expl3 2103 (18dec10)

git-svn-id: svn://tug.org/texlive/trunk@20793 c570f23f-e606-0410-a88d-b1316a301751

2 files changed, 1303 insertions, 186 deletions

diff --git a/Master/texmf-dist/tex/latex/expl3/l3fp.sty b/Master/texmf-dist/tex/latex/expl3/l3fp.sty
index 65366e3af16..b5bb0661edc 100644
--- a/Master/texmf-dist/tex/latex/expl3/l3fp.sty
+++ b/Master/texmf-dist/tex/latex/expl3/l3fp.sty
@@ -48,25 +48,18 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3fp.dtx 2092 2010-11-25 20:44:04Z joseph $
+\GetIdInfo$Id: l3fp.dtx 2104 2010-12-18 09:29:34Z joseph $
   {L3 Experimental floating-point operations}
 \ProvidesExplPackage
   {\filename}{\filedate}{\fileversion}{\filedescription}
 \package_check_loaded_expl:
-\int_new:N  \c_forty_four
-\int_set:Nn \c_forty_four { 44 }
-\int_new:N  \c_one_hundred
-\int_set:Nn \c_one_hundred { 100 }
-\int_new:N  \c_one_thousand
-\int_set:Nn \c_one_thousand { 1000 }
-\int_new:N  \c_one_million
-\int_set:Nn \c_one_million { 1 000 000 }
-\int_new:N  \c_one_hundred_million
-\int_set:Nn \c_one_hundred_million { 100 000 000 }
-\int_new:N  \c_five_hundred_million
-\int_set:Nn \c_five_hundred_million { 500 000 000 }
-\int_new:N  \c_one_thousand_million
-\int_set:Nn \c_one_thousand_million { 1 000 000 000 }
+\int_const:Nn \c_forty_four { 44 }
+\int_const:Nn \c_one_hundred { 100 }
+\int_const:Nn \c_one_thousand { 1000 }
+\int_const:Nn \c_one_million { 1 000 000 }
+\int_const:Nn \c_one_hundred_million { 100 000 000 }
+\int_const:Nn \c_five_hundred_million { 500 000 000 }
+\int_const:Nn \c_one_thousand_million { 1 000 000 000 }
 \int_new:N  \c_fp_pi_by_four_decimal_int
 \int_set:Nn \c_fp_pi_by_four_decimal_int { 785 398 158 }
 \int_new:N  \c_fp_pi_by_four_extended_int
@@ -79,16 +72,23 @@
 \int_set:Nn \c_fp_two_pi_decimal_int { 283 185 307 }
 \int_new:N  \c_fp_two_pi_extended_int
 \int_set:Nn \c_fp_two_pi_extended_int { 179 586 477 }
-\tl_new:N  \c_one_fp
+\tl_new:N \c_e_fp
+\tl_set:Nn \c_e_fp { + 2.718281828 e 0 }
+\tl_new:N \c_one_fp
 \tl_set:Nn \c_one_fp { + 1.000000000 e 0 }
-\tl_new:N  \c_pi_fp
+\tl_new:N \c_pi_fp
 \tl_set:Nn \c_pi_fp { + 3.141592654 e 0 }
-\tl_new:N  \c_undefined_fp
+\tl_new:N \c_undefined_fp
 \tl_set:Nn \c_undefined_fp { X 0.000000000 e 0 }
-\tl_new:N  \c_zero_fp
+\tl_new:N \c_zero_fp
 \tl_set:Nn \c_zero_fp { + 0.000000000 e 0 }
+\tl_new:N \l_fp_arg_tl
 \int_new:N \l_fp_count_int
 \int_new:N \l_fp_div_offset_int
+\int_new:N \l_fp_exp_integer_int
+\int_new:N \l_fp_exp_decimal_int
+\int_new:N \l_fp_exp_extended_int
+\int_new:N \l_fp_exp_exponent_int
 \int_new:N \l_fp_input_a_sign_int
 \int_new:N \l_fp_input_a_integer_int
 \int_new:N \l_fp_input_a_decimal_int
@@ -122,16 +122,16 @@
 \tl_new:N \l_fp_round_decimal_tl
 \int_new:N \l_fp_round_position_int
 \int_new:N \l_fp_round_target_int
+\tl_new:N \l_fp_sign_tl
 \int_new:N \l_fp_split_sign_int
 \int_new:N \l_fp_tmp_int
 \tl_new:N \l_fp_tmp_tl
-\tl_new:N \l_fp_trig_arg_tl
 \int_new:N \l_fp_trig_octant_int
 \int_new:N \l_fp_trig_sign_int
 \int_new:N \l_fp_trig_decimal_int
 \int_new:N \l_fp_trig_extended_int
 \cs_new_protected_nopar:Npn \fp_read:N #1 {
-  \exp_after:wN \fp_read_aux:w #1 \q_stop
+  \tex_expandafter:D \fp_read_aux:w #1 \q_stop
 }
 \cs_new_protected_nopar:Npn \fp_read_aux:w #1#2 . #3 e #4 \q_stop {
   \tex_if:D #1 -
@@ -150,29 +150,29 @@
   \l_fp_split_sign_int \c_one
   \fp_split_sign:
   \use:c { l_fp_input_ #1 _sign_int } \l_fp_split_sign_int
-  \exp_after:wN \fp_split_exponent:w \l_fp_tmp_tl e e \q_stop #1
+  \tex_expandafter:D \fp_split_exponent:w \l_fp_tmp_tl e e \q_stop #1
 }
 \cs_new_protected_nopar:Npn \fp_split_sign: {
   \tex_ifnum:D \pdf_strcmp:D
-    { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_stop } { - }
+    { \tex_expandafter:D \tl_head:w \l_fp_tmp_tl ? \q_stop } { - }
       = \c_zero
     \tl_set:Nx \l_fp_tmp_tl
       {
-        \exp_after:wN
+        \tex_expandafter:D
           \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_stop
       }
     \l_fp_split_sign_int -\l_fp_split_sign_int
-    \exp_after:wN \fp_split_sign:
+    \tex_expandafter:D \fp_split_sign:
   \tex_else:D
     \tex_ifnum:D \pdf_strcmp:D
-      { \exp_after:wN \tl_head:w \l_fp_tmp_tl ? \q_stop } { + }
+      { \tex_expandafter:D \tl_head:w \l_fp_tmp_tl ? \q_stop } { + }
         = \c_zero
       \tl_set:Nx \l_fp_tmp_tl
         {
-          \exp_after:wN
+          \tex_expandafter:D
             \tl_tail:w \l_fp_tmp_tl \prg_do_nothing: \q_stop
         }
-      \exp_after:wN \exp_after:wN \exp_after:wN
+      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
         \fp_split_sign:
      \tex_fi:D
   \tex_fi:D
@@ -193,7 +193,7 @@
 }
 \cs_new_protected_nopar:Npn \fp_split_aux_iii:w #1#2 \q_stop {
   \l_fp_tmp_int 1 #1 \scan_stop:
-  \exp_after:wN \fp_split_decimal:w
+  \tex_expandafter:D \fp_split_decimal:w
     \int_use:N \l_fp_tmp_int 000000000 \q_stop
 }
 \cs_new_protected_nopar:Npn \fp_split_decimal:w #1#2#3#4#5#6#7#8#9 {
@@ -212,7 +212,7 @@
   \tex_ifnum:D
     \use:c { l_fp_input_ #4 _integer_int } < \c_one_thousand_million
   \tex_else:D
-    \exp_after:wN \fp_overflow_msg:
+    \tex_expandafter:D \fp_overflow_msg:
   \tex_fi:D
 }
 \cs_new_protected_nopar:Npn \fp_standardise:NNNN #1#2#3#4 {
@@ -220,9 +220,9 @@
     \etex_numexpr:D #2 + #3 = \c_zero
     #1 \c_one
     #4 \c_zero
-    \exp_after:wN \use_none:nnnn
+    \tex_expandafter:D \use_none:nnnn
   \tex_else:D
-    \exp_after:wN \fp_standardise_aux:NNNN
+    \tex_expandafter:D \fp_standardise_aux:NNNN
   \tex_fi:D
   #1#2#3#4
 }
@@ -231,9 +231,9 @@
     {
       \tex_ifnum:D #2 = \c_zero
         \tex_advance:D #3 \c_one_thousand_million
-        \exp_after:wN \fp_standardise_aux:w
+        \tex_expandafter:D \fp_standardise_aux:w
           \int_use:N #3 \q_stop
-         \exp_after:wN \fp_standardise_aux:
+         \tex_expandafter:D \fp_standardise_aux:
        \tex_fi:D
     }
   \cs_set_protected_nopar:Npn
@@ -248,9 +248,9 @@
     {
       \tex_ifnum:D #2 > \c_nine
         \tex_advance:D #2 \c_one_thousand_million
-        \exp_after:wN \use_i:nn \exp_after:wN
+        \tex_expandafter:D \use_i:nn \tex_expandafter:D
           \fp_standardise_aux:w \int_use:N #2
-         \exp_after:wN \fp_standardise_aux:
+         \tex_expandafter:D \fp_standardise_aux:
        \tex_fi:D
     }
   \cs_set_protected_nopar:Npn
@@ -262,7 +262,7 @@
       \tl_set:Nx \l_fp_tmp_tl
         {
           ##9
-          \exp_after:wN \use_none:n \int_use:N #3
+          \tex_expandafter:D \use_none:n \int_use:N #3
         }
       #3 \l_fp_tmp_tl \scan_stop:
       \tex_advance:D #4 \c_one
@@ -277,25 +277,25 @@
       #4 \c_zero
     \tex_fi:D
   \tex_else:D
-    \exp_after:wN \fp_overflow_msg:
+    \tex_expandafter:D \fp_overflow_msg:
   \tex_fi:D
 }
 \cs_new_protected_nopar:Npn \fp_standardise_aux: { }
 \cs_new_protected_nopar:Npn \fp_standardise_aux:w { }
 \cs_new_protected_nopar:Npn \fp_level_input_exponents: {
   \tex_ifnum:D \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
-    \exp_after:wN \fp_level_input_exponents_a:
+    \tex_expandafter:D \fp_level_input_exponents_a:
   \tex_else:D
-    \exp_after:wN \fp_level_input_exponents_b:
+    \tex_expandafter:D \fp_level_input_exponents_b:
   \tex_fi:D
 }
 \cs_new_protected_nopar:Npn \fp_level_input_exponents_a: {
   \tex_ifnum:D \l_fp_input_a_exponent_int > \l_fp_input_b_exponent_int
     \tex_advance:D \l_fp_input_b_integer_int \c_one_thousand_million
-    \exp_after:wN \use_i:nn \exp_after:wN
+    \tex_expandafter:D \use_i:nn \tex_expandafter:D
       \fp_level_input_exponents_a:NNNNNNNNN
         \int_use:N \l_fp_input_b_integer_int
-    \exp_after:wN \fp_level_input_exponents_a:
+    \tex_expandafter:D \fp_level_input_exponents_a:
   \tex_fi:D
 }
 \cs_new_protected_nopar:Npn
@@ -306,7 +306,7 @@
   \tl_set:Nx \l_fp_tmp_tl
     {
       #9
-      \exp_after:wN \use_none:n
+      \tex_expandafter:D \use_none:n
         \int_use:N \l_fp_input_b_decimal_int
     }
   \l_fp_input_b_decimal_int \l_fp_tmp_tl \scan_stop:
@@ -315,10 +315,10 @@
 \cs_new_protected_nopar:Npn \fp_level_input_exponents_b: {
   \tex_ifnum:D \l_fp_input_b_exponent_int > \l_fp_input_a_exponent_int
     \tex_advance:D \l_fp_input_a_integer_int \c_one_thousand_million
-    \exp_after:wN \use_i:nn \exp_after:wN
+    \tex_expandafter:D \use_i:nn \tex_expandafter:D
       \fp_level_input_exponents_b:NNNNNNNNN
         \int_use:N \l_fp_input_a_integer_int
-    \exp_after:wN \fp_level_input_exponents_b:
+    \tex_expandafter:D \fp_level_input_exponents_b:
   \tex_fi:D
 }
 \cs_new_protected_nopar:Npn
@@ -329,7 +329,7 @@
   \tl_set:Nx \l_fp_tmp_tl
     {
       #9
-      \exp_after:wN \use_none:n
+      \tex_expandafter:D \use_none:n
         \int_use:N \l_fp_input_a_decimal_int
     }
   \l_fp_input_a_decimal_int \l_fp_tmp_tl \scan_stop:
@@ -341,6 +341,18 @@
   \tl_gset_eq:NN #1 \c_zero_fp
 }
 \cs_generate_variant:Nn \fp_new:N { c }
+\cs_new_protected_nopar:Npn \fp_const:Nn #1#2 {
+  \cs_if_free:NTF #1
+    {
+      \fp_new:N #1
+      \fp_gset:Nn #1 {#2}
+    }
+    {
+      \msg_kernel_error:nx { variable-already-defined }
+        { \token_to_str:N #1 }
+    }
+}
+\cs_generate_variant:Nn \fp_const:Nn { c }
 \cs_new_protected_nopar:Npn \fp_zero:N #1 {
   \tl_set_eq:NN #1 \c_zero_fp
 }
@@ -376,7 +388,7 @@
             \tex_fi:D
             \int_use:N \l_fp_input_a_integer_int
             .
