%%
%% This is file `xintfrac.sty',
%% generated with the docstrip utility.
%%
%% The original source files were:
%%
%% xint.dtx  (with options: `xintfrac')
%% 
%% IMPORTANT NOTICE:
%% 
%% For the copyright see the source file.
%% 
%% Any modified versions of this file must be renamed
%% with new filenames distinct from xintfrac.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 (version 1.09d of October 22, 2013)
%% xintfrac: Expandable operations on fractions
%% Copyright (C) 2013 by Jean-Francois Burnol
%%----------------------------------------------------------------
%%
\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   % :
  \def\space { }%
  \let\z\endgroup
  \expandafter\let\expandafter\x\csname ver@xintfrac.sty\endcsname
  \expandafter\let\expandafter\w\csname ver@xint.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{xintfrac}{\numexpr not available, aborting input}%
     \aftergroup\endinput
  \else
    \ifx\x\relax   % plain-TeX, first loading of xintfrac.sty
      \ifx\w\relax % but xint.sty not yet loaded.
         \y{xintfrac}{Package xint is required}%
         \y{xintfrac}{Will try \string\input\space xint.sty}%
         \def\z{\endgroup\input xint.sty\relax}%
      \fi
    \else
      \def\empty {}%
      \ifx\x\empty % LaTeX, first loading,
      % variable is initialized, but \ProvidesPackage not yet seen
          \ifx\w\relax % xint.sty not yet loaded.
            \y{xintfrac}{Package xint is required}%
            \y{xintfrac}{Will try \string\RequirePackage{xint}}%
            \def\z{\endgroup\RequirePackage{xint}}%
          \fi
      \else
        \y{xintfrac}{I was already loaded, aborting input}%
        \aftergroup\endinput
      \fi
    \fi
  \fi
\z%
\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   % :
  \ifdefined\PackageInfo
      \def\y#1#2{\PackageInfo{#1}{#2}}%
    \else
      \def\y#1#2{\immediate\write-1{Package #1 Info: #2.}}%
  \fi
  \def\empty {}%
  \expandafter\let\expandafter\w\csname ver@xint.sty\endcsname
  \ifx\w\relax % Plain TeX, user gave a file name at the prompt
      \y{xintfrac}{Loading of package xint failed, aborting input}%
      \aftergroup\endinput
  \fi
  \ifx\w\empty % LaTeX, user gave a file name at the prompt
      \y{xintfrac}{Loading of package xint failed, aborting input}%
      \aftergroup\endinput
  \fi
\endgroup%
\XINTsetupcatcodes%
\XINT_providespackage
\ProvidesPackage{xintfrac}%
  [2013/10/22 v1.09d Expandable operations on fractions (jfB)]%
\chardef\xint_c_vi     6
\chardef\xint_c_vii    7
\chardef\xint_c_xviii 18
\mathchardef\xint_c_x^iv 10000
\def\xintLen {\romannumeral0\xintlen }%
\def\xintlen #1%
{%
    \expandafter\XINT_flen\romannumeral0\XINT_infrac {#1}%
}%
\def\XINT_flen #1#2#3%
{%
    \expandafter\space
    \the\numexpr -1+\XINT_Abs {#1}+\XINT_Len {#2}+\XINT_Len {#3}\relax
}%
\def\XINT_lenrord_loop #1#2#3#4#5#6#7#8#9%
{%  faire \romannumeral-`0\XINT_lenrord_loop 0{}#1\Z\W\W\W\W\W\W\W\Z
    \xint_gob_til_W #9\XINT_lenrord_W\W
    \expandafter\XINT_lenrord_loop\expandafter
    {\the\numexpr #1+7}{#9#8#7#6#5#4#3#2}%
}%
\def\XINT_lenrord_W\W\expandafter\XINT_lenrord_loop\expandafter #1#2#3\Z
{%
    \expandafter\XINT_lenrord_X\expandafter {#1}#2\Z
}%
\def\XINT_lenrord_X #1#2\Z
{%
    \XINT_lenrord_Y #2\R\R\R\R\R\R\T {#1}%
}%
\def\XINT_lenrord_Y #1#2#3#4#5#6#7#8\T
{%
    \xint_gob_til_W
            #7\XINT_lenrord_Z \xint_c_viii
            #6\XINT_lenrord_Z \xint_c_vii
            #5\XINT_lenrord_Z \xint_c_vi
            #4\XINT_lenrord_Z \xint_c_v
            #3\XINT_lenrord_Z \xint_c_iv
            #2\XINT_lenrord_Z \xint_c_iii
            \W\XINT_lenrord_Z \xint_c_ii   \Z
}%
\def\XINT_lenrord_Z #1#2\Z #3% retourne: {longueur}renverse\Z
{%
    \expandafter{\the\numexpr #3-#1\relax}%
}%
\def\XINT_outfrac #1#2#3%
{%
    \ifcase\XINT_Sgn{#3}
        \expandafter \XINT_outfrac_divisionbyzero
    \or
        \expandafter \XINT_outfrac_P
    \else
        \expandafter \XINT_outfrac_N
    \fi
    {#2}{#3}[#1]%
}%
\def\XINT_outfrac_divisionbyzero #1#2{\xintError:DivisionByZero\space #1/0}%
\def\XINT_outfrac_P #1#2%
{%
    \ifcase\XINT_Sgn{#1}
        \expandafter\XINT_outfrac_Zero
    \fi
    \space #1/#2%
}%
\def\XINT_outfrac_Zero #1[#2]{ 0/1[0]}%
\def\XINT_outfrac_N #1#2%
{%
    \expandafter\XINT_outfrac_N_a\expandafter
    {\romannumeral0\XINT_opp #2}{\romannumeral0\XINT_opp #1}%
}%
\def\XINT_outfrac_N_a #1#2%
{%
    \expandafter\XINT_outfrac_P\expandafter {#2}{#1}%
}%
\def\XINT_inFrac {\romannumeral0\XINT_infrac }%
\def\XINT_infrac #1%
{%
    \expandafter\XINT_infrac_ \romannumeral-`0#1[\W]\Z\T
}%
\def\XINT_infrac_ #1[#2#3]#4\Z
{%
    \xint_UDwfork
      #2\dummy \XINT_infrac_A
      \W\dummy \XINT_infrac_B
    \krof
    #1[#2#3]#4%
}%
\def\XINT_infrac_A #1[\W]\T
{%
    \XINT_frac #1/\W\Z
}%
\def\XINT_infrac_B #1%
{%
    \xint_gob_til_zero #1\XINT_infrac_Zero0\XINT_infrac_BB #1%
}%
\def\XINT_infrac_BB #1[\W]\T {\XINT_infrac_BC #1/\W\Z }%
\def\XINT_infrac_BC #1/#2#3\Z
{%
    \xint_UDwfork
     #2\dummy \XINT_infrac_BCa
     \W\dummy {\expandafter\XINT_infrac_BCb \romannumeral-`0#2}%
    \krof
    #3\Z #1\Z
}%
\def\XINT_infrac_BCa \Z #1[#2]#3\Z { {#2}{#1}{1}}%
\def\XINT_infrac_BCb #1[#2]/\W\Z #3\Z { {#2}{#3}{#1}}%
\def\XINT_infrac_Zero #1\T { {0}{0}{1}}%
\def\XINT_frac #1/#2#3\Z
{%
    \xint_UDwfork
     #2\dummy \XINT_frac_A
     \W\dummy {\expandafter\XINT_frac_U \romannumeral-`0#2}%
    \krof
    #3e\W\Z #1e\W\Z
}%
\def\XINT_frac_U #1e#2#3\Z
{%
    \xint_UDwfork
      #2\dummy  \XINT_frac_Ua
      \W\dummy {\XINT_frac_Ub #2}%
    \krof
    #3\Z #1\Z
}%
\def\XINT_frac_Ua      \Z #1/\W\Z  {\XINT_frac_B #1.\W\Z {0}}%
\def\XINT_frac_Ub #1/\W e\W\Z #2\Z {\XINT_frac_B #2.\W\Z {#1}}%
\def\XINT_frac_B #1.#2#3\Z
{%
    \xint_UDwfork
      #2\dummy  \XINT_frac_Ba
      \W\dummy {\XINT_frac_Bb #2}%
    \krof
    #3\Z #1\Z
}%
\def\XINT_frac_Ba \Z #1\Z {\XINT_frac_T {0}{#1}}%
\def\XINT_frac_Bb #1.\W\Z #2\Z
{%
    \expandafter \XINT_frac_T \expandafter
    {\romannumeral0\XINT_length {#1}}{#2#1}%
}%
\def\XINT_frac_A e\W\Z {\XINT_frac_T {0}{1}{0}}%
\def\XINT_frac_T #1#2#3#4e#5#6\Z
{%
    \xint_UDwfork
      #5\dummy  \XINT_frac_Ta
      \W\dummy {\XINT_frac_Tb #5}%
    \krof
    #6\Z #4\Z {#1}{#2}{#3}%
}%
\def\XINT_frac_Ta \Z #1\Z      {\XINT_frac_C #1.\W\Z {0}}%
\def\XINT_frac_Tb #1e\W\Z #2\Z {\XINT_frac_C #2.\W\Z {#1}}%
\def\XINT_frac_C #1.#2#3\Z
{%
    \xint_UDwfork
      #2\dummy \XINT_frac_Ca
      \W\dummy {\XINT_frac_Cb #2}%
    \krof
    #3\Z #1\Z
}%
\def\XINT_frac_Ca \Z #1\Z {\XINT_frac_D {0}{#1}}%
\def\XINT_frac_Cb #1.\W\Z #2\Z
{%
    \expandafter\XINT_frac_D\expandafter
    {\romannumeral0\XINT_length {#1}}{#2#1}%
}%
\def\XINT_frac_D #1#2#3#4#5#6%
{%
    \expandafter \XINT_frac_E \expandafter
    {\the\numexpr -#1+#3+#4-#6\expandafter}\expandafter
    {\romannumeral0\XINT_num_loop #2%
     \xint_relax\xint_relax\xint_relax\xint_relax
     \xint_relax\xint_relax\xint_relax\xint_relax\Z }%
    {\romannumeral0\XINT_num_loop #5%
     \xint_relax\xint_relax\xint_relax\xint_relax
     \xint_relax\xint_relax\xint_relax\xint_relax\Z }%
}%
\def\XINT_frac_E #1#2#3%
{%
   \expandafter \XINT_frac_F  #3\Z {#2}{#1}%
}%
\def\XINT_frac_F #1%
{%
    \xint_UDzerominusfork
      #1-\dummy  \XINT_frac_Gdivisionbyzero
      0#1\dummy  \XINT_frac_Gneg
       0-\dummy  {\XINT_frac_Gpos #1}%
    \krof
}%
\def\XINT_frac_Gdivisionbyzero #1\Z #2#3%
{%
   \xintError:DivisionByZero\space {0}{#2}{0}%
}%
\def\XINT_frac_Gneg #1\Z #2#3%
{%
    \expandafter\XINT_frac_H \expandafter{\romannumeral0\XINT_opp #2}{#3}{#1}%
}%
\def\XINT_frac_H #1#2{ {#2}{#1}}%
\def\XINT_frac_Gpos #1\Z #2#3{ {#3}{#2}{#1}}%
\def\XINT_factortens #1%
{%
    \expandafter\XINT_cuz_cnt_loop\expandafter
    {\expandafter}\romannumeral0\XINT_rord_main {}#1%
      \xint_relax
        \xint_undef\xint_undef\xint_undef\xint_undef
        \xint_undef\xint_undef\xint_undef\xint_undef
      \xint_relax
    \R\R\R\R\R\R\R\R\Z
}%
\def\XINT_cuz_cnt #1%
{%
    \XINT_cuz_cnt_loop {}#1\R\R\R\R\R\R\R\R\Z
}%
\def\XINT_cuz_cnt_loop #1#2#3#4#5#6#7#8#9%
{%
    \xint_gob_til_R #9\XINT_cuz_cnt_toofara \R
    \expandafter\XINT_cuz_cnt_checka\expandafter
    {\the\numexpr #1+8\relax}{#2#3#4#5#6#7#8#9}%
}%
\def\XINT_cuz_cnt_toofara\R
    \expandafter\XINT_cuz_cnt_checka\expandafter #1#2%
{%
    \XINT_cuz_cnt_toofarb {#1}#2%
}%
\def\XINT_cuz_cnt_toofarb #1#2\Z {\XINT_cuz_cnt_toofarc #2\Z {#1}}%
\def\XINT_cuz_cnt_toofarc #1#2#3#4#5#6#7#8%
{%
    \xint_gob_til_R #2\XINT_cuz_cnt_toofard 7%
            #3\XINT_cuz_cnt_toofard 6%
