@DPmul{0}{43429448}{19032518}}%
+\def\MFP@RbaseE{\MFP@DPmul{2}{30258509}{29940457}}%
+\def\MFP@Rcos{%
+ \MFP@Rcopy xy\MFP@Rload x1{90}0\MFP@Rsub
+ \MFP@Rcopyzx\MFP@Rsin}%
+\def\MFP@Rsin{%
+ \MFP@tempa\MFP@x@Int
+ \MFP@tempb\MFP@x@Frc
+ \MFP@tempc\MFP@x@Sgn\relax
+ \MFP@reduce@angle
+ \ifnum\MFP@tempa>0 \MFP@@Rsin
+ \else\ifnum\MFP@tempb>0 \MFP@@Rsin
+ \else \MFP@Rzero
+ \fi\fi}%
\def\MFP@reduce@angle{%
- \ifnum\MFP@tempa<360
+ \ifnum\MFP@tempa<180
\else
- \advance\MFP@tempa-360
+ \advance\MFP@tempa-180
+ \MFP@tempc-\MFP@tempc
\@xp\MFP@reduce@angle
\fi}%
\def\MFP@@Rsin{%
\ifnum\MFP@tempa<90
\else
+ \MFP@tempa -\MFP@tempa
\ifnum\MFP@tempb>0
- \advance\MFP@tempa 1
\MFP@tempb -\MFP@tempb
\advance\MFP@tempb \MFP@ttteight\relax
+ \advance\MFP@tempa 179
+ \else \advance\MFP@tempa 180
\fi
- \MFP@tempa -\MFP@tempa
- \advance\MFP@tempa 180
\fi
\ifnum\MFP@tempa=90
- \MFP@Rloadz \MFP@sin@Sgn10%
+ \MFP@Rloadz \MFP@tempc10%
\else
\advance\MFP@tempb 50 \divide\MFP@tempb 100
\multiply\MFP@tempa 1000000 \advance\MFP@tempb\MFP@tempa
\ifnum\MFP@tempb=0
\MFP@Rzero
\else
- \MFP@Rload x10\MFP@tempb
- \MFP@Rcopy xs%
+ \MFP@Rload s\MFP@tempc0\MFP@tempb
+ \MFP@Rcopy sx%
\MFP@Rsq
\ifnum \MFP@z@Frc>0
\MFP@Rcopyz t\MFP@Rsin@prog
\else
\MFP@Rcopy sx%
\fi
- \MFP@Rload y11{74532925}\MFP@Rmul
- \ifnum\MFP@z@Sgn=0 \else
- \let\MFP@z@Sgn\MFP@sin@Sgn
- \fi
+ \MFP@DPmul 1{74532925}{19943296}%
\fi
\fi}%
\def\MFP@Rsin@prog{%
- \MFP@Rcopy tx%
- \MFP@Rload y10{00559959}\MFP@Rsmul\MFP@com@iter{01450559}%
- \MFP@com@iter{01952675}\MFP@com@iter{02769249}\MFP@com@iter{04230797}%
- \MFP@com@iter{07252796}\MFP@com@iter{15230871}\MFP@com@iter{50769570}%
- \MFP@flipz \MFP@Rcopyzx \MFP@Rcopy sy\MFP@Rsmul \MFP@Rcopyzx}%
+ \MFP@Rcopy tx\MFP@Rload y10{01952676}\MFP@Rsmul%
+ \MFP@com@iter{02769249}\MFP@com@iter{04230797}\MFP@com@iter{07252796}%
+ \MFP@com@iter{15230871}\MFP@com@iter{50769570}\MFP@flipz \MFP@Rcopyzx
+ \MFP@Rcopy sy\MFP@Rsmul\MFP@Rcopyzx\edef\MFP@x@Sgn{\MFP@s@Sgn}}%
\def\MFP@flipz{%
\ifnum\MFP@z@Sgn=0
\MFP@Rloadz 110%
@@ -161,16 +187,11 @@
\MFP@Rcopyzx\MFP@Rcopy ty\MFP@Rsmul
\MFP@Rcopyzx\MFP@Rload y10{#1}\MFP@Rsmul}%
\def\MFP@Rsmul{%
- \ifnum \MFP@x@Sgn=0
- \MFP@Rzero
- \else\ifnum \MFP@y@Sgn=0
- \MFP@Rzero
- \else\ifnum\MFP@x@Int>0
- \MFP@Rcopy yz%
- \else\ifnum\MFP@y@Int>0
- \MFP@Rcopy xz%
- \else
- \MFP@@Rsmul
+ \ifnum \MFP@x@Sgn=0 \MFP@Rzero
+ \else\ifnum \MFP@y@Sgn=0 \MFP@Rzero
+ \else\ifnum\MFP@x@Int>0 \MFP@Rcopy yz%
+ \else\ifnum\MFP@y@Int>0 \MFP@Rcopy xz%
+ \else \MFP@@Rsmul
\fi\fi\fi\fi}%
\def\MFP@@Rsmul{%
\MFP@split\MFP@x@Frc\MFP@x@Frc@i\MFP@x@Frc@ii
@@ -190,15 +211,11 @@
\advance\MFP@tempb1
\edef\MFP@z@Frc@ii{\number\MFP@tempb}\fi
\MFP@carrym\MFP@z@Frc@ii\MFP@z@Frc@i
- \makeMFP@fourdigits\MFP@z@Frc@iv
- \makeMFP@fourdigits\MFP@z@Frc@iii
\makeMFP@fourdigits\MFP@z@Frc@ii
\makeMFP@fourdigits\MFP@z@Frc@i
\def\MFP@z@Int{0}%
\edef\MFP@z@Frc{\MFP@z@Frc@i\MFP@z@Frc@ii}%
- \edef\MFP@z@Sgn{\ifnum\MFP@z@Frc=0 0\else 1\fi}%
- \edef\MFP@z@Und{\MFP@z@Frc@iii\MFP@z@Frc@iv}%
- \edef\MFP@z@Ovr{0}}%
+ \edef\MFP@z@Sgn{\ifnum\MFP@z@Frc=0 0\else 1\fi}}%
\def\MFP@Rangle{%
\ifcase\MFP@y@Sgn\relax
\ifcase\MFP@x@Sgn\relax
@@ -223,70 +240,72 @@
\def\MFP@x@Sgn{1}\MFP@@Rangle
\MFP@Rcopyzy\MFP@Rload x1{180}0\MFP@Rsub
\fi
- \let\MFP@z@Sgn\MFP@angle@Sgn
- }}%
+ \let\MFP@z@Sgn\MFP@angle@Sgn}}%
\def\MFP@@Rangle{%
\MFP@Rcmp
\ifMFP@neg
- \MFP@Rcopy xs\MFP@Rcopy yx\MFP@Rcopy sy%
+ \MFP@Rcopy xw\MFP@Rcopy yx\MFP@Rcopy wy%
\MFP@@@Rangle
\MFP@Rload x1{90}0\MFP@Rcopyzy\MFP@Rsub
\else
\MFP@@@Rangle
- \fi
-}%
+ \fi}%
\def\MFP@Rquad{\MFP@Rdbl\MFP@Rcopyzx\MFP@Rdbl}%
\def\MFP@@@Rangle{%
\MFP@Rcopy xs\MFP@Rcopy yt%
- \ifnum\MFP@y@Int<500000
+ \ifnum\MFP@x@Int<1000000
\else
- \MFP@Rload y1{200}0\MFP@Rdiv
- \MFP@Rcopyz s\MFP@Rcopy tx%
- \MFP@Rload y1{200}0\MFP@Rdiv
- \MFP@Rcopyz t%
+ \MFP@RdivC \MFP@Rcopyz s%
+ \MFP@Rcopy tx\MFP@RdivC \MFP@Rcopyz t%
\fi
- \MFP@Rcopy tx\MFP@Rdbl\MFP@Rcopyzx\MFP@Rcopy sy\MFP@Rcmp
- \ifMFP@pos
