diff --git a/src/drc/drc/built-in-macros/_drc_engine.rb b/src/drc/drc/built-in-macros/_drc_engine.rb
index bac80ca01..1f3caef99 100644
--- a/src/drc/drc/built-in-macros/_drc_engine.rb
+++ b/src/drc/drc/built-in-macros/_drc_engine.rb
@@ -212,15 +212,19 @@ module DRC
     end
     
     def tile_size(x, y = nil)
-      DRCTileSize::new(_make_numeric_value(x), _make_numeric_value(y || x))
+      DRCTileSize::new(_make_value(x) * self.dbu, _make_value(y || x) * self.dbu)
     end
     
     def tile_step(x, y = nil)
-      DRCTileStep::new(_make_numeric_value(x), _make_numeric_value(y || x))
+      DRCTileStep::new(_make_value(x) * self.dbu, _make_value(y || x) * self.dbu)
     end
     
     def tile_origin(x, y)
-      DRCTileOrigin::new(_make_numeric_value(x), _make_numeric_value(y))
+      DRCTileOrigin::new(_make_value(x) * self.dbu, _make_value(y) * self.dbu)
+    end
+    
+    def tile_count(x, y)
+      DRCTileCount::new(_make_numeric_value(x), _make_numeric_value(y))
     end
     
     def tile_boundary(b)
diff --git a/src/drc/drc/built-in-macros/_drc_layer.rb b/src/drc/drc/built-in-macros/_drc_layer.rb
index 4300a8b72..d66dfd0eb 100644
--- a/src/drc/drc/built-in-macros/_drc_layer.rb
+++ b/src/drc/drc/built-in-macros/_drc_layer.rb
@@ -983,8 +983,8 @@ CODE
     # @name corners
     # @brief Selects corners of polygons
     # @synopsis layer.corners([ options ])
-    # @synopsis layer.corners(angle, [ options ])
-    # @synopsis layer.corners(amin .. amax, [ options ])
+    # @synopsis layer.corners(angle [, options ])
+    # @synopsis layer.corners(amin .. amax [, options ])
     #
     # This method produces markers on the corners of the polygons. An angle criterion can be given which
     # selects corners based on the angle of the connecting edges. Positive angles indicate a left turn
@@ -3500,17 +3500,17 @@ CODE
     # %DRC%
     # @name with_density
     # @brief Returns tiles whose density is within a given range
-    # @synopsis layer.with_density(min_value, max_value, [options])
-    # @synopsis layer.with_density(min_value .. max_value, [options])
+    # @synopsis layer.with_density(min_value, max_value [, options ])
+    # @synopsis layer.with_density(min_value .. max_value [, options ])
     # 
-    # Runs a tiled analysis over the current layout. Reports the tiles whose density
+    # This method runs a tiled analysis over the current layout. It reports the tiles whose density
     # is between "min_value" and "max_value". "min_value" and "max_value" are given in
     # relative units, i.e. within the range of 0 to 1.0 corresponding to a density of 0 to 100%.
     #
     # "min_value" or "max_value" can be nil or omitted in the ".." range notation.
-    # In this case, they are taken as "0" or "100%".
+    # In this case, they are taken as "0" and "100%".
     #
-    # The tile size can be specified with the "tile_size" option:
+    # The tile size must be specified with the "tile_size" option:
     #
     # @code
     # # reports areas where layer 1/0 density is below 10% on 20x20 um tiles
@@ -3531,16 +3531,16 @@ CODE
     # low_density = input(1, 0).density(0.0 .. 0.1, tile_size(30.um), tile_step(20.um))
     # @/code
     #
-    # For "tile_step", anisotropic values can be given by using two values: the first for the
+    # For "tile_step", anisotropic values can be given as well by using two values: the first for the
     # horizontal and the second for the vertical tile step.
     #
     # Another option is "tile_origin" which specifies the location of the first tile's position. 
-    # This is the first tile's lower left corner. If no origin is given, the tiles are centered over the 
-    # area to cover.
+    # This is the lower left tile's lower left corner. If no origin is given, the tiles are centered over the 
+    # area investigated.