            #4\XINT_cuz_cnt_toofard 5%
            #5\XINT_cuz_cnt_toofard 4%
            #6\XINT_cuz_cnt_toofard 3%
            #7\XINT_cuz_cnt_toofard 2%
            #8\XINT_cuz_cnt_toofard 1%
            \Z #1#2#3#4#5#6#7#8%
}%
\def\XINT_cuz_cnt_toofard #1#2\Z #3\R #4\Z #5%
{%
    \expandafter\XINT_cuz_cnt_toofare
    \the\numexpr #3\relax \R\R\R\R\R\R\R\R\Z
    {\the\numexpr #5-#1\relax}\R\Z
}%
\def\XINT_cuz_cnt_toofare #1#2#3#4#5#6#7#8%
{%
    \xint_gob_til_R #2\XINT_cuz_cnt_stopc 1%
            #3\XINT_cuz_cnt_stopc 2%
            #4\XINT_cuz_cnt_stopc 3%
            #5\XINT_cuz_cnt_stopc 4%
            #6\XINT_cuz_cnt_stopc 5%
            #7\XINT_cuz_cnt_stopc 6%
            #8\XINT_cuz_cnt_stopc 7%
            \Z #1#2#3#4#5#6#7#8%
}%
\def\XINT_cuz_cnt_checka #1#2%
{%
    \expandafter\XINT_cuz_cnt_checkb\the\numexpr #2\relax \Z {#1}%
}%
\def\XINT_cuz_cnt_checkb #1%
{%
    \xint_gob_til_zero #1\expandafter\XINT_cuz_cnt_loop\xint_gob_til_Z
    0\XINT_cuz_cnt_stopa #1%
}%
\def\XINT_cuz_cnt_stopa #1\Z
{%
    \XINT_cuz_cnt_stopb #1\R\R\R\R\R\R\R\R\Z %
}%
\def\XINT_cuz_cnt_stopb #1#2#3#4#5#6#7#8#9%
{%
    \xint_gob_til_R #2\XINT_cuz_cnt_stopc 1%
            #3\XINT_cuz_cnt_stopc 2%
            #4\XINT_cuz_cnt_stopc 3%
            #5\XINT_cuz_cnt_stopc 4%
            #6\XINT_cuz_cnt_stopc 5%
            #7\XINT_cuz_cnt_stopc 6%
            #8\XINT_cuz_cnt_stopc 7%
            #9\XINT_cuz_cnt_stopc 8%
            \Z #1#2#3#4#5#6#7#8#9%
}%
\def\XINT_cuz_cnt_stopc #1#2\Z #3\R #4\Z #5%
{%
    \expandafter\XINT_cuz_cnt_stopd\expandafter
    {\the\numexpr #5-#1}#3%
}%
\def\XINT_cuz_cnt_stopd #1#2\R #3\Z
{%
    \expandafter\space\expandafter
     {\romannumeral0\XINT_rord_main {}#2%
      \xint_relax
        \xint_undef\xint_undef\xint_undef\xint_undef
        \xint_undef\xint_undef\xint_undef\xint_undef
      \xint_relax }{#1}%
}%
\def\xintRaw {\romannumeral0\xintraw }%
\def\xintraw
{%
    \expandafter\XINT_raw\romannumeral0\XINT_infrac
}%
\def\XINT_raw #1#2#3{ #2/#3[#1]}%
\def\xintPRaw {\romannumeral0\xintpraw }%
\def\xintpraw
{%
    \expandafter\XINT_praw\romannumeral0\XINT_infrac
}%
\def\XINT_praw #1%
{%
    \ifnum #1=\xint_c_ \expandafter\XINT_praw_a\fi \XINT_praw_A {#1}%
}%
\def\XINT_praw_A #1#2#3%
{%
    \if\XINT_isOne{#3}1\expandafter\xint_firstoftwo
                  \else\expandafter\xint_secondoftwo
    \fi { #2[#1]}{ #2/#3[#1]}%
}%
\def\XINT_praw_a\XINT_praw_A #1#2#3%
{%
    \if\XINT_isOne{#3}1\expandafter\xint_firstoftwo
                  \else\expandafter\xint_secondoftwo
    \fi { #2}{ #2/#3}%
}%
\def\xintRawWithZeros {\romannumeral0\xintrawwithzeros }%
\def\xintrawwithzeros
{%
    \expandafter\XINT_rawz\romannumeral0\XINT_infrac
}%
\def\XINT_rawz #1%
{%
    \ifcase\XINT_Sgn {#1}
      \expandafter\XINT_rawz_Ba
    \or
      \expandafter\XINT_rawz_A
    \else
      \expandafter\XINT_rawz_Ba
    \fi
    {#1}%
}%
\def\XINT_rawz_A  #1#2#3{\xint_dsh {#2}{-#1}/#3}%
\def\XINT_rawz_Ba #1#2#3{\expandafter\XINT_rawz_Bb
                        \expandafter{\romannumeral0\xint_dsh {#3}{#1}}{#2}}%
\def\XINT_rawz_Bb #1#2{ #2/#1}%
\def\xintFloor {\romannumeral0\xintfloor }%
\def\xintfloor #1{\expandafter\XINT_floor
                  \romannumeral0\xintrawwithzeros {#1}.}%
\def\XINT_floor #1/#2.{\xintiquo {#1}{#2}}%
\def\xintCeil {\romannumeral0\xintceil }%
\def\xintceil #1{\xintiiopp {\xintFloor {\xintOpp{#1}}}}%
\def\xintNumerator {\romannumeral0\xintnumerator }%
\def\xintnumerator
{%
    \expandafter\XINT_numer\romannumeral0\XINT_infrac
}%
\def\XINT_numer #1%
{%
    \ifcase\XINT_Sgn {#1}
      \expandafter\XINT_numer_B
    \or
      \expandafter\XINT_numer_A
    \else
      \expandafter\XINT_numer_B
    \fi
    {#1}%
}%
\def\XINT_numer_A #1#2#3{\xint_dsh {#2}{-#1}}%
\def\XINT_numer_B #1#2#3{ #2}%
\def\xintDenominator {\romannumeral0\xintdenominator }%
\def\xintdenominator
{%
    \expandafter\XINT_denom\romannumeral0\XINT_infrac
}%
\def\XINT_denom #1%
{%
    \ifcase\XINT_Sgn {#1}
      \expandafter\XINT_denom_B
    \or
      \expandafter\XINT_denom_A
    \else
      \expandafter\XINT_denom_B
    \fi
    {#1}%
}%
\def\XINT_denom_A #1#2#3{ #3}%
\def\XINT_denom_B #1#2#3{\xint_dsh {#3}{#1}}%
\def\xintFrac {\romannumeral0\xintfrac }%
\def\xintfrac #1%
{%
    \expandafter\XINT_fracfrac_A\romannumeral0\XINT_infrac {#1}%
}%
\def\XINT_fracfrac_A #1{\XINT_fracfrac_B #1\Z }%
\catcode`^=7
\def\XINT_fracfrac_B #1#2\Z
{%
    \xint_gob_til_zero #1\XINT_fracfrac_C 0\XINT_fracfrac_D {10^{#1#2}}%
}%
\def\XINT_fracfrac_C #1#2#3#4#5%
{%
    \ifcase\XINT_isOne {#5}
    \or \xint_afterfi {\expandafter\xint_firstoftwo_andstop\xint_gobble_ii }%
    \fi
    \space
    \frac {#4}{#5}%
}%
\def\XINT_fracfrac_D #1#2#3%
{%
    \ifcase\XINT_isOne {#3}
    \or \XINT_fracfrac_E
    \fi
    \space
    \frac {#2}{#3}#1%
}%
\def\XINT_fracfrac_E \fi #1#2#3#4{\fi \space #3\cdot }%
\def\xintSignedFrac {\romannumeral0\xintsignedfrac }%
\def\xintsignedfrac #1%
{%
    \expandafter\XINT_sgnfrac_a\romannumeral0\XINT_infrac {#1}%
}%
\def\XINT_sgnfrac_a #1#2%
{%
    \XINT_sgnfrac_b #2\Z {#1}%
}%
\def\XINT_sgnfrac_b #1%
{%
    \xint_UDsignfork
      #1\dummy \XINT_sgnfrac_N
       -\dummy {\XINT_sgnfrac_P #1}%
    \krof
}%
\def\XINT_sgnfrac_P #1\Z #2%
{%
    \XINT_fracfrac_A {#2}{#1}%
}%
\def\XINT_sgnfrac_N
{%
    \expandafter\xint_minus_andstop\romannumeral0\XINT_sgnfrac_P
}%
\def\xintFwOver {\romannumeral0\xintfwover }%
\def\xintfwover #1%
{%
    \expandafter\XINT_fwover_A\romannumeral0\XINT_infrac {#1}%
}%
\def\XINT_fwover_A #1{\XINT_fwover_B #1\Z }%
\def\XINT_fwover_B #1#2\Z
{%
    \xint_gob_til_zero #1\XINT_fwover_C 0\XINT_fwover_D {10^{#1#2}}%
}%
\catcode`^=11
\def\XINT_fwover_C #1#2#3#4#5%
{%
    \ifcase\XINT_isOne {#5}
       \xint_afterfi { {#4\over #5}}%
    \or
       \xint_afterfi { #4}%
    \fi
}%
\def\XINT_fwover_D #1#2#3%
{%
    \ifcase\XINT_isOne {#3}
      \xint_afterfi { {#2\over #3}}%
    \or
      \xint_afterfi { #2\cdot }%
    \fi
    #1%
}%
\def\xintSignedFwOver {\romannumeral0\xintsignedfwover }%
\def\xintsignedfwover #1%
{%
    \expandafter\XINT_sgnfwover_a\romannumeral0\XINT_infrac {#1}%
}%
\def\XINT_sgnfwover_a #1#2%
{%
    \XINT_sgnfwover_b #2\Z {#1}%
}%
\def\XINT_sgnfwover_b #1%
{%
    \xint_UDsignfork
      #1\dummy \XINT_sgnfwover_N
       -\dummy {\XINT_sgnfwover_P #1}%
    \krof
}%
\def\XINT_sgnfwover_P #1\Z #2%
{%
    \XINT_fwover_A {#2}{#1}%
}%
\def\XINT_sgnfwover_N
{%
    \expandafter\xint_minus_andstop\romannumeral0\XINT_sgnfwover_P
}%
\def\xintREZ {\romannumeral0\xintrez }%
\def\xintrez
{%
    \expandafter\XINT_rez_A\romannumeral0\XINT_infrac
}%
\def\XINT_rez_A #1#2%
{%
    \XINT_rez_AB #2\Z {#1}%
}%
\def\XINT_rez_AB #1%
{%
    \xint_UDzerominusfork
      #1-\dummy \XINT_rez_zero
      0#1\dummy \XINT_rez_neg
       0-\dummy {\XINT_rez_B #1}%
    \krof
}%
\def\XINT_rez_zero #1\Z #2#3{ 0/1[0]}%
\def\XINT_rez_neg {\expandafter\xint_minus_andstop\romannumeral0\XINT_rez_B }%
\def\XINT_rez_B #1\Z
{%
    \expandafter\XINT_rez_C\romannumeral0\XINT_factortens {#1}%
}%
\def\XINT_rez_C #1#2#3#4%
{%
    \expandafter\XINT_rez_D\romannumeral0\XINT_factortens {#4}{#3}{#2}{#1}%
}%
\def\XINT_rez_D #1#2#3#4#5%
{%
    \expandafter\XINT_rez_E\expandafter
    {\the\numexpr #3+#4-#2}{#1}{#5}%
}%
\def\XINT_rez_E #1#2#3{ #3/#2[#1]}%
\def\xintE {\romannumeral0\xinte }%
\def\xinte #1%
{%
    \expandafter\XINT_e \romannumeral0\XINT_infrac {#1}%
}%
\def\XINT_e #1#2#3#4%
{%
    \expandafter\XINT_e_end\expandafter{\the\numexpr #1+#4}{#2}{#3}%
}%
\def\xintfE {\romannumeral0\xintfe }%
\def\xintfe #1%
{%
    \expandafter\XINT_fe \romannumeral0\XINT_infrac {#1}%
}%
\def\XINT_fe #1#2#3#4%
{%
    \expandafter\XINT_e_end\expandafter{\the\numexpr #1+\xintNum{#4}}{#2}{#3}%
}%
\def\XINT_e_end #1#2#3{ #2/#3[#1]}%
\let\XINTinFloatfE\xintfE
\def\xintIrr {\romannumeral0\xintirr }%
\def\xintirr #1%
{%
    \expandafter\XINT_irr_start\romannumeral0\xintrawwithzeros {#1}\Z
}%
\def\XINT_irr_start #1#2/#3\Z
{%
    \ifcase\XINT_isOne {#3}
      \xint_afterfi
          {\xint_UDsignfork
               #1\dummy \XINT_irr_negative
                -\dummy {\XINT_irr_nonneg #1}%
           \krof}%
    \or
      \xint_afterfi{\XINT_irr_denomisone #1}%
    \fi
    #2\Z {#3}%
}%
\def\XINT_irr_denomisone #1\Z #2{ #1/1}% changed in 1.08
\def\XINT_irr_negative   #1\Z #2{\XINT_irr_D #1\Z #2\Z \xint_minus_andstop}%
\def\XINT_irr_nonneg     #1\Z #2{\XINT_irr_D #1\Z #2\Z \space}%
\def\XINT_irr_D #1#2\Z #3#4\Z
{%
    \xint_UDzerosfork
       #3#1\dummy \XINT_irr_indeterminate
