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-%--------------------------------------------
-%
-% Package sciformat.sty
-%
-% Provides support for floating point number representations of the
-% form
-%
-% S * M * 10^e
-%
-% with S in [-,+,0], 0<M<10, e in Z.
-%
-% Example:
-%
-% +1.62452*10^-8
-%
-% The conversion routines are complete text-based.
-%
-% Copyright 2007/2008 by Christian Feuersänger.
-%
-% This program is free software: you can redistribute it and/or modify
-% it under the terms of the GNU General Public License as published by
-% the Free Software Foundation, either version 3 of the License, or
-% (at your option) any later version.
-%
-% This program is distributed in the hope that it will be useful,
-% but WITHOUT ANY WARRANTY; without even the implied warranty of
-% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-% GNU General Public License for more details.
-%
-% You should have received a copy of the GNU General Public License
-% along with this program. If not, see <http://www.gnu.org/licenses/>.
-%
-%--------------------------------------------
-\ProvidesPackage{sciformat}[2008/02/17 v.0.9.4]
-\RequirePackage{pgf}[2007/01/01]
-\RequirePackage{pgfplotshelpers}[2008/02/17]
-
-% Computes a normalised floating point representation for #1 of the
-% form
-% [+-]X.XXXXXXX*10^C
-% where
-% X.XXXXXX is a mantisse with first number != 0
-% and C is a count.
-%
-% This method does NOT use TeX Registers to represent the numbers! The
-% computation is COMPLETELY STRING BASED.
-% This allows numbers such at 10000000 or 5.23e-10 to be represented
-% properly, although TeX-registers would produce overflow/underflow
-% errors in these cases.
-%
-% It is to be used to compute logs, because log(X*10^Y) = log(X) + log(10)*Y
-%
-% Arguments:
-% #1 a -possibly non-normalized- number representation. Accepted input
-% format is
-% [+-]XXXXX.XXXXXX
-% [+-]XXXXX.XXXXXXeXXXX
-% [+-]0.0000XXXXXX
-% [+-]0.0000XXXXXXeXXXX
-% NOT accepted input format is
-% [+-]0000.XXXXXX [leading zeros not supported]
-% [+-]XXXXX.XXXXXXEXXXXX [E notation not yet implemented]
-% #2 a macro name. \def#2{.....} will be used to assign the mantisse.
-% #3 a macro name. \def#3{.....} will be used to assign the exponent (base 10).
-%
-% Example:
-% \def\normalize#1{%
-% \sciparse#1\to\M\powten\E
-% \[ #1 \mapsto \M\cdot 10^{\E} \]
-% }
-% \normalize{123.41251}%
-% \normalize{3.26101452e-06}%
-%
-% REMARKS:
-% - the mantisse will ALWAYS have a period and one following number.
-% - Special case: the number +- 0 will always have the mantisse 0.0. The sign and
-% the exponent is undefined.
-\def\sciparse#1\to#2\powten#3{%
- \begingroup
- \sciparse@impl@possibly@signed#1\to#2\powten{#3}%
- \xdef\sciparseTMP{%
- \noexpand\def\noexpand#2{#2}%
- \noexpand\def\noexpand#3{#3}%
- }%
- \endgroup
- \sciparseTMP
-}
-
-% Overloaded scientific parser.
-%
-% In addition to '\sciparse', this method checks for '+- 0' cases
-% and sets #2 accordingly.
-%
-% \S #2: will be \def'ed to one of [0,1,2] with
-% 0 == '0', ( \def#2{0} )
-% 1 == '+',
-% 2 == '-',
-% -> can be used with \ifcase
-% \M #3: will be filled with a positive mantisse (undefined in case \S=0).
-% \E #4: the exponent basis 10 (an integer). Undefined in case \S = 0.