     #
     # By default, the tiles will cover the bounding box of the input layer. A separate layer
-    # can be used instead. This way, the layout's dimensions can be derived from some 
-    # drawn boundary layer. To specify a separate boundary layer, use the "tile_boundary" option:
+    # can be used in addition. This way, the layout's dimensions can be derived from some 
+    # drawn boundary layer. To specify a separate, additional layer included in the bounding box, use the "tile_boundary" option:
     #
     # @code
     # # reports density of layer 1/0 below 10% on 20x20 um tiles. The layout's boundary is taken from
@@ -3548,14 +3548,26 @@ CODE
     # cell_frame = input(0, 0)
     # low_density = input(1, 0).density(0.0 .. 0.1, tile_size(20.um), tile_boundary(cell_frame))
     # @/code
-    # 
-    # The complementary version of "with_density" is "without_density".
     #
+    # Note that the layer given in "tile_boundary" adds to the input layer for computing the bounding box.
+    # The computed area is at least the area of the input layer.
+    #
+    # Computation of the area can be skipped by explicitly giving a tile count in horizontal and vertical
+    # direction. With the "tile_origin" option this allows full control over the area covered:
+    #
+    # @code
+    # # reports density of layer 1/0 below 10% on 20x20 um tiles in the region 0,0 .. 2000,3000
+    # # (100 and 150 tiles of 20 um each are used in horizontal and vertical direction):
+    # low_density = input(1, 0).density(0.0 .. 0.1, tile_size(20.um), tile_origin(0.0, 0.0), tile_count(100, 150))
+    # @/code
+    # 
+    # The complementary version of "with_density" is \without_density.
     
+    # %DRC%
     # @name without_density
     # @brief Returns tiles whose density is not within a given range
-    # @synopsis layer.without_density(min_value, max_value, [options])
-    # @synopsis layer.without_density(min_value .. max_value, [options])
+    # @synopsis layer.without_density(min_value, max_value [, options ])
+    # @synopsis layer.without_density(min_value .. max_value [, options ])
     # 
     # For details about the operations and the operation see \with_density. This version will return the
     # tiles where the density is not within the given range.
@@ -3569,6 +3581,7 @@ CODE
       tile_size = nil
       tile_step = nil
       tile_origin = nil
+      tile_count = nil
       tile_boundary = nil
 
       n = 1
@@ -3579,6 +3592,8 @@ CODE
           tile_step = a.get
         elsif a.is_a?(DRCTileOrigin)
           tile_origin = a.get
+        elsif a.is_a?(DRCTileCount)
+          tile_count = a.get
         elsif a.is_a?(DRCTileBoundary)
           tile_boundary = a.get
         elsif a.is_a?(Float) || a.is_a?(1.class) || a == nil
@@ -3615,6 +3630,9 @@ CODE
       if tile_origin
         tp.tile_origin(*tile_origin)
       end
+      if tile_count
+        tp.tiles(*tile_count)
+      end
 
       res = RBA::Region.new      
       tp.output("res", res)
diff --git a/src/drc/drc/built-in-macros/_drc_tags.rb b/src/drc/drc/built-in-macros/_drc_tags.rb
index f87af0b6a..c6070cef1 100644
--- a/src/drc/drc/built-in-macros/_drc_tags.rb
+++ b/src/drc/drc/built-in-macros/_drc_tags.rb
@@ -211,6 +211,16 @@ module DRC
     end
   end
  
+  # A wrapper for the tile_count option
+  class DRCTileCount
+    def initialize(*args)
+      @xy = args
+    end
+    def get
+      @xy
+    end
+  end
+ 
   # A wrapper for the tile_boundary option
   class DRCTileBoundary
     def initialize(layer)
diff --git a/src/lay/lay/doc/about/drc_ref_drc.xml b/src/lay/lay/doc/about/drc_ref_drc.xml
index 16683f7cb..dc30e7fe4 100644
--- a/src/lay/lay/doc/about/drc_ref_drc.xml
+++ b/src/lay/lay/doc/about/drc_ref_drc.xml
@@ -72,6 +72,7 @@ The following global functions are relevant for the DRC expressions:
 <li><a href="/about/drc_ref_global.xml#space">space</a> </li>
 <li><a href="/about/drc_ref_global.xml#squares">squares</a> </li>
 <li><a href="/about/drc_ref_global.xml#width">width</a> </li>
+<li><a href="/about/drc_ref_global.xml#with_holes">with_holes</a> </li>
 </ul>
 </p><p>
 The following documentation will list the methods available for DRC expression objects.
