使用新的iFloat替代原先的ifloat_t

source/core/CMakeLists.txt

@@ -15,7 +15,7 @@ set(DV_CORE_MATH_INCLUDE_FILES
 	include/math/dvc_matrix3.h
 	include/math/dvc_matrix4.h
 	include/math/dvc_math_util.h
-	include/math/dvc_fixmath.h
+	include/math/dvc_fix_point.h
 )
 source_group("include/math" FILES ${DV_CORE_MATH_INCLUDE_FILES})
 
@@ -26,6 +26,7 @@ set(DV_CORE_MATH_SOURCE_FILES
 	source/math/dvc_matrix3.cpp
 	source/math/dvc_matrix4.cpp
 	source/math/dvc_math_util.cpp
+	source/math/dvc_fix_point.cpp
 )
 source_group("source/math" FILES ${DV_CORE_MATH_SOURCE_FILES})
 

source/core/include/math/dvc_fix_point.h

@@ -0,0 +1,456 @@
+#pragma once
+
+#include "dvc_config.h"
+
+DV_CORE_BEGIN_NAMESPACE
+
+class ifloat32
+{
+public:
+	static constexpr int32_t	kShift = 16;
+	static constexpr float32_t	kFloatScale = static_cast<float32_t>(1<<kShift);	//65536.0
+	static constexpr float32_t	kFloatInvScale = 1.f / kFloatScale;
+
+	static constexpr int32_t kZero_s1516 = 0;
+	static constexpr int32_t kOne_s1516 = 1 << kShift;
+	static constexpr int32_t kTwo_s1516 = 2 << kShift;
+	static constexpr int32_t kThree_s1516 = 3 << kShift;
+	static constexpr int32_t kFour_s1516 = 4 << kShift;
+	static constexpr int32_t kHalf_s1516 = kOne_s1516 >> 1;
+	static constexpr int32_t kPI_s1516 = 0x3243f;//(int32_t)(M_PI * kFloatScale);
+	static constexpr int32_t kPi2_s1516 = 0x6487e;
+	static constexpr int32_t kPiHalf_s1516 = 0x1921f;
+	static constexpr int32_t kE_s1516 = 0x2b7e1;
+
+	static constexpr int32_t kNegOne_s1516 = -1 << kShift;
+
+	static constexpr int32_t	kMax_s1516 = 0x7fffff80;	//(int32_t)(nextafter(INT32_MAX/kFloatScale, 0.f)*kFloatScale);
+	static constexpr int32_t	kMax_int32 = kMax_s1516 >> kShift;
+	static constexpr float32_t	kMax_float = (float32_t)kMax_s1516 * kFloatInvScale;
+
+	static constexpr int32_t	kMin_s1516 = 0x80000000;	// (int32_t)(nextafter(-INT32_MAX / ifloat32::kFloatScale, -FLT_MAX) * ifloat32::kFloatScale)
+	static constexpr int32_t	kMin_int32 = kMin_s1516 >> kShift;
+	static constexpr float32_t	kMin_float = (float32_t)kMin_s1516 * kFloatInvScale;
+
+public:
+	ifloat32() : s1516(0) {}
+	ifloat32(const ifloat32& other) : s1516(other.s1516) {}
+
+	//Converts a float to a fixed-point value.
+	ifloat32(float32_t f) {
+		s1516 = static_cast<int32_t>(f * kFloatScale);
+	}
+
+	//Converts a double to a fixed-point value.
+	ifloat32(float64_t f) {
+		s1516 = static_cast<int32_t>(f * kFloatScale);
+	}
+
+	//Converts an integer to a fixed-point value.
+	ifloat32(int32_t n) {
+		s1516 = static_cast<int32_t>(n << kShift);
+	}
+
+public:
+	//Converts into a float.
+	float32_t to_float() const {
+		return static_cast<float32_t>(s1516 * kFloatInvScale);
+	}
+
+	//Converts a fixed-point value into an integer by rounding it down to nearest integer. example: 3.94 -> 3, -2.1 -> -3
+	int32_t to_int32() const {
+		return static_cast<int32_t>(s1516 >> kShift);
+	}
+
+public:
+	inline ifloat32& operator = (const ifloat32& other) {
+		s1516 = other.s1516;
+		return *this;
+	}
+
+	inline bool operator == (const ifloat32& other) const {
+		return (s1516 == other.s1516);
+	}
+
+	inline bool operator != (const ifloat32& other) const {
+		return (s1516 != other.s1516);
+	}
+
+	inline bool operator < (const ifloat32& other) const {
+		return (s1516 < other.s1516);
+	}
+
+	inline bool operator > (const ifloat32& other) const {
+		return (s1516 > other.s1516);
+	}
+
+public:
+	inline ifloat32& operator += (const ifloat32 other) {
+		s1516 += other.s1516;
+		return *this;
+	}
+
+	inline ifloat32& operator -= (const ifloat32 other) {
+		s1516 -= other.s1516;
+		return *this;
+	}
+
+public:
+	//Adds the two FP numbers together.
+	inline friend ifloat32 operator + (const ifloat32& l, const ifloat32& r) {
+		int64_t t = static_cast<int64_t>(l.s1516) + static_cast<int64_t>(r.s1516);
+
+		ifloat32 ret;
+		ret.s1516 = static_cast<int32_t>(t);
+		return ret;
+	}
+
+	//Subtracts the two FP numbers from each other.
+	inline friend ifloat32 operator - (const ifloat32& l, const ifloat32& r) {
+		int64_t t = static_cast<int64_t>(l.s1516) - static_cast<int64_t>(r.s1516);
+
+		ifloat32 ret;
+		ret.s1516 = t;
+		return ret;
+	}
+
+	inline friend ifloat32 operator * (const ifloat32& a, const float32_t& b) {
+		int64_t t = static_cast<int64_t>(a.s1516) * static_cast<int64_t>(b * kFloatScale);
+
+		t = t >> kShift;
+
+		ifloat32 ret;
+		ret.s1516 = t;
+		return ret;
+	}
+
+	inline friend ifloat32 operator * (const ifloat32& a, const int32_t& b) {
+		ifloat32 ret;