       #30\dummy  \XINT_irr_divisionbyzero
       #10\dummy  \XINT_irr_zero
        00\dummy  \XINT_irr_loop_a
    \krof
    {#3#4}{#1#2}{#3#4}{#1#2}%
}%
\def\XINT_irr_indeterminate #1#2#3#4#5{\xintError:NaN\space 0/0}%
\def\XINT_irr_divisionbyzero #1#2#3#4#5{\xintError:DivisionByZero #5#2/0}%
\def\XINT_irr_zero #1#2#3#4#5{ 0/1}% changed in 1.08
\def\XINT_irr_loop_a #1#2%
{%
    \expandafter\XINT_irr_loop_d
    \romannumeral0\XINT_div_prepare {#1}{#2}{#1}%
}%
\def\XINT_irr_loop_d #1#2%
{%
    \XINT_irr_loop_e #2\Z
}%
\def\XINT_irr_loop_e #1#2\Z
{%
    \xint_gob_til_zero #1\xint_irr_loop_exit0\XINT_irr_loop_a {#1#2}%
}%
\def\xint_irr_loop_exit0\XINT_irr_loop_a #1#2#3#4%
{%
    \expandafter\XINT_irr_loop_exitb\expandafter
    {\romannumeral0\xintiquo {#3}{#2}}%
    {\romannumeral0\xintiquo {#4}{#2}}%
}%
\def\XINT_irr_loop_exitb #1#2%
{%
   \expandafter\XINT_irr_finish\expandafter {#2}{#1}%
}%
\def\XINT_irr_finish #1#2#3{#3#1/#2}% changed in 1.08
\def\xintNum {\romannumeral0\xintnum }%
\def\xintnum #1{\expandafter\XINT_intcheck\romannumeral0\xintirr {#1}\Z }%
\def\XINT_intcheck #1/#2\Z
{%
    \ifcase\XINT_isOne {#2}
      \xintError:NotAnInteger
    \fi\space #1%
}%
\def\xintJrr {\romannumeral0\xintjrr }%
\def\xintjrr #1%
{%
    \expandafter\XINT_jrr_start\romannumeral0\xintrawwithzeros {#1}\Z
}%
\def\XINT_jrr_start #1#2/#3\Z
{%
    \ifcase\XINT_isOne {#3}
      \xint_afterfi
          {\xint_UDsignfork
               #1\dummy \XINT_jrr_negative
                -\dummy {\XINT_jrr_nonneg #1}%
           \krof}%
    \or
      \xint_afterfi{\XINT_jrr_denomisone #1}%
    \fi
    #2\Z {#3}%
}%
\def\XINT_jrr_denomisone #1\Z #2{ #1/1}% changed in 1.08
\def\XINT_jrr_negative   #1\Z #2{\XINT_jrr_D #1\Z #2\Z \xint_minus_andstop }%
\def\XINT_jrr_nonneg     #1\Z #2{\XINT_jrr_D #1\Z #2\Z \space}%
\def\XINT_jrr_D #1#2\Z #3#4\Z
{%
    \xint_UDzerosfork
       #3#1\dummy \XINT_jrr_indeterminate
       #30\dummy  \XINT_jrr_divisionbyzero
       #10\dummy  \XINT_jrr_zero
        00\dummy  \XINT_jrr_loop_a
    \krof
    {#3#4}{#1#2}1001%
}%
\def\XINT_jrr_indeterminate #1#2#3#4#5#6#7{\xintError:NaN\space 0/0}%
\def\XINT_jrr_divisionbyzero #1#2#3#4#5#6#7{\xintError:DivisionByZero #7#2/0}%
\def\XINT_jrr_zero #1#2#3#4#5#6#7{ 0/1}% changed in 1.08
\def\XINT_jrr_loop_a #1#2%
{%
    \expandafter\XINT_jrr_loop_b
    \romannumeral0\XINT_div_prepare {#1}{#2}{#1}%
}%
\def\XINT_jrr_loop_b #1#2#3#4#5#6#7%
{%
    \expandafter \XINT_jrr_loop_c \expandafter
        {\romannumeral0\xintiiadd{\XINT_Mul{#4}{#1}}{#6}}%
        {\romannumeral0\xintiiadd{\XINT_Mul{#5}{#1}}{#7}}%
    {#2}{#3}{#4}{#5}%
}%
\def\XINT_jrr_loop_c #1#2%
{%
    \expandafter \XINT_jrr_loop_d \expandafter{#2}{#1}%
}%
\def\XINT_jrr_loop_d #1#2#3#4%
{%
    \XINT_jrr_loop_e #3\Z {#4}{#2}{#1}%
}%
\def\XINT_jrr_loop_e #1#2\Z
{%
    \xint_gob_til_zero #1\xint_jrr_loop_exit0\XINT_jrr_loop_a {#1#2}%
}%
\def\xint_jrr_loop_exit0\XINT_jrr_loop_a #1#2#3#4#5#6%
{%
    \XINT_irr_finish {#3}{#4}%
}%
\def\xintTrunc {\romannumeral0\xinttrunc }%
\def\xintiTrunc {\romannumeral0\xintitrunc }%
\def\xinttrunc #1%
{%
    \expandafter\XINT_trunc\expandafter {\the\numexpr #1}%
}%
\def\XINT_trunc #1#2%
{%
    \expandafter\XINT_trunc_G
    \romannumeral0\expandafter\XINT_trunc_A
    \romannumeral0\XINT_infrac {#2}{#1}{#1}%
}%
\def\xintitrunc #1%
{%
    \expandafter\XINT_itrunc\expandafter {\the\numexpr #1}%
}%
\def\XINT_itrunc #1#2%
{%
    \expandafter\XINT_itrunc_G
    \romannumeral0\expandafter\XINT_trunc_A
    \romannumeral0\XINT_infrac {#2}{#1}{#1}%
}%
\def\XINT_trunc_A #1#2#3#4%
{%
    \expandafter\XINT_trunc_checkifzero
    \expandafter{\the\numexpr #1+#4}#2\Z {#3}%
}%
\def\XINT_trunc_checkifzero #1#2#3\Z
{%
    \xint_gob_til_zero #2\XINT_trunc_iszero0\XINT_trunc_B {#1}{#2#3}%
}%
\def\XINT_trunc_iszero #1#2#3#4#5{ 0\Z 0}%
\def\XINT_trunc_B #1%
{%
    \ifcase\XINT_Sgn {#1}
      \expandafter\XINT_trunc_D
    \or
      \expandafter\XINT_trunc_D
    \else
      \expandafter\XINT_trunc_C
    \fi
    {#1}%
}%
\def\XINT_trunc_C #1#2#3%
{%
    \expandafter \XINT_trunc_E
    \romannumeral0\xint_dsh {#3}{#1}\Z #2\Z
}%
\def\XINT_trunc_D #1#2%
{%
    \expandafter \XINT_trunc_DE \expandafter
    {\romannumeral0\xint_dsh {#2}{-#1}}%
}%
\def\XINT_trunc_DE #1#2{\XINT_trunc_E #2\Z #1\Z }%
\def\XINT_trunc_E #1#2\Z #3#4\Z
{%
    \xint_UDsignsfork
          #1#3\dummy \XINT_trunc_minusminus
           #1-\dummy {\XINT_trunc_minusplus #3}%
           #3-\dummy {\XINT_trunc_plusminus #1}%
            --\dummy {\XINT_trunc_plusplus  #3#1}%
    \krof
    {#4}{#2}%
}%
\def\XINT_trunc_minusminus #1#2{\xintiquo {#1}{#2}\Z \space}%
\def\XINT_trunc_minusplus #1#2#3{\xintiquo {#1#2}{#3}\Z \xint_minus_andstop}%
\def\XINT_trunc_plusminus #1#2#3{\xintiquo {#2}{#1#3}\Z \xint_minus_andstop}%
\def\XINT_trunc_plusplus  #1#2#3#4{\xintiquo {#1#3}{#2#4}\Z \space}%
\def\XINT_itrunc_G #1#2\Z #3#4%
{%
    \xint_gob_til_zero #1\XINT_trunc_zero 0\xint_firstoftwo {#3#1#2}0%
}%
\def\XINT_trunc_G #1\Z #2#3%
{%
    \xint_gob_til_zero #2\XINT_trunc_zero 0%
    \expandafter\XINT_trunc_H\expandafter
    {\the\numexpr\romannumeral0\XINT_length {#1}-#3}{#3}{#1}#2%
}%
\def\XINT_trunc_zero 0#10{ 0}%
\def\XINT_trunc_H #1#2%
{%
    \ifnum #1 > 0
        \xint_afterfi {\XINT_trunc_Ha {#2}}%
    \else
        \xint_afterfi {\XINT_trunc_Hb {-#1}}% -0,--1,--2, ....
    \fi
}%
\def\XINT_trunc_Ha
{%
  \expandafter\XINT_trunc_Haa\romannumeral0\xintdecsplit
}%
\def\XINT_trunc_Haa #1#2#3%
{%
    #3#1.#2%
}%
\def\XINT_trunc_Hb #1#2#3%
{%
    \expandafter #3\expandafter0\expandafter.%
    \romannumeral0\XINT_dsx_zeroloop {#1}{}\Z {}#2% #1=-0 possible!
}%
\def\xintRound {\romannumeral0\xintround }%
\def\xintiRound {\romannumeral0\xintiround }%
\def\xintround #1%
{%
    \expandafter\XINT_round\expandafter {\the\numexpr #1}%
}%
\def\XINT_round
{%
    \expandafter\XINT_trunc_G\romannumeral0\XINT_round_A
}%
\def\xintiround #1%
{%
    \expandafter\XINT_iround\expandafter {\the\numexpr #1}%
}%
\def\XINT_iround
{%
    \expandafter\XINT_itrunc_G\romannumeral0\XINT_round_A
}%
\def\XINT_round_A #1#2%
{%
    \expandafter\XINT_round_B
    \romannumeral0\expandafter\XINT_trunc_A
    \romannumeral0\XINT_infrac {#2}{\the\numexpr #1+1\relax}{#1}%
}%
\def\XINT_round_B #1\Z
{%
    \expandafter\XINT_round_C
    \romannumeral0\XINT_rord_main {}#1%
      \xint_relax
        \xint_undef\xint_undef\xint_undef\xint_undef
        \xint_undef\xint_undef\xint_undef\xint_undef
      \xint_relax
    \Z
}%
\def\XINT_round_C #1%
{%
    \ifnum #1<5
        \expandafter\XINT_round_Daa
    \else
        \expandafter\XINT_round_Dba
    \fi
}%
\def\XINT_round_Daa #1%
{%
    \xint_gob_til_Z #1\XINT_round_Daz\Z \XINT_round_Da #1%
}%
\def\XINT_round_Daz\Z \XINT_round_Da \Z { 0\Z }%
\def\XINT_round_Da #1\Z
{%
    \XINT_rord_main {}#1%
      \xint_relax
        \xint_undef\xint_undef\xint_undef\xint_undef
        \xint_undef\xint_undef\xint_undef\xint_undef
      \xint_relax  \Z
}%
\def\XINT_round_Dba #1%
{%
    \xint_gob_til_Z #1\XINT_round_Dbz\Z \XINT_round_Db #1%
}%
\def\XINT_round_Dbz\Z \XINT_round_Db \Z { 1\Z }%
\def\XINT_round_Db #1\Z
{%
    \XINT_addm_A 0{}1000\W\X\Y\Z #1000\W\X\Y\Z \Z
}%
\def\xintRound:csv #1{\expandafter\XINT_round:_a\romannumeral-`0#1,,^}%
\def\XINT_round:_a {\XINT_round:_b {}}%
\def\XINT_round:_b #1#2,%
             {\expandafter\XINT_round:_c\romannumeral-`0#2,{#1}}%
\def\XINT_round:_c #1{\if #1,\expandafter\XINT_round:_f
                      \else\expandafter\XINT_round:_d\fi #1}%
\def\XINT_round:_d #1,%
         {\expandafter\XINT_round:_e\romannumeral0\xintiround 0{#1},}%
\def\XINT_round:_e #1,#2{\XINT_round:_b {#2,#1}}%
\def\XINT_round:_f ,#1#2^{\xint_gobble_i #1}%
\mathchardef\XINTdigits 16
\def\xintDigits #1#2%
   {\afterassignment \xint_gobble_i \mathchardef\XINTdigits=}%
\def\xinttheDigits {\number\XINTdigits }%
\def\xintFloat   {\romannumeral0\xintfloat }%
\def\xintfloat #1{\XINT_float_chkopt #1\Z }%
\def\XINT_float_chkopt #1%
{%
    \ifx [#1\expandafter\XINT_float_opt
       \else\expandafter\XINT_float_noopt
    \fi  #1%
}%
\def\XINT_float_noopt #1\Z
{%
    \expandafter\XINT_float_a\expandafter\XINTdigits
    \romannumeral0\XINT_infrac {#1}\XINT_float_Q
}%
\def\XINT_float_opt [\Z #1]#2%
{%
    \expandafter\XINT_float_a\expandafter
    {\the\numexpr #1\expandafter}%
    \romannumeral0\XINT_infrac {#2}\XINT_float_Q
}%
\def\XINT_float_a #1#2#3% #1=P, #2=n, #3=A, #4=B
{%
    \XINT_float_fork #3\Z {#1}{#2}% #1 = precision, #2=n
}%
\def\XINT_float_fork #1%
{%
    \xint_UDzerominusfork
