%%
%% This is file `xintcore.sty',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% xint.dtx  (with options: `xintcore')
%% 
%% IMPORTANT NOTICE:
%% 
%% For the copyright see the source file.
%% 
%% Any modified versions of this file must be renamed
%% with new filenames distinct from xintcore.sty.
%% 
%% For distribution of the original source see the terms
%% for copying and modification in the file xint.dtx.
%% 
%% This generated file may be distributed as long as the
%% original source files, as listed above, are part of the
%% same distribution. (The sources need not necessarily be
%% in the same archive or directory.)
%% ---------------------------------------------------------------
%% The xint bundle 1.3d 2019/01/06
%% Copyright (C) 2013-2019 by Jean-Francois Burnol
%% xintcore: Expandable arithmetic on big integers
%% ---------------------------------------------------------------
\begingroup\catcode61\catcode48\catcode32=10\relax%
  \catcode13=5    % ^^M
  \endlinechar=13 %
  \catcode123=1   % {
  \catcode125=2   % }
  \catcode64=11   % @
  \catcode35=6    % #
  \catcode44=12   % ,
  \catcode45=12   % -
  \catcode46=12   % .
  \catcode58=12   % :
  \let\z\endgroup
  \expandafter\let\expandafter\x\csname ver@xintcore.sty\endcsname
  \expandafter\let\expandafter\w\csname ver@xintkernel.sty\endcsname
  \expandafter
    \ifx\csname PackageInfo\endcsname\relax
      \def\y#1#2{\immediate\write-1{Package #1 Info: #2.}}%
    \else
      \def\y#1#2{\PackageInfo{#1}{#2}}%
    \fi
  \expandafter
  \ifx\csname numexpr\endcsname\relax
     \y{xintcore}{\numexpr not available, aborting input}%
     \aftergroup\endinput
  \else
    \ifx\x\relax   % plain-TeX, first loading of xintcore.sty
      \ifx\w\relax % but xintkernel.sty not yet loaded.
         \def\z{\endgroup\input xintkernel.sty\relax}%
      \fi
    \else
      \def\empty {}%
      \ifx\x\empty % LaTeX, first loading,
      % variable is initialized, but \ProvidesPackage not yet seen
          \ifx\w\relax % xintkernel.sty not yet loaded.
            \def\z{\endgroup\RequirePackage{xintkernel}}%
          \fi
      \else
        \aftergroup\endinput % xintkernel already loaded.
      \fi
    \fi
  \fi
\z%
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xintcore}%
  [2019/01/06 1.3d Expandable arithmetic on big integers (JFB)]%
\csname XINT_Clamped_istrapped\endcsname
\csname XINT_ConversionSyntax_istrapped\endcsname
\csname XINT_DivisionByZero_istrapped\endcsname
\csname XINT_DivisionImpossible_istrapped\endcsname
\csname XINT_DivisionUndefined_istrapped\endcsname
\csname XINT_InvalidOperation_istrapped\endcsname
\csname XINT_Overflow_istrapped\endcsname
\csname XINT_Underflow_istrapped\endcsname
\catcode`- 11
\def\XINT_ConversionSyntax-signal  {{InvalidOperation}}%
\let\XINT_DivisionImpossible-signal\XINT_ConversionSyntax-signal
\let\XINT_DivisionUndefined-signal \XINT_ConversionSyntax-signal
\let\XINT_InvalidContext-signal    \XINT_ConversionSyntax-signal
\catcode`- 12
\def\XINT_signalcondition #1{\expandafter\XINT_signalcondition_a
    \romannumeral0\ifcsname XINT_#1-signal\endcsname
                    \xint_dothis{\csname XINT_#1-signal\endcsname}%
                  \fi\xint_orthat{{#1}}{#1}}%
\def\XINT_signalcondition_a #1#2#3#4#5{% copied over from Python Decimal module
    \ifcsname XINT_#1_isignoredflag\endcsname
       \xint_dothis{\csname XINT_#1.handler\endcsname {#4}}%
    \fi
    \expandafter\xint_gobble_i\csname XINT_#1Flag_ON\endcsname
    \unless\ifcsname XINT_#1_istrapped\endcsname
       \xint_dothis{\csname XINT_#2.handler\endcsname {#4}}%
    \fi
    \xint_orthat{%
       % the flag raised is named after the signal #1, but we show condition #2
       \XINT_expandableerror{#2 (hit <RET> thrice)}%
       \XINT_expandableerror{#3}%
       \XINT_expandableerror{next: #5}%
       % not for X3.274
       %\XINT_expandableerror{<RET>, or I\xintUse{...}<RET>, or I\xintCTRLC<RET>}%
       \xint_stop_atfirstofone{#5}%
    }%
}%
%% \let\xintUse\xint_stop_atfirstofthree % defined in xint.sty
\def\XINT_ifFlagRaised #1{%
    \ifcsname XINT_#1Flag_ON\endcsname
        \expandafter\xint_firstoftwo
    \else
        \expandafter\xint_secondoftwo
    \fi}%
\def\XINT_resetFlag #1%
    {\expandafter\let\csname XINT_#1Flag_ON\endcsname\XINT_undefined}%
\def\XINT_resetFlags {% WIP
    \XINT_resetFlag{InvalidOperation}% also from DivisionUndefined
    \XINT_resetFlag{DivisionByZero}%
    \XINT_resetFlag{Underflow}% (\xintiiPow with negative exponent)
    \XINT_resetFlag{Overflow}%   not encountered so far in xint code 1.2l
    % .. others ..
}%
\def\XINT_RaiseFlag #1{\expandafter\xint_gobble_i\csname XINT_#1Flag_ON\endcsname}%
\catcode`. 11
\let\XINT_Clamped.handler\xint_firstofone % WIP
\def\XINT_InvalidOperation.handler#1{_NaN}% WIP
\def\XINT_ConversionSyntax.handler#1{_NaN}% WIP
\def\XINT_DivisionByZero.handler#1{_SignedInfinity(#1)}% WIP
\def\XINT_DivisionImpossible.handler#1{_NaN}% WIP
\def\XINT_DivisionUndefined.handler#1{_NaN}%  WIP
\let\XINT_Inexact.handler\xint_firstofone  %  WIP
\def\XINT_InvalidContext.handler#1{_NaN}%     WIP
\let\XINT_Rounded.handler\xint_firstofone  %  WIP
\let\XINT_Subnormal.handler\xint_firstofone%  WIP
\def\XINT_Overflow.handler#1{_NaN}%  WIP
\def\XINT_Underflow.handler#1{_NaN}% WIP
\catcode`. 12
\ifdefined\m@ne\let\xint_c_mone\m@ne
          \else\csname newcount\endcsname\xint_c_mone \xint_c_mone -1 \fi
\ifdefined\xint_c_x^viii\else
\csname newcount\endcsname\xint_c_x^viii \xint_c_x^viii   100000000
\fi
\ifdefined\xint_c_x^ix\else
\csname newcount\endcsname\xint_c_x^ix   \xint_c_x^ix    1000000000
\fi
\newcount\xint_c_x^viii_mone        \xint_c_x^viii_mone    99999999
\newcount\xint_c_xii_e_viii          \xint_c_xii_e_viii  1200000000
\newcount\xint_c_xi_e_viii_mone  \xint_c_xi_e_viii_mone  1099999999
\def\XINT_cuz_small#1{%
\def\XINT_cuz_small ##1##2##3##4##5##6##7##8%
{%
    \expandafter#1\the\numexpr ##1##2##3##4##5##6##7##8\relax
}}\XINT_cuz_small{ }%
\def\xintiNum {\romannumeral0\xintinum }%
\def\xintinum #1%
{%
    \expandafter\XINT_num_cleanup\the\numexpr\expandafter\XINT_num_loop
    \romannumeral`&&@#1\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
\def\xintNum {\romannumeral0\xintnum }%
\let\xintnum\xintinum
\def\XINT_num #1%
{%
    \expandafter\XINT_num_cleanup\the\numexpr\XINT_num_loop
    #1\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
\def\XINT_num_loop #1#2#3#4#5#6#7#8#9%
{%
    \xint_gob_til_xint: #9\XINT_num_end\xint:
    #1#2#3#4#5#6#7#8#9%
    \ifnum \numexpr #1#2#3#4#5#6#7#8#9+\xint_c_ = \xint_c_
      \expandafter\XINT_num_loop
    \else
     \expandafter\relax
    \fi
}%
\def\XINT_num_end\xint:#1\xint:{#1+\xint_c_\xint:}% empty input ok
\def\XINT_num_cleanup #1\xint:#2\Z { #1}%
\def\xintiiSgn {\romannumeral0\xintiisgn }%
\def\xintiisgn #1%
{%
    \expandafter\XINT_sgn \romannumeral`&&@#1\xint:
}%
\def\XINT_sgn #1#2\xint:
{%
    \xint_UDzerominusfork
      #1-{ 0}%
      0#1{-1}%
       0-{ 1}%
    \krof
}%
\def\XINT_Sgn #1#2\xint:
{%
    \xint_UDzerominusfork
      #1-{0}%
      0#1{-1}%
       0-{1}%
    \krof
}%
\def\XINT_cntSgn #1#2\xint:
{%
    \xint_UDzerominusfork
      #1-\xint_c_
      0#1\xint_c_mone
       0-\xint_c_i
    \krof
}%
\def\xintiiOpp {\romannumeral0\xintiiopp }%
\def\xintiiopp #1%
{%
    \expandafter\XINT_opp \romannumeral`&&@#1%
}%
\def\XINT_Opp #1{\romannumeral0\XINT_opp #1}%
\def\XINT_opp #1%
{%
    \xint_UDzerominusfork
      #1-{ 0}%      zero
      0#1{ }%     negative
       0-{ -#1}%  positive
    \krof
}%
\def\xintiiAbs {\romannumeral0\xintiiabs }%
\def\xintiiabs #1%
{%
    \expandafter\XINT_abs \romannumeral`&&@#1%
}%
\def\XINT_abs #1%
{%
    \xint_UDsignfork
      #1{ }%
       -{ #1}%
    \krof
}%
\def\xintFDg {\romannumeral0\xintfdg }%
\def\xintfdg #1{\expandafter\XINT_fdg \romannumeral`&&@#1\xint:\Z}%
\def\XINT_FDg #1%
   {\romannumeral0\expandafter\XINT_fdg\romannumeral`&&@\xintnum{#1}\xint:\Z }%
\def\XINT_fdg #1#2#3\Z
{%
    \xint_UDzerominusfork
      #1-{ 0}%   zero
      0#1{ #2}%  negative
       0-{ #1}%  positive
    \krof
}%
\def\xintLDg {\romannumeral0\xintldg }%
\def\xintldg #1{\expandafter\XINT_ldg_fork\romannumeral`&&@#1%
    \XINT_ldg_c{}{}{}{}{}{}{}{}\xint_bye\relax}%
\def\XINT_ldg_fork #1%
{%
    \xint_UDsignfork
      #1\XINT_ldg
       -{\XINT_ldg#1}%
    \krof
}%
\def\XINT_ldg #1{%
\def\XINT_ldg ##1##2##3##4##5##6##7##8##9%
   {\expandafter#1%
    \the\numexpr##9##8##7##6##5##4##3##2##1*\xint_c_+\XINT_ldg_a##9}%
}\XINT_ldg{ }%
\def\XINT_ldg_a#1#2{\XINT_ldg_cbye#2\XINT_ldg_d#1\XINT_ldg_c\XINT_ldg_b#2}%
\def\XINT_ldg_b#1#2#3#4#5#6#7#8#9{#9#8#7#6#5#4#3#2#1*\xint_c_+\XINT_ldg_a#9}%
\def\XINT_ldg_c    #1#2\xint_bye{#1}%
\def\XINT_ldg_cbye #1\XINT_ldg_c{}%
\def\XINT_ldg_d#1#2\xint_bye{#1}%
\def\xintDouble {\romannumeral0\xintdouble}%
\def\xintdouble #1{\expandafter\XINT_dbl_fork\romannumeral`&&@#1%
                   \xint_bye2345678\xint_bye*\xint_c_ii\relax}%
\def\XINT_dbl_fork #1%
{%
    \xint_UDsignfork
     #1\XINT_dbl_neg
