l3kernel 3160 (31aug12)

git-svn-id: svn://tug.org/texlive/trunk@27559 c570f23f-e606-0410-a88d-b1316a301751

15 files changed, 661 insertions, 513 deletions

diff --git a/Master/texmf-dist/tex/latex/l3kernel/expl3.sty b/Master/texmf-dist/tex/latex/l3kernel/expl3.sty
index 6adfc5fed60..edf7566552f 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/expl3.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/expl3.sty
@@ -60,8 +60,8 @@
   }
 \def\ExplFileName{expl3}
 \def\ExplFileDescription{L3 Experimental code bundle wrapper}
-\def\ExplFileDate{2012/08/14}
-\def\ExplFileVersion{4091}
+\def\ExplFileDate{2012/08/29}
+\def\ExplFileVersion{4160}
 \RequirePackage{etex}
 \reserveinserts{32}
 \ProvidesExplPackage
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3basics.sty b/Master/texmf-dist/tex/latex/l3kernel/l3basics.sty
index c7c5bcb0eb8..d9dfc41083c 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3basics.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3basics.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3basics.dtx 4069 2012-08-08 23:12:57Z bruno $
+\GetIdInfo$Id: l3basics.dtx 4144 2012-08-27 19:37:16Z bruno $
   {L3 Basic definitions}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -82,7 +82,10 @@
 \tex_let:D \if_int_compare:w   \tex_ifnum:D
 \tex_let:D \__int_to_roman:w     \tex_romannumeral:D
 \tex_let:D \group_insert_after:N \tex_aftergroup:D
-\tex_long:D \tex_def:D \exp_args:Nc #1#2 { \exp_after:wN #1 \cs:w #2 \cs_end: }
+\tex_long:D \tex_def:D \exp_args:Nc #1#2
+  { \exp_after:wN #1 \cs:w #2 \cs_end: }
+\tex_long:D \tex_def:D \exp_args:cc #1#2
+  { \cs:w #1 \exp_after:wN \cs_end: \cs:w #2 \cs_end: }
 \tex_def:D \token_to_str:c { \exp_args:Nc \token_to_str:N }
 \tex_long:D \tex_def:D \cs_meaning:c #1
   {
@@ -254,7 +257,7 @@
       \exp_after:wN \use_ii:nn
     \fi:
       {
-        \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 _p: #5 } #6
+        \exp_args:cc { cs_ #2 #3 :Npn } { #4 _p: #5 } #6
           { #7 \c_zero \c_true_bool \c_false_bool }
       }
       {
@@ -264,17 +267,17 @@
   }
 \cs_set_protected:Npn \__prg_generate_T_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
   {
-    \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 : #5 T } #6
+    \exp_args:cc { cs_ #2 #3 :Npn } { #4 : #5 T } #6
       { #7 \c_zero \use:n \use_none:n }
   }
 \cs_set_protected:Npn \__prg_generate_F_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
   {
-    \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 : #5 F } #6
+    \exp_args:cc { cs_ #2 #3 :Npn } { #4 : #5 F } #6
       { #7 \c_zero { } }
   }
 \cs_set_protected:Npn \__prg_generate_TF_form:wnnnnnn #1 \q_stop #2#3#4#5#6#7
   {
-    \exp_args:Nc \exp_args:Nc { cs_ #2 #3 :Npn } { #4 : #5 TF } #6
+    \exp_args:cc { cs_ #2 #3 :Npn } { #4 : #5 TF } #6
       { #7 \c_zero }
   }
 \cs_set_protected_nopar:Npn \prg_set_eq_conditional:NNn
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3clist.sty b/Master/texmf-dist/tex/latex/l3kernel/l3clist.sty
index 35d5381e677..18cee384adc 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3clist.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3clist.sty
@@ -48,7 +48,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3clist.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3clist.dtx 4102 2012-08-15 16:08:27Z bruno $
   {L3 Comma separated lists}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -146,7 +146,7 @@
 \cs_new_protected_nopar:Npn \clist_put_right:Nn
   { \__clist_put_right:NNNn \clist_concat:NNN \clist_set:Nn }
 \cs_new_protected_nopar:Npn \clist_gput_right:Nn
-  { \__clist_put_right:NNNn \clist_gconcat:NNN \clist_gset:Nn }
+  { \__clist_put_right:NNNn \clist_gconcat:NNN \clist_set:Nn }
 \cs_new_protected:Npn \__clist_put_right:NNNn #1#2#3#4
   {
     #2 \l__clist_internal_clist {#4}
@@ -419,18 +419,13 @@
   }
 \cs_new_protected:Npn \clist_show:N #1
   {
-    \__msg_show_variable:Nnn
-      #1
-      { clist }
+    \__msg_show_variable:Nnx #1 { clist }
       { \clist_map_function:NN #1 \__msg_show_item:n }
   }
 \cs_new_protected:Npn \clist_show:n #1
   {
     \clist_set:Nn \l__clist_internal_clist {#1}
-    \__msg_show_variable:Nnn
-      \l__clist_internal_clist
-      { clist }
-      { \clist_map_function:NN \l__clist_internal_clist \__msg_show_item:n }
+    \clist_show:N \l__clist_internal_clist
   }
 \cs_generate_variant:Nn \clist_show:N { c }
 \clist_new:N \l_tmpa_clist
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3coffins.sty b/Master/texmf-dist/tex/latex/l3kernel/l3coffins.sty
index a126e8fd5c4..1b8d88d4761 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3coffins.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3coffins.sty
@@ -47,7 +47,7 @@
 %% -----------------------------------------------------------------------
 %%
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3coffins.dtx 4011 2012-07-20 21:02:59Z joseph $
+\GetIdInfo$Id: l3coffins.dtx 4092 2012-08-14 14:04:41Z bruno $
   {L3 Coffin code layer}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -807,7 +807,7 @@
   {
     \__coffin_if_exist:NT #1
       {
-        \__msg_show_variable:Nnn #1 { coffins }
+        \__msg_show_variable:Nnx #1 { coffins }
           {
             \prop_map_function:cN
               { l__coffin_poles_ \__int_value:w #1 _prop }
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3color.sty b/Master/texmf-dist/tex/latex/l3kernel/l3color.sty
index 1584c055979..12b019250a5 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3color.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3color.sty
@@ -47,8 +47,8 @@
 %% -----------------------------------------------------------------------
 %%
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3color.dtx 3991 2012-07-16 19:00:35Z joseph $
-  {L3 Experimental colour support}
+\GetIdInfo$Id: l3color.dtx 4156 2012-08-29 11:10:09Z joseph $
+  {L3 Experimental color support}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
 \__expl_package_check:
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3doc.cls b/Master/texmf-dist/tex/latex/l3kernel/l3doc.cls
index 111db55e442..641a13ec78c 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3doc.cls
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3doc.cls
@@ -52,7 +52,7 @@
 \let     \fileversionOld        \ExplFileVersion
 \let \filedescriptionOld        \ExplFileDescription
 \RequirePackage{expl3,xparse,calc}
-\GetIdInfo$Id: l3doc.dtx 4070 2012-08-09 11:04:46Z joseph $
+\GetIdInfo$Id: l3doc.dtx 4130 2012-08-20 21:30:22Z joseph $
           {L3 Experimental documentation class}
 \ProvidesExplClass
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -71,7 +71,6 @@
 \tl_new:N \l__codedoc_macro_tl
 \int_new:N \l__codedoc_macro_int
 \int_new:N \g__codedoc_nested_macro_int
-\int_new:N \g__codedoc_codeline_int
 \prop_new:N \g__codedoc_missing_tests_prop
 \clist_new:N \g_docinput_clist
 \tl_new:N \l__codedoc_at_replaced_macro_tl
@@ -798,7 +797,7 @@
       \tl_to_str:N \l__codedoc_at_replaced_macro_tl
     }]
    }
-  \int_gincr:N \g__codedoc_codeline_int
+  \int_gincr:N \c@CodelineNo
 
   \bool_if:NF \l__codedoc_macro_aux_bool
    {
@@ -822,7 +821,7 @@
     \exp_args:Nx \DoNotIndex{ \tl_to_str:N \l__codedoc_at_replaced_macro_tl }
    }
 
-  \int_gdecr:N \g__codedoc_codeline_int
+  \int_gdecr:N \c@CodelineNo
   \ignorespaces
  }
 \tl_clear:N \l__codedoc_macro_tl
@@ -1250,7 +1249,7 @@
   \immediate\write\@indexfile
    {
     \string\indexentry{#1}
-    { \filesep \int_use:N \g__codedoc_codeline_int }
+    { \filesep \int_use:N \c@CodelineNo }
    }
  }
 \cs_set_eq:NN \filesep \@empty
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3expan.sty b/Master/texmf-dist/tex/latex/l3kernel/l3expan.sty
index f7a458e9a88..6dceea954ad 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3expan.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3expan.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3expan.dtx 4073 2012-08-10 01:33:13Z bruno $
+\GetIdInfo$Id: l3expan.dtx 4149 2012-08-28 10:50:40Z bruno $
   {L3 Argument expansion}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -56,6 +56,7 @@
 \cs_new:Npn \::: #1 {#1}
 \cs_new:Npn \::n #1 \::: #2#3 { #1 \::: { #2 {#3} } }
 \cs_new:Npn \::N #1 \::: #2#3 { #1 \::: {#2#3} }
+\cs_new:Npn \::p #1 \::: #2#3# { #1 \::: {#2#3} }
 \cs_new:Npn \::c #1 \::: #2#3
   { \exp_after:wN \__exp_arg_next:Nnn \cs:w #3 \cs_end: {#1} {#2} }
 \cs_new:Npn \::o #1 \::: #2#3
@@ -109,8 +110,6 @@
   { \exp_after:wN #1 \exp_after:wN #2 \exp_after:wN {#3} }
 \cs_new:Npn \exp_args:NNNo #1#2#3#4
   { \exp_after:wN #1 \exp_after:wN#2 \exp_after:wN #3 \exp_after:wN {#4} }
-\cs_new:Npn \exp_args:cc #1#2
-  { \cs:w #1 \exp_after:wN \cs_end: \cs:w #2 \cs_end: }
 \cs_new:Npn \exp_args:NNc #1#2#3
   { \exp_after:wN #1 \exp_after:wN #2 \cs:w # 3\cs_end: }
 \cs_new:Npn \exp_args:Ncc #1#2#3
@@ -313,80 +312,151 @@
     \exp_after:wN #1
     \exp_after:wN \__cs_generate_variant:nnNN
     \exp_after:wN #1
-    \etex_detokenize:D {#2} , ? , \q_recursion_stop
+    \etex_detokenize:D {#2} , \scan_stop: , \q_recursion_stop
   }
 \group_begin:
-  \tex_lccode:D `\Z = `\d \scan_stop:
-  \tex_lccode:D `\? =`\\ \scan_stop:
+  \tex_catcode:D `\M = 12 \scan_stop:
+  \tex_catcode:D `\A = 12 \scan_stop:
   \tex_catcode:D `\P = 12 \scan_stop:
   \tex_catcode:D `\R = 12 \scan_stop:
-  \tex_catcode:D `\O = 12 \scan_stop:
-  \tex_catcode:D `\T = 12 \scan_stop:
-  \tex_catcode:D `\E = 12 \scan_stop:
-  \tex_catcode:D `\C = 12 \scan_stop:
-  \tex_catcode:D `\Z = 12 \scan_stop:
 \tex_lowercase:D
   {
     \group_end:
     \cs_new_protected:Npn \__cs_generate_variant:N #1
       {
-        \exp_after:wN \__cs_generate_variant:w
-          \token_to_meaning:N #1
-          \q_mark \cs_new_protected_nopar:Npx
-          ? PROTECTEZ
-          \q_mark \cs_new_nopar:Npx
-          \q_stop
+        \exp_after:wN \if_meaning:w \exp_not:N #1 #1
+          \cs_set_eq:NN \__cs_tmp:w \cs_new_protected_nopar:Npx
+        \else:
+          \exp_after:wN \__cs_generate_variant:ww
+            \token_to_meaning:N #1 MA \q_mark
+            \q_mark \cs_new_protected_nopar:Npx
+            PR
+            \q_mark \cs_new_nopar:Npx
+            \q_stop
+        \fi:
       }
-    \cs_new_protected:Npn \__cs_generate_variant:w
-        #1 ? PROTECTEZ #2 \q_mark #3 #4 \q_stop
+    \cs_new_protected:Npn \__cs_generate_variant:ww #1 MA #2 \q_mark
+      { \__cs_generate_variant:wwNw #1 }
+    \cs_new_protected:Npn \__cs_generate_variant:wwNw
+        #1 PR #2 \q_mark #3 #4 \q_stop
       {
         \cs_set_eq:NN \__cs_tmp:w #3
       }
   }
 \cs_new_protected:Npn \__cs_generate_variant:nnNN #1#2#3#4
-  { \__cs_generate_variant:Nnnw #4 {#1}{#2} }
+  {
+    \if_meaning:w \c_false_bool #3
+      \__msg_kernel_error:nnx { kernel } { missing-colon }
+        { \token_to_str:c {#1} }
+      \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
+    \fi:
+    \__cs_generate_variant:Nnnw #4 {#1}{#2}
+  }
 \cs_new_protected:Npn \__cs_generate_variant:Nnnw #1#2#3#4 ,
   {
-    \if:w ? #4
+    \if_meaning:w \scan_stop: #4
       \exp_after:wN \use_none_delimit_by_q_recursion_stop:w
     \fi:
-    \exp_after:wN \__cs_generate_variant:NNn
-    \exp_after:wN #1
-      \cs:w
-        #2 :
-        \__cs_generate_variant_loop:NwN
-          ? #3
-          \q_mark #4 \__cs_generate_variant_loop_end:w
-          \q_mark \__cs_generate_variant_loop_error:wnNNnn
-        \q_stop
-      \cs_end:
-      {#4}
+    \use:x
+      {
+        \exp_not:N \__cs_generate_variant:wwNN
+        \__cs_generate_variant_loop:nNwN { }
+          #4
+          \__cs_generate_variant_loop_end:nwwwNNnn
+          \q_mark
+          #3 ~
+          { ~ { } \fi: \__cs_generate_variant_loop_long:wNNnn } ~
+          { }
+          \q_stop
+        \exp_not:N #1 {#2} {#4}
+      }
     \__cs_generate_variant:Nnnw #1 {#2} {#3}
   }
-\cs_new:Npn \__cs_generate_variant_loop:NwN #1 #2 \q_mark #3
-  { #3 \__cs_generate_variant_loop:NwN #2 \q_mark }
-\cs_new:Npn \__cs_generate_variant_loop_end:w #1#2 \q_mark #3 \q_stop {#2}
-\cs_new:Npn \__cs_generate_variant_loop_error:wnNNnn
-    #1 \q_stop \cs_end: #2 #3#4#5#6
+\cs_new:Npn \__cs_generate_variant_loop:nNwN #1#2#3 \q_mark #4
+  {
+    \if:w #2 #4
+      \exp_after:wN \__cs_generate_variant_loop_same:w
+    \else:
+      \if:w N #4 \else:
+        \if:w n #4 \else:
+          \__cs_generate_variant_loop_invalid:NNwNNnn #4#2
+        \fi:
+      \fi:
+    \fi:
+    #1
+    \prg_do_nothing:
+    #2
+    \__cs_generate_variant_loop:nNwN { } #3 \q_mark
+  }
+\cs_new:Npn \__cs_generate_variant_loop_same:w
+    #1 \prg_do_nothing: #2#3#4
+  {
+    #3 { #1 \__cs_generate_variant_same:N #2 }
+  }
+\cs_new:Npn \__cs_generate_variant_loop_end:nwwwNNnn
+    #1#2 \q_mark #3 ~ #4 \q_stop #5#6#7#8
   {
-    \cs_end: {#2}
-    \__msg_kernel_error:nnxx { kernel } { variant-too-long }
-      { \tl_to_str:n {#2} } { \token_to_str:N #4 }
-    #3 #4 {#5} {#6}
+    \scan_stop: \scan_stop: \fi:
+    \exp_not:N \q_mark
+    \exp_not:N \q_stop
+    \exp_not:N #6
+    \exp_not:c { #7 : #8 #1 #3 }
+  }
+\cs_new:Npn \__cs_generate_variant_loop_long:wNNnn #1 \q_stop #2#3#4#5
+  {
+    \exp_not:n
+      {
+        \q_mark
+        \__msg_kernel_error:nnxx { kernel } { variant-too-long }
+          {#5} { \token_to_str:N #3 }
+        \use_none:nnnn
+        \q_stop
+        #3
+        #3
+      }
+  }
+\cs_new:Npn \__cs_generate_variant_loop_invalid:NNwNNnn
+    #1#2 \fi: \fi: \fi: #3 \q_stop #4#5#6#7
+  {
+    \fi: \fi: \fi:
+    \exp_not:n
+      {
+        \q_mark
+        \__msg_kernel_error:nnxxxx { kernel } { invalid-variant }
+          {#7} { \token_to_str:N #5 } {#1} {#2}
+        \use_none:nnnn
+        \q_stop
+        #5
+        #5
+      }
+  }
+\cs_new:Npn \__cs_generate_variant_same:N #1
+  {
+    \if:w N #1
+      N
+    \else:
+      \if:w p #1
+        p
+      \else:
+        n
+      \fi:
+    \fi:
   }
-\cs_new_protected:Npn \__cs_generate_variant:NNn #1 #2 #3
+\cs_new_protected:Npn \__cs_generate_variant:wwNN
+    #1 \q_mark #2 \q_stop #3#4
   {
-    \cs_if_free:NTF #2
+    #2
+    \cs_if_free:NTF #4
       {
         \group_begin:
-          \__cs_generate_internal_variant:n {#3}
-          \__cs_tmp:w #2 { \exp_not:c { exp_args:N #3 } \exp_not:N #1 }
+          \__cs_generate_internal_variant:n {#1}
+          \__cs_tmp:w #4 { \exp_not:c { exp_args:N #1 } \exp_not:N #3 }
         \group_end:
       }
       {
         \iow_log:x
           {
-            Variant~\token_to_str:N #2~%
+            Variant~\token_to_str:N #4~%
             already~defined;~ not~ changing~ it~on~line~%
             \tex_the:D \tex_inputlineno:D
           }
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3file.sty b/Master/texmf-dist/tex/latex/l3kernel/l3file.sty
index c222c3a6358..44e02bdff7c 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3file.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3file.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3file.dtx 4059 2012-08-08 13:12:06Z bruno $
+\GetIdInfo$Id: l3file.dtx 4101 2012-08-15 16:05:33Z bruno $
   {L3 File and I/O operations}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -55,6 +55,7 @@
 \tl_gset_eq:NN \g_file_current_name_tl \@currname
 \seq_new:N \g__file_stack_seq
 \seq_new:N \g__file_record_seq
+\tl_new:N \l__file_internal_tl
 \tl_new:N \l__file_internal_name_tl
 \seq_new:N \l__file_search_path_seq
 \seq_new:N \l__file_saved_search_path_seq
@@ -141,10 +142,11 @@
     \clist_if_exist:NTF \@filelist
       { \@addtofilelist {#1} }
       { \seq_gput_right:Nn \g__file_record_seq {#1} }
-    \seq_gpush:Nn \g__file_stack_seq \g_file_current_name_tl
+    \seq_gpush:No \g__file_stack_seq \g_file_current_name_tl
     \tl_gset:Nn \g_file_current_name_tl {#1}
     \tex_input:D #1 \c_space_tl
-    \seq_gpop:NN \g__file_stack_seq \g_file_current_name_tl
+    \seq_gpop:NN \g__file_stack_seq \l__file_internal_tl
+    \tl_gset_eq:NN \g_file_current_name_tl \l__file_internal_tl
   }
 \cs_generate_variant:Nn \__file_input_aux:n { o }
 \cs_new_protected:Npn \file_path_include:n #1
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty b/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty
index 3918bd5a161..cd23b05bfc1 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3fp.sty
@@ -59,7 +59,7 @@
 %% -----------------------------------------------------------------------
 %%
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3fp.dtx 4089 2012-08-14 04:52:20Z bruno $
+\GetIdInfo$Id: l3fp.dtx 4151 2012-08-28 11:51:52Z bruno $
   {L3 Floating points}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -218,11 +218,15 @@
 \int_const:Nn \c__fp_middle_shift_int   { 5 0000 *  9999 }
 \int_const:Nn \c__fp_trailing_shift_int { 5 0000 * 10000 }
 \cs_new:Npn \__fp_pack:NNNNNw #1 #2#3#4#5 #6; { + #1#2#3#4#5 ; {#6} }
+\cs_new:Npn \__fp_pack:NNNNNwn #1 #2#3#4#5 #6; #7
+  { + #1#2#3#4#5 ; {#7} {#6} }
 \int_const:Nn \c__fp_big_leading_shift_int  { - 15 2374 }
 \int_const:Nn \c__fp_big_middle_shift_int   { 15 2374 *  9999 }
 \int_const:Nn \c__fp_big_trailing_shift_int { 15 2374 * 10000 }
 \cs_new:Npn \__fp_pack_big:NNNNNNw #1#2 #3#4#5#6 #7;
   { + #1#2#3#4#5#6 ; {#7} }
+\cs_new:Npn \__fp_pack_big:NNNNNNwn #1#2 #3#4#5#6 #7; #8
+  { + #1#2#3#4#5#6 ; {#8} {#7} }
 \int_const:Nn \c__fp_Bigg_leading_shift_int  { - 20 0000 }
 \int_const:Nn \c__fp_Bigg_middle_shift_int   { 20 0000 *  9999 }
 \int_const:Nn \c__fp_Bigg_trailing_shift_int { 20 0000 * 10000 }
@@ -417,7 +421,7 @@
       { \cs_set:Npn \__fp_invalid_operation:nnw ##1##2##3; }
       {
         #1
-        \__fp_error:nffn { invalid } {##2} { \__fp_to_tl:w ##3; } { }
+        \__fp_error:nnfn { invalid } {##2} { \__fp_to_tl:w ##3; } { }
         \fp_flag_on:n { invalid_operation }
         ##1
       }
@@ -431,11 +435,10 @@
         \exp_after:wN \c_nan_fp
       }
     \exp_args:Nno \use:n
-      { \cs_set:Npn \__fp_array_invalid_operation_o:nw ##1##2@ }
+      { \cs_set:Npn \__fp_invalid_operation_tl_o:nf ##1##2 }
       {
         #1
-        \__fp_error:nffn { invalid }
-          {##1} { \__fp_array_to_clist:w ##2 @ } { }
+        \__fp_error:nnfn { invalid } {##1} {##2} { }
         \fp_flag_on:n { invalid_operation }
         \exp_after:wN \c_nan_fp
       }
@@ -452,7 +455,7 @@
       { \cs_set:Npn \__fp_division_by_zero_o:Nnw ##1##2##3; }
       {
         #1
-        \__fp_error:nffn { zero-div } {##2} { \__fp_to_tl:w ##3; } { }
+        \__fp_error:nnfn { zero-div } {##2} { \__fp_to_tl:w ##3; } { }
         \fp_flag_on:n { division_by_zero }
         \exp_after:wN ##1
       }
@@ -499,7 +502,7 @@
   }
 \cs_new:Npn \__fp_invalid_operation:nnw #1#2#3; { }
 \cs_new:Npn \__fp_invalid_operation_o:Nww #1#2; #3; { }
-\cs_new:Npn \__fp_array_invalid_operation_o:nw #1 #2 @ { }