-            \exp_after:wN \use_none:n
+            \tex_expandafter:D \use_none:n
               \int_use:N \l_fp_input_a_decimal_int
             e
             \int_use:N \l_fp_input_a_exponent_int
@@ -398,7 +410,7 @@
     \l_fp_tmp_dim \l_fp_tmp_skip
     \fp_split:Nn a
       {
-        \exp_after:wN \fp_set_from_dim_aux:w
+        \tex_expandafter:D \fp_set_from_dim_aux:w
           \dim_use:N \l_fp_tmp_dim
       }
     \fp_standardise:NNNN
@@ -419,7 +431,7 @@
             \tex_fi:D
             \int_use:N \l_fp_input_a_integer_int
             .
-            \exp_after:wN \use_none:n
+            \tex_expandafter:D \use_none:n
               \int_use:N \l_fp_input_a_decimal_int
             e
             \int_use:N \l_fp_input_a_exponent_int
@@ -447,7 +459,7 @@
 \cs_new_eq:NN \fp_show:N \tl_show:N
 \cs_new_eq:NN \fp_show:c \tl_show:c
 \cs_new_nopar:Npn \fp_use:N #1 {
-  \exp_after:wN \fp_use_aux:w #1 \q_stop
+  \tex_expandafter:D \fp_use_aux:w #1 \q_stop
 }
 \cs_generate_variant:Nn \fp_use:N { c }
 \cs_new_nopar:Npn \fp_use_aux:w #1#2 e #3 \q_stop {
@@ -455,13 +467,13 @@
     -
   \tex_fi:D
   \tex_ifnum:D #3 > \c_zero
-    \exp_after:wN \fp_use_large:w
+    \tex_expandafter:D \fp_use_large:w
   \tex_else:D
     \tex_ifnum:D #3 < \c_zero
-      \exp_after:wN \exp_after:wN \exp_after:wN
+      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
         \fp_use_small:w
     \tex_else:D
-      \exp_after:wN \exp_after:wN \exp_after:wN
+      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
         \fp_use_none:w
     \tex_fi:D
   \tex_fi:D
@@ -475,9 +487,9 @@
 }
 \cs_new_nopar:Npn \fp_use_large:w #1 . #2 e #3 \q_stop {
   \tex_ifnum:D #3 < \c_ten
-    \exp_after:wN \fp_use_large_aux_i:w
+    \tex_expandafter:D \fp_use_large_aux_i:w
   \tex_else:D
-    \exp_after:wN \fp_use_large_aux_ii:w
+    \tex_expandafter:D \fp_use_large_aux_ii:w
   \tex_fi:D
   #1#2 e #3 \q_stop
 }
@@ -516,7 +528,7 @@
 \cs_new_nopar:Npn \fp_to_dim:N #1 { \fp_use:N #1 pt }
 \cs_generate_variant:Nn \fp_to_dim:N { c }
 \cs_new_nopar:Npn \fp_to_int:N #1 {
-  \exp_after:wN \fp_to_int_aux:w #1 \q_stop
+  \tex_expandafter:D \fp_to_int_aux:w #1 \q_stop
 }
 \cs_generate_variant:Nn \fp_to_int:N { c }
 \cs_new_nopar:Npn \fp_to_int_aux:w #1#2 e #3 \q_stop {
@@ -524,9 +536,9 @@
     -
   \tex_fi:D
   \tex_ifnum:D #3 < \c_zero
-    \exp_after:wN \fp_to_int_small:w
+    \tex_expandafter:D \fp_to_int_small:w
   \tex_else:D
-    \exp_after:wN \fp_to_int_large:w
+    \tex_expandafter:D \fp_to_int_large:w
   \tex_fi:D
   #2 e #3 \q_stop
 }
@@ -542,9 +554,9 @@
 }
 \cs_new_nopar:Npn \fp_to_int_large:w #1 . #2 e #3 \q_stop {
   \tex_ifnum:D #3 < \c_ten
-    \exp_after:wN \fp_to_int_large_aux_i:w
+    \tex_expandafter:D \fp_to_int_large_aux_i:w
   \tex_else:D
-    \exp_after:wN \fp_to_int_large_aux_ii:w
+    \tex_expandafter:D \fp_to_int_large_aux_ii:w
   \tex_fi:D
   #1#2 e #3 \q_stop
 }
@@ -590,7 +602,7 @@
   \prg_replicate:nn { #2 - 9 } { 0 }
 }
 \cs_new_nopar:Npn \fp_to_tl:N #1 {
-  \exp_after:wN \fp_to_tl_aux:w #1 \q_stop
+  \tex_expandafter:D \fp_to_tl_aux:w #1 \q_stop
 }
 \cs_generate_variant:Nn \fp_to_tl:N { c }
 \cs_new_nopar:Npn \fp_to_tl_aux:w #1#2 e #3 \q_stop {
@@ -598,17 +610,17 @@
     -
   \tex_fi:D
   \tex_ifnum:D #3 < \c_zero
-    \exp_after:wN \fp_to_tl_small:w
+    \tex_expandafter:D \fp_to_tl_small:w
   \tex_else:D
-    \exp_after:wN \fp_to_tl_large:w
+    \tex_expandafter:D \fp_to_tl_large:w
   \tex_fi:D
   #2 e #3 \q_stop
 }
 \cs_new_nopar:Npn \fp_to_tl_large:w #1 e #2 \q_stop {
   \tex_ifnum:D #2 < \c_ten
-    \exp_after:wN \fp_to_tl_large_aux_i:w
+    \tex_expandafter:D \fp_to_tl_large_aux_i:w
   \tex_else:D
-    \exp_after:wN \fp_to_tl_large_aux_ii:w
+    \tex_expandafter:D \fp_to_tl_large_aux_ii:w
   \tex_fi:D
   #1 e #2 \q_stop
 }
@@ -664,13 +676,13 @@
 \cs_new_nopar:cpn { fp_to_tl_large_9:w } #1 . #2 \q_stop {#1#2}
 \cs_new_nopar:Npn \fp_to_tl_small:w #1 e #2 \q_stop {
   \tex_ifnum:D #2 = \c_minus_one
-    \exp_after:wN \fp_to_tl_small_one:w
+    \tex_expandafter:D \fp_to_tl_small_one:w
   \tex_else:D
     \tex_ifnum:D #2 = -\c_two
-      \exp_after:wN \exp_after:wN \exp_after:wN
+      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
         \fp_to_tl_small_two:w
     \tex_else:D
-      \exp_after:wN \exp_after:wN \exp_after:wN
+      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
         \fp_to_tl_small_aux:w
     \tex_fi:D
   \tex_fi:D
@@ -682,7 +694,7 @@
       \etex_numexpr:D #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1
         < \c_one_thousand_million
       0.
-      \exp_after:wN \fp_to_tl_small_zeros:NNNNNNNNN
+      \tex_expandafter:D \fp_to_tl_small_zeros:NNNNNNNNN
         \tex_number:D
           \etex_numexpr:D
             #1 \fp_use_i_to_iix:NNNNNNNNN #2 + 1
@@ -701,7 +713,7 @@
       \etex_numexpr:D #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten
         < \c_one_thousand_million
       0.0
-      \exp_after:wN \fp_to_tl_small_zeros:NNNNNNNNN
+      \tex_expandafter:D \fp_to_tl_small_zeros:NNNNNNNNN
         \tex_number:D
           \etex_numexpr:D
             #1 \fp_use_i_to_vii:NNNNNNNNN #2 0 + \c_ten
@@ -817,7 +829,7 @@
     \fp_read:N #2
     \int_set:Nn \l_fp_round_target_int { #3 - 1 }
     \tex_ifnum:D \l_fp_round_target_int < \c_ten
-      \exp_after:wN \fp_round:
+      \tex_expandafter:D \fp_round:
     \tex_fi:D
     \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
     \cs_set_protected_nopar:Npx \fp_tmp:w
@@ -832,7 +844,7 @@
             \tex_fi:D
             \int_use:N \l_fp_input_a_integer_int
             .
-            \exp_after:wN \use_none:n
+            \tex_expandafter:D \use_none:n
               \int_use:N \l_fp_input_a_decimal_int
             e
             \int_use:N \l_fp_input_a_exponent_int
@@ -854,7 +866,7 @@
     \int_set:Nn \l_fp_round_target_int
       { #3 + \l_fp_input_a_exponent_int }
     \tex_ifnum:D \l_fp_round_target_int < \c_ten
-      \exp_after:wN \fp_round:
+      \tex_expandafter:D \fp_round:
     \tex_fi:D
     \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
     \cs_set_protected_nopar:Npx \fp_tmp:w
@@ -869,7 +881,7 @@
             \tex_fi:D
             \int_use:N \l_fp_input_a_integer_int
             .
-            \exp_after:wN \use_none:n
+            \tex_expandafter:D \use_none:n
               \int_use:N \l_fp_input_a_decimal_int
             e
             \int_use:N \l_fp_input_a_exponent_int
@@ -882,7 +894,7 @@
   \l_fp_round_position_int \c_eight
   \tl_clear:N \l_fp_round_decimal_tl
   \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-  \exp_after:wN \use_i:nn \exp_after:wN
+  \tex_expandafter:D \use_i:nn \tex_expandafter:D
     \fp_round_aux:NNNNNNNNN \int_use:N \l_fp_input_a_decimal_int
 }
 \cs_new_protected_nopar:Npn \fp_round_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
@@ -919,7 +931,7 @@
   \tex_fi:D
   \tex_advance:D \l_fp_round_position_int \c_minus_one
   \tex_ifnum:D \l_fp_round_position_int > \c_minus_one
-    \exp_after:wN \fp_round_loop:N
+    \tex_expandafter:D \fp_round_loop:N
   \tex_fi:D
 }
 \cs_new_protected_nopar:Npn \fp_abs:N {
@@ -942,7 +954,7 @@
             +
             \int_use:N \l_fp_input_a_integer_int
             .
-            \exp_after:wN \use_none:n
+            \tex_expandafter:D \use_none:n
               \int_use:N \l_fp_input_a_decimal_int
             e
             \int_use:N \l_fp_input_a_exponent_int
@@ -971,13 +983,13 @@
         \tex_fi:D
         \int_use:N \l_fp_input_a_integer_int
         .
-        \exp_after:wN \use_none:n
+        \tex_expandafter:D \use_none:n
           \int_use:N \l_fp_input_a_decimal_int
         e
         \int_use:N \l_fp_input_a_exponent_int
       }
-  \exp_after:wN \group_end: \exp_after:wN
-  #1 \exp_after:wN #2 \exp_after:wN { \l_fp_tmp_tl }
+  \tex_expandafter:D \group_end: \tex_expandafter:D
+  #1 \tex_expandafter:D #2 \tex_expandafter:D { \l_fp_tmp_tl }
 }
 \cs_new_protected_nopar:Npn \fp_add:Nn {
   \fp_add_aux:NNn \tl_set:Nn
@@ -1006,9 +1018,9 @@
       \l_fp_input_a_sign_int * \l_fp_input_b_sign_int
     \scan_stop:
       > \c_zero
-    \exp_after:wN \fp_add_sum:
+    \tex_expandafter:D \fp_add_sum:
   \tex_else:D
-    \exp_after:wN \fp_add_difference:
+    \tex_expandafter:D \fp_add_difference:
   \tex_fi:D
   \l_fp_output_exponent_int \l_fp_input_a_exponent_int
   \fp_standardise:NNNN
@@ -1028,7 +1040,7 @@
           \tex_fi:D
           \int_use:N \l_fp_output_integer_int
           .
-          \exp_after:wN \use_none:n
+          \tex_expandafter:D \use_none:n
             \tex_number:D \etex_numexpr:D
                \l_fp_output_decimal_int + \c_one_thousand_million
           e
@@ -1121,7 +1133,7 @@
       \l_fp_input_b_integer_int
       \l_fp_input_b_decimal_int
       \l_fp_input_b_exponent_int
-    \fp_mul_int:
+    \fp_mul_internal:
     \l_fp_output_exponent_int
       \etex_numexpr:D
         \l_fp_input_a_exponent_int + \l_fp_input_b_exponent_int
@@ -1153,7 +1165,7 @@
            \tex_fi:D
             \int_use:N \l_fp_output_integer_int
             .