-%
-% Example:
-% \sciparsesign141.212\S\M\E
-% -> \S = 1, \M = 1.41212, \E =2
-%
-\def\sciparsesign#1#2#3#4{%
- \begingroup
- \sciparsesign@impl@possibly@signed#1\S#2\M#3\E{#4}%
- \def\sciparseTMP{0}%
- \ifx\sciparseTMP#2\relax
- \def#4{0}%
- \fi
- \xdef\sciparseTMP{%
- \noexpand\def\noexpand#2{#2}%
- \noexpand\def\noexpand#3{#3}%
- \noexpand\def\noexpand#4{#4}%
- }%
- \endgroup
- \sciparseTMP
-}
-
-\def\sciparsesignsingle#1#2{%
- \begingroup
- \sciparsesign{#1}\sci@S\sci@M\sci@E
- \xdef\sciparseTMP{\noexpand\scisetcomponents{\noexpand#2}{\sci@S}{\sci@M}{\sci@E}}%
- \endgroup
- \sciparseTMP
-}
-
-% Compares
-% x = Sign(#1) #2 * 10^#3
-% with
-% y = Sign(#4) #5 * 10^#6
-%
-% example:
-% \scimathlessthan\S\M\E\and\SS\MM\EE
-% \ifscimathlessthan
-% is smaller!
-% \else
-% is not smaller.
-% \fi
-%
-% and sets the boolean
-% \ifscimathlessthan := (x<y).
-\def\scimathlessthan#1#2#3\and#4#5#6{%
- \scimathlessthanfalse
- \begingroup
- \let\S@first=\c@pgf@counta
- \let\S@second=\c@pgf@countb
- \S@first\expandafter=#1\relax
- \S@second\expandafter=#4\relax
- \ifcase\S@first
- % x = 0 -> (x<y <=> y >0)
- \ifnum1=\S@second
- \aftergroup\scimathlessthantrue
- \fi
- \or
- % x > 0 -> (x<y <=> ( y > 0 && |x| < |y|) )
- \ifnum1=\S@second
- % y>0:
- \scimathlessthan@positive\M#2\E#3\MM#5\EE{#6}%
- \fi
- \or
- % x < 0 -> (x<y <=> (y >= 0 || |x| > |y|) )
- \ifnum2=\S@second
- % 'y<0':
- \scimathlessthan@positive\M#5\E#6\MM#2\EE{#3}%
- \else
- \aftergroup\scimathlessthantrue
- \fi
- \fi
- \endgroup
-}
-
-\def\scimathmax#1#2#3\and#4#5#6\to#7#8#9{%
- \scimathlessthan#1#2#3\and#4#5#6\relax
- \ifscimathlessthan
- \let#7=#4
- \let#8=#5
- \let#9=#6
- \else
- \let#7=#1
- \let#8=#2
- \let#9=#3
- \fi
-}
-
-\def\scimathmin#1#2#3\and#4#5#6\to#7#8#9{%
- \scimathlessthan#1#2#3\and#4#5#6\relax
- \ifscimathlessthan
- \let#7=#1
- \let#8=#2
- \let#9=#3
- \else
- \let#7=#4
- \let#8=#5
- \let#9=#6
- \fi
-}
-
-% Takes \S, \M and \E as sign, mantisse and exponent and computes a
-% fixed point representation for that number.
-%
-% example:
-% \S=1
-% \M=4.2
-% \E=1
-% \scitofixed\S\M\E\result
-% -> 42.0
-\def\scitofixed#1#2#3#4{%
- \begingroup
- \let\sci@sign=\c@pgf@counta
- \sci@sign\expandafter=#1\relax
- \ifnum0=\sci@sign
- \xdef\sciparseTMP{0.0}%
- \else
- \expandafter\scitofixed@impl#2\E#3\END
- \ifnum2=\sci@sign
- \xdef\sciparseTMP{-\sciparseTMP}%
- \fi
- \fi
- \endgroup
- \let#4=\sciparseTMP
-}
-
-% Single macro SCI-representation to #2.
-\def\scitofixedsingle#1#2{%
- \begingroup
- \scigetcomponents{#1}\sci@S\sci@M\sci@E
- \scitofixed\sci@S\sci@M\sci@E{#2}%
- \global\let\sciparseTMP=#2%
- \endgroup
- \let#2=\sciparseTMP
-}
-
-% Takes a SINGLE macro representing a floating point and extracts
-% sign, mantisse and exponent.
-% #1: the name of the single macro.