- \MFP@Rsub\MFP@Rcopyz u\MFP@Rcopy sx\MFP@Rdbl
- \MFP@Rcopyzx\MFP@Rcopy ty\MFP@Radd
- \MFP@Rcopyz s\MFP@Rcopy ut%
- \MFP@Rload a1{2656}{50511771}%
+ \ifnum\MFP@t@Sgn=0 \MFP@Rzero
\else
- \MFP@Rload a000%
- \fi
- \MFP@Rcopy tx\MFP@Rquad\MFP@Rcopyzx\MFP@Rcopy sy\MFP@Rcmp
- \ifMFP@pos
- \MFP@Rsub\MFP@Rcopyz u\MFP@Rcopy sx\MFP@Rquad
- \MFP@Rcopyzx\MFP@Rcopy ty\MFP@Radd
- \MFP@Rcopyz s\MFP@Rcopy ut%
- \MFP@Rcopy ax\MFP@Rload y1{1403}{62434679}%
- \MFP@Radd\MFP@Rcopy za%
- \fi
- \MFP@Rcopy tx\MFP@RmulC
- \MFP@Rcopyzx\MFP@Rcopy sy\MFP@Rdiv
- \MFP@Rcopyzx\MFP@Ratanc
- \MFP@Rcopyzx\MFP@Rdeg
- \MFP@Rcopyzx\MFP@Rcopy ay\MFP@Radd
- \MFP@Rcopyzx\MFP@RdivC}%
+ \MFP@Rcopy tx\MFP@Rdbl\MFP@Rcopyzx\MFP@Rcopy sy\MFP@Rcmp
+ \ifMFP@pos
+ \MFP@Rsub\MFP@Rcopyz u\MFP@Rcopy sx\MFP@Rdbl
+ \MFP@Rcopyzx\MFP@Rcopy ty\MFP@Radd
+ \MFP@Rcopyz s\MFP@Rcopy ut%
+ \MFP@Rload a1{2656}{50511771}%
+ \else
+ \MFP@Rload a000%
+ \fi
+ \MFP@Rcopy tx\MFP@Rquad\MFP@Rcopyzx\MFP@Rcopy sy\MFP@Rcmp
+ \ifMFP@pos
+ \MFP@Rsub\MFP@Rcopyz u\MFP@Rcopy sx\MFP@Rquad
+ \MFP@Rcopyzx\MFP@Rcopy ty\MFP@Radd
+ \MFP@Rcopyz s\MFP@Rcopy ut%
+ \MFP@Rcopy ax\MFP@Rload y1{1403}{62434679}%
+ \MFP@Radd\MFP@Rcopy za%
+ \fi
+ \MFP@Rcopy tx\MFP@RmulC
+ \MFP@Rcopyzx\MFP@Rcopy sy\MFP@Rdiv
+ \MFP@Rcopyzx\MFP@Ratanc
+ \MFP@Rcopyzx\MFP@Rdeg
+ \MFP@Rcopyzx\MFP@Rcopy ay\MFP@Radd
+ \MFP@Rcopyzx\MFP@RdivC
+ \fi}%
+\def\MFP@twoofmany#1#2#3\MFP@end{#1#2}%
+\def\MFP@gobbletwo#1#2{}%
\def\MFP@RmulC{%
- \makeMFP@eightdigits\MFP@x@Frc
- \edef\MFP@Tmp{\number\MFP@x@Int.\MFP@x@Frc}%
- \@xp\MFP@@RmulC\MFP@Tmp\mfp@end}%
-\def\MFP@@RmulC#1.#2#3#4\mfp@end{%
- \MFP@Rloadz\MFP@x@Sgn{#1#2#3}{#400}}%
+ \edef\MFP@z@Int{\MFP@x@Int\@xp\MFP@twoofmany\MFP@x@Frc\MFP@end}%
+ \edef\MFP@z@Frc{\@xp\MFP@gobbletwo\MFP@x@Frc00}%
+ \edef\MFP@z@Sgn{\MFP@x@Sgn}}%
\def\MFP@RdivC{%
\makeMFP@eightdigits\MFP@x@Int
\makeMFP@eightdigits\MFP@x@Frc
- \@XP\MFP@@RdivC\@xp\MFP@x@Int\MFP@x@Frc\mfp@end}%
+ \@XP\MFP@@RdivC\@xp\MFP@x@Int\MFP@x@Frc\MFP@end}%
\def\MFP@@RdivC#1#2#3#4#5#6{%
\edef\MFP@z@Int{\number#1#2#3#4#5#6}%
\MFP@@@RdivC}%
-\def\MFP@@@RdivC#1#2#3#4#5#6#7#8#9\mfp@end{%
+\def\MFP@@@RdivC#1#2#3#4#5#6#7#8#9\MFP@end{%
\MFP@tempa#1#2#3#4#5#6#7#8\relax
\ifnum#9>49 \advance\MFP@tempa1 \fi
+ \edef\MFP@z@Frc{\number\MFP@tempa}%
+ \makeMFP@eightdigits\MFP@z@Frc
\edef\MFP@z@Sgn{\MFP@x@Sgn}%
- \ifnum\MFP@tempa=0 \ifnum\MFP@x@Int=0 \def\MFP@z@Sgn{0}\fi\fi
- \MFP@Rloadz\MFP@z@Sgn\MFP@z@Int\MFP@tempa}%
+ \ifnum\MFP@tempa=0
+ \ifnum\MFP@z@Int=0 \def\MFP@z@Sgn{0}\fi
+ \fi}%
\def\MFP@scaledmul{\MFP@Rmul\MFP@Rcopyzx\MFP@RdivC}%
\def\MFP@atan@iter#1#2{%
\MFP@Rcopy uy\MFP@scaledmul
@@ -294,82 +313,80 @@
\MFP@Rcopyzy\MFP@Rload x1{100}{00000000}%
\MFP@Rsub\MFP@Rcopyzx}%
\def\MFP@Ratanc{%
- \MFP@Rcopy xs%
- \MFP@Rcopy xy\MFP@scaledmul\MFP@Rcopyz u%
- \MFP@Rcopyzx\MFP@Rload y1{86}{66666667}%
- \MFP@scaledmul
- \MFP@Rcopyzy\MFP@Rload x1{100}{00000000}%
- \MFP@Rsub\MFP@Rcopyzx
- \MFP@atan@iter{84}{61538462}\MFP@atan@iter{81}{81818182}%
- \MFP@atan@iter{77}{77777778}\MFP@atan@iter{71}{42857143}%
- \MFP@atan@iter{60}{00000000}\MFP@atan@iter{33}{33333333}%
- \MFP@Rcopy sy\MFP@scaledmul}%
-\def\MFP@Rlog{%
+ \MFP@Rcopy xs\MFP@Rcopy xy\MFP@scaledmul
+ \ifnum \MFP@z@Sgn=0
+ \MFP@Rcopy sz%
+ \else
+ \MFP@Rcopyz u\MFP@Rcopyzx
+ \MFP@Rload y1{86}{66666667}\MFP@scaledmul
+ \MFP@Rcopyzy\MFP@Rload x1{100}{00000000}\MFP@Rsub\MFP@Rcopyzx
+ \MFP@atan@iter{84}{61538462}\MFP@atan@iter{81}{81818182}%
+ \MFP@atan@iter{77}{77777778}\MFP@atan@iter{71}{42857143}%
+ \MFP@atan@iter{60}{00000000}\MFP@atan@iter{33}{33333333}%
+ \MFP@Rcopy sy\MFP@scaledmul
+ \fi}%
+\newif\ifMFP@natural
+\def\MFP@Rlog{\MFP@naturalfalse\MFP@Rlog@}%
+\def\MFP@Rln{\MFP@naturaltrue\MFP@Rlog@}%
+\def\MFP@Rlog@{%
\ifnum\MFP@x@Sgn=0
\MFP@logofzero@err
\MFP@Rloadz{-1}\LogOfZeroInt\LogOfZeroFrac
\else
\ifnum \MFP@x@Sgn<0
- \MFP@warn{The logarithm of a negative number is complex.%
+ \MFP@warn{The logarithm of a negative number is complex.
