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% Copyright 2019 by Christian Feuersaenger
%
% This file may be distributed and/or modified
%
% 1. under the LaTeX Project Public License and/or
% 2. under the GNU Public License.
%
% See the file doc/generic/pgf/licenses/LICENSE for more details.
%
% This file contains methods for basic floating point arithmetics, rounding
% to arbitrary precision and number pretty printing.
%
\pgfkeys{
% The bug 3430171 (wrong minus sign spacing in pgfmathprintnumber)
% has been fixed in 2.10 CVS. Since it changes the spacing, its
% effects can be undone with this compatibility switch.
/pgf/compat/number printer/.is choice,
/pgf/compat/number printer/2.10/.code={%
\def\pgfmathprintnumber@begingroup{\bgroup}%
\def\pgfmathprintnumber@endgroup{\egroup}%
},
% I do not know the version number of the next release at this
% time. Please be so kind and KEEP THIS NAME INTACT. Add an alias
% if needed.
/pgf/compat/number printer/next after 2.10/.code={%
\def\pgfmathprintnumber@begingroup{\begingroup}%
\def\pgfmathprintnumber@endgroup{\endgroup}%
},
% activate the fix by default.
/pgf/compat/number printer/next after 2.10,%
}
\global\newif\ifpgfmathfloatcomparison
\newif\ifpgfmathfloatroundhasperiod
\newif\ifpgfmathprintnumberskipzeroperiod
% used internally in grouped macros:
\toksdef\pgfmathfloat@tmptoks=1
\newif\ifpgfmathfloat@fixed@digits@after@period
\newif\ifpgfmathfloatroundmayneedrenormalize
\toksdef\pgfmathfloat@a@Mtok=0
%% WARNING: avoid conflicting register names!
\let\pgfmathfloat@a@S=\c@pgf@counta
\let\pgfmathfloat@a@M=\pgf@xa
\let\pgfmathfloat@a@E=\c@pgf@countb
\let\pgfmathfloat@b@S=\c@pgf@countc
\let\pgfmathfloat@b@M=\pgf@xb
\let\pgfmathfloat@b@E=\c@pgf@countd
% can be changed with options.
\def\pgfmathfloat@round@precision{2}
% I introduced this to access the "original" precision in case a
% formatted changes it locally... in this case, the formatter may
% overwrite \pgfmathfloat@round@precision@orig to provide the original
% one.
% The default implementation here does nothing:
\def\pgfmathfloat@round@precision@orig{\pgfmathfloat@round@precision}%
\gdef\pgfmathfloat@glob@TMP{}
% Computes a normalised floating point representation for #1 of the
% form
% [FLAGS] MANTISSE EXPONENT
% meaning
% [+-]X.XXXXXXX*10^C
% where
% X.XXXXXX is a mantissa with first number != 0, C is an integer and
% FLAGS contains the sign and some other special cases.
%
% 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: an arbitrary number which shall be parsed. Maybe a macro.
% Examples:
% [+-]XXXXX.XXXXXX
% [+-]XXXXX.XXXXXXeXXXX
% [+-]0.0000XXXXXX
% [+-]0.0000XXXXXXeXXXX
% [+-]inf
% nan
% Maybe a macro containing such a number.
%
% Return value:
% \pgfmathresult will be \def'ed to
% FLAGS MANTISSE 'e' EXPONENT
% where
% FLAGS is a number in [0-5] where
% 0 == '0' (the number is +- 0.0),
% 1 == '+',
% 2 == '-',
% 3 == 'not a number'
% 4 == '+ infinity'
% 5 == '- infinity'
%
% MANTISSE is a normalised number 1 <= M < 10. It always contains a
% period and at least one digit after the period.
%
% EXPONENT is an integer value.
%
% Example:
% \pgfmathfloatparsenumber{1}
% -> \pgfmathresult = 11.0e0
% \pgfmathfloatparsenumber{141.212}
% -> \pgfmathresult = 11.41212e2
\def\pgfmathfloatparsenumber#1{%
\begingroup
\edef\pgfmathresult{#1}%
\expandafter\pgfflt@impl\pgfmathresult\pgfflt@EOI
\ifpgfmathfloatparsenumberpendingperiod
\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.0}%
\fi
\pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}%
\pgfmath@smuggleone\pgfmathresult
\endgroup
}
% The same as \pgfmathfloatparsenumber, but does not perform sanity checking.
% FIXME: there is no longer any difference here.
\let\pgfmathfloatqparsenumber=\pgfmathfloatparsenumber
% Takes a floating point number #1 as input and writes flags to count
% register #2, mantissa to dimen register #3 and exponent to count
% register #4.
\def\pgfmathfloattoregisters#1#2#3#4{%
\expandafter\pgfmathfloat@decompose#1\relax{#2}{#3}{#4}%
}
% the same, but writes the mantissa into a token register.
\def\pgfmathfloattoregisterstok#1#2#3#4{%
\expandafter\pgfmathfloat@decompose@tok#1\relax{#2}{#3}{#4}%
}
% Extracts the flags of #1 into the count register #2.
\def\pgfmathfloatgetflags#1#2{%
\expandafter\pgfmathfloat@decompose@F#1\relax{#2}%
}
% Extracts the flags of #1 into the macro #2.
\def\pgfmathfloatgetflagstomacro#1#2{%
\expandafter\pgfmathfloat@decompose@Fmacro#1\relax{#2}%
}%
% Extracts the mantissa of #1 into the dimen register #2.
\def\pgfmathfloatgetmantissa#1#2{%
\expandafter\pgfmathfloat@decompose@M#1\relax{#2}%
}
\let\pgfmathfloatgetmantisse=\pgfmathfloatgetmantissa
% Extracts the mantissa of #1 into the token register #2.
\def\pgfmathfloatgetmantissatok#1#2{%
\expandafter\pgfmathfloat@decompose@Mtok#1\relax{#2}%
}
\let\pgfmathfloatgetmantissetok=\pgfmathfloatgetmantissatok
% Extracts the exponent of #1 into the count register #2.
\def\pgfmathfloatgetexponent#1#2{%
\expandafter\pgfmathfloat@decompose@E#1\relax{#2}%
}
% Assigns \pgfmathresult to be a float encoded as
% <FLAGS><MANTISSE>e<EXPONENT>
%
% example:
% \pgfmathfloatcreate{1}{2.0}{10}
% \pgfmathfloat@to@FMeE@style\pgfmathresult
% ->
% \pgfmathresult is now '12.0e10' regardless of the internal float
% format.
\def\pgfmathfloat@to@FMeE@style#1{\expandafter\pgfmathfloat@to@FMeE@style@#1\relax\relax}%
\def\pgfmathfloat@to@FMeE@style@#1#2{%
\ifx#2Y%
\expandafter\pgfmathfloat@to@FMeE@style@@%
\else
\expandafter\pgfmathfloat@to@FMeE@style@error%
\fi
#1#2%
}%
\def\pgfmathfloat@to@FMeE@style@@#1Y#2e#3]\relax\relax{\def\pgfmathresult{#1#2e#3}}%
\def\pgfmathfloat@to@FMeE@style@error#1\relax\relax{%
\begingroup
\pgfmathfloatparsenumber@handleerror{wrong lowlevel format}{#1}{#1}%
\xdef\pgfmathfloat@decompose@TMP{%
\noexpand\pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}%
}%
\endgroup
\pgfmathfloat@decompose@TMP
}%
% decomposes a lowlevel floating point representation into flags,
% mantissa and exponent.
%
% #4: integer register for the flags.
% #5: dimen registers for the mantissa.
% #6: integer register for the exponent.
%
% \expandafter\pgfmathfloat@decompose\pgfmathresult\relax\pgfmathfloat@a@S\pgfmathfloat@a@M\pgfmathfloat@a@E
% -> the three temp registers contain flags, mantissa and exponent
\def\pgfmathfloat@decompose#1#2{% sanitize!
\ifx#2Y%
\expandafter\pgfmathfloat@decompose@%
\else
\expandafter\pgfmathfloat@decompose@error%
\fi
#1#2%
}
\def\pgfmathfloat@decompose@#1Y#2e#3]\relax#4#5#6{%
#4=#1\relax
#5=#2pt % keep space here.
#6=#3\relax%
}
% overloaded, #5 needs to be a token register for the mantissa.
% @see also \pgfmathfloatvalueof which does also employ the load
% level repr.
% \expandafter\pgfmathfloat@decompose@tok\pgfmathresult\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
% -> the three temp registers contain flags, mantissa and exponent
\def\pgfmathfloat@decompose@tok#1#2{%
\ifx#2Y%
\expandafter\pgfmathfloat@decompose@tok@%
\else
\expandafter\pgfmathfloat@decompose@tok@error%
\fi
#1#2%
}%
\def\pgfmathfloat@decompose@tok@#1Y#2e#3]\relax#4#5#6{%
#4=#1\relax
#5={#2}%
#6=#3\relax%
}
% overloaded, returns only ONE of the three components into #4:
% \expandafter\pgfmathfloat@decompose@tok\pgfmathresult\relax\pgfmathfloat@a@S
% -> \pgfmathfloat@a@S contains the flags field.
\def\pgfmathfloat@decompose@F#1#2{%
\ifx#2Y%
\expandafter\pgfmathfloat@decompose@F@%
\else
\expandafter\pgfmathfloat@decompose@F@error%
\fi
#1#2%
}%
\def\pgfmathfloat@decompose@Fmacro#1#2{%
\ifx#2Y%
\expandafter\pgfmathfloat@decompose@Fmacro@%
\else
\expandafter\pgfmathfloat@decompose@F@error%
\fi
#1#2%
}%
\def\pgfmathfloat@decompose@M#1#2{%
\ifx#2Y%
\expandafter\pgfmathfloat@decompose@M@%
\else
\expandafter\pgfmathfloat@decompose@M@error%
\fi
#1#2%
}%
\def\pgfmathfloat@decompose@E#1#2{%
\ifx#2Y%
\expandafter\pgfmathfloat@decompose@E@%
\else
\expandafter\pgfmathfloat@decompose@E@error%
\fi
#1#2%
}%
\def\pgfmathfloat@decompose@Mtok#1#2{%
\ifx#2Y%
\expandafter\pgfmathfloat@decompose@Mtok@%
\else
\expandafter\pgfmathfloat@decompose@Mtok@error%
\fi
#1#2%
}%
\def\pgfmathfloat@decompose@F@#1Y#2e#3]\relax#4{#4=#1\relax}%
\def\pgfmathfloat@decompose@Fmacro@#1Y#2e#3]\relax#4{\def#4{#1}}%
\def\pgfmathfloat@decompose@M@#1Y#2e#3]\relax#4{#4=#2pt}%
\def\pgfmathfloat@decompose@Mtok@#1Y#2e#3]\relax#4{#4={#2}}%
\def\pgfmathfloat@decompose@E@#1Y#2e#3]\relax#4{#4=#3\relax}%
\def\pgfmathfloat@decompose@error#1\relax#2#3#4{%
\begingroup
\pgfmathfloatparsenumber@handleerror{wrong lowlevel format}{#1}{#1}%
\xdef\pgfmathfloat@decompose@TMP{%
\noexpand#2=\the\pgfmathfloat@a@S\space
\noexpand#3=\the\pgfmathfloat@a@Mtok pt
\noexpand#4=\the\pgfmathfloat@a@E\space
}%
\endgroup
\pgfmathfloat@decompose@TMP
}%
\def\pgfmathfloat@decompose@tok@error#1\relax#2#3#4{%
\begingroup
\pgfmathfloatparsenumber@handleerror{wrong lowlevel format}{#1}{#1}%
\xdef\pgfmathfloat@decompose@TMP{%
\noexpand#2=\the\pgfmathfloat@a@S\space
\noexpand#3={\the\pgfmathfloat@a@Mtok}%
\noexpand#4=\the\pgfmathfloat@a@E\space
}%
\endgroup
\pgfmathfloat@decompose@TMP
}%
\def\pgfmathfloat@decompose@F@error#1\relax#2{%
\begingroup
\pgfmathfloatparsenumber@handleerror{wrong lowlevel format}{#1}{#1}%
\xdef\pgfmathfloat@decompose@TMP{\noexpand#2=\the\pgfmathfloat@a@S\space}%
\endgroup
\pgfmathfloat@decompose@TMP
}%
\def\pgfmathfloat@decompose@M@error#1\relax#2{%
\begingroup
\pgfmathfloatparsenumber@handleerror{wrong lowlevel format}{#1}{#1}%
\xdef\pgfmathfloat@decompose@TMP{\noexpand#2=\the\pgfmathfloat@a@Mtok pt }%
\endgroup
\pgfmathfloat@decompose@TMP
}%
\def\pgfmathfloat@decompose@Mtok@error#1\relax#2{%
\begingroup
\pgfmathfloatparsenumber@handleerror{wrong lowlevel format}{#1}{#1}%
\xdef\pgfmathfloat@decompose@TMP{\noexpand#2={\the\pgfmathfloat@a@Mtok}}%
\endgroup
\pgfmathfloat@decompose@TMP
}%
\def\pgfmathfloat@decompose@E@error#1\relax#2{%
\begingroup
\pgfmathfloatparsenumber@handleerror{wrong lowlevel format}{#1}{#1}%
\xdef\pgfmathfloat@decompose@TMP{\noexpand#2=\the\pgfmathfloat@a@E\space}%
\endgroup
\pgfmathfloat@decompose@TMP
}%
% Takes a floating point number #1 as input and writes flags to macro
% #2, mantissa to macro #3 and exponent to macro #4.
\def\pgfmathfloattomacro#1#2#3#4{%
\begingroup
\expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
\xdef\pgfmathfloat@glob@TMP{%
\noexpand\def\noexpand#2{\the\pgfmathfloat@a@S}%
\noexpand\def\noexpand#3{\the\pgfmathfloat@a@Mtok}%
\noexpand\def\noexpand#4{\the\pgfmathfloat@a@E}%
}%
\endgroup
\pgfmathfloat@glob@TMP
}
% Defines \pgfmathresult as the floating point number encoded by
% the flags #1, mantissa #2 and exponent #3.
%
% All arguments are characters and will be expanded using '\edef'.
\def\pgfmathfloatcreate#1#2#3{%
\edef\pgfmathresult{#1Y#2e#3]}%
}%
% This is the character present in any low-level floating point
% number. It is assumed to be the SECOND character of a float (after
% the flags integer).
\def\pgfmathfloat@POSTFLAGSCHAR{Y}
% Converts a composed floating point representation to fixed point.