-            \exp_after:wN \use_none:n
+            \tex_expandafter:D \use_none:n
               \tex_number:D \etex_numexpr:D
                  \l_fp_output_decimal_int + \c_one_thousand_million
             e
@@ -1162,7 +1174,7 @@
       }
   \fp_tmp:w
 }
-\cs_new_protected_nopar:Npn \fp_mul_int: {
+\cs_new_protected_nopar:Npn \fp_mul_internal: {
   \fp_mul_split:NNNN \l_fp_input_a_decimal_int
     \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
   \fp_mul_split:NNNN \l_fp_input_b_decimal_int
@@ -1199,7 +1211,7 @@
       #3 ##5##6##7 \scan_stop:
       #4 ##8##9    \scan_stop:
     }
-  \exp_after:wN \fp_mul_split_aux:w \int_use:N #1 \q_stop
+  \tex_expandafter:D \fp_mul_split_aux:w \int_use:N #1 \q_stop
   \tex_advance:D #1 -\c_one_thousand_million
 }
 \cs_new_protected_nopar:Npn \fp_mul_product:NN #1#2 {
@@ -1208,7 +1220,7 @@
 }
 \cs_new_protected_nopar:Npn \fp_mul_end_level: {
   \tex_advance:D \l_fp_mul_output_int \c_one_thousand_million
-  \exp_after:wN \use_i:nn \exp_after:wN
+  \tex_expandafter:D \use_i:nn \tex_expandafter:D
     \fp_mul_end_level:NNNNNNNNN \int_use:N \l_fp_mul_output_int
 }
 \cs_new_protected_nopar:Npn \fp_mul_end_level:NNNNNNNNN
@@ -1224,7 +1236,6 @@
 }
 \cs_generate_variant:Nn \fp_div:Nn  { c }
 \cs_generate_variant:Nn \fp_gdiv:Nn { c }
-
 \cs_new_protected_nopar:Npn \fp_div_aux:NNn #1#2#3 {
   \group_begin:
     \fp_read:N #2
@@ -1254,13 +1265,13 @@
             #1 \exp_not:N #2 { \c_zero_fp }
           }
       \tex_else:D
-        \exp_after:wN \exp_after:wN \exp_after:wN
-          \fp_div_aux:
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \fp_div_internal:
       \tex_fi:D
     \tex_fi:D
   \fp_tmp:w #1#2
 }
-\cs_new_protected_nopar:Npn \fp_div_aux: {
+\cs_new_protected_nopar:Npn \fp_div_internal: {
   \l_fp_output_integer_int \c_zero
   \l_fp_output_decimal_int \c_zero
   \cs_set_eq:NN \fp_div_store: \fp_div_store_integer:
@@ -1297,7 +1308,7 @@
           \tex_fi:D
           \int_use:N \l_fp_output_integer_int
           .
-          \exp_after:wN \use_none:n
+          \tex_expandafter:D \use_none:n
             \tex_number:D \etex_numexpr:D
                \l_fp_output_decimal_int + \c_one_thousand_million
              \scan_stop:
@@ -1312,30 +1323,30 @@
   \fp_div_store:
   \tex_multiply:D \l_fp_input_a_integer_int \c_ten
   \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-  \exp_after:wN \fp_div_loop_step:w
+  \tex_expandafter:D \fp_div_loop_step:w
     \int_use:N \l_fp_input_a_decimal_int \q_stop
   \tex_ifnum:D
     \etex_numexpr:D
       \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
       > \c_zero
       \tex_ifnum:D \l_fp_div_offset_int > \c_zero
-        \exp_after:wN \exp_after:wN \exp_after:wN
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
           \fp_div_loop:
       \tex_fi:D
   \tex_fi:D
 }
 \cs_new_protected_nopar:Npn \fp_div_divide: {
   \tex_ifnum:D \l_fp_input_a_integer_int > \l_fp_input_b_integer_int
-    \exp_after:wN \fp_div_divide_aux:
+    \tex_expandafter:D \fp_div_divide_aux:
   \tex_else:D
     \tex_ifnum:D \l_fp_input_a_integer_int < \l_fp_input_b_integer_int
     \tex_else:D
       \tex_ifnum:D
         \l_fp_input_a_decimal_int < \l_fp_input_b_decimal_int
       \tex_else:D
-        \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \fp_div_divide_aux:
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \fp_div_divide_aux:
       \tex_fi:D
     \tex_fi:D
   \tex_fi:D
@@ -1430,6 +1441,7 @@
   \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iv_int
   \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_iii_int
   \fp_mul_product:NN \l_fp_mul_a_iv_int       \l_fp_mul_b_ii_int
+  \fp_mul_product:NN \l_fp_mul_a_v_int        \l_fp_mul_b_i_int
   \fp_mul_end_level:
   \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_iv_int
   \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iii_int
@@ -1450,6 +1462,65 @@
   \fp_mul_end_level:
   #5 0 \l_fp_mul_output_tl \scan_stop:
 }
+\cs_new_protected_nopar:Npn \fp_mul:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+  \fp_mul_split:NNNN #2
+    \l_fp_mul_a_i_int \l_fp_mul_a_ii_int \l_fp_mul_a_iii_int
+  \fp_mul_split:NNNN #3
+    \l_fp_mul_a_iv_int \l_fp_mul_a_v_int \l_fp_mul_a_vi_int
+  \fp_mul_split:NNNN #5
+    \l_fp_mul_b_i_int \l_fp_mul_b_ii_int \l_fp_mul_b_iii_int
+  \fp_mul_split:NNNN #6
+    \l_fp_mul_b_iv_int \l_fp_mul_b_v_int \l_fp_mul_b_vi_int
+  \l_fp_mul_output_int \c_zero
+  \tl_clear:N \l_fp_mul_output_tl
+  \fp_mul_product:NN \l_fp_mul_a_i_int         \l_fp_mul_b_vi_int
+  \fp_mul_product:NN \l_fp_mul_a_ii_int        \l_fp_mul_b_v_int
+  \fp_mul_product:NN \l_fp_mul_a_iii_int       \l_fp_mul_b_iv_int
+  \fp_mul_product:NN \l_fp_mul_a_iv_int        \l_fp_mul_b_iii_int
+  \fp_mul_product:NN \l_fp_mul_a_v_int         \l_fp_mul_b_ii_int
+  \fp_mul_product:NN \l_fp_mul_a_vi_int        \l_fp_mul_b_i_int
+  \tex_divide:D \l_fp_mul_output_int \c_one_thousand
+  \fp_mul_product:NN #1                       \l_fp_mul_b_vi_int
+  \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_v_int
+  \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iv_int
+  \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_iii_int
+  \fp_mul_product:NN \l_fp_mul_a_iv_int       \l_fp_mul_b_ii_int
+  \fp_mul_product:NN \l_fp_mul_a_v_int        \l_fp_mul_b_i_int
+  \fp_mul_product:NN \l_fp_mul_a_vi_int       #4
+  \fp_mul_end_level:
+  \fp_mul_product:NN #1                       \l_fp_mul_b_v_int
+  \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_iv_int
+  \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_iii_int
+  \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_ii_int
+  \fp_mul_product:NN \l_fp_mul_a_iv_int       \l_fp_mul_b_i_int
+  \fp_mul_product:NN \l_fp_mul_a_v_int        #4
+  \fp_mul_end_level:
+  \fp_mul_product:NN #1                       \l_fp_mul_b_iv_int
+  \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_iii_int
+  \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_ii_int
+  \fp_mul_product:NN \l_fp_mul_a_iii_int      \l_fp_mul_b_i_int
+  \fp_mul_product:NN \l_fp_mul_a_iv_int       #4
+  \fp_mul_end_level:
+  #9 0 \l_fp_mul_output_tl \scan_stop:
+  \tl_clear:N \l_fp_mul_output_tl
+  \fp_mul_product:NN #1                       \l_fp_mul_b_iii_int
+  \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_ii_int
+  \fp_mul_product:NN \l_fp_mul_a_ii_int       \l_fp_mul_b_i_int
+  \fp_mul_product:NN \l_fp_mul_a_iii_int      #4
+  \fp_mul_end_level:
+  \fp_mul_product:NN #1                       \l_fp_mul_b_ii_int
+  \fp_mul_product:NN \l_fp_mul_a_i_int        \l_fp_mul_b_i_int
+  \fp_mul_product:NN \l_fp_mul_a_ii_int       #4
+  \fp_mul_end_level:
+  \fp_mul_product:NN #1                       \l_fp_mul_b_i_int
+  \fp_mul_product:NN \l_fp_mul_a_i_int        #4
+  \fp_mul_end_level:
+  #8 0 \l_fp_mul_output_tl \scan_stop:
+  \tl_clear:N \l_fp_mul_output_tl
+  \fp_mul_product:NN #1 #4
+  \fp_mul_end_level:
+  #7 0 \l_fp_mul_output_tl \scan_stop:
+}
 \cs_new_protected_nopar:Npn \fp_div_integer:NNNNN #1#2#3#4#5 {
   \l_fp_tmp_int #1
   \tex_divide:D \l_fp_tmp_int #3
@@ -1466,52 +1537,46 @@
     \tex_advancd:D #5 -\c_one_thousand_million
   \tex_fi:D
 }
-\cs_new_protected_nopar:Npn \fp_trig_normalise: {
-  \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
-    \l_fp_input_a_extended_int \c_zero
-    \fp_trig_normalise_aux_i:
-    \fp_trig_normalise_aux_ii:
-    \fp_trig_normalise_aux_iii:
-    \tex_ifnum:D \l_fp_input_a_integer_int < \c_zero
-      \l_fp_input_a_sign_int -\l_fp_input_a_sign_int
-      \l_fp_input_a_integer_int -\l_fp_input_a_integer_int
-    \tex_fi:D
-     \exp_after:wN \fp_trig_octant:
-  \tex_else:D
-    \l_fp_input_a_sign_int    \c_one
-    \l_fp_output_integer_int  \c_zero
-    \l_fp_output_decimal_int  \c_zero
-    \l_fp_output_exponent_int \c_zero
-    \exp_after:wN \fp_trig_overflow_msg:
-  \tex_fi:D
+\cs_new_protected_nopar:Npn \fp_extended_normalise: {
+  \fp_extended_normalise_aux_i:
+  \fp_extended_normalise_aux_ii:
 }
-\cs_new_protected_nopar:Npn \fp_trig_normalise_aux_i: {
+\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_i: {
   \tex_ifnum:D \l_fp_input_a_exponent_int > \c_zero
     \tex_multiply:D \l_fp_input_a_integer_int \c_ten
     \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \exp_after:wN \fp_trig_normalise_aux:w
+    \tex_expandafter:D \fp_extended_normalise_aux_i:w
       \int_use:N \l_fp_input_a_decimal_int \q_stop
-     \exp_after:wN \fp_trig_normalise_aux_i:
+     \tex_expandafter:D \fp_extended_normalise_aux_i:
    \tex_fi:D
 }
 \cs_new_protected_nopar:Npn
-  \fp_trig_normalise_aux:w #1#2#3#4#5#6#7#8#9 \q_stop {
+  \fp_extended_normalise_aux_i:w #1#2#3#4#5#6#7#8#9 \q_stop {
   \l_fp_input_a_integer_int
     \etex_numexpr:D \l_fp_input_a_integer_int + #2 \scan_stop:
   \l_fp_input_a_decimal_int #3#4#5#6#7#8#9 0 \scan_stop:
+  \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
+  \tex_expandafter:D \fp_extended_normalise_aux_ii:w
+      \int_use:N \l_fp_input_a_extended_int \q_stop
+}
+\cs_new_protected_nopar:Npn
+  \fp_extended_normalise_aux_ii:w #1#2#3#4#5#6#7#8#9 \q_stop {
+  \l_fp_input_a_decimal_int
+    \etex_numexpr:D \l_fp_input_a_decimal_int + #2 \scan_stop:
+  \l_fp_input_a_extended_int #3#4#5#6#7#8#9 0 \scan_stop:
   \tex_advance:D \l_fp_input_a_exponent_int \c_minus_one
 }
-\cs_new_protected_nopar:Npn \fp_trig_normalise_aux_ii: {
+\cs_new_protected_nopar:Npn \fp_extended_normalise_aux_ii: {
   \tex_ifnum:D \l_fp_input_a_exponent_int < \c_zero
     \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
-    \exp_after:wN \use_i:nn \exp_after:wN
-      \fp_trig_normalise_aux:NNNNNNNNN
+    \tex_expandafter:D \use_i:nn \tex_expandafter:D
+      \fp_extended_normalise_ii_aux:NNNNNNNNN
       \int_use:N \l_fp_input_a_decimal_int
-     \exp_after:wN \fp_trig_normalise_aux_ii:
+     \tex_expandafter:D \fp_extended_normalise_aux_ii:
    \tex_fi:D
 }
 \cs_new_protected_nopar:Npn
-  \fp_trig_normalise_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+  \fp_extended_normalise_ii_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
   \tex_ifnum:D \l_fp_input_a_integer_int = \c_zero
     \l_fp_input_a_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
   \tex_else:D
@@ -1532,7 +1597,64 @@
   \l_fp_input_a_extended_int \l_fp_tmp_tl \scan_stop:
   \tex_advance:D \l_fp_input_a_exponent_int \c_one
 }
-\cs_new_protected_nopar:Npn \fp_trig_normalise_aux_iii: {