-% The expansion of #1 is COMPLETELY independend of associated
-% floating point number. You can even use \def#1{foo bar}
-% so change the meaning of #1 without affecting the number.
-% #2: will be set to #1's sign
-% #3: will be set to #1's mantisse
-% #4: will be set to #1's exponent
-%
-% @see scisetcomponents
-\def\scigetcomponents#1#2#3#4{%
- \expandafter\let\expandafter#2\csname\string#1@S\endcsname
- \expandafter\let\expandafter#3\csname\string#1@M\endcsname
- \expandafter\let\expandafter#4\csname\string#1@E\endcsname
-}
-
-% Assigns sign #2, mantisse #3 and exponent #4 to a single macro
-% representing the floating point.
-%
-% #1: the target name. Will create macros #1@S, #1@M and #1@E
-% which will be filled with #2, #3 and #4.
-%
-% Remark:
-% It is perfectly save to use the macro name #1 for other uses since
-% only the '@{S,M,E}' - macros are used to maintain the numerical
-% information.
-%
-% @see scigetcomponents
-\def\scisetcomponents#1#2#3#4{%
- \expandafter\edef\csname\string#1@S\endcsname{#2}%
- \expandafter\edef\csname\string#1@M\endcsname{#3}%
- \expandafter\edef\csname\string#1@E\endcsname{#4}%
-}
-
-% Divides or multiplies the input number by 10^#4 using an arithmetic
-% left/right shift.
-%
-% Input:
-% #1 Sign macro
-% #2 Mantisse macro
-% #3 exponent macro
-% #4 a positive or negative integer number denoting the shift.
-%
-% Example:
-% \scimathshift\S\M\E4
-\def\scimathshift#1#2#3#4{%
- \begingroup
- \c@pgf@counta\expandafter=#3\relax
- \advance\c@pgf@counta by#4\relax
- \xdef\sciparseTMP{\the\c@pgf@counta}%
- \endgroup
- \let#3=\sciparseTMP
-}
-
-\def\scimathshiftsingle#1#2{%
- \begingroup
- \expandafter\let\expandafter\E\csname\string#1@E\endcsname
- \c@pgf@counta\expandafter=\E\relax
- \advance\c@pgf@counta by#2\relax
- \xdef\sciparseTMP{\the\c@pgf@counta}%
- \endgroup
- \expandafter\let\csname\string#1@E\endcsname\sciparseTMP%
-}
-
-
-% Rounds a fixed point number #1 to #2 digits precision and returns
-% the result into macro #3.
-%
-% This method is PURELY text based and can work with arbirtrary
-% precision (well, limited to TeX's stack size and integer size).
-\def\fixedpointround#1\prec#2\to#3{%
- \begingroup
- \pgfplots@toka={}%
- \let\fp@round@next=\empty
- \let\fp@round@prec=\c@pgf@countb
- \let\fp@offsetbehindperiod=\c@pgf@counta
- \let\fp@round@lastzeros=\c@pgf@countc
- \let\fp@round@trg=#3\relax
- \def\fp@round@input{#1}%
- \fp@round@prec=#2\relax
- \fp@round@lastzeros=0
- \fp@offsetbehindperiod=-1 % means: no period found so far
- \fixedpointround@impl@ITERATE@NODOT #1\fp@round@EOI
- \xdef\sciparseTMP{\fp@round@trg}%
- \endgroup
- \let#3=\sciparseTMP
-}
-
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-% IMPL
-%
-%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-% \fixedpointround implementation in WORDS:
-%
-% coarse idea:
-% 1. collect all digits/sign BEFORE the first period in REVERSE order
-% 2. then, collect UP TO \prec digits after the period in REVERSE order
-% Steps 1. and 2. lead to the digit [sign] sequence
-% "x_{-p} x_{-p+1} ... x_{-2} x_{-1} '.' x_0 ... x_r"
-% where 'r' is the total number of digits. The integer 'p' denotes the
-% ACTUALLY collected number of digits behind the period.
-%
-% Let 'k' be the desired precision.
-%
-% There are exactly TWO cases:
-% 1. The case with p<=k and x_{-p-1} = end of input.
-% 2. The case with p=k and x_{-p-1} is a further, next character.
