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#ifndef GL_VEC_HH
#define GL_VEC_HH

// This code implements a mathematical vector, comparable in functionality
// and syntax to the vector types in GLSL.
//
// Only vector sizes 2, 3 and 4 are supported. Though when it doesn't
// complicate stuff the code was written to support any size.
//
// Most basic functionality is already there, but this is not meant to be a
// full set of GLSL functions. We can always extend the functionality if/when
// required.
//
// In the past we had (some) manual SSE optimizations in this code. Though for
// the functions that matter (matrix-vector and matrix-matrix multiplication are
// built on top of the functions in this file), the compiler's
// auto-vectorization has become as good as the manually vectorized code.

#include "Math.hh"
#include "narrow.hh"
#include "unreachable.hh"
#include "xrange.hh"
#include <algorithm>
#include <array>
#include <cmath>
#include <iostream>
#include <utility>

namespace gl {

// Vector with N components of type T.
template<int N, typename T> class vecN;

// Specialization for N=2.
template<typename T> class vecN<2, T>
{
public:
	// Default copy-constructor and assignment operator.

	// Construct vector containing all zeros.
	constexpr vecN() : x(T(0)), y(T(0)) {}

	// Construct vector containing the same value repeated N times.
	constexpr explicit vecN(T t) : x(t), y(t) {}

	// Conversion constructor from vector of same size but different type.
	template<typename T2>
	constexpr explicit vecN(const vecN<2, T2>& v) : x(T(v.x)), y(T(v.y)) {}

	// Construct from larger vector (higher order elements are dropped).
	template<int N2> constexpr explicit vecN(const vecN<N2, T>& v) : x(v.x), y(v.y) {}

	// Construct vector from 2 given values.
	constexpr vecN(T a, T b) : x(a), y(b) {}

	// Access the i-th element of this vector.
	[[nodiscard]] constexpr T  operator[](unsigned i) const {
		if (i == 0) return x;
		if (i == 1) return y;
		UNREACHABLE;
	}
	[[nodiscard]] constexpr T& operator[](unsigned i) {
		if (i == 0) return x;
		if (i == 1) return y;
		UNREACHABLE;
	}

	[[nodiscard]] constexpr const T* data() const { return &x; }
	[[nodiscard]] constexpr       T* data()       { return &x; }

	// For structured bindings
	template<size_t I> [[nodiscard]] constexpr T  get() const noexcept { return (*this)[I]; }
	template<size_t I> [[nodiscard]] constexpr T& get()       noexcept { return (*this)[I]; }

	// Assignment version of the +,-,* operations defined below.
	constexpr vecN& operator+=(const vecN& v) { *this = *this + v; return *this; }
	constexpr vecN& operator-=(const vecN& v) { *this = *this - v; return *this; }
	constexpr vecN& operator*=(const vecN& v) { *this = *this * v; return *this; }
	constexpr vecN& operator*=(T           t) { *this = *this * t; return *this; }

	[[nodiscard]] constexpr bool operator==(const vecN&) const = default;

	// vector + vector
	[[nodiscard]] constexpr friend vecN operator+(const vecN& v1, const vecN& v2) {
		vecN r;
		for (auto i : xrange(2)) r[i] = v1[i] + v2[i];
		return r;
	}

	// vector - vector
	[[nodiscard]] constexpr friend vecN operator-(const vecN& v1, const vecN& v2) {
		vecN r;
		for (auto i : xrange(2)) r[i] = v1[i] - v2[i];
		return r;
	}

	// scalar * vector
	[[nodiscard]] constexpr friend vecN operator*(T a, const vecN& v) {
		vecN r;
		for (auto i : xrange(2)) r[i] = a * v[i];
		return r;
	}

	// vector * scalar
	[[nodiscard]] constexpr friend vecN operator*(const vecN& v, T a) {
		vecN r;
		for (auto i : xrange(2)) r[i] = v[i] * a;
		return r;
	}

	// vector * vector
	[[nodiscard]] constexpr friend vecN operator*(const vecN& v1, const vecN& v2)
	{
		vecN r;
		for (auto i : xrange(2)) r[i] = v1[i] * v2[i];
		return r;
	}

	// element-wise reciprocal
	[[nodiscard]] constexpr friend vecN recip(const vecN& v) {
		vecN r;
		for (auto i : xrange(2)) r[i] = T(1) / v[i];
		return r;
	}

	// scalar / vector
	[[nodiscard]] constexpr friend vecN operator/(T a, const vecN& v) {
		if constexpr (std::is_floating_point_v<T>) {
			return a * recip(v);
		} else {
			vecN r;
			for (auto i : xrange(2)) r[i] = a / v[i];
			return r;
		}
	}

	// vector / scalar
	[[nodiscard]] constexpr friend vecN operator/(const vecN& v, T a) {
		if constexpr (std::is_floating_point_v<T>) {
			return v * (T(1) / a);
		} else {
			vecN r;
			for (auto i : xrange(2)) r[i] = v[i] / a;
			return r;
		}
	}

	// vector / vector
	[[nodiscard]] constexpr friend vecN operator/(const vecN& v1, const vecN& v2) {
		if constexpr (std::is_floating_point_v<T>) {
			return v1 * recip(v2);
		} else {
			vecN r;
			for (auto i : xrange(2)) r[i] = v1[i] / v2[i];
			return r;
		}
	}