+\cs_new:Npn \__fp_invalid_operation_tl_o:nf #1 #2 { }
 \cs_new:Npn \__fp_division_by_zero_o:Nnw #1#2#3; { }
 \cs_new:Npn \__fp_division_by_zero_o:NNww #1#2#3; #4; { }
 \cs_new:Npn \__fp_overflow:w { }
@@ -512,21 +515,7 @@
   { \__fp_invalid_operation:nnw { \exp_after:wN \c_nan_fp } }
 \cs_new:Npn \__fp_error:nnnn #1
   { \__msg_kernel_expandable_error:nnnnn { kernel } { fp - #1 } }
-\cs_generate_variant:Nn \__fp_error:nnnn { nff }
-\cs_new:Npn \__fp_array_to_clist:w #1 @
-  {
-    \__fp_array_to_clist_i:wwww ;
-      #1
-      \__fp_array_to_clist_ii:ww \s__fp ; @
-  }
-\cs_new:Npn \__fp_array_to_clist_i:wwww #1; #2 \s__fp #3; #4 @
-  {
-    #2
-    \exp_after:wN \__fp_array_to_clist_i:wwww
-    \tex_romannumeral:D -`0 \__fp_to_tl:w \s__fp #3 ; ;
-    #4 , ~ #1 @
-  }
-\cs_new:Npn \__fp_array_to_clist_ii:ww #1 ; , ~ , ~ #2 @ {#2}
+\cs_generate_variant:Nn \__fp_error:nnnn { nnf, nff }
 \__msg_kernel_new:nnnn { kernel } { unknown-fpu-exception }
   { The~FPU~exception~'#1'~is~not~known:~that~trap~will~never~be~triggered. }
   {
@@ -687,7 +676,10 @@
 \cs_new:Npn \__fp_round:Nww #1#2 ; #3 ;
   {
     \__fp_small_int:wTF #3; { \__fp_round:Nwn #1#2; }
-      { \__fp_array_invalid_operation_o:nw { round } #2; #3; @ }
+      {
+        \__fp_invalid_operation_tl_o:nf
+          { round } { \__fp_array_to_clist:n { #2; #3; } }
+      }
   }
 \cs_new:Npn \__fp_round:Nwn #1 \s__fp \__fp_chk:w #2#3#4; #5
   {
@@ -808,7 +800,7 @@
     \cs_new:Npn \__fp_type_from_scan:N #1
       {
         \exp_after:wN \__fp_type_from_scan:w
-        \token_to_str:N #1 \q_mark S--FP \q_mark \q_stop
+        \token_to_str:N #1 \q_mark S--FP-? \q_mark \q_stop
       }
     \cs_new:Npn \__fp_type_from_scan:w #1 S--FP #2 \q_mark #3 \q_stop {#2}
   }
@@ -877,39 +869,26 @@
   }
 \cs_new:Npn \__fp_parse_operand_relax:NN #1#2
   {
-      \__fp_parse_operand_relax_aux:wwnw
-        #2 \s__fp_mark
-          {
-            \__fp_exp_after_o:nw
-              {
-                \tex_romannumeral:D -`0
-                \exp_after:wN \__fp_parse_infix:NN
-                \exp_after:wN #1 \tex_romannumeral:D \__fp_parse_expand:w
-              }
-            \s__fp
-          }
-        \s__fp #2
-          {
-            \__msg_kernel_expandable_error:nn { kernel } { fp-early-end }
-            \exp_after:wN \c_nan_fp
-            \tex_romannumeral:D -`0
-              \__fp_parse_infix:NN #1
-              \s__fp_mark
-          }
-        \s__fp_mark
-          {
-            \__msg_kernel_expandable_error:nnn
-              { kernel } { bad-variable } {#2}
-            \exp_after:wN \c_nan_fp
-            \tex_romannumeral:D -`0
-              \exp_after:wN \__fp_parse_infix:NN
-              \exp_after:wN #1
-              \tex_romannumeral:D \__fp_parse_expand:w
-          }
-        \s__fp_mark \s__fp_stop
+    \cs:w __fp_exp_after \__fp_type_from_scan:N #2 _f:nw \cs_end:
+      {
+        \exp_after:wN \__fp_parse_infix:NN
+        \exp_after:wN #1 \tex_romannumeral:D \__fp_parse_expand:w
+      }
+    #2
+  }
+\cs_new:Npn \__fp_exp_after_mark_f:nw #1
+  {
+    \__msg_kernel_expandable_error:nn { kernel } { fp-early-end }
+    \exp_after:wN \c_nan_fp
+    \tex_romannumeral:D -`0 #1
+  }
+\cs_new:cpn { __fp_exp_after_?_f:nw } #1#2
+  {
+    \__msg_kernel_expandable_error:nnn
+      { kernel } { bad-variable } {#2}
+    \exp_after:wN \c_nan_fp
+    \tex_romannumeral:D -`0 #1
   }
-\cs_new:Npn \__fp_parse_operand_relax_aux:wwnw
-    #1 \s__fp #2 \s__fp_mark #3 #4 \s__fp_mark \s__fp_stop { #3 }
 \cs_new:Npn \__fp_parse_operand_other:NN #1 #2
   {
     \if_int_compare:w
@@ -1447,8 +1426,9 @@
       \cs:w
         __fp
         \__fp_type_from_scan:N #2
+        _ #4
         \__fp_type_from_scan:N #5
-        _ #4 _o:ww
+        _o:ww
       \cs_end:
       #2#3 #5#6
     \tex_romannumeral:D -`0 #7 #1
@@ -1504,7 +1484,8 @@
         \tex_romannumeral:D -`0 \__fp_parse_infix:NN
       }
   }
-\tl_map_inline:nn { {abs} {cos} {cot} {exp} {ln} {sin} {tan} }
+\tl_map_inline:nn
+  { {abs} {cos} {cot} {csc} {exp} {ln} {sec} {sin} {tan} }
   {
     \cs_new:cpn { __fp_parse_word_#1:N } ##1
       {
@@ -1600,7 +1581,7 @@
     {
       \token_if_eq_meaning:NNTF #3 \__fp_parse_infix_):N
         {
-          \__fp_parse_exp_after_array:wf #2 \s__fp_stop
+          \__fp_exp_after_array_f:w #2 \s__fp_stop
           \exp_after:wN \__fp_parse_infix:NN
           \exp_after:wN #1
           \tex_romannumeral:D \__fp_parse_expand:w
@@ -1611,13 +1592,13 @@
         }
     }
 \group_end:
-\cs_new:Npn \__fp_parse_exp_after_array:wf #1
+\cs_new:Npn \__fp_exp_after_array_f:w #1
   {
-    \cs:w __fp \__fp_type_from_scan:N #1 _exp_after_f:nw \cs_end:
-      { \__fp_parse_exp_after_array:wf }
+    \cs:w __fp_exp_after \__fp_type_from_scan:N #1 _f:nw \cs_end:
+      { \__fp_exp_after_array_f:w }
     #1
   }
-\cs_new:Npn \__fp_stop_exp_after_f:nw #1#2 { }
+\cs_new:Npn \__fp_exp_after_stop_f:nw #1#2 { }
 \cs_new:cpn {__fp_parse_prefix_.:Nw} #1
   {
     \exp_after:wN \__fp_parse_infix_after_operand:NwN
@@ -1990,12 +1971,12 @@
 \cs_new:Npn \__fp_compare_npos:nwnw #1#2; #3#4;
   {
     \if_int_compare:w #1 = #3 \exp_stop_f:
-      \__fp_compare_mantissa:nnnnnnnn #2 #4
+      \__fp_compare_significand:nnnnnnnn #2 #4
     \else:
       \if_int_compare:w #1 < #3 - \fi: 1
     \fi:
   }
-\cs_new:Npn \__fp_compare_mantissa:nnnnnnnn #1#2#3#4#5#6#7#8
+\cs_new:Npn \__fp_compare_significand:nnnnnnnn #1#2#3#4#5#6#7#8
   {
     \if_int_compare:w #1#2 = #5#6 \exp_stop_f:
       \if_int_compare:w #3#4 = #7#8 \exp_stop_f:
@@ -2007,6 +1988,62 @@
       \if_int_compare:w #1#2 < #5#6 - \fi: 1
     \fi:
   }
+\cs_new:Npn \fp_do_until:nn #1#2
+  {
+    #2
+    \fp_compare:nF {#1}
+      { \fp_do_until:nn {#1} {#2} }
+  }
+\cs_new:Npn \fp_do_while:nn #1#2
+  {
+    #2
+    \fp_compare:nT {#1}
+      { \fp_do_while:nn {#1} {#2} }
+  }
+\cs_new:Npn \fp_until_do:nn #1#2
+  {
+    \fp_compare:nF {#1}
+      {
+        #2
+        \fp_until_do:nn {#1} {#2}
+      }
+  }
+\cs_new:Npn \fp_while_do:nn #1#2
+  {
+    \fp_compare:nT {#1}
+      {
+        #2
+        \fp_while_do:nn {#1} {#2}
+      }
+  }
+\cs_new:Npn \fp_do_until:nNnn #1#2#3#4
+  {
+    #4
+    \fp_compare:nNnF {#1} #2 {#3}
+      { \fp_do_until:nNnn {#1} #2 {#3} {#4} }
+  }
+\cs_new:Npn \fp_do_while:nNnn #1#2#3#4
+  {
+    #4
+    \fp_compare:nNnT {#1} #2 {#3}
+      { \fp_do_while:nNnn {#1} #2 {#3} {#4} }
+  }
+\cs_new:Npn \fp_until_do:nNnn #1#2#3#4
+  {
+    \fp_compare:nNnF {#1} #2 {#3}
+      {
+        #4
+        \fp_until_do:nNnn {#1} #2 {#3} {#4}
+      }
+  }
+\cs_new:Npn \fp_while_do:nNnn #1#2#3#4
+  {
+    \fp_compare:nNnT {#1} #2 {#3}
+      {
+        #4
+        \fp_while_do:nNnn {#1} #2 {#3} {#4}
+      }
+  }
 \cs_new:Npn \__fp_max_o:w #1 @
   {
     \exp_after:wN \__fp_minmax_loop:Nww
@@ -2083,7 +2120,7 @@
       \__fp_ternary_break_point:n { \exp_after:wN \__fp_ternary_i:NwwN }
       \exp_after:wN #1
       \tex_romannumeral:D -`0
-      \__fp_parse_exp_after_array:wf #3 \s__fp_stop
+      \__fp_exp_after_array_f:w #3 \s__fp_stop
       \exp_after:wN @
       \tex_romannumeral:D
         \__fp_parse_until:Nw \c_two
@@ -2094,7 +2131,7 @@
       \exp_after:wN \__fp_parse_until_test:NwN
       \exp_after:wN #1
       \tex_romannumeral:D -`0
-      \__fp_parse_exp_after_array:wf #3 \s__fp_stop
+      \__fp_exp_after_array_f:w #3 \s__fp_stop
       \exp_after:wN #4
       \exp_after:wN #1
     \fi:
@@ -2117,7 +2154,7 @@
     \exp_after:wN \__fp_parse_until_test:NwN
     \exp_after:wN #1
     \tex_romannumeral:D -`0
-    \__fp_parse_exp_after_array:wf #2 \s__fp_stop
+    \__fp_exp_after_array_f:w #2 \s__fp_stop
     #4 #1
   }
 \cs_new:Npn \__fp_ternary_ii:NwwN #1#2@#3@#4
@@ -2125,7 +2162,7 @@
     \exp_after:wN \__fp_parse_until_test:NwN
     \exp_after:wN #1
     \tex_romannumeral:D -`0
-    \__fp_parse_exp_after_array:wf #3 \s__fp_stop
+    \__fp_exp_after_array_f:w #3 \s__fp_stop
     #4 #1
   }
 %% File: l3fp-basics.dtx Copyright (C) 2011-2012 The LaTeX3 Project
@@ -2273,7 +2310,7 @@
 \cs_new:Npn \__fp_add_big_i_o:wNww #1; #2 #3; #4;
   {
     \__fp_decimate:nNnnnn {#1}
-      \__fp_add_mantissa_o:NnnwnnnnN
+      \__fp_add_significand_o:NnnwnnnnN
       #4
     #3
     #2
@@ -2281,34 +2318,34 @@
 \cs_new:Npn \__fp_add_big_ii_o:wNww #1; #2 #3; #4;
   {
     \__fp_decimate:nNnnnn {#1}
-      \__fp_add_mantissa_o:NnnwnnnnN
+      \__fp_add_significand_o:NnnwnnnnN
       #3
     #4
     #2
   }
-\cs_new:Npn \__fp_add_mantissa_o:NnnwnnnnN #1 #2#3 #4; #5#6#7#8
+\cs_new:Npn \__fp_add_significand_o:NnnwnnnnN #1 #2#3 #4; #5#6#7#8
   {
-    \exp_after:wN \__fp_add_mantissa_test_o:N
+    \exp_after:wN \__fp_add_significand_test_o:N
     \int_use:N \__int_eval:w 1#5#6 + #2
-      \exp_after:wN \__fp_add_mantissa_pack:NNNNNNN
+      \exp_after:wN \__fp_add_significand_pack:NNNNNNN
       \int_use:N \__int_eval:w 1#7#8 + #3 ; #1
   }
-\cs_new:Npn \__fp_add_mantissa_pack:NNNNNNN #1 #2#3#4#5#6#7
+\cs_new:Npn \__fp_add_significand_pack:NNNNNNN #1 #2#3#4#5#6#7
   {
     \if_meaning:w 2 #1
       + \c_one
     \fi:
     ; #2 #3 #4 #5 #6 #7 ;
   }
-\cs_new:Npn \__fp_add_mantissa_test_o:N #1
+\cs_new:Npn \__fp_add_significand_test_o:N #1
   {
     \if_meaning:w 2 #1
-      \exp_after:wN \__fp_add_mantissa_carry_o:wwwNN
+      \exp_after:wN \__fp_add_significand_carry_o:wwwNN
     \else:
-      \exp_after:wN \__fp_add_mantissa_no_carry_o:wwwNN
