xint (7apr19)

git-svn-id: svn://tug.org/texlive/trunk@50844 c570f23f-e606-0410-a88d-b1316a301751

12 files changed, 1223 insertions, 260 deletions

diff --git a/Master/texmf-dist/tex/generic/xint/xint.sty b/Master/texmf-dist/tex/generic/xint/xint.sty
index f8413488235..4137ad675a7 100644
--- a/Master/texmf-dist/tex/generic/xint/xint.sty
+++ b/Master/texmf-dist/tex/generic/xint/xint.sty
@@ -21,7 +21,7 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.3d 2019/01/06
+%% The xint bundle 1.3e 2019/04/05
 %% Copyright (C) 2013-2019 by Jean-Francois Burnol
 %% xint: Expandable operations on big integers
 %% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty (loaded by xintcore.sty)
 \XINT_providespackage
 \ProvidesPackage{xint}%
-  [2019/01/06 1.3d Expandable operations on big integers (JFB)]%
+  [2019/04/05 1.3e Expandable operations on big integers (JFB)]%
 \long\def\xint_firstofthree  #1#2#3{#1}%
 \long\def\xint_secondofthree #1#2#3{#2}%
 \long\def\xint_thirdofthree  #1#2#3{#3}%
@@ -98,6 +98,17 @@
 {%
     \expandafter\XINT_length_loop\xint_UDsignfork#1{}-#1\krof
 }%
+\def\xintiiLogTen {\the\numexpr\xintiilogten }%
+\def\xintiilogten #1%
+{%
+    \expandafter\XINT_iilogten\romannumeral`&&@#1%
+      \xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:\xint:
+      \xint_c_viii\xint_c_vii\xint_c_vi\xint_c_v
+      \xint_c_iv\xint_c_iii\xint_c_ii\xint_c_i\xint_c_\xint_bye
+    \relax
+}%
+\def\XINT_iilogten #1{\if#10-"7FFF8000\fi -1+%
+                      \expandafter\XINT_length_loop\xint_UDsignfork#1{}-#1\krof}%
 \def\xintReverseDigits {\romannumeral0\xintreversedigits }%
 \def\xintreversedigits #1%
 {%
diff --git a/Master/texmf-dist/tex/generic/xint/xintbinhex.sty b/Master/texmf-dist/tex/generic/xint/xintbinhex.sty
index a1799fbc3da..07e52be6dfc 100644
--- a/Master/texmf-dist/tex/generic/xint/xintbinhex.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintbinhex.sty
@@ -21,7 +21,7 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.3d 2019/01/06
+%% The xint bundle 1.3e 2019/04/05
 %% Copyright (C) 2013-2019 by Jean-Francois Burnol
 %% xintbinhex: Expandable binary and hexadecimal conversions
 %% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty
 \XINT_providespackage
 \ProvidesPackage{xintbinhex}%
-  [2019/01/06 1.3d Expandable binary and hexadecimal conversions (JFB)]%
+  [2019/04/05 1.3e Expandable binary and hexadecimal conversions (JFB)]%
 \newcount\xint_c_ii^xv  \xint_c_ii^xv   32768
 \newcount\xint_c_ii^xvi \xint_c_ii^xvi  65536
 \def\XINT_tmpa #1{\ifx\relax#1\else
diff --git a/Master/texmf-dist/tex/generic/xint/xintcfrac.sty b/Master/texmf-dist/tex/generic/xint/xintcfrac.sty
index 530d6e3db7e..c62037bbc24 100644
--- a/Master/texmf-dist/tex/generic/xint/xintcfrac.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintcfrac.sty
@@ -21,7 +21,7 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.3d 2019/01/06
+%% The xint bundle 1.3e 2019/04/05
 %% Copyright (C) 2013-2019 by Jean-Francois Burnol
 %% xintcfrac: Expandable continued fractions with xint package
 %% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty
 \XINT_providespackage
 \ProvidesPackage{xintcfrac}%
-  [2019/01/06 1.3d Expandable continued fractions with xint package (JFB)]%
+  [2019/04/05 1.3e Expandable continued fractions with xint package (JFB)]%
 \def\xintCFrac {\romannumeral0\xintcfrac }%
 \def\xintcfrac #1%
 {%
diff --git a/Master/texmf-dist/tex/generic/xint/xintcore.sty b/Master/texmf-dist/tex/generic/xint/xintcore.sty
index b93057a82bd..b0f8ff5d0f2 100644
--- a/Master/texmf-dist/tex/generic/xint/xintcore.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintcore.sty
@@ -21,7 +21,7 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.3d 2019/01/06
+%% The xint bundle 1.3e 2019/04/05
 %% Copyright (C) 2013-2019 by Jean-Francois Burnol
 %% xintcore: Expandable arithmetic on big integers
 %% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty
 \XINT_providespackage
 \ProvidesPackage{xintcore}%
-  [2019/01/06 1.3d Expandable arithmetic on big integers (JFB)]%
+  [2019/04/05 1.3e Expandable arithmetic on big integers (JFB)]%
 \csname XINT_Clamped_istrapped\endcsname
 \csname XINT_ConversionSyntax_istrapped\endcsname
 \csname XINT_DivisionByZero_istrapped\endcsname
diff --git a/Master/texmf-dist/tex/generic/xint/xintexpr.sty b/Master/texmf-dist/tex/generic/xint/xintexpr.sty
index 13bbb335437..8ed1191fb8a 100644
--- a/Master/texmf-dist/tex/generic/xint/xintexpr.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintexpr.sty
@@ -21,7 +21,7 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.3d 2019/01/06
+%% The xint bundle 1.3e 2019/04/05
 %% Copyright (C) 2013-2019 by Jean-Francois Burnol
 %% xintexpr: Expandable expression parser
 %% ---------------------------------------------------------------
@@ -81,142 +81,154 @@
 \XINTsetupcatcodes%
 \XINT_providespackage
 \ProvidesPackage{xintexpr}%
-  [2019/01/06 1.3d Expandable expression parser (JFB)]%
+  [2019/04/05 1.3e Expandable expression parser (JFB)]%
 \catcode`! 11
 \let\XINT_Cmp \xintiiCmp
-\def\xint_gob_til_! #1!{}% ! with catcode 11
-\def\XINT_expr_lockscan#1{% not used for decimal numbers in xintexpr 1.2
-\def\XINT_expr_lockscan##1!{\expandafter#1\csname .=##1\endcsname}%
-}\XINT_expr_lockscan{ }%
-\def\XINT_expr_lockit#1{%
-\def\XINT_expr_lockit##1{\expandafter#1\csname .=##1\endcsname}%
-}\XINT_expr_lockit{ }%
-\def\XINT_expr_unlock_hex_in #1%  expanded inside \csname..\endcsname
-   {\expandafter\XINT_expr_inhex\romannumeral`&&@\XINT_expr_unlock#1;}%
-\def\XINT_expr_inhex #1.#2#3;%    expanded inside \csname..\endcsname
-{%
-    \if#2>%
-      \xintHexToDec{#1}%
-    \else
-      \xintiiMul{\xintiiPow{625}{\xintLength{#3}}}{\xintHexToDec{#1#3}}%
-      [\the\numexpr-4*\xintLength{#3}]%
-    \fi
-}%
-\def\XINT_expr_unlock  {\expandafter\XINT_expr_unlock_a\string }%
-\def\XINT_expr_unlock_a #1.={}%
-\def\XINT_expr_unexpectedtoken {\xintError:ignored }%
-\let\XINT_expr_done\space
-\def\XINT_expr_wrap   { !\XINT_expr_usethe\XINT_protectii\XINT_expr_print }%
-\def\XINT_iiexpr_wrap { !\XINT_expr_usethe\XINT_protectii\XINT_iiexpr_print }%
-\def\XINT_protectii #1{\noexpand\XINT_protectii\noexpand #1\noexpand }%
-\protected\def\XINT_expr_usethe\XINT_protectii {\xintError:missing_xintthe!}%
-\def\XINT_expr_print     #1{\xintSPRaw::csv  {\XINT_expr_unlock #1}}%
-\def\XINT_iiexpr_print   #1{\xintCSV::csv    {\XINT_expr_unlock #1}}%
-\def\XINT_boolexpr_print #1{\xintIsTrue::csv {\XINT_expr_unlock #1}}%
 \def\xintexpr       {\romannumeral0\xintexpro      }%
 \def\xintiexpr      {\romannumeral0\xintiexpro     }%
 \def\xintfloatexpr  {\romannumeral0\xintfloatexpro }%
 \def\xintiiexpr     {\romannumeral0\xintiiexpro    }%
-\def\xinttheexpr
-   {\romannumeral`&&@\expandafter\XINT_expr_print\romannumeral0\xintbareeval}%
-\def\xinttheiexpr
-   {\romannumeral`&&@\expandafter\xint_gobble_iii\romannumeral`&&@\xintiexpr}%
-\def\xintthefloatexpr
-   {\romannumeral`&&@\expandafter\xint_gobble_iii\romannumeral`&&@\xintfloatexpr}%
-\def\xinttheiiexpr
-   {\romannumeral`&&@\expandafter\XINT_iiexpr_print\romannumeral0\xintbareiieval}%
-\def\xinteval #1%
-   {\romannumeral`&&@\expandafter\XINT_expr_print\romannumeral0\xintbareeval#1\relax}%
-\def\xintieval #1%
-   {\romannumeral`&&@\expandafter\xint_gobble_iii\romannumeral`&&@\xintiexpr#1\relax}%
-\def\xintfloateval #1%
-   {\romannumeral`&&@\expandafter\xint_gobble_iii\romannumeral`&&@\xintfloatexpr#1\relax}%
-\def\xintiieval #1%
-   {\romannumeral`&&@\expandafter\XINT_iiexpr_print\romannumeral0\xintbareiieval#1\relax}%
-\def\xintthe #1{\romannumeral`&&@\expandafter\xint_gobble_iii\romannumeral`&&@#1}%
-\def\xintthe_o #1{\expandafter\xint_gobble_iii\romannumeral`&&@#1}%
-\let\thexintexpr     \xinttheexpr
-\let\thexintiexpr    \xinttheiexpr
-\let\thexintfloatexpr\xintthefloatexpr
-\let\thexintiiexpr   \xinttheiiexpr
-\def\xintthecoords  #1{\romannumeral`&&@\expandafter\expandafter\expandafter
-                     \XINT_thecoords_a
-                     \expandafter\xint_gobble_iii\romannumeral0#1}%
-\def\XINT_thecoords_a #1#2% #1=print macro, indispensible for scientific notation
-   {\expandafter\XINT_expr_unlock\csname.=\expandafter\XINT_thecoords_b
-                         \romannumeral`&&@#1#2,!,!,^\endcsname }%
-\def\XINT_thecoords_b #1#2,#3#4,%
-   {\xint_gob_til_! #3\XINT_thecoords_c ! (#1#2, #3#4)\XINT_thecoords_b }%
-\def\XINT_thecoords_c #1^{}%
-\def\xintbareeval
-   {\expandafter\XINT_expr_until_end_a\romannumeral`&&@\XINT_expr_getnext }%
-\def\xintbarefloateval
-   {\expandafter\XINT_flexpr_until_end_a\romannumeral`&&@\XINT_expr_getnext }%
-\def\xintbareiieval
-   {\expandafter\XINT_iiexpr_until_end_a\romannumeral`&&@\XINT_expr_getnext }%
-\def\xintthebareeval      {\expandafter\XINT_expr_unlock\romannumeral0\xintbareeval}%
-\def\xintthebarefloateval {\expandafter\XINT_expr_unlock\romannumeral0\xintbarefloateval}%
-\def\xintthebareiieval    {\expandafter\XINT_expr_unlock\romannumeral0\xintbareiieval}%
 \def\xintexpro   {\expandafter\XINT_expr_wrap\romannumeral0\xintbareeval }%
 \def\xintiiexpro {\expandafter\XINT_iiexpr_wrap\romannumeral0\xintbareiieval }%
 \def\xintiexpro #1%
-   {\ifx [#1\expandafter\XINT_iexpr_withopt\else\expandafter\XINT_iexpr_noopt \fi #1}%
+{%
+    \ifx [#1\expandafter\XINT_iexpr_withopt\else\expandafter\XINT_iexpr_noopt
+    \fi #1%
+}%
 \def\XINT_iexpr_noopt
-   {\expandafter\XINT_iexpr_wrap \expandafter 0\romannumeral0\xintbareeval }%
+{%
+    \expandafter\XINT_iexpr_preprint\expandafter 0%
+    \romannumeral0\xintbareeval
+}%
 \def\XINT_iexpr_withopt [#1]%
 {%
-    \expandafter\XINT_iexpr_wrap\expandafter
+    \expandafter\XINT_iexpr_preprint\expandafter
     {\the\numexpr \xint_zapspaces #1 \xint_gobble_i\expandafter}%
     \romannumeral0\xintbareeval
 }%
-\def\XINT_iexpr_wrap #1#2%
+\def\XINT_iexpr_preprint #1#2%
 {%
     \expandafter\XINT_expr_wrap
     \csname .=\xintRound::csv {#1}{\XINT_expr_unlock #2}\endcsname
 }%
 \def\xintfloatexpro #1%
 {%
-    \ifx [#1\expandafter\XINT_flexpr_withopt_a\else\expandafter\XINT_flexpr_noopt
+    \ifx [#1\expandafter\XINT_flexpr_withopt\else\expandafter\XINT_flexpr_noopt
     \fi #1%
 }%
 \def\XINT_flexpr_noopt
 {%
-   \expandafter\XINT_flexpr_withopt_b\expandafter\xinttheDigits
-   \romannumeral0\xintbarefloateval