	// Textual representation. (Only) used to debug unittest.
	friend std::ostream& operator<<(std::ostream& os, const vecN& v) {
		os << "[ ";
		for (auto i : xrange(2)) {
			os << v[i] << ' ';
		}
		os << ']';
		return os;
	}

public:
	T x, y;
};

// Specialization for N=3.
template<typename T> class vecN<3, T>
{
public:
	constexpr vecN() : x(T(0)), y(T(0)), z(T(0)) {}
	constexpr explicit vecN(T t) : x(t), y(t), z(t) {}
	template<typename T2>
	constexpr explicit vecN(const vecN<3, T2>& v) : x(T(v.x)), y(T(v.y)), z(T(v.z)) {}
	constexpr explicit vecN(const vecN<4, T>& v) : x(v.x), y(v.y), z(v.z) {}
	constexpr vecN(T a, T b, T c) : x(a), y(b), z(c) {}
	constexpr vecN(T a, const vecN<2, T>& b) : x(a), y(b.x), z(b.y) {}
	constexpr vecN(const vecN<2, T>& a, T b) : x(a.x), y(a.y), z(b) {}

	[[nodiscard]] constexpr T  operator[](unsigned i) const {
		if (i == 0) return x;
		if (i == 1) return y;
		if (i == 2) return z;
		UNREACHABLE;
	}
	[[nodiscard]] constexpr T& operator[](unsigned i) {
		if (i == 0) return x;
		if (i == 1) return y;
		if (i == 2) return z;
		UNREACHABLE;
	}

	[[nodiscard]] constexpr const T* data() const { return &x; }
	[[nodiscard]] constexpr       T* data()       { return &x; }

	template<size_t I> [[nodiscard]] constexpr T  get() const noexcept { return (*this)[I]; }
	template<size_t I> [[nodiscard]] constexpr T& get()       noexcept { return (*this)[I]; }

	constexpr vecN& operator+=(const vecN& v) { *this = *this + v; return *this; }
	constexpr vecN& operator-=(const vecN& v) { *this = *this - v; return *this; }
	constexpr vecN& operator*=(const vecN& v) { *this = *this * v; return *this; }
	constexpr vecN& operator*=(T           t) { *this = *this * t; return *this; }

	[[nodiscard]] constexpr bool operator==(const vecN&) const = default;

	// vector + vector
	[[nodiscard]] constexpr friend vecN operator+(const vecN& v1, const vecN& v2) {
		vecN r;
		for (auto i : xrange(3)) r[i] = v1[i] + v2[i];
		return r;
	}

	// vector - vector
	[[nodiscard]] constexpr friend vecN operator-(const vecN& v1, const vecN& v2) {
		vecN r;
		for (auto i : xrange(3)) r[i] = v1[i] - v2[i];
		return r;
	}

	// scalar * vector
	[[nodiscard]] constexpr friend vecN operator*(T a, const vecN& v) {
		vecN r;
		for (auto i : xrange(3)) r[i] = a * v[i];
		return r;
	}

	// vector * scalar
	[[nodiscard]] constexpr friend vecN operator*(const vecN& v, T a) {
		vecN r;
		for (auto i : xrange(3)) r[i] = v[i] * a;
		return r;
	}

	// vector * vector
	[[nodiscard]] constexpr friend vecN operator*(const vecN& v1, const vecN& v2)
	{
		vecN r;
		for (auto i : xrange(3)) r[i] = v1[i] * v2[i];
		return r;
	}

	// element-wise reciprocal
	[[nodiscard]] constexpr friend vecN recip(const vecN& v) {
		vecN r;
		for (auto i : xrange(3)) r[i] = T(1) / v[i];
		return r;
	}

	// scalar / vector
	[[nodiscard]] constexpr friend vecN operator/(T a, const vecN& v) {
		return a * recip(v);
	}

	// vector / scalar
	[[nodiscard]] constexpr friend vecN operator/(const vecN& v, T a) {
		return v * (T(1) / a);
	}

	// vector / vector
	[[nodiscard]] constexpr friend vecN operator/(const vecN& v1, const vecN& v2) {
		return v1 * recip(v2);
	}

	// Textual representation. (Only) used to debug unittest.
	friend std::ostream& operator<<(std::ostream& os, const vecN& v) {
		os << "[ ";
		for (auto i : xrange(3)) {
			os << v[i] << ' ';
		}
		os << ']';
		return os;
	}

public:
	T x, y, z;
};

// Specialization for N=4.
template<typename T> class vecN<4, T>
{
public:
	constexpr vecN() : x(T(0)), y(T(0)), z(T(0)), w(T(0)) {}
	constexpr explicit vecN(T t) : x(t), y(t), z(t), w(t) {}
	template<typename T2>
	constexpr explicit vecN(const vecN<4, T2>& v) : x(T(v.x)), y(T(v.y)), z(T(v.z)), w(T(v.w)) {}
	constexpr vecN(T a, T b, T c, T d) : x(a), y(b), z(c), w(d) {}
	constexpr vecN(T a, const vecN<3, T>& b) : x(a), y(b.x), z(b.y), w(b.z) {}
	constexpr vecN(const vecN<3, T>& a, T b) : x(a.x), y(a.y), z(a.z), w(b) {}
	constexpr vecN(const vecN<2, T>& a, const vecN<2, T>& b) : x(a.x), y(a.y), z(b.x), w(b.y) {}

	[[nodiscard]] constexpr T  operator[](unsigned i) const {
		if (i == 0) return x;
		if (i == 1) return y;
		if (i == 2) return z;
		if (i == 3) return w;
		UNREACHABLE;
	}
	[[nodiscard]] constexpr T& operator[](unsigned i) {
		if (i == 0) return x;
		if (i == 1) return y;
		if (i == 2) return z;
		if (i == 3) return w;
		UNREACHABLE;
	}