+\cs_new_protected_nopar:Npn \fp_extended_normalise_output: {
+  \tex_ifnum:D \l_fp_output_integer_int > \c_nine
+    \tex_advance:D \l_fp_output_integer_int \c_one_thousand_million
+    \tex_expandafter:D \use_i:nn \tex_expandafter:D
+      \fp_extended_normalise_output_aux_i:NNNNNNNNN
+      \int_use:N \l_fp_output_integer_int
+    \tex_expandafter:D \fp_extended_normalise_output:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn
+  \fp_extended_normalise_output_aux_i:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+  \l_fp_output_integer_int #1#2#3#4#5#6#7#8 \scan_stop:
+  \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+  \tl_set:Nx \l_fp_tmp_tl
+    {
+      #9
+      \tex_expandafter:D \use_none:n
+      \int_use:N \l_fp_output_decimal_int
+    }
+  \tex_expandafter:D \fp_extended_normalise_output_aux_ii:NNNNNNNNN
+    \l_fp_tmp_tl
+}
+\cs_new_protected_nopar:Npn
+  \fp_extended_normalise_output_aux_ii:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+  \l_fp_output_decimal_int #1#2#3#4#5#6#7#8#9 \scan_stop:
+  \fp_extended_normalise_output_aux:N
+}
+\cs_new_protected_nopar:Npn \fp_extended_normalise_output_aux:N #1 {
+  \tex_advance:D \l_fp_output_extended_int \c_one_thousand_million
+  \tex_divide:D \l_fp_output_extended_int \c_ten
+  \tl_set:Nx \l_fp_tmp_tl
+    {
+      #1
+      \tex_expandafter:D \use_none:n
+        \int_use:N \l_fp_output_extended_int
+    }
+  \l_fp_output_extended_int \l_fp_tmp_tl \scan_stop:
+  \tex_advance:D \l_fp_output_exponent_int \c_one
+}
+\cs_new_protected_nopar:Npn \fp_trig_normalise: {
+  \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
+    \l_fp_input_a_extended_int \c_zero
+    \fp_extended_normalise:
+    \fp_trig_normalise_aux:
+    \tex_ifnum:D \l_fp_input_a_integer_int < \c_zero
+      \l_fp_input_a_sign_int -\l_fp_input_a_sign_int
+      \l_fp_input_a_integer_int -\l_fp_input_a_integer_int
+    \tex_fi:D
+     \tex_expandafter:D \fp_trig_octant:
+  \tex_else:D
+    \l_fp_input_a_sign_int    \c_one
+    \l_fp_output_integer_int  \c_zero
+    \l_fp_output_decimal_int  \c_zero
+    \l_fp_output_exponent_int \c_zero
+    \tex_expandafter:D \fp_trig_overflow_msg:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_trig_normalise_aux: {
   \tex_ifnum:D \l_fp_input_a_integer_int > \c_three
     \fp_sub:NNNNNNNNN
       \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
@@ -1540,7 +1662,7 @@
       \c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int
       \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
         \l_fp_input_a_extended_int
-    \exp_after:wN \fp_trig_normalise_aux_iii:
+    \tex_expandafter:D \fp_trig_normalise_aux:
   \tex_else:D
     \tex_ifnum:D \l_fp_input_a_integer_int > \c_two
       \tex_ifnum:D \l_fp_input_a_decimal_int > \c_fp_pi_decimal_int
@@ -1550,9 +1672,9 @@
           \c_six \c_fp_two_pi_decimal_int \c_fp_two_pi_extended_int
           \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
             \l_fp_input_a_extended_int
-        \exp_after:wN \exp_after:wN \exp_after:wN
-        \exp_after:wN \exp_after:wN \exp_after:wN
-          \exp_after:wN \fp_trig_normalise_aux_iii:
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \fp_trig_normalise_aux:
         \tex_fi:D
     \tex_fi:D
   \tex_fi:D
@@ -1583,7 +1705,7 @@
       \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
         \l_fp_input_a_extended_int
     \tex_advance:D \l_fp_trig_octant_int \c_one
-    \exp_after:wN \fp_trig_octant_aux:
+    \tex_expandafter:D \fp_trig_octant_aux:
   \tex_else:D
     \tex_ifnum:D
       \l_fp_input_a_decimal_int > \c_fp_pi_by_four_decimal_int
@@ -1595,7 +1717,7 @@
         \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
           \l_fp_input_a_extended_int
       \tex_advance:D \l_fp_trig_octant_int \c_one
-      \exp_after:wN \exp_after:wN \exp_after:wN
+      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
         \fp_trig_octant_aux:
     \tex_fi:D
   \tex_fi:D
@@ -1616,7 +1738,7 @@
       \l_fp_input_a_integer_int
       \l_fp_input_a_decimal_int
       \l_fp_input_a_exponent_int
-    \tl_set:Nx \l_fp_trig_arg_tl
+    \tl_set:Nx \l_fp_arg_tl
       {
         \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
           -
@@ -1625,7 +1747,7 @@
         \tex_fi:D
         \int_use:N \l_fp_input_a_integer_int
         .
-        \exp_after:wN \use_none:n
+        \tex_expandafter:D \use_none:n
           \tex_number:D \etex_numexpr:D
             \l_fp_input_a_decimal_int + \c_one_thousand_million
         e
@@ -1635,21 +1757,21 @@
       \cs_set_protected_nopar:Npx \fp_tmp:w
       {
         \group_end:
-        #1 \exp_not:N #2 { \l_fp_trig_arg_tl }
+        #1 \exp_not:N #2 { \l_fp_arg_tl }
       }
     \tex_else:D
       \etex_ifcsname:D
-        c_fp_sin ( \l_fp_trig_arg_tl ) _tl
+        c_fp_sin ( \l_fp_arg_tl ) _fp
       \tex_endcsname:D
       \tex_else:D
-        \exp_after:wN \exp_after:wN \exp_after:wN
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
           \fp_sin_aux_i:
       \tex_fi:D
       \cs_set_protected_nopar:Npx \fp_tmp:w
         {
           \group_end:
           #1 \exp_not:N #2
-            { \use:c { c_fp_sin ( \l_fp_trig_arg_tl ) _tl } }
+            { \use:c { c_fp_sin ( \l_fp_arg_tl ) _fp } }
         }
     \tex_fi:D
   \fp_tmp:w
@@ -1669,8 +1791,8 @@
     \l_fp_output_integer_int
     \l_fp_output_decimal_int
     \l_fp_output_exponent_int
-  \tl_new:c { c_fp_sin ( \l_fp_trig_arg_tl ) _tl }
-  \tl_gset:cx { c_fp_sin ( \l_fp_trig_arg_tl ) _tl }
+  \tl_new:c { c_fp_sin ( \l_fp_arg_tl ) _fp }
+  \tl_gset:cx { c_fp_sin ( \l_fp_arg_tl ) _fp }
     {
       \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
         +
@@ -1679,7 +1801,7 @@
       \tex_fi:D
       \int_use:N \l_fp_output_integer_int
       .
-      \exp_after:wN \use_none:n
+      \tex_expandafter:D \use_none:n
         \tex_number:D \etex_numexpr:D
            \l_fp_output_decimal_int + \c_one_thousand_million
          \scan_stop:
@@ -1690,13 +1812,13 @@
 \cs_new_protected_nopar:Npn \fp_sin_aux_ii: {
   \tex_ifcase:D \l_fp_trig_octant_int
   \tex_or:D
-    \exp_after:wN \fp_trig_calc_sin:
+    \tex_expandafter:D \fp_trig_calc_sin:
   \tex_or:D
-    \exp_after:wN \fp_trig_calc_cos:
+    \tex_expandafter:D \fp_trig_calc_cos:
   \tex_or:D
-    \exp_after:wN \fp_trig_calc_cos:
+    \tex_expandafter:D \fp_trig_calc_cos:
   \tex_or:D
-    \exp_after:wN \fp_trig_calc_sin:
+    \tex_expandafter:D \fp_trig_calc_sin:
   \tex_fi:D
 }
 \cs_new_protected_nopar:Npn \fp_cos:Nn {
@@ -1715,7 +1837,7 @@
       \l_fp_input_a_integer_int
       \l_fp_input_a_decimal_int
       \l_fp_input_a_exponent_int
-    \tl_set:Nx \l_fp_trig_arg_tl
+    \tl_set:Nx \l_fp_arg_tl
       {
         \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
           -
@@ -1724,21 +1846,21 @@
         \tex_fi:D
         \int_use:N \l_fp_input_a_integer_int
         .
-      \exp_after:wN \use_none:n
+      \tex_expandafter:D \use_none:n
         \tex_number:D \etex_numexpr:D
            \l_fp_input_a_decimal_int + \c_one_thousand_million
         e
         \int_use:N \l_fp_input_a_exponent_int
       }
-    \etex_ifcsname:D c_fp_cos ( \l_fp_trig_arg_tl ) _tl \tex_endcsname:D
+    \etex_ifcsname:D c_fp_cos ( \l_fp_arg_tl ) _fp \tex_endcsname:D
     \tex_else:D
-      \exp_after:wN \fp_cos_aux_i:
+      \tex_expandafter:D \fp_cos_aux_i:
     \tex_fi:D
     \cs_set_protected_nopar:Npx \fp_tmp:w
       {
         \group_end:
         #1 \exp_not:N #2
-          { \use:c { c_fp_cos ( \l_fp_trig_arg_tl ) _tl } }
+          { \use:c { c_fp_cos ( \l_fp_arg_tl ) _fp } }
       }
   \fp_tmp:w
 }
@@ -1757,8 +1879,8 @@
     \l_fp_output_integer_int
     \l_fp_output_decimal_int
     \l_fp_output_exponent_int
-  \tl_new:c { c_fp_cos ( \l_fp_trig_arg_tl ) _tl }
-  \tl_gset:cx { c_fp_cos ( \l_fp_trig_arg_tl ) _tl }
+  \tl_new:c { c_fp_cos ( \l_fp_arg_tl ) _fp }
+  \tl_gset:cx { c_fp_cos ( \l_fp_arg_tl ) _fp }
     {
       \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
         +
@@ -1767,7 +1889,7 @@
       \tex_fi:D
       \int_use:N \l_fp_output_integer_int
       .
-      \exp_after:wN \use_none:n
+      \tex_expandafter:D \use_none:n
         \tex_number:D \etex_numexpr:D
            \l_fp_output_decimal_int + \c_one_thousand_million
          \scan_stop:
@@ -1778,13 +1900,13 @@
 \cs_new_protected_nopar:Npn \fp_cos_aux_ii: {
   \tex_ifcase:D \l_fp_trig_octant_int
   \tex_or:D
-    \exp_after:wN \fp_trig_calc_cos:
+    \tex_expandafter:D \fp_trig_calc_cos:
   \tex_or:D
-    \exp_after:wN \fp_trig_calc_sin:
+    \tex_expandafter:D \fp_trig_calc_sin:
   \tex_or:D
-    \exp_after:wN \fp_trig_calc_sin:
+    \tex_expandafter:D \fp_trig_calc_sin:
   \tex_or:D
-    \exp_after:wN \fp_trig_calc_cos:
+    \tex_expandafter:D \fp_trig_calc_cos:
   \tex_fi:D
   \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
     \tex_ifnum:D \l_fp_trig_octant_int > \c_two
@@ -1829,7 +1951,7 @@
     \tex_fi:D
     \tex_advance:D \l_fp_output_extended_int -\l_fp_trig_extended_int
     \tex_advance:D \l_fp_output_decimal_int -\l_fp_trig_decimal_int
-    \exp_after:wN \fp_trig_calc_aux:
+    \tex_expandafter:D \fp_trig_calc_Taylor:
   \tex_fi:D
 }
 \cs_new_protected_nopar:Npn \fp_trig_calc_sin: {
@@ -1843,10 +1965,10 @@
     \l_fp_trig_decimal_int \l_fp_input_a_decimal_int
     \l_fp_trig_extended_int \l_fp_input_a_extended_int
     \l_fp_count_int \c_two
-    \exp_after:wN \fp_trig_calc_aux:
+    \tex_expandafter:D \fp_trig_calc_Taylor:
   \tex_fi:D
 }
-\cs_new_protected_nopar:Npn \fp_trig_calc_aux: {
+\cs_new_protected_nopar:Npn \fp_trig_calc_Taylor: {
   \l_fp_trig_sign_int -\l_fp_trig_sign_int
   \fp_mul:NNNNNN
     \l_fp_trig_decimal_int \l_fp_trig_extended_int
@@ -1896,7 +2018,7 @@
         \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
       \tex_fi:D
     \tex_fi:D
-    \exp_after:wN \fp_trig_calc_aux:
+    \tex_expandafter:D \fp_trig_calc_Taylor:
   \tex_fi:D
 }
 \cs_new_protected_nopar:Npn \fp_tan:Nn {
@@ -1915,7 +2037,7 @@
       \l_fp_input_a_integer_int
       \l_fp_input_a_decimal_int
       \l_fp_input_a_exponent_int
-    \tl_set:Nx \l_fp_trig_arg_tl
+    \tl_set:Nx \l_fp_arg_tl
       {
         \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
           -
@@ -1924,7 +2046,7 @@
         \tex_fi:D
         \int_use:N \l_fp_input_a_integer_int
         .
