Synchronize most shared variant code with Godot 4.4

include/godot_cpp/core/math.hpp

@@ -537,6 +537,26 @@ inline float bezier_interpolate(float p_start, float p_control_1, float p_contro
 	return p_start * omt3 + p_control_1 * omt2 * p_t * 3.0f + p_control_2 * omt * t2 * 3.0f + p_end * t3;
 }
 
+inline double bezier_derivative(double p_start, double p_control_1, double p_control_2, double p_end, double p_t) {
+	/* Formula from Wikipedia article on Bezier curves. */
+	double omt = (1.0 - p_t);
+	double omt2 = omt * omt;
+	double t2 = p_t * p_t;
+
+	double d = (p_control_1 - p_start) * 3.0 * omt2 + (p_control_2 - p_control_1) * 6.0 * omt * p_t + (p_end - p_control_2) * 3.0 * t2;
+	return d;
+}
+
+inline float bezier_derivative(float p_start, float p_control_1, float p_control_2, float p_end, float p_t) {
+	/* Formula from Wikipedia article on Bezier curves. */
+	float omt = (1.0f - p_t);
+	float omt2 = omt * omt;
+	float t2 = p_t * p_t;
+
+	float d = (p_control_1 - p_start) * 3.0f * omt2 + (p_control_2 - p_control_1) * 6.0f * omt * p_t + (p_end - p_control_2) * 3.0f * t2;
+	return d;
+}
+
 template <typename T>
 inline T clamp(T x, T minv, T maxv) {
 	if (x < minv) {

include/godot_cpp/variant/aabb.hpp

@@ -72,16 +72,21 @@ struct [[nodiscard]] AABB {
 	AABB merge(const AABB &p_with) const;
 	void merge_with(const AABB &p_aabb); ///merge with another AABB
 	AABB intersection(const AABB &p_aabb) const; ///get box where two intersect, empty if no intersection occurs
-	bool intersects_segment(const Vector3 &p_from, const Vector3 &p_to, Vector3 *r_clip = nullptr, Vector3 *r_normal = nullptr) const;
-	bool intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *r_clip = nullptr, Vector3 *r_normal = nullptr) const;
-	_FORCE_INLINE_ bool smits_intersect_ray(const Vector3 &p_from, const Vector3 &p_dir, real_t t0, real_t t1) const;
+	_FORCE_INLINE_ bool smits_intersect_ray(const Vector3 &p_from, const Vector3 &p_dir, real_t p_t0, real_t p_t1) const;
+
+	bool intersects_segment(const Vector3 &p_from, const Vector3 &p_to, Vector3 *r_intersection_point = nullptr, Vector3 *r_normal = nullptr) const;
+	bool intersects_ray(const Vector3 &p_from, const Vector3 &p_dir) const {
+		bool inside;
+		return find_intersects_ray(p_from, p_dir, inside);
+	}
+	bool find_intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, bool &r_inside, Vector3 *r_intersection_point = nullptr, Vector3 *r_normal = nullptr) const;
 
 	_FORCE_INLINE_ bool intersects_convex_shape(const Plane *p_planes, int p_plane_count, const Vector3 *p_points, int p_point_count) const;
 	_FORCE_INLINE_ bool inside_convex_shape(const Plane *p_planes, int p_plane_count) const;
 	bool intersects_plane(const Plane &p_plane) const;
 
 	_FORCE_INLINE_ bool has_point(const Vector3 &p_point) const;
-	_FORCE_INLINE_ Vector3 get_support(const Vector3 &p_normal) const;
+	_FORCE_INLINE_ Vector3 get_support(const Vector3 &p_direction) const;
 
 	Vector3 get_longest_axis() const;
 	int get_longest_axis_index() const;
@@ -208,15 +213,18 @@ inline bool AABB::encloses(const AABB &p_aabb) const {
 			(src_max.z >= dst_max.z));
 }
 
-Vector3 AABB::get_support(const Vector3 &p_normal) const {
-	Vector3 half_extents = size * 0.5f;
-	Vector3 ofs = position + half_extents;
-
-	return Vector3(
-				   (p_normal.x > 0) ? half_extents.x : -half_extents.x,
-				   (p_normal.y > 0) ? half_extents.y : -half_extents.y,
-				   (p_normal.z > 0) ? half_extents.z : -half_extents.z) +
-			ofs;
+Vector3 AABB::get_support(const Vector3 &p_direction) const {
+	Vector3 support = position;
+	if (p_direction.x > 0.0f) {
+		support.x += size.x;
+	}
+	if (p_direction.y > 0.0f) {
+		support.y += size.y;
+	}
+	if (p_direction.z > 0.0f) {
+		support.z += size.z;
+	}
+	return support;
 }
 
 Vector3 AABB::get_endpoint(int p_point) const {
@@ -402,7 +410,7 @@ inline real_t AABB::get_shortest_axis_size() const {
 	return max_size;
 }
 
-bool AABB::smits_intersect_ray(const Vector3 &p_from, const Vector3 &p_dir, real_t t0, real_t t1) const {
+bool AABB::smits_intersect_ray(const Vector3 &p_from, const Vector3 &p_dir, real_t p_t0, real_t p_t1) const {
 #ifdef MATH_CHECKS
 	if (unlikely(size.x < 0 || size.y < 0 || size.z < 0)) {
 		ERR_PRINT("AABB size is negative, this is not supported. Use AABB.abs() to get an AABB with a positive size.");
@@ -453,7 +461,7 @@ bool AABB::smits_intersect_ray(const Vector3 &p_from, const Vector3 &p_dir, real
 	if (tzmax < tmax) {
 		tmax = tzmax;
 	}
-	return ((tmin < t1) && (tmax > t0));
+	return ((tmin < p_t1) && (tmax > p_t0));
 }
 
 void AABB::grow_by(real_t p_amount) {

include/godot_cpp/variant/basis.hpp

@@ -43,11 +43,11 @@ struct [[nodiscard]] Basis {
 		Vector3(0, 0, 1)
 	};
 
-	_FORCE_INLINE_ const Vector3 &operator[](int axis) const {
-		return rows[axis];
+	_FORCE_INLINE_ const Vector3 &operator[](int p_row) const {
+		return rows[p_row];
 	}
-	_FORCE_INLINE_ Vector3 &operator[](int axis) {
-		return rows[axis];
+	_FORCE_INLINE_ Vector3 &operator[](int p_row) {
+		return rows[p_row];
 	}
 
 	void invert();
@@ -58,21 +58,19 @@ struct [[nodiscard]] Basis {
 
 	_FORCE_INLINE_ real_t determinant() const;
 
-	void from_z(const Vector3 &p_z);
-
 	void rotate(const Vector3 &p_axis, real_t p_angle);
 	Basis rotated(const Vector3 &p_axis, real_t p_angle) const;
 
 	void rotate_local(const Vector3 &p_axis, real_t p_angle);
 	Basis rotated_local(const Vector3 &p_axis, real_t p_angle) const;
 
-	void rotate(const Vector3 &p_euler, EulerOrder p_order = EULER_ORDER_YXZ);
-	Basis rotated(const Vector3 &p_euler, EulerOrder p_order = EULER_ORDER_YXZ) const;
+	void rotate(const Vector3 &p_euler, EulerOrder p_order = EulerOrder::EULER_ORDER_YXZ);
+	Basis rotated(const Vector3 &p_euler, EulerOrder p_order = EulerOrder::EULER_ORDER_YXZ) const;
 
 	void rotate(const Quaternion &p_quaternion);
 	Basis rotated(const Quaternion &p_quaternion) const;
 
-	Vector3 get_euler_normalized(EulerOrder p_order = EULER_ORDER_YXZ) const;
+	Vector3 get_euler_normalized(EulerOrder p_order = EulerOrder::EULER_ORDER_YXZ) const;
 	void get_rotation_axis_angle(Vector3 &p_axis, real_t &p_angle) const;
 	void get_rotation_axis_angle_local(Vector3 &p_axis, real_t &p_angle) const;
 	Quaternion get_rotation_quaternion() const;
@@ -81,9 +79,9 @@ struct [[nodiscard]] Basis {
 
 	Vector3 rotref_posscale_decomposition(Basis &rotref) const;
 
-	Vector3 get_euler(EulerOrder p_order = EULER_ORDER_YXZ) const;
-	void set_euler(const Vector3 &p_euler, EulerOrder p_order = EULER_ORDER_YXZ);
-	static Basis from_euler(const Vector3 &p_euler, EulerOrder p_order = EULER_ORDER_YXZ) {
+	Vector3 get_euler(EulerOrder p_order = EulerOrder::EULER_ORDER_YXZ) const;
+	void set_euler(const Vector3 &p_euler, EulerOrder p_order = EulerOrder::EULER_ORDER_YXZ);
+	static Basis from_euler(const Vector3 &p_euler, EulerOrder p_order = EulerOrder::EULER_ORDER_YXZ) {
 		Basis b;
 		b.set_euler(p_euler, p_order);
 		return b;
@@ -103,27 +101,25 @@ struct [[nodiscard]] Basis {
 
 	void scale_orthogonal(const Vector3 &p_scale);
 	Basis scaled_orthogonal(const Vector3 &p_scale) const;
-
-	void make_scale_uniform();
-	float get_uniform_scale() const;
+	real_t get_uniform_scale() const;
 
 	Vector3 get_scale() const;
 	Vector3 get_scale_abs() const;
-	Vector3 get_scale_local() const;
+	Vector3 get_scale_global() const;
 
 	void set_axis_angle_scale(const Vector3 &p_axis, real_t p_angle, const Vector3 &p_scale);
-	void set_euler_scale(const Vector3 &p_euler, const Vector3 &p_scale, EulerOrder p_order = EULER_ORDER_YXZ);
+	void set_euler_scale(const Vector3 &p_euler, const Vector3 &p_scale, EulerOrder p_order = EulerOrder::EULER_ORDER_YXZ);
 	void set_quaternion_scale(const Quaternion &p_quaternion, const Vector3 &p_scale);
 
 	// transposed dot products
-	_FORCE_INLINE_ real_t tdotx(const Vector3 &v) const {
-		return rows[0][0] * v[0] + rows[1][0] * v[1] + rows[2][0] * v[2];
+	_FORCE_INLINE_ real_t tdotx(const Vector3 &p_v) const {
+		return rows[0][0] * p_v[0] + rows[1][0] * p_v[1] + rows[2][0] * p_v[2];
 	}
-	_FORCE_INLINE_ real_t tdoty(const Vector3 &v) const {
-		return rows[0][1] * v[0] + rows[1][1] * v[1] + rows[2][1] * v[2];
+	_FORCE_INLINE_ real_t tdoty(const Vector3 &p_v) const {
+		return rows[0][1] * p_v[0] + rows[1][1] * p_v[1] + rows[2][1] * p_v[2];
 	}
-	_FORCE_INLINE_ real_t tdotz(const Vector3 &v) const {
-		return rows[0][2] * v[0] + rows[1][2] * v[1] + rows[2][2] * v[2];
+	_FORCE_INLINE_ real_t tdotz(const Vector3 &p_v) const {
+		return rows[0][2] * p_v[0] + rows[1][2] * p_v[1] + rows[2][2] * p_v[2];
 	}
 
 	bool is_equal_approx(const Basis &p_basis) const;
@@ -140,31 +136,35 @@ struct [[nodiscard]] Basis {
 	_FORCE_INLINE_ Basis operator+(const Basis &p_matrix) const;
 	_FORCE_INLINE_ void operator-=(const Basis &p_matrix);
 	_FORCE_INLINE_ Basis operator-(const Basis &p_matrix) const;
-	_FORCE_INLINE_ void operator*=(const real_t p_val);
-	_FORCE_INLINE_ Basis operator*(const real_t p_val) const;
+	_FORCE_INLINE_ void operator*=(real_t p_val);
+	_FORCE_INLINE_ Basis operator*(real_t p_val) const;
+	_FORCE_INLINE_ void operator/=(real_t p_val);
+	_FORCE_INLINE_ Basis operator/(real_t p_val) const;
 
 	bool is_orthogonal() const;
+	bool is_orthonormal() const;
+	bool is_conformal() const;
 	bool is_diagonal() const;
 	bool is_rotation() const;
 
-	Basis lerp(const Basis &p_to, const real_t &p_weight) const;
-	Basis slerp(const Basis &p_to, const real_t &p_weight) const;
+	Basis lerp(const Basis &p_to, real_t p_weight) const;
+	Basis slerp(const Basis &p_to, real_t p_weight) const;
 	void rotate_sh(real_t *p_values);
 
 	operator String() const;
 
 	/* create / set */
 
-	_FORCE_INLINE_ void set(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {
-		rows[0][0] = xx;
-		rows[0][1] = xy;
-		rows[0][2] = xz;
-		rows[1][0] = yx;
-		rows[1][1] = yy;
-		rows[1][2] = yz;
-		rows[2][0] = zx;
-		rows[2][1] = zy;
-		rows[2][2] = zz;
+	_FORCE_INLINE_ void set(real_t p_xx, real_t p_xy, real_t p_xz, real_t p_yx, real_t p_yy, real_t p_yz, real_t p_zx, real_t p_zy, real_t p_zz) {
+		rows[0][0] = p_xx;
+		rows[0][1] = p_xy;
+		rows[0][2] = p_xz;
+		rows[1][0] = p_yx;
+		rows[1][1] = p_yy;
+		rows[1][2] = p_yz;
+		rows[2][0] = p_zx;
+		rows[2][1] = p_zy;
+		rows[2][2] = p_zz;
 	}
 	_FORCE_INLINE_ void set_columns(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z) {
 		set_column(0, p_x);
@@ -194,20 +194,20 @@ struct [[nodiscard]] Basis {
 		rows[2].zero();
 	}
 
-	_FORCE_INLINE_ Basis transpose_xform(const Basis &m) const {
+	_FORCE_INLINE_ Basis transpose_xform(const Basis &p_m) const {
 		return Basis(
-				rows[0].x * m[0].x + rows[1].x * m[1].x + rows[2].x * m[2].x,
-				rows[0].x * m[0].y + rows[1].x * m[1].y + rows[2].x * m[2].y,
-				rows[0].x * m[0].z + rows[1].x * m[1].z + rows[2].x * m[2].z,
-				rows[0].y * m[0].x + rows[1].y * m[1].x + rows[2].y * m[2].x,
-				rows[0].y * m[0].y + rows[1].y * m[1].y + rows[2].y * m[2].y,
-				rows[0].y * m[0].z + rows[1].y * m[1].z + rows[2].y * m[2].z,
-				rows[0].z * m[0].x + rows[1].z * m[1].x + rows[2].z * m[2].x,
-				rows[0].z * m[0].y + rows[1].z * m[1].y + rows[2].z * m[2].y,
-				rows[0].z * m[0].z + rows[1].z * m[1].z + rows[2].z * m[2].z);
+				rows[0].x * p_m[0].x + rows[1].x * p_m[1].x + rows[2].x * p_m[2].x,
+				rows[0].x * p_m[0].y + rows[1].x * p_m[1].y + rows[2].x * p_m[2].y,
+				rows[0].x * p_m[0].z + rows[1].x * p_m[1].z + rows[2].x * p_m[2].z,
+				rows[0].y * p_m[0].x + rows[1].y * p_m[1].x + rows[2].y * p_m[2].x,
+				rows[0].y * p_m[0].y + rows[1].y * p_m[1].y + rows[2].y * p_m[2].y,
+				rows[0].y * p_m[0].z + rows[1].y * p_m[1].z + rows[2].y * p_m[2].z,
+				rows[0].z * p_m[0].x + rows[1].z * p_m[1].x + rows[2].z * p_m[2].x,
+				rows[0].z * p_m[0].y + rows[1].z * p_m[1].y + rows[2].z * p_m[2].y,
+				rows[0].z * p_m[0].z + rows[1].z * p_m[1].z + rows[2].z * p_m[2].z);
 	}
-	Basis(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {
-		set(xx, xy, xz, yx, yy, yz, zx, zy, zz);
+	Basis(real_t p_xx, real_t p_xy, real_t p_xz, real_t p_yx, real_t p_yy, real_t p_yz, real_t p_zx, real_t p_zy, real_t p_zz) {
+		set(p_xx, p_xy, p_xz, p_yx, p_yy, p_yz, p_zx, p_zy, p_zz);
 	}
 
 	void orthonormalize();
@@ -281,18 +281,30 @@ _FORCE_INLINE_ Basis Basis::operator-(const Basis &p_matrix) const {
 	return ret;
 }
 
-_FORCE_INLINE_ void Basis::operator*=(const real_t p_val) {
+_FORCE_INLINE_ void Basis::operator*=(real_t p_val) {
 	rows[0] *= p_val;
 	rows[1] *= p_val;
 	rows[2] *= p_val;
 }
 
-_FORCE_INLINE_ Basis Basis::operator*(const real_t p_val) const {
+_FORCE_INLINE_ Basis Basis::operator*(real_t p_val) const {
 	Basis ret(*this);
 	ret *= p_val;
 	return ret;
 }
 
+_FORCE_INLINE_ void Basis::operator/=(real_t p_val) {
+	rows[0] /= p_val;
+	rows[1] /= p_val;
+	rows[2] /= p_val;
+}
+
+_FORCE_INLINE_ Basis Basis::operator/(real_t p_val) const {
+	Basis ret(*this);
+	ret /= p_val;
+	return ret;
+}
+
 Vector3 Basis::xform(const Vector3 &p_vector) const {
 	return Vector3(
 			rows[0].dot(p_vector),

