% from TeXbook, appendix D
\protected\def\yquant@futurenonspacelet#1{%
   \def\yquant@futurenonspacelet@cs{#1}%
   \afterassignment\yquant@futurenonspacelet@i\let\yquant@futurenonspacelet@next= %
}

\def\yquant@futurenonspacelet@i{%
   \expandafter\futurelet\yquant@futurenonspacelet@cs\yquant@futurenonspacelet@ii%
}

\def\yquant@futurenonspacelet@ii{%
   \expandafter\ifx\yquant@futurenonspacelet@cs\@sptoken%
      \expandafter\yquant@futurenonspacelet@iii%
   \else%
      \expandafter\yquant@futurenonspacelet@next%
   \fi%
}

\def\yquant@futurenonspacelet@iii{%
   \afterassignment\yquant@futurenonspacelet@i%
   \let\@eattoken= %
}

% a bit faster than nested \@firstoftwo/\@secondoftwo
% note \@thirdofthree is defined in the latex kernel already.
\long\def\@firstofthree#1#2#3{#1}%
\long\def\@secondofthree#1#2#3{#2}%
\long\def\@firstoffour#1#2#3#4{#1}%
\long\def\@secondoffour#1#2#3#4{#2}%
\long\def\@thirdoffour#1#2#3#4{#3}%
\long\def\@fourthoffour#1#2#3#4{#4}%
\long\def\@thirdandfourthoffour#1#2#3#4{#3#4}%
\long\def\@secondandthirdoffive#1#2#3#4#5{{#2}{#3}}
\long\def\@firstoffive#1#2#3#4#5{#1} % unused
\long\def\@secondoffive#1#2#3#4#5{#2}
\long\def\@thirdoffive#1#2#3#4#5{#3}
\long\def\@fourthoffive#1#2#3#4#5{#4} % unused
\long\def\@fifthoffive#1#2#3#4#5{#5}

\protected\def\yquant@protectedempty{}

% Loop #1 from min(#2, #3) to max(#2, #3), executing #4
\protected\def\yquant@for #1:=#2to#3#{%
   \yquant@for@aux#1{#2}{#3}%
}

% Loop #1 from max(#2, #3) down to min(#2, #3), executing #4
\protected\def\yquant@fordown #1:=#2downto#3#{%
   \yquant@fordown@aux#1{#2}{#3}%
}

\long\def\yquant@for@aux#1#2#3#4{%
   \ifnum#2<#3\relax%
      \numdef#1{#2}%
      % to allow for things like \yquant@for \i := \i to ..., expand the boundaries
      \expandafter\yquant@for@loop\expandafter#1\expandafter{\the\numexpr#3+1\relax}{#4}%
   \else%
      \numdef#1{#3}%
      \expandafter\yquant@for@loop\expandafter#1\expandafter{\the\numexpr#2+1\relax}{#4}%
   \fi%
}

\long\def\yquant@fordown@aux#1#2#3#4{%
   \ifnum#2>#3\relax%
      \numdef#1{#2}%
      % to allow for things like \yquant@for \i := \i to ..., expand the boundaries
      \expandafter\yquant@fordown@loop\expandafter#1\expandafter{\the\numexpr#3-1\relax}{#4}%
   \else%
      \numdef#1{#3}%
      \expandafter\yquant@fordown@loop\expandafter#1\expandafter{\the\numexpr#2-1\relax}{#4}%
   \fi%
}

\long\def\yquant@for@loop#1#2#3{%
   \loop%
      \ifnum#1<#2\relax%
         #3%
         \numdef#1{#1+1}%
   \repeat%
}

\long\def\yquant@fordown@loop#1#2#3{%
   \loop%
      \ifnum#1>#2\relax%
         #3%
         \numdef#1{#1-1}%
   \repeat%
}

\def\yquant@for@break{%
   \fi%
   \iffalse%
}

% Def #1 to be the minimum of #2, ... until \relax
\protected\def\yquant@min#1{%
   \def#1{2147483647}%
   \def\yquant@min@var{#1}%
   \yquant@min@loop%
}

\def\yquant@min@loop#1{%
   \unless\ifx#1\relax\relax%
      \ifnum#1<\yquant@min@var\relax%
         \expandafter\edef\yquant@min@var{#1}%
      \fi%
      \expandafter\yquant@min@loop%
   \fi%
}