+    \expandafter\XINT_flexpr_preprint\expandafter\xinttheDigits
+    \romannumeral0\xintbarefloateval
 }%
-\def\XINT_flexpr_withopt_a [#1]%
+\def\XINT_flexpr_withopt [#1]%
 {%
-   \expandafter\XINT_flexpr_withopt_b\expandafter
+    \expandafter\XINT_flexpr_preprint\expandafter
     {\the\numexpr\xint_zapspaces #1 \xint_gobble_i\expandafter}%
     \romannumeral0\xintbarefloateval
 }%
-\def\XINT_flexpr_withopt_b #1#2%
+\def\XINT_flexpr_preprint #1#2%
 {%
-    \expandafter\XINT_flexpr_wrap\csname .;#1.=% ; and not : as before b'cause NewExpr
-    \XINTinFloat::csv {#1}{\XINT_expr_unlock #2}\endcsname
+    \expandafter\XINT_flexpr_wrap
+    \csname .;#1.=\XINTinFloat::csv {#1}{\XINT_expr_unlock #2}\endcsname
 }%
-\def\XINT_flexpr_wrap { !\XINT_expr_usethe\XINT_protectii\XINT_flexpr_print }%
+\def\XINT_expr_wrap   {!\XINT_expr_usethe\XINT_protectii\XINT_expr_print}%
+\def\XINT_iiexpr_wrap {!\XINT_expr_usethe\XINT_protectii\XINT_iiexpr_print}%
+\def\XINT_flexpr_wrap {!\XINT_expr_usethe\XINT_protectii\XINT_flexpr_print}%
+\def\XINT_protectii #1{\noexpand\XINT_protectii\noexpand #1\noexpand }%
+\protected\def\XINT_expr_usethe\XINT_protectii {\xintError:missing_xintthe!}%
+\def\XINT_expr_print   #1{\xintSPRaw::csv  {\XINT_expr_unlock #1}}%
+\def\XINT_iiexpr_print #1{\xintCSV::csv    {\XINT_expr_unlock #1}}%
 \def\XINT_flexpr_print #1%
 {%
     \expandafter\xintPFloat::csv
     \romannumeral`&&@\expandafter\XINT_expr_unlock_sp\string #1!%
 }%
 \def\XINT_expr_unlock_sp #1.;#2.=#3!{{#2}{#3}}%
-\def\xintboolexpr      {\romannumeral0\expandafter\expandafter\expandafter
-    \XINT_boolexpr_done \expandafter\xint_gobble_iv\romannumeral0\xintexpro }%
-\def\xinttheboolexpr   {\romannumeral`&&@\expandafter\expandafter\expandafter
-    \XINT_boolexpr_print\expandafter\xint_gobble_iv\romannumeral0\xintexpro }%
+\def\xinttheexpr
+   {\romannumeral`&&@\expandafter\XINT_expr_print\romannumeral0\xintbareeval}%
+\def\xinttheiexpr
+   {\romannumeral`&&@\expandafter\xint_gobble_iii\romannumeral`&&@\xintiexpr}%
+\def\xintthefloatexpr
+   {\romannumeral`&&@\expandafter\xint_gobble_iii\romannumeral`&&@\xintfloatexpr}%
+\def\xinttheiiexpr
+   {\romannumeral`&&@\expandafter\XINT_iiexpr_print\romannumeral0\xintbareiieval}%
+\let\thexintexpr     \xinttheexpr
+\let\thexintiexpr    \xinttheiexpr
+\let\thexintfloatexpr\xintthefloatexpr
+\let\thexintiiexpr   \xinttheiiexpr
+\def\xinteval #1%
+   {\romannumeral`&&@\expandafter\XINT_expr_print\romannumeral0\xintbareeval#1\relax}%
+\def\xintieval #1%
+   {\romannumeral`&&@\expandafter\xint_gobble_iii\romannumeral`&&@\xintiexpr#1\relax}%
+\def\xintfloateval #1%
+   {\romannumeral`&&@\expandafter\xint_gobble_iii\romannumeral`&&@\xintfloatexpr#1\relax}%
+\def\xintiieval #1%
+   {\romannumeral`&&@\expandafter\XINT_iiexpr_print\romannumeral0\xintbareiieval#1\relax}%
+\def\xintthe #1{\romannumeral`&&@\expandafter\xint_gobble_iii\romannumeral`&&@#1}%
+\def\xintbareeval
+   {\expandafter\XINT_expr_until_end_a\romannumeral`&&@\XINT_expr_getnext }%
+\def\xintbarefloateval
+   {\expandafter\XINT_flexpr_until_end_a\romannumeral`&&@\XINT_expr_getnext }%
+\def\xintbareiieval
+   {\expandafter\XINT_iiexpr_until_end_a\romannumeral`&&@\XINT_expr_getnext }%
+\def\xintthebareeval      {\expandafter\XINT_expr_unlock\romannumeral0\xintbareeval}%
+\def\xintthebarefloateval {\expandafter\XINT_expr_unlock\romannumeral0\xintbarefloateval}%
+\def\xintthebareiieval    {\expandafter\XINT_expr_unlock\romannumeral0\xintbareiieval}%
+\def\xintboolexpr
+{%
+    \romannumeral0\expandafter\expandafter\expandafter
+    \XINT_boolexpr_done\expandafter\xint_gobble_iv\romannumeral0\xintexpro
+}%
+\def\XINT_boolexpr_done {!\XINT_expr_usethe\XINT_protectii\XINT_boolexpr_print}%
+\def\XINT_boolexpr_print #1{\xintIsTrue::csv {\XINT_expr_unlock #1}}%
+\def\xinttheboolexpr
+{%
+    \romannumeral`&&@\expandafter\expandafter\expandafter
+    \XINT_boolexpr_print\expandafter\xint_gobble_iv\romannumeral0\xintexpro
+}%
 \let\thexintboolexpr\xinttheboolexpr
-\def\XINT_boolexpr_done { !\XINT_expr_usethe\XINT_protectii\XINT_boolexpr_print }%
 \def\xintifboolexpr      #1{\romannumeral0\xintiiifnotzero {\xinttheexpr #1\relax}}%
 \def\xintifboolfloatexpr #1{\romannumeral0\xintiiifnotzero {\xintthefloatexpr #1\relax}}%
 \def\xintifbooliiexpr    #1{\romannumeral0\xintiiifnotzero {\xinttheiiexpr #1\relax}}%
 \def\xintifsgnexpr      #1{\romannumeral0\xintiiifsgn {\xinttheexpr #1\relax}}%
 \def\xintifsgnfloatexpr #1{\romannumeral0\xintiiifsgn {\xintthefloatexpr #1\relax}}%
 \def\xintifsgniiexpr    #1{\romannumeral0\xintiiifsgn {\xinttheiiexpr #1\relax}}%
-\let\XINT:NEhook:two\empty
+\def\xintthecoords  #1{\romannumeral`&&@\expandafter\expandafter\expandafter
+                     \XINT_thecoords_a
+                     \expandafter\xint_gobble_iii\romannumeral0#1}%
+\def\XINT_thecoords_a #1#2% #1=print macro, indispensible for scientific notation
+   {\expandafter\XINT_expr_unlock\csname.=\expandafter\XINT_thecoords_b
+                         \romannumeral`&&@#1#2,!,!,^\endcsname }%
+\def\XINT_thecoords_b #1#2,#3#4,%
+   {\xint_gob_til_! #3\XINT_thecoords_c ! (#1#2, #3#4)\XINT_thecoords_b }%
+\def\XINT_thecoords_c #1^{}%
+\def\xint_gob_til_! #1!{}% ! with catcode 11
+\def\XINT_expr_lockscan#1{% not used for decimal numbers in xintexpr 1.2
+\def\XINT_expr_lockscan##1!{\expandafter#1\csname .=##1\endcsname}%
+}\XINT_expr_lockscan{ }%
+\def\XINT_expr_lockit#1{%
+\def\XINT_expr_lockit##1{\expandafter#1\csname .=##1\endcsname}%
+}\XINT_expr_lockit{ }%
+\def\XINT_expr_unlock_hex_in #1%  expanded inside \csname..\endcsname
+   {\expandafter\XINT_expr_inhex\romannumeral`&&@\XINT_expr_unlock#1;}%
+\def\XINT_expr_inhex #1.#2#3;%    expanded inside \csname..\endcsname
+{%
+    \if#2>%
+      \xintHexToDec{#1}%
+    \else
+      \xintiiMul{\xintiiPow{625}{\xintLength{#3}}}{\xintHexToDec{#1#3}}%
+      [\the\numexpr-4*\xintLength{#3}]%
+    \fi
+}%
+\def\XINT_expr_unlock  {\expandafter\XINT_expr_unlock_a\string }%
+\def\XINT_expr_unlock_a #1.={}%
+\def\XINT_expr_unexpectedtoken {\xintError:ignored }%
+\let\XINT_expr_done\space
 \let\XINT:NEhook:one\empty
+\let\XINT:NEhook:two\empty
 \let\XINT:NEhook:csv\empty
+\def\XINT:NEhook:twosp #1,#2,!#3{#3{#1}{#2}}%
 \def\XINT_::_end #1,#2{\xint_gobble_i #2}%
 \def\xintCSV::csv #1{\expandafter\XINT_csv::_a\romannumeral`&&@#1,^,}%
 \def\XINT_csv::_a {\XINT_csv::_b {}}%
@@ -245,34 +257,39 @@
 \def\XINT_istrue::_d #1,{\expandafter\XINT_istrue::_e\romannumeral0\xintisnotzero {#1},}%
 \def\XINT_istrue::_e #1,#2{\XINT_istrue::_b {#2, #1}}%
 \def\XINT_:::_end #1,#2#3{\xint_gobble_i #3}%
-\def\xintRound::csv #1#2{\romannumeral0\expandafter\XINT_round::_b\expandafter
-    {\the\numexpr#1\expandafter}\expandafter{\expandafter}\romannumeral`&&@#2,^,}%
-\def\XINT_round::_b #1#2#3,{\expandafter\XINT_round::_c \romannumeral`&&@#3,{#1}{#2}}%
+\def\xintRound::csv #1#2{\romannumeral0\expandafter\XINT_round::_a
+    \the\numexpr#1\expandafter.\romannumeral`&&@#2,^,}%
+\def\XINT_round::_a #1.{\XINT_round::_b #1.{}}%
+\def\XINT_round::_b #1.#2#3,{\expandafter\XINT_round::_c \romannumeral`&&@#3,{#1}{#2}}%
 \def\XINT_round::_c #1{\if ,#1\xint_dothis\XINT_round::_e\fi
                        \if ^#1\xint_dothis\XINT_:::_end\fi
                        \xint_orthat\XINT_round::_d #1}%
 \def\XINT_round::_d #1,#2{%
       \expandafter\XINT_round::_e\romannumeral0\ifnum#2>\xint_c_
       \expandafter\xintround\else\expandafter\xintiround\fi {#2}{#1},{#2}}%
-\def\XINT_round::_e #1,#2#3{\XINT_round::_b {#2}{#3, #1}}%
-\def\XINTinFloat::csv #1#2{\romannumeral0\expandafter\XINT_infloat::_b\expandafter
-   {\the\numexpr #1\expandafter}\expandafter{\expandafter}\romannumeral`&&@#2,^,}%
-\def\XINT_infloat::_b #1#2#3,{\XINT_infloat::_c #3,{#1}{#2}}%
+\def\XINT_round::_e #1,#2#3{\XINT_round::_b #2.{#3, #1}}%
+\def\XINTinFloat::csv #1#2{\romannumeral0\expandafter\XINT_infloat::_a
+   \the\numexpr #1\expandafter.\romannumeral`&&@#2,^,}%
+\def\XINT_infloat::_a #1#2.%
+   {\expandafter\XINT_infloat::_b\the\numexpr\if#1-\XINTdigits\fi#1#2.{}}%
+\def\XINT_infloat::_b #1.#2#3,{\XINT_infloat::_c #3,{#1}{#2}}%
 \def\XINT_infloat::_c #1{\if ,#1\xint_dothis\XINT_infloat::_e\fi
                        \if ^#1\xint_dothis\XINT_:::_end\fi
                        \xint_orthat\XINT_infloat::_d #1}%
 \def\XINT_infloat::_d #1,#2%
         {\expandafter\XINT_infloat::_e\romannumeral0\XINTinfloat [#2]{#1},{#2}}%
-\def\XINT_infloat::_e #1,#2#3{\XINT_infloat::_b {#2}{#3, #1}}%
-\def\xintPFloat::csv #1#2{\romannumeral0\expandafter\XINT_pfloat::_b\expandafter
-   {\the\numexpr #1\expandafter}\expandafter{\expandafter}\romannumeral`&&@#2,^,}%
-\def\XINT_pfloat::_b #1#2#3,{\expandafter\XINT_pfloat::_c \romannumeral`&&@#3,{#1}{#2}}%
+\def\XINT_infloat::_e #1,#2#3{\XINT_infloat::_b #2.{#3, #1}}%
+\def\xintPFloat::csv #1#2{\romannumeral0\expandafter\XINT_pfloat::_a
+    \the\numexpr #1\expandafter.\romannumeral`&&@#2,^,}%
+\def\XINT_pfloat::_a #1#2.%
+   {\expandafter\XINT_pfloat::_b\the\numexpr\if#1-\XINTdigits\fi#1#2.{}}%
+\def\XINT_pfloat::_b #1.#2#3,{\expandafter\XINT_pfloat::_c \romannumeral`&&@#3,{#1}{#2}}%
 \def\XINT_pfloat::_c #1{\if ,#1\xint_dothis\XINT_pfloat::_e\fi
                        \if ^#1\xint_dothis\XINT_:::_end\fi
                        \xint_orthat\XINT_pfloat::_d #1}%
 \def\XINT_pfloat::_d #1,#2%
  {\expandafter\XINT_pfloat::_e\romannumeral0\XINT_pfloat_opt [\xint:#2]{#1},{#2}}%
-\def\XINT_pfloat::_e #1,#2#3{\XINT_pfloat::_b {#2}{#3, #1}}%
+\def\XINT_pfloat::_e #1,#2#3{\XINT_pfloat::_b #2.{#3, #1}}%
 \def\XINT_expr_getnext #1%
 {%
     \expandafter\XINT_expr_getnext_a\romannumeral`&&@#1%
@@ -1446,7 +1463,7 @@
 \def\XINT_expr_onliteral_qfrac #1)%
         {\expandafter\XINT_expr_getop\csname .=\xintRaw{#1}\endcsname }%
 \def\XINT_expr_onliteral_qfloat #1)%
-        {\expandafter\XINT_expr_getop\csname .=\XINTinFloatdigits{#1}\endcsname }%
+        {\expandafter\XINT_expr_getop\csname .=\XINTinFloatSdigits{#1}\endcsname }%
 \def\XINT_expr_onliteral_qraw #1)%
         {\expandafter\XINT_expr_getop\csname .=#1\endcsname }%
 \def\XINT_expr_onliteral_random #1)%
@@ -1486,44 +1503,44 @@
 \catcode`~ 13
 \catcode`: 12
 \def\XINT_expr_defvar_getname #1:#2~{\endgroup
-    \def\XINT_expr_tmpa{#1}\edef\XINT_expr_tmpc{\xintCSVLength{#1}}}%