\MFP@msgbreak Only the real part will be computed}%
+ \def\MFP@x@Sgn{1}%
\fi
\MFP@Rload s000%
\ifnum \MFP@x@Int=0
\edef\MFP@x@Tmp{\number\MFP@x@Frc}%
- \MFP@tempa=\MFP@numzeros\MFP@x@Tmp\relax
+ \MFP@tempa=\MFP@numshiftL\MFP@x@Tmp\relax
\def\MFP@s@Sgn{-1}%
- \edef\MFP@t@Int{\@xp\MFP@firstofmany\MFP@x@Tmp\mfp@end}%
+ \edef\MFP@t@Int{\@xp\MFP@oneofmany\MFP@x@Tmp\MFP@end}%
\edef\MFP@t@Frc{\@xp\@gobble\MFP@x@Tmp0}%
- \MFPpadto@eight\MFP@t@Frc
+ \MFP@padtoeight\MFP@t@Frc
\else
- \MFP@tempa\MFP@numdigits\MFP@x@Int
- \edef\MFP@x@Tmp{\MFP@x@Int\MFP@x@Frc}% gather all digits
- \edef\MFP@s@Sgn{1}%
- \edef\MFP@t@Int{\@xp\MFP@firstofmany\MFP@x@Tmp\mfp@end}%
+ \MFP@tempa\MFP@numshiftR\MFP@x@Int
+ \edef\MFP@x@Tmp{\MFP@x@Int\MFP@x@Frc}%
+ \ifnum\MFP@tempa>0 \def\MFP@s@Sgn{1}\fi
+ \edef\MFP@t@Int{\@xp\MFP@oneofmany\MFP@x@Tmp\MFP@end}%
\edef\MFP@x@Tmp{\@xp\@gobble\MFP@x@Tmp}%
- \edef\MFP@t@Frc{\@xp\MFP@firsteightofmany\MFP@x@Tmp\mfp@end}%
+ \edef\MFP@t@Frc{\@xp\MFP@eightofmany\MFP@x@Tmp\MFP@end}%
\fi
\edef\MFP@s@Int{\number\MFP@tempa}%
\def\MFP@t@Sgn{1}%
\MFP@Rlog@reduce
+ \ifMFP@natural \MFP@Rcopy sx\MFP@RbaseE \MFP@Rcopy zs\fi
\ifnum\MFP@t@Frc=0
\MFP@Rcopy sz%
\else
- \MFP@Rlog@prog
+ \def\MFP@t@Int{0}\MFP@Rlog@prog
+ \ifMFP@natural\else \MFP@Rcopyzx \MFP@RbaseX \fi
+ \MFP@Rcopy sy\MFP@Rcopyzx\MFP@Radd
\fi
\fi}%
-\def\showreg #1{% for debugging
-\begingroup
- \edef\reg{%
- #1 = (\csname MFP@#1@Sgn\endcsname)%
- \csname MFP@#1@Int\endcsname.%
- \csname MFP@#1@Frc\endcsname}%
- \show\reg
-\endgroup}%
-\def\MFP@numdigits#1{\@xp\MFP@ninthofmany#176543210\mfp@end}%
-\def\MFP@numzeros#1{%
- \@xp\MFP@ninthofmany#112345678\mfp@end}%
+\def\MFP@numshiftR#1{\@xp\MFP@ninthofmany#176543210\MFP@end}%
+\def\MFP@numshiftL#1{\@xp\MFP@ninthofmany#112345678\MFP@end}%
\def\MFP@Rlog@reduce{%
- \MFP@reduceonce 3{16227766}{31622777}{50000000}%
- \MFP@reduceonce 1{77827941}{56234133}{25000000}%
- \MFP@reduceonce 1{33352143}{74989421}{12500000}%
- \MFP@reduceonce 1{15478198}{86596433}{06250000}}%
+ \MFP@Rcopy tx\MFP@RmulC\MFP@Rcopyz t%
+ \MFP@reduceonce {316}{31622776}{60168379}{50000000}%
+ \MFP@reduceonce {177}{56234132}{51903491}{25000000}%
+ \MFP@reduceonce {133}{74989420}{93324558}{12500000}%
+ \MFP@reduceonce {115}{86596432}{33600654}{06250000}%
+ \MFP@Rcopy tx\MFP@RdivC\MFP@Rcopyz t}%
\def\MFP@reduceonce#1#2#3#4{%
- \MFP@Rcopy tx\MFP@Rload y1{#1}{#2}\MFP@Rcmp
- \ifMFP@neg\else
- \MFP@Rload y10{#3}\MFP@Rmul
- \MFP@Rcopyz t\MFP@Rcopy sx\MFP@Rload y10{#4}\MFP@Radd
+ \ifnum\MFP@t@Int>#1\relax
+ \MFP@Rcopy tx%
+ \MFP@DPmul 0{#2}{#3}\MFP@Rcopyz t%
+ \MFP@Rcopy sx\MFP@Rload y10{#4}\MFP@Radd
\MFP@Rcopyz s%
\fi}%
\def\MFP@Rlog@prog{%
- \MFP@Rcopy tx\MFP@Rdecr
- \MFP@Rcopyz t%
- \MFP@Rcopyzx\MFP@Rload y10{43750000}\MFP@Rsmul
- \MFP@com@iter{85714286}\MFP@com@iter{83333333}\MFP@com@iter{80000000}%
- \MFP@com@iter{75000000}\MFP@com@iter{66666667}\MFP@com@iter{50000000}%
- \MFP@com@iter{43429448}\MFP@Rcopyzx\MFP@Rcopy sy\MFP@Radd}%
-\def\MFP@Rln{%
- \MFP@Rlog\MFP@Rcopyzx\MFP@Rload y12{30258509}\MFP@Rmul}%
+ \MFP@Rcopy tx\MFP@Rload y10{88888889}\MFP@Rsmul
+ \MFP@com@iter{87500000}\MFP@com@iter{85714286}\MFP@com@iter{83333333}%
+ \MFP@com@iter{80000000}\MFP@com@iter{75000000}\MFP@com@iter{66666667}%
+ \MFP@com@iter{50000000}\MFP@flipz\MFP@Rcopyzx\MFP@Rcopy ty\MFP@Rsmul}%
\def\MFP@Rexp{%
\ifcase\MFP@x@Sgn\relax
\MFP@Rloadz 110%
@@ -381,10 +398,10 @@
\fi}%
\def\MFP@Rexp@pos{%
\MFP@Rload y1{18}{42068074}\MFP@Rcmp
- \ifMFP@pos % overflow
+ \ifMFP@pos
\MFP@expoverflow@err
\MFP@Rloadz 1\MaxRealInt\MaxRealFrac
- \else % handle integer part
+ \else
\MFP@tempa\MFP@x@Int
\edef\MFP@powerof@e{%
1\ifcase\MFP@tempa
@@ -412,7 +429,7 @@
\ifnum\MFP@x@Frc=0
\else
\MFP@Rcopyz s%
- \MFP@tempa=\@xp\MFP@firstofmany\MFP@x@Frc\mfp@end
+ \MFP@tempa=\@xp\MFP@oneofmany\MFP@x@Frc\MFP@end
\edef\MFP@powerof@e{%
y1\ifcase\MFP@tempa
10\or
@@ -429,7 +446,7 @@
\edef\MFP@t@Frc{0\@xp\@gobble\MFP@x@Frc}%
\MFP@Rcopy sx\@xp\MFP@Rload\MFP@powerof@e\MFP@Rmul
\ifnum\MFP@t@Frc=0
- \else % handle the rest
+ \else
\MFP@Rcopyz s\MFP@Rload t10\MFP@t@Frc
\MFP@Rexp@pos@prog
\MFP@Rcopy sx\MFP@Rcopyzy\MFP@Rmul
@@ -437,9 +454,10 @@
\fi
\fi}%
\def\MFP@Rexp@pos@prog{%
- \MFP@Rcopy tz\MFP@Rexp@iter{16666667}\MFP@Rexp@iter{20000000}%
- \MFP@Rexp@iter{25000000}\MFP@Rexp@iter{33333333}%
- \MFP@Rexp@iter{50000000}\MFP@Rcopyzx\MFP@Rincr}%