+		ret.s1516 = a.s1516 * b;
+		return ret;
+	}
+
+	//Multiplies two FP values together.
+	inline friend ifloat32 operator * (const ifloat32& a, const ifloat32& b) {
+		int64_t t = static_cast<int64_t>(a.s1516) * static_cast<int64_t>(b.s1516);
+
+		t = t >> kShift;
+
+		ifloat32 ret;
+		ret.s1516 = static_cast<int32_t>(t);
+		return ret;
+	}
+
+	inline friend ifloat32 operator / (const ifloat32& a, const ifloat32& b) {
+		// pre-multiply by the base
+		int64_t t = static_cast<int64_t>(a.s1516) << kShift;
+		t /= b.s1516;
+
+		ifloat32 ret;
+		ret.s1516 = static_cast<int32_t>(t);
+		return ret;
+	}
+
+public:
+	int32_t s1516;
+};
+
+class ifloat64
+{
+public:
+	static constexpr int32_t	kShift = 32;
+	static constexpr float32_t	kFloatScale = static_cast<float32_t>(INT64_C(1) << kShift);	//4294967296.0
+	static constexpr float32_t	kFloatInvScale = 1.0f / kFloatScale;
+	static constexpr int64_t	kFractionMask = (INT64_C(1) << kShift) - 1; // Space before INT64_C(1) needed because of hacky C++ code generator
+
+	//static_cast<int64_t>(nextafter(INT64_MAX / iFloat64::kFloatScale, 0.0) * iFloat64::kFloatScale);
+	static constexpr int64_t	kMax_s3132 = INT64_C(0x7ffffffffffffc00);
+	static constexpr int32_t	kMax_int32 = static_cast<int32_t>(kMax_s3132 >> kShift);
+	static constexpr float32_t	kMax_float = 2.14748352e+09f;	//nextafter(static_cast<float32_t>(kS3132_Max * kFloatInvScale), 0.0f);
+
+	//(int32_t)(nextafter(-INT64_MAX / iFloat64::kFloatScale, -DBL_MAX) * iFloat64::kFloatScale);
+	static constexpr int64_t	kMin_s3132 = INT64_C(0x8000000000000000);
+	static constexpr int32_t	kMin_int32 = static_cast<int32_t>(kMin_s3132 >> kShift);
+	static constexpr float32_t	kMin_float = static_cast<float64_t>(kMin_s3132 * kFloatInvScale);
+
+	// special value
+	static DV_CORE_API const ifloat64 kMax;
+	static DV_CORE_API const ifloat64 kMin;
+	static DV_CORE_API const ifloat64 kZero;
+	static DV_CORE_API const ifloat64 kOne;
+	static DV_CORE_API const ifloat64 kTwo;
+	static DV_CORE_API const ifloat64 kThree;
+	static DV_CORE_API const ifloat64 kFour;
+	static DV_CORE_API const ifloat64 kHalf;
+	static DV_CORE_API const ifloat64 kPi;
+	static DV_CORE_API const ifloat64 kPi2;
+	static DV_CORE_API const ifloat64 kPiHalf;
+	static DV_CORE_API const ifloat64 kE;
+	static DV_CORE_API const ifloat64 kNegOne;
+
+public:
+	ifloat64() : s3132(0) {}
+	ifloat64(const ifloat64& other) : s3132(other.s3132) {}
+
+	//Converts a float to a fixed-point value.
+	ifloat64(float32_t f) {
+		s3132 = static_cast<int64_t>(std::round(f * kFloatScale));
+	}
+
+	//Converts a double to a fixed-point value.
+	ifloat64(float64_t f) {
+		s3132 = static_cast<int64_t>(std::round(f * kFloatScale));
+	}
+
+	//Converts an integer to a fixed-point value.
+	ifloat64(int32_t n) {
+		s3132 = static_cast<int64_t>(n) << kShift;
+	}
+
+private:
+	ifloat64(int64_t _s3132) {
+		s3132 = _s3132;
+	}
+
+public:
+	//Converts into a float.
+	float32_t to_float() const {
+		return static_cast<float32_t>(s3132 * kFloatInvScale);
+	}
+
+	//Converts a fixed-point value into an integer by rounding it down to nearest integer. example: 3.94 -> 3, -2.1 -> -3
+	int32_t to_int32() const {
+		return static_cast<int32_t>(s3132 >> kShift);
+	}
+
+public:
+	inline const ifloat64& operator + () const {
+		return *this;
+	}
+
+	inline ifloat64 operator - () const {
+		return ifloat64(-s3132);
+	}
+
+	inline ifloat64& operator = (const ifloat64& other) {
+		s3132 = other.s3132;
+		return *this;
+	}
+
+	inline bool operator == (const ifloat64& other) const {
+		return (s3132 == other.s3132);
+	}
+
+	inline bool operator != (const ifloat64& other) const {
+		return (s3132 != other.s3132);
+	}
+
+	inline bool operator < (const ifloat64& other) const {
+		return (s3132 < other.s3132);
+	}
+
+	inline bool operator > (const ifloat64& other) const {
+		return (s3132 > other.s3132);
+	}
+
+public:
+	inline ifloat64& operator += (const ifloat64 other) {
+		s3132 += other.s3132;
+		return *this;
+	}
+
+	inline ifloat64& operator -= (const ifloat64 other) {
+		s3132 -= other.s3132;
+		return *this;
+	}
+
+public:
+	//Adds the two FP numbers together.
+	inline friend ifloat64 operator + (const ifloat64& a, const ifloat64& b) {
+		ifloat64 ret;
+		ret.s3132 = a.s3132 + b.s3132;
+		return ret;
+	}
+
+	//Subtracts the two FP numbers from each other.
+	inline friend ifloat64 operator - (const ifloat64& a, const ifloat64& b) {
+		ifloat64 ret;
+		ret.s3132 = a.s3132 - b.s3132;
+		return ret;
+	}
+
