%%
%% 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 1.2g 2016/03/19
%% Copyright (C) 2013-2016 by Jean-Francois Burnol
%% xintfrac: Expandable operations on fractions
%% ---------------------------------------------------------------
\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@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.
         \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.
            \def\z{\endgroup\RequirePackage{xint}}%
          \fi
      \else
        \aftergroup\endinput % xintfrac already loaded.
      \fi
    \fi
  \fi
\z%
\XINTsetupcatcodes% defined in xintkernel.sty
\XINT_providespackage
\ProvidesPackage{xintfrac}%
  [2016/03/19 1.2g Expandable operations on fractions (JFB)]%
\def\XINT_cntSgnFork #1%
{%
    \ifcase #1\expandafter\xint_secondofthree
            \or\expandafter\xint_thirdofthree
          \else\expandafter\xint_firstofthree
    \fi
}%
\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%
{%
    \xint_gob_til_W #9\XINT_lenrord_W\W
    \expandafter\XINT_lenrord_loop\the\numexpr #1+\xint_c_vii.{#9#8#7#6#5#4#3#2}%
}%
\def\XINT_lenrord_W\W\expandafter\XINT_lenrord_loop #1.#2#3\Z
{%
    \expandafter\XINT_lenrord_X #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{\the\numexpr #3-#1.}%
\def\XINT_outfrac #1#2#3%
{%
    \ifcase\XINT_cntSgn #3\Z
        \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}%
\edef\XINT_outfrac_P #1#2%
{%
    \noexpand\if0\noexpand\XINT_Sgn #1\noexpand\Z
        \noexpand\expandafter\noexpand\XINT_outfrac_Zero
    \noexpand\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_fork\romannumeral`&&@#1/\XINT_W[\XINT_W\XINT_T
}%
\def\XINT_infrac_fork #1[#2%
{%
    \xint_UDXINTWfork
      #2\XINT_frac_gen
      \XINT_W\XINT_infrac_res_a % strict A[N] or A/B[N] input
    \krof
    #1[#2%
}%
\def\XINT_infrac_res_a #1%
{%
    \xint_gob_til_zero #1\XINT_infrac_res_zero 0\XINT_infrac_res_b #1%
}%
\def\XINT_infrac_res_zero 0\XINT_infrac_res_b #1\XINT_T {{0}{0}{1}}%
\def\XINT_infrac_res_b #1/#2%
{%
    \xint_UDXINTWfork
     #2\XINT_infrac_res_ca
     \XINT_W\XINT_infrac_res_cb
    \krof
    #1/#2%
}%
\def\XINT_infrac_res_ca #1[#2]/\XINT_W[\XINT_W\XINT_T
   {\expandafter{\the\numexpr #2}{#1}{1}}%
\def\XINT_infrac_res_cb #1/#2[%
   {\expandafter\XINT_infrac_res_cc\romannumeral`&&@#2~#1[}%
\def\XINT_infrac_res_cc #1~#2[#3]/\XINT_W[\XINT_W\XINT_T
   {\expandafter{\the\numexpr #3}{#2}{#1}}%
\def\XINT_frac_gen #1/#2%
{%
    \xint_UDXINTWfork
      #2\XINT_frac_gen_A
      \XINT_W\XINT_frac_gen_B
    \krof
    #1/#2%
}%
\def\XINT_frac_gen_A #1/\XINT_W [\XINT_W {\XINT_frac_gen_C 0~1!#1ee.\XINT_W }%
\def\XINT_frac_gen_B #1/#2/\XINT_W[%\XINT_W
{%
    \expandafter\XINT_frac_gen_Ba
    \romannumeral`&&@#2ee.\XINT_W\XINT_Z #1ee.%\XINT_W
}%
\def\XINT_frac_gen_Ba #1.#2%
{%
    \xint_UDXINTWfork
      #2\XINT_frac_gen_Bb
      \XINT_W\XINT_frac_gen_Bc
    \krof
    #1.#2%
}%
\def\XINT_frac_gen_Bb #1e#2e#3\XINT_Z
                {\expandafter\XINT_frac_gen_C\the\numexpr #2+\xint_c_~#1!}%
\def\XINT_frac_gen_Bc #1.#2e%
{%
    \expandafter\XINT_frac_gen_Bd\romannumeral`&&@#2.#1e%
}%
\def\XINT_frac_gen_Bd #1.#2e#3e#4\XINT_Z
{%
    \expandafter\XINT_frac_gen_C\the\numexpr #3-\romannumeral0\expandafter
    \XINT_length_loop
        0.#1\xint_relax\xint_relax\xint_relax\xint_relax
            \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye~#2#1!%
}%
\def\XINT_frac_gen_C #1!#2.#3%
{%
    \xint_UDXINTWfork
      #3\XINT_frac_gen_Ca
      \XINT_W\XINT_frac_gen_Cb
    \krof
    #1!#2.#3%
}%
\def\XINT_frac_gen_Ca #1~#2!#3e#4e#5\XINT_T
{%
    \expandafter\XINT_frac_gen_F\the\numexpr #4-#1\expandafter
    ~\romannumeral0\XINT_num_loop
     #2\xint_relax\xint_relax\xint_relax\xint_relax
      \xint_relax\xint_relax\xint_relax\xint_relax\Z~#3~%
}%
\def\XINT_frac_gen_Cb #1.#2e%
{%
    \expandafter\XINT_frac_gen_Cc\romannumeral`&&@#2.#1e%
}%
\def\XINT_frac_gen_Cc #1.#2~#3!#4e#5e#6\XINT_T
{%
    \expandafter\XINT_frac_gen_F\the\numexpr #5-#2-%
    \romannumeral0\XINT_length_loop
      0.#1\xint_relax\xint_relax\xint_relax\xint_relax
      \xint_relax\xint_relax\xint_relax\xint_relax\xint_bye\expandafter
    ~\romannumeral0\XINT_num_loop
     #3\xint_relax\xint_relax\xint_relax\xint_relax
      \xint_relax\xint_relax\xint_relax\xint_relax\Z
    ~#4#1~%
}%
\def\XINT_frac_gen_F #1~#2%
{%
    \xint_UDzerominusfork
      #2-\XINT_frac_gen_Gdivbyzero
      0#2{\XINT_frac_gen_G  -{}}%
       0-{\XINT_frac_gen_G {}#2}%
    \krof  #1~%
}%
\def\XINT_frac_gen_Gdivbyzero #1~~#2~%
{%
   \expandafter\XINT_frac_gen_Gdivbyzero_a
   \romannumeral0\XINT_num_loop
     #2\xint_relax\xint_relax\xint_relax\xint_relax
      \xint_relax\xint_relax\xint_relax\xint_relax\Z~#1~%
}%
\def\XINT_frac_gen_Gdivbyzero_a #1~#2~%
{%
    \xintError:DivisionByZero {#2}{#1}{0}%
}%
\def\XINT_frac_gen_G #1#2#3~#4~#5~%
{%
    \expandafter\XINT_frac_gen_Ga
    \romannumeral0\XINT_num_loop
      #1#5\xint_relax\xint_relax\xint_relax\xint_relax
      \xint_relax\xint_relax\xint_relax\xint_relax\Z~#3~{#2#4}%
}%
\def\XINT_frac_gen_Ga #1#2~#3~%
{%
    \xint_gob_til_zero #1\XINT_frac_gen_zero 0%
    {#3}{#1#2}%
}%
\def\XINT_frac_gen_zero 0#1#2#3{{0}{0}{1}}%
\def\XINT_factortens #1%
{%
    \expandafter\XINT_cuz_cnt_loop\expandafter
    {\expandafter}\romannumeral0\XINT_rord_main {}#1%
      \xint_relax
        \xint_bye\xint_bye\xint_bye\xint_bye
        \xint_bye\xint_bye\xint_bye\xint_bye
      \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_bye\xint_bye\xint_bye\xint_bye
        \xint_bye\xint_bye\xint_bye\xint_bye
      \xint_relax }{#1}%
}%
\def\XINT_addm_A #1#2#3#4#5#6%
{%
    \xint_gob_til_W #3\XINT_addm_az\W
    \XINT_addm_AB #1{#3#4#5#6}{#2}%
}%
\def\XINT_addm_az\W\XINT_addm_AB #1#2%
{%
    \XINT_addm_AC_checkcarry #1%
}%
\def\XINT_addm_AB #1#2#3#4\W\X\Y\Z #5#6#7#8%
{%
    \XINT_addm_ABE #1#2{#8#7#6#5}{#3}#4\W\X\Y\Z
}%
\def\XINT_addm_ABE #1#2#3#4#5#6%
{%
    \expandafter\XINT_addm_ABEA\the\numexpr #1+10#5#4#3#2+#6.%
}%
\def\XINT_addm_ABEA #1#2#3.#4%
{%
    \XINT_addm_A  #2{#3#4}%
}%
\def\XINT_addm_AC_checkcarry #1%
{%
    \xint_gob_til_zero #1\XINT_addm_AC_nocarry 0\XINT_addm_C
}%
\def\XINT_addm_AC_nocarry 0\XINT_addm_C #1#2\W\X\Y\Z
{%
    \expandafter
    \xint_cleanupzeros_andstop
    \romannumeral0%
    \XINT_rord_main {}#2%
      \xint_relax
        \xint_bye\xint_bye\xint_bye\xint_bye
        \xint_bye\xint_bye\xint_bye\xint_bye
      \xint_relax
    #1%
}%
\def\XINT_addm_C #1#2#3#4#5%
{%
    \xint_gob_til_W
    #5\XINT_addm_cw
    #4\XINT_addm_cx
    #3\XINT_addm_cy
    #2\XINT_addm_cz
    \W\XINT_addm_CD {#5#4#3#2}{#1}%
}%
\def\XINT_addm_CD #1%
{%
    \expandafter\XINT_addm_CC\the\numexpr 1+10#1.%
}%
\def\XINT_addm_CC #1#2#3.#4%
{%
    \XINT_addm_AC_checkcarry  #2{#3#4}%
}%
\def\XINT_addm_cw
    #1\XINT_addm_cx
    #2\XINT_addm_cy
    #3\XINT_addm_cz
    \W\XINT_addm_CD
{%
    \expandafter\XINT_addm_CDw\the\numexpr 1+#1#2#3.%
}%
\def\XINT_addm_CDw #1.#2#3\X\Y\Z
{%
    \XINT_addm_end #1#3%
}%
\def\XINT_addm_cx
    #1\XINT_addm_cy
    #2\XINT_addm_cz
    \W\XINT_addm_CD
{%
    \expandafter\XINT_addm_CDx\the\numexpr 1+#1#2.%
}%
\def\XINT_addm_CDx #1.#2#3\Y\Z
{%
    \XINT_addm_end #1#3%
}%
\def\XINT_addm_cy
    #1\XINT_addm_cz
    \W\XINT_addm_CD
{%
    \expandafter\XINT_addm_CDy\the\numexpr 1+#1.%
}%
\def\XINT_addm_CDy  #1.#2#3\Z
{%
    \XINT_addm_end #1#3%
}%
\def\XINT_addm_cz\W\XINT_addm_CD #1#2#3{\XINT_addm_end #1#3}%
\edef\XINT_addm_end #1#2#3#4#5%
    {\noexpand\expandafter\space\noexpand\the\numexpr #1#2#3#4#5\relax}%
\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_cntSgn #1\Z
      \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% devrais-je faire \xintREZ?