-        \exp_after:wN \use_none:n
+        \tex_expandafter:D \use_none:n
           \tex_number:D \etex_numexpr:D
             \l_fp_input_a_decimal_int + \c_one_thousand_million
         e
@@ -1934,32 +2056,32 @@
       \cs_set_protected_nopar:Npx \fp_tmp:w
       {
         \group_end:
-        #1 \exp_not:N #2 { \l_fp_trig_arg_tl }
+        #1 \exp_not:N #2 { \l_fp_arg_tl }
       }
     \tex_else:D
       \etex_ifcsname:D
-        c_fp_tan ( \l_fp_trig_arg_tl ) _tl
+        c_fp_tan ( \l_fp_arg_tl ) _fp
       \tex_endcsname:D
       \tex_else:D
-        \exp_after:wN \exp_after:wN \exp_after:wN
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
           \fp_tan_aux_i:
       \tex_fi:D
       \cs_set_protected_nopar:Npx \fp_tmp:w
         {
           \group_end:
           #1 \exp_not:N #2
-            { \use:c { c_fp_tan ( \l_fp_trig_arg_tl ) _tl } }
+            { \use:c { c_fp_tan ( \l_fp_arg_tl ) _fp } }
         }
     \tex_fi:D
   \fp_tmp:w
 }
 \cs_new_protected_nopar:Npn \fp_tan_aux_i: {
   \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
-    \exp_after:wN \fp_tan_aux_ii:
+    \tex_expandafter:D \fp_tan_aux_ii:
   \tex_else:D
-    \cs_new_eq:cN { c_fp_tan ( \l_fp_trig_arg_tl ) _tl }
+    \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
       \c_zero_fp
-    \exp_after:wN \fp_trig_overflow_msg:
+    \tex_expandafter:D \fp_trig_overflow_msg:
   \tex_fi:D
 }
 \cs_new_protected_nopar:Npn \fp_tan_aux_ii: {
@@ -1967,14 +2089,14 @@
   \fp_cos_aux_ii:
   \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero
     \tex_ifnum:D \l_fp_input_a_integer_int = \c_zero
-      \cs_new_eq:cN { c_fp_tan ( \l_fp_trig_arg_tl ) _tl }
+      \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
         \c_undefined_fp
     \tex_else:D
-      \exp_after:wN \exp_after:wN \exp_after:wN
+      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
         \fp_tan_aux_iii:
     \tex_fi:D
   \tex_else:D
-    \exp_after:wN \fp_tan_aux_iii:
+    \tex_expandafter:D \fp_tan_aux_iii:
   \tex_fi:D
 }
 \cs_new_protected_nopar:Npn \fp_tan_aux_iii: {
@@ -1997,14 +2119,14 @@
     \l_fp_input_a_exponent_int
   \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero
     \tex_ifnum:D \l_fp_input_a_integer_int = \c_zero
-      \cs_new_eq:cN { c_fp_tan ( \l_fp_trig_arg_tl ) _tl }
+      \cs_new_eq:cN { c_fp_tan ( \l_fp_arg_tl ) _fp }
         \c_zero_fp
     \tex_else:D
-      \exp_after:wN \exp_after:wN \exp_after:wN
+      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
         \fp_tan_aux_iv:
     \tex_fi:D
   \tex_else:D
-    \exp_after:wN \fp_tan_aux_iv:
+    \tex_expandafter:D \fp_tan_aux_iv:
   \tex_fi:D
 }
  \cs_new_protected_nopar:Npn \fp_tan_aux_iv: {
@@ -2027,8 +2149,563 @@
     \l_fp_output_integer_int
     \l_fp_output_decimal_int
     \l_fp_output_exponent_int
-  \tl_new:c { c_fp_tan ( \l_fp_trig_arg_tl ) _tl }
-  \tl_gset:cx { c_fp_tan ( \l_fp_trig_arg_tl ) _tl }
+  \tl_new:c { c_fp_tan ( \l_fp_arg_tl ) _fp }
+  \tl_gset:cx { c_fp_tan ( \l_fp_arg_tl ) _fp }
+    {
+      \tex_ifnum:D \l_fp_output_sign_int > \c_zero
+        +
+      \tex_else:D
+        -
+      \tex_fi:D
+      \int_use:N \l_fp_output_integer_int
+      .
+      \tex_expandafter:D \use_none:n
+        \tex_number:D \etex_numexpr:D
+           \l_fp_output_decimal_int + \c_one_thousand_million
+         \scan_stop:
+      e
+      \int_use:N \l_fp_output_exponent_int
+    }
+}
+\tl_new:c { c_fp_exp_1_tl }
+\tl_set:cn { c_fp_exp_1_tl }
+  { { 2 } { 718281828 } { 459045235 } { 0 } }
+\tl_new:c { c_fp_exp_2_tl }
+\tl_set:cn { c_fp_exp_2_tl }
+  { { 7 } { 389056098 } { 930650227 } { 0 } }
+\tl_new:c { c_fp_exp_3_tl }
+\tl_set:cn { c_fp_exp_3_tl }
+  { { 2 } { 008553692 } { 318766774 } { 1 } }
+\tl_new:c { c_fp_exp_4_tl }
+\tl_set:cn { c_fp_exp_4_tl }
+  { { 5 } { 459815003 } { 314423908 } { 1 } }
+\tl_new:c { c_fp_exp_5_tl }
+\tl_set:cn { c_fp_exp_5_tl }
+  { { 1 } { 484131591 } { 025766034 } { 2 } }
+\tl_new:c { c_fp_exp_6_tl }
+\tl_set:cn { c_fp_exp_6_tl }
+  { { 4 } { 034287934 } { 927351226 } { 2 } }
+\tl_new:c { c_fp_exp_7_tl }
+\tl_set:cn { c_fp_exp_7_tl }
+  { { 1 } { 096633158 } { 428458599 } { 3 } }
+\tl_new:c { c_fp_exp_8_tl }
+\tl_set:cn { c_fp_exp_8_tl }
+  { { 2 } { 980957987 } { 041728275 } { 3 } }
+\tl_new:c { c_fp_exp_9_tl }
+\tl_set:cn { c_fp_exp_9_tl }
+  { { 8 } { 103083927 } { 575384008 } { 3 } }
+\tl_new:c { c_fp_exp_10_tl }
+\tl_set:cn { c_fp_exp_10_tl }
+  { { 2 } { 202646579 } { 480671652 } { 4 } }
+\tl_new:c { c_fp_exp_20_tl }
+\tl_set:cn { c_fp_exp_20_tl }
+  { { 4 } { 851651954 } { 097902280 } { 8 } }
+\tl_new:c { c_fp_exp_30_tl }
+\tl_set:cn { c_fp_exp_30_tl }
+  { { 1 } { 068647458 } { 152446215 } { 13 } }
+\tl_new:c { c_fp_exp_40_tl }
+\tl_set:cn { c_fp_exp_40_tl }
+  { { 2 } { 353852668 } { 370199854 } { 17 } }
+\tl_new:c { c_fp_exp_50_tl }
+\tl_set:cn { c_fp_exp_50_tl }
+  { { 5 } { 184705528 } { 587072464 } { 21 } }
+\tl_new:c { c_fp_exp_60_tl }
+\tl_set:cn { c_fp_exp_60_tl }
+  { { 1 } { 142007389 } { 815684284 } { 26 } }
+\tl_new:c { c_fp_exp_70_tl }
+\tl_set:cn { c_fp_exp_70_tl }
+  { { 2 } { 515438670 } { 919167006 } { 30 } }
+\tl_new:c { c_fp_exp_80_tl }
+\tl_set:cn { c_fp_exp_80_tl }
+  { { 5 } { 540622384 } { 393510053 } { 34 } }
+\tl_new:c { c_fp_exp_90_tl }
+\tl_set:cn { c_fp_exp_90_tl }
+  { { 1 } { 220403294 } { 317840802 } { 39 } }
+\tl_new:c { c_fp_exp_100_tl }
+\tl_set:cn { c_fp_exp_100_tl }
+  { { 2 } { 688117141 } { 816135448 } { 43 } }
+\tl_new:c { c_fp_exp_200_tl }
+\tl_set:cn { c_fp_exp_200_tl }
+  { { 7 } { 225973768 } { 125749258 } { 86 } }
+\tl_new:c { c_fp_exp_-1_tl }
+\tl_set:cn { c_fp_exp_-1_tl }
+  { { 3 } { 678794411 } { 71442322 } { -1 } }
+\tl_new:c { c_fp_exp_-2_tl }
+\tl_set:cn { c_fp_exp_-2_tl }
+  { { 1 } { 353352832 } { 366132692 } { -1 } }
+\tl_new:c { c_fp_exp_-3_tl }
+\tl_set:cn { c_fp_exp_-3_tl }
+  { { 4 } { 978706836 } { 786394298 } { -2 } }
+\tl_new:c { c_fp_exp_-4_tl }
+\tl_set:cn { c_fp_exp_-4_tl }
+  { { 1 } { 831563888 } { 873418029 } { -2 } }
+\tl_new:c { c_fp_exp_-5_tl }
+\tl_set:cn { c_fp_exp_-5_tl }
+  { { 6 } { 737946999 } { 085467097 } { -3 } }
+\tl_new:c { c_fp_exp_-6_tl }
+\tl_set:cn { c_fp_exp_-6_tl }
+  { { 2 } { 478752176 } { 666358423 } { -3 } }
+\tl_new:c { c_fp_exp_-7_tl }
+\tl_set:cn { c_fp_exp_-7_tl }
+  { { 9 } { 118819655 } { 545162080 } { -4 } }
+\tl_new:c { c_fp_exp_-8_tl }
+\tl_set:cn { c_fp_exp_-8_tl }
+  { { 3 } { 354626279 } { 025118388 } { -4 } }
+\tl_new:c { c_fp_exp_-9_tl }
+\tl_set:cn { c_fp_exp_-9_tl }
+  { { 1 } { 234098040 } { 866795495 } { -4 } }
+\tl_new:c { c_fp_exp_-10_tl }
+\tl_set:cn { c_fp_exp_-10_tl }
+  { { 4 } { 539992976 } { 248451536 } { -5 } }
+\tl_new:c { c_fp_exp_-20_tl }
+\tl_set:cn { c_fp_exp_-20_tl }
+  { { 2 } { 061153622 } { 438557828 } { -9 } }
+\tl_new:c { c_fp_exp_-30_tl }
+\tl_set:cn { c_fp_exp_-30_tl }
+  { { 9 } { 357622968 } { 840174605 } { -14 } }
+\tl_new:c { c_fp_exp_-40_tl }
+\tl_set:cn { c_fp_exp_-40_tl }
+  { { 4 } { 248354255 } { 291588995 } { -18 } }
+\tl_new:c { c_fp_exp_-50_tl }
+\tl_set:cn { c_fp_exp_-50_tl }
+  { { 1 } { 928749847 } { 963917783 } { -22 } }
+\tl_new:c { c_fp_exp_-60_tl }
+\tl_set:cn { c_fp_exp_-60_tl }
+  { { 8 } { 756510762 } { 696520338 } { -27 } }
+\tl_new:c { c_fp_exp_-70_tl }
+\tl_set:cn { c_fp_exp_-70_tl }
+  { { 3 } { 975449735 } { 908646808 } { -31 } }
+\tl_new:c { c_fp_exp_-80_tl }
+\tl_set:cn { c_fp_exp_-80_tl }
+  { { 1 } { 804851387 } { 845415172 } { -35 } }
+\tl_new:c { c_fp_exp_-90_tl }
+\tl_set:cn { c_fp_exp_-90_tl }
+  { { 8 } { 194012623 } { 990515430 } { -40 } }
+\tl_new:c { c_fp_exp_-100_tl }
+\tl_set:cn { c_fp_exp_-100_tl }
+  { { 3 } { 720075976 } { 020835963 } { -44 } }
+\tl_new:c { c_fp_exp_-200_tl }
+\tl_set:cn { c_fp_exp_-200_tl }
+  { { 1 } { 383896526 } { 736737530 } { -87 } }
+\cs_new_protected_nopar:Npn \fp_exp:Nn {
+  \fp_exp_aux:NNn \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gexp:Nn {
+  \fp_exp_aux:NNn \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_exp:Nn  { c }
+\cs_generate_variant:Nn \fp_gexp:Nn { c }
+\cs_new_protected_nopar:Npn \fp_exp_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_split:Nn a {#3}
+    \fp_standardise:NNNN
+      \l_fp_input_a_sign_int
+      \l_fp_input_a_integer_int
+      \l_fp_input_a_decimal_int
+      \l_fp_input_a_exponent_int
+    \l_fp_input_a_extended_int \c_zero
+    \tl_set:Nx \l_fp_arg_tl
+      {
+        \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
+          -
+        \tex_else:D
+          +
+        \tex_fi:D
+        \int_use:N \l_fp_input_a_integer_int
+        .