@@ -921,6 +922,22 @@ out = in.drc(primary.squares)    # equivalent
 This method acts on edge expressions and delivers a specific part of each edge.
 See <a href="/about/drc_ref_layer.xml#start_segments">layer#start_segments</a> for details about this functionality.
 </p>
+<a name="with_holes"/><h2>"with_holes" - Selects all input polygons with the specified number of holes</h2>
+<keyword name="with_holes"/>
+<p>Usage:</p>
+<ul>
+<li><tt>expression.with_holes (in condition)</tt></li>
+</ul>
+<p>
+This operation can be used as a plain function in which case it acts on primary
+shapes or can be used as method on another DRC expression.
+The following example selects all polygons with more than 2 holes:
+</p><p>
+<pre>
+out = in.drc(with_holes &gt; 2)
+out = in.drc(primary.with_holes &gt; 2)   # equivalent
+</pre>
+</p>
 <a name="|"/><h2>"|" - Boolean OR between the results of two expressions</h2>
 <keyword name="|"/>
 <p>Usage:</p>
diff --git a/src/lay/lay/doc/about/drc_ref_global.xml b/src/lay/lay/doc/about/drc_ref_global.xml
index 6cff08384..bcfe6bc2f 100644
--- a/src/lay/lay/doc/about/drc_ref_global.xml
+++ b/src/lay/lay/doc/about/drc_ref_global.xml
@@ -1775,6 +1775,15 @@ In verbose mode, more output is generated in the log file
 <p>
 In verbose mode, more output is generated in the log file
 </p>
+<a name="warn"/><h2>"warn" - Prints a warning</h2>
+<keyword name="warn"/>
+<p>Usage:</p>
+<ul>
+<li><tt>warn(message)</tt></li>
+</ul>
+<p>
+Similar to <a href="#log">log</a>, but the message is printed formatted as a warning
+</p>
 <a name="width"/><h2>"width" - Performs a width check</h2>
 <keyword name="width"/>
 <p>Usage:</p>
@@ -1847,6 +1856,17 @@ shape.
 </tr>
 </table>
 </p>
+<a name="with_holes"/><h2>"with_holes" - Selects all input polygons according to their number of holes in DRC expressions</h2>
+<keyword name="with_holes"/>
+<p>Usage:</p>
+<ul>
+<li><tt>with_holes (in condition)</tt></li>
+</ul>
+<p>
+"with_holes" represents a polygon selector for
+<a href="/about/drc_ref_drc.xml">DRC</a> expressions selecting polygons of the primary by their number of holes
+(see <a href="/about/drc_ref_layer.xml#drc">Layer#drc</a> and <a href="/about/drc_ref_drc.xml#with_holes">DRC#with_holes</a> for more details).
+</p>
 <a name="write_spice"/><h2>"write_spice" - Defines SPICE output format (with options)</h2>
 <keyword name="write_spice"/>
 <p>Usage:</p>
diff --git a/src/lay/lay/doc/about/drc_ref_layer.xml b/src/lay/lay/doc/about/drc_ref_layer.xml
index f0964154e..702ec3f82 100644
--- a/src/lay/lay/doc/about/drc_ref_layer.xml
+++ b/src/lay/lay/doc/about/drc_ref_layer.xml
@@ -247,8 +247,8 @@ deliver objects that can be converted into polygons. Such objects are of class <
 <p>Usage:</p>
 <ul>
 <li><tt>layer.corners([ options ])</tt></li>
-<li><tt>layer.corners(angle, [ options ])</tt></li>
-<li><tt>layer.corners(amin .. amax, [ options ])</tt></li>
+<li><tt>layer.corners(angle [, options ])</tt></li>
+<li><tt>layer.corners(amin .. amax [, options ])</tt></li>
 </ul>
 <p>
 This method produces markers on the corners of the polygons. An angle criterion can be given which
@@ -3074,6 +3074,86 @@ bounding box.