+    \def\XINT_defvar_tmpa{#1}\edef\XINT_defvar_tmpc{\xintCSVLength{#1}}}%
 \def\XINT_expr_defvar #1#2#3;%
 {%
     \xintexprRestoreCatcodes
     \begingroup\lccode`~`: \lowercase{\let~}\empty
-    \edef\XINT_expr_tmpa{#2}%
-    \edef\XINT_expr_tmpa{\xint_zapspaces_o\XINT_expr_tmpa}%
+    \edef\XINT_defvar_tmpa{#2}%
+    \edef\XINT_defvar_tmpa{\xint_zapspaces_o\XINT_defvar_tmpa}%
     \expandafter\XINT_expr_defvar_getname
-                \detokenize\expandafter{\XINT_expr_tmpa}:~%
-    \ifcase\XINT_expr_tmpc
+                \detokenize\expandafter{\XINT_defvar_tmpa}:~%
+    \ifcase\XINT_defvar_tmpc\space
       \xintMessage {xintexpr}{Warning}
       {Aborting: not allowed to declare variable with empty name.}%
     \or
-     \edef\XINT_expr_tmpb{\romannumeral0#1#3\relax}%
-     \XINT_expr_defvar_one\XINT_expr_tmpa\XINT_expr_tmpb
+     \edef\XINT_defvar_tmpb{\romannumeral0#1#3\relax}%
+     \XINT_expr_defvar_one\XINT_defvar_tmpa\XINT_defvar_tmpb
     \else
-     \edef\XINT_expr_tmpb
+     \edef\XINT_defvar_tmpb
         {\expandafter\XINT_expr_unlock\romannumeral0#1#3\relax}%
-     \edef\XINT_expr_tmpd{\xintCSVLength{\XINT_expr_tmpb}}%
-     \ifnum\XINT_expr_tmpc=\XINT_expr_tmpd\space
-       \xintAssignArray\xintCSVtoList\XINT_expr_tmpa\to\XINT_expr_tmpvar
+     \edef\XINT_defvar_tmpd{\xintCSVLength{\XINT_defvar_tmpb}}%
+     \ifnum\XINT_defvar_tmpc=\XINT_defvar_tmpd\space
+       \xintAssignArray\xintCSVtoList\XINT_defvar_tmpa\to\XINT_defvar_tmpvar
        \xintAssignArray
-         \xintApply\XINT_expr_lockit{\xintCSVtoList\XINT_expr_tmpb}%
-       \to\XINT_expr_tmpval
-       \def\XINT_expr_tmpd{1}%
+         \xintApply\XINT_expr_lockit{\xintCSVtoList\XINT_defvar_tmpb}%
+       \to\XINT_defvar_tmpval
+       \def\XINT_defvar_tmpd{1}%
        \xintloop
            \expandafter\XINT_expr_defvar_one
-           \csname XINT_expr_tmpvar\XINT_expr_tmpd\expandafter\endcsname
-           \csname XINT_expr_tmpval\XINT_expr_tmpd\endcsname
-       \ifnum\XINT_expr_tmpd<\XINT_expr_tmpc\space
-           \edef\XINT_expr_tmpd{\the\numexpr\XINT_expr_tmpd+1}%
+           \csname XINT_defvar_tmpvar\XINT_defvar_tmpd\expandafter\endcsname
+           \csname XINT_defvar_tmpval\XINT_defvar_tmpd\endcsname
+       \ifnum\XINT_defvar_tmpd<\XINT_defvar_tmpc\space
+           \edef\XINT_defvar_tmpd{\the\numexpr\XINT_defvar_tmpd+1}%
        \repeat
-       \xintRelaxArray\XINT_expr_tmpvar
-       \xintRelaxArray\XINT_expr_tmpval
+       \xintRelaxArray\XINT_defvar_tmpvar
+       \xintRelaxArray\XINT_defvar_tmpval
      \else
        \xintMessage {xintexpr}{Warning}
-        {Aborting: mismatch between number of variables (\XINT_expr_tmpc)
-         and number of values (\XINT_expr_tmpd).}%
+        {Aborting: mismatch between number of variables (\XINT_defvar_tmpc)
+         and number of values (\XINT_defvar_tmpd).}%
      \fi
     \fi
 }%
@@ -1536,29 +1553,39 @@
 \def\xintdefiivar_a    #1={\XINT_expr_defvar\xintbareiieval    {#1}}%
 \def\xintdeffloatvar_a #1={\XINT_expr_defvar\xintbarefloateval {#1}}%
 \def\xintunassignvar #1{%
-   \edef\XINT_expr_tmpa{#1}%
-   \edef\XINT_expr_tmpa {\xint_zapspaces_o\XINT_expr_tmpa}%
-   \ifcsname XINT_expr_var_\XINT_expr_tmpa\endcsname
-       \ifnum\expandafter\xintLength\expandafter{\XINT_expr_tmpa}=\@ne
-         \expandafter\xintnewdummy\XINT_expr_tmpa
+   \edef\XINT_unvar_tmpa{#1}%
+   \edef\XINT_unvar_tmpa {\xint_zapspaces_o\XINT_unvar_tmpa}%
+   \ifcsname XINT_expr_var_\XINT_unvar_tmpa\endcsname
+       \ifnum\expandafter\xintLength\expandafter{\XINT_unvar_tmpa}=\@ne
+         \expandafter\xintnewdummy\XINT_unvar_tmpa
        \else
          \XINT_global\expandafter
-           \let\csname XINT_expr_var_\XINT_expr_tmpa\endcsname\xint_undefined
+           \let\csname XINT_expr_var_\XINT_unvar_tmpa\endcsname\xint_undefined
          \XINT_global\expandafter
-           \let\csname XINT_expr_onliteral_\XINT_expr_tmpa\endcsname\xint_undefined
+           \let\csname XINT_expr_onliteral_\XINT_unvar_tmpa\endcsname\xint_undefined
          \ifxintverbose\xintMessage {xintexpr}{Info}
-           {Variable \XINT_expr_tmpa\space has been
+           {Variable \XINT_unvar_tmpa\space has been
             \ifxintglobaldefs globally \fi ``unassigned''.}%
          \fi
        \fi
    \else
        \xintMessage {xintexpr}{Warning}
-           {Error: there was no such variable \XINT_expr_tmpa\space to unassign.}%
+           {Error: there was no such variable \XINT_unvar_tmpa\space to unassign.}%
    \fi
 }%
 \catcode`* 11
 \def\XINT_expr_makedummy #1%
 {%
+   \ifcsname XINT_expr_var_#1\endcsname
+     \XINT_global
+     \expandafter\let\csname XINT_expr_var_#1/old\expandafter\endcsname
+                     \csname XINT_expr_var_#1\expandafter\endcsname
+   \fi
+   \ifcsname XINT_expr_onliteral_#1\endcsname
+     \XINT_global
+     \expandafter\let\csname XINT_expr_onliteral_#1/old\expandafter\endcsname
+                     \csname XINT_expr_onliteral_#1\expandafter\endcsname
+   \fi
    \XINT_global
    \expandafter\def\csname XINT_expr_var_#1\endcsname ##1\relax !#1##2%
       {##2##1\relax !#1##2}%
@@ -1579,6 +1606,30 @@
 \edef\XINT_expr_onliteral_nil
       {\XINT_expr_precedence_*** *\expandafter\noexpand\csname .= \endcsname (}%
 \catcode`* 12
+\def\xintensuredummy #1{%
+    \XINT_expr_makedummy{#1}%
+    \ifxintverbose\xintMessage {xintexpr}{Info}%
+       {#1 (with letter catcode) now
+        \ifxintglobaldefs globally \fi usable as dummy variable.&&J
+        Use \string\xintrestoredummy{#1} to restore it to its former meaning.}%
+    \fi
+}%
+\def\xintrestorelettervar #1{%
+   \ifcsname XINT_expr_var_#1/old\endcsname
+     \XINT_global
+     \expandafter\let\csname XINT_expr_var_#1\expandafter\endcsname
+                     \csname XINT_expr_var_#1/old\expandafter\endcsname
+   \fi
+   \ifcsname XINT_expr_onliteral_#1/old\endcsname
+     \XINT_global
+     \expandafter\let\csname XINT_expr_onliteral_#1\expandafter\endcsname
+                     \csname XINT_expr_onliteral_#1/old\expandafter\endcsname
+   \fi
+    \ifxintverbose\xintMessage {xintexpr}{Info}%
+       {Character #1 (with letter catcode)
+        \ifxintglobaldefs globally \fi restored to its earlier status, if any.}%
+    \fi
+}%
 \edef\XINT_expr_var_omit  #1\relax !{1\string !?!\relax !}%
 \edef\XINT_expr_var_abort #1\relax !{1\string !?^\relax !}%
 \def\XINT_expr_op_!? #1#2\relax {\expandafter\XINT_expr_foundend\csname .=#2\endcsname}%
@@ -2114,16 +2165,18 @@
 \def\xintiiLCMof:csv #1{\expandafter\XINT_oncsv:_a\expandafter\xintiilcm
                       \expandafter\xint_firstofone\romannumeral`&&@#1,^,0}%
 \def\XINTinFloatdigits     {\XINTinFloat    [\XINTdigits]}%
+\def\XINTinFloatSdigits    {\XINTinFloatS   [\XINTdigits]}%
 \def\XINTinFloatSqrtdigits {\XINTinFloatSqrt[\XINTdigits]}%
 \def\XINTinFloatFacdigits  {\XINTinFloatFac [\XINTdigits]}%
+\def\XINTFloatiLogTendigits{\XINTFloatiLogTen[\XINTdigits]}%
 \def\XINTinFloatMaxof:csv #1{\expandafter\XINT_oncsv:_a\expandafter\xintmax
-                         \expandafter\XINTinFloatdigits\romannumeral`&&@#1,^,{0[0]}}%
+                         \expandafter\XINTinFloatSdigits\romannumeral`&&@#1,^,{0[0]}}%
 \def\XINTinFloatMinof:csv #1{\expandafter\XINT_oncsv:_a\expandafter\xintmin
-                         \expandafter\XINTinFloatdigits\romannumeral`&&@#1,^,{0[0]}}%
+                         \expandafter\XINTinFloatSdigits\romannumeral`&&@#1,^,{0[0]}}%
 \def\XINTinFloatSum:csv #1{\expandafter\XINT_oncsv:_a\expandafter\XINTinfloatadd
-                        \expandafter\XINTinFloatdigits\romannumeral`&&@#1,^,{0[0]}}%
+                        \expandafter\XINTinFloatSdigits\romannumeral`&&@#1,^,{0[0]}}%
 \def\XINTinFloatPrd:csv #1{\expandafter\XINT_oncsv:_a\expandafter\XINTinfloatmul
-                        \expandafter\XINTinFloatdigits\romannumeral`&&@#1,^,{1[0]}}%
+                        \expandafter\XINTinFloatSdigits\romannumeral`&&@#1,^,{1[0]}}%
 \def\XINT:expr:one:and:opt #1,#2,#3!#4#5%
 {%
     \if\relax#3\relax\expandafter\xint_firstoftwo\else
@@ -2145,18 +2198,10 @@
 \def\XINT:expr:totwo #1#2{#1,#2}%
 \def\XINT:expr:two:to:two #1,#2,!#3%
 {%
-    \expandafter\XINT:expr:totwo\romannumeral`&&@%
-    #3{#1}{#2}%
+    \expandafter\XINT:expr:totwo\romannumeral`&&@#3{#1}{#2}%
 }%
-\def\XINT:expr:two:to:one #1,#2,!#3%
-{%
-    #3{#1}{#2}%
-}%
-\def\XINT:flexpr:two:to:one #1,#2,!#3%
-{%
-    #3{#1}{#2}%
-}%
-\let\XINT:flexpr:two:to:two\XINT:flexpr:two:to:one
+\let\XINT:flexpr:two:to:two\XINT:expr:two:to:two
+\let\XINT:iiexpr:two:to:two\XINT:expr:two:to:two
 \def\XINT_expr_func_num #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
@@ -2352,6 +2397,16 @@
     \expandafter #1\expandafter #2\csname.=%
     \XINT:NEhook:one\xintiiSqrtR{\XINT_expr_unlock #3}\endcsname
 }%
+\def\XINT_expr_func_inv #1#2#3%
+{%
+    \expandafter #1\expandafter #2\csname.=%
+    \XINT:NEhook:one\xintInv{\XINT_expr_unlock #3}\endcsname
+}%
+\def\XINT_flexpr_func_inv #1#2#3%
+{%
+    \expandafter #1\expandafter #2\csname.=%
+    \XINT:NEhook:one\XINTinFloatInv{\XINT_expr_unlock #3}\endcsname
+}%
 \def\XINT_expr_func_round #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
@@ -2390,6 +2445,33 @@
     \endcsname
 }%
 \let\XINT_flexpr_func_float\XINT_expr_func_float
+\def\XINT_expr_func_sfloat #1#2#3%
+{%
+    \expandafter #1\expandafter #2\csname.=%
+    \expandafter\XINT:expr:one:and:opt
+    \romannumeral`&&@\XINT_expr_unlock #3,,!\XINTinFloatSdigits\XINTinFloatS
+    \endcsname
+}%
+\let\XINT_flexpr_func_sfloat\XINT_expr_func_sfloat
+\expandafter\def\csname XINT_expr_func_ilog10\endcsname #1#2#3%
+{%
+    \expandafter #1\expandafter #2\csname.=%
+    \expandafter\XINT:expr:one:and:opt
+    \romannumeral`&&@\XINT_expr_unlock #3,,!\xintiLogTen\XINTFloatiLogTen
+    \endcsname
+}%
+\expandafter\def\csname XINT_flexpr_func_ilog10\endcsname #1#2#3%
+{%
+    \expandafter #1\expandafter #2\csname.=%
+    \expandafter\XINT:expr:one:and:opt
+    \romannumeral`&&@\XINT_expr_unlock #3,,!\XINTFloatiLogTendigits\XINTFloatiLogTen
+    \endcsname
+}%
+\expandafter\def\csname XINT_iiexpr_func_ilog10\endcsname #1#2#3%
+{%
+    \expandafter #1\expandafter #2\csname.=%
+    \XINT:NEhook:one\xintiiLogTen{\XINT_expr_unlock #3}\endcsname
+}%