+      \exp_after:wN \__fp_add_significand_no_carry_o:wwwNN
     \fi:
   }
-\cs_new:Npn \__fp_add_mantissa_no_carry_o:wwwNN
+\cs_new:Npn \__fp_add_significand_no_carry_o:wwwNN
     #1; #2; #3#4 ; #5#6
   {
     \exp_after:wN \__fp_basics_pack_high:NNNNNw
@@ -2318,7 +2355,7 @@
         + \__fp_round:NNN #6 #4 #5
         \exp_after:wN ;
   }
-\cs_new:Npn \__fp_add_mantissa_carry_o:wwwNN
+\cs_new:Npn \__fp_add_significand_carry_o:wwwNN
     #1; #2; #3#4; #5#6
   {
     + \c_one
@@ -2527,41 +2564,41 @@
     \exp_after:wN #1
     \int_use:N \__int_eval:w
       #4 + #8
-      \__fp_mul_mantissa_o:nnnnNnnnn #5 #1 #9
+      \__fp_mul_significand_o:nnnnNnnnn #5 #1 #9
   }
-\cs_new:Npn \__fp_mul_mantissa_o:nnnnNnnnn #1#2#3#4 #5 #6#7#8#9
+\cs_new:Npn \__fp_mul_significand_o:nnnnNnnnn #1#2#3#4 #5 #6#7#8#9
   {
-    \exp_after:wN \__fp_mul_mantissa_test_f:NNN
+    \exp_after:wN \__fp_mul_significand_test_f:NNN
     \exp_after:wN #5
     \int_use:N \__int_eval:w 99990000 + #1*#6 +
-      \exp_after:wN \__fp_mul_mantissa_keep:NNNNNw
+      \exp_after:wN \__fp_mul_significand_keep:NNNNNw
       \int_use:N \__int_eval:w 99990000 + #1*#7 + #2*#6 +
-        \exp_after:wN \__fp_mul_mantissa_keep:NNNNNw
+        \exp_after:wN \__fp_mul_significand_keep:NNNNNw
         \int_use:N \__int_eval:w 99990000 + #1*#8 + #2*#7 + #3*#6 +
-          \exp_after:wN \__fp_mul_mantissa_drop:NNNNNw
+          \exp_after:wN \__fp_mul_significand_drop:NNNNNw
           \int_use:N \__int_eval:w  99990000 + #1*#9 + #2*#8 + #3*#7 + #4*#6 +
-            \exp_after:wN \__fp_mul_mantissa_drop:NNNNNw
+            \exp_after:wN \__fp_mul_significand_drop:NNNNNw
             \int_use:N \__int_eval:w  99990000 + #2*#9 + #3*#8 + #4*#7 +
-              \exp_after:wN \__fp_mul_mantissa_drop:NNNNNw
+              \exp_after:wN \__fp_mul_significand_drop:NNNNNw
               \int_use:N \__int_eval:w  99990000 + #3*#9 + #4*#8 +
-                \exp_after:wN \__fp_mul_mantissa_drop:NNNNNw
+                \exp_after:wN \__fp_mul_significand_drop:NNNNNw
                 \int_use:N \__int_eval:w 100000000 + #4*#9 ;
     ; \exp_after:wN ;
   }
-\cs_new:Npn \__fp_mul_mantissa_drop:NNNNNw #1#2#3#4#5 #6;
+\cs_new:Npn \__fp_mul_significand_drop:NNNNNw #1#2#3#4#5 #6;
   { #1#2#3#4#5 ; + #6 }
-\cs_new:Npn \__fp_mul_mantissa_keep:NNNNNw #1#2#3#4#5 #6;
+\cs_new:Npn \__fp_mul_significand_keep:NNNNNw #1#2#3#4#5 #6;
   { #1#2#3#4#5 ; #6 ; }
-\cs_new:Npn \__fp_mul_mantissa_test_f:NNN #1 #2 #3
+\cs_new:Npn \__fp_mul_significand_test_f:NNN #1 #2 #3
   {
     \if_meaning:w 0 #3
-      \exp_after:wN \__fp_mul_mantissa_small_f:NNwwwN
+      \exp_after:wN \__fp_mul_significand_small_f:NNwwwN
     \else:
-      \exp_after:wN \__fp_mul_mantissa_large_f:NwwNNNN
+      \exp_after:wN \__fp_mul_significand_large_f:NwwNNNN
     \fi:
     #1 #3
   }
-\cs_new:Npn \__fp_mul_mantissa_large_f:NwwNNNN #1 #2; #3; #4#5#6#7; +
+\cs_new:Npn \__fp_mul_significand_large_f:NwwNNNN #1 #2; #3; #4#5#6#7; +
   {
     \exp_after:wN \__fp_basics_pack_high:NNNNNw
     \int_use:N \__int_eval:w 1#2
@@ -2572,7 +2609,7 @@
           \exp_after:wN #7
           \__int_value:w \__fp_round_digit:Nw
   }
-\cs_new:Npn \__fp_mul_mantissa_small_f:NNwwwN #1 #2#3; #4#5; #6; + #7
+\cs_new:Npn \__fp_mul_significand_small_f:NNwwwN #1 #2#3; #4#5; #6; + #7
   {
     - \c_one
     \exp_after:wN \__fp_basics_pack_high:NNNNNw
@@ -2606,34 +2643,34 @@
     \exp_after:wN #1
     \int_use:N \__int_eval:w
       #3 - #6
-      \exp_after:wN \__fp_div_mantissa_i_o:wnnw
+      \exp_after:wN \__fp_div_significand_i_o:wnnw
         \int_use:N \__int_eval:w #7 \use_i:nnnn #8 + \c_one ;
         #4
         {#7}{#8}#9 ;
         #1
   }
-\cs_new:Npn \__fp_div_mantissa_i_o:wnnw #1 ; #2#3 #4 ;
+\cs_new:Npn \__fp_div_significand_i_o:wnnw #1 ; #2#3 #4 ;
   {
-    \exp_after:wN \__fp_div_mantissa_test_o:w
+    \exp_after:wN \__fp_div_significand_test_o:w
     \int_use:N \__int_eval:w
-      \exp_after:wN \__fp_div_mantissa_calc:wwnnnnnnn
+      \exp_after:wN \__fp_div_significand_calc:wwnnnnnnn
       \int_use:N \__int_eval:w 999999 + #2 #3 0 / #1 ;
         #2 #3 ;
         #4
-        { \exp_after:wN \__fp_div_mantissa_ii:wwn \__int_value:w #1 }
-        { \exp_after:wN \__fp_div_mantissa_ii:wwn \__int_value:w #1 }
-        { \exp_after:wN \__fp_div_mantissa_ii:wwn \__int_value:w #1 }
-        { \exp_after:wN \__fp_div_mantissa_iii:wwnnnnn \__int_value:w #1 }
+        { \exp_after:wN \__fp_div_significand_ii:wwn \__int_value:w #1 }
+        { \exp_after:wN \__fp_div_significand_ii:wwn \__int_value:w #1 }
+        { \exp_after:wN \__fp_div_significand_ii:wwn \__int_value:w #1 }
+        { \exp_after:wN \__fp_div_significand_iii:wwnnnnn \__int_value:w #1 }
   }
-\cs_new:Npn \__fp_div_mantissa_calc:wwnnnnnnn 1#1
+\cs_new:Npn \__fp_div_significand_calc:wwnnnnnnn 1#1
   {
     \if_meaning:w 1 #1
-      \exp_after:wN \__fp_div_mantissa_calc_i:wwnnnnnnn
+      \exp_after:wN \__fp_div_significand_calc_i:wwnnnnnnn
     \else:
-      \exp_after:wN \__fp_div_mantissa_calc_ii:wwnnnnnnn
+      \exp_after:wN \__fp_div_significand_calc_ii:wwnnnnnnn
     \fi:
   }
-\cs_new:Npn \__fp_div_mantissa_calc_i:wwnnnnnnn #1; #2;#3#4 #5#6#7#8 #9
+\cs_new:Npn \__fp_div_significand_calc_i:wwnnnnnnn #1; #2;#3#4 #5#6#7#8 #9
   {
     1 1 #1
     #9 \exp_after:wN ;
@@ -2650,7 +2687,7 @@
             - #1 * #8 ;
     {#5}{#6}{#7}{#8}
   }
-\cs_new:Npn \__fp_div_mantissa_calc_ii:wwnnnnnnn #1; #2;#3#4 #5#6#7#8 #9
+\cs_new:Npn \__fp_div_significand_calc_ii:wwnnnnnnn #1; #2;#3#4 #5#6#7#8 #9
   {
     1 0 #1
     #9 \exp_after:wN ;
@@ -2667,33 +2704,33 @@
             - #1 * #8 ;
     {#5}{#6}{#7}{#8}
   }
-\cs_new:Npn \__fp_div_mantissa_ii:wwn #1; #2;#3
+\cs_new:Npn \__fp_div_significand_ii:wwn #1; #2;#3
   {
-    \exp_after:wN \__fp_div_mantissa_pack:NNN
+    \exp_after:wN \__fp_div_significand_pack:NNN
     \int_use:N \__int_eval:w
-      \exp_after:wN \__fp_div_mantissa_calc:wwnnnnnnn
+      \exp_after:wN \__fp_div_significand_calc:wwnnnnnnn
       \int_use:N \__int_eval:w 999999 + #2 #3 0 / #1 ; #2 #3 ;
   }
-\cs_new:Npn \__fp_div_mantissa_iii:wwnnnnn #1; #2;#3#4#5 #6#7
+\cs_new:Npn \__fp_div_significand_iii:wwnnnnn #1; #2;#3#4#5 #6#7
   {
     0
-    \exp_after:wN \__fp_div_mantissa_iv:wwnnnnnnn
+    \exp_after:wN \__fp_div_significand_iv:wwnnnnnnn
     \int_use:N \__int_eval:w (\c_two * #2 #3) / #6 #7 ; % <- P
       #2 ; {#3} {#4} {#5}
       {#6} {#7}
   }
-\cs_new:Npn \__fp_div_mantissa_iv:wwnnnnnnn #1; #2;#3#4#5 #6#7#8#9
+\cs_new:Npn \__fp_div_significand_iv:wwnnnnnnn #1; #2;#3#4#5 #6#7#8#9
   {
     + \c_five * #1
-    \exp_after:wN \__fp_div_mantissa_vi:Nw
+    \exp_after:wN \__fp_div_significand_vi:Nw
     \int_use:N \__int_eval:w -20 + 2*#2#3 - #1*#6#7 +
-      \exp_after:wN \__fp_div_mantissa_v:NN
+      \exp_after:wN \__fp_div_significand_v:NN
       \int_use:N \__int_eval:w 199980 + 2*#4 - #1*#8 +
-        \exp_after:wN \__fp_div_mantissa_v:NN
+        \exp_after:wN \__fp_div_significand_v:NN
         \int_use:N \__int_eval:w 200000 + 2*#5 - #1*#9 ;
   }
-\cs_new:Npn \__fp_div_mantissa_v:NN #1#2 { #1#2 \__int_eval_end: + }
-\cs_new:Npn \__fp_div_mantissa_vi:Nw #1#2;
+\cs_new:Npn \__fp_div_significand_v:NN #1#2 { #1#2 \__int_eval_end: + }
+\cs_new:Npn \__fp_div_significand_vi:Nw #1#2;
   {
     \if_meaning:w 0 #1
       \if_int_compare:w \__int_eval:w #2 > \c_zero + \c_one \fi:
@@ -2702,17 +2739,17 @@
     \fi:
     ;
   }
-\cs_new:Npn \__fp_div_mantissa_pack:NNN 1 #1 #2 { + #1 #2 ; }
-\cs_new:Npn \__fp_div_mantissa_test_o:w 10 #1
+\cs_new:Npn \__fp_div_significand_pack:NNN 1 #1 #2 { + #1 #2 ; }
+\cs_new:Npn \__fp_div_significand_test_o:w 10 #1
   {
     \if_meaning:w 0 #1
-      \exp_after:wN \__fp_div_mantissa_small_o:wwwNNNNwN
+      \exp_after:wN \__fp_div_significand_small_o:wwwNNNNwN
     \else:
-      \exp_after:wN \__fp_div_mantissa_large_o:wwwNNNNwN
+      \exp_after:wN \__fp_div_significand_large_o:wwwNNNNwN
     \fi:
     #1
   }
-\cs_new:Npn \__fp_div_mantissa_small_o:wwwNNNNwN
+\cs_new:Npn \__fp_div_significand_small_o:wwwNNNNwN
     0 #1; #2; #3; #4#5#6#7#8; #9
   {
     \exp_after:wN \__fp_basics_pack_high:NNNNNw
@@ -2722,7 +2759,7 @@
         + \__fp_round:NNN #9 #7 #8
         \exp_after:wN ;
   }
-\cs_new:Npn \__fp_div_mantissa_large_o:wwwNNNNwN
+\cs_new:Npn \__fp_div_significand_large_o:wwwNNNNwN
     #1; #2; #3; #4#5#6#7#8; #9
   {
     + \c_one
@@ -2736,13 +2773,13 @@
         \__int_value:w \__fp_round_digit:Nw #7 #8 ;
       \exp_after:wN ;
   }
-\cs_new:Npn \__fp_neg_o:w \s__fp \__fp_chk:w #1 #2
+\cs_new:Npn \__fp_neg_o:w #1 \s__fp \__fp_chk:w #2 #3
   {
     \exp_after:wN \__fp_exp_after_o:w
     \exp_after:wN \s__fp
     \exp_after:wN \__fp_chk:w
-    \exp_after:wN #1
-    \int_use:N \__int_eval:w \c_two - #2 \__int_eval_end:
+    \exp_after:wN #2
+    \int_use:N \__int_eval:w \c_two - #3 \__int_eval_end:
   }
 \cs_new:Npn \__fp_abs_o:w \s__fp \__fp_chk:w #1 #2
   {
@@ -2788,6 +2825,12 @@
 \tl_const:Nn \c__fp_one_fixed_tl
   { {10000} {0000} {0000} {0000} {0000} {0000} }
 \cs_new:Npn \__fp_fixed_continue:wn #1; #2 { #2 #1; }
+\cs_new:Npn \__fp_fixed_add_one:wN #1#2; #3
+  {
+    \exp_after:wN #3 \exp_after:wN
+      { \int_use:N \__int_eval:w \c_ten_thousand + #1 } #2 ;
+  }
+\cs_new:Npn \__fp_fixed_mul_after:wn #1; #2 { #2 {#1} }
 \cs_new:Npn \__fp_fixed_div_int:wwN #1#2#3#4#5#6 ; #7 ; #8
   {
     \exp_after:wN \__fp_fixed_div_int_after:Nw