    {\expandafter\XINT_ifloor \romannumeral0\xintrawwithzeros {#1}./1[0]}%
\def\xintiFloor {\romannumeral0\xintifloor }%
\def\xintifloor #1%
    {\expandafter\XINT_ifloor \romannumeral0\xintrawwithzeros {#1}.}%
\def\XINT_ifloor #1/#2.{\xintiiquo {#1}{#2}}%
\def\xintCeil {\romannumeral0\xintceil }%
\def\xintceil #1{\xintiiopp {\xintFloor {\xintOpp{#1}}}}%
\def\xintiCeil {\romannumeral0\xinticeil }%
\def\xinticeil #1{\xintiiopp {\xintiFloor {\xintOpp{#1}}}}%
\def\xintNumerator {\romannumeral0\xintnumerator }%
\def\xintnumerator
{%
    \expandafter\XINT_numer\romannumeral0\XINT_infrac
}%
\def\XINT_numer #1%
{%
    \ifcase\XINT_cntSgn #1\Z
      \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_cntSgn #1\Z
      \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 0\XINT_fracfrac_D #1#2#3%
{%
    \if1\XINT_isOne {#3}%
        \xint_afterfi {\expandafter\xint_firstoftwo_thenstop\xint_gobble_ii }%
    \fi
    \space
    \frac {#2}{#3}%
}%
\def\XINT_fracfrac_D #1#2#3%
{%
    \if1\XINT_isOne {#3}\XINT_fracfrac_E\fi
    \space
    \frac {#2}{#3}#1%
}%
\def\XINT_fracfrac_E \fi\space\frac #1#2{\fi \space #1\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\XINT_sgnfrac_N
       -{\XINT_sgnfrac_P #1}%
    \krof
}%
\def\XINT_sgnfrac_P #1\Z #2%
{%
    \XINT_fracfrac_A {#2}{#1}%
}%
\def\XINT_sgnfrac_N
{%
    \expandafter-\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%
{%
    \if0\XINT_isOne {#5}\xint_afterfi { {#4\over #5}}%
                   \else\xint_afterfi { #4}%
    \fi
}%
\def\XINT_fwover_D #1#2#3%
{%
    \if0\XINT_isOne {#3}\xint_afterfi { {#2\over #3}}%
                   \else\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\XINT_sgnfwover_N
       -{\XINT_sgnfwover_P #1}%
    \krof
}%
\def\XINT_sgnfwover_P #1\Z #2%
{%
    \XINT_fwover_A {#2}{#1}%
}%
\def\XINT_sgnfwover_N
{%
    \expandafter-\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-\XINT_rez_zero
      0#1\XINT_rez_neg
       0-{\XINT_rez_B #1}%
    \krof
}%
\def\XINT_rez_zero #1\Z #2#3{ 0/1[0]}%
\def\XINT_rez_neg {\expandafter-\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\the\numexpr #1+#4.{#2}{#3}%
}%
\def\XINT_e_end #1.#2#3{ #2/#3[#1]}%
\def\xintIrr {\romannumeral0\xintirr }%
\def\xintirr #1%
{%
    \expandafter\XINT_irr_start\romannumeral0\xintrawwithzeros {#1}\Z
}%
\def\XINT_irr_start #1#2/#3\Z
{%
    \if0\XINT_isOne {#3}%
      \xint_afterfi
          {\xint_UDsignfork
               #1\XINT_irr_negative
                -{\XINT_irr_nonneg #1}%
           \krof}%
    \else
      \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 -}%
\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\XINT_irr_indeterminate
       #30\XINT_irr_divisionbyzero
       #10\XINT_irr_zero
        00\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\xintiiquo {#3}{#2}}%
    {\romannumeral0\xintiiquo {#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\xintifInt   {\romannumeral0\xintifint }%
\def\xintifint #1{\expandafter\XINT_ifint\romannumeral0\xintrawwithzeros {#1}.}%
\def\XINT_ifint #1/#2.%
{%
    \if 0\xintiiRem {#1}{#2}%
     \expandafter\xint_firstoftwo_thenstop
    \else
     \expandafter\xint_secondoftwo_thenstop
    \fi
}%
\def\xintJrr {\romannumeral0\xintjrr }%
\def\xintjrr #1%
{%
    \expandafter\XINT_jrr_start\romannumeral0\xintrawwithzeros {#1}\Z
}%
\def\XINT_jrr_start #1#2/#3\Z
{%
    \if0\XINT_isOne {#3}\xint_afterfi
          {\xint_UDsignfork
               #1\XINT_jrr_negative
                -{\XINT_jrr_nonneg #1}%
           \krof}%
    \else
      \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 -}%
\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\XINT_jrr_indeterminate
       #30\XINT_jrr_divisionbyzero
       #10\XINT_jrr_zero
        00\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_fork #4\Z #1\Z}{#6}}%
        {\romannumeral0\xintiiadd{\XINT_mul_fork #5\Z #1\Z}{#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\xintTFrac {\romannumeral0\xinttfrac }%
\def\xinttfrac #1{\expandafter\XINT_tfrac_fork\romannumeral0\xintrawwithzeros {#1}\Z }%
\def\XINT_tfrac_fork #1%
{%
    \xint_UDzerominusfork
        #1-\XINT_tfrac_zero
        0#1{\xintiiopp\XINT_tfrac_P }%
         0-{\XINT_tfrac_P #1}%
    \krof
}%
\def\XINT_tfrac_zero #1\Z { 0/1[0]}%
\def\XINT_tfrac_P #1/#2\Z {\expandafter\XINT_rez_AB
                           \romannumeral0\xintiirem{#1}{#2}\Z {0}{#2}}%
\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_iszero0\XINT_trunc_B #1#2#3{ 0\Z 0}%
\def\XINT_trunc_B #1%
{%
    \ifcase\XINT_cntSgn #1\Z
      \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_CE\expandafter
    {\romannumeral0\XINT_dsx_zeroloop -#1.{}\Z {#3}}{#2}%
}%
\def\XINT_trunc_CE #1#2{\XINT_trunc_E #2.{#1}}%
\def\XINT_trunc_D #1#2%
{%
    \expandafter\XINT_trunc_E
    \romannumeral0\XINT_dsx_zeroloop #1.{}\Z {#2}.%
}%
\def\XINT_trunc_E #1%
{%
    \xint_UDsignfork
       #1\XINT_trunc_Fneg
        -{\XINT_trunc_Fpos #1}%
    \krof
}%
\def\XINT_trunc_Fneg #1.#2{\expandafter\xint_firstoftwo_thenstop
           \romannumeral0\XINT_div_prepare {#2}{#1}\Z -}%
\def\XINT_trunc_Fpos #1.#2{\expandafter\xint_firstoftwo_thenstop
           \romannumeral0\XINT_div_prepare {#2}{#1}\Z \space }%
\def\XINT_itrunc_G #1#2\Z #3#4%
{%
    \xint_gob_til_zero #1\XINT_trunc_zero 0#3#1#2%
}%
\def\XINT_trunc_zero 0#1#20{ 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\xintlength {#1}-#3}{#3}{#1}#2%
}%
\def\XINT_trunc_H #1#2%
{%
    \ifnum #1 > \xint_c_
        \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 autoris\'e !
}%
\def\xintTTrunc {\romannumeral0\xintttrunc }%
\def\xintttrunc #1%
{%
    \expandafter\XINT_itrunc_G
    \romannumeral0\expandafter\XINT_ttrunc_A
    \romannumeral0\XINT_infrac {#1}0% this last 0 to let \XINT_itrunc_G be happy
}%
\def\XINT_ttrunc_A #1#2#3{\XINT_trunc_checkifzero {#1}#2\Z {#3}}%
\let\xintNum \xintTTrunc
\let\xintnum \xintttrunc
\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}{#1+\xint_c_i}{#1}%
}%
\def\XINT_round_B #1\Z
{%
    \expandafter\XINT_round_C
    \romannumeral0\XINT_rord_main {}#1%
      \xint_relax
        \xint_bye\xint_bye\xint_bye\xint_bye
        \xint_bye\xint_bye\xint_bye\xint_bye
      \xint_relax
    \Z
}%
\def\XINT_round_C #1%
{%
    \ifnum #1<\xint_c_v
        \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_bye\xint_bye\xint_bye\xint_bye
        \xint_bye\xint_bye\xint_bye\xint_bye
      \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\xintXTrunc #1#2%
{%
    \expandafter\XINT_xtrunc_a\expandafter
    {\the\numexpr #1\expandafter}\romannumeral0\xintraw {#2}%
}%
\def\XINT_xtrunc_a #1%
{%
    \expandafter\XINT_xtrunc_b\expandafter
    {\the\numexpr\ifnum#1<\xint_c_i \xint_c_i-\fi #1}%
}%
\def\XINT_xtrunc_b #1%
{%
    \expandafter\XINT_xtrunc_c\expandafter
    {\the\numexpr (#1+\xint_c_ii^v)/\xint_c_ii^vi-\xint_c_i}{#1}%
}%
\def\XINT_xtrunc_c #1#2%
{%
    \expandafter\XINT_xtrunc_d\expandafter
    {\the\numexpr #2-\xint_c_ii^vi*#1}{#1}{#2}%
}%
\def\XINT_xtrunc_d #1#2#3#4/#5[#6]%
{%
    \XINT_xtrunc_e #4.{#6}{#5}{#3}{#2}{#1}%
}%
\def\XINT_xtrunc_e #1%
{%
    \xint_UDzerominusfork
        #1-\XINT_xtrunc_zero
        0#1\XINT_xtrunc_N
        0-{\XINT_xtrunc_P #1}%
    \krof
}%
\def\XINT_xtrunc_zero .#1#2#3#4#5%
{%
    0.\romannumeral0\expandafter\XINT_dsx_zeroloop
                                \the\numexpr #5.{}\Z {}%
    \xintiloop [#4+-1]
    \ifnum \xintiloopindex>\xint_c_
    0000000000000000000000000000000000000000000000000000000000000000%
    \repeat
}%
\def\XINT_xtrunc_N {-\XINT_xtrunc_P }%
\def\XINT_xtrunc_P #1.#2%
{%
    \ifnum #2<\xint_c_
        \expandafter\XINT_xtrunc_negN_Q
    \else
        \expandafter\XINT_xtrunc_Q
    \fi  {#2}{#1}.%
}%
\def\XINT_xtrunc_negN_Q #1#2.#3#4#5#6%
{%
    \expandafter\XINT_xtrunc_negN_R
    \romannumeral0\XINT_div_prepare {#3}{#2}{#3}{#1}{#4}%
}%
\def\XINT_xtrunc_negN_R #1#2#3#4#5%
{%
    \expandafter\XINT_xtrunc_negN_S\expandafter
    {\the\numexpr -#4}{#5}{#2}{#3}{#1}%
}%
\def\XINT_xtrunc_negN_S #1#2%
{%
    \expandafter\XINT_xtrunc_negN_T\expandafter
    {\the\numexpr #2-#1}{#1}{#2}%
}%
\def\XINT_xtrunc_negN_T #1%
{%
    \ifnum \xint_c_<#1
      \expandafter\XINT_xtrunc_negNA
    \else
      \expandafter\XINT_xtrunc_negNW
    \fi {#1}%
}%
\def\XINT_xtrunc_unlock #10.{ }%
\def\XINT_xtrunc_negNA #1#2#3#4#5#6%
{%
   \expandafter\XINT_xtrunc_negNB\expandafter
   {\romannumeral0\expandafter\expandafter\expandafter
    \XINT_xtrunc_unlock\expandafter\string
    \csname\XINT_xtrunc_b {#1}#4/#5[0]\expandafter\endcsname
    \expandafter}\expandafter
    {\the\numexpr\xintLength{#6}-#2}{#6}%
}%
\def\XINT_xtrunc_negNB #1#2#3{\XINT_xtrunc_negNC {#2}{#3}#1}%
\def\XINT_xtrunc_negNC #1%
{%
    \ifnum \xint_c_ < #1
      \expandafter\XINT_xtrunc_negNDa
    \else
      \expandafter\XINT_xtrunc_negNE
    \fi {#1}%
}%
\def\XINT_xtrunc_negNDa #1#2%
{%
    \expandafter\XINT_xtrunc_negNDb%
    \romannumeral0\XINT_split_fromleft_loop #1.{}#2\W\W\W\W\W\W\W\W\Z
}%
\def\XINT_xtrunc_negNDb #1.#2.{#1.#2}%
\def\XINT_xtrunc_negNE #1#2%
{%
    0.\romannumeral0\XINT_dsx_zeroloop -#1.{}\Z {}#2%
}%
\def\XINT_xtrunc_negNW #1#2#3#4#5#6%
{%
    \expandafter\XINT_xtrunc_negNX\expandafter
    {\romannumeral0\xintnum{\xintDecSplitL {-#1}{#6}}}{#3}%
}%
\def\XINT_xtrunc_negNX #1#2%
{%
    \expandafter\XINT_xtrunc_negNC\expandafter
    {\the\numexpr\xintLength {#1}-#2}{#1}%
}%
\def\XINT_xtrunc_BisOne #1#2#3#4#5#6#7%
{%
    #5.\romannumeral0\expandafter\XINT_dsx_zeroloop
                                 \the\numexpr #7.{}\Z {}%
    \xintiloop [#6+-1]
    \ifnum \xintiloopindex>\xint_c_
    0000000000000000000000000000000000000000000000000000000000000000%
    \repeat
}%
\def\XINT_xtrunc_BisTwo #1#2#3#4#5#6#7%
{%
    \xintHalf {#5}.\ifodd\xintiiLDg{#5} 5\else 0\fi
    \romannumeral0\expandafter\XINT_dsx_zeroloop
                              \the\numexpr #7-\xint_c_i.{}\Z {}%
    \xintiloop [#6+-1]
    \ifnum \xintiloopindex>\xint_c_
    0000000000000000000000000000000000000000000000000000000000000000%
    \repeat
}%
\def\XINT_xtrunc_Q #1%
{%
    \expandafter\XINT_xtrunc_prepare
    \romannumeral0\XINT_dsx_zeroloop #1.{}\Z
}%
\def\XINT_xtrunc_prepare #1.#2#3%
{%
    \expandafter\XINT_xtrunc_Pa\expandafter
    {\romannumeral0%
    \XINT_xtrunc_prepare_a #2\R\R\R\R\R\R\R\R {10}0000001\W !{#2}}{#1}%
}%
\def\XINT_xtrunc_prepare_a #1#2#3#4#5#6#7#8#9%
{%
    \xint_gob_til_R #9\XINT_xtrunc_prepare_small\R
    \XINT_xtrunc_prepare_b #9%
}%
\def\XINT_xtrunc_prepare_small\R #1!#2%
{%
    \ifcase #2
    \or\xint_afterfi{ \XINT_div_BisOne}%
    \or\xint_afterfi{ \XINT_div_BisTwo}%
    \else\expandafter\XINT_xtrunc_small_aa
    \fi {#2}%
}%
\def\XINT_xtrunc_small_aa #1%
{%
    \expandafter\space\expandafter\XINT_xtrunc_small_a
    \the\numexpr #1/\xint_c_ii\expandafter
    .\the\numexpr \xint_c_x^viii+#1!%
}%
\def\XINT_xtrunc_small_a #1.#2!#3%
{%
    \expandafter\XINT_div_small_b\the\numexpr #1\expandafter
    .\the\numexpr #2\expandafter!%
    \romannumeral0\XINT_div_small_ba #3\R\R\R\R\R\R\R\R{10}0000001\W
       #3\XINT_sepbyviii_Z_end 2345678\relax
}%
\def\XINT_xtrunc_prepare_b
   {\expandafter\XINT_xtrunc_prepare_c\romannumeral0\XINT_zeroes_forviii }%
\def\XINT_xtrunc_prepare_c #1!%
{%
     \XINT_xtrunc_prepare_d  #1.00000000!{#1}%
}%
\def\XINT_xtrunc_prepare_d #1#2#3#4#5#6#7#8#9%
{%
    \expandafter\XINT_xtrunc_prepare_e\xint_gob_til_dot #1#2#3#4#5#6#7#8#9!%
}%
\def\XINT_xtrunc_prepare_e #1!#2!#3#4%
{%
    \XINT_xtrunc_prepare_f #4#3\X {#1}{#3}%
}%
\def\XINT_xtrunc_prepare_f #1#2#3#4#5#6#7#8#9\X
{%
    \expandafter\space\expandafter\XINT_div_prepare_g
     \the\numexpr  #1#2#3#4#5#6#7#8+\xint_c_i\expandafter
    .\the\numexpr (#1#2#3#4#5#6#7#8+\xint_c_i)/\xint_c_ii\expandafter
    .\the\numexpr #1#2#3#4#5#6#7#8\expandafter
    .\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_iii
        \R.\xint_c_vi\R.\xint_c_v\R.\xint_c_iv\R.\xint_c_iii
        \R.\xint_c_ii\R.\xint_c_i\R.\xint_c_\W
    \X
}%
\def\XINT_xtrunc_Pa #1#2%
{%
    \expandafter\XINT_xtrunc_Pb\romannumeral0#1{#2}{#1}%
}%
\def\XINT_xtrunc_Pb #1#2#3#4{#1.\XINT_xtrunc_A {#4}{#2}{#3}}%
\def\XINT_xtrunc_A #1%
{%
    \unless\ifnum #1>\xint_c_ \XINT_xtrunc_transition\fi
    \expandafter\XINT_xtrunc_B\expandafter{\the\numexpr #1-\xint_c_i}%
}%
\def\XINT_xtrunc_B #1#2#3%
{%
    \expandafter\XINT_xtrunc_D\romannumeral0#3%
    {#20000000000000000000000000000000000000000000000000000000000000000}%
    {#1}{#3}%
}%
\def\XINT_xtrunc_D #1#2#3%
{%
    \romannumeral0\expandafter\XINT_dsx_zeroloop
                  \the\numexpr \xint_c_ii^vi-\xintLength{#1}.{}\Z {}#1%
    \XINT_xtrunc_A {#3}{#2}%
}%
\def\XINT_xtrunc_transition\fi
    \expandafter\XINT_xtrunc_B\expandafter #1#2#3#4%
{%
    \fi
    \ifnum #4=\xint_c_ \XINT_xtrunc_abort\fi
    \expandafter\XINT_xtrunc_x\expandafter
    {\romannumeral0\XINT_dsx_zeroloop #4.{}\Z {#2}}{#3}{#4}%
}%
\def\XINT_xtrunc_x #1#2%
{%
    \expandafter\XINT_xtrunc_y\romannumeral0#2{#1}%
}%
\def\XINT_xtrunc_y #1#2#3%
{%
    \romannumeral0\expandafter\XINT_dsx_zeroloop
                  \the\numexpr #3-\xintLength{#1}.{}\Z {}#1%
}%
\def\XINT_xtrunc_abort\fi\expandafter\XINT_xtrunc_x\expandafter #1#2#3{\fi}%
\mathchardef\XINTdigits 16
\def\xintDigits #1#2%
   {\afterassignment \xint_gobble_i \mathchardef\XINTdigits=}%
\def\xinttheDigits {\number\XINTdigits }%
\def\xintAdd {\romannumeral0\xintadd }%
\def\xintadd #1{\expandafter\XINT_fadd\romannumeral0\xintraw {#1}}%
\def\XINT_fadd #1{\xint_gob_til_zero #1\XINT_fadd_Azero 0\XINT_fadd_a #1}%
\def\XINT_fadd_Azero #1]{\xintraw }%
\def\XINT_fadd_a #1/#2[#3]#4%
   {\expandafter\XINT_fadd_b\romannumeral0\xintraw {#4}{#3}{#1}{#2}}%
\def\XINT_fadd_b #1{\xint_gob_til_zero #1\XINT_fadd_Bzero 0\XINT_fadd_c #1}%
\def\XINT_fadd_Bzero #1]#2#3#4{ #3/#4[#2]}%
\def\XINT_fadd_c #1/#2[#3]#4%
{%
    \expandafter\XINT_fadd_Aa\expandafter{\the\numexpr #4-#3}{#3}{#4}{#1}{#2}%
}%
\def\XINT_fadd_Aa #1%
{%
    \ifcase\XINT_cntSgn #1\Z
       \expandafter\XINT_fadd_B
    \or
       \expandafter \XINT_fadd_Ba
    \else
       \expandafter \XINT_fadd_Bb
    \fi {#1}%
}%
\def\XINT_fadd_B   #1#2#3#4#5#6#7{\XINT_fadd_C {#4}{#5}{#7}{#6}[#3]}%
\def\XINT_fadd_Ba  #1#2#3#4#5#6#7%
{%
    \expandafter\XINT_fadd_C\expandafter
        {\romannumeral0\XINT_dsx_zeroloop #1.{}\Z {#6}}%
    {#7}{#5}{#4}[#2]%
}%
\def\XINT_fadd_Bb #1#2#3#4#5#6#7%
{%
    \expandafter\XINT_fadd_C\expandafter
        {\romannumeral0\XINT_dsx_zeroloop -#1.{}\Z {#4}}%
    {#5}{#7}{#6}[#3]%
}%
\def\XINT_fadd_C #1#2#3%
{%
   \ifcase\romannumeral0\xintiicmp {#2}{#3} %<- intentional space here.