	[[nodiscard]] constexpr const T* data() const { return &x; }
	[[nodiscard]] constexpr       T* data()       { return &x; }

	template<size_t I> [[nodiscard]] constexpr T  get() const noexcept { return (*this)[I]; }
	template<size_t I> [[nodiscard]] constexpr T& get()       noexcept { return (*this)[I]; }

	// Assignment version of the +,-,* operations defined below.
	constexpr vecN& operator+=(const vecN& v) { *this = *this + v; return *this; }
	constexpr vecN& operator-=(const vecN& v) { *this = *this - v; return *this; }
	constexpr vecN& operator*=(const vecN& v) { *this = *this * v; return *this; }
	constexpr vecN& operator*=(T           t) { *this = *this * t; return *this; }

	[[nodiscard]] constexpr bool operator==(const vecN&) const = default;

	// vector + vector
	[[nodiscard]] constexpr friend vecN operator+(const vecN& v1, const vecN& v2) {
		vecN r;
		for (auto i : xrange(4)) r[i] = v1[i] + v2[i];
		return r;
	}

	// vector - vector
	[[nodiscard]] constexpr friend vecN operator-(const vecN& v1, const vecN& v2) {
		vecN r;
		for (auto i : xrange(4)) r[i] = v1[i] - v2[i];
		return r;
	}

	// scalar * vector
	[[nodiscard]] constexpr friend vecN operator*(T a, const vecN& v) {
		vecN r;
		for (auto i : xrange(4)) r[i] = a * v[i];
		return r;
	}

	// vector * scalar
	[[nodiscard]] constexpr friend vecN operator*(const vecN& v, T a) {
		vecN r;
		for (auto i : xrange(4)) r[i] = v[i] * a;
		return r;
	}

	// vector * vector
	[[nodiscard]] constexpr friend vecN operator*(const vecN& v1, const vecN& v2)
	{
		vecN r;
		for (auto i : xrange(4)) r[i] = v1[i] * v2[i];
		return r;
	}

	// element-wise reciprocal
	[[nodiscard]] constexpr friend vecN recip(const vecN& v) {
		vecN r;
		for (auto i : xrange(4)) r[i] = T(1) / v[i];
		return r;
	}

	// scalar / vector
	[[nodiscard]] constexpr friend vecN operator/(T a, const vecN& v) {
		return a * recip(v);
	}

	// vector / scalar
	[[nodiscard]] constexpr friend vecN operator/(const vecN& v, T a) {
		return v * (T(1) / a);
	}

	// vector / vector
	[[nodiscard]] constexpr friend vecN operator/(const vecN& v1, const vecN& v2) {
		return v1 * recip(v2);
	}

	// Textual representation. (Only) used to debug unittest.
	friend std::ostream& operator<<(std::ostream& os, const vecN& v) {
		os << "[ ";
		for (auto i : xrange(4)) {
			os << v[i] << ' ';
		}
		os << ']';
		return os;
	}

public:
	T x, y, z, w;
};


// Convenience typedefs (same names as used by GLSL).
using  vec2 = vecN<2, float>;
using  vec3 = vecN<3, float>;
using  vec4 = vecN<4, float>;
using ivec2 = vecN<2, int>;
using ivec3 = vecN<3, int>;
using ivec4 = vecN<4, int>;

static_assert(sizeof( vec2) == 2 * sizeof(float));
static_assert(sizeof( vec3) == 3 * sizeof(float));
static_assert(sizeof( vec4) == 4 * sizeof(float));
static_assert(sizeof(ivec2) == 2 * sizeof(int));
static_assert(sizeof(ivec3) == 3 * sizeof(int));
static_assert(sizeof(ivec4) == 4 * sizeof(int));


// -- Scalar functions --

// reciprocal square root
[[nodiscard]] inline float rsqrt(float x)
{
	return 1.0f / sqrtf(x);
}
[[nodiscard]] inline double rsqrt(double x)
{
	return 1.0 / sqrt(x);
}

// convert radians <-> degrees
template<typename T> [[nodiscard]] constexpr T radians(T d)
{
	return d * T(Math::pi / 180.0);
}
template<typename T> [[nodiscard]] constexpr T degrees(T r)
{
	return r * T(180.0 / Math::pi);
}


// -- Vector functions --

// vector negation
template<int N, typename T>
[[nodiscard]] constexpr vecN<N, T> operator-(const vecN<N, T>& x)
{
	return vecN<N, T>() - x;
}

// min(vector, vector)
template<int N, typename T>
[[nodiscard]] constexpr vecN<N, T> min(const vecN<N, T>& x, const vecN<N, T>& y)
{
	vecN<N, T> r;
	for (auto i : xrange(N)) r[i] = std::min(x[i], y[i]);
	return r;
}

// max(vector, vector)
template<int N, typename T>
[[nodiscard]] constexpr vecN<N, T> max(const vecN<N, T>& x, const vecN<N, T>& y)
{
	vecN<N, T> r;
	for (auto i : xrange(N)) r[i] = std::max(x[i], y[i]);
	return r;
}

// min(vector.x, vector.y, ...)
template<int N, typename T>
[[nodiscard]] constexpr T min_component(const vecN<N, T>& x)
{
	T r = x[0];
	for (auto i : xrange(1, N)) r = std::min(r, x[i]);
	return r;
}

