odin-lang.Odin/core/math/linalg/specific.odin

package linalg

import "core:math"

F16_EPSILON :: 1e-3;
F32_EPSILON :: 1e-7;
F64_EPSILON :: 1e-15;

Vector2f16 :: distinct [2]f16;
Vector3f16 :: distinct [3]f16;
Vector4f16 :: distinct [4]f16;

Matrix1x1f16 :: distinct [1][1]f16;
Matrix1x2f16 :: distinct [1][2]f16;
Matrix1x3f16 :: distinct [1][3]f16;
Matrix1x4f16 :: distinct [1][4]f16;

Matrix2x1f16 :: distinct [2][1]f16;
Matrix2x2f16 :: distinct [2][2]f16;
Matrix2x3f16 :: distinct [2][3]f16;
Matrix2x4f16 :: distinct [2][4]f16;

Matrix3x1f16 :: distinct [3][1]f16;
Matrix3x2f16 :: distinct [3][2]f16;
Matrix3x3f16 :: distinct [3][3]f16;
Matrix3x4f16 :: distinct [3][4]f16;

Matrix4x1f16 :: distinct [4][1]f16;
Matrix4x2f16 :: distinct [4][2]f16;
Matrix4x3f16 :: distinct [4][3]f16;
Matrix4x4f16 :: distinct [4][4]f16;

Matrix1f16 :: Matrix1x1f16;
Matrix2f16 :: Matrix2x2f16;
Matrix3f16 :: Matrix3x3f16;
Matrix4f16 :: Matrix4x4f16;

Vector2f32 :: distinct [2]f32;
Vector3f32 :: distinct [3]f32;
Vector4f32 :: distinct [4]f32;

Matrix1x1f32 :: distinct [1][1]f32;
Matrix1x2f32 :: distinct [1][2]f32;
Matrix1x3f32 :: distinct [1][3]f32;
Matrix1x4f32 :: distinct [1][4]f32;

Matrix2x1f32 :: distinct [2][1]f32;
Matrix2x2f32 :: distinct [2][2]f32;
Matrix2x3f32 :: distinct [2][3]f32;
Matrix2x4f32 :: distinct [2][4]f32;

Matrix3x1f32 :: distinct [3][1]f32;
Matrix3x2f32 :: distinct [3][2]f32;
Matrix3x3f32 :: distinct [3][3]f32;
Matrix3x4f32 :: distinct [3][4]f32;

Matrix4x1f32 :: distinct [4][1]f32;
Matrix4x2f32 :: distinct [4][2]f32;
Matrix4x3f32 :: distinct [4][3]f32;
Matrix4x4f32 :: distinct [4][4]f32;

Matrix1f32 :: Matrix1x1f32;
Matrix2f32 :: Matrix2x2f32;
Matrix3f32 :: Matrix3x3f32;
Matrix4f32 :: Matrix4x4f32;

Vector2f64 :: distinct [2]f64;
Vector3f64 :: distinct [3]f64;
Vector4f64 :: distinct [4]f64;

Matrix1x1f64 :: distinct [1][1]f64;
Matrix1x2f64 :: distinct [1][2]f64;
Matrix1x3f64 :: distinct [1][3]f64;
Matrix1x4f64 :: distinct [1][4]f64;

Matrix2x1f64 :: distinct [2][1]f64;
Matrix2x2f64 :: distinct [2][2]f64;
Matrix2x3f64 :: distinct [2][3]f64;
Matrix2x4f64 :: distinct [2][4]f64;

Matrix3x1f64 :: distinct [3][1]f64;
Matrix3x2f64 :: distinct [3][2]f64;
Matrix3x3f64 :: distinct [3][3]f64;
Matrix3x4f64 :: distinct [3][4]f64;

Matrix4x1f64 :: distinct [4][1]f64;
Matrix4x2f64 :: distinct [4][2]f64;
Matrix4x3f64 :: distinct [4][3]f64;
Matrix4x4f64 :: distinct [4][4]f64;

Matrix1f64 :: Matrix1x1f64;
Matrix2f64 :: Matrix2x2f64;
Matrix3f64 :: Matrix3x3f64;
Matrix4f64 :: Matrix4x4f64;

Quaternionf16 :: distinct quaternion64;
Quaternionf32 :: distinct quaternion128;
Quaternionf64 :: distinct quaternion256;

MATRIX1F16_IDENTITY :: Matrix1f16{{1}};
MATRIX2F16_IDENTITY :: Matrix2f16{{1, 0}, {0, 1}};
MATRIX3F16_IDENTITY :: Matrix3f16{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
MATRIX4F16_IDENTITY :: Matrix4f16{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}};

MATRIX1F32_IDENTITY :: Matrix1f32{{1}};
MATRIX2F32_IDENTITY :: Matrix2f32{{1, 0}, {0, 1}};
MATRIX3F32_IDENTITY :: Matrix3f32{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
MATRIX4F32_IDENTITY :: Matrix4f32{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}};

