diff --git a/src/Shader/SamplerCore.cpp b/src/Shader/SamplerCore.cpp
index d0e420a..4255f80 100644
--- a/src/Shader/SamplerCore.cpp
+++ b/src/Shader/SamplerCore.cpp
@@ -1415,6 +1415,15 @@
 		return lod;
 	}
 
+	Float SamplerCore::log2(Float lod)
+	{
+		lod *= lod;                                      // Squaring doubles the exponent and produces an extra bit of precision.
+		lod = Float(As<Int>(lod)) - Float(0x3F800000);   // Interpret as integer and subtract the exponent bias.
+		lod *= As<Float>(Int(0x33800000));               // Scale by 0.5 * 2^-23 (mantissa length).
+
+		return lod;
+	}
+
 	void SamplerCore::computeLod(Pointer<Byte> &texture, Float &lod, Float &anisotropy, Float4 &uDelta, Float4 &vDelta, Float4 &uuuu, Float4 &vvvv, const Float &lodBias, Vector4f &dsx, Vector4f &dsy, SamplerFunction function)
 	{
 		if(function != Lod && function != Fetch)
@@ -1433,7 +1442,7 @@
 				duvdxy = Float4(dudxy.xz, dvdxy.xz);
 			}
 
-			// Scale by texture dimensions and LOD
+			// Scale by texture dimensions and global LOD.
 			Float4 dUVdxy = duvdxy * *Pointer<Float4>(texture + OFFSET(Texture,widthHeightLOD));
 
 			Float4 dUV2dxy = dUVdxy * dUVdxy;
@@ -1498,9 +1507,9 @@
 				Float4 V = v * M;
 				Float4 W = w * M;
 
-				dudxy = U - U.xxxx;
-				dvdxy = V - V.xxxx;
-				dsdxy = W - W.xxxx;
+				dudxy = Abs(U - U.xxxx);
+				dvdxy = Abs(V - V.xxxx);
+				dsdxy = Abs(W - W.xxxx);
 			}
 			else
 			{
@@ -1508,26 +1517,25 @@
 				dvdxy = Float4(dsx.y.xx, dsy.y.xx);
 				dsdxy = Float4(dsx.z.xx, dsy.z.xx);
 
-				dudxy *= Float4(M.x);
-				dvdxy *= Float4(M.x);
-				dsdxy *= Float4(M.x);
+				dudxy = Abs(dudxy * Float4(M.x));
+				dvdxy = Abs(dvdxy * Float4(M.x));
+				dsdxy = Abs(dsdxy * Float4(M.x));
 			}
 
-			// Scale by texture dimensions and LOD
-			dudxy *= *Pointer<Float4>(texture + OFFSET(Texture,widthLOD));
-			dvdxy *= *Pointer<Float4>(texture + OFFSET(Texture,widthLOD));
-			dsdxy *= *Pointer<Float4>(texture + OFFSET(Texture,widthLOD));
+			// Compute the largest Manhattan distance in two dimensions.
+			// This takes the footprint across adjacent faces into account.
+			Float4 duvdxy = dudxy + dvdxy;
+			Float4 dusdxy = dudxy + dsdxy;
+			Float4 dvsdxy = dvdxy + dsdxy;
 
-			dudxy *= dudxy;
-			dvdxy *= dvdxy;
-			dsdxy *= dsdxy;
-
-			dudxy += dvdxy;
-			dudxy += dsdxy;
+			dudxy = Max(Max(duvdxy, dusdxy), dvsdxy);
 
 			lod = Max(Float(dudxy.y), Float(dudxy.z));   // FIXME: Max(dudxy.y, dudxy.z);
 
-			lod = log2sqrt(lod);   // log2(sqrt(lod))
+			// Scale by texture dimension and global LOD.
+			lod *= *Pointer<Float>(texture + OFFSET(Texture,widthLOD));
+
+			lod = log2(lod);
 
 			if(function == Bias)
 			{
@@ -1577,7 +1585,7 @@
 					dsdxy = Float4(dsx.z.xx, dsy.z.xx);
 				}
 
-				// Scale by texture dimensions and LOD
+				// Scale by texture dimensions and global LOD.
 				dudxy *= *Pointer<Float4>(texture + OFFSET(Texture,widthLOD));
 				dvdxy *= *Pointer<Float4>(texture + OFFSET(Texture,heightLOD));
 				dsdxy *= *Pointer<Float4>(texture + OFFSET(Texture,depthLOD));
diff --git a/src/Shader/SamplerCore.hpp b/src/Shader/SamplerCore.hpp
index c31f398..6004bd7 100644
--- a/src/Shader/SamplerCore.hpp
+++ b/src/Shader/SamplerCore.hpp
@@ -71,6 +71,7 @@
 		Vector4f sampleFloat2D(Pointer<Byte> &texture, Float4 &u, Float4 &v, Float4 &w, Float4 &q, Vector4f &offset, Float &lod, Int face[4], bool secondLOD, SamplerFunction function);
 		Vector4f sampleFloat3D(Pointer<Byte> &texture, Float4 &u, Float4 &v, Float4 &w, Vector4f &offset, Float &lod, bool secondLOD, SamplerFunction function);
 		Float log2sqrt(Float lod);
+		Float log2(Float lod);
 		void computeLod(Pointer<Byte> &texture, Float &lod, Float &anisotropy, Float4 &uDelta, Float4 &vDelta, Float4 &u, Float4 &v, const Float &lodBias, Vector4f &dsx, Vector4f &dsy, SamplerFunction function);
 		void computeLodCube(Pointer<Byte> &texture, Float &lod, Float4 &u, Float4 &v, Float4 &w, const Float &lodBias, Vector4f &dsx, Vector4f &dsy, Float4 &M, SamplerFunction function);
 		void computeLod3D(Pointer<Byte> &texture, Float &lod, Float4 &u, Float4 &v, Float4 &w, const Float &lodBias, Vector4f &dsx, Vector4f &dsy, SamplerFunction function);