      \expandafter\XINT_fadd_eq
   \or\expandafter\XINT_fadd_D
   \else\expandafter\XINT_fadd_Da
   \fi {#2}{#3}{#1}%
}%
\def\XINT_fadd_eq #1#2#3#4%#5%
{%
   \expandafter\XINT_fadd_G
   \romannumeral0\xintiiadd {#3}{#4}/#1%[#5]%
}%
\def\XINT_fadd_D #1#2%
{%
   \expandafter\XINT_fadd_E\romannumeral0\XINT_div_prepare {#2}{#1}{#1}{#2}%
}%
\def\XINT_fadd_E #1#2%
{%
   \if0\XINT_Sgn #2\Z
        \expandafter\XINT_fadd_F
   \else\expandafter\XINT_fadd_K
   \fi {#1}%
}%
\def\XINT_fadd_F #1#2#3#4#5%#6%
{%
   \expandafter\XINT_fadd_G
   \romannumeral0\xintiiadd {\xintiiMul {#5}{#1}}{#4}/#2%[#6]%
}%
\def\XINT_fadd_Da #1#2%
{%
   \expandafter\XINT_fadd_Ea\romannumeral0\XINT_div_prepare {#1}{#2}{#1}{#2}%
}%
\def\XINT_fadd_Ea #1#2%
{%
   \if0\XINT_Sgn #2\Z
        \expandafter\XINT_fadd_Fa
   \else\expandafter\XINT_fadd_K
   \fi {#1}%
}%
\def\XINT_fadd_Fa #1#2#3#4#5%#6%
{%
   \expandafter\XINT_fadd_G
   \romannumeral0\xintiiadd {\xintiiMul {#4}{#1}}{#5}/#3%[#6]%
}%
\def\XINT_fadd_G #1{\if0#1\XINT_fadd_iszero\fi\space #1}%
\def\XINT_fadd_K #1#2#3#4#5%
{%
    \expandafter\XINT_fadd_L
    \romannumeral0\xintiiadd {\xintiiMul {#2}{#5}}{\xintiiMul {#3}{#4}}.%
    {{#2}{#3}}%
}%
\def\XINT_fadd_L #1{\if0#1\XINT_fadd_iszero\fi \XINT_fadd_M #1}%
\def\XINT_fadd_M #1.#2{\expandafter\XINT_fadd_N \expandafter
                       {\romannumeral0\xintiimul #2}{#1}}%
\def\XINT_fadd_N #1#2{ #2/#1}%
\edef\XINT_fadd_iszero\fi #1[#2]{\noexpand\fi\space 0/1[0]}% ou [#2] originel?
\def\xintSub   {\romannumeral0\xintsub }%
\def\xintsub #1{\expandafter\XINT_fsub\romannumeral0\xintraw {#1}}%
\def\XINT_fsub #1{\xint_gob_til_zero #1\XINT_fsub_Azero 0\XINT_fsub_a #1}%
\def\XINT_fsub_Azero #1]{\xintopp }%
\def\XINT_fsub_a #1/#2[#3]#4%
   {\expandafter\XINT_fsub_b\romannumeral0\xintraw {#4}{#3}{#1}{#2}}%
\def\XINT_fsub_b #1{\xint_UDzerominusfork
                      #1-\XINT_fadd_Bzero
                       0#1\XINT_fadd_c
                       0-{\XINT_fadd_c -#1}%
                     \krof }%
\def\xintSum {\romannumeral0\xintsum }%
\def\xintsum #1{\xintsumexpr #1\relax }%
\def\xintSumExpr {\romannumeral0\xintsumexpr }%
\def\xintsumexpr {\expandafter\XINT_fsumexpr\romannumeral`&&@}%
\def\XINT_fsumexpr {\XINT_fsum_loop_a {0/1[0]}}%
\def\XINT_fsum_loop_a #1#2%
{%
    \expandafter\XINT_fsum_loop_b \romannumeral`&&@#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\xintMul {\romannumeral0\xintmul }%
\def\xintmul #1{\expandafter\XINT_fmul\romannumeral0\xintraw {#1}.}%
\def\XINT_fmul #1{\xint_gob_til_zero #1\XINT_fmul_zero 0\XINT_fmul_a #1}%
\def\XINT_fmul_a #1[#2].#3%
   {\expandafter\XINT_fmul_b\romannumeral0\xintraw {#3}#1[#2.]}%
\def\XINT_fmul_b #1{\xint_gob_til_zero #1\XINT_fmul_zero 0\XINT_fmul_c #1}%
\def\XINT_fmul_c #1/#2[#3]#4/#5[#6.]%
{%
    \expandafter\XINT_fmul_d
    \expandafter{\the\numexpr #3+#6\expandafter}%
    \expandafter{\romannumeral0\xintiimul {#5}{#2}}%
    {\romannumeral0\xintiimul {#4}{#1}}%
}%
\def\XINT_fmul_d #1#2#3%
{%
    \expandafter \XINT_fmul_e \expandafter{#3}{#1}{#2}%
}%
\def\XINT_fmul_e #1#2{\XINT_outfrac {#2}{#1}}%
\def\XINT_fmul_zero #1.#2{ 0/1[0]}%
\def\xintSqr {\romannumeral0\xintsqr }%
\def\xintsqr #1{\expandafter\XINT_fsqr\romannumeral0\xintraw {#1}}%
\def\XINT_fsqr #1{\xint_gob_til_zero #1\XINT_fsqr_zero 0\XINT_fsqr_a #1}%
\def\XINT_fsqr_a #1/#2[#3]%
{%
    \expandafter\XINT_fsqr_b
    \expandafter{\the\numexpr #3+#3\expandafter}%
    \expandafter{\romannumeral0\xintiisqr {#2}}%
    {\romannumeral0\xintiisqr {#1}}%
}%
\def\XINT_fsqr_b #1#2#3{\expandafter \XINT_fmul_e \expandafter{#3}{#1}{#2}}%
\def\XINT_fsqr_zero #1]{ 0/1[0]}%
\def\xintipow #1#2%
{%
    \expandafter\xint_pow\the\numexpr \xintNum{#2}\expandafter.\romannumeral0\xintnum{#1}\Z%
}%
\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-\XINT_fpow_zero
      0#1\XINT_fpow_neg
       0-{\XINT_fpow_pos #1}%
    \krof
    {#2}%
}%
\def\XINT_fpow_zero #1#2#3#4{ 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\xintiipow {#5}{#1#2}}%
    {\romannumeral0\xintiipow {#4}{#1#2}}%
}%
\def\XINT_fpow_neg #1#2#3#4%
{%
    \expandafter\XINT_fpow_pos_A\expandafter
    {\the\numexpr -#1*#2\expandafter}\expandafter
    {\romannumeral0\xintiipow {#3}{#1}}%
    {\romannumeral0\xintiipow {#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\xintifac #1{\expandafter\XINT_fac_fork\the\numexpr \xintNum{#1}.}%
\def\xintibinomial #1#2%
{%
    \expandafter\XINT_binom_pre
    \the\numexpr\xintNum{#1}\expandafter.\the\numexpr\xintNum{#2}.%
}%
\def\xintipfactorial #1#2%
{%
    \expandafter\XINT_pfac_fork
    \the\numexpr\xintNum{#1}\expandafter.\the\numexpr\xintNum{#2}.%
}%
\def\xintPrd {\romannumeral0\xintprd }%
\def\xintprd #1{\xintprdexpr #1\relax }%
\def\xintPrdExpr {\romannumeral0\xintprdexpr }%
\def\xintprdexpr {\expandafter\XINT_fprdexpr \romannumeral`&&@}%
\def\XINT_fprdexpr {\XINT_fprod_loop_a {1/1[0]}}%
\def\XINT_fprod_loop_a #1#2%
{%
    \expandafter\XINT_fprod_loop_b \romannumeral`&&@#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\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\xintDivFloor     {\romannumeral0\xintdivfloor }%
\def\xintdivfloor #1#2{\xintfloor{\xintDiv {#1}{#2}}}%
\def\xintDivTrunc     {\romannumeral0\xintdivtrunc }%
\def\xintdivtrunc #1#2{\xintttrunc {\xintDiv {#1}{#2}}}%
\def\xintDivRound     {\romannumeral0\xintdivround }%
\def\xintdivround #1#2{\xintiround 0{\xintDiv {#1}{#2}}}%
\def\xintMod {\romannumeral0\xintmod }%
\def\xintmod #1{\expandafter\XINT_mod_a\romannumeral0\xintraw{#1}.}%
\def\XINT_mod_a #1#2.#3%
   {\expandafter\XINT_mod_b\expandafter #1\romannumeral0\xintraw{#3}#2.}%
\def\XINT_mod_b #1#2% #1 de A, #2 de B.