%
% Example:
% \pgfmathfloattofixed{142e1}
% -> \pgfmathresult = 42.0
\def\pgfmathfloattofixed@#1{%
\begingroup
\expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
\ifcase\pgfmathfloat@a@S
\def\pgfmathresult{0.0}%
\or
\expandafter\pgfmathfloattofixed@impl\the\pgfmathfloat@a@Mtok\relax
\or
\expandafter\pgfmathfloattofixed@impl\the\pgfmathfloat@a@Mtok\relax
\pgfmathfloat@a@Mtok=\expandafter{\pgfmathresult}%
\edef\pgfmathresult{-\the\pgfmathfloat@a@Mtok}%
\or\def\pgfmathresult{nan}%
\or\def\pgfmathresult{inf}%
\or\def\pgfmathresult{-inf}%
\fi
\pgfmath@smuggleone\pgfmathresult
\endgroup
}
\let\pgfmathfloattofixed=\pgfmathfloattofixed@
% Converts a float to an integer (in integer format).
%
% @see \pgfmathfloatint
\def\pgfmathfloattoint#1{%
\pgfmathfloattofixed{#1}%
\expandafter\pgfmathfloattoint@@\pgfmathresult\relax
}%
\def\pgfmathfloattoint@@#1.#2\relax{%
\def\pgfmathresult{#1}%
}%
% Converts a floating point number to scientific format 1.234e5.
%
% This operation is very fast.
\def\pgfmathfloattosci@#1{%
\begingroup
\expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
\ifcase\pgfmathfloat@a@S
\def\pgfmathresult{0.0e0}%
\or
\edef\pgfmathresult{\the\pgfmathfloat@a@Mtok e\the\pgfmathfloat@a@E}%
\or
\edef\pgfmathresult{-\the\pgfmathfloat@a@Mtok e\the\pgfmathfloat@a@E}%
\or\def\pgfmathresult{nan}%
\or\def\pgfmathresult{inf}%
\or\def\pgfmathresult{-inf}%
\fi
\pgfmath@smuggleone\pgfmathresult
\endgroup
}%
\let\pgfmathfloattosci=\pgfmathfloattosci@
% Expands a floating point number to scientific format 1.234e5.
%
% This operation is very fast.
\def\pgfmathfloatvalueof#1{\expandafter\pgfmathfloatvalueof@@#1@@}%
% Make it fool proof such that the following arguments work:
% \pgfmathfloatvalueof{1Y1.0e1} -> 1.0e1
% \pgfmathfloatvalueof{2Y1.0e1} -> -1.0e1
% and wrong arguments as well:
% \pgfmathfloatvalueof{1} -> 1
% \pgfmathfloatvalueof{1e2} -> 1e2
\def\pgfmathfloatvalueof@@#1#2{%
\if#2Y%
% keep in mind that \pgfmathfloatvalueof should be expandable!
% We must not use \let here. Let's hope that #1 and #2 are
% single tokens (not something which was enclosed by curly
% braces...)
\expandafter\pgfmathfloatvalueof@@@\expandafter#1\expandafter#2%
\else
% Oh - no float!? Ok, we cannot report errors in this context.
% So: make it a feature and return the input argument as-is.
% Might be useful, in fact...
\expandafter\pgfmathfloatvalueof@abort\expandafter#1\expandafter#2%
\fi
}
\def\pgfmathfloatvalueof@@@#1Y#2e#3]@@{%
\ifcase#1 %
0.0e0%
\or
#2e#3%
\or
-#2e#3%
\or nan%
\or inf%
\or -inf%
\fi
}%
\def\pgfmathfloatvalueof@abort#1@@{#1}%
% Rounds a fixed point number #1 to \pgfmathfloat@round@precision digits precision and returns
% the result into \pgfmathresult.
%
% Any trailing zeros after the period are discarded.
% See \pgfmathroundtozerofill if you want trailing zeros and fixed
% width.
%
% This method is PURELY text based and can work with arbitrary
% precision (well, limited to TeX's stack size and integer size).
%
% Examples:
% \pgfmathroundto{1}
% -> \pgfmathresult = '1'
%
% \pgfmathroundto{19999.9996}
% -> \pgfmathresult = '20000'
%
% Arguments:
% #1 may be either a number or a macro (\pgfmathresult is allowed) expanding to a number.
%
% SIDE EFFECT: the global variable \ifpgfmathfloatroundhasperiod will be set.
\def\pgfmathroundto#1{%
\pgfmathfloatroundhasperiodtrue
\begingroup
\pgfmathfloat@fixed@digits@after@periodfalse
\pgfmathroundto@impl{#1}%
\pgfmath@smuggleone\pgfmathresult
\endgroup
}
% Overloaded method.
%
% This variant always uses a FIXED number behind the period and fills
% in zeros if necessary.
% Examples:
% \pgfmathroundtozerofill{1}
% -> \pgfmathresult = '1.00'
%
% \pgfmathroundtozerofill{19999.9996}
% -> \pgfmathresult = '20000.00'
%
% SIDE EFFECT: the global variable \ifpgfmathfloatroundhasperiod will be set.
\def\pgfmathroundtozerofill#1{%
\pgfmathfloatroundhasperiodtrue
\begingroup
\pgfmathfloat@fixed@digits@after@periodtrue
\pgfmathroundto@impl{#1}%
\pgfmath@smuggleone\pgfmathresult
\endgroup
}
% see \pgfmathprintnumber@fixed@style for docs
\def\pgfmathprintnumber@fixed@styleDEFAULT#1#2#3e#4\relax{%
\begingroup
\pgfkeysgetvalue{/pgf/number format/set decimal separator}\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP
\pgfkeysgetvalue{/pgf/number format/@dec sep mark}\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP@MARK
\pgfkeysgetvalue{/pgf/number format/set thousands separator}\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP
\c@pgf@counta=#4\relax % it is the exponent here.
\ifnum#2=0
\c@pgf@counta=0
\fi
\def\pgfmathresult{}%
\ifpgfmathfloatroundhasperiod
\expandafter\pgfmathprintnumber@fixed@styleDEFAULT@impl@period#1\pgfmathfloat@EOI
\else
\expandafter\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod#1\pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI%
\begingroup
\toks0=\expandafter{\pgfmathresult}%
\toks1=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP@MARK}%
\xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 }%
\endgroup
\let\pgfmathresult=\pgfmathfloat@glob@TMP
\fi
\pgfmath@smuggleone\pgfmathresult
\endgroup
}
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@period#1.#2\pgfmathfloat@EOI{%
\ifpgfmathprintnumberskipzeroperiod
\def\pgfmathfloat@loc@TMPb{#1}%
\ifx\pgfmathfloatparsenumber@tok@ZERO\pgfmathfloat@loc@TMPb
\else
\def\pgfmathfloat@loc@TMPc{-0}%
\ifx\pgfmathfloat@loc@TMPc\pgfmathfloat@loc@TMPb
\def\pgfmathresult{-}%
\else
\def\pgfmathfloat@loc@TMPc{+0}%
\ifx\pgfmathfloat@loc@TMPc\pgfmathfloat@loc@TMPb
\def\pgfmathresult{+}%
\else
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod#1\pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI
\fi
\fi
\fi
\else
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod#1\pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI
\fi
\ifpgfmathprintnumber@thousand@sep@in@fractional
\let\pgfmathresultfractional\pgfutil@empty%
\pgfmathprintnumber@thousand@sep@in@fractional#2MMMM\@@
\else
\def\pgfmathresultfractional{#2}%
\fi
\begingroup
\toks0=\expandafter{\pgfmathresult}%
\toks1=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP@MARK}%
\toks2=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP}%
\toks3=\expandafter{\pgfmathresultfractional}%
\xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 \the\toks2 \the\toks3 }%
\endgroup
\let\pgfmathresult=\pgfmathfloat@glob@TMP
}%
% assigns \pgfmathresult such that it contains the formatted result.
% It assumes that none of the following tokens contains a period.
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod{%
\ifx\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP\pgfutil@empty
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall}%
\else
\ifnum\c@pgf@counta<0\relax % exponent of the number in this context
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall}%
\else
\ifnum\c@pgf@counta<\pgfkeysvalueof{/pgf/number format/min exponent for 1000 sep}\relax
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall}%
\else
\advance\c@pgf@counta by1 % counta:= total number of digits, N.
\c@pgf@countb=\c@pgf@counta
\divide\c@pgf@countb by3 % countb := N DIV 3
\c@pgf@countc=\c@pgf@countb
\multiply\c@pgf@countc by3
\advance\c@pgf@counta by-\c@pgf@countc% now counta := N MOD 3
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printsign
}%
\fi
\fi
\fi
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT
}
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printsign#1{%
\def\pgfmathfloat@loc@TMPb{#1}%
\ifx\pgfmathfloat@loc@TMPb\pgfmathfloatparsenumber@tok@MINUS
\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1}%
\let\pgfmathfloat@loc@TMPb=\pgfutil@empty
\else
\ifx\pgfmathfloat@loc@TMPb\pgfmathfloatparsenumber@tok@PLUS
\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1}%
\let\pgfmathfloat@loc@TMPb=\pgfutil@empty
\else
\ifpgfmathprintnumber@showpositive
\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult +}%
\fi
\fi
\fi
\ifnum\c@pgf@counta>0 % \c@pgf@counta = N MOD 3 in this context
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
\expandafter\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printtrailingdigits\pgfmathfloat@loc@TMPb
}%
\else
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
\expandafter\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird\pgfmathfloat@loc@TMPb
}%
\fi
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT
}
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printtrailingdigits#1#2{%
\ifcase\c@pgf@counta % = N MOD 3 in this context
% does not happen per construction
\or
\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1}%
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird#2%
}%
\or
\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1#2}%
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird%
}%
\fi
\ifnum\c@pgf@countb>0\relax % \c@pgf@countb = N DIV 3 in this context
\begingroup
\toks0=\expandafter{\pgfmathresult}%
\toks1=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP}%
\xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 }%
\endgroup
\let\pgfmathresult=\pgfmathfloat@glob@TMP
\fi
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT
}
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird#1#2#3{%
\ifnum\c@pgf@countb>0\relax
\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1#2#3}%
\advance\c@pgf@countb by-1
\ifnum\c@pgf@countb>0\relax
\begingroup
\toks0=\expandafter{\pgfmathresult}%
\toks1=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP}%
\xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 }%
\endgroup
\let\pgfmathresult=\pgfmathfloat@glob@TMP
\fi
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{%
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird%
}%
\else
% in this case, #1#2#3 are expected to be
% \pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI
%--------------------------------------------------
% \def\pgfmathfloat@loc@TMPb{\pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI}%
% \def\pgfmathfloat@loc@TMPc{#1#2#3}%
% \ifx\pgfmathfloat@loc@TMPc\pgfmathfloat@loc@TMPb
% \else
% \pgfmath@error{INTERNAL ERROR in fixed style - The input sequence did not terminate as expected; which indicates a wrong exponent argument provided to \string\pgfmathprintnumber@fixed@style}{}%
% \fi
%--------------------------------------------------
\let\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT=\relax
\fi
\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT
}
% \pgfmathprintnumber@thousand@sep@in@fractional 01234525MMMM\@@
% ->
% 012<sep>345<sep>25
\def\pgfmathprintnumber@thousand@sep@in@fractional#1#2#3#4{%
\if#4M%
% Ok, no further separator
\def\pgfmathprint@next{\pgfmathprintnumber@thousand@sep@in@fractional@finish#1#2#3#4}%
\else
\begingroup
\toks0=\expandafter{\pgfmathresultfractional}%
\toks1={#1#2#3}%
\toks2=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP}%
\xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 \the\toks2 }%
\endgroup
\let\pgfmathresultfractional=\pgfmathfloat@glob@TMP
\def\pgfmathprint@next{\pgfmathprintnumber@thousand@sep@in@fractional#4}%
\fi
\pgfmathprint@next
}%
\def\pgfmathprintnumber@thousand@sep@in@fractional@finish#1M{%
\expandafter\def\expandafter\pgfmathresultfractional\expandafter{\pgfmathresultfractional #1}%
\pgfmathprintnumber@thousand@sep@in@fractional@finish@
}%
\def\pgfmathprintnumber@thousand@sep@in@fractional@finish@#1\@@{}%
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall#1{%
\def\pgfmathfloat@loc@TMPb{#1}%
\let\pgfmathfloat@loc@TMPc=\pgfutil@empty
\ifx\pgfmathfloat@loc@TMPb\pgfmathfloatparsenumber@tok@MINUS
\else
\ifx\pgfmathfloat@loc@TMPb\pgfmathfloatparsenumber@tok@PLUS
\else
\ifpgfmathprintnumber@showpositive
\def\pgfmathfloat@loc@TMPc{+}%
\fi
\fi
\fi
\expandafter\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall@\pgfmathfloat@loc@TMPc#1%
}
\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall@#1\pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI{%
\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1}%
}%
% @deprecated. It has been replaced by \pgfmathprintnumber@fixed@styleDEFAULT
% #1 maybe a macro
\def\pgfmathprintnumber@fixed@stylePERIOD#1#2#3e#4\relax{%
\def\pgfmathresult{#1}%
}
% @deprecated. It has been replaced by \pgfmathprintnumber@fixed@styleDEFAULT
% #1 maybe a macro
\def\pgfmathprintnumber@fixed@styleCOMMA#1#2#3e#4\relax{%
\ifpgfmathfloatroundhasperiod
\expandafter\pgfmathprintnumber@fixed@styleCOMMA@impl#1\pgfmathfloat@EOI
\else
\def\pgfmathresult{#1}%
\fi
}
\def\pgfmathprintnumber@fixed@styleCOMMA@impl#1.#2\pgfmathfloat@EOI{\def\pgfmathresult{#1{,}#2}}
% The default style to display fixed point numbers.
%
% It does not apply numerics, but it is responsible for typesetting the
% rounded number.
% It can access the \ifpgfmathfloatroundhasperiod boolean.
%
% Arguments:
% #1#2#3e#4\relax
% Input:
% #1 the fixed point number to be displayed (maybe a macro).
% #2#3e#4: the (possibly unformatted) floating point representation
% which belongs to #1. This format is returned (only!) by
% \pgfmathfloat@to@FMeE@style.
% It is used to determine sign and exponent.
\let\pgfmathprintnumber@fixed@style=\pgfmathprintnumber@fixed@styleDEFAULT
% Rounds a normalized floating point number to \pgfmathfloat@round@precision
% digits precision and writes the result to \pgfmathresult.