 \def\XINT_expr_func_divmod #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
@@ -2400,7 +2482,7 @@
 \def\XINT_flexpr_func_divmod #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
-    \expandafter\XINT:flexpr:two:to:two
+    \expandafter\XINT:NEhook:twosp
     \romannumeral`&&@\XINT_expr_unlock #3,!\XINTinFloatDivMod
     \endcsname
 }%
@@ -2414,63 +2496,63 @@
 \def\XINT_expr_func_mod #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
-    \expandafter\XINT:expr:two:to:one
+    \expandafter\XINT:NEhook:twosp
     \romannumeral`&&@\XINT_expr_unlock #3,!\xintMod
     \endcsname
 }%
 \def\XINT_flexpr_func_mod #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
-    \expandafter\XINT:flexpr:two:to:one
+    \expandafter\XINT:NEhook:twosp
     \romannumeral`&&@\XINT_expr_unlock #3,!\XINTinFloatMod
     \endcsname
 }%
 \def\XINT_iiexpr_func_mod #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
-    \expandafter\XINT:expr:two:to:one
+    \expandafter\XINT:NEhook:twosp
     \romannumeral`&&@\XINT_expr_unlock #3,!\xintiiMod
     \endcsname
 }%
 \def\XINT_expr_func_binomial #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
-    \expandafter\XINT:expr:two:to:one
+    \expandafter\XINT:NEhook:twosp
     \romannumeral`&&@\XINT_expr_unlock #3,!\xintBinomial
     \endcsname
 }%
 \def\XINT_flexpr_func_binomial #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
-    \expandafter\XINT:flexpr:two:to:one
+    \expandafter\XINT:NEhook:twosp
     \romannumeral`&&@\XINT_expr_unlock #3,!\XINTinFloatBinomial
     \endcsname
 }%
 \def\XINT_iiexpr_func_binomial #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
-    \expandafter\XINT:expr:two:to:one
+    \expandafter\XINT:NEhook:twosp
     \romannumeral`&&@\XINT_expr_unlock #3,!\xintiiBinomial
     \endcsname
 }%
 \def\XINT_expr_func_pfactorial #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
-    \expandafter\XINT:expr:two:to:one
+    \expandafter\XINT:NEhook:twosp
     \romannumeral`&&@\XINT_expr_unlock #3,!\xintPFactorial
     \endcsname
 }%
 \def\XINT_flexpr_func_pfactorial #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
-    \expandafter\XINT:flexpr:two:to:one
+    \expandafter\XINT:NEhook:twosp
     \romannumeral`&&@\XINT_expr_unlock #3,!\XINTinFloatPFactorial
     \endcsname
 }%
 \def\XINT_iiexpr_func_pfactorial #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
-    \expandafter\XINT:expr:two:to:one
+    \expandafter\XINT:NEhook:twosp
     \romannumeral`&&@\XINT_expr_unlock #3,!\xintiiPFactorial
     \endcsname
 }%
@@ -2506,7 +2588,7 @@
 \def\XINT_expr_func_quo #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
-    \expandafter\XINT:expr:two:to:one
+    \expandafter\XINT:NEhook:twosp
     \romannumeral`&&@\XINT_expr_unlock #3,!\xintiQuo
     \endcsname
 }%
@@ -2514,14 +2596,14 @@
 \def\XINT_iiexpr_func_quo #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
-    \expandafter\XINT:expr:two:to:one
+    \expandafter\XINT:NEhook:twosp
     \romannumeral`&&@\XINT_expr_unlock #3,!\xintiiQuo
     \endcsname
 }%
 \def\XINT_expr_func_rem #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
-    \expandafter\XINT:expr:two:to:one
+    \expandafter\XINT:NEhook:twosp
     \romannumeral`&&@\XINT_expr_unlock #3,!\xintiRem
     \endcsname
 }%
@@ -2529,7 +2611,7 @@
 \def\XINT_iiexpr_func_rem #1#2#3%
 {%
     \expandafter #1\expandafter #2\csname.=%
-    \expandafter\XINT:expr:two:to:one
+    \expandafter\XINT:NEhook:twosp
     \romannumeral`&&@\XINT_expr_unlock #3,!\xintiiRem
     \endcsname
 }%
@@ -2806,25 +2888,32 @@
 \def\XINT_tmpa #1#2#3#4%
 {%
   \def #1##1(##2)##3=##4;{%
-   \edef\XINT_expr_tmpa {##1}%
-   \edef\XINT_expr_tmpa {\xint_zapspaces_o \XINT_expr_tmpa}%
-   \def\XINT_expr_tmpb {0}%
-   \def\XINT_expr_tmpc {(##4)}%
-   \xintFor ####1 in {##2} \do
-      {\edef\XINT_expr_tmpb {\the\numexpr\XINT_expr_tmpb+\xint_c_i}%
-       \edef\XINT_expr_tmpc {subs(\unexpanded\expandafter{\XINT_expr_tmpc},%
-                             ####1=################\XINT_expr_tmpb)}%
+   \edef\XINT_deffunc_tmpa {##1}%
+   \edef\XINT_deffunc_tmpa {\xint_zapspaces_o \XINT_deffunc_tmpa}%
+   \def\XINT_deffunc_tmpb {0}%
+   \def\XINT_deffunc_tmpc {(##4)}%
+   \edef\XINT_deffunc_tmpd {##2}%
+   \ifnum\xintLength:f:csv{\XINT_deffunc_tmpd}>\xint_c_
+     \xintFor ####1 in {\XINT_deffunc_tmpd}\do
+      {\edef\XINT_deffunc_tmpb {\the\numexpr\XINT_deffunc_tmpb+\xint_c_i}%
+       \edef\XINT_deffunc_tmpc {subs(\unexpanded\expandafter{\XINT_deffunc_tmpc},%
+                             ####1=################\XINT_deffunc_tmpb)}%
       }%
-   \expandafter\XINT_expr_defuserfunc
-     \csname XINT_#2_func_\XINT_expr_tmpa\expandafter\endcsname
-     \expandafter{\XINT_expr_tmpa}{#2}%
-   \expandafter#3\csname XINT_#2_userfunc_\XINT_expr_tmpa\endcsname
-                              [\XINT_expr_tmpb]{\XINT_expr_tmpc}%
+   \fi
+   \ifnum\XINT_deffunc_tmpb=\xint_c_
+    \expandafter\XINT_expr_defuserfunc_none\csname
+   \else
+   \expandafter\XINT_expr_defuserfunc\csname
+   \fi
+      XINT_#2_func_\XINT_deffunc_tmpa\expandafter\endcsname
+     \expandafter{\XINT_deffunc_tmpa}{#2}%
+   \expandafter#3\csname XINT_#2_userfunc_\XINT_deffunc_tmpa\endcsname
+                              [\XINT_deffunc_tmpb]{\XINT_deffunc_tmpc}%
    \ifxintverbose\xintMessage {xintexpr}{Info}
-        {Function \XINT_expr_tmpa\space for \string\xint #4 parser
-         associated to \string\XINT_#2_userfunc_\XINT_expr_tmpa\space
+        {Function \XINT_deffunc_tmpa\space for \string\xint #4 parser
+         associated to \string\XINT_#2_userfunc_\XINT_deffunc_tmpa\space
          with \ifxintglobaldefs global \fi meaning \expandafter\meaning
-         \csname XINT_#2_userfunc_\XINT_expr_tmpa\endcsname}%
+         \csname XINT_#2_userfunc_\XINT_deffunc_tmpa\endcsname}%
    \fi
    \xintexprRestoreCatcodes
   }%
@@ -2839,34 +2928,157 @@
 {%
     \XINT_global
     \def #1##1##2##3{\expandafter ##1\expandafter ##2%
-     \csname .=\XINT:expr:userfunc{#3}{#2}{\XINT_expr_unlock ##3}\endcsname
+     \csname.=\XINT:expr:userfunc{#3}{#2}{\XINT_expr_unlock ##3}\endcsname
     }%
 }%
 \def\XINT:expr:userfunc #1#2#3%
-   {\csname XINT_#1_userfunc_#2\expandafter\endcsname
-    \romannumeral0\xintcsvtolistnonstripped{#3}}%
-\catcode`~ 12
-\def\XINT:newexpr:userfunc #1#2#3%
-   {~xintExpandArgs{XINT_#1_userfunc_#2}{\xintCSVtoListNonStripped{#3}}}%
-\catcode`~ 3
+{%
+    \csname XINT_#1_userfunc_#2\expandafter\endcsname
+       \romannumeral0\xintcsvtolistnonstripped{#3}%
+}%
+\def\XINT_expr_defuserfunc_none #1#2#3%
+{%
+    \XINT_global
+    \def #1##1##2##3{\expandafter ##1\expandafter ##2%
+     \csname.=\XINT:expr:userfunc:none{#3}{#2}\endcsname
+    }%
+}%
+\def\XINT:expr:userfunc:none #1#2{\csname XINT_#1_userfunc_#2\endcsname}%
+\def\XINT_tmpa #1#2#3#4%
+{%
+  \def #1##1(##2)##3=##4;{%
+   \edef\XINT_defefunc_tmpa {##1}%
+   \edef\XINT_defefunc_tmpa {\xint_zapspaces_o \XINT_defefunc_tmpa}%
+   \def\XINT_defefunc_tmpb {0}%
+   \def\XINT_defefunc_tmpc {(##4)}%
+   \edef\XINT_defefunc_tmpd {##2}%
+   \ifnum\xintLength:f:csv{\XINT_defefunc_tmpd}>\xint_c_
+     \xintFor ####1 in {\XINT_defefunc_tmpd}\do
+      {\edef\XINT_defefunc_tmpb {\the\numexpr\XINT_defefunc_tmpb+\xint_c_i}%
+       \edef\XINT_defefunc_tmpc {subs(\unexpanded\expandafter{\XINT_defefunc_tmpc},%
+                             ####1=################\XINT_defefunc_tmpb)}%
+      }%
+   \fi
+   \expandafter#3\csname XINT_#2_userefunc_\XINT_defefunc_tmpa\endcsname
+                              [\XINT_defefunc_tmpb]{\XINT_defefunc_tmpc}%
+   \edef\XINT_defefunc_tmpd{\xintLength:f:csv
+       {\expandafter\meaning\csname
+         XINT_#2_userfunc_\XINT_defefunc_tmpa\endcsname}}%
+   \ifcase\XINT_defefunc_tmpb\space
+    \expandafter\XINT_expr_defuserefunc_none\csname
+   \or
+        \expandafter\XINT_expr_defuserefunc_one\csname
+   \or
+        \expandafter\XINT_expr_defuserefunc_two\csname
+   \else
+        \expandafter\XINT_expr_defuserefunc_many\csname
+   \fi
+      XINT_#2_func_\XINT_defefunc_tmpa\expandafter\endcsname
+     \expandafter{\XINT_defefunc_tmpa}{#2}%
+   \ifxintverbose\xintMessage {xintexpr}{Info}
+        {Function \XINT_defefunc_tmpa\space for \string\xint #4 parser
+         associated to \string\XINT_#2_userefunc_\XINT_defefunc_tmpa\space
+         with \ifxintglobaldefs global \fi meaning \expandafter\meaning
+         \csname XINT_#2_userefunc_\XINT_defefunc_tmpa\endcsname}%
+   \fi
+   \xintexprRestoreCatcodes
+  }%
+}%
+\def\xintdefefunc      {\xintexprSafeCatcodes\xintdefefunc_a}%
+\def\xintdefiiefunc    {\xintexprSafeCatcodes\xintdefiiefunc_a}%
+\def\xintdeffloatefunc {\xintexprSafeCatcodes\xintdeffloatefunc_a}%
+\XINT_tmpa\xintdefefunc_a     {expr}  \XINT_NewFunc     {expr}%
+\XINT_tmpa\xintdefiiefunc_a   {iiexpr}\XINT_NewIIFunc   {iiexpr}%
+\XINT_tmpa\xintdeffloatefunc_a{flexpr}\XINT_NewFloatFunc{floatexpr}%
+\def\XINT_expr_defuserefunc_none #1#2#3%
+{%
+    \expandafter\XINT_expr_defuserefunc_none_a
+    \csname XINT_#3_userefunc_#2\endcsname
+}%
+\def\XINT_expr_defuserefunc_none_a #1#2%
+{%
+    \XINT_global
+    \def #2##1##2##3{\expandafter ##1\expandafter ##2\csname.=#1\endcsname}%
+}%
+\def\XINT_expr_defuserefunc_one #1#2#3%
+{%
+    \expandafter\XINT_expr_defuserefunc_one_a
+    \csname XINT_#3_userefunc_#2\expandafter\endcsname
+    \csname XINT_#3_userefunc:f_#2\endcsname #1{#2}{#3}%
+}%
+\def\XINT_expr_defuserefunc_one_a #1#2#3#4#5%
+{%
+    \XINT_global
+    \def #2##1{\expandafter#1\expandafter{\romannumeral`&&@##1}}%
+    \XINT_global
+    \def #3##1##2##3%
+    {%
+       \expandafter ##1\expandafter ##2%
+       \csname.=\XINT:expr:userefunc:one{#5}{#4}{\XINT_expr_unlock##3}\endcsname
+    }%
+}%
+\def\XINT:expr:userefunc:one #1#2#3%
+{%
+    \csname XINT_#1_userefunc_#2\expandafter\endcsname\expandafter
+    {\romannumeral`&&@#3}%
+}%
+\def\XINT_expr_defuserefunc_two #1#2#3%
+{%
+    \expandafter\XINT_expr_defuserefunc_two_a
+    \csname XINT_#3_userefunc:f_#2\endcsname #1{#2}{#3}%
+}%
+\def\XINT_expr_defuserefunc_two_a #1#2#3#4%
+{%
+    \XINT_global
+    \def #1##1##2{\xintExpandArgs{XINT_#4_userefunc_#3}{{##1}{##2}}}%
+    \XINT_global
+    \def #2##1##2##3%
+    {%
+       \expandafter ##1\expandafter ##2%
+       \csname.=\XINT:expr:userefunc:two{#4}{#3}{\XINT_expr_unlock##3}\endcsname