% Def #1 to be the maximum of #2, ... until \relax
\protected\def\yquant@max#1{%
   \def#1{-2147483647}%
   \def\yquant@max@var{#1}%
   \yquant@max@loop%
}

\def\yquant@max@loop#1{%
   \unless\ifx#1\relax\relax%
      \ifnum#1>\yquant@max@var\relax%
         \expandafter\edef\yquant@max@var{#1}%
      \fi%
      \expandafter\yquant@max@loop%
   \fi%
}

% Cleanup global tokens after environment
\protected\def\yquant@cleanup@csadd#1{%
   \csxappto{\yquant@prefix cleanup}{\expandafter\noexpand\csname#1\endcsname}%
}

\def\yquant@cleanup#1#2{%
   \global\undef#1%
   \unless\ifx|#2%
      \expandafter\yquant@cleanup\expandafter#2%
   \fi%
}

% Executes #3 if #1 (single token!) is equal (\ifx) to the first token of #2, and #4 else.
\def\ifyquant@firsttoken#1#2{%
   % First check whether #2 is present at all...
   \ifstrempty{#2}{%
      \expandafter\@secondoftwo%
   }{%
      \ifyquant@firsttoken@aux#1#2\yquant@sep%
   }%
}

\def\ifyquant@firsttoken@aux#1#2#3\yquant@sep{%
   \ifx#1#2%
      \expandafter\expandafter\expandafter\@firstoftwo%
   \else%
      \expandafter\expandafter\expandafter\@secondoftwo%
   \fi%
}

% Executes #3 if #1 begins with #2, and #4 else - non-expandable
\protected\def\ifyquant@beginswith#1#2{%
   \def\ifyquant@beginswith@##1#2##2\yquant@end{%
      \ifstrempty{##1}%
   }%
   \ifyquant@beginswith@#1#2\yquant@end%
}

% absolute value of a dimension
\def\yquant@abs#1{%
   \ifdim#1<0pt %
      \the\dimexpr-\dimexpr#1\relax\relax%
   \else%
      #1%
   \fi%
}

% Sortlist related macros.
\newcount\yquant@sort@count

\protected\def\yquant@sort@clear{%
   % Probably cleanup used macros?
   \yquant@sort@count=0 %
}

\protected\def\yquant@sort@eadd#1{%
   \csedef{yquant@sort@item\the\yquant@sort@count}{#1}%
   \advance \yquant@sort@count by 1 %
}

% Perform quicksort on the stored sortlist.
% #1: compare macro that expands to ##3 if its second argument is strictly larger than its first or to ##4 else
\protected\def\yquant@sort#1{%
   \let\yquant@sort@cmp=#1%
   \expandafter\yquant@sort@aux\expandafter0\expandafter{\the\numexpr\yquant@sort@count-1\relax}%
}

% Returns the first item in the unordered sortlist when compared according to #1 and stores it in #2.
\protected\def\yquant@sort@findfirst#1#2{%
   \ifnum\yquant@sort@count<1 %
      \let#2=\empty%
   \else%
      \letcs#2{yquant@sort@item0}%
      \count0=1 %
      \loop%
         \ifnum\count0<\yquant@sort@count\relax%
            \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter#1%
               \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter{%
               \expandafter\expandafter\expandafter#2%
               \expandafter\expandafter\expandafter}%
               \expandafter\expandafter\expandafter{%
                  \csname yquant@sort@item\the\count0\endcsname%
               }%
               \relax{%
               \letcs#2{yquant@sort@item\the\count0}%
            }%
            \advance\count0 by 1 %
      \repeat%
   \fi%
}

\def\yquant@sort@ascending#1#2{%
   \ifnum#2>#1 %
      \expandafter\@firstoftwo%
   \else%
      \expandafter\@secondoftwo%
   \fi%
}

\protected\def\yquant@sort@aux#1#2{%
   \ifnum#1<#2\relax%
      \yquant@sort@divide{#1}{#2}%
      \edef\cmd{%
         \noexpand\yquant@sort@aux{#1}{\the\numexpr\count0-1\relax}%
         \noexpand\yquant@sort@aux{\the\numexpr\count0+1\relax}{#2}%
      }%
      \cmd%
   \fi%
}