 </p><p>
 This method is available for polygon layers only.
 </p>
+<a name="with_density"/><h2>"with_density" - Returns tiles whose density is within a given range</h2>
+<keyword name="with_density"/>
+<p>Usage:</p>
+<ul>
+<li><tt>layer.with_density(min_value, max_value [, options ])</tt></li>
+<li><tt>layer.with_density(min_value .. max_value [, options ])</tt></li>
+</ul>
+<p>
+This method runs a tiled analysis over the current layout. It reports the tiles whose density
+is between "min_value" and "max_value". "min_value" and "max_value" are given in
+relative units, i.e. within the range of 0 to 1.0 corresponding to a density of 0 to 100%.
+</p><p>
+"min_value" or "max_value" can be nil or omitted in the ".." range notation.
+In this case, they are taken as "0" and "100%".
+</p><p>
+The tile size must be specified with the "tile_size" option:
+</p><p>
+<pre>
+# reports areas where layer 1/0 density is below 10% on 20x20 um tiles
+low_density = input(1, 0).density(0.0 .. 0.1, tile_size(20.um))
+</pre>
+</p><p>
+Anisotropic tiles can be specified by giving two values, like "tile_size(10.um, 20.um)".
+The first value is the horizontal tile dimension, the second value is the vertical tile
+dimension.
+</p><p>
+A tile overlap can be specified using "tile_step". If the tile step is less than the
+tile size, the tiles will overlap. The layout window given by "tile_size" is moved
+in increments of the tile step:
+</p><p>
+<pre>
+# reports areas where layer 1/0 density is below 10% on 30x30 um tiles
+# with a tile step of 20x20 um:
+low_density = input(1, 0).density(0.0 .. 0.1, tile_size(30.um), tile_step(20.um))
+</pre>
+</p><p>
+For "tile_step", anisotropic values can be given as well by using two values: the first for the
+horizontal and the second for the vertical tile step.
+</p><p>
+Another option is "tile_origin" which specifies the location of the first tile's position. 
+This is the lower left tile's lower left corner. If no origin is given, the tiles are centered over the 
+area investigated.
+</p><p>
+By default, the tiles will cover the bounding box of the input layer. A separate layer
+can be used in addition. This way, the layout's dimensions can be derived from some 
+drawn boundary layer. To specify a separate, additional layer included in the bounding box, use the "tile_boundary" option:
+</p><p>
+<pre>
+# reports density of layer 1/0 below 10% on 20x20 um tiles. The layout's boundary is taken from
+# layer 0/0:
+cell_frame = input(0, 0)
+low_density = input(1, 0).density(0.0 .. 0.1, tile_size(20.um), tile_boundary(cell_frame))
+</pre>
+</p><p>
+Note that the layer given in "tile_boundary" adds to the input layer for computing the bounding box.
+The computed area is at least the area of the input layer.
+</p><p>
+Computation of the area can be skipped by explicitly giving a tile count in horizontal and vertical
+direction. With the "tile_origin" option this allows full control over the area covered:
+</p><p>
+<pre>
+# reports density of layer 1/0 below 10% on 20x20 um tiles in the region 0,0 .. 2000,3000
+# (100 and 150 tiles of 20 um each are used in horizontal and vertical direction):
+low_density = input(1, 0).density(0.0 .. 0.1, tile_size(20.um), tile_origin(0.0, 0.0), tile_count(100, 150))
+</pre>
+</p><p>
+The complementary version of "with_density" is <a href="#without_density">without_density</a>.
+</p>
+<a name="with_holes"/><h2>"with_holes" - Selects all polygons with the specified number of holes</h2>
+<keyword name="with_holes"/>
+<p>Usage:</p>
+<ul>
+<li><tt>layer.with_holes(count)</tt></li>
+<li><tt>layer.with_holes(min_count, max_count)</tt></li>
+<li><tt>layer.with_holes(min_count .. max_count)</tt></li>
+</ul>
+<p>
+This method is available for polygon layers. It will select all polygons from the input layer
+which have the specified number of holes.