+    }%
+}%
+\def\XINT:expr:userefunc:two #1#2#3%
+{%
+    \expandafter\XINT:expr:userefunc:two_a
+    \csname XINT_#1_userefunc_#2\expandafter\endcsname
+    \romannumeral`&&@#3,%
+}%
+\def\XINT:expr:userefunc:two_a #1#2,#3,{#1{#2}{#3}}%
+\def\XINT_expr_defuserefunc_many #1#2#3%
+{%
+    \XINT_global
+    \def #1##1##2##3%
+    {%
+         \expandafter ##1\expandafter ##2%
+         \csname.=\XINT:expr:userefunc{#3}{#2}{\XINT_expr_unlock##3}\endcsname
+    }%
+}%
+\def\XINT:expr:userefunc #1#2#3%
+{%
+    \csname XINT_#1_userefunc_#2\expandafter\endcsname
+       \romannumeral0\xintcsvtolistnonstripped{#3}%
+}%
 \def\XINT_tmpa #1{\expandafter\def\csname xintunassign#1func\endcsname ##1{%
-   \edef\XINT_expr_tmpa{##1}%
-   \edef\XINT_expr_tmpa {\xint_zapspaces_o\XINT_expr_tmpa}%
+   \edef\XINT_unfunc_tmpa{##1}%
+   \edef\XINT_unfunc_tmpa {\xint_zapspaces_o\XINT_unfunc_tmpa}%
+   \XINT_global\expandafter
+     \let\csname XINT_#1_func_\XINT_unfunc_tmpa\endcsname\xint_undefined
    \XINT_global\expandafter
-     \let\csname XINT_#1_func_\XINT_expr_tmpa\endcsname\xint_undefined
+     \let\csname XINT_#1_userfunc_\XINT_unfunc_tmpa\endcsname\xint_undefined
    \XINT_global\expandafter
-     \let\csname XINT_#1_userfunc_\XINT_expr_tmpa\endcsname\xint_undefined
+     \let\csname XINT_#1_userefunc_\XINT_unfunc_tmpa\endcsname\xint_undefined
    \ifxintverbose\xintMessage {xintexpr}{Info}
-    {Function \XINT_expr_tmpa\space for \string\xint #1 parser now
+    {Function \XINT_unfunc_tmpa\space for \string\xint #1 parser now
      \ifxintglobaldefs globally \fi undefined.}%
    \fi}}%
 \XINT_tmpa{expr}\XINT_tmpa{iiexpr}\XINT_tmpa{floatexpr}%
 \def\XINT_expr_wrapit #1{\expandafter\XINT_expr_wrap\csname.=#1\endcsname}%
 \def\xintNewFunction #1#2[#3]#4%
 {%
-  \edef\XINT_expr_tmpa {#1}%
-  \edef\XINT_expr_tmpa {\xint_zapspaces_o \XINT_expr_tmpa}%
-  \def\XINT_expr_tmpb ##1##2##3##4##5##6##7##8##9{#4}%
+  \edef\XINT_newfunc_tmpa {#1}%
+  \edef\XINT_newfunc_tmpa {\xint_zapspaces_o \XINT_newfunc_tmpa}%
+  \def\XINT_newfunc_tmpb ##1##2##3##4##5##6##7##8##9{#4}%
   \begingroup
     \ifcase #3\relax
         \toks0{}%
@@ -2883,26 +3095,26 @@
     \expandafter
   \endgroup\expandafter
   \XINT_global\expandafter
-  \def\csname XINT_expr_macrofunc_\XINT_expr_tmpa\expandafter\endcsname
-  \the\toks0\expandafter{\XINT_expr_tmpb
+  \def\csname XINT_expr_macrofunc_\XINT_newfunc_tmpa\expandafter\endcsname
+  \the\toks0\expandafter{\XINT_newfunc_tmpb
     {\XINT_expr_wrapit{##1}}{\XINT_expr_wrapit{##2}}{\XINT_expr_wrapit{##3}}%
     {\XINT_expr_wrapit{##4}}{\XINT_expr_wrapit{##5}}{\XINT_expr_wrapit{##6}}%
     {\XINT_expr_wrapit{##7}}{\XINT_expr_wrapit{##8}}{\XINT_expr_wrapit{##9}}}%
   \expandafter\XINT_expr_newfunction
-    \csname XINT_expr_func_\XINT_expr_tmpa\expandafter\endcsname
-    \expandafter{\XINT_expr_tmpa}{eval}\xintbareeval
+    \csname XINT_expr_func_\XINT_newfunc_tmpa\expandafter\endcsname
+    \expandafter{\XINT_newfunc_tmpa}{eval}\xintbareeval
   \expandafter\XINT_expr_newfunction
-    \csname XINT_iiexpr_func_\XINT_expr_tmpa\expandafter\endcsname
-    \expandafter{\XINT_expr_tmpa}{iieval}\xintbareiieval
+    \csname XINT_iiexpr_func_\XINT_newfunc_tmpa\expandafter\endcsname
+    \expandafter{\XINT_newfunc_tmpa}{iieval}\xintbareiieval
   \expandafter\XINT_expr_newfunction
-    \csname XINT_flexpr_func_\XINT_expr_tmpa\expandafter\endcsname
-    \expandafter{\XINT_expr_tmpa}{floateval}\xintbarefloateval
+    \csname XINT_flexpr_func_\XINT_newfunc_tmpa\expandafter\endcsname
+    \expandafter{\XINT_newfunc_tmpa}{floateval}\xintbarefloateval
   \ifxintverbose
     \xintMessage {xintexpr}{Info}
-        {Function \XINT_expr_tmpa\space for the expression parsers is
-         associated to \string\XINT_expr_macrofunc_\XINT_expr_tmpa\space
+        {Function \XINT_newfunc_tmpa\space for the expression parsers is
+         associated to \string\XINT_expr_macrofunc_\XINT_newfunc_tmpa\space
          with \ifxintglobaldefs global \fi meaning \expandafter\meaning
-         \csname XINT_expr_macrofunc_\XINT_expr_tmpa\endcsname}%
+         \csname XINT_expr_macrofunc_\XINT_newfunc_tmpa\endcsname}%
   \fi
 }%
 \def\XINT_expr_newfunction #1#2#3#4%
@@ -2953,6 +3165,7 @@
 \def\XINT_applyon:::_end #1,#2#3#4{\xint_secondoftwo #4}%
 \catcode`~ 12
 \catcode`$ 12 % $
+\def\xint_dfork  #1$#2#3\krof {#2}% $
 \def\xint_ddfork #1$$#2#3\krof {#2}% $$
 \def\XINT:NE:RApply::csv #1#2#3#4%
    {~xintApply::csv{~expandafter #2~xint_exchangetwo_keepbraces{#4}}{#3}}%
@@ -2979,13 +3192,75 @@
     \if  #2~\xint_dothis{#4}\fi
     \xint_orthat{#3}%
 }%
+\def\XINT:NE:twosp#1#2,#3#4,!#5%
+{%
+    \XINT:NE:two_fork_dd#1#3{#5}{\detokenize{#5}}{#1#2}{#3#4}%
+}%
 \def\XINT:NE:one#1#2{\expandafter\XINT:NE:one_a\romannumeral`&&@#2!#1}%
-\def\XINT:NE:one_a#1#2!#3{%
+\def\XINT:NE:one_a#1#2!#3%
+{%
     \if ###1\xint_dothis {\detokenize{#3}}\fi
     \if  ~#1\xint_dothis {\detokenize{#3}}\fi
     \if  $#1\xint_dothis {~xintApply::csv{\detokenize{#3}}}\fi %$
     \xint_orthat #3{#1#2}%
 }%
+\def\XINT:NE:userfunc #1#2#3%
+   {~xintExpandArgs{XINT_#1_userfunc_#2}{\xintCSVtoListNonStripped{#3}}}%
+\def\XINT:NE:userfunc:none #1#2{~!{XINT_#1_userfunc_#2}}%
+\def\XINT:NE:userefunc:one#1#2#3%
+   {\expandafter\XINT:NE:userefunc:one_a\romannumeral`&&@#3!{#1}{#2}}%
+\def\XINT:NE:userefunc:one_a#1#2!#3#4%
+{%
+    \if ###1\xint_dothis {~!{XINT_#3_userefunc:f_#4}}\fi
+    \if  ~#1\xint_dothis {~!{XINT_#3_userefunc:f_#4}}\fi
+    \if  $#1\xint_dothis {~xintApply::csv~!{XINT_#3_userefunc:f_#4}}\fi %$
+    \xint_orthat {\csname XINT_#3_userefunc_#4\endcsname}%
+    {#1#2}%
+}%
+\def\XINT:NE:twosp#1#2,#3#4,!#5%
+{%
+    \XINT:NE:two_fork_dd#1#3{#5}{\detokenize{#5}}{#1#2}{#3#4}%
+}%
+\def\XINT:NE:userefunc:two#1#2#3%
+    {\expandafter\XINT:NE:userefunc:two_a\romannumeral`&&@#3,!{#1}{#2}}%
+\def\XINT:NE:userefunc:two_a#1#2,#3#4,!#5#6%
+{%
+    \XINT:NE:two_fork_dd#1#3{\csname XINT_#5_userefunc_#6\endcsname}%
+                            {~!{XINT_#5_userefunc:f_#6}}%
+    {#1#2}{#3#4}%
+}%
+\def\XINT:NE:userefunc#1#2#3%
+{%
+    \expandafter\XINT:NE:userefunc_a\romannumeral`&&@#3,2,3,4,5,6,7,8,9,!%
+    {#1}{#2}{#3}%
+}%
+\def\XINT:NE:userefunc_a#1#2,#3#4,#5#6,#7#8,#9%
+{%
+    \XINT:NE:userefunc_b{#1#3#5#7#9}%
+}%
+\def\XINT:NE:userefunc_b#1#2,#3#4,#5#6,#7#8,#9%
+{%
+    \XINT:NE:userefunc_c{#1#3#5#7#9}%
+}%
+\def\XINT:NE:iftilde  #1~#2#3\relax{\unless\if !#21\fi}%
+\def\XINT:NE:ifdollar #1$#2#3\relax{\unless\if !#21\fi}%$
+\def\XINT:NE:ifhash#1{%
+\def\XINT:NE:ifhash##1#1##2##3\relax{\unless\if !##21\fi}%
+}\expandafter\XINT:NE:ifhash\string#%
+\def\XINT:NE:userefunc_c#1#2!%
+{%
+    \if0\XINT:NE:iftilde #1~!\relax\XINT:NE:ifdollar #1$!\relax%$
+        \XINT:NE:ifhash #1##!\relax 0%
+      \expandafter\XINT:NE:userefunc_x
+    \else
+      \expandafter\XINT:NE:userefunc_p
+    \fi
+}%
+\def\XINT:NE:userefunc_x#1#2%
+   {\csname XINT_#1_userefunc_#2\expandafter\endcsname
+    \romannumeral0\xintcsvtolistnonstripped}%
+\def\XINT:NE:userefunc_p #1#2#3%
+   {~xintExpandArgs{XINT_#1_userefunc_#2}{\xintCSVtoListNonStripped{#3}}}%
 \def\XINT:NE:oneopt#1[#2]#3%
    {\expandafter\XINT:NE:oneopt_a\romannumeral`&&@#3!{#2}#1}%
 \def\XINT:NE:oneopt_a#1#2!#3#4%
@@ -3032,11 +3307,6 @@
     {\expandafter\XINT:newexpr:insertdollar\detokenize{#3}}%
     {#1}{#2}%
 }%
-\def\XINT:newexpr:two:to:one #1,#2,!#3%
-{%
-    \XINT:NE:two#3{#1}{#2}%
-}%
-\let\XINT:newflexpr:two:to:one\XINT:newexpr:two:to:one
 \def\xintiiifNotZeroNE:#1#2,#3,#4,%
 {%
     \if1\if###11\else\if~#11\else\if$#11\else0%$
@@ -3086,20 +3356,23 @@
     {#1#2}{#3}{#4}{#5}%
 }%
 \def\XINT_expr_redefinemacros {%
-  \let\XINT:NEhook:one\XINT:NE:one
-  \let\XINT:NEhook:two\XINT:NE:two
-  \let\XINT:NEhook:csv\XINT:NE:csv
+  \let\XINT:NEhook:one  \XINT:NE:one
+  \let\XINT:NEhook:two  \XINT:NE:two
+  \let\XINT:NEhook:csv  \XINT:NE:csv
+  \let\XINT:NEhook:twosp\XINT:NE:twosp
+  \let\XINT:expr:userfunc      \XINT:NE:userfunc
+  \let\XINT:expr:userfunc:none \XINT:NE:userfunc:none
+  \let\XINT:expr:userefunc     \XINT:NE:userefunc
+  \let\XINT:expr:userefunc:one \XINT:NE:userefunc:one
+  \let\XINT:expr:userefunc:two \XINT:NE:userefunc:two
+  \let\XINT:expr:macrofunc     \XINT:newexpr:macrofunc
   \let\XINT:expr:one:and:opt         \XINT:newexpr:one:and:opt
   \let\XINT:expr:one:or:two:nums     \XINT:newexpr:one:or:two:nums
   \let\XINT:iiexpr:one:or:two:       \XINT:newiiexpr:one:or:two:
   \let\XINT:expr:tacitzeroifonearg   \XINT:newexpr:tacitzeroifonearg
   \let\XINT:iiexpr:tacitzeroifonearg \XINT:newiiexpr:tacitzeroifonearg
-  \let\XINT:expr:two:to:two   \XINT:newexpr:two:to:two
-  \let\XINT:expr:two:to:one   \XINT:newexpr:two:to:one
-  \let\XINT:flexpr:two:to:one \XINT:newflexpr:two:to:one
-  \let\XINT:expr:two:to:one   \XINT:newexpr:two:to:one
-  \let\XINT:flexpr:two:to:two \XINT:newflexpr:two:to:two
-  \let\XINT:flexpr:two:to:one \XINT:newflexpr:two:to:one
+  \let\XINT:expr:two:to:two          \XINT:newexpr:two:to:two
+  \let\XINT:flexpr:two:to:two        \XINT:newflexpr:two:to:two
   \let\xintiiifNotZero:       \xintiiifNotZeroNE:
   \let\xintifInt:             \xintifIntNE:
   \let\xintifFloatInt:        \xintifFloatIntNE:
@@ -3125,8 +3398,6 @@
   \def\XINTinFloatSeqB::csv
     {\XINT:NE:two_\XINTinFloatSeqBNumeric::csv{$noexpand$XINTinFloatSeqB:f:csv}}%
   \def\xintListSel:x:csv  {~xintListSel:f:csv }%
-  \let\XINT:expr:userfunc \XINT:newexpr:userfunc
-  \let\XINT:expr:macrofunc\XINT:newexpr:macrofunc
   \def\XINTinRandomFloatSdigits{~XINTinRandomFloatSdigits }%
   \def\XINTinRandomFloatSixteen{~XINTinRandomFloatSixteen }%
   \def\xintiiRandRange{~xintiiRandRange }%
@@ -3135,21 +3406,26 @@
 \def\XINT_expr_redefineprints
 {%
    \def\XINT_flexpr_noopt
-     {\expandafter\XINT_flexpr_withopt_b\expandafter-\romannumeral0\xintbarefloateval }%
-   \def\XINT_flexpr_withopt_b ##1##2%
-     {\expandafter\XINT_flexpr_wrap\csname .;##1.=\XINT_expr_unlock  ##2\endcsname }%
+   {%
+       \expandafter
+       \XINT_flexpr_preprint\expandafter-\romannumeral0\xintbarefloateval
+   }%
+   \def\XINT_flexpr_preprint ##1##2%
+   {%
+       \expandafter\XINT_flexpr_wrap
+       \csname .;##1.=\XINT_expr_unlock##2\endcsname
+   }%
    \def\XINT_expr_unlock_sp ##1.;##2##3.=##4!%