      -\XINT_dbl
    \krof #1%
}%
\def\XINT_dbl_neg-{\expandafter-\romannumeral0\XINT_dbl}%
\def\XINT_dbl #1{%
\def\XINT_dbl ##1##2##3##4##5##6##7##8%
   {\expandafter#1\the\numexpr##1##2##3##4##5##6##7##8\XINT_dbl_a}%
}\XINT_dbl{ }%
\def\XINT_dbl_a #1#2#3#4#5#6#7#8%
   {\expandafter\XINT_dbl_e\the\numexpr 1#1#2#3#4#5#6#7#8\XINT_dbl_a}%
\def\XINT_dbl_e#1{*\xint_c_ii\if#13+\xint_c_i\fi\relax}%
\def\xintHalf {\romannumeral0\xinthalf}%
\def\xinthalf #1{\expandafter\XINT_half_fork\romannumeral`&&@#1%
    \xint_bye\xint_Bye345678\xint_bye
    *\xint_c_v+\xint_c_v)/\xint_c_x-\xint_c_i\relax}%
\def\XINT_half_fork #1%
{%
    \xint_UDsignfork
     #1\XINT_half_neg
      -\XINT_half
    \krof #1%
}%
\def\XINT_half_neg-{\xintiiopp\XINT_half}%
\def\XINT_half #1{%
\def\XINT_half ##1##2##3##4##5##6##7##8%
   {\expandafter#1\the\numexpr(##1##2##3##4##5##6##7##8\XINT_half_a}%
}\XINT_half{ }%
\def\XINT_half_a#1{\xint_Bye#1\xint_bye\XINT_half_b#1}%
\def\XINT_half_b #1#2#3#4#5#6#7#8%
   {\expandafter\XINT_half_e\the\numexpr(1#1#2#3#4#5#6#7#8\XINT_half_a}%
\def\XINT_half_e#1{*\xint_c_v+#1-\xint_c_v)\relax}%
\def\xintInc {\romannumeral0\xintinc}%
\def\xintinc #1{\expandafter\XINT_inc_fork\romannumeral`&&@#1%
                \xint_bye23456789\xint_bye+\xint_c_i\relax}%
\def\XINT_inc_fork #1%
{%
    \xint_UDsignfork
      #1\XINT_inc_neg
       -\XINT_inc
    \krof #1%
}%
\def\XINT_inc_neg-#1\xint_bye#2\relax
   {\xintiiopp\XINT_dec #1\XINT_dec_bye234567890\xint_bye}%
\def\XINT_inc #1{%
\def\XINT_inc ##1##2##3##4##5##6##7##8##9%
   {\expandafter#1\the\numexpr##1##2##3##4##5##6##7##8##9\XINT_inc_a}%
}\XINT_inc{ }%
\def\XINT_inc_a #1#2#3#4#5#6#7#8#9%
   {\expandafter\XINT_inc_e\the\numexpr 1#1#2#3#4#5#6#7#8#9\XINT_inc_a}%
\def\XINT_inc_e#1{\if#12+\xint_c_i\fi\relax}%
\def\xintDec {\romannumeral0\xintdec}%
\def\xintdec #1{\expandafter\XINT_dec_fork\romannumeral`&&@#1%
                \XINT_dec_bye234567890\xint_bye}%
\def\XINT_dec_fork #1%
{%
    \xint_UDsignfork
      #1\XINT_dec_neg
       -\XINT_dec
    \krof #1%
}%
\def\XINT_dec_neg-#1\XINT_dec_bye#2\xint_bye
   {\expandafter-%
    \romannumeral0\XINT_inc #1\xint_bye23456789\xint_bye+\xint_c_i\relax}%
\def\XINT_dec #1{%
\def\XINT_dec ##1##2##3##4##5##6##7##8##9%
   {\expandafter#1\the\numexpr##1##2##3##4##5##6##7##8##9\XINT_dec_a}%
}\XINT_dec{ }%
\def\XINT_dec_a #1#2#3#4#5#6#7#8#9%
   {\expandafter\XINT_dec_e\the\numexpr 1#1#2#3#4#5#6#7#8#9\XINT_dec_a}%
\def\XINT_dec_bye #1\XINT_dec_a#2#3\xint_bye
         {\if#20-\xint_c_ii\relax+\else-\fi\xint_c_i\relax}%
\def\XINT_dec_e#1{\unless\if#11\xint_dothis{-\xint_c_i#1}\fi\xint_orthat\relax}%
\def\xintDSL {\romannumeral0\xintdsl }%
\def\xintdsl #1{\expandafter\XINT_dsl\romannumeral`&&@#10}%
\def\XINT_dsl#1{%
\def\XINT_dsl ##1{\xint_gob_til_zero ##1\xint_dsl_zero 0#1##1}%
}\XINT_dsl{ }%
\def\xint_dsl_zero 0 0{ }%
\def\xintDSR{\romannumeral0\xintdsr}%
\def\xintdsr #1{\expandafter\XINT_dsr_fork\romannumeral`&&@#1%
    \xint_bye\xint_Bye3456789\xint_bye+\xint_c_v)/\xint_c_x-\xint_c_i\relax}%
\def\XINT_dsr_fork #1%
{%
    \xint_UDsignfork
      #1\XINT_dsr_neg
       -\XINT_dsr
    \krof #1%
}%
\def\XINT_dsr_neg-{\xintiiopp\XINT_dsr}%
\def\XINT_dsr #1{%
\def\XINT_dsr ##1##2##3##4##5##6##7##8##9%
   {\expandafter#1\the\numexpr(##1##2##3##4##5##6##7##8##9\XINT_dsr_a}%
}\XINT_dsr{ }%
\def\XINT_dsr_a#1{\xint_Bye#1\xint_bye\XINT_dsr_b#1}%
\def\XINT_dsr_b #1#2#3#4#5#6#7#8#9%
   {\expandafter\XINT_dsr_e\the\numexpr(1#1#2#3#4#5#6#7#8#9\XINT_dsr_a}%
\def\XINT_dsr_e #1{)\relax}%
\def\xintDSRr{\romannumeral0\xintdsrr}%
\def\xintdsrr #1{\expandafter\XINT_dsrr_fork\romannumeral`&&@#1%
                \xint_bye\xint_Bye3456789\xint_bye/\xint_c_x\relax}%
\def\XINT_dsrr_fork #1%
{%
    \xint_UDsignfork
      #1\XINT_dsrr_neg
       -\XINT_dsrr
    \krof #1%
}%
\def\XINT_dsrr_neg-{\xintiiopp\XINT_dsrr}%
\def\XINT_dsrr #1{%
\def\XINT_dsrr ##1##2##3##4##5##6##7##8##9%
   {\expandafter#1\the\numexpr##1##2##3##4##5##6##7##8##9\XINT_dsrr_a}%
}\XINT_dsrr{ }%
\def\XINT_dsrr_a#1{\xint_Bye#1\xint_bye\XINT_dsrr_b#1}%
\def\XINT_dsrr_b #1#2#3#4#5#6#7#8#9%
   {\expandafter\XINT_dsrr_e\the\numexpr1#1#2#3#4#5#6#7#8#9\XINT_dsrr_a}%
\let\XINT_dsrr_e\XINT_inc_e
\def\XINT_cuz #1{%
\def\XINT_cuz {\expandafter#1\the\numexpr\XINT_cuz_loop}%
}\XINT_cuz{ }%
\def\XINT_cuz_loop #1#2#3#4#5#6#7#8#9%
{%
    #1#2#3#4#5#6#7#8%
       \xint_gob_til_R #9\XINT_cuz_hitend\R
       \ifnum #1#2#3#4#5#6#7#8>\xint_c_
             \expandafter\XINT_cuz_cleantoend
       \else\expandafter\XINT_cuz_loop
       \fi #9%
}%
\def\XINT_cuz_hitend\R #1\R{\relax}%
\def\XINT_cuz_cleantoend #1\R{\relax #1}%
\def\XINT_cuz_byviii #1#2#3#4#5#6#7#8#9%
{%
    \xint_gob_til_R #9\XINT_cuz_byviii_e \R
    \xint_gob_til_eightzeroes #1#2#3#4#5#6#7#8\XINT_cuz_byviii_z 00000000%
    \XINT_cuz_byviii_done #1#2#3#4#5#6#7#8#9%
}%
\def\XINT_cuz_byviii_z 00000000\XINT_cuz_byviii_done 00000000{\XINT_cuz_byviii}%
\def\XINT_cuz_byviii_done #1\R { #1}%
\def\XINT_cuz_byviii_e\R #1\XINT_cuz_byviii_done #2\R{ #2}%
\def\XINT_unsep_loop #1!#2!#3!#4!#5!#6!#7!#8!#9!%
{%
    \expandafter\XINT_unsep_clean
    \the\numexpr #1\expandafter\XINT_unsep_clean
    \the\numexpr #2\expandafter\XINT_unsep_clean
    \the\numexpr #3\expandafter\XINT_unsep_clean
    \the\numexpr #4\expandafter\XINT_unsep_clean
    \the\numexpr #5\expandafter\XINT_unsep_clean
    \the\numexpr #6\expandafter\XINT_unsep_clean
    \the\numexpr #7\expandafter\XINT_unsep_clean
    \the\numexpr #8\expandafter\XINT_unsep_clean
    \the\numexpr #9\XINT_unsep_loop
}%
\def\XINT_unsep_clean 1{\relax}%
\def\XINT_unsep_cuzsmall
{%
    \expandafter\XINT_unsep_cuzsmall_x\the\numexpr0\XINT_unsep_loop
}%
\def\XINT_unsep_cuzsmall_x #1{%
\def\XINT_unsep_cuzsmall_x 0##1##2##3##4##5##6##7##8%
{%
    \expandafter#1\the\numexpr ##1##2##3##4##5##6##7##8\relax
}}\XINT_unsep_cuzsmall_x{ }%
\def\XINT_div_unsepQ_delim {\xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax\Z}%
\def\XINT_div_unsepQ
{%
    \expandafter\XINT_div_unsepQ_x\the\numexpr0\XINT_unsep_loop
}%
\def\XINT_div_unsepQ_x #1{%
\def\XINT_div_unsepQ_x 0##1##2##3##4##5##6##7##8##9%
{%
    \xint_gob_til_Z ##9\XINT_div_unsepQ_one\Z
    \xint_gob_til_eightzeroes ##1##2##3##4##5##6##7##8\XINT_div_unsepQ_y 00000000%
    \expandafter#1\the\numexpr ##1##2##3##4##5##6##7##8\relax ##9%
}}\XINT_div_unsepQ_x{ }%
\def\XINT_div_unsepQ_y #1{%
\def\XINT_div_unsepQ_y ##1\relax ##2##3##4##5##6##7##8##9%
{%
    \expandafter#1\the\numexpr ##2##3##4##5##6##7##8##9\relax
}}\XINT_div_unsepQ_y{ }%
\def\XINT_div_unsepQ_one#1\expandafter{\expandafter}%
\def\XINT_div_unsepR
{%
    \expandafter\XINT_div_unsepR_x\the\numexpr0\XINT_unsep_loop
}%
\def\XINT_div_unsepR_x#1{%
\def\XINT_div_unsepR_x 0{\expandafter#1\the\numexpr\XINT_cuz_loop}%
}\XINT_div_unsepR_x{ }%
\def\XINT_zeroes_forviii #1#2#3#4#5#6#7#8%
{%
    \xint_gob_til_R #8\XINT_zeroes_forviii_end\R\XINT_zeroes_forviii
}%
\def\XINT_zeroes_forviii_end#1{%
\def\XINT_zeroes_forviii_end\R\XINT_zeroes_forviii ##1##2##3##4##5##6##7##8##9\W
{%
    \expandafter#1\xint_gob_til_one ##2##3##4##5##6##7##8%
}}\XINT_zeroes_forviii_end{ }%
\def\XINT_sepbyviii_Z #1#2#3#4#5#6#7#8%
{%
    1#1#2#3#4#5#6#7#8\expandafter!\the\numexpr\XINT_sepbyviii_Z
}%
\def\XINT_sepbyviii_Z_end #1\relax {;!}%
\def\XINT_sepbyviii_andcount
{%
    \expandafter\XINT_sepbyviii_andcount_a\the\numexpr\XINT_sepbyviii
}%
\def\XINT_sepbyviii #1#2#3#4#5#6#7#8%
{%
    1#1#2#3#4#5#6#7#8\expandafter!\the\numexpr\XINT_sepbyviii
}%
\def\XINT_sepbyviii_end #1\relax {\relax\XINT_sepbyviii_andcount_end!}%
\def\XINT_sepbyviii_andcount_a {\XINT_sepbyviii_andcount_b \xint_c_\xint:}%
\def\XINT_sepbyviii_andcount_b #1\xint:#2!#3!#4!#5!#6!#7!#8!#9!%
{%
    #2\expandafter!\the\numexpr#3\expandafter!\the\numexpr#4\expandafter
    !\the\numexpr#5\expandafter!\the\numexpr#6\expandafter!\the\numexpr
    #7\expandafter!\the\numexpr#8\expandafter!\the\numexpr#9\expandafter!\the\numexpr
    \expandafter\XINT_sepbyviii_andcount_b\the\numexpr #1+\xint_c_viii\xint:%
}%
\def\XINT_sepbyviii_andcount_end #1\XINT_sepbyviii_andcount_b\the\numexpr
    #2+\xint_c_viii\xint:#3#4\W {\expandafter\xint:\the\numexpr #2+#3\xint:}%
\def\XINT_rsepbyviii #1#2#3#4#5#6#7#8%
{%
    \XINT_rsepbyviii_b {#1#2#3#4#5#6#7#8}%
}%
\def\XINT_rsepbyviii_b #1#2#3#4#5#6#7#8#9%
{%
    #2#3#4#5#6#7#8#9\expandafter!\the\numexpr
    1#1\expandafter\xint:\the\numexpr 1\XINT_rsepbyviii
}%
\def\XINT_rsepbyviii_end_B #1\relax #2#3{#2\xint:}%
\def\XINT_rsepbyviii_end_A #11#2\expandafter #3\relax #4#5{#5!1#2\xint:}%
\def\XINT_sepandrev
{%
    \expandafter\XINT_sepandrev_a\the\numexpr 1\XINT_rsepbyviii
}%
\def\XINT_sepandrev_a {\XINT_sepandrev_b {}}%
\def\XINT_sepandrev_b #1#2\xint:#3\xint:#4\xint:#5\xint:#6\xint:#7\xint:#8\xint:#9\xint:%
{%
    \xint_gob_til_R #9\XINT_sepandrev_end\R
    \XINT_sepandrev_b {#9!#8!#7!#6!#5!#4!#3!#2!#1}%
}%
\def\XINT_sepandrev_end\R\XINT_sepandrev_b #1#2\W {\XINT_sepandrev_done #1}%
\def\XINT_sepandrev_done #11#2!{ }%
\def\XINT_sepandrev_andcount
{%
    \expandafter\XINT_sepandrev_andcount_a\the\numexpr 1\XINT_rsepbyviii