+	inline friend ifloat64 operator * (const ifloat64& a, const int32_t& b) {
+		ifloat64 ret;
+		ret.s3132 = a.s3132 * b;
+		return ret;
+	}
+
+	inline friend ifloat64 operator * (const ifloat64& a, const float32_t& b) {
+		ifloat64 ret;
+		ret.s3132 = _safeMulti(a.s3132, static_cast<int64_t>(b * kFloatScale));
+		return ret;
+	}
+
+	//Multiplies two FP values together.
+	inline friend ifloat64 operator * (const ifloat64& a, const ifloat64& b) {
+		ifloat64 ret;
+		ret.s3132 = _safeMulti(a.s3132, b.s3132);
+		return ret;
+	}
+
+	inline friend ifloat64 operator / (const ifloat64& a, const ifloat64& b) {
+		// From http://www.hackersdelight.org/hdcodetxt/divlu.c.txt
+
+		int64_t sign_dif = a.s3132 ^ b.s3132;
+
+		static const uint64_t B = INT64_C(0x100000000); // Number base (32 bits)
+
+		uint64_t abs_a = (uint64_t)((a.s3132 < 0) ? -a.s3132 : a.s3132);
+		uint64_t u1 = abs_a >> 32;
+		uint64_t u0 = abs_a << 32;
+		uint64_t v = (uint64_t)((b.s3132 < 0) ? -b.s3132 : b.s3132);
+
+		// Overflow?
+		if (u1 >= v)
+		{
+			//invalid number
+			ifloat64 ret;
+			ret.s3132 = 0x7fffffffffffffff;
+			return ret;
+		}
+
+		// Shift amount for norm
+		int32_t s = _nlz(v); // 0 <= s <= 63
+		v = v << s; // Normalize the divisor
+		uint64_t vn1 = v >> 32; // Break the divisor into two 32-bit digits
+		uint64_t vn0 = v & INT64_C(0xffffffff);
+
+		uint64_t un32 = (u1 << s) | (u0 >> (64 - s)) & (uint64_t)((int64_t)-s >> 63);
+		uint64_t un10 = u0 << s; // Shift dividend left
+
+		uint64_t un1 = un10 >> 32; // Break the right half of dividend into two digits
+		uint64_t un0 = un10 & INT64_C(0xffffffff);
+
+		// Compute the first quotient digit, q1
+		uint64_t q1 = un32 / vn1;
+		uint64_t rhat = un32 - q1 * vn1;
+		do
+		{
+			if ((q1 >= B) || ((q1 * vn0) > (B * rhat + un1)))
+			{
+				q1 = q1 - 1;
+				rhat = rhat + vn1;
+			}
+			else break;
+		} while (rhat < B);
+
+		uint64_t un21 = un32 * B + un1 - q1 * v; // Multiply and subtract
+
+		// Compute the second quotient digit, q0
+		uint64_t q0 = un21 / vn1;
+		rhat = un21 - q0 * vn1;
+		do
+		{
+			if ((q0 >= B) || ((q0 * vn0) > (B * rhat + un0)))
+			{
+				q0 = q0 - 1;
+				rhat = rhat + vn1;
+			}
+			else break;
+		} while (rhat < B);
+
+		// Calculate the remainder
+		// uint64_t r = (un21 * b + un0 - q0 * v) >> s;
+		// rem = (int64_t)r;
+
+		int64_t t = q1 * B + q0;
+
+		ifloat64 ret;
+		ret.s3132 = (sign_dif < 0) ? -(int64_t)t : (int64_t)t;
+		return ret;
+	}
+
+public:
+	static int64_t _safeMulti(const int64_t a, const int64_t b) {
+		int64_t sign_diff = a ^ b;
+		uint64_t abs_a = a < 0 ? -a : a;
+		uint64_t abs_b = b < 0 ? -b : b;
+
+		uint64_t ai = abs_a >> kShift;
+		uint64_t af = (abs_a & kFractionMask);
+		uint64_t bi = abs_b >> kShift;
+		uint64_t bf = (abs_b & kFractionMask);
+
+		// (Ai+Af)*(Bi+Bf)=Af*Bf + Ai*(Bi+Bf) + Af*Bi
+		int64_t t = ((af * bf) >> kShift) + ai * abs_b + af * bi;
+		return (sign_diff < 0) ? -t : t;
+	}
+
+	static int32_t _nlz(uint64_t x)
+	{
+		int32_t n = 0;
+		if (x <= INT64_C(0x00000000FFFFFFFF)) { n = n + 32; x = x << 32; }
+		if (x <= INT64_C(0x0000FFFFFFFFFFFF)) { n = n + 16; x = x << 16; }
+		if (x <= INT64_C(0x00FFFFFFFFFFFFFF)) { n = n + 8; x = x << 8; }
+		if (x <= INT64_C(0x0FFFFFFFFFFFFFFF)) { n = n + 4; x = x << 4; }
+		if (x <= INT64_C(0x3FFFFFFFFFFFFFFF)) { n = n + 2; x = x << 2; }
+		if (x <= INT64_C(0x7FFFFFFFFFFFFFFF)) { n = n + 1; }
+		if (x == 0) return 64;
+		return n;
+	}
+
+public:
+	int64_t s3132;
+};
+
+typedef ifloat32 iFloat32;
+typedef ifloat64 iFloat64;
+
+typedef ifloat64 iFloat;
+
+struct iFloat2
+{
+	iFloat x, y;
+
+	iFloat2() : x(0), y(0) {}
+	iFloat2(const iFloat2& other) : x(other.x), y(other.y) {}
+	iFloat2(float32_t _x, float32_t _y) : x(_x), y(_y) {}
+};
+
+struct iFloat3
+{
+	iFloat x, y, z;
+
+	inline void add(const iFloat3& other) {
+		x += other.x;
+		y += other.y;
+		z += other.z;
+	}
+
+	inline void sub(const iFloat3& other) {
+		x -= other.x;
+		y -= other.y;
+		z -= other.z;
+	}
+
+	inline void mul(const iFloat& multiplier) {
+		x = x * multiplier;
+		y = y * multiplier;
+		z = z * multiplier;
+	}
+
+	inline iFloat operator [] (const size_t i) const {
+		return *(&x + i);
+	}
+
+	inline iFloat& operator [] (const size_t i) {
+		return *(&x + i);
+	}
+
+	iFloat3() : x(0), y(0), z(0) {}
+	iFloat3(const iFloat3& other) : x(other.x), y(other.y), z(other.z) {}
+	iFloat3(float32_t _x, float32_t _y, float32_t _z) : x(_x), y(_y), z(_z) {}
+	iFloat3(iFloat _x, iFloat _y, iFloat _z) : x(_x), y(_y), z(_z) {}
+};
+
+DV_CORE_END_NAMESPACE