include/godot_cpp/variant/char_range.inc.hpp

@@ -0,0 +1,3631 @@
+/**************************************************************************/
+/*  char_range.inc.hpp                                                    */
+/**************************************************************************/
+/*                         This file is part of:                          */
+/*                             GODOT ENGINE                               */
+/*                        https://godotengine.org                         */
+/**************************************************************************/
+/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
+/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur.                  */
+/*                                                                        */
+/* Permission is hereby granted, free of charge, to any person obtaining  */
+/* a copy of this software and associated documentation files (the        */
+/* "Software"), to deal in the Software without restriction, including    */
+/* without limitation the rights to use, copy, modify, merge, publish,    */
+/* distribute, sublicense, and/or sell copies of the Software, and to     */
+/* permit persons to whom the Software is furnished to do so, subject to  */
+/* the following conditions:                                              */
+/*                                                                        */
+/* The above copyright notice and this permission notice shall be         */
+/* included in all copies or substantial portions of the Software.        */
+/*                                                                        */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,        */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF     */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. */
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY   */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,   */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE      */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                 */
+/**************************************************************************/
+
+#pragma once
+
+// Unicode Derived Core Properties
+// Source: https://www.unicode.org/Public/16.0.0/ucd/DerivedCoreProperties.txt
+
+namespace godot {
+
+struct CharRange {
+	char32_t start;
+	char32_t end;
+};
+
+constexpr inline CharRange xid_start[] = {
+	{ 0x41, 0x5a },
+	{ 0x5f, 0x5f }, // Underscore technically isn't in XID_Start, but for our purposes it's included.
+	{ 0x61, 0x7a },
+	{ 0xaa, 0xaa },
+	{ 0xb5, 0xb5 },
+	{ 0xba, 0xba },
+	{ 0xc0, 0xd6 },
+	{ 0xd8, 0xf6 },
+	{ 0xf8, 0x2c1 },
+	{ 0x2c6, 0x2d1 },
+	{ 0x2e0, 0x2e4 },
+	{ 0x2ec, 0x2ec },
+	{ 0x2ee, 0x2ee },
+	{ 0x370, 0x374 },
+	{ 0x376, 0x377 },
+	{ 0x37b, 0x37d },
+	{ 0x37f, 0x37f },
+	{ 0x386, 0x386 },
+	{ 0x388, 0x38a },
+	{ 0x38c, 0x38c },
+	{ 0x38e, 0x3a1 },
+	{ 0x3a3, 0x3f5 },
+	{ 0x3f7, 0x481 },
+	{ 0x48a, 0x52f },
+	{ 0x531, 0x556 },
+	{ 0x559, 0x559 },
+	{ 0x560, 0x588 },
+	{ 0x5d0, 0x5ea },
+	{ 0x5ef, 0x5f2 },
+	{ 0x620, 0x64a },
+	{ 0x66e, 0x66f },
+	{ 0x671, 0x6d3 },
+	{ 0x6d5, 0x6d5 },
+	{ 0x6e5, 0x6e6 },
+	{ 0x6ee, 0x6ef },
+	{ 0x6fa, 0x6fc },
+	{ 0x6ff, 0x6ff },
+	{ 0x710, 0x710 },
+	{ 0x712, 0x72f },
+	{ 0x74d, 0x7a5 },
+	{ 0x7b1, 0x7b1 },
+	{ 0x7ca, 0x7ea },
+	{ 0x7f4, 0x7f5 },
+	{ 0x7fa, 0x7fa },
+	{ 0x800, 0x815 },
+	{ 0x81a, 0x81a },
+	{ 0x824, 0x824 },
+	{ 0x828, 0x828 },
+	{ 0x840, 0x858 },
+	{ 0x860, 0x86a },
+	{ 0x870, 0x887 },
+	{ 0x889, 0x88e },
+	{ 0x8a0, 0x8c9 },
+	{ 0x904, 0x939 },
+	{ 0x93d, 0x93d },
+	{ 0x950, 0x950 },
+	{ 0x958, 0x961 },
+	{ 0x971, 0x980 },
+	{ 0x985, 0x98c },
+	{ 0x98f, 0x990 },
+	{ 0x993, 0x9a8 },
+	{ 0x9aa, 0x9b0 },
+	{ 0x9b2, 0x9b2 },
+	{ 0x9b6, 0x9b9 },
+	{ 0x9bd, 0x9bd },
+	{ 0x9ce, 0x9ce },
+	{ 0x9dc, 0x9dd },
+	{ 0x9df, 0x9e1 },
+	{ 0x9f0, 0x9f1 },
+	{ 0x9fc, 0x9fc },
+	{ 0xa05, 0xa0a },
+	{ 0xa0f, 0xa10 },
+	{ 0xa13, 0xa28 },
+	{ 0xa2a, 0xa30 },
+	{ 0xa32, 0xa33 },
+	{ 0xa35, 0xa36 },
+	{ 0xa38, 0xa39 },
+	{ 0xa59, 0xa5c },
+	{ 0xa5e, 0xa5e },
+	{ 0xa72, 0xa74 },
+	{ 0xa85, 0xa8d },
+	{ 0xa8f, 0xa91 },
+	{ 0xa93, 0xaa8 },
+	{ 0xaaa, 0xab0 },
+	{ 0xab2, 0xab3 },
+	{ 0xab5, 0xab9 },
+	{ 0xabd, 0xabd },
+	{ 0xad0, 0xad0 },
+	{ 0xae0, 0xae1 },
+	{ 0xaf9, 0xaf9 },
+	{ 0xb05, 0xb0c },
+	{ 0xb0f, 0xb10 },
+	{ 0xb13, 0xb28 },
+	{ 0xb2a, 0xb30 },
+	{ 0xb32, 0xb33 },
+	{ 0xb35, 0xb39 },
+	{ 0xb3d, 0xb3d },
+	{ 0xb5c, 0xb5d },
+	{ 0xb5f, 0xb61 },
+	{ 0xb71, 0xb71 },
+	{ 0xb83, 0xb83 },
+	{ 0xb85, 0xb8a },
+	{ 0xb8e, 0xb90 },
+	{ 0xb92, 0xb95 },
+	{ 0xb99, 0xb9a },
+	{ 0xb9c, 0xb9c },
+	{ 0xb9e, 0xb9f },
+	{ 0xba3, 0xba4 },
+	{ 0xba8, 0xbaa },
+	{ 0xbae, 0xbb9 },
+	{ 0xbd0, 0xbd0 },
+	{ 0xc05, 0xc0c },
+	{ 0xc0e, 0xc10 },
+	{ 0xc12, 0xc28 },
+	{ 0xc2a, 0xc39 },
+	{ 0xc3d, 0xc3d },
+	{ 0xc58, 0xc5a },
+	{ 0xc5d, 0xc5d },
+	{ 0xc60, 0xc61 },
+	{ 0xc80, 0xc80 },
+	{ 0xc85, 0xc8c },
+	{ 0xc8e, 0xc90 },
+	{ 0xc92, 0xca8 },
+	{ 0xcaa, 0xcb3 },
+	{ 0xcb5, 0xcb9 },
+	{ 0xcbd, 0xcbd },
+	{ 0xcdd, 0xcde },
+	{ 0xce0, 0xce1 },
+	{ 0xcf1, 0xcf2 },
+	{ 0xd04, 0xd0c },
+	{ 0xd0e, 0xd10 },
+	{ 0xd12, 0xd3a },
+	{ 0xd3d, 0xd3d },
+	{ 0xd4e, 0xd4e },
+	{ 0xd54, 0xd56 },
+	{ 0xd5f, 0xd61 },
+	{ 0xd7a, 0xd7f },
+	{ 0xd85, 0xd96 },
+	{ 0xd9a, 0xdb1 },
+	{ 0xdb3, 0xdbb },
+	{ 0xdbd, 0xdbd },
+	{ 0xdc0, 0xdc6 },
+	{ 0xe01, 0xe30 },
+	{ 0xe32, 0xe32 },
+	{ 0xe40, 0xe46 },
+	{ 0xe81, 0xe82 },
+	{ 0xe84, 0xe84 },
+	{ 0xe86, 0xe8a },
+	{ 0xe8c, 0xea3 },
+	{ 0xea5, 0xea5 },
+	{ 0xea7, 0xeb0 },
+	{ 0xeb2, 0xeb2 },
+	{ 0xebd, 0xebd },
+	{ 0xec0, 0xec4 },
+	{ 0xec6, 0xec6 },
+	{ 0xedc, 0xedf },
+	{ 0xf00, 0xf00 },
+	{ 0xf40, 0xf47 },
+	{ 0xf49, 0xf6c },
+	{ 0xf88, 0xf8c },
+	{ 0x1000, 0x102a },
+	{ 0x103f, 0x103f },
+	{ 0x1050, 0x1055 },
+	{ 0x105a, 0x105d },
+	{ 0x1061, 0x1061 },
+	{ 0x1065, 0x1066 },
+	{ 0x106e, 0x1070 },
+	{ 0x1075, 0x1081 },
+	{ 0x108e, 0x108e },
+	{ 0x10a0, 0x10c5 },
+	{ 0x10c7, 0x10c7 },
+	{ 0x10cd, 0x10cd },
+	{ 0x10d0, 0x10fa },
+	{ 0x10fc, 0x1248 },
+	{ 0x124a, 0x124d },
+	{ 0x1250, 0x1256 },
+	{ 0x1258, 0x1258 },
+	{ 0x125a, 0x125d },
+	{ 0x1260, 0x1288 },
+	{ 0x128a, 0x128d },
+	{ 0x1290, 0x12b0 },
+	{ 0x12b2, 0x12b5 },
+	{ 0x12b8, 0x12be },
+	{ 0x12c0, 0x12c0 },
+	{ 0x12c2, 0x12c5 },
+	{ 0x12c8, 0x12d6 },
+	{ 0x12d8, 0x1310 },
+	{ 0x1312, 0x1315 },
+	{ 0x1318, 0x135a },
+	{ 0x1380, 0x138f },
+	{ 0x13a0, 0x13f5 },
+	{ 0x13f8, 0x13fd },
+	{ 0x1401, 0x166c },
+	{ 0x166f, 0x167f },
+	{ 0x1681, 0x169a },
+	{ 0x16a0, 0x16ea },
+	{ 0x16ee, 0x16f8 },
+	{ 0x1700, 0x1711 },
+	{ 0x171f, 0x1731 },
+	{ 0x1740, 0x1751 },
+	{ 0x1760, 0x176c },
+	{ 0x176e, 0x1770 },
+	{ 0x1780, 0x17b3 },
+	{ 0x17d7, 0x17d7 },
+	{ 0x17dc, 0x17dc },
+	{ 0x1820, 0x1878 },
+	{ 0x1880, 0x18a8 },
+	{ 0x18aa, 0x18aa },
+	{ 0x18b0, 0x18f5 },
+	{ 0x1900, 0x191e },
+	{ 0x1950, 0x196d },
+	{ 0x1970, 0x1974 },
+	{ 0x1980, 0x19ab },
+	{ 0x19b0, 0x19c9 },
+	{ 0x1a00, 0x1a16 },
+	{ 0x1a20, 0x1a54 },
+	{ 0x1aa7, 0x1aa7 },
+	{ 0x1b05, 0x1b33 },
+	{ 0x1b45, 0x1b4c },
+	{ 0x1b83, 0x1ba0 },
+	{ 0x1bae, 0x1baf },
+	{ 0x1bba, 0x1be5 },
+	{ 0x1c00, 0x1c23 },
+	{ 0x1c4d, 0x1c4f },
+	{ 0x1c5a, 0x1c7d },
+	{ 0x1c80, 0x1c8a },
+	{ 0x1c90, 0x1cba },
+	{ 0x1cbd, 0x1cbf },
+	{ 0x1ce9, 0x1cec },
+	{ 0x1cee, 0x1cf3 },
+	{ 0x1cf5, 0x1cf6 },
+	{ 0x1cfa, 0x1cfa },
+	{ 0x1d00, 0x1dbf },
+	{ 0x1e00, 0x1f15 },
+	{ 0x1f18, 0x1f1d },
+	{ 0x1f20, 0x1f45 },
+	{ 0x1f48, 0x1f4d },
+	{ 0x1f50, 0x1f57 },
+	{ 0x1f59, 0x1f59 },
+	{ 0x1f5b, 0x1f5b },
+	{ 0x1f5d, 0x1f5d },
+	{ 0x1f5f, 0x1f7d },
+	{ 0x1f80, 0x1fb4 },
+	{ 0x1fb6, 0x1fbc },
+	{ 0x1fbe, 0x1fbe },
+	{ 0x1fc2, 0x1fc4 },
+	{ 0x1fc6, 0x1fcc },
+	{ 0x1fd0, 0x1fd3 },
+	{ 0x1fd6, 0x1fdb },
+	{ 0x1fe0, 0x1fec },
+	{ 0x1ff2, 0x1ff4 },
+	{ 0x1ff6, 0x1ffc },
+	{ 0x2071, 0x2071 },
+	{ 0x207f, 0x207f },
+	{ 0x2090, 0x209c },
+	{ 0x2102, 0x2102 },
+	{ 0x2107, 0x2107 },
+	{ 0x210a, 0x2113 },
+	{ 0x2115, 0x2115 },
+	{ 0x2118, 0x211d },
+	{ 0x2124, 0x2124 },
+	{ 0x2126, 0x2126 },
+	{ 0x2128, 0x2128 },
+	{ 0x212a, 0x2139 },
+	{ 0x213c, 0x213f },
+	{ 0x2145, 0x2149 },
+	{ 0x214e, 0x214e },
+	{ 0x2160, 0x2188 },
+	{ 0x2c00, 0x2ce4 },
+	{ 0x2ceb, 0x2cee },
+	{ 0x2cf2, 0x2cf3 },
+	{ 0x2d00, 0x2d25 },
+	{ 0x2d27, 0x2d27 },
+	{ 0x2d2d, 0x2d2d },
+	{ 0x2d30, 0x2d67 },
+	{ 0x2d6f, 0x2d6f },
+	{ 0x2d80, 0x2d96 },
+	{ 0x2da0, 0x2da6 },
+	{ 0x2da8, 0x2dae },
+	{ 0x2db0, 0x2db6 },
+	{ 0x2db8, 0x2dbe },
+	{ 0x2dc0, 0x2dc6 },
+	{ 0x2dc8, 0x2dce },
+	{ 0x2dd0, 0x2dd6 },
+	{ 0x2dd8, 0x2dde },
+	{ 0x3005, 0x3007 },
+	{ 0x3021, 0x3029 },
+	{ 0x3031, 0x3035 },
+	{ 0x3038, 0x303c },
+	{ 0x3041, 0x3096 },
+	{ 0x309d, 0x309f },
+	{ 0x30a1, 0x30fa },
+	{ 0x30fc, 0x30ff },
+	{ 0x3105, 0x312f },
+	{ 0x3131, 0x318e },
+	{ 0x31a0, 0x31bf },
+	{ 0x31f0, 0x31ff },
+	{ 0x3400, 0x4dbf },
+	{ 0x4e00, 0xa48c },
+	{ 0xa4d0, 0xa4fd },
+	{ 0xa500, 0xa60c },
+	{ 0xa610, 0xa61f },
+	{ 0xa62a, 0xa62b },
+	{ 0xa640, 0xa66e },
+	{ 0xa67f, 0xa69d },
+	{ 0xa6a0, 0xa6ef },
+	{ 0xa717, 0xa71f },
+	{ 0xa722, 0xa788 },
+	{ 0xa78b, 0xa7cd },
+	{ 0xa7d0, 0xa7d1 },
+	{ 0xa7d3, 0xa7d3 },
+	{ 0xa7d5, 0xa7dc },
+	{ 0xa7f2, 0xa801 },
+	{ 0xa803, 0xa805 },
+	{ 0xa807, 0xa80a },
+	{ 0xa80c, 0xa822 },
+	{ 0xa840, 0xa873 },
+	{ 0xa882, 0xa8b3 },
+	{ 0xa8f2, 0xa8f7 },
+	{ 0xa8fb, 0xa8fb },
+	{ 0xa8fd, 0xa8fe },
+	{ 0xa90a, 0xa925 },
+	{ 0xa930, 0xa946 },
+	{ 0xa960, 0xa97c },
+	{ 0xa984, 0xa9b2 },
+	{ 0xa9cf, 0xa9cf },
+	{ 0xa9e0, 0xa9e4 },
+	{ 0xa9e6, 0xa9ef },
+	{ 0xa9fa, 0xa9fe },
+	{ 0xaa00, 0xaa28 },
+	{ 0xaa40, 0xaa42 },
+	{ 0xaa44, 0xaa4b },
+	{ 0xaa60, 0xaa76 },
+	{ 0xaa7a, 0xaa7a },
+	{ 0xaa7e, 0xaaaf },
+	{ 0xaab1, 0xaab1 },
+	{ 0xaab5, 0xaab6 },
+	{ 0xaab9, 0xaabd },
+	{ 0xaac0, 0xaac0 },
+	{ 0xaac2, 0xaac2 },
+	{ 0xaadb, 0xaadd },
+	{ 0xaae0, 0xaaea },
+	{ 0xaaf2, 0xaaf4 },
+	{ 0xab01, 0xab06 },
+	{ 0xab09, 0xab0e },
+	{ 0xab11, 0xab16 },
+	{ 0xab20, 0xab26 },
+	{ 0xab28, 0xab2e },
+	{ 0xab30, 0xab5a },
+	{ 0xab5c, 0xab69 },
+	{ 0xab70, 0xabe2 },
+	{ 0xac00, 0xd7a3 },
+	{ 0xd7b0, 0xd7c6 },
+	{ 0xd7cb, 0xd7fb },
+	{ 0xf900, 0xfa6d },
+	{ 0xfa70, 0xfad9 },
+	{ 0xfb00, 0xfb06 },
+	{ 0xfb13, 0xfb17 },
+	{ 0xfb1d, 0xfb1d },
+	{ 0xfb1f, 0xfb28 },
+	{ 0xfb2a, 0xfb36 },
+	{ 0xfb38, 0xfb3c },
+	{ 0xfb3e, 0xfb3e },
+	{ 0xfb40, 0xfb41 },
+	{ 0xfb43, 0xfb44 },
+	{ 0xfb46, 0xfbb1 },
+	{ 0xfbd3, 0xfc5d },
+	{ 0xfc64, 0xfd3d },
+	{ 0xfd50, 0xfd8f },
+	{ 0xfd92, 0xfdc7 },
+	{ 0xfdf0, 0xfdf9 },
+	{ 0xfe71, 0xfe71 },
+	{ 0xfe73, 0xfe73 },
+	{ 0xfe77, 0xfe77 },
+	{ 0xfe79, 0xfe79 },
+	{ 0xfe7b, 0xfe7b },
+	{ 0xfe7d, 0xfe7d },
+	{ 0xfe7f, 0xfefc },
+	{ 0xff21, 0xff3a },
+	{ 0xff41, 0xff5a },
+	{ 0xff66, 0xff9d },
+	{ 0xffa0, 0xffbe },
+	{ 0xffc2, 0xffc7 },
+	{ 0xffca, 0xffcf },
+	{ 0xffd2, 0xffd7 },
+	{ 0xffda, 0xffdc },
+	{ 0x10000, 0x1000b },
+	{ 0x1000d, 0x10026 },
+	{ 0x10028, 0x1003a },
+	{ 0x1003c, 0x1003d },
+	{ 0x1003f, 0x1004d },
+	{ 0x10050, 0x1005d },
+	{ 0x10080, 0x100fa },
+	{ 0x10140, 0x10174 },
+	{ 0x10280, 0x1029c },
+	{ 0x102a0, 0x102d0 },
+	{ 0x10300, 0x1031f },
+	{ 0x1032d, 0x1034a },
+	{ 0x10350, 0x10375 },
+	{ 0x10380, 0x1039d },
+	{ 0x103a0, 0x103c3 },
+	{ 0x103c8, 0x103cf },
+	{ 0x103d1, 0x103d5 },
+	{ 0x10400, 0x1049d },
+	{ 0x104b0, 0x104d3 },
+	{ 0x104d8, 0x104fb },
+	{ 0x10500, 0x10527 },
+	{ 0x10530, 0x10563 },
+	{ 0x10570, 0x1057a },
+	{ 0x1057c, 0x1058a },
+	{ 0x1058c, 0x10592 },
+	{ 0x10594, 0x10595 },
+	{ 0x10597, 0x105a1 },
+	{ 0x105a3, 0x105b1 },
+	{ 0x105b3, 0x105b9 },
+	{ 0x105bb, 0x105bc },
+	{ 0x105c0, 0x105f3 },
+	{ 0x10600, 0x10736 },
+	{ 0x10740, 0x10755 },
+	{ 0x10760, 0x10767 },
+	{ 0x10780, 0x10785 },
+	{ 0x10787, 0x107b0 },
+	{ 0x107b2, 0x107ba },
+	{ 0x10800, 0x10805 },
+	{ 0x10808, 0x10808 },
+	{ 0x1080a, 0x10835 },
+	{ 0x10837, 0x10838 },
+	{ 0x1083c, 0x1083c },
+	{ 0x1083f, 0x10855 },
+	{ 0x10860, 0x10876 },
+	{ 0x10880, 0x1089e },
+	{ 0x108e0, 0x108f2 },
+	{ 0x108f4, 0x108f5 },
+	{ 0x10900, 0x10915 },
+	{ 0x10920, 0x10939 },
+	{ 0x10980, 0x109b7 },
+	{ 0x109be, 0x109bf },
+	{ 0x10a00, 0x10a00 },
+	{ 0x10a10, 0x10a13 },
+	{ 0x10a15, 0x10a17 },
+	{ 0x10a19, 0x10a35 },
+	{ 0x10a60, 0x10a7c },
+	{ 0x10a80, 0x10a9c },
+	{ 0x10ac0, 0x10ac7 },
+	{ 0x10ac9, 0x10ae4 },
+	{ 0x10b00, 0x10b35 },
+	{ 0x10b40, 0x10b55 },
+	{ 0x10b60, 0x10b72 },
+	{ 0x10b80, 0x10b91 },
+	{ 0x10c00, 0x10c48 },
+	{ 0x10c80, 0x10cb2 },
+	{ 0x10cc0, 0x10cf2 },
+	{ 0x10d00, 0x10d23 },
+	{ 0x10d4a, 0x10d65 },
+	{ 0x10d6f, 0x10d85 },
+	{ 0x10e80, 0x10ea9 },
+	{ 0x10eb0, 0x10eb1 },
+	{ 0x10ec2, 0x10ec4 },
+	{ 0x10f00, 0x10f1c },
+	{ 0x10f27, 0x10f27 },
+	{ 0x10f30, 0x10f45 },
+	{ 0x10f70, 0x10f81 },
+	{ 0x10fb0, 0x10fc4 },
+	{ 0x10fe0, 0x10ff6 },
+	{ 0x11003, 0x11037 },
+	{ 0x11071, 0x11072 },
+	{ 0x11075, 0x11075 },
+	{ 0x11083, 0x110af },
+	{ 0x110d0, 0x110e8 },
+	{ 0x11103, 0x11126 },
+	{ 0x11144, 0x11144 },
+	{ 0x11147, 0x11147 },
+	{ 0x11150, 0x11172 },
+	{ 0x11176, 0x11176 },
+	{ 0x11183, 0x111b2 },
+	{ 0x111c1, 0x111c4 },
+	{ 0x111da, 0x111da },
+	{ 0x111dc, 0x111dc },
+	{ 0x11200, 0x11211 },
+	{ 0x11213, 0x1122b },
+	{ 0x1123f, 0x11240 },
+	{ 0x11280, 0x11286 },
+	{ 0x11288, 0x11288 },
+	{ 0x1128a, 0x1128d },
+	{ 0x1128f, 0x1129d },
+	{ 0x1129f, 0x112a8 },
+	{ 0x112b0, 0x112de },
+	{ 0x11305, 0x1130c },
+	{ 0x1130f, 0x11310 },
+	{ 0x11313, 0x11328 },
+	{ 0x1132a, 0x11330 },
+	{ 0x11332, 0x11333 },
+	{ 0x11335, 0x11339 },
+	{ 0x1133d, 0x1133d },
+	{ 0x11350, 0x11350 },
+	{ 0x1135d, 0x11361 },
+	{ 0x11380, 0x11389 },
+	{ 0x1138b, 0x1138b },
+	{ 0x1138e, 0x1138e },
+	{ 0x11390, 0x113b5 },
+	{ 0x113b7, 0x113b7 },
+	{ 0x113d1, 0x113d1 },
+	{ 0x113d3, 0x113d3 },
+	{ 0x11400, 0x11434 },
+	{ 0x11447, 0x1144a },
+	{ 0x1145f, 0x11461 },
+	{ 0x11480, 0x114af },
+	{ 0x114c4, 0x114c5 },
+	{ 0x114c7, 0x114c7 },
+	{ 0x11580, 0x115ae },
+	{ 0x115d8, 0x115db },
+	{ 0x11600, 0x1162f },
+	{ 0x11644, 0x11644 },
+	{ 0x11680, 0x116aa },
+	{ 0x116b8, 0x116b8 },
+	{ 0x11700, 0x1171a },
+	{ 0x11740, 0x11746 },
+	{ 0x11800, 0x1182b },
+	{ 0x118a0, 0x118df },
+	{ 0x118ff, 0x11906 },
+	{ 0x11909, 0x11909 },
+	{ 0x1190c, 0x11913 },
+	{ 0x11915, 0x11916 },
+	{ 0x11918, 0x1192f },
+	{ 0x1193f, 0x1193f },
+	{ 0x11941, 0x11941 },
+	{ 0x119a0, 0x119a7 },
+	{ 0x119aa, 0x119d0 },
+	{ 0x119e1, 0x119e1 },
+	{ 0x119e3, 0x119e3 },
+	{ 0x11a00, 0x11a00 },
+	{ 0x11a0b, 0x11a32 },
+	{ 0x11a3a, 0x11a3a },
+	{ 0x11a50, 0x11a50 },
+	{ 0x11a5c, 0x11a89 },
+	{ 0x11a9d, 0x11a9d },
+	{ 0x11ab0, 0x11af8 },
+	{ 0x11bc0, 0x11be0 },
+	{ 0x11c00, 0x11c08 },
+	{ 0x11c0a, 0x11c2e },
+	{ 0x11c40, 0x11c40 },
+	{ 0x11c72, 0x11c8f },
+	{ 0x11d00, 0x11d06 },
+	{ 0x11d08, 0x11d09 },
+	{ 0x11d0b, 0x11d30 },
+	{ 0x11d46, 0x11d46 },
+	{ 0x11d60, 0x11d65 },
+	{ 0x11d67, 0x11d68 },
+	{ 0x11d6a, 0x11d89 },
+	{ 0x11d98, 0x11d98 },
+	{ 0x11ee0, 0x11ef2 },
+	{ 0x11f02, 0x11f02 },
+	{ 0x11f04, 0x11f10 },
+	{ 0x11f12, 0x11f33 },
+	{ 0x11fb0, 0x11fb0 },
+	{ 0x12000, 0x12399 },
+	{ 0x12400, 0x1246e },
+	{ 0x12480, 0x12543 },
+	{ 0x12f90, 0x12ff0 },
+	{ 0x13000, 0x1342f },
+	{ 0x13441, 0x13446 },
+	{ 0x13460, 0x143fa },
+	{ 0x14400, 0x14646 },
+	{ 0x16100, 0x1611d },
+	{ 0x16800, 0x16a38 },
+	{ 0x16a40, 0x16a5e },
+	{ 0x16a70, 0x16abe },
+	{ 0x16ad0, 0x16aed },
+	{ 0x16b00, 0x16b2f },
+	{ 0x16b40, 0x16b43 },
+	{ 0x16b63, 0x16b77 },
+	{ 0x16b7d, 0x16b8f },
+	{ 0x16d40, 0x16d6c },
+	{ 0x16e40, 0x16e7f },
+	{ 0x16f00, 0x16f4a },
+	{ 0x16f50, 0x16f50 },
+	{ 0x16f93, 0x16f9f },
+	{ 0x16fe0, 0x16fe1 },
+	{ 0x16fe3, 0x16fe3 },
+	{ 0x17000, 0x187f7 },
+	{ 0x18800, 0x18cd5 },
+	{ 0x18cff, 0x18d08 },
+	{ 0x1aff0, 0x1aff3 },
+	{ 0x1aff5, 0x1affb },
+	{ 0x1affd, 0x1affe },
+	{ 0x1b000, 0x1b122 },
+	{ 0x1b132, 0x1b132 },
+	{ 0x1b150, 0x1b152 },
+	{ 0x1b155, 0x1b155 },
+	{ 0x1b164, 0x1b167 },
+	{ 0x1b170, 0x1b2fb },
+	{ 0x1bc00, 0x1bc6a },
+	{ 0x1bc70, 0x1bc7c },
+	{ 0x1bc80, 0x1bc88 },
+	{ 0x1bc90, 0x1bc99 },
+	{ 0x1d400, 0x1d454 },
+	{ 0x1d456, 0x1d49c },
+	{ 0x1d49e, 0x1d49f },
+	{ 0x1d4a2, 0x1d4a2 },
+	{ 0x1d4a5, 0x1d4a6 },
+	{ 0x1d4a9, 0x1d4ac },
+	{ 0x1d4ae, 0x1d4b9 },
+	{ 0x1d4bb, 0x1d4bb },
+	{ 0x1d4bd, 0x1d4c3 },
+	{ 0x1d4c5, 0x1d505 },
+	{ 0x1d507, 0x1d50a },
+	{ 0x1d50d, 0x1d514 },
+	{ 0x1d516, 0x1d51c },
+	{ 0x1d51e, 0x1d539 },
+	{ 0x1d53b, 0x1d53e },
+	{ 0x1d540, 0x1d544 },
+	{ 0x1d546, 0x1d546 },
+	{ 0x1d54a, 0x1d550 },
+	{ 0x1d552, 0x1d6a5 },
+	{ 0x1d6a8, 0x1d6c0 },
+	{ 0x1d6c2, 0x1d6da },
+	{ 0x1d6dc, 0x1d6fa },
+	{ 0x1d6fc, 0x1d714 },
+	{ 0x1d716, 0x1d734 },
+	{ 0x1d736, 0x1d74e },
+	{ 0x1d750, 0x1d76e },
+	{ 0x1d770, 0x1d788 },
+	{ 0x1d78a, 0x1d7a8 },
+	{ 0x1d7aa, 0x1d7c2 },
+	{ 0x1d7c4, 0x1d7cb },
+	{ 0x1df00, 0x1df1e },
+	{ 0x1df25, 0x1df2a },
+	{ 0x1e030, 0x1e06d },
+	{ 0x1e100, 0x1e12c },
+	{ 0x1e137, 0x1e13d },
+	{ 0x1e14e, 0x1e14e },
+	{ 0x1e290, 0x1e2ad },
+	{ 0x1e2c0, 0x1e2eb },
+	{ 0x1e4d0, 0x1e4eb },
+	{ 0x1e5d0, 0x1e5ed },
+	{ 0x1e5f0, 0x1e5f0 },
+	{ 0x1e7e0, 0x1e7e6 },
+	{ 0x1e7e8, 0x1e7eb },
+	{ 0x1e7ed, 0x1e7ee },
+	{ 0x1e7f0, 0x1e7fe },
+	{ 0x1e800, 0x1e8c4 },
+	{ 0x1e900, 0x1e943 },
+	{ 0x1e94b, 0x1e94b },
+	{ 0x1ee00, 0x1ee03 },
+	{ 0x1ee05, 0x1ee1f },
+	{ 0x1ee21, 0x1ee22 },
+	{ 0x1ee24, 0x1ee24 },
+	{ 0x1ee27, 0x1ee27 },
+	{ 0x1ee29, 0x1ee32 },
+	{ 0x1ee34, 0x1ee37 },
+	{ 0x1ee39, 0x1ee39 },
+	{ 0x1ee3b, 0x1ee3b },
+	{ 0x1ee42, 0x1ee42 },
+	{ 0x1ee47, 0x1ee47 },
+	{ 0x1ee49, 0x1ee49 },
+	{ 0x1ee4b, 0x1ee4b },
+	{ 0x1ee4d, 0x1ee4f },
+	{ 0x1ee51, 0x1ee52 },
+	{ 0x1ee54, 0x1ee54 },
+	{ 0x1ee57, 0x1ee57 },
+	{ 0x1ee59, 0x1ee59 },
+	{ 0x1ee5b, 0x1ee5b },
+	{ 0x1ee5d, 0x1ee5d },
+	{ 0x1ee5f, 0x1ee5f },
+	{ 0x1ee61, 0x1ee62 },
+	{ 0x1ee64, 0x1ee64 },
+	{ 0x1ee67, 0x1ee6a },
+	{ 0x1ee6c, 0x1ee72 },
+	{ 0x1ee74, 0x1ee77 },
+	{ 0x1ee79, 0x1ee7c },
+	{ 0x1ee7e, 0x1ee7e },
+	{ 0x1ee80, 0x1ee89 },
+	{ 0x1ee8b, 0x1ee9b },
+	{ 0x1eea1, 0x1eea3 },
+	{ 0x1eea5, 0x1eea9 },
+	{ 0x1eeab, 0x1eebb },
+	{ 0x20000, 0x2a6df },
+	{ 0x2a700, 0x2b739 },
+	{ 0x2b740, 0x2b81d },
+	{ 0x2b820, 0x2cea1 },
+	{ 0x2ceb0, 0x2ebe0 },
+	{ 0x2ebf0, 0x2ee5d },
+	{ 0x2f800, 0x2fa1d },
+	{ 0x30000, 0x3134a },
+	{ 0x31350, 0x323af },
+};
+
+constexpr inline CharRange xid_continue[] = {
+	{ 0x30, 0x39 },
+	{ 0x41, 0x5a },
+	{ 0x5f, 0x5f },
+	{ 0x61, 0x7a },
+	{ 0xaa, 0xaa },
+	{ 0xb5, 0xb5 },
+	{ 0xb7, 0xb7 },
+	{ 0xba, 0xba },
+	{ 0xc0, 0xd6 },
+	{ 0xd8, 0xf6 },
+	{ 0xf8, 0x2c1 },
+	{ 0x2c6, 0x2d1 },
+	{ 0x2e0, 0x2e4 },
+	{ 0x2ec, 0x2ec },
+	{ 0x2ee, 0x2ee },
+	{ 0x300, 0x374 },
+	{ 0x376, 0x377 },
+	{ 0x37b, 0x37d },
+	{ 0x37f, 0x37f },
+	{ 0x386, 0x38a },
+	{ 0x38c, 0x38c },
+	{ 0x38e, 0x3a1 },
+	{ 0x3a3, 0x3f5 },
+	{ 0x3f7, 0x481 },
+	{ 0x483, 0x487 },
+	{ 0x48a, 0x52f },
+	{ 0x531, 0x556 },
+	{ 0x559, 0x559 },
+	{ 0x560, 0x588 },
+	{ 0x591, 0x5bd },
+	{ 0x5bf, 0x5bf },
+	{ 0x5c1, 0x5c2 },
+	{ 0x5c4, 0x5c5 },
+	{ 0x5c7, 0x5c7 },
+	{ 0x5d0, 0x5ea },
+	{ 0x5ef, 0x5f2 },
+	{ 0x610, 0x61a },
+	{ 0x620, 0x669 },
+	{ 0x66e, 0x6d3 },
+	{ 0x6d5, 0x6dc },
+	{ 0x6df, 0x6e8 },
+	{ 0x6ea, 0x6fc },
+	{ 0x6ff, 0x6ff },
+	{ 0x710, 0x74a },
+	{ 0x74d, 0x7b1 },
+	{ 0x7c0, 0x7f5 },
+	{ 0x7fa, 0x7fa },
+	{ 0x7fd, 0x7fd },
+	{ 0x800, 0x82d },
+	{ 0x840, 0x85b },
+	{ 0x860, 0x86a },
+	{ 0x870, 0x887 },
+	{ 0x889, 0x88e },
+	{ 0x897, 0x8e1 },
+	{ 0x8e3, 0x963 },
+	{ 0x966, 0x96f },
+	{ 0x971, 0x983 },
+	{ 0x985, 0x98c },
+	{ 0x98f, 0x990 },
+	{ 0x993, 0x9a8 },
+	{ 0x9aa, 0x9b0 },
+	{ 0x9b2, 0x9b2 },
+	{ 0x9b6, 0x9b9 },
+	{ 0x9bc, 0x9c4 },
+	{ 0x9c7, 0x9c8 },
+	{ 0x9cb, 0x9ce },
+	{ 0x9d7, 0x9d7 },
+	{ 0x9dc, 0x9dd },
+	{ 0x9df, 0x9e3 },
+	{ 0x9e6, 0x9f1 },
+	{ 0x9fc, 0x9fc },
+	{ 0x9fe, 0x9fe },
+	{ 0xa01, 0xa03 },
+	{ 0xa05, 0xa0a },
+	{ 0xa0f, 0xa10 },
+	{ 0xa13, 0xa28 },
+	{ 0xa2a, 0xa30 },
+	{ 0xa32, 0xa33 },
+	{ 0xa35, 0xa36 },
+	{ 0xa38, 0xa39 },
+	{ 0xa3c, 0xa3c },
+	{ 0xa3e, 0xa42 },
+	{ 0xa47, 0xa48 },
+	{ 0xa4b, 0xa4d },
+	{ 0xa51, 0xa51 },
+	{ 0xa59, 0xa5c },
+	{ 0xa5e, 0xa5e },
+	{ 0xa66, 0xa75 },
+	{ 0xa81, 0xa83 },
+	{ 0xa85, 0xa8d },
+	{ 0xa8f, 0xa91 },
+	{ 0xa93, 0xaa8 },
+	{ 0xaaa, 0xab0 },
+	{ 0xab2, 0xab3 },
+	{ 0xab5, 0xab9 },
+	{ 0xabc, 0xac5 },
+	{ 0xac7, 0xac9 },
+	{ 0xacb, 0xacd },
+	{ 0xad0, 0xad0 },
+	{ 0xae0, 0xae3 },
+	{ 0xae6, 0xaef },
+	{ 0xaf9, 0xaff },
+	{ 0xb01, 0xb03 },
+	{ 0xb05, 0xb0c },
+	{ 0xb0f, 0xb10 },
+	{ 0xb13, 0xb28 },
+	{ 0xb2a, 0xb30 },
+	{ 0xb32, 0xb33 },
+	{ 0xb35, 0xb39 },
+	{ 0xb3c, 0xb44 },
+	{ 0xb47, 0xb48 },
+	{ 0xb4b, 0xb4d },
+	{ 0xb55, 0xb57 },
+	{ 0xb5c, 0xb5d },
+	{ 0xb5f, 0xb63 },
+	{ 0xb66, 0xb6f },
+	{ 0xb71, 0xb71 },
+	{ 0xb82, 0xb83 },
+	{ 0xb85, 0xb8a },
+	{ 0xb8e, 0xb90 },
+	{ 0xb92, 0xb95 },
+	{ 0xb99, 0xb9a },
+	{ 0xb9c, 0xb9c },
+	{ 0xb9e, 0xb9f },
+	{ 0xba3, 0xba4 },
+	{ 0xba8, 0xbaa },
+	{ 0xbae, 0xbb9 },
+	{ 0xbbe, 0xbc2 },
+	{ 0xbc6, 0xbc8 },
+	{ 0xbca, 0xbcd },
+	{ 0xbd0, 0xbd0 },
+	{ 0xbd7, 0xbd7 },
+	{ 0xbe6, 0xbef },
+	{ 0xc00, 0xc0c },
+	{ 0xc0e, 0xc10 },
+	{ 0xc12, 0xc28 },
+	{ 0xc2a, 0xc39 },
+	{ 0xc3c, 0xc44 },
+	{ 0xc46, 0xc48 },
+	{ 0xc4a, 0xc4d },
+	{ 0xc55, 0xc56 },
+	{ 0xc58, 0xc5a },
+	{ 0xc5d, 0xc5d },
+	{ 0xc60, 0xc63 },
+	{ 0xc66, 0xc6f },
+	{ 0xc80, 0xc83 },
+	{ 0xc85, 0xc8c },
+	{ 0xc8e, 0xc90 },
+	{ 0xc92, 0xca8 },
+	{ 0xcaa, 0xcb3 },
+	{ 0xcb5, 0xcb9 },
+	{ 0xcbc, 0xcc4 },
+	{ 0xcc6, 0xcc8 },
+	{ 0xcca, 0xccd },
+	{ 0xcd5, 0xcd6 },
+	{ 0xcdd, 0xcde },
+	{ 0xce0, 0xce3 },
+	{ 0xce6, 0xcef },
+	{ 0xcf1, 0xcf3 },
+	{ 0xd00, 0xd0c },
+	{ 0xd0e, 0xd10 },
+	{ 0xd12, 0xd44 },
+	{ 0xd46, 0xd48 },
+	{ 0xd4a, 0xd4e },
+	{ 0xd54, 0xd57 },
+	{ 0xd5f, 0xd63 },
+	{ 0xd66, 0xd6f },
+	{ 0xd7a, 0xd7f },
+	{ 0xd81, 0xd83 },
+	{ 0xd85, 0xd96 },
+	{ 0xd9a, 0xdb1 },
+	{ 0xdb3, 0xdbb },
+	{ 0xdbd, 0xdbd },
+	{ 0xdc0, 0xdc6 },
+	{ 0xdca, 0xdca },
+	{ 0xdcf, 0xdd4 },
+	{ 0xdd6, 0xdd6 },
+	{ 0xdd8, 0xddf },
+	{ 0xde6, 0xdef },
+	{ 0xdf2, 0xdf3 },
+	{ 0xe01, 0xe3a },
+	{ 0xe40, 0xe4e },
+	{ 0xe50, 0xe59 },
+	{ 0xe81, 0xe82 },
+	{ 0xe84, 0xe84 },
+	{ 0xe86, 0xe8a },
+	{ 0xe8c, 0xea3 },
+	{ 0xea5, 0xea5 },
+	{ 0xea7, 0xebd },
+	{ 0xec0, 0xec4 },
+	{ 0xec6, 0xec6 },
+	{ 0xec8, 0xece },
+	{ 0xed0, 0xed9 },
+	{ 0xedc, 0xedf },
+	{ 0xf00, 0xf00 },
+	{ 0xf18, 0xf19 },
+	{ 0xf20, 0xf29 },
+	{ 0xf35, 0xf35 },
+	{ 0xf37, 0xf37 },
+	{ 0xf39, 0xf39 },
+	{ 0xf3e, 0xf47 },
+	{ 0xf49, 0xf6c },
+	{ 0xf71, 0xf84 },
+	{ 0xf86, 0xf97 },
+	{ 0xf99, 0xfbc },
+	{ 0xfc6, 0xfc6 },
+	{ 0x1000, 0x1049 },
+	{ 0x1050, 0x109d },
+	{ 0x10a0, 0x10c5 },
+	{ 0x10c7, 0x10c7 },
+	{ 0x10cd, 0x10cd },
+	{ 0x10d0, 0x10fa },
+	{ 0x10fc, 0x1248 },
+	{ 0x124a, 0x124d },
+	{ 0x1250, 0x1256 },
+	{ 0x1258, 0x1258 },
+	{ 0x125a, 0x125d },
+	{ 0x1260, 0x1288 },
+	{ 0x128a, 0x128d },
+	{ 0x1290, 0x12b0 },
+	{ 0x12b2, 0x12b5 },
+	{ 0x12b8, 0x12be },
+	{ 0x12c0, 0x12c0 },
+	{ 0x12c2, 0x12c5 },
+	{ 0x12c8, 0x12d6 },
+	{ 0x12d8, 0x1310 },
+	{ 0x1312, 0x1315 },
+	{ 0x1318, 0x135a },
+	{ 0x135d, 0x135f },
+	{ 0x1369, 0x1371 },
+	{ 0x1380, 0x138f },
+	{ 0x13a0, 0x13f5 },
+	{ 0x13f8, 0x13fd },
+	{ 0x1401, 0x166c },
+	{ 0x166f, 0x167f },
+	{ 0x1681, 0x169a },
+	{ 0x16a0, 0x16ea },
+	{ 0x16ee, 0x16f8 },
+	{ 0x1700, 0x1715 },
+	{ 0x171f, 0x1734 },
+	{ 0x1740, 0x1753 },
+	{ 0x1760, 0x176c },
+	{ 0x176e, 0x1770 },
+	{ 0x1772, 0x1773 },
+	{ 0x1780, 0x17d3 },
+	{ 0x17d7, 0x17d7 },
+	{ 0x17dc, 0x17dd },
+	{ 0x17e0, 0x17e9 },
+	{ 0x180b, 0x180d },
+	{ 0x180f, 0x1819 },
+	{ 0x1820, 0x1878 },
+	{ 0x1880, 0x18aa },
+	{ 0x18b0, 0x18f5 },
+	{ 0x1900, 0x191e },
+	{ 0x1920, 0x192b },
+	{ 0x1930, 0x193b },
+	{ 0x1946, 0x196d },
+	{ 0x1970, 0x1974 },
+	{ 0x1980, 0x19ab },
+	{ 0x19b0, 0x19c9 },
+	{ 0x19d0, 0x19da },
+	{ 0x1a00, 0x1a1b },
+	{ 0x1a20, 0x1a5e },
+	{ 0x1a60, 0x1a7c },
+	{ 0x1a7f, 0x1a89 },
+	{ 0x1a90, 0x1a99 },
+	{ 0x1aa7, 0x1aa7 },
+	{ 0x1ab0, 0x1abd },
+	{ 0x1abf, 0x1ace },
+	{ 0x1b00, 0x1b4c },
+	{ 0x1b50, 0x1b59 },
+	{ 0x1b6b, 0x1b73 },
+	{ 0x1b80, 0x1bf3 },
+	{ 0x1c00, 0x1c37 },
+	{ 0x1c40, 0x1c49 },
+	{ 0x1c4d, 0x1c7d },
+	{ 0x1c80, 0x1c8a },
+	{ 0x1c90, 0x1cba },
+	{ 0x1cbd, 0x1cbf },
+	{ 0x1cd0, 0x1cd2 },
+	{ 0x1cd4, 0x1cfa },
+	{ 0x1d00, 0x1f15 },
+	{ 0x1f18, 0x1f1d },
+	{ 0x1f20, 0x1f45 },
+	{ 0x1f48, 0x1f4d },
+	{ 0x1f50, 0x1f57 },
+	{ 0x1f59, 0x1f59 },
+	{ 0x1f5b, 0x1f5b },
+	{ 0x1f5d, 0x1f5d },
+	{ 0x1f5f, 0x1f7d },
+	{ 0x1f80, 0x1fb4 },
+	{ 0x1fb6, 0x1fbc },
+	{ 0x1fbe, 0x1fbe },
+	{ 0x1fc2, 0x1fc4 },
+	{ 0x1fc6, 0x1fcc },
+	{ 0x1fd0, 0x1fd3 },
+	{ 0x1fd6, 0x1fdb },
+	{ 0x1fe0, 0x1fec },
+	{ 0x1ff2, 0x1ff4 },
+	{ 0x1ff6, 0x1ffc },
+	{ 0x200c, 0x200d },
+	{ 0x203f, 0x2040 },
+	{ 0x2054, 0x2054 },
+	{ 0x2071, 0x2071 },
+	{ 0x207f, 0x207f },
+	{ 0x2090, 0x209c },
+	{ 0x20d0, 0x20dc },
+	{ 0x20e1, 0x20e1 },
+	{ 0x20e5, 0x20f0 },
+	{ 0x2102, 0x2102 },
+	{ 0x2107, 0x2107 },
+	{ 0x210a, 0x2113 },
+	{ 0x2115, 0x2115 },
+	{ 0x2118, 0x211d },
+	{ 0x2124, 0x2124 },
+	{ 0x2126, 0x2126 },
+	{ 0x2128, 0x2128 },
+	{ 0x212a, 0x2139 },
+	{ 0x213c, 0x213f },
+	{ 0x2145, 0x2149 },
+	{ 0x214e, 0x214e },
+	{ 0x2160, 0x2188 },
+	{ 0x2c00, 0x2ce4 },
+	{ 0x2ceb, 0x2cf3 },
+	{ 0x2d00, 0x2d25 },
+	{ 0x2d27, 0x2d27 },
+	{ 0x2d2d, 0x2d2d },
+	{ 0x2d30, 0x2d67 },
+	{ 0x2d6f, 0x2d6f },
+	{ 0x2d7f, 0x2d96 },
+	{ 0x2da0, 0x2da6 },
+	{ 0x2da8, 0x2dae },
+	{ 0x2db0, 0x2db6 },
+	{ 0x2db8, 0x2dbe },
+	{ 0x2dc0, 0x2dc6 },
+	{ 0x2dc8, 0x2dce },
+	{ 0x2dd0, 0x2dd6 },
+	{ 0x2dd8, 0x2dde },
+	{ 0x2de0, 0x2dff },
+	{ 0x3005, 0x3007 },
+	{ 0x3021, 0x302f },
+	{ 0x3031, 0x3035 },
+	{ 0x3038, 0x303c },
+	{ 0x3041, 0x3096 },
+	{ 0x3099, 0x309a },
+	{ 0x309d, 0x309f },
+	{ 0x30a1, 0x30ff },
+	{ 0x3105, 0x312f },
+	{ 0x3131, 0x318e },
+	{ 0x31a0, 0x31bf },
+	{ 0x31f0, 0x31ff },
+	{ 0x3400, 0x4dbf },
+	{ 0x4e00, 0xa48c },
+	{ 0xa4d0, 0xa4fd },
+	{ 0xa500, 0xa60c },
+	{ 0xa610, 0xa62b },
+	{ 0xa640, 0xa66f },
+	{ 0xa674, 0xa67d },
+	{ 0xa67f, 0xa6f1 },
+	{ 0xa717, 0xa71f },
+	{ 0xa722, 0xa788 },
+	{ 0xa78b, 0xa7cd },
+	{ 0xa7d0, 0xa7d1 },
+	{ 0xa7d3, 0xa7d3 },
+	{ 0xa7d5, 0xa7dc },
+	{ 0xa7f2, 0xa827 },
+	{ 0xa82c, 0xa82c },
+	{ 0xa840, 0xa873 },
+	{ 0xa880, 0xa8c5 },
+	{ 0xa8d0, 0xa8d9 },
+	{ 0xa8e0, 0xa8f7 },
+	{ 0xa8fb, 0xa8fb },
+	{ 0xa8fd, 0xa92d },
+	{ 0xa930, 0xa953 },
+	{ 0xa960, 0xa97c },
+	{ 0xa980, 0xa9c0 },
+	{ 0xa9cf, 0xa9d9 },
+	{ 0xa9e0, 0xa9fe },
+	{ 0xaa00, 0xaa36 },
+	{ 0xaa40, 0xaa4d },
+	{ 0xaa50, 0xaa59 },
+	{ 0xaa60, 0xaa76 },
+	{ 0xaa7a, 0xaac2 },
+	{ 0xaadb, 0xaadd },
+	{ 0xaae0, 0xaaef },
+	{ 0xaaf2, 0xaaf6 },
+	{ 0xab01, 0xab06 },
+	{ 0xab09, 0xab0e },
+	{ 0xab11, 0xab16 },
+	{ 0xab20, 0xab26 },
+	{ 0xab28, 0xab2e },
+	{ 0xab30, 0xab5a },
+	{ 0xab5c, 0xab69 },
+	{ 0xab70, 0xabea },
+	{ 0xabec, 0xabed },
+	{ 0xabf0, 0xabf9 },
+	{ 0xac00, 0xd7a3 },
+	{ 0xd7b0, 0xd7c6 },
+	{ 0xd7cb, 0xd7fb },
+	{ 0xf900, 0xfa6d },
+	{ 0xfa70, 0xfad9 },
+	{ 0xfb00, 0xfb06 },
+	{ 0xfb13, 0xfb17 },
+	{ 0xfb1d, 0xfb28 },
+	{ 0xfb2a, 0xfb36 },
+	{ 0xfb38, 0xfb3c },
+	{ 0xfb3e, 0xfb3e },
+	{ 0xfb40, 0xfb41 },
+	{ 0xfb43, 0xfb44 },
+	{ 0xfb46, 0xfbb1 },
+	{ 0xfbd3, 0xfc5d },
+	{ 0xfc64, 0xfd3d },
+	{ 0xfd50, 0xfd8f },
+	{ 0xfd92, 0xfdc7 },
+	{ 0xfdf0, 0xfdf9 },
+	{ 0xfe00, 0xfe0f },
+	{ 0xfe20, 0xfe2f },
+	{ 0xfe33, 0xfe34 },
+	{ 0xfe4d, 0xfe4f },
+	{ 0xfe71, 0xfe71 },
+	{ 0xfe73, 0xfe73 },
+	{ 0xfe77, 0xfe77 },
+	{ 0xfe79, 0xfe79 },
+	{ 0xfe7b, 0xfe7b },
+	{ 0xfe7d, 0xfe7d },
+	{ 0xfe7f, 0xfefc },
+	{ 0xff10, 0xff19 },
+	{ 0xff21, 0xff3a },
+	{ 0xff3f, 0xff3f },
+	{ 0xff41, 0xff5a },
+	{ 0xff65, 0xffbe },
+	{ 0xffc2, 0xffc7 },
+	{ 0xffca, 0xffcf },
+	{ 0xffd2, 0xffd7 },
+	{ 0xffda, 0xffdc },
+	{ 0x10000, 0x1000b },
+	{ 0x1000d, 0x10026 },
+	{ 0x10028, 0x1003a },
+	{ 0x1003c, 0x1003d },
+	{ 0x1003f, 0x1004d },
+	{ 0x10050, 0x1005d },
+	{ 0x10080, 0x100fa },
+	{ 0x10140, 0x10174 },
+	{ 0x101fd, 0x101fd },
+	{ 0x10280, 0x1029c },
+	{ 0x102a0, 0x102d0 },
+	{ 0x102e0, 0x102e0 },
+	{ 0x10300, 0x1031f },
+	{ 0x1032d, 0x1034a },
+	{ 0x10350, 0x1037a },
+	{ 0x10380, 0x1039d },
+	{ 0x103a0, 0x103c3 },
+	{ 0x103c8, 0x103cf },
+	{ 0x103d1, 0x103d5 },
+	{ 0x10400, 0x1049d },
+	{ 0x104a0, 0x104a9 },
+	{ 0x104b0, 0x104d3 },
+	{ 0x104d8, 0x104fb },
+	{ 0x10500, 0x10527 },
+	{ 0x10530, 0x10563 },
+	{ 0x10570, 0x1057a },
+	{ 0x1057c, 0x1058a },
+	{ 0x1058c, 0x10592 },
+	{ 0x10594, 0x10595 },
+	{ 0x10597, 0x105a1 },
+	{ 0x105a3, 0x105b1 },
+	{ 0x105b3, 0x105b9 },
+	{ 0x105bb, 0x105bc },
+	{ 0x105c0, 0x105f3 },
+	{ 0x10600, 0x10736 },
+	{ 0x10740, 0x10755 },
+	{ 0x10760, 0x10767 },
+	{ 0x10780, 0x10785 },
+	{ 0x10787, 0x107b0 },
+	{ 0x107b2, 0x107ba },
+	{ 0x10800, 0x10805 },
+	{ 0x10808, 0x10808 },
+	{ 0x1080a, 0x10835 },
+	{ 0x10837, 0x10838 },
+	{ 0x1083c, 0x1083c },
+	{ 0x1083f, 0x10855 },
+	{ 0x10860, 0x10876 },
+	{ 0x10880, 0x1089e },
+	{ 0x108e0, 0x108f2 },
+	{ 0x108f4, 0x108f5 },
+	{ 0x10900, 0x10915 },
+	{ 0x10920, 0x10939 },
+	{ 0x10980, 0x109b7 },
+	{ 0x109be, 0x109bf },
+	{ 0x10a00, 0x10a03 },
+	{ 0x10a05, 0x10a06 },
+	{ 0x10a0c, 0x10a13 },
+	{ 0x10a15, 0x10a17 },
+	{ 0x10a19, 0x10a35 },
+	{ 0x10a38, 0x10a3a },
+	{ 0x10a3f, 0x10a3f },
+	{ 0x10a60, 0x10a7c },
+	{ 0x10a80, 0x10a9c },
+	{ 0x10ac0, 0x10ac7 },
+	{ 0x10ac9, 0x10ae6 },
+	{ 0x10b00, 0x10b35 },
+	{ 0x10b40, 0x10b55 },
+	{ 0x10b60, 0x10b72 },
+	{ 0x10b80, 0x10b91 },
+	{ 0x10c00, 0x10c48 },
+	{ 0x10c80, 0x10cb2 },
+	{ 0x10cc0, 0x10cf2 },
+	{ 0x10d00, 0x10d27 },
+	{ 0x10d30, 0x10d39 },
+	{ 0x10d40, 0x10d65 },
+	{ 0x10d69, 0x10d6d },
+	{ 0x10d6f, 0x10d85 },
+	{ 0x10e80, 0x10ea9 },
+	{ 0x10eab, 0x10eac },
+	{ 0x10eb0, 0x10eb1 },
+	{ 0x10ec2, 0x10ec4 },
+	{ 0x10efc, 0x10f1c },
+	{ 0x10f27, 0x10f27 },
+	{ 0x10f30, 0x10f50 },
+	{ 0x10f70, 0x10f85 },
+	{ 0x10fb0, 0x10fc4 },
+	{ 0x10fe0, 0x10ff6 },
+	{ 0x11000, 0x11046 },
+	{ 0x11066, 0x11075 },
+	{ 0x1107f, 0x110ba },
+	{ 0x110c2, 0x110c2 },
+	{ 0x110d0, 0x110e8 },
+	{ 0x110f0, 0x110f9 },
+	{ 0x11100, 0x11134 },
+	{ 0x11136, 0x1113f },
+	{ 0x11144, 0x11147 },
+	{ 0x11150, 0x11173 },
+	{ 0x11176, 0x11176 },
+	{ 0x11180, 0x111c4 },
+	{ 0x111c9, 0x111cc },
+	{ 0x111ce, 0x111da },
+	{ 0x111dc, 0x111dc },
+	{ 0x11200, 0x11211 },
+	{ 0x11213, 0x11237 },
+	{ 0x1123e, 0x11241 },
+	{ 0x11280, 0x11286 },
+	{ 0x11288, 0x11288 },
+	{ 0x1128a, 0x1128d },
+	{ 0x1128f, 0x1129d },
+	{ 0x1129f, 0x112a8 },
+	{ 0x112b0, 0x112ea },
+	{ 0x112f0, 0x112f9 },
+	{ 0x11300, 0x11303 },
+	{ 0x11305, 0x1130c },
+	{ 0x1130f, 0x11310 },
+	{ 0x11313, 0x11328 },
+	{ 0x1132a, 0x11330 },
+	{ 0x11332, 0x11333 },
+	{ 0x11335, 0x11339 },
+	{ 0x1133b, 0x11344 },
+	{ 0x11347, 0x11348 },
+	{ 0x1134b, 0x1134d },
+	{ 0x11350, 0x11350 },
+	{ 0x11357, 0x11357 },
+	{ 0x1135d, 0x11363 },
+	{ 0x11366, 0x1136c },
+	{ 0x11370, 0x11374 },
+	{ 0x11380, 0x11389 },
+	{ 0x1138b, 0x1138b },
+	{ 0x1138e, 0x1138e },
+	{ 0x11390, 0x113b5 },
+	{ 0x113b7, 0x113c0 },
+	{ 0x113c2, 0x113c2 },
+	{ 0x113c5, 0x113c5 },
+	{ 0x113c7, 0x113ca },
+	{ 0x113cc, 0x113d3 },
+	{ 0x113e1, 0x113e2 },
+	{ 0x11400, 0x1144a },
+	{ 0x11450, 0x11459 },
+	{ 0x1145e, 0x11461 },
+	{ 0x11480, 0x114c5 },
+	{ 0x114c7, 0x114c7 },
+	{ 0x114d0, 0x114d9 },
+	{ 0x11580, 0x115b5 },
+	{ 0x115b8, 0x115c0 },
+	{ 0x115d8, 0x115dd },
+	{ 0x11600, 0x11640 },
+	{ 0x11644, 0x11644 },
+	{ 0x11650, 0x11659 },
+	{ 0x11680, 0x116b8 },
+	{ 0x116c0, 0x116c9 },
+	{ 0x116d0, 0x116e3 },
+	{ 0x11700, 0x1171a },
+	{ 0x1171d, 0x1172b },
+	{ 0x11730, 0x11739 },
+	{ 0x11740, 0x11746 },
+	{ 0x11800, 0x1183a },
+	{ 0x118a0, 0x118e9 },
+	{ 0x118ff, 0x11906 },
+	{ 0x11909, 0x11909 },
+	{ 0x1190c, 0x11913 },
+	{ 0x11915, 0x11916 },
+	{ 0x11918, 0x11935 },
+	{ 0x11937, 0x11938 },
+	{ 0x1193b, 0x11943 },
+	{ 0x11950, 0x11959 },
+	{ 0x119a0, 0x119a7 },
+	{ 0x119aa, 0x119d7 },
+	{ 0x119da, 0x119e1 },
+	{ 0x119e3, 0x119e4 },
+	{ 0x11a00, 0x11a3e },
+	{ 0x11a47, 0x11a47 },
+	{ 0x11a50, 0x11a99 },
+	{ 0x11a9d, 0x11a9d },
+	{ 0x11ab0, 0x11af8 },
+	{ 0x11bc0, 0x11be0 },
+	{ 0x11bf0, 0x11bf9 },
+	{ 0x11c00, 0x11c08 },
+	{ 0x11c0a, 0x11c36 },
+	{ 0x11c38, 0x11c40 },
+	{ 0x11c50, 0x11c59 },
+	{ 0x11c72, 0x11c8f },
+	{ 0x11c92, 0x11ca7 },
+	{ 0x11ca9, 0x11cb6 },
+	{ 0x11d00, 0x11d06 },
+	{ 0x11d08, 0x11d09 },
+	{ 0x11d0b, 0x11d36 },
+	{ 0x11d3a, 0x11d3a },
+	{ 0x11d3c, 0x11d3d },
+	{ 0x11d3f, 0x11d47 },
+	{ 0x11d50, 0x11d59 },
+	{ 0x11d60, 0x11d65 },
+	{ 0x11d67, 0x11d68 },
+	{ 0x11d6a, 0x11d8e },
+	{ 0x11d90, 0x11d91 },
+	{ 0x11d93, 0x11d98 },
+	{ 0x11da0, 0x11da9 },
+	{ 0x11ee0, 0x11ef6 },
+	{ 0x11f00, 0x11f10 },
+	{ 0x11f12, 0x11f3a },
+	{ 0x11f3e, 0x11f42 },
+	{ 0x11f50, 0x11f5a },
+	{ 0x11fb0, 0x11fb0 },
+	{ 0x12000, 0x12399 },
+	{ 0x12400, 0x1246e },
+	{ 0x12480, 0x12543 },
+	{ 0x12f90, 0x12ff0 },
+	{ 0x13000, 0x1342f },
+	{ 0x13440, 0x13455 },
+	{ 0x13460, 0x143fa },
+	{ 0x14400, 0x14646 },
+	{ 0x16100, 0x16139 },
+	{ 0x16800, 0x16a38 },
+	{ 0x16a40, 0x16a5e },
+	{ 0x16a60, 0x16a69 },
+	{ 0x16a70, 0x16abe },
+	{ 0x16ac0, 0x16ac9 },
+	{ 0x16ad0, 0x16aed },
+	{ 0x16af0, 0x16af4 },
+	{ 0x16b00, 0x16b36 },
+	{ 0x16b40, 0x16b43 },
+	{ 0x16b50, 0x16b59 },
+	{ 0x16b63, 0x16b77 },
+	{ 0x16b7d, 0x16b8f },
+	{ 0x16d40, 0x16d6c },
+	{ 0x16d70, 0x16d79 },
+	{ 0x16e40, 0x16e7f },
+	{ 0x16f00, 0x16f4a },
+	{ 0x16f4f, 0x16f87 },
+	{ 0x16f8f, 0x16f9f },
+	{ 0x16fe0, 0x16fe1 },
+	{ 0x16fe3, 0x16fe4 },
+	{ 0x16ff0, 0x16ff1 },
+	{ 0x17000, 0x187f7 },
+	{ 0x18800, 0x18cd5 },
+	{ 0x18cff, 0x18d08 },
+	{ 0x1aff0, 0x1aff3 },
+	{ 0x1aff5, 0x1affb },
+	{ 0x1affd, 0x1affe },
+	{ 0x1b000, 0x1b122 },
+	{ 0x1b132, 0x1b132 },
+	{ 0x1b150, 0x1b152 },
+	{ 0x1b155, 0x1b155 },
+	{ 0x1b164, 0x1b167 },
+	{ 0x1b170, 0x1b2fb },
+	{ 0x1bc00, 0x1bc6a },
+	{ 0x1bc70, 0x1bc7c },
+	{ 0x1bc80, 0x1bc88 },
+	{ 0x1bc90, 0x1bc99 },
+	{ 0x1bc9d, 0x1bc9e },
+	{ 0x1ccf0, 0x1ccf9 },
+	{ 0x1cf00, 0x1cf2d },
+	{ 0x1cf30, 0x1cf46 },
+	{ 0x1d165, 0x1d169 },
+	{ 0x1d16d, 0x1d172 },
+	{ 0x1d17b, 0x1d182 },
+	{ 0x1d185, 0x1d18b },
+	{ 0x1d1aa, 0x1d1ad },
+	{ 0x1d242, 0x1d244 },
+	{ 0x1d400, 0x1d454 },
+	{ 0x1d456, 0x1d49c },
+	{ 0x1d49e, 0x1d49f },
+	{ 0x1d4a2, 0x1d4a2 },
+	{ 0x1d4a5, 0x1d4a6 },
+	{ 0x1d4a9, 0x1d4ac },
+	{ 0x1d4ae, 0x1d4b9 },
+	{ 0x1d4bb, 0x1d4bb },
+	{ 0x1d4bd, 0x1d4c3 },
+	{ 0x1d4c5, 0x1d505 },
+	{ 0x1d507, 0x1d50a },
+	{ 0x1d50d, 0x1d514 },
+	{ 0x1d516, 0x1d51c },
+	{ 0x1d51e, 0x1d539 },
+	{ 0x1d53b, 0x1d53e },
+	{ 0x1d540, 0x1d544 },
+	{ 0x1d546, 0x1d546 },
+	{ 0x1d54a, 0x1d550 },
+	{ 0x1d552, 0x1d6a5 },
+	{ 0x1d6a8, 0x1d6c0 },
+	{ 0x1d6c2, 0x1d6da },
+	{ 0x1d6dc, 0x1d6fa },
+	{ 0x1d6fc, 0x1d714 },
+	{ 0x1d716, 0x1d734 },
+	{ 0x1d736, 0x1d74e },
+	{ 0x1d750, 0x1d76e },
+	{ 0x1d770, 0x1d788 },
+	{ 0x1d78a, 0x1d7a8 },
+	{ 0x1d7aa, 0x1d7c2 },
+	{ 0x1d7c4, 0x1d7cb },
+	{ 0x1d7ce, 0x1d7ff },
+	{ 0x1da00, 0x1da36 },
+	{ 0x1da3b, 0x1da6c },
+	{ 0x1da75, 0x1da75 },
+	{ 0x1da84, 0x1da84 },
+	{ 0x1da9b, 0x1da9f },
+	{ 0x1daa1, 0x1daaf },
+	{ 0x1df00, 0x1df1e },
+	{ 0x1df25, 0x1df2a },
+	{ 0x1e000, 0x1e006 },
+	{ 0x1e008, 0x1e018 },
+	{ 0x1e01b, 0x1e021 },
+	{ 0x1e023, 0x1e024 },
+	{ 0x1e026, 0x1e02a },
+	{ 0x1e030, 0x1e06d },
+	{ 0x1e08f, 0x1e08f },
+	{ 0x1e100, 0x1e12c },
+	{ 0x1e130, 0x1e13d },
+	{ 0x1e140, 0x1e149 },
+	{ 0x1e14e, 0x1e14e },
+	{ 0x1e290, 0x1e2ae },
+	{ 0x1e2c0, 0x1e2f9 },
+	{ 0x1e4d0, 0x1e4f9 },
+	{ 0x1e5d0, 0x1e5fa },
+	{ 0x1e7e0, 0x1e7e6 },
+	{ 0x1e7e8, 0x1e7eb },
+	{ 0x1e7ed, 0x1e7ee },
+	{ 0x1e7f0, 0x1e7fe },
+	{ 0x1e800, 0x1e8c4 },
+	{ 0x1e8d0, 0x1e8d6 },
+	{ 0x1e900, 0x1e94b },
+	{ 0x1e950, 0x1e959 },
+	{ 0x1ee00, 0x1ee03 },
+	{ 0x1ee05, 0x1ee1f },
+	{ 0x1ee21, 0x1ee22 },
+	{ 0x1ee24, 0x1ee24 },
+	{ 0x1ee27, 0x1ee27 },
+	{ 0x1ee29, 0x1ee32 },
+	{ 0x1ee34, 0x1ee37 },
+	{ 0x1ee39, 0x1ee39 },
+	{ 0x1ee3b, 0x1ee3b },
+	{ 0x1ee42, 0x1ee42 },
+	{ 0x1ee47, 0x1ee47 },
+	{ 0x1ee49, 0x1ee49 },
+	{ 0x1ee4b, 0x1ee4b },
+	{ 0x1ee4d, 0x1ee4f },
+	{ 0x1ee51, 0x1ee52 },
+	{ 0x1ee54, 0x1ee54 },
+	{ 0x1ee57, 0x1ee57 },
+	{ 0x1ee59, 0x1ee59 },
+	{ 0x1ee5b, 0x1ee5b },
+	{ 0x1ee5d, 0x1ee5d },
+	{ 0x1ee5f, 0x1ee5f },
+	{ 0x1ee61, 0x1ee62 },
+	{ 0x1ee64, 0x1ee64 },
+	{ 0x1ee67, 0x1ee6a },
+	{ 0x1ee6c, 0x1ee72 },
+	{ 0x1ee74, 0x1ee77 },
+	{ 0x1ee79, 0x1ee7c },
+	{ 0x1ee7e, 0x1ee7e },
+	{ 0x1ee80, 0x1ee89 },
+	{ 0x1ee8b, 0x1ee9b },
+	{ 0x1eea1, 0x1eea3 },
+	{ 0x1eea5, 0x1eea9 },
+	{ 0x1eeab, 0x1eebb },
+	{ 0x1fbf0, 0x1fbf9 },
+	{ 0x20000, 0x2a6df },
+	{ 0x2a700, 0x2b739 },
+	{ 0x2b740, 0x2b81d },
+	{ 0x2b820, 0x2cea1 },
+	{ 0x2ceb0, 0x2ebe0 },
+	{ 0x2ebf0, 0x2ee5d },
+	{ 0x2f800, 0x2fa1d },
+	{ 0x30000, 0x3134a },
+	{ 0x31350, 0x323af },
+	{ 0xe0100, 0xe01ef },
+};
+
+constexpr inline CharRange uppercase_letter[] = {
+	{ 0x41, 0x5a },
+	{ 0xc0, 0xd6 },
+	{ 0xd8, 0xde },
+	{ 0x100, 0x100 },
+	{ 0x102, 0x102 },
+	{ 0x104, 0x104 },
+	{ 0x106, 0x106 },
+	{ 0x108, 0x108 },
+	{ 0x10a, 0x10a },
+	{ 0x10c, 0x10c },
+	{ 0x10e, 0x10e },
+	{ 0x110, 0x110 },
+	{ 0x112, 0x112 },
+	{ 0x114, 0x114 },
+	{ 0x116, 0x116 },
+	{ 0x118, 0x118 },
+	{ 0x11a, 0x11a },
+	{ 0x11c, 0x11c },
+	{ 0x11e, 0x11e },
+	{ 0x120, 0x120 },
+	{ 0x122, 0x122 },
+	{ 0x124, 0x124 },
+	{ 0x126, 0x126 },
+	{ 0x128, 0x128 },
+	{ 0x12a, 0x12a },
+	{ 0x12c, 0x12c },
+	{ 0x12e, 0x12e },
+	{ 0x130, 0x130 },
+	{ 0x132, 0x132 },
+	{ 0x134, 0x134 },
+	{ 0x136, 0x136 },
+	{ 0x139, 0x139 },
+	{ 0x13b, 0x13b },
+	{ 0x13d, 0x13d },
+	{ 0x13f, 0x13f },
+	{ 0x141, 0x141 },
+	{ 0x143, 0x143 },
+	{ 0x145, 0x145 },
+	{ 0x147, 0x147 },
+	{ 0x14a, 0x14a },
+	{ 0x14c, 0x14c },
+	{ 0x14e, 0x14e },
+	{ 0x150, 0x150 },
+	{ 0x152, 0x152 },
+	{ 0x154, 0x154 },
+	{ 0x156, 0x156 },
+	{ 0x158, 0x158 },
+	{ 0x15a, 0x15a },
+	{ 0x15c, 0x15c },
+	{ 0x15e, 0x15e },
+	{ 0x160, 0x160 },
+	{ 0x162, 0x162 },
+	{ 0x164, 0x164 },
+	{ 0x166, 0x166 },
+	{ 0x168, 0x168 },
+	{ 0x16a, 0x16a },
+	{ 0x16c, 0x16c },
+	{ 0x16e, 0x16e },
+	{ 0x170, 0x170 },
+	{ 0x172, 0x172 },
+	{ 0x174, 0x174 },
+	{ 0x176, 0x176 },
+	{ 0x178, 0x179 },
+	{ 0x17b, 0x17b },
+	{ 0x17d, 0x17d },
+	{ 0x181, 0x182 },
+	{ 0x184, 0x184 },
+	{ 0x186, 0x187 },
+	{ 0x189, 0x18b },
+	{ 0x18e, 0x191 },
+	{ 0x193, 0x194 },
+	{ 0x196, 0x198 },
+	{ 0x19c, 0x19d },
+	{ 0x19f, 0x1a0 },
+	{ 0x1a2, 0x1a2 },
+	{ 0x1a4, 0x1a4 },
+	{ 0x1a6, 0x1a7 },
+	{ 0x1a9, 0x1a9 },
+	{ 0x1ac, 0x1ac },
+	{ 0x1ae, 0x1af },
+	{ 0x1b1, 0x1b3 },
+	{ 0x1b5, 0x1b5 },
+	{ 0x1b7, 0x1b8 },
+	{ 0x1bc, 0x1bc },
+	{ 0x1c4, 0x1c4 },
+	{ 0x1c7, 0x1c7 },
+	{ 0x1ca, 0x1ca },
+	{ 0x1cd, 0x1cd },
+	{ 0x1cf, 0x1cf },
+	{ 0x1d1, 0x1d1 },
+	{ 0x1d3, 0x1d3 },
+	{ 0x1d5, 0x1d5 },
+	{ 0x1d7, 0x1d7 },
+	{ 0x1d9, 0x1d9 },
+	{ 0x1db, 0x1db },
+	{ 0x1de, 0x1de },
+	{ 0x1e0, 0x1e0 },
+	{ 0x1e2, 0x1e2 },
+	{ 0x1e4, 0x1e4 },
+	{ 0x1e6, 0x1e6 },
+	{ 0x1e8, 0x1e8 },
+	{ 0x1ea, 0x1ea },
+	{ 0x1ec, 0x1ec },
+	{ 0x1ee, 0x1ee },
+	{ 0x1f1, 0x1f1 },
+	{ 0x1f4, 0x1f4 },
+	{ 0x1f6, 0x1f8 },
+	{ 0x1fa, 0x1fa },
+	{ 0x1fc, 0x1fc },
+	{ 0x1fe, 0x1fe },
+	{ 0x200, 0x200 },
+	{ 0x202, 0x202 },
+	{ 0x204, 0x204 },
+	{ 0x206, 0x206 },
+	{ 0x208, 0x208 },
+	{ 0x20a, 0x20a },
+	{ 0x20c, 0x20c },
+	{ 0x20e, 0x20e },
+	{ 0x210, 0x210 },
+	{ 0x212, 0x212 },
+	{ 0x214, 0x214 },
+	{ 0x216, 0x216 },
+	{ 0x218, 0x218 },
+	{ 0x21a, 0x21a },
+	{ 0x21c, 0x21c },
+	{ 0x21e, 0x21e },
+	{ 0x220, 0x220 },
+	{ 0x222, 0x222 },
+	{ 0x224, 0x224 },
+	{ 0x226, 0x226 },
+	{ 0x228, 0x228 },
+	{ 0x22a, 0x22a },
+	{ 0x22c, 0x22c },
+	{ 0x22e, 0x22e },
+	{ 0x230, 0x230 },
+	{ 0x232, 0x232 },
+	{ 0x23a, 0x23b },
+	{ 0x23d, 0x23e },
+	{ 0x241, 0x241 },
+	{ 0x243, 0x246 },
+	{ 0x248, 0x248 },
+	{ 0x24a, 0x24a },
+	{ 0x24c, 0x24c },
+	{ 0x24e, 0x24e },
+	{ 0x370, 0x370 },
+	{ 0x372, 0x372 },
+	{ 0x376, 0x376 },
+	{ 0x37f, 0x37f },
+	{ 0x386, 0x386 },
+	{ 0x388, 0x38a },
+	{ 0x38c, 0x38c },
+	{ 0x38e, 0x38f },
+	{ 0x391, 0x3a1 },
+	{ 0x3a3, 0x3ab },
+	{ 0x3cf, 0x3cf },
+	{ 0x3d2, 0x3d4 },
+	{ 0x3d8, 0x3d8 },
+	{ 0x3da, 0x3da },
+	{ 0x3dc, 0x3dc },
+	{ 0x3de, 0x3de },
+	{ 0x3e0, 0x3e0 },
+	{ 0x3e2, 0x3e2 },
+	{ 0x3e4, 0x3e4 },
+	{ 0x3e6, 0x3e6 },
+	{ 0x3e8, 0x3e8 },
+	{ 0x3ea, 0x3ea },
+	{ 0x3ec, 0x3ec },
+	{ 0x3ee, 0x3ee },
+	{ 0x3f4, 0x3f4 },
+	{ 0x3f7, 0x3f7 },
+	{ 0x3f9, 0x3fa },
+	{ 0x3fd, 0x42f },
+	{ 0x460, 0x460 },
+	{ 0x462, 0x462 },
+	{ 0x464, 0x464 },
+	{ 0x466, 0x466 },
+	{ 0x468, 0x468 },
+	{ 0x46a, 0x46a },
+	{ 0x46c, 0x46c },
+	{ 0x46e, 0x46e },
+	{ 0x470, 0x470 },
+	{ 0x472, 0x472 },
+	{ 0x474, 0x474 },
+	{ 0x476, 0x476 },
+	{ 0x478, 0x478 },
+	{ 0x47a, 0x47a },
+	{ 0x47c, 0x47c },
+	{ 0x47e, 0x47e },
+	{ 0x480, 0x480 },
+	{ 0x48a, 0x48a },
+	{ 0x48c, 0x48c },
+	{ 0x48e, 0x48e },
+	{ 0x490, 0x490 },
+	{ 0x492, 0x492 },
+	{ 0x494, 0x494 },
+	{ 0x496, 0x496 },
+	{ 0x498, 0x498 },
+	{ 0x49a, 0x49a },
+	{ 0x49c, 0x49c },
+	{ 0x49e, 0x49e },
+	{ 0x4a0, 0x4a0 },
+	{ 0x4a2, 0x4a2 },
+	{ 0x4a4, 0x4a4 },
+	{ 0x4a6, 0x4a6 },
+	{ 0x4a8, 0x4a8 },
+	{ 0x4aa, 0x4aa },
+	{ 0x4ac, 0x4ac },
+	{ 0x4ae, 0x4ae },
+	{ 0x4b0, 0x4b0 },
+	{ 0x4b2, 0x4b2 },
+	{ 0x4b4, 0x4b4 },
+	{ 0x4b6, 0x4b6 },
+	{ 0x4b8, 0x4b8 },
+	{ 0x4ba, 0x4ba },
+	{ 0x4bc, 0x4bc },
+	{ 0x4be, 0x4be },
+	{ 0x4c0, 0x4c1 },
+	{ 0x4c3, 0x4c3 },
+	{ 0x4c5, 0x4c5 },
+	{ 0x4c7, 0x4c7 },
+	{ 0x4c9, 0x4c9 },
+	{ 0x4cb, 0x4cb },
+	{ 0x4cd, 0x4cd },
+	{ 0x4d0, 0x4d0 },
+	{ 0x4d2, 0x4d2 },
+	{ 0x4d4, 0x4d4 },
+	{ 0x4d6, 0x4d6 },
+	{ 0x4d8, 0x4d8 },
+	{ 0x4da, 0x4da },
+	{ 0x4dc, 0x4dc },
+	{ 0x4de, 0x4de },
+	{ 0x4e0, 0x4e0 },
+	{ 0x4e2, 0x4e2 },
+	{ 0x4e4, 0x4e4 },
+	{ 0x4e6, 0x4e6 },
+	{ 0x4e8, 0x4e8 },
+	{ 0x4ea, 0x4ea },
+	{ 0x4ec, 0x4ec },
+	{ 0x4ee, 0x4ee },