}%
\def\XINT_sepandrev_andcount_a {\XINT_sepandrev_andcount_b 0!{}}%
\def\XINT_sepandrev_andcount_b #1!#2#3\xint:#4\xint:#5\xint:#6\xint:#7\xint:#8\xint:#9\xint:%
{%
    \xint_gob_til_R #9\XINT_sepandrev_andcount_end\R
    \expandafter\XINT_sepandrev_andcount_b \the\numexpr #1+\xint_c_i!%
    {#9!#8!#7!#6!#5!#4!#3!#2}%
}%
\def\XINT_sepandrev_andcount_end\R
    \expandafter\XINT_sepandrev_andcount_b\the\numexpr #1+\xint_c_i!#2#3#4\W
{\expandafter\XINT_sepandrev_andcount_done\the\numexpr #3+\xint_c_xiv*#1!#2}%
\def\XINT_sepandrev_andcount_done#1{%
\def\XINT_sepandrev_andcount_done##1!##21##3!{\expandafter#1\the\numexpr##1-##3\xint:}%
}\XINT_sepandrev_andcount_done{ }%
\def\XINT_rev_nounsep #1#2!#3!#4!#5!#6!#7!#8!#9!%
{%
    \xint_gob_til_R #9\XINT_rev_nounsep_end\R
    \XINT_rev_nounsep {#9!#8!#7!#6!#5!#4!#3!#2!#1}%
}%
\def\XINT_rev_nounsep_end\R\XINT_rev_nounsep #1#2\W {\XINT_rev_nounsep_done #1}%
\def\XINT_rev_nounsep_done #11{ 1}%
\def\XINT_unrevbyviii #11#2!1#3!1#4!1#5!1#6!1#7!1#8!1#9!%
{%
    \xint_gob_til_R #9\XINT_unrevbyviii_a\R
    \XINT_unrevbyviii {#9#8#7#6#5#4#3#2#1}%
}%
\def\XINT_unrevbyviii_a#1{%
\def\XINT_unrevbyviii_a\R\XINT_unrevbyviii ##1##2\W
    {\expandafter#1\romannumeral`&&@\xint_gob_til_sc ##1}%
}\XINT_unrevbyviii_a{ }%
\def\XINT_smallunrevbyviii 1#1!1#2!1#3!1#4!1#5!1#6!1#7!1#8!#9\W%
{%
    \expandafter\XINT_cuz_small\xint_gob_til_sc #8#7#6#5#4#3#2#1%
}%
\def\xintiiAdd   {\romannumeral0\xintiiadd }%
\def\xintiiadd #1{\expandafter\XINT_iiadd\romannumeral`&&@#1\xint:}%
\def\XINT_iiadd #1#2\xint:#3%
{%
    \expandafter\XINT_add_nfork\expandafter#1\romannumeral`&&@#3\xint:#2\xint:
}%
\def\XINT_iadd #1#2\xint:#3%
{%
    \expandafter\XINT_add_nfork\expandafter
    #1\romannumeral0\xintnum{#3}\xint:#2\xint:
}%
\def\XINT_add_fork #1#2\xint:#3\xint:{\XINT_add_nfork #1#3\xint:#2\xint:}%
\def\XINT_add_nfork #1#2%
{%
    \xint_UDzerofork
      #1\XINT_add_firstiszero
      #2\XINT_add_secondiszero
       0{}%
    \krof
    \xint_UDsignsfork
          #1#2\XINT_add_minusminus
           #1-\XINT_add_minusplus
           #2-\XINT_add_plusminus
            --\XINT_add_plusplus
    \krof #1#2%
}%
\def\XINT_add_firstiszero  #1\krof 0#2#3\xint:#4\xint:{ #2#3}%
\def\XINT_add_secondiszero #1\krof #20#3\xint:#4\xint:{ #2#4}%
\def\XINT_add_minusminus   #1#2%
   {\expandafter-\romannumeral0\XINT_add_pp_a {}{}}%
\def\XINT_add_minusplus    #1#2{\XINT_sub_mm_a {}#2}%
\def\XINT_add_plusminus    #1#2%
   {\expandafter\XINT_opp\romannumeral0\XINT_sub_mm_a #1{}}%
\def\XINT_add_pp_a #1#2#3\xint:
{%
  \expandafter\XINT_add_pp_b
      \romannumeral0\expandafter\XINT_sepandrev_andcount
      \romannumeral0\XINT_zeroes_forviii #2#3\R\R\R\R\R\R\R\R{10}0000001\W
      #2#3\XINT_rsepbyviii_end_A 2345678%
          \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
              \R\xint:\xint_c_xii \R\xint:\xint_c_x  \R\xint:\xint_c_viii \R\xint:\xint_c_vi
              \R\xint:\xint_c_iv  \R\xint:\xint_c_ii \R\xint:\xint_c_\W
   \X #1%
}%
\let\XINT_add_plusplus \XINT_add_pp_a
\def\XINT_add_pp_b #1\xint:#2\X #3\xint:
{%
    \expandafter\XINT_add_checklengths
    \the\numexpr #1\expandafter\xint:%
    \romannumeral0\expandafter\XINT_sepandrev_andcount
    \romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
    #3\XINT_rsepbyviii_end_A 2345678%
      \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
              \R\xint:\xint_c_xii \R\xint:\xint_c_x  \R\xint:\xint_c_viii \R\xint:\xint_c_vi
              \R\xint:\xint_c_iv  \R\xint:\xint_c_ii \R\xint:\xint_c_\W
     1;!1;!1;!1;!\W #21;!1;!1;!1;!\W
     1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
}%
\def\XINT_add_checklengths #1\xint:#2\xint:%
{%
    \ifnum #2>#1
       \expandafter\XINT_add_exchange
    \else
       \expandafter\XINT_add_A
    \fi
    #1\xint:#2\xint:%
}%
\def\XINT_add_exchange #1\xint:#2\xint:#3\W #4\W
{%
    \XINT_add_A #2\xint:#1\xint:#4\W #3\W
}%
\def\XINT_add_A #1\xint:#2\xint:%
{%
    \ifnum #1>\xint_c_vi
          \expandafter\XINT_add_aa
    \else \expandafter\XINT_add_aa_small
    \fi
}%
\def\XINT_add_aa {\expandafter\XINT_add_out\the\numexpr\XINT_add_a \xint_c_ii}%
\def\XINT_add_out{\expandafter\XINT_cuz_small\romannumeral0\XINT_unrevbyviii {}}%
\def\XINT_add_aa_small
    {\expandafter\XINT_smallunrevbyviii\the\numexpr\XINT_add_a \xint_c_ii}%
\def\XINT_add_a #1!#2!#3!#4!#5\W
                #6!#7!#8!#9!%
{%
    \XINT_add_b
        #1!#6!#2!#7!#3!#8!#4!#9!%
        #5\W
}%
\def\XINT_add_b #11#2#3!#4!%
{%
    \xint_gob_til_sc #2\XINT_add_bi ;%
    \expandafter\XINT_add_c\the\numexpr#1+1#2#3+#4-\xint_c_ii\xint:%
}%
\def\XINT_add_bi;\expandafter\XINT_add_c
    \the\numexpr#1+#2+#3-\xint_c_ii\xint:#4!#5!#6!#7!#8!#9!\W
{%
    \XINT_add_k #1#3!#5!#7!#9!%
}%
\def\XINT_add_c #1#2\xint:%
{%
    1#2\expandafter!\the\numexpr\XINT_add_d #1%
}%
\def\XINT_add_d #11#2#3!#4!%
{%
    \xint_gob_til_sc #2\XINT_add_di ;%
    \expandafter\XINT_add_e\the\numexpr#1+1#2#3+#4-\xint_c_ii\xint:%
}%
\def\XINT_add_di;\expandafter\XINT_add_e
    \the\numexpr#1+#2+#3-\xint_c_ii\xint:#4!#5!#6!#7!#8\W
{%
    \XINT_add_k #1#3!#5!#7!%
}%
\def\XINT_add_e #1#2\xint:%
{%
    1#2\expandafter!\the\numexpr\XINT_add_f #1%
}%
\def\XINT_add_f #11#2#3!#4!%
{%
    \xint_gob_til_sc #2\XINT_add_fi ;%
    \expandafter\XINT_add_g\the\numexpr#1+1#2#3+#4-\xint_c_ii\xint:%
}%
\def\XINT_add_fi;\expandafter\XINT_add_g
    \the\numexpr#1+#2+#3-\xint_c_ii\xint:#4!#5!#6\W
{%
    \XINT_add_k #1#3!#5!%
}%
\def\XINT_add_g #1#2\xint:%
{%
    1#2\expandafter!\the\numexpr\XINT_add_h #1%
}%
\def\XINT_add_h #11#2#3!#4!%
{%
    \xint_gob_til_sc #2\XINT_add_hi ;%
    \expandafter\XINT_add_i\the\numexpr#1+1#2#3+#4-\xint_c_ii\xint:%
}%
\def\XINT_add_hi;%
    \expandafter\XINT_add_i\the\numexpr#1+#2+#3-\xint_c_ii\xint:#4\W
{%
    \XINT_add_k #1#3!%
}%
\def\XINT_add_i #1#2\xint:%
{%
    1#2\expandafter!\the\numexpr\XINT_add_a #1%
}%
\def\XINT_add_k #1{\if #12\expandafter\XINT_add_ke\else\expandafter\XINT_add_l \fi}%
\def\XINT_add_ke #11;#2\W {\XINT_add_kf #11;!}%
\def\XINT_add_kf 1{1\relax }%
\def\XINT_add_l 1#1#2{\xint_gob_til_sc #1\XINT_add_lf ;\XINT_add_m 1#1#2}%
\def\XINT_add_lf #1\W {1\relax 00000001!1;!}%
\def\XINT_add_m #1!{\expandafter\XINT_add_n\the\numexpr\xint_c_i+#1\xint:}%
\def\XINT_add_n #1#2\xint:{1#2\expandafter!\the\numexpr\XINT_add_o #1}%
\def\XINT_add_o #1{\if #12\expandafter\XINT_add_l\else\expandafter\XINT_add_ke \fi}%
\def\xintiiCmp   {\romannumeral0\xintiicmp }%
\def\xintiicmp #1{\expandafter\XINT_iicmp\romannumeral`&&@#1\xint:}%
\def\XINT_iicmp #1#2\xint:#3%
{%
    \expandafter\XINT_cmp_nfork\expandafter #1\romannumeral`&&@#3\xint:#2\xint:
}%
\def\XINT_icmp #1#2\xint:#3%
{%
    \expandafter\XINT_cmp_nfork\expandafter #1\romannumeral0\xintnum{#3}\xint:#2\xint:
}%
\def\XINT_cmp_nfork #1#2%
{%
    \xint_UDzerofork
      #1\XINT_cmp_firstiszero
      #2\XINT_cmp_secondiszero
       0{}%
    \krof
    \xint_UDsignsfork
          #1#2\XINT_cmp_minusminus
           #1-\XINT_cmp_minusplus
           #2-\XINT_cmp_plusminus
            --\XINT_cmp_plusplus
    \krof #1#2%
}%
\def\XINT_cmp_firstiszero  #1\krof 0#2#3\xint:#4\xint:
{%
    \xint_UDzerominusfork
      #2-{ 0}%
      0#2{ 1}%
       0-{ -1}%
    \krof
}%
\def\XINT_cmp_secondiszero #1\krof #20#3\xint:#4\xint:
{%
    \xint_UDzerominusfork
      #2-{ 0}%
      0#2{ -1}%
       0-{ 1}%
    \krof
}%
\def\XINT_cmp_plusminus    #1\xint:#2\xint:{ 1}%
\def\XINT_cmp_minusplus    #1\xint:#2\xint:{ -1}%
\def\XINT_cmp_minusminus
    --{\expandafter\XINT_opp\romannumeral0\XINT_cmp_plusplus {}{}}%
\def\XINT_cmp_plusplus  #1#2#3\xint:
{%
    \expandafter\XINT_cmp_pp
    \the\numexpr\expandafter\XINT_sepbyviii_andcount
    \romannumeral0\XINT_zeroes_forviii #2#3\R\R\R\R\R\R\R\R{10}0000001\W
    #2#3\XINT_sepbyviii_end 2345678\relax
        \xint_c_vii!\xint_c_vi!\xint_c_v!\xint_c_iv!%
        \xint_c_iii!\xint_c_ii!\xint_c_i!\xint_c_\W
    #1%
}%
\def\XINT_cmp_pp #1\xint:#2\xint:#3\xint:
{%
    \expandafter\XINT_cmp_checklengths
    \the\numexpr #2\expandafter\xint:%
    \the\numexpr\expandafter\XINT_sepbyviii_andcount
    \romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
    #3\XINT_sepbyviii_end 2345678\relax
        \xint_c_vii!\xint_c_vi!\xint_c_v!\xint_c_iv!%
        \xint_c_iii!\xint_c_ii!\xint_c_i!\xint_c_\W
    #1;!1;!1;!1;!\W
}%
\def\XINT_cmp_checklengths #1\xint:#2\xint:#3\xint:
{%
    \ifnum #1=#3
       \expandafter\xint_firstoftwo
    \else
       \expandafter\xint_secondoftwo
    \fi
    \XINT_cmp_a {\XINT_cmp_distinctlengths {#1}{#3}}#2;!1;!1;!1;!\W
}%
\def\XINT_cmp_distinctlengths #1#2#3\W #4\W
{%
    \ifnum #1>#2
        \expandafter\xint_firstoftwo
    \else
        \expandafter\xint_secondoftwo
    \fi
    { -1}{ 1}%
}%
\def\XINT_cmp_a 1#1!1#2!1#3!1#4!#5\W 1#6!1#7!1#8!1#9!%
{%
    \xint_gob_til_sc #1\XINT_cmp_equal ;%
    \ifnum #1>#6 \XINT_cmp_gt\fi
    \ifnum #1<#6 \XINT_cmp_lt\fi
    \xint_gob_til_sc #2\XINT_cmp_equal ;%
    \ifnum #2>#7 \XINT_cmp_gt\fi
    \ifnum #2<#7 \XINT_cmp_lt\fi