MATRIX1F64_IDENTITY :: Matrix1f64{{1}};
MATRIX2F64_IDENTITY :: Matrix2f64{{1, 0}, {0, 1}};
MATRIX3F64_IDENTITY :: Matrix3f64{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}};
MATRIX4F64_IDENTITY :: Matrix4f64{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}};

QUATERNIONF16_IDENTITY :: Quaternionf16(1);
QUATERNIONF32_IDENTITY :: Quaternionf32(1);
QUATERNIONF64_IDENTITY :: Quaternionf64(1);

VECTOR3F16_X_AXIS :: Vector3f16{1, 0, 0};
VECTOR3F16_Y_AXIS :: Vector3f16{0, 1, 0};
VECTOR3F16_Z_AXIS :: Vector3f16{0, 0, 1};

VECTOR3F32_X_AXIS :: Vector3f32{1, 0, 0};
VECTOR3F32_Y_AXIS :: Vector3f32{0, 1, 0};
VECTOR3F32_Z_AXIS :: Vector3f32{0, 0, 1};

VECTOR3F64_X_AXIS :: Vector3f64{1, 0, 0};
VECTOR3F64_Y_AXIS :: Vector3f64{0, 1, 0};
VECTOR3F64_Z_AXIS :: Vector3f64{0, 0, 1};


vector2_orthogonal :: proc(v: $V/[2]$E) -> V where !IS_ARRAY(E), IS_FLOAT(E) {
	return {-v.y, v.x};
}

vector3_orthogonal :: proc(v: $V/[3]$E) -> V where !IS_ARRAY(E), IS_FLOAT(E) {
	x := abs(v.x);
	y := abs(v.y);
	z := abs(v.z);

	other: V;
	if x < y {
		if x < z {
			other = {1, 0, 0};
		} else {
			other = {0, 0, 1};
		}
	} else {
		if y < z {
			other = {0, 1, 0};
		} else {
			other = {0, 0, 1};
		}
	}
	return normalize(cross(v, other));
}

orthogonal :: proc{vector2_orthogonal, vector3_orthogonal};



vector4_srgb_to_linear_f16 :: proc(col: Vector4f16) -> Vector4f16 {
	r := math.pow(col.x, 2.2);
	g := math.pow(col.y, 2.2);
	b := math.pow(col.z, 2.2);
	a := col.w;
	return {r, g, b, a};
}
vector4_srgb_to_linear_f32 :: proc(col: Vector4f32) -> Vector4f32 {
	r := math.pow(col.x, 2.2);
	g := math.pow(col.y, 2.2);
	b := math.pow(col.z, 2.2);
	a := col.w;
	return {r, g, b, a};
}
vector4_srgb_to_linear_f64 :: proc(col: Vector4f64) -> Vector4f64 {
	r := math.pow(col.x, 2.2);
	g := math.pow(col.y, 2.2);
	b := math.pow(col.z, 2.2);
	a := col.w;
	return {r, g, b, a};
}
vector4_srgb_to_linear :: proc{
	vector4_srgb_to_linear_f16,
	vector4_srgb_to_linear_f32,
	vector4_srgb_to_linear_f64,
};


vector4_linear_to_srgb_f16 :: proc(col: Vector4f16) -> Vector4f16 {
	a :: 2.51;
	b :: 0.03;
	c :: 2.43;
	d :: 0.59;
	e :: 0.14;

	x := col.x;
	y := col.y;
	z := col.z;

	x = (x * (a * x + b)) / (x * (c * x + d) + e);
	y = (y * (a * y + b)) / (y * (c * y + d) + e);
	z = (z * (a * z + b)) / (z * (c * z + d) + e);

	x = math.pow(clamp(x, 0, 1), 1.0 / 2.2);
	y = math.pow(clamp(y, 0, 1), 1.0 / 2.2);
	z = math.pow(clamp(z, 0, 1), 1.0 / 2.2);

	return {x, y, z, col.w};
}
vector4_linear_to_srgb_f32 :: proc(col: Vector4f32) -> Vector4f32 {
	a :: 2.51;
	b :: 0.03;
	c :: 2.43;
	d :: 0.59;
	e :: 0.14;

	x := col.x;
	y := col.y;
	z := col.z;

	x = (x * (a * x + b)) / (x * (c * x + d) + e);
	y = (y * (a * y + b)) / (y * (c * y + d) + e);
	z = (z * (a * z + b)) / (z * (c * z + d) + e);

	x = math.pow(clamp(x, 0, 1), 1.0 / 2.2);
	y = math.pow(clamp(y, 0, 1), 1.0 / 2.2);
	z = math.pow(clamp(z, 0, 1), 1.0 / 2.2);

	return {x, y, z, col.w};
}
vector4_linear_to_srgb_f64 :: proc(col: Vector4f64) -> Vector4f64 {
	a :: 2.51;
	b :: 0.03;
	c :: 2.43;
	d :: 0.59;
	e :: 0.14;

	x := col.x;
	y := col.y;
	z := col.z;

	x = (x * (a * x + b)) / (x * (c * x + d) + e);
	y = (y * (a * y + b)) / (y * (c * y + d) + e);
	z = (z * (a * z + b)) / (z * (c * z + d) + e);