source/core/include/math/dvc_fixmath.h

@@ -1,98 +0,0 @@
-#pragma once
-
-#include "dvc_config.h"
-
-DV_CORE_BEGIN_NAMESPACE
-
-typedef int64_t ifloat_t;
-//typedef int64_t ifloat2_t[2];
-//typedef int64_t ifloat3_t[3];
-
-#define IFLOAT_SHIFT (16)
-#define IFLOAT_SCALE ((float64_t)(1<<IFLOAT_SHIFT))
-
-//-------------------------------------------------------------------------------------
-inline ifloat_t ifloat_init(float32_t a)
-{
-	return (ifloat_t)((float64_t)a * IFLOAT_SCALE + 0.5);
-}
-
-//-------------------------------------------------------------------------------------
-inline ifloat_t ifloat_init(int32_t a)
-{
-	return (int64_t)(a)<< IFLOAT_SHIFT;
-}
-
-//-------------------------------------------------------------------------------------
-inline float32_t ifloat_get_float(ifloat_t a)
-{
-	return (float32_t)((float64_t)a/ IFLOAT_SCALE);
-}
-
-//-------------------------------------------------------------------------------------
-inline ifloat_t ifloat_multiply(ifloat_t a, ifloat_t b)
-{
-	return (ifloat_t)((a * b) >> IFLOAT_SHIFT);
-}
-
-//-------------------------------------------------------------------------------------
-//inline void ifloat3_add(ifloat3_t& a, const ifloat3_t& b)
-//{
-//	a[0] += b[0]; a[1] += b[1]; a[2] += b[2];
-//}
-
-//-------------------------------------------------------------------------------------
-//inline void ifloat3_sub(ifloat3_t& a, const ifloat3_t& b)
-//{
-//	a[0] -= b[0]; a[1] -= b[1]; a[2] -= b[2];
-//}
-
-//-------------------------------------------------------------------------------------
-//inline void ifloat3_cpy(ifloat3_t& a, const ifloat3_t& b)
-//{
-//	a[0] = b[0]; a[1] = b[1]; a[2] = b[2];
-//}
-
-//-------------------------------------------------------------------------------------
-struct ifloat2_t
-{
-	ifloat_t x, y;
-
-	ifloat2_t() : x(0ll), y(0ll) {}
-	ifloat2_t(const ifloat2_t& other) : x(other.x), y(other.y) {}
-	ifloat2_t(float32_t _x, float32_t _y) : x(ifloat_init(_x)), y(ifloat_init(_y)) {}
-};
-
-struct ifloat3_t
-{
-	ifloat_t x, y, z;
-
-	inline void add(const ifloat3_t& other) {
-		x += other.x;
-		y += other.y;
-		z += other.z;
-	}
-
-	inline void sub(const ifloat3_t& other) {
-		x -= other.x;
-		y -= other.y;
-		z -= other.z;
-	}
-
-	inline ifloat_t operator [] (const size_t i) const {
-		return *(&x + i);
-	}
-
-	inline ifloat_t& operator [] (const size_t i) {
-		return *(&x + i);
-	}
-
-	ifloat3_t() : x(0ll), y(0ll), z(0ll) {}
-	ifloat3_t(const ifloat3_t& other) : x(other.x), y(other.y), z(other.z) {}
-	ifloat3_t(float32_t _x, float32_t _y, float32_t _z) : x(ifloat_init(_x)), y(ifloat_init(_y)), z(ifloat_init(_z)) {}
-	ifloat3_t(ifloat_t _x, ifloat_t _y, ifloat_t _z) : x(_x), y(_y), z(_z) {}
-};
-
-
-DV_CORE_END_NAMESPACE
-

source/core/include/pipe/dvc_rasterizer.h

@@ -21,10 +21,24 @@ public:
 public:
 	typedef std::function<void(const std::pair<int32_t, int32_t>& pos, const fVector3& percent)> DrawTriangleCallback;
 
+	struct DebugParam
+	{
+		bool debug;
+		const char* szOutputFileName;
+		int32_t x;
+		int32_t y;
+
+		FILE* fpOutput;
+		int32_t tile_id;
+		int32_t coarse_id;
+		int32_t fine_id;
+		int32_t edge_id;
+	};
+
 	//Larrabee algorithm
 	static void drawTriangleLarrabee(int32_t canvasWidth, int32_t canvasHeight,
 		const fVector2& v0, const fVector2& v1, const fVector2& v2, 
-		DrawTriangleCallback callback, bool ccw=true);
+		DrawTriangleCallback callback, bool ccw=true, const DebugParam* debugParam=nullptr);
 