\def\iftrue@hidden{\iftrue}%
\def\iffalse@hidden{\iffalse}%
\protected\def\yquant@sort@divide#1#2{%
   \count0=#1\relax% i
   \count2=#2\relax% j
   \advance\count2 by -1 %
   \letcs\yquant@sort@pivot{yquant@sort@item#2}%
   \loop%
      % search an item from the left that is larger or equal to the pivot
      {% protect the outer loop from finding \repeat
         \loop%
            \ifnum\count0<#2\relax%
               \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\yquant@sort@cmp%
                  \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter{%
                  \expandafter\expandafter\expandafter\yquant@sort@pivot%
                  \expandafter\expandafter\expandafter}%
                  \expandafter\expandafter\expandafter{%
                     \csname yquant@sort@item\the\count0\endcsname%
                  }{%
                     \expandafter\iffalse@hidden%
                  }{%
                     \advance\count0 by 1 %
                     \expandafter\iftrue@hidden%
                  }%
            \else%
               \expandafter\iffalse@hidden%
            \fi%
         \repeat%
         \expandafter%
      }%
      \expandafter\count\expandafter0\expandafter=\the\count0\relax%
      % search an item from the right that is small than the pivot
      {% protect the outer loop from finding \repeat
         \loop%
            \ifnum\count2>#1\relax%
               \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\yquant@sort@cmp%
                  \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter{%
                  \expandafter\expandafter\expandafter\yquant@sort@pivot%
                  \expandafter\expandafter\expandafter}%
                  \expandafter\expandafter\expandafter{%
                     \csname yquant@sort@item\the\count2\endcsname%
                  }{%
                     \advance\count2 by -1 %
                     \expandafter\iftrue@hidden%
                  }{%
                     \expandafter\iffalse@hidden%
                  }%
            \else%
               \expandafter\iffalse@hidden%
            \fi%
         \repeat%
         \expandafter%
      }%
      \expandafter\count\expandafter2\expandafter=\the\count2\relax%
      \ifnum\count0<\count2 %
         % swap item i <> item j
         \letcs\tmp{yquant@sort@item\the\count0}%
         \csletcs{yquant@sort@item\the\count0}{yquant@sort@item\the\count2}%
         \cslet{yquant@sort@item\the\count2}\tmp%
      \fi%
      \ifnum\count0<\count2 %
   \repeat%
   \letcs\tmp{yquant@sort@item\the\count0}%
   \csletcs{yquant@sort@item\the\count0}{yquant@sort@item#2}%
   \cslet{yquant@sort@item#2}\tmp%
}

% Add an internal etoolbox list to the sorted items
\def\yquant@sort@addlist#1{%
   \forlistloop\yquant@sort@addlist@aux#1%
}

\protected\def\yquant@sort@addlist@aux#1{%
   \csdef{yquant@sort@item\the\yquant@sort@count}{#1}%
   \advance\yquant@sort@count by 1 %
}

% Sorts an internal etoolbox list #1 using macro #2
\protected\def\yquant@sort@list#1#2{%
   \begingroup%
      \yquant@sort@count=0 %
      \yquant@sort@addlist#1%
      \yquant@sort#2%
      \let#1=\empty%
      \count0=0 %
      \loop%
         \ifnum\count0<\yquant@sort@count%
            \expandafter\expandafter\expandafter\listadd%
            \expandafter\expandafter\expandafter#1%
            \expandafter\expandafter\expandafter{%
               \csname yquant@sort@item\the\count0\endcsname%
            }%
            \advance\count0 by 1 %
      \repeat%
      \expandafter%
   \endgroup%
   \expandafter\def\expandafter#1\expandafter{#1}%
}

\protected\def\yquant@sort@dolistloop{%
   \count0=0 %
   \loop%
      \ifnum\count0<\yquant@sort@count%
         \expandafter\expandafter\expandafter\do%
         \expandafter\expandafter\expandafter{%
            \csname yquant@sort@item\the\count0\endcsname%
         }%
         \advance\count0 by 1 %
   \repeat%
}

\begingroup
\catcode`\|=3
\catcode`\&=3
\gdef\yquant@list@delim{|}

\protected\gdef\yquant@list@dequeue#1#2{%
   \expandafter\ifblank\expandafter{#1}{%
      \let#2=\empty%
   }{%
      \expandafter\yquant@list@dequeue@i#1\etb@lst@q@end{#1}{#2}\def%
   }%
}%

\protected\gdef\yquant@list@dequeue@i#1|#2\etb@lst@q@end#3#4#5{%
   \def#4{#1}%
   #5#3{#2}%
}