-%
-% Then, we do in case 1.)
-% discard any unused zeros at the tail of our number (possibly
-% including the period)
-%
-% and in case 2.)
-% if NEXT DIGIT < 5:
-% do exactly the same as in case 1.) above and discard any
-% following digits.
-% else
-% let q := -p
-% while(x_q = 9 and q<=r )
-% if q>=0
-% set x_q = '0'
-% else
-% discard digit x_q='9'
-% fi
-% ++q
-% if q=0
-% discard the period
-% fi
-% end while
-% if q = r+1
-% insert a '1'
-% else
-% set x_q = x_q + 1
-% fi
-% fi
-%
-% All these loops have been implemented in spaghetti-code below.
-% Sorry, I fear its hard to understand. In principle, everything is
-% realised using more or less finite state machines (with some number
-% counting logic).
-%
-% Some comments:
-% - The token register \pgfplots@toka is used to accumulate the REVERSED input number.
-% - \fp@round@EOI always denotes 'END OF INPUT'.
-% - in the second stage, we need to reverse \pgfplots@toka.
-% This is -again- done with \pgfplots@toka.
-
-\def\fixedpointround@impl@discard@period#1.#2\fp@round@EOI{%
- \def\fp@round@trg{#1}%
-}
-
-\def\fixedpointround@impl@gobble@rest@and@start#1\fp@round@EOI{%
- \fixedpointround@impl@start
-}
-\def\fixedpointround@impl@gobble@and@start\fp@round@EOI{%
- \fixedpointround@impl@start
-}
-\def\fixedpointround@impl@gobble\fp@round@EOI{}%
-
-\def\fixedpointround@impl@start{%
- \ifx\fp@round@next\empty
- \ifnum\fp@offsetbehindperiod<0
- \edef\fp@round@trg{\fp@round@input}%
- \else
- \ifnum\fp@offsetbehindperiod>\fp@round@prec
- \errmessage{Internal logic error in fixedpointround at [I] - should not have happened!?}%
- \fi
- \fixedpointround@impl@discard@suffix@zeros
- \fi
- \else
- \ifnum\fp@offsetbehindperiod=\fp@round@prec
- \else
- \errmessage{Internal logic error in fixedpointround at [II] - should not have happened!? I have offsetbehindperiod=\the\fp@offsetbehindperiod and prec = \the\fp@round@prec}%
- \fi
- \expandafter\ifnum\fp@round@next<5
- \fixedpointround@impl@discard@suffix@zeros
- \else
- \multiply\fp@offsetbehindperiod by-1
- %\edef\fp@round@trg{B\the\pgfplots@toka B}%
- \expandafter\fixedpointround@impl@ADD@ONE\the\pgfplots@toka\fp@round@EOI
- \fi
- \fi
-}
-
-\def\fixedpointround@impl@ADD@ONE{%
- \pgfplots@toka={}%
- \fixedpointround@impl@ADD@ONE@ITERATE
-}
-\def\fixedpointround@impl@ADD@ONE@ITERATE{%
- \@ifnextchar\fp@round@EOI{%
- \edef\fp@round@trg{1\the\pgfplots@toka}%
- \fixedpointround@impl@gobble
- }{%
- \@ifnextchar.{%
- \fixedpointround@impl@ADD@ONE@NEXT@COLLECT
- }{%
- \@ifnextchar+{%
- \fixedpointround@impl@ADD@ONE@NEXT@COLLECT
- }{%
- \@ifnextchar-{%
- \fixedpointround@impl@ADD@ONE@NEXT@COLLECT
- }{%
- \fixedpointround@impl@ADD@ONE@NEXT
- }%
- }%
- }%
- }%
-}
-
-\def\fixedpointround@impl@ADD@ONE@ITERATE@gobble@dot.{%
- \fixedpointround@impl@ADD@ONE@ITERATE
-}
-
-\def\fixedpointround@impl@ADD@ONE@NEXT@COLLECT#1{%
- \pgfplots@toka=\expandafter{\expandafter#1\the\pgfplots@toka}%
- \fixedpointround@impl@ADD@ONE@ITERATE
-}
-\def\fixedpointround@impl@ADD@ONE@NEXT#1{%
- \ifnum#1=9
- \ifnum\fp@offsetbehindperiod<0
- % silently DROP digit
- \else