@@ -2799,7 +2842,7 @@
       #3; {#7} \__fp_fixed_div_int_ii:wnn
       #4; {#7} \__fp_fixed_div_int_ii:wnn
       #5; {#7} \__fp_fixed_div_int_ii:wnn
-      #6; {#7} \__fp_fixed_div_int_end:wnn ;
+      #6; {#7} \__fp_fixed_div_int_iii:wnn ;
   }
 \cs_new:Npn \__fp_fixed_div_int_i:wnN #1; #2 #3
   {
@@ -2816,110 +2859,104 @@
       \exp_after:wN \__fp_fixed_div_int_i:wnN
       \int_use:N \__int_eval:w #3 - #1*#2 \__int_eval_end:
   }
-\cs_new:Npn \__fp_fixed_div_int_end:wnn #1; #2 #3 { + #1 + \c_two ; }
+\cs_new:Npn \__fp_fixed_div_int_iii:wnn #1; #2 #3 { + #1 + \c_two ; }
 \cs_new:Npn \__fp_fixed_div_int_pack:Nw #1 #2; { + #1; {#2} }
 \cs_new:Npn \__fp_fixed_div_int_after:Nw #1 #2; { #1 {#2} }
-\cs_new:Npn \__fp_fixed_add_one:wN #1#2; #3
-  {
-    \exp_after:wN #3 \exp_after:wN
-      { \int_use:N \__int_eval:w 10000 + #1 } #2 ;
-  }
-\cs_new_nopar:Npn \__fp_fixed_add:wwN { \__fp_fixed_add_i:NNnnnnwnn + + }
-\cs_new_nopar:Npn \__fp_fixed_sub:wwN { \__fp_fixed_add_i:NNnnnnwnn + - }
-\cs_new_nopar:Npn \__fp_fixed_sub_back:wwN { \__fp_fixed_add_i:NNnnnnwnn - + }
-\cs_new:Npn \__fp_fixed_add_i:NNnnnnwnn #1#2 #3#4#5#6 #7; #8#9
-  {
-    \exp_after:wN \__fp_fixed_add_after:NNNNNwN
-    \int_use:N \__int_eval:w 1 9999 9998 #1 #3#4 #2 #8#9
-      \exp_after:wN \__fp_fixed_add_pack:NNNNNwN
-      \int_use:N \__int_eval:w 1 9999 9998 #1 #5#6
-        \__fp_fixed_add_ii:NnnNnnnnw #1 #7 #2
-  }
-\cs_new:Npn \__fp_fixed_add_ii:NnnNnnnnw #1 #2#3 #4 #5#6 #7#8 ; #9
-  {
-    #4 #5#6
-    \exp_after:wN \__fp_fixed_add_pack:NNNNNwN
-    \int_use:N \__int_eval:w 2 0000 0000 #4 #7#8 #1 #2#3 ; #9 ;
-  }
-\cs_new:Npn \__fp_fixed_add_pack:NNNNNwN #1 #2#3#4#5 #6; #7
-  { + #1 ; #7 {#2#3#4#5} {#6} }
-\cs_new:Npn \__fp_fixed_add_after:NNNNNwN #1 #2#3#4#5 #6; #7
-  {
-    \exp_after:wN #7
-    \exp_after:wN { \int_use:N \__int_eval:w - 2 0000 + #1#2#3#4#5 }
-    {#6}
-  }
+\cs_new_nopar:Npn \__fp_fixed_add:wwn { \__fp_fixed_add_i:Nnnnnwnn + }
+\cs_new_nopar:Npn \__fp_fixed_sub:wwn { \__fp_fixed_add_i:Nnnnnwnn - }
+\cs_new:Npn \__fp_fixed_add_i:Nnnnnwnn #1 #2#3#4#5 #6; #7#8
+  {
+    \exp_after:wN \__fp_fixed_add_after:NNNNNwn
+    \int_use:N \__int_eval:w 9 9999 9998 + #2#3 #1 #7#8
+      \exp_after:wN \__fp_fixed_add_pack:NNNNNwn
+      \int_use:N \__int_eval:w 1 9999 9998 + #4#5
+        \__fp_fixed_add_ii:nnNnnnwn #6 #1
+  }
+\cs_new:Npn \__fp_fixed_add_ii:nnNnnnwn #1#2 #3 #4#5 #6#7 ; #8
+  {
+    #3 #4#5
+    \exp_after:wN \__fp_fixed_add_pack:NNNNNwn
+    \int_use:N \__int_eval:w 2 0000 0000 #3 #6#7 + #1#2 ; {#8} ;
+  }
+\cs_new:Npn \__fp_fixed_add_pack:NNNNNwn #1 #2#3#4#5 #6; #7
+  { + #1 ; {#7} {#2#3#4#5} {#6} }
+\cs_new:Npn \__fp_fixed_add_after:NNNNNwn 1 #1 #2#3#4#5 #6; #7
+  { #7 {#1#2#3#4#5} {#6} }
 \cs_new:Npn \__fp_fixed_mul:wwn #1#2#3#4 #5; #6#7#8#9
   {
-    \exp_after:wN \__fp_fixed_mul_after:wwn
+    \exp_after:wN \__fp_fixed_mul_after:wn
     \int_use:N \__int_eval:w \c__fp_leading_shift_int
-      \exp_after:wN \__fp_pack:NNNNNw
+      \exp_after:wN \__fp_pack:NNNNNwn
       \int_use:N \__int_eval:w \c__fp_middle_shift_int
         + #1*#6
-        \exp_after:wN \__fp_pack:NNNNNw
+        \exp_after:wN \__fp_pack:NNNNNwn
         \int_use:N \__int_eval:w \c__fp_middle_shift_int
           + #1*#7 + #2*#6
-          \exp_after:wN \__fp_pack:NNNNNw
+          \exp_after:wN \__fp_pack:NNNNNwn
           \int_use:N \__int_eval:w \c__fp_middle_shift_int
             + #1*#8 + #2*#7 + #3*#6
-            \exp_after:wN \__fp_pack:NNNNNw
+            \exp_after:wN \__fp_pack:NNNNNwn
             \int_use:N \__int_eval:w \c__fp_middle_shift_int
               + #1*#9 + #2*#8 + #3*#7 + #4*#6
-              \exp_after:wN \__fp_pack:NNNNNw
+              \exp_after:wN \__fp_pack:NNNNNwn
               \int_use:N \__int_eval:w \c__fp_trailing_shift_int
                 + #2*#9 + #3*#8 + #4*#7
                 + ( #3*#9 + #4*#8
-                  + \__fp_fixed_mul_i:nnnnnnnn #5 {#6}{#7}  {#1}{#2}
-  }
-\cs_new:Npn \__fp_fixed_mul_i:nnnnnnnn #1#2 #3#4 #5#6 #7#8
-  { #1*#4 + #2*#3 + #5*#8 + #6*#7 )/10000 + #1*#3 + #5*#7 ; }
-\cs_new:Npn \__fp_fixed_mul_pack:NNNNNw
-    #1 #2#3#4#5 #6; { + #1#2#3#4#5 ; {#6} }
-\cs_new:Npn \__fp_fixed_mul_after:wwn #1; #2; #3 { #3 {#1} #2 ; }
-\cs_new:Npn \__fp_fixed_one_minus_mul:wwn #1; #2#3#4#5;
-  {
-    \exp_after:wN \__fp_fixed_mul_after:wwn
-    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int + \c_ten_thousand
-      \exp_after:wN \__fp_pack_big:NNNNNNw
+                  + \__fp_fixed_mul_i:nnnnnnnwn #5 {#6}{#7}  {#1}{#2}
+  }
+\cs_new:Npn \__fp_fixed_mul_i:nnnnnnnwn #1#2 #3#4 #5#6 #7#8 ; #9
+  {
+    #1*#4 + #2*#3 + #5*#8 + #6*#7 ) / \c_ten_thousand
+    + #1*#3 + #5*#7 ;
+    {#9} ;
+  }
+\cs_new:Npn \__fp_fixed_mul_add:wwwn #1; #2; #3#4#5#6#7#8; #9
+  {
+    \exp_after:wN \__fp_fixed_mul_after:wn
+    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int
+      \exp_after:wN \__fp_pack_big:NNNNNNwn
+      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #3 #4
+        \__fp_fixed_mul_add_i:Nwnnnwnnn +
+          + #5 #6 ; #2 ; #1 ; #2 ; +
+          + #7 #8 ; {#9} ;
+  }
+\cs_new:Npn \__fp_fixed_mul_sub_back:wwwn #1; #2; #3#4#5#6#7#8; #9
+  {
+    \exp_after:wN \__fp_fixed_mul_after:wn
+    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int
+      \exp_after:wN \__fp_pack_big:NNNNNNwn
+      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #3 #4
+        \__fp_fixed_mul_add_i:Nwnnnwnnn -
+          + #5 #6 ; #2 ; #1 ; #2 ; -
+          + #7 #8 ; {#9} ;
+  }
+\cs_new:Npn \__fp_fixed_one_minus_mul:wwn #1; #2; #3
+  {
+    \exp_after:wN \__fp_fixed_mul_after:wn
+    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int
+      \exp_after:wN \__fp_pack_big:NNNNNNwn
+      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + 1 0000 0000
+        \__fp_fixed_mul_add_i:Nwnnnwnnn -
+          ; #2 ; #1 ; #2 ; -
+          ; {#3} ;
+  }
+\cs_new:Npn \__fp_fixed_mul_add_i:Nwnnnwnnn #1 #2; #3#4#5#6; #7#8#9
+  {
+    #1 #7*#3
+    \exp_after:wN \__fp_pack_big:NNNNNNwn
+    \int_use:N \__int_eval:w \c__fp_big_middle_shift_int
+      #1 #7*#4 #1 #8*#3
+      \exp_after:wN \__fp_pack_big:NNNNNNwn
       \int_use:N \__int_eval:w \c__fp_big_middle_shift_int
-        \__fp_fixed_mul_add_i:Nnwnnwnnn
-          - 00; {#2}{#3}{#4}; #1; {#2}{#3}{#4}#5; - 00 ;
-  }
-\cs_new:Npn \__fp_fixed_mul_add:wwwn #1; #2#3#4#5; #6#7#8#9
-  {
-    \exp_after:wN \__fp_fixed_mul_after:wwn
-    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int + #6
-      \exp_after:wN \__fp_pack_big:NNNNNNw
-      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #7
-        \__fp_fixed_mul_add_i:Nnwnnwnnn
-          + {#8}{#9}; {#2}{#3}{#4}; #1; {#2}{#3}{#4}#5; +
-  }
-\cs_new:Npn \__fp_fixed_mul_sub_back:wwwn #1; #2#3#4#5; #6#7#8#9
-  {
-    \exp_after:wN \__fp_fixed_mul_after:wwn
-    \int_use:N \__int_eval:w \c__fp_big_leading_shift_int + #6
-      \exp_after:wN \__fp_pack_big:NNNNNNw
-      \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #7
-        \__fp_fixed_mul_add_i:Nnwnnwnnn
-          - {#8}{#9}; {#2}{#3}{#4}; #1; {#2}{#3}{#4}#5; -
-  }
-\cs_new:Npn \__fp_fixed_mul_add_i:Nnwnnwnnn #1 #2#3; #4#5#6; #7#8#9
-  { % sg z3z4; y1y2y3; x1x2x3  x4x5x6; y1y2y3y4y5y6; sg z5z6;
-        #1 #7*#4
-        \exp_after:wN \__fp_pack_big:NNNNNNw
-        \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #2
-          #1 #7*#5 #1 #8*#4
-          \exp_after:wN \__fp_pack_big:NNNNNNw
-          \int_use:N \__int_eval:w \c__fp_big_middle_shift_int + #3
-            #1 #7*#6 #1 #8*#5 #1 #9*#4
-            \exp_after:wN \__fp_pack_big:NNNNNNw
-            \int_use:N \__int_eval:w \c__fp_big_middle_shift_int
-              #1 \__fp_fixed_mul_add_ii:nnnnwnnnn {#7}{#8}{#9}
+        #1 #7*#5 #1 #8*#4 #1 #9*#3 #2
+        \exp_after:wN \__fp_pack_big:NNNNNNwn
+        \int_use:N \__int_eval:w \c__fp_big_middle_shift_int
+          #1 \__fp_fixed_mul_add_ii:nnnnwnnnn {#7}{#8}{#9}
   }
 \cs_new:Npn \__fp_fixed_mul_add_ii:nnnnwnnnn #1#2#3#4#5; #6#7#8#9
-  { % x1x2x3x4 x5x6; y1y2y3y4  y5y6; sg z5z6;
+  {
     ( #1*#9 + #2*#8 + #3*#7 + #4*#6 )
-    \exp_after:wN \__fp_pack_big:NNNNNNw
+    \exp_after:wN \__fp_pack_big:NNNNNNwn
     \int_use:N \__int_eval:w \c__fp_big_trailing_shift_int
       \__fp_fixed_mul_add_iii:nnnnwnnwN
         { #6 + #4*#7 + #3*#8 + #2*#9 + #1 }
@@ -2928,15 +2965,9 @@
         {#6}
   }
 \cs_new:Npn \__fp_fixed_mul_add_iii:nnnnwnnwN #1#2 #3#4#5; #6#7#8; #9
-  { % {y1+x4*y2+x3*y3+x2*y4+x1} {y2+x4*y3+x3*y4+x2}
-    % x1x5x6; y1y5y6; sg z5z6;
-    % =>
-    % sg (x5*y1+x4*y2+x3*y3+x2*y4+x1*y5)
-    % sg (x6*y1+x5*y2+x4*y3+x3*y4+x2*y5+x1*y6)/10000
-    % + z5z6;
+  {
     #9 (#4* #1 *#7)
     #9 (#5*#6+#4* #2 *#7+#3*#8) / \c_ten_thousand
-    + \__fp_use_s:nn
   }
 \cs_new:Npn \__fp_fixed_to_float:Nw #1#2; { \__fp_fixed_to_float:wN #2; #1 }
 \cs_new:Npn \__fp_fixed_to_float:wN #1#2#3#4#5#6; #7
@@ -2996,7 +3027,7 @@
   }
 \cs_new:Npn \__fp_fixed_inv_to_float:wN #1#2; #3
   {
-    - \__int_eval:w
+    + \__int_eval:w % ^^A todo: remove the +?
         \if_int_compare:w #1 < \c_one_thousand
           \__fp_fixed_dtf_zeros:wNnnnnnn
         \fi:
@@ -3092,7 +3123,7 @@
   { #1 ; {#2#3#4#5} {#6} }
 \cs_new:Npn \__fp_fixed_dtf_epsilon_ii:NNNNNww #1#2#3#4#5#6; #7;
   {
-    \__fp_fixed_mul:wwn %^^A todo: optimize to use \__fp_mul_mantissa.
+    \__fp_fixed_mul:wwn %^^A todo: optimize to use \__fp_mul_significand.