-     {\if -##2\expandafter\xint_firstoftwo\else\expandafter\xint_secondoftwo\fi
-      \XINTdigits{{##2##3}}{##4}}%
-   \def\XINT_expr_print ##1%
-     {\expandafter\xintSPRaw::csv\expandafter
-                 {\romannumeral`&&@\XINT_expr_unlock ##1}}%
-   \def\XINT_iiexpr_print ##1%
-     {\expandafter\xintCSV::csv\expandafter
-                 {\romannumeral`&&@\XINT_expr_unlock ##1}}%
-   \def\XINT_boolexpr_print ##1%
-     {\expandafter\xintIsTrue::csv\expandafter
-                 {\romannumeral`&&@\XINT_expr_unlock ##1}}%
+   {%
+       \if -##2\expandafter\xint_firstoftwo\else\expandafter\xint_secondoftwo\fi
+       \XINTdigits{{##2##3}}{##4}%
+   }%
+   \def\XINT_expr_print ##1{\expandafter
+       \xintSPRaw::csv\expandafter{\romannumeral`&&@\XINT_expr_unlock ##1}}%
+   \def\XINT_iiexpr_print ##1{\expandafter
+       \xintCSV::csv\expandafter{\romannumeral`&&@\XINT_expr_unlock ##1}}%
+   \def\XINT_boolexpr_print ##1{\expandafter
+       \xintIsTrue::csv\expandafter{\romannumeral`&&@\XINT_expr_unlock ##1}}%
    \def\xintCSV::csv     {~xintCSV::csv    }%
    \def\xintSPRaw::csv   {~xintSPRaw::csv  }%
    \def\xintPFloat::csv  {~xintPFloat::csv }%
@@ -3168,11 +3444,11 @@
                                  \xinttheboolexpr\XINT_newexpr_clean}%
 \def\XINT_newexpr_clean #1>{\noexpand\romannumeral`&&@}%
 \def\XINT_NewFunc
- {\XINT_NewExpr{}\xint_gobble_i\xintthebareeval\XINT_newfunc_clean}%
+ {\XINT_NewExpr\XINT_expr_redefineprints\xint_gobble_i\xintthebareeval\XINT_newfunc_clean}%
 \def\XINT_NewFloatFunc
- {\XINT_NewExpr{}\xint_gobble_i\xintthebarefloateval\XINT_newfunc_clean}%
+ {\XINT_NewExpr\XINT_expr_redefineprints\xint_gobble_i\xintthebarefloateval\XINT_newfunc_clean}%
 \def\XINT_NewIIFunc
- {\XINT_NewExpr{}\xint_gobble_i\xintthebareiieval\XINT_newfunc_clean}%
+ {\XINT_NewExpr\XINT_expr_redefineprints\xint_gobble_i\xintthebareiieval\XINT_newfunc_clean}%
 \def\XINT_newfunc_clean #1>{}%
 \def\XINT_NewExpr #1#2#3#4#5#6[#7]%
 {%
@@ -3198,7 +3474,7 @@
 \def\XINT_NewExpr_a %1%2%3%4%5@
 {@
     \def\XINT_tmpa %%1%%2%%3%%4%%5%%6%%7%%8%%9{%5}@
-    \def~{$noexpand$}@
+    \def~%%1{\if !%%1\noexpand~\else $noexpand$%%1\fi}@
     \catcode`: 11 \catcode`_ 11
     \catcode`# 12 \catcode`~ 13 \escapechar 126
     \endlinechar -1 \everyeof {\noexpand }@
@@ -3207,6 +3483,7 @@
      %2\XINT_tmpa{#1}{#2}{#3}{#4}{#5}{#6}{#7}{#8}{#9}\relax}@
     }@
     \escapechar 92 \catcode`# 6 \catcode`$ 0 @ $
+    \def~%%1{\expandafter\noexpand\csname %%1\endcsname}@
     \edef\XINT_tmpa %%1%%2%%3%%4%%5%%6%%7%%8%%9@
       {\scantokens\expandafter{\expandafter%3\meaning\XINT_tmpb}}@
     \the\toks0\expandafter
@@ -3218,6 +3495,7 @@
        \fi}@
 }@
 \catcode`% 14
+\XINT_setcatcodes % clean up to avoid surprises if something changes
 \newif\ifxintexprsafecatcodes
 \let\xintexprRestoreCatcodes\empty
 \def\xintexprSafeCatcodes
@@ -3277,7 +3555,13 @@
         \catcode96=12  % `
         \catcode32=10  % space
 }%
-\let\XINT_tmpa\relax \let\XINT_tmpb\relax \let\XINT_tmpc\relax
+\let\XINT_tmpa\undefined \let\XINT_tmpb\undefined \let\XINT_tmpc\undefined
+\ifdefined\RequirePackage\expandafter\xint_firstoftwo\else\expandafter\xint_secondoftwo\fi
+{\RequirePackage{xinttrig}%
+\RequirePackage{xintlog}}%
+{\input xinttrig.sty
+\input xintlog.sty
+}%
 \XINT_restorecatcodes_endinput%
 \endinput
 %%
diff --git a/Master/texmf-dist/tex/generic/xint/xintfrac.sty b/Master/texmf-dist/tex/generic/xint/xintfrac.sty
index 09b2c87192d..11d4185c722 100644
--- a/Master/texmf-dist/tex/generic/xint/xintfrac.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintfrac.sty
@@ -21,7 +21,7 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.3d 2019/01/06
+%% The xint bundle 1.3e 2019/04/05
 %% Copyright (C) 2013-2019 by Jean-Francois Burnol
 %% xintfrac: Expandable operations on fractions
 %% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty
 \XINT_providespackage
 \ProvidesPackage{xintfrac}%
-  [2019/01/06 1.3d Expandable operations on fractions (JFB)]%
+  [2019/04/05 1.3e Expandable operations on fractions (JFB)]%
 \def\XINT_cntSgnFork #1%
 {%
     \ifcase #1\expandafter\xint_secondofthree
@@ -397,6 +397,41 @@
     \expandafter\XINT_raw\romannumeral0\XINT_infrac
 }%
 \def\XINT_raw #1#2#3{ #2/#3[#1]}%
+\def\xintiLogTen {\the\numexpr\xintilogten}%
+\def\xintilogten
+{%
+    \expandafter\XINT_ilogten\romannumeral0\xintraw
+}%
+\def\XINT_ilogten #1%
+{%
+    \xint_UDzerominusfork
+      0#1\XINT_ilogten_p
+      #1-\XINT_ilogten_z
+      0-{\XINT_ilogten_p#1}%
+    \krof
+}%
+\def\XINT_ilogten_z #1[#2]{-"7FFF8000\relax}%
+\def\XINT_ilogten_p #1/#2[#3]%
+{%
+    #3+\expandafter\XINT_ilogten_a
+       \the\numexpr\xintLength{#1}\expandafter.\the\numexpr\xintLength{#2}.#1.#2.%
+}%
+\def\XINT_ilogten_a #1.#2.%
+{%
+    #1-#2\ifnum#1>#2
+      \expandafter\XINT_ilogten_aa
+    \else
+      \expandafter\XINT_ilogten_ab
+    \fi #1.#2.%
+}%
+\def\XINT_ilogten_aa #1.#2.#3.#4.%
+{%
+    \xintiiifLt{#3}{\XINT_dsx_addzerosnofuss{#1-#2}#4;}{-1}{}\relax
+}%
+\def\XINT_ilogten_ab #1.#2.#3.#4.%
+{%
+    \xintiiifLt{\XINT_dsx_addzerosnofuss{#2-#1}#3;}{#4}{-1}{}\relax
+}%
 \def\xintPRaw {\romannumeral0\xintpraw }%
 \def\xintpraw
 {%
@@ -1902,6 +1937,17 @@
 \def\XINT_infloatS_clean #1%
    {\if #1!\xint_dothis\XINT_infloatS_clean_a\fi\xint_orthat{ }#1}%
 \def\XINT_infloatS_clean_a !#1.{ }%
+\def\XINTFloatiLogTen {\the\numexpr\XINTfloatilogten}%
+\def\XINTfloatilogten [#1]#2%
+    {\expandafter\XINT_floatilogten\romannumeral0\XINT_infloat[#1]{#2}#1.}%
+\def\XINT_floatilogten #1{%
+    \if #10\xint_dothis\XINT_floatilogten_z\fi
+    \if #1!\xint_dothis\XINT_floatilogten_a\fi
+    \xint_orthat\XINT_floatilogten_b #1%
+}%
+\def\XINT_floatilogten_z 0[0]#1.{-"7FFF8000\relax}%
+\def\XINT_floatilogten_a !#1.#2[#3]#4.{#3-#1+#4-1\relax}%
+\def\XINT_floatilogten_b #1[#2]#3.{#2+#3-1\relax}%
 \def\XINT_infloat [#1]#2%
 {%
     \expandafter\XINT_infloat_a\the\numexpr #1\expandafter.%
@@ -2255,6 +2301,7 @@
     \expandafter\XINT_FL_mul_b\romannumeral0\XINTinfloatS[#3]{#4}#1[#2]%
 }%
 \def\XINT_FL_mul_b #1[#2]#3[#4]{\xintiiMul{#3}{#1}/1[#4+#2]}%
+\def\XINTinFloatInv#1{\XINTinFloatS[\XINTdigits]{\xintInv{#1}}}%
 \def\xintFloatDiv   {\romannumeral0\xintfloatdiv   }%
 \def\xintfloatdiv   #1{\XINT_fldiv_chkopt \xintfloat #1\xint:}%
 \def\XINTinFloatDiv {\romannumeral0\XINTinfloatdiv }%
@@ -2609,7 +2656,7 @@
 \def\xintFloatFac     {\romannumeral0\xintfloatfac}%
 \def\xintfloatfac   #1{\XINT_flfac_chkopt \xintfloat #1\xint:}%
 \def\XINTinFloatFac   {\romannumeral0\XINTinfloatfac }%
-\def\XINTinfloatfac #1{\XINT_flfac_chkopt \XINTinfloat #1\xint:}%
+\def\XINTinfloatfac #1{\XINT_flfac_chkopt \XINTinfloatS #1\xint:}%
 \def\XINT_flfac_chkopt #1#2%
 {%
     \ifx [#2\expandafter\XINT_flfac_opt
diff --git a/Master/texmf-dist/tex/generic/xint/xintgcd.sty b/Master/texmf-dist/tex/generic/xint/xintgcd.sty
index 60a38048466..ecd3d3f8532 100644
--- a/Master/texmf-dist/tex/generic/xint/xintgcd.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintgcd.sty
@@ -21,7 +21,7 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.3d 2019/01/06
+%% The xint bundle 1.3e 2019/04/05
 %% Copyright (C) 2013-2019 by Jean-Francois Burnol
 %% xintgcd: Euclidean algorithm with xint package
 %% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty
 \XINT_providespackage
 \ProvidesPackage{xintgcd}%
-  [2019/01/06 1.3d Euclide algorithm with xint package (JFB)]%
+  [2019/04/05 1.3e Euclide algorithm with xint package (JFB)]%
 \def\xintGCD {\romannumeral0\xintgcd }%
 \def\xintgcd #1#2{\xintiigcd {\xintNum{#1}}{\xintNum{#2}}}%
 \def\xintiiGCD {\romannumeral0\xintiigcd }%
diff --git a/Master/texmf-dist/tex/generic/xint/xintkernel.sty b/Master/texmf-dist/tex/generic/xint/xintkernel.sty
index 63719d70a97..2b03201a5f5 100644
--- a/Master/texmf-dist/tex/generic/xint/xintkernel.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintkernel.sty
@@ -21,7 +21,7 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.3d 2019/01/06
+%% The xint bundle 1.3e 2019/04/05
 %% Copyright (C) 2013-2019 by Jean-Francois Burnol
 %% xintkernel: Paraphernalia for the xint packages
 %% ---------------------------------------------------------------
@@ -156,7 +156,7 @@
 \fi
 \XINT_providespackage
 \ProvidesPackage {xintkernel}%
-  [2019/01/06 1.3d Paraphernalia for the xint packages (JFB)]%
+  [2019/04/05 1.3e Paraphernalia for the xint packages (JFB)]%
 \chardef\xint_c_     0
 \chardef\xint_c_i    1
 \chardef\xint_c_ii   2
@@ -564,8 +564,11 @@
   }%
 }%
 \def\xintMessage #1#2#3{%
+    \edef\XINT_newlinechar{\the\newlinechar}%
+    \newlinechar10
     \immediate\write128{Package #1 #2: (on line \the\inputlineno)}%
     \immediate\write128{\space\space\space\space#3}%
+    \newlinechar\XINT_newlinechar\space
 }%
 \newif\ifxintverbose
 \newif\ifxintglobaldefs
diff --git a/Master/texmf-dist/tex/generic/xint/xintlog.sty b/Master/texmf-dist/tex/generic/xint/xintlog.sty
new file mode 100644
index 00000000000..0ba983d2530
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/xint/xintlog.sty
@@ -0,0 +1,118 @@
+%%
+%% This is file `xintlog.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% xint.dtx  (with options: `xintlog')
+%% 
+%% IMPORTANT NOTICE:
+%% 
+%% For the copyright see the source file.
+%% 
+%% Any modified versions of this file must be renamed
+%% with new filenames distinct from xintlog.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 1.3e 2019/04/05
+%% Copyright (C) 2013-2019 by Jean-Francois Burnol
+%% xintlog: Logarithms and exponentials for xintexpr
+%% ---------------------------------------------------------------
+\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   % :
+  \catcode94=7    % ^
+  \def\z{\endgroup}%
+  \def\empty{}\def\space{ }\newlinechar10
+  \expandafter\let\expandafter\w\csname ver@xintexpr.sty\endcsname
+  \expandafter\let\expandafter\x\csname ver@xintlog.sty\endcsname
+  \expandafter
+    \ifx\csname PackageInfo\endcsname\relax
+      \def\y#1#2{\immediate\write-1{Package #1 Info:^^J%
+                 \space\space\space\space#2.}}%
+    \else
+      \def\y#1#2{\PackageInfo{#1}{#2}}%
+    \fi
+  \expandafter
+  \ifx\csname numexpr\endcsname\relax
+     \y{xintlog}{\numexpr not available, aborting input}%
+     \aftergroup\endinput
+  \else
+    \ifx\w\relax % xintexpr.sty not yet loaded.
