Merge branch 'house_placing' into jgrpp

# Conflicts:
#	src/settings_gui.cpp
#	src/settings_type.h
#	src/town_gui.cpp

src/core/math_func.hpp

@@ -346,6 +346,33 @@ static inline int RoundDivSU(int a, uint b)
 	}
 }
 
+/**
+ * Test if <tt> sqrt(a) <= sqrt(b) + sqrt(c) </tt>
+ *
+ * This function can tell you what's the relation between some of your values
+ * even thought you know only squares of them. Useful when comparing euclidean
+ * distances, it's easier to calculate them squared (#DistanceSquare) e.g.
+ * having a squared town radius R and squared distance D, to tell if the distance
+ * is further then N tiles beyond the town you may check if !SqrtCmp(D, R, N * N).
+ *
+ * @param a first value squared
+ * @param b second value squared
+ * @param c third value squared
+ * @return sqrt(a) <= sqrt(b) + sqrt(c)
+ *
+ * @pre 4 * b * c <= UINT32_MAX
+ */
+inline bool SqrtCmp(uint32 a, uint32 b, uint32 c)
+{
+	assert(c == 0 || b <= UINT32_MAX / 4 / c);
+
+	/* we can square the inequality twice to get rid of square roots
+	 * but some edge case must be checked first */
+	if (a <= b + c) return true;
+	uint32 d = a - (b + c);
+	return d <= UINT16_MAX && d * d <= 4 * b * c;
+}
+
 uint32 IntSqrt(uint32 num);
 
 #endif /* MATH_FUNC_HPP */