+	{ 0x4f0, 0x4f0 },
+	{ 0x4f2, 0x4f2 },
+	{ 0x4f4, 0x4f4 },
+	{ 0x4f6, 0x4f6 },
+	{ 0x4f8, 0x4f8 },
+	{ 0x4fa, 0x4fa },
+	{ 0x4fc, 0x4fc },
+	{ 0x4fe, 0x4fe },
+	{ 0x500, 0x500 },
+	{ 0x502, 0x502 },
+	{ 0x504, 0x504 },
+	{ 0x506, 0x506 },
+	{ 0x508, 0x508 },
+	{ 0x50a, 0x50a },
+	{ 0x50c, 0x50c },
+	{ 0x50e, 0x50e },
+	{ 0x510, 0x510 },
+	{ 0x512, 0x512 },
+	{ 0x514, 0x514 },
+	{ 0x516, 0x516 },
+	{ 0x518, 0x518 },
+	{ 0x51a, 0x51a },
+	{ 0x51c, 0x51c },
+	{ 0x51e, 0x51e },
+	{ 0x520, 0x520 },
+	{ 0x522, 0x522 },
+	{ 0x524, 0x524 },
+	{ 0x526, 0x526 },
+	{ 0x528, 0x528 },
+	{ 0x52a, 0x52a },
+	{ 0x52c, 0x52c },
+	{ 0x52e, 0x52e },
+	{ 0x531, 0x556 },
+	{ 0x10a0, 0x10c5 },
+	{ 0x10c7, 0x10c7 },
+	{ 0x10cd, 0x10cd },
+	{ 0x13a0, 0x13f5 },
+	{ 0x1c89, 0x1c89 },
+	{ 0x1c90, 0x1cba },
+	{ 0x1cbd, 0x1cbf },
+	{ 0x1e00, 0x1e00 },
+	{ 0x1e02, 0x1e02 },
+	{ 0x1e04, 0x1e04 },
+	{ 0x1e06, 0x1e06 },
+	{ 0x1e08, 0x1e08 },
+	{ 0x1e0a, 0x1e0a },
+	{ 0x1e0c, 0x1e0c },
+	{ 0x1e0e, 0x1e0e },
+	{ 0x1e10, 0x1e10 },
+	{ 0x1e12, 0x1e12 },
+	{ 0x1e14, 0x1e14 },
+	{ 0x1e16, 0x1e16 },
+	{ 0x1e18, 0x1e18 },
+	{ 0x1e1a, 0x1e1a },
+	{ 0x1e1c, 0x1e1c },
+	{ 0x1e1e, 0x1e1e },
+	{ 0x1e20, 0x1e20 },
+	{ 0x1e22, 0x1e22 },
+	{ 0x1e24, 0x1e24 },
+	{ 0x1e26, 0x1e26 },
+	{ 0x1e28, 0x1e28 },
+	{ 0x1e2a, 0x1e2a },
+	{ 0x1e2c, 0x1e2c },
+	{ 0x1e2e, 0x1e2e },
+	{ 0x1e30, 0x1e30 },
+	{ 0x1e32, 0x1e32 },
+	{ 0x1e34, 0x1e34 },
+	{ 0x1e36, 0x1e36 },
+	{ 0x1e38, 0x1e38 },
+	{ 0x1e3a, 0x1e3a },
+	{ 0x1e3c, 0x1e3c },
+	{ 0x1e3e, 0x1e3e },
+	{ 0x1e40, 0x1e40 },
+	{ 0x1e42, 0x1e42 },
+	{ 0x1e44, 0x1e44 },
+	{ 0x1e46, 0x1e46 },
+	{ 0x1e48, 0x1e48 },
+	{ 0x1e4a, 0x1e4a },
+	{ 0x1e4c, 0x1e4c },
+	{ 0x1e4e, 0x1e4e },
+	{ 0x1e50, 0x1e50 },
+	{ 0x1e52, 0x1e52 },
+	{ 0x1e54, 0x1e54 },
+	{ 0x1e56, 0x1e56 },
+	{ 0x1e58, 0x1e58 },
+	{ 0x1e5a, 0x1e5a },
+	{ 0x1e5c, 0x1e5c },
+	{ 0x1e5e, 0x1e5e },
+	{ 0x1e60, 0x1e60 },
+	{ 0x1e62, 0x1e62 },
+	{ 0x1e64, 0x1e64 },
+	{ 0x1e66, 0x1e66 },
+	{ 0x1e68, 0x1e68 },
+	{ 0x1e6a, 0x1e6a },
+	{ 0x1e6c, 0x1e6c },
+	{ 0x1e6e, 0x1e6e },
+	{ 0x1e70, 0x1e70 },
+	{ 0x1e72, 0x1e72 },
+	{ 0x1e74, 0x1e74 },
+	{ 0x1e76, 0x1e76 },
+	{ 0x1e78, 0x1e78 },
+	{ 0x1e7a, 0x1e7a },
+	{ 0x1e7c, 0x1e7c },
+	{ 0x1e7e, 0x1e7e },
+	{ 0x1e80, 0x1e80 },
+	{ 0x1e82, 0x1e82 },
+	{ 0x1e84, 0x1e84 },
+	{ 0x1e86, 0x1e86 },
+	{ 0x1e88, 0x1e88 },
+	{ 0x1e8a, 0x1e8a },
+	{ 0x1e8c, 0x1e8c },
+	{ 0x1e8e, 0x1e8e },
+	{ 0x1e90, 0x1e90 },
+	{ 0x1e92, 0x1e92 },
+	{ 0x1e94, 0x1e94 },
+	{ 0x1e9e, 0x1e9e },
+	{ 0x1ea0, 0x1ea0 },
+	{ 0x1ea2, 0x1ea2 },
+	{ 0x1ea4, 0x1ea4 },
+	{ 0x1ea6, 0x1ea6 },
+	{ 0x1ea8, 0x1ea8 },
+	{ 0x1eaa, 0x1eaa },
+	{ 0x1eac, 0x1eac },
+	{ 0x1eae, 0x1eae },
+	{ 0x1eb0, 0x1eb0 },
+	{ 0x1eb2, 0x1eb2 },
+	{ 0x1eb4, 0x1eb4 },
+	{ 0x1eb6, 0x1eb6 },
+	{ 0x1eb8, 0x1eb8 },
+	{ 0x1eba, 0x1eba },
+	{ 0x1ebc, 0x1ebc },
+	{ 0x1ebe, 0x1ebe },
+	{ 0x1ec0, 0x1ec0 },
+	{ 0x1ec2, 0x1ec2 },
+	{ 0x1ec4, 0x1ec4 },
+	{ 0x1ec6, 0x1ec6 },
+	{ 0x1ec8, 0x1ec8 },
+	{ 0x1eca, 0x1eca },
+	{ 0x1ecc, 0x1ecc },
+	{ 0x1ece, 0x1ece },
+	{ 0x1ed0, 0x1ed0 },
+	{ 0x1ed2, 0x1ed2 },
+	{ 0x1ed4, 0x1ed4 },
+	{ 0x1ed6, 0x1ed6 },
+	{ 0x1ed8, 0x1ed8 },
+	{ 0x1eda, 0x1eda },
+	{ 0x1edc, 0x1edc },
+	{ 0x1ede, 0x1ede },
+	{ 0x1ee0, 0x1ee0 },
+	{ 0x1ee2, 0x1ee2 },
+	{ 0x1ee4, 0x1ee4 },
+	{ 0x1ee6, 0x1ee6 },
+	{ 0x1ee8, 0x1ee8 },
+	{ 0x1eea, 0x1eea },
+	{ 0x1eec, 0x1eec },
+	{ 0x1eee, 0x1eee },
+	{ 0x1ef0, 0x1ef0 },
+	{ 0x1ef2, 0x1ef2 },
+	{ 0x1ef4, 0x1ef4 },
+	{ 0x1ef6, 0x1ef6 },
+	{ 0x1ef8, 0x1ef8 },
+	{ 0x1efa, 0x1efa },
+	{ 0x1efc, 0x1efc },
+	{ 0x1efe, 0x1efe },
+	{ 0x1f08, 0x1f0f },
+	{ 0x1f18, 0x1f1d },
+	{ 0x1f28, 0x1f2f },
+	{ 0x1f38, 0x1f3f },
+	{ 0x1f48, 0x1f4d },
+	{ 0x1f59, 0x1f59 },
+	{ 0x1f5b, 0x1f5b },
+	{ 0x1f5d, 0x1f5d },
+	{ 0x1f5f, 0x1f5f },
+	{ 0x1f68, 0x1f6f },
+	{ 0x1fb8, 0x1fbb },
+	{ 0x1fc8, 0x1fcb },
+	{ 0x1fd8, 0x1fdb },
+	{ 0x1fe8, 0x1fec },
+	{ 0x1ff8, 0x1ffb },
+	{ 0x2102, 0x2102 },
+	{ 0x2107, 0x2107 },
+	{ 0x210b, 0x210d },
+	{ 0x2110, 0x2112 },
+	{ 0x2115, 0x2115 },
+	{ 0x2119, 0x211d },
+	{ 0x2124, 0x2124 },
+	{ 0x2126, 0x2126 },
+	{ 0x2128, 0x2128 },
+	{ 0x212a, 0x212d },
+	{ 0x2130, 0x2133 },
+	{ 0x213e, 0x213f },
+	{ 0x2145, 0x2145 },
+	{ 0x2160, 0x216f },
+	{ 0x2183, 0x2183 },
+	{ 0x24b6, 0x24cf },
+	{ 0x2c00, 0x2c2f },
+	{ 0x2c60, 0x2c60 },
+	{ 0x2c62, 0x2c64 },
+	{ 0x2c67, 0x2c67 },
+	{ 0x2c69, 0x2c69 },
+	{ 0x2c6b, 0x2c6b },
+	{ 0x2c6d, 0x2c70 },
+	{ 0x2c72, 0x2c72 },
+	{ 0x2c75, 0x2c75 },
+	{ 0x2c7e, 0x2c80 },
+	{ 0x2c82, 0x2c82 },
+	{ 0x2c84, 0x2c84 },
+	{ 0x2c86, 0x2c86 },
+	{ 0x2c88, 0x2c88 },
+	{ 0x2c8a, 0x2c8a },
+	{ 0x2c8c, 0x2c8c },
+	{ 0x2c8e, 0x2c8e },
+	{ 0x2c90, 0x2c90 },
+	{ 0x2c92, 0x2c92 },
+	{ 0x2c94, 0x2c94 },
+	{ 0x2c96, 0x2c96 },
+	{ 0x2c98, 0x2c98 },
+	{ 0x2c9a, 0x2c9a },
+	{ 0x2c9c, 0x2c9c },
+	{ 0x2c9e, 0x2c9e },
+	{ 0x2ca0, 0x2ca0 },
+	{ 0x2ca2, 0x2ca2 },
+	{ 0x2ca4, 0x2ca4 },
+	{ 0x2ca6, 0x2ca6 },
+	{ 0x2ca8, 0x2ca8 },
+	{ 0x2caa, 0x2caa },
+	{ 0x2cac, 0x2cac },
+	{ 0x2cae, 0x2cae },
+	{ 0x2cb0, 0x2cb0 },
+	{ 0x2cb2, 0x2cb2 },
+	{ 0x2cb4, 0x2cb4 },
+	{ 0x2cb6, 0x2cb6 },
+	{ 0x2cb8, 0x2cb8 },
+	{ 0x2cba, 0x2cba },
+	{ 0x2cbc, 0x2cbc },
+	{ 0x2cbe, 0x2cbe },
+	{ 0x2cc0, 0x2cc0 },
+	{ 0x2cc2, 0x2cc2 },
+	{ 0x2cc4, 0x2cc4 },
+	{ 0x2cc6, 0x2cc6 },
+	{ 0x2cc8, 0x2cc8 },
+	{ 0x2cca, 0x2cca },
+	{ 0x2ccc, 0x2ccc },
+	{ 0x2cce, 0x2cce },
+	{ 0x2cd0, 0x2cd0 },
+	{ 0x2cd2, 0x2cd2 },
+	{ 0x2cd4, 0x2cd4 },
+	{ 0x2cd6, 0x2cd6 },
+	{ 0x2cd8, 0x2cd8 },
+	{ 0x2cda, 0x2cda },
+	{ 0x2cdc, 0x2cdc },
+	{ 0x2cde, 0x2cde },
+	{ 0x2ce0, 0x2ce0 },
+	{ 0x2ce2, 0x2ce2 },
+	{ 0x2ceb, 0x2ceb },
+	{ 0x2ced, 0x2ced },
+	{ 0x2cf2, 0x2cf2 },
+	{ 0xa640, 0xa640 },
+	{ 0xa642, 0xa642 },
+	{ 0xa644, 0xa644 },
+	{ 0xa646, 0xa646 },
+	{ 0xa648, 0xa648 },
+	{ 0xa64a, 0xa64a },
+	{ 0xa64c, 0xa64c },
+	{ 0xa64e, 0xa64e },
+	{ 0xa650, 0xa650 },
+	{ 0xa652, 0xa652 },
+	{ 0xa654, 0xa654 },
+	{ 0xa656, 0xa656 },
+	{ 0xa658, 0xa658 },
+	{ 0xa65a, 0xa65a },
+	{ 0xa65c, 0xa65c },
+	{ 0xa65e, 0xa65e },
+	{ 0xa660, 0xa660 },
+	{ 0xa662, 0xa662 },
+	{ 0xa664, 0xa664 },
+	{ 0xa666, 0xa666 },
+	{ 0xa668, 0xa668 },
+	{ 0xa66a, 0xa66a },
+	{ 0xa66c, 0xa66c },
+	{ 0xa680, 0xa680 },
+	{ 0xa682, 0xa682 },
+	{ 0xa684, 0xa684 },
+	{ 0xa686, 0xa686 },
+	{ 0xa688, 0xa688 },
+	{ 0xa68a, 0xa68a },
+	{ 0xa68c, 0xa68c },
+	{ 0xa68e, 0xa68e },
+	{ 0xa690, 0xa690 },
+	{ 0xa692, 0xa692 },
+	{ 0xa694, 0xa694 },
+	{ 0xa696, 0xa696 },
+	{ 0xa698, 0xa698 },
+	{ 0xa69a, 0xa69a },
+	{ 0xa722, 0xa722 },
+	{ 0xa724, 0xa724 },
+	{ 0xa726, 0xa726 },
+	{ 0xa728, 0xa728 },
+	{ 0xa72a, 0xa72a },
+	{ 0xa72c, 0xa72c },
+	{ 0xa72e, 0xa72e },
+	{ 0xa732, 0xa732 },
+	{ 0xa734, 0xa734 },
+	{ 0xa736, 0xa736 },
+	{ 0xa738, 0xa738 },
+	{ 0xa73a, 0xa73a },
+	{ 0xa73c, 0xa73c },
+	{ 0xa73e, 0xa73e },
+	{ 0xa740, 0xa740 },
+	{ 0xa742, 0xa742 },
+	{ 0xa744, 0xa744 },
+	{ 0xa746, 0xa746 },
+	{ 0xa748, 0xa748 },
+	{ 0xa74a, 0xa74a },
+	{ 0xa74c, 0xa74c },
+	{ 0xa74e, 0xa74e },
+	{ 0xa750, 0xa750 },
+	{ 0xa752, 0xa752 },
+	{ 0xa754, 0xa754 },
+	{ 0xa756, 0xa756 },
+	{ 0xa758, 0xa758 },
+	{ 0xa75a, 0xa75a },
+	{ 0xa75c, 0xa75c },
+	{ 0xa75e, 0xa75e },
+	{ 0xa760, 0xa760 },
+	{ 0xa762, 0xa762 },
+	{ 0xa764, 0xa764 },
+	{ 0xa766, 0xa766 },
+	{ 0xa768, 0xa768 },
+	{ 0xa76a, 0xa76a },
+	{ 0xa76c, 0xa76c },
+	{ 0xa76e, 0xa76e },
+	{ 0xa779, 0xa779 },
+	{ 0xa77b, 0xa77b },
+	{ 0xa77d, 0xa77e },
+	{ 0xa780, 0xa780 },
+	{ 0xa782, 0xa782 },
+	{ 0xa784, 0xa784 },
+	{ 0xa786, 0xa786 },
+	{ 0xa78b, 0xa78b },
+	{ 0xa78d, 0xa78d },
+	{ 0xa790, 0xa790 },
+	{ 0xa792, 0xa792 },
+	{ 0xa796, 0xa796 },
+	{ 0xa798, 0xa798 },
+	{ 0xa79a, 0xa79a },
+	{ 0xa79c, 0xa79c },
+	{ 0xa79e, 0xa79e },
+	{ 0xa7a0, 0xa7a0 },
+	{ 0xa7a2, 0xa7a2 },
+	{ 0xa7a4, 0xa7a4 },
+	{ 0xa7a6, 0xa7a6 },
+	{ 0xa7a8, 0xa7a8 },
+	{ 0xa7aa, 0xa7ae },
+	{ 0xa7b0, 0xa7b4 },
+	{ 0xa7b6, 0xa7b6 },
+	{ 0xa7b8, 0xa7b8 },
+	{ 0xa7ba, 0xa7ba },
+	{ 0xa7bc, 0xa7bc },
+	{ 0xa7be, 0xa7be },
+	{ 0xa7c0, 0xa7c0 },
+	{ 0xa7c2, 0xa7c2 },
+	{ 0xa7c4, 0xa7c7 },
+	{ 0xa7c9, 0xa7c9 },
+	{ 0xa7cb, 0xa7cc },
+	{ 0xa7d0, 0xa7d0 },
+	{ 0xa7d6, 0xa7d6 },
+	{ 0xa7d8, 0xa7d8 },
+	{ 0xa7da, 0xa7da },
+	{ 0xa7dc, 0xa7dc },
+	{ 0xa7f5, 0xa7f5 },
+	{ 0xff21, 0xff3a },
+	{ 0x10400, 0x10427 },
+	{ 0x104b0, 0x104d3 },
+	{ 0x10570, 0x1057a },
+	{ 0x1057c, 0x1058a },
+	{ 0x1058c, 0x10592 },
+	{ 0x10594, 0x10595 },
+	{ 0x10c80, 0x10cb2 },
+	{ 0x10d50, 0x10d65 },
+	{ 0x118a0, 0x118bf },
+	{ 0x16e40, 0x16e5f },
+	{ 0x1d400, 0x1d419 },
+	{ 0x1d434, 0x1d44d },
+	{ 0x1d468, 0x1d481 },
+	{ 0x1d49c, 0x1d49c },
+	{ 0x1d49e, 0x1d49f },
+	{ 0x1d4a2, 0x1d4a2 },
+	{ 0x1d4a5, 0x1d4a6 },
+	{ 0x1d4a9, 0x1d4ac },
+	{ 0x1d4ae, 0x1d4b5 },
+	{ 0x1d4d0, 0x1d4e9 },
+	{ 0x1d504, 0x1d505 },
+	{ 0x1d507, 0x1d50a },
+	{ 0x1d50d, 0x1d514 },
+	{ 0x1d516, 0x1d51c },
+	{ 0x1d538, 0x1d539 },
+	{ 0x1d53b, 0x1d53e },
+	{ 0x1d540, 0x1d544 },
+	{ 0x1d546, 0x1d546 },
+	{ 0x1d54a, 0x1d550 },
+	{ 0x1d56c, 0x1d585 },
+	{ 0x1d5a0, 0x1d5b9 },
+	{ 0x1d5d4, 0x1d5ed },
+	{ 0x1d608, 0x1d621 },
+	{ 0x1d63c, 0x1d655 },
+	{ 0x1d670, 0x1d689 },
+	{ 0x1d6a8, 0x1d6c0 },
+	{ 0x1d6e2, 0x1d6fa },
+	{ 0x1d71c, 0x1d734 },
+	{ 0x1d756, 0x1d76e },
+	{ 0x1d790, 0x1d7a8 },
+	{ 0x1d7ca, 0x1d7ca },
+	{ 0x1e900, 0x1e921 },
+	{ 0x1f130, 0x1f149 },
+	{ 0x1f150, 0x1f169 },
+	{ 0x1f170, 0x1f189 },
+};
+
+constexpr inline CharRange lowercase_letter[] = {
+	{ 0x61, 0x7a },
+	{ 0xaa, 0xaa },
+	{ 0xb5, 0xb5 },
+	{ 0xba, 0xba },
+	{ 0xdf, 0xf6 },
+	{ 0xf8, 0xff },
+	{ 0x101, 0x101 },
+	{ 0x103, 0x103 },
+	{ 0x105, 0x105 },
+	{ 0x107, 0x107 },
+	{ 0x109, 0x109 },
+	{ 0x10b, 0x10b },
+	{ 0x10d, 0x10d },
+	{ 0x10f, 0x10f },
+	{ 0x111, 0x111 },
+	{ 0x113, 0x113 },
+	{ 0x115, 0x115 },
+	{ 0x117, 0x117 },
+	{ 0x119, 0x119 },
+	{ 0x11b, 0x11b },
+	{ 0x11d, 0x11d },
+	{ 0x11f, 0x11f },
+	{ 0x121, 0x121 },
+	{ 0x123, 0x123 },
+	{ 0x125, 0x125 },
+	{ 0x127, 0x127 },
+	{ 0x129, 0x129 },
+	{ 0x12b, 0x12b },
+	{ 0x12d, 0x12d },
+	{ 0x12f, 0x12f },
+	{ 0x131, 0x131 },
+	{ 0x133, 0x133 },
+	{ 0x135, 0x135 },
+	{ 0x137, 0x138 },
+	{ 0x13a, 0x13a },
+	{ 0x13c, 0x13c },
+	{ 0x13e, 0x13e },
+	{ 0x140, 0x140 },
+	{ 0x142, 0x142 },
+	{ 0x144, 0x144 },
+	{ 0x146, 0x146 },
+	{ 0x148, 0x149 },
+	{ 0x14b, 0x14b },
+	{ 0x14d, 0x14d },
+	{ 0x14f, 0x14f },
+	{ 0x151, 0x151 },
+	{ 0x153, 0x153 },
+	{ 0x155, 0x155 },
+	{ 0x157, 0x157 },
+	{ 0x159, 0x159 },
+	{ 0x15b, 0x15b },
+	{ 0x15d, 0x15d },
+	{ 0x15f, 0x15f },
+	{ 0x161, 0x161 },
+	{ 0x163, 0x163 },
+	{ 0x165, 0x165 },
+	{ 0x167, 0x167 },
+	{ 0x169, 0x169 },
+	{ 0x16b, 0x16b },
+	{ 0x16d, 0x16d },
+	{ 0x16f, 0x16f },
+	{ 0x171, 0x171 },
+	{ 0x173, 0x173 },
+	{ 0x175, 0x175 },
+	{ 0x177, 0x177 },
+	{ 0x17a, 0x17a },
+	{ 0x17c, 0x17c },
+	{ 0x17e, 0x180 },
+	{ 0x183, 0x183 },
+	{ 0x185, 0x185 },
+	{ 0x188, 0x188 },
+	{ 0x18c, 0x18d },
+	{ 0x192, 0x192 },
+	{ 0x195, 0x195 },
+	{ 0x199, 0x19b },
+	{ 0x19e, 0x19e },
+	{ 0x1a1, 0x1a1 },
+	{ 0x1a3, 0x1a3 },
+	{ 0x1a5, 0x1a5 },
+	{ 0x1a8, 0x1a8 },
+	{ 0x1aa, 0x1ab },
+	{ 0x1ad, 0x1ad },
+	{ 0x1b0, 0x1b0 },
+	{ 0x1b4, 0x1b4 },
+	{ 0x1b6, 0x1b6 },
+	{ 0x1b9, 0x1ba },
+	{ 0x1bd, 0x1bf },
+	{ 0x1c6, 0x1c6 },
+	{ 0x1c9, 0x1c9 },
+	{ 0x1cc, 0x1cc },
+	{ 0x1ce, 0x1ce },
+	{ 0x1d0, 0x1d0 },
+	{ 0x1d2, 0x1d2 },
+	{ 0x1d4, 0x1d4 },
+	{ 0x1d6, 0x1d6 },
+	{ 0x1d8, 0x1d8 },
+	{ 0x1da, 0x1da },
+	{ 0x1dc, 0x1dd },
+	{ 0x1df, 0x1df },
+	{ 0x1e1, 0x1e1 },
+	{ 0x1e3, 0x1e3 },
+	{ 0x1e5, 0x1e5 },
+	{ 0x1e7, 0x1e7 },
+	{ 0x1e9, 0x1e9 },
+	{ 0x1eb, 0x1eb },
+	{ 0x1ed, 0x1ed },
+	{ 0x1ef, 0x1f0 },
+	{ 0x1f3, 0x1f3 },
+	{ 0x1f5, 0x1f5 },
+	{ 0x1f9, 0x1f9 },
+	{ 0x1fb, 0x1fb },
+	{ 0x1fd, 0x1fd },
+	{ 0x1ff, 0x1ff },
+	{ 0x201, 0x201 },
+	{ 0x203, 0x203 },
+	{ 0x205, 0x205 },
+	{ 0x207, 0x207 },
+	{ 0x209, 0x209 },
+	{ 0x20b, 0x20b },
+	{ 0x20d, 0x20d },
+	{ 0x20f, 0x20f },
+	{ 0x211, 0x211 },
+	{ 0x213, 0x213 },
+	{ 0x215, 0x215 },
+	{ 0x217, 0x217 },
+	{ 0x219, 0x219 },
+	{ 0x21b, 0x21b },
+	{ 0x21d, 0x21d },
+	{ 0x21f, 0x21f },
+	{ 0x221, 0x221 },
+	{ 0x223, 0x223 },
+	{ 0x225, 0x225 },
+	{ 0x227, 0x227 },
+	{ 0x229, 0x229 },
+	{ 0x22b, 0x22b },
+	{ 0x22d, 0x22d },
+	{ 0x22f, 0x22f },
+	{ 0x231, 0x231 },
+	{ 0x233, 0x239 },
+	{ 0x23c, 0x23c },
+	{ 0x23f, 0x240 },
+	{ 0x242, 0x242 },
+	{ 0x247, 0x247 },
+	{ 0x249, 0x249 },
+	{ 0x24b, 0x24b },
+	{ 0x24d, 0x24d },
+	{ 0x24f, 0x293 },
+	{ 0x295, 0x2b8 },
+	{ 0x2c0, 0x2c1 },
+	{ 0x2e0, 0x2e4 },
+	{ 0x345, 0x345 },
+	{ 0x371, 0x371 },
+	{ 0x373, 0x373 },
+	{ 0x377, 0x377 },
+	{ 0x37a, 0x37d },
+	{ 0x390, 0x390 },
+	{ 0x3ac, 0x3ce },
+	{ 0x3d0, 0x3d1 },
+	{ 0x3d5, 0x3d7 },
+	{ 0x3d9, 0x3d9 },
+	{ 0x3db, 0x3db },
+	{ 0x3dd, 0x3dd },
+	{ 0x3df, 0x3df },
+	{ 0x3e1, 0x3e1 },
+	{ 0x3e3, 0x3e3 },
+	{ 0x3e5, 0x3e5 },
+	{ 0x3e7, 0x3e7 },
+	{ 0x3e9, 0x3e9 },
+	{ 0x3eb, 0x3eb },
+	{ 0x3ed, 0x3ed },
+	{ 0x3ef, 0x3f3 },
+	{ 0x3f5, 0x3f5 },
+	{ 0x3f8, 0x3f8 },
+	{ 0x3fb, 0x3fc },
+	{ 0x430, 0x45f },
+	{ 0x461, 0x461 },
+	{ 0x463, 0x463 },
+	{ 0x465, 0x465 },
+	{ 0x467, 0x467 },
+	{ 0x469, 0x469 },
+	{ 0x46b, 0x46b },
+	{ 0x46d, 0x46d },
+	{ 0x46f, 0x46f },
+	{ 0x471, 0x471 },
+	{ 0x473, 0x473 },
+	{ 0x475, 0x475 },
+	{ 0x477, 0x477 },
+	{ 0x479, 0x479 },
+	{ 0x47b, 0x47b },
+	{ 0x47d, 0x47d },
+	{ 0x47f, 0x47f },
+	{ 0x481, 0x481 },
+	{ 0x48b, 0x48b },
+	{ 0x48d, 0x48d },
+	{ 0x48f, 0x48f },
+	{ 0x491, 0x491 },
+	{ 0x493, 0x493 },
+	{ 0x495, 0x495 },
+	{ 0x497, 0x497 },
+	{ 0x499, 0x499 },
+	{ 0x49b, 0x49b },
+	{ 0x49d, 0x49d },
+	{ 0x49f, 0x49f },
+	{ 0x4a1, 0x4a1 },
+	{ 0x4a3, 0x4a3 },
+	{ 0x4a5, 0x4a5 },
+	{ 0x4a7, 0x4a7 },
+	{ 0x4a9, 0x4a9 },
+	{ 0x4ab, 0x4ab },
+	{ 0x4ad, 0x4ad },
+	{ 0x4af, 0x4af },
+	{ 0x4b1, 0x4b1 },
+	{ 0x4b3, 0x4b3 },
+	{ 0x4b5, 0x4b5 },
+	{ 0x4b7, 0x4b7 },
+	{ 0x4b9, 0x4b9 },
+	{ 0x4bb, 0x4bb },
+	{ 0x4bd, 0x4bd },
+	{ 0x4bf, 0x4bf },
+	{ 0x4c2, 0x4c2 },
+	{ 0x4c4, 0x4c4 },
+	{ 0x4c6, 0x4c6 },
+	{ 0x4c8, 0x4c8 },
+	{ 0x4ca, 0x4ca },
+	{ 0x4cc, 0x4cc },
+	{ 0x4ce, 0x4cf },
+	{ 0x4d1, 0x4d1 },
+	{ 0x4d3, 0x4d3 },
+	{ 0x4d5, 0x4d5 },
+	{ 0x4d7, 0x4d7 },
+	{ 0x4d9, 0x4d9 },
+	{ 0x4db, 0x4db },
+	{ 0x4dd, 0x4dd },
+	{ 0x4df, 0x4df },
+	{ 0x4e1, 0x4e1 },
+	{ 0x4e3, 0x4e3 },
+	{ 0x4e5, 0x4e5 },
+	{ 0x4e7, 0x4e7 },
+	{ 0x4e9, 0x4e9 },
+	{ 0x4eb, 0x4eb },
+	{ 0x4ed, 0x4ed },
+	{ 0x4ef, 0x4ef },
+	{ 0x4f1, 0x4f1 },
+	{ 0x4f3, 0x4f3 },
+	{ 0x4f5, 0x4f5 },
+	{ 0x4f7, 0x4f7 },
+	{ 0x4f9, 0x4f9 },
+	{ 0x4fb, 0x4fb },
+	{ 0x4fd, 0x4fd },
+	{ 0x4ff, 0x4ff },
+	{ 0x501, 0x501 },
+	{ 0x503, 0x503 },
+	{ 0x505, 0x505 },
+	{ 0x507, 0x507 },
+	{ 0x509, 0x509 },
+	{ 0x50b, 0x50b },
+	{ 0x50d, 0x50d },
+	{ 0x50f, 0x50f },
+	{ 0x511, 0x511 },
+	{ 0x513, 0x513 },
+	{ 0x515, 0x515 },
+	{ 0x517, 0x517 },
+	{ 0x519, 0x519 },
+	{ 0x51b, 0x51b },
+	{ 0x51d, 0x51d },
+	{ 0x51f, 0x51f },
+	{ 0x521, 0x521 },
+	{ 0x523, 0x523 },
+	{ 0x525, 0x525 },
+	{ 0x527, 0x527 },
+	{ 0x529, 0x529 },
+	{ 0x52b, 0x52b },
+	{ 0x52d, 0x52d },
+	{ 0x52f, 0x52f },
+	{ 0x560, 0x588 },
+	{ 0x10d0, 0x10fa },
+	{ 0x10fc, 0x10ff },
+	{ 0x13f8, 0x13fd },
+	{ 0x1c80, 0x1c88 },
+	{ 0x1c8a, 0x1c8a },
+	{ 0x1d00, 0x1dbf },
+	{ 0x1e01, 0x1e01 },
+	{ 0x1e03, 0x1e03 },
+	{ 0x1e05, 0x1e05 },
+	{ 0x1e07, 0x1e07 },
+	{ 0x1e09, 0x1e09 },
+	{ 0x1e0b, 0x1e0b },
+	{ 0x1e0d, 0x1e0d },
+	{ 0x1e0f, 0x1e0f },
+	{ 0x1e11, 0x1e11 },
+	{ 0x1e13, 0x1e13 },
+	{ 0x1e15, 0x1e15 },
+	{ 0x1e17, 0x1e17 },
+	{ 0x1e19, 0x1e19 },
+	{ 0x1e1b, 0x1e1b },
+	{ 0x1e1d, 0x1e1d },
+	{ 0x1e1f, 0x1e1f },
+	{ 0x1e21, 0x1e21 },
+	{ 0x1e23, 0x1e23 },
+	{ 0x1e25, 0x1e25 },
+	{ 0x1e27, 0x1e27 },
+	{ 0x1e29, 0x1e29 },
+	{ 0x1e2b, 0x1e2b },
+	{ 0x1e2d, 0x1e2d },
+	{ 0x1e2f, 0x1e2f },
+	{ 0x1e31, 0x1e31 },
+	{ 0x1e33, 0x1e33 },
+	{ 0x1e35, 0x1e35 },
+	{ 0x1e37, 0x1e37 },
+	{ 0x1e39, 0x1e39 },
+	{ 0x1e3b, 0x1e3b },
+	{ 0x1e3d, 0x1e3d },
+	{ 0x1e3f, 0x1e3f },
+	{ 0x1e41, 0x1e41 },
+	{ 0x1e43, 0x1e43 },
+	{ 0x1e45, 0x1e45 },
+	{ 0x1e47, 0x1e47 },
+	{ 0x1e49, 0x1e49 },
+	{ 0x1e4b, 0x1e4b },
+	{ 0x1e4d, 0x1e4d },
+	{ 0x1e4f, 0x1e4f },
+	{ 0x1e51, 0x1e51 },
+	{ 0x1e53, 0x1e53 },
+	{ 0x1e55, 0x1e55 },
+	{ 0x1e57, 0x1e57 },
+	{ 0x1e59, 0x1e59 },
+	{ 0x1e5b, 0x1e5b },
+	{ 0x1e5d, 0x1e5d },
+	{ 0x1e5f, 0x1e5f },
+	{ 0x1e61, 0x1e61 },
+	{ 0x1e63, 0x1e63 },
+	{ 0x1e65, 0x1e65 },
+	{ 0x1e67, 0x1e67 },
+	{ 0x1e69, 0x1e69 },
+	{ 0x1e6b, 0x1e6b },
+	{ 0x1e6d, 0x1e6d },
+	{ 0x1e6f, 0x1e6f },
+	{ 0x1e71, 0x1e71 },
+	{ 0x1e73, 0x1e73 },
+	{ 0x1e75, 0x1e75 },
+	{ 0x1e77, 0x1e77 },
+	{ 0x1e79, 0x1e79 },
+	{ 0x1e7b, 0x1e7b },
+	{ 0x1e7d, 0x1e7d },
+	{ 0x1e7f, 0x1e7f },
+	{ 0x1e81, 0x1e81 },
+	{ 0x1e83, 0x1e83 },
+	{ 0x1e85, 0x1e85 },
+	{ 0x1e87, 0x1e87 },
+	{ 0x1e89, 0x1e89 },
+	{ 0x1e8b, 0x1e8b },
+	{ 0x1e8d, 0x1e8d },
+	{ 0x1e8f, 0x1e8f },
+	{ 0x1e91, 0x1e91 },
+	{ 0x1e93, 0x1e93 },
+	{ 0x1e95, 0x1e9d },
+	{ 0x1e9f, 0x1e9f },
+	{ 0x1ea1, 0x1ea1 },
+	{ 0x1ea3, 0x1ea3 },
+	{ 0x1ea5, 0x1ea5 },
+	{ 0x1ea7, 0x1ea7 },
+	{ 0x1ea9, 0x1ea9 },
+	{ 0x1eab, 0x1eab },
+	{ 0x1ead, 0x1ead },
+	{ 0x1eaf, 0x1eaf },
+	{ 0x1eb1, 0x1eb1 },
+	{ 0x1eb3, 0x1eb3 },
+	{ 0x1eb5, 0x1eb5 },
+	{ 0x1eb7, 0x1eb7 },
+	{ 0x1eb9, 0x1eb9 },
+	{ 0x1ebb, 0x1ebb },
+	{ 0x1ebd, 0x1ebd },
+	{ 0x1ebf, 0x1ebf },
+	{ 0x1ec1, 0x1ec1 },
+	{ 0x1ec3, 0x1ec3 },
+	{ 0x1ec5, 0x1ec5 },
+	{ 0x1ec7, 0x1ec7 },
+	{ 0x1ec9, 0x1ec9 },
+	{ 0x1ecb, 0x1ecb },
+	{ 0x1ecd, 0x1ecd },
+	{ 0x1ecf, 0x1ecf },
+	{ 0x1ed1, 0x1ed1 },
+	{ 0x1ed3, 0x1ed3 },
+	{ 0x1ed5, 0x1ed5 },
+	{ 0x1ed7, 0x1ed7 },
+	{ 0x1ed9, 0x1ed9 },
+	{ 0x1edb, 0x1edb },
+	{ 0x1edd, 0x1edd },
+	{ 0x1edf, 0x1edf },
+	{ 0x1ee1, 0x1ee1 },
+	{ 0x1ee3, 0x1ee3 },
+	{ 0x1ee5, 0x1ee5 },
+	{ 0x1ee7, 0x1ee7 },
+	{ 0x1ee9, 0x1ee9 },
+	{ 0x1eeb, 0x1eeb },
+	{ 0x1eed, 0x1eed },
+	{ 0x1eef, 0x1eef },
+	{ 0x1ef1, 0x1ef1 },
+	{ 0x1ef3, 0x1ef3 },
+	{ 0x1ef5, 0x1ef5 },
+	{ 0x1ef7, 0x1ef7 },
+	{ 0x1ef9, 0x1ef9 },
+	{ 0x1efb, 0x1efb },
+	{ 0x1efd, 0x1efd },
+	{ 0x1eff, 0x1f07 },
+	{ 0x1f10, 0x1f15 },
+	{ 0x1f20, 0x1f27 },
+	{ 0x1f30, 0x1f37 },
+	{ 0x1f40, 0x1f45 },
+	{ 0x1f50, 0x1f57 },
+	{ 0x1f60, 0x1f67 },
+	{ 0x1f70, 0x1f7d },
+	{ 0x1f80, 0x1f87 },
+	{ 0x1f90, 0x1f97 },
+	{ 0x1fa0, 0x1fa7 },
+	{ 0x1fb0, 0x1fb4 },
+	{ 0x1fb6, 0x1fb7 },
+	{ 0x1fbe, 0x1fbe },
+	{ 0x1fc2, 0x1fc4 },
+	{ 0x1fc6, 0x1fc7 },
+	{ 0x1fd0, 0x1fd3 },
+	{ 0x1fd6, 0x1fd7 },
+	{ 0x1fe0, 0x1fe7 },
+	{ 0x1ff2, 0x1ff4 },
+	{ 0x1ff6, 0x1ff7 },
+	{ 0x2071, 0x2071 },
+	{ 0x207f, 0x207f },
+	{ 0x2090, 0x209c },
+	{ 0x210a, 0x210a },
+	{ 0x210e, 0x210f },
+	{ 0x2113, 0x2113 },
+	{ 0x212f, 0x212f },
+	{ 0x2134, 0x2134 },
+	{ 0x2139, 0x2139 },
+	{ 0x213c, 0x213d },
+	{ 0x2146, 0x2149 },
+	{ 0x214e, 0x214e },
+	{ 0x2170, 0x217f },
+	{ 0x2184, 0x2184 },
+	{ 0x24d0, 0x24e9 },
+	{ 0x2c30, 0x2c5f },
+	{ 0x2c61, 0x2c61 },
+	{ 0x2c65, 0x2c66 },
+	{ 0x2c68, 0x2c68 },
+	{ 0x2c6a, 0x2c6a },
+	{ 0x2c6c, 0x2c6c },
+	{ 0x2c71, 0x2c71 },
+	{ 0x2c73, 0x2c74 },
+	{ 0x2c76, 0x2c7d },
+	{ 0x2c81, 0x2c81 },
+	{ 0x2c83, 0x2c83 },
+	{ 0x2c85, 0x2c85 },
+	{ 0x2c87, 0x2c87 },
+	{ 0x2c89, 0x2c89 },
+	{ 0x2c8b, 0x2c8b },
+	{ 0x2c8d, 0x2c8d },
+	{ 0x2c8f, 0x2c8f },
+	{ 0x2c91, 0x2c91 },
+	{ 0x2c93, 0x2c93 },
+	{ 0x2c95, 0x2c95 },
+	{ 0x2c97, 0x2c97 },
+	{ 0x2c99, 0x2c99 },
+	{ 0x2c9b, 0x2c9b },
+	{ 0x2c9d, 0x2c9d },
+	{ 0x2c9f, 0x2c9f },
+	{ 0x2ca1, 0x2ca1 },
+	{ 0x2ca3, 0x2ca3 },
+	{ 0x2ca5, 0x2ca5 },
+	{ 0x2ca7, 0x2ca7 },
+	{ 0x2ca9, 0x2ca9 },
+	{ 0x2cab, 0x2cab },
+	{ 0x2cad, 0x2cad },
+	{ 0x2caf, 0x2caf },
+	{ 0x2cb1, 0x2cb1 },
+	{ 0x2cb3, 0x2cb3 },
+	{ 0x2cb5, 0x2cb5 },
+	{ 0x2cb7, 0x2cb7 },
+	{ 0x2cb9, 0x2cb9 },
+	{ 0x2cbb, 0x2cbb },
+	{ 0x2cbd, 0x2cbd },
+	{ 0x2cbf, 0x2cbf },
+	{ 0x2cc1, 0x2cc1 },
+	{ 0x2cc3, 0x2cc3 },
+	{ 0x2cc5, 0x2cc5 },
+	{ 0x2cc7, 0x2cc7 },
+	{ 0x2cc9, 0x2cc9 },
+	{ 0x2ccb, 0x2ccb },
+	{ 0x2ccd, 0x2ccd },
+	{ 0x2ccf, 0x2ccf },
+	{ 0x2cd1, 0x2cd1 },
+	{ 0x2cd3, 0x2cd3 },
+	{ 0x2cd5, 0x2cd5 },
+	{ 0x2cd7, 0x2cd7 },
+	{ 0x2cd9, 0x2cd9 },
+	{ 0x2cdb, 0x2cdb },
+	{ 0x2cdd, 0x2cdd },
+	{ 0x2cdf, 0x2cdf },
+	{ 0x2ce1, 0x2ce1 },
+	{ 0x2ce3, 0x2ce4 },
+	{ 0x2cec, 0x2cec },
+	{ 0x2cee, 0x2cee },
+	{ 0x2cf3, 0x2cf3 },
+	{ 0x2d00, 0x2d25 },
+	{ 0x2d27, 0x2d27 },
+	{ 0x2d2d, 0x2d2d },
+	{ 0xa641, 0xa641 },
+	{ 0xa643, 0xa643 },
+	{ 0xa645, 0xa645 },
+	{ 0xa647, 0xa647 },
+	{ 0xa649, 0xa649 },
+	{ 0xa64b, 0xa64b },
+	{ 0xa64d, 0xa64d },
+	{ 0xa64f, 0xa64f },
+	{ 0xa651, 0xa651 },
+	{ 0xa653, 0xa653 },
+	{ 0xa655, 0xa655 },
+	{ 0xa657, 0xa657 },
+	{ 0xa659, 0xa659 },
+	{ 0xa65b, 0xa65b },
+	{ 0xa65d, 0xa65d },
+	{ 0xa65f, 0xa65f },
+	{ 0xa661, 0xa661 },
+	{ 0xa663, 0xa663 },
+	{ 0xa665, 0xa665 },
+	{ 0xa667, 0xa667 },
+	{ 0xa669, 0xa669 },
+	{ 0xa66b, 0xa66b },
+	{ 0xa66d, 0xa66d },
+	{ 0xa681, 0xa681 },
+	{ 0xa683, 0xa683 },
+	{ 0xa685, 0xa685 },
+	{ 0xa687, 0xa687 },
+	{ 0xa689, 0xa689 },
+	{ 0xa68b, 0xa68b },
+	{ 0xa68d, 0xa68d },
+	{ 0xa68f, 0xa68f },
+	{ 0xa691, 0xa691 },
+	{ 0xa693, 0xa693 },
+	{ 0xa695, 0xa695 },
+	{ 0xa697, 0xa697 },
+	{ 0xa699, 0xa699 },
+	{ 0xa69b, 0xa69d },
+	{ 0xa723, 0xa723 },
+	{ 0xa725, 0xa725 },
+	{ 0xa727, 0xa727 },
+	{ 0xa729, 0xa729 },
+	{ 0xa72b, 0xa72b },
+	{ 0xa72d, 0xa72d },
+	{ 0xa72f, 0xa731 },
+	{ 0xa733, 0xa733 },
+	{ 0xa735, 0xa735 },
+	{ 0xa737, 0xa737 },
+	{ 0xa739, 0xa739 },
+	{ 0xa73b, 0xa73b },
+	{ 0xa73d, 0xa73d },
+	{ 0xa73f, 0xa73f },
+	{ 0xa741, 0xa741 },
+	{ 0xa743, 0xa743 },
+	{ 0xa745, 0xa745 },
+	{ 0xa747, 0xa747 },
+	{ 0xa749, 0xa749 },
+	{ 0xa74b, 0xa74b },
+	{ 0xa74d, 0xa74d },
+	{ 0xa74f, 0xa74f },
+	{ 0xa751, 0xa751 },
+	{ 0xa753, 0xa753 },
+	{ 0xa755, 0xa755 },
+	{ 0xa757, 0xa757 },
+	{ 0xa759, 0xa759 },
+	{ 0xa75b, 0xa75b },
+	{ 0xa75d, 0xa75d },
+	{ 0xa75f, 0xa75f },
+	{ 0xa761, 0xa761 },
+	{ 0xa763, 0xa763 },
+	{ 0xa765, 0xa765 },
+	{ 0xa767, 0xa767 },
+	{ 0xa769, 0xa769 },
+	{ 0xa76b, 0xa76b },
+	{ 0xa76d, 0xa76d },
+	{ 0xa76f, 0xa778 },
+	{ 0xa77a, 0xa77a },
+	{ 0xa77c, 0xa77c },
+	{ 0xa77f, 0xa77f },
+	{ 0xa781, 0xa781 },
+	{ 0xa783, 0xa783 },
+	{ 0xa785, 0xa785 },
+	{ 0xa787, 0xa787 },
+	{ 0xa78c, 0xa78c },
+	{ 0xa78e, 0xa78e },
+	{ 0xa791, 0xa791 },
+	{ 0xa793, 0xa795 },
+	{ 0xa797, 0xa797 },
+	{ 0xa799, 0xa799 },
+	{ 0xa79b, 0xa79b },
+	{ 0xa79d, 0xa79d },
+	{ 0xa79f, 0xa79f },
+	{ 0xa7a1, 0xa7a1 },
+	{ 0xa7a3, 0xa7a3 },
+	{ 0xa7a5, 0xa7a5 },
+	{ 0xa7a7, 0xa7a7 },
+	{ 0xa7a9, 0xa7a9 },
+	{ 0xa7af, 0xa7af },
+	{ 0xa7b5, 0xa7b5 },
+	{ 0xa7b7, 0xa7b7 },
+	{ 0xa7b9, 0xa7b9 },
+	{ 0xa7bb, 0xa7bb },
+	{ 0xa7bd, 0xa7bd },
+	{ 0xa7bf, 0xa7bf },
+	{ 0xa7c1, 0xa7c1 },
+	{ 0xa7c3, 0xa7c3 },
+	{ 0xa7c8, 0xa7c8 },
+	{ 0xa7ca, 0xa7ca },
+	{ 0xa7cd, 0xa7cd },
+	{ 0xa7d1, 0xa7d1 },
+	{ 0xa7d3, 0xa7d3 },
+	{ 0xa7d5, 0xa7d5 },
+	{ 0xa7d7, 0xa7d7 },
+	{ 0xa7d9, 0xa7d9 },
+	{ 0xa7db, 0xa7db },
+	{ 0xa7f2, 0xa7f4 },
+	{ 0xa7f6, 0xa7f6 },
+	{ 0xa7f8, 0xa7fa },
+	{ 0xab30, 0xab5a },
+	{ 0xab5c, 0xab69 },
+	{ 0xab70, 0xabbf },
+	{ 0xfb00, 0xfb06 },
+	{ 0xfb13, 0xfb17 },
+	{ 0xff41, 0xff5a },
+	{ 0x10428, 0x1044f },
+	{ 0x104d8, 0x104fb },
+	{ 0x10597, 0x105a1 },
+	{ 0x105a3, 0x105b1 },
+	{ 0x105b3, 0x105b9 },
+	{ 0x105bb, 0x105bc },
+	{ 0x10780, 0x10780 },
+	{ 0x10783, 0x10785 },
+	{ 0x10787, 0x107b0 },
+	{ 0x107b2, 0x107ba },
+	{ 0x10cc0, 0x10cf2 },
+	{ 0x10d70, 0x10d85 },
+	{ 0x118c0, 0x118df },
+	{ 0x16e60, 0x16e7f },
+	{ 0x1d41a, 0x1d433 },
+	{ 0x1d44e, 0x1d454 },
+	{ 0x1d456, 0x1d467 },
+	{ 0x1d482, 0x1d49b },
+	{ 0x1d4b6, 0x1d4b9 },
+	{ 0x1d4bb, 0x1d4bb },
+	{ 0x1d4bd, 0x1d4c3 },
+	{ 0x1d4c5, 0x1d4cf },
+	{ 0x1d4ea, 0x1d503 },
+	{ 0x1d51e, 0x1d537 },
+	{ 0x1d552, 0x1d56b },
+	{ 0x1d586, 0x1d59f },
+	{ 0x1d5ba, 0x1d5d3 },
+	{ 0x1d5ee, 0x1d607 },
+	{ 0x1d622, 0x1d63b },
+	{ 0x1d656, 0x1d66f },
+	{ 0x1d68a, 0x1d6a5 },
+	{ 0x1d6c2, 0x1d6da },
+	{ 0x1d6dc, 0x1d6e1 },
+	{ 0x1d6fc, 0x1d714 },
+	{ 0x1d716, 0x1d71b },
+	{ 0x1d736, 0x1d74e },
+	{ 0x1d750, 0x1d755 },
+	{ 0x1d770, 0x1d788 },
+	{ 0x1d78a, 0x1d78f },
+	{ 0x1d7aa, 0x1d7c2 },
+	{ 0x1d7c4, 0x1d7c9 },
+	{ 0x1d7cb, 0x1d7cb },
+	{ 0x1df00, 0x1df09 },
+	{ 0x1df0b, 0x1df1e },
+	{ 0x1df25, 0x1df2a },
+	{ 0x1e030, 0x1e06d },
+	{ 0x1e922, 0x1e943 },
+};
+
+constexpr inline CharRange unicode_letter[] = {
+	{ 0x41, 0x5a },
+	{ 0x61, 0x7a },
+	{ 0xaa, 0xaa },
+	{ 0xb5, 0xb5 },
+	{ 0xba, 0xba },
+	{ 0xc0, 0xd6 },
+	{ 0xd8, 0xf6 },
+	{ 0xf8, 0x2c1 },
+	{ 0x2c6, 0x2d1 },
+	{ 0x2e0, 0x2e4 },
+	{ 0x2ec, 0x2ec },
+	{ 0x2ee, 0x2ee },
+	{ 0x345, 0x345 },
+	{ 0x363, 0x374 },
+	{ 0x376, 0x377 },
+	{ 0x37a, 0x37d },
+	{ 0x37f, 0x37f },
+	{ 0x386, 0x386 },
+	{ 0x388, 0x38a },
+	{ 0x38c, 0x38c },
+	{ 0x38e, 0x3a1 },
+	{ 0x3a3, 0x3f5 },
+	{ 0x3f7, 0x481 },
+	{ 0x48a, 0x52f },
+	{ 0x531, 0x556 },
+	{ 0x559, 0x559 },
+	{ 0x560, 0x588 },
+	{ 0x5b0, 0x5bd },
+	{ 0x5bf, 0x5bf },
+	{ 0x5c1, 0x5c2 },
+	{ 0x5c4, 0x5c5 },
+	{ 0x5c7, 0x5c7 },
+	{ 0x5d0, 0x5ea },
+	{ 0x5ef, 0x5f2 },
+	{ 0x610, 0x61a },
+	{ 0x620, 0x657 },
+	{ 0x659, 0x65f },
+	{ 0x66e, 0x6d3 },
+	{ 0x6d5, 0x6dc },
+	{ 0x6e1, 0x6e8 },
+	{ 0x6ed, 0x6ef },
+	{ 0x6fa, 0x6fc },
+	{ 0x6ff, 0x6ff },
+	{ 0x710, 0x73f },
+	{ 0x74d, 0x7b1 },
+	{ 0x7ca, 0x7ea },
+	{ 0x7f4, 0x7f5 },
+	{ 0x7fa, 0x7fa },
+	{ 0x800, 0x817 },
+	{ 0x81a, 0x82c },
+	{ 0x840, 0x858 },
+	{ 0x860, 0x86a },
+	{ 0x870, 0x887 },
+	{ 0x889, 0x88e },
+	{ 0x897, 0x897 },
+	{ 0x8a0, 0x8c9 },
+	{ 0x8d4, 0x8df },
+	{ 0x8e3, 0x8e9 },
+	{ 0x8f0, 0x93b },
+	{ 0x93d, 0x94c },
+	{ 0x94e, 0x950 },
+	{ 0x955, 0x963 },
+	{ 0x971, 0x983 },
+	{ 0x985, 0x98c },
+	{ 0x98f, 0x990 },
+	{ 0x993, 0x9a8 },
+	{ 0x9aa, 0x9b0 },
+	{ 0x9b2, 0x9b2 },
+	{ 0x9b6, 0x9b9 },
+	{ 0x9bd, 0x9c4 },
+	{ 0x9c7, 0x9c8 },
+	{ 0x9cb, 0x9cc },
+	{ 0x9ce, 0x9ce },
+	{ 0x9d7, 0x9d7 },
+	{ 0x9dc, 0x9dd },
+	{ 0x9df, 0x9e3 },
+	{ 0x9f0, 0x9f1 },
+	{ 0x9fc, 0x9fc },
+	{ 0xa01, 0xa03 },
+	{ 0xa05, 0xa0a },
+	{ 0xa0f, 0xa10 },
+	{ 0xa13, 0xa28 },
+	{ 0xa2a, 0xa30 },
+	{ 0xa32, 0xa33 },
+	{ 0xa35, 0xa36 },
+	{ 0xa38, 0xa39 },
+	{ 0xa3e, 0xa42 },
+	{ 0xa47, 0xa48 },
+	{ 0xa4b, 0xa4c },
+	{ 0xa51, 0xa51 },
+	{ 0xa59, 0xa5c },
+	{ 0xa5e, 0xa5e },
+	{ 0xa70, 0xa75 },
+	{ 0xa81, 0xa83 },
+	{ 0xa85, 0xa8d },
+	{ 0xa8f, 0xa91 },
+	{ 0xa93, 0xaa8 },
+	{ 0xaaa, 0xab0 },
+	{ 0xab2, 0xab3 },
+	{ 0xab5, 0xab9 },
+	{ 0xabd, 0xac5 },
+	{ 0xac7, 0xac9 },
+	{ 0xacb, 0xacc },
+	{ 0xad0, 0xad0 },
+	{ 0xae0, 0xae3 },
+	{ 0xaf9, 0xafc },
+	{ 0xb01, 0xb03 },
+	{ 0xb05, 0xb0c },
+	{ 0xb0f, 0xb10 },
+	{ 0xb13, 0xb28 },
+	{ 0xb2a, 0xb30 },
+	{ 0xb32, 0xb33 },
+	{ 0xb35, 0xb39 },
+	{ 0xb3d, 0xb44 },
+	{ 0xb47, 0xb48 },
+	{ 0xb4b, 0xb4c },
+	{ 0xb56, 0xb57 },
+	{ 0xb5c, 0xb5d },
+	{ 0xb5f, 0xb63 },
+	{ 0xb71, 0xb71 },
+	{ 0xb82, 0xb83 },
+	{ 0xb85, 0xb8a },
+	{ 0xb8e, 0xb90 },
+	{ 0xb92, 0xb95 },
+	{ 0xb99, 0xb9a },
+	{ 0xb9c, 0xb9c },
+	{ 0xb9e, 0xb9f },
+	{ 0xba3, 0xba4 },
+	{ 0xba8, 0xbaa },
+	{ 0xbae, 0xbb9 },
+	{ 0xbbe, 0xbc2 },
+	{ 0xbc6, 0xbc8 },
+	{ 0xbca, 0xbcc },
+	{ 0xbd0, 0xbd0 },
+	{ 0xbd7, 0xbd7 },
+	{ 0xc00, 0xc0c },
+	{ 0xc0e, 0xc10 },
+	{ 0xc12, 0xc28 },
+	{ 0xc2a, 0xc39 },
+	{ 0xc3d, 0xc44 },
+	{ 0xc46, 0xc48 },
+	{ 0xc4a, 0xc4c },
+	{ 0xc55, 0xc56 },
+	{ 0xc58, 0xc5a },
+	{ 0xc5d, 0xc5d },
+	{ 0xc60, 0xc63 },
+	{ 0xc80, 0xc83 },
+	{ 0xc85, 0xc8c },
+	{ 0xc8e, 0xc90 },
+	{ 0xc92, 0xca8 },
+	{ 0xcaa, 0xcb3 },
+	{ 0xcb5, 0xcb9 },
+	{ 0xcbd, 0xcc4 },
+	{ 0xcc6, 0xcc8 },
+	{ 0xcca, 0xccc },
+	{ 0xcd5, 0xcd6 },
+	{ 0xcdd, 0xcde },
+	{ 0xce0, 0xce3 },
+	{ 0xcf1, 0xcf3 },
+	{ 0xd00, 0xd0c },
+	{ 0xd0e, 0xd10 },
+	{ 0xd12, 0xd3a },
+	{ 0xd3d, 0xd44 },
+	{ 0xd46, 0xd48 },
+	{ 0xd4a, 0xd4c },
+	{ 0xd4e, 0xd4e },
+	{ 0xd54, 0xd57 },
+	{ 0xd5f, 0xd63 },
+	{ 0xd7a, 0xd7f },
+	{ 0xd81, 0xd83 },
+	{ 0xd85, 0xd96 },
+	{ 0xd9a, 0xdb1 },
+	{ 0xdb3, 0xdbb },
+	{ 0xdbd, 0xdbd },
+	{ 0xdc0, 0xdc6 },
+	{ 0xdcf, 0xdd4 },
+	{ 0xdd6, 0xdd6 },
+	{ 0xdd8, 0xddf },
+	{ 0xdf2, 0xdf3 },
+	{ 0xe01, 0xe3a },
+	{ 0xe40, 0xe46 },
+	{ 0xe4d, 0xe4d },
+	{ 0xe81, 0xe82 },
+	{ 0xe84, 0xe84 },
+	{ 0xe86, 0xe8a },
+	{ 0xe8c, 0xea3 },
+	{ 0xea5, 0xea5 },
+	{ 0xea7, 0xeb9 },
+	{ 0xebb, 0xebd },
+	{ 0xec0, 0xec4 },
+	{ 0xec6, 0xec6 },
+	{ 0xecd, 0xecd },
+	{ 0xedc, 0xedf },
+	{ 0xf00, 0xf00 },
+	{ 0xf40, 0xf47 },
+	{ 0xf49, 0xf6c },
+	{ 0xf71, 0xf83 },
+	{ 0xf88, 0xf97 },
+	{ 0xf99, 0xfbc },
+	{ 0x1000, 0x1036 },
+	{ 0x1038, 0x1038 },
+	{ 0x103b, 0x103f },
+	{ 0x1050, 0x108f },
+	{ 0x109a, 0x109d },
+	{ 0x10a0, 0x10c5 },
+	{ 0x10c7, 0x10c7 },
+	{ 0x10cd, 0x10cd },
+	{ 0x10d0, 0x10fa },
+	{ 0x10fc, 0x1248 },
+	{ 0x124a, 0x124d },
+	{ 0x1250, 0x1256 },
+	{ 0x1258, 0x1258 },
+	{ 0x125a, 0x125d },
+	{ 0x1260, 0x1288 },
+	{ 0x128a, 0x128d },
+	{ 0x1290, 0x12b0 },
+	{ 0x12b2, 0x12b5 },
+	{ 0x12b8, 0x12be },
+	{ 0x12c0, 0x12c0 },
+	{ 0x12c2, 0x12c5 },
+	{ 0x12c8, 0x12d6 },
+	{ 0x12d8, 0x1310 },
+	{ 0x1312, 0x1315 },
+	{ 0x1318, 0x135a },
+	{ 0x1380, 0x138f },
+	{ 0x13a0, 0x13f5 },
+	{ 0x13f8, 0x13fd },
+	{ 0x1401, 0x166c },
+	{ 0x166f, 0x167f },
+	{ 0x1681, 0x169a },
+	{ 0x16a0, 0x16ea },
+	{ 0x16ee, 0x16f8 },
+	{ 0x1700, 0x1713 },
+	{ 0x171f, 0x1733 },
+	{ 0x1740, 0x1753 },
+	{ 0x1760, 0x176c },
+	{ 0x176e, 0x1770 },
+	{ 0x1772, 0x1773 },
+	{ 0x1780, 0x17b3 },
+	{ 0x17b6, 0x17c8 },
+	{ 0x17d7, 0x17d7 },
+	{ 0x17dc, 0x17dc },
+	{ 0x1820, 0x1878 },
+	{ 0x1880, 0x18aa },
+	{ 0x18b0, 0x18f5 },
+	{ 0x1900, 0x191e },
+	{ 0x1920, 0x192b },
+	{ 0x1930, 0x1938 },
+	{ 0x1950, 0x196d },
+	{ 0x1970, 0x1974 },
+	{ 0x1980, 0x19ab },
+	{ 0x19b0, 0x19c9 },
+	{ 0x1a00, 0x1a1b },
+	{ 0x1a20, 0x1a5e },
+	{ 0x1a61, 0x1a74 },
+	{ 0x1aa7, 0x1aa7 },
+	{ 0x1abf, 0x1ac0 },
+	{ 0x1acc, 0x1ace },
+	{ 0x1b00, 0x1b33 },
+	{ 0x1b35, 0x1b43 },
+	{ 0x1b45, 0x1b4c },
+	{ 0x1b80, 0x1ba9 },
+	{ 0x1bac, 0x1baf },
+	{ 0x1bba, 0x1be5 },
+	{ 0x1be7, 0x1bf1 },
+	{ 0x1c00, 0x1c36 },
+	{ 0x1c4d, 0x1c4f },
+	{ 0x1c5a, 0x1c7d },
+	{ 0x1c80, 0x1c8a },
+	{ 0x1c90, 0x1cba },
+	{ 0x1cbd, 0x1cbf },
+	{ 0x1ce9, 0x1cec },
+	{ 0x1cee, 0x1cf3 },
+	{ 0x1cf5, 0x1cf6 },
+	{ 0x1cfa, 0x1cfa },
+	{ 0x1d00, 0x1dbf },
+	{ 0x1dd3, 0x1df4 },
+	{ 0x1e00, 0x1f15 },
+	{ 0x1f18, 0x1f1d },
+	{ 0x1f20, 0x1f45 },
+	{ 0x1f48, 0x1f4d },
+	{ 0x1f50, 0x1f57 },
+	{ 0x1f59, 0x1f59 },
+	{ 0x1f5b, 0x1f5b },
+	{ 0x1f5d, 0x1f5d },
+	{ 0x1f5f, 0x1f7d },
+	{ 0x1f80, 0x1fb4 },
+	{ 0x1fb6, 0x1fbc },
+	{ 0x1fbe, 0x1fbe },
+	{ 0x1fc2, 0x1fc4 },
+	{ 0x1fc6, 0x1fcc },
+	{ 0x1fd0, 0x1fd3 },
+	{ 0x1fd6, 0x1fdb },
+	{ 0x1fe0, 0x1fec },
+	{ 0x1ff2, 0x1ff4 },
+	{ 0x1ff6, 0x1ffc },
+	{ 0x2071, 0x2071 },
+	{ 0x207f, 0x207f },
+	{ 0x2090, 0x209c },
+	{ 0x2102, 0x2102 },
+	{ 0x2107, 0x2107 },
+	{ 0x210a, 0x2113 },
+	{ 0x2115, 0x2115 },
+	{ 0x2119, 0x211d },
+	{ 0x2124, 0x2124 },
+	{ 0x2126, 0x2126 },
+	{ 0x2128, 0x2128 },
+	{ 0x212a, 0x212d },
+	{ 0x212f, 0x2139 },
+	{ 0x213c, 0x213f },
+	{ 0x2145, 0x2149 },
+	{ 0x214e, 0x214e },
+	{ 0x2160, 0x2188 },
+	{ 0x24b6, 0x24e9 },
+	{ 0x2c00, 0x2ce4 },
+	{ 0x2ceb, 0x2cee },
+	{ 0x2cf2, 0x2cf3 },
+	{ 0x2d00, 0x2d25 },
+	{ 0x2d27, 0x2d27 },
+	{ 0x2d2d, 0x2d2d },
+	{ 0x2d30, 0x2d67 },
+	{ 0x2d6f, 0x2d6f },
+	{ 0x2d80, 0x2d96 },
+	{ 0x2da0, 0x2da6 },
+	{ 0x2da8, 0x2dae },
+	{ 0x2db0, 0x2db6 },
+	{ 0x2db8, 0x2dbe },
+	{ 0x2dc0, 0x2dc6 },
+	{ 0x2dc8, 0x2dce },
+	{ 0x2dd0, 0x2dd6 },
+	{ 0x2dd8, 0x2dde },
+	{ 0x2de0, 0x2dff },
+	{ 0x2e2f, 0x2e2f },
+	{ 0x3005, 0x3007 },
+	{ 0x3021, 0x3029 },
+	{ 0x3031, 0x3035 },
+	{ 0x3038, 0x303c },
+	{ 0x3041, 0x3096 },
+	{ 0x309d, 0x309f },
+	{ 0x30a1, 0x30fa },
+	{ 0x30fc, 0x30ff },
+	{ 0x3105, 0x312f },
+	{ 0x3131, 0x318e },
+	{ 0x31a0, 0x31bf },
+	{ 0x31f0, 0x31ff },
+	{ 0x3400, 0x4dbf },
+	{ 0x4e00, 0xa48c },
+	{ 0xa4d0, 0xa4fd },
+	{ 0xa500, 0xa60c },
+	{ 0xa610, 0xa61f },
+	{ 0xa62a, 0xa62b },
+	{ 0xa640, 0xa66e },
+	{ 0xa674, 0xa67b },
+	{ 0xa67f, 0xa6ef },
+	{ 0xa717, 0xa71f },
+	{ 0xa722, 0xa788 },
+	{ 0xa78b, 0xa7cd },
+	{ 0xa7d0, 0xa7d1 },
+	{ 0xa7d3, 0xa7d3 },
+	{ 0xa7d5, 0xa7dc },
+	{ 0xa7f2, 0xa805 },
+	{ 0xa807, 0xa827 },
+	{ 0xa840, 0xa873 },
+	{ 0xa880, 0xa8c3 },
+	{ 0xa8c5, 0xa8c5 },
+	{ 0xa8f2, 0xa8f7 },
+	{ 0xa8fb, 0xa8fb },
+	{ 0xa8fd, 0xa8ff },
+	{ 0xa90a, 0xa92a },
+	{ 0xa930, 0xa952 },
+	{ 0xa960, 0xa97c },
+	{ 0xa980, 0xa9b2 },
+	{ 0xa9b4, 0xa9bf },
+	{ 0xa9cf, 0xa9cf },
+	{ 0xa9e0, 0xa9ef },
+	{ 0xa9fa, 0xa9fe },
+	{ 0xaa00, 0xaa36 },
+	{ 0xaa40, 0xaa4d },
+	{ 0xaa60, 0xaa76 },
+	{ 0xaa7a, 0xaabe },
+	{ 0xaac0, 0xaac0 },
+	{ 0xaac2, 0xaac2 },
+	{ 0xaadb, 0xaadd },
+	{ 0xaae0, 0xaaef },
+	{ 0xaaf2, 0xaaf5 },
+	{ 0xab01, 0xab06 },
+	{ 0xab09, 0xab0e },
+	{ 0xab11, 0xab16 },
+	{ 0xab20, 0xab26 },
+	{ 0xab28, 0xab2e },
+	{ 0xab30, 0xab5a },
+	{ 0xab5c, 0xab69 },
+	{ 0xab70, 0xabea },
+	{ 0xac00, 0xd7a3 },
+	{ 0xd7b0, 0xd7c6 },
+	{ 0xd7cb, 0xd7fb },
+	{ 0xf900, 0xfa6d },
+	{ 0xfa70, 0xfad9 },
+	{ 0xfb00, 0xfb06 },
+	{ 0xfb13, 0xfb17 },
+	{ 0xfb1d, 0xfb28 },
+	{ 0xfb2a, 0xfb36 },
+	{ 0xfb38, 0xfb3c },
+	{ 0xfb3e, 0xfb3e },
+	{ 0xfb40, 0xfb41 },
+	{ 0xfb43, 0xfb44 },
+	{ 0xfb46, 0xfbb1 },
+	{ 0xfbd3, 0xfd3d },
+	{ 0xfd50, 0xfd8f },
+	{ 0xfd92, 0xfdc7 },
+	{ 0xfdf0, 0xfdfb },
+	{ 0xfe70, 0xfe74 },
+	{ 0xfe76, 0xfefc },
+	{ 0xff21, 0xff3a },
+	{ 0xff41, 0xff5a },
+	{ 0xff66, 0xffbe },
+	{ 0xffc2, 0xffc7 },
+	{ 0xffca, 0xffcf },
+	{ 0xffd2, 0xffd7 },
+	{ 0xffda, 0xffdc },
+	{ 0x10000, 0x1000b },
+	{ 0x1000d, 0x10026 },
+	{ 0x10028, 0x1003a },
+	{ 0x1003c, 0x1003d },
+	{ 0x1003f, 0x1004d },
+	{ 0x10050, 0x1005d },
+	{ 0x10080, 0x100fa },
+	{ 0x10140, 0x10174 },
+	{ 0x10280, 0x1029c },
+	{ 0x102a0, 0x102d0 },
+	{ 0x10300, 0x1031f },
+	{ 0x1032d, 0x1034a },
+	{ 0x10350, 0x1037a },
+	{ 0x10380, 0x1039d },
+	{ 0x103a0, 0x103c3 },
+	{ 0x103c8, 0x103cf },
+	{ 0x103d1, 0x103d5 },
+	{ 0x10400, 0x1049d },
+	{ 0x104b0, 0x104d3 },
+	{ 0x104d8, 0x104fb },
+	{ 0x10500, 0x10527 },
+	{ 0x10530, 0x10563 },
+	{ 0x10570, 0x1057a },
+	{ 0x1057c, 0x1058a },
+	{ 0x1058c, 0x10592 },
+	{ 0x10594, 0x10595 },
+	{ 0x10597, 0x105a1 },
+	{ 0x105a3, 0x105b1 },
+	{ 0x105b3, 0x105b9 },
+	{ 0x105bb, 0x105bc },
+	{ 0x105c0, 0x105f3 },
+	{ 0x10600, 0x10736 },
+	{ 0x10740, 0x10755 },
+	{ 0x10760, 0x10767 },
+	{ 0x10780, 0x10785 },
+	{ 0x10787, 0x107b0 },
+	{ 0x107b2, 0x107ba },
+	{ 0x10800, 0x10805 },
+	{ 0x10808, 0x10808 },
+	{ 0x1080a, 0x10835 },
+	{ 0x10837, 0x10838 },
+	{ 0x1083c, 0x1083c },
+	{ 0x1083f, 0x10855 },
+	{ 0x10860, 0x10876 },
+	{ 0x10880, 0x1089e },
+	{ 0x108e0, 0x108f2 },
+	{ 0x108f4, 0x108f5 },
+	{ 0x10900, 0x10915 },
+	{ 0x10920, 0x10939 },
+	{ 0x10980, 0x109b7 },
+	{ 0x109be, 0x109bf },
+	{ 0x10a00, 0x10a03 },
+	{ 0x10a05, 0x10a06 },
+	{ 0x10a0c, 0x10a13 },
+	{ 0x10a15, 0x10a17 },
+	{ 0x10a19, 0x10a35 },
+	{ 0x10a60, 0x10a7c },
+	{ 0x10a80, 0x10a9c },
+	{ 0x10ac0, 0x10ac7 },
+	{ 0x10ac9, 0x10ae4 },
+	{ 0x10b00, 0x10b35 },
+	{ 0x10b40, 0x10b55 },
+	{ 0x10b60, 0x10b72 },
+	{ 0x10b80, 0x10b91 },
+	{ 0x10c00, 0x10c48 },
+	{ 0x10c80, 0x10cb2 },
+	{ 0x10cc0, 0x10cf2 },
+	{ 0x10d00, 0x10d27 },
+	{ 0x10d4a, 0x10d65 },
+	{ 0x10d69, 0x10d69 },
+	{ 0x10d6f, 0x10d85 },
+	{ 0x10e80, 0x10ea9 },
+	{ 0x10eab, 0x10eac },
+	{ 0x10eb0, 0x10eb1 },
+	{ 0x10ec2, 0x10ec4 },
+	{ 0x10efc, 0x10efc },
+	{ 0x10f00, 0x10f1c },
+	{ 0x10f27, 0x10f27 },
+	{ 0x10f30, 0x10f45 },
+	{ 0x10f70, 0x10f81 },
+	{ 0x10fb0, 0x10fc4 },
+	{ 0x10fe0, 0x10ff6 },
+	{ 0x11000, 0x11045 },
+	{ 0x11071, 0x11075 },
+	{ 0x11080, 0x110b8 },
+	{ 0x110c2, 0x110c2 },
+	{ 0x110d0, 0x110e8 },
+	{ 0x11100, 0x11132 },
+	{ 0x11144, 0x11147 },
+	{ 0x11150, 0x11172 },
+	{ 0x11176, 0x11176 },
+	{ 0x11180, 0x111bf },
+	{ 0x111c1, 0x111c4 },
+	{ 0x111ce, 0x111cf },
+	{ 0x111da, 0x111da },
+	{ 0x111dc, 0x111dc },
+	{ 0x11200, 0x11211 },
+	{ 0x11213, 0x11234 },
+	{ 0x11237, 0x11237 },
+	{ 0x1123e, 0x11241 },
+	{ 0x11280, 0x11286 },
+	{ 0x11288, 0x11288 },
+	{ 0x1128a, 0x1128d },
+	{ 0x1128f, 0x1129d },
+	{ 0x1129f, 0x112a8 },
+	{ 0x112b0, 0x112e8 },
+	{ 0x11300, 0x11303 },
+	{ 0x11305, 0x1130c },
+	{ 0x1130f, 0x11310 },
+	{ 0x11313, 0x11328 },
+	{ 0x1132a, 0x11330 },
+	{ 0x11332, 0x11333 },
+	{ 0x11335, 0x11339 },
+	{ 0x1133d, 0x11344 },
+	{ 0x11347, 0x11348 },
+	{ 0x1134b, 0x1134c },
+	{ 0x11350, 0x11350 },
+	{ 0x11357, 0x11357 },
+	{ 0x1135d, 0x11363 },
+	{ 0x11380, 0x11389 },
+	{ 0x1138b, 0x1138b },
+	{ 0x1138e, 0x1138e },
+	{ 0x11390, 0x113b5 },
+	{ 0x113b7, 0x113c0 },
+	{ 0x113c2, 0x113c2 },
+	{ 0x113c5, 0x113c5 },
+	{ 0x113c7, 0x113ca },
+	{ 0x113cc, 0x113cd },
+	{ 0x113d1, 0x113d1 },
+	{ 0x113d3, 0x113d3 },
+	{ 0x11400, 0x11441 },
+	{ 0x11443, 0x11445 },
+	{ 0x11447, 0x1144a },
+	{ 0x1145f, 0x11461 },
+	{ 0x11480, 0x114c1 },
+	{ 0x114c4, 0x114c5 },
+	{ 0x114c7, 0x114c7 },
+	{ 0x11580, 0x115b5 },
+	{ 0x115b8, 0x115be },
+	{ 0x115d8, 0x115dd },
+	{ 0x11600, 0x1163e },
+	{ 0x11640, 0x11640 },
+	{ 0x11644, 0x11644 },
+	{ 0x11680, 0x116b5 },
+	{ 0x116b8, 0x116b8 },
+	{ 0x11700, 0x1171a },
+	{ 0x1171d, 0x1172a },
+	{ 0x11740, 0x11746 },
+	{ 0x11800, 0x11838 },
+	{ 0x118a0, 0x118df },
+	{ 0x118ff, 0x11906 },
+	{ 0x11909, 0x11909 },
+	{ 0x1190c, 0x11913 },
+	{ 0x11915, 0x11916 },
+	{ 0x11918, 0x11935 },
+	{ 0x11937, 0x11938 },
+	{ 0x1193b, 0x1193c },
+	{ 0x1193f, 0x11942 },
+	{ 0x119a0, 0x119a7 },
+	{ 0x119aa, 0x119d7 },
+	{ 0x119da, 0x119df },
+	{ 0x119e1, 0x119e1 },
+	{ 0x119e3, 0x119e4 },
+	{ 0x11a00, 0x11a32 },
+	{ 0x11a35, 0x11a3e },
+	{ 0x11a50, 0x11a97 },
+	{ 0x11a9d, 0x11a9d },
+	{ 0x11ab0, 0x11af8 },
+	{ 0x11bc0, 0x11be0 },
+	{ 0x11c00, 0x11c08 },
+	{ 0x11c0a, 0x11c36 },
+	{ 0x11c38, 0x11c3e },
+	{ 0x11c40, 0x11c40 },
+	{ 0x11c72, 0x11c8f },
+	{ 0x11c92, 0x11ca7 },
+	{ 0x11ca9, 0x11cb6 },
+	{ 0x11d00, 0x11d06 },
+	{ 0x11d08, 0x11d09 },
+	{ 0x11d0b, 0x11d36 },
+	{ 0x11d3a, 0x11d3a },
+	{ 0x11d3c, 0x11d3d },
+	{ 0x11d3f, 0x11d41 },
+	{ 0x11d43, 0x11d43 },
+	{ 0x11d46, 0x11d47 },
+	{ 0x11d60, 0x11d65 },
+	{ 0x11d67, 0x11d68 },
+	{ 0x11d6a, 0x11d8e },
+	{ 0x11d90, 0x11d91 },
+	{ 0x11d93, 0x11d96 },
+	{ 0x11d98, 0x11d98 },
+	{ 0x11ee0, 0x11ef6 },
+	{ 0x11f00, 0x11f10 },
+	{ 0x11f12, 0x11f3a },
+	{ 0x11f3e, 0x11f40 },
+	{ 0x11fb0, 0x11fb0 },
+	{ 0x12000, 0x12399 },
+	{ 0x12400, 0x1246e },
+	{ 0x12480, 0x12543 },
+	{ 0x12f90, 0x12ff0 },
+	{ 0x13000, 0x1342f },
+	{ 0x13441, 0x13446 },
+	{ 0x13460, 0x143fa },
+	{ 0x14400, 0x14646 },
+	{ 0x16100, 0x1612e },
+	{ 0x16800, 0x16a38 },
+	{ 0x16a40, 0x16a5e },
+	{ 0x16a70, 0x16abe },
+	{ 0x16ad0, 0x16aed },
+	{ 0x16b00, 0x16b2f },
+	{ 0x16b40, 0x16b43 },
+	{ 0x16b63, 0x16b77 },
+	{ 0x16b7d, 0x16b8f },
+	{ 0x16d40, 0x16d6c },
+	{ 0x16e40, 0x16e7f },
+	{ 0x16f00, 0x16f4a },
+	{ 0x16f4f, 0x16f87 },
+	{ 0x16f8f, 0x16f9f },
+	{ 0x16fe0, 0x16fe1 },
+	{ 0x16fe3, 0x16fe3 },
+	{ 0x16ff0, 0x16ff1 },
+	{ 0x17000, 0x187f7 },
+	{ 0x18800, 0x18cd5 },
+	{ 0x18cff, 0x18d08 },
+	{ 0x1aff0, 0x1aff3 },
+	{ 0x1aff5, 0x1affb },
+	{ 0x1affd, 0x1affe },
+	{ 0x1b000, 0x1b122 },
+	{ 0x1b132, 0x1b132 },
+	{ 0x1b150, 0x1b152 },
+	{ 0x1b155, 0x1b155 },
+	{ 0x1b164, 0x1b167 },
+	{ 0x1b170, 0x1b2fb },
+	{ 0x1bc00, 0x1bc6a },
+	{ 0x1bc70, 0x1bc7c },
+	{ 0x1bc80, 0x1bc88 },
+	{ 0x1bc90, 0x1bc99 },
+	{ 0x1bc9e, 0x1bc9e },
+	{ 0x1d400, 0x1d454 },
+	{ 0x1d456, 0x1d49c },
+	{ 0x1d49e, 0x1d49f },
+	{ 0x1d4a2, 0x1d4a2 },
+	{ 0x1d4a5, 0x1d4a6 },
+	{ 0x1d4a9, 0x1d4ac },
+	{ 0x1d4ae, 0x1d4b9 },
+	{ 0x1d4bb, 0x1d4bb },
+	{ 0x1d4bd, 0x1d4c3 },
+	{ 0x1d4c5, 0x1d505 },
+	{ 0x1d507, 0x1d50a },
+	{ 0x1d50d, 0x1d514 },
+	{ 0x1d516, 0x1d51c },
+	{ 0x1d51e, 0x1d539 },
+	{ 0x1d53b, 0x1d53e },
+	{ 0x1d540, 0x1d544 },
+	{ 0x1d546, 0x1d546 },
+	{ 0x1d54a, 0x1d550 },
+	{ 0x1d552, 0x1d6a5 },
+	{ 0x1d6a8, 0x1d6c0 },
+	{ 0x1d6c2, 0x1d6da },
+	{ 0x1d6dc, 0x1d6fa },
+	{ 0x1d6fc, 0x1d714 },
+	{ 0x1d716, 0x1d734 },
+	{ 0x1d736, 0x1d74e },
+	{ 0x1d750, 0x1d76e },
+	{ 0x1d770, 0x1d788 },
+	{ 0x1d78a, 0x1d7a8 },
+	{ 0x1d7aa, 0x1d7c2 },
+	{ 0x1d7c4, 0x1d7cb },
+	{ 0x1df00, 0x1df1e },
+	{ 0x1df25, 0x1df2a },
+	{ 0x1e000, 0x1e006 },
+	{ 0x1e008, 0x1e018 },
+	{ 0x1e01b, 0x1e021 },
+	{ 0x1e023, 0x1e024 },
+	{ 0x1e026, 0x1e02a },
+	{ 0x1e030, 0x1e06d },
+	{ 0x1e08f, 0x1e08f },
+	{ 0x1e100, 0x1e12c },
+	{ 0x1e137, 0x1e13d },
+	{ 0x1e14e, 0x1e14e },
+	{ 0x1e290, 0x1e2ad },
+	{ 0x1e2c0, 0x1e2eb },
+	{ 0x1e4d0, 0x1e4eb },
+	{ 0x1e5d0, 0x1e5ed },
+	{ 0x1e5f0, 0x1e5f0 },
+	{ 0x1e7e0, 0x1e7e6 },
+	{ 0x1e7e8, 0x1e7eb },
+	{ 0x1e7ed, 0x1e7ee },
+	{ 0x1e7f0, 0x1e7fe },
+	{ 0x1e800, 0x1e8c4 },
+	{ 0x1e900, 0x1e943 },
+	{ 0x1e947, 0x1e947 },
+	{ 0x1e94b, 0x1e94b },
+	{ 0x1ee00, 0x1ee03 },
+	{ 0x1ee05, 0x1ee1f },
+	{ 0x1ee21, 0x1ee22 },
+	{ 0x1ee24, 0x1ee24 },
+	{ 0x1ee27, 0x1ee27 },
+	{ 0x1ee29, 0x1ee32 },
+	{ 0x1ee34, 0x1ee37 },
+	{ 0x1ee39, 0x1ee39 },
+	{ 0x1ee3b, 0x1ee3b },
+	{ 0x1ee42, 0x1ee42 },
+	{ 0x1ee47, 0x1ee47 },
+	{ 0x1ee49, 0x1ee49 },
+	{ 0x1ee4b, 0x1ee4b },
+	{ 0x1ee4d, 0x1ee4f },
+	{ 0x1ee51, 0x1ee52 },
+	{ 0x1ee54, 0x1ee54 },
+	{ 0x1ee57, 0x1ee57 },
+	{ 0x1ee59, 0x1ee59 },
+	{ 0x1ee5b, 0x1ee5b },
+	{ 0x1ee5d, 0x1ee5d },
+	{ 0x1ee5f, 0x1ee5f },
+	{ 0x1ee61, 0x1ee62 },
+	{ 0x1ee64, 0x1ee64 },
+	{ 0x1ee67, 0x1ee6a },
+	{ 0x1ee6c, 0x1ee72 },
+	{ 0x1ee74, 0x1ee77 },
+	{ 0x1ee79, 0x1ee7c },
+	{ 0x1ee7e, 0x1ee7e },
+	{ 0x1ee80, 0x1ee89 },
+	{ 0x1ee8b, 0x1ee9b },
+	{ 0x1eea1, 0x1eea3 },
+	{ 0x1eea5, 0x1eea9 },
+	{ 0x1eeab, 0x1eebb },
+	{ 0x1f130, 0x1f149 },
+	{ 0x1f150, 0x1f169 },
+	{ 0x1f170, 0x1f189 },
+	{ 0x20000, 0x2a6df },
+	{ 0x2a700, 0x2b739 },
+	{ 0x2b740, 0x2b81d },
+	{ 0x2b820, 0x2cea1 },
+	{ 0x2ceb0, 0x2ebe0 },
+	{ 0x2ebf0, 0x2ee5d },
+	{ 0x2f800, 0x2fa1d },
+	{ 0x30000, 0x3134a },
+	{ 0x31350, 0x323af },
+};
+
+} // namespace godot