	x = math.pow(clamp(x, 0, 1), 1.0 / 2.2);
	y = math.pow(clamp(y, 0, 1), 1.0 / 2.2);
	z = math.pow(clamp(z, 0, 1), 1.0 / 2.2);

	return {x, y, z, col.w};
}
vector4_linear_to_srgb :: proc{
	vector4_linear_to_srgb_f16,
	vector4_linear_to_srgb_f32,
	vector4_linear_to_srgb_f64,
};


vector4_hsl_to_rgb_f16 :: proc(h, s, l: f16, a: f16 = 1) -> Vector4f16 {
	hue_to_rgb :: proc(p, q, t: f16) -> f16 {
		t := t;
		if t < 0 { t += 1; }
		if t > 1 { t -= 1; }
		switch {
		case t < 1.0/6.0: return p + (q - p) * 6.0 * t;
		case t < 1.0/2.0: return q;
		case t < 2.0/3.0: return p + (q - p) * 6.0 * (2.0/3.0 - t);
		}
		return p;
	}

	r, g, b: f16;
	if s == 0 {
		r = l;
		g = l;
		b = l;
	} else {
		q := l * (1+s) if l < 0.5 else l+s - l*s;
		p := 2*l - q;
		r = hue_to_rgb(p, q, h + 1.0/3.0);
		g = hue_to_rgb(p, q, h);
		b = hue_to_rgb(p, q, h - 1.0/3.0);
	}
	return {r, g, b, a};
}
vector4_hsl_to_rgb_f32 :: proc(h, s, l: f32, a: f32 = 1) -> Vector4f32 {
	hue_to_rgb :: proc(p, q, t: f32) -> f32 {
		t := t;
		if t < 0 { t += 1; }
		if t > 1 { t -= 1; }
		switch {
		case t < 1.0/6.0: return p + (q - p) * 6.0 * t;
		case t < 1.0/2.0: return q;
		case t < 2.0/3.0: return p + (q - p) * 6.0 * (2.0/3.0 - t);
		}
		return p;
	}

	r, g, b: f32;
	if s == 0 {
		r = l;
		g = l;
		b = l;
	} else {
		q := l * (1+s) if l < 0.5 else l+s - l*s;
		p := 2*l - q;
		r = hue_to_rgb(p, q, h + 1.0/3.0);
		g = hue_to_rgb(p, q, h);
		b = hue_to_rgb(p, q, h - 1.0/3.0);
	}
	return {r, g, b, a};
}
vector4_hsl_to_rgb_f64 :: proc(h, s, l: f64, a: f64 = 1) -> Vector4f64 {
	hue_to_rgb :: proc(p, q, t: f64) -> f64 {
		t := t;
		if t < 0 { t += 1; }
		if t > 1 { t -= 1; }
		switch {
		case t < 1.0/6.0: return p + (q - p) * 6.0 * t;
		case t < 1.0/2.0: return q;
		case t < 2.0/3.0: return p + (q - p) * 6.0 * (2.0/3.0 - t);
		}
		return p;
	}

	r, g, b: f64;
	if s == 0 {
		r = l;
		g = l;
		b = l;
	} else {
		q := l * (1+s) if l < 0.5 else l+s - l*s;
		p := 2*l - q;
		r = hue_to_rgb(p, q, h + 1.0/3.0);
		g = hue_to_rgb(p, q, h);
		b = hue_to_rgb(p, q, h - 1.0/3.0);
	}
	return {r, g, b, a};
}
vector4_hsl_to_rgb :: proc{
	vector4_hsl_to_rgb_f16,
	vector4_hsl_to_rgb_f32,
	vector4_hsl_to_rgb_f64,
};


vector4_rgb_to_hsl_f16 :: proc(col: Vector4f16) -> Vector4f16 {
	r := col.x;
	g := col.y;
	b := col.z;
	a := col.w;
	v_min := min(r, g, b);
	v_max := max(r, g, b);
	h, s, l: f16;
	h  = 0.0;
	s  = 0.0;
	l  = (v_min + v_max) * 0.5;

	if v_max != v_min {
		d: = v_max - v_min;
		s = d / (2.0 - v_max - v_min) if l > 0.5 else d / (v_max + v_min);
		switch {
		case v_max == r:
			h = (g - b) / d + (6.0 if g < b else 0.0);
		case v_max == g:
			h = (b - r) / d + 2.0;
		case v_max == b:
			h = (r - g) / d + 4.0;
		}

		h *= 1.0/6.0;
	}

	return {h, s, l, a};
}
vector4_rgb_to_hsl_f32 :: proc(col: Vector4f32) -> Vector4f32 {
	r := col.x;
	g := col.y;
	b := col.z;
	a := col.w;
	v_min := min(r, g, b);
	v_max := max(r, g, b);
	h, s, l: f32;
	h  = 0.0;
	s  = 0.0;
	l  = (v_min + v_max) * 0.5;