- \pgfplots@toka=\expandafter{\expandafter0\the\pgfplots@toka}%
- \fi
- \advance\fp@offsetbehindperiod by1
- \ifnum\fp@offsetbehindperiod=0
- \def\fp@round@nextcmd{\fixedpointround@impl@ADD@ONE@ITERATE@gobble@dot}%
- \else
- \def\fp@round@nextcmd{\fixedpointround@impl@ADD@ONE@ITERATE}%
- \fi
- \else
- % re-use this counter:
- \fp@round@lastzeros=#1
- \advance\fp@round@lastzeros by1
- \edef\fp@round@trg{\the\fp@round@lastzeros\the\pgfplots@toka}%
- \pgfplots@toka=\expandafter{\fp@round@trg}%
- \def\fp@round@nextcmd{\fixedpointround@impl@REVERSE@ITERATE}%
- \fi
- \fp@round@nextcmd
-}
-
-
-\def\fixedpointround@impl@discard@suffix@zeros{%
- \ifnum\fp@round@lastzeros=\fp@offsetbehindperiod
- \expandafter\fixedpointround@impl@discard@period\fp@round@input\fp@round@EOI
- \else
- \ifnum\fp@round@lastzeros=0
- \expandafter\fixedpointround@impl@REVERSE\the\pgfplots@toka\fp@round@EOI
- \else
- \expandafter\fixedpointround@impl@discard@suffix@zeros@ITERATE\the\pgfplots@toka\fp@round@EOI
- \fi
- \fi
-}
-
-% PRECONDITION:
-% \fp@round@lastzeros > 0
-\def\fixedpointround@impl@discard@suffix@zeros@ITERATE#1{%
- \advance\fp@round@lastzeros by-1
- \ifnum\fp@round@lastzeros=0
- \def\fp@round@nextcmd{\fixedpointround@impl@REVERSE}%
- \else
- \def\fp@round@nextcmd{\fixedpointround@impl@discard@suffix@zeros@ITERATE}%
- \fi
- \fp@round@nextcmd
-}
-
-\def\fixedpointround@impl@REVERSE{%
- \pgfplots@toka={}%
- \fixedpointround@impl@REVERSE@ITERATE
-}
-
-\def\fixedpointround@impl@REVERSE@ITERATE{%
- \@ifnextchar\fp@round@EOI{%
- \edef\fp@round@trg{\the\pgfplots@toka}%
- \fixedpointround@impl@gobble
- }{%
- \fixedpointround@impl@REVERSE@NEXT
- }%
-}
-
-\def\fixedpointround@impl@REVERSE@NEXT#1{%
- \pgfplots@toka=\expandafter{\expandafter#1\the\pgfplots@toka}%
- \fixedpointround@impl@REVERSE@ITERATE
-}
-
-\def\fixedpointround@impl@BEGIN@DOT.{%
- \pgfplots@toka=\expandafter{\expandafter.\the\pgfplots@toka}%
- \fp@offsetbehindperiod=0
- \fixedpointround@impl@ITERATE@DOT
-}
-\def\fixedpointround@impl@ITERATE@DOT{%
- \@ifnextchar\fp@round@EOI{%
- % finished.
- \fixedpointround@impl@gobble@and@start
- }{%
- \fixedpointround@impl@NEXT@DOT
- }%
-}
-\def\fixedpointround@impl@NEXT@DOT#1{%
- \ifnum\fp@offsetbehindperiod=\fp@round@prec
- \def\fp@round@next{#1}%
- \def\fp@round@nextcmd{\fixedpointround@impl@gobble@rest@and@start}%
- \else
- \advance\fp@offsetbehindperiod by1
- \ifnum#1=0
- \advance\fp@round@lastzeros by1
- \else
- \fp@round@lastzeros=0
- \fi
- \pgfplots@toka=\expandafter{\expandafter#1\the\pgfplots@toka}%
- \def\fp@round@nextcmd{\fixedpointround@impl@ITERATE@DOT}%
- \fi
- \fp@round@nextcmd
-}%
-
-\def\fixedpointround@impl@ITERATE@NODOT{%
- \@ifnextchar\fp@round@EOI{%
- \fixedpointround@impl@gobble@and@start
- }{%
- \@ifnextchar.{%
- \fixedpointround@impl@BEGIN@DOT
- }{%
- \fixedpointround@impl@NEXT@NODOT
- }%
- }%
-}
-\def\fixedpointround@impl@NEXT@NODOT#1{%
- \pgfplots@toka=\expandafter{\expandafter#1\the\pgfplots@toka}%
- \fixedpointround@impl@ITERATE@NODOT
-}%
-
-%--------------------------------------------
-% END of fixedpointround implementation.