include/godot_cpp/variant/char_utils.hpp

@@ -30,58 +30,105 @@
 
 #pragma once
 
-static _FORCE_INLINE_ bool is_ascii_upper_case(char32_t c) {
-	return (c >= 'A' && c <= 'Z');
+#include "char_range.inc.hpp"
+
+namespace godot {
+
+#define BSEARCH_CHAR_RANGE(m_array)                      \
+	int low = 0;                                         \
+	int high = sizeof(m_array) / sizeof(m_array[0]) - 1; \
+	int middle = (low + high) / 2;                       \
+                                                         \
+	while (low <= high) {                                \
+		if (p_char < m_array[middle].start) {            \
+			high = middle - 1;                           \
+		} else if (p_char > m_array[middle].end) {       \
+			low = middle + 1;                            \
+		} else {                                         \
+			return true;                                 \
+		}                                                \
+                                                         \
+		middle = (low + high) / 2;                       \
+	}                                                    \
+                                                         \
+	return false
+
+constexpr bool is_unicode_identifier_start(char32_t p_char) {
+	BSEARCH_CHAR_RANGE(xid_start);
+}
+
+constexpr bool is_unicode_identifier_continue(char32_t p_char) {
+	BSEARCH_CHAR_RANGE(xid_continue);
+}
+
+constexpr bool is_unicode_upper_case(char32_t p_char) {
+	BSEARCH_CHAR_RANGE(uppercase_letter);
 }
 