    \xint_gob_til_sc #3\XINT_cmp_equal ;%
    \ifnum #3>#8 \XINT_cmp_gt\fi
    \ifnum #3<#8 \XINT_cmp_lt\fi
    \xint_gob_til_sc #4\XINT_cmp_equal ;%
    \ifnum #4>#9 \XINT_cmp_gt\fi
    \ifnum #4<#9 \XINT_cmp_lt\fi
    \XINT_cmp_a #5\W
}%
\def\XINT_cmp_lt#1{\def\XINT_cmp_lt\fi ##1\W ##2\W {\fi#1-1}}\XINT_cmp_lt{ }%
\def\XINT_cmp_gt#1{\def\XINT_cmp_gt\fi ##1\W ##2\W {\fi#11}}\XINT_cmp_gt{ }%
\def\XINT_cmp_equal #1\W #2\W { 0}%
\def\xintiiSub   {\romannumeral0\xintiisub }%
\def\xintiisub #1{\expandafter\XINT_iisub\romannumeral`&&@#1\xint:}%
\def\XINT_iisub #1#2\xint:#3%
{%
    \expandafter\XINT_sub_nfork\expandafter
    #1\romannumeral`&&@#3\xint:#2\xint:
}%
\def\XINT_isub #1#2\xint:#3%
{%
   \expandafter\XINT_sub_nfork\expandafter
   #1\romannumeral0\xintnum{#3}\xint:#2\xint:
}%
\def\XINT_sub_nfork #1#2%
{%
    \xint_UDzerofork
      #1\XINT_sub_firstiszero
      #2\XINT_sub_secondiszero
       0{}%
    \krof
    \xint_UDsignsfork
          #1#2\XINT_sub_minusminus
           #1-\XINT_sub_minusplus
           #2-\XINT_sub_plusminus
            --\XINT_sub_plusplus
    \krof #1#2%
}%
\def\XINT_sub_firstiszero  #1\krof 0#2#3\xint:#4\xint:{\XINT_opp #2#3}%
\def\XINT_sub_secondiszero #1\krof #20#3\xint:#4\xint:{ #2#4}%
\def\XINT_sub_plusminus    #1#2{\XINT_add_pp_a #1{}}%
\def\XINT_sub_plusplus   #1#2%
   {\expandafter\XINT_opp\romannumeral0\XINT_sub_mm_a #1#2}%
\def\XINT_sub_minusplus    #1#2%
   {\expandafter-\romannumeral0\XINT_add_pp_a {}#2}%
\def\XINT_sub_minusminus #1#2{\XINT_sub_mm_a {}{}}%
\def\XINT_sub_mm_a  #1#2#3\xint:
{%
  \expandafter\XINT_sub_mm_b
      \romannumeral0\expandafter\XINT_sepandrev_andcount
      \romannumeral0\XINT_zeroes_forviii #2#3\R\R\R\R\R\R\R\R{10}0000001\W
      #2#3\XINT_rsepbyviii_end_A 2345678%
          \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
              \R\xint:\xint_c_xii \R\xint:\xint_c_x  \R\xint:\xint_c_viii \R\xint:\xint_c_vi
              \R\xint:\xint_c_iv  \R\xint:\xint_c_ii \R\xint:\xint_c_\W
  \X #1%
}%
\def\XINT_sub_mm_b #1\xint:#2\X #3\xint:
{%
    \expandafter\XINT_sub_checklengths
    \the\numexpr #1\expandafter\xint:%
    \romannumeral0\expandafter\XINT_sepandrev_andcount
    \romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
    #3\XINT_rsepbyviii_end_A 2345678%
      \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
              \R\xint:\xint_c_xii \R\xint:\xint_c_x  \R\xint:\xint_c_viii \R\xint:\xint_c_vi
              \R\xint:\xint_c_iv  \R\xint:\xint_c_ii \R\xint:\xint_c_\W
      1;!1;!1;!1;!\W
    #21;!1;!1;!1;!\W
    1;!1\R!1\R!1\R!1\R!%
    1\R!1\R!1\R!1\R!\W
}%
\def\XINT_sub_checklengths #1\xint:#2\xint:%
{%
    \ifnum #2>#1
       \expandafter\XINT_sub_exchange
    \else
       \expandafter\XINT_sub_aa
    \fi
}%
\def\XINT_sub_exchange #1\W #2\W
{%
    \expandafter\XINT_opp\romannumeral0\XINT_sub_aa #2\W #1\W
}%
\def\XINT_sub_aa
{%
    \expandafter\XINT_sub_out\the\numexpr\XINT_sub_a\xint_c_i
}%
\def\XINT_sub_out {\XINT_unrevbyviii{}}%
\def\XINT_sub_a #1!#2!#3!#4!#5\W #6!#7!#8!#9!%
{%
    \XINT_sub_b
    #1!#6!#2!#7!#3!#8!#4!#9!%
    #5\W
}%
\def\XINT_sub_b #1#2#3#4!#5!%
{%
    \xint_gob_til_sc #3\XINT_sub_bi ;%
    \expandafter\XINT_sub_c\the\numexpr#1+1#5-#3#4-\xint_c_i\xint:%
}%
\def\XINT_sub_c 1#1#2\xint:%
{%
    1#2\expandafter!\the\numexpr\XINT_sub_d #1%
}%
\def\XINT_sub_d #1#2#3#4!#5!%
{%
    \xint_gob_til_sc #3\XINT_sub_di ;%
    \expandafter\XINT_sub_e\the\numexpr#1+1#5-#3#4-\xint_c_i\xint:
}%
\def\XINT_sub_e 1#1#2\xint:%
{%
    1#2\expandafter!\the\numexpr\XINT_sub_f #1%
}%
\def\XINT_sub_f #1#2#3#4!#5!%
{%
    \xint_gob_til_sc #3\XINT_sub_fi ;%
    \expandafter\XINT_sub_g\the\numexpr#1+1#5-#3#4-\xint_c_i\xint:
}%
\def\XINT_sub_g 1#1#2\xint:%
{%
    1#2\expandafter!\the\numexpr\XINT_sub_h #1%
}%
\def\XINT_sub_h #1#2#3#4!#5!%
{%
    \xint_gob_til_sc #3\XINT_sub_hi ;%
    \expandafter\XINT_sub_i\the\numexpr#1+1#5-#3#4-\xint_c_i\xint:
}%
\def\XINT_sub_i 1#1#2\xint:%
{%
    1#2\expandafter!\the\numexpr\XINT_sub_a #1%
}%
\def\XINT_sub_bi;%
    \expandafter\XINT_sub_c\the\numexpr#1+1#2-#3\xint:
    #4!#5!#6!#7!#8!#9!\W
{%
    \XINT_sub_k #1#2!#5!#7!#9!%
}%
\def\XINT_sub_di;%
    \expandafter\XINT_sub_e\the\numexpr#1+1#2-#3\xint:
    #4!#5!#6!#7!#8\W
{%
    \XINT_sub_k #1#2!#5!#7!%
}%
\def\XINT_sub_fi;%
    \expandafter\XINT_sub_g\the\numexpr#1+1#2-#3\xint:
    #4!#5!#6\W
{%
    \XINT_sub_k #1#2!#5!%
}%
\def\XINT_sub_hi;%
    \expandafter\XINT_sub_i\the\numexpr#1+1#2-#3\xint:
    #4\W
{%
    \XINT_sub_k #1#2!%
}%
\def\XINT_sub_k #1#2#3%
{%
    \xint_gob_til_sc #3\XINT_sub_p;\XINT_sub_l #1#2#3%
}%
\def\XINT_sub_l #1%
   {\xint_UDzerofork #1\XINT_sub_l_carry 0\XINT_sub_l_Ia\krof}%
\def\XINT_sub_l_Ia 1#1;!#2\W{1\relax#1;!1\XINT_sub_fix_none!}%
\def\XINT_sub_l_carry 1#1!{\ifcase #1
         \expandafter \XINT_sub_l_Id
    \or  \expandafter \XINT_sub_l_Ic
    \else\expandafter \XINT_sub_l_Ib\fi 1#1!}%
\def\XINT_sub_l_Ib #1;#2\W {-\xint_c_i+#1;!1\XINT_sub_fix_none!}%
\def\XINT_sub_l_Ic 1#1!1#2#3!#4;#5\W
{%
    \xint_gob_til_sc #2\XINT_sub_l_Ica;%
    1\relax 00000000!1#2#3!#4;!1\XINT_sub_fix_none!%
}%
\def\XINT_sub_l_Ica#1\W
{%
    1;!1\XINT_sub_fix_cuz!%
    1;!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
    \xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
\def\XINT_sub_l_Id 1#1!%
    {199999999\expandafter!\the\numexpr \XINT_sub_l_Id_a}%
\def\XINT_sub_l_Id_a 1#1!{\ifcase #1
         \expandafter \XINT_sub_l_Id
    \or  \expandafter \XINT_sub_l_Id_b
    \else\expandafter \XINT_sub_l_Ib\fi 1#1!}%
\def\XINT_sub_l_Id_b 1#1!1#2#3!#4;#5\W
{%
    \xint_gob_til_sc #2\XINT_sub_l_Ida;%
    1\relax 00000000!1#2#3!#4;!1\XINT_sub_fix_none!%
}%
\def\XINT_sub_l_Ida#1\XINT_sub_fix_none{1;!1\XINT_sub_fix_none}%
\def\XINT_sub_p;\XINT_sub_l #1#2\W #3\W
{%
    \xint_UDzerofork
       #1{1;!1\XINT_sub_fix_neg!%
          1;!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
          \xint_bye2345678\xint_bye1099999988\relax}% A - B, B > A
        0{1;!1\XINT_sub_fix_cuz!%
          1;!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W}%
    \krof
    \xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\Z
}%
\def\XINT_sub_fix_none;{\XINT_cuz_small}%
\def\XINT_sub_fix_cuz ;{\expandafter\XINT_num_cleanup\the\numexpr\XINT_num_loop}%
\def\XINT_sub_fix_neg;%
{%
    \expandafter-\romannumeral0\expandafter
    \XINT_sub_comp_finish\the\numexpr\XINT_sub_comp_loop
}%
\def\XINT_sub_comp_finish 0{\XINT_sub_fix_cuz;}%
\def\XINT_sub_comp_loop #1#2#3#4#5#6#7#8%
{%
    \expandafter\XINT_sub_comp_clean
    \the\numexpr \xint_c_xi_e_viii_mone-#1#2#3#4#5#6#7#8\XINT_sub_comp_loop
}%
\def\XINT_sub_comp_clean 1#1{+#1\relax}%
\def\xintiiMul {\romannumeral0\xintiimul }%
\def\xintiimul #1%
{%
    \expandafter\XINT_iimul\romannumeral`&&@#1\xint:
}%
\def\XINT_iimul #1#2\xint:#3%
{%
    \expandafter\XINT_mul_nfork\expandafter #1\romannumeral`&&@#3\xint:#2\xint:
}%
\def\XINT_mul_fork #1#2\xint:#3\xint:{\XINT_mul_nfork #1#3\xint:#2\xint:}%
\def\XINT_mul_nfork #1#2%
{%
    \xint_UDzerofork
      #1\XINT_mul_zero
      #2\XINT_mul_zero
       0{}%
    \krof
    \xint_UDsignsfork
          #1#2\XINT_mul_minusminus
           #1-\XINT_mul_minusplus
           #2-\XINT_mul_plusminus
            --\XINT_mul_plusplus
    \krof #1#2%
}%
\def\XINT_mul_zero  #1\krof #2#3\xint:#4\xint:{ 0}%
\def\XINT_mul_minusminus   #1#2{\XINT_mul_plusplus {}{}}%
\def\XINT_mul_minusplus    #1#2%
   {\expandafter-\romannumeral0\XINT_mul_plusplus {}#2}%
\def\XINT_mul_plusminus    #1#2%
   {\expandafter-\romannumeral0\XINT_mul_plusplus #1{}}%
\def\XINT_mul_plusplus #1#2#3\xint:
{%
  \expandafter\XINT_mul_pre_b
      \romannumeral0\expandafter\XINT_sepandrev_andcount
      \romannumeral0\XINT_zeroes_forviii #2#3\R\R\R\R\R\R\R\R{10}0000001\W
      #2#3\XINT_rsepbyviii_end_A 2345678%
          \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
              \R\xint:\xint_c_xii \R\xint:\xint_c_x  \R\xint:\xint_c_viii \R\xint:\xint_c_vi
              \R\xint:\xint_c_iv  \R\xint:\xint_c_ii \R\xint:\xint_c_\W
  \W #1%
}%
\def\XINT_mul_pre_b #1\xint:#2\W #3\xint:
{%
    \expandafter\XINT_mul_checklengths
    \the\numexpr #1\expandafter\xint:%
    \romannumeral0\expandafter\XINT_sepandrev_andcount
    \romannumeral0\XINT_zeroes_forviii #3\R\R\R\R\R\R\R\R{10}0000001\W
    #3\XINT_rsepbyviii_end_A 2345678%
      \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
              \R\xint:\xint_c_xii \R\xint:\xint_c_x  \R\xint:\xint_c_viii \R\xint:\xint_c_vi
              \R\xint:\xint_c_iv  \R\xint:\xint_c_ii \R\xint:\xint_c_\W
     1;!\W #21;!%
    1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
}%
\def\XINT_mul_checklengths #1\xint:#2\xint:%
{%
    \ifnum #2=\xint_c_i\expandafter\XINT_mul_smallbyfirst\fi
    \ifnum #1=\xint_c_i\expandafter\XINT_mul_smallbysecond\fi
    \ifnum #2<#1
       \ifnum \numexpr (#2-\xint_c_i)*(#1-#2)<383
          \XINT_mul_exchange
       \fi
    \else
       \ifnum \numexpr (#1-\xint_c_i)*(#2-#1)>383
          \XINT_mul_exchange
       \fi
    \fi