%
% This method uses \pgfmathroundto for the mantissa.
%
% @see pgfmathfloatroundzerofill
%
% SIDE EFFECT: the global variable \ifpgfmathfloatroundhasperiod will be set to
% whether the final mantissa #5 has a period or not.
\def\pgfmathfloatround#1{%
\pgfmathfloatroundhasperiodtrue
\begingroup
\pgfmathfloat@fixed@digits@after@periodfalse
\expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
\pgfmathfloatround@impl
\pgfmath@smuggleone\pgfmathresult
\endgroup
}
% Overload.
%
% This method uses a fixed width for the mantissa and fills in zeros
% if necessary.
%
% This method uses \pgfmathroundtozerofill for the mantissa.
%
% SIDE EFFECT: the global variable \ifpgfmathfloatroundhasperiod will be set to
% whether the final mantissa #5 has a period or not.
\def\pgfmathfloatroundzerofill#1{%
\pgfmathfloatroundhasperiodtrue
\begingroup
\pgfmathfloat@fixed@digits@after@periodtrue
\expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
\pgfmathfloatround@impl
\pgfmath@smuggleone\pgfmathresult
\endgroup
}
\newif\ifpgfmathfloatround@allow@empty@mantissa
\def\pgfmathfloatround@mantissa@ONE{1pt }%
% #1: sign
% #2: mantissa
% #3: exponent
% #4: CODE to display if the mantissa is drawn.
% This code will be shown just before the exponent.
% Example: #4=\cdot
% #5: CODE to display if the mantissa is NOT draw. (unused currently)
% Might be used to display '10^1' instead of '1*10^1'.
% #6: CODE to display the exponent.
\def\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax#4#5#6{%
\pgfkeysgetvalue{/pgf/number format/@sci exponent mark}\pgfmathfloatrounddisplaystyle@e@mark
\ifcase#1\relax
\pgfmathprintnumber@fixed@style{#2}#1#2e0\relax%
\expandafter\pgfmathfloatrounddisplaystyle@shared@impl@\expandafter{\pgfmathresult}{#4#6}%
\or
\def\pgfmathfloat@loc@TMPa{1}% "should draw mantissa=1"
\ifpgfmathfloatround@allow@empty@mantissa
\else
\ifdim#2pt=\pgfmathfloatround@mantissa@ONE
\def\pgfmathfloat@loc@TMPa{0}% do not draw it.
\fi
\fi
%
\if1\pgfmathfloat@loc@TMPa
\pgfmathprintnumber@fixed@style{#2}#1#2e0\relax%
\expandafter\pgfmathfloatrounddisplaystyle@shared@impl@\expandafter{\pgfmathresult}{#4#6}%
\else
\def\pgfmathfloat@loc@TMPa{0}%
\pgfmathfloatrounddisplaystyle@shared@impl@{#5}{#6}%
\fi
\or
\def\pgfmathfloat@loc@TMPa{1}% "should draw mantissa=1"
\ifpgfmathfloatround@allow@empty@mantissa
\else
\ifdim#2pt=\pgfmathfloatround@mantissa@ONE
\def\pgfmathfloat@loc@TMPa{0}% do not draw it.
\fi
\fi
%
\if1\pgfmathfloat@loc@TMPa
\pgfmathprintnumber@fixed@style{-#2}#1#2e0\relax%
\expandafter\pgfmathfloatrounddisplaystyle@shared@impl@\expandafter{\pgfmathresult}{#4#6}%
\else
\def\pgfmathfloat@loc@TMPa{0}%
\pgfmathfloatrounddisplaystyle@shared@impl@{-#5}{#6}%
\fi
\or
\pgfmathfloatrounddisplaystyle@shared@impl@@{\hbox{NaN}}{}%
\or
\ifpgfmathprintnumber@showpositive
\pgfmathfloatrounddisplaystyle@shared@impl@@{+\infty}{}%
\else
\pgfmathfloatrounddisplaystyle@shared@impl@@{\infty}{}%
\fi
\or
\pgfmathfloatrounddisplaystyle@shared@impl@@{-\infty}{}%
\fi
}
% #1: the part before the exponent code
% #2: the part for the exponent code.
\def\pgfmathfloatrounddisplaystyle@shared@impl@#1#2{%
\pgfmathprintnumber@begingroup
\toks0={#1}%
\toks1=\expandafter{\pgfmathfloatrounddisplaystyle@e@mark #2}%
\xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 }%
\pgfmathprintnumber@endgroup
\let\pgfmathresult=\pgfmathfloat@glob@TMP
}%
% Same as \pgfmathfloatrounddisplaystyle@shared@impl@, but it also
% inserts the '@dec sep mark' at the end.
\def\pgfmathfloatrounddisplaystyle@shared@impl@@#1#2{%
\pgfmathprintnumber@begingroup
\toks0={#1}%
\toks1=\expandafter{\pgfmathfloatrounddisplaystyle@e@mark #2}%
\pgfkeysgetvalue{/pgf/number format/@dec sep mark}\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP@MARK
\toks2=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP@MARK}%
\xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 \the\toks2 }%
\pgfmathprintnumber@endgroup
\let\pgfmathresult=\pgfmathfloat@glob@TMP
}
\def\pgfmathfloatrounddisplaystyle@std#1#2e#3\relax{%
\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax{\cdot}{}{10^{#3}}%
}
\def\pgfmathfloatrounddisplaystyle@subscript#1#2e#3\relax{%
\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax{}{1}{_{#3}}%
}
\def\pgfmathfloatrounddisplaystyle@superscript#1#2e#3\relax{%
\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax{}{1}{^{#3}}%
}
\def\pgfmathfloatrounddisplaystyle@e#1#2e#3\relax{%
\ifnum#3<0\relax
\pgfmathprintnumber@begingroup
\count0=#3\relax
\multiply\count0 by-1
\xdef\pgfmathfloat@glob@TMP{e{-}\the\count0}%
\pgfmathprintnumber@endgroup%
\let\pgfmathresult=\pgfmathfloat@glob@TMP
\else
\def\pgfmathresult{e{+}#3}%
\fi
\def\pgfmathfloat@loc@TMPb{\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax{}{1}}%
\expandafter\pgfmathfloat@loc@TMPb\expandafter{\pgfmathresult}%
}
\def\pgfmathfloatrounddisplaystyle@E#1#2e#3\relax{%
\ifnum#3<0\relax
\pgfmathprintnumber@begingroup
\count0=#3\relax
\multiply\count0 by-1
\xdef\pgfmathfloat@glob@TMP{E{-}\the\count0}%
\pgfmathprintnumber@endgroup%
\let\pgfmathresult=\pgfmathfloat@glob@TMP
\else
\def\pgfmathresult{E{+}#3}%
\fi
\def\pgfmathfloat@loc@TMPb{\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax{}{1}}%
\expandafter\pgfmathfloat@loc@TMPb\expandafter{\pgfmathresult}%
}
\def\pgfmathfloatrounddisplaystyle@generic#1#2e#3\relax{%
\begingroup
\pgfkeysvalueof {/pgf/number format/sci generic/@/.@cmd}{#3}{#1}{#2}\pgfeov
\pgfkeysgetvalue{/pgf/number format/sci generic/mantissa sep}\pgfmathdisplay@aftermantissa
\pgfkeysgetvalue{/pgf/number format/sci generic/empty mantissa sep}\pgfmathdisplay@nomantissa
\pgfkeysgetvalue{/pgf/number format/sci generic/exponent}\pgfmathdisplay@e
\toks0=\expandafter{\pgfmathdisplay@aftermantissa}%
\toks1=\expandafter{\pgfmathdisplay@nomantissa}%
\toks2=\expandafter{\pgfmathdisplay@e}%
\xdef\pgfmathfloat@glob@TMP{\noexpand\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\noexpand\relax{\the\toks0}{\the\toks1}{\the\toks2}}%
\endgroup
\pgfmathfloat@glob@TMP
}
% A macro which takes the argument '<SIGN><MANTISSE>e<EXPONENT>' and
% expands to the final TeX-representation for that floating point
% number.
%
% PRECONDITION:
% the floating point number has already been rounded properly and
% the mantissa has been rounded correctly.
%
% The argument needs to be in the format returned by
% \pgfmathfloat@to@FMeE@style and terminated by '\relax'.
\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@std
\newif\ifpgfmathfloat@usezerofill@sci
\newif\ifpgfmathfloat@usezerofill@fixed
\newif\ifpgfmathprintnumber@assumemathmode
\newif\ifpgfmathprintnumber@showpositive
\newif\ifpgfmathprintnumber@frac@warn
\newif\ifpgfmathprintnumber@frac@whole
\newif\ifpgfmathparsenumber@comma@as@period
\long\def\pgfmathfloatfrac@verbatim#1#2{#1/#2}%
\let\pgfmathround@@orig=\pgfmathround@
% 2 = compatible
% 0 = no
% 1 = yes
\def\pgfmathprintnumber@RELATIVE@choice@roundtofixed{2}%
\newif\ifpgfmathprintnumber@thousand@sep@in@fractional
\pgfkeys{%
/pgf/number format/.is family,
/pgf/number format,
fixed/.code= \pgfmath@set@number@printer{pgfmathprintnumber@FIXED},
sci/.code= \pgfmath@set@number@printer{pgfmathprintnumber@SCI},
std/.code= {\pgfmath@set@number@printer{pgfmathprintnumber@STD}\pgfmathprintnumber@STD@setparam{#1}},
std/.default=,%
relative round mode/.is choice,
relative round mode/fixed/.code={\def\pgfmathprintnumber@RELATIVE@choice@roundtofixed{1}},
relative round mode/mantissa/.code={\def\pgfmathprintnumber@RELATIVE@choice@roundtofixed{0}},
relative round mode/compatible/.code={\def\pgfmathprintnumber@RELATIVE@choice@roundtofixed{2}},
% relative={<exponent base 10>}
relative/.code={%
\pgfmath@set@number@printer{pgfmathprintnumber@RELATIVE}%
\pgfmathround@@orig{#1}%
\expandafter\pgfmathfloattoint@@\pgfmathresult\relax
\let\pgfmathprintnumber@RELATIVE@param=\pgfmathresult
},%
relative/.value required,
relative*/.style={/pgf/number format/relative={#1},/pgf/number format/relative round mode=fixed},
every relative/.style=std,
relative style/.style={/pgf/number format/every relative/.append style={#1}},
fixed relative/.code= \pgfmath@set@number@printer{pgfmathprintnumber@FIXED@RELATIVE},
int detect/.code= \pgfmath@set@number@printer{pgfmathprintnumber@INT@DETECT},
int trunc/.code= \pgfmath@set@number@printer{pgfmathprintnumber@INT@TRUNC},
frac/.code= \pgfmath@set@number@printer{pgfmathprintnumber@frac},%
frac TeX/.initial=\frac,
frac whole format/.code={\def\pgfmathresult{#1}},
frac denom/.initial=,
frac whole/.is if=pgfmathprintnumber@frac@whole,
frac whole=true,
frac shift/.initial=4,
frac warning/.is if=pgfmathprintnumber@frac@warn,
frac warning=true,
assume math mode/.is if=pgfmathprintnumber@assumemathmode,
assume math mode/.default=true,
fixed zerofill/.is if= pgfmathfloat@usezerofill@fixed,
fixed zerofill/.default=true,
sci zerofill/.is if= pgfmathfloat@usezerofill@sci,
sci zerofill/.default=true,
zerofill/.style= {/pgf/number format/fixed zerofill=#1,/pgf/number format/sci zerofill=#1},
zerofill/.default= true,
precision/.store in= \pgfmathfloat@round@precision,
sci precision/.code={%
\edef\pgfmathfloat@loc@TMPa{#1}%
\ifx\pgfmathfloat@loc@TMPa\pgfutil@empty
\def\pgfmathprintnumber@sci@precision{\pgfmathfloat@round@precision}%
\else
\let\pgfmathprintnumber@sci@precision=\pgfmathfloat@loc@TMPa
\fi
},%
sci precision/.default=,
sci precision=,
fixed default/.code= {\let\pgfmathprintnumber@fixed@style=\pgfmathprintnumber@fixed@styleDEFAULT},
set decimal separator/.initial=,
dec sep/.style={/pgf/number format/set decimal separator={#1}},
@dec sep mark/.initial=,
@sci exponent mark/.initial=,
set thousands separator/.initial=,
1000 sep in fractionals/.is if=pgfmathprintnumber@thousand@sep@in@fractional,
1000 sep in fractionals/.default=true,
1000 sep/.style={/pgf/number format/set thousands separator={#1}},
min exponent for 1000 sep/.initial=0,
use period/.style= {/pgf/number format/set decimal separator={.},/pgf/number format/set thousands separator={{{,}}}},
use comma/.style= {/pgf/number format/set decimal separator={{{,}}},/pgf/number format/set thousands separator={.}},
showpos/.is if=pgfmathprintnumber@showpositive,
showpos/.default=true,
print sign/.is if=pgfmathprintnumber@showpositive,
print sign/.default=true,
read comma as period/.is if=pgfmathparsenumber@comma@as@period,
read comma as period/.default=true,
skip 0./.is if=pgfmathprintnumberskipzeroperiod,
skip 0./.default=true,
skip 0.= false,
use period,
sci 10^e/.code= {\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@std},
sci 10e/.code= {\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@std},
sci e/.code= {\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@e},
sci E/.code= {\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@E},
sci subscript/.code= {\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@subscript},
sci superscript/.code= {\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@superscript},
sci generic/.code= {%
\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@generic
\pgfkeysdefargs{/pgf/number format/sci generic/@}%
{##1##2##3}%
{\pgfqkeys{/pgf/number format/sci generic}{#1}}%
},
sci generic/mantissa sep/.initial=,%
sci generic/empty mantissa sep/.initial=,%
sci generic/mantisse sep/.style={/pgf/number format/sci generic/mantissa sep={#1}},%
sci generic/empty mantisse sep/.style={/pgf/number format/sci generic/empty mantissa sep={#1}},%
sci generic/exponent/.initial=,%
sci generic/.value required,
verbatim/.code={%
\pgfqkeys{/pgf/number format}{%
sci generic={mantissa sep=,exponent={e##1}},
1000 sep=,
skip 0.=false,
print sign=false,
dec sep=.,
assume math mode,
frac TeX=\pgfmathfloatfrac@verbatim,
frac whole format/.code={\def\pgfmathresult{##1 }},
@dec sep mark=,
@sci exponent mark=,
}%
},
retain unit mantissa/.is if=pgfmathfloatround@allow@empty@mantissa,
retain unit mantissa/.default=true,
retain unit mantissa=true,
%
% allows to replace the implementation, for example
% 'implementation=\num'. This is experimental -- it is unclear
% if all consumers work well since they rely on the keys in
% /pgf/number format.
implementation/.code={\def\pgfmathprintnumber@protected{#1}},
}
\def\pgfmathprintnumber@STD#1{%
% parse the input:
\pgfmathfloatparsenumber{#1}%
\pgfmathfloat@to@FMeE@style\pgfmathresult
\expandafter\pgfmathprintnumber@STD@issci\pgfmathresult\relax
}
\def\pgfmathprintnumber@STD@setparam#1{%
\edef\pgfmathfloat@loc@TMPb{#1}%
\ifx\pgfmathfloat@loc@TMPb\pgfutil@empty
% DEFAULT for lower and upper bound.