     #1-\dummy  \XINT_float_zero
     0#1\dummy  \XINT_float_J
      0-\dummy  {\XINT_float_K #1}%
    \krof
}%
\def\XINT_float_zero #1\Z #2#3#4#5{ 0.e0}%
\def\XINT_float_J {\expandafter\xint_minus_andstop\romannumeral0\XINT_float_K }%
\def\XINT_float_K #1\Z #2% #1=A, #2=P, #3=n, #4=B
{%
    \expandafter\XINT_float_L\expandafter
    {\the\numexpr\xintLength{#1}\expandafter}\expandafter
    {\the\numexpr #2+\xint_c_ii}{#1}{#2}%
}%
\def\XINT_float_L #1#2%
{%
    \ifnum #1>#2
      \expandafter\XINT_float_Ma
    \else
      \expandafter\XINT_float_Mc
    \fi {#1}{#2}%
}%
\def\XINT_float_Ma #1#2#3%
{%
    \expandafter\XINT_float_Mb\expandafter
    {\the\numexpr #1-#2\expandafter\expandafter\expandafter}%
    \expandafter\expandafter\expandafter
    {\expandafter\xint_firstoftwo
     \romannumeral0\XINT_split_fromleft_loop {#2}{}#3\W\W\W\W\W\W\W\W\Z
     }{#2}%
}%
\def\XINT_float_Mb #1#2#3#4#5#6% #2=A', #3=P+2, #4=P, #5=n, #6=B
{%
   \expandafter\XINT_float_N\expandafter
   {\the\numexpr\xintLength{#6}\expandafter}\expandafter
   {\the\numexpr #3\expandafter}\expandafter
   {\the\numexpr #1+#5}%
   {#6}{#3}{#2}{#4}%
}% long de B, P+2, n', B, |A'|=P+2, A', P
\def\XINT_float_Mc #1#2#3#4#5#6%
{%
   \expandafter\XINT_float_N\expandafter
   {\romannumeral0\XINT_length{#6}}{#2}{#5}{#6}{#1}{#3}{#4}%
}% long de B, P+2, n, B, |A|, A, P
\def\XINT_float_N #1#2%
{%
    \ifnum #1>#2
      \expandafter\XINT_float_O
    \else
      \expandafter\XINT_float_P
    \fi {#1}{#2}%
}%
\def\XINT_float_O #1#2#3#4%
{%
    \expandafter\XINT_float_P\expandafter
    {\the\numexpr #2\expandafter}\expandafter
    {\the\numexpr #2\expandafter}\expandafter
    {\the\numexpr #3-#1+#2\expandafter\expandafter\expandafter}%
    \expandafter\expandafter\expandafter
    {\expandafter\xint_firstoftwo
     \romannumeral0\XINT_split_fromleft_loop {#2}{}#4\W\W\W\W\W\W\W\W\Z
     }%
}% |B|,P+2,n,B,|A|,A,P
\def\XINT_float_P #1#2#3#4#5#6#7#8%
{%
    \expandafter #8\expandafter {\the\numexpr #1-#5+#2-\xint_c_i}%
    {#6}{#4}{#7}{#3}%
}% |B|-|A|+P+1,A,B,P,n
\def\XINT_float_Q #1%
{%
    \ifnum #1<\xint_c_
      \expandafter\XINT_float_Ri
    \else
      \expandafter\XINT_float_Rii
    \fi {#1}%
}%
\def\XINT_float_Ri #1#2#3%
{%
    \expandafter\XINT_float_Sa
    \romannumeral0\xintiquo {#2}%
         {\XINT_dsx_addzerosnofuss {-#1}{#3}}\Z {#1}%
}%
\def\XINT_float_Rii #1#2#3%
{%
    \expandafter\XINT_float_Sa
    \romannumeral0\xintiquo
         {\XINT_dsx_addzerosnofuss {#1}{#2}}{#3}\Z {#1}%
}%
\def\XINT_float_Sa #1%
{%
    \if #19%
        \xint_afterfi {\XINT_float_Sb\XINT_float_Wb }%
    \else
        \xint_afterfi {\XINT_float_Sb\XINT_float_Wa }%
    \fi #1%
}%
\def\XINT_float_Sb #1#2\Z #3#4%
{%
    \expandafter\XINT_float_T\expandafter
    {\the\numexpr #4+\xint_c_i\expandafter}%
    \romannumeral-`0\XINT_lenrord_loop 0{}#2\Z\W\W\W\W\W\W\W\Z #1{#3}{#4}%
}%
\def\XINT_float_T #1#2#3%
{%
    \ifnum #2>#1
      \xint_afterfi{\XINT_float_U\XINT_float_Xb}%
    \else
      \xint_afterfi{\XINT_float_U\XINT_float_Xa #3}%
    \fi
}%
\def\XINT_float_U #1#2%
{%
    \ifnum #2<\xint_c_v
      \expandafter\XINT_float_Va
    \else
      \expandafter\XINT_float_Vb
    \fi #1%
}%
\def\XINT_float_Va #1#2\Z #3%
{%
    \expandafter#1%
    \romannumeral0\expandafter\XINT_float_Wa
    \romannumeral0\XINT_rord_main {}#2%
      \xint_relax
        \xint_undef\xint_undef\xint_undef\xint_undef
        \xint_undef\xint_undef\xint_undef\xint_undef
      \xint_relax \Z
}%
\def\XINT_float_Vb #1#2\Z #3%
{%
    \expandafter #1%
    \romannumeral0\expandafter #3%
    \romannumeral0\XINT_addm_A 0{}1000\W\X\Y\Z #2000\W\X\Y\Z \Z
}%
\def\XINT_float_Wa #1{ #1.}%
\def\XINT_float_Wb #1#2%
    {\if #11\xint_afterfi{ 10.}\else\xint_afterfi{ #1.#2}\fi }%
\def\XINT_float_Xa #1\Z #2#3#4%
{%
    \expandafter\XINT_float_Y\expandafter
    {\the\numexpr #3+#4-#2}{#1}%
}%
\def\XINT_float_Xb #1\Z #2#3#4%
{%
    \expandafter\XINT_float_Y\expandafter
    {\the\numexpr #3+#4+\xint_c_i-#2}{#1}%
}%
\def\XINT_float_Y #1#2{ #2e#1}%
\def\xintFloat:csv #1{\expandafter\XINT_float:_a\romannumeral-`0#1,,^}%
\def\XINT_float:_a {\XINT_float:_b {}}%
\def\XINT_float:_b #1#2,%
             {\expandafter\XINT_float:_c\romannumeral-`0#2,{#1}}%
\def\XINT_float:_c #1{\if #1,\expandafter\XINT_float:_f
                      \else\expandafter\XINT_float:_d\fi #1}%
\def\XINT_float:_d #1,%
         {\expandafter\XINT_float:_e\romannumeral0\xintfloat {#1},}%
\def\XINT_float:_e #1,#2{\XINT_float:_b {#2,#1}}%
\def\XINT_float:_f ,#1#2^{\xint_gobble_i #1}%
\def\XINTinFloat {\romannumeral0\XINT_inFloat }%
\def\XINT_inFloat [#1]#2%
{%
    \expandafter\XINT_infloat_a\expandafter
    {\the\numexpr #1\expandafter}%
    \romannumeral0\XINT_infrac {#2}\XINT_infloat_Q
}%
\def\XINT_infloat_a #1#2#3% #1=P, #2=n, #3=A, #4=B
{%
    \XINT_infloat_fork #3\Z {#1}{#2}% #1 = precision, #2=n
}%
\def\XINT_infloat_fork #1%
{%
    \xint_UDzerominusfork
     #1-\dummy  \XINT_infloat_zero
     0#1\dummy  \XINT_infloat_J
      0-\dummy  {\XINT_float_K #1}%
    \krof
}%
\def\XINT_infloat_zero #1\Z #2#3#4#5{ 0[0]}%
\def\XINT_infloat_J {\expandafter-\romannumeral0\XINT_float_K }%
\def\XINT_infloat_Q #1%
{%
    \ifnum #1<\xint_c_
      \expandafter\XINT_infloat_Ri
    \else
      \expandafter\XINT_infloat_Rii
    \fi {#1}%
}%
\def\XINT_infloat_Ri #1#2#3%
{%
    \expandafter\XINT_infloat_S\expandafter
    {\romannumeral0\xintiquo {#2}%
         {\XINT_dsx_addzerosnofuss {-#1}{#3}}}{#1}%
}%
\def\XINT_infloat_Rii #1#2#3%
{%
    \expandafter\XINT_infloat_S\expandafter
    {\romannumeral0\xintiquo
         {\XINT_dsx_addzerosnofuss {#1}{#2}}{#3}}{#1}%
}%
\def\XINT_infloat_S #1#2#3%
{%
    \expandafter\XINT_infloat_T\expandafter
    {\the\numexpr #3+\xint_c_i\expandafter}%
    \romannumeral-`0\XINT_lenrord_loop 0{}#1\Z\W\W\W\W\W\W\W\Z
    {#2}%
}%
\def\XINT_infloat_T #1#2#3%
{%
    \ifnum #2>#1
      \xint_afterfi{\XINT_infloat_U\XINT_infloat_Wb}%
    \else
      \xint_afterfi{\XINT_infloat_U\XINT_infloat_Wa #3}%
    \fi
}%
\def\XINT_infloat_U #1#2%
{%
    \ifnum #2<\xint_c_v
      \expandafter\XINT_infloat_Va
    \else
      \expandafter\XINT_infloat_Vb
    \fi #1%
}%
\def\XINT_infloat_Va #1#2\Z
{%
    \expandafter#1%
    \romannumeral0\XINT_rord_main {}#2%
      \xint_relax
        \xint_undef\xint_undef\xint_undef\xint_undef
        \xint_undef\xint_undef\xint_undef\xint_undef
      \xint_relax \Z
}%
\def\XINT_infloat_Vb #1#2\Z
{%
    \expandafter #1%
    \romannumeral0\XINT_addm_A 0{}1000\W\X\Y\Z #2000\W\X\Y\Z \Z
}%
\def\XINT_infloat_Wa #1\Z #2#3%
{%
    \expandafter\XINT_infloat_X\expandafter
    {\the\numexpr #3+\xint_c_i-#2}{#1}%
}%
\def\XINT_infloat_Wb #1\Z #2#3%
{%
    \expandafter\XINT_infloat_X\expandafter
    {\the\numexpr #3+\xint_c_ii-#2}{#1}%
}%
\def\XINT_infloat_X #1#2{ #2[#1]}%
\def\xintAdd {\romannumeral0\xintadd }%
\def\xintadd #1%
{%
    \expandafter\xint_fadd\expandafter {\romannumeral0\XINT_infrac {#1}}%
}%
\def\xint_fadd #1#2{\expandafter\XINT_fadd_A\romannumeral0\XINT_infrac{#2}#1}%
\def\XINT_fadd_A #1#2#3#4%
{%
    \ifnum #4 > #1
       \xint_afterfi {\XINT_fadd_B {#1}}%
    \else
       \xint_afterfi {\XINT_fadd_B {#4}}%
    \fi
    {#1}{#4}{#2}{#3}%
}%
\def\XINT_fadd_B #1#2#3#4#5#6#7%
{%
    \expandafter\XINT_fadd_C\expandafter
    {\romannumeral0\xintiimul {#7}{#5}}%
    {\romannumeral0\xintiiadd
    {\romannumeral0\xintiimul {\xintDSH {\the\numexpr -#3+#1\relax}{#6}}{#5}}%
    {\romannumeral0\xintiimul {#7}{\xintDSH {\the\numexpr -#2+#1\relax}{#4}}}%
    }%
    {#1}%
}%
\def\XINT_fadd_C #1#2#3%
{%
    \expandafter\XINT_fadd_D\expandafter {#2}{#3}{#1}%
}%
\def\XINT_fadd_D #1#2{\XINT_outfrac {#2}{#1}}%
\def\xintSub {\romannumeral0\xintsub }%
\def\xintsub #1%
{%
    \expandafter\xint_fsub\expandafter {\romannumeral0\XINT_infrac {#1}}%
}%
\def\xint_fsub #1#2%
   {\expandafter\XINT_fsub_A\romannumeral0\XINT_infrac {#2}#1}%
\def\XINT_fsub_A #1#2#3#4%
{%
    \ifnum #4 > #1
       \xint_afterfi {\XINT_fsub_B {#1}}%
    \else
       \xint_afterfi {\XINT_fsub_B {#4}}%
    \fi
    {#1}{#4}{#2}{#3}%
}%
\def\XINT_fsub_B #1#2#3#4#5#6#7%
{%
    \expandafter\XINT_fsub_C\expandafter
    {\romannumeral0\xintiimul {#7}{#5}}%
    {\romannumeral0\xintiisub
    {\romannumeral0\xintiimul {\xintDSH {\the\numexpr -#3+#1\relax}{#6}}{#5}}%
    {\romannumeral0\xintiimul {#7}{\xintDSH {\the\numexpr -#2+#1\relax}{#4}}}%
    }%
    {#1}%
}%
\def\XINT_fsub_C #1#2#3%
{%
    \expandafter\XINT_fsub_D\expandafter {#2}{#3}{#1}%
}%
\def\XINT_fsub_D #1#2{\XINT_outfrac {#2}{#1}}%
\def\xintSum {\romannumeral0\xintsum }%