-static _FORCE_INLINE_ bool is_ascii_lower_case(char32_t c) {
-	return (c >= 'a' && c <= 'z');
+constexpr bool is_unicode_lower_case(char32_t p_char) {
+	BSEARCH_CHAR_RANGE(lowercase_letter);
 }
 
-static _FORCE_INLINE_ bool is_digit(char32_t c) {
-	return (c >= '0' && c <= '9');
+constexpr bool is_unicode_letter(char32_t p_char) {
+	BSEARCH_CHAR_RANGE(unicode_letter);
 }
 
-static _FORCE_INLINE_ bool is_hex_digit(char32_t c) {
-	return (is_digit(c) || (c >= 'a' && c <= 'f') || (c >= 'A' && c <= 'F'));
+#undef BSEARCH_CHAR_RANGE
+
+constexpr bool is_ascii_upper_case(char32_t p_char) {
+	return (p_char >= 'A' && p_char <= 'Z');
 }
 
-static _FORCE_INLINE_ bool is_binary_digit(char32_t c) {
-	return (c == '0' || c == '1');
+constexpr bool is_ascii_lower_case(char32_t p_char) {
+	return (p_char >= 'a' && p_char <= 'z');
 }
 
-static _FORCE_INLINE_ bool is_ascii_char(char32_t c) {
-	return (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z');
+constexpr bool is_digit(char32_t p_char) {
+	return (p_char >= '0' && p_char <= '9');
 }
 
-static _FORCE_INLINE_ bool is_ascii_alphanumeric_char(char32_t c) {
-	return (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z') || (c >= '0' && c <= '9');
+constexpr bool is_hex_digit(char32_t p_char) {
+	return (is_digit(p_char) || (p_char >= 'a' && p_char <= 'f') || (p_char >= 'A' && p_char <= 'F'));
 }
 
-static _FORCE_INLINE_ bool is_ascii_identifier_char(char32_t c) {
-	return (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z') || (c >= '0' && c <= '9') || c == '_';
+constexpr bool is_binary_digit(char32_t p_char) {
+	return (p_char == '0' || p_char == '1');
 }
 
-static _FORCE_INLINE_ bool is_symbol(char32_t c) {
-	return c != '_' && ((c >= '!' && c <= '/') || (c >= ':' && c <= '@') || (c >= '[' && c <= '`') || (c >= '{' && c <= '~') || c == '\t' || c == ' ');
+constexpr bool is_ascii_alphabet_char(char32_t p_char) {
+	return (p_char >= 'a' && p_char <= 'z') || (p_char >= 'A' && p_char <= 'Z');
 }
 
-static _FORCE_INLINE_ bool is_control(char32_t p_char) {
+constexpr bool is_ascii_alphanumeric_char(char32_t p_char) {
+	return (p_char >= 'a' && p_char <= 'z') || (p_char >= 'A' && p_char <= 'Z') || (p_char >= '0' && p_char <= '9');
+}
+
+constexpr bool is_ascii_identifier_char(char32_t p_char) {
+	return (p_char >= 'a' && p_char <= 'z') || (p_char >= 'A' && p_char <= 'Z') || (p_char >= '0' && p_char <= '9') || p_char == '_';
+}
+
+constexpr bool is_symbol(char32_t p_char) {
+	return p_char != '_' && ((p_char >= '!' && p_char <= '/') || (p_char >= ':' && p_char <= '@') || (p_char >= '[' && p_char <= '`') || (p_char >= '{' && p_char <= '~') || p_char == '\t' || p_char == ' ');
+}
+
+constexpr bool is_control(char32_t p_char) {
 	return (p_char <= 0x001f) || (p_char >= 0x007f && p_char <= 0x009f);
 }
 
-static _FORCE_INLINE_ bool is_whitespace(char32_t p_char) {
-	return (p_char == ' ') || (p_char == 0x00a0) || (p_char == 0x1680) || (p_char >= 0x2000 && p_char <= 0x200a) || (p_char == 0x202f) || (p_char == 0x205f) || (p_char == 0x3000) || (p_char == 0x2028) || (p_char == 0x2029) || (p_char >= 0x0009 && p_char <= 0x000d) || (p_char == 0x0085);
+constexpr bool is_whitespace(char32_t p_char) {
+	return (p_char == ' ') || (p_char == 0x00a0) || (p_char == 0x1680) || (p_char >= 0x2000 && p_char <= 0x200b) || (p_char == 0x202f) || (p_char == 0x205f) || (p_char == 0x3000) || (p_char == 0x2028) || (p_char == 0x2029) || (p_char >= 0x0009 && p_char <= 0x000d) || (p_char == 0x0085);
 }
 
-static _FORCE_INLINE_ bool is_linebreak(char32_t p_char) {
+constexpr bool is_linebreak(char32_t p_char) {
 	return (p_char >= 0x000a && p_char <= 0x000d) || (p_char == 0x0085) || (p_char == 0x2028) || (p_char == 0x2029);
 }
 
-static _FORCE_INLINE_ bool is_punct(char32_t p_char) {
+constexpr bool is_punct(char32_t p_char) {
 	return (p_char >= ' ' && p_char <= '/') || (p_char >= ':' && p_char <= '@') || (p_char >= '[' && p_char <= '^') || (p_char == '`') || (p_char >= '{' && p_char <= '~') || (p_char >= 0x2000 && p_char <= 0x206f) || (p_char >= 0x3000 && p_char <= 0x303f);
 }
 
-static _FORCE_INLINE_ bool is_underscore(char32_t p_char) {
+constexpr bool is_underscore(char32_t p_char) {
 	return (p_char == '_');
 }
+
+} // namespace godot

include/godot_cpp/variant/color.hpp

@@ -102,12 +102,10 @@ struct [[nodiscard]] Color {
 
 	_FORCE_INLINE_ Color lerp(const Color &p_to, float p_weight) const {
 		Color res = *this;
-
-		res.r += (p_weight * (p_to.r - r));
-		res.g += (p_weight * (p_to.g - g));
-		res.b += (p_weight * (p_to.b - b));
-		res.a += (p_weight * (p_to.a - a));
-
+		res.r = Math::lerp(res.r, p_to.r, p_weight);
+		res.g = Math::lerp(res.g, p_to.g, p_weight);
+		res.b = Math::lerp(res.b, p_to.b, p_weight);
+		res.a = Math::lerp(res.a, p_to.a, p_weight);
 		return res;
 	}
 
@@ -128,33 +126,46 @@ struct [[nodiscard]] Color {
 	}
 
 	_FORCE_INLINE_ uint32_t to_rgbe9995() const {
-		const float pow2to9 = 512.0f;
-		const float B = 15.0f;
-		const float N = 9.0f;
-
-		float sharedexp = 65408.000f; // Result of: ((pow2to9 - 1.0f) / pow2to9) * powf(2.0f, 31.0f - 15.0f)
-
-		float cRed = MAX(0.0f, MIN(sharedexp, r));
-		float cGreen = MAX(0.0f, MIN(sharedexp, g));
-		float cBlue = MAX(0.0f, MIN(sharedexp, b));
-
-		float cMax = MAX(cRed, MAX(cGreen, cBlue));
-
-		float expp = MAX(-B - 1.0f, floor(Math::log(cMax) / (real_t)Math_LN2)) + 1.0f + B;
-
-		float sMax = (float)floor((cMax / Math::pow(2.0f, expp - B - N)) + 0.5f);
-
-		float exps = expp + 1.0f;
-
-		if (0.0f <= sMax && sMax < pow2to9) {
-			exps = expp;
-		}
-
-		float sRed = Math::floor((cRed / pow(2.0f, exps - B - N)) + 0.5f);
-		float sGreen = Math::floor((cGreen / pow(2.0f, exps - B - N)) + 0.5f);
-		float sBlue = Math::floor((cBlue / pow(2.0f, exps - B - N)) + 0.5f);
-
-		return (uint32_t(Math::fast_ftoi(sRed)) & 0x1FF) | ((uint32_t(Math::fast_ftoi(sGreen)) & 0x1FF) << 9) | ((uint32_t(Math::fast_ftoi(sBlue)) & 0x1FF) << 18) | ((uint32_t(Math::fast_ftoi(exps)) & 0x1F) << 27);
+		// https://github.com/microsoft/DirectX-Graphics-Samples/blob/v10.0.19041.0/MiniEngine/Core/Color.cpp
+		static const float kMaxVal = float(0x1FF << 7);
+		static const float kMinVal = float(1.f / (1 << 16));
+
+		// Clamp RGB to [0, 1.FF*2^16]
+		const float _r = CLAMP(r, 0.0f, kMaxVal);
+		const float _g = CLAMP(g, 0.0f, kMaxVal);
+		const float _b = CLAMP(b, 0.0f, kMaxVal);
+
+		// Compute the maximum channel, no less than 1.0*2^-15
+		const float MaxChannel = MAX(MAX(_r, _g), MAX(_b, kMinVal));
+
+		// Take the exponent of the maximum channel (rounding up the 9th bit) and
+		// add 15 to it.  When added to the channels, it causes the implicit '1.0'
+		// bit and the first 8 mantissa bits to be shifted down to the low 9 bits
+		// of the mantissa, rounding the truncated bits.
+		union {
+			float f;
+			uint32_t i;
+		} R, G, B, E;
+
+		E.f = MaxChannel;
+		E.i += 0x07804000; // Add 15 to the exponent and 0x4000 to the mantissa
+		E.i &= 0x7F800000; // Zero the mantissa
+
+		// This shifts the 9-bit values we need into the lowest bits, rounding as
+		// needed. Note that if the channel has a smaller exponent than the max
+		// channel, it will shift even more.  This is intentional.
+		R.f = _r + E.f;
+		G.f = _g + E.f;
+		B.f = _b + E.f;
+
+		// Convert the Bias to the correct exponent in the upper 5 bits.
+		E.i <<= 4;
+		E.i += 0x10000000;
+
+		// Combine the fields. RGB floats have unwanted data in the upper 9
+		// bits. Only red needs to mask them off because green and blue shift
+		// it out to the left.
+		return E.i | (B.i << 18U) | (G.i << 9U) | (R.i & 511U);
 	}
 
 	_FORCE_INLINE_ Color blend(const Color &p_over) const {
@@ -173,16 +184,16 @@ struct [[nodiscard]] Color {
 
 	_FORCE_INLINE_ Color srgb_to_linear() const {
 		return Color(
-				r < 0.04045f ? r * (1.0f / 12.92f) : Math::pow((r + 0.055f) * (float)(1.0 / (1.0 + 0.055)), 2.4f),
-				g < 0.04045f ? g * (1.0f / 12.92f) : Math::pow((g + 0.055f) * (float)(1.0 / (1.0 + 0.055)), 2.4f),
-				b < 0.04045f ? b * (1.0f / 12.92f) : Math::pow((b + 0.055f) * (float)(1.0 / (1.0 + 0.055)), 2.4f),
+				r < 0.04045f ? r * (1.0f / 12.92f) : Math::pow(float((r + 0.055) * (1.0 / (1.0 + 0.055))), 2.4f),
+				g < 0.04045f ? g * (1.0f / 12.92f) : Math::pow(float((g + 0.055) * (1.0 / (1.0 + 0.055))), 2.4f),
+				b < 0.04045f ? b * (1.0f / 12.92f) : Math::pow(float((b + 0.055) * (1.0 / (1.0 + 0.055))), 2.4f),
 				a);
 	}
 	_FORCE_INLINE_ Color linear_to_srgb() const {
 		return Color(
-				r < 0.0031308f ? 12.92f * r : (1.0f + 0.055f) * Math::pow(r, 1.0f / 2.4f) - 0.055f,
-				g < 0.0031308f ? 12.92f * g : (1.0f + 0.055f) * Math::pow(g, 1.0f / 2.4f) - 0.055f,
-				b < 0.0031308f ? 12.92f * b : (1.0f + 0.055f) * Math::pow(b, 1.0f / 2.4f) - 0.055f, a);
+				r < 0.0031308f ? 12.92f * r : (1.0 + 0.055) * Math::pow(r, 1.0f / 2.4f) - 0.055,
+				g < 0.0031308f ? 12.92f * g : (1.0 + 0.055) * Math::pow(g, 1.0f / 2.4f) - 0.055,
+				b < 0.0031308f ? 12.92f * b : (1.0 + 0.055) * Math::pow(b, 1.0f / 2.4f) - 0.055, a);
 	}
 
 	static Color hex(uint32_t p_hex);
@@ -198,6 +209,7 @@ struct [[nodiscard]] Color {
 	static Color from_string(const String &p_string, const Color &p_default);
 	static Color from_hsv(float p_h, float p_s, float p_v, float p_alpha = 1.0f);
 	static Color from_rgbe9995(uint32_t p_rgbe);
+	static Color from_rgba8(int64_t p_r8, int64_t p_g8, int64_t p_b8, int64_t p_a8 = 255);
 
 	_FORCE_INLINE_ bool operator<(const Color &p_color) const; // Used in set keys.
 	operator String() const;

include/godot_cpp/variant/color_names.inc.hpp

@@ -187,7 +187,6 @@ static NamedColor named_colors[] = {
 	{ "WHITE_SMOKE", Color::hex(0xF5F5F5FF) },
 	{ "YELLOW", Color::hex(0xFFFF00FF) },
 	{ "YELLOW_GREEN", Color::hex(0x9ACD32FF) },
-	{ nullptr, Color() },
 };
 
 } // namespace godot

include/godot_cpp/variant/plane.hpp

@@ -49,7 +49,7 @@ struct [[nodiscard]] Plane {
 
 	/* Plane-Point operations */
 
-	_FORCE_INLINE_ Vector3 center() const { return normal * d; }
+	_FORCE_INLINE_ Vector3 get_center() const { return normal * d; }
 	Vector3 get_any_perpendicular_normal() const;
 
 	_FORCE_INLINE_ bool is_point_over(const Vector3 &p_point) const; ///< Point is over plane
@@ -102,7 +102,7 @@ real_t Plane::distance_to(const Vector3 &p_point) const {
 
 bool Plane::has_point(const Vector3 &p_point, real_t p_tolerance) const {
 	real_t dist = normal.dot(p_point) - d;
-	dist = Math::abs(dist);
+	dist = ABS(dist);
 	return (dist <= p_tolerance);
 }
 

include/godot_cpp/variant/projection.hpp

@@ -31,6 +31,7 @@
 #pragma once
 
 #include <godot_cpp/core/math.hpp>
+#include <godot_cpp/templates/vector.hpp>
 #include <godot_cpp/variant/vector3.hpp>
 #include <godot_cpp/variant/vector4.hpp>
 
@@ -55,21 +56,21 @@ struct [[nodiscard]] Projection {
 
 	Vector4 columns[4];
 
-	_FORCE_INLINE_ const Vector4 &operator[](const int p_axis) const {
+	_FORCE_INLINE_ const Vector4 &operator[](int p_axis) const {
 		DEV_ASSERT((unsigned int)p_axis < 4);
 		return columns[p_axis];
 	}
 
-	_FORCE_INLINE_ Vector4 &operator[](const int p_axis) {
+	_FORCE_INLINE_ Vector4 &operator[](int p_axis) {
 		DEV_ASSERT((unsigned int)p_axis < 4);
 		return columns[p_axis];
 	}
 
-	float determinant() const;
+	real_t determinant() const;
 	void set_identity();
 	void set_zero();
 	void set_light_bias();
-	void set_depth_correction(bool p_flip_y = true);
+	void set_depth_correction(bool p_flip_y = true, bool p_reverse_z = true, bool p_remap_z = true);
 
 	void set_light_atlas_rect(const Rect2 &p_rect);
 	void set_perspective(real_t p_fovy_degrees, real_t p_aspect, real_t p_z_near, real_t p_z_far, bool p_flip_fov = false);
@@ -106,7 +107,7 @@ struct [[nodiscard]] Projection {
 	real_t get_fov() const;
 	bool is_orthogonal() const;
 
-	Array get_projection_planes(const Transform3D &p_transform) const;
+	Vector<Plane> get_projection_planes(const Transform3D &p_transform) const;
 
 	bool get_endpoints(const Transform3D &p_transform, Vector3 *p_8points) const;
 	Vector2 get_viewport_half_extents() const;
@@ -148,7 +149,7 @@ struct [[nodiscard]] Projection {
 		return !(*this == p_cam);
 	}
 
-	float get_lod_multiplier() const;
+	real_t get_lod_multiplier() const;
 
 	Projection();
 	Projection(const Vector4 &p_x, const Vector4 &p_y, const Vector4 &p_z, const Vector4 &p_w);

include/godot_cpp/variant/quaternion.hpp

@@ -142,15 +142,24 @@ struct [[nodiscard]] Quaternion {
 	}
 
 	Quaternion(const Vector3 &p_v0, const Vector3 &p_v1) { // Shortest arc.
-		Vector3 c = p_v0.cross(p_v1);
-		real_t d = p_v0.dot(p_v1);
-
-		if (d < -1.0f + (real_t)CMP_EPSILON) {
-			x = 0;
-			y = 1;
-			z = 0;
+#ifdef MATH_CHECKS
+		ERR_FAIL_COND_MSG(p_v0.is_zero_approx() || p_v1.is_zero_approx(), "The vectors must not be zero.");
+#endif
+		constexpr real_t ALMOST_ONE = 1.0f - (real_t)CMP_EPSILON;
+		Vector3 n0 = p_v0.normalized();
+		Vector3 n1 = p_v1.normalized();
+		real_t d = n0.dot(n1);
+		if (abs(d) > ALMOST_ONE) {
+			if (d >= 0) {
+				return; // Vectors are same.
+			}
+			Vector3 axis = n0.get_any_perpendicular();
+			x = axis.x;
+			y = axis.y;
+			z = axis.z;
 			w = 0;
 		} else {
+			Vector3 c = n0.cross(n1);
 			real_t s = Math::sqrt((1.0f + d) * 2.0f);
 			real_t rs = 1.0f / s;
 

include/godot_cpp/variant/rect2.hpp

@@ -52,7 +52,7 @@ struct [[nodiscard]] Rect2 {
 
 	_FORCE_INLINE_ Vector2 get_center() const { return position + (size * 0.5f); }
 
-	inline bool intersects(const Rect2 &p_rect, const bool p_include_borders = false) const {
+	inline bool intersects(const Rect2 &p_rect, bool p_include_borders = false) const {
 #ifdef MATH_CHECKS
 		if (unlikely(size.x < 0 || size.y < 0 || p_rect.size.x < 0 || p_rect.size.y < 0)) {
 			ERR_PRINT("Rect2 size is negative, this is not supported. Use Rect2.abs() to get a Rect2 with a positive size.");
@@ -105,17 +105,17 @@ struct [[nodiscard]] Rect2 {
 		}
 		if (p_point.y < position.y) {
 			real_t d = position.y - p_point.y;
-			dist = inside ? d : Math::min(dist, d);
+			dist = inside ? d : MIN(dist, d);
 			inside = false;
 		}
 		if (p_point.x >= (position.x + size.x)) {
 			real_t d = p_point.x - (position.x + size.x);
-			dist = inside ? d : Math::min(dist, d);
+			dist = inside ? d : MIN(dist, d);
 			inside = false;
 		}
 		if (p_point.y >= (position.y + size.y)) {
 			real_t d = p_point.y - (position.y + size.y);
-			dist = inside ? d : Math::min(dist, d);
+			dist = inside ? d : MIN(dist, d);
 			inside = false;
 		}
 
@@ -145,7 +145,7 @@ struct [[nodiscard]] Rect2 {
 		return size.x > 0.0f && size.y > 0.0f;
 	}
 
-	// Returns the intersection between two Rect2s or an empty Rect2 if there is no intersection
+	// Returns the intersection between two Rect2s or an empty Rect2 if there is no intersection.
 	inline Rect2 intersection(const Rect2 &p_rect) const {
 		Rect2 new_rect = p_rect;
 
@@ -282,13 +282,19 @@ struct [[nodiscard]] Rect2 {
 		return Rect2(position + size.minf(0), size.abs());
 	}
 
-	Vector2 get_support(const Vector2 &p_normal) const {
-		Vector2 half_extents = size * 0.5f;
-		Vector2 ofs = position + half_extents;
-		return Vector2(
-					   (p_normal.x > 0) ? -half_extents.x : half_extents.x,
-					   (p_normal.y > 0) ? -half_extents.y : half_extents.y) +
-				ofs;
+	_FORCE_INLINE_ Rect2 round() const {
+		return Rect2(position.round(), size.round());
+	}
+
+	Vector2 get_support(const Vector2 &p_direction) const {
+		Vector2 support = position;
+		if (p_direction.x > 0.0f) {
+			support.x += size.x;
+		}
+		if (p_direction.y > 0.0f) {
+			support.y += size.y;
+		}
+		return support;
 	}
 
 	_FORCE_INLINE_ bool intersects_filled_polygon(const Vector2 *p_points, int p_point_count) const {
@@ -304,14 +310,14 @@ struct [[nodiscard]] Rect2 {
 			i_f = i;
 
 			Vector2 r = (b - a);
-			float l = r.length();
+			const real_t l = r.length();
 			if (l == 0.0f) {
 				continue;
 			}
 
 			// Check inside.
 			Vector2 tg = r.orthogonal();
-			float s = tg.dot(center) - tg.dot(a);
+			const real_t s = tg.dot(center) - tg.dot(a);
 			if (s < 0.0f) {
 				side_plus++;
 			} else {
@@ -327,8 +333,8 @@ struct [[nodiscard]] Rect2 {
 			Vector2 t13 = (position - a) * ir;
 			Vector2 t24 = (end - a) * ir;
 
-			float tmin = Math::max(Math::min(t13.x, t24.x), Math::min(t13.y, t24.y));
-			float tmax = Math::min(Math::max(t13.x, t24.x), Math::max(t13.y, t24.y));
+			const real_t tmin = MAX(MIN(t13.x, t24.x), MIN(t13.y, t24.y));
+			const real_t tmax = MIN(MAX(t13.x, t24.x), MAX(t13.y, t24.y));
 
 			// if tmax < 0, ray (line) is intersecting AABB, but the whole AABB is behind us
 			if (tmax < 0 || tmin > tmax || tmin >= l) {

include/godot_cpp/variant/rect2i.hpp

@@ -88,7 +88,7 @@ struct [[nodiscard]] Rect2i {
 		return size.x > 0 && size.y > 0;
 	}
 
-	// Returns the intersection between two Rect2is or an empty Rect2i if there is no intersection
+	// Returns the intersection between two Rect2is or an empty Rect2i if there is no intersection.
 	inline Rect2i intersection(const Rect2i &p_rect) const {
 		Rect2i new_rect = p_rect;
 

include/godot_cpp/variant/transform2d.hpp

@@ -39,21 +39,24 @@ namespace godot {
 class String;
 
 struct [[nodiscard]] Transform2D {
-	// Warning #1: basis of Transform2D is stored differently from Basis. In terms of columns array, the basis matrix looks like "on paper":
+	// WARNING: The basis of Transform2D is stored differently from Basis.
+	// In terms of columns array, the basis matrix looks like "on paper":
 	// M = (columns[0][0] columns[1][0])
 	//     (columns[0][1] columns[1][1])
-	// This is such that the columns, which can be interpreted as basis vectors of the coordinate system "painted" on the object, can be accessed as columns[i].
-	// Note that this is the opposite of the indices in mathematical texts, meaning: $M_{12}$ in a math book corresponds to columns[1][0] here.
+	// This is such that the columns, which can be interpreted as basis vectors
+	// of the coordinate system "painted" on the object, can be accessed as columns[i].
+	// NOTE: This is the opposite of the indices in mathematical texts,
+	// meaning: $M_{12}$ in a math book corresponds to columns[1][0] here.
 	// This requires additional care when working with explicit indices.
 	// See https://en.wikipedia.org/wiki/Row-_and_column-major_order for further reading.
 
-	// Warning #2: 2D be aware that unlike 3D code, 2D code uses a left-handed coordinate system: Y-axis points down,
-	// and angle is measure from +X to +Y in a clockwise-fashion.
+	// WARNING: Be aware that unlike 3D code, 2D code uses a left-handed coordinate system:
+	// Y-axis points down, and angle is measure from +X to +Y in a clockwise-fashion.
 
 	Vector2 columns[3];
 
-	_FORCE_INLINE_ real_t tdotx(const Vector2 &v) const { return columns[0][0] * v.x + columns[1][0] * v.y; }
-	_FORCE_INLINE_ real_t tdoty(const Vector2 &v) const { return columns[0][1] * v.x + columns[1][1] * v.y; }
+	_FORCE_INLINE_ real_t tdotx(const Vector2 &p_v) const { return columns[0][0] * p_v.x + columns[1][0] * p_v.y; }
+	_FORCE_INLINE_ real_t tdoty(const Vector2 &p_v) const { return columns[0][1] * p_v.x + columns[1][1] * p_v.y; }
 
 	const Vector2 &operator[](int p_idx) const { return columns[p_idx]; }
 	Vector2 &operator[](int p_idx) { return columns[p_idx]; }
@@ -64,20 +67,20 @@ struct [[nodiscard]] Transform2D {
 	void affine_invert();
 	Transform2D affine_inverse() const;
 
-	void set_rotation(const real_t p_rot);
+	void set_rotation(real_t p_rot);
 	real_t get_rotation() const;
 	real_t get_skew() const;
-	void set_skew(const real_t p_angle);
-	_FORCE_INLINE_ void set_rotation_and_scale(const real_t p_rot, const Size2 &p_scale);
-	_FORCE_INLINE_ void set_rotation_scale_and_skew(const real_t p_rot, const Size2 &p_scale, const real_t p_skew);
-	void rotate(const real_t p_angle);
+	void set_skew(real_t p_angle);
+	_FORCE_INLINE_ void set_rotation_and_scale(real_t p_rot, const Size2 &p_scale);
+	_FORCE_INLINE_ void set_rotation_scale_and_skew(real_t p_rot, const Size2 &p_scale, real_t p_skew);
+	void rotate(real_t p_angle);
 
 	void scale(const Size2 &p_scale);
 	void scale_basis(const Size2 &p_scale);
-	void translate_local(const real_t p_tx, const real_t p_ty);
+	void translate_local(real_t p_tx, real_t p_ty);
 	void translate_local(const Vector2 &p_translation);
 
-	real_t basis_determinant() const;
+	real_t determinant() const;
 
 	Size2 get_scale() const;
 	void set_scale(const Size2 &p_scale);
@@ -85,18 +88,18 @@ struct [[nodiscard]] Transform2D {
 	_FORCE_INLINE_ const Vector2 &get_origin() const { return columns[2]; }
 	_FORCE_INLINE_ void set_origin(const Vector2 &p_origin) { columns[2] = p_origin; }
 
-	Transform2D basis_scaled(const Size2 &p_scale) const;
 	Transform2D scaled(const Size2 &p_scale) const;
 	Transform2D scaled_local(const Size2 &p_scale) const;
 	Transform2D translated(const Vector2 &p_offset) const;
 	Transform2D translated_local(const Vector2 &p_offset) const;
-	Transform2D rotated(const real_t p_angle) const;
-	Transform2D rotated_local(const real_t p_angle) const;
+	Transform2D rotated(real_t p_angle) const;
+	Transform2D rotated_local(real_t p_angle) const;
 
 	Transform2D untranslated() const;
 
 	void orthonormalize();
 	Transform2D orthonormalized() const;
+	bool is_conformal() const;
 	bool is_equal_approx(const Transform2D &p_transform) const;
 	bool is_finite() const;
 
@@ -107,10 +110,12 @@ struct [[nodiscard]] Transform2D {
 
 	void operator*=(const Transform2D &p_transform);
 	Transform2D operator*(const Transform2D &p_transform) const;
-	void operator*=(const real_t p_val);
-	Transform2D operator*(const real_t p_val) const;
+	void operator*=(real_t p_val);
+	Transform2D operator*(real_t p_val) const;
+	void operator/=(real_t p_val);
+	Transform2D operator/(real_t p_val) const;
 
-	Transform2D interpolate_with(const Transform2D &p_transform, const real_t p_c) const;
+	Transform2D interpolate_with(const Transform2D &p_transform, real_t p_c) const;
 
 	_FORCE_INLINE_ Vector2 basis_xform(const Vector2 &p_vec) const;
 	_FORCE_INLINE_ Vector2 basis_xform_inv(const Vector2 &p_vec) const;
@@ -123,13 +128,13 @@ struct [[nodiscard]] Transform2D {
 
 	operator String() const;
 
-	Transform2D(const real_t xx, const real_t xy, const real_t yx, const real_t yy, const real_t ox, const real_t oy) {
-		columns[0][0] = xx;
-		columns[0][1] = xy;
-		columns[1][0] = yx;
-		columns[1][1] = yy;
-		columns[2][0] = ox;
-		columns[2][1] = oy;
+	Transform2D(real_t p_xx, real_t p_xy, real_t p_yx, real_t p_yy, real_t p_ox, real_t p_oy) {
+		columns[0][0] = p_xx;
+		columns[0][1] = p_xy;
+		columns[1][0] = p_yx;
+		columns[1][1] = p_yy;
+		columns[2][0] = p_ox;
+		columns[2][1] = p_oy;
 	}
 
 	Transform2D(const Vector2 &p_x, const Vector2 &p_y, const Vector2 &p_origin) {
@@ -138,9 +143,9 @@ struct [[nodiscard]] Transform2D {
 		columns[2] = p_origin;
 	}
 
-	Transform2D(const real_t p_rot, const Vector2 &p_pos);
+	Transform2D(real_t p_rot, const Vector2 &p_pos);
 
-	Transform2D(const real_t p_rot, const Size2 &p_scale, const real_t p_skew, const Vector2 &p_pos);
+	Transform2D(real_t p_rot, const Size2 &p_scale, real_t p_skew, const Vector2 &p_pos);
 
 	Transform2D() {
 		columns[0][0] = 1.0;
@@ -188,14 +193,14 @@ Rect2 Transform2D::xform(const Rect2 &p_rect) const {
 	return new_rect;
 }
 
-void Transform2D::set_rotation_and_scale(const real_t p_rot, const Size2 &p_scale) {
+void Transform2D::set_rotation_and_scale(real_t p_rot, const Size2 &p_scale) {
 	columns[0][0] = Math::cos(p_rot) * p_scale.x;
 	columns[1][1] = Math::cos(p_rot) * p_scale.y;
 	columns[1][0] = -Math::sin(p_rot) * p_scale.y;
 	columns[0][1] = Math::sin(p_rot) * p_scale.x;
 }
 
-void Transform2D::set_rotation_scale_and_skew(const real_t p_rot, const Size2 &p_scale, const real_t p_skew) {
+void Transform2D::set_rotation_scale_and_skew(real_t p_rot, const Size2 &p_scale, real_t p_skew) {
 	columns[0][0] = Math::cos(p_rot) * p_scale.x;
 	columns[1][1] = Math::cos(p_rot + p_skew) * p_scale.y;
 	columns[1][0] = -Math::sin(p_rot + p_skew) * p_scale.y;

include/godot_cpp/variant/transform3d.hpp

@@ -54,8 +54,8 @@ struct [[nodiscard]] Transform3D {
 	void rotate(const Vector3 &p_axis, real_t p_angle);
 	void rotate_basis(const Vector3 &p_axis, real_t p_angle);
 
-	void set_look_at(const Vector3 &p_eye, const Vector3 &p_target, const Vector3 &p_up = Vector3(0, 1, 0));
-	Transform3D looking_at(const Vector3 &p_target, const Vector3 &p_up = Vector3(0, 1, 0)) const;
+	void set_look_at(const Vector3 &p_eye, const Vector3 &p_target, const Vector3 &p_up = Vector3(0, 1, 0), bool p_use_model_front = false);
+	Transform3D looking_at(const Vector3 &p_target, const Vector3 &p_up = Vector3(0, 1, 0), bool p_use_model_front = false) const;
 
 	void scale(const Vector3 &p_scale);
 	Transform3D scaled(const Vector3 &p_scale) const;
@@ -104,8 +104,10 @@ struct [[nodiscard]] Transform3D {
 
 	void operator*=(const Transform3D &p_transform);
 	Transform3D operator*(const Transform3D &p_transform) const;
-	void operator*=(const real_t p_val);
-	Transform3D operator*(const real_t p_val) const;
+	void operator*=(real_t p_val);
+	Transform3D operator*(real_t p_val) const;
+	void operator/=(real_t p_val);
+	Transform3D operator/(real_t p_val) const;
 
 	Transform3D interpolate_with(const Transform3D &p_transform, real_t p_c) const;
 
@@ -115,11 +117,11 @@ struct [[nodiscard]] Transform3D {
 				basis.xform(v));
 	}
 
-	void set(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz, real_t tx, real_t ty, real_t tz) {
-		basis.set(xx, xy, xz, yx, yy, yz, zx, zy, zz);
-		origin.x = tx;
-		origin.y = ty;
-		origin.z = tz;
+	void set(real_t p_xx, real_t p_xy, real_t p_xz, real_t p_yx, real_t p_yy, real_t p_yz, real_t p_zx, real_t p_zy, real_t p_zz, real_t p_tx, real_t p_ty, real_t p_tz) {
+		basis.set(p_xx, p_xy, p_xz, p_yx, p_yy, p_yz, p_zx, p_zy, p_zz);
+		origin.x = p_tx;
+		origin.y = p_ty;
+		origin.z = p_tz;
 	}
 
 	operator String() const;
@@ -127,7 +129,7 @@ struct [[nodiscard]] Transform3D {
 	Transform3D() {}
 	Transform3D(const Basis &p_basis, const Vector3 &p_origin = Vector3());
 	Transform3D(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z, const Vector3 &p_origin);
-	Transform3D(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz, real_t ox, real_t oy, real_t oz);
+	Transform3D(real_t p_xx, real_t p_xy, real_t p_xz, real_t p_yx, real_t p_yy, real_t p_yz, real_t p_zx, real_t p_zy, real_t p_zz, real_t p_ox, real_t p_oy, real_t p_oz);
 };
 
 _FORCE_INLINE_ Vector3 Transform3D::xform(const Vector3 &p_vector) const {

include/godot_cpp/variant/vector2.hpp

@@ -61,13 +61,13 @@ struct [[nodiscard]] Vector2 {
 		real_t coord[2] = { 0 };
 	};
 
-	_FORCE_INLINE_ real_t &operator[](int p_idx) {
-		DEV_ASSERT((unsigned int)p_idx < 2);
-		return coord[p_idx];
+	_FORCE_INLINE_ real_t &operator[](int p_axis) {
+		DEV_ASSERT((unsigned int)p_axis < 2);
+		return coord[p_axis];
 	}
-	_FORCE_INLINE_ const real_t &operator[](int p_idx) const {
-		DEV_ASSERT((unsigned int)p_idx < 2);
-		return coord[p_idx];
+	_FORCE_INLINE_ const real_t &operator[](int p_axis) const {
+		DEV_ASSERT((unsigned int)p_axis < 2);
+		return coord[p_axis];
 	}
 
 	_FORCE_INLINE_ Vector2::Axis min_axis_index() const {
@@ -84,7 +84,7 @@ struct [[nodiscard]] Vector2 {
 
 	real_t length() const;
 	real_t length_squared() const;
-	Vector2 limit_length(const real_t p_len = 1.0) const;
+	Vector2 limit_length(real_t p_len = 1.0) const;
 
 	Vector2 min(const Vector2 &p_vector2) const {
 		return Vector2(MIN(x, p_vector2.x), MIN(y, p_vector2.y));
@@ -110,19 +110,20 @@ struct [[nodiscard]] Vector2 {
 
 	real_t dot(const Vector2 &p_other) const;
 	real_t cross(const Vector2 &p_other) const;
-	Vector2 posmod(const real_t p_mod) const;
+	Vector2 posmod(real_t p_mod) const;
 	Vector2 posmodv(const Vector2 &p_modv) const;
 	Vector2 project(const Vector2 &p_to) const;
 
-	Vector2 plane_project(const real_t p_d, const Vector2 &p_vec) const;
+	Vector2 plane_project(real_t p_d, const Vector2 &p_vec) const;
 
-	_FORCE_INLINE_ Vector2 lerp(const Vector2 &p_to, const real_t p_weight) const;
-	_FORCE_INLINE_ Vector2 slerp(const Vector2 &p_to, const real_t p_weight) const;
-	_FORCE_INLINE_ Vector2 cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, const real_t p_weight) const;
-	_FORCE_INLINE_ Vector2 cubic_interpolate_in_time(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, const real_t p_weight, const real_t &p_b_t, const real_t &p_pre_a_t, const real_t &p_post_b_t) const;
-	_FORCE_INLINE_ Vector2 bezier_interpolate(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, const real_t p_t) const;
+	_FORCE_INLINE_ Vector2 lerp(const Vector2 &p_to, real_t p_weight) const;
+	_FORCE_INLINE_ Vector2 slerp(const Vector2 &p_to, real_t p_weight) const;
+	_FORCE_INLINE_ Vector2 cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, real_t p_weight) const;
+	_FORCE_INLINE_ Vector2 cubic_interpolate_in_time(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, real_t p_weight, real_t p_b_t, real_t p_pre_a_t, real_t p_post_b_t) const;
+	_FORCE_INLINE_ Vector2 bezier_interpolate(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, real_t p_t) const;
+	_FORCE_INLINE_ Vector2 bezier_derivative(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, real_t p_t) const;
 
-	Vector2 move_toward(const Vector2 &p_to, const real_t p_delta) const;
+	Vector2 move_toward(const Vector2 &p_to, real_t p_delta) const;
 
 	Vector2 slide(const Vector2 &p_normal) const;
 	Vector2 bounce(const Vector2 &p_normal) const;
@@ -138,16 +139,16 @@ struct [[nodiscard]] Vector2 {
 	void operator-=(const Vector2 &p_v);
 	Vector2 operator*(const Vector2 &p_v1) const;
 
-	Vector2 operator*(const real_t &rvalue) const;
-	void operator*=(const real_t &rvalue);
-	void operator*=(const Vector2 &rvalue) { *this = *this * rvalue; }
+	Vector2 operator*(real_t p_rvalue) const;
+	void operator*=(real_t p_rvalue);
+	void operator*=(const Vector2 &p_rvalue) { *this = *this * p_rvalue; }
 
 	Vector2 operator/(const Vector2 &p_v1) const;
 
-	Vector2 operator/(const real_t &rvalue) const;
+	Vector2 operator/(real_t p_rvalue) const;
 
-	void operator/=(const real_t &rvalue);
-	void operator/=(const Vector2 &rvalue) { *this = *this / rvalue; }
+	void operator/=(real_t p_rvalue);
+	void operator/=(const Vector2 &p_rvalue) { *this = *this / p_rvalue; }
 
 	Vector2 operator-() const;
 
@@ -160,13 +161,13 @@ struct [[nodiscard]] Vector2 {
 	bool operator>=(const Vector2 &p_vec2) const { return x == p_vec2.x ? (y >= p_vec2.y) : (x > p_vec2.x); }
 
 	real_t angle() const;
-	static Vector2 from_angle(const real_t p_angle);
+	static Vector2 from_angle(real_t p_angle);
 
 	_FORCE_INLINE_ Vector2 abs() const {
 		return Vector2(Math::abs(x), Math::abs(y));
 	}
 
-	Vector2 rotated(const real_t p_by) const;
+	Vector2 rotated(real_t p_by) const;
 	Vector2 orthogonal() const {
 		return Vector2(y, -x);
 	}
@@ -185,13 +186,13 @@ struct [[nodiscard]] Vector2 {
 	operator Vector2i() const;
 
 	_FORCE_INLINE_ Vector2() {}
-	_FORCE_INLINE_ Vector2(const real_t p_x, const real_t p_y) {
+	_FORCE_INLINE_ Vector2(real_t p_x, real_t p_y) {
 		x = p_x;
 		y = p_y;
 	}
 };
 
-_FORCE_INLINE_ Vector2 Vector2::plane_project(const real_t p_d, const Vector2 &p_vec) const {
+_FORCE_INLINE_ Vector2 Vector2::plane_project(real_t p_d, const Vector2 &p_vec) const {
 	return p_vec - *this * (dot(p_vec) - p_d);
 }
 
@@ -217,26 +218,26 @@ _FORCE_INLINE_ Vector2 Vector2::operator*(const Vector2 &p_v1) const {
 	return Vector2(x * p_v1.x, y * p_v1.y);
 }
 
-_FORCE_INLINE_ Vector2 Vector2::operator*(const real_t &rvalue) const {
-	return Vector2(x * rvalue, y * rvalue);
+_FORCE_INLINE_ Vector2 Vector2::operator*(real_t p_rvalue) const {
+	return Vector2(x * p_rvalue, y * p_rvalue);
 }
 
-_FORCE_INLINE_ void Vector2::operator*=(const real_t &rvalue) {
-	x *= rvalue;
-	y *= rvalue;
+_FORCE_INLINE_ void Vector2::operator*=(real_t p_rvalue) {
+	x *= p_rvalue;
+	y *= p_rvalue;
 }
 
 _FORCE_INLINE_ Vector2 Vector2::operator/(const Vector2 &p_v1) const {
 	return Vector2(x / p_v1.x, y / p_v1.y);
 }
 
-_FORCE_INLINE_ Vector2 Vector2::operator/(const real_t &rvalue) const {
-	return Vector2(x / rvalue, y / rvalue);
+_FORCE_INLINE_ Vector2 Vector2::operator/(real_t p_rvalue) const {
+	return Vector2(x / p_rvalue, y / p_rvalue);
 }
 
-_FORCE_INLINE_ void Vector2::operator/=(const real_t &rvalue) {
-	x /= rvalue;
-	y /= rvalue;
+_FORCE_INLINE_ void Vector2::operator/=(real_t p_rvalue) {
+	x /= p_rvalue;
+	y /= p_rvalue;
 }
 
 _FORCE_INLINE_ Vector2 Vector2::operator-() const {
@@ -251,16 +252,14 @@ _FORCE_INLINE_ bool Vector2::operator!=(const Vector2 &p_vec2) const {
 	return x != p_vec2.x || y != p_vec2.y;
 }
 
-Vector2 Vector2::lerp(const Vector2 &p_to, const real_t p_weight) const {
+Vector2 Vector2::lerp(const Vector2 &p_to, real_t p_weight) const {
 	Vector2 res = *this;
-
-	res.x += (p_weight * (p_to.x - x));
-	res.y += (p_weight * (p_to.y - y));
-
+	res.x = Math::lerp(res.x, p_to.x, p_weight);
+	res.y = Math::lerp(res.y, p_to.y, p_weight);
 	return res;
 }
 
-Vector2 Vector2::slerp(const Vector2 &p_to, const real_t p_weight) const {
+Vector2 Vector2::slerp(const Vector2 &p_to, real_t p_weight) const {
 	real_t start_length_sq = length_squared();
 	real_t end_length_sq = p_to.length_squared();
 	if (unlikely(start_length_sq == 0.0f || end_length_sq == 0.0f)) {
@@ -273,31 +272,32 @@ Vector2 Vector2::slerp(const Vector2 &p_to, const real_t p_weight) const {
 	return rotated(angle * p_weight) * (result_length / start_length);
 }
 
-Vector2 Vector2::cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, const real_t p_weight) const {
+Vector2 Vector2::cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, real_t p_weight) const {
 	Vector2 res = *this;
 	res.x = Math::cubic_interpolate(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight);
 	res.y = Math::cubic_interpolate(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight);
 	return res;
 }
 
-Vector2 Vector2::cubic_interpolate_in_time(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, const real_t p_weight, const real_t &p_b_t, const real_t &p_pre_a_t, const real_t &p_post_b_t) const {
+Vector2 Vector2::cubic_interpolate_in_time(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, real_t p_weight, real_t p_b_t, real_t p_pre_a_t, real_t p_post_b_t) const {
 	Vector2 res = *this;
 	res.x = Math::cubic_interpolate_in_time(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
 	res.y = Math::cubic_interpolate_in_time(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
 	return res;
 }
 
-Vector2 Vector2::bezier_interpolate(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, const real_t p_t) const {
+Vector2 Vector2::bezier_interpolate(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, real_t p_t) const {
 	Vector2 res = *this;
+	res.x = Math::bezier_interpolate(res.x, p_control_1.x, p_control_2.x, p_end.x, p_t);
+	res.y = Math::bezier_interpolate(res.y, p_control_1.y, p_control_2.y, p_end.y, p_t);
+	return res;
+}
 
-	/* Formula from Wikipedia article on Bezier curves. */
-	real_t omt = (1.0 - p_t);
-	real_t omt2 = omt * omt;
-	real_t omt3 = omt2 * omt;
-	real_t t2 = p_t * p_t;
-	real_t t3 = t2 * p_t;
-
-	return res * omt3 + p_control_1 * omt2 * p_t * 3.0 + p_control_2 * omt * t2 * 3.0 + p_end * t3;
+Vector2 Vector2::bezier_derivative(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, real_t p_t) const {
+	Vector2 res = *this;
+	res.x = Math::bezier_derivative(res.x, p_control_1.x, p_control_2.x, p_end.x, p_t);
+	res.y = Math::bezier_derivative(res.y, p_control_1.y, p_control_2.y, p_end.y, p_t);
+	return res;
 }
 
 Vector2 Vector2::direction_to(const Vector2 &p_to) const {
@@ -309,19 +309,19 @@ Vector2 Vector2::direction_to(const Vector2 &p_to) const {
 // Multiplication operators required to workaround issues with LLVM using implicit conversion
 // to Vector2i instead for integers where it should not.
 