 	//Scaleline algorithm
 	static void drawTriangleScanline(int32_t canvasWidth, int32_t canvasHeight,

source/core/source/math/dvc_fix_point.cpp

@@ -0,0 +1,20 @@
+#include "math/dvc_fix_point.h"
+
+DV_CORE_BEGIN_NAMESPACE
+
+const ifloat64 ifloat64::kMax{ ifloat64::kMax_s3132 };
+const ifloat64 ifloat64::kMin{ ifloat64::kMin_s3132 };
+const ifloat64 ifloat64::kZero{ 0 };
+const ifloat64 ifloat64::kOne{ INT64_C(1) << ifloat64::kShift };
+const ifloat64 ifloat64::kTwo{ INT64_C(2) << kShift };
+const ifloat64 ifloat64::kThree{ INT64_C(3) << ifloat64::kShift };
+const ifloat64 ifloat64::kFour{ INT64_C(4) << ifloat64::kShift };
+const ifloat64 ifloat64::kHalf{ INT64_C(1) << (ifloat64::kShift-1) };
+const ifloat64 ifloat64::kPi{ INT64_C(0x3243f6a89) }; //static_cast<int64_t>(std::round(M_PI * kFloatScale));
+const ifloat64 ifloat64::kPi2{ INT64_C(0x6487ed511) };
+const ifloat64 ifloat64::kPiHalf{ INT64_C(0x1921fb544) };
+const ifloat64 ifloat64::kE{ INT64_C(0x2b7e15163) };
+const ifloat64 ifloat64::kNegOne{ INT64_C(-1) << kShift };
+
+DV_CORE_END_NAMESPACE
+

source/core/source/pipe/dvc_rasterizer_triangle.cpp

@@ -1,5 +1,5 @@
 #include "pipe/dvc_rasterizer.h"
-#include "math/dvc_fixmath.h"
+#include "math/dvc_fix_point.h"
 #include "math/dvc_math_util.h"
 
 /*
@@ -21,7 +21,8 @@ struct DrawTriangleParam
 	float32_t	bbox_max_y;
 	bool		tlBorder[3];
 	float32_t	area;
-	ifloat3_t	edgesDX, edgesDY;
+	iFloat3		edgesDX, edgesDY;
+	Rasterizer::DebugParam	debugParam;
 };
 
 //-------------------------------------------------------------------------------------
@@ -29,10 +30,15 @@ enum { TILE_WIDTH_IN_PIXELS = 64, COARSE_BLOCK_WIDTH_IN_PIXELS = 16, FINE_BLOCK_
 
 //-------------------------------------------------------------------------------------
 void _drawTriangle_Fine(int32_t tile_id, int32_t coarse_id, int32_t fine_id,
-	const DrawTriangleParam& param, const ifloat3_t& edges0, uint32_t testEdgeMask, 
+	const DrawTriangleParam& param, const iFloat3& edges0, uint32_t testEdgeMask, 
 	Rasterizer::DrawTriangleCallback callback)
 {
-	ifloat3_t pixelEdges(edges0);
+	iFloat3 kHalfDX = param.edgesDX; kHalfDX.mul(iFloat::kHalf);
+	iFloat3 kHalfDY = param.edgesDY; kHalfDY.mul(iFloat::kHalf);
+
+	iFloat3 pixelEdges(edges0);
+	pixelEdges.sub(kHalfDY);
+	pixelEdges.add(kHalfDX);
 
 	const fVector2 v0(param.verts[0]), v1(param.verts[1]), v2(param.verts[2]);
 	const bool edgeMask[3] = { (testEdgeMask & 1) != 0 , (testEdgeMask & 2) != 0 , (testEdgeMask & 4) != 0 };
@@ -45,10 +51,39 @@ void _drawTriangle_Fine(int32_t tile_id, int32_t coarse_id, int32_t fine_id,
 
 	for (int32_t y_index=0, y= fine_start_y; y_index < 4; y_index++, y++) 
 	{
-		ifloat3_t edgesRow(pixelEdges);
+		iFloat3 edgesRow(pixelEdges);
 
 		for (int32_t x_index = 0, x=fine_start_x; x_index < 4; x_index++, x++) 
 		{
+			if (param.debugParam.debug)
+			{
+				if (x == param.debugParam.x && y == param.debugParam.y)
+				{
+					iFloat3 LBEdges(edges0);
+					LBEdges.sub(kHalfDY);
+					LBEdges.add(kHalfDX);
+
+					fprintf(param.debugParam.fpOutput, "======= Fine =======\n");
+					fprintf(param.debugParam.fpOutput, "LeftBottom=[%d,%d](%f,%f)\n", fine_start_x, fine_start_y, fine_start_x+0.5f, fine_start_y+0.5f);
+					fprintf(param.debugParam.fpOutput, "Edge0=(%f,%f,%f)[%lld,%lld,%lld]\n",
+						edges0.x.to_float(), edges0.y.to_float(), edges0.z.to_float(),
+						edges0.x.s3132, edges0.y.s3132, edges0.z.s3132
+					);
+					fprintf(param.debugParam.fpOutput, "Edge0+0.5=(%f,%f,%f)[%lld,%lld,%lld]\n",
+						LBEdges.x.to_float(), LBEdges.y.to_float(), LBEdges.z.to_float(), 
+						LBEdges.x.s3132, LBEdges.y.s3132, LBEdges.z.s3132
+					);
+
+					fprintf(param.debugParam.fpOutput, "======= Pixel =======\n");
+					fprintf(param.debugParam.fpOutput, "Position=[%d,%d](%f,%f)\n", x, y, x+0.5f, y+0.5f);
+					fprintf(param.debugParam.fpOutput, "IndexInFind=[%d,%d]\n", x_index, y_index);
+					fprintf(param.debugParam.fpOutput, "Edge=(%f,%f,%f)[%lld,%lld,%lld]\n",
+						edgesRow.x.to_float(), edgesRow.y.to_float(), edgesRow.z.to_float(),
+						edgesRow.x.s3132, edgesRow.y.s3132, edgesRow.z.s3132
+					);
+				}
+			}
+
 			bool rejected =
 				(edgeMask[0] && (edgesRow.x < 0 || (!param.tlBorder[0] && edgesRow.x == 0))) ||
 				(edgeMask[1] && (edgesRow.y < 0 || (!param.tlBorder[1] && edgesRow.y == 0))) ||
@@ -74,24 +109,24 @@ void _drawTriangle_Fine(int32_t tile_id, int32_t coarse_id, int32_t fine_id,
 