       {0000} {#2#3#4#5} {#6} #7 ;
       {0000} {#2#3#4#5} {#6} #7 ;
     \__fp_fixed_add_one:wN
@@ -3209,7 +3240,7 @@
   }
 \cs_new:Npn \__fp_ln_x_iv:wnnnnnnnn #1; #2#3#4#5 #6#7#8#9
   {
-    \exp_after:wN \__fp_div_mantissa_pack:NNN
+    \exp_after:wN \__fp_div_significand_pack:NNN
     \int_use:N \__int_eval:w
     \__fp_ln_div_i:w #1 ;
       #6 #7 ; {#8} {#9}
@@ -3222,20 +3253,20 @@
   }
 \cs_new:Npn \__fp_ln_div_i:w #1;
   {
-    \exp_after:wN \__fp_div_mantissa_calc:wwnnnnnnn
+    \exp_after:wN \__fp_div_significand_calc:wwnnnnnnn
     \int_use:N \__int_eval:w 999999 + 2 0000 0000 / #1 ; % Q1
   }
 \cs_new:Npn \__fp_ln_div_ii:wwn #1; #2;#3 % y; B1;B2 <- for k=1
   {
-    \exp_after:wN \__fp_div_mantissa_pack:NNN
+    \exp_after:wN \__fp_div_significand_pack:NNN
     \int_use:N \__int_eval:w
-      \exp_after:wN \__fp_div_mantissa_calc:wwnnnnnnn
+      \exp_after:wN \__fp_div_significand_calc:wwnnnnnnn
       \int_use:N \__int_eval:w 999999 + #2 #3 / #1 ; % Q2
       #2 #3 ;
   }
 \cs_new:Npn \__fp_ln_div_vi:wwn #1; #2;#3#4#5 #6#7#8#9 %y;F1;F2F3F4x1x2x3x4
   {
-    \exp_after:wN \__fp_div_mantissa_pack:NNN
+    \exp_after:wN \__fp_div_significand_pack:NNN
     \int_use:N \__int_eval:w 1000000 + #2 #3 / #1 ; % Q6
   }
 \cs_new:Npn \__fp_ln_div_after:Nw #1#2;
@@ -3303,7 +3334,7 @@
       \__fp_ln_Taylor_break:w
     \fi:
     \exp_after:wN \__fp_fixed_div_int:wwN \c__fp_one_fixed_tl ; #1;
-    \__fp_fixed_add:wwN #2;
+    \__fp_fixed_add:wwn #2;
     \__fp_fixed_mul:wwn #3;
     {
       \exp_after:wN \__fp_ln_Taylor_loop:www
@@ -3311,7 +3342,7 @@
     }
     #3;
   }
-\cs_new:Npn \__fp_ln_Taylor_break:w \fi: #1 \__fp_fixed_add:wwN #2#3; #4 ;;
+\cs_new:Npn \__fp_ln_Taylor_break:w \fi: #1 \__fp_fixed_add:wwn #2#3; #4 ;;
   {
     \fi:
     \exp_after:wN \__fp_fixed_mul:wwn
@@ -3320,9 +3351,9 @@
 \cs_new:Npn \__fp_ln_c:NwNw #1 #2; #3
   {
     \if_meaning:w + #1
-      \exp_after:wN \exp_after:wN \exp_after:wN \__fp_fixed_sub:wwN
+      \exp_after:wN \exp_after:wN \exp_after:wN \__fp_fixed_sub:wwn
     \else:
-      \exp_after:wN \exp_after:wN \exp_after:wN \__fp_fixed_add:wwN
+      \exp_after:wN \exp_after:wN \exp_after:wN \__fp_fixed_add:wwn
     \fi:
     #3 ; #2 ;
   }
@@ -3336,11 +3367,11 @@
       \if_int_compare:w #2 > \c_zero
         \exp_after:wN \__fp_ln_exponent_small:NNww
         \exp_after:wN 0
-        \exp_after:wN \__fp_fixed_sub:wwN \__int_value:w
+        \exp_after:wN \__fp_fixed_sub:wwn \__int_value:w
       \else:
         \exp_after:wN \__fp_ln_exponent_small:NNww
         \exp_after:wN 2
-        \exp_after:wN \__fp_fixed_add:wwN \__int_value:w -
+        \exp_after:wN \__fp_fixed_add:wwn \__int_value:w -
       \fi:
     \fi:
     #2; #1;
@@ -3348,7 +3379,7 @@
 \cs_new:Npn \__fp_ln_exponent_one:ww 1; #1;
   {
     \c_zero
-    \exp_after:wN \__fp_fixed_sub:wwN \c__fp_ln_x_fixed_tl ; #1;
+    \exp_after:wN \__fp_fixed_sub:wwn \c__fp_ln_x_fixed_tl ; #1;
     \__fp_fixed_to_float:wN 0
   }
 \cs_new:Npn \__fp_ln_exponent_small:NNww #1#2#3; #4#5#6#7#8#9;
@@ -3421,7 +3452,7 @@
           }
           #5
           {#4}
-          #2 0
+          #1 #2 0
           \tex_romannumeral:D
         \fi:
       \fi:
@@ -3429,8 +3460,9 @@
   }
 \cs_new:Npn \__fp_exp_overflow:
   { + \c_two * \c__fp_max_exponent_int ; {1000} {0000} {0000} {0000} ; }
-\cs_new:Npn \__fp_exp_Taylor:Nnnwn #1#2#3 #4; #5
+\cs_new:Npn \__fp_exp_Taylor:Nnnwn #1#2#3 #4; #5 #6
   {
+    #6
     \__fp_pack_twice_four:wNNNNNNNN
     \__fp_pack_twice_four:wNNNNNNNN
     \__fp_pack_twice_four:wNNNNNNNN
@@ -3562,9 +3594,9 @@
     #1;
     \__fp_exp_large_after:wwn
   }
-\cs_new:Npn \__fp_exp_large_after:wwn #1; #2;
+\cs_new:Npn \__fp_exp_large_after:wwn #1; #2; #3
   {
-    \__fp_exp_Taylor:Nnnwn ? { } { } 0 #2; {}
+    \__fp_exp_Taylor:Nnnwn ? { } { } 0 #2; {} #3
     \__fp_fixed_mul:wwn #1;
   }
 \cs_new:cpn { __fp_ \iow_char:N \^ _o:ww }
@@ -3599,6 +3631,13 @@
     \fi:
     \if_meaning:w #1 #4
       \__fp_case_return_o:Nw \c_zero_fp
+    \fi:
+    \if_meaning:w 0 #1
+      \__fp_case_use:nw
+        {
+          \__fp_division_by_zero_o:NNww \c_inf_fp ^
+            \s__fp \__fp_chk:w #1 #2 ;
+        }
     \else:
       \__fp_case_return_o:Nw \c_inf_fp
     \fi:
@@ -3613,7 +3652,7 @@
       \fi:
       \__fp_case_return_o:Nww \c_one_fp
     \fi:
-    \if_case:w #4 ~
+    \if_case:w #4 \exp_stop_f:
     \or:
       \exp_after:wN \__fp_pow_npos:Nww
       \exp_after:wN #5
@@ -3638,50 +3677,57 @@
     \exp_after:wN 0
     \__int_value:w
       \if:w #1 \if_int_compare:w #3 > \c_zero 0 \else: 2 \fi:
-        \exp_after:wN \__fp_pow_npos_aux:Nnww
+        \exp_after:wN \__fp_pow_npos_aux:NNnww
+        \exp_after:wN +
         \exp_after:wN \__fp_fixed_to_float:wN
       \else:
-        -
-        \exp_after:wN \__fp_pow_npos_aux:Nnww
+        \exp_after:wN \__fp_pow_npos_aux:NNnww
+        \exp_after:wN -
         \exp_after:wN \__fp_fixed_inv_to_float:wN
       \fi:
       {#3}
   }
-\cs_new:Npn \__fp_pow_npos_aux:Nnww #1#2#3#4; \s__fp \__fp_chk:w 1#5#6#7;
+\cs_new:Npn \__fp_pow_npos_aux:NNnww #1#2#3#4#5; \s__fp \__fp_chk:w 1#6#7#8;
   {
+    #1
     \__int_eval:w
-      \__fp_ln_significand:NNNNnnnN #3#4
-      \__fp_pow_exponent:wnN {#2}
-      \__fp_fixed_mul:wwn #7 {0000}{0000} ;
-      \__fp_pow_B:wwN #6;
-      #1 0 % fixed_to_float:wN
+      \__fp_ln_significand:NNNNnnnN #4#5
+      \__fp_pow_exponent:wnN {#3}
+      \__fp_fixed_mul:wwn #8 {0000}{0000} ;
+      \__fp_pow_B:wwN #7;
+      #1 #2 0 % fixed_to_float:wN
   }
 \cs_new:Npn \__fp_pow_exponent:wnN #1; #2
   {
     \if_int_compare:w #2 > \c_zero
-      \exp_after:wN \__fp_pow_exponent:Nwnnnnnn % n\ln(10) - (-\ln(x))
+      \exp_after:wN \__fp_pow_exponent:Nwnnnnnwn % n\ln(10) - (-\ln(x))
       \exp_after:wN +
     \else:
-      \exp_after:wN \__fp_pow_exponent:Nwnnnnnn % -( |n|\ln(10) + (-\ln(x)) )
+      \exp_after:wN \__fp_pow_exponent:Nwnnnnnwn % -( |n|\ln(10) + (-\ln(x)) )
       \exp_after:wN -
     \fi:
     #2; #1;
   }
-\cs_new:Npn \__fp_pow_exponent:Nwnnnnnn #1#2; #3#4#5#6#7#8;
-  { %^^A todo: use that in ln. %^^A todo: log(1.00...) too inaccurate?
-    \exp_after:wN \__fp_fixed_mul_after:wwn
-    \int_use:N \__int_eval:w -5 0000
-      \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-      \int_use:N \__int_eval:w 4 9995 0000 #1#2*23025 - #1 #3
-        \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-        \int_use:N \__int_eval:w 4 9995 0000 #1 #2*8509 - #1 #4
-          \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-          \int_use:N \__int_eval:w 4 9995 0000 #1 #2*2994 - #1 #5
-            \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-            \int_use:N \__int_eval:w 4 9995 0000 #1 #2*0456 - #1 #6
-              \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-              \int_use:N \__int_eval:w 5 0000 0000 #1 #2*8401 - #1 #7
-                #1 ( #2*7991 - #8 ) / 1 0000 ; ;
+\cs_new:Npn \__fp_pow_exponent:Nwnnnnnwn #1#2; #3#4#5#6#7#8; #9
+  { %^^A todo: use that in ln.
+    \exp_after:wN \__fp_fixed_mul_after:wn
+    \int_use:N \__int_eval:w \c__fp_leading_shift_int
+      \exp_after:wN \__fp_pack:NNNNNwn
+      \int_use:N \__int_eval:w \c__fp_middle_shift_int
+        #1#2*23025 - #1 #3
+        \exp_after:wN \__fp_pack:NNNNNwn
+        \int_use:N \__int_eval:w \c__fp_middle_shift_int
+          #1 #2*8509 - #1 #4
+          \exp_after:wN \__fp_pack:NNNNNwn
+          \int_use:N \__int_eval:w \c__fp_middle_shift_int
+            #1 #2*2994 - #1 #5
+            \exp_after:wN \__fp_pack:NNNNNwn
+            \int_use:N \__int_eval:w \c__fp_middle_shift_int
+              #1 #2*0456 - #1 #6
+              \exp_after:wN \__fp_pack:NNNNNwn
+              \int_use:N \__int_eval:w \c__fp_trailing_shift_int
+                #1 #2*8401 - #1 #7
+                #1 ( #2*7991 - #8 ) / 1 0000 ; {#9} ;
   }
 \cs_new:Npn \__fp_pow_B:wwN #1#2#3#4#5#6; #7;
   {
@@ -3698,7 +3744,7 @@
     \int_use:N \__int_eval:w 10 0000 + #1 \__int_eval_end:
     #2#3#4#5#6 0000 0000 0000 0000 0000 0000 ; %^^A todo: how many 0?
   }
-\cs_new:Npn \__fp_pow_C_overflow:w #1; #2;
+\cs_new:Npn \__fp_pow_C_overflow:w #1; #2; #3
   {
     + \c_two * \c__fp_max_exponent_int
     \exp_after:wN \__fp_fixed_continue:wn \c__fp_one_fixed_tl ;
@@ -3729,7 +3775,7 @@
 \cs_new:Npn \__fp_pow_neg:www \s__fp \__fp_chk:w #1#2; #3; #4;
   {
     \if_case:w \__fp_pow_neg_case:w #4 ;
-      \exp_after:wN \__fp_pow_neg_neg:w
+      \exp_after:wN \__fp_neg_o:w
     \or:
       \if_int_compare:w \__int_eval:w #1 / \c_two = \c_one
         \__fp_invalid_operation_o:Nww ^ #3; #4;
@@ -3741,14 +3787,6 @@
     \__fp_exp_after_o:w
     \s__fp \__fp_chk:w #1#2;
   }
-\cs_new:Npn \__fp_pow_neg_neg:w \__fp_exp_after_o:w \s__fp \__fp_chk:w #1#2
-  {
-    \exp_after:wN \__fp_exp_after_o:w
-    \exp_after:wN \s__fp
-    \exp_after:wN \__fp_chk:w
-    \exp_after:wN #1
-    \int_use:N \__int_eval:w \c_two - #2 \__int_eval_end:
-  }
 \cs_new:Npn \__fp_pow_neg_case:w \s__fp \__fp_chk:w #1#2#3;
   {
     \if_case:w #1 \exp_stop_f:
@@ -3826,24 +3864,17 @@
 %%
 %% -----------------------------------------------------------------------
 %%
-\cs_new_nopar:Npx \__fp_one_over:w
-  {
-    \exp_not:N \exp_after:wN
-    \exp_not:c { __fp_/_o:ww }
-    \exp_not:N \c_one_fp
-  }
 \cs_new:Npn \__fp_sin_o:w \s__fp \__fp_chk:w #1#2
   {
     \if_case:w #1 \exp_stop_f:
            \__fp_case_return_same_o:w
     \or:
-      \exp_after:wN \__fp_trig_exponent:NNNNwn
-      \exp_after:wN \__fp_sin_series:NNwww
-      \exp_after:wN ?
-      \exp_after:wN #2
-      \exp_after:wN \c_zero
-    \or:
-      \__fp_case_use:nw { \__fp_invalid_operation_o:nw { sin } }
+      \__fp_case_use:nw
+        {
+          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_o:w
+            \__fp_sin_series:NNwww \__fp_fixed_to_float:wN #2 \c_zero
+        }
+    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { sin } }
     \else: \__fp_case_return_same_o:w
     \fi:
     \s__fp \__fp_chk:w #1#2
@@ -3853,16 +3884,42 @@
     \if_case:w #1 \exp_stop_f:
            \__fp_case_return_o:Nw \c_one_fp
     \or:
-      \__fp_case_use:nw %^^A todo: is that faster than the exp_after route?