{%
    \if0#2\xint_dothis\XINT_mod_divbyzero\fi
    \if0#1\xint_dothis\XINT_mod_aiszero\fi
    \if-#2\xint_dothis{\XINT_mod_bneg #1}\fi
          \xint_orthat{\XINT_mod_bpos #1#2}%
}%
\def\XINT_mod_bpos #1%
{%
    \xint_UDsignfork
            #1{\xintiiopp\XINT_mod_pos {}}%
             -{\XINT_mod_pos #1}%
    \krof
}%
\def\XINT_mod_bneg #1%
{%
    \xint_UDsignfork
            #1{\xintiiopp\XINT_mod_pos {}}%
             -{\XINT_mod_pos #1}%
    \krof
}%
\def\XINT_mod_divbyzero #1.{\xintError:DivisionByZero\space 0/1[0]}%
\def\XINT_mod_aiszero #1.{ 0/1[0]}%
\def\XINT_mod_pos #1#2/#3[#4]#5/#6[#7].%
{%
    \expandafter\XINT_mod_pos_a
    \the\numexpr\ifnum#7>#4 #4\else #7\fi\expandafter.\expandafter
    {\romannumeral0\xintiimul {#6}{#3}}%       n fois u
    {\xintiiE{\xintiiMul {#1#5}{#3}}{#7-#4}}%  m fois u
    {\xintiiE{\xintiiMul {#2}{#6}}{#4-#7}}%    t fois n
}%
\def\XINT_mod_pos_a #1.#2#3#4{\xintiirem {#3}{#4}/#2[#1]}%
\def\xintIsOne   {\romannumeral0\xintisone }%
\def\xintisone #1{\expandafter\XINT_fracisone
                  \romannumeral0\xintrawwithzeros{#1}\Z }%
\def\XINT_fracisone #1/#2\Z
    {\if0\XINT_Cmp {#1}{#2}\xint_afterfi{ 1}\else\xint_afterfi{ 0}\fi}%
\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%
{%
    \expandafter\XINT_cntSgnFork\romannumeral`&&@\expandafter\XINT_cntSgn
     \the\numexpr #2+\xintLength{#3}-\xintLength{#1}\relax\Z
    { 0}{\XINT_fgeq_E #2\Z {#3}{#1}}{ 1}%
}%
\def\XINT_fgeq_E #1%
{%
    \xint_UDsignfork
        #1\XINT_fgeq_Fd
         -{\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\XINT_fmax_minusminus
       -#5\XINT_fmax_firstneg
       #1-\XINT_fmax_secondneg
        --\XINT_fmax_nonneg_a
    \krof
    #1#5{#2/#3[#4]}{#6/#7[#8]}%
}%
\def\XINT_fmax_minusminus --%
   {\expandafter-\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%
{%
    \if0\romannumeral0\XINT_fgeq_A #1#2%
          \xint_afterfi{ #1}%
    \else \xint_afterfi{ #2}%
    \fi
}%
\def\xintMaxof      {\romannumeral0\xintmaxof }%
\def\xintmaxof    #1{\expandafter\XINT_maxof_a\romannumeral`&&@#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`&&@#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\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\XINT_fmin_minusminus
       -#5\XINT_fmin_firstneg
       #1-\XINT_fmin_secondneg
        --\XINT_fmin_nonneg_a
    \krof
    #1#5{#2/#3[#4]}{#6/#7[#8]}%
}%
\def\XINT_fmin_minusminus --%
   {\expandafter-\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%
{%
    \if0\romannumeral0\XINT_fgeq_A #1#2%
          \xint_afterfi{ #2}%
    \else \xint_afterfi{ #1}%
    \fi
}%
\def\xintMinof      {\romannumeral0\xintminof }%
\def\xintminof    #1{\expandafter\XINT_minof_a\romannumeral`&&@#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`&&@#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\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\XINT_fcmp_minusminus
       -#5\XINT_fcmp_firstneg
       #1-\XINT_fcmp_secondneg
        --\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\XINT_fcmp_zerozero
       0#2\XINT_fcmp_firstzero
       #10\XINT_fcmp_secondzero
        00\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%
{%
    \expandafter\XINT_cntSgnFork\romannumeral`&&@\expandafter\XINT_cntSgn
    \the\numexpr #2+\xintLength{#3}-\xintLength{#1}\relax\Z
    { -1}{\XINT_fcmp_E #2\Z {#3}{#1}}{ 1}%
}%
\def\XINT_fcmp_E #1%
{%
    \xint_UDsignfork
        #1\XINT_fcmp_Fd
         -{\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{\xintiicmp {#2}{#1}}%
\def\XINT_fcmp_Fn #1\Z #2#3%
{%
    \expandafter\xintiicmp\expandafter
    {\romannumeral0\XINT_dsx_addzerosnofuss {#1}{#2}}{#3}%
}%
\def\xintAbs   {\romannumeral0\xintabs }%
\def\xintabs #1{\expandafter\XINT_abs\romannumeral0\xintraw {#1}}%
\def\xintOpp   {\romannumeral0\xintopp }%
\def\xintopp #1{\expandafter\XINT_opp\romannumeral0\xintraw {#1}}%
\def\xintSgn   {\romannumeral0\xintsgn }%
\def\xintsgn #1{\expandafter\XINT_sgn\romannumeral0\xintraw {#1}\Z }%
\def\xintFloat   {\romannumeral0\xintfloat }%
\def\xintfloat #1{\XINT_float_chkopt #1\xint_relax }%
\def\XINT_float_chkopt #1%
{%
    \ifx [#1\expandafter\XINT_float_opt
       \else\expandafter\XINT_float_noopt
    \fi  #1%
}%
\def\XINT_float_noopt #1\xint_relax
{%
    \expandafter\XINT_float_a\expandafter\XINTdigits\expandafter.%
    \romannumeral0\XINT_infrac {#1}\XINT_float_Q
}%
\def\XINT_float_opt [\xint_relax #1]#2%
{%
    \expandafter\XINT_float_a\the\numexpr #1\expandafter.%
    \romannumeral0\XINT_infrac {#2}\XINT_float_Q
}%
\def\XINT_float_a #1.#2#3#4%
{%
    \if\romannumeral0\XINT_isone#4XY1\expandafter\XINT_float_sp
    \else\expandafter\XINT_float_fork\fi #3.{#1}{#2}{#4}%
}%
\def\XINT_float_sp #1%
{%
    \xint_UDzerominusfork
     #1-\XINT_float_spzero
     0#1\XINT_float_spneg
      0-{\XINT_float_sppos #1}%
    \krof
}%
\def\XINT_float_spzero .#1#2#3#4{ 0.e0}%
\def\XINT_float_spneg {\expandafter-\romannumeral0\XINT_float_sppos}%
\def\XINT_float_sppos #1.#2#3#4#5%
{%
    \expandafter\XINT_float_sp_b\the\numexpr#2-\xintLength{#1}.#1.#2.#3.%
}%
\def\XINT_float_sp_b #1%
{%
    \xint_UDzerominusfork
     #1-\XINT_float_sp_quick
     0#1\XINT_float_sp_c
      0-{\XINT_float_sp_addzeros #1}%
    \krof
}%
\def\XINT_float_sp_quick .#1.#2.#3.%
{%
    \expandafter\XINT_float_sp_done\the\numexpr #3+#2-\xint_c_i.#1;%
}%
\def\XINT_float_sp_addzeros #1.#2.#3.#4.%
{%
    \expandafter\XINT_float_sp_done
    \the\numexpr #4-#1+#3-\xint_c_i\expandafter.%
    \romannumeral0\XINT_dsx_addzerosnofuss {#1}{#2};%
}%
\def\XINT_float_sp_done #1.#2#3;{ #2.#3e#1}%
\def\XINT_float_sp_c #1.#2%
{%
    \if #29\xint_dothis {\XINT_float_sp_d\XINT_float_Wb }\fi
           \xint_orthat {\XINT_float_sp_d\XINT_float_sp_Wa }#1.#2%
}%
\def\XINT_float_sp_d #1#2.#3.#4.#5.%
{%
    \expandafter\XINT_float_sp_e
    \the\numexpr #5+#2+#4-\xint_c_i\expandafter.%
    \romannumeral0\expandafter\XINT_split_fromleft_loop
       \the\numexpr #4+\xint_c_i.{}#3\W\W\W\W\W\W\W\W\Z #1%
}%
\def\XINT_float_sp_e #1.#2.#3.%
{%
    \expandafter\XINT_float_sp_f
    \romannumeral0\XINT_rord_main {}#2%
      \xint_relax
        \xint_bye\xint_bye\xint_bye\xint_bye
        \xint_bye\xint_bye\xint_bye\xint_bye
      \xint_relax ;#1.%
}%
\def\XINT_float_sp_f #1%
{%
    \ifnum #1<\xint_c_v
    \expandafter\XINT_float_sp_ga\else\expandafter\XINT_float_sp_h\fi
}%
\def\XINT_float_sp_ga #1;#2.#3%
{%
    \expandafter\XINT_float_sp_Wa
    \romannumeral0\XINT_rord_main {}#1%
      \xint_relax
        \xint_bye\xint_bye\xint_bye\xint_bye
        \xint_bye\xint_bye\xint_bye\xint_bye
      \xint_relax e#2%
}%
\def\XINT_float_sp_h  #1;#2.#3%
{%
    \expandafter#3%
    \romannumeral0\XINT_addm_A 0{}1000\W\X\Y\Z #1000\W\X\Y\Z e#2%
}%
\def\XINT_float_sp_Wa #1{ #1.}%
\def\XINT_float_fork #1%
{%
    \xint_UDsignfork
     #1\XINT_float_J
     -{\XINT_float_K #1}%
    \krof
}%
\def\XINT_float_J {\expandafter-\romannumeral0\XINT_float_K }%
\def\XINT_float_K #1.#2%
{%
    \expandafter\XINT_float_L
    \the\numexpr\xintLength{#1}\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_Mb
    \fi #1.#2.%
}%
\def\XINT_float_Ma #1.#2.#3%
{%
    \expandafter\XINT_float_MatoN
    \the\numexpr #1-#2\expandafter.%
    \romannumeral0\XINT_split_fromleft_loop #2.{}#3\W\W\W\W\W\W\W\W\Z
    {#2}%
}%
\def\XINT_float_MatoN #1.#2.#3.#4#5#6#7%
{%
   \expandafter\XINT_float_N
   \the\numexpr\xintLength{#7}\expandafter.\the\numexpr #1+#6.#4.%
   {#7}{#4}{#2}{#5}%
}%
\def\XINT_float_Mb #1.#2.#3#4#5#6%
{%
   \expandafter\XINT_float_N
   \romannumeral0\xintlength{#6}.#5.#2.{#6}{#1}{#3}{#4}%
}%
\def\XINT_float_N #1.#2.#3.%
{%
    \ifnum #1>#3
         \expandafter\XINT_float_N_Blong
    \else\expandafter\XINT_float_P\fi
    #1.#2.#3.%
}%
\def\XINT_float_N_Blong #1.#2.#3.#4%
{%
    \expandafter\XINT_float_NaP
    \the\numexpr #2-#1+#3\expandafter.%
    \romannumeral0\XINT_split_fromleft_loop #3.{}#4\W\W\W\W\W\W\W\W\Z {#3}%
}%
\def\XINT_float_NaP #1.#2.#3.#4{\XINT_float_P #4.#1.#4.{#2}}%
\def\XINT_float_P #1.#2.#3.#4#5#6#7#8%
{%
    \expandafter #8\the\numexpr #1-#5+#3-\xint_c_i.{#6}{#4}{#7}{#2}%
}%
\def\XINT_float_Q #1.#2#3%
{%
    \expandafter\XINT_float_Sa
    \romannumeral0\xintiiquo{\XINT_dsx_addzerosnofuss {#1}{#2}}{#3}\Z {#1}%
}%
\def\XINT_float_Sa #1%
{%
    \if #19\xint_dothis {\XINT_float_Sb\XINT_float_Wb }\fi
           \xint_orthat {\XINT_float_Sb\XINT_float_Wa }#1%
}%
\def\XINT_float_Sb #1#2\Z #3#4%
{%
    \expandafter\XINT_float_T
    \the\numexpr #4+\xint_c_i\expandafter.%
    \romannumeral`&&@\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_dothis{\XINT_float_U\XINT_float_Xb}\fi
                 \xint_orthat{\XINT_float_U\XINT_float_Xa #3}%
}%
\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_bye\xint_bye\xint_bye\xint_bye
        \xint_bye\xint_bye\xint_bye\xint_bye
      \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_dothis{ 10.}\fi\xint_orthat{ #1.#2}}%
\def\XINT_float_Xa #1\Z #2#3#4%
{%
    \expandafter\XINT_float_Y\the\numexpr #3+#4-#2.{#1}%
}%
\def\XINT_float_Xb #1\Z #2#3#4%
{%
    \expandafter\XINT_float_Y\the\numexpr #3+#4+\xint_c_i-#2.{#1}%
}%
\def\XINT_float_Y #1.#2{ #2e#1}%
\def\XINTinFloat {\romannumeral0\XINTinfloat }%
\def\XINTinfloat
   {\expandafter\XINT_infloat_clean\romannumeral0\XINT_infloat}%
\def\XINT_infloat_clean #1%
   {\if #1!\xint_dothis\XINT_infloat_clean_a\fi\xint_orthat{ }#1}%
\def\XINT_infloat_clean_a !#1.#2[#3]%
{%
    \expandafter\XINT_infloat_sp_done
    \the\numexpr #3-#1\expandafter.%
    \romannumeral0\XINT_dsx_addzerosnofuss {#1}{#2};%
}%
\def\XINT_infloat_sp_done #1.#2;{ #2[#1]}%
\def\XINTinFloatS {\romannumeral0\XINTinfloatS}%
\def\XINTinfloatS