\def\pgfmathprintnumber@STD@getlowerbound{%
\c@pgf@counta=\pgfmathfloat@round@precision@orig\relax
\divide\c@pgf@counta by-2\relax
}%
\def\pgfmathprintnumber@STD@upperbound{4}%
\else
\expandafter\pgfutil@in@\expandafter:\expandafter{\pgfmathfloat@loc@TMPb}%
\ifpgfutil@in@
% we have -4:5 or something like that.
% parse both values:
\def\pgfmathfloat@loc@TMPa##1:##2\relax{%
\edef\pgfmathprintnumber@STD@getlowerbound{%
\noexpand\c@pgf@counta=##1\space
}%
\edef\pgfmathprintnumber@STD@upperbound{##2}%
}%
\expandafter\pgfmathfloat@loc@TMPa\pgfmathfloat@loc@TMPb\relax
\else
% we have just the lower bound:
\def\pgfmathprintnumber@STD@upperbound{4}%
\edef\pgfmathprintnumber@STD@getlowerbound{%
\noexpand\c@pgf@counta=\pgfmathfloat@loc@TMPb\space
}%
\fi
\fi
}%
\def\pgfmathprintnumber@STD@issci#1#2e#3\relax{%
\expandafter\ifnum#1<3
\expandafter\ifnum#3>\pgfmathprintnumber@STD@upperbound\relax
\pgfmathprintnumber@SCI@issci#1#2e#3\relax%
\else
\begingroup
\pgfmathprintnumber@STD@getlowerbound
\ifnum#3<\c@pgf@counta
\pgfmathprintnumber@SCI@issci#1#2e#3\relax%
\else
\pgfmathprintnumber@FIXED@issci#1#2e#3\relax%
\fi
\pgfmath@smuggleone\pgfmathresult
\endgroup
\fi
\else% nan or inf:
\pgfmathfloatrounddisplaystyle#1#2e#3\relax%
\fi
}
\def\pgfmathprintnumber@RELATIVE#1{%
% parse the input:
\pgfmathfloatparsenumber{#1}%
\pgfmathfloat@to@FMeE@style\pgfmathresult
\expandafter\pgfmathprintnumber@RELATIVE@issci\pgfmathresult\relax
}
\def\pgfmathprintnumber@RELATIVE@choice@roundtofixed@warn{%
\pgf@typeout{! Package pgf warning: the use of /pgf/number format/relative is discouraged (buggy). Please use 'relative*' instead or type \string\pgfkeys{/pgf/number format/relative round mode=fixed} into your preamble.}%
\global\let\pgfmathprintnumber@RELATIVE@choice@roundtofixed@warn=\relax
}
\def\pgfmathprintnumber@RELATIVE@issci#1#2e#3\relax{%
\begingroup
% format X / 10^{relative}:
\c@pgf@counta=#3\relax
\advance\c@pgf@counta by-\pgfmathprintnumber@RELATIVE@param\relax
\pgfmathfloatcreate{#1}{#2}{\the\c@pgf@counta}%
% OK, round it to the desired precision:
\if0\pgfmathprintnumber@RELATIVE@choice@roundtofixed
% relative round mode=mantissa
\def\b@round@fixed{0}%
\else
\if1\pgfmathprintnumber@RELATIVE@choice@roundtofixed
% relative round mode=fixed
\def\b@round@fixed{1}%
\else
\pgfmathprintnumber@RELATIVE@choice@roundtofixed@warn
% relative round mode=compatible
\ifnum\c@pgf@counta>0
% hm. for positive exponents, we should round the
% mantissa rather than only the fractional part.
\def\b@round@fixed{0}%
\else
% negative exponent -> round fixed representation:
\def\b@round@fixed{1}%
\fi
\fi
\fi
\if1\b@round@fixed
% round fixed representation:
\pgfmathfloattofixed\pgfmathresult
\expandafter\pgfmathroundto\expandafter{\pgfmathresult}%
\pgfmathfloatparsenumber{\pgfmathresult}%
\pgfmathfloatroundhasperiodtrue% make sure the code below works:
\else
% round the mantissa:
\expandafter\pgfmathfloatround\expandafter{\pgfmathresult}%
\fi
% Now, compute result * 10^{relative} and format the result:
\pgfmathfloattoregisterstok\pgfmathresult\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
\ifnum\pgfmathfloat@a@S=0
\pgfmathfloat@a@E=\pgfmathfloat@a@S % avoid 0 * 10^8
\else
\advance\pgfmathfloat@a@E by+\pgfmathprintnumber@RELATIVE@param\relax
\fi
\edef\pgfmathresultX{%
\the\pgfmathfloat@a@S
\the\pgfmathfloat@a@Mtok
\ifpgfmathfloatroundhasperiod\else.0\fi
e\the\pgfmathfloat@a@E}%
% call another formatter for the result (but avoid rounding inside of it):
\pgfqkeys{/pgf/number format}{/pgf/number format/every relative,
fixed zerofill=false,% useless here!
sci zerofill=false}%
\ifx\pgfmathprintnumber@issci\pgfmathprintnumber@RELATIVE@issci
\pgfmath@error{The '/pgf/number format/every relative' style should set a valid display style}{}%
\fi
\let\pgfmathfloat@round@precision@orig=\pgfmathfloat@round@precision
\def\pgfmathfloat@round@precision{9999}%
\expandafter\pgfmathprintnumber@issci\pgfmathresultX\relax%
\pgfmath@smuggleone\pgfmathresult
\endgroup
}
\def\pgfmathprintnumber@FIXED@RELATIVE#1{%
% parse the input:
\pgfmathfloatparsenumber{#1}%
\pgfmathfloat@to@FMeE@style\pgfmathresult
\expandafter\pgfmathprintnumber@FIXED@RELATIVE@issci\pgfmathresult\relax
}
\def\pgfmathprintnumber@FIXED@RELATIVE@issci#1#2e#3\relax{%
\begingroup
\pgfmathfloatcreate{#1}{#2}{#3}%
% we want the first <precision> digits - not the first
% <precision>+1 digits:
\c@pgf@counta=\pgfmathfloat@round@precision\relax
\advance\c@pgf@counta by-1
\edef\pgfmathfloat@round@precision{\the\c@pgf@counta}%
\pgfmathfloatround{\pgfmathresult}%
\pgfmathfloattoregisterstok\pgfmathresult\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
\ifnum\pgfmathfloat@a@S=0
\pgfmathfloat@a@E=\pgfmathfloat@a@S % avoid 0 * 10^8
\fi
\edef\pgfmathresultX{%
\the\pgfmathfloat@a@S
\the\pgfmathfloat@a@Mtok
\ifpgfmathfloatroundhasperiod\else.0\fi
e\the\pgfmathfloat@a@E}%
\let\pgfmathfloat@round@precision@orig=\pgfmathfloat@round@precision
\pgfmathfloat@usezerofill@fixedfalse
\def\pgfmathfloat@round@precision{9999}% typeset all remaining digits!
\expandafter\pgfmathprintnumber@FIXED@issci\pgfmathresultX\relax%
\pgfmath@smuggleone\pgfmathresult
\endgroup
}
\def\pgfmathprintnumber@frac#1{%
% parse the input:
\pgfmathfloatparsenumber{#1}%
\pgfmathfloatgetfrac{\pgfmathresult}%
\expandafter\pgfmathprintnumber@frac@formatresult\pgfmathresult
}
\def\pgfmathprintnumber@frac@issci#1#2e#3\relax{%
\pgfmathfloatcreate{#1}{#2}{#3}%
\pgfmathfloatgetfrac{\pgfmathresult}%
\expandafter\pgfmathprintnumber@frac@formatresult\pgfmathresult
}
\def\pgfmathprintnumber@frac@formatresult#1#2#3{%
\begingroup
\pgfkeysgetvalue{/pgf/number format/frac TeX}\pgfmathresult
\toks0=\expandafter{\pgfmathresult}%
\def\pgfmathfloat@loc@TMPa{#1}%
\ifx\pgfmathfloat@loc@TMPa\pgfutil@empty
\ifpgfmathprintnumber@showpositive
\def\pgfmathfloat@loc@TMPa{+}%
\fi
\else
\ifx\pgfmathfloat@loc@TMPa-%
\else
\ifx\pgfmathfloat@loc@TMPa+%
\else
\ifpgfmathprintnumber@showpositive
\edef\pgfmathfloat@loc@TMPa{+\pgfmathfloat@loc@TMPa}%
\fi
\def\pgfmathfloat@loc@TMPb{\pgfkeysvalueof{/pgf/number format/frac whole format/.@cmd}}%
\expandafter\pgfmathfloat@loc@TMPb\pgfmathfloat@loc@TMPa\pgfeov
\let\pgfmathfloat@loc@TMPa=\pgfmathresult
\fi
\fi
\fi
\toks1=\expandafter{\pgfmathfloat@loc@TMPa}%
\edef\pgfmathresult{%
\the\toks1 \ifnum#2=0 \else\the\toks0 {#2}{#3}\fi%
}%
\pgfmath@smuggleone\pgfmathresult
\endgroup
}%
% Defines \pgfmathresult to contain three sets of braces containing
% the sign (optionally containing any components >1), the numerator and the denominator for #1.
%
% \pgfmathfloatgetfrac{0.5} -> \pgfmathresult contains {}{1}{2}
% \pgfmathfloatgetfrac{-0.5} -> \pgfmathresult contains {-}{1}{2}
% \pgfmathfloatgetfrac{1.5} -> \pgfmathresult contains {1}{1}{2}
%
% special cases:
% \pgfmathfloatgetfrac{0} -> \pgfmathresult contains {0}{0}{1}
% \pgfmathfloatgetfrac{1} -> \pgfmathresult contains {1}{0}{1}
%
% The numerator and denominator is always a number (not empty)
\def\pgfmathfloatgetfrac#1{%
\pgfutil@ifundefined{pgfmathfloatmultiply@}{%
\pgfmath@error{Sorry, the number format 'frac' requires '\string\usetikzlibrary{fpu}' (and, optionally, \string\usepackage{fp}) in order to work correctly}{}%
\edef\pgfmathresult{{#1}{0}{1}}%
}{%
\pgfmathfloatgetfrac@{#1}%
}%
}%
\def\pgfmathfloatgetfrac@#1{%
\begingroup
\edef\pgfmathfloat@arg{#1}%
\expandafter\pgfmathfloat@decompose@tok\pgfmathfloat@arg\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
\def\pgfmathfloat@loc@TMPa{0}%
\ifcase\pgfmathfloat@a@S
% #1 = 0:
\def\pgfmathresult{{0}{0}{1}}%
\or% #1 > 0
\pgfmathfloat@a@S=1
\def\pgfmathfloat@loc@TMPa{1}%
\or% #1 < 0
\pgfmathfloat@a@S=-1
\def\pgfmathfloat@loc@TMPa{1}%
\or
\edef\pgfmathresult{{}{NaN}{1}}%
\or
\edef\pgfmathresult{{}{\infty}{1}}%
\or
\edef\pgfmathresult{{-}{\infty}{1}}%
\fi
\if1\pgfmathfloat@loc@TMPa
\ifnum\pgfmathfloat@a@E<0
\def\pgfmathfloat@wholenumber{}%
\else
\pgfmathfloatcreate{1}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}%
\pgfmathfloattofixed\pgfmathresult%
\def\pgfmathfloat@loc@TMPa##1.##2\relax{%
\def\pgfmathfloat@wholenumber{##1}%
\pgfmathfloatparsenumber{0.##2}%
}%
\expandafter\pgfmathfloat@loc@TMPa\pgfmathresult\relax
\expandafter\pgfmathfloat@decompose@tok\pgfmathresult\relax\pgfmathfloat@b@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
\fi
%
\def\pgfmathfloat@loc@TMPa##1.##2\relax{%
\def\pgfmathfloat@mantissa@first{##1}%
\def\pgfmathfloat@mantissa@ltone{0.##2}%
}%
\expandafter\pgfmathfloat@loc@TMPa\the\pgfmathfloat@a@Mtok\relax
%
\def\pgfmathfloat@loc@@to@int##1.##2\relax##3{%
##3=##1
\ifdim0.##2pt>0.5pt
\advance##3 by1
\fi
}%
%
% alias registers names:
\let\pgfmathresultnumerator=\pgfmathfloat@b@S
\let\pgfmathresultdenom=\pgfmathfloat@b@E
%
\pgfkeysgetvalue{/pgf/number format/frac denom}\pgfmath@target@denominator
\ifx\pgfmath@target@denominator\pgfutil@empty
%
\pgfmathfloat@a@E=-\pgfmathfloat@a@E
\ifdim\pgfmathfloat@mantissa@ltone pt=0pt
\def\pgfmathfloat@factor{1}%
\edef\pgfmathfloat@scaled@numerator{\the\pgfmathfloat@a@Mtok}%
\else
% FIXME : this here is numerically instable.
%
% The errors of 1/r are magnified by 10^k which
% doesn't work.
\pgfutil@ifundefined{FPdiv}{%
\pgfmathfloatparsenumber{\pgfmathfloat@mantissa@ltone}%
\pgfmathfloatreciprocal@{\pgfmathresult}%
}{%
% \usepackage{fp}.
% yields higher absolute precision.