+      \__fp_case_use:nw
         {
-          \__fp_trig_exponent:NNNNwn
-          \__fp_sin_series:NNwww
-          ?
-          0
-          \c_two
+          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_one_o:w
+            \__fp_sin_series:NNwww \__fp_fixed_to_float:wN 0 \c_two
         }
+    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { cos } }
+    \else: \__fp_case_return_same_o:w
+    \fi:
+    \s__fp \__fp_chk:w #1#2
+  }
+\cs_new:Npn \__fp_csc_o:w \s__fp \__fp_chk:w #1#2
+  {
+    \if_case:w #1 \exp_stop_f:
+           \__fp_cot_zero_o:Nnw #2 { csc }
+    \or:
+      \__fp_case_use:nw
+        {
+          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_inv_o:w
+            \__fp_sin_series:NNwww \__fp_fixed_inv_to_float:wN #2 \c_zero
+        }
+    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { csc } }
+    \else: \__fp_case_return_same_o:w
+    \fi:
+    \s__fp \__fp_chk:w #1#2
+  }
+\cs_new:Npn \__fp_sec_o:w \s__fp \__fp_chk:w #1#2
+  {
+    \if_case:w #1 \exp_stop_f:
+           \__fp_case_return_o:Nw \c_one_fp
     \or:
-      \__fp_case_use:nw { \__fp_invalid_operation_o:nw { cos } }
+      \__fp_case_use:nw
+        {
+          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_one_o:w
+            \__fp_sin_series:NNwww \__fp_fixed_inv_to_float:wN 0 \c_two
+        }
+    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { sec } }
     \else: \__fp_case_return_same_o:w
     \fi:
     \s__fp \__fp_chk:w #1#2
@@ -3872,13 +3929,12 @@
     \if_case:w #1 \exp_stop_f:
            \__fp_case_return_same_o:w
     \or:
-      \exp_after:wN \__fp_trig_exponent:NNNNwn
-      \exp_after:wN \__fp_tan_series:NNwww
-      \exp_after:wN 0
-      \exp_after:wN #2
-      \exp_after:wN \c_one
-    \or:
-      \__fp_case_use:nw { \__fp_invalid_operation_o:nw { tan } }
+      \__fp_case_use:nw
+        {
+          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_o:w
+            \__fp_tan_series_o:NNwww 0 #2 \c_one
+        }
+    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { tan } }
     \else: \__fp_case_return_same_o:w
     \fi:
     \s__fp \__fp_chk:w #1#2
@@ -3886,129 +3942,126 @@
 \cs_new:Npn \__fp_cot_o:w \s__fp \__fp_chk:w #1#2
   {
     \if_case:w #1 \exp_stop_f:
-           \exp_after:wN \__fp_one_over:w
-    \or:
-      \exp_after:wN \__fp_trig_exponent:NNNNwn
-      \exp_after:wN \__fp_tan_series:NNwww
-      \exp_after:wN 2
-      \exp_after:wN #2
-      \exp_after:wN \c_three
+           \__fp_cot_zero_o:Nnw #2 { cot }
     \or:
-      \__fp_case_use:nw { \__fp_invalid_operation_o:nw { cot } }
+      \__fp_case_use:nw
+        {
+          \__fp_trig_exponent:NNNNNwn \__fp_trig_epsilon_inv_o:w
+            \__fp_tan_series_o:NNwww 2 #2 \c_three
+        }
+    \or:   \__fp_case_use:nw { \__fp_invalid_operation_o:nw { cot } }
     \else: \__fp_case_return_same_o:w
     \fi:
     \s__fp \__fp_chk:w #1#2
   }
-\cs_new:Npn \__fp_trig_exponent:NNNNwn #1#2#3#4 \s__fp \__fp_chk:w 1#5#6
+\cs_new:Npn \__fp_cot_zero_o:Nnw #1 #2 #3 \fi:
   {
-    \if_int_compare:w #6 > - \c_eight
-      \exp_after:wN #1
+    \fi:
+    \if_meaning:w 0 #1
+      \exp_after:wN \__fp_division_by_zero_o:Nnw \exp_after:wN \c_inf_fp
+    \else:
+      \exp_after:wN \__fp_division_by_zero_o:Nnw \exp_after:wN \c_minus_inf_fp
+    \fi:
+    {#2}
+  }
+\cs_new:Npn \__fp_trig_exponent:NNNNNwn #1#2#3#4#5 \s__fp \__fp_chk:w 1#6#7
+  {
+    \if_int_compare:w #7 > - \c_eight
       \exp_after:wN #2
       \exp_after:wN #3
-      \int_use:N \__int_eval:w #4
-        \if_int_compare:w #6 > \c_zero
-          \exp_after:wN \__fp_trig_large:w \__int_value:w
+      \exp_after:wN #4
+      \int_use:N \__int_eval:w #5
+        \if_int_compare:w #7 > \c_zero
+          \exp_after:wN \__fp_trig_large:ww \__int_value:w
         \else:
-          \exp_after:wN \__fp_trig_small:w \__int_value:w
+          \exp_after:wN \__fp_trig_small:ww \__int_value:w
         \fi:
     \else:
-      \if_case:w #4
-             \__fp_sin_epsilon:w
-      \or:   \__fp_sin_epsilon:w
-      \or:   \__fp_cos_epsilon:w
-      \else: \__fp_cot_epsilon:w
-      \fi:
-      #5
+      \exp_after:wN #1
+      \exp_after:wN #6
     \fi:
-    #6 ;
-  }
-\cs_new:Npn \__fp_sin_epsilon:w #1 \fi: #2 \fi: #3 ;
-  { \fi: \fi: \__fp_exp_after_o:w \s__fp \__fp_chk:w 1 #2 {#3} }
-\cs_new:Npn \__fp_cos_epsilon:w #1 \fi: #2 \fi: #3 ; #4 ;
-  { \fi: \fi: \exp_after:wN \c_one_fp }
-\cs_new:Npn \__fp_cot_epsilon:w \fi: #1 \fi: #2 ;
-  { \fi: \fi: \__fp_one_over:w \s__fp \__fp_chk:w 1 #1 {#2} }
-\cs_new:Npn \__fp_trig_small:w #1;
-  {
-    \exp_after:wN \exp_after:wN \exp_after:wN \__fp_trig_small_aux:wwNN
-    \prg_replicate:nn { - #1 } { 0 } ;
+    #7 ;
   }
-\cs_new:Npn \__fp_trig_small_aux:wwNN #1; #2#3#4#5;
+\cs_new:Npn \__fp_trig_epsilon_o:w #1 #2 ;
+  { \__fp_exp_after_o:w \s__fp \__fp_chk:w 1 #1 {#2} }
+\cs_new:Npn \__fp_trig_epsilon_one_o:w #1 ; #2 ;
+  { \exp_after:wN \c_one_fp }
+\group_begin:
+  \char_set_catcode_letter:N /
+  \cs_new:Npn \__fp_trig_epsilon_inv_o:w #1 #2 ;
+    {
+      \exp_after:wN \__fp_/_o:ww
+        \c_one_fp
+        \s__fp \__fp_chk:w 1 #1 {#2}
+    }
+\group_end:
+\cs_new:Npn \__fp_trig_small:ww #1; #2#3#4#5;
   {
-    \__fp_pack_twice_four:wNNNNNNNN
-    \__fp_pack_twice_four:wNNNNNNNN
-    \__fp_pack_twice_four:wNNNNNNNN
-    .
-    ;
-    #1#2#3#4#5 0000 0000;
+    \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN
+    \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN
+    \exp_after:wN \__fp_pack_twice_four:wNNNNNNNN
+    \exp_after:wN .
+    \exp_after:wN ;
+    \tex_romannumeral:D -`0
+      \prg_replicate:nn { - #1 } { 0 } #2#3#4#5 0000 0000 ;
   }
-\cs_new:Npn \__fp_trig_large:w #1; #2#3;
+\cs_new:Npn \__fp_trig_large:ww #1; #2#3;
   { \__fp_trig_large_i:www #2; #3 ;  #1; }
 \cs_new:Npn \__fp_trig_large_i:www #1; #2; #3;
   {
     \if_meaning:w 0 #3 \__fp_trig_large_break:w \fi:
-    \exp_after:wN \__fp_trig_large_ii:wnnnnnn
+    \exp_after:wN \__fp_trig_large_ii_o:wnnnn
     \int_use:N \__int_eval:w ( #1 - 3141 ) / 6283 ;
-    {#1} #2;
+    {#1} #2
+    \exp_after:wN ;
     \int_use:N \__int_eval:w \c_minus_one + #3;
   }
-\cs_new:Npn \__fp_trig_large_ii:wnnnnnn #1; #2#3#4#5;
+\cs_new:Npn \__fp_trig_large_ii_o:wnnnn #1; #2#3#4#5
   {
     \exp_after:wN \__fp_trig_large_i:www
-    \int_use:N \__int_eval:w -5 0000 + #20 - #1*62831
-      \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-      \int_use:N \__int_eval:w 4 9995 0000 + #30 - #1*8530
-        \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-        \int_use:N \__int_eval:w 4 9995 0000 + #40 - #1*7179
-          \exp_after:wN \__fp_fixed_mul_pack:NNNNNw
-          \int_use:N \__int_eval:w 5 0000 0000 + #50 - #1*5880
-    \exp_after:wN ;
+    \int_use:N \__int_eval:w \c__fp_leading_shift_int + #20 - #1*62831
+      \exp_after:wN \__fp_pack:NNNNNw
+      \int_use:N \__int_eval:w \c__fp_middle_shift_int + #30 - #1*8530
+        \exp_after:wN \__fp_pack:NNNNNw
+        \int_use:N \__int_eval:w \c__fp_middle_shift_int + #40 - #1*7179
+          \exp_after:wN \__fp_pack:NNNNNw
+          \int_use:N \__int_eval:w \c__fp_trailing_shift_int + #50 - #1*5880
     \exp_after:wN ;
   }
 \cs_new:Npn \__fp_trig_large_break:w \fi: #1; #2;
-  { \fi: \__fp_trig_octant_loop:nw #2 {0000} {0000} ; }
-\cs_new:Npn \__fp_trig_octant_loop:nw #1#2;
+  { \fi: \__fp_trig_octant_loop:nnnnnw #2 {0000} {0000} ; }
+\cs_new:Npn \__fp_trig_octant_loop:nnnnnw #1#2#3#4#5#6;
   {
-    \if_int_compare:w #1 < 15707 \exp_stop_f:
+    \if_int_compare:w #1#2 < 157079633 \exp_stop_f:
+      \if_int_compare:w #1#2 = 157079632 \exp_stop_f:
+        \if_int_compare:w #3#4 > 67948969 \exp_stop_f:
+          \use_i_ii:nnn
+        \fi:
+      \fi:
       \__fp_trig_octant_break:w
     \fi:
     + \c_two
-    \__fp_fixed_sub_back:wwN
+    \__fp_fixed_sub:wwn
+      {#1} {#2} {#3} {#4} {0000} {0000} ;
       {15707} {9632} {6794} {8970} {0000} {0000} ;
-      {#1} #2;
-    \__fp_trig_octant_loop:nw
+    \__fp_trig_octant_loop:nnnnnw
   }
-\cs_new:Npn \__fp_trig_octant_break:w #1 \fi: + #2#3 #4; #5#6; #7;
+\cs_new:Npn \__fp_trig_octant_break:w #1 \fi: + #2#3 #4#5; #6; #7;
   {
     \fi:
-    \if_int_compare:w #5 < 7854 \exp_stop_f:
-      \if_int_compare:w #5 < \c_zero
-        \exp_after:wN \__fp_trig_octant_neg:w
-      \fi:
+    \if_int_compare:w #4 < 7854 \exp_stop_f:
       \exp_after:wN \__fp_use_i_until_s:nw
       \exp_after:wN .
     \fi:
     + \c_one
-    \__fp_fixed_sub:wwN
-    {15707} {9632} {6794} {8970} {0000} {0000} ;
-    {#5} #6 ; . ;
-  }
-\cs_new:Npn \__fp_trig_octant_neg:w #1\fi: #2; #3#4#5#6#7#8; #9
-  {
-    \fi:
-    + \c_seven
-    \exp_after:wN \__fp_fixed_add_after:NNNNNwN
-    \int_use:N \__int_eval:w 1 9999 9998 - #30000 - #4
-      \exp_after:wN \__fp_fixed_add_pack:NNNNNwN
-      \int_use:N \__int_eval:w 1 9999 9998 - #5#6
-        \exp_after:wN \__fp_fixed_add_pack:NNNNNwN
-        \int_use:N \__int_eval:w 2 0000 0000 - #7#8 ; {#9} ;
+    \__fp_fixed_sub:wwn #6 ; {#4} #5 ; . ;
   }
 \cs_new:Npn \__fp_sin_series:NNwww #1#2#3 . #4; #5;
   {
     \__fp_fixed_mul:wwn #4; #4;
     {
-      \exp_after:wN \__fp_sin_series_aux:Nnww
+      \exp_after:wN \__fp_sin_series_aux:NNnww
+      \exp_after:wN #1
       \__int_value:w
         \if_int_odd:w \__int_eval:w ( #3 + \c_two ) / \c_four \__int_eval_end:
           #2
@@ -4019,49 +4072,49 @@
     }
     #4 ;
   }
-\cs_new:Npn \__fp_sin_series_aux:Nnww #1#2 #3; #4;
+\cs_new:Npn \__fp_sin_series_aux:NNnww #1#2#3 #4; #5;
   {
-    \if_int_odd:w \__int_eval:w #2 / \c_two \__int_eval_end:
+    \if_int_odd:w \__int_eval:w #3 / \c_two \__int_eval_end:
       \exp_after:wN \use_i:nn
     \else:
       \exp_after:wN \use_ii:nn
     \fi:
-    {
-      \__fp_fixed_continue:wn {0000}{0000}{0000}{0001}{5619}{2070}; % 1/18!