   {\expandafter\XINT_infloatS_clean\romannumeral0\XINT_infloat}%
\def\XINT_infloatS_clean #1%
   {\if #1!\xint_dothis\XINT_infloatS_clean_a\fi\xint_orthat{ }#1}%
\def\XINT_infloatS_clean_a !#1.{ }%
\def\XINT_infloat [#1]#2%
{%
    \expandafter\XINT_infloat_a\the\numexpr #1\expandafter.%
    \romannumeral0\XINT_infrac {#2}\XINT_infloat_Q
}%
\def\XINT_infloat_a #1.#2#3#4%
{%
    \if\romannumeral0\XINT_isone#4XY1\expandafter\XINT_infloat_sp
    \else\expandafter\XINT_float_fork\fi #3.{#1}{#2}{#4}%
}%
\def\XINT_infloat_sp #1%
{%
    \xint_UDzerominusfork
     #1-\XINT_infloat_spzero
     0#1\XINT_infloat_spneg
      0-{\XINT_infloat_sppos #1}%
    \krof
}%
\def\XINT_infloat_spzero .#1#2#3#4{ 0[0]}%
\def\XINT_infloat_spneg
    {\expandafter\XINT_infloat_spnegend\romannumeral0\XINT_infloat_sppos}%
\def\XINT_infloat_spnegend #1%
    {\if#1!\expandafter\XINT_infloat_spneg_needzeros\fi -#1}%
\def\XINT_infloat_spneg_needzeros -!#1.{!#1.-}%
\def\XINT_infloat_sppos #1.#2#3#4#5%
{%
    \expandafter\XINT_infloat_sp_b\the\numexpr#2-\xintLength{#1}.#1.#2.#3.%
}%
\def\XINT_infloat_sp_b #1%
{%
    \xint_UDzerominusfork
     #1-\XINT_infloat_sp_quick
     0#1\XINT_infloat_sp_c
      0-{\XINT_infloat_sp_needzeros #1}%
    \krof
}%
\def\XINT_infloat_sp_quick .#1.#2.#3.{ #1[#3]}%
\def\XINT_infloat_sp_needzeros #1.#2.#3.#4.{!#1.#2[#4]}%
\def\XINT_infloat_sp_c #1.#2%
{%
    \if #29\xint_dothis {\XINT_infloat_sp_d\XINT_infloat_Wb }\fi
           \xint_orthat {\XINT_infloat_sp_d\xint_c_ }#1.#2%
}%
\def\XINT_infloat_sp_d #1#2.#3.#4.%#5.%
{%
    \expandafter\XINT_infloat_sp_e
    \romannumeral0\expandafter\XINT_split_fromleft_loop
       \the\numexpr #4+\xint_c_i.{}#3\W\W\W\W\W\W\W\W\Z #1#2.%
}%
\def\XINT_infloat_sp_e #1.#2.%
{%
    \expandafter\XINT_infloat_sp_f
    \romannumeral0\XINT_rord_main {}#1%
      \xint_relax
        \xint_bye\xint_bye\xint_bye\xint_bye
        \xint_bye\xint_bye\xint_bye\xint_bye
      \xint_relax ;%
}%
\def\XINT_infloat_sp_f #1%
{%
    \ifnum #1<\xint_c_v
    \expandafter\XINT_infloat_sp_ga\else\expandafter\XINT_infloat_sp_h\fi
}%
\def\XINT_infloat_sp_ga #1;#2#3.#4.%
{%
    \expandafter\XINT_infloat_sp_done\the\numexpr #3+#4\expandafter.%
    \romannumeral0\XINT_rord_main {}#1%
      \xint_relax
        \xint_bye\xint_bye\xint_bye\xint_bye
        \xint_bye\xint_bye\xint_bye\xint_bye
      \xint_relax ;%
}%
\def\XINT_infloat_sp_h  #1;#2%
{%
    \expandafter\XINT_infloat_sp_i
    \romannumeral0\expandafter#2%
    \romannumeral0\XINT_addm_A 0{}1000\W\X\Y\Z #1000\W\X\Y\Z;%
}%
\def\XINT_infloat_sp_i #1#2;#3.#4.%
{%
    \expandafter\XINT_infloat_sp_done\the\numexpr #1+#3+#4.#2;%
}%
\def\XINT_infloat_Q #1.#2#3%
{%
    \expandafter\XINT_infloat_Sa
    \romannumeral0\xintiiquo{\XINT_dsx_addzerosnofuss {#1}{#2}}{#3}\Z {#1}%
}%
\def\XINT_infloat_Sa #1%
{%
    \if #19\xint_dothis {\XINT_infloat_Sb\XINT_infloat_Wb }\fi
           \xint_orthat {\XINT_infloat_Sb\xint_c_ }#1%
}%
\def\XINT_infloat_Sb #1#2\Z #3#4%
{%
    \expandafter\XINT_infloat_T
    \the\numexpr #4+\xint_c_i\expandafter.%
    \romannumeral`&&@\XINT_lenrord_loop 0.{}#2\Z\W\W\W\W\W\W\W\Z #1{#3}%
}%
\def\XINT_infloat_T #1.#2.#3%
{%
    \ifnum #2>#1 \xint_dothis{\XINT_infloat_U\XINT_infloat_Xb}\fi
                 \xint_orthat{\XINT_infloat_U\XINT_infloat_Xa #3}%
}%
\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 #3%
{%
    \expandafter#1%
    \romannumeral0\expandafter\xint_c_
    \romannumeral0\XINT_rord_main {}#2%
      \xint_relax
        \xint_bye\xint_bye\xint_bye\xint_bye
        \xint_bye\xint_bye\xint_bye\xint_bye
      \xint_relax \Z
}%
\def\XINT_infloat_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_infloat_Wb #1#2%
    {\if #11\xint_dothis{\xint_c_i1}\fi\xint_orthat{\xint_c_#1#2}}%
\def\XINT_infloat_Xa #1#2\Z #3#4%
{%
    \expandafter\XINT_infloat_Y\the\numexpr #1+\xint_c_i+#4-#3.{#2}%
}%
\def\XINT_infloat_Xb #1#2\Z #3#4%
{%
    \expandafter\XINT_infloat_Y\the\numexpr #1+\xint_c_ii+#4-#3.{#2}%
}%
\def\XINT_infloat_Y #1.#2{ #2[#1]}%
\def\xintPFloat   {\romannumeral0\xintpfloat }%
\def\xintpfloat #1{\XINT_pfloat_chkopt #1\xint_relax }%
\def\XINT_pfloat_chkopt #1%
{%
    \ifx [#1\expandafter\XINT_pfloat_opt
       \else\expandafter\XINT_pfloat_noopt
    \fi  #1%
}%
\def\XINT_pfloat_noopt #1\xint_relax
{%
    \expandafter\XINT_pfloat_a
    \romannumeral0\xintfloat [\XINTdigits]{#1};\XINTdigits.%
}%
\def\XINT_pfloat_opt [\xint_relax #1]%#2%
{%
    \expandafter\XINT_pfloat_opt_a \the\numexpr #1.%
}%
\def\XINT_pfloat_opt_a #1.#2%
{%
    \expandafter\XINT_pfloat_a\romannumeral0\xintfloat [#1]{#2};#1.%
}%
\def\XINT_pfloat_a #1%
{%
    \xint_UDzerominusfork
        #1-\XINT_pfloat_zero
        0#1\XINT_pfloat_neg
        0-{\XINT_pfloat_pos #1}%
    \krof
}%
\def\XINT_pfloat_zero #1;#2.{ 0.}%
\def\XINT_pfloat_neg {\expandafter-\romannumeral0\XINT_pfloat_pos }%
\def\XINT_pfloat_pos #1e#2;#3.%
{%
    \ifnum #2>\xint_c_v  \xint_dothis\XINT_pfloat_no\fi
    \ifnum #2<-\xint_c_v \xint_dothis\XINT_pfloat_no\fi
    \ifnum #2<\xint_c_   \xint_dothis\XINT_pfloat_N\fi
    \ifnum #2>\numexpr #3-\xint_c_i\relax \xint_dothis\XINT_pfloat_Ps\fi
    \xint_orthat\XINT_pfloat_P #1e#2;%
}%
\def\XINT_pfloat_no #1;{ #1}%
\def\XINT_pfloat_N #1#2.#3e#4;%
{%
    \csname XINT_pfloat_N\romannumeral-#4\endcsname #2#10.#3;%
}%
\def\XINT_pfloat_Ni  #1#2#3.#4;{ #2.#1#4}%
\def\XINT_pfloat_Nii #1#2#3.#4;{ 0.#2#1#4}%
\def\XINT_pfloat_Niii#1#2#3.#4;{ 0.0#2#1#4}%
\def\XINT_pfloat_Niv #1#2#3.#4;{ 0.00#2#1#4}%
\def\XINT_pfloat_Nv  #1#2#3.#4;{ 0.000#2#1#4}%
\def\XINT_pfloat_P #1#2.#3e#4;%
{%
    \csname XINT_pfloat_P_\romannumeral#4\endcsname #3.#1#2;%
}%
\def\XINT_pfloat_P_   #1.#2;{ #2.#1}%
\def\XINT_pfloat_P_i  #1#2.#3;{ #3#1.#2}%
\def\XINT_pfloat_P_ii #1#2#3.#4;{ #4#1#2.#3}%
\def\XINT_pfloat_P_iii#1#2#3#4.#5;{ #5#1#2#3.#4}%
\def\XINT_pfloat_P_iv #1#2#3#4#5.#6;{ #6#1#2#3#4.#5}%
\def\XINT_pfloat_P_v  #1#2#3#4#5#6.#7;{ #7#1#2#3#4#5.#6}%
\def\XINT_pfloat_Ps #1#2.#3e#4;%
{%
    \csname XINT_pfloat_Ps\romannumeral#4\endcsname #300000.#1#2;%
}%
\def\XINT_pfloat_Psi  #1#2.#3;{ #3#1.}%
\def\XINT_pfloat_Psii #1#2#3.#4;{ #4#1#2.}%
\def\XINT_pfloat_Psiii#1#2#3#4.#5;{ #5#1#2#3.}%
\def\XINT_pfloat_Psiv #1#2#3#4#5.#6;{ #6#1#2#3#4.}%
\def\XINT_pfloat_Psv  #1#2#3#4#5#6.#7;{ #7#1#2#3#4#5.}%
\def\XINTinFloatFracdigits {\romannumeral0\XINTinfloatfracdigits }%
\def\XINTinfloatfracdigits #1%
{%
    \expandafter\XINT_infloatfracdg_a\expandafter {\romannumeral0\xinttfrac{#1}}%
}%
\def\XINT_infloatfracdg_a {\XINTinfloat [\XINTdigits]}%
\def\xintFloatAdd      {\romannumeral0\xintfloatadd }%
\def\xintfloatadd    #1{\XINT_fladd_chkopt \xintfloat #1\xint_relax }%
\def\XINTinFloatAdd    {\romannumeral0\XINTinfloatadd }%
\def\XINTinfloatadd  #1{\XINT_fladd_chkopt \XINTinfloatS #1\xint_relax }%
\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\xint_relax #3%
{%
    #1[\XINTdigits]%
    {\expandafter\XINT_FL_add_a
     \romannumeral0\XINTinfloat[\XINTdigits]{#2}\XINTdigits.{#3}}%
}%
\def\XINT_fladd_opt #1[\xint_relax #2]%#3#4%
{%
    \expandafter\XINT_fladd_opt_a\the\numexpr #2.#1%
}%
\def\XINT_fladd_opt_a #1.#2#3#4%
{%
    #2[#1]{\expandafter\XINT_FL_add_a\romannumeral0\XINTinfloat[#1]{#3}#1.{#4}}%
}%
\def\XINT_FL_add_a #1%
{%
    \xint_gob_til_zero #1\XINT_FL_add_zero 0\XINT_FL_add_b #1%
}%
\def\XINT_FL_add_zero #1.#2{#2}%
\def\XINT_FL_add_b #1]#2.#3%
{%
    \expandafter\XINT_FL_add_c\romannumeral0\XINTinfloat[#2]{#3}#2.#1]%
}%
\def\XINT_FL_add_c #1%
{%
    \xint_gob_til_zero #1\XINT_FL_add_zero 0\XINT_FL_add_d #1%
}%
\def\XINT_FL_add_d #1[#2]#3.#4[#5]%
{%
    \ifnum\numexpr #2-#3-#5>\xint_c_\xint_dothis\xint_firstoftwo\fi
    \ifnum\numexpr #5-#3-#2>\xint_c_\xint_dothis\xint_secondoftwo\fi
    \xint_orthat\xintAdd {#1[#2]}{#4[#5]}%
}%
\def\xintFloatSub      {\romannumeral0\xintfloatsub }%
\def\xintfloatsub    #1{\XINT_flsub_chkopt \xintfloat #1\xint_relax }%
\def\XINTinFloatSub    {\romannumeral0\XINTinfloatsub }%
\def\XINTinfloatsub  #1{\XINT_flsub_chkopt \XINTinfloatS #1\xint_relax }%
\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\xint_relax #3%
{%
    #1[\XINTdigits]%
    {\expandafter\XINT_FL_add_a
     \romannumeral0\XINTinfloat[\XINTdigits]{#2}\XINTdigits.{\xintOpp{#3}}}%
}%
\def\XINT_flsub_opt #1[\xint_relax #2]%#3#4%
{%
    \expandafter\XINT_flsub_opt_a\the\numexpr #2.#1%
}%
\def\XINT_flsub_opt_a #1.#2#3#4%
{%
    #2[#1]{\expandafter\XINT_FL_add_a\romannumeral0\XINTinfloat[#1]{#3}#1.{\xintOpp{#4}}}%
}%
\def\xintFloatMul   {\romannumeral0\xintfloatmul   }%
\def\xintfloatmul   #1{\XINT_flmul_chkopt \xintfloat #1\xint_relax }%
\def\XINTinFloatMul {\romannumeral0\XINTinfloatmul }%
\def\XINTinfloatmul #1{\XINT_flmul_chkopt \XINTinfloatS #1\xint_relax }%
\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\xint_relax #3%
{%
    #1[\XINTdigits]%
    {\expandafter\XINT_FL_mul_a
     \romannumeral0\XINTinfloatS[\XINTdigits]{#2}\XINTdigits.{#3}}%
}%
\def\XINT_flmul_opt #1[\xint_relax #2]%#3#4%
{%
    \expandafter\XINT_flmul_opt_a\the\numexpr #2.#1%
}%
\def\XINT_flmul_opt_a #1.#2#3#4%
{%
    #2[#1]{\expandafter\XINT_FL_mul_a\romannumeral0\XINTinfloatS[#1]{#3}#1.{#4}}%
}%
\def\XINT_FL_mul_a #1[#2]#3.#4%
{%
    \expandafter\XINT_FL_mul_b\romannumeral0\XINTinfloatS[#3]{#4}#1[#2]%
}%
\def\XINT_FL_mul_b #1[#2]#3[#4]{\xintE{\xintiiMul {#3}{#1}}{#4+#2}}%
\def\xintFloatDiv   {\romannumeral0\xintfloatdiv   }%
\def\xintfloatdiv   #1{\XINT_fldiv_chkopt \xintfloat #1\xint_relax }%
\def\XINTinFloatDiv {\romannumeral0\XINTinfloatdiv }%
\def\XINTinfloatdiv #1{\XINT_fldiv_chkopt \XINTinfloatS #1\xint_relax }%
\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\xint_relax #3%
{%
    #1[\XINTdigits]%
    {\expandafter\XINT_FL_div_a