+        \y{xintlog}%
+          {Loading should be via \ifx\x\empty\string\usepackage{xintexpr.sty}
+                          \else\string\input\space xintexpr.sty \fi
+           rather, aborting}%
+        \aftergroup\endinput
+    \else
+      \ifx\x\relax % first loading (initiated from xintexpr.sty)
+      \else
+        \ifx\x\empty % LaTeX first loading, \ProvidesPackage not yet seen
+        \else
+          \y{xintlog}{Already loaded, aborting}%
+          \aftergroup\endinput
+        \fi
+      \fi
+    \fi
+  \fi
+\z%
+\xintexprSafeCatcodes\catcode`_ 11
+\XINT_providespackage
+\ProvidesPackage{xintlog}%
+[2019/04/05 1.3e Logarithms and exponentials for xintexpr (JFB)]%
+\ifdefined\RequirePackage
+  \RequirePackage{poormanlog}%
+\else
+  \input poormanlog.tex
+\fi
+\xintexprRestoreCatcodes\csname XINT_setcatcodes\endcsname\catcode`\! 11
+\def\xintLog#1{\xintMul{\PoorManLogBaseTen{#1}}{23025850923[-10]}}%
+\def\XINTinFloatLog#1{\XINTinFloatMul{\PoorManLogBaseTen{#1}}{23025850923[-10]}}%
+\def\xintExp#1{\PoorManPowerOfTen{\xintMul{#1}{434294481903[-12]}}}%
+\def\XINTinFloatExp#1{\PoorManPowerOfTen{\XINTinFloatMul{#1}{434294481903[-12]}}}%
+\def\XINT_expr_func_log #1#2#3%
+{%
+    \expandafter #1\expandafter #2\csname.=%
+    \XINT:NEhook:one\xintLog{\XINT_expr_unlock #3}\endcsname
+}%
+\def\XINT_flexpr_func_log #1#2#3%
+{%
+    \expandafter #1\expandafter #2\csname.=%
+    \XINT:NEhook:one\XINTinFloatLog{\XINT_expr_unlock #3}\endcsname
+}%
+\def\XINT_expr_func_exp #1#2#3%
+{%
+    \expandafter #1\expandafter #2\csname.=%
+    \XINT:NEhook:one\xintExp{\XINT_expr_unlock #3}\endcsname
+}%
+\def\XINT_flexpr_func_exp #1#2#3%
+{%
+    \expandafter #1\expandafter #2\csname.=%
+    \XINT:NEhook:one\XINTinFloatExp{\XINT_expr_unlock #3}\endcsname
+}%
+\def\XINT_expr_func_pow #1#2#3%
+{%
+    \expandafter #1\expandafter #2\csname.=%
+    \expandafter\XINT:NEhook:twosp
+    \romannumeral`&&@\XINT_expr_unlock #3,!\PoorManPower
+    \endcsname
+}%
+\let\XINT_flexpr_func_pow\XINT_expr_func_pow
+\endinput
+%%
+%% End of file `xintlog.sty'.
diff --git a/Master/texmf-dist/tex/generic/xint/xintseries.sty b/Master/texmf-dist/tex/generic/xint/xintseries.sty
index 7958c90d75d..38ea5b473c4 100644
--- a/Master/texmf-dist/tex/generic/xint/xintseries.sty
+++ b/Master/texmf-dist/tex/generic/xint/xintseries.sty
@@ -21,7 +21,7 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.3d 2019/01/06
+%% The xint bundle 1.3e 2019/04/05
 %% Copyright (C) 2013-2019 by Jean-Francois Burnol
 %% xintseries: Expandable partial sums with xint package
 %% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty
 \XINT_providespackage
 \ProvidesPackage{xintseries}%
-  [2019/01/06 1.3d Expandable partial sums with xint package (JFB)]%
+  [2019/04/05 1.3e Expandable partial sums with xint package (JFB)]%
 \def\xintSeries {\romannumeral0\xintseries }%
 \def\xintseries #1#2%
 {%
diff --git a/Master/texmf-dist/tex/generic/xint/xinttools.sty b/Master/texmf-dist/tex/generic/xint/xinttools.sty
index f6d378e7c24..c38614a2a1e 100644
--- a/Master/texmf-dist/tex/generic/xint/xinttools.sty
+++ b/Master/texmf-dist/tex/generic/xint/xinttools.sty
@@ -21,7 +21,7 @@
 %% same distribution. (The sources need not necessarily be
 %% in the same archive or directory.)
 %% ---------------------------------------------------------------
-%% The xint bundle 1.3d 2019/01/06
+%% The xint bundle 1.3e 2019/04/05
 %% Copyright (C) 2013-2019 by Jean-Francois Burnol
 %% xinttools: Expandable and non-expandable utilities
 %% ---------------------------------------------------------------
@@ -70,7 +70,7 @@
 \XINTsetupcatcodes% defined in xintkernel.sty
 \XINT_providespackage
 \ProvidesPackage{xinttools}%
-  [2019/01/06 1.3d Expandable and non-expandable utilities (JFB)]%
+  [2019/04/05 1.3e Expandable and non-expandable utilities (JFB)]%
 \newtoks\XINT_toks
 \xint_firstofone{\let\XINT_sptoken= } %<- space here!
 \def\xintgodef  {\global\xintodef }%
diff --git a/Master/texmf-dist/tex/generic/xint/xinttrig.sty b/Master/texmf-dist/tex/generic/xint/xinttrig.sty
new file mode 100644
index 00000000000..b2e41c7b21f
--- /dev/null
+++ b/Master/texmf-dist/tex/generic/xint/xinttrig.sty
@@ -0,0 +1,500 @@
+%%
+%% This is file `xinttrig.sty',
+%% generated with the docstrip utility.
+%%
+%% The original source files were:
+%%
+%% xint.dtx  (with options: `xinttrig')
+%% 
+%% IMPORTANT NOTICE:
+%% 
+%% For the copyright see the source file.
+%% 
+%% Any modified versions of this file must be renamed
+%% with new filenames distinct from xinttrig.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 1.3e 2019/04/05
+%% Copyright (C) 2013-2019 by Jean-Francois Burnol
+%% xinttrig: Trigonometry for the xintexpr package
+%% ---------------------------------------------------------------
+\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   % :
+  \catcode94=7    % ^
+  \def\z{\endgroup}%
+  \def\empty{}\def\space{ }\newlinechar10
+  \expandafter\let\expandafter\w\csname ver@xintexpr.sty\endcsname
+  \expandafter
+    \ifx\csname PackageInfo\endcsname\relax
+      \def\y#1#2{\immediate\write-1{Package #1 Info:^^J%
+                 \space\space\space\space#2.}}%
+    \else
+      \def\y#1#2{\PackageInfo{#1}{#2}}%
+    \fi
+  \expandafter
+  \ifx\csname numexpr\endcsname\relax
+     \y{xinttrig}{\numexpr not available, aborting input}%
+     \aftergroup\endinput
+  \else
+    \ifx\w\relax % xintexpr.sty not yet loaded.
+        \y{xinttrig}%
+          {Loading should be via \ifx\x\empty\string\usepackage{xintexpr.sty}
+                          \else\string\input\space xintexpr.sty \fi
+           rather, aborting}%
+         \aftergroup\endinput
+    \fi
+  \fi
+\z%
+\catcode`_ 11 \XINT_setcatcodes \catcode`? 12
+\ifcsname xintlibver@trig\endcsname
+  \expandafter\xint_firstoftwo
+\else
+  \expandafter\xint_secondoftwo
+\fi
+{\immediate\write-1{Reloading xinttrig library using Digits=\xinttheDigits.}}%
+{\expandafter\gdef\csname xintlibver@trig\endcsname{2019/04/05 1.3e}%
+\XINT_providespackage
+\ProvidesPackage{xinttrig}%
+[2019/04/05 1.3e Trigonometrical functions for xintexpr (JFB)]%
+}%
+\xintFor* #1 in {iDTVtuwxyzX}\do{\xintensuredummy{#1}}%
+\def\xintreloadxinttrig
+   {\edef\XINT_restorecatcodes_now{\XINT_restorecatcodes}%
+    \XINT_setcatcodes\catcode`? 12
+    \input xinttrig.sty
+    \XINT_restorecatcodes_now}%
+\xintdeffloatvar twoPi        := 0 +
+    6.28318530717958647692528676655900576839433879875021164194989;%
+\xintdeffloatvar threePiover2 := 0 +
+    4.71238898038468985769396507491925432629575409906265873146242;%
+\xintdeffloatvar Pi           := 0 +
+    3.14159265358979323846264338327950288419716939937510582097494;%
+\xintdeffloatvar Piover2      := 0 +
+    1.57079632679489661923132169163975144209858469968755291048747;%
+\xintdeffloatvar oneDegree := 0 +
+    0.0174532925199432957692369076848861271344287188854172545609719;% Pi/180
+\xintdeffloatvar oneRadian := 0 +
+    57.2957795130823208767981548141051703324054724665643215491602;%   180/Pi
+\xintdeffloatvar invfact\xintListWithSep{, invfact}{\xintSeq{2}{44}}%
+     := seq(0+x, x=\xintexpr rseq(1/2{;}@/i, i=3..44)\relax);% need to hide inner ;
+\xintdeffloatefunc sin_aux(X) := 1 - X(invfact3 - X(invfact5
+\ifnum\XINTdigits>4
+                           - X(invfact7
+\ifnum\XINTdigits>6
+                           - X(invfact9
+\ifnum\XINTdigits>8
+                           - X(invfact11
+\ifnum\XINTdigits>10
+                           - X(invfact13
+\ifnum\XINTdigits>13
+                           - X(invfact15
+\ifnum\XINTdigits>15
+                           - X(invfact17
+\ifnum\XINTdigits>18
+                           - X(invfact19
+\ifnum\XINTdigits>21
+                           - X(invfact21
+\ifnum\XINTdigits>24
+                           - X(invfact23
+\ifnum\XINTdigits>27
+                           - X(invfact25
+\ifnum\XINTdigits>30
+                           - X(invfact27
+\ifnum\XINTdigits>33
+                           - X(invfact29
+\ifnum\XINTdigits>36
+                           - X(invfact31
+\ifnum\XINTdigits>39
+                           - X(invfact33
+\ifnum\XINTdigits>43
+                           - X(invfact35
+\ifnum\XINTdigits>46
+                           - X(invfact37
+\ifnum\XINTdigits>49
+                           - X(invfact39
+\ifnum\XINTdigits>53
+                           - X(invfact41
+\ifnum\XINTdigits>59
+                           - X(invfact43
+    )\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi));%
+\xintdeffloatefunc cos_aux(X) := 1 - X(invfact2 - X(invfact4
+\ifnum\XINTdigits>3
+                           - X(invfact6
+\ifnum\XINTdigits>5
+                           - X(invfact8
+\ifnum\XINTdigits>7
+                           - X(invfact10
+\ifnum\XINTdigits>9
+                           - X(invfact12
+\ifnum\XINTdigits>12
+                           - X(invfact14
+\ifnum\XINTdigits>14
+                           - X(invfact16
+\ifnum\XINTdigits>17
+                           - X(invfact18
+\ifnum\XINTdigits>20
+                           - X(invfact20
+\ifnum\XINTdigits>23
+                           - X(invfact22
+\ifnum\XINTdigits>25
+                           - X(invfact24
+\ifnum\XINTdigits>28
+                           - X(invfact26
+\ifnum\XINTdigits>32
+                           - X(invfact28
+\ifnum\XINTdigits>35
+                           - X(invfact30
+\ifnum\XINTdigits>38
+                           - X(invfact32
+\ifnum\XINTdigits>41
+                           - X(invfact34
+\ifnum\XINTdigits>44
+                           - X(invfact36
+\ifnum\XINTdigits>48
+                           - X(invfact38
+\ifnum\XINTdigits>51
+                           - X(invfact40
+\ifnum\XINTdigits>55
+                           - X(invfact42
+\ifnum\XINTdigits>58
+                           - X(invfact44
+    )\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi)\fi));%
+\expandafter\let\csname XINT_expr_func_sin_aux\expandafter\endcsname
+                \csname XINT_flexpr_func_sin_aux\endcsname
+\expandafter\let\csname XINT_expr_func_cos_aux\expandafter\endcsname
+                \csname XINT_flexpr_func_cos_aux\endcsname
+\xintdeffloatefunc sin_(x) := x * sin_aux(sqr(x));%
+\xintdeffloatefunc cos_(x) := cos_aux(sqr(x));%
+\def\XINT_mod_ccclx_i #1.% input <k>.<N>. k is a non-negative exponent
+{%
+    \expandafter\XINT_mod_ccclx_e\the\numexpr
+    \expandafter\XINT_mod_ccclx_j\the\numexpr1\ifcase#1 \or0\or00\else000\fi.%
+}%
+\def\XINT_mod_ccclx_j 1#1.#2.% #2=N is a non-negative mantissa
+{%
+    (\XINT_mod_ccclx_ja {++}#2#1\XINT_mod_ccclx_jb 0000000\relax
+}%                                   1     2345678
+\def\XINT_mod_ccclx_ja #1#2#3#4#5#6#7#8#9%
+{%
+    #9+#8+#7+#6+#5+#4+#3+#2\xint_firstoftwo{+\XINT_mod_ccclx_ja{+#9+#8+#7}}{#1}%
+}%
+\def\XINT_mod_ccclx_jb #1\xint_firstoftwo#2#3{#1+0)*280\XINT_mod_ccclx_jc #1#3}%
+\def\XINT_mod_ccclx_jc  +#1+#2+#3#4\relax{+80*(#3+#2+#1)+#3#2#1.}%
+\def\XINT_mod_ccclx_e#1.{\expandafter\XINT_mod_ccclx_z\the\numexpr(#1+180)/360-1.#1.}%
+\def\XINT_mod_ccclx_z#1.#2.{#2-360*#1.}%
+\def\XINT_flexpr_func_sind_ #1#2#3%
+{%
+    \expandafter #1\expandafter #2\csname.=%
+    \XINT:NEhook:one\xintSind{\XINT_expr_unlock#3}\endcsname
+}%
+\def\xintSind#1{\romannumeral`&&@\expandafter\xintsind
+                \romannumeral0\XINTinfloatS[\XINTdigits]{#1}}%
+\def\xintsind #1[#2#3]%
+{%
+    \xint_UDsignfork
+      #2\XINT_sind
+       -\XINT_sind_int
+    \krof#2#3.#1..%<< attention extra dot
+}%
+\def\XINT_sind #1.#2.% NOT TO BE USED WITH VANISHING (OR NEGATIVE) #2.