-_FORCE_INLINE_ Vector2 operator*(const float p_scalar, const Vector2 &p_vec) {
+_FORCE_INLINE_ Vector2 operator*(float p_scalar, const Vector2 &p_vec) {
 	return p_vec * p_scalar;
 }
 
-_FORCE_INLINE_ Vector2 operator*(const double p_scalar, const Vector2 &p_vec) {
+_FORCE_INLINE_ Vector2 operator*(double p_scalar, const Vector2 &p_vec) {
 	return p_vec * p_scalar;
 }
 
-_FORCE_INLINE_ Vector2 operator*(const int32_t p_scalar, const Vector2 &p_vec) {
+_FORCE_INLINE_ Vector2 operator*(int32_t p_scalar, const Vector2 &p_vec) {
 	return p_vec * p_scalar;
 }
 
-_FORCE_INLINE_ Vector2 operator*(const int64_t p_scalar, const Vector2 &p_vec) {
+_FORCE_INLINE_ Vector2 operator*(int64_t p_scalar, const Vector2 &p_vec) {
 	return p_vec * p_scalar;
 }
 

include/godot_cpp/variant/vector2i.hpp

@@ -61,13 +61,13 @@ struct [[nodiscard]] Vector2i {
 		int32_t coord[2] = { 0 };
 	};
 
-	_FORCE_INLINE_ int32_t &operator[](int p_idx) {
-		DEV_ASSERT((unsigned int)p_idx < 2);
-		return coord[p_idx];
+	_FORCE_INLINE_ int32_t &operator[](int p_axis) {
+		DEV_ASSERT((unsigned int)p_axis < 2);
+		return coord[p_axis];
 	}
-	_FORCE_INLINE_ const int32_t &operator[](int p_idx) const {
-		DEV_ASSERT((unsigned int)p_idx < 2);
-		return coord[p_idx];
+	_FORCE_INLINE_ const int32_t &operator[](int p_axis) const {
+		DEV_ASSERT((unsigned int)p_axis < 2);
+		return coord[p_axis];
 	}
 
 	_FORCE_INLINE_ Vector2i::Axis min_axis_index() const {
@@ -94,22 +94,30 @@ struct [[nodiscard]] Vector2i {
 		return Vector2i(MAX(x, p_scalar), MAX(y, p_scalar));
 	}
 
+	double distance_to(const Vector2i &p_to) const {
+		return (p_to - *this).length();
+	}
+
+	int64_t distance_squared_to(const Vector2i &p_to) const {
+		return (p_to - *this).length_squared();
+	}
+
 	Vector2i operator+(const Vector2i &p_v) const;
 	void operator+=(const Vector2i &p_v);
 	Vector2i operator-(const Vector2i &p_v) const;
 	void operator-=(const Vector2i &p_v);
 	Vector2i operator*(const Vector2i &p_v1) const;
 
-	Vector2i operator*(const int32_t &rvalue) const;
-	void operator*=(const int32_t &rvalue);
+	Vector2i operator*(int32_t p_rvalue) const;
+	void operator*=(int32_t p_rvalue);
 
 	Vector2i operator/(const Vector2i &p_v1) const;
-	Vector2i operator/(const int32_t &rvalue) const;
-	void operator/=(const int32_t &rvalue);
+	Vector2i operator/(int32_t p_rvalue) const;
+	void operator/=(int32_t p_rvalue);
 
 	Vector2i operator%(const Vector2i &p_v1) const;
-	Vector2i operator%(const int32_t &rvalue) const;
-	void operator%=(const int32_t &rvalue);
+	Vector2i operator%(int32_t p_rvalue) const;
+	void operator%=(int32_t p_rvalue);
 
 	Vector2i operator-() const;
 	bool operator<(const Vector2i &p_vec2) const { return (x == p_vec2.x) ? (y < p_vec2.y) : (x < p_vec2.x); }
@@ -124,22 +132,19 @@ struct [[nodiscard]] Vector2i {
 	int64_t length_squared() const;
 	double length() const;
 
-	int64_t distance_squared_to(const Vector2i &p_to) const;
-	double distance_to(const Vector2i &p_to) const;
-
 	real_t aspect() const { return width / (real_t)height; }
 	Vector2i sign() const { return Vector2i(SIGN(x), SIGN(y)); }
 	Vector2i abs() const { return Vector2i(Math::abs(x), Math::abs(y)); }
-	Vector2i snapped(const Vector2i &p_step) const;
-	Vector2i snappedi(int32_t p_step) const;
 	Vector2i clamp(const Vector2i &p_min, const Vector2i &p_max) const;
 	Vector2i clampi(int32_t p_min, int32_t p_max) const;
+	Vector2i snapped(const Vector2i &p_step) const;
+	Vector2i snappedi(int32_t p_step) const;
 
 	operator String() const;
 	operator Vector2() const;
 
 	inline Vector2i() {}
-	inline Vector2i(const int32_t p_x, const int32_t p_y) {
+	inline Vector2i(int32_t p_x, int32_t p_y) {
 		x = p_x;
 		y = p_y;
 	}
@@ -147,19 +152,19 @@ struct [[nodiscard]] Vector2i {
 
 // Multiplication operators required to workaround issues with LLVM using implicit conversion.
 
-_FORCE_INLINE_ Vector2i operator*(const int32_t p_scalar, const Vector2i &p_vector) {
+_FORCE_INLINE_ Vector2i operator*(int32_t p_scalar, const Vector2i &p_vector) {
 	return p_vector * p_scalar;
 }
 
-_FORCE_INLINE_ Vector2i operator*(const int64_t p_scalar, const Vector2i &p_vector) {
+_FORCE_INLINE_ Vector2i operator*(int64_t p_scalar, const Vector2i &p_vector) {
 	return p_vector * p_scalar;
 }
 
-_FORCE_INLINE_ Vector2i operator*(const float p_scalar, const Vector2i &p_vector) {
+_FORCE_INLINE_ Vector2i operator*(float p_scalar, const Vector2i &p_vector) {
 	return p_vector * p_scalar;
 }
 
-_FORCE_INLINE_ Vector2i operator*(const double p_scalar, const Vector2i &p_vector) {
+_FORCE_INLINE_ Vector2i operator*(double p_scalar, const Vector2i &p_vector) {
 	return p_vector * p_scalar;
 }
 

include/godot_cpp/variant/vector3.hpp

@@ -59,12 +59,12 @@ struct [[nodiscard]] Vector3 {
 		real_t coord[3] = { 0 };
 	};
 
-	_FORCE_INLINE_ const real_t &operator[](const int p_axis) const {
+	_FORCE_INLINE_ const real_t &operator[](int p_axis) const {
 		DEV_ASSERT((unsigned int)p_axis < 3);
 		return coord[p_axis];
 	}
 
-	_FORCE_INLINE_ real_t &operator[](const int p_axis) {
+	_FORCE_INLINE_ real_t &operator[](int p_axis) {
 		DEV_ASSERT((unsigned int)p_axis < 3);
 		return coord[p_axis];
 	}
@@ -100,36 +100,38 @@ struct [[nodiscard]] Vector3 {
 	_FORCE_INLINE_ Vector3 normalized() const;
 	_FORCE_INLINE_ bool is_normalized() const;
 	_FORCE_INLINE_ Vector3 inverse() const;
-	Vector3 limit_length(const real_t p_len = 1.0) const;
+	Vector3 limit_length(real_t p_len = 1.0) const;
 
 	_FORCE_INLINE_ void zero();
 
-	void snap(const Vector3 p_val);
-	void snapf(real_t p_val);
-	Vector3 snapped(const Vector3 p_val) const;
-	Vector3 snappedf(real_t p_val) const;
+	void snap(const Vector3 &p_step);
+	void snapf(real_t p_step);
+	Vector3 snapped(const Vector3 &p_step) const;
+	Vector3 snappedf(real_t p_step) const;
 
-	void rotate(const Vector3 &p_axis, const real_t p_angle);
-	Vector3 rotated(const Vector3 &p_axis, const real_t p_angle) const;
+	void rotate(const Vector3 &p_axis, real_t p_angle);
+	Vector3 rotated(const Vector3 &p_axis, real_t p_angle) const;
 
 	/* Static Methods between 2 vector3s */
 
-	_FORCE_INLINE_ Vector3 lerp(const Vector3 &p_to, const real_t p_weight) const;
-	_FORCE_INLINE_ Vector3 slerp(const Vector3 &p_to, const real_t p_weight) const;
-	_FORCE_INLINE_ Vector3 cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight) const;
-	_FORCE_INLINE_ Vector3 cubic_interpolate_in_time(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight, const real_t &p_b_t, const real_t &p_pre_a_t, const real_t &p_post_b_t) const;
-	_FORCE_INLINE_ Vector3 bezier_interpolate(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const;
+	_FORCE_INLINE_ Vector3 lerp(const Vector3 &p_to, real_t p_weight) const;
+	_FORCE_INLINE_ Vector3 slerp(const Vector3 &p_to, real_t p_weight) const;
+	_FORCE_INLINE_ Vector3 cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, real_t p_weight) const;
+	_FORCE_INLINE_ Vector3 cubic_interpolate_in_time(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, real_t p_weight, real_t p_b_t, real_t p_pre_a_t, real_t p_post_b_t) const;
+	_FORCE_INLINE_ Vector3 bezier_interpolate(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, real_t p_t) const;
+	_FORCE_INLINE_ Vector3 bezier_derivative(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, real_t p_t) const;
 
-	Vector3 move_toward(const Vector3 &p_to, const real_t p_delta) const;
+	Vector3 move_toward(const Vector3 &p_to, real_t p_delta) const;
 
 	Vector2 octahedron_encode() const;
 	static Vector3 octahedron_decode(const Vector2 &p_oct);
-	Vector2 octahedron_tangent_encode(const float sign) const;
-	static Vector3 octahedron_tangent_decode(const Vector2 &p_oct, float *sign);
+	Vector2 octahedron_tangent_encode(float p_sign) const;
+	static Vector3 octahedron_tangent_decode(const Vector2 &p_oct, float *r_sign);
 
 	_FORCE_INLINE_ Vector3 cross(const Vector3 &p_with) const;
 	_FORCE_INLINE_ real_t dot(const Vector3 &p_with) const;
 	Basis outer(const Vector3 &p_with) const;
+	_FORCE_INLINE_ Vector3 get_any_perpendicular() const;
 
 	_FORCE_INLINE_ Vector3 abs() const;
 	_FORCE_INLINE_ Vector3 floor() const;
@@ -142,7 +144,7 @@ struct [[nodiscard]] Vector3 {
 	_FORCE_INLINE_ real_t distance_to(const Vector3 &p_to) const;
 	_FORCE_INLINE_ real_t distance_squared_to(const Vector3 &p_to) const;
 
-	_FORCE_INLINE_ Vector3 posmod(const real_t p_mod) const;
+	_FORCE_INLINE_ Vector3 posmod(real_t p_mod) const;
 	_FORCE_INLINE_ Vector3 posmodv(const Vector3 &p_modv) const;
 	_FORCE_INLINE_ Vector3 project(const Vector3 &p_to) const;
 
@@ -169,10 +171,10 @@ struct [[nodiscard]] Vector3 {
 	_FORCE_INLINE_ Vector3 &operator/=(const Vector3 &p_v);
 	_FORCE_INLINE_ Vector3 operator/(const Vector3 &p_v) const;
 
-	_FORCE_INLINE_ Vector3 &operator*=(const real_t p_scalar);
-	_FORCE_INLINE_ Vector3 operator*(const real_t p_scalar) const;
-	_FORCE_INLINE_ Vector3 &operator/=(const real_t p_scalar);
-	_FORCE_INLINE_ Vector3 operator/(const real_t p_scalar) const;
+	_FORCE_INLINE_ Vector3 &operator*=(real_t p_scalar);
+	_FORCE_INLINE_ Vector3 operator*(real_t p_scalar) const;
+	_FORCE_INLINE_ Vector3 &operator/=(real_t p_scalar);
+	_FORCE_INLINE_ Vector3 operator/(real_t p_scalar) const;
 
 	_FORCE_INLINE_ Vector3 operator-() const;
 
@@ -187,7 +189,7 @@ struct [[nodiscard]] Vector3 {
 	operator Vector3i() const;
 
 	_FORCE_INLINE_ Vector3() {}
-	_FORCE_INLINE_ Vector3(const real_t p_x, const real_t p_y, const real_t p_z) {
+	_FORCE_INLINE_ Vector3(real_t p_x, real_t p_y, real_t p_z) {
 		x = p_x;
 		y = p_y;
 		z = p_z;
@@ -227,14 +229,15 @@ Vector3 Vector3::round() const {
 	return Vector3(Math::round(x), Math::round(y), Math::round(z));
 }
 
-Vector3 Vector3::lerp(const Vector3 &p_to, const real_t p_weight) const {
-	return Vector3(
-			x + (p_weight * (p_to.x - x)),
-			y + (p_weight * (p_to.y - y)),
-			z + (p_weight * (p_to.z - z)));
+Vector3 Vector3::lerp(const Vector3 &p_to, real_t p_weight) const {
+	Vector3 res = *this;
+	res.x = Math::lerp(res.x, p_to.x, p_weight);
+	res.y = Math::lerp(res.y, p_to.y, p_weight);
+	res.z = Math::lerp(res.z, p_to.z, p_weight);
+	return res;
 }
 
-Vector3 Vector3::slerp(const Vector3 &p_to, const real_t p_weight) const {
+Vector3 Vector3::slerp(const Vector3 &p_to, real_t p_weight) const {
 	// This method seems more complicated than it really is, since we write out
 	// the internals of some methods for efficiency (mainly, checking length).
 	real_t start_length_sq = length_squared();
@@ -256,7 +259,7 @@ Vector3 Vector3::slerp(const Vector3 &p_to, const real_t p_weight) const {
 	return rotated(axis, angle * p_weight) * (result_length / start_length);
 }
 
-Vector3 Vector3::cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight) const {
+Vector3 Vector3::cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, real_t p_weight) const {
 	Vector3 res = *this;
 	res.x = Math::cubic_interpolate(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight);
 	res.y = Math::cubic_interpolate(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight);
@@ -264,7 +267,7 @@ Vector3 Vector3::cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, c
 	return res;
 }
 
-Vector3 Vector3::cubic_interpolate_in_time(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight, const real_t &p_b_t, const real_t &p_pre_a_t, const real_t &p_post_b_t) const {
+Vector3 Vector3::cubic_interpolate_in_time(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, real_t p_weight, real_t p_b_t, real_t p_pre_a_t, real_t p_post_b_t) const {
 	Vector3 res = *this;
 	res.x = Math::cubic_interpolate_in_time(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
 	res.y = Math::cubic_interpolate_in_time(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
@@ -272,17 +275,20 @@ Vector3 Vector3::cubic_interpolate_in_time(const Vector3 &p_b, const Vector3 &p_
 	return res;
 }
 
-Vector3 Vector3::bezier_interpolate(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const {
+Vector3 Vector3::bezier_interpolate(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, real_t p_t) const {
 	Vector3 res = *this;
+	res.x = Math::bezier_interpolate(res.x, p_control_1.x, p_control_2.x, p_end.x, p_t);
+	res.y = Math::bezier_interpolate(res.y, p_control_1.y, p_control_2.y, p_end.y, p_t);
+	res.z = Math::bezier_interpolate(res.z, p_control_1.z, p_control_2.z, p_end.z, p_t);
+	return res;
+}
 
-	/* Formula from Wikipedia article on Bezier curves. */
-	real_t omt = (1.0 - p_t);
-	real_t omt2 = omt * omt;
-	real_t omt3 = omt2 * omt;
-	real_t t2 = p_t * p_t;
-	real_t t3 = t2 * p_t;
-
-	return res * omt3 + p_control_1 * omt2 * p_t * 3.0 + p_control_2 * omt * t2 * 3.0 + p_end * t3;
+Vector3 Vector3::bezier_derivative(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, real_t p_t) const {
+	Vector3 res = *this;
+	res.x = Math::bezier_derivative(res.x, p_control_1.x, p_control_2.x, p_end.x, p_t);
+	res.y = Math::bezier_derivative(res.y, p_control_1.y, p_control_2.y, p_end.y, p_t);
+	res.z = Math::bezier_derivative(res.z, p_control_1.z, p_control_2.z, p_end.z, p_t);
+	return res;
 }
 
 real_t Vector3::distance_to(const Vector3 &p_to) const {
@@ -293,7 +299,7 @@ real_t Vector3::distance_squared_to(const Vector3 &p_to) const {
 	return (p_to - *this).length_squared();
 }
 
-Vector3 Vector3::posmod(const real_t p_mod) const {
+Vector3 Vector3::posmod(real_t p_mod) const {
 	return Vector3(Math::fposmod(x, p_mod), Math::fposmod(y, p_mod), Math::fposmod(z, p_mod));
 }
 
@@ -322,6 +328,16 @@ Vector3 Vector3::direction_to(const Vector3 &p_to) const {
 	return ret;
 }
 
+Vector3 Vector3::get_any_perpendicular() const {
+	// Return the any perpendicular vector by cross product with the Vector3.RIGHT or Vector3.UP,
+	// whichever has the greater angle to the current vector with the sign of each element positive.
+	// The only essence is "to avoid being parallel to the current vector", and there is no mathematical basis for using Vector3.RIGHT and Vector3.UP,
+	// since it could be a different vector depending on the prior branching code Math::abs(x) <= Math::abs(y) && Math::abs(x) <= Math::abs(z).
+	// However, it would be reasonable to use any of the axes of the basis, as it is simpler to calculate.
+	ERR_FAIL_COND_V_MSG(is_zero_approx(), Vector3(0, 0, 0), "The Vector3 must not be zero.");
+	return cross((Math::abs(x) <= Math::abs(y) && Math::abs(x) <= Math::abs(z)) ? Vector3(1, 0, 0) : Vector3(0, 1, 0)).normalized();
+}
+
 /* Operators */
 
 Vector3 &Vector3::operator+=(const Vector3 &p_v) {
@@ -368,7 +384,7 @@ Vector3 Vector3::operator/(const Vector3 &p_v) const {
 	return Vector3(x / p_v.x, y / p_v.y, z / p_v.z);
 }
 
-Vector3 &Vector3::operator*=(const real_t p_scalar) {
+Vector3 &Vector3::operator*=(real_t p_scalar) {
 	x *= p_scalar;
 	y *= p_scalar;
 	z *= p_scalar;
@@ -378,34 +394,34 @@ Vector3 &Vector3::operator*=(const real_t p_scalar) {
 // Multiplication operators required to workaround issues with LLVM using implicit conversion
 // to Vector3i instead for integers where it should not.
 
-_FORCE_INLINE_ Vector3 operator*(const float p_scalar, const Vector3 &p_vec) {
+_FORCE_INLINE_ Vector3 operator*(float p_scalar, const Vector3 &p_vec) {
 	return p_vec * p_scalar;
 }
 
-_FORCE_INLINE_ Vector3 operator*(const double p_scalar, const Vector3 &p_vec) {
+_FORCE_INLINE_ Vector3 operator*(double p_scalar, const Vector3 &p_vec) {
 	return p_vec * p_scalar;
 }
 
-_FORCE_INLINE_ Vector3 operator*(const int32_t p_scalar, const Vector3 &p_vec) {
+_FORCE_INLINE_ Vector3 operator*(int32_t p_scalar, const Vector3 &p_vec) {
 	return p_vec * p_scalar;
 }
 
-_FORCE_INLINE_ Vector3 operator*(const int64_t p_scalar, const Vector3 &p_vec) {
+_FORCE_INLINE_ Vector3 operator*(int64_t p_scalar, const Vector3 &p_vec) {
 	return p_vec * p_scalar;
 }
 
-Vector3 Vector3::operator*(const real_t p_scalar) const {
+Vector3 Vector3::operator*(real_t p_scalar) const {
 	return Vector3(x * p_scalar, y * p_scalar, z * p_scalar);
 }
 
-Vector3 &Vector3::operator/=(const real_t p_scalar) {
+Vector3 &Vector3::operator/=(real_t p_scalar) {
 	x /= p_scalar;
 	y /= p_scalar;
 	z /= p_scalar;
 	return *this;
 }
 
-Vector3 Vector3::operator/(const real_t p_scalar) const {
+Vector3 Vector3::operator/(real_t p_scalar) const {
 	return Vector3(x / p_scalar, y / p_scalar, z / p_scalar);
 }
 
@@ -519,9 +535,9 @@ void Vector3::zero() {
 // slide returns the component of the vector along the given plane, specified by its normal vector.
 Vector3 Vector3::slide(const Vector3 &p_normal) const {
 #ifdef MATH_CHECKS
-	ERR_FAIL_COND_V_MSG(!p_normal.is_normalized(), Vector3(), "The normal Vector3 must be normalized.");
+	ERR_FAIL_COND_V_MSG(!p_normal.is_normalized(), Vector3(), "The normal Vector3 " + p_normal.operator String() + " must be normalized.");
 #endif
-	return *this - p_normal * this->dot(p_normal);
+	return *this - p_normal * dot(p_normal);
 }
 
 Vector3 Vector3::bounce(const Vector3 &p_normal) const {
@@ -530,9 +546,9 @@ Vector3 Vector3::bounce(const Vector3 &p_normal) const {
 
 Vector3 Vector3::reflect(const Vector3 &p_normal) const {
 #ifdef MATH_CHECKS
-	ERR_FAIL_COND_V_MSG(!p_normal.is_normalized(), Vector3(), "The normal Vector3 must be normalized.");
+	ERR_FAIL_COND_V_MSG(!p_normal.is_normalized(), Vector3(), "The normal Vector3 " + p_normal.operator String() + " must be normalized.");
 #endif
-	return 2.0f * p_normal * this->dot(p_normal) - *this;
+	return 2.0f * p_normal * dot(p_normal) - *this;
 }
 
 } // namespace godot

include/godot_cpp/variant/vector3i.hpp

@@ -57,12 +57,12 @@ struct [[nodiscard]] Vector3i {
 		int32_t coord[3] = { 0 };
 	};
 
-	_FORCE_INLINE_ const int32_t &operator[](const int p_axis) const {
+	_FORCE_INLINE_ const int32_t &operator[](int p_axis) const {
 		DEV_ASSERT((unsigned int)p_axis < 3);
 		return coord[p_axis];
 	}
 
-	_FORCE_INLINE_ int32_t &operator[](const int p_axis) {
+	_FORCE_INLINE_ int32_t &operator[](int p_axis) {
 		DEV_ASSERT((unsigned int)p_axis < 3);
 		return coord[p_axis];
 	}
@@ -89,17 +89,17 @@ struct [[nodiscard]] Vector3i {
 	_FORCE_INLINE_ int64_t length_squared() const;
 	_FORCE_INLINE_ double length() const;
 
-	_FORCE_INLINE_ int64_t distance_squared_to(const Vector3i &p_to) const;
-	_FORCE_INLINE_ double distance_to(const Vector3i &p_to) const;
-
 	_FORCE_INLINE_ void zero();
 
 	_FORCE_INLINE_ Vector3i abs() const;
 	_FORCE_INLINE_ Vector3i sign() const;
-	Vector3i snapped(const Vector3i &p_step) const;
-	Vector3i snappedi(int32_t p_step) const;
 	Vector3i clamp(const Vector3i &p_min, const Vector3i &p_max) const;
 	Vector3i clampi(int32_t p_min, int32_t p_max) const;
+	Vector3i snapped(const Vector3i &p_step) const;
+	Vector3i snappedi(int32_t p_step) const;
+
+	_FORCE_INLINE_ double distance_to(const Vector3i &p_to) const;
+	_FORCE_INLINE_ int64_t distance_squared_to(const Vector3i &p_to) const;
 
 	/* Operators */
 
@@ -114,12 +114,12 @@ struct [[nodiscard]] Vector3i {
 	_FORCE_INLINE_ Vector3i &operator%=(const Vector3i &p_v);
 	_FORCE_INLINE_ Vector3i operator%(const Vector3i &p_v) const;
 
-	_FORCE_INLINE_ Vector3i &operator*=(const int32_t p_scalar);
-	_FORCE_INLINE_ Vector3i operator*(const int32_t p_scalar) const;
-	_FORCE_INLINE_ Vector3i &operator/=(const int32_t p_scalar);
-	_FORCE_INLINE_ Vector3i operator/(const int32_t p_scalar) const;
-	_FORCE_INLINE_ Vector3i &operator%=(const int32_t p_scalar);
-	_FORCE_INLINE_ Vector3i operator%(const int32_t p_scalar) const;
+	_FORCE_INLINE_ Vector3i &operator*=(int32_t p_scalar);
+	_FORCE_INLINE_ Vector3i operator*(int32_t p_scalar) const;
+	_FORCE_INLINE_ Vector3i &operator/=(int32_t p_scalar);
+	_FORCE_INLINE_ Vector3i operator/(int32_t p_scalar) const;
+	_FORCE_INLINE_ Vector3i &operator%=(int32_t p_scalar);
+	_FORCE_INLINE_ Vector3i operator%(int32_t p_scalar) const;
 
 	_FORCE_INLINE_ Vector3i operator-() const;
 
@@ -134,7 +134,7 @@ struct [[nodiscard]] Vector3i {
 	operator Vector3() const;
 
 	_FORCE_INLINE_ Vector3i() {}
-	_FORCE_INLINE_ Vector3i(const int32_t p_x, const int32_t p_y, const int32_t p_z) {
+	_FORCE_INLINE_ Vector3i(int32_t p_x, int32_t p_y, int32_t p_z) {
 		x = p_x;
 		y = p_y;
 		z = p_z;
@@ -149,14 +149,6 @@ double Vector3i::length() const {
 	return Math::sqrt((double)length_squared());
 }
 
-int64_t Vector3i::distance_squared_to(const Vector3i &p_to) const {
-	return (p_to - *this).length_squared();
-}
-
-double Vector3i::distance_to(const Vector3i &p_to) const {
-	return (p_to - *this).length();
-}
-
 Vector3i Vector3i::abs() const {
 	return Vector3i(Math::abs(x), Math::abs(y), Math::abs(z));
 }
@@ -165,6 +157,14 @@ Vector3i Vector3i::sign() const {
 	return Vector3i(SIGN(x), SIGN(y), SIGN(z));
 }
 
+double Vector3i::distance_to(const Vector3i &p_to) const {
+	return (p_to - *this).length();
+}
+
+int64_t Vector3i::distance_squared_to(const Vector3i &p_to) const {
+	return (p_to - *this).length_squared();
+}
+
 /* Operators */
 
 Vector3i &Vector3i::operator+=(const Vector3i &p_v) {
@@ -222,54 +222,54 @@ Vector3i Vector3i::operator%(const Vector3i &p_v) const {
 	return Vector3i(x % p_v.x, y % p_v.y, z % p_v.z);
 }
 
-Vector3i &Vector3i::operator*=(const int32_t p_scalar) {
+Vector3i &Vector3i::operator*=(int32_t p_scalar) {
 	x *= p_scalar;
 	y *= p_scalar;
 	z *= p_scalar;
 	return *this;
 }
 
-Vector3i Vector3i::operator*(const int32_t p_scalar) const {
+Vector3i Vector3i::operator*(int32_t p_scalar) const {
 	return Vector3i(x * p_scalar, y * p_scalar, z * p_scalar);
 }
 
 // Multiplication operators required to workaround issues with LLVM using implicit conversion.
 
-_FORCE_INLINE_ Vector3i operator*(const int32_t p_scalar, const Vector3i &p_vector) {
+_FORCE_INLINE_ Vector3i operator*(int32_t p_scalar, const Vector3i &p_vector) {
 	return p_vector * p_scalar;
 }
 
-_FORCE_INLINE_ Vector3i operator*(const int64_t p_scalar, const Vector3i &p_vector) {
+_FORCE_INLINE_ Vector3i operator*(int64_t p_scalar, const Vector3i &p_vector) {
 	return p_vector * p_scalar;
 }
 
-_FORCE_INLINE_ Vector3i operator*(const float p_scalar, const Vector3i &p_vector) {
+_FORCE_INLINE_ Vector3i operator*(float p_scalar, const Vector3i &p_vector) {
 	return p_vector * p_scalar;
 }
 
-_FORCE_INLINE_ Vector3i operator*(const double p_scalar, const Vector3i &p_vector) {
+_FORCE_INLINE_ Vector3i operator*(double p_scalar, const Vector3i &p_vector) {
 	return p_vector * p_scalar;
 }
 
-Vector3i &Vector3i::operator/=(const int32_t p_scalar) {
+Vector3i &Vector3i::operator/=(int32_t p_scalar) {
 	x /= p_scalar;
 	y /= p_scalar;
 	z /= p_scalar;
 	return *this;
 }
 
-Vector3i Vector3i::operator/(const int32_t p_scalar) const {
+Vector3i Vector3i::operator/(int32_t p_scalar) const {
 	return Vector3i(x / p_scalar, y / p_scalar, z / p_scalar);
 }
 
-Vector3i &Vector3i::operator%=(const int32_t p_scalar) {
+Vector3i &Vector3i::operator%=(int32_t p_scalar) {
 	x %= p_scalar;
 	y %= p_scalar;
 	z %= p_scalar;
 	return *this;
 }
 
-Vector3i Vector3i::operator%(const int32_t p_scalar) const {
+Vector3i Vector3i::operator%(int32_t p_scalar) const {
 	return Vector3i(x % p_scalar, y % p_scalar, z % p_scalar);
 }
 

include/godot_cpp/variant/vector4.hpp

@@ -36,6 +36,7 @@
 namespace godot {
 
 class String;
+struct Vector4i;
 
 struct [[nodiscard]] Vector4 {
 	static const int AXIS_COUNT = 4;
@@ -54,15 +55,14 @@ struct [[nodiscard]] Vector4 {
 			real_t z;
 			real_t w;
 		};
-		[[deprecated("Use coord instead")]] real_t components[4];
 		real_t coord[4] = { 0, 0, 0, 0 };
 	};
 
-	_FORCE_INLINE_ real_t &operator[](const int p_axis) {
+	_FORCE_INLINE_ real_t &operator[](int p_axis) {
 		DEV_ASSERT((unsigned int)p_axis < 4);
 		return coord[p_axis];
 	}
-	_FORCE_INLINE_ const real_t &operator[](const int p_axis) const {
+	_FORCE_INLINE_ const real_t &operator[](int p_axis) const {
 		DEV_ASSERT((unsigned int)p_axis < 4);
 		return coord[p_axis];
 	}
@@ -104,11 +104,11 @@ struct [[nodiscard]] Vector4 {
 	Vector4 floor() const;
 	Vector4 ceil() const;
 	Vector4 round() const;
-	Vector4 lerp(const Vector4 &p_to, const real_t p_weight) const;
-	Vector4 cubic_interpolate(const Vector4 &p_b, const Vector4 &p_pre_a, const Vector4 &p_post_b, const real_t p_weight) const;
-	Vector4 cubic_interpolate_in_time(const Vector4 &p_b, const Vector4 &p_pre_a, const Vector4 &p_post_b, const real_t p_weight, const real_t &p_b_t, const real_t &p_pre_a_t, const real_t &p_post_b_t) const;
+	Vector4 lerp(const Vector4 &p_to, real_t p_weight) const;
+	Vector4 cubic_interpolate(const Vector4 &p_b, const Vector4 &p_pre_a, const Vector4 &p_post_b, real_t p_weight) const;
+	Vector4 cubic_interpolate_in_time(const Vector4 &p_b, const Vector4 &p_pre_a, const Vector4 &p_post_b, real_t p_weight, real_t p_b_t, real_t p_pre_a_t, real_t p_post_b_t) const;
 
-	Vector4 posmod(const real_t p_mod) const;
+	Vector4 posmod(real_t p_mod) const;
 	Vector4 posmodv(const Vector4 &p_modv) const;
 	void snap(const Vector4 &p_step);
 	void snapf(real_t p_step);
@@ -124,15 +124,15 @@ struct [[nodiscard]] Vector4 {
 	_FORCE_INLINE_ void operator-=(const Vector4 &p_vec4);
 	_FORCE_INLINE_ void operator*=(const Vector4 &p_vec4);
 	_FORCE_INLINE_ void operator/=(const Vector4 &p_vec4);
-	_FORCE_INLINE_ void operator*=(const real_t &s);
-	_FORCE_INLINE_ void operator/=(const real_t &s);
+	_FORCE_INLINE_ void operator*=(real_t p_s);
+	_FORCE_INLINE_ void operator/=(real_t p_s);
 	_FORCE_INLINE_ Vector4 operator+(const Vector4 &p_vec4) const;
 	_FORCE_INLINE_ Vector4 operator-(const Vector4 &p_vec4) const;
 	_FORCE_INLINE_ Vector4 operator*(const Vector4 &p_vec4) const;
 	_FORCE_INLINE_ Vector4 operator/(const Vector4 &p_vec4) const;
 	_FORCE_INLINE_ Vector4 operator-() const;
-	_FORCE_INLINE_ Vector4 operator*(const real_t &s) const;
-	_FORCE_INLINE_ Vector4 operator/(const real_t &s) const;
+	_FORCE_INLINE_ Vector4 operator*(real_t p_s) const;
+	_FORCE_INLINE_ Vector4 operator/(real_t p_s) const;
 
 	_FORCE_INLINE_ bool operator==(const Vector4 &p_vec4) const;
 	_FORCE_INLINE_ bool operator!=(const Vector4 &p_vec4) const;
@@ -142,28 +142,14 @@ struct [[nodiscard]] Vector4 {
 	_FORCE_INLINE_ bool operator<=(const Vector4 &p_vec4) const;
 
 	operator String() const;
+	operator Vector4i() const;
 
 	_FORCE_INLINE_ Vector4() {}
-
-	_FORCE_INLINE_ Vector4(real_t p_x, real_t p_y, real_t p_z, real_t p_w) :
-			x(p_x),
-			y(p_y),
-			z(p_z),
-			w(p_w) {
-	}
-
-	Vector4(const Vector4 &p_vec4) :
-			x(p_vec4.x),
-			y(p_vec4.y),
-			z(p_vec4.z),
-			w(p_vec4.w) {
-	}
-
-	void operator=(const Vector4 &p_vec4) {
-		x = p_vec4.x;
-		y = p_vec4.y;
-		z = p_vec4.z;
-		w = p_vec4.w;
+	_FORCE_INLINE_ Vector4(real_t p_x, real_t p_y, real_t p_z, real_t p_w) {
+		x = p_x;
+		y = p_y;
+		z = p_z;
+		w = p_w;
 	}
 };
 
@@ -202,15 +188,15 @@ void Vector4::operator/=(const Vector4 &p_vec4) {
 	z /= p_vec4.z;
 	w /= p_vec4.w;
 }
-void Vector4::operator*=(const real_t &s) {
-	x *= s;
-	y *= s;
-	z *= s;
-	w *= s;
+void Vector4::operator*=(real_t p_s) {
+	x *= p_s;
+	y *= p_s;
+	z *= p_s;
+	w *= p_s;
 }
 
-void Vector4::operator/=(const real_t &s) {
-	*this *= 1.0f / s;
+void Vector4::operator/=(real_t p_s) {
+	*this *= 1.0f / p_s;
 }
 
 Vector4 Vector4::operator+(const Vector4 &p_vec4) const {
@@ -233,12 +219,12 @@ Vector4 Vector4::operator-() const {
 	return Vector4(-x, -y, -z, -w);
 }
 
-Vector4 Vector4::operator*(const real_t &s) const {
-	return Vector4(x * s, y * s, z * s, w * s);
+Vector4 Vector4::operator*(real_t p_s) const {
+	return Vector4(x * p_s, y * p_s, z * p_s, w * p_s);
 }
 
-Vector4 Vector4::operator/(const real_t &s) const {
-	return *this * (1.0f / s);
+Vector4 Vector4::operator/(real_t p_s) const {
+	return *this * (1.0f / p_s);
 }
 
 bool Vector4::operator==(const Vector4 &p_vec4) const {
@@ -301,19 +287,19 @@ bool Vector4::operator>=(const Vector4 &p_v) const {
 	return x > p_v.x;
 }
 
-_FORCE_INLINE_ Vector4 operator*(const float p_scalar, const Vector4 &p_vec) {
+_FORCE_INLINE_ Vector4 operator*(float p_scalar, const Vector4 &p_vec) {
 	return p_vec * p_scalar;
 }
 
-_FORCE_INLINE_ Vector4 operator*(const double p_scalar, const Vector4 &p_vec) {
+_FORCE_INLINE_ Vector4 operator*(double p_scalar, const Vector4 &p_vec) {
 	return p_vec * p_scalar;
 }
 
-_FORCE_INLINE_ Vector4 operator*(const int32_t p_scalar, const Vector4 &p_vec) {
+_FORCE_INLINE_ Vector4 operator*(int32_t p_scalar, const Vector4 &p_vec) {
 	return p_vec * p_scalar;
 }
 
-_FORCE_INLINE_ Vector4 operator*(const int64_t p_scalar, const Vector4 &p_vec) {
+_FORCE_INLINE_ Vector4 operator*(int64_t p_scalar, const Vector4 &p_vec) {
 	return p_vec * p_scalar;
 }
 

include/godot_cpp/variant/vector4i.hpp

@@ -59,12 +59,12 @@ struct [[nodiscard]] Vector4i {
 		int32_t coord[4] = { 0 };
 	};
 
-	_FORCE_INLINE_ const int32_t &operator[](const int p_axis) const {
+	_FORCE_INLINE_ const int32_t &operator[](int p_axis) const {
 		DEV_ASSERT((unsigned int)p_axis < 4);
 		return coord[p_axis];
 	}
 
-	_FORCE_INLINE_ int32_t &operator[](const int p_axis) {
+	_FORCE_INLINE_ int32_t &operator[](int p_axis) {
 		DEV_ASSERT((unsigned int)p_axis < 4);
 		return coord[p_axis];
 	}
@@ -91,17 +91,17 @@ struct [[nodiscard]] Vector4i {
 	_FORCE_INLINE_ int64_t length_squared() const;
 	_FORCE_INLINE_ double length() const;
 
-	_FORCE_INLINE_ int64_t distance_squared_to(const Vector4i &p_to) const;
-	_FORCE_INLINE_ double distance_to(const Vector4i &p_to) const;
-
 	_FORCE_INLINE_ void zero();
 
+	_FORCE_INLINE_ double distance_to(const Vector4i &p_to) const;
+	_FORCE_INLINE_ int64_t distance_squared_to(const Vector4i &p_to) const;
+
 	_FORCE_INLINE_ Vector4i abs() const;
 	_FORCE_INLINE_ Vector4i sign() const;
-	Vector4i snapped(const Vector4i &p_step) const;
-	Vector4i snappedi(int32_t p_step) const;
 	Vector4i clamp(const Vector4i &p_min, const Vector4i &p_max) const;
 	Vector4i clampi(int32_t p_min, int32_t p_max) const;
+	Vector4i snapped(const Vector4i &p_step) const;
+	Vector4i snappedi(int32_t p_step) const;
 
 	/* Operators */
 
@@ -116,12 +116,12 @@ struct [[nodiscard]] Vector4i {
 	_FORCE_INLINE_ Vector4i &operator%=(const Vector4i &p_v);
 	_FORCE_INLINE_ Vector4i operator%(const Vector4i &p_v) const;
 
-	_FORCE_INLINE_ Vector4i &operator*=(const int32_t p_scalar);
-	_FORCE_INLINE_ Vector4i operator*(const int32_t p_scalar) const;
-	_FORCE_INLINE_ Vector4i &operator/=(const int32_t p_scalar);
-	_FORCE_INLINE_ Vector4i operator/(const int32_t p_scalar) const;
-	_FORCE_INLINE_ Vector4i &operator%=(const int32_t p_scalar);
-	_FORCE_INLINE_ Vector4i operator%(const int32_t p_scalar) const;
+	_FORCE_INLINE_ Vector4i &operator*=(int32_t p_scalar);
+	_FORCE_INLINE_ Vector4i operator*(int32_t p_scalar) const;
+	_FORCE_INLINE_ Vector4i &operator/=(int32_t p_scalar);
+	_FORCE_INLINE_ Vector4i operator/(int32_t p_scalar) const;
+	_FORCE_INLINE_ Vector4i &operator%=(int32_t p_scalar);
+	_FORCE_INLINE_ Vector4i operator%(int32_t p_scalar) const;
 
 	_FORCE_INLINE_ Vector4i operator-() const;
 
@@ -137,7 +137,7 @@ struct [[nodiscard]] Vector4i {
 
 	_FORCE_INLINE_ Vector4i() {}
 	Vector4i(const Vector4 &p_vec4);
-	_FORCE_INLINE_ Vector4i(const int32_t p_x, const int32_t p_y, const int32_t p_z, const int32_t p_w) {
+	_FORCE_INLINE_ Vector4i(int32_t p_x, int32_t p_y, int32_t p_z, int32_t p_w) {
 		x = p_x;
 		y = p_y;
 		z = p_z;
@@ -153,20 +153,20 @@ double Vector4i::length() const {
 	return Math::sqrt((double)length_squared());
 }
 
-int64_t Vector4i::distance_squared_to(const Vector4i &p_to) const {
-	return (p_to - *this).length_squared();
-}
-
 double Vector4i::distance_to(const Vector4i &p_to) const {
 	return (p_to - *this).length();
 }
 
+int64_t Vector4i::distance_squared_to(const Vector4i &p_to) const {
+	return (p_to - *this).length_squared();
+}
+
 Vector4i Vector4i::abs() const {
 	return Vector4i(Math::abs(x), Math::abs(y), Math::abs(z), Math::abs(w));
 }
 
 Vector4i Vector4i::sign() const {
-	return Vector4i(Math::sign(x), Math::sign(y), Math::sign(z), Math::sign(w));
+	return Vector4i(SIGN(x), SIGN(y), SIGN(z), SIGN(w));
 }
 
 /* Operators */
@@ -231,7 +231,7 @@ Vector4i Vector4i::operator%(const Vector4i &p_v) const {
 	return Vector4i(x % p_v.x, y % p_v.y, z % p_v.z, w % p_v.w);
 }
 
-Vector4i &Vector4i::operator*=(const int32_t p_scalar) {
+Vector4i &Vector4i::operator*=(int32_t p_scalar) {
 	x *= p_scalar;
 	y *= p_scalar;
 	z *= p_scalar;
@@ -239,29 +239,29 @@ Vector4i &Vector4i::operator*=(const int32_t p_scalar) {
 	return *this;
 }
 
-Vector4i Vector4i::operator*(const int32_t p_scalar) const {
+Vector4i Vector4i::operator*(int32_t p_scalar) const {
 	return Vector4i(x * p_scalar, y * p_scalar, z * p_scalar, w * p_scalar);
 }
 
 // Multiplication operators required to workaround issues with LLVM using implicit conversion.
 