\protected\gdef\yquant@list@gdequeue#1#2{%
   \expandafter\ifblank\expandafter{#1}{%
      \let#2=\empty%
   }{%
      \expandafter\yquant@list@dequeue@i#1\etb@lst@q@end{#1}{#2}\gdef%
   }%
}

\protected\gdef\yquant@list@eupdateorinsert#1#2#3{%
   % the list items are of the form <number>:<value>. If an item is present where <number> = #2, then set its <value> to #3, if #3 is greater. If no item is present, add it.
   \begingroup%
      \def\etb@tempa##1|#2:##2|##3&{%
         \endgroup%
         \ifstrempty{##3}{%
            \eappto#1{#2:#3|}%
         }{%
            \ifdim##2<#3 %
               \yquant@list@ereplace#1{#2:##2}{#2:#3}%
            \fi%
         }%
      }%
   \expandafter\etb@tempa\expandafter|#1|#2:#3|&%
}

\protected\gdef\yquant@list@ereplace#1#2#3{%
   \begingroup%
      \def\etb@tempa##1|#2|##2&{%
         \endgroup%
         \ifstrempty{##1}{%
            \edef#1{%
               \unexpanded{##1}|#3|\unexpanded{##2}%
            }%
         }{%
            \edef#1{%
               \unexpanded\expandafter{\@gobble##1}|#3|\unexpanded{##2}%
            }%
         }%
      }%
   \expandafter\etb@tempa\expandafter|#1&
}

% expands to the contents of a list ranging from #1 to #2 (ascending)
\gdef\yquant@list@range#1#2{%
   \ifnum#1>#2 %
      \expandafter\@firstoftwo%
   \else%
      \expandafter\@secondoftwo%
   \fi{}{%
      #1|%
      \expandafter\yquant@list@range\expandafter{\the\numexpr#1+1\relax}{#2}%
   }%
}
\endgroup

% performs #3 if #1 is a subset of #2; else, performs #4
\protected\def\ifyquant@registersubset#1#2{%
   \begingroup%
      \let\yquant@register@multi=\@fourthoffour
      \def\yquant@register@multi@contiguous##1##2##3{\yquant@list@range{##1}{##2}}%
      \edef\listA{#1}%
      \edef\listB{#2}%
      \let\ifsuccess=\iftrue%
      \forlistloop\yquant@registersubset@loop\listA%
      \expandafter%
   \endgroup%
   \ifsuccess%
      \expandafter\@firstoftwo%
   \else%
      \expandafter\@secondoftwo%
   \fi%
}

\protected\def\yquant@registersubset@loop#1{%
   \ifinlist{#1}\listB\relax{%
      \let\ifsuccess=\iffalse%
      \listbreak%
   }%
}

\def\ifyquant@OR#1\fi#2\fi{%
   #1%
      \expandafter\@firstoftwo%
   \else%
      #2%
         \expandafter\expandafter\expandafter\@firstoftwo%
      \else%
         \expandafter\expandafter\expandafter\@secondoftwo%
      \fi%
   \fi%
}

\def\ifyquant@AND#1\fi#2\fi{%
   #1%
      #2%
         \expandafter\expandafter\expandafter\@firstoftwo%
      \else%
         \expandafter\expandafter\expandafter\@secondoftwo%
      \fi%
   \else%
      \expandafter\@secondoftwo%
   \fi%
}

% There are a couple of pgf states that are always set globally and only protected by a scope. We don't want this, so we provide our own grouping - essentially, a scope without the scope in the output. This is because we deem changes to the variables within the group as unlikely, but possible, so it is more economical (in the output) to reset them explicitly only if a change occurred.
\protected\def\yquant@begingroup{%
   \edef\pgfscope@linewidth{\the\pgflinewidth}%
   \let\pgfscope@stroke@color=\pgf@strokecolor@global%
   \let\pgfscope@fill@color=\pgf@fillcolor@global%
   \begingroup%
}

\protected\def\yquant@endgroup{%
   \endgroup%
   \unless\ifdim\pgflinewidth=\pgfscope@linewidth\space%
      % we can be sure that if it is not #1 in this group, it won't be globally, as it is always set globally (unless a bad user breaks this behavior).
      \global\pgflinewidth=\pgfscope@linewidth%
      % but we must make sure that this is also reflected in the PDF (since we didn't actually start a scope). So set it (and this is why we check for equality, as we don't need to pollute the PDF with unnecessary linewidth changes)
      \pgfsys@setlinewidth{\the\pgflinewidth}%
   \fi%
   \unless\ifx\pgfscope@stroke@color\pgf@strokecolor@global%
      \global\let\pgf@strokecolor@global=\pgfscope@stroke@color%
      \expandafter\pgf@setstrokecolor\pgf@strokecolor@global%
   \fi%
   \unless\ifx\pgfscope@fill@color\pgf@fillcolor@global%
      \global\let\pgf@fillcolor@global=\pgfscope@fill@color%
      \expandafter\pgf@setfillcolor\pgf@fillcolor@global%
   \fi%
}