     \romannumeral0\XINTinfloatS[\XINTdigits]{#2}\XINTdigits.{#3}}%
}%
\def\XINT_fldiv_opt #1[\xint_relax #2]%#3#4%
{%
    \expandafter\XINT_fldiv_opt_a\the\numexpr #2.#1%
}%
\def\XINT_fldiv_opt_a #1.#2#3#4%
{%
    #2[#1]{\expandafter\XINT_FL_div_a\romannumeral0\XINTinfloatS[#1]{#3}#1.{#4}}%
}%
\def\XINT_FL_div_a #1[#2]#3.#4%
{%
    \expandafter\XINT_FL_div_b\romannumeral0\XINTinfloatS[#3]{#4}#1[#2]%
}%
\def\XINT_FL_div_b #1[#2]#3[#4]{\xintE{#3/#1}{#4-#2}}%
\def\xintFloatPow   {\romannumeral0\xintfloatpow}%
\def\xintfloatpow #1{\XINT_flpow_chkopt \xintfloat #1\xint_relax }%
\def\XINTinFloatPow {\romannumeral0\XINTinfloatpow }%
\def\XINTinfloatpow #1{\XINT_flpow_chkopt \XINTinfloatS #1\xint_relax }%
\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\xint_relax #3%
{%
   \expandafter\XINT_flpow_checkB_a
   \the\numexpr #3.\XINTdigits.{#2}{#1[\XINTdigits]}%
}%
\def\XINT_flpow_opt #1[\xint_relax #2]%
{%
   \expandafter\XINT_flpow_opt_a\the\numexpr #2.#1%
}%
\def\XINT_flpow_opt_a #1.#2#3#4%
{%
   \expandafter\XINT_flpow_checkB_a\the\numexpr #4.#1.{#3}{#2[#1]}%
}%
\def\XINT_flpow_checkB_a #1%
{%
    \xint_UDzerominusfork
      #1-\XINT_flpow_BisZero
      0#1{\XINT_flpow_checkB_b -}%
       0-{\XINT_flpow_checkB_b {}#1}%
    \krof
}%
\def\XINT_flpow_BisZero .#1.#2#3{#3{1[0]}}%
\def\XINT_flpow_checkB_b #1#2.#3.%
{%
    \expandafter\XINT_flpow_checkB_c
    \the\numexpr\xintLength{#2}+\xint_c_iii.#3.#2.{#1}%
}%
\def\XINT_flpow_checkB_c #1.#2.%
{%
    \expandafter\XINT_flpow_checkB_d\the\numexpr#1+#2.#1.#2.%
}%
\def\XINT_flpow_checkB_d #1.#2.#3.#4.#5#6%
{%
    \expandafter \XINT_flpow_aa
    \romannumeral0\XINTinfloat [#3]{#6}{#2}{#1}{#4}{#5}%
}%
\def\XINT_flpow_aa #1[#2]#3%
{%
    \expandafter\XINT_flpow_ab\the\numexpr #2-#3\expandafter.%
    \romannumeral0\XINT_dsx_addzerosnofuss {#3}{}.#1.%
}%
\def\XINT_flpow_ab #1.#2.#3.{\XINT_flpow_a #3#2[#1]}%
\def\XINT_flpow_a #1%
{%
    \xint_UDzerominusfork
      #1-\XINT_flpow_zero
      0#1{\XINT_flpow_b \iftrue}%
       0-{\XINT_flpow_b \iffalse#1}%
    \krof
}%
\def\XINT_flpow_zero #1[#2]#3#4#5#6%
{%
    \if 1#51\xint_afterfi {#6{0[0]}}\else
    \xint_afterfi {\xintError:DivisionByZero #6{1[2147483648]}}\fi
}%
\def\XINT_flpow_b #1#2[#3]#4#5%
{%
    \XINT_flpow_loopI #5.#3.#2.#4.{#1\ifodd #5 \xint_c_i\fi\fi}%
}%
\def\XINT_flpow_truncate #1.#2.#3.%
{%
    \expandafter\XINT_flpow_truncate_a
    \romannumeral0\XINT_split_fromleft_loop #3.{}#2\W\W\W\W\W\W\W\W\Z
    #1.#3.%
}%
\def\XINT_flpow_truncate_a #1.#2.#3.{#3+\xintLength{#2}.#1.}%
\def\XINT_flpow_loopI #1.%
{%
    \ifnum #1=\xint_c_i\expandafter\XINT_flpow_ItoIII\fi
    \ifodd #1
       \expandafter\XINT_flpow_loopI_odd
    \else
       \expandafter\XINT_flpow_loopI_even
    \fi
    #1.%
}%
\def\XINT_flpow_ItoIII\ifodd #1\fi #2.#3.#4.#5.#6%
{%
    \expandafter\XINT_flpow_III\the\numexpr #6+\xint_c_.#3.#4.#5.%
}%
\def\XINT_flpow_loopI_even #1.#2.#3.%#4.%
{%
    \expandafter\XINT_flpow_loopI
    \the\numexpr #1/\xint_c_ii\expandafter.%
    \the\numexpr\expandafter\XINT_flpow_truncate
    \the\numexpr\xint_c_ii*#2\expandafter.\romannumeral0\xintiisqr{#3}.%
}%
\def\XINT_flpow_loopI_odd #1.#2.#3.#4.%
{%
    \expandafter\XINT_flpow_loopII
    \the\numexpr #1/\xint_c_ii-\xint_c_i\expandafter.%
    \the\numexpr\expandafter\XINT_flpow_truncate
    \the\numexpr\xint_c_ii*#2\expandafter.\romannumeral0\xintiisqr{#3}.#4.#2.#3.%
}%
\def\XINT_flpow_loopII #1.%
{%
    \ifnum #1 = \xint_c_i\expandafter\XINT_flpow_IItoIII\fi
    \ifodd #1
       \expandafter\XINT_flpow_loopII_odd
    \else
       \expandafter\XINT_flpow_loopII_even
    \fi
    #1.%
}%
\def\XINT_flpow_loopII_even #1.#2.#3.%#4.%
{%
    \expandafter\XINT_flpow_loopII
    \the\numexpr #1/\xint_c_ii\expandafter.%
    \the\numexpr\expandafter\XINT_flpow_truncate
    \the\numexpr\xint_c_ii*#2\expandafter.\romannumeral0\xintiisqr{#3}.%
}%
\def\XINT_flpow_loopII_odd #1.#2.#3.#4.#5.#6.%
{%
    \expandafter\XINT_flpow_loopII_odda
    \the\numexpr\expandafter\XINT_flpow_truncate
    \the\numexpr#2+#5\expandafter.\romannumeral0\xintiimul{#3}{#6}.#4.%
    #1.#2.#3.%
}%
\def\XINT_flpow_loopII_odda #1.#2.#3.#4.#5.#6.%
{%
    \expandafter\XINT_flpow_loopII
    \the\numexpr #4/\xint_c_ii-\xint_c_i\expandafter.%
    \the\numexpr\expandafter\XINT_flpow_truncate
    \the\numexpr\xint_c_ii*#5\expandafter.\romannumeral0\xintiisqr{#6}.#3.%
    #1.#2.%
}%
\def\XINT_flpow_IItoIII\ifodd #1\fi #2.#3.#4.#5.#6.#7.#8%
{%
    \expandafter\XINT_flpow_III\the\numexpr #8+\xint_c_\expandafter.%
    \the\numexpr\expandafter\XINT_flpow_truncate
    \the\numexpr#3+#6\expandafter.\romannumeral0\xintiimul{#4}{#7}.#5.%
}%
\def\XINT_flpow_III #1.#2.#3.#4.#5%
{%
    \expandafter\XINT_flpow_IIIend
    \xint_UDsignfork
        #5{{\xintNum{1/#3[\xint_c_ii*#4-\xint_c_i]}[\xint_c_i-\xint_c_ii*#4-#2]}}%
         -{{#3[#2]}}%
    \krof #1%
}%
\def\XINT_flpow_IIIend #1#2#3%
    {#3{\if#21\xint_afterfi{\expandafter-\romannumeral`&&@}\fi#1}}%
\def\xintFloatPower   {\romannumeral0\xintfloatpower}%
\def\xintfloatpower #1{\XINT_flpower_chkopt \xintfloat #1\xint_relax }%
\def\XINTinFloatPower {\romannumeral0\XINTinfloatpower }%
\def\XINTinfloatpower #1{\XINT_flpower_chkopt \XINTinfloatS #1\xint_relax }%
\def\XINTinFloatPowerH {\romannumeral0\XINTinfloatpowerH }%
\def\XINTinfloatpowerH #1#2%
   {\expandafter\XINT_flpowerh_a \romannumeral0\xinttrunc 1{#2}.0;%
    \XINTdigits.{#1}{\XINTinfloatS[\XINTdigits]}}%
\def\XINT_flpowerh_a #1.#2%
{%
    \ifnum#2>\xint_c_iv\xint_dothis\XINT_flpowerh_b\fi
    \xint_orthat\XINT_flpowerh_i #1.#2%
}%
\def\XINT_flpowerh_i #1.#2;%
   {\expandafter\XINT_flpower_checkB_a\romannumeral0\xintinum{#1}.}%
\def\XINT_flpowerh_b #1%
{%
    \if#1-\xint_dothis\XINT_flpowerh_bneg\fi
          \xint_orthat{\XINT_flpowerh_bpos #1}%
}%
\def\XINT_flpowerh_bpos #1.#2;\XINTdigits.#3#4%
{%
    \expandafter\XINT_flpower_checkB_a
    \romannumeral0\xintinc{\xintDouble{#1}}.%
    \XINTdigits.{#3}{\XINTinfloatsqrt[\XINTdigits]}%
}%
\def\XINT_flpowerh_bneg #1.#2;\XINTdigits.#3#4%
{%
    \expandafter\XINT_flpower_checkB_a
    \expandafter-\romannumeral0\xintinc{\xintDouble{#1}}.%
    \XINTdigits.{#3}{\XINTinfloatsqrt[\XINTdigits]}%
}%
\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\xint_relax #3%
{%
   \expandafter\XINT_flpower_checkB_a
   \romannumeral0\xintnum{#3}.\XINTdigits.{#2}{#1[\XINTdigits]}%
}%
\def\XINT_flpower_opt #1[\xint_relax #2]%
{%
   \expandafter\XINT_flpower_opt_a\the\numexpr #2.#1%
}%
\def\XINT_flpower_opt_a #1.#2#3#4%
{%
   \expandafter\XINT_flpower_checkB_a
   \romannumeral0\xintnum{#4}.#1.{#3}{#2[#1]}%
}%
\def\XINT_flpower_checkB_a #1%
{%
    \xint_UDzerominusfork
      #1-\XINT_flpower_BisZero
      0#1{\XINT_flpower_checkB_b -}%
       0-{\XINT_flpower_checkB_b {}#1}%
    \krof
}%
\def\XINT_flpower_BisZero .#1.#2#3{#3{1[0]}}%
\def\XINT_flpower_checkB_b #1#2.#3.%
{%
    \expandafter\XINT_flpower_checkB_c
    \the\numexpr\xintLength{#2}+\xint_c_iii.#3.#2.{#1}%
}%
\def\XINT_flpower_checkB_c #1.#2.%
{%
    \expandafter\XINT_flpower_checkB_d\the\numexpr#1+#2.#1.#2.%
}%
\def\XINT_flpower_checkB_d #1.#2.#3.#4.#5#6%
{%
    \expandafter \XINT_flpower_aa
    \romannumeral0\XINTinfloat [#3]{#6}{#2}{#1}{#4}{#5}%
}%
\def\XINT_flpower_aa #1[#2]#3%
{%
    \expandafter\XINT_flpower_ab\the\numexpr #2-#3\expandafter.%
    \romannumeral0\XINT_dsx_addzerosnofuss {#3}{}.#1.%
}%
\def\XINT_flpower_ab #1.#2.#3.{\XINT_flpower_a #3#2[#1]}%
\def\XINT_flpower_a #1%
{%
    \xint_UDzerominusfork
      #1-\XINT_flpow_zero
      0#1{\XINT_flpower_b \iftrue}%
       0-{\XINT_flpower_b \iffalse#1}%
    \krof
}%
\def\XINT_flpower_b #1#2[#3]#4#5%
{%
    \XINT_flpower_loopI #5.#3.#2.#4.{#1\xintiiOdd{#5}\fi}%
}%
\def\XINT_flpower_loopI #1.%
{%
    \if1\XINT_isOne {#1}\xint_dothis\XINT_flpower_ItoIII\fi
    \if1\xintiiOdd {#1}\xint_dothis{\expandafter\XINT_flpower_loopI_odd}\fi
                       \xint_orthat{\expandafter\XINT_flpower_loopI_even}%
    \romannumeral0\xinthalf{#1}.%
}%
\def\XINT_flpower_ItoIII #1.#2.#3.#4.#5%
{%
    \expandafter\XINT_flpow_III\the\numexpr #5+\xint_c_.#2.#3.#4.%
}%
\def\XINT_flpower_loopI_even #1.#2.#3.#4.%
{%
    \expandafter\XINT_flpower_toloopI
    \the\numexpr\expandafter\XINT_flpow_truncate
    \the\numexpr\xint_c_ii*#2\expandafter.\romannumeral0\xintiisqr{#3}.#4.#1.%
}%
\def\XINT_flpower_toloopI #1.#2.#3.#4.{\XINT_flpower_loopI #4.#1.#2.#3.}%
\def\XINT_flpower_loopI_odd #1.#2.#3.#4.%
{%
    \expandafter\XINT_flpower_toloopII
    \the\numexpr\expandafter\XINT_flpow_truncate
    \the\numexpr\xint_c_ii*#2\expandafter.\romannumeral0\xintiisqr{#3}.#4.%
    #1.#2.#3.%
}%
\def\XINT_flpower_toloopII #1.#2.#3.#4.{\XINT_flpower_loopII #4.#1.#2.#3.}%
\def\XINT_flpower_loopII #1.%
{%
    \if1\XINT_isOne{#1}\xint_dothis\XINT_flpower_IItoIII\fi
    \if1\xintiiOdd{#1}\xint_dothis{\expandafter\XINT_flpower_loopII_odd}\fi
                      \xint_orthat{\expandafter\XINT_flpower_loopII_even}%
    \romannumeral0\xinthalf{#1}.%
}%
\def\XINT_flpower_loopII_even #1.#2.#3.#4.%
{%
    \expandafter\XINT_flpower_toloopII
    \the\numexpr\expandafter\XINT_flpow_truncate
    \the\numexpr\xint_c_ii*#2\expandafter.\romannumeral0\xintiisqr{#3}.#4.#1.%
}%
\def\XINT_flpower_loopII_odd #1.#2.#3.#4.#5.#6.%
{%
    \expandafter\XINT_flpower_loopII_odda
    \the\numexpr\expandafter\XINT_flpow_truncate
    \the\numexpr#2+#5\expandafter.\romannumeral0\xintiimul{#3}{#6}.#4.%
    #1.#2.#3.%
}%
\def\XINT_flpower_loopII_odda #1.#2.#3.#4.#5.#6.%
{%
    \expandafter\XINT_flpower_toloopII
    \the\numexpr\expandafter\XINT_flpow_truncate
    \the\numexpr\xint_c_ii*#5\expandafter.\romannumeral0\xintiisqr{#6}.#3.%
    #4.#1.#2.%