\FPmessagesfalse%
\FPdebugfalse%
\FPdiv\pgfmathresult{1}{\pgfmathfloat@mantissa@ltone}%
\pgfmathfloatparsenumber{\pgfmathresult}%
}%
\let\pgfmathfloat@inv=\pgfmathresult
\pgfmathfloatcreate{1}{1.0}{\pgfkeysvalueof{/pgf/number format/frac shift}}%
\let\pgfmathfloat@scalebaseten=\pgfmathresult
\pgfmathfloatmultiply@{\pgfmathfloat@inv}{\pgfmathfloat@scalebaseten}%
\let\pgfmathfloat@factor=\pgfmathresult
%
\expandafter\pgfmathfloatparsenumber\expandafter{\the\pgfmathfloat@a@Mtok}%
\let\pgfmathfloat@loc@TMPa=\pgfmathresult
\pgfmathfloatmultiply@{\pgfmathfloat@factor}{\pgfmathfloat@loc@TMPa}%
\pgfmathfloattofixed\pgfmathresult
\let\pgfmathfloat@scaled@numerator=\pgfmathresult
%
\pgfmathfloattofixed\pgfmathfloat@factor
\expandafter\pgfmathfloat@loc@@to@int\pgfmathresult\relax{\pgfmathfloat@b@S}%
\edef\pgfmathfloat@factor{\the\pgfmathfloat@b@S}%
\fi
%
%
\pgfmathresultdenom=\pgfmathfloat@factor\relax
\pgfmathfloat@multiply@ten@to@the@E\pgfmathresultdenom
%
\expandafter\pgfmathfloat@loc@@to@int\pgfmathfloat@scaled@numerator\relax{\pgfmathresultnumerator}%
%\message{scale = \pgfmathfloat@factor; Z = \the\pgfmathresultnumerator\space ( von \pgfmathfloat@scaled@numerator), N = \the\pgfmathresultdenom.}%
%
\pgfmathgreatestcommondivisor{\pgfmathresultnumerator}{\pgfmathresultdenom}%
\divide\pgfmathresultnumerator by\pgfmathresult\relax
\divide\pgfmathresultdenom by\pgfmathresult\relax
\ifpgfmathprintnumber@frac@warn
\ifnum\pgfmathresultdenom>1000
\pgfutil@ifundefined{FPdiv}{%
\pgfmathfloattosci@\pgfmathfloat@arg
\pgf@typeout{! Package pgf /pgf/number format/frac warning=true: /pgf/number format/frac of `\pgfmathresult' = \the\pgfmathresultnumerator\space / \the\pgfmathresultdenom\space might be large due to instabilities. Try \string\usepackage{fp} to improve accuracy.}%
}{}%
\fi
\fi
\else
% use target denominator:
\pgfmathresultdenom=\pgfmath@target@denominator\relax
\pgfmathfloatcreate{1}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}%
\pgfmathfloattofixed\pgfmathresult
\pgf@xa=\pgfmathresult pt
\multiply\pgf@xa by\pgfmathresultdenom
\edef\pgfmathfloat@scaled@numerator{\pgfmath@tonumber\pgf@xa}%
\expandafter\pgfmathfloat@loc@@to@int\pgfmathfloat@scaled@numerator\relax{\pgfmathresultnumerator}%
\fi
\ifpgfmathprintnumber@frac@whole
\else
\ifx\pgfmathfloat@wholenumber\pgfutil@empty
\else
\count0=\pgfmathfloat@wholenumber\relax
\multiply\count0 by\pgfmathresultdenom
\advance\pgfmathresultnumerator by\count0
\def\pgfmathfloat@wholenumber{}%
\fi
\fi
\ifnum\pgfmathfloat@a@S<0
\edef\pgfmathresult{{-\pgfmathfloat@wholenumber}{\the\pgfmathresultnumerator}{\the\pgfmathresultdenom}}%
\else
\edef\pgfmathresult{{\pgfmathfloat@wholenumber}{\the\pgfmathresultnumerator}{\the\pgfmathresultdenom}}%
\fi
\fi
\pgfmath@smuggleone\pgfmathresult
\endgroup
}%
\def\pgfmathfloat@gobble@until@relax#1\relax{}
% computes the greatest common divisor of two integer numbers (in
% integer arithmetics).
\def\pgfmathgreatestcommondivisor#1#2{%
\begingroup
\count0=#1\relax
\count1=#2\relax
\ifnum\count0=0
\edef\pgfmathresult{\the\count1}%
\else
\pgfmathgreatestcommondivisor@loop
\edef\pgfmathresult{\the\count0}%
\fi
\pgfmath@smuggleone\pgfmathresult
\endgroup
}
\def\pgfmathgreatestcommondivisor@loop{%
\ifnum\count1=0
\else
\ifnum\count0>\count1
\advance\count0 by-\count1
\else
\advance\count1 by-\count0
\fi
\expandafter\pgfmathgreatestcommondivisor@loop
\fi
}%
% multiplies a TeX register by 10^E where E is stored in the register
% \pgfmathfloat@a@E (and it should be positive!)%
%
% #1 a TeX register
\def\pgfmathfloat@multiply@ten@to@the@E#1{%
\ifnum\pgfmathfloat@a@E>0
\multiply#1 by10
\advance\pgfmathfloat@a@E by-1
\def\pgfmathfloat@multiply@ten@to@the@E@next{\pgfmathfloat@multiply@ten@to@the@E{#1}}%
\else
\let\pgfmathfloat@multiply@ten@to@the@E@next=\relax%
\fi
\pgfmathfloat@multiply@ten@to@the@E@next
}%
\def\pgfmathprintnumber@INT@TRUNC#1{%
\pgfmathfloatparsenumber{#1}%
\pgfmathfloat@to@FMeE@style\pgfmathresult
\expandafter\pgfmathprintnumber@INT@TRUNC@issci\pgfmathresult\relax
}
\def\pgfmathprintnumber@INT@TRUNC@impl#1.#2\relax#3#4e#5\relax{%
\pgfmathfloatroundhasperiodfalse
\pgfmathprintnumber@fixed@style{#1}#3#4e#5\relax%
}
\def\pgfmathprintnumber@INT@TRUNC@issci#1#2e#3\relax{%
\ifnum#1<3\relax
\pgfmathfloatcreate{#1}{#2}{#3}%
\pgfmathfloattofixed{\pgfmathresult}%
\expandafter\pgfmathprintnumber@INT@TRUNC@impl\pgfmathresult\relax#1#2e#3\relax
\else
\pgfmathfloatrounddisplaystyle#1#2e#3\relax%
\fi
}
% Invokes '#2' if '#1' is actually an integer or '#3' if not.
%
% As a side-effect, \pgfretval will be set to the integer value if it
% actually *is* an integer. Otherwise, \pgfretval will contain the
% parsed floating point number.
%
% #1 a number constant (not necessarily a parsed float).
\def\pgfmathifisint#1#2#3{%
\gdef\pgfmathfloatisint@@{0}%
\begingroup
\pgfmathfloatparsenumber{#1}%
\let\pgfretval\pgfmathresult
\pgfmathfloat@to@FMeE@style\pgfmathresult
\expandafter\pgfmathfloatisint@\pgfmathresult\relax
\pgfmath@smuggleone\pgfretval
\endgroup
\if1\pgfmathfloatisint@@ #2\else #3\fi
}%
\def\pgfmathfloatisint@#1#2e#3\relax{%
\ifnum#1<3\relax
\pgfmathfloatcreate{#1}{#2}{#3}%
\pgfmathfloattofixed{\pgfmathresult}%
\def\pgfmathfloat@round@precision{6}%
\expandafter\pgfmathroundto\expandafter{\pgfmathresult}%
\ifpgfmathfloatroundhasperiod
\else
\let\pgfretval\pgfmathresult%
\gdef\pgfmathfloatisint@@{1}%
\fi
\fi
}
\def\pgfmathprintnumber@INT@DETECT#1{%
\pgfmathfloatparsenumber{#1}%
\pgfmathfloat@to@FMeE@style\pgfmathresult
\expandafter\pgfmathprintnumber@INT@DETECT@issci\pgfmathresult\relax
}
\def\pgfmathprintnumber@INT@DETECT@issci#1#2e#3\relax{%
\begingroup
\ifnum#1<3\relax
\pgfmathfloatcreate{#1}{#2}{#3}%
\pgfmathfloattofixed{\pgfmathresult}%
\let\pgfmathfloat@round@precision@=\pgfmathfloat@round@precision
\def\pgfmathfloat@round@precision{6}%
\expandafter\pgfmathroundto\expandafter{\pgfmathresult}%
\let\pgfmathfloat@round@precision=\pgfmathfloat@round@precision@
\ifpgfmathfloatroundhasperiod
\pgfmathprintnumber@SCI@issci#1#2e#3\relax
\else
\expandafter\pgfmathprintnumber@fixed@style\expandafter{\pgfmathresult}#1#2e#3\relax
\fi
\else
\pgfmathfloatrounddisplaystyle#1#2e#3\relax%
\fi
\pgfmath@smuggleone\pgfmathresult
\endgroup
}
\def\pgfmathprintnumber@FIXED#1{%
\pgfmathfloatparsenumber{#1}%
\pgfmathfloat@to@FMeE@style\pgfmathresult
\expandafter\pgfmathprintnumber@FIXED@issci\pgfmathresult\relax
}
\def\pgfmathprintnumber@FIXED@issci#1#2e#3\relax{%
\begingroup
\ifnum#1<3
\pgfmathfloatcreate{#1}{#2}{#3}%
\pgfmathfloattofixed{\pgfmathresult}%
\ifpgfmathfloat@usezerofill@fixed
\expandafter\pgfmathroundtozerofill\expandafter{\pgfmathresult}%
\else
\expandafter\pgfmathroundto\expandafter{\pgfmathresult}%
\fi
\ifpgfmathfloatroundmayneedrenormalize
\pgfmathfloat@a@E=#3\relax
\advance\pgfmathfloat@a@E by1
\edef\pgfmathfloat@loc@TMPb{\noexpand\pgfmathprintnumber@fixed@style{\pgfmathresult}#1#2e\the\pgfmathfloat@a@E}%
\pgfmathfloat@loc@TMPb\relax%
\else
\expandafter\pgfmathprintnumber@fixed@style\expandafter{\pgfmathresult}#1#2e#3\relax%
\fi
\else% nan or inf:
\pgfmathfloatrounddisplaystyle#1#2e#3\relax%
\fi
\pgfmath@smuggleone\pgfmathresult
\endgroup
}
\def\pgfmathprintnumber@SCI#1{%
\pgfmathfloatparsenumber{#1}%
\pgfmathfloat@to@FMeE@style\pgfmathresult
\expandafter\pgfmathprintnumber@SCI@issci\pgfmathresult\relax
}
\def\pgfmathprintnumber@SCI@issci#1#2e#3\relax{%
\begingroup
\pgfmathfloatcreate{#1}{#2}{#3}%
\edef\pgfmathfloat@round@precision{\pgfmathprintnumber@sci@precision}%
\ifpgfmathfloat@usezerofill@sci
\pgfmathfloatroundzerofill{\pgfmathresult}%
\else
\pgfmathfloatround{\pgfmathresult}%
\fi
\pgfmathfloat@to@FMeE@style\pgfmathresult
\expandafter\pgfmathfloatrounddisplaystyle\pgfmathresult\relax
\pgfmath@smuggleone\pgfmathresult
\endgroup
}
% Prints argument #1 using the current pretty printer environment (all
% variables in /pgf/number format).
%
% You may specify optional arguments with \pgfmathprintnumber[...].
\def\pgfmathprintnumber{%
% \protect allows to supply \pgfmathprintnumber inside of latex
% captions. The \csname yields \relax in case protect is undefined.
\pgf@texdist@protect\pgfmathprintnumber@protected
}%
\def\pgfmathprintnumber@protected{%
\pgfutil@ifnextchar[%
{\pgfmathprintnumber@OPT}%
{\pgfmathprintnumber@noopt}%
}
\def\pgfmathprintnumber@noopt#1{%
\pgfmathprintnumber@{#1}%
\ifpgfmathprintnumber@assumemathmode
\pgfmathresult
\else
\pgfutilensuremath{\pgfmathresult}%
\fi
}%
\def\pgfmathprintnumber@OPT[#1]#2{%
\begingroup
\pgfqkeys{/pgf/number format}{#1}%
\pgfmathprintnumber@{#2}%
\ifpgfmathprintnumber@assumemathmode
\pgfmathresult
\else
\pgfutilensuremath{\pgfmathresult}%
\fi
\endgroup
}%
% As \pgfmathprintnumber, but it produces its output into the second
% argument.
\def\pgfmathprintnumberto{%
\pgfutil@ifnextchar[%
{\pgfmathprintnumberto@OPT}%
{\pgfmathprintnumberto@noopt}%
}
\def\pgfmathprintnumberto@noopt#1#2{%
\begingroup
\pgfmathprintnumber@{#1}%
\ifpgfmathprintnumber@assumemathmode
\global\let\pgfmathfloat@glob@TMP=\pgfmathresult
\else
\toks0=\expandafter{\pgfmathresult}%
\xdef\pgfmathfloat@glob@TMP{\noexpand\pgfutilensuremath{\the\toks0 }}%
\fi
\endgroup
\let#2=\pgfmathfloat@glob@TMP
}%
\def\pgfmathprintnumberto@OPT[#1]#2#3{%
\begingroup
\pgfqkeys{/pgf/number format}{#1}%
\pgfmathprintnumber@{#2}%
\ifpgfmathprintnumber@assumemathmode
\global\let\pgfmathfloat@glob@TMP=\pgfmathresult
\else
\toks0=\expandafter{\pgfmathresult}%
\xdef\pgfmathfloat@glob@TMP{\noexpand\pgfutilensuremath{\the\toks0 }}%
\fi
\endgroup
\let#3=\pgfmathfloat@glob@TMP
}%
% Changes the current number pretty printer to #1.
%
% #1 is the macro base name for the pretty print routine, without the
% leading '\'.
\def\pgfmath@set@number@printer#1{%
\expandafter\let\expandafter\pgfmathprintnumber@\csname #1\endcsname
\expandafter\let\expandafter\pgfmathprintnumber@issci\csname #1@issci\endcsname
}
\pgfkeys{/pgf/number format/std}
%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% IMPL
%
%%%%%%%%%%%%%%%%%%%%%%%%%%
% equals only itself when compared with \ifx:
\def\pgfmathfloat@EOI{\pgfmathfloat@EOI}%
% Re-use counters internally.
%
% They are always grouped and only used inside of the rounding
% routines.
\let\c@pgfmathroundto@prec=\pgfmathfloat@b@S% ATTENTION: DOUBLE-USED REGISTERS!
\let\c@pgfmathroundto@offsetbehindperiod=\pgfmathfloat@b@E
\newcount\c@pgfmathroundto@lastzeros
\newif\ifpgfmathround@impl@PREPERIOD@is@negative@zero
% PRECONDITION:
% \ifpgfmathfloatroundhasperiod=\iftrue holds outside of the current TeX group.
