diff --git a/GPU/Math3D.h b/GPU/Math3D.h
index dd1991f917..a87cce8318 100644
--- a/GPU/Math3D.h
+++ b/GPU/Math3D.h
@@ -228,11 +228,11 @@ public:
 
 	Vec3() {}
 	Vec3(const T a[3]) : x(a[0]), y(a[1]), z(a[2]) {}
-	Vec3(const T& _x, const T& _y, const T& _z) : x(_x), y(_y), z(_z) {}
+	constexpr Vec3(const T& _x, const T& _y, const T& _z) : x(_x), y(_y), z(_z) {}
 	Vec3(const Vec2<T>& _xy, const T& _z) : x(_xy.x), y(_xy.y), z(_z) {}
 #if defined(_M_SSE)
-	Vec3(const __m128 &_vec) : vec(_vec) {}
-	Vec3(const __m128i &_ivec) : ivec(_ivec) {}
+	constexpr Vec3(const __m128 &_vec) : vec(_vec) {}
+	constexpr Vec3(const __m128i &_ivec) : ivec(_ivec) {}
 	Vec3(const Vec3Packed<T> &_xyz) {
 		vec = _mm_loadu_ps(_xyz.AsArray());
 	}
@@ -249,7 +249,7 @@ public:
 #endif
 
 	template<typename T2>
-	Vec3<T2> Cast() const
+	constexpr Vec3<T2> Cast() const
 	{
 		return Vec3<T2>((T2)x, (T2)y, (T2)z);
 	}
@@ -258,7 +258,7 @@ public:
 	static Vec3 FromRGB(unsigned int rgb);
 	unsigned int ToRGB() const; // alpha bits set to zero
 
-	static Vec3 AssignToAll(const T& f)
+	static constexpr Vec3 AssignToAll(const T& f)
 	{
 		return Vec3<T>(f, f, f);
 	}
diff --git a/GPU/Software/DrawPixel.cpp b/GPU/Software/DrawPixel.cpp
index ab244aacf8..2194c69e55 100644
--- a/GPU/Software/DrawPixel.cpp
+++ b/GPU/Software/DrawPixel.cpp
@@ -415,7 +415,9 @@ void SOFTRAST_CALL DrawSinglePixel(int x, int y, int z, int fog, Vec4IntArg colo
 	// Fog is applied prior to color test.
 	if (pixelID.applyFog && !clearMode) {
 		Vec3<int> fogColor = Vec3<int>::FromRGB(pixelID.cached.fogColor);
-		fogColor = (prim_color.rgb() * fog + fogColor * (255 - fog)) / 255;
+		// This is very similar to the BLEND texfunc, and simply always rounds up.
+		static constexpr Vec3<int> roundup = Vec3<int>::AssignToAll(255);
+		fogColor = (prim_color.rgb() * fog + fogColor * (255 - fog) + roundup) / 256;
 		prim_color.r() = fogColor.r();
 		prim_color.g() = fogColor.g();
 		prim_color.b() = fogColor.b();
diff --git a/GPU/Software/Rasterizer.cpp b/GPU/Software/Rasterizer.cpp
index ed8848ce80..0348f6d57a 100644
--- a/GPU/Software/Rasterizer.cpp
+++ b/GPU/Software/Rasterizer.cpp
@@ -348,7 +348,7 @@ Vec3<int> AlphaBlendingResult(const PixelFuncID &pixelID, const Vec4<int> &sourc
 
 		return Vec3<int>(_mm_unpacklo_epi16(_mm_adds_epi16(s, d), _mm_setzero_si128()));
 #else
-		Vec3<int> half = Vec3<int>::AssignToAll(1);
+		static constexpr Vec3<int> half = Vec3<int>::AssignToAll(1);
 		Vec3<int> lhs = ((source.rgb() * 2 + half) * (srcfactor * 2 + half)) / 1024;
 		Vec3<int> rhs = ((dst.rgb() * 2 + half) * (dstfactor * 2 + half)) / 1024;
 		return lhs + rhs;
@@ -370,7 +370,7 @@ Vec3<int> AlphaBlendingResult(const PixelFuncID &pixelID, const Vec4<int> &sourc
 
 		return Vec3<int>(_mm_unpacklo_epi16(_mm_max_epi16(_mm_subs_epi16(s, d), _mm_setzero_si128()), _mm_setzero_si128()));
 #else
-		Vec3<int> half = Vec3<int>::AssignToAll(1);
+		static constexpr Vec3<int> half = Vec3<int>::AssignToAll(1);
 		Vec3<int> lhs = ((source.rgb() * 2 + half) * (srcfactor * 2 + half)) / 1024;
 		Vec3<int> rhs = ((dst.rgb() * 2 + half) * (dstfactor * 2 + half)) / 1024;
 		return lhs - rhs;
@@ -392,7 +392,7 @@ Vec3<int> AlphaBlendingResult(const PixelFuncID &pixelID, const Vec4<int> &sourc
 
 		return Vec3<int>(_mm_unpacklo_epi16(_mm_max_epi16(_mm_subs_epi16(d, s), _mm_setzero_si128()), _mm_setzero_si128()));
 #else
-		Vec3<int> half = Vec3<int>::AssignToAll(1);
+		static constexpr Vec3<int> half = Vec3<int>::AssignToAll(1);
 		Vec3<int> lhs = ((source.rgb() * 2 + half) * (srcfactor * 2 + half)) / 1024;
 		Vec3<int> rhs = ((dst.rgb() * 2 + half) * (dstfactor * 2 + half)) / 1024;
 		return rhs - lhs;