+        \tex_expandafter:D \use_none:n
+          \tex_number:D \etex_numexpr:D
+             \l_fp_input_a_decimal_int + \c_one_thousand_million
+        e
+        \int_use:N \l_fp_input_a_exponent_int
+      }
+    \etex_ifcsname:D c_fp_exp ( \l_fp_arg_tl ) _fp \tex_endcsname:D
+    \tex_else:D
+      \tex_expandafter:D \fp_exp_internal:
+    \tex_fi:D
+    \cs_set_protected_nopar:Npx \fp_tmp:w
+      {
+        \group_end:
+        #1 \exp_not:N #2
+          {
+            \etex_ifcsname:D c_fp_exp ( \l_fp_arg_tl ) _fp
+              \tex_endcsname:D
+              \use:c { c_fp_exp ( \l_fp_arg_tl ) _fp }
+            \tex_else:D
+              \c_zero_fp
+            \tex_fi:D
+          }
+      }
+  \fp_tmp:w
+}
+\cs_new_protected_nopar:Npn \fp_exp_internal: {
+  \tex_ifnum:D \l_fp_input_a_exponent_int < \c_three
+    \fp_extended_normalise:
+    \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+      \tex_ifnum:D \l_fp_input_a_integer_int < 230 \scan_stop:
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \fp_exp_aux:
+      \tex_else:D
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \fp_exp_overflow_msg:
+        \tex_fi:D
+    \tex_else:D
+      \tex_ifnum:D \l_fp_input_a_integer_int < 230 \scan_stop:
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D  \fp_exp_aux:
+      \tex_else:D
+        \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
+          { \c_zero_fp }
+      \tex_fi:D
+    \tex_fi:D
+  \tex_else:D
+    \tex_expandafter:D \fp_exp_overflow_msg:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_exp_aux: {
+  \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero
+    \tex_expandafter:D \fp_exp_integer:
+  \tex_else:D
+    \l_fp_output_integer_int  \c_one
+    \l_fp_output_decimal_int  \c_zero
+    \l_fp_output_extended_int \c_zero
+    \l_fp_output_exponent_int \c_zero
+    \tex_expandafter:D \fp_exp_decimal:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_exp_integer: {
+  \tex_ifnum:D \l_fp_input_a_integer_int < \c_one_hundred
+    \l_fp_exp_integer_int  \c_one
+    \l_fp_exp_decimal_int  \c_zero
+    \l_fp_exp_extended_int \c_zero
+    \l_fp_exp_exponent_int \c_zero
+    \tex_expandafter:D \fp_exp_integer_tens:
+  \tex_else:D
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_expandafter:D \use_i:nnn
+          \int_use:N \l_fp_input_a_integer_int
+      }
+    \l_fp_input_a_integer_int
+      \etex_numexpr:D
+        \l_fp_input_a_integer_int - \l_fp_tmp_tl 00
+      \scan_stop:
+    \tex_ifnum:D \l_fp_input_a_sign_int < \c_zero
+      \tex_ifnum:D \l_fp_output_integer_int > 200 \scan_stop:
+        \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
+          { \c_zero_fp }
+      \tex_else:D
+        \fp_exp_integer_const:n { - \l_fp_tmp_tl 00 }
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \fp_exp_integer_tens:
+      \tex_fi:D
+    \tex_else:D
+      \fp_exp_integer_const:n { \l_fp_tmp_tl 00 }
+      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+        \tex_expandafter:D \fp_exp_integer_tens:
+    \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_exp_integer_tens: {
+  \l_fp_output_integer_int  \l_fp_exp_integer_int
+  \l_fp_output_decimal_int  \l_fp_exp_decimal_int
+  \l_fp_output_extended_int \l_fp_exp_extended_int
+  \l_fp_output_exponent_int \l_fp_exp_exponent_int
+  \tex_ifnum:D \l_fp_input_a_integer_int > \c_nine
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_expandafter:D \use_i:nn
+          \int_use:N \l_fp_input_a_integer_int
+      }
+    \l_fp_input_a_integer_int
+      \etex_numexpr:D
+        \l_fp_input_a_integer_int - \l_fp_tmp_tl 0
+      \scan_stop:
+    \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+      \fp_exp_integer_const:n { \l_fp_tmp_tl 0 }
+    \tex_else:D
+      \fp_exp_integer_const:n { - \l_fp_tmp_tl 0 }
+    \tex_fi:D
+    \fp_mul:NNNNNNNNN
+      \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+      \l_fp_output_integer_int \l_fp_output_decimal_int
+        \l_fp_output_extended_int
+      \l_fp_output_integer_int \l_fp_output_decimal_int
+        \l_fp_output_extended_int
+    \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int
+    \fp_extended_normalise_output:
+  \tex_fi:D
+  \fp_exp_integer_units:
+}
+\cs_new_protected_nopar:Npn \fp_exp_integer_units: {
+  \tex_ifnum:D \l_fp_input_a_integer_int > \c_zero
+    \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+      \fp_exp_integer_const:n { \int_use:N \l_fp_input_a_integer_int }
+    \tex_else:D
+      \fp_exp_integer_const:n
+        { - \int_use:N \l_fp_input_a_integer_int }
+    \tex_fi:D
+    \fp_mul:NNNNNNNNN
+      \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+      \l_fp_output_integer_int \l_fp_output_decimal_int
+        \l_fp_output_extended_int
+      \l_fp_output_integer_int \l_fp_output_decimal_int
+        \l_fp_output_extended_int
+    \tex_advance:D \l_fp_output_exponent_int \l_fp_exp_exponent_int
+    \fp_extended_normalise_output:
+  \tex_fi:D
+  \fp_exp_decimal:
+}
+\cs_new_protected_nopar:Npn \fp_exp_integer_const:n #1 {
+  \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+    \fp_exp_integer_const:nnnn
+    \tex_csname:D c_fp_exp_ #1 _tl \tex_endcsname:D
+}
+\cs_new_protected_nopar:Npn \fp_exp_integer_const:nnnn #1#2#3#4 {
+  \l_fp_exp_integer_int  #1 \scan_stop:
+  \l_fp_exp_decimal_int  #2 \scan_stop:
+  \l_fp_exp_extended_int #3 \scan_stop:
+  \l_fp_exp_exponent_int #4 \scan_stop:
+}
+\cs_new_protected_nopar:Npn \fp_exp_decimal: {
+  \tex_ifnum:D \l_fp_input_a_decimal_int > \c_zero
+    \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+      \l_fp_exp_integer_int  \c_one
+      \l_fp_exp_decimal_int  \l_fp_input_a_decimal_int
+      \l_fp_exp_extended_int \l_fp_input_a_extended_int
+    \tex_else:D
+      \l_fp_exp_integer_int \c_zero
+      \tex_ifnum:D \l_fp_exp_extended_int = \c_zero
+        \l_fp_exp_decimal_int
+          \etex_numexpr:D
+            \c_one_thousand_million - \l_fp_input_a_decimal_int
+          \scan_stop:
+        \l_fp_exp_extended_int \c_zero
+      \tex_else:D
+        \l_fp_exp_decimal_int
+          \etex_numexpr:D
+            999999999 - \l_fp_input_a_decimal_int
+          \scan_stop:
+        \l_fp_exp_extended_int
+          \etex_numexpr:D
+            \c_one_thousand_million - \l_fp_input_a_extended_int
+          \scan_stop:
+      \tex_fi:D
+    \tex_fi:D
+    \l_fp_input_b_sign_int     \l_fp_input_a_sign_int
+    \l_fp_input_b_decimal_int  \l_fp_input_a_decimal_int
+    \l_fp_input_b_extended_int \l_fp_input_a_extended_int
+    \l_fp_count_int \c_one
+    \fp_exp_Taylor:
+    \fp_mul:NNNNNNNNN
+      \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+      \l_fp_output_integer_int \l_fp_output_decimal_int
+        \l_fp_output_extended_int
+      \l_fp_output_integer_int \l_fp_output_decimal_int
+        \l_fp_output_extended_int
+  \tex_fi:D
+  \tex_ifnum:D \l_fp_output_extended_int < \c_five_hundred_million
+  \tex_else:D
+    \tex_advance:D \l_fp_output_decimal_int \c_one
+    \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
+    \tex_else:D
+      \l_fp_output_decimal_int \c_zero
+      \tex_advance:D \l_fp_output_integer_int \c_one
+    \tex_fi:D
+  \tex_fi:D
+  \fp_standardise:NNNN
+    \l_fp_output_sign_int
+    \l_fp_output_integer_int
+    \l_fp_output_decimal_int
+    \l_fp_output_exponent_int
+  \fp_exp_const:cx { c_fp_exp ( \l_fp_arg_tl ) _fp }
+    {
+      +
+      \int_use:N \l_fp_output_integer_int
+      .
+      \tex_expandafter:D \use_none:n
+        \tex_number:D \etex_numexpr:D
+           \l_fp_output_decimal_int + \c_one_thousand_million
+         \scan_stop:
+      e
+      \int_use:N \l_fp_output_exponent_int
+    }
+}
+\cs_new_protected_nopar:Npn \fp_exp_Taylor: {
+  \tex_advance:D \l_fp_count_int \c_one
+  \tex_multiply:D \l_fp_input_b_sign_int \l_fp_input_a_sign_int
+  \fp_mul:NNNNNN
+    \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+    \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+    \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+  \fp_div_integer:NNNNN
+    \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+    \l_fp_count_int
+    \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+  \tex_ifnum:D
+    \etex_numexpr:D
+      \l_fp_input_b_decimal_int + \l_fp_input_b_extended_int
+      > \c_zero
+    \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero
+      \tex_advance:D \l_fp_exp_decimal_int \l_fp_input_b_decimal_int
+      \tex_advance:D \l_fp_exp_extended_int
+        \l_fp_input_b_extended_int
+      \tex_ifnum:D \l_fp_exp_extended_int < \c_one_thousand_million
+      \tex_else:D
+        \tex_advance:D \l_fp_exp_decimal_int \c_one
+        \tex_advance:D \l_fp_exp_extended_int
+          -\c_one_thousand_million
+      \tex_fi:D
+      \tex_ifnum:D \l_fp_exp_decimal_int < \c_one_thousand_million
+      \tex_else:D
+        \tex_advance:D \l_fp_exp_integer_int \c_one
+        \tex_advance:D \l_fp_exp_decimal_int
+          -\c_one_thousand_million
+      \tex_fi:D
+    \tex_else:D
+      \tex_advance:D \l_fp_exp_decimal_int -\l_fp_input_b_decimal_int
+      \tex_advance:D \l_fp_exp_extended_int
+        -\l_fp_input_a_extended_int
+      \tex_ifnum:D \l_fp_exp_extended_int < \c_zero
+        \tex_advance:D \l_fp_exp_decimal_int \c_minus_one
+        \tex_advance:D \l_fp_exp_extended_int \c_one_thousand_million
+      \tex_fi:D
+      \tex_ifnum:D \l_fp_exp_decimal_int < \c_zero
+        \tex_advance:D \l_fp_exp_integer_int \c_minus_one
+        \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million
+      \tex_fi:D
+    \tex_fi:D
+    \tex_expandafter:D \fp_exp_Taylor:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_exp_const:Nx #1#2 {
+  \tl_new:N #1
+  \tl_gset:Nx #1 {#2}
+}
+\cs_generate_variant:Nn \fp_exp_const:Nx { c }
+\tl_new:c { c_fp_ln_10_1_tl }
+\tl_set:cn { c_fp_ln_10_1_tl }
+  { { 2 } { 302585092 } { 994045684 } { 0 } }
+\tl_new:c { c_fp_ln_10_2_tl }
+\tl_set:cn { c_fp_ln_10_2_tl }
+  { { 4 } { 605170185 } { 988091368 } { 0 } }
+\tl_new:c { c_fp_ln_10_3_tl }
+\tl_set:cn { c_fp_ln_10_3_tl }
+  { { 6 } { 907755278 } { 982137052 } { 0 } }
+\tl_new:c { c_fp_ln_10_4_tl }
+\tl_set:cn { c_fp_ln_10_4_tl }
+  { { 9 } { 210340371 } { 976182736 } { 0 } }
+\tl_new:c { c_fp_ln_10_5_tl }
+\tl_set:cn { c_fp_ln_10_5_tl }
+  { { 1 } { 151292546 } { 497022842 } { 1 } }
+\tl_new:c { c_fp_ln_10_6_tl }
+\tl_set:cn { c_fp_ln_10_6_tl }
+  { { 1 } { 381551055 } { 796427410 } { 1 } }
+\tl_new:c { c_fp_ln_10_7_tl }
+\tl_set:cn { c_fp_ln_10_7_tl }
+  { { 1 } { 611809565 } { 095831979 } { 1 } }
+\tl_new:c { c_fp_ln_10_8_tl }
+\tl_set:cn { c_fp_ln_10_8_tl }
+  { { 1 } { 842068074 } { 395226547 } { 1 } }
+\tl_new:c { c_fp_ln_10_9_tl }
+\tl_set:cn { c_fp_ln_10_9_tl }
+  { { 2 } { 072326583 } { 694641116 } { 1 } }
+\tl_new:c { c_fp_ln_2_1_tl }
+\tl_set:cn { c_fp_ln_2_1_tl }
+  { { 0 } { 693147180 } { 559945309 } { 0 } }
+\tl_new:c { c_fp_ln_2_2_tl }
+\tl_set:cn { c_fp_ln_2_2_tl }
+  { { 1 } { 386294361 } { 119890618 } { 0 } }
+\tl_new:c { c_fp_ln_2_3_tl }
+\tl_set:cn { c_fp_ln_2_3_tl }
+  { { 2 } { 079441541 } { 679835928 } { 0 } }
+\cs_new_protected_nopar:Npn \fp_ln:Nn {
+  \fp_ln_aux:NNn \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gln:Nn {
+  \fp_ln_aux:NNn \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_ln:Nn  { c }
+\cs_generate_variant:Nn \fp_gln:Nn { c }
+\cs_new_protected_nopar:Npn \fp_ln_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_split:Nn a {#3}
+    \fp_standardise:NNNN
+      \l_fp_input_a_sign_int
+      \l_fp_input_a_integer_int
+      \l_fp_input_a_decimal_int
+      \l_fp_input_a_exponent_int
+    \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+      \tex_ifnum:D
+        \etex_numexpr:D
+          \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+          > \c_zero
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \fp_ln_aux:
+      \tex_else:D
+        \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+          {
+            \group_end:
+            ##1 \exp_not:N ##2 { \c_zero_fp }
+          }
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \fp_ln_error_msg:
+      \tex_fi:D
+    \tex_else:D
+      \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+        {
+          \group_end:
+          ##1 \exp_not:N ##2 { \c_zero_fp }
+        }
+      \tex_expandafter:D \fp_ln_error_msg:
+    \tex_fi:D
+  \fp_tmp:w #1 #2
+}
+\cs_new_protected_nopar:Npn \fp_ln_aux: {
+  \tl_set:Nx \l_fp_arg_tl
+    {
+      +
+      \int_use:N \l_fp_input_a_integer_int
+      .