%
% POSTCONDITION:
% \ifpgfmathfloatroundhasperiod will be set correctly AFTER the
% current TeX group.
% \ifpgfmathfloatroundmayneedrenormalize will be set globally
\def\pgfmathroundto@impl#1{%
\edef\pgfmathround@input{#1}%
\global\pgfmathfloatroundmayneedrenormalizefalse
\pgfmathfloat@tmptoks={}%
\let\pgfmathround@next=\pgfutil@empty
\let\pgfmathround@cur=\pgfutil@empty
\let\pgfmathresult=\pgfutil@empty
\expandafter\c@pgfmathroundto@prec\pgfmathfloat@round@precision\relax
\c@pgfmathroundto@lastzeros=0
\c@pgfmathroundto@offsetbehindperiod=-1 % means: no period found so far
\pgfmathround@impl@PREPERIOD@is@negative@zerotrue
\expandafter\pgfmathroundto@impl@ITERATE@NODOT@firstcall\pgfmathround@input\pgfmathfloat@EOI
}
% \pgfmathroundto 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.
%
% Please note that pgfmathroundto rounds the mantissa, that means |abs(x)|.
%
% 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, for 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 \pgfmathfloat@tmptoks is used to accumulate the REVERSED input number.
% - \pgfmathfloat@EOI always denotes 'END OF INPUT'.
% - in the second stage, we need to reverse \pgfmathfloat@tmptoks.
% This is -- again -- done with \pgfmathfloat@tmptoks.
\def\pgfmathroundto@impl@discard@period#1.#2\pgfmathfloat@EOI{%
\pgfmathfloatroundhasperiodfalse
\aftergroup\pgfmathfloatroundhasperiodfalse
\def\pgfmathresult{#1}%
}
\def\pgfmathroundto@impl@gobble@rest@and@start#1\pgfmathfloat@EOI{%
\pgfmathroundto@impl@start
}
\def\pgfmathroundto@impl@gobble@and@start\pgfmathfloat@EOI{%
\pgfmathroundto@impl@start
}
\def\pgfmathroundto@impl@gobble\pgfmathfloat@EOI{}%
\def\pgfmathroundto@impl@gobble@rest#1\pgfmathfloat@EOI{}%
% This method will be invoked as soon as the first step, the reverse
% collection of up to PREC digits after the period, has finished.
\def\pgfmathroundto@impl@start{%
\ifx\pgfmathround@next\pgfutil@empty
\ifnum\c@pgfmathroundto@offsetbehindperiod<0
% no period found.
\ifpgfmathfloat@fixed@digits@after@period
\ifnum\c@pgfmathroundto@prec=0\relax
\pgfmathfloatroundhasperiodfalse
\aftergroup\pgfmathfloatroundhasperiodfalse
\edef\pgfmathresult{\pgfmathround@input}%
\else
\pgfmathfloat@tmptoks=\expandafter{\pgfmathround@input.}%
\c@pgfmathroundto@offsetbehindperiod=\c@pgfmathroundto@prec
\pgfmathroundto@impl@append@zeros
\edef\pgfmathresult{\the\pgfmathfloat@tmptoks}%
\fi
\else
\pgfmathfloatroundhasperiodfalse
\aftergroup\pgfmathfloatroundhasperiodfalse
\edef\pgfmathresult{\pgfmathround@input}%
\fi
\else
%\ifnum\c@pgfmathroundto@offsetbehindperiod>\c@pgfmathroundto@prec
% \pgfmath@error{Internal logic error in pgfmathroundto at [I] - should not have happened!?}{}%
%\fi
\pgfmathroundto@impl@finish@with@truncation
\fi
\else
%\ifnum\c@pgfmathroundto@offsetbehindperiod=\c@pgfmathroundto@prec
%\else
% \pgfmath@error{Internal logic error in pgfmathroundto at [II] - should not have happened!? I have offsetbehindperiod=\the\c@pgfmathroundto@offsetbehindperiod and prec = \the\c@pgfmathroundto@prec}{}%
%\fi
\expandafter\ifnum\pgfmathround@next<5\relax
\pgfmathroundto@impl@finish@with@truncation
\else
\multiply\c@pgfmathroundto@offsetbehindperiod by-1
\expandafter\pgfmathroundto@impl@ADD@ONE\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI
\fi
\fi
}
% takes the current input and decides whether trailing zeros shall be
% discarded or more zeros need to be filled in.
\def\pgfmathroundto@impl@finish@with@truncation{%
\ifpgfmathfloat@fixed@digits@after@period
\expandafter\pgfmathroundto@impl@REVERSE\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI
\ifnum\c@pgfmathroundto@lastzeros=\c@pgfmathroundto@offsetbehindperiod
\ifpgfmathround@impl@PREPERIOD@is@negative@zero
% write '0.0000' instead of '-0.0000':
\expandafter\pgfmathroundto@impl@discard@minus\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI
\fi
\fi
\ifnum\c@pgfmathroundto@prec=0\relax
\expandafter\pgfmathroundto@impl@discard@period\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI
\else
\advance\c@pgfmathroundto@prec by-\c@pgfmathroundto@offsetbehindperiod
\c@pgfmathroundto@offsetbehindperiod=\c@pgfmathroundto@prec
\pgfmathroundto@impl@append@zeros
\edef\pgfmathresult{\the\pgfmathfloat@tmptoks}%
\fi
\else
\pgfmathroundto@impl@discard@suffix@zeros
\fi
}
\def\pgfmathroundto@impl@discard@minus-#1\pgfmathfloat@EOI{\pgfmathfloat@tmptoks={#1}}%
% appends \c@pgfmathroundto@offsetbehindperiod zeros at the end of \pgfmathfloat@tmptoks.
\def\pgfmathroundto@impl@append@zeros{%
\ifnum\c@pgfmathroundto@offsetbehindperiod>0
\pgfmathfloat@tmptoks=\expandafter{\the\pgfmathfloat@tmptoks0}%
\advance\c@pgfmathroundto@offsetbehindperiod by-1
\pgfmathroundto@impl@append@zeros
\fi
}
\def\pgfmathroundto@impl@ADD@ONE{%
\pgfmathfloat@tmptoks={}% no longer needed because its old value will be read from input
\pgfmathroundto@impl@ADD@ONE@ITERATE
}
\def\pgfmathroundto@impl@ADD@ONE@ITERATE{%
\pgfutil@ifnextchar\pgfmathfloat@EOI{%
\global\pgfmathfloatroundmayneedrenormalizetrue
\edef\pgfmathresult{1\the\pgfmathfloat@tmptoks}%
\pgfmathroundto@impl@gobble
}{%
\pgfutil@ifnextchar.{%
\ifnum\c@pgfmathroundto@prec=0
% silently discard period in special case precision=0
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ADD@ONE@ITERATE@gobble@dot}%
\else
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ADD@ONE@NEXT@COLLECT}%
\fi
\pgfmathround@nextcmd
}{%
\pgfutil@ifnextchar+{%
\global\pgfmathfloatroundmayneedrenormalizetrue
\edef\pgfmathresult{1\the\pgfmathfloat@tmptoks}%
\pgfmathroundto@impl@gobble@rest
}{%
\pgfutil@ifnextchar-{%
\global\pgfmathfloatroundmayneedrenormalizetrue
\edef\pgfmathresult{-1\the\pgfmathfloat@tmptoks}%
\pgfmathroundto@impl@gobble@rest
}{%
\pgfmathroundto@impl@ADD@ONE@NEXT
}%
}%
}%
}%
}
\def\pgfmathroundto@impl@ADD@ONE@ITERATE@gobble@dot.{%
\pgfmathfloatroundhasperiodfalse
\aftergroup\pgfmathfloatroundhasperiodfalse
\pgfmathroundto@impl@ADD@ONE@ITERATE
}
\def\pgfmathroundto@impl@ADD@ONE@NEXT@COLLECT#1{%
\pgfmathfloat@tmptoks=\expandafter{\expandafter#1\the\pgfmathfloat@tmptoks}%
\pgfmathroundto@impl@ADD@ONE@ITERATE
}
\def\pgfmathroundto@impl@ADD@ONE@NEXT#1{%
\ifnum#1=9
\ifnum\c@pgfmathroundto@offsetbehindperiod<0
\ifpgfmathfloat@fixed@digits@after@period
\pgfmathfloat@tmptoks=\expandafter{\expandafter0\the\pgfmathfloat@tmptoks}%
\else
% silently DROP digit
\fi
\else
\pgfmathfloat@tmptoks=\expandafter{\expandafter0\the\pgfmathfloat@tmptoks}%
\fi
\advance\c@pgfmathroundto@offsetbehindperiod by1
\ifnum\c@pgfmathroundto@offsetbehindperiod=0
\ifpgfmathfloat@fixed@digits@after@period
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ADD@ONE@ITERATE}%
\else
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ADD@ONE@ITERATE@gobble@dot}%
\fi
\else
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ADD@ONE@ITERATE}%
\fi
\else
% re-use this counter:
\c@pgfmathroundto@lastzeros=#1
\advance\c@pgfmathroundto@lastzeros by1
\edef\pgfmathresult{\the\c@pgfmathroundto@lastzeros\the\pgfmathfloat@tmptoks}%
\pgfmathfloat@tmptoks=\expandafter{\pgfmathresult}%
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@REVERSE@ITERATE}%
\fi
\pgfmathround@nextcmd
}
\def\pgfmathroundto@impl@discard@suffix@zeros{%
\ifnum\c@pgfmathroundto@lastzeros=\c@pgfmathroundto@offsetbehindperiod
\ifpgfmathround@impl@PREPERIOD@is@negative@zero
\pgfmathfloatroundhasperiodfalse
\aftergroup\pgfmathfloatroundhasperiodfalse
\def\pgfmathresult{0}% write '0' instead of '-0'
\else
\expandafter\pgfmathroundto@impl@discard@period\pgfmathround@input\pgfmathfloat@EOI
\fi
\else
\ifnum\c@pgfmathroundto@lastzeros=0
\expandafter\pgfmathroundto@impl@REVERSE\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI
\else
\expandafter\pgfmathroundto@impl@discard@suffix@zeros@ITERATE\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI
\fi
\fi
}
% PRECONDITION:
% \c@pgfmathroundto@lastzeros > 0
\def\pgfmathroundto@impl@discard@suffix@zeros@ITERATE#1{%
\advance\c@pgfmathroundto@lastzeros by-1
\ifnum\c@pgfmathroundto@lastzeros=0
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@REVERSE}%
\else
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@discard@suffix@zeros@ITERATE}%
\fi
\pgfmathround@nextcmd
}
% Usage:
% \pgfmathroundto@impl@REVERSE#1\pgfmathfloat@EOI
% -> writes #1 reversed into \pgfmathfloat@tmptoks
\def\pgfmathroundto@impl@REVERSE{%
\pgfmathfloat@tmptoks={}%
\pgfmathroundto@impl@REVERSE@ITERATE
}
\def\pgfmathroundto@impl@REVERSE@ITERATE{%
\pgfutil@ifnextchar\pgfmathfloat@EOI{%
\edef\pgfmathresult{\the\pgfmathfloat@tmptoks}%
\pgfmathroundto@impl@gobble
}{%
\pgfmathroundto@impl@REVERSE@NEXT
}%
}
\def\pgfmathroundto@impl@REVERSE@NEXT#1{%
\pgfmathfloat@tmptoks=\expandafter{\expandafter#1\the\pgfmathfloat@tmptoks}%
\pgfmathroundto@impl@REVERSE@ITERATE
}
\def\pgfmathroundto@impl@BEGIN@DOT.{%
\pgfmathfloat@tmptoks=\expandafter{\expandafter.\the\pgfmathfloat@tmptoks}%
\c@pgfmathroundto@offsetbehindperiod=0
\pgfmathroundto@impl@ITERATE@DOT
}
\def\pgfmathroundto@impl@ITERATE@DOT{%
\pgfutil@ifnextchar\pgfmathfloat@EOI{%
% finished.
\pgfmathroundto@impl@gobble@and@start
}{%
\pgfmathroundto@impl@NEXT@DOT
}%
}
\def\pgfmathroundto@impl@NEXT@DOT#1{%
\ifnum\c@pgfmathroundto@offsetbehindperiod=\c@pgfmathroundto@prec
\def\pgfmathround@next{#1}%
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@gobble@rest@and@start}%
\else
\advance\c@pgfmathroundto@offsetbehindperiod by1
\ifnum#1=0
\advance\c@pgfmathroundto@lastzeros by1
\else
\c@pgfmathroundto@lastzeros=0
\fi
\pgfmathfloat@tmptoks=\expandafter{\expandafter#1\the\pgfmathfloat@tmptoks}%
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ITERATE@DOT}%
\fi
\pgfmathround@nextcmd
}%
% in contrast to pgfmathroundto@impl@ITERATE@NODOT, this method here
% checks also for signs
\def\pgfmathroundto@impl@ITERATE@NODOT@firstcall#1{%
\def\pgfmathround@cur{#1}%
\ifx\pgfmathround@cur\pgfmathfloat@EOI
\pgfmathround@impl@PREPERIOD@is@negative@zerofalse
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@start}%
\else
\ifx\pgfmathround@cur\pgfmathfloatparsenumber@tok@PERIOD
\pgfmathround@impl@PREPERIOD@is@negative@zerofalse
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@BEGIN@DOT.}%
\else
\ifx\pgfmathround@cur\pgfmathfloatparsenumber@tok@MINUS
\else
\pgfmathround@impl@PREPERIOD@is@negative@zerofalse
\fi
\pgfmathfloat@tmptoks=\expandafter{\expandafter#1\the\pgfmathfloat@tmptoks}%
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ITERATE@NODOT}%
\fi
\fi
\pgfmathround@nextcmd
}
\def\pgfmathroundto@impl@ITERATE@NODOT#1{%
\def\pgfmathround@cur{#1}%
\ifx\pgfmathround@cur\pgfmathfloat@EOI
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@start}%
\else
\ifx\pgfmathround@cur\pgfmathfloatparsenumber@tok@PERIOD
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@BEGIN@DOT.}%
\else
\ifx\pgfmathround@cur\pgfmathfloatparsenumber@tok@ZERO
\else
\pgfmathround@impl@PREPERIOD@is@negative@zerofalse
\fi
\pgfmathfloat@tmptoks=\expandafter{\expandafter#1\the\pgfmathfloat@tmptoks}%
\def\pgfmathround@nextcmd{\pgfmathroundto@impl@ITERATE@NODOT}%
\fi
\fi
\pgfmathround@nextcmd
}
%--------------------------------------------
% END of pgfmathroundto implementation.