+ \MFP@Rcopy tz\MFP@Rexp@iter{14285714}\MFP@Rexp@iter{16666667}%
+ \MFP@Rexp@iter{20000000}\MFP@Rexp@iter{25000000}%
+ \MFP@Rexp@iter{33333333}\MFP@Rexp@iter{50000000}\MFP@Rcopyzx
+ \MFP@Rincr}%
\def\MFP@Rexp@iter#1{%
\MFP@Rcopyzx\MFP@Rload y10{#1}\MFP@Rsmul
\MFP@Rcopyzx\MFP@Rcopy ty\MFP@Rsmul
@@ -449,7 +467,7 @@
\MFP@Rcmp
\ifMFP@pos
\MFP@Rloadz 000%
- \else % handle integer part
+ \else
\MFP@tempa\MFP@x@Int
\edef\MFP@powerof@e{%
\ifcase\MFP@tempa
@@ -476,9 +494,9 @@
000\fi}%
\@xp\MFP@Rloadz\MFP@powerof@e
\ifnum\MFP@x@Frc=0
- \else % handle first decimal digit
+ \else
\MFP@Rcopyz s%
- \MFP@tempa=\@xp\MFP@firstofmany\MFP@x@Frc\mfp@end
+ \MFP@tempa=\@xp\MFP@oneofmany\MFP@x@Frc\MFP@end
\edef\MFP@powerof@e{%
y1\ifcase\MFP@tempa
10\or
@@ -495,18 +513,19 @@
\edef\MFP@t@Frc{0\@xp\@gobble\MFP@x@Frc}%
\MFP@Rcopy sx\@xp\MFP@Rload\MFP@powerof@e\MFP@Rmul
\ifnum\MFP@t@Frc=0
- \else % handle the rest
+ \else
\MFP@Rcopyz s\MFP@Rload t10\MFP@t@Frc
\MFP@Rexp@neg@prog
- \MFP@Rcopy sx\MFP@Rcopyzy\MFP@Rmul
+ \MFP@Rcopyzx\MFP@Rcopy sy\MFP@Rmul
\fi
\fi
\fi}%
\def\MFP@Rexp@neg@prog{%
- \MFP@Rcopy tx\MFP@Rload y10{16666667}\MFP@Rsmul
- \MFP@com@iter{20000000}\MFP@com@iter{25000000}%
- \MFP@com@iter{33333333}\MFP@com@iter{50000000}%
- \MFP@flipz\MFP@Rcopyzx\MFP@Rcopy ty\MFP@Rsmul\MFP@flipz}%
+ \MFP@Rcopy tx\MFP@Rload y10{14285712}\MFP@Rsmul
+ \MFP@com@iter{16666667}\MFP@com@iter{20000000}%
+ \MFP@com@iter{25000000}\MFP@com@iter{33333333}%
+ \MFP@com@iter{50000000}\MFP@flipz\MFP@Rcopyzx
+ \MFP@Rcopy ty\MFP@Rsmul\MFP@flipz}%
\def\MFP@Rpow{%
\ifnum\MFP@y@Frc>0
\MFP@warn{The "pow" function requires an integer power.
@@ -523,30 +542,23 @@
\MFP@badpower@err
\MFP@Rloadz 1\xOverZeroInt\xOverZeroFrac
\fi
- \else % integer power of nonzero number
- % get the sign in case an overflow interrupts the calculations.
+ \else
\ifnum\MFP@x@Sgn>0
\def\MFP@power@Sgn{1}%
\else
\edef\MFP@power@Sgn{\ifodd\MFP@loopctr -\fi 1}%
-\ifMFPdebug
- \show\MFP@power@Sgn
-\fi
\fi
\ifnum\MFP@y@Sgn<0 \MFP@Rinv \MFP@Rcopyzx\fi
\ifnum\MFP@loopctr=1
\MFP@Rloadz \MFP@power@Sgn\MFP@x@Int\MFP@x@Frc
\else
\MFP@@Rpow
-\ifMFPdebug
- \showreg z%
-\fi
\fi
\fi
- \fi}% %
+ \fi}%
\def\MFP@@Rpow{%
- \MFP@Rcopy xq% initialize register to be squared
- \MFP@Rload p110% initialize register to hold partial products
+ \MFP@Rcopy xq%
+ \MFP@Rload p110%
\MFP@Rpow@loop}%
\def\MFP@Rpow@loop{%
\ifodd\MFP@loopctr
@@ -568,32 +580,40 @@
\def\MFP@handle@expoverflow{%
\MFP@expoverflow@err
\MFP@loopctr=0
- \MFP@Rloadz\MFP@power@Sgn\MaxRealInt\MaxRealFrac
-}%
+ \MFP@Rloadz\MFP@power@Sgn\MaxRealInt\MaxRealFrac}%
\def\MFP@Rsqrt{%
\ifcase\MFP@x@Sgn\relax
\MFP@Rzero
\or
\ifnum\MFP@x@Int=0
- \let\MFP@sqrt@reduce=Y%
+ \def\MFP@sqrt@reduce{2}%
\edef\MFP@x@Int{\number\MFP@x@Frc}%
\edef\MFP@x@Frc{00000000}%
+ \else\ifnum\MFP@x@Int<10000
+ \def\MFP@sqrt@reduce{1}%
+ \edef\MFP@x@Int{\MFP@x@Int\@xp\MFP@fourofmany\MFP@x@Frc\MFP@end}%
+ \edef\MFP@x@Frc{\@xp\MFP@gobblefour\MFP@x@Frc0000}%
\else
- \let\MFP@sqrt@reduce=N%
- \fi
+ \def\MFP@sqrt@reduce{0}%
+ \fi\fi
\MFP@Rcopy xt%
\MFP@Isqrt
\MFP@Rcopyz s\MFP@Rcopyzy
\MFP@Rcopy tx\MFP@Rdiv
\MFP@Rcopy sx\MFP@Rcopyzy\MFP@Radd
\MFP@Rcopyzx\MFP@Rhalve
- \ifx Y\MFP@sqrt@reduce
- \MFP@Rcopyzx\MFP@Rload y10{10000}\MFP@Rmul
+ \ifcase \MFP@sqrt@reduce\relax
+ \or
+ \MFP@Rcopyzx\MFP@Rload y10{01000000}\MFP@Rmul
+ \or
+ \MFP@Rcopyzx\MFP@Rload y10{00010000}\MFP@Rmul
\fi
\else
- \MFP@sqrtofneg@err
+ \MFP@warn{Square root of a negative number. Zero will be returned.}%
\MFP@Rzero
\fi}%
+\def\MFP@fourofmany#1#2#3#4#5\MFP@end{#1#2#3#4}%
+\def\MFP@gobblefour#1#2#3#4{}%
\def\MFP@ItoQ#1#2{%
\MFP@tempa#1\relax\MFP@tempb#2\relax
\def\MFP@ItoQ@Tmp{}\MFP@ItoQ@loop}%
@@ -617,7 +637,7 @@
\def\MFP@Isqrt{%
\MFP@ItoQ\MFP@x@Int\MFP@x@Frc
\MFP@tempa=0 \MFP@tempb=0 \MFP@tempc=0
- \expandafter\MFP@Isqrt@loop\MFP@ItoQ@Tmp\mfp@end
+ \expandafter\MFP@Isqrt@loop\MFP@ItoQ@Tmp\MFP@end
\MFP@tempa=\MFP@tempc
\divide\MFP@tempc\MFP@tttfour
\edef\MFP@z@Int{\number\MFP@tempc}%
@@ -628,7 +648,7 @@
\edef\MFP@z@Frc{\MFP@z@Frc0000}%
\def\MFP@z@Sgn{1}}%
\def\MFP@Isqrt@loop#1{%
- \ifx\mfp@end #1%
+ \ifx\MFP@end #1%
\else
\multiply\MFP@tempa 2 \multiply\MFP@tempb 4 \multiply\MFP@tempc 2
\advance \MFP@tempb#1\relax
@@ -638,8 +658,8 @@
\advance\MFP@tempa 1
\fi
\expandafter\MFP@Isqrt@loop
- \fi
-}%
+ \fi}%
+\MFP@xfinish
\endinput
%%
%% End of file `mfpextra.tex'.