}%
\def\XINT_flpower_IItoIII #1.#2.#3.#4.#5.#6.#7%
{%
    \expandafter\XINT_flpow_III\the\numexpr #7+\xint_c_\expandafter.%
    \the\numexpr\expandafter\XINT_flpow_truncate
    \the\numexpr#2+#5\expandafter.\romannumeral0\xintiimul{#3}{#6}.#4.%
}%
\def\xintFloatFac     {\romannumeral0\xintfloatfac}%
\def\xintfloatfac   #1{\XINT_flfac_chkopt \xintfloat #1\xint_relax }%
\def\XINTinFloatFac   {\romannumeral0\XINTinfloatfac }%
\def\XINTinfloatfac #1{\XINT_flfac_chkopt \XINTinfloat #1\xint_relax }%
\def\XINT_flfac_chkopt #1#2%
{%
    \ifx [#2\expandafter\XINT_flfac_opt
       \else\expandafter\XINT_flfac_noopt
    \fi
     #1#2%
}%
\def\XINT_flfac_noopt  #1#2\xint_relax
{%
   \expandafter\XINT_FL_fac_fork_a
   \the\numexpr \xintNum{#2}.\xint_c_i \XINTdigits\XINT_FL_fac_out{#1[\XINTdigits]}%
}%
\def\XINT_flfac_opt #1[\xint_relax #2]%
{%
   \expandafter\XINT_flfac_opt_a\the\numexpr #2.#1%
}%
\def\XINT_flfac_opt_a #1.#2#3%
{%
   \expandafter\XINT_FL_fac_fork_a\the\numexpr \xintNum{#3}.\xint_c_i {#1}\XINT_FL_fac_out{#2[#1]}%
}%
\def\XINT_FL_fac_fork_a #1%
{%
     \xint_UDzerominusfork
     #1-\XINT_FL_fac_iszero
     0#1\XINT_FL_fac_isneg
      0-{\XINT_FL_fac_fork_b #1}%
    \krof
}%
\def\XINT_FL_fac_iszero #1.#2#3#4#5{#5{1[0]}}%
\def\XINT_FL_fac_isneg  #1.#2#3#4#5{\expandafter\xintError:FactorialOfNegative #5{0[0]}}%
\def\XINT_FL_fac_fork_b #1.%
{%
    \ifnum #1>\xint_c_x^viii_mone\xint_dothis\XINT_FL_fac_toobig\fi
    \ifnum #1>\xint_c_x^iv\xint_dothis\XINT_FL_fac_vbig \fi
    \ifnum #1>465  \xint_dothis\XINT_FL_fac_big\fi
    \ifnum #1>101  \xint_dothis\XINT_FL_fac_med\fi
                   \xint_orthat\XINT_FL_fac_small
    #1.%
}%
\def\XINT_FL_fac_toobig #1.#2#3#4#5{\expandafter\xintError:TooBigFactorial #5{1[0]}}%
\def\XINT_FL_fac_vbig
   {\expandafter\XINT_FL_fac_vbigloop_a
    \the\numexpr \XINT_FL_fac_increaseP \xint_c_i   }%
\def\XINT_FL_fac_big
   {\expandafter\XINT_FL_fac_bigloop_a
    \the\numexpr \XINT_FL_fac_increaseP \xint_c_ii  }%
\def\XINT_FL_fac_med
   {\expandafter\XINT_FL_fac_medloop_a
    \the\numexpr \XINT_FL_fac_increaseP \xint_c_iii }%
\def\XINT_FL_fac_small
   {\expandafter\XINT_FL_fac_smallloop_a
    \the\numexpr \XINT_FL_fac_increaseP \xint_c_iv  }%
\def\XINT_FL_fac_increaseP #1#2.#3#4%
{%
    #2\expandafter.\the\numexpr\xint_c_viii*%
    ((\xint_c_iv+#4+\expandafter\XINT_FL_fac_countdigits
                    \the\numexpr #2/(#1*#3)\relax 87654321\Z)/\xint_c_viii).%
}%
\def\XINT_FL_fac_countdigits #1#2#3#4#5#6#7#8{\XINT_FL_fac_countdone }%
\def\XINT_FL_fac_countdone   #1#2\Z {#1}%
\def\XINT_FL_fac_out #1\Z![#2]#3{#3{\romannumeral0\XINT_mul_out
                                 #1\Z!1\R!1\R!1\R!1\R!1\R!1\R!1\R!1\R!\W [#2]}}%
\def\XINT_FL_fac_vbigloop_a #1.#2.%
{%
    \XINT_FL_fac_bigloop_a \xint_c_x^iv.#2.%
    {\expandafter\XINT_FL_fac_vbigloop_loop\the\numexpr 100010001\expandafter.%
     \the\numexpr \xint_c_x^viii+#1.}%
}%
\def\XINT_FL_fac_vbigloop_loop #1.#2.%
{%
    \ifnum #1>#2 \expandafter\XINT_FL_fac_loop_exit\fi
    \expandafter\XINT_FL_fac_vbigloop_loop
    \the\numexpr #1+\xint_c_i\expandafter.%
    \the\numexpr #2\expandafter.\the\numexpr\XINT_FL_fac_mul #1!%
}%
\def\XINT_FL_fac_bigloop_a #1.%
{%
    \expandafter\XINT_FL_fac_bigloop_b \the\numexpr
    #1+\xint_c_i-\xint_c_ii*((#1-464)/\xint_c_ii).#1.%
}%
\def\XINT_FL_fac_bigloop_b #1.#2.#3.%
{%
    \expandafter\XINT_FL_fac_medloop_a
        \the\numexpr #1-\xint_c_i.#3.{\XINT_FL_fac_bigloop_loop #1.#2.}%
}%
\def\XINT_FL_fac_bigloop_loop #1.#2.%
{%
    \ifnum #1>#2 \expandafter\XINT_FL_fac_loop_exit\fi
    \expandafter\XINT_FL_fac_bigloop_loop
    \the\numexpr #1+\xint_c_ii\expandafter.%
    \the\numexpr #2\expandafter.\the\numexpr\XINT_FL_fac_bigloop_mul #1!%
}%
\def\XINT_FL_fac_bigloop_mul #1!%
{%
    \expandafter\XINT_FL_fac_mul
        \the\numexpr \xint_c_x^viii+#1*(#1+\xint_c_i)!%
}%
\def\XINT_FL_fac_medloop_a #1.%
{%
    \expandafter\XINT_FL_fac_medloop_b
        \the\numexpr #1+\xint_c_i-\xint_c_iii*((#1-100)/\xint_c_iii).#1.%
}%
\def\XINT_FL_fac_medloop_b #1.#2.#3.%
{%
    \expandafter\XINT_FL_fac_smallloop_a
        \the\numexpr #1-\xint_c_i.#3.{\XINT_FL_fac_medloop_loop #1.#2.}%
}%
\def\XINT_FL_fac_medloop_loop #1.#2.%
{%
    \ifnum #1>#2 \expandafter\XINT_FL_fac_loop_exit\fi
    \expandafter\XINT_FL_fac_medloop_loop
    \the\numexpr #1+\xint_c_iii\expandafter.%
    \the\numexpr #2\expandafter.\the\numexpr\XINT_FL_fac_medloop_mul #1!%
}%
\def\XINT_FL_fac_medloop_mul #1!%
{%
    \expandafter\XINT_FL_fac_mul
    \the\numexpr
        \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)!%
}%
\def\XINT_FL_fac_smallloop_a #1.%
{%
    \csname
       XINT_FL_fac_smallloop_\the\numexpr #1-\xint_c_iv*(#1/\xint_c_iv)\relax
    \endcsname #1.%
}%
\expandafter\def\csname XINT_FL_fac_smallloop_1\endcsname #1.#2.%
{%
    \XINT_FL_fac_addzeros #2.100000001!.{2.#1.}{#2}%
}%
\expandafter\def\csname XINT_FL_fac_smallloop_-2\endcsname #1.#2.%
{%
    \XINT_FL_fac_addzeros #2.100000002!.{3.#1.}{#2}%
}%
\expandafter\def\csname XINT_FL_fac_smallloop_-1\endcsname #1.#2.%
{%
    \XINT_FL_fac_addzeros #2.100000006!.{4.#1.}{#2}%
}%
\expandafter\def\csname XINT_FL_fac_smallloop_0\endcsname #1.#2.%
{%
    \XINT_FL_fac_addzeros #2.100000024!.{5.#1.}{#2}%
}%
\def\XINT_FL_fac_addzeros #1.%
{%
    \ifnum #1=\xint_c_viii \expandafter\XINT_FL_fac_addzeros_exit\fi
    \expandafter\XINT_FL_fac_addzeros\the\numexpr #1-\xint_c_viii.100000000!%
}%
\def\XINT_FL_fac_addzeros_exit #1.#2.#3#4{\XINT_FL_fac_smallloop_loop #3#21\Z![-#4]}%
\def\XINT_FL_fac_smallloop_loop #1.#2.%
{%
    \ifnum #1>#2 \expandafter\XINT_FL_fac_loop_exit\fi
    \expandafter\XINT_FL_fac_smallloop_loop
    \the\numexpr #1+\xint_c_iv\expandafter.%
    \the\numexpr #2\expandafter.\romannumeral0\XINT_FL_fac_smallloop_mul #1!%
}%
\def\XINT_FL_fac_smallloop_mul #1!%
{%
    \expandafter\XINT_FL_fac_mul
    \the\numexpr
        \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)*(#1+\xint_c_iii)!%
}%[[
\def\XINT_FL_fac_loop_exit #1!#2]#3{#3#2]}%
\def\XINT_FL_fac_mul 1#1!%
   {\expandafter\XINT_FL_fac_mul_a\the\numexpr\XINT_FL_fac_smallmul 10!{#1}}%
\def\XINT_FL_fac_mul_a #1-#2%
{%
    \if#21\xint_afterfi{\expandafter\space\xint_gob_til_exclam}\else
    \expandafter\space\fi #11\Z!%
}%
\def\XINT_FL_fac_minimulwc_a #1#2#3#4#5!#6#7#8#9%
{%
    \XINT_FL_fac_minimulwc_b {#1#2#3#4}{#5}{#6#7#8#9}%
}%
\def\XINT_FL_fac_minimulwc_b #1#2#3#4!#5%
{%
    \expandafter\XINT_FL_fac_minimulwc_c
    \the\numexpr \xint_c_x^ix+#5+#2*#4.{{#1}{#2}{#3}{#4}}%
}%
\def\XINT_FL_fac_minimulwc_c 1#1#2#3#4#5#6.#7%
{%
    \expandafter\XINT_FL_fac_minimulwc_d {#1#2#3#4#5}#7{#6}%
}%
\def\XINT_FL_fac_minimulwc_d #1#2#3#4#5%
{%
    \expandafter\XINT_FL_fac_minimulwc_e
    \the\numexpr \xint_c_x^ix+#1+#2*#5+#3*#4.{#2}{#4}%
}%
\def\XINT_FL_fac_minimulwc_e 1#1#2#3#4#5#6.#7#8#9%
{%
    1#6#9\expandafter!%
    \the\numexpr\expandafter\XINT_FL_fac_smallmul
    \the\numexpr \xint_c_x^viii+#1#2#3#4#5+#7*#8!%
}%
\def\XINT_FL_fac_smallmul 1#1!#21#3!%
{%
    \xint_gob_til_Z #3\XINT_FL_fac_smallmul_end\Z
    \XINT_FL_fac_minimulwc_a #2!#3!{#1}{#2}%
}%
\def\XINT_FL_fac_smallmul_end\Z\XINT_FL_fac_minimulwc_a #1!\Z!#2#3[#4]%
{%
   \ifnum #2=\xint_c_
       \expandafter\xint_firstoftwo\else
       \expandafter\xint_secondoftwo
   \fi
   {-2\relax[#4]}%
   {1#2\expandafter!\expandafter-\expandafter1\expandafter
                  [\the\numexpr #4+\xint_c_viii]}%
}%
\def\xintFloatPFactorial {\romannumeral0\xintfloatpfactorial}%
\def\xintfloatpfactorial #1{\XINT_flpfac_chkopt \xintfloat #1\xint_relax }%
\def\XINTinFloatPFactorial {\romannumeral0\XINTinfloatpfactorial }%
\def\XINTinfloatpfactorial #1{\XINT_flpfac_chkopt \XINTinfloat #1\xint_relax }%
\def\XINT_flpfac_chkopt #1#2%
{%
    \ifx [#2\expandafter\XINT_flpfac_opt
       \else\expandafter\XINT_flpfac_noopt
    \fi
     #1#2%
}%
\def\XINT_flpfac_noopt  #1#2\xint_relax #3%
{%
   \expandafter\XINT_FL_pfac_fork
   \the\numexpr \xintNum{#2}\expandafter.%
   \the\numexpr \xintNum{#3}.\xint_c_i{\XINTdigits}{#1[\XINTdigits]}%
}%
\def\XINT_flpfac_opt #1[\xint_relax #2]%
{%
   \expandafter\XINT_flpfac_opt_b\the\numexpr #2.#1%
}%
\def\XINT_flpfac_opt_b #1.#2#3#4%
{%
   \expandafter\XINT_FL_pfac_fork
   \the\numexpr \xintNum{#3}\expandafter.%
   \the\numexpr \xintNum{#4}.\xint_c_i{#1}{#2[#1]}%
}%
\def\XINT_FL_pfac_fork #1#2.#3.%
{%
    \if-#1\xint_dothis\XINT_FL_pfac_outofrange\fi
    \ifnum #1#2=#3  \xint_dothis\XINT_FL_pfac_one\fi
    \ifnum #1#2>#3  \xint_dothis\XINT_FL_pfac_outofrange\fi
    \ifnum #3>\xint_c_x^viii_mone
                     \xint_dothis\XINT_FL_pfac_outofrange\fi
    \xint_orthat \XINT_FL_pfac_increaseP #1#2.#3.%
}%
\def\XINT_FL_pfac_outofrange #1.#2.#3#4#5{\xintError:OutOfRangePFac #5{0[0]}}%
\def\XINT_FL_pfac_one #1.#2.#3#4#5{#5{1[0]}}%
\def\XINT_FL_pfac_increaseP #1.#2.#3#4%
{%
    \expandafter\XINT_FL_pfac_a
    \the\numexpr \xint_c_viii*((\xint_c_iv+#4+\expandafter
                 \XINT_FL_fac_countdigits\the\numexpr (#2-#1-\xint_c_i)%
                    /\ifnum #2>\xint_c_x^iv #3\else(#3*\xint_c_ii)\fi\relax
                 87654321\Z)/\xint_c_viii).#1.#2.%
}%
\def\XINT_FL_pfac_a #1.#2.#3.%
{%
    \expandafter\XINT_FL_pfac_b\the\numexpr \xint_c_i+#2\expandafter.%
    \the\numexpr#3\expandafter.%
    \romannumeral0\XINT_FL_pfac_addzeroes #1.100000001!1\Z![-#1]%
}%
\def\XINT_FL_pfac_addzeroes #1.%
{%
    \ifnum #1=\xint_c_viii \expandafter\XINT_FL_pfac_addzeroes_exit\fi
    \expandafter\XINT_FL_pfac_addzeroes\the\numexpr #1-\xint_c_viii.100000000!%
}%
\def\XINT_FL_pfac_addzeroes_exit #1.{ }%
\def\XINT_FL_pfac_b #1.%
{%
    \ifnum #1>9999 \xint_dothis\XINT_FL_pfac_vbigloop \fi