-_FORCE_INLINE_ Vector4i operator*(const int32_t p_scalar, const Vector4i &p_vector) {
+_FORCE_INLINE_ Vector4i operator*(int32_t p_scalar, const Vector4i &p_vector) {
 	return p_vector * p_scalar;
 }
 
-_FORCE_INLINE_ Vector4i operator*(const int64_t p_scalar, const Vector4i &p_vector) {
+_FORCE_INLINE_ Vector4i operator*(int64_t p_scalar, const Vector4i &p_vector) {
 	return p_vector * p_scalar;
 }
 
-_FORCE_INLINE_ Vector4i operator*(const float p_scalar, const Vector4i &p_vector) {
+_FORCE_INLINE_ Vector4i operator*(float p_scalar, const Vector4i &p_vector) {
 	return p_vector * p_scalar;
 }
 
-_FORCE_INLINE_ Vector4i operator*(const double p_scalar, const Vector4i &p_vector) {
+_FORCE_INLINE_ Vector4i operator*(double p_scalar, const Vector4i &p_vector) {
 	return p_vector * p_scalar;
 }
 
-Vector4i &Vector4i::operator/=(const int32_t p_scalar) {
+Vector4i &Vector4i::operator/=(int32_t p_scalar) {
 	x /= p_scalar;
 	y /= p_scalar;
 	z /= p_scalar;
@@ -269,11 +269,11 @@ Vector4i &Vector4i::operator/=(const int32_t p_scalar) {
 	return *this;
 }
 
-Vector4i Vector4i::operator/(const int32_t p_scalar) const {
+Vector4i Vector4i::operator/(int32_t p_scalar) const {
 	return Vector4i(x / p_scalar, y / p_scalar, z / p_scalar, w / p_scalar);
 }
 
-Vector4i &Vector4i::operator%=(const int32_t p_scalar) {
+Vector4i &Vector4i::operator%=(int32_t p_scalar) {
 	x %= p_scalar;
 	y %= p_scalar;
 	z %= p_scalar;
@@ -281,7 +281,7 @@ Vector4i &Vector4i::operator%=(const int32_t p_scalar) {
 	return *this;
 }
 
-Vector4i Vector4i::operator%(const int32_t p_scalar) const {
+Vector4i Vector4i::operator%(int32_t p_scalar) const {
 	return Vector4i(x % p_scalar, y % p_scalar, z % p_scalar, w % p_scalar);
 }
 

src/variant/aabb.cpp

@@ -119,55 +119,75 @@ AABB AABB::intersection(const AABB &p_aabb) const {
 	return AABB(min, max - min);
 }
 
-bool AABB::intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *r_clip, Vector3 *r_normal) const {
+// Note that this routine returns the BACKTRACKED (i.e. behind the ray origin)
+// intersection point + normal if INSIDE the AABB.
+// The caller can therefore decide when INSIDE whether to use the
+// backtracked intersection, or use p_from as the intersection, and
+// carry on progressing without e.g. reflecting against the normal.
+bool AABB::find_intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, bool &r_inside, Vector3 *r_intersection_point, Vector3 *r_normal) const {
 #ifdef MATH_CHECKS
 	if (unlikely(size.x < 0 || size.y < 0 || size.z < 0)) {
 		ERR_PRINT("AABB size is negative, this is not supported. Use AABB.abs() to get an AABB with a positive size.");
 	}
 #endif
-	Vector3 c1, c2;
 	Vector3 end = position + size;
-	real_t near = -1e20;
-	real_t far = 1e20;
+	real_t tmin = -1e20;
+	real_t tmax = 1e20;
 	int axis = 0;
 
+	// Make sure r_inside is always initialized,
+	// to prevent reading uninitialized data in the client code.
+	r_inside = false;
+
 	for (int i = 0; i < 3; i++) {
 		if (p_dir[i] == 0) {
 			if ((p_from[i] < position[i]) || (p_from[i] > end[i])) {
 				return false;
 			}
 		} else { // ray not parallel to planes in this direction
-			c1[i] = (position[i] - p_from[i]) / p_dir[i];
-			c2[i] = (end[i] - p_from[i]) / p_dir[i];
+			real_t t1 = (position[i] - p_from[i]) / p_dir[i];
+			real_t t2 = (end[i] - p_from[i]) / p_dir[i];
 
-			if (c1[i] > c2[i]) {
-				SWAP(c1, c2);
+			if (t1 > t2) {
+				SWAP(t1, t2);
 			}
-			if (c1[i] > near) {
-				near = c1[i];
+			if (t1 >= tmin) {
+				tmin = t1;
 				axis = i;
 			}
-			if (c2[i] < far) {
-				far = c2[i];
+			if (t2 < tmax) {
+				if (t2 < 0) {
+					return false;
+				}
+				tmax = t2;
 			}
-			if ((near > far) || (far < 0)) {
+			if (tmin > tmax) {
 				return false;
 			}
 		}
 	}
 
-	if (r_clip) {
-		*r_clip = c1;
+	// Did the ray start from inside the box?
+	// In which case the intersection returned is the point of entry
+	// (behind the ray start) or the calling routine can use the ray origin as intersection point.
+	r_inside = tmin < 0;
+
+	if (r_intersection_point) {
+		*r_intersection_point = p_from + p_dir * tmin;
+
+		// Prevent float error by making sure the point is exactly
+		// on the AABB border on the relevant axis.
+		r_intersection_point->coord[axis] = (p_dir[axis] >= 0) ? position.coord[axis] : end.coord[axis];
 	}
 	if (r_normal) {
 		*r_normal = Vector3();
-		(*r_normal)[axis] = p_dir[axis] ? -1 : 1;
+		(*r_normal)[axis] = (p_dir[axis] >= 0) ? -1 : 1;
 	}
 
 	return true;
 }
 
-bool AABB::intersects_segment(const Vector3 &p_from, const Vector3 &p_to, Vector3 *r_clip, Vector3 *r_normal) const {
+bool AABB::intersects_segment(const Vector3 &p_from, const Vector3 &p_to, Vector3 *r_intersection_point, Vector3 *r_normal) const {
 #ifdef MATH_CHECKS
 	if (unlikely(size.x < 0 || size.y < 0 || size.z < 0)) {
 		ERR_PRINT("AABB size is negative, this is not supported. Use AABB.abs() to get an AABB with a positive size.");
@@ -225,8 +245,8 @@ bool AABB::intersects_segment(const Vector3 &p_from, const Vector3 &p_to, Vector
 		*r_normal = normal;
 	}
 
-	if (r_clip) {
-		*r_clip = p_from + rel * min;
+	if (r_intersection_point) {
+		*r_intersection_point = p_from + rel * min;
 	}
 
 	return true;
@@ -412,7 +432,15 @@ Variant AABB::intersects_segment_bind(const Vector3 &p_from, const Vector3 &p_to
 
 Variant AABB::intersects_ray_bind(const Vector3 &p_from, const Vector3 &p_dir) const {
 	Vector3 inters;
-	if (intersects_ray(p_from, p_dir, &inters)) {
+	bool inside = false;
+
+	if (find_intersects_ray(p_from, p_dir, inside, &inters)) {
+		// When inside the intersection point may be BEHIND the ray,
+		// so for general use we return the ray origin.
+		if (inside) {
+			return p_from;
+		}
+
 		return inters;
 	}
 	return Variant();

src/variant/basis.cpp

@@ -29,31 +29,17 @@
 /**************************************************************************/
 
 #include <godot_cpp/core/error_macros.hpp>
+#include <godot_cpp/core/math.hpp>
 #include <godot_cpp/variant/basis.hpp>
 #include <godot_cpp/variant/string.hpp>
 
+using namespace godot;
+
 #define cofac(row1, col1, row2, col2) \
 	(rows[row1][col1] * rows[row2][col2] - rows[row1][col2] * rows[row2][col1])
 
 namespace godot {
 
-void Basis::from_z(const Vector3 &p_z) {
-	if (Math::abs(p_z.z) > (real_t)Math_SQRT12) {
-		// choose p in y-z plane
-		real_t a = p_z[1] * p_z[1] + p_z[2] * p_z[2];
-		real_t k = 1.0f / Math::sqrt(a);
-		rows[0] = Vector3(0, -p_z[2] * k, p_z[1] * k);
-		rows[1] = Vector3(a * k, -p_z[0] * rows[0][2], p_z[0] * rows[0][1]);
-	} else {
-		// choose p in x-y plane
-		real_t a = p_z.x * p_z.x + p_z.y * p_z.y;
-		real_t k = 1.0f / Math::sqrt(a);
-		rows[0] = Vector3(-p_z.y * k, p_z.x * k, 0);
-		rows[1] = Vector3(-p_z.z * rows[0].y, p_z.z * rows[0].x, a * k);
-	}
-	rows[2] = p_z;
-}
-
 void Basis::invert() {
 	real_t co[3] = {
 		cofac(1, 1, 2, 2), cofac(1, 2, 2, 0), cofac(1, 0, 2, 1)
@@ -107,13 +93,35 @@ Basis Basis::orthogonalized() const {
 	return c;
 }
 
+// Returns true if the basis vectors are orthogonal (perpendicular), so it has no skew or shear, and can be decomposed into rotation and scale.
+// See https://en.wikipedia.org/wiki/Orthogonal_basis
 bool Basis::is_orthogonal() const {
-	Basis identity;
-	Basis m = (*this) * transposed();
+	const Vector3 x = get_column(0);
+	const Vector3 y = get_column(1);
+	const Vector3 z = get_column(2);
+	return Math::is_zero_approx(x.dot(y)) && Math::is_zero_approx(x.dot(z)) && Math::is_zero_approx(y.dot(z));
+}
 
-	return m.is_equal_approx(identity);
+// Returns true if the basis vectors are orthonormal (orthogonal and normalized), so it has no scale, skew, or shear.
+// See https://en.wikipedia.org/wiki/Orthonormal_basis
+bool Basis::is_orthonormal() const {
+	const Vector3 x = get_column(0);
+	const Vector3 y = get_column(1);
+	const Vector3 z = get_column(2);
+	return Math::is_equal_approx(x.length_squared(), 1) && Math::is_equal_approx(y.length_squared(), 1) && Math::is_equal_approx(z.length_squared(), 1) && Math::is_zero_approx(x.dot(y)) && Math::is_zero_approx(x.dot(z)) && Math::is_zero_approx(y.dot(z));
 }
 
+// Returns true if the basis is conformal (orthogonal, uniform scale, preserves angles and distance ratios).
+// See https://en.wikipedia.org/wiki/Conformal_linear_transformation
+bool Basis::is_conformal() const {
+	const Vector3 x = get_column(0);
+	const Vector3 y = get_column(1);
+	const Vector3 z = get_column(2);
+	const real_t x_len_sq = x.length_squared();
+	return Math::is_equal_approx(x_len_sq, y.length_squared()) && Math::is_equal_approx(x_len_sq, z.length_squared()) && Math::is_zero_approx(x.dot(y)) && Math::is_zero_approx(x.dot(z)) && Math::is_zero_approx(y.dot(z));
+}
+
+// Returns true if the basis only has diagonal elements, so it may only have scale or flip, but no rotation, skew, or shear.
 bool Basis::is_diagonal() const {
 	return (
 			Math::is_zero_approx(rows[0][1]) && Math::is_zero_approx(rows[0][2]) &&
@@ -121,8 +129,9 @@ bool Basis::is_diagonal() const {
 			Math::is_zero_approx(rows[2][0]) && Math::is_zero_approx(rows[2][1]));
 }
 
+// Returns true if the basis is a pure rotation matrix, so it has no scale, skew, shear, or flip.
 bool Basis::is_rotation() const {
-	return Math::is_equal_approx(determinant(), 1, (real_t)UNIT_EPSILON) && is_orthogonal();
+	return is_conformal() && Math::is_equal_approx(determinant(), 1, (real_t)UNIT_EPSILON);
 }
 
 #ifdef MATH_CHECKS
@@ -257,29 +266,26 @@ void Basis::scale_orthogonal(const Vector3 &p_scale) {
 Basis Basis::scaled_orthogonal(const Vector3 &p_scale) const {
 	Basis m = *this;
 	Vector3 s = Vector3(-1, -1, -1) + p_scale;
+	bool sign = std::signbit(s.x + s.y + s.z);
+	Basis b = m.orthonormalized();
+	s = b.xform_inv(s);
 	Vector3 dots;
-	Basis b;
 	for (int i = 0; i < 3; i++) {
 		for (int j = 0; j < 3; j++) {
-			dots[j] += s[i] * Math::abs(m.get_column(i).normalized().dot(b.get_column(j)));
+			dots[j] += s[i] * abs(m.get_column(i).normalized().dot(b.get_column(j)));
 		}
 	}
+	if (sign != std::signbit(dots.x + dots.y + dots.z)) {
+		dots = -dots;
+	}
 	m.scale_local(Vector3(1, 1, 1) + dots);
 	return m;
 }
 
-float Basis::get_uniform_scale() const {
+real_t Basis::get_uniform_scale() const {
 	return (rows[0].length() + rows[1].length() + rows[2].length()) / 3.0f;
 }
 
-void Basis::make_scale_uniform() {
-	float l = (rows[0].length() + rows[1].length() + rows[2].length()) / 3.0f;
-	for (int i = 0; i < 3; i++) {
-		rows[i].normalize();
-		rows[i] *= l;
-	}
-}
-
 Basis Basis::scaled_local(const Vector3 &p_scale) const {
 	return (*this) * Basis::from_scale(p_scale);
 }
@@ -291,7 +297,7 @@ Vector3 Basis::get_scale_abs() const {
 			Vector3(rows[0][2], rows[1][2], rows[2][2]).length());
 }
 
-Vector3 Basis::get_scale_local() const {
+Vector3 Basis::get_scale_global() const {
 	real_t det_sign = SIGN(determinant());
 	return det_sign * Vector3(rows[0].length(), rows[1].length(), rows[2].length());
 }
@@ -418,7 +424,7 @@ void Basis::rotate_to_align(Vector3 p_start_direction, Vector3 p_end_direction)
 		real_t dot = p_start_direction.dot(p_end_direction);
 		dot = CLAMP(dot, -1.0f, 1.0f);
 		const real_t angle_rads = Math::acos(dot);
-		set_axis_angle(axis, angle_rads);
+		*this = Basis(axis, angle_rads) * (*this);
 	}
 }
 
@@ -453,8 +459,13 @@ void Basis::get_rotation_axis_angle_local(Vector3 &p_axis, real_t &p_angle) cons
 }
 
 Vector3 Basis::get_euler(EulerOrder p_order) const {
+	// This epsilon value results in angles within a +/- 0.04 degree range being simplified/truncated.
+	// Based on testing, this is the largest the epsilon can be without the angle truncation becoming
+	// visually noticeable.
+	const real_t epsilon = 0.00000025;
+
 	switch (p_order) {
-		case EULER_ORDER_XYZ: {
+		case EulerOrder::EULER_ORDER_XYZ: {
 			// Euler angles in XYZ convention.
 			// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
 			//
@@ -464,8 +475,8 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 
 			Vector3 euler;
 			real_t sy = rows[0][2];
-			if (sy < (1.0f - (real_t)CMP_EPSILON)) {
-				if (sy > -(1.0f - (real_t)CMP_EPSILON)) {
+			if (sy < (1.0f - epsilon)) {
+				if (sy > -(1.0f - epsilon)) {
 					// is this a pure Y rotation?
 					if (rows[1][0] == 0 && rows[0][1] == 0 && rows[1][2] == 0 && rows[2][1] == 0 && rows[1][1] == 1) {
 						// return the simplest form (human friendlier in editor and scripts)
@@ -489,7 +500,7 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 			}
 			return euler;
 		}
-		case EULER_ORDER_XZY: {
+		case EulerOrder::EULER_ORDER_XZY: {
 			// Euler angles in XZY convention.
 			// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
 			//
@@ -499,8 +510,8 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 
 			Vector3 euler;
 			real_t sz = rows[0][1];
-			if (sz < (1.0f - (real_t)CMP_EPSILON)) {
-				if (sz > -(1.0f - (real_t)CMP_EPSILON)) {
+			if (sz < (1.0f - epsilon)) {
+				if (sz > -(1.0f - epsilon)) {
 					euler.x = Math::atan2(rows[2][1], rows[1][1]);
 					euler.y = Math::atan2(rows[0][2], rows[0][0]);
 					euler.z = Math::asin(-sz);
@@ -518,7 +529,7 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 			}
 			return euler;
 		}
-		case EULER_ORDER_YXZ: {
+		case EulerOrder::EULER_ORDER_YXZ: {
 			// Euler angles in YXZ convention.
 			// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
 			//
@@ -530,8 +541,8 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 
 			real_t m12 = rows[1][2];
 
-			if (m12 < (1 - (real_t)CMP_EPSILON)) {
-				if (m12 > -(1 - (real_t)CMP_EPSILON)) {
+			if (m12 < (1 - epsilon)) {
+				if (m12 > -(1 - epsilon)) {
 					// is this a pure X rotation?
 					if (rows[1][0] == 0 && rows[0][1] == 0 && rows[0][2] == 0 && rows[2][0] == 0 && rows[0][0] == 1) {
 						// return the simplest form (human friendlier in editor and scripts)
@@ -556,7 +567,7 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 
 			return euler;
 		}
-		case EULER_ORDER_YZX: {
+		case EulerOrder::EULER_ORDER_YZX: {
 			// Euler angles in YZX convention.
 			// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
 			//
@@ -566,8 +577,8 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 
 			Vector3 euler;
 			real_t sz = rows[1][0];
-			if (sz < (1.0f - (real_t)CMP_EPSILON)) {
-				if (sz > -(1.0f - (real_t)CMP_EPSILON)) {
+			if (sz < (1.0f - epsilon)) {
+				if (sz > -(1.0f - epsilon)) {
 					euler.x = Math::atan2(-rows[1][2], rows[1][1]);
 					euler.y = Math::atan2(-rows[2][0], rows[0][0]);
 					euler.z = Math::asin(sz);
@@ -584,8 +595,8 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 				euler.z = Math_PI / 2.0f;
 			}
 			return euler;
-		}
-		case EULER_ORDER_ZXY: {
+		} break;
+		case EulerOrder::EULER_ORDER_ZXY: {
 			// Euler angles in ZXY convention.
 			// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
 			//
@@ -594,8 +605,8 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 			//        -cx*sy            sx                    cx*cy
 			Vector3 euler;
 			real_t sx = rows[2][1];
-			if (sx < (1.0f - (real_t)CMP_EPSILON)) {
-				if (sx > -(1.0f - (real_t)CMP_EPSILON)) {
+			if (sx < (1.0f - epsilon)) {
+				if (sx > -(1.0f - epsilon)) {
 					euler.x = Math::asin(sx);
 					euler.y = Math::atan2(-rows[2][0], rows[2][2]);
 					euler.z = Math::atan2(-rows[0][1], rows[1][1]);
@@ -612,8 +623,8 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 				euler.z = 0;
 			}
 			return euler;
-		}
-		case EULER_ORDER_ZYX: {
+		} break;
+		case EulerOrder::EULER_ORDER_ZYX: {
 			// Euler angles in ZYX convention.
 			// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
 			//
@@ -622,8 +633,8 @@ Vector3 Basis::get_euler(EulerOrder p_order) const {
 			//        -sy               cy*sx                 cy*cx
 			Vector3 euler;
 			real_t sy = rows[2][0];
-			if (sy < (1.0f - (real_t)CMP_EPSILON)) {
-				if (sy > -(1.0f - (real_t)CMP_EPSILON)) {
+			if (sy < (1.0f - epsilon)) {
+				if (sy > -(1.0f - epsilon)) {
 					euler.x = Math::atan2(rows[2][1], rows[2][2]);
 					euler.y = Math::asin(-sy);
 					euler.z = Math::atan2(rows[1][0], rows[0][0]);
@@ -664,26 +675,26 @@ void Basis::set_euler(const Vector3 &p_euler, EulerOrder p_order) {
 	Basis zmat(c, -s, 0, s, c, 0, 0, 0, 1);
 
 	switch (p_order) {
-		case EULER_ORDER_XYZ: {
+		case EulerOrder::EULER_ORDER_XYZ: {
 			*this = xmat * (ymat * zmat);
 		} break;
-		case EULER_ORDER_XZY: {
+		case EulerOrder::EULER_ORDER_XZY: {
 			*this = xmat * zmat * ymat;
 		} break;
-		case EULER_ORDER_YXZ: {
+		case EulerOrder::EULER_ORDER_YXZ: {
 			*this = ymat * xmat * zmat;
 		} break;
-		case EULER_ORDER_YZX: {
+		case EulerOrder::EULER_ORDER_YZX: {
 			*this = ymat * zmat * xmat;
 		} break;
-		case EULER_ORDER_ZXY: {
+		case EulerOrder::EULER_ORDER_ZXY: {
 			*this = zmat * xmat * ymat;
 		} break;
-		case EULER_ORDER_ZYX: {
+		case EulerOrder::EULER_ORDER_ZYX: {
 			*this = zmat * ymat * xmat;
 		} break;
 		default: {
-			ERR_FAIL_MSG("Invalid order parameter for set_euler(vec3,order)");
+			ERR_FAIL_MSG("Invalid Euler order parameter.");
 		}
 	}
 }
@@ -720,7 +731,7 @@ Basis::operator String() const {
 
 Quaternion Basis::get_quaternion() const {
 #ifdef MATH_CHECKS
-	ERR_FAIL_COND_V_MSG(!is_rotation(), Quaternion(), "Basis must be normalized in order to be casted to a Quaternion. Use get_rotation_quaternion() or call orthonormalized() if the Basis contains linearly independent vectors.");
+	ERR_FAIL_COND_V_MSG(!is_rotation(), Quaternion(), "Basis " + operator String() + " must be normalized in order to be casted to a Quaternion. Use get_rotation_quaternion() or call orthonormalized() if the Basis contains linearly independent vectors.");
 #endif
 	/* Allow getting a quaternion from an unnormalized transform */
 	Basis m = *this;
@@ -828,8 +839,8 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
 	z = (rows[1][0] - rows[0][1]) / s;
 
 	r_axis = Vector3(x, y, z);
-	// CLAMP to avoid NaN if the value passed to acos is not in [0,1].
-	r_angle = Math::acos(CLAMP((rows[0][0] + rows[1][1] + rows[2][2] - 1) / 2, (real_t)0.0, (real_t)1.0));
+	// acos does clamping.
+	r_angle = Math::acos((rows[0][0] + rows[1][1] + rows[2][2] - 1) / 2);
 }
 
 void Basis::set_quaternion(const Quaternion &p_quaternion) {
@@ -847,7 +858,7 @@ void Basis::set_quaternion(const Quaternion &p_quaternion) {
 void Basis::set_axis_angle(const Vector3 &p_axis, real_t p_angle) {
 // Rotation matrix from axis and angle, see https://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_angle
 #ifdef MATH_CHECKS
-	ERR_FAIL_COND_MSG(!p_axis.is_normalized(), "The axis Vector3 must be normalized.");
+	ERR_FAIL_COND_MSG(!p_axis.is_normalized(), "The axis Vector3 " + p_axis.operator String() + " must be normalized.");
 #endif
 	Vector3 axis_sq(p_axis.x * p_axis.x, p_axis.y * p_axis.y, p_axis.z * p_axis.z);
 	real_t cosine = Math::cos(p_angle);
@@ -905,7 +916,7 @@ void Basis::_set_diagonal(const Vector3 &p_diag) {
 	rows[2][2] = p_diag.z;
 }
 
-Basis Basis::lerp(const Basis &p_to, const real_t &p_weight) const {
+Basis Basis::lerp(const Basis &p_to, real_t p_weight) const {
 	Basis b;
 	b.rows[0] = rows[0].lerp(p_to.rows[0], p_weight);
 	b.rows[1] = rows[1].lerp(p_to.rows[1], p_weight);
@@ -914,7 +925,7 @@ Basis Basis::lerp(const Basis &p_to, const real_t &p_weight) const {
 	return b;
 }
 
-Basis Basis::slerp(const Basis &p_to, const real_t &p_weight) const {
+Basis Basis::slerp(const Basis &p_to, real_t p_weight) const {
 	//consider scale
 	Quaternion from(*this);
 	Quaternion to(p_to);
@@ -1047,9 +1058,10 @@ Basis Basis::looking_at(const Vector3 &p_target, const Vector3 &p_up, bool p_use
 		v_z = -v_z;
 	}
 	Vector3 v_x = p_up.cross(v_z);
-#ifdef MATH_CHECKS
-	ERR_FAIL_COND_V_MSG(v_x.is_zero_approx(), Basis(), "The target vector and up vector can't be parallel to each other.");
-#endif
+	if (v_x.is_zero_approx()) {
+		WARN_PRINT("Target and up vectors are colinear. This is not advised as it may cause unwanted rotation around local Z axis.");
+		v_x = p_up.get_any_perpendicular(); // Vectors are almost parallel.
+	}
 	v_x.normalize();
 	Vector3 v_y = v_z.cross(v_x);
 

src/variant/color.cpp

@@ -29,6 +29,7 @@
 /**************************************************************************/
 
 #include <godot_cpp/core/error_macros.hpp>
+#include <godot_cpp/templates/hash_map.hpp>
 #include <godot_cpp/variant/color.hpp>
 #include <godot_cpp/variant/color_names.inc.hpp>
 #include <godot_cpp/variant/string.hpp>
@@ -131,20 +132,20 @@ String _to_hex(float p_val) {
 
 String Color::to_html(bool p_alpha) const {
 	String txt;
-	txt = txt + _to_hex(r);
-	txt = txt + _to_hex(g);
-	txt = txt + _to_hex(b);
+	txt += _to_hex(r);
+	txt += _to_hex(g);
+	txt += _to_hex(b);
 	if (p_alpha) {
-		txt = txt + _to_hex(a);
+		txt += _to_hex(a);
 	}
 	return txt;
 }
 
 float Color::get_h() const {
-	float min = Math::min(r, g);
-	min = Math::min(min, b);
-	float max = Math::max(r, g);
-	max = Math::max(max, b);
+	float min = MIN(r, g);
+	min = MIN(min, b);
+	float max = MAX(r, g);
+	max = MAX(max, b);
 
 	float delta = max - min;
 
@@ -170,10 +171,10 @@ float Color::get_h() const {
 }
 
 float Color::get_s() const {
-	float min = Math::min(r, g);
-	min = Math::min(min, b);
-	float max = Math::max(r, g);
-	max = Math::max(max, b);
+	float min = MIN(r, g);
+	min = MIN(min, b);
+	float max = MAX(r, g);
+	max = MAX(max, b);
 
 	float delta = max - min;
 
@@ -181,8 +182,8 @@ float Color::get_s() const {
 }
 
 float Color::get_v() const {
-	float max = Math::max(r, g);
-	max = Math::max(max, b);
+	float max = MAX(r, g);
+	max = MAX(max, b);
 	return max;
 }
 
@@ -385,7 +386,6 @@ Color Color::named(const String &p_name) {
 	int idx = find_named_color(p_name);
 	if (idx == -1) {
 		ERR_FAIL_V_MSG(Color(), "Invalid color name: " + p_name + ".");
-		return Color();
 	}
 	return named_colors[idx].color;
 }
@@ -400,7 +400,7 @@ Color Color::named(const String &p_name, const Color &p_default) {
 
 int Color::find_named_color(const String &p_name) {
 	String name = p_name;
-	// Normalize name
+	// Normalize name.
 	name = name.replace(" ", "");
 	name = name.replace("-", "");
 	name = name.replace("_", "");
@@ -408,23 +408,24 @@ int Color::find_named_color(const String &p_name) {
 	name = name.replace(".", "");
 	name = name.to_upper();
 
-	int idx = 0;
-	while (named_colors[idx].name != nullptr) {
-		if (name == String(named_colors[idx].name).replace("_", "")) {
-			return idx;
+	static HashMap<String, int> named_colors_hashmap;
+	if (unlikely(named_colors_hashmap.is_empty())) {
+		const int named_color_count = get_named_color_count();
+		for (int i = 0; i < named_color_count; i++) {
+			named_colors_hashmap[String(named_colors[i].name).replace("_", "")] = i;
 		}
-		idx++;
+	}
+
+	const HashMap<String, int>::ConstIterator E = named_colors_hashmap.find(name);
+	if (E) {
+		return E->value;
 	}
 
 	return -1;
 }
 
 int Color::get_named_color_count() {
-	int idx = 0;
-	while (named_colors[idx].name != nullptr) {
-		idx++;
-	}
-	return idx;
+	return sizeof(named_colors) / sizeof(NamedColor);
 }
 
 String Color::get_named_color_name(int p_idx) {
@@ -467,6 +468,10 @@ Color Color::from_rgbe9995(uint32_t p_rgbe) {
 	return Color(rd, gd, bd, 1.0f);
 }
 
+Color Color::from_rgba8(int64_t p_r8, int64_t p_g8, int64_t p_b8, int64_t p_a8) {
+	return Color(p_r8 / 255.0f, p_g8 / 255.0f, p_b8 / 255.0f, p_a8 / 255.0f);
+}
+
 Color::operator String() const {
 	return "(" + String::num(r, 4) + ", " + String::num(g, 4) + ", " + String::num(b, 4) + ", " + String::num(a, 4) + ")";
 }

src/variant/plane.cpp

@@ -60,7 +60,7 @@ Vector3 Plane::get_any_perpendicular_normal() const {
 	static const Vector3 p2 = Vector3(0, 1, 0);
 	Vector3 p;
 
-	if (Math::abs(normal.dot(p1)) > 0.99f) { // if too similar to p1
+	if (ABS(normal.dot(p1)) > 0.99f) { // if too similar to p1
 		p = p2; // use p2
 	} else {
 		p = p1; // use p1
@@ -100,13 +100,11 @@ bool Plane::intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3
 	Vector3 segment = p_dir;
 	real_t den = normal.dot(segment);
 
-	//printf("den is %i\n",den);
 	if (Math::is_zero_approx(den)) {
 		return false;
 	}
 
 	real_t dist = (normal.dot(p_from) - d) / den;
-	//printf("dist is %i\n",dist);
 
 	if (dist > (real_t)CMP_EPSILON) { //this is a ray, before the emitting pos (p_from) doesn't exist
 
@@ -123,13 +121,11 @@ bool Plane::intersects_segment(const Vector3 &p_begin, const Vector3 &p_end, Vec
 	Vector3 segment = p_begin - p_end;
 	real_t den = normal.dot(segment);
 
-	//printf("den is %i\n",den);
 	if (Math::is_zero_approx(den)) {
 		return false;
 	}
 
 	real_t dist = (normal.dot(p_begin) - d) / den;
-	//printf("dist is %i\n",dist);
 
 	if (dist < (real_t)-CMP_EPSILON || dist > (1.0f + (real_t)CMP_EPSILON)) {
 		return false;

src/variant/projection.cpp

@@ -39,7 +39,7 @@
 
 namespace godot {
 
-float Projection::determinant() const {
+real_t Projection::determinant() const {
 	return columns[0][3] * columns[1][2] * columns[2][1] * columns[3][0] - columns[0][2] * columns[1][3] * columns[2][1] * columns[3][0] -
 			columns[0][3] * columns[1][1] * columns[2][2] * columns[3][0] + columns[0][1] * columns[1][3] * columns[2][2] * columns[3][0] +
 			columns[0][2] * columns[1][1] * columns[2][3] * columns[3][0] - columns[0][1] * columns[1][2] * columns[2][3] * columns[3][0] -
@@ -171,7 +171,7 @@ Projection Projection::perspective_znear_adjusted(real_t p_new_znear) const {
 }
 
 Plane Projection::get_projection_plane(Planes p_plane) const {
-	const real_t *matrix = (const real_t *)this->columns;
+	const real_t *matrix = (const real_t *)columns;
 
 	switch (p_plane) {
 		case PLANE_NEAR: {
@@ -404,20 +404,19 @@ void Projection::set_frustum(real_t p_size, real_t p_aspect, Vector2 p_offset, r
 }
 
 real_t Projection::get_z_far() const {
-	const real_t *matrix = (const real_t *)this->columns;
+	const real_t *matrix = (const real_t *)columns;
 	Plane new_plane = Plane(matrix[3] - matrix[2],
 			matrix[7] - matrix[6],
 			matrix[11] - matrix[10],
 			matrix[15] - matrix[14]);
 
-	new_plane.normal = -new_plane.normal;
 	new_plane.normalize();
 
 	return new_plane.d;
 }
 
 real_t Projection::get_z_near() const {
-	const real_t *matrix = (const real_t *)this->columns;
+	const real_t *matrix = (const real_t *)columns;
 	Plane new_plane = Plane(matrix[3] + matrix[2],
 			matrix[7] + matrix[6],
 			matrix[11] + matrix[10],
@@ -428,7 +427,7 @@ real_t Projection::get_z_near() const {
 }
 
 Vector2 Projection::get_viewport_half_extents() const {
-	const real_t *matrix = (const real_t *)this->columns;
+	const real_t *matrix = (const real_t *)columns;
 	///////--- Near Plane ---///////
 	Plane near_plane = Plane(matrix[3] + matrix[2],
 			matrix[7] + matrix[6],
@@ -456,7 +455,7 @@ Vector2 Projection::get_viewport_half_extents() const {
 }
 
 Vector2 Projection::get_far_plane_half_extents() const {
-	const real_t *matrix = (const real_t *)this->columns;
+	const real_t *matrix = (const real_t *)columns;
 	///////--- Far Plane ---///////
 	Plane far_plane = Plane(matrix[3] - matrix[2],
 			matrix[7] - matrix[6],
@@ -484,7 +483,7 @@ Vector2 Projection::get_far_plane_half_extents() const {
 }
 
 bool Projection::get_endpoints(const Transform3D &p_transform, Vector3 *p_8points) const {
-	Array planes = get_projection_planes(Transform3D());
+	Vector<Plane> planes = get_projection_planes(Transform3D());
 	const Planes intersections[8][3] = {
 		{ PLANE_FAR, PLANE_LEFT, PLANE_TOP },
 		{ PLANE_FAR, PLANE_LEFT, PLANE_BOTTOM },
@@ -509,17 +508,17 @@ bool Projection::get_endpoints(const Transform3D &p_transform, Vector3 *p_8point
 	return true;
 }
 
-Array Projection::get_projection_planes(const Transform3D &p_transform) const {
+Vector<Plane> Projection::get_projection_planes(const Transform3D &p_transform) const {
 	/** Fast Plane Extraction from combined modelview/projection matrices.
 	 * References:
 	 * https://web.archive.org/web/20011221205252/https://www.markmorley.com/opengl/frustumculling.html
 	 * https://web.archive.org/web/20061020020112/https://www2.ravensoft.com/users/ggribb/plane%20extraction.pdf
 	 */
 
-	Array planes;
+	Vector<Plane> planes;
 	planes.resize(6);
 
-	const real_t *matrix = (const real_t *)this->columns;
+	const real_t *matrix = (const real_t *)columns;
 
 	Plane new_plane;
 
@@ -532,7 +531,7 @@ Array Projection::get_projection_planes(const Transform3D &p_transform) const {
 	new_plane.normal = -new_plane.normal;
 	new_plane.normalize();
 
-	planes[0] = p_transform.xform(new_plane);
+	planes.write[0] = p_transform.xform(new_plane);
 
 	///////--- Far Plane ---///////
 	new_plane = Plane(matrix[3] - matrix[2],
@@ -543,7 +542,7 @@ Array Projection::get_projection_planes(const Transform3D &p_transform) const {
 	new_plane.normal = -new_plane.normal;
 	new_plane.normalize();
 
-	planes[1] = p_transform.xform(new_plane);
+	planes.write[1] = p_transform.xform(new_plane);
 
 	///////--- Left Plane ---///////
 	new_plane = Plane(matrix[3] + matrix[0],
@@ -554,7 +553,7 @@ Array Projection::get_projection_planes(const Transform3D &p_transform) const {
 	new_plane.normal = -new_plane.normal;
 	new_plane.normalize();
 
-	planes[2] = p_transform.xform(new_plane);
+	planes.write[2] = p_transform.xform(new_plane);
 
 	///////--- Top Plane ---///////
 	new_plane = Plane(matrix[3] - matrix[1],
@@ -565,7 +564,7 @@ Array Projection::get_projection_planes(const Transform3D &p_transform) const {
 	new_plane.normal = -new_plane.normal;
 	new_plane.normalize();
 
-	planes[3] = p_transform.xform(new_plane);
+	planes.write[3] = p_transform.xform(new_plane);
 
 	///////--- Right Plane ---///////
 	new_plane = Plane(matrix[3] - matrix[0],
@@ -576,7 +575,7 @@ Array Projection::get_projection_planes(const Transform3D &p_transform) const {
 	new_plane.normal = -new_plane.normal;
 	new_plane.normalize();
 
-	planes[4] = p_transform.xform(new_plane);
+	planes.write[4] = p_transform.xform(new_plane);
 
 	///////--- Bottom Plane ---///////
 	new_plane = Plane(matrix[3] + matrix[1],
@@ -587,7 +586,7 @@ Array Projection::get_projection_planes(const Transform3D &p_transform) const {
 	new_plane.normal = -new_plane.normal;
 	new_plane.normalize();
 
-	planes[5] = p_transform.xform(new_plane);
+	planes.write[5] = p_transform.xform(new_plane);
 
 	return planes;
 }
@@ -599,101 +598,229 @@ Projection Projection::inverse() const {
 }
 
 void Projection::invert() {
-	int i, j, k;
-	int pvt_i[4], pvt_j[4]; /* Locations of pivot matrix */
-	real_t pvt_val; /* Value of current pivot element */
-	real_t hold; /* Temporary storage */
-	real_t determinant = 1.0f;
-	for (k = 0; k < 4; k++) {
-		/** Locate k'th pivot element **/
-		pvt_val = columns[k][k]; /** Initialize for search **/
-		pvt_i[k] = k;
-		pvt_j[k] = k;
-		for (i = k; i < 4; i++) {
-			for (j = k; j < 4; j++) {
-				if (Math::abs(columns[i][j]) > Math::abs(pvt_val)) {
-					pvt_i[k] = i;
-					pvt_j[k] = j;
-					pvt_val = columns[i][j];
-				}
-			}
-		}
-
-		/** Product of pivots, gives determinant when finished **/
-		determinant *= pvt_val;
-		if (Math::is_zero_approx(determinant)) {
-			return; /** Matrix is singular (zero determinant). **/
-		}
-
-		/** "Interchange" rows (with sign change stuff) **/
-		i = pvt_i[k];
-		if (i != k) { /** If rows are different **/
-			for (j = 0; j < 4; j++) {
-				hold = -columns[k][j];
-				columns[k][j] = columns[i][j];
-				columns[i][j] = hold;
-			}
-		}
-
-		/** "Interchange" columns **/
-		j = pvt_j[k];
-		if (j != k) { /** If columns are different **/
-			for (i = 0; i < 4; i++) {
-				hold = -columns[i][k];
-				columns[i][k] = columns[i][j];
-				columns[i][j] = hold;
-			}
-		}
-
-		/** Divide column by minus pivot value **/
-		for (i = 0; i < 4; i++) {
-			if (i != k) {
-				columns[i][k] /= (-pvt_val);
-			}
-		}
-
-		/** Reduce the matrix **/
-		for (i = 0; i < 4; i++) {
-			hold = columns[i][k];
-			for (j = 0; j < 4; j++) {
-				if (i != k && j != k) {
-					columns[i][j] += hold * columns[k][j];
-				}
-			}
-		}
-
-		/** Divide row by pivot **/
-		for (j = 0; j < 4; j++) {
-			if (j != k) {
-				columns[k][j] /= pvt_val;
-			}
-		}
-
-		/** Replace pivot by reciprocal (at last we can touch it). **/
-		columns[k][k] = 1.0 / pvt_val;
+	// Adapted from Mesa's `src/util/u_math.c` `util_invert_mat4x4`.
+	// MIT licensed. Copyright 2008 VMware, Inc. Authored by Jacques Leroy.
+	Projection temp;
+	real_t *out = (real_t *)temp.columns;
+	real_t *m = (real_t *)columns;
+
+	real_t wtmp[4][8];
+	real_t m0, m1, m2, m3, s;
+	real_t *r0, *r1, *r2, *r3;
+
+#define MAT(m, r, c) (m)[(c) * 4 + (r)]
+
+	r0 = wtmp[0];
+	r1 = wtmp[1];
+	r2 = wtmp[2];
+	r3 = wtmp[3];
+
+	r0[0] = MAT(m, 0, 0);
+	r0[1] = MAT(m, 0, 1);
+	r0[2] = MAT(m, 0, 2);
+	r0[3] = MAT(m, 0, 3);
+	r0[4] = 1.0;
+	r0[5] = 0.0;
+	r0[6] = 0.0;
+	r0[7] = 0.0;
+
+	r1[0] = MAT(m, 1, 0);
+	r1[1] = MAT(m, 1, 1);
+	r1[2] = MAT(m, 1, 2);
+	r1[3] = MAT(m, 1, 3);
+	r1[5] = 1.0;
+	r1[4] = 0.0;
+	r1[6] = 0.0;
+	r1[7] = 0.0;
+
+	r2[0] = MAT(m, 2, 0);
+	r2[1] = MAT(m, 2, 1);
+	r2[2] = MAT(m, 2, 2);
+	r2[3] = MAT(m, 2, 3);
+	r2[6] = 1.0;
+	r2[4] = 0.0;
+	r2[5] = 0.0;
+	r2[7] = 0.0;
+
+	r3[0] = MAT(m, 3, 0);
+	r3[1] = MAT(m, 3, 1);
+	r3[2] = MAT(m, 3, 2);
+	r3[3] = MAT(m, 3, 3);
+
+	r3[7] = 1.0;
+	r3[4] = 0.0;
+	r3[5] = 0.0;
+	r3[6] = 0.0;
+
+	/* choose pivot - or die */
+	if (Math::abs(r3[0]) > Math::abs(r2[0])) {
+		SWAP(r3, r2);
+	}
+	if (Math::abs(r2[0]) > Math::abs(r1[0])) {
+		SWAP(r2, r1);
+	}
+	if (Math::abs(r1[0]) > Math::abs(r0[0])) {
+		SWAP(r1, r0);
+	}
+	ERR_FAIL_COND(0.0 == r0[0]);
+
+	/* eliminate first variable     */
+	m1 = r1[0] / r0[0];
+	m2 = r2[0] / r0[0];
+	m3 = r3[0] / r0[0];
+	s = r0[1];
+	r1[1] -= m1 * s;
+	r2[1] -= m2 * s;
+	r3[1] -= m3 * s;
+	s = r0[2];
+	r1[2] -= m1 * s;
+	r2[2] -= m2 * s;
+	r3[2] -= m3 * s;
+	s = r0[3];
+	r1[3] -= m1 * s;
+	r2[3] -= m2 * s;
+	r3[3] -= m3 * s;
+	s = r0[4];
+	if (s != 0.0) {
+		r1[4] -= m1 * s;
+		r2[4] -= m2 * s;
+		r3[4] -= m3 * s;
+	}
+	s = r0[5];
+	if (s != 0.0) {
+		r1[5] -= m1 * s;
+		r2[5] -= m2 * s;
+		r3[5] -= m3 * s;
+	}
+	s = r0[6];
+	if (s != 0.0) {
+		r1[6] -= m1 * s;
+		r2[6] -= m2 * s;
+		r3[6] -= m3 * s;
+	}
+	s = r0[7];
+	if (s != 0.0) {
+		r1[7] -= m1 * s;
+		r2[7] -= m2 * s;
+		r3[7] -= m3 * s;
 	}
 