    \XINT_mul_start
}%
\def\XINT_mul_smallbyfirst #1\XINT_mul_start 1#2!1;!\W
{%
    \ifnum#2=\xint_c_i\expandafter\XINT_mul_oneisone\fi
    \ifnum#2<\xint_c_xxii\expandafter\XINT_mul_verysmall\fi
    \expandafter\XINT_mul_out\the\numexpr\XINT_smallmul 1#2!%
}%
\def\XINT_mul_smallbysecond #1\XINT_mul_start #2\W 1#3!1;!%
{%
    \ifnum#3=\xint_c_i\expandafter\XINT_mul_oneisone\fi
    \ifnum#3<\xint_c_xxii\expandafter\XINT_mul_verysmall\fi
    \expandafter\XINT_mul_out\the\numexpr\XINT_smallmul 1#3!#2%
}%
\def\XINT_mul_oneisone #1!{\XINT_mul_out }%
\def\XINT_mul_verysmall\expandafter\XINT_mul_out
                       \the\numexpr\XINT_smallmul 1#1!%
    {\expandafter\XINT_mul_out\the\numexpr\XINT_verysmallmul 0\xint:#1!}%
\def\XINT_mul_exchange #1\XINT_mul_start #2\W #31;!%
   {\fi\fi\XINT_mul_start #31;!\W #2}%
\def\XINT_mul_start
   {\expandafter\XINT_mul_out\the\numexpr\XINT_mul_loop 100000000!1;!\W}%
\def\XINT_mul_out
   {\expandafter\XINT_cuz_small\romannumeral0\XINT_unrevbyviii {}}%
\def\XINT_mul_loop #1\W #2\W 1#3!%
{%
    \xint_gob_til_sc #3\XINT_mul_e ;%
    \expandafter\XINT_mul_a\the\numexpr \XINT_smallmul 1#3!#2\W
    #1\W #2\W
}%
\def\XINT_mul_a #1\W #2\W
{%
    \expandafter\XINT_mul_b\the\numexpr
    \XINT_add_a \xint_c_ii #21;!1;!1;!\W #11;!1;!1;!\W\W
}%
\def\XINT_mul_b 1#1!{1#1\expandafter!\the\numexpr\XINT_mul_loop }%
\def\XINT_mul_e;#1\W 1#2\W #3\W {1\relax #2}%
\def\XINT_minimulwc_a 1#1\xint:#2\xint:#3!#4#5#6#7#8\xint:%
{%
    \expandafter\XINT_minimulwc_b
    \the\numexpr \xint_c_x^ix+#1+#3*#8\xint:
                     #3*#4#5#6#7+#2*#8\xint:
                           #2*#4#5#6#7\xint:%
}%
\def\XINT_minimulwc_b 1#1#2#3#4#5#6\xint:#7\xint:%
{%
    \expandafter\XINT_minimulwc_c
    \the\numexpr \xint_c_x^ix+#1#2#3#4#5+#7\xint:#6\xint:%
}%
\def\XINT_minimulwc_c 1#1#2#3#4#5#6\xint:#7\xint:#8\xint:%
{%
    1#6#7\expandafter!%
    \the\numexpr\expandafter\XINT_smallmul_a
    \the\numexpr \xint_c_x^viii+#1#2#3#4#5+#8\xint:%
}%
\def\XINT_smallmul 1#1#2#3#4#5!{\XINT_smallmul_a 100000000\xint:#1#2#3#4\xint:#5!}%
\def\XINT_smallmul_a #1\xint:#2\xint:#3!1#4!%
{%
    \xint_gob_til_sc #4\XINT_smallmul_e;%
    \XINT_minimulwc_a #1\xint:#2\xint:#3!#4\xint:#2\xint:#3!%
}%
\def\XINT_smallmul_e;\XINT_minimulwc_a 1#1\xint:#2;#3!%
    {\xint_gob_til_eightzeroes #1\XINT_smallmul_f 000000001\relax #1!1;!}%
\def\XINT_smallmul_f 000000001\relax 00000000!1{1\relax}%
\def\XINT_verysmallmul #1\xint:#2!1#3!%
{%
    \xint_gob_til_sc #3\XINT_verysmallmul_e;%
    \expandafter\XINT_verysmallmul_a
    \the\numexpr #2*#3+#1\xint:#2!%
}%
\def\XINT_verysmallmul_e;\expandafter\XINT_verysmallmul_a\the\numexpr
    #1+#2#3\xint:#4!%
{\xint_gob_til_zero #2\XINT_verysmallmul_f 0\xint_c_x^viii+#2#3!1;!}%
\def\XINT_verysmallmul_f #1!1{1\relax}%
\def\XINT_verysmallmul_a #1#2\xint:%
{%
    \unless\ifnum #1#2<\xint_c_x^ix
    \expandafter\XINT_verysmallmul_bi\else
    \expandafter\XINT_verysmallmul_bj\fi
    \the\numexpr \xint_c_x^ix+#1#2\xint:%
}%
\def\XINT_verysmallmul_bj{\expandafter\XINT_verysmallmul_cj }%
\def\XINT_verysmallmul_cj 1#1#2\xint:%
    {1#2\expandafter!\the\numexpr\XINT_verysmallmul #1\xint:}%
\def\XINT_verysmallmul_bi\the\numexpr\xint_c_x^ix+#1#2#3\xint:%
    {1#3\expandafter!\the\numexpr\XINT_verysmallmul #1#2\xint:}%
\def\XINT_minimul_a #1\xint:#2!#3#4#5#6#7!%
{%
    \expandafter\XINT_minimul_b
    \the\numexpr \xint_c_x^viii+#2*#7\xint:#2*#3#4#5#6+#1*#7\xint:#1*#3#4#5#6\xint:%
}%
\def\XINT_minimul_b 1#1#2#3#4#5\xint:#6\xint:%
{%
    \expandafter\XINT_minimul_c
    \the\numexpr \xint_c_x^ix+#1#2#3#4+#6\xint:#5\xint:%
}%
\def\XINT_minimul_c 1#1#2#3#4#5#6\xint:#7\xint:#8\xint:%
{%
    1#6#7\expandafter!\the\numexpr \xint_c_x^viii+#1#2#3#4#5+#8!%
}%
\def\xintiiDivision   {\romannumeral0\xintiidivision }%
\def\xintiidivision  #1{\expandafter\XINT_iidivision \romannumeral`&&@#1\xint:}%
\def\XINT_iidivision #1#2\xint:#3{\expandafter\XINT_iidivision_a\expandafter #1%
                             \romannumeral`&&@#3\xint:#2\xint:}%
\def\XINT_iidivision_a #1#2% #1 de A, #2 de B.
{%
    \if0#2\xint_dothis{\XINT_iidivision_divbyzero #1#2}\fi
    \if0#1\xint_dothis\XINT_iidivision_aiszero\fi
    \if-#2\xint_dothis{\expandafter\XINT_iidivision_bneg
                       \romannumeral0\XINT_iidivision_bpos #1}\fi
    \xint_orthat{\XINT_iidivision_bpos #1#2}%
}%
\def\XINT_iidivision_divbyzero#1#2#3\xint:#4\xint:
   {\if0#1\xint_dothis{\XINT_signalcondition{DivisionUndefined}}\fi
          \xint_orthat{\XINT_signalcondition{DivisionByZero}}%
    {Division of #1#4 by #2#3}{}{{0}{0}}}%
\def\XINT_iidivision_aiszero #1\xint:#2\xint:{{0}{0}}%
\def\XINT_iidivision_bneg #1% q->-q, r unchanged
                          {\expandafter{\romannumeral0\XINT_opp #1}}%
\def\XINT_iidivision_bpos #1%
{%
    \xint_UDsignfork
            #1\XINT_iidivision_aneg
             -{\XINT_iidivision_apos #1}%
    \krof
}%
\def\XINT_iidivision_apos #1#2\xint:#3\xint:{\XINT_div_prepare {#2}{#1#3}}%
\def\XINT_iidivision_aneg #1\xint:#2\xint:
   {\expandafter
    \XINT_iidivision_aneg_b\romannumeral0\XINT_div_prepare {#1}{#2}{#1}}%
\def\XINT_iidivision_aneg_b #1#2{\if0\XINT_Sgn #2\xint:
                              \expandafter\XINT_iidivision_aneg_rzero
                           \else
                              \expandafter\XINT_iidivision_aneg_rpos
                           \fi {#1}{#2}}%
\def\XINT_iidivision_aneg_rzero #1#2#3{{-#1}{0}}% necessarily q was >0
\def\XINT_iidivision_aneg_rpos #1%
{%
    \expandafter\XINT_iidivision_aneg_end\expandafter
               {\expandafter-\romannumeral0\xintinc {#1}}% q-> -(1+q)
}%
\def\XINT_iidivision_aneg_end #1#2#3%
{%
     \expandafter\xint_exchangetwo_keepbraces
     \expandafter{\romannumeral0\XINT_sub_mm_a {}{}#3\xint:#2\xint:}{#1}% r-> b-r
}%
\def\XINT_div_prepare #1%
{%
    \XINT_div_prepare_a #1\R\R\R\R\R\R\R\R {10}0000001\W !{#1}%
}%
\def\XINT_div_prepare_a #1#2#3#4#5#6#7#8#9%
{%
    \xint_gob_til_R #9\XINT_div_prepare_small\R
    \XINT_div_prepare_b #9%
}%
\def\XINT_div_prepare_small\R #1!#2%
{%
    \ifcase #2
    \or\expandafter\XINT_div_BisOne
    \or\expandafter\XINT_div_BisTwo
    \else\expandafter\XINT_div_small_a
    \fi {#2}%
}%
\def\XINT_div_BisOne #1#2{{#2}{0}}%
\def\XINT_div_BisTwo #1#2%
{%
    \expandafter\expandafter\expandafter\XINT_div_BisTwo_a
    \ifodd\xintLDg{#2} \expandafter1\else \expandafter0\fi {#2}%
}%
\def\XINT_div_BisTwo_a #1#2%
{%
    \expandafter{\romannumeral0\XINT_half
     #2\xint_bye\xint_Bye345678\xint_bye
     *\xint_c_v+\xint_c_v)/\xint_c_x-\xint_c_i\relax}{#1}%
}%
\def\XINT_div_small_a #1#2%
{%
    \expandafter\XINT_div_small_b
    \the\numexpr #1/\xint_c_ii\expandafter
    \xint:\the\numexpr \xint_c_x^viii+#1\expandafter!%
    \romannumeral0%
    \XINT_div_small_ba #2\R\R\R\R\R\R\R\R{10}0000001\W
       #2\XINT_sepbyviii_Z_end 2345678\relax
}%
\def\XINT_div_small_b #1!#2{#2#1!}%
\def\XINT_div_small_ba #1#2#3#4#5#6#7#8#9%
{%
    \xint_gob_til_R #9\XINT_div_smallsmall\R
    \expandafter\XINT_div_dosmalldiv
    \the\numexpr\expandafter\XINT_sepbyviii_Z
           \romannumeral0\XINT_zeroes_forviii
    #1#2#3#4#5#6#7#8#9%
}%
\def\XINT_div_smallsmall\R
    \expandafter\XINT_div_dosmalldiv
    \the\numexpr\expandafter\XINT_sepbyviii_Z
    \romannumeral0\XINT_zeroes_forviii #1\R #2\relax
   {{\XINT_div_dosmallsmall}{#1}}%
\def\XINT_div_dosmallsmall #1\xint:1#2!#3%
{%
    \expandafter\XINT_div_smallsmallend
    \the\numexpr (#3+#1)/#2-\xint_c_i\xint:#2\xint:#3\xint:%
}%
\def\XINT_div_smallsmallend #1\xint:#2\xint:#3\xint:{\expandafter
    {\the\numexpr #1\expandafter}\expandafter{\the\numexpr #3-#1*#2}}%
\def\XINT_div_dosmalldiv
    {{\expandafter\XINT_sdiv_out\the\numexpr\XINT_smalldivx_a}}%
\def\XINT_div_prepare_b
   {\expandafter\XINT_div_prepare_c\romannumeral0\XINT_zeroes_forviii }%
\def\XINT_div_prepare_c #1!%
{%
     \XINT_div_prepare_d  #1.00000000!{#1}%
}%
\def\XINT_div_prepare_d #1#2#3#4#5#6#7#8#9%
{%
    \expandafter\XINT_div_prepare_e\xint_gob_til_dot #1#2#3#4#5#6#7#8#9!%
}%
\def\XINT_div_prepare_e #1!#2!#3#4%
{%
    \XINT_div_prepare_f #4#3\X {#1}{#3}%
}%
\def\XINT_div_prepare_f #1#2#3#4#5#6#7#8#9\X
{%
    \expandafter\XINT_div_prepare_g
     \the\numexpr  #1#2#3#4#5#6#7#8+\xint_c_i\expandafter
    \xint:\the\numexpr (#1#2#3#4#5#6#7#8+\xint_c_i)/\xint_c_ii\expandafter
    \xint:\the\numexpr #1#2#3#4#5#6#7#8\expandafter
    \xint:\romannumeral0\XINT_sepandrev_andcount
    #1#2#3#4#5#6#7#8#9\XINT_rsepbyviii_end_A 2345678%
                      \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
              \R\xint:\xint_c_xii \R\xint:\xint_c_x  \R\xint:\xint_c_viii \R\xint:\xint_c_vi
              \R\xint:\xint_c_iv  \R\xint:\xint_c_ii \R\xint:\xint_c_\W
    \X
}%
\def\XINT_div_prepare_g #1\xint:#2\xint:#3\xint:#4\xint:#5\X #6#7#8%
{%
    \expandafter\XINT_div_prepare_h
    \the\numexpr\expandafter\XINT_sepbyviii_andcount
    \romannumeral0\XINT_zeroes_forviii #8#7\R\R\R\R\R\R\R\R{10}0000001\W
    #8#7\XINT_sepbyviii_end 2345678\relax
     \xint_c_vii!\xint_c_vi!\xint_c_v!\xint_c_iv!%