	if v_max != v_min {
		d: = v_max - v_min;
		s = d / (2.0 - v_max - v_min) if l > 0.5 else d / (v_max + v_min);
		switch {
		case v_max == r:
			h = (g - b) / d + (6.0 if g < b else 0.0);
		case v_max == g:
			h = (b - r) / d + 2.0;
		case v_max == b:
			h = (r - g) / d + 4.0;
		}

		h *= 1.0/6.0;
	}

	return {h, s, l, a};
}
vector4_rgb_to_hsl_f64 :: proc(col: Vector4f64) -> Vector4f64 {
	r := col.x;
	g := col.y;
	b := col.z;
	a := col.w;
	v_min := min(r, g, b);
	v_max := max(r, g, b);
	h, s, l: f64;
	h  = 0.0;
	s  = 0.0;
	l  = (v_min + v_max) * 0.5;

	if v_max != v_min {
		d: = v_max - v_min;
		s = d / (2.0 - v_max - v_min) if l > 0.5 else d / (v_max + v_min);
		switch {
		case v_max == r:
			h = (g - b) / d + (6.0 if g < b else 0.0);
		case v_max == g:
			h = (b - r) / d + 2.0;
		case v_max == b:
			h = (r - g) / d + 4.0;
		}

		h *= 1.0/6.0;
	}

	return {h, s, l, a};
}
vector4_rgb_to_hsl :: proc{
	vector4_rgb_to_hsl_f16,
	vector4_rgb_to_hsl_f32,
	vector4_rgb_to_hsl_f64,
};



quaternion_angle_axis_f16 :: proc(angle_radians: f16, axis: Vector3f16) -> (q: Quaternionf16) {
	t := angle_radians*0.5;
	v := normalize(axis) * math.sin(t);
	q.x = v.x;
	q.y = v.y;
	q.z = v.z;
	q.w = math.cos(t);
	return;
}
quaternion_angle_axis_f32 :: proc(angle_radians: f32, axis: Vector3f32) -> (q: Quaternionf32) {
	t := angle_radians*0.5;
	v := normalize(axis) * math.sin(t);
	q.x = v.x;
	q.y = v.y;
	q.z = v.z;
	q.w = math.cos(t);
	return;
}
quaternion_angle_axis_f64 :: proc(angle_radians: f64, axis: Vector3f64) -> (q: Quaternionf64) {
	t := angle_radians*0.5;
	v := normalize(axis) * math.sin(t);
	q.x = v.x;
	q.y = v.y;
	q.z = v.z;
	q.w = math.cos(t);
	return;
}
quaternion_angle_axis :: proc{
	quaternion_angle_axis_f16,
	quaternion_angle_axis_f32,
	quaternion_angle_axis_f64,
};

angle_from_quaternion_f16 :: proc(q: Quaternionf16) -> f16 {
	if abs(q.w) > math.SQRT_THREE*0.5 {
		return math.asin(q.x*q.x + q.y*q.y + q.z*q.z) * 2;
	}

	return math.cos(q.x) * 2;
}
angle_from_quaternion_f32 :: proc(q: Quaternionf32) -> f32 {
	if abs(q.w) > math.SQRT_THREE*0.5 {
		return math.asin(q.x*q.x + q.y*q.y + q.z*q.z) * 2;
	}

	return math.cos(q.x) * 2;
}
angle_from_quaternion_f64 :: proc(q: Quaternionf64) -> f64 {
	if abs(q.w) > math.SQRT_THREE*0.5 {
		return math.asin(q.x*q.x + q.y*q.y + q.z*q.z) * 2;
	}

	return math.cos(q.x) * 2;
}
angle_from_quaternion :: proc{
	angle_from_quaternion_f16,
	angle_from_quaternion_f32,
	angle_from_quaternion_f64,
};

axis_from_quaternion_f16 :: proc(q: Quaternionf16) -> Vector3f16 {
	t1 := 1 - q.w*q.w;
	if t1 < 0 {
		return {0, 0, 1};
	}
	t2 := 1.0 / math.sqrt(t1);
	return {q.x*t2, q.y*t2, q.z*t2};
}
axis_from_quaternion_f32 :: proc(q: Quaternionf32) -> Vector3f32 {
	t1 := 1 - q.w*q.w;
	if t1 < 0 {
		return {0, 0, 1};
	}
	t2 := 1.0 / math.sqrt(t1);
	return {q.x*t2, q.y*t2, q.z*t2};
}
axis_from_quaternion_f64 :: proc(q: Quaternionf64) -> Vector3f64 {
	t1 := 1 - q.w*q.w;
	if t1 < 0 {
		return {0, 0, 1};
	}
	t2 := 1.0 / math.sqrt(t1);
	return {q.x*t2, q.y*t2, q.z*t2};
}
axis_from_quaternion :: proc{
	axis_from_quaternion_f16,
	axis_from_quaternion_f32,
	axis_from_quaternion_f64,
};