-	/* That was most of the work, one final pass of row/column interchange */
-	/* to finish */
-	for (k = 4 - 2; k >= 0; k--) { /* Don't need to work with 1 by 1 corner*/
-		i = pvt_j[k]; /* Rows to swap correspond to pivot COLUMN */
-		if (i != k) { /* If rows are different */
-			for (j = 0; j < 4; j++) {
-				hold = columns[k][j];
-				columns[k][j] = -columns[i][j];
-				columns[i][j] = hold;
-			}
-		}
+	/* choose pivot - or die */
+	if (Math::abs(r3[1]) > Math::abs(r2[1])) {
+		SWAP(r3, r2);
+	}
+	if (Math::abs(r2[1]) > Math::abs(r1[1])) {
+		SWAP(r2, r1);
+	}
+	ERR_FAIL_COND(0.0 == r1[1]);
+
+	/* eliminate second variable */
+	m2 = r2[1] / r1[1];
+	m3 = r3[1] / r1[1];
+	r2[2] -= m2 * r1[2];
+	r3[2] -= m3 * r1[2];
+	r2[3] -= m2 * r1[3];
+	r3[3] -= m3 * r1[3];
+	s = r1[4];
+	if (0.0 != s) {
+		r2[4] -= m2 * s;
+		r3[4] -= m3 * s;
+	}
+	s = r1[5];
+	if (0.0 != s) {
+		r2[5] -= m2 * s;
+		r3[5] -= m3 * s;
+	}
+	s = r1[6];
+	if (0.0 != s) {
+		r2[6] -= m2 * s;
+		r3[6] -= m3 * s;
+	}
+	s = r1[7];
+	if (0.0 != s) {
+		r2[7] -= m2 * s;
+		r3[7] -= m3 * s;
+	}
 
-		j = pvt_i[k]; /* Columns to swap correspond to pivot ROW */
-		if (j != k) { /* If columns are different */
-			for (i = 0; i < 4; i++) {
-				hold = columns[i][k];
-				columns[i][k] = -columns[i][j];
-				columns[i][j] = hold;
-			}
-		}
+	/* choose pivot - or die */
+	if (Math::abs(r3[2]) > Math::abs(r2[2])) {
+		SWAP(r3, r2);
 	}
+	ERR_FAIL_COND(0.0 == r2[2]);
+
+	/* eliminate third variable */
+	m3 = r3[2] / r2[2];
+	r3[3] -= m3 * r2[3];
+	r3[4] -= m3 * r2[4];
+	r3[5] -= m3 * r2[5];
+	r3[6] -= m3 * r2[6];
+	r3[7] -= m3 * r2[7];
+
+	/* last check */
+	ERR_FAIL_COND(0.0 == r3[3]);
+
+	s = 1.0 / r3[3]; /* now back substitute row 3 */
+	r3[4] *= s;
+	r3[5] *= s;
+	r3[6] *= s;
+	r3[7] *= s;
+
+	m2 = r2[3]; /* now back substitute row 2 */
+	s = 1.0 / r2[2];
+	r2[4] = s * (r2[4] - r3[4] * m2);
+	r2[5] = s * (r2[5] - r3[5] * m2);
+	r2[6] = s * (r2[6] - r3[6] * m2);
+	r2[7] = s * (r2[7] - r3[7] * m2);
+	m1 = r1[3];
+	r1[4] -= r3[4] * m1;
+	r1[5] -= r3[5] * m1;
+	r1[6] -= r3[6] * m1;
+	r1[7] -= r3[7] * m1;
+	m0 = r0[3];
+	r0[4] -= r3[4] * m0;
+	r0[5] -= r3[5] * m0;
+	r0[6] -= r3[6] * m0;
+	r0[7] -= r3[7] * m0;
+
+	m1 = r1[2]; /* now back substitute row 1 */
+	s = 1.0 / r1[1];
+	r1[4] = s * (r1[4] - r2[4] * m1);
+	r1[5] = s * (r1[5] - r2[5] * m1),
+	r1[6] = s * (r1[6] - r2[6] * m1);
+	r1[7] = s * (r1[7] - r2[7] * m1);
+	m0 = r0[2];
+	r0[4] -= r2[4] * m0;
+	r0[5] -= r2[5] * m0;
+	r0[6] -= r2[6] * m0;
+	r0[7] -= r2[7] * m0;
+
+	m0 = r0[1]; /* now back substitute row 0 */
+	s = 1.0 / r0[0];
+	r0[4] = s * (r0[4] - r1[4] * m0);
+	r0[5] = s * (r0[5] - r1[5] * m0),
+	r0[6] = s * (r0[6] - r1[6] * m0);
+	r0[7] = s * (r0[7] - r1[7] * m0);
+
+	MAT(out, 0, 0) = r0[4];
+	MAT(out, 0, 1) = r0[5];
+	MAT(out, 0, 2) = r0[6];
+	MAT(out, 0, 3) = r0[7];
+	MAT(out, 1, 0) = r1[4];
+	MAT(out, 1, 1) = r1[5];
+	MAT(out, 1, 2) = r1[6];
+	MAT(out, 1, 3) = r1[7];
+	MAT(out, 2, 0) = r2[4];
+	MAT(out, 2, 1) = r2[5];
+	MAT(out, 2, 2) = r2[6];
+	MAT(out, 2, 3) = r2[7];
+	MAT(out, 3, 0) = r3[4];
+	MAT(out, 3, 1) = r3[5];
+	MAT(out, 3, 2) = r3[6];
+	MAT(out, 3, 3) = r3[7];
+
+#undef MAT
+
+	*this = temp;
 }
 
 void Projection::flip_y() {
@@ -722,7 +849,8 @@ Projection Projection::operator*(const Projection &p_matrix) const {
 	return new_matrix;
 }
 
-void Projection::set_depth_correction(bool p_flip_y) {
+void Projection::set_depth_correction(bool p_flip_y, bool p_reverse_z, bool p_remap_z) {
+	// p_remap_z is used to convert from OpenGL-style clip space (-1 - 1) to Vulkan style (0 - 1).
 	real_t *m = &columns[0][0];
 
 	m[0] = 1;
@@ -735,11 +863,11 @@ void Projection::set_depth_correction(bool p_flip_y) {
 	m[7] = 0.0;
 	m[8] = 0.0;
 	m[9] = 0.0;
-	m[10] = 0.5;
+	m[10] = p_remap_z ? (p_reverse_z ? -0.5 : 0.5) : (p_reverse_z ? -1.0 : 1.0);
 	m[11] = 0.0;
 	m[12] = 0.0;
 	m[13] = 0.0;
-	m[14] = 0.5;
+	m[14] = p_remap_z ? 0.5 : 0.0;
 	m[15] = 1.0;
 }
 
@@ -786,14 +914,10 @@ void Projection::set_light_atlas_rect(const Rect2 &p_rect) {
 }
 
 Projection::operator String() const {
-	String str;
-	for (int i = 0; i < 4; i++) {
-		for (int j = 0; j < 4; j++) {
-			str = str + String((j > 0) ? ", " : "\n") + rtos(columns[i][j]);
-		}
-	}
-
-	return str;
+	return "[X: " + columns[0].operator String() +
+			", Y: " + columns[1].operator String() +
+			", Z: " + columns[2].operator String() +
+			", W: " + columns[3].operator String() + "]";
 }
 
 real_t Projection::get_aspect() const {
@@ -812,7 +936,7 @@ bool Projection::is_orthogonal() const {
 }
 
 real_t Projection::get_fov() const {
-	const real_t *matrix = (const real_t *)this->columns;
+	const real_t *matrix = (const real_t *)columns;
 
 	Plane right_plane = Plane(matrix[3] - matrix[0],
 			matrix[7] - matrix[4],
@@ -834,13 +958,13 @@ real_t Projection::get_fov() const {
 	}
 }
 
-float Projection::get_lod_multiplier() const {
+real_t Projection::get_lod_multiplier() const {
 	if (is_orthogonal()) {
 		return get_viewport_half_extents().x;
 	} else {
-		float zn = get_z_near();
-		float width = get_viewport_half_extents().x * 2.0;
-		return 1.0 / (zn / width);
+		const real_t zn = get_z_near();
+		const real_t width = get_viewport_half_extents().x * 2.0f;
+		return 1.0f / (zn / width);
 	}
 
 	// Usage is lod_size / (lod_distance * multiplier) < threshold

src/variant/quaternion.cpp

@@ -194,11 +194,11 @@ Quaternion Quaternion::spherical_cubic_interpolate(const Quaternion &p_b, const
 	post_q = Basis(post_q).get_rotation_quaternion();
 
 	// Flip quaternions to shortest path if necessary.
-	bool flip1 = Math::sign(from_q.dot(pre_q));
+	bool flip1 = std::signbit(from_q.dot(pre_q));
 	pre_q = flip1 ? -pre_q : pre_q;
-	bool flip2 = Math::sign(from_q.dot(to_q));
+	bool flip2 = std::signbit(from_q.dot(to_q));
 	to_q = flip2 ? -to_q : to_q;
-	bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : Math::sign(to_q.dot(post_q));
+	bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : std::signbit(to_q.dot(post_q));
 	post_q = flip3 ? -post_q : post_q;
 
 	// Calc by Expmap in from_q space.
@@ -245,11 +245,11 @@ Quaternion Quaternion::spherical_cubic_interpolate_in_time(const Quaternion &p_b
 	post_q = Basis(post_q).get_rotation_quaternion();
 
 	// Flip quaternions to shortest path if necessary.
-	bool flip1 = Math::sign(from_q.dot(pre_q));
+	bool flip1 = std::signbit(from_q.dot(pre_q));
 	pre_q = flip1 ? -pre_q : pre_q;
-	bool flip2 = Math::sign(from_q.dot(to_q));
+	bool flip2 = std::signbit(from_q.dot(to_q));
 	to_q = flip2 ? -to_q : to_q;
-	bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : Math::sign(to_q.dot(post_q));
+	bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : std::signbit(to_q.dot(post_q));
 	post_q = flip3 ? -post_q : post_q;
 
 	// Calc by Expmap in from_q space.

src/variant/rect2.cpp

@@ -211,31 +211,31 @@ next4:
 	real_t mina = maxa;
 
 	real_t dp = p_xform.columns[0].dot(xf_points2[1]);
-	maxa = Math::max(dp, maxa);
-	mina = Math::min(dp, mina);
+	maxa = MAX(dp, maxa);
+	mina = MIN(dp, mina);
 
 	dp = p_xform.columns[0].dot(xf_points2[2]);
-	maxa = Math::max(dp, maxa);
-	mina = Math::min(dp, mina);
+	maxa = MAX(dp, maxa);
+	mina = MIN(dp, mina);
 
 	dp = p_xform.columns[0].dot(xf_points2[3]);
-	maxa = Math::max(dp, maxa);
-	mina = Math::min(dp, mina);
+	maxa = MAX(dp, maxa);
+	mina = MIN(dp, mina);
 
 	real_t maxb = p_xform.columns[0].dot(xf_points[0]);
 	real_t minb = maxb;
 
 	dp = p_xform.columns[0].dot(xf_points[1]);
-	maxb = Math::max(dp, maxb);
-	minb = Math::min(dp, minb);
+	maxb = MAX(dp, maxb);
+	minb = MIN(dp, minb);
 
 	dp = p_xform.columns[0].dot(xf_points[2]);
-	maxb = Math::max(dp, maxb);
-	minb = Math::min(dp, minb);
+	maxb = MAX(dp, maxb);
+	minb = MIN(dp, minb);
 
 	dp = p_xform.columns[0].dot(xf_points[3]);
-	maxb = Math::max(dp, maxb);
-	minb = Math::min(dp, minb);
+	maxb = MAX(dp, maxb);
+	minb = MIN(dp, minb);
 
 	if (mina > maxb) {
 		return false;
@@ -248,31 +248,31 @@ next4:
 	mina = maxa;
 
 	dp = p_xform.columns[1].dot(xf_points2[1]);
-	maxa = Math::max(dp, maxa);
-	mina = Math::min(dp, mina);
+	maxa = MAX(dp, maxa);
+	mina = MIN(dp, mina);
 
 	dp = p_xform.columns[1].dot(xf_points2[2]);
-	maxa = Math::max(dp, maxa);
-	mina = Math::min(dp, mina);
+	maxa = MAX(dp, maxa);
+	mina = MIN(dp, mina);
 
 	dp = p_xform.columns[1].dot(xf_points2[3]);
-	maxa = Math::max(dp, maxa);
-	mina = Math::min(dp, mina);
+	maxa = MAX(dp, maxa);
+	mina = MIN(dp, mina);
 
 	maxb = p_xform.columns[1].dot(xf_points[0]);
 	minb = maxb;
 
 	dp = p_xform.columns[1].dot(xf_points[1]);
-	maxb = Math::max(dp, maxb);
-	minb = Math::min(dp, minb);
+	maxb = MAX(dp, maxb);
+	minb = MIN(dp, minb);
 
 	dp = p_xform.columns[1].dot(xf_points[2]);
-	maxb = Math::max(dp, maxb);
-	minb = Math::min(dp, minb);
+	maxb = MAX(dp, maxb);
+	minb = MIN(dp, minb);
 
 	dp = p_xform.columns[1].dot(xf_points[3]);
-	maxb = Math::max(dp, maxb);
-	minb = Math::min(dp, minb);
+	maxb = MAX(dp, maxb);
+	minb = MIN(dp, minb);
 
 	if (mina > maxb) {
 		return false;
@@ -285,7 +285,7 @@ next4:
 }
 
 Rect2::operator String() const {
-	return "[P: " + position.operator String() + ", S: " + size + "]";
+	return "[P: " + position.operator String() + ", S: " + size.operator String() + "]";
 }
 
 Rect2::operator Rect2i() const {

src/variant/transform2d.cpp

@@ -48,7 +48,7 @@ Transform2D Transform2D::inverse() const {
 }
 
 void Transform2D::affine_invert() {
-	real_t det = basis_determinant();
+	real_t det = determinant();
 #ifdef MATH_CHECKS
 	ERR_FAIL_COND(det == 0);
 #endif
@@ -67,17 +67,17 @@ Transform2D Transform2D::affine_inverse() const {
 	return inv;
 }
 
-void Transform2D::rotate(const real_t p_angle) {
+void Transform2D::rotate(real_t p_angle) {
 	*this = Transform2D(p_angle, Vector2()) * (*this);
 }
 
 real_t Transform2D::get_skew() const {
-	real_t det = basis_determinant();
+	real_t det = determinant();
 	return Math::acos(columns[0].normalized().dot(SIGN(det) * columns[1].normalized())) - (real_t)Math_PI * 0.5f;
 }
 
-void Transform2D::set_skew(const real_t p_angle) {
-	real_t det = basis_determinant();
+void Transform2D::set_skew(real_t p_angle) {
+	real_t det = determinant();
 	columns[1] = SIGN(det) * columns[0].rotated(((real_t)Math_PI * 0.5f + p_angle)).normalized() * columns[1].length();
 }
 
@@ -85,7 +85,7 @@ real_t Transform2D::get_rotation() const {
 	return Math::atan2(columns[0].y, columns[0].x);
 }
 
-void Transform2D::set_rotation(const real_t p_rot) {
+void Transform2D::set_rotation(real_t p_rot) {
 	Size2 scale = get_scale();
 	real_t cr = Math::cos(p_rot);
 	real_t sr = Math::sin(p_rot);
@@ -96,7 +96,7 @@ void Transform2D::set_rotation(const real_t p_rot) {
 	set_scale(scale);
 }
 
-Transform2D::Transform2D(const real_t p_rot, const Vector2 &p_pos) {
+Transform2D::Transform2D(real_t p_rot, const Vector2 &p_pos) {
 	real_t cr = Math::cos(p_rot);
 	real_t sr = Math::sin(p_rot);
 	columns[0][0] = cr;
@@ -106,7 +106,7 @@ Transform2D::Transform2D(const real_t p_rot, const Vector2 &p_pos) {
 	columns[2] = p_pos;
 }
 
-Transform2D::Transform2D(const real_t p_rot, const Size2 &p_scale, const real_t p_skew, const Vector2 &p_pos) {
+Transform2D::Transform2D(real_t p_rot, const Size2 &p_scale, real_t p_skew, const Vector2 &p_pos) {
 	columns[0][0] = Math::cos(p_rot) * p_scale.x;
 	columns[1][1] = Math::cos(p_rot + p_skew) * p_scale.y;
 	columns[1][0] = -Math::sin(p_rot + p_skew) * p_scale.y;
@@ -115,7 +115,7 @@ Transform2D::Transform2D(const real_t p_rot, const Size2 &p_scale, const real_t
 }
 
 Size2 Transform2D::get_scale() const {
-	real_t det_sign = Math::sign(basis_determinant());
+	real_t det_sign = SIGN(determinant());
 	return Size2(columns[0].length(), det_sign * columns[1].length());
 }
 
@@ -138,7 +138,7 @@ void Transform2D::scale_basis(const Size2 &p_scale) {
 	columns[1][1] *= p_scale.y;
 }
 
-void Transform2D::translate_local(const real_t p_tx, const real_t p_ty) {
+void Transform2D::translate_local(real_t p_tx, real_t p_ty) {
 	translate_local(Vector2(p_tx, p_ty));
 }
 
@@ -153,7 +153,7 @@ void Transform2D::orthonormalize() {
 	Vector2 y = columns[1];
 
 	x.normalize();
-	y = (y - x * (x.dot(y)));
+	y = y - x * x.dot(y);
 	y.normalize();
 
 	columns[0] = x;
@@ -161,9 +161,21 @@ void Transform2D::orthonormalize() {
 }
 
 Transform2D Transform2D::orthonormalized() const {
-	Transform2D on = *this;
-	on.orthonormalize();
-	return on;
+	Transform2D ortho = *this;
+	ortho.orthonormalize();
+	return ortho;
+}
+
+bool Transform2D::is_conformal() const {
+	// Non-flipped case.
+	if (Math::is_equal_approx(columns[0][0], columns[1][1]) && Math::is_equal_approx(columns[0][1], -columns[1][0])) {
+		return true;
+	}
+	// Flipped case.
+	if (Math::is_equal_approx(columns[0][0], -columns[1][1]) && Math::is_equal_approx(columns[0][1], columns[1][0])) {
+		return true;
+	}
+	return false;
 }
 
 bool Transform2D::is_equal_approx(const Transform2D &p_transform) const {
@@ -223,12 +235,6 @@ Transform2D Transform2D::operator*(const Transform2D &p_transform) const {
 	return t;
 }
 
-Transform2D Transform2D::basis_scaled(const Size2 &p_scale) const {
-	Transform2D copy = *this;
-	copy.scale_basis(p_scale);
-	return copy;
-}
-
 Transform2D Transform2D::scaled(const Size2 &p_scale) const {
 	// Equivalent to left multiplication
 	Transform2D copy = *this;
@@ -257,67 +263,52 @@ Transform2D Transform2D::translated_local(const Vector2 &p_offset) const {
 	return Transform2D(columns[0], columns[1], columns[2] + basis_xform(p_offset));
 }
 
-Transform2D Transform2D::rotated(const real_t p_angle) const {
+Transform2D Transform2D::rotated(real_t p_angle) const {
 	// Equivalent to left multiplication
 	return Transform2D(p_angle, Vector2()) * (*this);
 }
 
-Transform2D Transform2D::rotated_local(const real_t p_angle) const {
+Transform2D Transform2D::rotated_local(real_t p_angle) const {
 	// Equivalent to right multiplication
 	return (*this) * Transform2D(p_angle, Vector2()); // Could be optimized, because origin transform can be skipped.
 }
 
-real_t Transform2D::basis_determinant() const {
+real_t Transform2D::determinant() const {
 	return columns[0].x * columns[1].y - columns[0].y * columns[1].x;
 }
 
-Transform2D Transform2D::interpolate_with(const Transform2D &p_transform, const real_t p_c) const {
-	//extract parameters
-	Vector2 p1 = get_origin();
-	Vector2 p2 = p_transform.get_origin();
-
-	real_t r1 = get_rotation();
-	real_t r2 = p_transform.get_rotation();
-
-	Size2 s1 = get_scale();
-	Size2 s2 = p_transform.get_scale();
-
-	//slerp rotation
-	Vector2 v1(Math::cos(r1), Math::sin(r1));
-	Vector2 v2(Math::cos(r2), Math::sin(r2));
-
-	real_t dot = v1.dot(v2);
-
-	dot = Math::clamp(dot, (real_t)-1.0, (real_t)1.0);
-
-	Vector2 v;
-
-	if (dot > 0.9995f) {
-		v = v1.lerp(v2, p_c).normalized(); //linearly interpolate to avoid numerical precision issues
-	} else {
-		real_t angle = p_c * Math::acos(dot);
-		Vector2 v3 = (v2 - v1 * dot).normalized();
-		v = v1 * Math::cos(angle) + v3 * Math::sin(angle);
-	}
-
-	//construct matrix
-	Transform2D res(v.angle(), p1.lerp(p2, p_c));
-	res.scale_basis(s1.lerp(s2, p_c));
-	return res;
+Transform2D Transform2D::interpolate_with(const Transform2D &p_transform, real_t p_weight) const {
+	return Transform2D(
+			Math::lerp_angle(get_rotation(), p_transform.get_rotation(), p_weight),
+			get_scale().lerp(p_transform.get_scale(), p_weight),
+			Math::lerp_angle(get_skew(), p_transform.get_skew(), p_weight),
+			get_origin().lerp(p_transform.get_origin(), p_weight));
 }
 
-void Transform2D::operator*=(const real_t p_val) {
+void Transform2D::operator*=(real_t p_val) {
 	columns[0] *= p_val;
 	columns[1] *= p_val;
 	columns[2] *= p_val;
 }
 
-Transform2D Transform2D::operator*(const real_t p_val) const {
+Transform2D Transform2D::operator*(real_t p_val) const {
 	Transform2D ret(*this);
 	ret *= p_val;
 	return ret;
 }
 
+void Transform2D::operator/=(real_t p_val) {
+	columns[0] /= p_val;
+	columns[1] /= p_val;
+	columns[2] /= p_val;
+}
+
+Transform2D Transform2D::operator/(real_t p_val) const {
+	Transform2D ret(*this);
+	ret /= p_val;
+	return ret;
+}
+
 Transform2D::operator String() const {
 	return "[X: " + columns[0].operator String() +
 			", Y: " + columns[1].operator String() +

src/variant/transform3d.cpp

@@ -78,20 +78,20 @@ void Transform3D::rotate_basis(const Vector3 &p_axis, real_t p_angle) {
 	basis.rotate(p_axis, p_angle);
 }
 
-Transform3D Transform3D::looking_at(const Vector3 &p_target, const Vector3 &p_up) const {
+Transform3D Transform3D::looking_at(const Vector3 &p_target, const Vector3 &p_up, bool p_use_model_front) const {
 #ifdef MATH_CHECKS
 	ERR_FAIL_COND_V_MSG(origin.is_equal_approx(p_target), Transform3D(), "The transform's origin and target can't be equal.");
 #endif
 	Transform3D t = *this;
-	t.basis = Basis::looking_at(p_target - origin, p_up);
+	t.basis = Basis::looking_at(p_target - origin, p_up, p_use_model_front);
 	return t;
 }
 
-void Transform3D::set_look_at(const Vector3 &p_eye, const Vector3 &p_target, const Vector3 &p_up) {
+void Transform3D::set_look_at(const Vector3 &p_eye, const Vector3 &p_target, const Vector3 &p_up, bool p_use_model_front) {
 #ifdef MATH_CHECKS
 	ERR_FAIL_COND_MSG(p_eye.is_equal_approx(p_target), "The eye and target vectors can't be equal.");
 #endif
-	basis = Basis::looking_at(p_target - p_eye, p_up);
+	basis = Basis::looking_at(p_target - p_eye, p_up, p_use_model_front);
 	origin = p_eye;
 }
 
@@ -198,17 +198,28 @@ Transform3D Transform3D::operator*(const Transform3D &p_transform) const {
 	return t;
 }
 
-void Transform3D::operator*=(const real_t p_val) {
+void Transform3D::operator*=(real_t p_val) {
 	origin *= p_val;
 	basis *= p_val;
 }
 
-Transform3D Transform3D::operator*(const real_t p_val) const {
+Transform3D Transform3D::operator*(real_t p_val) const {
 	Transform3D ret(*this);
 	ret *= p_val;
 	return ret;
 }
 
+void Transform3D::operator/=(real_t p_val) {
+	basis /= p_val;
+	origin /= p_val;
+}
+
+Transform3D Transform3D::operator/(real_t p_val) const {
+	Transform3D ret(*this);
+	ret /= p_val;
+	return ret;
+}
+
 Transform3D::operator String() const {
 	return "[X: " + basis.get_column(0).operator String() +
 			", Y: " + basis.get_column(1).operator String() +
@@ -228,9 +239,9 @@ Transform3D::Transform3D(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &
 	basis.set_column(2, p_z);
 }
 
-Transform3D::Transform3D(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz, real_t ox, real_t oy, real_t oz) {
-	basis = Basis(xx, xy, xz, yx, yy, yz, zx, zy, zz);
-	origin = Vector3(ox, oy, oz);
+Transform3D::Transform3D(real_t p_xx, real_t p_xy, real_t p_xz, real_t p_yx, real_t p_yy, real_t p_yz, real_t p_zx, real_t p_zy, real_t p_zz, real_t p_ox, real_t p_oy, real_t p_oz) {
+	basis = Basis(p_xx, p_xy, p_xz, p_yx, p_yy, p_yz, p_zx, p_zy, p_zz);
+	origin = Vector3(p_ox, p_oy, p_oz);
 }
 
 } // namespace godot

src/variant/vector2.cpp

@@ -39,7 +39,7 @@ real_t Vector2::angle() const {
 	return Math::atan2(y, x);
 }
 
-Vector2 Vector2::from_angle(const real_t p_angle) {
+Vector2 Vector2::from_angle(real_t p_angle) {
 	return Vector2(Math::cos(p_angle), Math::sin(p_angle));
 }
 
@@ -111,7 +111,7 @@ Vector2 Vector2::round() const {
 	return Vector2(Math::round(x), Math::round(y));
 }
 
-Vector2 Vector2::rotated(const real_t p_by) const {
+Vector2 Vector2::rotated(real_t p_by) const {
 	real_t sine = Math::sin(p_by);
 	real_t cosi = Math::cos(p_by);
 	return Vector2(
@@ -119,7 +119,7 @@ Vector2 Vector2::rotated(const real_t p_by) const {
 			x * sine + y * cosi);
 }
 
-Vector2 Vector2::posmod(const real_t p_mod) const {
+Vector2 Vector2::posmod(real_t p_mod) const {
 	return Vector2(Math::fposmod(x, p_mod), Math::fposmod(y, p_mod));
 }
 
@@ -155,7 +155,7 @@ Vector2 Vector2::snappedf(real_t p_step) const {
 			Math::snapped(y, p_step));
 }
 
-Vector2 Vector2::limit_length(const real_t p_len) const {
+Vector2 Vector2::limit_length(real_t p_len) const {
 	const real_t l = length();
 	Vector2 v = *this;
 	if (l > 0 && p_len < l) {
@@ -166,7 +166,7 @@ Vector2 Vector2::limit_length(const real_t p_len) const {
 	return v;
 }
 
-Vector2 Vector2::move_toward(const Vector2 &p_to, const real_t p_delta) const {
+Vector2 Vector2::move_toward(const Vector2 &p_to, real_t p_delta) const {
 	Vector2 v = *this;
 	Vector2 vd = p_to - v;
 	real_t len = vd.length();
@@ -176,9 +176,9 @@ Vector2 Vector2::move_toward(const Vector2 &p_to, const real_t p_delta) const {
 // slide returns the component of the vector along the given plane, specified by its normal vector.
 Vector2 Vector2::slide(const Vector2 &p_normal) const {
 #ifdef MATH_CHECKS
-	ERR_FAIL_COND_V_MSG(!p_normal.is_normalized(), Vector2(), "The normal Vector2 must be normalized.");
+	ERR_FAIL_COND_V_MSG(!p_normal.is_normalized(), Vector2(), "The normal Vector2 " + p_normal.operator String() + "must be normalized.");
 #endif
-	return *this - p_normal * this->dot(p_normal);
+	return *this - p_normal * dot(p_normal);
 }
 
 Vector2 Vector2::bounce(const Vector2 &p_normal) const {
@@ -187,9 +187,9 @@ Vector2 Vector2::bounce(const Vector2 &p_normal) const {
 
 Vector2 Vector2::reflect(const Vector2 &p_normal) const {
 #ifdef MATH_CHECKS
-	ERR_FAIL_COND_V_MSG(!p_normal.is_normalized(), Vector2(), "The normal Vector2 must be normalized.");
+	ERR_FAIL_COND_V_MSG(!p_normal.is_normalized(), Vector2(), "The normal Vector2 " + p_normal.operator String() + "must be normalized.");
 #endif
-	return 2.0f * p_normal * this->dot(p_normal) - *this;
+	return 2.0f * p_normal * dot(p_normal) - *this;
 }
 
 bool Vector2::is_equal_approx(const Vector2 &p_v) const {
@@ -205,7 +205,7 @@ bool Vector2::is_finite() const {
 }
 
 Vector2::operator String() const {
-	return "(" + String::num_real(x, false) + ", " + String::num_real(y, false) + ")";
+	return "(" + String::num_real(x, true) + ", " + String::num_real(y, true) + ")";
 }
 
 Vector2::operator Vector2i() const {

src/variant/vector2i.cpp

@@ -35,18 +35,6 @@
 
 namespace godot {
 
-Vector2i Vector2i::snapped(const Vector2i &p_step) const {
-	return Vector2i(
-			Math::snapped(x, p_step.x),
-			Math::snapped(y, p_step.y));
-}
-
-Vector2i Vector2i::snappedi(int32_t p_step) const {
-	return Vector2i(
-			Math::snapped(x, p_step),
-			Math::snapped(y, p_step));
-}
-
 Vector2i Vector2i::clamp(const Vector2i &p_min, const Vector2i &p_max) const {
 	return Vector2i(
 			CLAMP(x, p_min.x, p_max.x),
@@ -59,20 +47,24 @@ Vector2i Vector2i::clampi(int32_t p_min, int32_t p_max) const {
 			CLAMP(y, p_min, p_max));
 }
 
-int64_t Vector2i::length_squared() const {
-	return x * (int64_t)x + y * (int64_t)y;
+Vector2i Vector2i::snapped(const Vector2i &p_step) const {
+	return Vector2i(
+			Math::snapped(x, p_step.x),
+			Math::snapped(y, p_step.y));
 }
 
-double Vector2i::length() const {
-	return Math::sqrt((double)length_squared());
+Vector2i Vector2i::snappedi(int32_t p_step) const {
+	return Vector2i(
+			Math::snapped(x, p_step),
+			Math::snapped(y, p_step));
 }
 
-int64_t Vector2i::distance_squared_to(const Vector2i &p_to) const {
-	return (p_to - *this).length_squared();
+int64_t Vector2i::length_squared() const {
+	return x * (int64_t)x + y * (int64_t)y;
 }
 
-double Vector2i::distance_to(const Vector2i &p_to) const {
-	return (p_to - *this).length();
+double Vector2i::length() const {
+	return Math::sqrt((double)length_squared());
 }
 
 Vector2i Vector2i::operator+(const Vector2i &p_v) const {
@@ -97,39 +89,39 @@ Vector2i Vector2i::operator*(const Vector2i &p_v1) const {
 	return Vector2i(x * p_v1.x, y * p_v1.y);
 }
 
-Vector2i Vector2i::operator*(const int32_t &rvalue) const {
-	return Vector2i(x * rvalue, y * rvalue);
+Vector2i Vector2i::operator*(int32_t p_rvalue) const {
+	return Vector2i(x * p_rvalue, y * p_rvalue);
 }
 
-void Vector2i::operator*=(const int32_t &rvalue) {
-	x *= rvalue;
-	y *= rvalue;
+void Vector2i::operator*=(int32_t p_rvalue) {
+	x *= p_rvalue;
+	y *= p_rvalue;
 }
 
 Vector2i Vector2i::operator/(const Vector2i &p_v1) const {
 	return Vector2i(x / p_v1.x, y / p_v1.y);
 }
 
-Vector2i Vector2i::operator/(const int32_t &rvalue) const {
-	return Vector2i(x / rvalue, y / rvalue);
+Vector2i Vector2i::operator/(int32_t p_rvalue) const {
+	return Vector2i(x / p_rvalue, y / p_rvalue);
 }
 
-void Vector2i::operator/=(const int32_t &rvalue) {
-	x /= rvalue;
-	y /= rvalue;
+void Vector2i::operator/=(int32_t p_rvalue) {
+	x /= p_rvalue;
+	y /= p_rvalue;
 }
 
 Vector2i Vector2i::operator%(const Vector2i &p_v1) const {
 	return Vector2i(x % p_v1.x, y % p_v1.y);
 }
 
-Vector2i Vector2i::operator%(const int32_t &rvalue) const {
-	return Vector2i(x % rvalue, y % rvalue);
+Vector2i Vector2i::operator%(int32_t p_rvalue) const {
+	return Vector2i(x % p_rvalue, y % p_rvalue);
 }
 
-void Vector2i::operator%=(const int32_t &rvalue) {
-	x %= rvalue;
-	y %= rvalue;
+void Vector2i::operator%=(int32_t p_rvalue) {
+	x %= p_rvalue;
+	y %= p_rvalue;
 }
 
 Vector2i Vector2i::operator-() const {

src/variant/vector3.cpp

@@ -37,11 +37,11 @@
 
 namespace godot {
 
-void Vector3::rotate(const Vector3 &p_axis, const real_t p_angle) {
+void Vector3::rotate(const Vector3 &p_axis, real_t p_angle) {
 	*this = Basis(p_axis, p_angle).xform(*this);
 }
 
-Vector3 Vector3::rotated(const Vector3 &p_axis, const real_t p_angle) const {
+Vector3 Vector3::rotated(const Vector3 &p_axis, real_t p_angle) const {
 	Vector3 r = *this;
 	r.rotate(p_axis, p_angle);
 	return r;
@@ -61,31 +61,31 @@ Vector3 Vector3::clampf(real_t p_min, real_t p_max) const {
 			CLAMP(z, p_min, p_max));
 }
 
-void Vector3::snap(const Vector3 p_step) {
+void Vector3::snap(const Vector3 &p_step) {
 	x = Math::snapped(x, p_step.x);
 	y = Math::snapped(y, p_step.y);
 	z = Math::snapped(z, p_step.z);
 }
 
+Vector3 Vector3::snapped(const Vector3 &p_step) const {
+	Vector3 v = *this;
+	v.snap(p_step);
+	return v;
+}
+
 void Vector3::snapf(real_t p_step) {
 	x = Math::snapped(x, p_step);
 	y = Math::snapped(y, p_step);
 	z = Math::snapped(z, p_step);
 }
 
-Vector3 Vector3::snapped(const Vector3 p_step) const {
-	Vector3 v = *this;
-	v.snap(p_step);
-	return v;
-}
-
 Vector3 Vector3::snappedf(real_t p_step) const {
 	Vector3 v = *this;
 	v.snapf(p_step);
 	return v;
 }
 
-Vector3 Vector3::limit_length(const real_t p_len) const {
+Vector3 Vector3::limit_length(real_t p_len) const {
 	const real_t l = length();
 	Vector3 v = *this;
 	if (l > 0 && p_len < l) {
@@ -96,7 +96,7 @@ Vector3 Vector3::limit_length(const real_t p_len) const {
 	return v;
 }
 
-Vector3 Vector3::move_toward(const Vector3 &p_to, const real_t p_delta) const {
+Vector3 Vector3::move_toward(const Vector3 &p_to, real_t p_delta) const {
 	Vector3 v = *this;
 	Vector3 vd = p_to - v;
 	real_t len = vd.length();
@@ -122,23 +122,25 @@ Vector2 Vector3::octahedron_encode() const {
 Vector3 Vector3::octahedron_decode(const Vector2 &p_oct) {
 	Vector2 f(p_oct.x * 2.0f - 1.0f, p_oct.y * 2.0f - 1.0f);
 	Vector3 n(f.x, f.y, 1.0f - Math::abs(f.x) - Math::abs(f.y));
-	float t = CLAMP(-n.z, 0.0f, 1.0f);
+	const real_t t = CLAMP(-n.z, 0.0f, 1.0f);
 	n.x += n.x >= 0 ? -t : t;
 	n.y += n.y >= 0 ? -t : t;
 	return n.normalized();
 }
 
-Vector2 Vector3::octahedron_tangent_encode(const float sign) const {
-	Vector2 res = this->octahedron_encode();
+Vector2 Vector3::octahedron_tangent_encode(float p_sign) const {
+	const real_t bias = 1.0f / (real_t)32767.0f;
+	Vector2 res = octahedron_encode();
+	res.y = MAX(res.y, bias);
 	res.y = res.y * 0.5f + 0.5f;
-	res.y = sign >= 0.0f ? res.y : 1 - res.y;
+	res.y = p_sign >= 0.0f ? res.y : 1 - res.y;
 	return res;
 }
 
-Vector3 Vector3::octahedron_tangent_decode(const Vector2 &p_oct, float *sign) {
+Vector3 Vector3::octahedron_tangent_decode(const Vector2 &p_oct, float *r_sign) {
 	Vector2 oct_compressed = p_oct;
 	oct_compressed.y = oct_compressed.y * 2 - 1;
-	*sign = oct_compressed.y >= 0.0f ? 1.0f : -1.0f;
+	*r_sign = oct_compressed.y >= 0.0f ? 1.0f : -1.0f;
 	oct_compressed.y = Math::abs(oct_compressed.y);
 	Vector3 res = Vector3::octahedron_decode(oct_compressed);
 	return res;
@@ -165,7 +167,7 @@ bool Vector3::is_finite() const {
 }
 
 Vector3::operator String() const {
-	return "(" + String::num_real(x, false) + ", " + String::num_real(y, false) + ", " + String::num_real(z, false) + ")";
+	return "(" + String::num_real(x, true) + ", " + String::num_real(y, true) + ", " + String::num_real(z, true) + ")";
 }
 
 Vector3::operator Vector3i() const {

src/variant/vector3i.cpp

@@ -35,20 +35,6 @@
 
 namespace godot {
 
-Vector3i Vector3i::snapped(const Vector3i &p_step) const {
-	return Vector3i(
-			Math::snapped(x, p_step.x),
-			Math::snapped(y, p_step.y),
-			Math::snapped(z, p_step.z));
-}
-
-Vector3i Vector3i::snappedi(int32_t p_step) const {
-	return Vector3i(
-			Math::snapped(x, p_step),
-			Math::snapped(y, p_step),
-			Math::snapped(z, p_step));
-}
-
 Vector3i::Axis Vector3i::min_axis_index() const {
 	return x < y ? (x < z ? Vector3i::AXIS_X : Vector3i::AXIS_Z) : (y < z ? Vector3i::AXIS_Y : Vector3i::AXIS_Z);
 }
@@ -71,6 +57,20 @@ Vector3i Vector3i::clampi(int32_t p_min, int32_t p_max) const {
 			CLAMP(z, p_min, p_max));
 }
 
+Vector3i Vector3i::snapped(const Vector3i &p_step) const {
+	return Vector3i(
+			Math::snapped(x, p_step.x),
+			Math::snapped(y, p_step.y),
+			Math::snapped(z, p_step.z));
+}
+
+Vector3i Vector3i::snappedi(int32_t p_step) const {
+	return Vector3i(
+			Math::snapped(x, p_step),
+			Math::snapped(y, p_step),
+			Math::snapped(z, p_step));
+}
+
 Vector3i::operator String() const {
 	return "(" + itos(x) + ", " + itos(y) + ", " + itos(z) + ")";
 }

src/variant/vector4.cpp

@@ -117,7 +117,7 @@ Vector4 Vector4::abs() const {
 }
 
 Vector4 Vector4::sign() const {
-	return Vector4(Math::sign(x), Math::sign(y), Math::sign(z), Math::sign(w));
+	return Vector4(SIGN(x), SIGN(y), SIGN(z), SIGN(w));
 }
 
 Vector4 Vector4::floor() const {
@@ -132,15 +132,16 @@ Vector4 Vector4::round() const {
 	return Vector4(Math::round(x), Math::round(y), Math::round(z), Math::round(w));
 }
 
-Vector4 Vector4::lerp(const Vector4 &p_to, const real_t p_weight) const {
-	return Vector4(
-			x + (p_weight * (p_to.x - x)),
-			y + (p_weight * (p_to.y - y)),
-			z + (p_weight * (p_to.z - z)),
-			w + (p_weight * (p_to.w - w)));
+Vector4 Vector4::lerp(const Vector4 &p_to, real_t p_weight) const {
+	Vector4 res = *this;
+	res.x = Math::lerp(res.x, p_to.x, p_weight);
+	res.y = Math::lerp(res.y, p_to.y, p_weight);
+	res.z = Math::lerp(res.z, p_to.z, p_weight);
+	res.w = Math::lerp(res.w, p_to.w, p_weight);
+	return res;
 }
 
-Vector4 Vector4::cubic_interpolate(const Vector4 &p_b, const Vector4 &p_pre_a, const Vector4 &p_post_b, const real_t p_weight) const {
+Vector4 Vector4::cubic_interpolate(const Vector4 &p_b, const Vector4 &p_pre_a, const Vector4 &p_post_b, real_t p_weight) const {
 	Vector4 res = *this;
 	res.x = Math::cubic_interpolate(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight);
 	res.y = Math::cubic_interpolate(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight);
@@ -149,7 +150,7 @@ Vector4 Vector4::cubic_interpolate(const Vector4 &p_b, const Vector4 &p_pre_a, c
 	return res;
 }
 
-Vector4 Vector4::cubic_interpolate_in_time(const Vector4 &p_b, const Vector4 &p_pre_a, const Vector4 &p_post_b, const real_t p_weight, const real_t &p_b_t, const real_t &p_pre_a_t, const real_t &p_post_b_t) const {
+Vector4 Vector4::cubic_interpolate_in_time(const Vector4 &p_b, const Vector4 &p_pre_a, const Vector4 &p_post_b, real_t p_weight, real_t p_b_t, real_t p_pre_a_t, real_t p_post_b_t) const {
 	Vector4 res = *this;
 	res.x = Math::cubic_interpolate_in_time(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
 	res.y = Math::cubic_interpolate_in_time(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
@@ -158,7 +159,7 @@ Vector4 Vector4::cubic_interpolate_in_time(const Vector4 &p_b, const Vector4 &p_
 	return res;
 }
 
-Vector4 Vector4::posmod(const real_t p_mod) const {
+Vector4 Vector4::posmod(real_t p_mod) const {
 	return Vector4(Math::fposmod(x, p_mod), Math::fposmod(y, p_mod), Math::fposmod(z, p_mod), Math::fposmod(w, p_mod));
 }
 
@@ -213,9 +214,13 @@ Vector4 Vector4::clampf(real_t p_min, real_t p_max) const {
 }
 
 Vector4::operator String() const {
-	return "(" + String::num_real(x, false) + ", " + String::num_real(y, false) + ", " + String::num_real(z, false) + ", " + String::num_real(w, false) + ")";
+	return "(" + String::num_real(x, true) + ", " + String::num_real(y, true) + ", " + String::num_real(z, true) + ", " + String::num_real(w, true) + ")";
 }
 
 static_assert(sizeof(Vector4) == 4 * sizeof(real_t));
 
+Vector4::operator Vector4i() const {
+	return Vector4i(x, y, z, w);
+}
+
 } // namespace godot

src/variant/vector4i.cpp

@@ -35,22 +35,6 @@
 
 namespace godot {
 
-Vector4i Vector4i::snapped(const Vector4i &p_step) const {
-	return Vector4i(
-			Math::snapped(x, p_step.x),
-			Math::snapped(y, p_step.y),
-			Math::snapped(z, p_step.z),
-			Math::snapped(w, p_step.w));
-}
-
-Vector4i Vector4i::snappedi(int32_t p_step) const {
-	return Vector4i(
-			Math::snapped(x, p_step),
-			Math::snapped(y, p_step),
-			Math::snapped(z, p_step),
-			Math::snapped(w, p_step));
-}
-
 Vector4i::Axis Vector4i::min_axis_index() const {
 	uint32_t min_index = 0;
 	int32_t min_value = x;
@@ -91,6 +75,22 @@ Vector4i Vector4i::clampi(int32_t p_min, int32_t p_max) const {
 			CLAMP(w, p_min, p_max));
 }
 
+Vector4i Vector4i::snapped(const Vector4i &p_step) const {
+	return Vector4i(
+			Math::snapped(x, p_step.x),
+			Math::snapped(y, p_step.y),
+			Math::snapped(z, p_step.z),
+			Math::snapped(w, p_step.w));
+}
+
+Vector4i Vector4i::snappedi(int32_t p_step) const {
+	return Vector4i(
+			Math::snapped(x, p_step),
+			Math::snapped(y, p_step),
+			Math::snapped(z, p_step),
+			Math::snapped(w, p_step));
+}
+
 Vector4i::operator String() const {
 	return "(" + itos(x) + ", " + itos(y) + ", " + itos(z) + ", " + itos(w) + ")";
 }