-%--------------------------------------------
-
-\newif\ifscimathlessthan
-
-% first character MAY be + or -. This is checked, then
-% \sciparse@impl@positive will be called for the
-% absolute value. The sign is inserted afterwards.
-\def\sciparse@impl@possibly@signed#1#2\to#3\powten#4{%
- \def\sciparseTMP{#1}%
- \def\sciparseTMPB{-}%
- \if\sciparseTMP\sciparseTMPB
- \sciparse@impl@positive@possibly@noperiod#2.\to#3\powten#4\S\sciparseTMPB%
- \edef#3{-#3}%
- \else
- \def\sciparseTMPB{+}%
- \if\sciparseTMP\sciparseTMPB
- \sciparse@impl@positive@possibly@noperiod#2.\to#3\powten#4\S\sciparseTMPB%
- \else
- \sciparse@impl@positive@possibly@noperiod#1#2.\to#3\powten#4\S\sciparseTMPB%
- \fi
- \fi
-}
-
-% the same as above, only the return value is different.
-\def\sciparsesign@impl@possibly@signed#1#2\S#3\M#4\E#5{%
- \def\sciparseTMP{#1}%
- \def\sciparseTMPB{-}%
- \if\sciparseTMP\sciparseTMPB
- \def#3{2}%
- \sciparse@impl@positive@possibly@noperiod#2.\to#4\powten#5\S#3%
- \else
- \def#3{1}%
- \def\sciparseTMPB{+}%
- \if\sciparseTMP\sciparseTMPB
- \sciparse@impl@positive@possibly@noperiod#2.\to#4\powten#5\S#3%
- \else
- \sciparse@impl@positive@possibly@noperiod#1#2.\to#4\powten#5\S#3%
- \fi
- \fi
-}
-
-% XXXX -> XXXX.0
-% XXXX.YYY -> XXXX.YYYY
-\def\sciparse@impl@positive@possibly@noperiod#1.#2\to#3\powten#4\S#5{%
-%\tracingmacros=2\tracingcommands=2
- \def\sciparseTMP{#2}%
- \ifx\sciparseTMP\empty
- \sciparse@impl@positive@noperiod@possibly@SCI#1e\to#3\powten#4\S{#5}%
- \else
- \expandafter\sciparse@impl@positive\sciformat@pop@last@of@two@dots#1.#2\to#3\powten#4\S{#5}%
- \fi
-}
-\def\sciformat@pop@last@of@two@dots#1.#2.{#1.#2}%
-
-\def\sciparse@impl@positive@noperiod@possibly@SCI#1e#2\to#3\powten#4\S#5{%
- \def\sciparseTMP{#2}%
- \ifx\sciparseTMP\empty
- % this case applies to
- % 1234 -> 1234.0
- \sciparse@impl@positive#1.0\to#3\powten#4\S{#5}%
- \else
- % this case applies to
- % 1e1 -> 1.0e1
- % in this case, #1e#2 = 1e1e, so we have to discard a suffix 'e'.
- \edef\sciparseTMP{#1.0e\sciformat@popsuffix@e@expansion#2}%
- \expandafter\sciparse@impl@positive\sciparseTMP\to#3\powten#4\S{#5}%
- \fi
-}
-
-% XXXXX.XXXXX -> X.XXXXXXX * 10^4
-% 0.0000XXXXX -> X.XXXX * 10^{-5}
-%
-% or
-% XXXX.XXXXXeYYY -> X.XXXXXX* 10^{3+YYY}
-% 0.0000XXXXeYYY -> X.XXX* 10^{-5+YYY}
-%
-% this version does not accept a sign. A period is required.