// max(vector.x, vector.y, ...)
template<int N, typename T>
[[nodiscard]] constexpr T max_component(const vecN<N, T>& x)
{
	T r = x[0];
	for (auto i : xrange(1, N)) r = std::max(r, x[i]);
	return r;
}

// clamp(vector, vector, vector)
template<int N, typename T>
[[nodiscard]] constexpr vecN<N, T> clamp(const vecN<N, T>& x, const vecN<N, T>& minVal, const vecN<N, T>& maxVal)
{
	return min(maxVal, max(minVal, x));
}

// clamp(vector, scalar, scalar)
template<int N, typename T>
[[nodiscard]] constexpr vecN<N, T> clamp(const vecN<N, T>& x, T minVal, T maxVal)
{
	return clamp(x, vecN<N, T>(minVal), vecN<N, T>(maxVal));
}

// sum of components
template<int N, typename T>
[[nodiscard]] constexpr T sum(const vecN<N, T>& x)
{
	T result(0);
	for (auto i : xrange(N)) result += x[i];
	return result;
}
template<int N, typename T>
[[nodiscard]] constexpr vecN<N, T> sum_broadcast(const vecN<N, T>& x)
{
	return vecN<N, T>(sum(x));
}

// dot product
template<int N, typename T>
[[nodiscard]] constexpr T dot(const vecN<N, T>& x, const vecN<N, T>& y)
{
	return sum(x * y);
}
template<int N, typename T>
[[nodiscard]] constexpr vecN<N, T> dot_broadcast(const vecN<N, T>& x, const vecN<N, T>& y)
{
	return sum_broadcast(x * y);
}

// squared length (norm-2)
template<int N, typename T>
[[nodiscard]] constexpr T length2(const vecN<N, T>& x)
{
	return dot(x, x);
}

// length (norm-2)
template<int N, typename T>
[[nodiscard]] inline T length(const vecN<N, T>& x)
{
	return std::sqrt(length2(x));
}

// normalize vector
template<int N, typename T>
[[nodiscard]] inline vecN<N, T> normalize(const vecN<N, T>& x)
{
	return x * gl::rsqrt(length2(x));
}

// cross product (only defined for vectors of length 3)
template<typename T>
[[nodiscard]] constexpr vecN<3, T> cross(const vecN<3, T>& a, const vecN<3, T>& b)
{
	return vecN<3, T>(a.y * b.z - a.z * b.y,
	                  a.z * b.x - a.x * b.z,
	                  a.x * b.y - a.y * b.x);
}

// round each component to the nearest integer (returns a vector of integers)
template<int N, typename T>
[[nodiscard]] inline vecN<N, int> round(const vecN<N, T>& x)
{
	vecN<N, int> r;
	for (auto i : xrange(N)) r[i] = narrow_cast<int>(std::lrint(x[i]));
	return r;
}

// truncate each component to the nearest integer that is not bigger in
// absolute value (returns a vector of integers)
template<int N, typename T>
[[nodiscard]] constexpr vecN<N, int> trunc(const vecN<N, T>& x)
{
	vecN<N, int> r;
	for (auto i : xrange(N)) r[i] = int(x[i]);
	return r;
}
// Similar, but floor.
template<int N, typename T>
[[nodiscard]] inline vecN<N, int> floor(const vecN<N, T>& x)
{
	vecN<N, int> r;
	for (auto i : xrange(N)) r[i] = int(std::floor(x[i]));
	return r;
}
// Similar, but ceil.
template<int N, typename T>
[[nodiscard]] inline vecN<N, int> ceil(const vecN<N, T>& x)
{
	vecN<N, int> r;
	for (auto i : xrange(N)) r[i] = int(std::ceil(x[i]));
	return r;
}

} // namespace gl

// Support for structured bindings
namespace std {
// On some platforms tuple_size is a class and on others it is a struct.
// Such a mismatch is only a problem when targeting the Microsoft C++ ABI,
// which we don't do when compiling with Clang.
#ifdef __clang__
#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Wmismatched-tags"
#endif
	template<int N, typename T> class tuple_size<gl::vecN<N, T>>
		: public std::integral_constant<size_t, N> {};
#ifdef __clang__
#pragma clang diagnostic pop
#endif
	template<size_t I, int N, typename T> class tuple_element<I, gl::vecN<N, T>> {
	public:
		using type = T;
	};
}