+      \tex_expandafter:D \use_none:n
+        \tex_number:D \etex_numexpr:D
+           \l_fp_input_a_decimal_int + \c_one_thousand_million
+      e
+      \int_use:N \l_fp_input_a_exponent_int
+    }
+  \etex_ifcsname:D c_fp_ln ( \l_fp_arg_tl ) _fp \tex_endcsname:D
+  \tex_else:D
+    \tex_expandafter:D \fp_ln_exponent:
+  \tex_fi:D
+  \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+    {
+      \group_end:
+      ##1 \exp_not:N ##2
+        { \use:c { c_fp_ln ( \l_fp_arg_tl ) _fp } }
+    }
+}
+\cs_new_protected_nopar:Npn \fp_ln_exponent: {
+  \fp_ln_internal:
+  \tex_ifnum:D \l_fp_output_extended_int < \c_five_hundred_million
+  \tex_else:D
+    \tex_advance:D \l_fp_output_decimal_int \c_one
+    \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
+    \tex_else:D
+      \l_fp_output_decimal_int \c_zero
+      \tex_advance:D \l_fp_output_integer_int \c_one
+    \tex_fi:D
+  \tex_fi:D
+  \fp_standardise:NNNN
+    \l_fp_output_sign_int
+    \l_fp_output_integer_int
+    \l_fp_output_decimal_int
+    \l_fp_output_exponent_int
+  \tl_new:c { c_fp_ln ( \l_fp_arg_tl ) _fp }
+  \tl_gset:cx { c_fp_ln ( \l_fp_arg_tl ) _fp }
     {
       \tex_ifnum:D \l_fp_output_sign_int > \c_zero
         +
@@ -2037,7 +2714,7 @@
       \tex_fi:D
       \int_use:N \l_fp_output_integer_int
       .
-      \exp_after:wN \use_none:n
+      \tex_expandafter:D \use_none:n
         \tex_number:D \etex_numexpr:D
            \l_fp_output_decimal_int + \c_one_thousand_million
          \scan_stop:
@@ -2045,21 +2722,445 @@
       \int_use:N \l_fp_output_exponent_int
     }
 }
-\prg_new_conditional:Npnn \fp_if_undefined:N #1 { p , T , F , TF } {
+\cs_new_protected_nopar:Npn \fp_ln_internal: {
+  \tex_ifnum:D \l_fp_input_a_exponent_int < \c_zero
+    \l_fp_input_a_exponent_int -\l_fp_input_a_exponent_int
+    \l_fp_output_sign_int \c_minus_one
+  \tex_else:D
+    \l_fp_output_sign_int \c_one
+  \tex_fi:D
+  \tex_ifnum:D \l_fp_input_a_exponent_int > \c_nine
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \tex_expandafter:D \use_i:nn
+          \int_use:N \l_fp_input_a_exponent_int
+      }
+    \l_fp_input_a_exponent_int
+      \etex_numexpr:D
+        \l_fp_input_a_exponent_int - \l_fp_tmp_tl 0
+      \scan_stop:
+    \fp_ln_const:nn { 10 } { \l_fp_tmp_tl }
+    \tex_advance:D \l_fp_exp_exponent_int \c_one
+    \l_fp_output_integer_int  \l_fp_exp_integer_int
+    \l_fp_output_decimal_int  \l_fp_exp_decimal_int
+    \l_fp_output_extended_int \l_fp_exp_extended_int
+    \l_fp_output_exponent_int \l_fp_exp_exponent_int
+  \tex_else:D
+    \l_fp_output_integer_int  \c_zero
+    \l_fp_output_decimal_int  \c_zero
+    \l_fp_output_extended_int \c_zero
+    \l_fp_output_exponent_int \c_zero
+  \tex_fi:D
+  \fp_ln_exponent_units:
+}
+\cs_new_protected_nopar:Npn \fp_ln_exponent_units: {
+  \tex_ifnum:D \l_fp_input_a_exponent_int > \c_zero
+    \fp_ln_const:nn { 10 } { \int_use:N \l_fp_input_a_exponent_int }
+    \fp_ln_normalise:
+    \fp_add:NNNNNNNNN
+      \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+      \l_fp_output_integer_int \l_fp_output_decimal_int
+        \l_fp_output_extended_int
+      \l_fp_output_integer_int \l_fp_output_decimal_int
+        \l_fp_output_extended_int
+  \tex_fi:D
+  \fp_ln_mantissa:
+}
+\cs_new_protected_nopar:Npn \fp_ln_normalise: {
+  \tex_ifnum:D \l_fp_exp_exponent_int < \l_fp_output_exponent_int
+    \tex_advance:D \l_fp_exp_decimal_int \c_one_thousand_million
+    \tex_expandafter:D \use_i:nn \tex_expandafter:D
+      \fp_ln_normalise_aux:NNNNNNNNN
+      \int_use:N \l_fp_exp_decimal_int
+     \tex_expandafter:D \fp_ln_normalise:
+   \tex_fi:D
+}
+\cs_new_protected_nopar:Npn
+  \fp_ln_normalise_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+  \tex_ifnum:D \l_fp_exp_integer_int = \c_zero
+    \l_fp_exp_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
+  \tex_else:D
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \int_use:N \l_fp_exp_integer_int
+        #1#2#3#4#5#6#7#8
+      }
+    \l_fp_exp_integer_int \c_zero
+    \l_fp_exp_decimal_int \l_fp_tmp_tl \scan_stop:
+  \tex_fi:D
+  \tex_divide:D \l_fp_exp_extended_int \c_ten
+  \tl_set:Nx \l_fp_tmp_tl
+    {
+      #9
+      \int_use:N \l_fp_exp_extended_int
+    }
+  \l_fp_exp_extended_int \l_fp_tmp_tl \scan_stop:
+  \tex_advance:D \l_fp_exp_exponent_int \c_one
+}
+\cs_new_protected_nopar:Npn \fp_ln_mantissa: {
+  \l_fp_count_int \c_zero
+  \l_fp_input_a_extended_int \c_zero
+  \fp_ln_mantissa_aux:
+  \tex_ifnum:D \l_fp_count_int > \c_zero
+    \fp_ln_const:nn { 2 } { \int_use:N \l_fp_count_int }
+    \fp_ln_normalise:
+    \tex_ifnum:D \l_fp_output_sign_int > \c_zero
+      \tex_expandafter:D \fp_add:NNNNNNNNN
+    \tex_else:D
+      \tex_expandafter:D \fp_sub:NNNNNNNNN
+    \tex_fi:D
+    \l_fp_output_integer_int \l_fp_output_decimal_int
+      \l_fp_output_extended_int
+    \l_fp_exp_integer_int \l_fp_exp_decimal_int \l_fp_exp_extended_int
+    \l_fp_output_integer_int \l_fp_output_decimal_int
+      \l_fp_output_extended_int
+  \tex_fi:D
+  \tex_ifnum:D
+    \etex_numexpr:D
+      \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int > \c_one
+    \scan_stop:
+    \tex_expandafter:D \fp_ln_Taylor:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_ln_mantissa_aux: {
+  \tex_ifnum:D \l_fp_input_a_integer_int > \c_one
+    \tex_advance:D \l_fp_count_int \c_one
+    \fp_ln_mantissa_divide_two:
+    \tex_expandafter:D \fp_ln_mantissa_aux:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_ln_mantissa_divide_two: {
+  \tex_ifodd:D \l_fp_input_a_decimal_int
+    \tex_advance:D \l_fp_input_a_extended_int \c_one_thousand_million
+  \tex_fi:D
+  \tex_ifodd:D \l_fp_input_a_integer_int
+    \tex_advance:D \l_fp_input_a_decimal_int \c_one_thousand_million
+  \tex_fi:D
+  \tex_divide:D \l_fp_input_a_integer_int  \c_two
+  \tex_divide:D \l_fp_input_a_decimal_int  \c_two
+  \tex_divide:D \l_fp_input_a_extended_int \c_two
+}
+\cs_new_protected_nopar:Npn \fp_ln_const:nn #1#2 {
+  \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+    \fp_exp_integer_const:nnnn
+    \tex_csname:D c_fp_ln_ #1 _ #2 _tl \tex_endcsname:D
+}
+\cs_new_protected_nopar:Npn \fp_ln_Taylor: {
+  \group_begin:
+    \l_fp_input_a_integer_int \c_zero
+    \l_fp_input_a_exponent_int \c_zero
+    \l_fp_input_b_integer_int \c_two
+    \l_fp_input_b_decimal_int \l_fp_input_a_decimal_int
+    \l_fp_input_b_exponent_int \c_zero
+    \fp_div_internal:
+    \fp_ln_fixed:
+    \l_fp_input_a_integer_int  \l_fp_output_integer_int
+    \l_fp_input_a_decimal_int  \l_fp_output_decimal_int
+    \l_fp_input_a_exponent_int \l_fp_output_exponent_int
+    \l_fp_input_a_extended_int \c_zero
+    \l_fp_output_decimal_int \c_zero
+    \l_fp_output_decimal_int  \l_fp_input_a_decimal_int
+    \l_fp_output_extended_int \l_fp_input_a_extended_int
+    \fp_mul:NNNNNN
+      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+      \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+    \l_fp_count_int \c_one
+    \fp_ln_Taylor_aux:
+    \cs_set_protected_nopar:Npx \fp_tmp:w
+      {
+        \group_end:
+        \exp_not:N \l_fp_exp_decimal_int
+          \int_use:N \l_fp_output_decimal_int \scan_stop:
+        \exp_not:N \l_fp_exp_extended_int
+          \int_use:N \l_fp_output_extended_int \scan_stop:
+        \exp_not:N \l_fp_exp_exponent_int
+          \int_use:N \l_fp_output_exponent_int \scan_stop:
+      }
+  \fp_tmp:w
+  \tex_advance:D \l_fp_exp_decimal_int \l_fp_exp_decimal_int
+  \tex_ifnum:D \l_fp_exp_extended_int < \c_five_hundred_million
+  \tex_else:D
+    \tex_advance:D \l_fp_exp_extended_int -\c_five_hundred_million
+    \tex_advance:D \l_fp_exp_decimal_int \c_one
+  \tex_fi:D
+  \tex_advance:D \l_fp_exp_extended_int \l_fp_exp_extended_int
+  \tex_ifnum:D \l_fp_output_sign_int > \c_zero
+    \tex_expandafter:D \fp_add:NNNNNNNNN
+  \tex_else:D
+    \tex_expandafter:D \fp_sub:NNNNNNNNN
+  \tex_fi:D
+  \l_fp_output_integer_int \l_fp_output_decimal_int
+    \l_fp_output_extended_int
+  \c_zero \l_fp_exp_decimal_int \l_fp_exp_extended_int
+  \l_fp_output_integer_int \l_fp_output_decimal_int
+    \l_fp_output_extended_int
+}
+\cs_new_protected_nopar:Npn \fp_ln_fixed: {
+  \tex_ifnum:D \l_fp_output_exponent_int < \c_zero
+    \tex_advance:D \l_fp_output_decimal_int \c_one_thousand_million
+    \tex_expandafter:D \use_i:nn \tex_expandafter:D
+      \fp_ln_fixed_aux:NNNNNNNNN
+      \int_use:N \l_fp_output_decimal_int
+     \tex_expandafter:D \fp_ln_fixed:
+   \tex_fi:D
+}
+\cs_new_protected_nopar:Npn
+  \fp_ln_fixed_aux:NNNNNNNNN #1#2#3#4#5#6#7#8#9 {
+  \tex_ifnum:D \l_fp_output_integer_int = \c_zero
+    \l_fp_output_decimal_int #1#2#3#4#5#6#7#8 \scan_stop:
+  \tex_else:D
+    \tl_set:Nx \l_fp_tmp_tl
+      {
+        \int_use:N \l_fp_output_integer_int
+        #1#2#3#4#5#6#7#8
+      }
+    \l_fp_output_integer_int \c_zero
+    \l_fp_output_decimal_int \l_fp_tmp_tl \scan_stop:
+  \tex_fi:D
+  \tex_advance:D \l_fp_output_exponent_int \c_one
+}
+\cs_new_protected_nopar:Npn \fp_ln_Taylor_aux: {
+  \tex_advance:D \l_fp_count_int \c_two
+  \fp_mul:NNNNNN
+    \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+    \l_fp_input_b_decimal_int \l_fp_input_b_extended_int
+    \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+  \tex_ifnum:D
+    \etex_numexpr:D
+      \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
+      > \c_zero
+    \fp_div_integer:NNNNN
+      \l_fp_input_a_decimal_int \l_fp_input_a_extended_int
+      \l_fp_count_int
+      \l_fp_exp_decimal_int \l_fp_exp_extended_int
+      \tex_advance:D \l_fp_output_decimal_int \l_fp_exp_decimal_int