 //-------------------------------------------------------------------------------------
 void _drawTriangle_Coarse(int32_t tile_id, int32_t coarse_id,
-	DrawTriangleParam& param, const ifloat3_t& edges0, uint32_t testEdgeMask, 
+	DrawTriangleParam& param, const iFloat3& edges0, uint32_t testEdgeMask, 
 	Rasterizer::DrawTriangleCallback callback)
 {
-	const ifloat3_t blockEdgesDX(
+	const iFloat3 blockEdgesDX(
 		param.edgesDX.x * FINE_BLOCK_WIDTH_IN_PIXELS, 
 		param.edgesDX.y * FINE_BLOCK_WIDTH_IN_PIXELS, 
 		param.edgesDX.z * FINE_BLOCK_WIDTH_IN_PIXELS 
 	);
-	const ifloat3_t blockEdgesDY(
+	const iFloat3 blockEdgesDY(
 		param.edgesDY.x * FINE_BLOCK_WIDTH_IN_PIXELS,
 		param.edgesDY.y * FINE_BLOCK_WIDTH_IN_PIXELS, 
 		param.edgesDY.z * FINE_BLOCK_WIDTH_IN_PIXELS 
 	);
 	const bool edgeMask[3] = { (testEdgeMask & 1) != 0 , (testEdgeMask & 2) != 0 , (testEdgeMask & 4) != 0 };
 
-	ifloat3_t blockReject(edges0);
-	ifloat3_t blockAccept(edges0);
-	ifloat3_t blockEdges(edges0);
+	iFloat3 blockReject(edges0);
+	iFloat3 blockAccept(edges0);
+	iFloat3 blockEdges(edges0);
 
 	for (size_t v = 0; v < 3; v++) 
 	{
@@ -117,8 +152,8 @@ void _drawTriangle_Coarse(int32_t tile_id, int32_t coarse_id,
 
 		if (block_start_y + (y_index + 1)*FINE_BLOCK_WIDTH_IN_PIXELS >= param.bbox_min_y) 
 		{
-			ifloat3_t edgesRow(blockEdges);
-			ifloat3_t edgesRowReject, edgesRowAccept;
+			iFloat3 edgesRow(blockEdges);
+			iFloat3 edgesRowReject, edgesRowAccept;
 
 			for (size_t v = 0; v < 3; v++) 
 			{
@@ -182,25 +217,25 @@ void _drawTriangle_Coarse(int32_t tile_id, int32_t coarse_id,
 
 //-------------------------------------------------------------------------------------
 void _drawTriangle_Title(int32_t tile_id,
-	DrawTriangleParam& param, const ifloat3_t& edges0, uint32_t testEdgeMask, 
+	DrawTriangleParam& param, const iFloat3& edges0, uint32_t testEdgeMask, 
 	Rasterizer::DrawTriangleCallback callback)
 {
-	const ifloat3_t blockEdgesDX( 
+	const iFloat3 blockEdgesDX( 
 		param.edgesDX[0] * COARSE_BLOCK_WIDTH_IN_PIXELS, 
 		param.edgesDX[1] * COARSE_BLOCK_WIDTH_IN_PIXELS,
 		param.edgesDX[2] * COARSE_BLOCK_WIDTH_IN_PIXELS
 	);
 
-	const ifloat3_t blockEdgesDY(
+	const iFloat3 blockEdgesDY(
 		param.edgesDY[0] * COARSE_BLOCK_WIDTH_IN_PIXELS, 
 		param.edgesDY[1] * COARSE_BLOCK_WIDTH_IN_PIXELS, 
 		param.edgesDY[2] * COARSE_BLOCK_WIDTH_IN_PIXELS 
 	);
 	const bool edgeMask[3] = { (testEdgeMask & 1) != 0 , (testEdgeMask & 2) != 0 , (testEdgeMask & 4) != 0 };
 
-	ifloat3_t blockReject(edges0);
-	ifloat3_t blockAccept(edges0);
-	ifloat3_t blockEdges(edges0);
+	iFloat3 blockReject(edges0);
+	iFloat3 blockAccept(edges0);
+	iFloat3 blockEdges(edges0);
 
 	for (size_t v = 0; v < 3; v++) 
 	{
@@ -226,8 +261,8 @@ void _drawTriangle_Title(int32_t tile_id,
 
 		if (block_start_y + (y_index + 1)*COARSE_BLOCK_WIDTH_IN_PIXELS >= param.bbox_min_y) 
 		{
-			ifloat3_t edges(blockEdges);
-			ifloat3_t edgesRowReject, edgesRowAccept;
+			iFloat3 edges(blockEdges);
+			iFloat3 edgesRowReject, edgesRowAccept;
 
 			for (size_t v = 0; v < 3; v++) 
 			{
@@ -298,7 +333,7 @@ void _drawTriangle_Title(int32_t tile_id,
 //-------------------------------------------------------------------------------------
 void Rasterizer::drawTriangleLarrabee(int32_t canvasWidth, int32_t canvasHeight, 
 	const fVector2& v0, const fVector2& v1, const fVector2& v2, 
-	DrawTriangleCallback callback, bool ccw)
+	DrawTriangleCallback callback, bool ccw, const DebugParam* debugParam)
 {
 	assert(canvasWidth >= TILE_WIDTH_IN_PIXELS && canvasHeight >= TILE_WIDTH_IN_PIXELS);
 	assert(canvasWidth%TILE_WIDTH_IN_PIXELS == 0 && canvasHeight%TILE_WIDTH_IN_PIXELS == 0);
@@ -306,20 +341,23 @@ void Rasterizer::drawTriangleLarrabee(int32_t canvasWidth, int32_t canvasHeight,
 	DrawTriangleParam param;
 	param.widthInTiles = canvasWidth / TILE_WIDTH_IN_PIXELS;
 