angle_axis_from_quaternion_f16 :: proc(q: Quaternionf16) -> (angle: f16, axis: Vector3f16) {
	angle = angle_from_quaternion(q);
	axis  = axis_from_quaternion(q);
	return;
}
angle_axis_from_quaternion_f32 :: proc(q: Quaternionf32) -> (angle: f32, axis: Vector3f32) {
	angle = angle_from_quaternion(q);
	axis  = axis_from_quaternion(q);
	return;
}
angle_axis_from_quaternion_f64 :: proc(q: Quaternionf64) -> (angle: f64, axis: Vector3f64) {
	angle = angle_from_quaternion(q);
	axis  = axis_from_quaternion(q);
	return;
}
angle_axis_from_quaternion :: proc {
	angle_axis_from_quaternion_f16,
	angle_axis_from_quaternion_f32,
	angle_axis_from_quaternion_f64,
};


quaternion_from_forward_and_up_f16 :: proc(forward, up: Vector3f16) -> Quaternionf16 {
	f := normalize(forward);
	s := normalize(cross(f, up));
	u := cross(s, f);
	m := Matrix3f16{
		{+s.x, +u.x, -f.x},
		{+s.y, +u.y, -f.y},
		{+s.z, +u.z, -f.z},
	};

	tr := trace(m);

	q: Quaternionf16;

	switch {
	case tr > 0:
		S := 2 * math.sqrt(1 + tr);
		q.w = 0.25 * S;
		q.x = (m[2][1] - m[1][2]) / S;
		q.y = (m[0][2] - m[2][0]) / S;
		q.z = (m[1][0] - m[0][1]) / S;
	case (m[0][0] > m[1][1]) && (m[0][0] > m[2][2]):
		S := 2 * math.sqrt(1 + m[0][0] - m[1][1] - m[2][2]);
		q.w = (m[2][1] - m[1][2]) / S;
		q.x = 0.25 * S;
		q.y = (m[0][1] + m[1][0]) / S;
		q.z = (m[0][2] + m[2][0]) / S;
	case m[1][1] > m[2][2]:
		S := 2 * math.sqrt(1 + m[1][1] - m[0][0] - m[2][2]);
		q.w = (m[0][2] - m[2][0]) / S;
		q.x = (m[0][1] + m[1][0]) / S;
		q.y = 0.25 * S;
		q.z = (m[1][2] + m[2][1]) / S;
	case:
		S := 2 * math.sqrt(1 + m[2][2] - m[0][0] - m[1][1]);
		q.w = (m[1][0] - m[0][1]) / S;
		q.x = (m[0][2] - m[2][0]) / S;
		q.y = (m[1][2] + m[2][1]) / S;
		q.z = 0.25 * S;
	}

	return normalize(q);
}
quaternion_from_forward_and_up_f32 :: proc(forward, up: Vector3f32) -> Quaternionf32 {
	f := normalize(forward);
	s := normalize(cross(f, up));
	u := cross(s, f);
	m := Matrix3f32{
		{+s.x, +u.x, -f.x},
		{+s.y, +u.y, -f.y},
		{+s.z, +u.z, -f.z},
	};

	tr := trace(m);

	q: Quaternionf32;

	switch {
	case tr > 0:
		S := 2 * math.sqrt(1 + tr);
		q.w = 0.25 * S;
		q.x = (m[2][1] - m[1][2]) / S;
		q.y = (m[0][2] - m[2][0]) / S;
		q.z = (m[1][0] - m[0][1]) / S;
	case (m[0][0] > m[1][1]) && (m[0][0] > m[2][2]):
		S := 2 * math.sqrt(1 + m[0][0] - m[1][1] - m[2][2]);
		q.w = (m[2][1] - m[1][2]) / S;
		q.x = 0.25 * S;
		q.y = (m[0][1] + m[1][0]) / S;
		q.z = (m[0][2] + m[2][0]) / S;
	case m[1][1] > m[2][2]:
		S := 2 * math.sqrt(1 + m[1][1] - m[0][0] - m[2][2]);
		q.w = (m[0][2] - m[2][0]) / S;
		q.x = (m[0][1] + m[1][0]) / S;
		q.y = 0.25 * S;
		q.z = (m[1][2] + m[2][1]) / S;
	case:
		S := 2 * math.sqrt(1 + m[2][2] - m[0][0] - m[1][1]);
		q.w = (m[1][0] - m[0][1]) / S;
		q.x = (m[0][2] - m[2][0]) / S;
		q.y = (m[1][2] + m[2][1]) / S;
		q.z = 0.25 * S;
	}

	return normalize(q);
}
quaternion_from_forward_and_up_f64 :: proc(forward, up: Vector3f64) -> Quaternionf64 {
	f := normalize(forward);
	s := normalize(cross(f, up));
	u := cross(s, f);
	m := Matrix3f64{
		{+s.x, +u.x, -f.x},
		{+s.y, +u.y, -f.y},
		{+s.z, +u.z, -f.z},
	};

	tr := trace(m);

	q: Quaternionf64;