+</p>
 <a name="with_length"/><h2>"with_length" - Selects edges by their length</h2>
 <keyword name="with_length"/>
 <p>Usage:</p>
@@ -3228,6 +3308,29 @@ bounding box.
 </p><p>
 This method is available for polygon layers only.
 </p>
+<a name="without_density"/><h2>"without_density" - Returns tiles whose density is not within a given range</h2>
+<keyword name="without_density"/>
+<p>Usage:</p>
+<ul>
+<li><tt>layer.without_density(min_value, max_value [, options ])</tt></li>
+<li><tt>layer.without_density(min_value .. max_value [, options ])</tt></li>
+</ul>
+<p>
+For details about the operations and the operation see <a href="#with_density">with_density</a>. This version will return the
+tiles where the density is not within the given range.
+</p>
+<a name="without_holes"/><h2>"without_holes" - Selects all polygons with the specified number of holes</h2>
+<keyword name="without_holes"/>
+<p>Usage:</p>
+<ul>
+<li><tt>layer.without_holes(count)</tt></li>
+<li><tt>layer.without_holes(min_count, max_count)</tt></li>
+<li><tt>layer.without_holes(min_count .. max_count)</tt></li>
+</ul>
+<p>
+This method is available for polygon layers. It will select all polygons from the input layer
+which do not have the specified number of holes.
+</p>
 <a name="without_length"/><h2>"without_length" - Selects edges by the their length</h2>
 <keyword name="without_length"/>
 <p>Usage:</p>
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diff --git a/src/lay/lay/doc/images/drc_shielded1.png b/src/lay/lay/doc/images/drc_shielded1.png
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diff --git a/src/lay/lay/doc/images/drc_shielded2.png b/src/lay/lay/doc/images/drc_shielded2.png
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diff --git a/src/lay/lay/doc/images/drc_shielded3.png b/src/lay/lay/doc/images/drc_shielded3.png
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diff --git a/src/lay/lay/doc/images/drc_sized1.png b/src/lay/lay/doc/images/drc_sized1.png
index 445a60538..daae1b5ec 100644
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diff --git a/src/lay/lay/doc/images/drc_sized3.png b/src/lay/lay/doc/images/drc_sized3.png
index 247bda8b2..63946cc16 100644
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diff --git a/src/lay/lay/doc/images/drc_sized4.png b/src/lay/lay/doc/images/drc_sized4.png
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diff --git a/src/lay/lay/doc/images/drc_sized5.png b/src/lay/lay/doc/images/drc_sized5.png
index 7caace4de..4426443b4 100644
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index 83677eef9..0849455da 100644
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diff --git a/src/lay/lay/doc/images/drc_space2.png b/src/lay/lay/doc/images/drc_space2.png
index 5b7b015c6..713378517 100644
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diff --git a/src/lay/lay/doc/images/drc_space3.png b/src/lay/lay/doc/images/drc_space3.png
index 9273739f0..a9ddcd213 100644
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diff --git a/src/lay/lay/doc/images/drc_space3u.png b/src/lay/lay/doc/images/drc_space3u.png
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diff --git a/src/lay/lay/doc/images/drc_start_segments1.png b/src/lay/lay/doc/images/drc_start_segments1.png
index 377a6ac57..bdd7c7051 100644
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diff --git a/src/lay/lay/doc/images/drc_start_segments2.png b/src/lay/lay/doc/images/drc_start_segments2.png
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diff --git a/src/lay/lay/doc/images/drc_textpoly1.png b/src/lay/lay/doc/images/drc_textpoly1.png
index 487cfcc9c..d43240264 100644
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diff --git a/src/lay/lay/doc/images/drc_textpoly2.png b/src/lay/lay/doc/images/drc_textpoly2.png
index e6eec02b4..ff84fb7b0 100644
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diff --git a/src/lay/lay/doc/images/drc_texts1.png b/src/lay/lay/doc/images/drc_texts1.png
index a3c5eabf2..44e30c5bb 100644