% #1 is a pgf soft path. We extract the maximum x position at the y position specified in #2 and assign it to \dimen0, which is translated to the user coordinate system.
% If the circuit is currently vertical, we extract the minimum y position at the x position specified in #2.
\protected\def\yquant@softpath@extractmaxxat#1#2{%
   \begingroup%
      \dimen0=\yquant@orientation@minus16000pt %
      \dimen2=#2 %
      \pgftransforminvert%
      \let\pgfsyssoftpath@movetotoken=\yquant@softpath@extractmaxxat@moveto%
      \let\pgfsyssoftpath@linetotoken=\yquant@softpath@extractmaxxat@lineto%
      \let\pgfsyssoftpath@curvetosupportatoken=\yquant@softpath@extractmaxxat@curveto%
      \let\pgfsyssoftpath@rectcornertoken=\yquant@softpath@extractmaxxat@rectto%
      \let\pgfsyssoftpath@closepath=\@gobbletwo%
      % the specialroundtoken (undocumented) is \@gobbletwo by default.
      #1%
      \expandafter%
   \endgroup%
   \expandafter\dimen\expandafter0\expandafter=\the\dimen0\relax%
}

% We work with transformed coordinate systems and inversions, so it may happen that we don't end up exactly within a boundary, but are slightly off.
\newdimen\yquant@softpath@extracttol
\yquant@softpath@extracttol=99sp %

\protected\def\yquant@softpath@extractmaxxat@update#1{%
   \ifdim\yquant@orientation@plus\dimen0<\yquant@orientation@plus#1 %
      \dimen0=#1 %
   \fi%
}

\protected\def\yquant@softpath@extractmaxxat@moveto#1#2{%
   \pgfpointtransformed{\pgfqpoint{#1}{#2}}%
   \dimen4=\yquant@pgf@x %
   \dimen6=\yquant@pgf@y %
}

\protected\def\yquant@softpath@extractmaxxat@lineto#1#2{%
   \pgfpointtransformed{\pgfqpoint{#1}{#2}}%
   \ifyquant@OR\ifdim\yquant@orientation@plus\dimen4>\yquant@orientation@plus\dimen0 \fi%
               \ifdim\yquant@orientation@plus\yquant@pgf@x>\yquant@orientation@plus\dimen0 \fi{%
      \ifyquant@AND\unless\ifdim\dimexpr\dimen6-\yquant@softpath@extracttol\relax>\dimen2 \fi%
                   \unless\ifdim\dimexpr\dimen6+\yquant@softpath@extracttol\relax<\dimen2 \fi{%
         \yquant@softpath@extractmaxxat@update{\dimen4}%
      }{%
         \ifdim\dimen6<\dimen2 %
            \unless\ifdim\dimexpr\yquant@pgf@y+\yquant@softpath@extracttol\relax<\dimen2 %
               \expandafter\yquant@softpath@extractmaxxat@update\expandafter{\the\dimexpr%
                  \dimen4+% x0
                  \dimexpr\yquant@pgf@x-\dimen4\relax*% (x1-x0)
                  \dimexpr\dimen2-\dimen6\relax/\dimexpr\yquant@pgf@y-\dimen6\relax% (y-y0)/(y1-y0)
               \relax}%
            \fi%
         \else%
            \unless\ifdim\dimexpr\yquant@pgf@y-\yquant@softpath@extracttol\relax>\dimen2 %
               \expandafter\yquant@softpath@extractmaxxat@update\expandafter{\the\dimexpr%
                  \dimen4+% x0
                  \dimexpr\yquant@pgf@x-\dimen4\relax*% (x1-x0)
                  \dimexpr\dimen2-\dimen6\relax/\dimexpr\yquant@pgf@y-\dimen6\relax% (y-y0)/(y1-y0)
               \relax}%
            \fi%
         \fi%
      }%
   }\relax%
   \dimen4=\yquant@pgf@x%
   \dimen6=\yquant@pgf@y%
}