	switch {
	case tr > 0:
		S := 2 * math.sqrt(1 + tr);
		q.w = 0.25 * S;
		q.x = (m[2][1] - m[1][2]) / S;
		q.y = (m[0][2] - m[2][0]) / S;
		q.z = (m[1][0] - m[0][1]) / S;
	case (m[0][0] > m[1][1]) && (m[0][0] > m[2][2]):
		S := 2 * math.sqrt(1 + m[0][0] - m[1][1] - m[2][2]);
		q.w = (m[2][1] - m[1][2]) / S;
		q.x = 0.25 * S;
		q.y = (m[0][1] + m[1][0]) / S;
		q.z = (m[0][2] + m[2][0]) / S;
	case m[1][1] > m[2][2]:
		S := 2 * math.sqrt(1 + m[1][1] - m[0][0] - m[2][2]);
		q.w = (m[0][2] - m[2][0]) / S;
		q.x = (m[0][1] + m[1][0]) / S;
		q.y = 0.25 * S;
		q.z = (m[1][2] + m[2][1]) / S;
	case:
		S := 2 * math.sqrt(1 + m[2][2] - m[0][0] - m[1][1]);
		q.w = (m[1][0] - m[0][1]) / S;
		q.x = (m[0][2] - m[2][0]) / S;
		q.y = (m[1][2] + m[2][1]) / S;
		q.z = 0.25 * S;
	}

	return normalize(q);
}
quaternion_from_forward_and_up :: proc{
	quaternion_from_forward_and_up_f16,
	quaternion_from_forward_and_up_f32,
	quaternion_from_forward_and_up_f64,
};

quaternion_look_at_f16 :: proc(eye, centre: Vector3f16, up: Vector3f16) -> Quaternionf16 {
	return quaternion_from_matrix3(matrix3_look_at(eye, centre, up));
}
quaternion_look_at_f32 :: proc(eye, centre: Vector3f32, up: Vector3f32) -> Quaternionf32 {
	return quaternion_from_matrix3(matrix3_look_at(eye, centre, up));
}
quaternion_look_at_f64 :: proc(eye, centre: Vector3f64, up: Vector3f64) -> Quaternionf64 {
	return quaternion_from_matrix3(matrix3_look_at(eye, centre, up));
}
quaternion_look_at :: proc{
	quaternion_look_at_f16,
	quaternion_look_at_f32,
	quaternion_look_at_f64,
};



quaternion_nlerp_f16 :: proc(a, b: Quaternionf16, t: f16) -> (c: Quaternionf16) {
	c.x = a.x + (b.x-a.x)*t;
	c.y = a.y + (b.y-a.y)*t;
	c.z = a.z + (b.z-a.z)*t;
	c.w = a.w + (b.w-a.w)*t;
	return normalize(c);
}
quaternion_nlerp_f32 :: proc(a, b: Quaternionf32, t: f32) -> (c: Quaternionf32) {
	c.x = a.x + (b.x-a.x)*t;
	c.y = a.y + (b.y-a.y)*t;
	c.z = a.z + (b.z-a.z)*t;
	c.w = a.w + (b.w-a.w)*t;
	return normalize(c);
}
quaternion_nlerp_f64 :: proc(a, b: Quaternionf64, t: f64) -> (c: Quaternionf64) {
	c.x = a.x + (b.x-a.x)*t;
	c.y = a.y + (b.y-a.y)*t;
	c.z = a.z + (b.z-a.z)*t;
	c.w = a.w + (b.w-a.w)*t;
	return normalize(c);
}
quaternion_nlerp :: proc{
	quaternion_nlerp_f16,
	quaternion_nlerp_f32,
	quaternion_nlerp_f64,
};


quaternion_slerp_f16 :: proc(x, y: Quaternionf16, t: f16) -> (q: Quaternionf16) {
	a, b := x, y;
	cos_angle := dot(a, b);
	if cos_angle < 0 {
		b = -b;
		cos_angle = -cos_angle;
	}
	if cos_angle > 1 - F32_EPSILON {
		q.x = a.x + (b.x-a.x)*t;
		q.y = a.y + (b.y-a.y)*t;
		q.z = a.z + (b.z-a.z)*t;
		q.w = a.w + (b.w-a.w)*t;
		return;
	}

	angle := math.acos(cos_angle);
	sin_angle := math.sin(angle);
	factor_a := math.sin((1-t) * angle) / sin_angle;
	factor_b := math.sin(t * angle)     / sin_angle;


	q.x = factor_a * a.x + factor_b * b.x;
	q.y = factor_a * a.y + factor_b * b.y;
	q.z = factor_a * a.z + factor_b * b.z;
	q.w = factor_a * a.w + factor_b * b.w;
	return;
}
quaternion_slerp_f32 :: proc(x, y: Quaternionf32, t: f32) -> (q: Quaternionf32) {
	a, b := x, y;
	cos_angle := dot(a, b);
	if cos_angle < 0 {
		b = -b;
		cos_angle = -cos_angle;
	}
	if cos_angle > 1 - F32_EPSILON {
		q.x = a.x + (b.x-a.x)*t;
		q.y = a.y + (b.y-a.y)*t;
		q.z = a.z + (b.z-a.z)*t;
		q.w = a.w + (b.w-a.w)*t;
		return;
	}