#endif // GL_VEC_HH

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1	#ifndef GL_VEC_HH
2	#define GL_VEC_HH
3
4	// This code implements a mathematical vector, comparable in functionality
5	// and syntax to the vector types in GLSL.
6	//
7	// Only vector sizes 2, 3 and 4 are supported. Though when it doesn't
8	// complicate stuff the code was written to support any size.
9	//
10	// Most basic functionality is already there, but this is not meant to be a
11	// full set of GLSL functions. We can always extend the functionality if/when
12	// required.
13	//
14	// In the past we had (some) manual SSE optimizations in this code. Though for
15	// the functions that matter (matrix-vector and matrix-matrix multiplication are
16	// built on top of the functions in this file), the compiler's
17	// auto-vectorization has become as good as the manually vectorized code.
18
19	#include "Math.hh"
20	#include "narrow.hh"
21	#include "unreachable.hh"
22	#include "xrange.hh"
23	#include <algorithm>
24	#include <array>
25	#include <cmath>
26	#include <iostream>
27	#include <utility>
28
29	namespace gl {
30
31	// Vector with N components of type T.
32	template<int N, typename T> class vecN;
33
34	// Specialization for N=2.
35	template<typename T> class vecN<2, T>
36	{
37	public:
38	// Default copy-constructor and assignment operator.
39
40	// Construct vector containing all zeros.
41	constexpr vecN() : x(T(0)), y(T(0)) {}
42
43	// Construct vector containing the same value repeated N times.
44	constexpr explicit vecN(T t) : x(t), y(t) {}
45
46	// Conversion constructor from vector of same size but different type.
47	template<typename T2>
48	constexpr explicit vecN(const vecN<2, T2>& v) : x(T(v.x)), y(T(v.y)) {}
49
50	// Construct from larger vector (higher order elements are dropped).
51	template<int N2> constexpr explicit vecN(const vecN<N2, T>& v) : x(v.x), y(v.y) {}
52
53	// Construct vector from 2 given values.
54	constexpr vecN(T a, T b) : x(a), y(b) {}
55
56	// Access the i-th element of this vector.
57	[[nodiscard]] constexpr T operator[](unsigned i) const {
58	if (i == 0) return x;
59	if (i == 1) return y;
60	UNREACHABLE;
61	}
62	[[nodiscard]] constexpr T& operator[](unsigned i) {
63	if (i == 0) return x;
64	if (i == 1) return y;
65	UNREACHABLE;
66	}
67
68	[[nodiscard]] constexpr const T* data() const { return &x; }
69	[[nodiscard]] constexpr T* data() { return &x; }
70
71	// For structured bindings
72	template<size_t I> [[nodiscard]] constexpr T get() const noexcept { return (*this)[I]; }
73	template<size_t I> [[nodiscard]] constexpr T& get() noexcept { return (*this)[I]; }
74
75	// Assignment version of the +,-,* operations defined below.
76	constexpr vecN& operator+=(const vecN& v) { this = this + v; return *this; }
77	constexpr vecN& operator-=(const vecN& v) { this = this - v; return *this; }
78	constexpr vecN& operator=(const vecN& v) { this = this v; return *this; }
79	constexpr vecN& operator=(T t) { this = this t; return *this; }
80
81	[[nodiscard]] constexpr bool operator==(const vecN&) const = default;
82
83	// vector + vector
84	[[nodiscard]] constexpr friend vecN operator+(const vecN& v1, const vecN& v2) {
85	vecN r;
86	for (auto i : xrange(2)) r[i] = v1[i] + v2[i];
87	return r;
88	}
89
90	// vector - vector
91	[[nodiscard]] constexpr friend vecN operator-(const vecN& v1, const vecN& v2) {
92	vecN r;
93	for (auto i : xrange(2)) r[i] = v1[i] - v2[i];
94	return r;
95	}
96
97	// scalar * vector
98	[[nodiscard]] constexpr friend vecN operator*(T a, const vecN& v) {
99	vecN r;
100	for (auto i : xrange(2)) r[i] = a * v[i];
101	return r;
102	}
103
104	// vector * scalar
105	[[nodiscard]] constexpr friend vecN operator*(const vecN& v, T a) {
106	vecN r;
107	for (auto i : xrange(2)) r[i] = v[i] * a;
108	return r;
109	}
110
111	// vector * vector
112	[[nodiscard]] constexpr friend vecN operator*(const vecN& v1, const vecN& v2)
113	{
114	vecN r;
115	for (auto i : xrange(2)) r[i] = v1[i] * v2[i];
116	return r;
117	}
118
119	// element-wise reciprocal
120	[[nodiscard]] constexpr friend vecN recip(const vecN& v) {
121	vecN r;
122	for (auto i : xrange(2)) r[i] = T(1) / v[i];
123	return r;
124	}
125
126	// scalar / vector
127	[[nodiscard]] constexpr friend vecN operator/(T a, const vecN& v) {
128	if constexpr (std::is_floating_point_v<T>) {
129	return a * recip(v);
130	} else {
131	vecN r;
132	for (auto i : xrange(2)) r[i] = a / v[i];
133	return r;
134	}
135	}
136
137	// vector / scalar
138	[[nodiscard]] constexpr friend vecN operator/(const vecN& v, T a) {
139	if constexpr (std::is_floating_point_v<T>) {
140	return v * (T(1) / a);
