l3kernel (14aug19)

git-svn-id: svn://tug.org/texlive/trunk@51881 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 71 insertions, 101 deletions

diff --git a/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx b/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx
index 963d61b7ae7..aca74650f23 100644
--- a/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx
+++ b/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx
@@ -43,7 +43,7 @@
 %    }^^A
 % }
 %
-% \date{Released 2019-07-25}
+% \date{Released 2019-08-14}
 %
 % \maketitle
 %
@@ -464,12 +464,12 @@
 %    \end{macrocode}
 % \end{variable}
 %
-% \begin{variable}{\l_@@_slope_x_fp}
-% \begin{variable}{\l_@@_slope_y_fp}
+% \begin{variable}{\l_@@_slope_A_fp}
+% \begin{variable}{\l_@@_slope_B_fp}
 %   Used for calculations of intersections.
 %    \begin{macrocode}
-\fp_new:N \l_@@_slope_x_fp
-\fp_new:N \l_@@_slope_y_fp
+\fp_new:N \l_@@_slope_A_fp
+\fp_new:N \l_@@_slope_B_fp
 %    \end{macrocode}
 % \end{variable}
 % \end{variable}
@@ -1123,7 +1123,7 @@
 %
 % \begin{macro}{\@@_calculate_intersection:Nnn}
 % \begin{macro}{\@@_calculate_intersection:nnnnnnnn}
-% \begin{macro}{\@@_calculate_intersection_aux:nnnnnN}
+% \begin{macro}{\@@_calculate_intersection:nnnnnn}
 %   The lead off in finding intersections is to recover the two poles
 %   and then hand off to the auxiliary for the actual calculation. There
 %   may of course not be an intersection, for which an error trap is
@@ -1159,7 +1159,7 @@
 \cs_new_protected:Npn \@@_calculate_intersection:nnnnnnnn
   #1#2#3#4#5#6#7#8
   {
-    \dim_compare:nNnTF {#3} = { \c_zero_dim }
+    \dim_compare:nNnTF {#3} = \c_zero_dim
 %    \end{macrocode}
 %   The case where the first pole is vertical.  So the $x$-component
 %   of the interaction is at $a$. There is then a test on the
@@ -1173,17 +1173,23 @@
 %   The second pole may still be horizontal, in which case the
 %   $y$-component of the intersection is $b'$. If not,
 %   \[
-%     y = \frac{d'}{c'} \left ( x - a' \right ) + b'
+%     y = \frac{d'}{c'} \left ( a - a' \right ) + b'
 %   \]
-%   with the $x$-component already known to be |#1|. This calculation
-%   is done as a generalised auxiliary.
+%   with the $x$-component already known to be |#1|.
 %    \begin{macrocode}
           {
-            \dim_compare:nNnTF {#8} = \c_zero_dim
-              { \dim_set:Nn \l_@@_y_dim {#6} }
+            \dim_set:Nn \l_@@_y_dim
               {
-                \@@_calculate_intersection_aux:nnnnnN
-                  {#1} {#5} {#6} {#7} {#8} \l_@@_y_dim
+                \dim_compare:nNnTF {#8} = \c_zero_dim
+                  {#6}
+                  {
+                    \fp_to_dim:n
+                      {
+                          ( \dim_to_fp:n {#8} / \dim_to_fp:n {#7} )
+                        * ( \dim_to_fp:n {#1} - \dim_to_fp:n {#5} )
+                        + \dim_to_fp:n {#6}
+                      }
+                  }
               }
           }
       }
@@ -1199,117 +1205,81 @@
             \dim_compare:nNnTF {#8} = { \c_zero_dim }
               { \bool_set_true:N \l_@@_error_bool }
               {
-                \dim_compare:nNnTF {#7} = \c_zero_dim
-                  { \dim_set:Nn \l_@@_x_dim {#5} }
 %    \end{macrocode}
-%   The formula for the case where the second pole is neither horizontal
-%   nor vertical is
+%   Now we deal with the case where the second pole may be vertical, or
+%   if not we have
 %   \[
-%     x = \frac{c'}{d'} \left ( y - b' \right ) + a'
+%     x = \frac{c'}{d'} \left ( b - b' \right ) + a'
 %   \]
 %   which is again handled by the same auxiliary.
 %    \begin{macrocode}
+                \dim_set:Nn \l_@@_x_dim
                   {
-                    \@@_calculate_intersection_aux:nnnnnN
-                      {#2} {#6} {#5} {#8} {#7} \l_@@_x_dim
+                    \dim_compare:nNnTF {#7} = \c_zero_dim
+                      {#5}
+                      {
+                        \fp_to_dim:n
+                          {
+                              ( \dim_to_fp:n {#7} / \dim_to_fp:n {#8} )
+                            * ( \dim_to_fp:n {#4} - \dim_to_fp:n {#6} )
+                             + \dim_to_fp:n {#5}
+                          }
+                      }
                   }
               }
           }
 %    \end{macrocode}
-%   The first pole is neither horizontal nor vertical. This still leaves
-%   the second pole, which may be a special case. For those possibilities,
-%   the calculations are the same as above with the first and second poles
-%   interchanged.