	angle := math.acos(cos_angle);
	sin_angle := math.sin(angle);
	factor_a := math.sin((1-t) * angle) / sin_angle;
	factor_b := math.sin(t * angle)     / sin_angle;


	q.x = factor_a * a.x + factor_b * b.x;
	q.y = factor_a * a.y + factor_b * b.y;
	q.z = factor_a * a.z + factor_b * b.z;
	q.w = factor_a * a.w + factor_b * b.w;
	return;
}
quaternion_slerp_f64 :: proc(x, y: Quaternionf64, t: f64) -> (q: Quaternionf64) {
	a, b := x, y;
	cos_angle := dot(a, b);
	if cos_angle < 0 {
		b = -b;
		cos_angle = -cos_angle;
	}
	if cos_angle > 1 - F64_EPSILON {
		q.x = a.x + (b.x-a.x)*t;
		q.y = a.y + (b.y-a.y)*t;
		q.z = a.z + (b.z-a.z)*t;
		q.w = a.w + (b.w-a.w)*t;
		return;
	}

	angle := math.acos(cos_angle);
	sin_angle := math.sin(angle);
	factor_a := math.sin((1-t) * angle) / sin_angle;
	factor_b := math.sin(t * angle)     / sin_angle;


	q.x = factor_a * a.x + factor_b * b.x;
	q.y = factor_a * a.y + factor_b * b.y;
	q.z = factor_a * a.z + factor_b * b.z;
	q.w = factor_a * a.w + factor_b * b.w;
	return;
}
quaternion_slerp :: proc{
	quaternion_slerp_f16,
	quaternion_slerp_f32,
	quaternion_slerp_f64,
};


quaternion_squad_f16 :: proc(q1, q2, s1, s2: Quaternionf16, h: f16) -> Quaternionf16 {
	slerp :: quaternion_slerp;
	return slerp(slerp(q1, q2, h), slerp(s1, s2, h), 2 * (1 - h) * h);
}
quaternion_squad_f32 :: proc(q1, q2, s1, s2: Quaternionf32, h: f32) -> Quaternionf32 {
	slerp :: quaternion_slerp;
	return slerp(slerp(q1, q2, h), slerp(s1, s2, h), 2 * (1 - h) * h);
}
quaternion_squad_f64 :: proc(q1, q2, s1, s2: Quaternionf64, h: f64) -> Quaternionf64 {
	slerp :: quaternion_slerp;
	return slerp(slerp(q1, q2, h), slerp(s1, s2, h), 2 * (1 - h) * h);
}
quaternion_squad :: proc{
	quaternion_squad_f16,
	quaternion_squad_f32,
	quaternion_squad_f64,
};


quaternion_from_matrix4_f16 :: proc(m: Matrix4f16) -> (q: Quaternionf16) {
	m3: Matrix3f16 = ---;
	m3[0][0], m3[0][1], m3[0][2] = m[0][0], m[0][1], m[0][2];
	m3[1][0], m3[1][1], m3[1][2] = m[1][0], m[1][1], m[1][2];
	m3[2][0], m3[2][1], m3[2][2] = m[2][0], m[2][1], m[2][2];
	return quaternion_from_matrix3(m3);
}
quaternion_from_matrix4_f32 :: proc(m: Matrix4f32) -> (q: Quaternionf32) {
	m3: Matrix3f32 = ---;
	m3[0][0], m3[0][1], m3[0][2] = m[0][0], m[0][1], m[0][2];
	m3[1][0], m3[1][1], m3[1][2] = m[1][0], m[1][1], m[1][2];
	m3[2][0], m3[2][1], m3[2][2] = m[2][0], m[2][1], m[2][2];
	return quaternion_from_matrix3(m3);
}
quaternion_from_matrix4_f64 :: proc(m: Matrix4f64) -> (q: Quaternionf64) {
	m3: Matrix3f64 = ---;
	m3[0][0], m3[0][1], m3[0][2] = m[0][0], m[0][1], m[0][2];
	m3[1][0], m3[1][1], m3[1][2] = m[1][0], m[1][1], m[1][2];
	m3[2][0], m3[2][1], m3[2][2] = m[2][0], m[2][1], m[2][2];
	return quaternion_from_matrix3(m3);
}
quaternion_from_matrix4 :: proc{
	quaternion_from_matrix4_f16,
	quaternion_from_matrix4_f32,
	quaternion_from_matrix4_f64,
};


quaternion_from_matrix3_f16 :: proc(m: Matrix3f16) -> (q: Quaternionf16) {
	four_x_squared_minus_1 := m[0][0] - m[1][1] - m[2][2];
	four_y_squared_minus_1 := m[1][1] - m[0][0] - m[2][2];
	four_z_squared_minus_1 := m[2][2] - m[0][0] - m[1][1];
	four_w_squared_minus_1 := m[0][0] + m[1][1] + m[2][2];