141	} else {
142	vecN r;
143	for (auto i : xrange(2)) r[i] = v[i] / a;
144	return r;
145	}
146	}
147
148	// vector / vector
149	[[nodiscard]] constexpr friend vecN operator/(const vecN& v1, const vecN& v2) {
150	if constexpr (std::is_floating_point_v<T>) {
151	return v1 * recip(v2);
152	} else {
153	vecN r;
154	for (auto i : xrange(2)) r[i] = v1[i] / v2[i];
155	return r;
156	}
157	}
158
159	// Textual representation. (Only) used to debug unittest.
160	friend std::ostream& operator<<(std::ostream& os, const vecN& v) {
161	os << "[ ";
162	for (auto i : xrange(2)) {
163	os << v[i] << ' ';
164	}
165	os << ']';
166	return os;
167	}
168
169	public:
170	T x, y;
171	};
172
173	// Specialization for N=3.
174	template<typename T> class vecN<3, T>
175	{
176	public:
177	constexpr vecN() : x(T(0)), y(T(0)), z(T(0)) {}
178	constexpr explicit vecN(T t) : x(t), y(t), z(t) {}
179	template<typename T2>
180	constexpr explicit vecN(const vecN<3, T2>& v) : x(T(v.x)), y(T(v.y)), z(T(v.z)) {}
181	constexpr explicit vecN(const vecN<4, T>& v) : x(v.x), y(v.y), z(v.z) {}
182	constexpr vecN(T a, T b, T c) : x(a), y(b), z(c) {}
183	constexpr vecN(T a, const vecN<2, T>& b) : x(a), y(b.x), z(b.y) {}
184	constexpr vecN(const vecN<2, T>& a, T b) : x(a.x), y(a.y), z(b) {}
185
186	[[nodiscard]] constexpr T operator[](unsigned i) const {
187	if (i == 0) return x;
188	if (i == 1) return y;
189	if (i == 2) return z;
190	UNREACHABLE;
191	}
192	[[nodiscard]] constexpr T& operator[](unsigned i) {
193	if (i == 0) return x;
194	if (i == 1) return y;
195	if (i == 2) return z;
196	UNREACHABLE;
197	}
198
199	[[nodiscard]] constexpr const T* data() const { return &x; }
200	[[nodiscard]] constexpr T* data() { return &x; }
201
202	template<size_t I> [[nodiscard]] constexpr T get() const noexcept { return (*this)[I]; }
203	template<size_t I> [[nodiscard]] constexpr T& get() noexcept { return (*this)[I]; }
204
205	constexpr vecN& operator+=(const vecN& v) { this = this + v; return *this; }
206	constexpr vecN& operator-=(const vecN& v) { this = this - v; return *this; }
207	constexpr vecN& operator=(const vecN& v) { this = this v; return *this; }
208	constexpr vecN& operator=(T t) { this = this t; return *this; }
209
210	[[nodiscard]] constexpr bool operator==(const vecN&) const = default;
211
212	// vector + vector
213	[[nodiscard]] constexpr friend vecN operator+(const vecN& v1, const vecN& v2) {
214	vecN r;
215	for (auto i : xrange(3)) r[i] = v1[i] + v2[i];
216	return r;
217	}
218
219	// vector - vector
220	[[nodiscard]] constexpr friend vecN operator-(const vecN& v1, const vecN& v2) {
221	vecN r;
222	for (auto i : xrange(3)) r[i] = v1[i] - v2[i];
223	return r;
224	}
225
226	// scalar * vector
227	[[nodiscard]] constexpr friend vecN operator*(T a, const vecN& v) {
228	vecN r;
229	for (auto i : xrange(3)) r[i] = a * v[i];
230	return r;
231	}
232
233	// vector * scalar
234	[[nodiscard]] constexpr friend vecN operator*(const vecN& v, T a) {
235	vecN r;
236	for (auto i : xrange(3)) r[i] = v[i] * a;
237	return r;
238	}
239
240	// vector * vector
241	[[nodiscard]] constexpr friend vecN operator*(const vecN& v1, const vecN& v2)
242	{
243	vecN r;
244	for (auto i : xrange(3)) r[i] = v1[i] * v2[i];
245	return r;
246	}
247
248	// element-wise reciprocal
249	[[nodiscard]] constexpr friend vecN recip(const vecN& v) {
250	vecN r;
251	for (auto i : xrange(3)) r[i] = T(1) / v[i];
252	return r;
253	}
254
255	// scalar / vector
256	[[nodiscard]] constexpr friend vecN operator/(T a, const vecN& v) {
257	return a * recip(v);
258	}
259
260	// vector / scalar
261	[[nodiscard]] constexpr friend vecN operator/(const vecN& v, T a) {
262	return v * (T(1) / a);
263	}
264
265	// vector / vector
266	[[nodiscard]] constexpr friend vecN operator/(const vecN& v1, const vecN& v2) {
267	return v1 * recip(v2);
268	}
269
270	// Textual representation. (Only) used to debug unittest.
271	friend std::ostream& operator<<(std::ostream& os, const vecN& v) {
272	os << "[ ";
273	for (auto i : xrange(3)) {
274	os << v[i] << ' ';
275	}
276	os << ']';
277	return os;
278	}
279
280	public:
281	T x, y, z;
282	};
283
284	// Specialization for N=4.
285	template<typename T> class vecN<4, T>
286	{
287	public:
288	constexpr vecN() : x(T(0)), y(T(0)), z(T(0)), w(T(0)) {}
289	constexpr explicit vecN(T t) : x(t), y(t), z(t), w(t) {}
290	template<typename T2>
291	constexpr explicit vecN(const vecN<4, T2>& v) : x(T(v.x)), y(T(v.y)), z(T(v.z)), w(T(v.w)) {}
292	constexpr vecN(T a, T b, T c, T d) : x(a), y(b), z(c), w(d) {}
293	constexpr vecN(T a, const vecN<3, T>& b) : x(a), y(b.x), z(b.y), w(b.z) {}