diff --git a/Master/texmf-dist/tex/generic/minifp/minifp.sty b/Master/texmf-dist/tex/generic/minifp/minifp.sty
index 321ec4197f1..0566ae33e1e 100644
--- a/Master/texmf-dist/tex/generic/minifp/minifp.sty
+++ b/Master/texmf-dist/tex/generic/minifp/minifp.sty
@@ -21,16 +21,16 @@
%% is Daniel H. Luecking. The Base Interpreters associated
%% with minifp are plain TeX and LaTeX.
%%
-\def\MFPfiledate{2013/02/01}%
-\def\MFPfileversion{0.92}%
+\def\MFPfiledate{2013/05/28}%
+\def\MFPfileversion{0.95}%
\expandafter
\ifx \csname MFP@finish\endcsname\relax
\else \expandafter\endinput \fi
\expandafter\edef\csname MFP@finish\endcsname{%
- \catcode64=\the\catcode64 \space % @
- \catcode46=\the\catcode46 \space % .
- \catcode60=\the\catcode60 \space % <
- \catcode62=\the\catcode62 \space}% >
+ \catcode64=\the\catcode64 \space
+ \catcode46=\the\catcode46 \space
+ \catcode60=\the\catcode60 \space
+ \catcode62=\the\catcode62 \space}%
\ifx\ProvidesPackage\UndEfInEd
\newlinechar`\^^J%
\message{%
@@ -44,28 +44,22 @@
\DeclareOption{extra}{\def\MFPextra{}}%
\ProcessOptions\relax
\fi
-\catcode64=11 % @=letter (already is in LaTeX)
+\catcode64=11
\ifx\MFPextra\UndEfInEd
\def\MFP@loadextra{}%
\else
\def\MFP@loadextra{\input mfpextra\relax}%
\fi
-\def\MFPloadextra{%
- \edef\MFP@load@extra{%
- \catcode46=12 \catcode60=12 \catcode62=12 \catcode64=11
- \noexpand\input mfpextra\relax
- \catcode46=\the\catcode46\relax\catcode60=\the\catcode60\relax
- \catcode62=\the\catcode62\relax\catcode64=\the\catcode64\relax}%
- \MFP@load@extra}%
-\catcode46=12 % .
-\catcode60=12 % <
-\catcode62=12 % >
-\long\def\gobbleto@mfp@end#1\mfp@end{}%
-\ifx\mfp@end\UndEfInEd\def\mfp@end{\@empty}\fi
+\def\MFPloadextra{\input mfpextra\relax}%
+\catcode46=12
+\catcode60=12
+\catcode62=12
+\long\def\gobbleto@MFP@end#1\MFP@end{}%
+\def\MFP@end{\@empty}%
\ifx\documentclass\UndEfInEd
\def\MFP@ifnoLaTeX{}%
\else
- \let\MFP@ifnoLaTeX\gobbleto@mfp@end
+ \let\MFP@ifnoLaTeX\gobbleto@MFP@end
\fi
\let\@xp\expandafter
\def\@XP{\@xp\@xp\@xp}%
@@ -97,13 +91,13 @@
\long\def\@firstofone #1{#1}%
\long\def\@firstoftwo #1#2{#1}%
\long\def\@secondoftwo#1#2{#2}%
-\mfp@end
+\MFP@end
\def\MFP@tttfour {10000}% ttt = Ten To The
\def\MFP@ttteight{100000000}%
-\def\MFP@firstofmany#1#2\mfp@end{#1}%
-\def\MFP@fifthofmany#1#2#3#4#5#6\mfp@end{#5}%
-\def\MFP@ninthofmany#1#2#3#4#5#6#7#8{\MFP@firstofmany}%
-\def\MFP@firsteightofmany#1#2#3#4#5#6#7#8#9\mfp@end{#1#2#3#4#5#6#7#8}%
+\def\MFP@oneofmany#1#2\MFP@end{#1}%
+\def\MFP@fifthofmany#1#2#3#4#5#6\MFP@end{#5}%
+\def\MFP@ninthofmany#1#2#3#4#5#6#7#8{\MFP@oneofmany}%
+\def\MFP@eightofmany#1#2#3#4#5#6#7#8#9\MFP@end{#1#2#3#4#5#6#7#8}%
\let\MFP@eos\relax
\def\MFP@EOS{\MFP@eos}%
\def\MFP@initRstack{\def\MFP@Rstack{\MFP@eos}}%
@@ -116,22 +110,19 @@
\countdef \MFP@tempf 10
\newcount \MFP@loopctr
\def\MFP@endgroup@after#1{\edef\x{\endgroup#1}\x}%
-\def\MFP@endgroup@return{\MFP@endgroup@after\MFP@returned@values}%
-\def\MFP@def@after{\def\noexpand}%
+\def\MFP@afterdef{\def\noexpand}%
\def\MFP@returned@values{%
- \MFP@def@after\MFP@z@Val{\MFP@z@Sign\MFP@z@Int.\MFP@z@Frc}%
- \MFP@def@after\MFP@z@Ovr{\MFP@z@Ovr}%
- \MFP@def@after\MFP@z@Und{\MFP@z@Und}%
- \MFP@def@after\MFPcurr@Sgn{\MFP@z@Sgn}}%
+ \MFP@afterdef\MFP@z@Val{\MFP@z@Sign\MFP@z@Int.\MFP@z@Frc}%
+ \MFP@afterdef\MFP@z@Ovr{\MFP@z@Ovr}%
+ \MFP@afterdef\MFP@z@Und{\MFP@z@Und}%
+ \MFP@afterdef\MFPcurr@Sgn{\MFP@z@Sgn}}%
\def\MFP@subroutine#1{%
\begingroup
- \MFP@basic@init@z
+ \MFP@Rzero
+ \def\MFP@z@Ovr{0}%
+ \def\MFP@z@Und{0}%
#1%
- \MFP@endgroup@return}%
-\def\MFP@basic@init@z{%
- \MFP@Rzero
- \def\MFP@z@Ovr{0}%
- \def\MFP@z@Und{0}}%
+ \MFP@endgroup@after\MFP@returned@values}%
\def\MFP@Rzero{%
\def\MFP@z@Sgn{0}%
\def\MFP@z@Int{0}%
@@ -170,28 +161,24 @@
\def\MFPparse@real#1#2#3#4{%
\MFPnospace@def\MFPtemp@Val{#4}%
\MFPprocess@into@parts\MFPtemp@Val#1#2#3%
- \MFPpadto@eight#3}%
+ \MFP@padtoeight#3}%
\def\MFPparse@x{\MFPparse@real\MFP@x@Sgn\MFP@x@Int\MFP@x@Frc}%
\def\MFPparse@y{\MFPparse@real\MFP@y@Sgn\MFP@y@Int\MFP@y@Frc}%
\def\MFPnospace@def#1#2{%