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diff --git a/src/lay/lay/doc/images/drc_texts2.png b/src/lay/lay/doc/images/drc_texts2.png
index 2e672d4ce..010c0abca 100644
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diff --git a/src/lay/lay/doc/images/drc_transformed1.png b/src/lay/lay/doc/images/drc_transformed1.png
index 1c8f240f0..3fbbc5af2 100644
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diff --git a/src/lay/lay/doc/images/drc_width1.png b/src/lay/lay/doc/images/drc_width1.png
index e603ea2ec..afc906e51 100644
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diff --git a/src/lay/lay/doc/images/drc_width1u.png b/src/lay/lay/doc/images/drc_width1u.png
index 0620c9f52..dfdc2267f 100644
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index adbd23e3e..e27d018ef 100644
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diff --git a/src/lay/lay/doc/images/drc_width2u.png b/src/lay/lay/doc/images/drc_width2u.png
index 72059ed49..da04841dd 100644
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diff --git a/src/lay/lay/doc/images/drc_width3.png b/src/lay/lay/doc/images/drc_width3.png
index b6e4f245d..47a5c108f 100644
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diff --git a/src/lay/lay/doc/images/drc_width3u.png b/src/lay/lay/doc/images/drc_width3u.png
index d8b9975fa..3766720b1 100644
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diff --git a/src/lay/lay/doc/images/drc_width4.png b/src/lay/lay/doc/images/drc_width4.png
index 10024dbfd..afef4849c 100644
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diff --git a/src/lay/lay/doc/images/drc_width4u.png b/src/lay/lay/doc/images/drc_width4u.png
index 481c252f2..6434c0e14 100644
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diff --git a/src/lay/lay/doc/images/drc_width5u.png b/src/lay/lay/doc/images/drc_width5u.png
index df054f8b5..9bcd5eadf 100644
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diff --git a/src/lay/lay/doc/images/drc_width6u.png b/src/lay/lay/doc/images/drc_width6u.png
index 5c25d49a4..664e44a3e 100644
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diff --git a/src/lay/lay/doc/images/drc_with_angle1.png b/src/lay/lay/doc/images/drc_with_angle1.png
index 77e234653..ec941dbbb 100644
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diff --git a/src/lay/lay/doc/images/drc_with_angle2.png b/src/lay/lay/doc/images/drc_with_angle2.png
index c122a281b..7deb564f0 100644
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diff --git a/src/lay/lay/doc/images/drc_with_angle3.png b/src/lay/lay/doc/images/drc_with_angle3.png
index 1e04a839b..98df2c5f8 100644
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diff --git a/src/lay/lay/doc/images/drc_with_angle4.png b/src/lay/lay/doc/images/drc_with_angle4.png
index 2fc74b3c7..605b45d14 100644
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diff --git a/src/lay/lay/doc/images/drc_xor1.png b/src/lay/lay/doc/images/drc_xor1.png
index d33f65b84..9e7b24970 100644
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diff --git a/src/lay/lay/doc/images/drc_xor2.png b/src/lay/lay/doc/images/drc_xor2.png
index ec9da5c2b..246364a18 100644
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diff --git a/testdata/drc/drcSimpleTests_30.drc b/testdata/drc/drcSimpleTests_30.drc
index ca278452d..de3b78fee 100644
--- a/testdata/drc/drcSimpleTests_30.drc
+++ b/testdata/drc/drcSimpleTests_30.drc
@@ -13,5 +13,6 @@ a.without_density(0..0.1, tile_size(10.um)).output(101, 0)
 a.with_density(0.1, nil, tile_size(10.um), tile_origin(25.um, 10.um)).output(102, 0)
 a.with_density(0.1, nil, tile_size(10.um, 20.um)).output(103, 0)
 a.with_density(0.1, 1.0, tile_size(10.um), tile_step(10.um, 20.um)).output(104, 0)
+a.with_density(0.1, nil, tile_size(10.um), tile_origin(25.um, 10.um), tile_count(10, 15)).output(105, 0)
 a.with_density(0..0.1, tile_size(100.um), tile_step(10.um)).output(110, 0)
 
diff --git a/testdata/drc/drcSimpleTests_au30.gds b/testdata/drc/drcSimpleTests_au30.gds
index 14b2f86b8..f09ab94b3 100644
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