%--------------------------------------------
% flags, mantissa and exponent has already been stored into
% \pgfmathfloat@a@* [using ...@Mtok]
%
% PRECONDITION:
% \ifpgfmathfloatroundhasperiod = \iftrue outside of the current
% group
%
% POSTCONDITION:
% \ifpgfmathfloatroundhasperiod will be set after the current TeX
% group.
\def\pgfmathfloatround@impl{%
\expandafter\pgfmathroundto@impl\expandafter{\the\pgfmathfloat@a@Mtok}%
\ifpgfmathfloatroundmayneedrenormalize
\ifpgfmathfloatroundhasperiod
\expandafter\pgfmathfloatround@impl@renormalize\pgfmathresult\pgfmathfloat@EOI%
\else
\expandafter\pgfmathfloatround@impl@renormalize\pgfmathresult.\pgfmathfloat@EOI%
\fi
\advance\pgfmathfloat@a@E by1
\fi
\pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\pgfmathresult}{\the\pgfmathfloat@a@E}%
}
\def\pgfmathfloatround@impl@renormalize#1#2.#3\pgfmathfloat@EOI{%
\pgfmathroundto@impl{#1.#2#3}%
}
% ATTENTION: this thing REQUIRES a period in the mantissa!
% collects everything into \pgfmathresult
\def\pgfmathfloattofixed@impl#1.#2\relax{%
\ifnum\pgfmathfloat@a@E<0
\ifcase-\pgfmathfloat@a@E
\or%e-1
\pgfmathfloat@a@Mtok={0.}%
\or%e-2
\pgfmathfloat@a@Mtok={0.0}%
\or%e-3
\pgfmathfloat@a@Mtok={0.00}%
\or%e-4
\pgfmathfloat@a@Mtok={0.000}%
\or%e-5
\pgfmathfloat@a@Mtok={0.0000}%
\or%e-6
\pgfmathfloat@a@Mtok={0.00000}%
\or%e-7
\pgfmathfloat@a@Mtok={0.000000}%
\or%e-8
\pgfmathfloat@a@Mtok={0.0000000}%
\or%e-9
\pgfmathfloat@a@Mtok={0.00000000}%
\or%e-10
\pgfmathfloat@a@Mtok={0.000000000}%
\else%<= -11
\pgfmathfloat@a@Mtok={0.0000000000}%
\advance\pgfmathfloat@a@E by10
\pgfutil@loop
\ifnum\pgfmathfloat@a@E<-1
\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok 0}%
\advance\pgfmathfloat@a@E by1
\pgfutil@repeat
\fi
\def\pgfmathfloat@loc@TMPb{#2}%
\def\pgfmathfloat@loc@TMPc{0}%
\ifx\pgfmathfloat@loc@TMPb\pgfmathfloat@loc@TMPc
\edef\pgfmathresult{\the\pgfmathfloat@a@Mtok #1}%
\else
\edef\pgfmathresult{\the\pgfmathfloat@a@Mtok #1#2}%
\fi
\else
%--------------------------------------------------
% \ifnum\pgfmathfloat@a@E=0%
% \edef\pgfmathresult{#1.#2}%
% \else
% \pgfmathfloat@a@Mtok={#1}%
% \pgfmathfloattofixed@impl@collectmantissa#2\count\pgfmathfloat@a@E
% \edef\pgfmathresult{\the\pgfmathfloat@a@Mtok}%
% \fi
%--------------------------------------------------
\pgfmathfloat@a@Mtok{#1}%
\pgfmathfloattofixed@impl@pos#2000000000\pgfmathfloat@EOI
\edef\pgfmathresult{\the\pgfmathfloat@a@Mtok}%
\fi
}
% FIXME: this implementation here is very fast, but it introduces trailing zeros. Is that acceptable?
\def\pgfmathfloattofixed@impl@pos#1#2#3#4#5#6#7#8#9\pgfmathfloat@EOI{%
\ifcase\pgfmathfloat@a@E
% e+0
\pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok .#1#2#3#4#5#6#7#8#9}%
\or%e+1
\pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1.#2#3#4#5#6#7#8#9}%
\or%e+2
\pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2.#3#4#5#6#7#8#9}%
\or%e+3
\pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2#3.#4#5#6#7#8#9}%
\or%e+4
\pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2#3#4.#5#6#7#8#9}%
\or%e+5
\pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2#3#4#5.#6#7#8#9}%
\or%e+6
\pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2#3#4#5#6.#7#8#9}%
\or%e+7
\pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2#3#4#5#6#7.#8#9}%
\or%e+8
\pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2#3#4#5#6#7#8.#9}%
\else%>=9
\pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2#3#4#5#6#7#8}%
\advance\pgfmathfloat@a@E by-8
\pgfmathfloattofixed@impl@collectmantissa#9\count\pgfmathfloat@a@E
\fi
}%
\def\pgfmathfloattofixed@impl@collectmantissa#1#2\count#3{%
\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok #1}%
\advance\pgfmathfloat@a@E by-1%
\def\pgfmathfloat@loc@TMPb{#2}%
\ifx\pgfmathfloat@loc@TMPb\pgfutil@empty
\pgfutil@loop
\ifnum\pgfmathfloat@a@E>0%
\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok 0}%
\advance\pgfmathfloat@a@E by-1%
\pgfutil@repeat
\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok .0}%
\else
\ifnum\pgfmathfloat@a@E=0
\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok .#2}%
\else
\pgfmathfloattofixed@impl@collectmantissa#2\count#3%
\fi
\fi
}
% ============================================
%
%
% \pgfmathfloatparsenumber implementation
%
%
% ============================================
% accepted parser tokens:
\def\pgfmathfloatparsenumber@tok@ZERO{0}
\def\pgfmathfloatparsenumber@tok@PLUS{+}
\def\pgfmathfloatparsenumber@tok@MINUS{-}
\def\pgfmathfloatparsenumber@tok@PERIOD{.}
\newif\ifpgfmathfloatparsenumberpendingperiod
\def\pgfflt@EOI{p@EOI}%
\def\pgfflt@EOI@unexpanded{\pgfflt@EOI}%
% Starts a finite-start-machine parser to read a number.
%
% The machine's state is represented by the macro which is currently
% processed; state transitions are realised using \csname...#1\endcsname
% constructions.
%
% It assigns \pgfmathfloat@a@S, \pgfmathfloat@a@Mtok, \pgfmathfloat@a@E.
\def\pgfflt@impl#1{%
\pgfmathfloatparsenumberpendingperiodfalse
\pgfmathfloat@tmptoks={}% this register is used to collect PENDING ZEROS
\pgfmathfloat@a@E=0
% start parsing: check for sign:
\expandafter\ifx\csname pgfflt@#1\endcsname\relax
\pgfmathfloat@a@S=1
\expandafter\pgfflt@init\expandafter#1%
\else
\expandafter\expandafter\csname pgfflt@#1\endcsname
\fi
}
% State transitions:
\expandafter\def\csname pgfflt@+\endcsname{%
\pgfmathfloat@a@S=1 %
\pgfflt@init}%
\expandafter\def\csname pgfflt@-\endcsname{%
\pgfmathfloat@a@S=2 %
\pgfflt@init}%
\expandafter\def\csname pgfflt@\pgfflt@EOI\endcsname{%
\pgfmathfloatparsenumber@handleerror{empty number}{}{}}%
\pgfkeys{
/pgf/fpu/handlers/empty number/.style 2 args={%
/pgf/fpu/handlers/invalid number={#1}{#2}%
},
/pgf/fpu/empty number is zero/.style={%
/pgf/fpu/handlers/empty number/.code 2 args={%
\pgfmathfloatcreate{0}{0.0}{0}%
}%
},%
/pgf/fpu/handlers/invalid separator/.code 2 args={%
\pgfmath@error{Could not parse input '#1' as a floating point number, sorry. The unreadable part was near the decimal separator '#2'. Do you need the option 'read comma as period'?}{}%
},
/pgf/fpu/handlers/invalid number/.code 2 args={%
\pgfmath@error{Could not parse input '#1' as a floating point number, sorry. The unreadable part was near '#2'.}{}%
},
/pgf/fpu/handlers/wrong lowlevel format/.code 2 args={%
\pgfmath@error{Sorry, an internal routine of the floating point unit got an ill-formatted floating point number `#1'. The unreadable part was near '#2'.}{}%
\let\pgfmathresult=\pgfutil@empty
},
}
% #1 the error handler
% #2 the number which was invalid.
% #3 the part which produced the error
%
% POSTCONDITION: the three registers
% \pgfmathfloat@a@S
% \pgfmathfloat@a@Mtok
% \pgfmathfloat@a@E
% will contain the number which results from the error handler.
\def\pgfmathfloatparsenumber@handleerror#1#2#3{%
\let\pgfmathresult=\pgfutil@empty
\pgfmathfloatparsenumberpendingperiodfalse
\pgfkeys{/pgf/fpu/handlers/#1={#2}{#3}}%
\ifx\pgfmathresult\pgfutil@empty
\pgfmathfloat@a@S=3
\pgfmathfloat@a@Mtok={0.0}%
\pgfmathfloat@a@E=0
\else
\expandafter\pgfmathfloat@decompose@tok\pgfmathresult\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E
\fi
}
\def\pgfflt@error#1\pgfflt@EOI{%
\begingroup
\pgfmathfloat@a@Mtok={#1}%
\xdef\pgfmathfloat@glob@TMP{%
\noexpand\pgfmathfloatparsenumber@handleerror
{invalid number}{\pgfmathresult}{\the\pgfmathfloat@a@Mtok}}%
\endgroup
\pgfmathfloat@glob@TMP
}%
% FROM: checksign.
%
\def\pgfflt@init#1{%
\expandafter\ifx\csname pgffltA@#1\endcsname\relax
\expandafter\pgfflt@error\expandafter#1%
\else
\expandafter\expandafter\csname pgffltA@#1\endcsname
\fi}
% state transitions:
\expandafter\def\csname pgffltA@0\endcsname{\pgfflt@leadingzero}% FIXME: inline optimization!
\expandafter\def\csname pgffltA@1\endcsname{\pgfflt@nonzerodigit1}%
\expandafter\def\csname pgffltA@2\endcsname{\pgfflt@nonzerodigit2}%
\expandafter\def\csname pgffltA@3\endcsname{\pgfflt@nonzerodigit3}%
\expandafter\def\csname pgffltA@4\endcsname{\pgfflt@nonzerodigit4}%
\expandafter\def\csname pgffltA@5\endcsname{\pgfflt@nonzerodigit5}%
\expandafter\def\csname pgffltA@6\endcsname{\pgfflt@nonzerodigit6}%
\expandafter\def\csname pgffltA@7\endcsname{\pgfflt@nonzerodigit7}%
\expandafter\def\csname pgffltA@8\endcsname{\pgfflt@nonzerodigit8}%
\expandafter\def\csname pgffltA@9\endcsname{\pgfflt@nonzerodigit9}%
\def\pgfflt@nonzerodigit#1{%
\pgfmathfloat@a@Mtok={#1}%
\pgfmathfloatparsenumberpendingperiodtrue
\pgfflt@positiveexp}%
\expandafter\def\csname pgffltA@n\endcsname{\pgfflt@readnan}% FIXME: inlining?
\expandafter\def\csname pgffltA@N\endcsname{\pgfflt@readnan}% FIXME: inlining?
\expandafter\def\csname pgffltA@i\endcsname{\pgfflt@readinf}% FIXME: inlining?
\expandafter\def\csname pgffltA@I\endcsname{\pgfflt@readinf}% FIXME: inlining?