    \ifnum #1>463  \xint_dothis\XINT_FL_pfac_bigloop   \fi
    \ifnum #1>98   \xint_dothis\XINT_FL_pfac_medloop   \fi
                   \xint_orthat\XINT_FL_pfac_smallloop #1.%
}%
\def\XINT_FL_pfac_smallloop #1.#2.%
{%
    \ifcase\numexpr #2-#1\relax
        \expandafter\XINT_FL_pfac_end_
    \or \expandafter\XINT_FL_pfac_end_i
    \or \expandafter\XINT_FL_pfac_end_ii
    \or \expandafter\XINT_FL_pfac_end_iii
    \else\expandafter\XINT_FL_pfac_smallloop_a
    \fi #1.#2.%
}%
\def\XINT_FL_pfac_smallloop_a #1.#2.%
{%
    \expandafter\XINT_FL_pfac_smallloop_b
    \the\numexpr #1+\xint_c_iv\expandafter.%
    \the\numexpr #2\expandafter.%
    \romannumeral0\expandafter\XINT_FL_fac_mul
    \the\numexpr \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)*(#1+\xint_c_iii)!%
}%
\def\XINT_FL_pfac_smallloop_b #1.%
{%
    \ifnum #1>98  \expandafter\XINT_FL_pfac_medloop   \else
                  \expandafter\XINT_FL_pfac_smallloop \fi #1.%
}%
\def\XINT_FL_pfac_medloop #1.#2.%
{%
    \ifcase\numexpr #2-#1\relax
        \expandafter\XINT_FL_pfac_end_
    \or \expandafter\XINT_FL_pfac_end_i
    \or \expandafter\XINT_FL_pfac_end_ii
    \else\expandafter\XINT_FL_pfac_medloop_a
    \fi #1.#2.%
}%
\def\XINT_FL_pfac_medloop_a #1.#2.%
{%
    \expandafter\XINT_FL_pfac_medloop_b
    \the\numexpr #1+\xint_c_iii\expandafter.%
    \the\numexpr #2\expandafter.%
    \romannumeral0\expandafter\XINT_FL_fac_mul
    \the\numexpr \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)!%
}%
\def\XINT_FL_pfac_medloop_b #1.%
{%
    \ifnum #1>463 \expandafter\XINT_FL_pfac_bigloop   \else
                  \expandafter\XINT_FL_pfac_medloop   \fi #1.%
}%
\def\XINT_FL_pfac_bigloop #1.#2.%
{%
    \ifcase\numexpr #2-#1\relax
        \expandafter\XINT_FL_pfac_end_
    \or \expandafter\XINT_FL_pfac_end_i
    \else\expandafter\XINT_FL_pfac_bigloop_a
    \fi #1.#2.%
}%
\def\XINT_FL_pfac_bigloop_a #1.#2.%
{%
    \expandafter\XINT_FL_pfac_bigloop_b
    \the\numexpr #1+\xint_c_ii\expandafter.%
    \the\numexpr #2\expandafter.%
    \romannumeral0\expandafter\XINT_FL_fac_mul
    \the\numexpr \xint_c_x^viii+#1*(#1+\xint_c_i)!%
}%
\def\XINT_FL_pfac_bigloop_b #1.%
{%
    \ifnum #1>9999 \expandafter\XINT_FL_pfac_vbigloop  \else
                   \expandafter\XINT_FL_pfac_bigloop   \fi #1.%
}%
\def\XINT_FL_pfac_vbigloop #1.#2.%
{%
    \ifnum #2=#1
         \expandafter\XINT_FL_pfac_end_
    \else\expandafter\XINT_FL_pfac_vbigloop_a
    \fi #1.#2.%
}%
\def\XINT_FL_pfac_vbigloop_a #1.#2.%
{%
    \expandafter\XINT_FL_pfac_vbigloop
    \the\numexpr #1+\xint_c_i\expandafter.%
    \the\numexpr #2\expandafter.%
    \romannumeral0\expandafter\XINT_FL_fac_mul
    \the\numexpr\xint_c_x^viii+#1!%
}%
\def\XINT_FL_pfac_end_iii #1.#2.%
{%
    \expandafter\XINT_FL_fac_out
    \romannumeral0\expandafter\XINT_FL_fac_mul
    \the\numexpr \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)*(#1+\xint_c_iii)!%
}%
\def\XINT_FL_pfac_end_ii #1.#2.%
{%
    \expandafter\XINT_FL_fac_out
    \romannumeral0\expandafter\XINT_FL_fac_mul
    \the\numexpr \xint_c_x^viii+#1*(#1+\xint_c_i)*(#1+\xint_c_ii)!%
}%
\def\XINT_FL_pfac_end_i #1.#2.%
{%
    \expandafter\XINT_FL_fac_out
    \romannumeral0\expandafter\XINT_FL_fac_mul
    \the\numexpr \xint_c_x^viii+#1*(#1+\xint_c_i)!%
}%
\def\XINT_FL_pfac_end_ #1.#2.%
{%
    \expandafter\XINT_FL_fac_out
    \romannumeral0\expandafter\XINT_FL_fac_mul
    \the\numexpr \xint_c_x^viii+#1!%
}%
\def\xintFloatBinomial    {\romannumeral0\xintfloatbinomial}%
\def\xintfloatbinomial   #1{\XINT_flbinom_chkopt \xintfloat #1\xint_relax }%
\def\XINTinFloatBinomial   {\romannumeral0\XINTinfloatbinomial }%
\def\XINTinfloatbinomial #1{\XINT_flbinom_chkopt \XINTinfloat #1\xint_relax }%
\def\XINT_flbinom_chkopt #1#2%
{%
    \ifx [#2\expandafter\XINT_flbinom_opt
       \else\expandafter\XINT_flbinom_noopt
    \fi  #1#2%
}%
\def\XINT_flbinom_noopt #1#2\xint_relax #3%
{%
    \expandafter\XINT_FL_binom_a
    \the\numexpr\xintNum{#2}\expandafter.\the\numexpr\xintNum{#3}.\XINTdigits.#1%
}%
\def\XINT_flbinom_opt #1[\xint_relax #2]#3#4%
{%
    \expandafter\XINT_FL_binom_a
    \the\numexpr\xintNum{#3}\expandafter.\the\numexpr\xintNum{#4}\expandafter.%
    \the\numexpr #2.#1%
}%
\def\XINT_FL_binom_a #1.#2.%
{%
    \expandafter\XINT_FL_binom_fork \the\numexpr #1-#2.#2.#1.%
}%
\def\XINT_FL_binom_fork #1#2.#3#4.#5.%
{%
    \if-#1\xint_dothis \XINT_FL_binom_outofrange\fi
    \if-#3\xint_dothis \XINT_FL_binom_outofrange\fi
    \if0#1\xint_dothis \XINT_FL_binom_one\fi
    \if0#3\xint_dothis \XINT_FL_binom_one\fi
    \ifnum #5>\xint_c_x^viii_mone \xint_dothis\XINT_FL_binom_outofrange\fi
    \ifnum #1#2>#3#4  \xint_dothis\XINT_FL_binom_ab \fi
                      \xint_orthat\XINT_FL_binom_aa
    #1#2.#3#4.#5.%
}%
\def\XINT_FL_binom_outofrange #1.#2.#3.#4.#5%
       {\xintError:OutOfRangeBinomial #5[#4]{0[0]}}%
\def\XINT_FL_binom_one #1.#2.#3.#4.#5{#5[#4]{1[0]}}%
\def\XINT_FL_binom_aa  #1.#2.#3.#4.#5%
{%
    #5[#4]{\xintDiv{\XINT_FL_pfac_increaseP
           #2.#3.\xint_c_iv{#4+\xint_c_i}{\XINTinfloat[#4+\xint_c_iii]}}%
           {\XINT_FL_fac_fork_b
           #1.\xint_c_iv{#4+\xint_c_i}\XINT_FL_fac_out{\XINTinfloat[#4+\xint_c_iii]}}}%
}%
\def\XINT_FL_binom_ab  #1.#2.#3.#4.#5%
{%
    #5[#4]{\xintDiv{\XINT_FL_pfac_increaseP
           #1.#3.\xint_c_iv{#4+\xint_c_i}{\XINTinfloat[#4+\xint_c_iii]}}%
           {\XINT_FL_fac_fork_b
           #2.\xint_c_iv{#4+\xint_c_i}\XINT_FL_fac_out{\XINTinfloat[#4+\xint_c_iii]}}}%
}%
\def\xintFloatSqrt     {\romannumeral0\xintfloatsqrt }%
\def\xintfloatsqrt   #1{\XINT_flsqrt_chkopt \xintfloat #1\xint_relax }%
\def\XINTinFloatSqrt   {\romannumeral0\XINTinfloatsqrt }%
\def\XINTinfloatsqrt #1{\XINT_flsqrt_chkopt \XINTinfloat #1\xint_relax }%
\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\xint_relax
{%
    \expandafter\XINT_FL_sqrt_a
                \romannumeral0\XINTinfloat[\XINTdigits]{#2}\XINTdigits.#1%
}%
\def\XINT_flsqrt_opt #1[\xint_relax #2]%#3%
{%
    \expandafter\XINT_flsqrt_opt_a\the\numexpr #2.#1%
}%
\def\XINT_flsqrt_opt_a #1.#2#3%
{%
    \expandafter\XINT_FL_sqrt_a\romannumeral0\XINTinfloat[#1]{#3}#1.#2%
}%
\def\XINT_FL_sqrt_a #1%
{%
    \xint_UDzerominusfork
     #1-\XINT_FL_sqrt_iszero
     0#1\XINT_FL_sqrt_isneg
      0-{\XINT_FL_sqrt_pos #1}%
    \krof
}%[
\def\XINT_FL_sqrt_iszero #1]#2.#3{#3[#2]{0[0]}}%
\def\XINT_FL_sqrt_isneg  #1]#2.#3{\xintError:RootOfNegative #3[#2]{0[0]}}%
\def\XINT_FL_sqrt_pos #1[#2]#3.%
{%
    \expandafter\XINT_flsqrt
    \the\numexpr #3\ifodd #2 \xint_dothis {+\xint_c_iii.(#2+\xint_c_i).0}\fi
    \xint_orthat {+\xint_c_ii.#2.{}}#100.#3.%
}%
\def\XINT_flsqrt #1.#2.%
{%
    \expandafter\XINT_flsqrt_a
    \the\numexpr #2/\xint_c_ii-(#1-\xint_c_i)/\xint_c_ii.#1.%
}%
\def\XINT_flsqrt_a #1.#2.#3#4.#5.%
{%
    \expandafter\XINT_flsqrt_b
    \the\numexpr (#2-\xint_c_i)/\xint_c_ii\expandafter.%
    \romannumeral0\XINT_sqrt_start #2.#4#3.#5.#2.#4#3.#5.#1.%
}%
\def\XINT_flsqrt_b #1.#2#3%
{%
   \expandafter\XINT_flsqrt_c
   \romannumeral0\xintiisub
    {\XINT_dsx_addzerosnofuss {#1}{#2}}%
    {\xintiiDivRound{\XINT_dsx_addzerosnofuss {#1}{#3}}{\XINT_dbl_pos#2\Z}}.%
}%
\def\XINT_flsqrt_c #1.#2.%
{%
    \expandafter\XINT_flsqrt_d
    \romannumeral0\XINT_split_fromleft_loop #2.{}#1\W\W\W\W\W\W\W\W\Z
}%
\def\XINT_flsqrt_d #1.#2#3.%
{%
    \ifnum #2=\xint_c_v
    \expandafter\XINT_flsqrt_f\else\expandafter\XINT_flsqrt_finish\fi
    #2#3.#1.%
}%
\def\XINT_flsqrt_finish #1#2.#3.#4.#5.#6.#7.#8{#8[#6]{#3#1[#7]}}%
\def\XINT_flsqrt_f 5#1.%
   {\expandafter\XINT_flsqrt_g\romannumeral0\xintinum{#1}\relax.}%
\def\XINT_flsqrt_g #1#2#3.{\if\relax#2\xint_dothis{\XINT_flsqrt_h #1}\fi
                           \xint_orthat{\XINT_flsqrt_finish 5.}}%
\def\XINT_flsqrt_h #1{\ifnum #1<\xint_c_iii\xint_dothis{\XINT_flsqrt_again}\fi
                      \xint_orthat{\XINT_flsqrt_finish 5.}}%
\def\XINT_flsqrt_again #1.#2.%
{%
    \expandafter\XINT_flsqrt_again_a\the\numexpr #2+\xint_c_viii.%
}%
\def\XINT_flsqrt_again_a #1.#2.#3.%
{%
    \expandafter\XINT_flsqrt_b
    \the\numexpr (#1-\xint_c_i)/\xint_c_ii\expandafter.%
    \romannumeral0\XINT_sqrt_start #1.#200000000.#3.%
                                   #1.#200000000.#3.%
}%
\def\xintFloatE   {\romannumeral0\xintfloate }%
\def\xintfloate #1{\XINT_floate_chkopt #1\xint_relax }%
\def\XINT_floate_chkopt #1%
{%
    \ifx [#1\expandafter\XINT_floate_opt
       \else\expandafter\XINT_floate_noopt
    \fi  #1%
}%
\def\XINT_floate_noopt #1\xint_relax
{%
    \expandafter\XINT_floate_a\expandafter\XINTdigits
                \romannumeral0\XINT_infrac {#1}%
}%
\def\XINT_floate_opt [\xint_relax #1]#2%
{%
    \expandafter\XINT_floate_a\expandafter
    {\the\numexpr #1\expandafter}\romannumeral0\XINT_infrac {#2}%
}%
\def\XINT_floate_a #1#2#3#4#5%
{%
    \expandafter\XINT_float_a\the\numexpr#1\expandafter.%
    \expandafter{\the\numexpr #2+#5}{#3}{#4}\XINT_float_Q
}%
\def\XINTinFloatE {\romannumeral0\XINTinfloate }%
\def\XINTinfloate
   {\expandafter\XINT_infloate\romannumeral0\XINTinfloat [\XINTdigits]}%
\def\XINT_infloate #1[#2]#3%
   {\expandafter\XINT_infloate_end\the\numexpr #3+#2.{#1}}%
\def\XINT_infloate_end #1.#2{ #2[#1]}%
\def\XINTinFloatMod {\romannumeral0\XINTinfloatmod [\XINTdigits]}%
\def\XINTinfloatmod [#1]#2#3{\expandafter\XINT_infloatmod\expandafter
                           {\romannumeral0\XINTinfloat[#1]{#2}}%
                           {\romannumeral0\XINTinfloat[#1]{#3}}{#1}}%
\def\XINT_infloatmod #1#2{\expandafter\XINT_infloatmod_a\expandafter {#2}{#1}}%
\def\XINT_infloatmod_a #1#2#3{\XINTinfloat [#3]{\xintMod {#2}{#1}}}%
\XINT_restorecatcodes_endinput%
\endinput
%%
%% End of file `xintfrac.sty'.