     \xint_c_iii!\xint_c_ii!\xint_c_i!\xint_c_\W
    {#1}{#2}{#3}{#4}{#5}{#6}%
}%
\def\XINT_div_prepare_h #11\xint:#2\xint:#3#4#5#6%#7#8%
{%
    \XINT_div_start_a {#2}{#6}{#1}{#3}{#4}{#5}%{#7}{#8}%
}%
\def\XINT_div_start_a #1#2%
{%
    \ifnum #1 < #2
      \expandafter\XINT_div_zeroQ
    \else
      \expandafter\XINT_div_start_b
    \fi
    {#1}{#2}%
}%
\def\XINT_div_zeroQ #1#2#3#4#5#6#7%
{%
    \expandafter\XINT_div_zeroQ_end
    \romannumeral0\XINT_unsep_cuzsmall
    #3\xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax\xint:
}%
\def\XINT_div_zeroQ_end #1\xint:#2%
    {\expandafter{\expandafter0\expandafter}\XINT_div_cleanR #1#2\xint:}%
\def\XINT_div_start_b #1#2#3#4#5#6%
{%
    \expandafter\XINT_div_finish\the\numexpr
    \XINT_div_start_c {#2}\xint:#3\xint:{#6}{{#1}{#2}{{#4}{#5}}{#6}}%
}%
\def\XINT_div_finish
{%
    \expandafter\XINT_div_finish_a \romannumeral`&&@\XINT_div_unsepQ
}%
\def\XINT_div_finish_a #1\Z #2\xint:{\XINT_div_finish_b #2\xint:{#1}}%
\def\XINT_div_finish_b #1%
{%
    \if0#1%
       \expandafter\XINT_div_finish_bRzero
    \else
       \expandafter\XINT_div_finish_bRpos
    \fi
    #1%
}%
\def\XINT_div_finish_bRzero 0\xint:#1#2{{#1}{0}}%
\def\XINT_div_finish_bRpos #1\xint:#2#3%
{%
    \expandafter\xint_exchangetwo_keepbraces\XINT_div_cleanR  #1#3\xint:{#2}%
}%
\def\XINT_div_cleanR #100000000\xint:{{#1}}%
\def\XINT_div_start_c #1%
{%
    \ifnum #1>\xint_c_vi
       \expandafter\XINT_div_start_ca
    \else
       \expandafter\XINT_div_start_cb
    \fi {#1}%
}%
\def\XINT_div_start_ca #1#2\xint:#3!#4!#5!#6!#7!#8!#9!%
{%
    \expandafter\XINT_div_start_c\expandafter
    {\the\numexpr #1-\xint_c_vii}#2#3!#4!#5!#6!#7!#8!#9!\xint:%
}%
\def\XINT_div_start_cb #1%
   {\csname XINT_div_start_c_\romannumeral\numexpr#1\endcsname}%
\def\XINT_div_start_c_i   #1\xint:#2!%
    {\XINT_div_start_c_   #1#2!\xint:}%
\def\XINT_div_start_c_ii  #1\xint:#2!#3!%
    {\XINT_div_start_c_   #1#2!#3!\xint:}%
\def\XINT_div_start_c_iii #1\xint:#2!#3!#4!%
    {\XINT_div_start_c_   #1#2!#3!#4!\xint:}%
\def\XINT_div_start_c_iv  #1\xint:#2!#3!#4!#5!%
    {\XINT_div_start_c_   #1#2!#3!#4!#5!\xint:}%
\def\XINT_div_start_c_v   #1\xint:#2!#3!#4!#5!#6!%
    {\XINT_div_start_c_   #1#2!#3!#4!#5!#6!\xint:}%
\def\XINT_div_start_c_vi  #1\xint:#2!#3!#4!#5!#6!#7!%
    {\XINT_div_start_c_   #1#2!#3!#4!#5!#6!#7!\xint:}%
\def\XINT_div_start_c_ 1#1!#2\xint:#3\xint:#4#5#6%
{%
    \XINT_div_I_a {#1}{#4}{1#1!#2}{#6}{00000000}#5{#3}{#6}%
}%
\def\XINT_div_I_a #1#2%
{%
    \expandafter\XINT_div_I_b\the\numexpr #1/#2\xint:{#1}{#2}%
}%
\def\XINT_div_I_b #1%
{%
    \xint_gob_til_zero #1\XINT_div_I_czero 0\XINT_div_I_c #1%
}%
\def\XINT_div_I_czero 0\XINT_div_I_c 0\xint:#1#2#3#4#5{1#5\XINT_div_I_g {#3}}%
\def\XINT_div_I_c #1\xint:#2#3%
{%
    \expandafter\XINT_div_I_da\the\numexpr #2-#1*#3\xint:#1\xint:{#2}{#3}%
}%
\def\XINT_div_I_da #1\xint:%
{%
    \ifnum #1>\xint_c_ix
       \expandafter\XINT_div_I_dP
    \else
       \ifnum #1<\xint_c_
        \expandafter\expandafter\expandafter\XINT_div_I_dN
       \else
        \expandafter\expandafter\expandafter\XINT_div_I_db
       \fi
    \fi
}%
\def\XINT_div_I_dN #1\xint:%
{%
    \expandafter\XINT_div_I_b\the\numexpr #1-\xint_c_i\xint:%
}%
\def\XINT_div_I_db #1\xint:#2#3#4#5%
{%
    \expandafter\XINT_div_I_dc\expandafter #1%
    \romannumeral0\expandafter\XINT_div_sub\expandafter
       {\romannumeral0\XINT_rev_nounsep {}#4\R!\R!\R!\R!\R!\R!\R!\R!\W}%
       {\the\numexpr\XINT_div_verysmallmul #1!#51;!}%
    \Z {#4}{#5}%
}%
\def\XINT_div_I_dc #1#2%
{%
    \if-#2\expandafter\XINT_div_I_dd\else\expandafter\XINT_div_I_de\fi
     #1#2%
}%
\def\XINT_div_I_dd #1-\Z
{%
    \if #11\expandafter\XINT_div_I_dz\fi
    \expandafter\XINT_div_I_dP\the\numexpr #1-\xint_c_i\xint: XX%
}%
\def\XINT_div_I_dz #1XX#2#3#4%
{%
    1#4\XINT_div_I_g {#2}%
}%
\def\XINT_div_I_de #1#2\Z #3#4#5{1#5+#1\XINT_div_I_g {#2}}%
\def\XINT_div_I_dP #1\xint:#2#3#4#5#6%
{%
    1#6+#1\expandafter\XINT_div_I_g\expandafter
    {\romannumeral0\expandafter\XINT_div_sub\expandafter
      {\romannumeral0\XINT_rev_nounsep {}#4\R!\R!\R!\R!\R!\R!\R!\R!\W}%
      {\the\numexpr\XINT_div_verysmallmul #1!#51;!}%
    }%
}%
\def\XINT_div_I_g #1#2#3#4#5#6#7%
{%
     \expandafter !\the\numexpr
     \ifnum#2=#3
          \expandafter\XINT_div_exittofinish
     \else
          \expandafter\XINT_div_I_h
     \fi
     {#4}#1\xint:#6\xint:{{#4}{#5}{#3}{#2}}{#7}%
}%
\def\XINT_div_exittofinish #1#2\xint:#3\xint:#4#5%
{%
    1\expandafter\expandafter\expandafter!\expandafter\XINT_div_unsepQ_delim
    \romannumeral0\XINT_div_unsepR #2#3%
    \xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax\R\xint:
}%
\def\XINT_div_I_h #1\xint:#2!#3\xint:#4#5%
{%
    \XINT_div_II_b #1#2!\xint:{#5}{#4}{#3}{#5}%
}%
\def\XINT_div_II_b #11#2!#3!%
{%
    \xint_gob_til_eightzeroes #2\XINT_div_II_skipc 00000000%
    \XINT_div_II_c #1{1#2}{#3}%
}%
\def\XINT_div_II_skipc 00000000\XINT_div_II_c #1#2#3#4#5\xint:#6#7%
{%
    \XINT_div_II_k #7{#4!#5}{#6}{00000000}%
}%
\def\XINT_div_II_c #1#2#3#4%
{%
     \expandafter\XINT_div_II_d\the\numexpr\XINT_div_xmini
     #1\xint:#2!#3!#4!{#1}{#2}#3!#4!%
}%
\def\XINT_div_xmini #1%
{%
    \xint_gob_til_one #1\XINT_div_xmini_a 1\XINT_div_mini #1%
}%
\def\XINT_div_xmini_a 1\XINT_div_mini 1#1%
{%
    \xint_gob_til_zero #1\XINT_div_xmini_b 0\XINT_div_mini 1#1%
}%
\def\XINT_div_xmini_b 0\XINT_div_mini 10#1#2#3#4#5#6#7%
{%
    \xint_gob_til_zero #7\XINT_div_xmini_c 0\XINT_div_mini 10#1#2#3#4#5#6#7%
}%
\def\XINT_div_xmini_c 0\XINT_div_mini 100000000\xint:50000000!#1!#2!{#1!}%
\def\XINT_div_II_d 1#1#2#3#4#5!#6#7#8\xint:#9%
{%
    \expandafter\XINT_div_II_e
    \romannumeral0\expandafter\XINT_div_sub\expandafter
      {\romannumeral0\XINT_rev_nounsep {}#8\R!\R!\R!\R!\R!\R!\R!\R!\W}%
      {\the\numexpr\XINT_div_smallmul_a 100000000\xint:#1#2#3#4\xint:#5!#91;!}%
    \xint:{#6}{#7}{#9}{#1#2#3#4#5}%
}%
\def\XINT_div_II_e 1#1!%
{%
    \xint_gob_til_eightzeroes #1\XINT_div_II_skipf 00000000%
    \XINT_div_II_f 1#1!%
}%
\def\XINT_div_II_skipf 00000000\XINT_div_II_f 100000000!#1\xint:#2#3#4#5#6%
{%
    \XINT_div_II_k #6{#1}{#4}{#5}%
}%
\def\XINT_div_II_f #1!#2!#3\xint:%
{%
    \XINT_div_II_fa {#1!#2!}{#1!#2!#3}%
}%
\def\XINT_div_II_fa #1#2#3#4%
{%
    \expandafter\XINT_div_II_g \the\numexpr\XINT_div_xmini #3\xint:#4!#1{#2}%
}%
\def\XINT_div_II_g 1#1#2#3#4#5!#6#7#8%
{%
    \expandafter \XINT_div_II_h
    \the\numexpr 1#1#2#3#4#5+#8\expandafter\expandafter\expandafter
    \xint:\expandafter\expandafter\expandafter
    {\expandafter\xint_gob_til_exclam
     \romannumeral0\expandafter\XINT_div_sub\expandafter
       {\romannumeral0\XINT_rev_nounsep {}#6\R!\R!\R!\R!\R!\R!\R!\R!\W}%
       {\the\numexpr\XINT_div_smallmul_a 100000000\xint:#1#2#3#4\xint:#5!#71;!}}%
    {#7}%
}%
\def\XINT_div_II_h 1#1\xint:#2#3#4%
{%
    \XINT_div_II_k #4{#2}{#3}{#1}%
}%
\def\XINT_div_II_k #1#2#3#4#5%
{%
    \expandafter\XINT_div_II_l \the\numexpr #4-\xint_c_i\xint:{#3}#1{#2}#5\xint:%
}%
\def\XINT_div_II_l #1\xint:#2#3#4#51#6!%
{%
    \XINT_div_II_m {{#1}{#2}{{#3}{#4}}{#5}}{#5}{#6}1#6!%
}%
\def\XINT_div_II_m #1#2#3#4\xint:#5#6%
{%
     \XINT_div_I_a {#3}{#2}{#4}{#5}{#6}#1%
}%
\def\XINT_div_minimulwc_a 1#1\xint:#2\xint:#3!#4#5#6#7#8\xint:%
{%
    \expandafter\XINT_div_minimulwc_b
    \the\numexpr \xint_c_x^ix+#1+#3*#8\xint:#3*#4#5#6#7+#2*#8\xint:#2*#4#5#6#7\xint:%
}%
\def\XINT_div_minimulwc_b 1#1#2#3#4#5#6\xint:#7\xint:%
{%
    \expandafter\XINT_div_minimulwc_c
    \the\numexpr \xint_c_x^ix+#1#2#3#4#5+#7\xint:#6\xint:%
}%
\def\XINT_div_minimulwc_c 1#1#2#3#4#5#6\xint:#7\xint:#8\xint:%
{%
    1#6#7\expandafter!%
    \the\numexpr\expandafter\XINT_div_smallmul_a
    \the\numexpr \xint_c_x^viii+#1#2#3#4#5+#8\xint:%
}%
\def\XINT_div_smallmul_a #1\xint:#2\xint:#3!1#4!%
{%
    \xint_gob_til_sc #4\XINT_div_smallmul_e;%
    \XINT_div_minimulwc_a #1\xint:#2\xint:#3!#4\xint:#2\xint:#3!%
}%
\def\XINT_div_smallmul_e;\XINT_div_minimulwc_a 1#1\xint:#2;#3!{1\relax #1!}%
\def\XINT_div_verysmallmul #1%
   {\xint_gob_til_one #1\XINT_div_verysmallisone 1\XINT_div_verysmallmul_a 0\xint:#1}%
\def\XINT_div_verysmallisone 1\XINT_div_verysmallmul_a 0\xint:1!1#11;!%
   {1\relax #1100000000!}%
\def\XINT_div_verysmallmul_a #1\xint:#2!1#3!%
{%
    \xint_gob_til_sc #3\XINT_div_verysmallmul_e;%
    \expandafter\XINT_div_verysmallmul_b
    \the\numexpr \xint_c_x^ix+#2*#3+#1\xint:#2!%
}%
\def\XINT_div_verysmallmul_b 1#1#2\xint:%
    {1#2\expandafter!\the\numexpr\XINT_div_verysmallmul_a #1\xint:}%
\def\XINT_div_verysmallmul_e;#1;+#2#3!{1\relax 0000000#2!}%
\def\XINT_div_sub #1#2%
{%
    \expandafter\XINT_div_sub_clean
    \the\numexpr\expandafter\XINT_div_sub_a\expandafter
    1#2;!;!;!;!;!\W #1;!;!;!;!;!\W
}%
\def\XINT_div_sub_clean #1-#2#3\W
{%
    \if1#2\expandafter\XINT_rev_nounsep\else\expandafter\XINT_div_sub_neg\fi
    {}#1\R!\R!\R!\R!\R!\R!\R!\R!\W
}%
\def\XINT_div_sub_neg #1\W { -}%
\def\XINT_div_sub_a #1!#2!#3!#4!#5\W #6!#7!#8!#9!%
{%
    \XINT_div_sub_b #1!#6!#2!#7!#3!#8!#4!#9!#5\W
}%
\def\XINT_div_sub_b #1#2#3!#4!%