294	constexpr vecN(const vecN<3, T>& a, T b) : x(a.x), y(a.y), z(a.z), w(b) {}
295	constexpr vecN(const vecN<2, T>& a, const vecN<2, T>& b) : x(a.x), y(a.y), z(b.x), w(b.y) {}
296
297	[[nodiscard]] constexpr T operator[](unsigned i) const {
298	if (i == 0) return x;
299	if (i == 1) return y;
300	if (i == 2) return z;
301	if (i == 3) return w;
302	UNREACHABLE;
303	}
304	[[nodiscard]] constexpr T& operator[](unsigned i) {
305	if (i == 0) return x;
306	if (i == 1) return y;
307	if (i == 2) return z;
308	if (i == 3) return w;
309	UNREACHABLE;
310	}
311
312	[[nodiscard]] constexpr const T* data() const { return &x; }
313	[[nodiscard]] constexpr T* data() { return &x; }
314
315	template<size_t I> [[nodiscard]] constexpr T get() const noexcept { return (*this)[I]; }
316	template<size_t I> [[nodiscard]] constexpr T& get() noexcept { return (*this)[I]; }
317
318	// Assignment version of the +,-,* operations defined below.
319	constexpr vecN& operator+=(const vecN& v) { this = this + v; return *this; }
320	constexpr vecN& operator-=(const vecN& v) { this = this - v; return *this; }
321	constexpr vecN& operator=(const vecN& v) { this = this v; return *this; }
322	constexpr vecN& operator=(T t) { this = this t; return *this; }
323
324	[[nodiscard]] constexpr bool operator==(const vecN&) const = default;
325
326	// vector + vector
327	[[nodiscard]] constexpr friend vecN operator+(const vecN& v1, const vecN& v2) {
328	vecN r;
329	for (auto i : xrange(4)) r[i] = v1[i] + v2[i];
330	return r;
331	}
332
333	// vector - vector
334	[[nodiscard]] constexpr friend vecN operator-(const vecN& v1, const vecN& v2) {
335	vecN r;
336	for (auto i : xrange(4)) r[i] = v1[i] - v2[i];
337	return r;
338	}
339
340	// scalar * vector
341	[[nodiscard]] constexpr friend vecN operator*(T a, const vecN& v) {
342	vecN r;
343	for (auto i : xrange(4)) r[i] = a * v[i];
344	return r;
345	}
346
347	// vector * scalar
348	[[nodiscard]] constexpr friend vecN operator*(const vecN& v, T a) {
349	vecN r;
350	for (auto i : xrange(4)) r[i] = v[i] * a;
351	return r;
352	}
353
354	// vector * vector
355	[[nodiscard]] constexpr friend vecN operator*(const vecN& v1, const vecN& v2)
356	{
357	vecN r;
358	for (auto i : xrange(4)) r[i] = v1[i] * v2[i];
359	return r;
360	}
361
362	// element-wise reciprocal
363	[[nodiscard]] constexpr friend vecN recip(const vecN& v) {
364	vecN r;
365	for (auto i : xrange(4)) r[i] = T(1) / v[i];
366	return r;
367	}
368
369	// scalar / vector
370	[[nodiscard]] constexpr friend vecN operator/(T a, const vecN& v) {
371	return a * recip(v);
372	}
373
374	// vector / scalar
375	[[nodiscard]] constexpr friend vecN operator/(const vecN& v, T a) {
376	return v * (T(1) / a);
377	}
378
379	// vector / vector
380	[[nodiscard]] constexpr friend vecN operator/(const vecN& v1, const vecN& v2) {
381	return v1 * recip(v2);
382	}
383
384	// Textual representation. (Only) used to debug unittest.
385	friend std::ostream& operator<<(std::ostream& os, const vecN& v) {
386	os << "[ ";
387	for (auto i : xrange(4)) {
388	os << v[i] << ' ';
389	}
390	os << ']';
391	return os;
392	}
393
394	public:
395	T x, y, z, w;
396	};
397
398
399	// Convenience typedefs (same names as used by GLSL).
400	using vec2 = vecN<2, float>;
401	using vec3 = vecN<3, float>;
402	using vec4 = vecN<4, float>;
403	using ivec2 = vecN<2, int>;
404	using ivec3 = vecN<3, int>;
405	using ivec4 = vecN<4, int>;
406
407	static_assert(sizeof( vec2) == 2 * sizeof(float));
408	static_assert(sizeof( vec3) == 3 * sizeof(float));
409	static_assert(sizeof( vec4) == 4 * sizeof(float));
410	static_assert(sizeof(ivec2) == 2 * sizeof(int));
411	static_assert(sizeof(ivec3) == 3 * sizeof(int));
412	static_assert(sizeof(ivec4) == 4 * sizeof(int));
413
414
415	// -- Scalar functions --
416
417	// reciprocal square root
418	[[nodiscard]] inline float rsqrt(float x)
419	{
420	return 1.0f / sqrtf(x);
421	}
422	[[nodiscard]] inline double rsqrt(double x)
423	{
424	return 1.0 / sqrt(x);
425	}
426
427	// convert radians <-> degrees
428	template<typename T> [[nodiscard]] constexpr T radians(T d)
429	{
430	return d * T(Math::pi / 180.0);
431	}
432	template<typename T> [[nodiscard]] constexpr T degrees(T r)
433	{
434	return r * T(180.0 / Math::pi);
435	}
436
437
438	// -- Vector functions --
439
440	// vector negation
441	template<int N, typename T>
442	[[nodiscard]] constexpr vecN<N, T> operator-(const vecN<N, T>& x)
443	{
444	return vecN<N, T>() - x;
445	}
446
447	// min(vector, vector)
448	template<int N, typename T>
449	[[nodiscard]] constexpr vecN<N, T> min(const vecN<N, T>& x, const vecN<N, T>& y)
450	{
451	vecN<N, T> r;
452	for (auto i : xrange(N)) r[i] = std::min(x[i], y[i]);