-%
-% The return value #6 will be \def'ed to '0' if the resulting mantisse is '0'.
-% Won't be touched otherwise.
-\def\sciparse@impl@positive#1#2.#3\to#4\powten#5\S#6{%
-% \begingroup
-% FIXME! restore variables!!
-%\tracingmacros=2\tracingcommands=2
-%\tracingmacros=0\tracingcommands=0
- \sciparse@positive@getexisting@exponent@e#3e\preexponentto\preexponentstring\exponenttocount\c@pgf@counta
- % will \c@pgf@counta will be initialised in the line above
- % \c@pgf@counta=0
- \ifnum#1=0
- % the case 0.0000XXXX
- % does also handle 0.0000XXXXeXXX
- \def\sciparseTMP{#2}%
- \ifx\sciparseTMP\empty
- \c@pgf@countb=0
- \expandafter\sciformat@count@leading@zeros\preexponentstring\to\c@pgf@countb
- \advance\c@pgf@countb by1
- \advance\c@pgf@counta by-\c@pgf@countb
- \edef#5{\the\c@pgf@counta}%
- \expandafter\sciformat@assignmantisse\preexponentstring\to#4\countdownzerosfrom\c@pgf@countb\S{#6}%
- \else
- % the case 000.0000XXXXX
- % is not allowed and does not make sense.
- \errmessage{INVALID NUMBER FORMAT: leading zeros 00*.* not supported yet}%
- \fi
- \else
- % the case NXXXXX.XXXXXXX
- % or NXXXXXX.XXXXXXeXXXX
- % where N in [1-9]
- \sciformat@strlen#1#2\to\c@pgf@counta
- \advance\c@pgf@counta by-1
- \edef#4{#1.#2\preexponentstring}%
- \edef#5{\the\c@pgf@counta}%
- \fi
-%\tracingmacros=0\tracingcommands=0
-% \endgroup
-}
-
-% parses scientific notation and returns the exponent and everything
-% before the exponent like
-%
-% XXXXXXXeYYYY -> \def#2{XXXXXXX} #3=YYYY
-% or
-% XXXXXXXXe -> \def#2{XXXXXXXX} #3=0
-%
-% Examples:
-% - \sciparse@exponent@e123456e\preexponentto\M\exponenttocount\acount
-% \M->123456
-% \acount=0
-% Please note that the input was 123456e -> at least 'e' is expected!
-%
-% - \sciparse@exponent@e123456e-10e\preexponentto\M\exponenttocount\acount
-% \M->123456
-% \acount=-10
-% Again, the suffix 'e' is REQUIRED. This allows to reduce \ifs.
-\def\sciparse@positive@getexisting@exponent@e#1e#2\preexponentto#3\exponenttocount#4{%
- \def#3{#1}%
- \def\sciparseTMP{#2}%
- \ifx\sciparseTMP\empty
- #4=0
- \else
- \sciformat@popsuffix@e#2\tocount{#4}%
- \fi
-}
-
-% XXXXXe -> #2=XXXXX where X in [+-0-9].
-\def\sciformat@popsuffix@e#1e\tocount#2{%
- #2=#1
-}
-
-\def\sciformat@popsuffix@e@expansion#1e{%
- #1%
-}%
-
-% 00000XXXXXX -> X.XXXXX
-% Inputs:
-% #1 = 00000XXXXXX
-% #2 a macro name
-% #3 a count in which the number of zeros plus one is contained (i.e.
-% the number of shifts).
-% #4 a macro name which will be \def'ed to '0' if the resulting
-% mantisse is 0. Won't be touched otherwise.