-	//ccw
+	//Whether the three input vertices are in the agreed clockwise order or not, 
+	// it indicates that the triangle is invisible
 	bool isCCW = (v1 - v0).crossProduct(v2 - v1)>0;
 	if (isCCW != ccw) return;
 
+	//By default, the order is counterclockwise. So if the input data is clockwise, a reversal is needed. 
+	// Swap v1 and v2, and then reverse it back when the final callback is made
 	param.ccw = ccw;
 	param.verts[0] = v0;
 	param.verts[1] = ccw ? v1 : v2;
 	param.verts[2] = ccw ? v2 : v1;
 	param.area = (param.verts[1] - param.verts[0]).crossProduct(param.verts[2] - param.verts[1]);
 
-	ifloat2_t vertices[3];
+	iFloat2 vertices[3];
 	for (size_t i = 0; i < 3; i++) 
 	{
-		vertices[i] = ifloat2_t(param.verts[i].x, param.verts[i].y);
+		vertices[i] = iFloat2(param.verts[i].x, param.verts[i].y);
 	}
 
 	//get window coordinates bounding box
@@ -329,8 +367,8 @@ void Rasterizer::drawTriangleLarrabee(int32_t canvasWidth, int32_t canvasHeight,
 	param.bbox_max_y = MathUtil::max3(v0.y, v1.y, v2.y);
 
 	//canvas size
-	ifloat_t iCanvasWidth = ifloat_init(canvasWidth);
-	ifloat_t iCanvasHeight = ifloat_init(canvasHeight);
+	iFloat iCanvasWidth(canvasWidth);
+	iFloat iCanvasHeight(canvasHeight);
 
 	// clip triangles that are fully outside the scissor rect (scissor rect = whole window)
 	if (param.bbox_max_x < 0 || param.bbox_max_y < 0 || param.bbox_min_x >= canvasWidth || param.bbox_min_y >= canvasHeight) 
@@ -348,13 +386,13 @@ void Rasterizer::drawTriangleLarrabee(int32_t canvasWidth, int32_t canvasHeight,
 	int32_t last_tile_x = (int32_t)(param.bbox_max_x / TILE_WIDTH_IN_PIXELS);
 	int32_t last_tile_y = (int32_t)(param.bbox_max_y / TILE_WIDTH_IN_PIXELS);
 
-	// evaluate edge equation at the top left tile
-	ifloat_t firstTileX = first_tile_x * ifloat_init(TILE_WIDTH_IN_PIXELS);
-	ifloat_t firstTileY = first_tile_y * ifloat_init(TILE_WIDTH_IN_PIXELS);
+	//The first Title is the Title at the lower left corner within the bounding box range covered by the triangle
+	iFloat firstTileX = iFloat(first_tile_x * TILE_WIDTH_IN_PIXELS);
+	iFloat firstTileY = iFloat(first_tile_y * TILE_WIDTH_IN_PIXELS);
 
-	ifloat3_t edges0;
-	ifloat3_t tileEdgesDX, tileEdgesDY, edgesReject, edgesAccept;
-	const ifloat_t kZeroPointFive = ifloat_init(0.5f);
+	iFloat3 edgesLB; //The edge value at the lower left corner of the first title
+	iFloat3 tileEdgesDX, tileEdgesDY;
+	iFloat3 edgesReject, edgesAccept;
 
 	for (size_t v = 0; v < 3; v++)
 	{
@@ -366,8 +404,8 @@ void Rasterizer::drawTriangleLarrabee(int32_t canvasWidth, int32_t canvasHeight,
 		tileEdgesDY[v] = param.edgesDY[v] * TILE_WIDTH_IN_PIXELS;
 
 		//(V0,V1) X (V0, P) = (x1-x0)(py-y0)-(y1-y0)(px-x0)
-		edges0[v] = ifloat_multiply(param.edgesDX[v], (firstTileY + kZeroPointFive - vertices[v].y))
-				  - ifloat_multiply(param.edgesDY[v], (firstTileX + kZeroPointFive - vertices[v].x));
+		edgesLB[v] = param.edgesDX[v] * (firstTileY - vertices[v].y)
+				  - param.edgesDY[v] * (firstTileX - vertices[v].x);
 
 		// Top-left rule: 
 		//   shift top-left edges ever so slightly outward to make the top-left edges be 
@@ -382,7 +420,7 @@ void Rasterizer::drawTriangleLarrabee(int32_t canvasWidth, int32_t canvasHeight,
 			param.tlBorder[v] = false;
 		}
 
-		edgesReject[v] = edgesAccept[v] = edges0[v];
+		edgesReject[v] = edgesAccept[v] = edgesLB[v];
 
 		if (tileEdgesDX[v] > 0) edgesReject[v] += tileEdgesDX[v];
 		else if (tileEdgesDX[v] < 0) edgesAccept[v] += tileEdgesDX[v];
@@ -391,18 +429,77 @@ void Rasterizer::drawTriangleLarrabee(int32_t canvasWidth, int32_t canvasHeight,
 		else if (tileEdgesDY[v] < 0) edgesReject[v] -= tileEdgesDY[v];
 	}
 