\def\xintsum #1{\xintsumexpr #1\relax }%
\def\xintSumExpr {\romannumeral0\xintsumexpr }%
\def\xintsumexpr {\expandafter\XINT_fsumexpr\romannumeral-`0}%
\def\XINT_fsumexpr {\XINT_fsum_loop_a {0/1[0]}}%
\def\XINT_fsum_loop_a #1#2%
{%
    \expandafter\XINT_fsum_loop_b \romannumeral-`0#2\Z {#1}%
}%
\def\XINT_fsum_loop_b #1%
{%
    \xint_gob_til_relax #1\XINT_fsum_finished\relax
    \XINT_fsum_loop_c #1%
}%
\def\XINT_fsum_loop_c #1\Z #2%
{%
    \expandafter\XINT_fsum_loop_a\expandafter{\romannumeral0\xintadd {#2}{#1}}%
}%
\def\XINT_fsum_finished #1\Z #2{ #2}%
\def\xintSum:csv #1{\expandafter\XINT_sum:_a\romannumeral-`0#1,,^}%
\def\XINT_sum:_a {\XINT_sum:_b {0/1[0]}}%
\def\XINT_sum:_b #1#2,{\expandafter\XINT_sum:_c\romannumeral-`0#2,{#1}}%
\def\XINT_sum:_c #1{\if #1,\expandafter\XINT_sum:_e
                      \else\expandafter\XINT_sum:_d\fi #1}%
\def\XINT_sum:_d #1,#2{\expandafter\XINT_sum:_b\expandafter
                        {\romannumeral0\xintadd {#2}{#1}}}%
\def\XINT_sum:_e  ,#1#2^{#1}% allows empty list
\def\xintMul {\romannumeral0\xintmul }%
\def\xintmul #1%
{%
    \expandafter\xint_fmul\expandafter {\romannumeral0\XINT_infrac {#1}}%
}%
\def\xint_fmul #1#2%
   {\expandafter\XINT_fmul_A\romannumeral0\XINT_infrac {#2}#1}%
\def\XINT_fmul_A #1#2#3#4#5#6%
{%
    \expandafter\XINT_fmul_B
    \expandafter{\the\numexpr #1+#4\expandafter}%
    \expandafter{\romannumeral0\xintiimul {#6}{#3}}%
    {\romannumeral0\xintiimul {#5}{#2}}%
}%
\def\XINT_fmul_B #1#2#3%
{%
    \expandafter \XINT_fmul_C \expandafter{#3}{#1}{#2}%
}%
\def\XINT_fmul_C #1#2{\XINT_outfrac {#2}{#1}}%
\def\xintSqr {\romannumeral0\xintsqr }%
\def\xintsqr #1%
{%
    \expandafter\xint_fsqr\expandafter{\romannumeral0\XINT_infrac {#1}}%
}%
\def\xint_fsqr #1{\XINT_fmul_A #1#1}%
\def\xintPow {\romannumeral0\xintpow }%
\def\xintpow #1%
{%
    \expandafter\xint_fpow\expandafter {\romannumeral0\XINT_infrac {#1}}%
}%
\def\xint_fpow #1#2%
{%
    \expandafter\XINT_fpow_fork\the\numexpr \xintNum{#2}\relax\Z #1%
}%
\def\XINT_fpow_fork #1#2\Z
{%
    \xint_UDzerominusfork
      #1-\dummy  \XINT_fpow_zero
      0#1\dummy  \XINT_fpow_neg
       0-\dummy  {\XINT_fpow_pos #1}%
    \krof
    {#2}%
}%
\def\XINT_fpow_zero #1#2#3#4%
{%
    \space 1/1[0]%
}%
\def\XINT_fpow_pos #1#2#3#4#5%
{%
    \expandafter\XINT_fpow_pos_A\expandafter
    {\the\numexpr #1#2*#3\expandafter}\expandafter
    {\romannumeral0\xintipow {#5}{#1#2}}%
    {\romannumeral0\xintipow {#4}{#1#2}}%
}%
\def\XINT_fpow_neg #1#2#3#4%
{%
    \expandafter\XINT_fpow_pos_A\expandafter
    {\the\numexpr -#1*#2\expandafter}\expandafter
    {\romannumeral0\xintipow {#3}{#1}}%
    {\romannumeral0\xintipow {#4}{#1}}%
}%
\def\XINT_fpow_pos_A #1#2#3%
{%
    \expandafter\XINT_fpow_pos_B\expandafter {#3}{#1}{#2}%
}%
\def\XINT_fpow_pos_B #1#2{\XINT_outfrac {#2}{#1}}%
\def\xintFac {\romannumeral0\xintfac }%
\def\xintfac #1%
{%
    \expandafter\XINT_fac_fork\expandafter{\the\numexpr \xintNum{#1}}%
}%
\def\xintPrd {\romannumeral0\xintprd }%
\def\xintprd #1{\xintprdexpr #1\relax }%
\def\xintPrdExpr {\romannumeral0\xintprdexpr }%
\def\xintprdexpr {\expandafter\XINT_fprdexpr \romannumeral-`0}%
\def\XINT_fprdexpr {\XINT_fprod_loop_a {1/1[0]}}%
\def\XINT_fprod_loop_a #1#2%
{%
    \expandafter\XINT_fprod_loop_b \romannumeral-`0#2\Z {#1}%
}%
\def\XINT_fprod_loop_b #1%
{%
    \xint_gob_til_relax #1\XINT_fprod_finished\relax
    \XINT_fprod_loop_c #1%
}%
\def\XINT_fprod_loop_c #1\Z #2%
{%
  \expandafter\XINT_fprod_loop_a\expandafter{\romannumeral0\xintmul {#1}{#2}}%
}%
\def\XINT_fprod_finished #1\Z #2{ #2}%
\def\xintPrd:csv #1{\expandafter\XINT_prd:_a\romannumeral-`0#1,,^}%
\def\XINT_prd:_a {\XINT_prd:_b {1/1[0]}}%
\def\XINT_prd:_b #1#2,{\expandafter\XINT_prd:_c\romannumeral-`0#2,{#1}}%
\def\XINT_prd:_c #1{\if #1,\expandafter\XINT_prd:_e
                      \else\expandafter\XINT_prd:_d\fi #1}%
\def\XINT_prd:_d #1,#2{\expandafter\XINT_prd:_b\expandafter
                        {\romannumeral0\xintmul {#2}{#1}}}%
\def\XINT_prd:_e  ,#1#2^{#1}% allows empty list
\def\xintDiv {\romannumeral0\xintdiv }%
\def\xintdiv #1%
{%
    \expandafter\xint_fdiv\expandafter {\romannumeral0\XINT_infrac {#1}}%
}%
\def\xint_fdiv #1#2%
   {\expandafter\XINT_fdiv_A\romannumeral0\XINT_infrac {#2}#1}%
\def\XINT_fdiv_A #1#2#3#4#5#6%
{%
    \expandafter\XINT_fdiv_B
    \expandafter{\the\numexpr #4-#1\expandafter}%
    \expandafter{\romannumeral0\xintiimul {#2}{#6}}%
    {\romannumeral0\xintiimul {#3}{#5}}%
}%
\def\XINT_fdiv_B #1#2#3%
{%
    \expandafter\XINT_fdiv_C
    \expandafter{#3}{#1}{#2}%
}%
\def\XINT_fdiv_C #1#2{\XINT_outfrac {#2}{#1}}%
\def\xintIsOne {\romannumeral0\xintisone }%
\def\xintisone #1{\expandafter\XINT_fracisone
                \romannumeral0\xintrawwithzeros{#1}\Z }%
\def\XINT_fracisone #1/#2\Z{\xintsgnfork{\XINT_Cmp {#1}{#2}}{0}{1}{0}}%
\def\xintGeq {\romannumeral0\xintgeq }%
\def\xintgeq #1%
{%
    \expandafter\xint_fgeq\expandafter {\romannumeral0\xintabs {#1}}%
}%
\def\xint_fgeq #1#2%
{%
    \expandafter\XINT_fgeq_A \romannumeral0\xintabs {#2}#1%
}%
\def\XINT_fgeq_A #1%
{%
    \xint_gob_til_zero #1\XINT_fgeq_Zii 0%
    \XINT_fgeq_B #1%
}%
\def\XINT_fgeq_Zii 0\XINT_fgeq_B #1[#2]#3[#4]{ 1}%
\def\XINT_fgeq_B #1/#2[#3]#4#5/#6[#7]%
{%
    \xint_gob_til_zero #4\XINT_fgeq_Zi 0%
    \expandafter\XINT_fgeq_C\expandafter
    {\the\numexpr #7-#3\expandafter}\expandafter
    {\romannumeral0\xintiimul {#4#5}{#2}}%
    {\romannumeral0\xintiimul {#6}{#1}}%
}%
\def\XINT_fgeq_Zi 0#1#2#3#4#5#6#7{ 0}%
\def\XINT_fgeq_C #1#2#3%
{%
    \expandafter\XINT_fgeq_D\expandafter
    {#3}{#1}{#2}%
}%
\def\XINT_fgeq_D #1#2#3%
{%
    \xintSgnFork
    {\xintiSgn{\the\numexpr #2+\xintLength{#3}-\xintLength{#1}\relax}}%
    { 0}{\XINT_fgeq_E #2\Z {#3}{#1}}{ 1}%
}%
\def\XINT_fgeq_E #1%
{%
    \xint_UDsignfork
        #1\dummy  \XINT_fgeq_Fd
         -\dummy {\XINT_fgeq_Fn #1}%
    \krof
}%
\def\XINT_fgeq_Fd #1\Z #2#3%
{%
    \expandafter\XINT_fgeq_Fe\expandafter
    {\romannumeral0\XINT_dsx_addzerosnofuss {#1}{#3}}{#2}%
}%
\def\XINT_fgeq_Fe #1#2{\XINT_geq_pre {#2}{#1}}%
\def\XINT_fgeq_Fn #1\Z #2#3%
{%
    \expandafter\XINT_geq_pre\expandafter
    {\romannumeral0\XINT_dsx_addzerosnofuss {#1}{#2}}{#3}%
}%
\def\xintMax {\romannumeral0\xintmax }%
\def\xintmax #1%
{%
    \expandafter\xint_fmax\expandafter {\romannumeral0\xintraw {#1}}%
}%
\def\xint_fmax #1#2%
{%
    \expandafter\XINT_fmax_A\romannumeral0\xintraw {#2}#1%
}%
\def\XINT_fmax_A #1#2/#3[#4]#5#6/#7[#8]%
{%
    \xint_UDsignsfork
      #1#5\dummy \XINT_fmax_minusminus
       -#5\dummy \XINT_fmax_firstneg
       #1-\dummy \XINT_fmax_secondneg
        --\dummy \XINT_fmax_nonneg_a
    \krof
    #1#5{#2/#3[#4]}{#6/#7[#8]}%
}%
\def\XINT_fmax_minusminus --%
   {\expandafter\xint_minus_andstop\romannumeral0\XINT_fmin_nonneg_b }%
\def\XINT_fmax_firstneg #1-#2#3{ #1#2}%
\def\XINT_fmax_secondneg -#1#2#3{ #1#3}%
\def\XINT_fmax_nonneg_a #1#2#3#4%
{%
    \XINT_fmax_nonneg_b {#1#3}{#2#4}%
}%
\def\XINT_fmax_nonneg_b #1#2%
{%
    \ifcase\romannumeral0\XINT_fgeq_A #1#2
        \xint_afterfi{ #1}%
    \or \xint_afterfi{ #2}%
    \fi
}%
\def\xintMaxof      {\romannumeral0\xintmaxof }%
\def\xintmaxof    #1{\expandafter\XINT_maxof_a\romannumeral-`0#1\relax }%
\def\XINT_maxof_a #1{\expandafter\XINT_maxof_b\romannumeral0\xintraw{#1}\Z }%
\def\XINT_maxof_b #1\Z #2%
           {\expandafter\XINT_maxof_c\romannumeral-`0#2\Z {#1}\Z}%
\def\XINT_maxof_c #1%
           {\xint_gob_til_relax #1\XINT_maxof_e\relax\XINT_maxof_d #1}%
\def\XINT_maxof_d #1\Z
           {\expandafter\XINT_maxof_b\romannumeral0\xintmax {#1}}%
\def\XINT_maxof_e #1\Z #2\Z { #2}%
\def\xintMaxof:csv #1{\expandafter\XINT_maxof:_b\romannumeral-`0#1,,}%
\def\XINT_maxof:_b #1,#2,{\expandafter\XINT_maxof:_c\romannumeral-`0#2,{#1},}%
\def\XINT_maxof:_c #1{\if #1,\expandafter\XINT_maxof:_e
                       \else\expandafter\XINT_maxof:_d\fi #1}%
\def\XINT_maxof:_d #1,{\expandafter\XINT_maxof:_b\romannumeral0\xintmax {#1}}%
\def\XINT_maxof:_e ,#1,{#1}%
\def\xintFloatMaxof      {\romannumeral0\xintflmaxof }%
\def\xintflmaxof    #1{\expandafter\XINT_flmaxof_a\romannumeral-`0#1\relax }%
\def\XINT_flmaxof_a #1{\expandafter\XINT_flmaxof_b
                       \romannumeral0\XINT_inFloat [\XINTdigits]{#1}\Z }%
\def\XINT_flmaxof_b #1\Z #2%
           {\expandafter\XINT_flmaxof_c\romannumeral-`0#2\Z {#1}\Z}%
\def\XINT_flmaxof_c #1%
           {\xint_gob_til_relax #1\XINT_flmaxof_e\relax\XINT_flmaxof_d #1}%
\def\XINT_flmaxof_d #1\Z
           {\expandafter\XINT_flmaxof_b\romannumeral0\xintmax