\protected\def\yquant@softpath@extractmaxxat@curveto@checkx{%
   % \dimen11 holds our only candidate for t. Is it within the curve?
   \ifyquant@AND\unless\ifdim\dimen11<0pt \fi\unless\ifdim\dimen11>1pt \fi{%
      % it is. \dimen4: x0, \pgf@xa: xa, \pgf@xb: xb, \pgf@xc: x1
      \begingroup%
         \dimen12=\dimexpr1pt-\dimen11\relax% 1 - t
         \dimen13=\dimexpr\dimen11*\dimen11/65536\relax% t^2
         \dimen14=\dimexpr\dimen12*\dimen12/65536\relax% (1 - t)^2
         \dimen255=\dimexpr\dimen13*\dimen11/65536*\pgf@xc/65536+% t^3 x1
                           3\dimen13*\dimen12/65536*\pgf@xb/65536+% t^2(1 - t) xb
                           \dimen14*\dimen12/65536*\dimen4/65536+% (1 - t)^3 x0
                           3\dimen11*\dimen14/65536*\pgf@xa/65536% 3t(1 - t)^2 xa
                   \relax%
         \expandafter%
      \endgroup%
      \expandafter\yquant@softpath@extractmaxxat@update\expandafter{\the\dimen255}%
   }\relax%
}

