diff --git a/src/newgdi/glyphruninfo.c b/src/newgdi/glyphruninfo.c
index 966d7d95..662cf7a8 100644
--- a/src/newgdi/glyphruninfo.c
+++ b/src/newgdi/glyphruninfo.c
@@ -80,6 +80,8 @@ GLYPHRUNINFO* GUIAPI CreateGlyphRunInfo(
     BidiBracketType local_brk_ts[LOCAL_ARRAY_SIZE];
     BidiBracketType *brk_ts = NULL;
 
+    BidiLevel level_or, level_and;
+
     ScriptType script_type = SCRIPT_COMMON;
 
     int i, j;
@@ -122,10 +124,15 @@ GLYPHRUNINFO* GUIAPI CreateGlyphRunInfo(
 
     // remove the bidi marks from embedding levels and original string.
     j = 0;
+    level_or = 0, level_and = 1;
     for (i = 0; i < nr_ucs; i++) {
         if (!BIDI_IS_EXPLICIT_OR_BN (bidi_ts[i])) {
             els[j] = els[i];
             ucs[j] = ucs[i];
+
+            level_or |= els[j];
+            level_and &= els[j];
+
             j++;
         }
     }
@@ -137,6 +144,12 @@ GLYPHRUNINFO* GUIAPI CreateGlyphRunInfo(
         goto out;
     }
 
+    // check for all even or odd
+    /* If none of the levels had the LSB set, all chars were even. */
+    runinfo->all_even = (level_or & 0x1) == 0;
+    /* If all of the levels had the LSB set, all chars were odd. */
+    runinfo->all_odd = (level_and & 0x1) == 1;
+
     runinfo->ucs = ucs;
     runinfo->nr_ucs = nr_ucs;
     runinfo->els = els;
diff --git a/src/newgdi/glyphruninfo.h b/src/newgdi/glyphruninfo.h
index de5ca153..042afc22 100644
--- a/src/newgdi/glyphruninfo.h
+++ b/src/newgdi/glyphruninfo.h
@@ -78,6 +78,8 @@ typedef enum {
     GR_DIRECTION_BTT
 } GlyphRunDir;
 
+// NOTE: we arrange the fields carefully to avoid wasting space when
+// we allocate an array of this structure.
 typedef struct _MAPL2G {
     // Glyph index in the run; Less than 0 if it is ignored.
     Sint32          glyph_index;
@@ -116,6 +118,10 @@ struct _GLYPHRUNINFO {
     int             nr_ucs;
     int             nr_runs;
     ParagraphDir    base_dir;
+
+    /* The following fields will be initialized by CreateGlyphRunInfo. */
+    Uint8           all_even;
+    Uint8           all_odd;
 };
 
 #ifdef __cplusplus