+      \tex_advance:D \l_fp_output_extended_int \l_fp_exp_extended_int
+      \tex_ifnum:D \l_fp_output_extended_int < \c_one_thousand_million
+      \tex_else:D
+        \tex_advance:D \l_fp_output_decimal_int \c_one
+        \tex_advance:D \l_fp_output_extended_int
+          -\c_one_thousand_million
+      \tex_fi:D
+      \tex_ifnum:D \l_fp_output_decimal_int < \c_one_thousand_million
+      \tex_else:D
+        \tex_advance:D \l_fp_output_integer_int \c_one
+        \tex_advance:D \l_fp_output_decimal_int
+          -\c_one_thousand_million
+      \tex_fi:D
+    \tex_expandafter:D \fp_ln_Taylor_aux:
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_pow:Nn {
+  \fp_pow_aux:NNn \tl_set:Nn
+}
+\cs_new_protected_nopar:Npn \fp_gpow:Nn {
+  \fp_pow_aux:NNn \tl_gset:Nn
+}
+\cs_generate_variant:Nn \fp_pow:Nn  { c }
+\cs_generate_variant:Nn \fp_gpow:Nn { c }
+\cs_new_protected_nopar:Npn \fp_pow_aux:NNn #1#2#3 {
+  \group_begin:
+    \fp_read:N #2
+    \l_fp_input_b_sign_int     \l_fp_input_a_sign_int
+    \l_fp_input_b_integer_int  \l_fp_input_a_integer_int
+    \l_fp_input_b_decimal_int  \l_fp_input_a_decimal_int
+    \l_fp_input_b_exponent_int \l_fp_input_a_exponent_int
+    \fp_split:Nn a {#3}
+    \fp_standardise:NNNN
+      \l_fp_input_a_sign_int
+      \l_fp_input_a_integer_int
+      \l_fp_input_a_decimal_int
+      \l_fp_input_a_exponent_int
+    \tex_ifnum:D
+      \etex_numexpr:D
+        \l_fp_input_b_integer_int + \l_fp_input_b_decimal_int
+        = \c_zero
+       \tex_ifnum:D
+         \etex_numexpr:D
+           \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+           = \c_zero
+           \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+             {
+               \group_end:
+               ##1 ##2 { \c_undefined_fp }
+             }
+         \tex_else:D
+           \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+             {
+               \group_end:
+               ##1 ##2 { \c_zero_fp }
+             }
+        \tex_fi:D
+     \tex_else:D
+       \tex_ifnum:D
+         \etex_numexpr:D
+           \l_fp_input_a_integer_int + \l_fp_input_a_decimal_int
+           = \c_zero
+           \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+             {
+               \group_end:
+               ##1 ##2 { \c_one_fp }
+             }
+         \tex_else:D
+           \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+             \fp_pow_aux_i:
+        \tex_fi:D
+     \tex_fi:D
+  \fp_tmp:w #1 #2
+}
+\cs_new_protected_nopar:Npn \fp_pow_aux_i: {
+  \tex_ifnum:D \l_fp_input_b_sign_int > \c_zero
+    \tl_set:Nn \l_fp_sign_tl { + }
+    \tex_expandafter:D \fp_pow_aux_ii:
+  \tex_else:D
+    \l_fp_input_a_extended_int \c_zero
+    \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
+      \group_begin:
+      \fp_extended_normalise:
+      \tex_ifnum:D
+        \etex_numexpr:D
+          \l_fp_input_a_decimal_int + \l_fp_input_a_extended_int
+          = \c_zero
+         \group_end:
+        \tl_set:Nn \l_fp_sign_tl { - }
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+        \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \fp_pow_aux_ii:
+      \tex_else:D
+        \group_end:
+        \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+          {
+            \group_end:
+            ##1 ##2 { \c_undefined_fp }
+         }
+      \tex_fi:D
+    \tex_else:D
+      \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+        {
+          \group_end:
+          ##1 ##2 { \c_undefined_fp }
+       }
+    \tex_fi:D
+  \tex_fi:D
+}
+\cs_new_protected_nopar:Npn \fp_pow_aux_ii: {
+  \tex_ifnum:D \l_fp_input_a_sign_int > \c_zero
+    \tex_expandafter:D \fp_pow_aux_iv:
+  \tex_else:D
+    \tex_ifnum:D \l_fp_input_a_exponent_int < \c_ten
+      \group_begin:
+      \l_fp_input_a_extended_int \c_zero
+      \fp_extended_normalise:
+      \tex_ifnum:D \l_fp_input_a_decimal_int = \c_zero
+        \tex_ifnum:D \l_fp_input_a_integer_int > \c_ten
+          \group_end:
+          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+            \fp_pow_aux_iv:
+        \tex_else:D
+          \group_end:
+          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+            \tex_expandafter:D \fp_pow_aux_iii:
+        \tex_fi:D
+      \tex_else:D
+        \group_end:
+          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+          \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+            \tex_expandafter:D \fp_pow_aux_iv:
+      \tex_fi:D
+    \tex_else:D
+      \tex_expandafter:D \tex_expandafter:D \tex_expandafter:D
+        \fp_pow_aux_iv:
+    \tex_fi:D
+  \tex_fi:D
+  \cs_set_protected_nopar:Npx \fp_tmp:w ##1##2
+    {
+      \group_end:
+      ##1 ##2
+        {
+          \l_fp_sign_tl
+          \int_use:N \l_fp_output_integer_int
+          .
+          \tex_expandafter:D \use_none:n
+            \tex_number:D \etex_numexpr:D
+               \l_fp_output_decimal_int + \c_one_thousand_million
+             \scan_stop:
+          e
+          \int_use:N \l_fp_output_exponent_int
+        }
+    }
+}
+\cs_new_protected_nopar:Npn \fp_pow_aux_iii: {
+  \l_fp_input_a_sign_int \c_one
+  \fp_pow_aux_iv:
+  \l_fp_input_a_integer_int  \c_one
+  \l_fp_input_a_decimal_int  \c_zero
+  \l_fp_input_a_exponent_int \c_zero
+  \l_fp_input_b_integer_int  \l_fp_output_integer_int
+  \l_fp_input_b_decimal_int  \l_fp_output_decimal_int
+  \l_fp_input_b_exponent_int \l_fp_output_exponent_int
+  \fp_div_internal:
+}
+\cs_new_protected_nopar:Npn \fp_pow_aux_iv: {
+  \group_begin:
+    \l_fp_input_a_integer_int  \l_fp_input_b_integer_int
+    \l_fp_input_a_decimal_int  \l_fp_input_b_decimal_int
+    \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int
+    \fp_ln_internal:
+    \cs_set_protected_nopar:Npx \fp_tmp:w
+      {
+        \group_end:
+        \exp_not:N \l_fp_input_b_sign_int
+          \int_use:N \l_fp_output_sign_int \scan_stop:
+        \exp_not:N \l_fp_input_b_integer_int
+          \int_use:N \l_fp_output_integer_int \scan_stop:
+        \exp_not:N \l_fp_input_b_decimal_int
+          \int_use:N \l_fp_output_decimal_int \scan_stop:
+        \exp_not:N \l_fp_input_b_extended_int
+          \int_use:N \l_fp_output_extended_int \scan_stop:
+        \exp_not:N \l_fp_input_b_exponent_int
+          \int_use:N \l_fp_output_exponent_int \scan_stop:
+      }
+  \fp_tmp:w
+  \l_fp_input_a_extended_int  \c_zero
+  \fp_mul:NNNNNNNNN
+    \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
+      \l_fp_input_a_extended_int
+    \l_fp_input_b_integer_int \l_fp_input_b_decimal_int
+      \l_fp_input_b_extended_int
+    \l_fp_input_a_integer_int \l_fp_input_a_decimal_int
+      \l_fp_input_a_extended_int
+  \tex_advance:D \l_fp_input_a_exponent_int \l_fp_input_b_exponent_int
+  \l_fp_output_integer_int  \c_zero
+  \l_fp_output_decimal_int  \c_zero
+  \l_fp_output_exponent_int \c_zero
+  \cs_set_eq:NN \fp_exp_const:Nx \use_none:nn
+  \fp_exp_internal:
+}
+\prg_new_conditional:Npnn \fp_if_undefined:N #1 { T , F , TF , p } {
   \tex_ifx:D #1 \c_undefined_fp
     \prg_return_true:
   \tex_else:D
     \prg_return_false:
   \tex_fi:D
 }
-\prg_new_conditional:Npnn \fp_if_zero:N #1 { p , T , F , TF } {
+\prg_new_conditional:Npnn \fp_if_zero:N #1 { T , F , TF , p } {
   \tex_ifx:D #1 \c_zero_fp
     \prg_return_true:
   \tex_else:D
     \prg_return_false:
   \tex_fi:D
 }
-\prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3 { T , F , TF }
+\prg_new_protected_conditional:Npnn \fp_compare:nNn #1#2#3
+  { T , F , TF }
   {
   \group_begin:
     \fp_split:Nn a {#1}
@@ -2076,7 +3177,8 @@
       \l_fp_input_b_exponent_int
     \fp_compare_aux:N #2
 }
-\prg_new_protected_conditional:Npnn \fp_compare:NNN #1#2#3 { T , F , TF }
+\prg_new_protected_conditional:Npnn \fp_compare:NNN #1#2#3
+  { T , F , TF }
   {
   \group_begin:
     \fp_read:N #3
@@ -2265,6 +3367,21 @@
 \cs_new_protected_nopar:Npn \fp_overflow_msg: {
   \msg_kernel_error:nn { fpu } { overflow }
 }
+\msg_kernel_new:nnnn { fpu } { exponent-overflow }
+  { Number~too~big~for~exponent~unit. }
+  {
+    The~exponent~of~the~input~given~is~too~big~for~the~floating~point~
+    unit:~the~maximum~input~value~for~an~exponent~is~230.
+  }
+\cs_new_protected_nopar:Npn \fp_exp_overflow_msg: {
+  \msg_kernel_error:nn { fpu } { exponent-overflow }
+}
+\msg_kernel_new:nnnn { fpu } { logarithm-input-error }
+  { Invalid~input~to~ln~function. }
+  { Logarithms~can~only~be~calculated~for~positive~numbers. }
+\cs_new_protected_nopar:Npn \fp_ln_error_msg: {
+  \msg_kernel_error:nn { fpu } { logarithm-input-error }
+}
 \msg_kernel_new:nnnn { fpu } { trigonometric-overflow }
   { Number~too~big~for~trigonometry~unit. }
   {
diff --git a/Master/texmf-dist/tex/latex/expl3/l3tl.sty b/Master/texmf-dist/tex/latex/expl3/l3tl.sty
index 14719daf74b..cd8125b8d1b 100644
--- a/Master/texmf-dist/tex/latex/expl3/l3tl.sty
+++ b/Master/texmf-dist/tex/latex/expl3/l3tl.sty
@@ -48,7 +48,7 @@
 %%
 %% -----------------------------------------------------------------------
 \RequirePackage{l3names}
-\GetIdInfo$Id: l3tl.dtx 2084 2010-11-17 19:12:14Z joseph $
+\GetIdInfo$Id: l3tl.dtx 2103 2010-12-18 07:40:03Z joseph $
           {L3 Experimental Token Lists}
 \ProvidesExplPackage
   {\filename}{\filedate}{\fileversion}{\filedescription}
@@ -235,7 +235,7 @@
     \tl_set:Nn \l_tl_tmpb_tl {#2}
     \tex_ifx:D \l_tl_tmpa_tl \l_tl_tmpb_tl
       \group_end:
-      \prg_return_false:
+      \prg_return_true:
     \tex_else:D
       \group_end:
       \prg_return_false: