master ce7a95711c0: Improve rounding of projection vector versors

[Po Lu]

branch: master
commit ce7a95711c0746eb7320ea18799b66599764c49a
Author: Po Lu <luangruo@yahoo.com>
Commit: Po Lu <luangruo@yahoo.com>

    Improve rounding of projection vector versors
    
    * src/sfnt.c (sfnt_short_frac_dot): New function.
    (sfnt_validate_gs): Guarantee dot product of freedom and
    projection vectors are properly rounded.  If the final product
    is short of 1/16th of a vector, reset it to an entire vector.
---
 src/sfnt.c | 26 +++++++++++++++++++++-----
 1 file changed, 21 insertions(+), 5 deletions(-)

diff --git a/src/sfnt.c b/src/sfnt.c
index ead41b89025..e66292c6ad8 100644
--- a/src/sfnt.c
+++ b/src/sfnt.c
@@ -10721,6 +10721,15 @@ sfnt_move (sfnt_f26dot6 *restrict x, sfnt_f26dot6 
*restrict y,
     }
 }
 
+/* Compute the dot product of the two versors A and B with
+   rounding.  */
+
+static sfnt_f2dot14
+sfnt_short_frac_dot (sfnt_f2dot14 a, sfnt_f2dot14 b)
+{
+  return (sfnt_f2dot14) ((((long) a * b) + 8192) / 16384);
+}
+
 /* Validate the graphics state GS.
    Establish function pointers for rounding and projection.
    Establish dot product used to convert vector distances between
@@ -10797,11 +10806,18 @@ sfnt_validate_gs (struct sfnt_graphics_state *gs)
     gs->vector_dot_product = gs->projection_vector.y;
   else
     /* Actually calculate the dot product.  */
-    gs->vector_dot_product = ((((long) gs->projection_vector.x
-                               * gs->freedom_vector.x)
-                              + ((long) gs->projection_vector.y
-                                 * gs->freedom_vector.y))
-                             / 16384);
+    gs->vector_dot_product = (sfnt_short_frac_dot (gs->projection_vector.x,
+                                                  gs->freedom_vector.x)
+                             + sfnt_short_frac_dot (gs->projection_vector.y,
+                                                    gs->freedom_vector.y));
+
+  /* If the product is less than 1/16th of a vector, prevent overflow
+     by resetting it to 1.  */
+
+  if (gs->vector_dot_product > -0x400
+      && gs->vector_dot_product < 0x400)
+    gs->vector_dot_product = (gs->vector_dot_product < 0
+                             ? -0x4000 : 0x4000);
 
   /* Now figure out which function to use to move distances.  Handle
      the common case where both the freedom and projection vectors are