+%   The first pole is neither horizontal nor vertical. To avoid even
+%   more complexity, we now work out both slopes and pass to an auxiliary.
 %    \begin{macrocode}
           {
-            \dim_compare:nNnTF {#7} = \c_zero_dim
+            \use:x
               {
-                \dim_set:Nn \l_@@_x_dim {#5}
-                \@@_calculate_intersection_aux:nnnnnN
-                  {#5} {#1} {#2} {#3} {#4} \l_@@_y_dim
-              }
-              {
-                \dim_compare:nNnTF {#8} = \c_zero_dim
-                  {
-                    \dim_set:Nn \l_@@_y_dim {#6}
-                    \@@_calculate_intersection_aux:nnnnnN
-                      {#6} {#2} {#1} {#4} {#3} \l_@@_x_dim
-                  }
-%    \end{macrocode}
-%   If none of the special cases apply then there is still a need to
-%   check that there is a unique intersection between the two pole. This
-%   is the case if they have different slopes.
-%    \begin{macrocode}
-                  {
-                    \fp_set:Nn \l_@@_slope_x_fp
-                      { \dim_to_fp:n {#4} / \dim_to_fp:n {#3} }
-                    \fp_set:Nn \l_@@_slope_y_fp
-                      { \dim_to_fp:n {#8} / \dim_to_fp:n {#7} }
-                    \fp_compare:nNnTF
-                      \l_@@_slope_x_fp = \l_@@_slope_y_fp
-                      { \bool_set_true:N \l_@@_error_bool }
-%    \end{macrocode}
-%   All of the tests pass, so there is the full complexity of the
-%   calculation:
-%   \[
-%     x = \frac { a ( d / c ) - a' ( d' / c' ) - b + b' }
-%              { ( d / c ) - ( d' / c' ) }
-%   \]
-%   and noting that the two ratios are already worked out from the test
-%   just performed. There is quite a bit of shuffling from dimensions to
-%   floating points in order to do the work. The $y$-values is then
-%   worked out using the standard auxiliary starting from the
-%   $x$-position.
-%    \begin{macrocode}
-                      {
-                        \dim_set:Nn \l_@@_x_dim
-                          {
-                            \fp_to_dim:n
-                              {
-                                (
-                                      \dim_to_fp:n {#1} *
-                                        \l_@@_slope_x_fp
-                                  - ( \dim_to_fp:n {#5} *
-                                        \l_@@_slope_y_fp )
-                                  -   \dim_to_fp:n {#2}
-                                  +   \dim_to_fp:n {#6}
-                                )
-                                /
-                                (
-                                  \l_@@_slope_x_fp -
-                                  \l_@@_slope_y_fp
-                                )
-                            }
-                          }
-                        \@@_calculate_intersection_aux:nnnnnN
-                          { \l_@@_x_dim }
-                          {#5} {#6} {#8} {#7} \l_@@_y_dim
-                      }
-                  }
+                \@@_calculate_intersection:nnnnnn
+                  { \dim_to_fp:n {#4} / \dim_to_fp:n {#3} }
+                  { \dim_to_fp:n {#8} / \dim_to_fp:n {#7} }
               }
+                {#1} {#2} {#5} {#6}
           }
       }
   }
 %    \end{macrocode}
-%   The formula for finding the intersection point is in most cases the
-%   same. The formula here is
+%   Assuming the two poles are not parallel, then the intersection point is
+%   found in two steps. First we find the $x$-value with
 %   \[
-%     \#6 = \#4 \cdot \left( \frac { \#1 - \#2 } { \#5 } \right)\#3
+%     x = \frac { sa - s'a'  - b + b' }{ s - s' }
+%   \]
+%   and then finding the $y$-value with
+%   \[
+%     y = s ( x - a ) + b
 %   \]
-%   Thus |#4| and |#5| should be the directions of the pole while
-%   |#2| and |#3| are co-ordinates.
 %    \begin{macrocode}
-\cs_new_protected:Npn \@@_calculate_intersection_aux:nnnnnN
-    #1#2#3#4#5#6
+\cs_set_protected:Npn \@@_calculate_intersection:nnnnnn #1#2#3#4#5#6
   {
-    \dim_set:Nn #6
+    \fp_compare:nNnTF {#1} = {#2}
+      { \bool_set_true:N \l_@@_error_bool }
       {
-        \fp_to_dim:n
+        \dim_set:Nn \l_@@_x_dim
+          {
+            \fp_to_dim:n
+              {
+                (
+                    #1 * \dim_to_fp:n {#3}
+                  - #2 * \dim_to_fp:n {#5}
+                  - \dim_to_fp:n {#4}
+                  + \dim_to_fp:n {#6}
+                )
+                /
+                ( #1 - #2 )
+              }
+          }
+        \dim_set:Nn \l_@@_y_dim
           {
-            \dim_to_fp:n {#4} *
-            ( \dim_to_fp:n {#1} - \dim_to_fp:n {#2} ) /
-            \dim_to_fp:n {#5}
-            + \dim_to_fp:n {#3}
+            \fp_to_dim:n
+              {
+                  #1 * ( \l_@@_x_dim - \dim_to_fp:n {#3} )
+                + \dim_to_fp:n {#4}
+              }
           }
       }
   }