                         {\XINTinFloat [\XINTdigits]{#1}}}%
\def\XINT_flmaxof_e #1\Z #2\Z { #2}%
\def\xintFloatMaxof:csv #1{\expandafter\XINT_flmaxof:_a\romannumeral-`0#1,,}%
\def\XINT_flmaxof:_a #1,{\expandafter\XINT_flmaxof:_b
                         \romannumeral0\XINT_inFloat [\XINTdigits]{#1},}%
\def\XINT_flmaxof:_b #1,#2,%
      {\expandafter\XINT_flmaxof:_c\romannumeral-`0#2,{#1},}%
\def\XINT_flmaxof:_c #1{\if #1,\expandafter\XINT_flmaxof:_e
                       \else\expandafter\XINT_flmaxof:_d\fi #1}%
\def\XINT_flmaxof:_d #1,%
      {\expandafter\XINT_flmaxof:_b\romannumeral0\xintmax
                   {\XINTinFloat [\XINTdigits]{#1}}}%
\def\XINT_flmaxof:_e ,#1,{#1}%
\def\xintMin {\romannumeral0\xintmin }%
\def\xintmin #1%
{%
    \expandafter\xint_fmin\expandafter {\romannumeral0\xintraw {#1}}%
}%
\def\xint_fmin #1#2%
{%
    \expandafter\XINT_fmin_A\romannumeral0\xintraw {#2}#1%
}%
\def\XINT_fmin_A #1#2/#3[#4]#5#6/#7[#8]%
{%
    \xint_UDsignsfork
      #1#5\dummy \XINT_fmin_minusminus
       -#5\dummy \XINT_fmin_firstneg
       #1-\dummy \XINT_fmin_secondneg
        --\dummy \XINT_fmin_nonneg_a
    \krof
    #1#5{#2/#3[#4]}{#6/#7[#8]}%
}%
\def\XINT_fmin_minusminus --%
   {\expandafter\xint_minus_andstop\romannumeral0\XINT_fmax_nonneg_b }%
\def\XINT_fmin_firstneg #1-#2#3{ -#3}%
\def\XINT_fmin_secondneg -#1#2#3{ -#2}%
\def\XINT_fmin_nonneg_a #1#2#3#4%
{%
    \XINT_fmin_nonneg_b {#1#3}{#2#4}%
}%
\def\XINT_fmin_nonneg_b #1#2%
{%
    \ifcase\romannumeral0\XINT_fgeq_A #1#2
        \xint_afterfi{ #2}%
    \or \xint_afterfi{ #1}%
    \fi
}%
\def\xintMinof      {\romannumeral0\xintminof }%
\def\xintminof    #1{\expandafter\XINT_minof_a\romannumeral-`0#1\relax }%
\def\XINT_minof_a #1{\expandafter\XINT_minof_b\romannumeral0\xintraw{#1}\Z }%
\def\XINT_minof_b #1\Z #2%
           {\expandafter\XINT_minof_c\romannumeral-`0#2\Z {#1}\Z}%
\def\XINT_minof_c #1%
           {\xint_gob_til_relax #1\XINT_minof_e\relax\XINT_minof_d #1}%
\def\XINT_minof_d #1\Z
           {\expandafter\XINT_minof_b\romannumeral0\xintmin {#1}}%
\def\XINT_minof_e #1\Z #2\Z { #2}%
\def\xintMinof:csv #1{\expandafter\XINT_minof:_b\romannumeral-`0#1,,}%
\def\XINT_minof:_b #1,#2,{\expandafter\XINT_minof:_c\romannumeral-`0#2,{#1},}%
\def\XINT_minof:_c #1{\if #1,\expandafter\XINT_minof:_e
                       \else\expandafter\XINT_minof:_d\fi #1}%
\def\XINT_minof:_d #1,{\expandafter\XINT_minof:_b\romannumeral0\xintmin {#1}}%
\def\XINT_minof:_e ,#1,{#1}%
\def\xintFloatMinof      {\romannumeral0\xintflminof }%
\def\xintflminof    #1{\expandafter\XINT_flminof_a\romannumeral-`0#1\relax }%
\def\XINT_flminof_a #1{\expandafter\XINT_flminof_b
                       \romannumeral0\XINT_inFloat [\XINTdigits]{#1}\Z }%
\def\XINT_flminof_b #1\Z #2%
           {\expandafter\XINT_flminof_c\romannumeral-`0#2\Z {#1}\Z}%
\def\XINT_flminof_c #1%
           {\xint_gob_til_relax #1\XINT_flminof_e\relax\XINT_flminof_d #1}%
\def\XINT_flminof_d #1\Z
           {\expandafter\XINT_flminof_b\romannumeral0\xintmin
                         {\XINTinFloat [\XINTdigits]{#1}}}%
\def\XINT_flminof_e #1\Z #2\Z { #2}%
\def\xintFloatMinof:csv #1{\expandafter\XINT_flminof:_a\romannumeral-`0#1,,}%
\def\XINT_flminof:_a #1,{\expandafter\XINT_flminof:_b
                         \romannumeral0\XINT_inFloat [\XINTdigits]{#1},}%
\def\XINT_flminof:_b #1,#2,%
      {\expandafter\XINT_flminof:_c\romannumeral-`0#2,{#1},}%
\def\XINT_flminof:_c #1{\if #1,\expandafter\XINT_flminof:_e
                       \else\expandafter\XINT_flminof:_d\fi #1}%
\def\XINT_flminof:_d #1,%
      {\expandafter\XINT_flminof:_b\romannumeral0\xintmin
                   {\XINTinFloat [\XINTdigits]{#1}}}%
\def\XINT_flminof:_e ,#1,{#1}%
\def\xintCmp {\romannumeral0\xintcmp }%
\def\xintcmp #1%
{%
    \expandafter\xint_fcmp\expandafter {\romannumeral0\xintraw {#1}}%
}%
\def\xint_fcmp #1#2%
{%
    \expandafter\XINT_fcmp_A\romannumeral0\xintraw {#2}#1%
}%
\def\XINT_fcmp_A #1#2/#3[#4]#5#6/#7[#8]%
{%
    \xint_UDsignsfork
      #1#5\dummy \XINT_fcmp_minusminus
       -#5\dummy \XINT_fcmp_firstneg
       #1-\dummy \XINT_fcmp_secondneg
        --\dummy \XINT_fcmp_nonneg_a
    \krof
    #1#5{#2/#3[#4]}{#6/#7[#8]}%
}%
\def\XINT_fcmp_minusminus --#1#2{\XINT_fcmp_B #2#1}%
\def\XINT_fcmp_firstneg #1-#2#3{ -1}%
\def\XINT_fcmp_secondneg -#1#2#3{ 1}%
\def\XINT_fcmp_nonneg_a #1#2%
{%
    \xint_UDzerosfork
      #1#2\dummy \XINT_fcmp_zerozero
       0#2\dummy \XINT_fcmp_firstzero
       #10\dummy \XINT_fcmp_secondzero
        00\dummy \XINT_fcmp_pos
    \krof
    #1#2%
}%
\def\XINT_fcmp_zerozero   #1#2#3#4{ 0}%  1.08b had some [ and ] here!!!
\def\XINT_fcmp_firstzero  #1#2#3#4{ -1}% incredibly I never saw that until
\def\XINT_fcmp_secondzero #1#2#3#4{ 1}%  preparing 1.09a.
\def\XINT_fcmp_pos #1#2#3#4%
{%
    \XINT_fcmp_B #1#3#2#4%
}%
\def\XINT_fcmp_B #1/#2[#3]#4/#5[#6]%
{%
    \expandafter\XINT_fcmp_C\expandafter
    {\the\numexpr #6-#3\expandafter}\expandafter
    {\romannumeral0\xintiimul {#4}{#2}}%
    {\romannumeral0\xintiimul {#5}{#1}}%
}%
\def\XINT_fcmp_C #1#2#3%
{%
    \expandafter\XINT_fcmp_D\expandafter
    {#3}{#1}{#2}%
}%
\def\XINT_fcmp_D #1#2#3%
{%
    \xintSgnFork
    {\xintiSgn{\the\numexpr #2+\xintLength{#3}-\xintLength{#1}\relax}}%
    { -1}{\XINT_fcmp_E #2\Z {#3}{#1}}{ 1}%
}%
\def\XINT_fcmp_E #1%
{%
    \xint_UDsignfork
        #1\dummy  \XINT_fcmp_Fd
         -\dummy {\XINT_fcmp_Fn #1}%
    \krof
}%
\def\XINT_fcmp_Fd #1\Z #2#3%
{%
    \expandafter\XINT_fcmp_Fe\expandafter
    {\romannumeral0\XINT_dsx_addzerosnofuss {#1}{#3}}{#2}%
}%
\def\XINT_fcmp_Fe #1#2{\XINT_cmp_pre {#2}{#1}}%
\def\XINT_fcmp_Fn #1\Z #2#3%
{%
    \expandafter\XINT_cmp_pre\expandafter
    {\romannumeral0\XINT_dsx_addzerosnofuss {#1}{#2}}{#3}%
}%
\def\xintAbs {\romannumeral0\xintabs }%
\def\xintabs #1%
{%
    \expandafter\xint_fabs\romannumeral0\XINT_infrac {#1}%
}%
\def\xint_fabs #1#2%
{%
    \expandafter\XINT_outfrac\expandafter
    {\the\numexpr #1\expandafter}\expandafter
    {\romannumeral0\XINT_abs #2}%
}%
\def\xintOpp {\romannumeral0\xintopp }%
\def\xintopp #1%
{%
    \expandafter\xint_fopp\romannumeral0\XINT_infrac {#1}%
}%
\def\xint_fopp #1#2%
{%
    \expandafter\XINT_outfrac\expandafter
    {\the\numexpr #1\expandafter}\expandafter
    {\romannumeral0\XINT_opp #2}%
}%
\def\xintSgn {\romannumeral0\xintsgn }%
\def\xintsgn #1%
{%
    \expandafter\xint_fsgn\romannumeral0\XINT_infrac {#1}%
}%
\def\xint_fsgn #1#2#3{\xintisgn {#2}}%
\def\xintDivision {\romannumeral0\xintdivision }%
\def\xintdivision #1%
{%
    \expandafter\xint_xdivision\expandafter{\romannumeral0\xintnum {#1}}%
}%
\def\xint_xdivision #1#2%
{%
    \expandafter\XINT_div_fork\romannumeral0\xintnum {#2}\Z #1\Z
}%
\def\xintQuo {\romannumeral0\xintquo }%
\def\xintRem {\romannumeral0\xintrem }%
\def\xintquo {\expandafter\xint_firstoftwo_andstop
               \romannumeral0\xintdivision }%
\def\xintrem {\expandafter\xint_secondoftwo_andstop
               \romannumeral0\xintdivision }%
\def\xintFDg {\romannumeral0\xintfdg }%
\def\xintfdg #1%
{%
    \expandafter\XINT_fdg\romannumeral0\xintnum {#1}\W\Z
}%
\def\xintLDg {\romannumeral0\xintldg }%
\def\xintldg #1%
{%
    \expandafter\XINT_ldg\expandafter{\romannumeral0\xintnum {#1}}%
}%
\def\xintMON {\romannumeral0\xintmon }%
\def\xintmon #1%
{%
    \ifodd\xintLDg {#1}
        \xint_afterfi{ -1}%
    \else
        \xint_afterfi{ 1}%
    \fi
}%
\def\xintMMON {\romannumeral0\xintmmon }%
\def\xintmmon #1%
{%
    \ifodd\xintLDg {#1}
        \xint_afterfi{ 1}%
    \else
        \xint_afterfi{ -1}%
    \fi
}%
\def\xintOdd {\romannumeral0\xintodd }%
\def\xintodd #1%
{%
    \ifodd\xintLDg{#1}
        \xint_afterfi{ 1}%
    \else
        \xint_afterfi{ 0}%
    \fi
}%
\def\xintFloatAdd      {\romannumeral0\xintfloatadd }%
\def\xintfloatadd    #1{\XINT_fladd_chkopt \xintfloat #1\Z }%
\def\XINTinFloatAdd   {\romannumeral0\XINTinfloatadd }%
\def\XINTinfloatadd #1{\XINT_fladd_chkopt \XINT_inFloat #1\Z }%
\def\XINT_fladd_chkopt #1#2%
{%
    \ifx [#2\expandafter\XINT_fladd_opt
       \else\expandafter\XINT_fladd_noopt
    \fi  #1#2%
}%
\def\XINT_fladd_noopt #1#2\Z #3%
{%
    #1[\XINTdigits]{\XINT_FL_Add {\XINTdigits+2}{#2}{#3}}%
}%
\def\XINT_fladd_opt #1[\Z #2]#3#4%
{%
    #1[#2]{\XINT_FL_Add {#2+2}{#3}{#4}}%
}%
\def\XINT_FL_Add #1#2%
{%
    \expandafter\XINT_FL_Add_a\expandafter{\the\numexpr #1\expandafter}%
    \expandafter{\romannumeral0\XINT_inFloat [#1]{#2}}%
}%
\def\XINT_FL_Add_a #1#2#3%
{%
    \expandafter\XINT_FL_Add_b\romannumeral0\XINT_inFloat [#1]{#3}#2{#1}%