\protected\def\yquant@softpath@extractmaxxat@curveto#1#2\pgfsyssoftpath@curvetosupportbtoken#3#4\pgfsyssoftpath@curvetotoken#5#6{%
   % There's really no good way to do this apart from solving the Bézier curve (a third-order polynomial). Let's do it. (Yes, this is inefficient, but if someone substitutes the rectangular box of a subcircuit by a more fancy design, this is not our fault).
   % Parametrized by t, the x coordinates of the curve are
   % x0 + 3 (xa - x0) t + 3 (x0 - 2xa + xb) t^2 + (3xa - 3xb + x1 - x0) t^3
   % where x0 = \dimen4 (the moveto point), xa = #1, xb = #3, x1 = #5.
   % Likewise for y:
   %       y0 = \dimen6 (the moveto point), ya = #2, yb = #4, y1 = #6.
   \pgfpointtransformed{\pgfqpoint{#1}{#2}}%
   \pgf@xa=\yquant@pgf@x%
   \pgf@ya=\yquant@pgf@y%
   \pgfpointtransformed{\pgfqpoint{#3}{#4}}%
   \pgf@xb=\yquant@pgf@x%
   \pgf@yb=\yquant@pgf@y%
   \pgfpointtransformed{\pgfqpoint{#5}{#6}}%
   \pgf@xc=\yquant@pgf@x%
   \pgf@yc=\yquant@pgf@y%
   % We first solve the third-order polynomial for t using the y value, then plug it back into the x value.
   % TODO: this is accurate to approx. 3 digits (so we don't use \yquant@softpath@extracttol, but much higher tolerances). Can this be improved by reformulating Cardanos formula to involve less divisions?
   \begingroup%
      % We need so many dimensions that we break with TeX's convention for their use.
      % for the multiplications with and divisions by dimensions, we exploit that eTeX fuses muldiv to 64 bits. Further note that each dimension has a scaling factor of 65536 for sp<->pt conversion. This is why don't factor out divisions (which would be more efficient, but not give the benefit of 64bit accuracy).
      % a = 3(ya - yb) + (y1 - y0)
      \dimen1=\dimexpr3\pgf@ya-3\pgf@yb+\pgf@yc-\dimen6\relax%
      \ifyquant@AND\ifdim\dimen1<1pt \fi\ifdim\dimen1>-1pt \fi{%
         \dimen1=0pt % this is almost or exactly a quadratic curve
         % this is only a quadratic curve!
         % b = 3(y0 - 2ya + yb)
         \dimen3=3\dimexpr\dimen6-2\pgf@ya+\pgf@yb\relax%
         % c: 3(ya - y0)
         \dimen5=3\dimexpr\pgf@ya-\dimen6\relax%
         % d: y0 - <desired y>
         \dimen7=\dimexpr\dimen6-\dimen2\relax%
         \ifyquant@AND\ifdim\dimen3<1pt \fi\ifdim\dimen3>-1pt \fi{%
            % this is almost a linear curve!
            \dimen11=\dimexpr-\dimen7*65536/\dimen5\relax%
            \yquant@softpath@extractmaxxat@curveto@checkx%
            \expandafter\@gobble%
         }{%
            % check the discriminant of the equation
            \dimen8=\dimexpr\dimen3*\dimen3/65536-4\dimen3*\dimen7/65536\relax%
            \unless\ifdim\dimen8<0pt%
               % there are two potential candidates, (-c +- sqrt(c^2 - 4b d))/2b
               \pgfmathsqrt@{\the\dimen8\@gobbletwo}%
               \dimen11=\dimexpr\dimexpr-\dimen5+\pgfmathresult pt\relax*65536/%
                                \dimexpr2\dimen3\relax\relax%
               \yquant@softpath@extractmaxxat@curveto@checkx%
               \dimen11=\dimexpr\dimexpr-\dimen5-\pgfmathresult pt\relax*65536/%
                                \dimexpr2\dimen3\relax\relax%
               \yquant@softpath@extractmaxxat@curveto@checkx%
            \fi%
         }%
      }{%
         % We will simplify by directly dividing all coefficients by a
         % b = 3(y0 - 2ya + yb)
         \dimen3=\dimexpr3\dimexpr\dimen6-2\pgf@ya+\pgf@yb\relax*65536/\dimen1\relax%
         % c: 3(ya - y0)
         \dimen5=\dimexpr3\dimexpr\pgf@ya-\dimen6\relax*65536/\dimen1\relax%
         % d: y0 - <desired y>
         \dimen7=\dimexpr\dimexpr\dimen6-\dimen2\relax*65536/\dimen1\relax%
         % Note that now our a value (\dimen1) is no longer needed, it is one.
         % check the discriminant of the equation
         % Q = (3c - b^2)/9
         \dimen8=\dimexpr\dimexpr3\dimen5-\dimen3*\dimen3/65536\relax/9\relax%
         % R = (9bc - 27d - 2b^3)/54 = bc/6 - d/2 - b^3/27
         \dimen9=\dimexpr\dimen3*\dimen5/393216-% 6*65536
                          .5\dimen7-%
                          \dimen3*\dimen3/65536*\dimen3/1769472% 27*65536
                  \relax%
         % D = Q^3 + R^2
         \dimen10=\dimexpr\dimen8*\dimen8/65536*\dimen8/65536+\dimen9*\dimen9/65536\relax%
         \ifdim\dimen10>0pt %
            % only one real root: y_1 = S + T - b/3a
            % S = cbrt(R + sqrt(Q^3 + R^2))
            % T = cbrt(R - sqrt(Q^3 + R^2))
            \pgfmathsqrt@{\the\dimen10\@gobbletwo}%
            \dimen12=\dimexpr\dimen9+\pgfmathresult pt\relax%
            \dimen13=\dimexpr\dimen9-\pgfmathresult pt\relax%
            \ifdim\dimen12>0pt %
               \pgfmathpow@{\the\dimen12\@gobbletwo}{.3333333333}%
               \dimen11=\pgfmathresult pt %
            \else%
               \pgfmathpow@{\the\dimexpr-\dimen12\relax\@gobbletwo}{.3333333333}%
               \dimen11=-\pgfmathresult pt %
            \fi%
            \ifdim\dimen13>0pt %
               \pgfmathpow@{\the\dimen13\@gobbletwo}{.3333333333}%
               \dimen11=\dimexpr\dimen11+\pgfmathresult pt-.33333333333\dimen3\relax%
            \else%
               \pgfmathpow@{\the\dimexpr-\dimen13\relax\@gobbletwo}{.3333333333}%
               \dimen11=\dimexpr\dimen11-\pgfmathresult pt-.33333333333\dimen3\relax%
            \fi%
            \yquant@softpath@extractmaxxat@curveto@checkx%
         \else%
            \ifdim\dimen10=0pt %
               % easiest case, three real roots, two of which are equal:
               % y_1 = 2cbrt(R) - b/3a
               % y_2, x_3 = -cbrt(R) - b/3a
               \ifdim\dimen9>0pt %
                  \pgfmathpow@{\the\dimen9\@gobbletwo}{.3333333333}%
                  \dimen15=\pgfmathresult pt %
               \else%
                  \pgfmathpow@{\the\dimexpr-\dimen9\relax\@gobbletwo}{.3333333333}%
                  \dimen15=-\pgfmathresult pt %
               \fi%
               \dimen11=\dimexpr2\dimen15-.33333333333\dimen3\relax%
               \yquant@softpath@extractmaxxat@curveto@checkx%
               % check the next candidate
               \dimen11=\dimexpr-\dimen15-.33333333333\dimen3\relax%
               \yquant@softpath@extractmaxxat@curveto@checkx%
            \else%
               % nastiest case, three distinct real roots which we can find only by taking a complex-valued cube root.
               % p + i q = cbrt(R + i sqrt(|D|))
               \pgfmathsqrt@{\the\dimexpr-\dimen10\relax\@gobbletwo}%
               \dimen10=\pgfmathresult pt %
               % Let us first find the absolute value
               \dimen12=\dimexpr\dimen9*\dimen9/65536+\dimen10*\dimen10/65536\relax%
               \pgfmathpow@{\the\dimen12\@gobbletwo}{.1666666667}%
               \dimen12=\pgfmathresult pt%
               % then we need 1/3 the argument of R + i sqrt(|D|).
               \pgfmathatantwo@{\the\dimen10\@gobbletwo}{\the\dimen9\@gobbletwo}%
               \dimen13=.3333333333\dimexpr\pgfmathresult pt\relax%
               % and then the real and imaginary parts as cosine and sine.
               \pgfmathcos@{\the\dimen13\@gobbletwo}%
               \dimen14=\dimexpr\pgfmathresult\dimen12\relax%
               \pgfmathsin@{\the\dimen13\@gobbletwo}%
               \dimen15=\dimexpr\pgfmathresult\dimen12\relax%
               % Now the candidates are
               % y_1 = 2p - b/3a
               % y_2 = -p - sqrt(3)q - b/3a
               % y_3 = -p + sqrt(3)q - b/3a
               \dimen11=\dimexpr2\dimen14-.33333333333\dimen3\relax%
               \yquant@softpath@extractmaxxat@curveto@checkx%
               \dimen11=\dimexpr-\dimen14-1.732050808\dimen15-.33333333333\dimen3\relax%
               \yquant@softpath@extractmaxxat@curveto@checkx%
               \dimen11=\dimexpr-\dimen14+1.732050808\dimen15-.33333333333\dimen3\relax%
               \yquant@softpath@extractmaxxat@curveto@checkx%
            \fi%
         \fi%
      }%
      % Now after all these calculations, \dimen0 was updated within the group. Make available outside.
      \expandafter%
   \endgroup%
   \expandafter\dimen\expandafter0\expandafter=\the\dimen0\relax%
   \dimen4=\pgf@xc %
   \dimen6=\pgf@yc %
}