{%
    \xint_gob_til_sc #4\XINT_div_sub_bi ;%
    \expandafter\XINT_div_sub_c\the\numexpr#1-#3+1#4-\xint_c_i\xint:%
}%
\def\XINT_div_sub_c 1#1#2\xint:%
{%
    1#2\expandafter!\the\numexpr\XINT_div_sub_d #1%
}%
\def\XINT_div_sub_d #1#2#3!#4!%
{%
    \xint_gob_til_sc #4\XINT_div_sub_di ;%
    \expandafter\XINT_div_sub_e\the\numexpr#1-#3+1#4-\xint_c_i\xint:%
}%
\def\XINT_div_sub_e 1#1#2\xint:%
{%
    1#2\expandafter!\the\numexpr\XINT_div_sub_f #1%
}%
\def\XINT_div_sub_f #1#2#3!#4!%
{%
    \xint_gob_til_sc #4\XINT_div_sub_fi ;%
    \expandafter\XINT_div_sub_g\the\numexpr#1-#3+1#4-\xint_c_i\xint:%
}%
\def\XINT_div_sub_g 1#1#2\xint:%
{%
    1#2\expandafter!\the\numexpr\XINT_div_sub_h #1%
}%
\def\XINT_div_sub_h #1#2#3!#4!%
{%
    \xint_gob_til_sc #4\XINT_div_sub_hi ;%
    \expandafter\XINT_div_sub_i\the\numexpr#1-#3+1#4-\xint_c_i\xint:%
}%
\def\XINT_div_sub_i 1#1#2\xint:%
{%
    1#2\expandafter!\the\numexpr\XINT_div_sub_a #1%
}%
\def\XINT_div_sub_bi;%
    \expandafter\XINT_div_sub_c\the\numexpr#1-#2+#3\xint:#4!#5!#6!#7!#8!#9!;!\W
{%
    \XINT_div_sub_l #1#2!#5!#7!#9!%
}%
\def\XINT_div_sub_di;%
    \expandafter\XINT_div_sub_e\the\numexpr#1-#2+#3\xint:#4!#5!#6!#7!#8\W
{%
    \XINT_div_sub_l #1#2!#5!#7!%
}%
\def\XINT_div_sub_fi;%
    \expandafter\XINT_div_sub_g\the\numexpr#1-#2+#3\xint:#4!#5!#6\W
{%
    \XINT_div_sub_l #1#2!#5!%
}%
\def\XINT_div_sub_hi;%
    \expandafter\XINT_div_sub_i\the\numexpr#1-#2+#3\xint:#4\W
{%
    \XINT_div_sub_l #1#2!%
}%
\def\XINT_div_sub_l #1%
{%
   \xint_UDzerofork
      #1{-2\relax}%
       0\XINT_div_sub_r
   \krof
}%
\def\XINT_div_sub_r #1!%
{%
    -\ifnum 0#1=\xint_c_ 1\else2\fi\relax
}%
\def\XINT_sdiv_out #1;!#2!%
    {\expandafter
     {\romannumeral0\XINT_unsep_cuzsmall
      #1\xint_bye!2!3!4!5!6!7!8!9!\xint_bye\xint_c_i\relax}%
     {#2}}%
\def\XINT_smalldivx_a #1\xint:1#2!1#3!%
{%
    \expandafter\XINT_smalldivx_b
    \the\numexpr (#3+#1)/#2-\xint_c_i!#1\xint:#2!#3!%
}%
\def\XINT_smalldivx_b #1#2!%
{%
    \if0#1\else
          \xint_c_x^viii+#1#2\xint_afterfi{\expandafter!\the\numexpr}\fi
    \XINT_smalldiv_c #1#2!%
}%
\def\XINT_smalldiv_c #1!#2\xint:#3!#4!%
{%
    \expandafter\XINT_smalldiv_d\the\numexpr #4-#1*#3!#2\xint:#3!%
}%
\def\XINT_smalldiv_d #1!#2!1#3#4!%
{%
    \xint_gob_til_sc #3\XINT_smalldiv_end ;%
    \XINT_smalldiv_e #1!#2!1#3#4!%
}%
\def\XINT_smalldiv_end;\XINT_smalldiv_e #1!#2!1;!{1!;!#1!}%
\def\XINT_smalldiv_e #1!#2\xint:#3!%
{%
    \expandafter\XINT_smalldiv_f\the\numexpr
    \xint_c_xi_e_viii_mone+#1*\xint_c_x^viii/#3!#2\xint:#3!#1!%
}%
\def\XINT_smalldiv_f 1#1#2#3#4#5#6!#7\xint:#8!%
{%
     \xint_gob_til_zero #1\XINT_smalldiv_fz 0%
     \expandafter\XINT_smalldiv_g
     \the\numexpr\XINT_minimul_a #2#3#4#5\xint:#6!#8!#2#3#4#5#6!#7\xint:#8!%
}%
\def\XINT_smalldiv_fz 0%
    \expandafter\XINT_smalldiv_g\the\numexpr\XINT_minimul_a
    9999\xint:9999!#1!99999999!#2!0!1#3!%
{%
    \XINT_smalldiv_i \xint:#3!\xint_c_!#2!%
}%
\def\XINT_smalldiv_g 1#1!1#2!#3!#4!#5!#6!%
{%
    \expandafter\XINT_smalldiv_h\the\numexpr 1#6-#1\xint:#2!#5!#3!#4!%
}%
\def\XINT_smalldiv_h 1#1#2\xint:#3!#4!%
{%
    \expandafter\XINT_smalldiv_i\the\numexpr #4-#3+#1-\xint_c_i\xint:#2!%
}%
\def\XINT_smalldiv_i #1\xint:#2!#3!#4\xint:#5!%
{%
    \expandafter\XINT_smalldiv_j\the\numexpr (#1#2+#4)/#5-\xint_c_i!#3!#1#2!#4\xint:#5!%
}%
\def\XINT_smalldiv_j #1!#2!%
{%
    \xint_c_x^viii+#1+#2\expandafter!\the\numexpr\XINT_smalldiv_k
    #1!%
}%
\def\XINT_smalldiv_k #1!#2!#3\xint:#4!%
{%
    \expandafter\XINT_smalldiv_d\the\numexpr #2-#1*#4!#3\xint:#4!%
}%
\def\XINT_div_mini #1\xint:#2!1#3!%
{%
    \expandafter\XINT_div_mini_a\the\numexpr
    \xint_c_xi_e_viii_mone+#3*\xint_c_x^viii/#1!#1\xint:#2!#3!%
}%
\def\XINT_div_mini_a 1#1#2#3#4#5#6!#7\xint:#8!%
{%
     \xint_gob_til_zero #1\XINT_div_mini_w 0%
     \expandafter\XINT_div_mini_b
     \the\numexpr\XINT_minimul_a #2#3#4#5\xint:#6!#7!#2#3#4#5#6!#7\xint:#8!%
}%
\def\XINT_div_mini_w 0%
    \expandafter\XINT_div_mini_b\the\numexpr\XINT_minimul_a
    9999\xint:9999!#1!99999999!#2\xint:#3!00000000!#4!%
{%
    \xint_c_x^viii_mone+(#4+#3)/#2!%
}%
\def\XINT_div_mini_b 1#1!1#2!#3!#4!#5!#6!%
{%
    \expandafter\XINT_div_mini_c
    \the\numexpr 1#6-#1\xint:#2!#5!#3!#4!%
}%
\def\XINT_div_mini_c 1#1#2\xint:#3!#4!%
{%
    \expandafter\XINT_div_mini_d
    \the\numexpr #4-#3+#1-\xint_c_i\xint:#2!%
}%
\def\XINT_div_mini_d #1\xint:#2!#3!#4\xint:#5!%
{%
    \xint_c_x^viii_mone+#3+(#1#2+#5)/#4!%
}%
\def\xintiiQuo {\romannumeral0\xintiiquo }%
\def\xintiiRem {\romannumeral0\xintiirem }%
\def\xintiiquo
   {\expandafter\xint_stop_atfirstoftwo\romannumeral0\xintiidivision }%
\def\xintiirem
   {\expandafter\xint_stop_atsecondoftwo\romannumeral0\xintiidivision }%
\def\xintiiDivRound   {\romannumeral0\xintiidivround }%
\def\xintiidivround #1{\expandafter\XINT_iidivround\romannumeral`&&@#1\xint:}%
\def\XINT_idivround #1#2\xint:#3%
    {\expandafter\XINT_iidivround_a\expandafter #1%
                 \romannumeral0\xintnum{#3}\xint:#2\xint:}%
\def\XINT_iidivround #1#2\xint:#3%
    {\expandafter\XINT_iidivround_a\expandafter #1\romannumeral`&&@#3\xint:#2\xint:}%
\def\XINT_iidivround_a #1#2% #1 de A, #2 de B.
{%
    \if0#2\xint_dothis{\XINT_iidivround_divbyzero#1#2}\fi
    \if0#1\xint_dothis\XINT_iidivround_aiszero\fi
    \if-#2\xint_dothis{\XINT_iidivround_bneg #1}\fi
          \xint_orthat{\XINT_iidivround_bpos #1#2}%
}%
\def\XINT_iidivround_divbyzero #1#2#3\xint:#4\xint:
   {\XINT_signalcondition{DivisionByZero}{Division of #1#4 by #2#3}{}{0}}%
\def\XINT_iidivround_aiszero   #1\xint:#2\xint:{ 0}%
\def\XINT_iidivround_bpos #1%
{%
    \xint_UDsignfork
            #1{\xintiiopp\XINT_iidivround_pos {}}%
             -{\XINT_iidivround_pos #1}%
    \krof
}%
\def\XINT_iidivround_bneg #1%
{%
    \xint_UDsignfork
            #1{\XINT_iidivround_pos {}}%
             -{\xintiiopp\XINT_iidivround_pos #1}%
    \krof
}%
\def\XINT_iidivround_pos #1#2\xint:#3\xint:
{%
    \expandafter\expandafter\expandafter\XINT_dsrr
    \expandafter\xint_firstoftwo
    \romannumeral0\XINT_div_prepare {#2}{#1#30}%
    \xint_bye\xint_Bye3456789\xint_bye/\xint_c_x\relax
}%
\def\xintiiDivTrunc   {\romannumeral0\xintiidivtrunc }%
\def\xintiidivtrunc #1{\expandafter\XINT_iidivtrunc\romannumeral`&&@#1\xint:}%
\def\XINT_iidivtrunc #1#2\xint:#3{\expandafter\XINT_iidivtrunc_a\expandafter #1%
                             \romannumeral`&&@#3\xint:#2\xint:}%
\def\XINT_iidivtrunc_a #1#2% #1 de A, #2 de B.
{%
    \if0#2\xint_dothis{\XINT_iidivtrunc_divbyzero#1#2}\fi
    \if0#1\xint_dothis\XINT_iidivtrunc_aiszero\fi
    \if-#2\xint_dothis{\XINT_iidivtrunc_bneg #1}\fi
          \xint_orthat{\XINT_iidivtrunc_bpos #1#2}%
}%
\let\XINT_iidivtrunc_divbyzero\XINT_iidivround_divbyzero
\let\XINT_iidivtrunc_aiszero  \XINT_iidivround_aiszero
\def\XINT_iidivtrunc_bpos #1%
{%
    \xint_UDsignfork
            #1{\xintiiopp\XINT_iidivtrunc_pos {}}%
             -{\XINT_iidivtrunc_pos #1}%
    \krof
}%
\def\XINT_iidivtrunc_bneg #1%
{%
    \xint_UDsignfork
            #1{\XINT_iidivtrunc_pos {}}%
             -{\xintiiopp\XINT_iidivtrunc_pos #1}%
    \krof
}%
\def\XINT_iidivtrunc_pos #1#2\xint:#3\xint:
    {\expandafter\xint_stop_atfirstoftwo
     \romannumeral0\XINT_div_prepare {#2}{#1#3}}%
\def\xintiiModTrunc {\romannumeral0\xintiimodtrunc }%
\def\xintiimodtrunc #1{\expandafter\XINT_iimodtrunc\romannumeral`&&@#1\xint:}%
\def\XINT_iimodtrunc #1#2\xint:#3{\expandafter\XINT_iimodtrunc_a\expandafter #1%
                             \romannumeral`&&@#3\xint:#2\xint:}%
\def\XINT_iimodtrunc_a #1#2% #1 de A, #2 de B.
{%
    \if0#2\xint_dothis{\XINT_iimodtrunc_divbyzero#1#2}\fi
    \if0#1\xint_dothis\XINT_iimodtrunc_aiszero\fi
    \if-#2\xint_dothis{\XINT_iimodtrunc_bneg #1}\fi
          \xint_orthat{\XINT_iimodtrunc_bpos #1#2}%
}%
\let\XINT_iimodtrunc_divbyzero\XINT_iidivround_divbyzero
\let\XINT_iimodtrunc_aiszero  \XINT_iidivround_aiszero
\def\XINT_iimodtrunc_bpos #1%
{%
    \xint_UDsignfork
            #1{\xintiiopp\XINT_iimodtrunc_pos {}}%
             -{\XINT_iimodtrunc_pos #1}%
    \krof
}%
\def\XINT_iimodtrunc_bneg #1%
{%
    \xint_UDsignfork
            #1{\xintiiopp\XINT_iimodtrunc_pos {}}%
             -{\XINT_iimodtrunc_pos #1}%
    \krof
}%
\def\XINT_iimodtrunc_pos #1#2\xint:#3\xint:
    {\expandafter\xint_stop_atsecondoftwo\romannumeral0\XINT_div_prepare
      {#2}{#1#3}}%
\def\xintiiDivMod   {\romannumeral0\xintiidivmod }%
\def\xintiidivmod #1{\expandafter\XINT_iidivmod\romannumeral`&&@#1\xint:}%
\def\XINT_iidivmod #1#2\xint:#3{\expandafter\XINT_iidivmod_a\expandafter #1%
                             \romannumeral`&&@#3\xint:#2\xint:}%
\def\XINT_iidivmod_a #1#2% #1 de A, #2 de B.
{%
    \if0#2\xint_dothis{\XINT_iidivmod_divbyzero#1#2}\fi
    \if0#1\xint_dothis\XINT_iidivmod_aiszero\fi
    \if-#2\xint_dothis{\XINT_iidivmod_bneg #1}\fi
          \xint_orthat{\XINT_iidivmod_bpos #1#2}%
}%
\def\XINT_iidivmod_divbyzero #1#2\xint:#3\xint:
{%
    \XINT_signalcondition{DivisionByZero}{Division by #2 of #1#3}{}%
    {{0}{0}}% ^^c3^^a0 revoir...