}%
\def\XINT_FL_Add_b #1%
{%
    \xint_gob_til_zero #1\XINT_FL_Add_zero 0\XINT_FL_Add_c #1%
}%
\def\XINT_FL_Add_c #1[#2]#3%
{%
    \xint_gob_til_zero #3\XINT_FL_Add_zerobis 0\XINT_FL_Add_d #1[#2]#3%
}%
\def\XINT_FL_Add_d #1[#2]#3[#4]#5%
{%
    \xintSgnFork {\ifnum \numexpr #2-#4-#5>1 \expandafter 1%
                  \else\ifnum \numexpr #4-#2-#5>1
                       \xint_afterfi {\expandafter-\expandafter1}%
                       \else \expandafter\expandafter\expandafter0%
                       \fi
                  \fi}%
    {#3[#4]}{\xintAdd {#1[#2]}{#3[#4]}}{#1[#2]}%
}%
\def\XINT_FL_Add_zero 0\XINT_FL_Add_c 0[0]#1[#2]#3{#1[#2]}%
\def\XINT_FL_Add_zerobis 0\XINT_FL_Add_d #1[#2]0[0]#3{#1[#2]}%
\def\xintFloatSub {\romannumeral0\xintfloatsub }%
\def\xintfloatsub    #1{\XINT_flsub_chkopt \xintfloat #1\Z }%
\def\XINTinFloatSub {\romannumeral0\XINTinfloatsub }%
\def\XINTinfloatsub #1{\XINT_flsub_chkopt \XINT_inFloat #1\Z }%
\def\XINT_flsub_chkopt #1#2%
{%
    \ifx [#2\expandafter\XINT_flsub_opt
       \else\expandafter\XINT_flsub_noopt
    \fi  #1#2%
}%
\def\XINT_flsub_noopt #1#2\Z #3%
{%
    #1[\XINTdigits]{\XINT_FL_Add {\XINTdigits+2}{#2}{\xintOpp{#3}}}%
}%
\def\XINT_flsub_opt #1[\Z #2]#3#4%
{%
    #1[#2]{\XINT_FL_Add {#2+2}{#3}{\xintOpp{#4}}}%
}%
\def\xintFloatMul    {\romannumeral0\xintfloatmul}%
\def\xintfloatmul    #1{\XINT_flmul_chkopt \xintfloat #1\Z }%
\def\XINTinFloatMul {\romannumeral0\XINTinfloatmul }%
\def\XINTinfloatmul #1{\XINT_flmul_chkopt \XINT_inFloat #1\Z }%
\def\XINT_flmul_chkopt #1#2%
{%
    \ifx [#2\expandafter\XINT_flmul_opt
       \else\expandafter\XINT_flmul_noopt
    \fi  #1#2%
}%
\def\XINT_flmul_noopt #1#2\Z #3%
{%
    #1[\XINTdigits]{\XINT_FL_Mul {\XINTdigits+2}{#2}{#3}}%
}%
\def\XINT_flmul_opt #1[\Z #2]#3#4%
{%
    #1[#2]{\XINT_FL_Mul {#2+2}{#3}{#4}}%
}%
\def\XINT_FL_Mul #1#2%
{%
    \expandafter\XINT_FL_Mul_a\expandafter{\the\numexpr #1\expandafter}%
    \expandafter{\romannumeral0\XINT_inFloat [#1]{#2}}%
}%
\def\XINT_FL_Mul_a #1#2#3%
{%
    \expandafter\XINT_FL_Mul_b\romannumeral0\XINT_inFloat [#1]{#3}#2%
}%
\def\XINT_FL_Mul_b #1[#2]#3[#4]{\xintE{\xintiiMul {#1}{#3}}{#2+#4}}%
\def\xintFloatDiv    {\romannumeral0\xintfloatdiv}%
\def\xintfloatdiv    #1{\XINT_fldiv_chkopt \xintfloat #1\Z }%
\def\XINTinFloatDiv  {\romannumeral0\XINTinfloatdiv }%
\def\XINTinfloatdiv  #1{\XINT_fldiv_chkopt \XINT_inFloat #1\Z }%
\def\XINT_fldiv_chkopt #1#2%
{%
    \ifx [#2\expandafter\XINT_fldiv_opt
       \else\expandafter\XINT_fldiv_noopt
    \fi  #1#2%
}%
\def\XINT_fldiv_noopt #1#2\Z #3%
{%
    #1[\XINTdigits]{\XINT_FL_Div {\XINTdigits+2}{#2}{#3}}%
}%
\def\XINT_fldiv_opt #1[\Z #2]#3#4%
{%
    #1[#2]{\XINT_FL_Div {#2+2}{#3}{#4}}%
}%
\def\XINT_FL_Div #1#2%
{%
    \expandafter\XINT_FL_Div_a\expandafter{\the\numexpr #1\expandafter}%
    \expandafter{\romannumeral0\XINT_inFloat [#1]{#2}}%
}%
\def\XINT_FL_Div_a #1#2#3%
{%
    \expandafter\XINT_FL_Div_b\romannumeral0\XINT_inFloat [#1]{#3}#2%
}%
\def\XINT_FL_Div_b #1[#2]#3[#4]{\xintE{#3/#1}{#4-#2}}%
\def\xintFloatSum      {\romannumeral0\xintfloatsum }%
\def\xintfloatsum    #1{\expandafter\XINT_floatsum_a\romannumeral-`0#1\relax }%
\def\XINT_floatsum_a #1{\expandafter\XINT_floatsum_b
                         \romannumeral0\xintraw{#1}\Z }% normalizes if only 1
\def\XINT_floatsum_b #1\Z #2%            but a bit wasteful
           {\expandafter\XINT_floatsum_c\romannumeral-`0#2\Z {#1}\Z}%
\def\XINT_floatsum_c #1%
           {\xint_gob_til_relax #1\XINT_floatsum_e\relax\XINT_floatsum_d #1}%
\def\XINT_floatsum_d #1\Z
           {\expandafter\XINT_floatsum_b\romannumeral0\XINTinfloatadd {#1}}%
\def\XINT_floatsum_e #1\Z #2\Z { #2}%
\def\xintFloatSum:csv #1{\expandafter\XINT_floatsum:_a\romannumeral-`0#1,,^}%
\def\XINT_floatsum:_a {\XINT_floatsum:_b {0/1[0]}}%
\def\XINT_floatsum:_b #1#2,%
             {\expandafter\XINT_floatsum:_c\romannumeral-`0#2,{#1}}%
\def\XINT_floatsum:_c #1{\if #1,\expandafter\XINT_floatsum:_e
                      \else\expandafter\XINT_floatsum:_d\fi #1}%
\def\XINT_floatsum:_d #1,#2{\expandafter\XINT_floatsum:_b\expandafter
                        {\romannumeral0\XINTinfloatadd {#2}{#1}}}%
\def\XINT_floatsum:_e  ,#1#2^{#1}% allows empty list
\def\xintFloatPrd      {\romannumeral0\xintfloatprd }%
\def\xintfloatprd    #1{\expandafter\XINT_floatprd_a\romannumeral-`0#1\relax }%
\def\XINT_floatprd_a #1{\expandafter\XINT_floatprd_b
                         \romannumeral0\xintraw{#1}\Z }%
\def\XINT_floatprd_b #1\Z #2%
           {\expandafter\XINT_floatprd_c\romannumeral-`0#2\Z {#1}\Z}%
\def\XINT_floatprd_c #1%
           {\xint_gob_til_relax #1\XINT_floatprd_e\relax\XINT_floatprd_d #1}%
\def\XINT_floatprd_d #1\Z
           {\expandafter\XINT_floatprd_b\romannumeral0\XINTinfloatmul {#1}}%
\def\XINT_floatprd_e #1\Z #2\Z { #2}%
\def\xintFloatPrd:csv #1{\expandafter\XINT_floatprd:_a\romannumeral-`0#1,,^}%
\def\XINT_floatprd:_a {\XINT_floatprd:_b {1/1[0]}}%
\def\XINT_floatprd:_b #1#2,%
             {\expandafter\XINT_floatprd:_c\romannumeral-`0#2,{#1}}%
\def\XINT_floatprd:_c #1{\if #1,\expandafter\XINT_floatprd:_e
                      \else\expandafter\XINT_floatprd:_d\fi #1}%
\def\XINT_floatprd:_d #1,#2{\expandafter\XINT_floatprd:_b\expandafter
                        {\romannumeral0\XINTinfloatmul {#2}{#1}}}%
\def\XINT_floatprd:_e  ,#1#2^{#1}% allows empty list
\def\xintFloatPow {\romannumeral0\xintfloatpow}%
\def\xintfloatpow #1{\XINT_flpow_chkopt \xintfloat #1\Z }%
\def\XINTinFloatPow {\romannumeral0\XINTinfloatpow }%
\def\XINTinfloatpow #1{\XINT_flpow_chkopt \XINT_inFloat #1\Z }%
\def\XINT_flpow_chkopt #1#2%
{%
    \ifx [#2\expandafter\XINT_flpow_opt
       \else\expandafter\XINT_flpow_noopt
    \fi
     #1#2%
}%
\def\XINT_flpow_noopt  #1#2\Z #3%
{%
   \expandafter\XINT_flpow_checkB_start\expandafter
                {\the\numexpr #3\expandafter}\expandafter
                {\the\numexpr \XINTdigits}{#2}{#1[\XINTdigits]}%
}%
\def\XINT_flpow_opt #1[\Z #2]#3#4%
{%
   \expandafter\XINT_flpow_checkB_start\expandafter
               {\the\numexpr #4\expandafter}\expandafter
               {\the\numexpr #2}{#3}{#1[#2]}%
}%
\def\XINT_flpow_checkB_start #1{\XINT_flpow_checkB_a #1\Z }%
\def\XINT_flpow_checkB_a #1%
{%
    \xint_UDzerominusfork
      #1-\dummy  \XINT_flpow_BisZero
      0#1\dummy  {\XINT_flpow_checkB_b 1}%
       0-\dummy  {\XINT_flpow_checkB_b 0#1}%
    \krof
}%
\def\XINT_flpow_BisZero \Z #1#2#3{#3{1/1[0]}}%
\def\XINT_flpow_checkB_b #1#2\Z #3%
{%
    \expandafter\XINT_flpow_checkB_c \expandafter
    {\romannumeral0\XINT_length{#2}}{#3}{#2}#1%
}%
\def\XINT_flpow_checkB_c #1#2%
{%
    \expandafter\XINT_flpow_checkB_d \expandafter
    {\the\numexpr \expandafter\XINT_Length\expandafter
                  {\the\numexpr #1*20/3}+#1+#2+1}%
}%
\def\XINT_flpow_checkB_d #1#2#3#4%
{%
    \expandafter \XINT_flpow_a
    \romannumeral0\XINT_inFloat [#1]{#4}{#1}{#2}#3%
}%
\def\XINT_flpow_a #1%
{%
    \xint_UDzerominusfork
      #1-\dummy \XINT_flpow_zero
      0#1\dummy {\XINT_flpow_b 1}%
       0-\dummy {\XINT_flpow_b 0#1}%
    \krof
}%
\def\XINT_flpow_zero [#1]#2#3#4#5%
{%
    \if #41 \xint_afterfi {\xintError:DivisionByZero\space 1.e2147483647}%
    \else \xint_afterfi { 0.e0}\fi
}%
\def\XINT_flpow_b #1#2[#3]#4#5%
{%
    \XINT_flpow_c {#4}{#5}{#2[#3]}{#1*\ifodd #5 1\else 0\fi}%
}%
\def\XINT_flpow_c #1#2#3#4%
{%
    \XINT_flpow_loop {#1}{#2}{#3}{{#1}}\XINT_flpow_prd
      \xint_relax
        \xint_undef\xint_undef\xint_undef\xint_undef
        \xint_undef\xint_undef\xint_undef\xint_undef
      \xint_relax {#4}%
}%
\def\XINT_flpow_loop #1#2#3%
{%
    \ifnum #2 = 1
        \expandafter\XINT_flpow_loop_end
    \else
        \xint_afterfi{\expandafter\XINT_flpow_loop_a
            \expandafter{\the\numexpr 2*(#2/2)-#2\expandafter }% b mod 2
            \expandafter{\the\numexpr #2-#2/2\expandafter }%     [b/2]
            \expandafter{\romannumeral0\XINTinfloatmul [#1]{#3}{#3}}}%
    \fi
    {#1}{{#3}}%
}%
\def\XINT_flpow_loop_a #1#2#3#4%
{%
    \ifnum #1 = 1
        \expandafter\XINT_flpow_loop
    \else
        \expandafter\XINT_flpow_loop_throwaway
    \fi
    {#4}{#2}{#3}%
}%
\def\XINT_flpow_loop_throwaway #1#2#3#4%
{%
   \XINT_flpow_loop {#1}{#2}{#3}%
}%
\def\XINT_flpow_loop_end #1{\romannumeral0\XINT_rord_main {}\relax }%
\def\XINT_flpow_prd #1#2%
{%
    \XINT_flpow_prd_getnext {#2}{#1}%
}%
\def\XINT_flpow_prd_getnext #1#2#3%
{%
    \XINT_flpow_prd_checkiffinished #3\Z {#1}{#2}%
}%
\def\XINT_flpow_prd_checkiffinished #1%
{%