-	ifloat3_t rowEdges(edges0);
+	if (debugParam != nullptr)
+	{
+		param.debugParam.debug = debugParam->debug;
+		param.debugParam.szOutputFileName = debugParam->szOutputFileName;
+		param.debugParam.x = debugParam->x;
+		param.debugParam.y = debugParam->y;
+
+		if (param.debugParam.debug) {
+			param.debugParam.fpOutput = fopen(debugParam->szOutputFileName, "w");
+
+			fprintf(param.debugParam.fpOutput, "===== Triangle ====\n");
+			for (int32_t i = 0; i < 3; i++) {
+				fprintf(param.debugParam.fpOutput, "v%d=(%f,%f)[%lld,%lld]\n", i,
+					param.verts[i].x, param.verts[i].y, vertices[i].x.s3132, vertices[i].y.s3132);
+			}
+			fprintf(param.debugParam.fpOutput, "===== TitleRange ====\n");
+			fprintf(param.debugParam.fpOutput,
+				"tile_x={%d, %d}\ntile_y={%d, %d}\n",
+				first_tile_x, last_tile_x, first_tile_y, last_tile_y);
+			fprintf(param.debugParam.fpOutput,
+				"FirstTitle=(%f,%f)[%lld,%lld]\n", firstTileX.to_float(), firstTileY.to_float(),
+				firstTileX.s3132, firstTileY.s3132
+			);
+
+			fprintf(param.debugParam.fpOutput, "===== Edge ====\n");
+			for (int32_t i = 0; i < 3; i++) {
+				fprintf(param.debugParam.fpOutput, "DX%d=(%f)[%lld]\tDY%d=(%f)[%lld]\n",
+					i,
+					param.edgesDX[i].to_float(), param.edgesDX[i].s3132,
+					i,
+					param.edgesDY[i].to_float(), param.edgesDY[i].s3132);
+			}
+			fprintf(param.debugParam.fpOutput, "\n");
+			for (int32_t i = 0; i < 3; i++) {
+				fprintf(param.debugParam.fpOutput, "Edge%d=(%lld)*(y-%lld)-(%lld)*(x-%lld)\n\t=(%f)*(y-%f)-(%f)*(x-%f)\n", i,
+					param.edgesDX[i].s3132, vertices[i].y.s3132, param.edgesDY[i].s3132, vertices[i].x.s3132,
+					param.edgesDX[i].to_float(), vertices[i].y.to_float(), param.edgesDY[i].to_float(), vertices[i].x.to_float()
+				);
+			}
+			fprintf(param.debugParam.fpOutput, "EdgeLB=(%f,%f,%f)[%lld,%lld,%lld]\n",
+				edgesLB.x.to_float(), edgesLB.y.to_float(), edgesLB.z.to_float(),
+				edgesLB.x.s3132, edgesLB.y.s3132, edgesLB.z.s3132
+			);
+			for (int32_t i = 0; i < 3; i++)
+			{
+				fprintf(param.debugParam.fpOutput, "EdgeLB.%d=%lld*(%lld-%lld)-%lld*(%lld-%lld)\n", i,
+					param.edgesDX[i].s3132, firstTileY.s3132, vertices[i].y.s3132, 
+					param.edgesDY[i].s3132, firstTileX.s3132, vertices[i].x.s3132
+				);
+			}
+
+			fprintf(param.debugParam.fpOutput, "TopLeft=%s,%s,%s\n",
+				param.tlBorder[0] ? "true" : "false", param.tlBorder[1] ? "true" : "false", param.tlBorder[2] ? "true" : "false"
+			);
+		}
+	}
+
+	iFloat3 rowEdges(edgesLB);
 
 	int32_t tile_row_start = first_tile_y * param.widthInTiles + first_tile_x;
 	for (int32_t tile_y = first_tile_y; tile_y <= last_tile_y; tile_y++)
 	{
-		ifloat3_t edges(rowEdges);
-		ifloat3_t tileEdgesReject(edgesReject);
-		ifloat3_t tileEdgesAccept(edgesAccept);
+		iFloat3 edges(rowEdges);
+		iFloat3 tileEdgesReject(edgesReject);
+		iFloat3 tileEdgesAccept(edgesAccept);
 
 		int32_t tile_i = tile_row_start;
 		for (int32_t tile_x = first_tile_x; tile_x <= last_tile_x; tile_x++) 
 		{
+			//If the title is excluded by any edge, 
+			// it indicates that the title is completely outside the triangle and does not require rendering
 			bool rejected =
 				((tileEdgesReject[0] < 0 || (!param.tlBorder[0] && tileEdgesReject[0] == 0))) ||
 				((tileEdgesReject[1] < 0 || (!param.tlBorder[1] && tileEdgesReject[1] == 0))) ||
@@ -416,7 +513,9 @@ void Rasterizer::drawTriangleLarrabee(int32_t canvasWidth, int32_t canvasHeight,
 				{
 					if (tileEdgesAccept[v] < 0 || (tileEdgesAccept[v] == 0 && !param.tlBorder[v])) 
 					{
-						testEdgeMask += (1 << v);
+						//whether the accepting vertex of this title is on the "outside" of the three edges, 
+						// that is, it may intersect or be completely outside
+						testEdgeMask += (1 << v); 
 					}
 				}
 
@@ -436,6 +535,12 @@ void Rasterizer::drawTriangleLarrabee(int32_t canvasWidth, int32_t canvasHeight,
 		edgesAccept.add(tileEdgesDX);
 		tile_row_start += param.widthInTiles;
 	}
+
+	if (debugParam != nullptr && debugParam->debug)
+	{
+		fclose(param.debugParam.fpOutput);
+		param.debugParam.fpOutput = nullptr;
+	}
 }
 
 //-------------------------------------------------------------------------------------