Rope: Use integer sqrt algorithm for calculating distances

src/lib/C4Real.cpp

@@ -29,6 +29,16 @@
 
 #ifdef C4REAL_USE_FIXNUM
 
+C4Fixed Sqrt(C4Fixed x)
+{
+	assert(x.val >= 0);
+	assert(FIXED_SHIFT % 2 == 0);
+
+	C4Fixed ret;
+	ret.val = SqrtI(x.val) << (FIXED_SHIFT >> 1);
+	return ret;
+}
+
 // static table with sinus values from 0.00 degree to 90.00 degree inclusively
 long SineTable[9001] =
 {

src/lib/C4Real.h

@@ -71,6 +71,7 @@ class C4Fixed
 	friend C4Fixed itofix(int32_t x, int32_t prec);
 	friend float fixtof(const C4Fixed &x);
 	friend C4Fixed ftofix(float x);
+	friend C4Fixed Sqrt(C4Fixed x);
 #else
 	friend void FIXED_TO_FLOAT(float *pVal);
 #endif
@@ -296,6 +297,8 @@ inline C4Real C4REAL100(int x) { return itofix(x, 100); }
 inline C4Real C4REAL256(int x) { C4Fixed r; r.val = x * FIXED_FPF / 256; return r; }
 inline C4Real C4REAL10(int x) { return itofix(x, 10); }
 
+C4Fixed Sqrt(C4Fixed x);
+
 #else
 
 // *** wrap C4Real to float

src/lib/Standard.cpp

@@ -71,6 +71,28 @@ int Pow(int base, int exponent)
 	return result;
 }
 
+/* Fast(?) Integer square root */
+uint32_t SqrtI(uint32_t a)
+{
+	uint32_t rem = 0;
+	uint32_t root = 0;
+	for(unsigned int i = 0; i < (sizeof(a)*8)/2; i++)
+	{
+		root <<= 1;
+		rem = ((rem << 2) + (a >> (sizeof(a)*8 - 2)));
+		a <<= 2;
+		root ++;
+		if(root <= rem)
+		{
+			rem -= root;
+			root++;
+		}
+		else
+			root--;
+	}
+	return root >> 1;
+}
+
 bool ForLine(int32_t x1, int32_t y1, int32_t x2, int32_t y2,
              bool (*fnCallback)(int32_t, int32_t, int32_t), int32_t iPar,
              int32_t *lastx, int32_t *lasty)

src/lib/Standard.h

@@ -48,6 +48,7 @@ int32_t Distance(int32_t iX1, int32_t iY1, int32_t iX2, int32_t iY2);
 int Angle(int iX1, int iY1, int iX2, int iY2);
 int Pow(int base, int exponent);
 int32_t StrToI32(const char *s, int base, const char **scan_end);
+uint32_t SqrtI(uint32_t a);
 
 #include <cstring>
 inline void ZeroMem(void *lpMem, size_t dwSize)

src/object/C4Rope.cpp

@@ -36,17 +36,15 @@ namespace
 		float v;
 	};
 
-	// TODO: For all square roots, we must avoid floating point by using an
-	// integer-based Sqrt algorithm
-	// TODO: Could also use an approximation which works without Sqrt, especially
-	// if this becomes a performance bottleneck. http://www.azillionmonkeys.com/qed/sqroot.html
+	// TODO: If the sqrts become a performance bottleneck we could also use an
+	// approximation which works without Sqrt, cf. http://www.azillionmonkeys.com/qed/sqroot.html
 	C4Real Len(C4Real dx, C4Real dy)
 	{
 		// Prevent possible overflow
 		if(Abs(dx) > 120 || Abs(dy) > 120)
-			return ftofix(sqrt(fixtoi(dx)*fixtoi(dx) + fixtoi(dy)*fixtoi(dy)));
+			return itofix(SqrtI(fixtoi(dx)*fixtoi(dx) + fixtoi(dy)*fixtoi(dy)));// ftofix(sqrt(fixtoi(dx)*fixtoi(dx) + fixtoi(dy)*fixtoi(dy)));
 		else
-			return ftofix(sqrt(fixtof(dx*dx + dy*dy)));
+			return Sqrt(dx*dx + dy*dy);//ftofix(sqrt(fixtof(dx*dx + dy*dy)));
 	}
 
 	// For use in initializer list