    \xint_gob_til_relax #1\XINT_flpow_prd_end\relax
    \XINT_flpow_prd_compute #1%
}%
\def\XINT_flpow_prd_compute #1\Z #2#3%
{%
    \expandafter\XINT_flpow_prd_getnext\expandafter
    {\romannumeral0\XINTinfloatmul [#3]{#1}{#2}}{#3}%
}%
\def\XINT_flpow_prd_end\relax\XINT_flpow_prd_compute
    \relax\Z #1#2#3%
{%
    \expandafter\XINT_flpow_conclude \the\numexpr #3\relax #1%
}%
\def\XINT_flpow_conclude #1#2[#3]#4%
{%
    \expandafter\XINT_flpow_conclude_really\expandafter
    {\the\numexpr\if #41 -\fi#3\expandafter}%
    \xint_UDzerofork
        #4\dummy {{#2}}%
         0\dummy {{1/#2}}%
    \krof #1%
}%
\def\XINT_flpow_conclude_really #1#2#3#4%
{%
    \xint_UDzerofork
    #3\dummy {#4{#2[#1]}}%
     0\dummy {#4{-#2[#1]}}%
    \krof
}%
\def\xintFloatPower {\romannumeral0\xintfloatpower}%
\def\xintfloatpower #1{\XINT_flpower_chkopt \xintfloat #1\Z }%
\def\XINTinFloatPower {\romannumeral0\XINTinfloatpower}%
\def\XINTinfloatpower #1{\XINT_flpower_chkopt \XINT_inFloat #1\Z }%
\def\XINT_flpower_chkopt #1#2%
{%
    \ifx [#2\expandafter\XINT_flpower_opt
       \else\expandafter\XINT_flpower_noopt
    \fi
     #1#2%
}%
\def\XINT_flpower_noopt  #1#2\Z #3%
{%
   \expandafter\XINT_flpower_checkB_start\expandafter
                {\the\numexpr \XINTdigits\expandafter}\expandafter
                {\romannumeral0\xintnum{#3}}{#2}{#1[\XINTdigits]}%
}%
\def\XINT_flpower_opt #1[\Z #2]#3#4%
{%
   \expandafter\XINT_flpower_checkB_start\expandafter
               {\the\numexpr #2\expandafter}\expandafter
               {\romannumeral0\xintnum{#4}}{#3}{#1[#2]}%
}%
\def\XINT_flpower_checkB_start #1#2{\XINT_flpower_checkB_a #2\Z {#1}}%
\def\XINT_flpower_checkB_a #1%
{%
    \xint_UDzerominusfork
      #1-\dummy  \XINT_flpower_BisZero
      0#1\dummy  {\XINT_flpower_checkB_b 1}%
       0-\dummy  {\XINT_flpower_checkB_b 0#1}%
    \krof
}%
\def\XINT_flpower_BisZero \Z #1#2#3{#3{1/1[0]}}%
\def\XINT_flpower_checkB_b #1#2\Z #3%
{%
    \expandafter\XINT_flpower_checkB_c \expandafter
    {\romannumeral0\XINT_length{#2}}{#3}{#2}#1%
}%
\def\XINT_flpower_checkB_c #1#2%
{%
    \expandafter\XINT_flpower_checkB_d \expandafter
    {\the\numexpr \expandafter\XINT_Length\expandafter
                  {\the\numexpr #1*20/3}+#1+#2+1}%
}%
\def\XINT_flpower_checkB_d #1#2#3#4%
{%
    \expandafter \XINT_flpower_a
    \romannumeral0\XINT_inFloat [#1]{#4}{#1}{#2}#3%
}%
\def\XINT_flpower_a #1%
{%
    \xint_UDzerominusfork
      #1-\dummy \XINT_flpower_zero
      0#1\dummy {\XINT_flpower_b 1}%
       0-\dummy {\XINT_flpower_b 0#1}%
    \krof
}%
\def\XINT_flpower_zero [#1]#2#3#4#5%
{%
    \if #41
          \xint_afterfi {\xintError:DivisionByZero\space 1.e2147483647}%
    \else \xint_afterfi { 0.e0}\fi
}%
\def\XINT_flpower_b #1#2[#3]#4#5%
{%
    \XINT_flpower_c {#4}{#5}{#2[#3]}{#1*\xintOdd {#5}}%
}%
\def\XINT_flpower_c #1#2#3#4%
{%
    \XINT_flpower_loop {#1}{#2}{#3}{{#1}}\XINT_flpow_prd
      \xint_relax
        \xint_undef\xint_undef\xint_undef\xint_undef
        \xint_undef\xint_undef\xint_undef\xint_undef
      \xint_relax {#4}%
}%
\def\XINT_flpower_loop #1#2#3%
{%
    \ifcase\XINT_isOne {#2}
        \xint_afterfi{\expandafter\XINT_flpower_loop_x\expandafter
            {\romannumeral0\XINTinfloatmul [#1]{#3}{#3}}%
            {\romannumeral0\xintdivision {#2}{2}}}%
    \or \expandafter\XINT_flpow_loop_end
    \fi
    {#1}{{#3}}%
}%
\def\XINT_flpower_loop_x #1#2{\expandafter\XINT_flpower_loop_a #2{#1}}%
\def\XINT_flpower_loop_a #1#2#3#4%
{%
    \ifnum #2 = 1
        \expandafter\XINT_flpower_loop
    \else
        \expandafter\XINT_flpower_loop_throwaway
    \fi
    {#4}{#1}{#3}%
}%
\def\XINT_flpower_loop_throwaway #1#2#3#4%
{%
   \XINT_flpower_loop {#1}{#2}{#3}%
}%
\def\xintFloatSqrt     {\romannumeral0\xintfloatsqrt }%
\def\xintfloatsqrt   #1{\XINT_flsqrt_chkopt \xintfloat #1\Z }%
\def\XINTinFloatSqrt   {\romannumeral0\XINTinfloatsqrt }%
\def\XINTinfloatsqrt #1{\XINT_flsqrt_chkopt \XINT_inFloat #1\Z }%
\def\XINT_flsqrt_chkopt #1#2%
{%
    \ifx [#2\expandafter\XINT_flsqrt_opt
       \else\expandafter\XINT_flsqrt_noopt
    \fi  #1#2%
}%
\def\XINT_flsqrt_noopt #1#2\Z
{%
    #1[\XINTdigits]{\XINT_FL_sqrt \XINTdigits {#2}}%
}%
\def\XINT_flsqrt_opt #1[\Z #2]#3%
{%
    #1[#2]{\XINT_FL_sqrt {#2}{#3}}%
}%
\def\XINT_FL_sqrt #1%
{%
    \ifnum\numexpr #1<\xint_c_xviii
        \xint_afterfi {\XINT_FL_sqrt_a\xint_c_xviii}%
    \else
        \xint_afterfi {\XINT_FL_sqrt_a {#1+\xint_c_i}}%
    \fi
}%
\def\XINT_FL_sqrt_a #1#2%
{%
    \expandafter\XINT_FL_sqrt_checkifzeroorneg
    \romannumeral0\XINT_inFloat [#1]{#2}%
}%
\def\XINT_FL_sqrt_checkifzeroorneg #1%
{%
    \xint_UDzerominusfork
     #1-\dummy  \XINT_FL_sqrt_iszero
     0#1\dummy  \XINT_FL_sqrt_isneg
      0-\dummy {\XINT_FL_sqrt_b #1}%
    \krof
}%
\def\XINT_FL_sqrt_iszero #1[#2]{0[0]}%
\def\XINT_FL_sqrt_isneg  #1[#2]{\xintError:RootOfNegative 0[0]}%
\def\XINT_FL_sqrt_b #1[#2]%
{%
    \ifodd #2
        \xint_afterfi{\XINT_FL_sqrt_c 01}%
    \else
        \xint_afterfi{\XINT_FL_sqrt_c {}0}%
    \fi
    {#1}{#2}%
}%
\def\XINT_FL_sqrt_c #1#2#3#4%
{%
    \expandafter\XINT_flsqrt\expandafter {\the\numexpr #4-#2}{#3#1}%
}%
\def\XINT_flsqrt #1#2%
{%
    \expandafter\XINT_sqrt_a
    \expandafter{\romannumeral0\XINT_length {#2}}\XINT_flsqrt_big_d {#2}{#1}%
}%
\def\XINT_flsqrt_big_d #1\or #2\fi #3%
{%
   \fi
   \ifodd #3
     \xint_afterfi{\expandafter\XINT_flsqrt_big_eB}%
   \else
     \xint_afterfi{\expandafter\XINT_flsqrt_big_eA}%
   \fi
   \expandafter {\the\numexpr (#3-\xint_c_i)/\xint_c_ii }{#1}%
}%
\def\XINT_flsqrt_big_eA  #1#2#3%
{%
    \XINT_flsqrt_big_eA_a #3\Z {#2}{#1}{#3}%
}%
\def\XINT_flsqrt_big_eA_a #1#2#3#4#5#6#7#8#9\Z
{%
    \XINT_flsqrt_big_eA_b {#1#2#3#4#5#6#7#8}%
}%
\def\XINT_flsqrt_big_eA_b #1#2%
{%
    \expandafter\XINT_flsqrt_big_f
    \romannumeral0\XINT_flsqrt_small_e {#2001}{#1}%
}%
\def\XINT_flsqrt_big_eB #1#2#3%
{%
    \XINT_flsqrt_big_eB_a #3\Z {#2}{#1}{#3}%
}%
\def\XINT_flsqrt_big_eB_a #1#2#3#4#5#6#7#8#9%
{%
    \XINT_flsqrt_big_eB_b {#1#2#3#4#5#6#7#8#9}%
}%
\def\XINT_flsqrt_big_eB_b #1#2\Z #3%
{%
    \expandafter\XINT_flsqrt_big_f
    \romannumeral0\XINT_flsqrt_small_e {#30001}{#1}%
}%
\def\XINT_flsqrt_small_e #1#2%
{%
   \expandafter\XINT_flsqrt_small_f\expandafter
   {\the\numexpr #1*#1-#2-\xint_c_i}{#1}%
}%
\def\XINT_flsqrt_small_f #1#2%
{%
   \expandafter\XINT_flsqrt_small_g\expandafter
   {\the\numexpr (#1+#2)/(2*#2)-\xint_c_i }{#1}{#2}%
}%
\def\XINT_flsqrt_small_g #1%
{%
    \ifnum #1>\xint_c_
       \expandafter\XINT_flsqrt_small_h
    \else
       \expandafter\XINT_flsqrt_small_end
    \fi
    {#1}%
}%
\def\XINT_flsqrt_small_h #1#2#3%
{%
    \expandafter\XINT_flsqrt_small_f\expandafter
    {\the\numexpr #2-\xint_c_ii*#1*#3+#1*#1\expandafter}\expandafter
    {\the\numexpr #3-#1}%
}%
\def\XINT_flsqrt_small_end #1#2#3%
{%
    \expandafter\space\expandafter
    {\the\numexpr \xint_c_i+#3*\xint_c_x^iv-
                      (#2*\xint_c_x^iv+#3)/(\xint_c_ii*#3)}%
}%
\def\XINT_flsqrt_big_f #1%
{%
    \expandafter\XINT_flsqrt_big_fa\expandafter
    {\romannumeral0\xintiisqr {#1}}{#1}%
}%
\def\XINT_flsqrt_big_fa #1#2#3#4%
{%
    \expandafter\XINT_flsqrt_big_fb\expandafter
    {\romannumeral0\XINT_dsx_addzerosnofuss
                     {\numexpr #3-\xint_c_viii\relax}{#2}}%
    {\romannumeral0\xintiisub
      {\XINT_dsx_addzerosnofuss
           {\numexpr \xint_c_ii*(#3-\xint_c_viii)\relax}{#1}}{#4}}%
    {#3}%
}%
\def\XINT_flsqrt_big_fb #1#2%
{%
    \expandafter\XINT_flsqrt_big_g\expandafter {#2}{#1}%
}%
\def\XINT_flsqrt_big_g #1#2%
{%
    \expandafter\XINT_flsqrt_big_j
    \romannumeral0\xintidivision
    {#1}{\romannumeral0\XINT_dbl_pos #2\R\R\R\R\R\R\R\Z \W\W\W\W\W\W\W }{#2}%
}%
\def\XINT_flsqrt_big_j #1%
{%
    \ifcase\XINT_Sgn {#1}
        \expandafter \XINT_flsqrt_big_end_a
    \or \expandafter \XINT_flsqrt_big_k
    \fi {#1}%
}%
\def\XINT_flsqrt_big_k #1#2#3%
{%
    \expandafter\XINT_flsqrt_big_l\expandafter
    {\romannumeral0\XINT_sub_pre {#3}{#1}}%
    {\romannumeral0\xintiiadd {#2}{\romannumeral0\XINT_sqr {#1}}}%
}%
\def\XINT_flsqrt_big_l #1#2%
{%
   \expandafter\XINT_flsqrt_big_g\expandafter
   {#2}{#1}%
}%
\def\XINT_flsqrt_big_end_a #1#2#3#4#5%
{%
   \expandafter\XINT_flsqrt_big_end_b\expandafter
   {\the\numexpr -#4+#5/\xint_c_ii\expandafter}\expandafter
   {\romannumeral0\xintiisub
    {\XINT_dsx_addzerosnofuss {#4}{#3}}%
    {\xintHalf{\xintiQuo{\XINT_dsx_addzerosnofuss {#4}{#2}}{#3}}}}%
}%
\def\XINT_flsqrt_big_end_b #1#2{#2[#1]}%
\XINT_restorecatcodes_endinput%
\endinput
%%
%% End of file `xintfrac.sty'.