\edef#1{#2\space}\edef#1{\@xp\zap@space#1\@empty}}%
\def\MFPprocess@into@parts#1#2#3#4{%
- \@xp\MFPsplit@dot#1..\mfp@end #3#4%
- \ifnum#31<0
- \def#2{-1}%
- \else
- \def#2{1}%
+ \@xp\MFPsplit@dot#1..\MFP@end #3#4%
+ \ifnum#31<0 \def#2{-1}%
+ \else \def#2{1}%
\fi
\ifnum #30=0
\def#3{0}%
- \ifnum 0#4=0
- \def#2{0}%
- \fi
+ \ifnum 0#4=0 \def#2{0}\fi
\fi
\edef#3{\number \ifnum #2<0 -\fi#3}}%
-\def\MFPsplit@dot#1.#2.#3\mfp@end#4#5{\edef#4{#1}\edef#5{#2}}%
-\def\MFPpadto@eight#1{%
- \edef#1{\@xp\MFP@firsteightofmany#100000000\mfp@end}}%
+\def\MFPsplit@dot#1.#2.#3\MFP@end#4#5{\edef#4{#1}\edef#5{#2}}%
+\def\MFP@padtoeight#1{%
+ \edef#1{\@xp\MFP@eightofmany#100000000\MFP@end}}%
\def\MFPgetoperand@x{\Rpop\MFP@x@Val
\MFPprocess@into@parts\MFP@x@Val\MFP@x@Sgn\MFP@x@Int\MFP@x@Frc}%
\def\MFPgetoperand@y{\Rpop\MFP@y@Val
@@ -211,8 +198,8 @@
\@xp\@secondoftwo
\fi}%
\def\MFP@popit{\if@EndofStack\doMFP@EOS\doMFP@popit}%
-\def\doMFP@EOS#1\mfp@end#2{\MFP@popempty@err\let#2\EndofStack}%
-\def\doMFP@popit#1#2\mfp@end#3{\edef\MFP@Rstack{#2}\edef#3{#1}}%
+\def\doMFP@EOS#1\MFP@end#2{\MFP@popempty@err\let#2\EndofStack}%
+\def\doMFP@popit#1#2\MFP@end#3{\edef\MFP@Rstack{#2}\edef#3{#1}}%
\def\MFPchk#1{%
\MFPparse@x{#1}%
\MFP@Rchk\MFP@x@Sgn}%
@@ -267,8 +254,8 @@
\def\Rmax {\MFP@stack@Binary\MFP@Rmax}%
\let\Rnoop\relax
\def\Rcmp{%
- \MFPgetoperand@y\MFPgetoperand@x % get operands (last pushed is y)
- \MFP@Rcat\MFP@x@Val\MFP@Rcat\MFP@y@Val % put back: LOFI
+ \MFPgetoperand@y\MFPgetoperand@x
+ \MFP@Rcat\MFP@x@Val\MFP@Rcat\MFP@y@Val
\MFP@Rcmp}%
\def\Rchk{%
\MFPgetoperand@x
@@ -279,7 +266,7 @@
\edef\MFP@z@Val{\MFP@x@Sign\MFP@x@Int.\MFP@x@Frc}%
\edef\MFPcurr@Sgn{\MFP@x@Sgn}%
\MFPpush@result}%
- \def\Rpop{\@xp\MFP@popit\MFP@Rstack\mfp@end}%
+ \def\Rpop{\@xp\MFP@popit\MFP@Rstack\MFP@end}%
\def\Rexch{%
\Rpop\MFP@x@Val\Rpop\MFP@y@Val
\MFP@Rcattwo\MFP@y@Val\MFP@x@Val}%
@@ -316,6 +303,10 @@
\def\MFPdiv{\MFP@op@Binary\MFP@Rdiv}%
\def\MFPmin{\MFP@op@Binary\MFP@Rmin}%
\def\MFPmax{\MFP@op@Binary\MFP@Rmax}%
+\def\MFP@stack@Nullary#1{%
+ \MFP@subroutine{#1}\MFPpush@result}%
+\def\MFP@op@Nullary#1{%
+ \MFP@subroutine{#1}\MFPstore@result}%
\def\MFP@stack@Unary#1{%
\MFPgetoperand@x
\MFP@subroutine{#1}\MFPpush@result}%
@@ -339,7 +330,7 @@
\MFP@tempb\MFP@x@Frc\relax
\ifodd\MFP@tempb
\def\MFP@z@Und{5}%
- \advance\MFP@tempb 1 % round up
+ \advance\MFP@tempb 1
\ifnum\MFP@ttteight=\MFP@tempb
\MFP@tempb0 \advance\MFP@tempa1
\fi
@@ -379,17 +370,17 @@
\edef\MFP@x@Sgn{\number -\MFP@x@Sgn}\MFP@Rincr
\edef\MFP@z@Sgn{\number -\MFP@z@Sgn}}%
\def\MFP@Rstore{\MFP@Rcopy xz}%
-\def\MFP@Rfloororceil#1{%
+\def\MFP@Rfloorceil#1{%
\MFP@tempa\MFP@x@Int\relax
- \ifnum 0#1\MFP@x@Sgn
+ \ifnum \MFP@x@Sgn #10
\ifnum\MFP@x@Frc=0
\else
\advance\MFP@tempa1
\fi
\fi
\MFP@Rloadz{\ifnum\MFP@x@Int=0 0\else\MFP@x@Sgn\fi}\MFP@tempa0}%
-\def\MFP@Rfloor{\MFP@Rfloororceil>}%
-\def\MFP@Rceil {\MFP@Rfloororceil<}%
+\def\MFP@Rfloor{\MFP@Rfloorceil<}%
+\def\MFP@Rceil {\MFP@Rfloorceil>}%
\def\MFP@split#1#2#3{%
\begingroup
\MFP@tempa#1\relax
@@ -399,38 +390,27 @@
\multiply\MFP@tempb by\MFP@tttfour
\advance\MFP@tempa-\MFP@tempb
\MFP@endgroup@after{%
- \MFP@def@after#2{#2}%
- \MFP@def@after#3{\number\MFP@tempa}%
+ \MFP@afterdef#2{#2}%
+ \MFP@afterdef#3{\number\MFP@tempa}%
}}%
-\def\MFP@x@split{%
+\def\MFP@@split{%
\MFP@split\MFP@x@Int\MFP@x@Int@ii\MFP@x@Int@i
- \MFP@split\MFP@x@Frc\MFP@x@Frc@i\MFP@x@Frc@ii}%
-\def\MFP@y@split{%
+ \MFP@split\MFP@x@Frc\MFP@x@Frc@i\MFP@x@Frc@ii
\MFP@split\MFP@y@Int\MFP@y@Int@ii\MFP@y@Int@i
\MFP@split\MFP@y@Frc\MFP@y@Frc@i\MFP@y@Frc@ii}%
-\def\MFPmore@init@z{%
- \def\MFP@z@Frc@iv {0}%
- \def\MFP@z@Frc@iii{0}%
- \def\MFP@z@Frc@ii {0}%
- \def\MFP@z@Frc@i {0}%
- \def\MFP@z@Int@i {0}%
- \def\MFP@z@Int@ii {0}%
- \def\MFP@z@Int@iii{0}}%
-\def\MFP@fourdigits#1{%
- \@xp\MFP@fifthofmany\number#1{}{0}{00}{000}\mfp@end\number#1}%
-\def\makeMFP@fourdigits#1{\edef#1{\MFP@fourdigits{#1}}}%
-\def\MFP@eightdigits#1{%
- \@xp\MFP@ninthofmany\number#1%
- {}{0}{00}{000}{0000}{00000}{000000}{0000000}\mfp@end\number#1}%