}%
\def\XINT_iidivmod_aiszero #1\xint:#2\xint:{{0}{0}}%
\def\XINT_iidivmod_bneg #1%
{%
    \expandafter\XINT_iidivmod_bneg_finish
    \romannumeral0\xint_UDsignfork
            #1{\XINT_iidivmod_bpos {}}%
             -{\XINT_iidivmod_bpos {-#1}}%
    \krof
}%
\def\XINT_iidivmod_bneg_finish#1#2%
{%
    \expandafter\xint_exchangetwo_keepbraces\expandafter
    {\romannumeral0\xintiiopp#2}{#1}%
}%
\def\XINT_iidivmod_bpos #1#2\xint:#3\xint:{\xintiidivision{#1#3}{#2}}%
\def\xintiiDivFloor {\romannumeral0\xintiidivfloor}%
\def\xintiidivfloor {\expandafter\xint_stop_atfirstoftwo
                \romannumeral0\xintiidivmod}%
\def\xintiiMod {\romannumeral0\xintiimod}%
\def\xintiimod {\expandafter\xint_stop_atsecondoftwo
                \romannumeral0\xintiidivmod}%
\def\xintiiSqr {\romannumeral0\xintiisqr }%
\def\xintiisqr #1%
{%
    \expandafter\XINT_sqr\romannumeral0\xintiiabs{#1}\xint:
}%
\def\XINT_sqr #1\xint:
{%
    \expandafter\XINT_sqr_a
      \romannumeral0\expandafter\XINT_sepandrev_andcount
      \romannumeral0\XINT_zeroes_forviii #1\R\R\R\R\R\R\R\R{10}0000001\W
      #1\XINT_rsepbyviii_end_A 2345678%
        \XINT_rsepbyviii_end_B 2345678\relax\xint_c_ii\xint_c_i
              \R\xint:\xint_c_xii \R\xint:\xint_c_x  \R\xint:\xint_c_viii \R\xint:\xint_c_vi
              \R\xint:\xint_c_iv  \R\xint:\xint_c_ii \R\xint:\xint_c_\W
      \xint:
}%
\def\XINT_sqr_a #1\xint:
{%
    \ifnum #1=\xint_c_i \expandafter\XINT_sqr_small
                   \else\expandafter\XINT_sqr_start\fi
}%
\def\XINT_sqr_small 1#1#2#3#4#5!\xint:
{%
    \ifnum #1#2#3#4#5<46341 \expandafter\XINT_sqr_verysmall\fi
    \expandafter\XINT_sqr_small_out
    \the\numexpr\XINT_minimul_a #1#2#3#4\xint:#5!#1#2#3#4#5!%
}%
\def\XINT_sqr_verysmall#1{%
\def\XINT_sqr_verysmall
    \expandafter\XINT_sqr_small_out\the\numexpr\XINT_minimul_a ##1!##2!%
    {\expandafter#1\the\numexpr ##2*##2\relax}%
}\XINT_sqr_verysmall{ }%
\def\XINT_sqr_small_out 1#1!1#2!%
{%
    \XINT_cuz #2#1\R
}%
\def\XINT_sqr_start #1\xint:
{%
    \expandafter\XINT_mul_out
    \the\numexpr\XINT_mul_loop
                100000000!1;!\W #11;!\W #11;!%
    1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
}%
\def\xintiiPow {\romannumeral0\xintiipow }%
\def\xintiipow #1#2%
{%
    \expandafter\xint_pow\the\numexpr #2\expandafter
    .\romannumeral`&&@#1\xint:
}%
\def\xint_pow #1.#2%#3\xint:
{%
    \xint_UDzerominusfork
      #2-\XINT_pow_AisZero
      0#2\XINT_pow_Aneg
      0-{\XINT_pow_Apos #2}%
    \krof {#1}%
}%
\def\XINT_pow_AisZero #1#2\xint:
{%
     \ifcase\XINT_cntSgn #1\xint:
         \xint_afterfi { 1}%
     \or
         \xint_afterfi { 0}%
     \else
         \xint_afterfi
        {\XINT_signalcondition{DivisionByZero}{Zero to power #1}{}{0}}%
     \fi
}%
\def\XINT_pow_Aneg #1%
{%
   \ifodd #1
       \expandafter\XINT_opp\romannumeral0%
   \fi
   \XINT_pow_Apos {}{#1}%
}%
\def\XINT_pow_Apos #1#2{\XINT_pow_Apos_a {#2}#1}%
\def\XINT_pow_Apos_a #1#2#3%
{%
    \xint_gob_til_xint: #3\XINT_pow_Apos_short\xint:
    \XINT_pow_AatleastTwo {#1}#2#3%
}%
\def\XINT_pow_Apos_short\xint:\XINT_pow_AatleastTwo #1#2\xint:
{%
    \ifcase #2
         \xintError:thiscannothappen
    \or  \expandafter\XINT_pow_AisOne
    \else\expandafter\XINT_pow_AatleastTwo
    \fi {#1}#2\xint:
}%
\def\XINT_pow_AisOne #1\xint:{ 1}%
\def\XINT_pow_AatleastTwo #1%
{%
    \ifcase\XINT_cntSgn #1\xint:
        \expandafter\XINT_pow_BisZero
    \or
        \expandafter\XINT_pow_I_in
    \else
        \expandafter\XINT_pow_BisNegative
    \fi
    {#1}%
}%
\def\XINT_pow_BisNegative #1\xint:{\XINT_signalcondition{Underflow}{Inverse power
    can not be represented by an integer}{}{0}}%
\def\XINT_pow_BisZero #1\xint:{ 1}%
\def\XINT_pow_I_in #1#2\xint:
{%
    \expandafter\XINT_pow_I_loop
    \the\numexpr #1\expandafter\xint:%
    \romannumeral0\expandafter\XINT_sepandrev
    \romannumeral0\XINT_zeroes_forviii #2\R\R\R\R\R\R\R\R{10}0000001\W
    #2\XINT_rsepbyviii_end_A 2345678%
      \XINT_rsepbyviii_end_B 2345678\relax XX%
    \R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\R\xint:\W
    1;!\W
    1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
}%
\def\XINT_pow_I_loop #1\xint:%
{%
    \ifnum #1 = \xint_c_i\expandafter\XINT_pow_I_exit\fi
    \ifodd #1
       \expandafter\XINT_pow_II_in
    \else
       \expandafter\XINT_pow_I_squareit
    \fi #1\xint:%
}%
\def\XINT_pow_I_exit \ifodd #1\fi #2\xint:#3\W {\XINT_mul_out #3}%
\def\XINT_pow_I_squareit #1\xint:#2\W%
{%
    \expandafter\XINT_pow_I_loop
    \the\numexpr #1/\xint_c_ii\expandafter\xint:%
    \the\numexpr\XINT_pow_mulbutcheckifsmall #2\W #2\W
}%
\def\XINT_pow_mulbutcheckifsmall #1!1#2%
{%
    \xint_gob_til_sc #2\XINT_pow_mul_small;%
    \XINT_mul_loop 100000000!1;!\W #1!1#2%
}%
\def\XINT_pow_mul_small;\XINT_mul_loop
    100000000!1;!\W 1#1!1;!\W
{%
    \XINT_smallmul 1#1!%
}%
\def\XINT_pow_II_in #1\xint:#2\W
{%
    \expandafter\XINT_pow_II_loop
    \the\numexpr #1/\xint_c_ii-\xint_c_i\expandafter\xint:%
    \the\numexpr\XINT_pow_mulbutcheckifsmall #2\W #2\W #2\W
}%
\def\XINT_pow_II_loop #1\xint:%
{%
    \ifnum #1 = \xint_c_i\expandafter\XINT_pow_II_exit\fi
    \ifodd #1
       \expandafter\XINT_pow_II_odda
    \else
       \expandafter\XINT_pow_II_even
    \fi #1\xint:%
}%
\def\XINT_pow_II_exit\ifodd #1\fi #2\xint:#3\W #4\W
{%
    \expandafter\XINT_mul_out
    \the\numexpr\XINT_pow_mulbutcheckifsmall #4\W #3%
}%
\def\XINT_pow_II_even #1\xint:#2\W
{%
    \expandafter\XINT_pow_II_loop
    \the\numexpr #1/\xint_c_ii\expandafter\xint:%
    \the\numexpr\XINT_pow_mulbutcheckifsmall #2\W #2\W
}%
\def\XINT_pow_II_odda #1\xint:#2\W #3\W
{%
    \expandafter\XINT_pow_II_oddb
    \the\numexpr #1/\xint_c_ii-\xint_c_i\expandafter\xint:%
    \the\numexpr\XINT_pow_mulbutcheckifsmall #3\W #2\W #2\W
}%
\def\XINT_pow_II_oddb #1\xint:#2\W #3\W
{%
    \expandafter\XINT_pow_II_loop
    \the\numexpr #1\expandafter\xint:%
    \the\numexpr\XINT_pow_mulbutcheckifsmall #3\W #3\W #2\W
}%
\def\xintiiFac {\romannumeral0\xintiifac }%
\def\xintiifac #1{\expandafter\XINT_fac_fork\the\numexpr#1.}%
\def\XINT_fac_fork #1#2.%
{%
    \xint_UDzerominusfork
     #1-\XINT_fac_zero
     0#1\XINT_fac_neg
      0-\XINT_fac_checksize
    \krof #1#2.%
}%
\def\XINT_fac_zero #1.{ 1}%
\def\XINT_fac_neg  #1.{\XINT_signalcondition{InvalidOperation}{Factorial of
    negative: (#1)!}{}{0}}%
\def\XINT_fac_checksize #1.%
{%
    \ifnum #1>\xint_c_x^iv \xint_dothis{\XINT_fac_toobig #1.}\fi
    \ifnum #1>465 \xint_dothis{\XINT_fac_bigloop_a   #1.}\fi
    \ifnum #1>101 \xint_dothis{\XINT_fac_medloop_a   #1.\XINT_mul_out}\fi
                  \xint_orthat{\XINT_fac_smallloop_a #1.\XINT_mul_out}%
    1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W
}%
\def\XINT_fac_toobig #1.#2\W{\XINT_signalcondition{InvalidOperation}{Factorial
    of too big argument: #1 > 10000}{}{0}}%
\def\XINT_fac_bigloop_a #1.%
{%
    \expandafter\XINT_fac_bigloop_b \the\numexpr
    #1+\xint_c_i-\xint_c_ii*((#1-464)/\xint_c_ii).#1.%
}%
\def\XINT_fac_bigloop_b #1.#2.%
{%
    \expandafter\XINT_fac_medloop_a
        \the\numexpr #1-\xint_c_i.{\XINT_fac_bigloop_loop #1.#2.}%
}%
\def\XINT_fac_bigloop_loop #1.#2.%
{%
    \ifnum #1>#2 \expandafter\XINT_fac_bigloop_exit\fi
    \expandafter\XINT_fac_bigloop_loop
    \the\numexpr #1+\xint_c_ii\expandafter.%
    \the\numexpr #2\expandafter.\the\numexpr\XINT_fac_bigloop_mul #1!%
}%
\def\XINT_fac_bigloop_exit #1!{\XINT_mul_out}%
\def\XINT_fac_bigloop_mul #1!%
{%
    \expandafter\XINT_smallmul
        \the\numexpr \xint_c_x^viii+#1*(#1+\xint_c_i)!%
}%
\def\XINT_fac_medloop_a #1.%
{%
    \expandafter\XINT_fac_medloop_b
        \the\numexpr #1+\xint_c_i-\xint_c_iii*((#1-100)/\xint_c_iii).#1.%
}%
\def\XINT_fac_medloop_b #1.#2.%
{%
    \expandafter\XINT_fac_smallloop_a
        \the\numexpr #1-\xint_c_i.{\XINT_fac_medloop_loop #1.#2.}%
}%
\def\XINT_fac_medloop_loop #1.#2.%
{%
    \ifnum #1>#2 \expandafter\XINT_fac_loop_exit\fi
    \expandafter\XINT_fac_medloop_loop
    \the\numexpr #1+\xint_c_iii\expandafter.%
    \the\numexpr #2\expandafter.\the\numexpr\XINT_fac_medloop_mul #1!%
}%
\def\XINT_fac_medloop_mul #1!%
{%
    \expandafter\XINT_smallmul
    \the\numexpr
        \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)!%
}%
\def\XINT_fac_smallloop_a #1.%
{%
    \csname
       XINT_fac_smallloop_\the\numexpr #1-\xint_c_iv*(#1/\xint_c_iv)\relax
    \endcsname #1.%
}%
\expandafter\def\csname XINT_fac_smallloop_1\endcsname #1.%
{%
    \XINT_fac_smallloop_loop 2.#1.100000001!1;!%
}%
\expandafter\def\csname XINT_fac_smallloop_-2\endcsname #1.%
{%
    \XINT_fac_smallloop_loop 3.#1.100000002!1;!%
}%
\expandafter\def\csname XINT_fac_smallloop_-1\endcsname #1.%
{%
    \XINT_fac_smallloop_loop 4.#1.100000006!1;!%
}%
\expandafter\def\csname XINT_fac_smallloop_0\endcsname #1.%
{%
    \XINT_fac_smallloop_loop 5.#1.1000000024!1;!%
}%
\def\XINT_fac_smallloop_loop #1.#2.%
{%
    \ifnum #1>#2 \expandafter\XINT_fac_loop_exit\fi
    \expandafter\XINT_fac_smallloop_loop
    \the\numexpr #1+\xint_c_iv\expandafter.%
    \the\numexpr #2\expandafter.\the\numexpr\XINT_fac_smallloop_mul #1!%
}%
\def\XINT_fac_smallloop_mul #1!%
{%
    \expandafter\XINT_smallmul
    \the\numexpr
        \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)*(#1+\xint_c_iii)!%
}%
\def\XINT_fac_loop_exit #1!#2;!#3{#3#2;!}%
\def\XINT_useiimessage #1% used in LaTeX only
{%
    \XINT_ifFlagRaised {#1}%
    {\@backslashchar#1
     (load xintfrac or use \@backslashchar xintii\xint_gobble_iv#1!)\MessageBreak}%
    {}%
}%
\XINT_restorecatcodes_endinput%
\endinput
%%
%% End of file `xintcore.sty'.