453	return r;
454	}
455
456	// max(vector, vector)
457	template<int N, typename T>
458	[[nodiscard]] constexpr vecN<N, T> max(const vecN<N, T>& x, const vecN<N, T>& y)
459	{
460	vecN<N, T> r;
461	for (auto i : xrange(N)) r[i] = std::max(x[i], y[i]);
462	return r;
463	}
464
465	// min(vector.x, vector.y, ...)
466	template<int N, typename T>
467	[[nodiscard]] constexpr T min_component(const vecN<N, T>& x)
468	{
469	T r = x[0];
470	for (auto i : xrange(1, N)) r = std::min(r, x[i]);
471	return r;
472	}
473
474	// max(vector.x, vector.y, ...)
475	template<int N, typename T>
476	[[nodiscard]] constexpr T max_component(const vecN<N, T>& x)
477	{
478	T r = x[0];
479	for (auto i : xrange(1, N)) r = std::max(r, x[i]);
480	return r;
481	}
482
483	// clamp(vector, vector, vector)
484	template<int N, typename T>
485	[[nodiscard]] constexpr vecN<N, T> clamp(const vecN<N, T>& x, const vecN<N, T>& minVal, const vecN<N, T>& maxVal)
486	{
487	return min(maxVal, max(minVal, x));
488	}
489
490	// clamp(vector, scalar, scalar)
491	template<int N, typename T>
492	[[nodiscard]] constexpr vecN<N, T> clamp(const vecN<N, T>& x, T minVal, T maxVal)
493	{
494	return clamp(x, vecN<N, T>(minVal), vecN<N, T>(maxVal));
495	}
496
497	// sum of components
498	template<int N, typename T>
499	[[nodiscard]] constexpr T sum(const vecN<N, T>& x)
500	{
501	T result(0);
502	for (auto i : xrange(N)) result += x[i];
503	return result;
504	}
505	template<int N, typename T>
506	[[nodiscard]] constexpr vecN<N, T> sum_broadcast(const vecN<N, T>& x)
507	{
508	return vecN<N, T>(sum(x));
509	}
510
511	// dot product
512	template<int N, typename T>
513	[[nodiscard]] constexpr T dot(const vecN<N, T>& x, const vecN<N, T>& y)
514	{
515	return sum(x * y);
516	}
517	template<int N, typename T>
518	[[nodiscard]] constexpr vecN<N, T> dot_broadcast(const vecN<N, T>& x, const vecN<N, T>& y)
519	{
520	return sum_broadcast(x * y);
521	}
522
523	// squared length (norm-2)
524	template<int N, typename T>
525	[[nodiscard]] constexpr T length2(const vecN<N, T>& x)
526	{
527	return dot(x, x);
528	}
529
530	// length (norm-2)
531	template<int N, typename T>
532	[[nodiscard]] inline T length(const vecN<N, T>& x)
533	{
534	return std::sqrt(length2(x));
535	}
536
537	// normalize vector
538	template<int N, typename T>
539	[[nodiscard]] inline vecN<N, T> normalize(const vecN<N, T>& x)
540	{
541	return x * gl::rsqrt(length2(x));
542	}
543
544	// cross product (only defined for vectors of length 3)
545	template<typename T>
546	[[nodiscard]] constexpr vecN<3, T> cross(const vecN<3, T>& a, const vecN<3, T>& b)
547	{
548	return vecN<3, T>(a.y * b.z - a.z * b.y,
549	a.z * b.x - a.x * b.z,
550	a.x * b.y - a.y * b.x);
551	}
552
553	// round each component to the nearest integer (returns a vector of integers)
554	template<int N, typename T>
555	[[nodiscard]] inline vecN<N, int> round(const vecN<N, T>& x)
556	{
557	vecN<N, int> r;
558	for (auto i : xrange(N)) r[i] = narrow_cast<int>(std::lrint(x[i]));
559	return r;
560	}
561
562	// truncate each component to the nearest integer that is not bigger in
563	// absolute value (returns a vector of integers)
564	template<int N, typename T>
565	[[nodiscard]] constexpr vecN<N, int> trunc(const vecN<N, T>& x)
566	{
567	vecN<N, int> r;
568	for (auto i : xrange(N)) r[i] = int(x[i]);
569	return r;
570	}
571	// Similar, but floor.
572	template<int N, typename T>
573	[[nodiscard]] inline vecN<N, int> floor(const vecN<N, T>& x)
574	{
575	vecN<N, int> r;
576	for (auto i : xrange(N)) r[i] = int(std::floor(x[i]));
577	return r;
578	}
579	// Similar, but ceil.
580	template<int N, typename T>
581	[[nodiscard]] inline vecN<N, int> ceil(const vecN<N, T>& x)
582	{
583	vecN<N, int> r;
584	for (auto i : xrange(N)) r[i] = int(std::ceil(x[i]));
585	return r;
586	}
587
588	} // namespace gl
589
590	// Support for structured bindings
591	namespace std {
592	// On some platforms tuple_size is a class and on others it is a struct.
593	// Such a mismatch is only a problem when targeting the Microsoft C++ ABI,
594	// which we don't do when compiling with Clang.
595	#ifdef __clang__
596	#pragma clang diagnostic push
597	#pragma clang diagnostic ignored "-Wmismatched-tags"
598	#endif
599	template<int N, typename T> class tuple_size<gl::vecN<N, T>>
600	: public std::integral_constant<size_t, N> {};
601	#ifdef __clang__
602	#pragma clang diagnostic pop
603	#endif
604	template<size_t I, int N, typename T> class tuple_element<I, gl::vecN<N, T>> {
605	public:
606	using type = T;
607	};
608	}
609
610	#endif // GL_VEC_HH

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