-\def\makeMFP@eightdigits#1{\edef#1{\MFP@eightdigits{#1}}}%
+\def\makeMFP@fourdigits#1{%
+ \edef#1{\@xp\MFP@fifthofmany\number#1{}{0}{00}{000}\MFP@end\number#1}}%
+\def\makeMFP@eightdigits#1{%
+ \edef#1{\@xp\MFP@ninthofmany\number#1%
+ {}{0}{00}{000}{0000}{00000}{000000}{0000000}\MFP@end\number#1}}%
\def\MFP@carrya{\MFP@carry\MFP@ttteight}%
\def\MFP@carrym{\MFP@carry\MFP@tttfour}%
\def\MFP@carry#1#2#3{%
\begingroup
\MFP@carryi{#1}#2#3%
\MFP@endgroup@after{%
- \MFP@def@after#3{\number\MFP@tempa}%
- \MFP@def@after#2{\number\MFP@tempb}%
+ \MFP@afterdef#3{\number\MFP@tempa}%
+ \MFP@afterdef#2{\number\MFP@tempb}%
}}%
\def\MFP@carryi#1#2#3{%
\MFP@tempa=#3\relax
@@ -445,7 +425,7 @@
\MFP@tempa#1%
\advance\MFP@tempa#2\relax
\MFP@endgroup@after{%
- \MFP@def@after#3{\number\MFP@tempa}%
+ \MFP@afterdef#3{\number\MFP@tempa}%
}}%
\def\MFP@multiplyone#1#2{%
\MFP@tempa#1%
@@ -500,24 +480,25 @@
\edef\MFP@z@Frc{\number\MFP@tempb}%
\makeMFP@eightdigits\MFP@z@Frc}%
\def\MFP@Rmul{%
- \MFP@tempa\MFP@x@Sgn \multiply\MFP@tempa\MFP@y@Sgn\relax
- \ifnum 0=\MFP@tempa
- \MFP@Rzero
- \else
- \edef\MFP@z@Sgn{\number\MFP@tempa}%
- \@xp\MFP@@Rmul
- \fi}%
+ \ifnum\MFP@x@Sgn=0 \MFP@Rzero
+ \else\ifnum\MFP@y@Sgn=0 \MFP@Rzero
+ \else \edef\MFP@z@Sgn{\number\MFP@x@Sign\MFP@y@Sgn}%
+ \@XP\MFP@@Rmul
+ \fi\fi}%
\def\MFP@@Rmul{%
- \MFPmore@init@z
- \MFP@x@split\MFP@y@split
+ \def\MFP@z@Frc@iv {0}\def\MFP@z@Frc@iii{0}%
+ \def\MFP@z@Frc@ii {0}\def\MFP@z@Frc@i {0}%
+ \def\MFP@z@Int@i {0}\def\MFP@z@Int@ii {0}%
+ \def\MFP@z@Int@iii{0}%
+ \MFP@@split
\MFP@multiplyfour \MFP@y@Frc@ii \MFP@z@Frc@i
- \MFP@z@Frc@ii \MFP@z@Frc@iii\MFP@z@Frc@iv
+ \MFP@z@Frc@ii \MFP@z@Frc@iii \MFP@z@Frc@iv
\MFP@multiplyfour \MFP@y@Frc@i \MFP@z@Int@i
- \MFP@z@Frc@i \MFP@z@Frc@ii \MFP@z@Frc@iii
+ \MFP@z@Frc@i \MFP@z@Frc@ii \MFP@z@Frc@iii
\MFP@multiplyfour \MFP@y@Int@i \MFP@z@Int@ii
- \MFP@z@Int@i \MFP@z@Frc@i \MFP@z@Frc@ii
+ \MFP@z@Int@i \MFP@z@Frc@i \MFP@z@Frc@ii
\MFP@multiplyfour \MFP@y@Int@ii \MFP@z@Int@iii
- \MFP@z@Int@ii \MFP@z@Int@i \MFP@z@Frc@i
+ \MFP@z@Int@ii \MFP@z@Int@i \MFP@z@Frc@i
\MFP@carrym\MFP@z@Frc@iv\MFP@z@Frc@iii
\MFP@carrym\MFP@z@Frc@iii\MFP@z@Frc@ii
\ifnum\MFP@z@Frc@iii<5000 \else
@@ -540,12 +521,10 @@
\edef\MFP@z@Und{\MFP@z@Frc@iii\MFP@z@Frc@iv}%
\ifnum\MFP@z@Int>0
\else\ifnum\MFP@z@Frc>0
- \else
- \def\MFP@z@Sgn{0}%
+ \else \def\MFP@z@Sgn{0}%
\fi\fi}%
\def\MFP@Rdiv{%
- \ifnum\MFP@y@Sgn=0
- \MFP@dividebyzero@err
+ \ifnum\MFP@y@Sgn=0 \MFP@dividebyzero@err
\ifnum\MFP@x@Sgn=0
\edef\MFP@z@Int{\ZeroOverZeroInt}%
\edef\MFP@z@Frc{\ZeroOverZeroFrac}%
@@ -554,13 +533,8 @@
\edef\MFP@z@Frc{\xOverZeroFrac}%
\fi
\edef\MFP@z@Sgn{\MFP@x@Sgn}%
- \else\ifnum\MFP@x@Sgn=0
- \MFP@Rzero
- \else
- \MFP@tempa\MFP@x@Sgn
- \multiply\MFP@tempa\MFP@y@Sgn
- \edef\MFP@z@Sgn{\number\MFP@tempa}%
- \MFP@@Rdiv
+ \else\ifnum\MFP@x@Sgn=0 \MFP@Rzero
+ \else \edef\MFP@z@Sgn{\number\MFP@x@Sign\MFP@y@Sgn}\MFP@@Rdiv
\fi\fi}%
\def\MFP@@Rdiv{%
\ifnum\MFP@y@Int=0
@@ -571,14 +545,14 @@
\MFP@tempa=0
\fi
\advance\MFP@tempa\MFP@numdigits@toshift\MFP@y@Int\relax
- \@XP\MFP@doshift@y\@xp\MFP@y@Int\MFP@y@Frc0000000\mfp@end
+ \@XP\MFP@doshift@y\@xp\MFP@y@Int\MFP@y@Frc0000000\MFP@end
\ifnum\MFP@x@Int=0
\edef\MFP@x@Int{\number\MFP@x@Frc}%
\def\MFP@x@Frc{00000000}%
\advance\MFP@tempa -8
\fi
\advance\MFP@tempa-\MFP@numdigits@toshift\MFP@x@Int\relax
- \@XP\MFP@doshift@x\@xp\MFP@x@Int\MFP@x@Frc0000000\mfp@end
+ \@XP\MFP@doshift@x\@xp\MFP@x@Int\MFP@x@Frc0000000\MFP@end
\ifnum\MFP@tempa<-9
\else
\MFP@tempf\MFP@tempa
@@ -593,13 +567,13 @@
\makeMFP@eightdigits\MFP@z@Frc
\fi
\fi}%
-\def\MFP@numdigits@toshift#1{\@xp\MFP@ninthofmany#101234567\mfp@end}%
-\def\MFP@doshift@x#1#2#3#4#5#6#7#8#9\mfp@end{%
+\def\MFP@numdigits@toshift#1{\@xp\MFP@ninthofmany#101234567\MFP@end}%
+\def\MFP@doshift@x#1#2#3#4#5#6#7#8#9\MFP@end{%
\def\MFP@x@Int{#1#2#3#4#5#6#7#8}%
- \edef\MFP@x@Frc{\MFP@firsteightofmany#9\mfp@end}}%
-\def\MFP@doshift@y#1#2#3#4#5#6#7#8#9\mfp@end{%
+ \edef\MFP@x@Frc{\MFP@eightofmany#9\MFP@end}}%
+\def\MFP@doshift@y#1#2#3#4#5#6#7#8#9\MFP@end{%
\def \MFP@y@Int{#1#2#3#4#5#6#7#8}%