+{%
+    \expandafter\XINT_sind_a
+    \romannumeral0\xinttrunc{\XINTdigits}{#2[#1]}%
+}%
+\def\XINT_sind_a{\expandafter\XINT_sind_i\the\numexpr\XINT_mod_ccclx_i0.}%
+\def\XINT_sind_int
+{%
+    \expandafter\XINT_sind_i\the\numexpr\expandafter\XINT_mod_ccclx_i
+}%
+\def\XINT_sind_i #1.% range reduction inside [0, 360[
+{%
+    \ifcase\numexpr#1/90\relax
+       \expandafter\XINT_sind_A
+    \or\expandafter\XINT_sind_B\the\numexpr-90+%
+    \or\expandafter\XINT_sind_C\the\numexpr-180+%
+    \or\expandafter\XINT_sind_D\the\numexpr-270+%
+    \else\expandafter\XINT_sind_E\the\numexpr-360+%
+    \fi#1.%
+}%
+\def\XINT_sind_A#1{%
+\def\XINT_sind_A##1.##2.%
+{%
+    \expandafter\XINT_flexpr_userefunc_sin_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{##1.##2}{#1}}}%
+}%
+}\expandafter
+\XINT_sind_A\expandafter{\romannumeral`&&@\xintthebarefloateval oneDegree\relax}%
+\def\XINT_sind_B#1{\xint_UDsignfork#1\XINT_sind_B_n-\XINT_sind_B_p\krof #1}%
+\def\XINT_tmpa#1{%
+\def\XINT_sind_B_n-##1.##2.%
+{%
+    \expandafter\XINT_flexpr_userefunc_cos_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{\xintSub{##1[0]}{.##2}}{#1}}}%
+}%
+\def\XINT_sind_B_p##1.##2.%
+{%
+    \expandafter\XINT_flexpr_userefunc_cos_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{##1.##2}{#1}}}%
+}%
+}\expandafter
+\XINT_tmpa\expandafter{\romannumeral`&&@\xintthebarefloateval oneDegree\relax}%
+\def\XINT_sind_C#1{\xint_UDsignfork#1\XINT_sind_C_n-\XINT_sind_C_p\krof #1}%
+\def\XINT_tmpa#1{%
+\def\XINT_sind_C_n-##1.##2.%
+{%
+    \expandafter\XINT_flexpr_userefunc_sin_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{\xintSub{##1[0]}{.##2}}{#1}}}%
+}%
+\def\XINT_sind_C_p##1.##2.%
+{%
+    \xintiiopp\expandafter\XINT_flexpr_userefunc_sin_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{##1.##2}{#1}}}%
+}%
+}\expandafter
+\XINT_tmpa\expandafter{\romannumeral`&&@\xintthebarefloateval oneDegree\relax}%
+\def\XINT_sind_D#1{\xint_UDsignfork#1\XINT_sind_D_n-\XINT_sind_D_p\krof #1}%
+\def\XINT_tmpa#1{%
+\def\XINT_sind_D_n-##1.##2.%
+{%
+    \xintiiopp\expandafter\XINT_flexpr_userefunc_cos_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{\xintSub{##1[0]}{.##2}}{#1}}}%
+}%
+\def\XINT_sind_D_p##1.##2.%
+{%
+    \xintiiopp\expandafter\XINT_flexpr_userefunc_cos_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{##1.##2}{#1}}}%
+}%
+}\expandafter
+\XINT_tmpa\expandafter{\romannumeral`&&@\xintthebarefloateval oneDegree\relax}%
+\def\XINT_sind_E#1{%
+\def\XINT_sind_E-##1.##2.%
+{%
+    \xintiiopp\expandafter\XINT_flexpr_userefunc_sin_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{\xintSub{##1[0]}{.##2}}{#1}}}%
+}%
+}\expandafter
+\XINT_sind_E\expandafter{\romannumeral`&&@\xintthebarefloateval oneDegree\relax}%
+\def\XINT_flexpr_func_cosd_ #1#2#3%
+{%
+    \expandafter #1\expandafter #2\csname.=%
+    \XINT:NEhook:one\xintCosd{\XINT_expr_unlock#3}\endcsname
+}%
+\def\xintCosd#1{\romannumeral`&&@\expandafter\xintcosd
+                    \romannumeral0\XINTinfloatS[\XINTdigits]{#1}}%
+\def\xintcosd #1[#2#3]%
+{%
+    \xint_UDsignfork
+      #2\XINT_cosd
+       -\XINT_cosd_int
+    \krof#2#3.#1..%<< attention extra dot
+}%
+\def\XINT_cosd #1.#2.% NOT TO BE USED WITH VANISHING (OR NEGATIVE) #2.
+{%
+    \expandafter\XINT_cosd_a
+    \romannumeral0\xinttrunc{\XINTdigits}{#2[#1]}%
+}%
+\def\XINT_cosd_a{\expandafter\XINT_cosd_i\the\numexpr\XINT_mod_ccclx_i0.}%
+\def\XINT_cosd_int
+{%
+    \expandafter\XINT_cosd_i\the\numexpr\expandafter\XINT_mod_ccclx_i
+}%
+\def\XINT_cosd_i #1.%
+{%
+    \ifcase\numexpr#1/90\relax
+       \expandafter\XINT_cosd_A
+    \or\expandafter\XINT_cosd_B\the\numexpr-90+%
+    \or\expandafter\XINT_cosd_C\the\numexpr-180+%
+    \or\expandafter\XINT_cosd_D\the\numexpr-270+%
+    \else\expandafter\XINT_cosd_E\the\numexpr-360+%
+    \fi#1.%
+}%
+\def\XINT_cosd_A#1{%
+\def\XINT_cosd_A##1.##2.%
+{%
+    \expandafter\XINT_flexpr_userefunc_cos_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{##1.##2}{#1}}}%
+}%
+}\expandafter
+\XINT_cosd_A\expandafter{\romannumeral`&&@\xintthebarefloateval oneDegree\relax}%
+\def\XINT_cosd_B#1{\xint_UDsignfork#1\XINT_cosd_B_n-\XINT_cosd_B_p\krof #1}%
+\def\XINT_tmpa#1{%
+\def\XINT_cosd_B_n-##1.##2.%
+{%
+    \expandafter\XINT_flexpr_userefunc_sin_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{\xintSub{##1[0]}{.##2}}{#1}}}%
+}%
+\def\XINT_cosd_B_p##1.##2.%
+{%
+    \xintiiopp\expandafter\XINT_flexpr_userefunc_sin_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{##1.##2}{#1}}}%
+}%
+}\expandafter
+\XINT_tmpa\expandafter{\romannumeral`&&@\xintthebarefloateval oneDegree\relax}%
+\def\XINT_cosd_C#1{\xint_UDsignfork#1\XINT_cosd_C_n-\XINT_cosd_C_p\krof #1}%
+\def\XINT_tmpa#1{%
+\def\XINT_cosd_C_n-##1.##2.%
+{%
+    \xintiiopp\expandafter\XINT_flexpr_userefunc_cos_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{\xintSub{##1[0]}{.##2}}{#1}}}%
+}%
+\def\XINT_cosd_C_p##1.##2.%
+{%
+    \xintiiopp\expandafter\XINT_flexpr_userefunc_cos_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{##1.##2}{#1}}}%
+}%
+}\expandafter
+\XINT_tmpa\expandafter{\romannumeral`&&@\xintthebarefloateval oneDegree\relax}%
+\def\XINT_cosd_D#1{\xint_UDsignfork#1\XINT_cosd_D_n-\XINT_cosd_D_p\krof #1}%
+\def\XINT_tmpa#1{%
+\def\XINT_cosd_D_n-##1.##2.%
+{%
+    \xintiiopp\expandafter\XINT_flexpr_userefunc_sin_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{\xintSub{##1[0]}{.##2}}{#1}}}%
+}%
+\def\XINT_cosd_D_p##1.##2.%
+{%
+    \expandafter\XINT_flexpr_userefunc_sin_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{##1.##2}{#1}}}%
+}%
+}\expandafter
+\XINT_tmpa\expandafter{\romannumeral`&&@\xintthebarefloateval oneDegree\relax}%
+\def\XINT_cosd_E#1{%
+\def\XINT_cosd_E-##1.##2.%
+{%
+    \expandafter\XINT_flexpr_userefunc_cos_\expandafter
+         {\romannumeral0\XINTinfloat[\XINTdigits]{\xintMul{\xintSub{##1[0]}{.##2}}{#1}}}%
+}%
+}\expandafter
+\XINT_cosd_E\expandafter{\romannumeral`&&@\xintthebarefloateval oneDegree\relax}%
+\xintdeffloatefunc sind(x) := ifsgn(x, if(x>=-45, sin_(x*oneDegree), -sind_(-x)),
+                                      0,
+                                      if(x<=45, sin_(x*oneDegree), sind_(x)));%
+\xintdeffloatefunc cosd(x) := ifsgn(x, if(x>=-45, cos_(x*oneDegree), cosd_(-x)),
+                                      1,
+                                      if(x<=45, cos_(x*oneDegree), cosd_(x)));%
+\xintdeffloatefunc sin(x):= if(abs(x)<0.79, sin_(x),%
+                                          ifsgn(x, -sind_(-x*oneRadian),
+                                                   0,
+                                                   sind_(x*oneRadian))
+                              );%
+\xintdeffloatefunc cos(x):= if(abs(x)<0.79, cos_(x), cosd_(abs(x*oneRadian)));%
+\xintdeffloatefunc sinc(x):=
+    if(abs(x)<0.79, sin_aux(sqr(x)), sind_(abs(x)*oneRadian)/abs(x));%
+\xintdeffloatefunc tand(x):= sind(x)/cosd(x);%
+\xintdeffloatefunc cotd(x):= cosd(x)/sind(x);%
+\xintdeffloatefunc tan(x) := ifsgn(x, if(x>-0.79, sin(x)/cos(x), -cotd(90+x*oneRadian)),
+                                     0,
+                                     if(x<0.79, sin(x)/cos(x), cotd(90-x*oneRadian))
+                                  );%
+\xintdeffloatefunc cot(x) := if(abs(x)<0.79, cos(x)/sin(x),
+                                           ifsgn(x, -tand(90+x*oneRadian),
+                                                    0,
+                                                    tand(90-x*oneRadian))
+                                  );%
+\xintdeffloatefunc sec(x) := inv(cos(x));%
+\xintdeffloatefunc csc(x) := inv(sin(x));%
+\xintdeffloatefunc secd(x):= inv(cosd(x));%
+\xintdeffloatefunc cscd(x):= inv(sind(x));%
+\xintdeffloatefunc asin_aux(X) := 1
+\ifnum\XINTdigits>3 % actually 4 would achieve 1ulp in place of <0.5ulp
+                           + X(1/6
+\ifnum\XINTdigits>9
+                           + X(3/40
+\ifnum\XINTdigits>16
+                           + X(5/112
+\ifnum\XINTdigits>25
+                           + X(35/1152
+\ifnum\XINTdigits>35
+                           + X(63/2816
+\ifnum\XINTdigits>46
+                           + X(231/13312
+                           )\fi)\fi)\fi)\fi)\fi)\fi;%
+\xintdeffloatefunc asin_o(D, T) := T + D*asin_aux(sqr(D));%
+\xintdeffloatefunc asin_n(V, T, t, u) :=% V is square of T
+                   asin_o (\xintexpr t*cos_aux(V) - u*T*sin_aux(V)\relax, T);%
+\xintdeffloatefunc asin_m(T, t, u) := asin_n(sqr(T), T, t, u);%
+\xintdeffloatefunc asin_l(t, u)    := asin_m(t*asin_aux(sqr(t)), t, u);%
+\xintdeffloatefunc asin_a(t, u) :=
+    if(t<u, asin_l(t, u), Piover2 - asin_l(u, t));%
+\xintdeffloatefunc asind_a(t, u):=
+    if(t<u, asin_l(t, u) * oneRadian, 90 - asin_l(u, t) * oneRadian);%
+\xintdeffloatefunc asin(t) := ifsgn(t, -asin_a(-t, sqrt(1-sqr(t))),
+                                      0,
+                                      asin_a(t, sqrt(1-sqr(t))));%
+\xintdeffloatefunc asind(t) := ifsgn(t, -asind_a(-t, sqrt(1-sqr(t))),
+                                      0,
+                                      asind_a(t, sqrt(1-sqr(t))));%
+\xintdeffloatefunc acos(t) := Piover2 - asin(t);%
+\xintdeffloatefunc acosd(t):= 90 - asind(t);%
+\xintdeffloatefunc atan_b(t, w, z):=%
+    0.5 * if(w< 0, Pi - asin_a(2z * t, -w*z), asin_a(2z * t, w*z));%
+\xintdeffloatefunc atan_a(t, T) := atan_b(t, 1-T, inv(1+T));%
+\xintdeffloatefunc atan(t):= ifsgn(t,-atan_a(-t, sqr(t)), 0, atan_a(t, sqr(t)));%
+\xintdeffloatefunc atand_b(t, w, z) :=
+    0.5 * if(w< 0, 180 - asind_a(2z * t, -w*z), asind_a(2z * t, w*z));%
+\xintdeffloatefunc atand_a(t, T) := atand_b(t, 1-T, inv(1+T));%
+\xintdeffloatefunc atand(t):= ifsgn(t,-atand_a(-t, sqr(t)), 0, atand_a(t, sqr(t)));%
+\xintdeffloatefunc Arg(x, y):=
+    if(y>x,
+       if(y>-x, Piover2 - atan(x/y),
+                if(y<0, -Pi + atan(y/x), Pi + atan(y/x))),
+       if(y>-x, atan(y/x), -Piover2 + atan(x/-y))
+       );%
+\xintdeffloatefunc atan2(y,x) := Arg(x, y);%
+\xintdeffloatefunc Argd(x, y):=
+    if(y>x,
+       if(y>-x, 90 - atand(x/y),
+                if(y<0, -180 + atand(y/x), 180 + atand(y/x))),
+       if(y>-x, atand(y/x), -90 + atand(x/-y))
+       );%
+\xintdeffloatefunc atan2d(y,x) := Argd(x, y);%
+\xintdeffloatefunc pArg(x, y):=
+    if(y>x,
+       if(y>-x, Piover2 - atan(x/y), Pi + atan(y/x)),
+       if(y>-x, if(y<0, twoPi + atan(y/x), atan(y/x)),
+                threePiover2 + atan(x/-y))
+       );%
+\xintdeffloatefunc pArgd(x, y):=
+    if(y>x,
+       if(y>-x, 90 - atan(x/y)*oneRadian, 180 + atan(y/x)*oneRadian),
+       if(y>-x, if(y<0, 360 + atan(y/x)*oneRadian, atan(y/x)*oneRadian),
+                270 + atan(x/-y)*oneRadian)
+       );%
+\expandafter\let\csname XINT_flexpr_func_tg\expandafter\endcsname
+                \csname XINT_flexpr_func_tan\endcsname
+\expandafter\let\csname XINT_flexpr_func_cotg\expandafter\endcsname
+                \csname XINT_flexpr_func_cot\endcsname
+\xintFor #1 in {sin, cos, tan, sec, csc, cot,
+                asin, acos, atan}\do
+{%
+    \xintdefefunc #1(x) := \xintfloatexpr #1(sfloat(x))\relax;%
+    \xintdefefunc #1d(x):= \xintfloatexpr #1d(sfloat(x))\relax;%
+}%
+\xintFor #1 in {Arg, pArg, atan2}\do
+{%
+    \xintdefefunc #1(x, y) := \xintfloatexpr #1(sfloat(x), sfloat(y))\relax;%
+    \xintdefefunc #1d(x, y):= \xintfloatexpr #1d(sfloat(x), sfloat(y))\relax;%
+}%
+\xintdefefunc tg(x)  := \xintfloatexpr tg(sfloat(x))\relax;%
+\xintdefefunc cotg(x):= \xintfloatexpr cotg(sfloat(x))\relax;%
+\xintdefefunc sinc(x):= \xintfloatexpr sinc(sfloat(x))\relax;%
+\xintFor* #1 in {iDTVtuwxyzX}\do{\xintrestorelettervar{#1}}%
+\endinput
+%%
+%% End of file `xinttrig.sty'.