\expandafter\def\csname pgffltA@.\endcsname{% read '.9' like '0.9'
\pgfmathfloat@a@E=-1
\pgfflt@leadingzero@foundperiod}%
\expandafter\def\csname pgffltA@,\endcsname{% read ',9' like '0,9'
\pgfmathfloat@frenchinput{%
\pgfmathfloat@a@E=-1
\pgfflt@leadingzero@foundperiod
}%
}%
\def\pgfmathfloat@frenchinput#1{%
\ifpgfmathparsenumber@comma@as@period
\def\pgf@marshal{#1}%
\expandafter\pgf@marshal
\else
\expandafter\pgfflt@error@separator\expandafter,%
\fi
}%
\def\pgfflt@error@separator#1\pgfflt@EOI{%
\begingroup
\pgfmathfloat@a@Mtok={#1}%
\xdef\pgfmathfloat@glob@TMP{%
\noexpand\pgfmathfloatparsenumber@handleerror
{invalid separator}{\pgfmathresult}{\the\pgfmathfloat@a@Mtok}}%
\endgroup
\pgfmathfloat@glob@TMP
}%
\def\pgfflt@finish#1\pgfflt@EOI{}
\def\pgfflt@readnan #1#2{%
\def\pgfflt@readnan@ok{1}%
\if#1a\else\if#1A\else\def\pgfflt@readnan@ok{0}\fi\fi
\if#2n\else\if#2N\else\def\pgfflt@readnan@ok{0}\fi\fi
\if\pgfflt@readnan@ok1%
\pgfmathfloat@a@S=3\relax%
\pgfmathfloat@a@Mtok={0.0}%
\pgfmathfloat@a@E=0%
\expandafter\pgfflt@finish
\else
\def\pgfflt@readnan@{\pgfflt@error #1#2}%
\expandafter\pgfflt@readnan@
\fi
}
\def\pgfflt@readinf #1#2{%
\def\pgfflt@readinf@ok{1}%
\if#1n\else\if#1N\else\def\pgfflt@readinf@ok{0}\fi\fi
\if#2f\else\if#2F\else\def\pgfflt@readinf@ok{0}\fi\fi
\if\pgfflt@readinf@ok1%
\ifnum\pgfmathfloat@a@S=1 %
\pgfmathfloat@a@S=4 %
\pgfmathfloat@a@Mtok={0.0}%
\else
\pgfmathfloat@a@S=5 %
\pgfmathfloat@a@Mtok={0.0}%
\fi
\pgfmathfloat@a@E=0 %
\expandafter\pgfflt@finish
\else
\def\pgfflt@readinf@{\pgfflt@error #1#2}%
\expandafter\pgfflt@readinf@
\fi
}
\def\pgfflt@leadingzero#1{%
\expandafter\ifx\csname pgffltB@#1\endcsname\relax
\expandafter\pgfflt@error\expandafter#1%
\else
\expandafter\expandafter\csname pgffltB@#1\endcsname
\fi}
% State transitions:
\expandafter\def\csname pgffltB@0\endcsname{\pgfflt@leadingzero}%
\expandafter\def\csname pgffltB@1\endcsname{\pgfmathfloat@a@Mtok={1}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp}
\expandafter\def\csname pgffltB@2\endcsname{\pgfmathfloat@a@Mtok={2}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp}
\expandafter\def\csname pgffltB@3\endcsname{\pgfmathfloat@a@Mtok={3}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp}
\expandafter\def\csname pgffltB@4\endcsname{\pgfmathfloat@a@Mtok={4}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp}
\expandafter\def\csname pgffltB@5\endcsname{\pgfmathfloat@a@Mtok={5}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp}
\expandafter\def\csname pgffltB@6\endcsname{\pgfmathfloat@a@Mtok={6}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp}
\expandafter\def\csname pgffltB@7\endcsname{\pgfmathfloat@a@Mtok={7}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp}
\expandafter\def\csname pgffltB@8\endcsname{\pgfmathfloat@a@Mtok={8}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp}
\expandafter\def\csname pgffltB@9\endcsname{\pgfmathfloat@a@Mtok={9}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp}
\expandafter\def\csname pgffltB@\pgfmathfloat@POSTFLAGSCHAR\endcsname{\pgfmathfloat@a@Mtok={0}\pgfflt@readlowlevelfloat}%
\expandafter\def\csname pgffltB@.\endcsname{%
\pgfmathfloat@a@E=-1
\pgfflt@leadingzero@foundperiod}%
\expandafter\def\csname pgffltB@,\endcsname{%
\pgfmathfloat@frenchinput{%
\pgfmathfloat@a@E=-1
\pgfflt@leadingzero@foundperiod
}%
}%
\expandafter\def\csname pgffltB@e\endcsname{%
\pgfmathfloat@a@S=0\relax%
\pgfmathfloat@a@Mtok={0.0}%
\pgfmathfloat@a@E=0%
\pgfflt@readexponent}%
\let\pgffltB@E=\pgffltB@e
\expandafter\def\csname pgffltB@\pgfflt@EOI\endcsname{%
\pgfmathfloat@a@S=0\relax%
\pgfmathfloat@a@Mtok={0.0}%
\pgfmathfloat@a@E=0}%
\def\pgfflt@leadingzero@foundperiod#1{%
\expandafter\ifx\csname pgffltC@#1\endcsname\relax
\expandafter\pgfflt@error\expandafter#1%
\else
\expandafter\expandafter\csname pgffltC@#1\endcsname
\fi}
% State transitions:
\expandafter\def\csname pgffltC@0\endcsname{%
\advance\pgfmathfloat@a@E by-1
\pgfflt@leadingzero@foundperiod}%
\expandafter\def\csname pgffltC@1\endcsname{\pgfmathfloat@a@Mtok={1}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}%
\expandafter\def\csname pgffltC@2\endcsname{\pgfmathfloat@a@Mtok={2}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}%
\expandafter\def\csname pgffltC@3\endcsname{\pgfmathfloat@a@Mtok={3}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}%
\expandafter\def\csname pgffltC@4\endcsname{\pgfmathfloat@a@Mtok={4}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}%
\expandafter\def\csname pgffltC@5\endcsname{\pgfmathfloat@a@Mtok={5}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}%
\expandafter\def\csname pgffltC@6\endcsname{\pgfmathfloat@a@Mtok={6}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}%
\expandafter\def\csname pgffltC@7\endcsname{\pgfmathfloat@a@Mtok={7}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}%
\expandafter\def\csname pgffltC@8\endcsname{\pgfmathfloat@a@Mtok={8}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}%
\expandafter\def\csname pgffltC@9\endcsname{\pgfmathfloat@a@Mtok={9}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}%
\expandafter\def\csname pgffltC@e\endcsname{%
\pgfmathfloat@a@S=0\relax%
\pgfmathfloat@a@Mtok={0.0}%
\pgfmathfloat@a@E=0%
\pgfflt@readexponent}%
\let\pgffltC@E=\pgffltC@e
\expandafter\def\csname pgffltC@\pgfflt@EOI\endcsname{%
\pgfmathfloat@a@S=0\relax%
\pgfmathfloat@a@Mtok={0.0}%
\pgfmathfloat@a@E=0}%
\def\pgfflt@positiveexp#1{%
\expandafter\ifx\csname pgffltD@#1\endcsname\relax
\expandafter\pgfflt@error\expandafter#1%
\else
\expandafter\expandafter\csname pgffltD@#1\endcsname
\fi}
% State transitions:
\expandafter\def\csname pgffltD@0\endcsname{%
\advance\pgfmathfloat@a@E by1
\pgfmathfloat@tmptoks=\expandafter{\the\pgfmathfloat@tmptoks0}%
\pgfflt@pendingzeros@positiveexp}%
\expandafter\def\csname pgffltD@1\endcsname{\pgffltD@nonzerodigit1}%
\expandafter\def\csname pgffltD@2\endcsname{\pgffltD@nonzerodigit2}%
\expandafter\def\csname pgffltD@3\endcsname{\pgffltD@nonzerodigit3}%
\expandafter\def\csname pgffltD@4\endcsname{\pgffltD@nonzerodigit4}%
\expandafter\def\csname pgffltD@5\endcsname{\pgffltD@nonzerodigit5}%
\expandafter\def\csname pgffltD@6\endcsname{\pgffltD@nonzerodigit6}%
\expandafter\def\csname pgffltD@7\endcsname{\pgffltD@nonzerodigit7}%
\expandafter\def\csname pgffltD@8\endcsname{\pgffltD@nonzerodigit8}%
\expandafter\def\csname pgffltD@9\endcsname{\pgffltD@nonzerodigit9}%
\expandafter\def\csname pgffltD@\pgfmathfloat@POSTFLAGSCHAR\endcsname{\pgfflt@readlowlevelfloat}%
\expandafter\def\csname pgffltD@.\endcsname{\pgfflt@finish@number@after@period}% FIXME : inlining?
\expandafter\def\csname pgffltD@,\endcsname{\pgfmathfloat@frenchinput{\pgfflt@finish@number@after@period}}%
\expandafter\def\csname pgffltD@e\endcsname{\pgfflt@readexponent}% FIXME : inlining?
\let\pgffltD@E=\pgffltD@e
\expandafter\def\csname pgffltD@\pgfflt@EOI\endcsname{}% NOP
\def\pgffltD@nonzerodigit#1{%
\advance\pgfmathfloat@a@E by1
\ifpgfmathfloatparsenumberpendingperiod
\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.}%
\pgfmathfloatparsenumberpendingperiodfalse
\fi
\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok#1}%
\pgfflt@positiveexp}%
% Read a low-level floating point.
% Since we are in the second state, \pgfmathfloat@a@Mtok contains the
% FLAGS. The post-flags-char has also been read.
\def\pgfflt@readlowlevelfloat#1e#2]\pgfflt@EOI{%
\pgfmathfloatparsenumberpendingperiodfalse
\pgfmathfloat@a@S=\the\pgfmathfloat@a@Mtok\relax
\pgfmathfloat@a@Mtok={#1}%
\pgfmathfloat@a@E=#2
}%
\def\pgfflt@readexponent#1\pgfflt@EOI{%
\afterassignment\pgfflt@readexponent@
\pgfmathfloat@b@E=#1 \pgfflt@EOI% the white space is important, otherwise \pgfflt@EOI will be expanded.
}
\def\pgfflt@readexponent@#1{%
\advance\pgfmathfloat@a@E by\pgfmathfloat@b@E\relax
%
% sanity checking:
\def\pgfmathfloat@loc@TMPb{#1}%
\ifx\pgfmathfloat@loc@TMPb\pgfflt@EOI@unexpanded
\else
\def\pgfmathfloat@loc@TMPb{\pgfflt@error#1}%
\expandafter\pgfmathfloat@loc@TMPb
\fi
}
\def\pgfflt@pendingzeros@positiveexp#1{%
\expandafter\ifx\csname pgffltE@#1\endcsname\relax
\expandafter\pgfflt@error\expandafter#1%
\else
\expandafter\expandafter\csname pgffltE@#1\endcsname
\fi}
% State transitions:
\expandafter\def\csname pgffltE@0\endcsname{%
\pgfmathfloat@tmptoks=\expandafter{\the\pgfmathfloat@tmptoks0}%
\advance\pgfmathfloat@a@E by1
\pgfflt@pendingzeros@positiveexp}%
\expandafter\def\csname pgffltE@1\endcsname{\pgffltE@nonzerodigit1}%
\expandafter\def\csname pgffltE@2\endcsname{\pgffltE@nonzerodigit2}%
\expandafter\def\csname pgffltE@3\endcsname{\pgffltE@nonzerodigit3}%
\expandafter\def\csname pgffltE@4\endcsname{\pgffltE@nonzerodigit4}%
\expandafter\def\csname pgffltE@5\endcsname{\pgffltE@nonzerodigit5}%
\expandafter\def\csname pgffltE@6\endcsname{\pgffltE@nonzerodigit6}%
\expandafter\def\csname pgffltE@7\endcsname{\pgffltE@nonzerodigit7}%
\expandafter\def\csname pgffltE@8\endcsname{\pgffltE@nonzerodigit8}%
\expandafter\def\csname pgffltE@9\endcsname{\pgffltE@nonzerodigit9}%
\expandafter\def\csname pgffltE@.\endcsname{\pgfflt@finish@number@after@period}% FIXME : inlining?
\expandafter\def\csname pgffltE@,\endcsname{\pgfmathfloat@frenchinput{\pgfflt@finish@number@after@period}}% FIXME : inlining?
\def\pgffltE@e{\pgfflt@readexponent}% FIXME : inlining?
\let\pgffltE@E=\pgffltE@e
\expandafter\def\csname pgffltE@\pgfflt@EOI\endcsname{}% NOP
\def\pgffltE@nonzerodigit#1{%
\advance\pgfmathfloat@a@E by1
\ifpgfmathfloatparsenumberpendingperiod
\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.}%
\pgfmathfloatparsenumberpendingperiodfalse
\fi
\pgfmathfloat@a@Mtok=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfmathfloat@a@Mtok\the\pgfmathfloat@tmptoks}%
\pgfmathfloat@tmptoks={}%
\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok#1}%
\pgfflt@positiveexp}%
\def\pgfflt@finish@number@after@period#1{%
\expandafter\ifx\csname pgffltF@#1\endcsname\relax
\expandafter\pgfflt@error\expandafter#1%
\else
\expandafter\expandafter\csname pgffltF@#1\endcsname
\fi}
% State transitions:
\expandafter\def\csname pgffltF@0\endcsname{%
\pgfmathfloat@tmptoks=\expandafter{\the\pgfmathfloat@tmptoks0}%
\pgfflt@pendingzeros}%
\expandafter\def\csname pgffltF@1\endcsname{\pgffltF@nonzerodigit1}%
\expandafter\def\csname pgffltF@2\endcsname{\pgffltF@nonzerodigit2}%
\expandafter\def\csname pgffltF@3\endcsname{\pgffltF@nonzerodigit3}%
\expandafter\def\csname pgffltF@4\endcsname{\pgffltF@nonzerodigit4}%
\expandafter\def\csname pgffltF@5\endcsname{\pgffltF@nonzerodigit5}%
\expandafter\def\csname pgffltF@6\endcsname{\pgffltF@nonzerodigit6}%
\expandafter\def\csname pgffltF@7\endcsname{\pgffltF@nonzerodigit7}%
\expandafter\def\csname pgffltF@8\endcsname{\pgffltF@nonzerodigit8}%
\expandafter\def\csname pgffltF@9\endcsname{\pgffltF@nonzerodigit9}%
\def\pgffltF@e{\pgfflt@readexponent}%
\let\pgffltF@E=\pgffltF@e
\expandafter\def\csname pgffltF@\pgfflt@EOI\endcsname{}% NOP
\def\pgffltF@nonzerodigit#1{%
\ifpgfmathfloatparsenumberpendingperiod
\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.}%
\pgfmathfloatparsenumberpendingperiodfalse
\fi
\pgfmathfloat@a@Mtok=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfmathfloat@a@Mtok\the\pgfmathfloat@tmptoks}%
\pgfmathfloat@tmptoks={}%
\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok#1}%
\pgfflt@finish@number@after@period}%
\def\pgfflt@pendingzeros#1{%
\expandafter\ifx\csname pgffltG@#1\endcsname\relax
\expandafter\pgfflt@error\expandafter#1%
\else
\expandafter\expandafter\csname pgffltG@#1\endcsname
\fi}
% State transitions:
\expandafter\def\csname pgffltG@0\endcsname{%
\pgfmathfloat@tmptoks=\expandafter{\the\pgfmathfloat@tmptoks0}%
\pgfflt@pendingzeros}%
\expandafter\def\csname pgffltG@1\endcsname{\pgffltG@nonzerodigit1}%
\expandafter\def\csname pgffltG@2\endcsname{\pgffltG@nonzerodigit2}%
\expandafter\def\csname pgffltG@3\endcsname{\pgffltG@nonzerodigit3}%
\expandafter\def\csname pgffltG@4\endcsname{\pgffltG@nonzerodigit4}%
\expandafter\def\csname pgffltG@5\endcsname{\pgffltG@nonzerodigit5}%
\expandafter\def\csname pgffltG@6\endcsname{\pgffltG@nonzerodigit6}%
\expandafter\def\csname pgffltG@7\endcsname{\pgffltG@nonzerodigit7}%
\expandafter\def\csname pgffltG@8\endcsname{\pgffltG@nonzerodigit8}%
\expandafter\def\csname pgffltG@9\endcsname{\pgffltG@nonzerodigit9}%
\def\pgffltG@e{\pgfflt@readexponent}% FIXME: inlining?
\let\pgffltG@E=\pgffltG@e
\expandafter\def\csname pgffltG@\pgfflt@EOI\endcsname{}% NOP
\def\pgffltG@nonzerodigit#1{%
\ifpgfmathfloatparsenumberpendingperiod
\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.}%
\pgfmathfloatparsenumberpendingperiodfalse
\fi
\pgfmathfloat@a@Mtok=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfmathfloat@a@Mtok\the\pgfmathfloat@tmptoks}%
\pgfmathfloat@tmptoks={}%
\pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok#1}%
\pgfflt@finish@number@after@period}%
\endinput