-\def\sciformat@assignmantisse#1\to#2\countdownzerosfrom#3\S#4{%
- \pgfplots@toka={#1}%
- \loop
- \ifnum#3=1
- \else
- \expandafter\sciformat@popfirst\the\pgfplots@toka\to{\pgfplots@toka}%
- \advance#3 by-1
- \repeat
- \edef\sciformat@assignmantisseTMP{\the\pgfplots@toka}%
- \ifx\sciformat@assignmantisseTMP\empty
- % The case 0.0 * 10^0
- \def#2{0.0}%
- \def#4{0}%
- \else
- \expandafter\sciformat@insertperiod\the\pgfplots@toka\to{#2}%
- \fi
-}
-
-% XXXXXX -> X.XXXXX into #3
-\def\sciformat@insertperiod#1#2\to#3{%
- \def\sciparseTMP{#2}%
- \ifx\sciparseTMP\empty
- \def#3{#1.0}%
- \else
- \def#3{#1.#2}%
- \fi
-}
-
-% discards the first token.
-\def\sciformat@popfirst#1#2\to#3{%
- #3={#2}%
-}
-
-% adds the string length of #1#2 into the count register #3.
-%
-% The register won't be initialised to zero!
-\def\sciformat@strlen#1#2\to#3{%
- \advance#3 by1
- \def\sciparseTMP{#2}%
- \ifx\sciparseTMP\empty
- \else
- \sciformat@strlen#2\to{#3}%
- \fi
-}
-
-% Adds the number of leadings zeros of #1#2 into the count register
-% #3.
-%
-% The register won't be initialised to zero!
-\def\sciformat@count@leading@zeros#1#2\to#3{%
- \ifnum#1=0
- \advance#3 by1
- \def\sciparseTMP{#2}%
- \ifx\sciparseTMP\empty
- \else
- \sciformat@count@leading@zeros#2\to{#3}%
- \fi
- \fi
-}
-
-
-
-
-
-
-\def\scimathlessthan@positive\M#1\E#2\MM#3\EE#4{%
- \c@pgf@counta\expandafter=#2\relax
- \c@pgf@countb\expandafter=#4\relax
- \ifnum\c@pgf@counta<\c@pgf@countb
- \aftergroup\scimathlessthantrue
- \else
- \ifnum\c@pgf@counta=\c@pgf@countb\relax
- \pgfmath@xa\expandafter=#1 pt\relax
- \pgfmath@xb\expandafter=#3 pt\relax
- \ifdim\pgfmath@xa<\pgfmath@xb
- \aftergroup\scimathlessthantrue
- \fi
- \fi
- \fi
-}
-
-\def\scitofixed@impl#1.#2\E#3\END{%
- \let\scitofixed@exponent=\c@pgf@countb
- \scitofixed@exponent\expandafter=#3\relax
- \ifnum\scitofixed@exponent<0
- \pgfplots@toka={0.}%
- \loop
- \ifnum\scitofixed@exponent<-1
- \pgfplots@toka=\expandafter{\the\pgfplots@toka 0}%
- \advance\scitofixed@exponent by1
- \repeat
- \def\sciparseTMPB{#2}%
- \def\sciparseTMPC{0}%
- \ifx\sciparseTMPB\sciparseTMPC
- \xdef\sciparseTMP{\the\pgfplots@toka #1}%
- \else
- \xdef\sciparseTMP{\the\pgfplots@toka #1#2}%
- \fi
- \else
- \ifnum\scitofixed@exponent=0
- \xdef\sciparseTMP{#1.#2}%
- \else
- \pgfplots@toka={#1}%
- \scitofixed@impl@collectmantisse#2\count\scitofixed@exponent
- \xdef\sciparseTMP{\the\pgfplots@toka}%
- \fi
- \fi
-}
-
-\def\scitofixed@impl@collectmantisse#1#2\count#3{%
- \pgfplots@toka=\expandafter{\the\pgfplots@toka #1}%
- \advance\scitofixed@exponent by-1
- \def\sciparseTMPB{#2}%
- \ifx\sciparseTMPB\empty
- \loop
- \ifnum\scitofixed@exponent>0
- \pgfplots@toka=\expandafter{\the\pgfplots@toka 0}%
- \advance\scitofixed@exponent by-1
- \repeat
- \else
- \ifnum\scitofixed@exponent=0
- \pgfplots@toka=\expandafter{\the\pgfplots@toka .#2}%
- \else
- \scitofixed@impl@collectmantisse#2\count#3%
- \fi
- \fi
-}