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0000}{0477}{9477}{3324};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0011}{4707}{4559}{7730};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0000}{2087}{6756}{9878}{6810};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0027}{5573}{1922}{3985}{8907};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{2480}{1587}{3015}{8730}{1587};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0013}{8888}{8888}{8888}{8888}{8889};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0416}{6666}{6666}{6666}{6666}{6667};
-      \__fp_fixed_mul_sub_back:wwwn #3; {5000}{0000}{0000}{0000}{0000}{0000};
-      \__fp_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
+    { % 1/18!
+      \__fp_fixed_mul_sub_back:wwwn     {0000}{0000}{0000}{0001}{5619}{2070};
+                                  #4; {0000}{0000}{0000}{0477}{9477}{3324};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0000}{0011}{4707}{4559}{7730};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0000}{2087}{6756}{9878}{6810};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0027}{5573}{1922}{3985}{8907};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{2480}{1587}{3015}{8730}{1587};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0013}{8888}{8888}{8888}{8888}{8889};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0416}{6666}{6666}{6666}{6666}{6667};
+      \__fp_fixed_mul_sub_back:wwwn #4; {5000}{0000}{0000}{0000}{0000}{0000};
+      \__fp_fixed_mul_sub_back:wwwn #4;{10000}{0000}{0000}{0000}{0000}{0000};
     }
-    {
-      \__fp_fixed_continue:wn {0000}{0000}{0000}{0028}{1145}{7254}; % 1/17!
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0000}{7647}{1637}{3182};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0000}{0160}{5904}{3836}{8216};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0002}{5052}{1083}{8544}{1719};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0275}{5731}{9223}{9858}{9065};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0001}{9841}{2698}{4126}{9841}{2698};
-      \__fp_fixed_mul_sub_back:wwwn #3; {0083}{3333}{3333}{3333}{3333}{3333};
-      \__fp_fixed_mul_sub_back:wwwn #3; {1666}{6666}{6666}{6666}{6666}{6667};
-      \__fp_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
-      \__fp_fixed_mul:wwn #4;
+    { % 1/17!
+      \__fp_fixed_mul_sub_back:wwwn     {0000}{0000}{0000}{0028}{1145}{7254};
+                                  #4; {0000}{0000}{0000}{7647}{1637}{3182};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0000}{0160}{5904}{3836}{8216};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0002}{5052}{1083}{8544}{1719};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0000}{0275}{5731}{9223}{9858}{9065};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0001}{9841}{2698}{4126}{9841}{2698};
+      \__fp_fixed_mul_sub_back:wwwn #4; {0083}{3333}{3333}{3333}{3333}{3333};
+      \__fp_fixed_mul_sub_back:wwwn #4; {1666}{6666}{6666}{6666}{6666}{6667};
+      \__fp_fixed_mul_sub_back:wwwn #4;{10000}{0000}{0000}{0000}{0000}{0000};
+      \__fp_fixed_mul:wwn #5;
     }
     {
       \exp_after:wN \__fp_sanitize:Nw
-      \exp_after:wN #1
-      \int_use:N \__int_eval:w \__fp_fixed_to_float:wN
+      \exp_after:wN #2
+      \int_use:N \__int_eval:w #1
     }
-    #1
+    #2
   }
-\cs_new:Npn \__fp_tan_series:NNwww #1#2#3. #4; #5;
+\cs_new:Npn \__fp_tan_series_o:NNwww #1#2#3. #4; #5;
   {
     \__fp_fixed_mul:wwn #4; #4;
     {
-      \exp_after:wN \__fp_tan_series_aux:Nnww
+      \exp_after:wN \__fp_tan_series_aux_o:Nnww
       \__int_value:w
         \if_int_odd:w \__int_eval:w #3 / \c_two \__int_eval_end:
           \exp_after:wN \reverse_if:N
@@ -4071,18 +4124,18 @@
     }
     #4 ;
   }
-\cs_new:Npn \__fp_tan_series_aux:Nnww #1 #2 #3; #4;
+\cs_new:Npn \__fp_tan_series_aux_o:Nnww #1 #2 #3; #4;
   {
-    \__fp_fixed_continue:wn {0000}{0000}{1527}{3493}{0856}{7059};
-    \__fp_fixed_mul_sub_back:wwwn #3; {0000}{0159}{6080}{0274}{5257}{6472};
+    \__fp_fixed_mul_sub_back:wwwn     {0000}{0000}{1527}{3493}{0856}{7059};
+                                #3; {0000}{0159}{6080}{0274}{5257}{6472};
     \__fp_fixed_mul_sub_back:wwwn #3; {0002}{4571}{2320}{0157}{2558}{8481};
     \__fp_fixed_mul_sub_back:wwwn #3; {0115}{5830}{7533}{5397}{3168}{2147};
     \__fp_fixed_mul_sub_back:wwwn #3; {1929}{8245}{6140}{3508}{7719}{2982};
     \__fp_fixed_mul_sub_back:wwwn #3;{10000}{0000}{0000}{0000}{0000}{0000};
     \__fp_fixed_mul:wwn #4;
       {
-        \__fp_fixed_continue:wn {0000}{0007}{0258}{0681}{9408}{4706};
-        \__fp_fixed_mul_sub_back:wwwn #3; {0000}{2343}{7175}{1399}{6151}{7670};
+        \__fp_fixed_mul_sub_back:wwwn     {0000}{0007}{0258}{0681}{9408}{4706};
+                                    #3; {0000}{2343}{7175}{1399}{6151}{7670};
         \__fp_fixed_mul_sub_back:wwwn #3; {0019}{2638}{4588}{9232}{8861}{3691};
         \__fp_fixed_mul_sub_back:wwwn #3; {0536}{6357}{0691}{4344}{6852}{4252};
         \__fp_fixed_mul_sub_back:wwwn #3; {5263}{1578}{9473}{6842}{1052}{6315};
@@ -4350,6 +4403,21 @@
 \cs_new_eq:NN \fp_eval:n \fp_to_decimal:n
 \cs_new:Npn \fp_abs:n #1
   { \fp_to_decimal:n { abs \__fp_parse:n {#1} } }
+\cs_new:Npn \__fp_array_to_clist:n #1
+  {
+    \__fp_array_to_clist_i:wwww ;
+      #1
+      \__fp_array_to_clist_ii:ww \s__fp ; @
+      ; , ~ , ~ @ \s_stop
+  }
+\cs_new:Npn \__fp_array_to_clist_i:wwww #1; #2 \s__fp #3; #4 @
+  {
+    #2
+    \exp_after:wN \__fp_array_to_clist_i:wwww
+    \tex_romannumeral:D -`0 \__fp_to_tl:w \s__fp #3 ; ;
+    #4 , ~ #1 @
+  }
+\cs_new:Npn \__fp_array_to_clist_ii:ww #1 ; , ~ , ~ #2 @ #3 \s_stop {#2}
 %%
 %% File: l3fp-assign.dtx Copyright (C) 2011-2012 The LaTeX3 project
 %%
@@ -4421,7 +4489,14 @@
 \cs_generate_variant:Nn \fp_sub:Nn  { c }
 \cs_generate_variant:Nn \fp_gsub:Nn { c }
 \cs_new_protected:Npn \fp_show:N #1
-  { \__msg_show_variable:x { > \fp_to_tl:N #1 } }
+  {
+    \fp_if_exist:NTF #1
+      { \__msg_show_variable:x { > \fp_to_tl:N #1 } }
+      {
+        \__msg_kernel_error:nnx { kernel } { variable-not-defined }
+          { \token_to_str:N #1 }
+      }
+  }
 \cs_new_protected:Npn \fp_show:n #1
   { \__msg_show_variable:x { > \fp_to_tl:n {#1} } }
 \cs_generate_variant:Nn \fp_show:N { c }
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3int.sty b/Master/texmf-dist/tex/latex/l3kernel/l3int.sty
index 531f0a0e7c9..25667fc8c75 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3int.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3int.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3int.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3int.dtx 4121 2012-08-17 01:36:30Z bruno $
   {L3 Integers}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -329,11 +329,11 @@
   }
 \cs_new:Npn \int_until_do:nNnn #1#2#3#4
   {
-  \int_compare:nNnF {#1} #2 {#3}
-    {
-      #4
-      \int_until_do:nNnn {#1} #2 {#3} {#4}
-    }
+    \int_compare:nNnF {#1} #2 {#3}
+      {
+        #4
+        \int_until_do:nNnn {#1} #2 {#3} {#4}
+      }
   }
 \cs_new:Npn \int_do_while:nNnn #1#2#3#4
   {
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3msg.sty b/Master/texmf-dist/tex/latex/l3kernel/l3msg.sty
index 3845880de85..0d717006172 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3msg.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3msg.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3msg.dtx 4077 2012-08-10 23:30:52Z bruno $
+\GetIdInfo$Id: l3msg.dtx 4147 2012-08-28 10:27:33Z bruno $
   {L3 Messages}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -591,7 +591,7 @@
     \c_msg_coding_error_text_tl
     Code-level~functions~must~contain~':'~to~separate~the~
     argument~specification~from~the~function~name.~This~is~
-    needed~when~defining~conditionals~or~when~building~a~
+    needed~when~defining~conditionals~or~variants,~or~when~building~a~
     parameter~text~from~the~number~of~arguments~of~the~function.
   }
 \__msg_kernel_new:nnnn { kernel } { protected-predicate }
@@ -630,6 +630,14 @@
     with~a~signature~starting~with~'#1',~but~that~is~longer~than~
     the~signature~(part~after~the~colon)~of~'#2'.
   }
+\__msg_kernel_new:nnnn { kernel } { invalid-variant }
+  { Variant~form~'#1'~invalid~for~base~form~'#2'. }
+  {
+    \c_msg_coding_error_text_tl
+    LaTeX~has~been~asked~to~create~a~variant~of~the~function~'#2'~
+    with~a~signature~starting~with~'#1',~but~cannot~change~an~argument~
+    from~type~'#3'~to~type~'#4'.
+  }
 \__msg_kernel_new:nnn { kernel } { bad-variable }
   { Erroneous~variable~#1 used! }
 \__msg_kernel_new:nnn { kernel } { misused-sequence }
@@ -736,7 +744,7 @@
     \cs_if_exist:NTF #1
       {
         \__msg_term:nnn { LaTeX / kernel } { show- #2 } {#1}
-        \__msg_show_variable:x {#3}
+        \__msg_show_variable:x { \tl_to_str:n {#3} }
       }
       {
         \__msg_kernel_error:nnx { kernel } { variable-not-defined }
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3prg.sty b/Master/texmf-dist/tex/latex/l3kernel/l3prg.sty
index 22fa6688784..93ef25ee4b6 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3prg.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3prg.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3prg.dtx 4061 2012-08-08 15:19:07Z bruno $
+\GetIdInfo$Id: l3prg.dtx 4114 2012-08-16 01:57:02Z bruno $
   {L3 Control structures}
 %%
 \ProvidesExplPackage
@@ -106,8 +106,8 @@
 \cs_new_protected:Npn \bool_show:n #1
   {
     \bool_if:nTF {#1}
-      { \__msg_show_variable:x { > true } }
-      { \__msg_show_variable:x { > false } }
+      { \__msg_show_variable:n { > true } }
+      { \__msg_show_variable:n { > false } }
   }
 \cs_generate_variant:Nn \bool_show:N { c }
 \bool_new:N \l_tmpa_bool
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3prop.sty b/Master/texmf-dist/tex/latex/l3kernel/l3prop.sty
index e65ebc5e2bc..1e692963872 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3prop.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3prop.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3prop.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3prop.dtx 4092 2012-08-14 14:04:41Z bruno $
   {L3 Property lists}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -295,9 +295,7 @@
   { \__prg_map_break:Nn \prop_map_break: }
 \cs_new_protected:Npn \prop_show:N #1
   {
-    \__msg_show_variable:Nnn
-      #1
-      { prop }
+    \__msg_show_variable:Nnx #1 { prop }
       { \prop_map_function:NN #1 \__msg_show_item:nn }
   }
 \cs_generate_variant:Nn \prop_show:N { c }
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3seq.sty b/Master/texmf-dist/tex/latex/l3kernel/l3seq.sty
index 5b4fe8c3790..58e3b205359 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3seq.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3seq.sty
@@ -46,7 +46,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3seq.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3seq.dtx 4092 2012-08-14 14:04:41Z bruno $
   {L3 Sequences and stacks}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
@@ -433,9 +433,7 @@
 \prg_new_eq_conditional:NNn \seq_gpop:cN \seq_gpop_left:cN { T , F , TF }
 \cs_new_protected:Npn \seq_show:N #1
   {
-    \__msg_show_variable:Nnn
-      #1
-      { seq }
+    \__msg_show_variable:Nnx #1 { seq }
       { \seq_map_function:NN #1 \__msg_show_item:n }
   }
 \cs_generate_variant:Nn \seq_show:N { c }
diff --git a/Master/texmf-dist/tex/latex/l3kernel/l3skip.sty b/Master/texmf-dist/tex/latex/l3kernel/l3skip.sty
index 8888a5b9056..adbdbc68d8c 100644
--- a/Master/texmf-dist/tex/latex/l3kernel/l3skip.sty
+++ b/Master/texmf-dist/tex/latex/l3kernel/l3skip.sty
@@ -47,7 +47,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3bootstrap}
-\GetIdInfo$Id: l3skip.dtx 3991 2012-07-16 19:00:35Z joseph $
+\GetIdInfo$Id: l3skip.dtx 4121 2012-08-17 01:36:30Z bruno $
   {L3 Dimensions and skips}
 \ProvidesExplPackage
   {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}