- \edef\MFP@y@Frc{\MFP@firsteightofmany#9\mfp@end}}%
+ \edef\MFP@y@Frc{\MFP@eightofmany#9\MFP@end}}%
\def\MFP@Rdivloop{%
\MFP@tempb\MFP@x@Int % \MFP@tempb = n_1
\MFP@tempc\MFP@y@Int % \MFP@tempc = d_1
@@ -634,7 +608,7 @@
\fi
\advance\MFP@tempf -1
\ifnum\MFP@tempf>0
- \edef\MFP@x@Int{\MFP@x@Int0}% easy multiplications by 10
+ \edef\MFP@x@Int{\MFP@x@Int0}%
\edef\MFP@x@Frc{\MFP@x@Frc0}%
\MFP@carrya\MFP@x@Frc\MFP@x@Int
\@xp\MFP@Rdivloop
@@ -643,7 +617,7 @@
\advance \MFP@tempa -7
\ifnum\MFP@tempa>0
\def\MFP@z@Ovr{}%
- \@xp\MFPget@Ovrdigits\MFP@z@digits\mfp@end
+ \@xp\MFPget@Ovrdigits\MFP@z@digits\MFP@end
\else
\ifnum\MFP@tempa<-7
\edef\MFP@z@digits{00000000\MFP@z@digits}%
@@ -661,7 +635,7 @@
0000\else
00000%
\fi \MFP@z@digits}%
- \@xp\MFPget@Intdigits\MFP@z@digits\mfp@end
+ \@xp\MFPget@Intdigits\MFP@z@digits\MFP@end
\fi}%
\def\MFPget@Ovrdigits#1{%
\edef\MFP@z@Ovr{\MFP@z@Ovr#1}%
@@ -676,7 +650,7 @@
\MFPget@Frcdigits}%
\def\MFPget@Frcdigits#1#2#3#4#5#6#7#8#9{%
\def\MFP@z@Frc{#1#2#3#4#5#6#7#8}%
- \def\MFP@z@Und{#9}\gobbleto@mfp@end}%
+ \def\MFP@z@Und{#9}\gobbleto@MFP@end}%
\def\MFP@Rmax{%
\MFP@Rcmp \ifMFP@neg \MFP@Rcopy yz\else\MFP@Rcopy xz\fi}%
\def\MFP@Rmin{%
@@ -691,15 +665,15 @@
\@xp\MFP@Rtrunc
\fi}%
\def\MFP@Rtrunc#1{%
- \edef\MFP@x@Frc{\@xp\MFP@@Rtrunc\MFP@x@Frc\mfp@end}%
- \ifnum\MFP@x@Int=0 % possibly returns 0
+ \edef\MFP@x@Frc{\@xp\MFP@@Rtrunc\MFP@x@Frc\MFP@end}%
+ \ifnum\MFP@x@Int=0
\ifnum\MFP@x@Frc=0
\def\MFP@x@Sgn{0}%
\fi
\fi
\MFP@endgroup@after{%
- \MFP@def@after#1{\MFP@x@Sign\MFP@x@Int.\MFP@x@Frc}}}%
-\def\MFP@@Rtrunc#1#2#3#4#5#6#7#8#9\mfp@end{%
+ \MFP@afterdef#1{\MFP@x@Sign\MFP@x@Int.\MFP@x@Frc}}}%
+\def\MFP@@Rtrunc#1#2#3#4#5#6#7#8#9\MFP@end{%
\ifcase\MFP@tempa\or
#1\or
#1#2\or
@@ -711,9 +685,9 @@
#1#2#3#4#5#6#7#8\fi}%
\def\MFP@iRtrunc#1{%
\makeMFP@eightdigits\MFP@x@Int
- \edef\MFP@x@Val{\number\MFP@x@Sign\@xp\MFP@@iRtrunc\MFP@x@Int\mfp@end}%
- \MFP@endgroup@after{\MFP@def@after#1{\MFP@x@Val}}}%
-\def\MFP@@iRtrunc#1#2#3#4#5#6#7#8#9\mfp@end{%
+ \edef\MFP@x@Val{\number\MFP@x@Sign\@xp\MFP@@iRtrunc\MFP@x@Int\MFP@end}%
+ \MFP@endgroup@after{\MFP@afterdef#1{\MFP@x@Val}}}%
+\def\MFP@@iRtrunc#1#2#3#4#5#6#7#8#9\MFP@end{%
\ifcase-\MFP@tempa
#1#2#3#4#5#6#7#8\or
#1#2#3#4#5#6#70\or
@@ -730,32 +704,32 @@
\ifnum 0>\MFP@tempa
\edef\MFP@y@Tmp{%
\ifcase-\MFP@tempa\or
- 5\or % .5 x 10^1
- 50\or % .5 x 10^2
- 500\or % .5 x 10^3
- 5000\or % .5 x 10^4
- 50000\or % .5 x 10^5
- 500000\or % .5 x 10^6
- 5000000\else % .5 x 10^7
- 50000000\fi % .5 x 10^8
+ 5\or
+ 50\or
+ 500\or
+ 5000\or
+ 50000\or
+ 500000\or
+ 5000000\else
+ 50000000\fi
}%
\else
\edef\MFP@y@Tmp{%
\ifcase\MFP@tempa
- .5\or % .5 x 10^0
- .05\or % .5 x 10^{-1}
- .005\or % .5 x 10^{-2}
- .0005\or % .5 x 10^{-3}
- .00005\or % .5 x 10^{-4}
- .000005\or % .5 x 10^{-5}
- .0000005\or % .5 x 10^{-6}
- .00000005\else% .5 x 10^{-7}
- 0\fi %
+ .5\or
+ .05\or
+ .005\or
+ .0005\or
+ .00005\or
+ .000005\or
+ .0000005\or
+ .00000005\else
+ 0\fi
}%
\fi
\MFPchk{#2}\ifMFP@neg\edef\MFP@y@Tmp{-\MFP@y@Tmp}\fi
\MFPadd{#2}\MFP@y@Tmp\MFP@z@Tmp
- \MFP@endgroup@after{\MFP@def@after\MFP@z@Tmp{\MFP@z@Tmp}}%
+ \MFP@endgroup@after{\MFP@afterdef\MFP@z@Tmp{\MFP@z@Tmp}}%
\MFPtruncate{#1}\MFP@z@Tmp}%
\def\MFPstrip{%
\@ifstar{\MFP@strip{}}{\MFP@strip{.0}}}%
@@ -764,22 +738,22 @@
\ifnum \MFP@x@Frc=0
\edef#3{\MFP@x@Sign\MFP@x@Int#1}%
\else
- \edef#3{\MFP@x@Sign\MFP@x@Int.\@xp\MFP@@strip\MFP@x@Frc\mfp@end}%
+ \edef#3{\MFP@x@Sign\MFP@x@Int.\@xp\MFP@@strip\MFP@x@Frc\MFP@end}%
\fi}%
-\def\MFP@@strip#1#2\mfp@end{%
+\def\MFP@@strip#1#2\MFP@end{%
#1%
\ifnum 0#2>0
\@xp\MFP@@strip
\else
- \@xp\gobbleto@mfp@end
- \fi#2\mfp@end}%
+ \@xp\gobbleto@MFP@end
+ \fi#2\MFP@end}%
\def\MFP@Global#1{\toks@\@xp{#1}\xdef#1{\the\toks@}}%
\def\MFP@GlobalStack{\MFP@Global\MFP@Rstack}%
\def\MFP@Export#1{%
\begingroup
\toks@\@xp{\MFPprogram@returns}%
\MFP@endgroup@after{%
- \MFP@def@after\MFPprogram@returns{\the\toks@ \MFP@def@after#1{#1}}%
+ \MFP@afterdef\MFPprogram@returns{\the\toks@ \MFP@afterdef#1{#1}}%
}}%
\def\MFP@ExportStack{\MFP@Export\MFP@Rstack}%
\def\MFP@Rload #1#2#3#4{%