\protected\def\yquant@softpath@extractmaxxat@rectto#1#2\pgfsyssoftpath@rectsizetoken#3#4{%
   % #1: lower left x, #2: lower left y, #3: width, #4: height
   \pgfpointtransformed{\pgfqpoint{#1}{#2}}%
   \pgf@xa=\yquant@pgf@x%
   \pgf@ya=\yquant@pgf@y%
   \pgfpointtransformed{\pgfqpoint{\dimexpr#1+#3\relax}{\dimexpr#2+#4\relax}}%
   % (\pgf@xa, \pgf@ya) one corner, (\pgf@x, \pgf@y) other corner
   % We should include some tolerance; the transform inversion is not exact.
   \ifdim\yquant@pgf@y>\pgf@ya %
      \unless\ifdim\dimexpr\pgf@ya-\yquant@softpath@extracttol\relax>\dimen2 %
         \unless\ifdim\dimexpr\yquant@pgf@y+\yquant@softpath@extracttol\relax<\dimen2 %
            \ifdim\yquant@orientation@plus\yquant@pgf@x>\yquant@orientation@plus\pgf@xa %
               \yquant@softpath@extractmaxxat@update\yquant@pgf@x%
            \else%
               \yquant@softpath@extractmaxxat@update\pgf@xa%
            \fi%
         \fi%
      \fi%
   \else%
      \unless\ifdim\dimexpr\pgf@ya+\yquant@softpath@extracttol\relax<\dimen2 %
         \unless\ifdim\dimexpr\yquant@pgf@y-\yquant@softpath@extracttol\relax>\dimen2 %
            \ifdim\yquant@orientation@plus\yquant@pgf@x>\yquant@orientation@plus\pgf@xa %
               \yquant@softpath@extractmaxxat@update\yquant@pgf@x%
            \else%
               \yquant@softpath@extractmaxxat@update\pgf@xa%
            \fi%
         \fi%
      \fi%
   \fi%
}