	biggest_index := 0;
	four_biggest_squared_minus_1 := four_w_squared_minus_1;
	if four_x_squared_minus_1 > four_biggest_squared_minus_1 {
		four_biggest_squared_minus_1 = four_x_squared_minus_1;
		biggest_index = 1;
	}
	if four_y_squared_minus_1 > four_biggest_squared_minus_1 {
		four_biggest_squared_minus_1 = four_y_squared_minus_1;
		biggest_index = 2;
	}
	if four_z_squared_minus_1 > four_biggest_squared_minus_1 {
		four_biggest_squared_minus_1 = four_z_squared_minus_1;
		biggest_index = 3;
	}

	biggest_val := math.sqrt(four_biggest_squared_minus_1 + 1) * 0.5;
	mult := 0.25 / biggest_val;

	q = 1;
	switch biggest_index {
	case 0:
		q.w = biggest_val;
		q.x = (m[1][2] - m[2][1]) * mult;
		q.y = (m[2][0] - m[0][2]) * mult;
		q.z = (m[0][1] - m[1][0]) * mult;
	case 1:
		q.w = (m[1][2] - m[2][1]) * mult;
		q.x = biggest_val;
		q.y = (m[0][1] + m[1][0]) * mult;
		q.z = (m[2][0] + m[0][2]) * mult;
	case 2:
		q.w = (m[2][0] - m[0][2]) * mult;
		q.x = (m[0][1] + m[1][0]) * mult;
		q.y = biggest_val;
		q.z = (m[1][2] + m[2][1]) * mult;
	case 3:
		q.w = (m[0][1] - m[1][0]) * mult;
		q.x = (m[2][0] + m[0][2]) * mult;
		q.y = (m[1][2] + m[2][1]) * mult;
		q.z = biggest_val;
	}
	return;
}
quaternion_from_matrix3_f32 :: proc(m: Matrix3f32) -> (q: Quaternionf32) {
	four_x_squared_minus_1 := m[0][0] - m[1][1] - m[2][2];
	four_y_squared_minus_1 := m[1][1] - m[0][0] - m[2][2];
	four_z_squared_minus_1 := m[2][2] - m[0][0] - m[1][1];
	four_w_squared_minus_1 := m[0][0] + m[1][1] + m[2][2];

	biggest_index := 0;
	four_biggest_squared_minus_1 := four_w_squared_minus_1;
	if four_x_squared_minus_1 > four_biggest_squared_minus_1 {
		four_biggest_squared_minus_1 = four_x_squared_minus_1;
		biggest_index = 1;
	}
	if four_y_squared_minus_1 > four_biggest_squared_minus_1 {
		four_biggest_squared_minus_1 = four_y_squared_minus_1;
		biggest_index = 2;
	}
	if four_z_squared_minus_1 > four_biggest_squared_minus_1 {
		four_biggest_squared_minus_1 = four_z_squared_minus_1;
		biggest_index = 3;
	}

	biggest_val := math.sqrt(four_biggest_squared_minus_1 + 1) * 0.5;
	mult := 0.25 / biggest_val;

	q = 1;
	switch biggest_index {
	case 0:
		q.w = biggest_val;
		q.x = (m[1][2] - m[2][1]) * mult;
		q.y = (m[2][0] - m[0][2]) * mult;
		q.z = (m[0][1] - m[1][0]) * mult;
	case 1:
		q.w = (m[1][2] - m[2][1]) * mult;
		q.x = biggest_val;
		q.y = (m[0][1] + m[1][0]) * mult;
		q.z = (m[2][0] + m[0][2]) * mult;
	case 2:
		q.w = (m[2][0] - m[0][2]) * mult;
		q.x = (m[0][1] + m[1][0]) * mult;
		q.y = biggest_val;
		q.z = (m[1][2] + m[2][1]) * mult;
	case 3:
		q.w = (m[0][1] - m[1][0]) * mult;
		q.x = (m[2][0] + m[0][2]) * mult;
		q.y = (m[1][2] + m[2][1]) * mult;
		q.z = biggest_val;
	}
	return;
}
quaternion_from_matrix3_f64 :: proc(m: Matrix3f64) -> (q: Quaternionf64) {
	four_x_squared_minus_1 := m[0][0] - m[1][1] - m[2][2];
	four_y_squared_minus_1 := m[1][1] - m[0][0] - m[2][2];
	four_z_squared_minus_1 := m[2][2] - m[0][0] - m[1][1];
	four_w_squared_minus_1 := m[0][0] + m[1][1] + m[2][2];

	biggest_index := 0;
	four_biggest_squared_minus_1 := four_w_squared_minus_1;
	if four_x_squared_minus_1 > four_biggest_squared_minus_1 {
		four_biggest_squared_minus_1 = four_x_squared_minus_1;
		biggest_index = 1;
	}
	if four_y_squared_minus_1 > four_biggest_squared_minus_1 {
		four_biggest_squared_minus_1 = four_y_squared_minus_1;
		biggest_index = 2;
	}
	if four_z_squared_minus_1 > four_biggest_squared_minus_1 {
		four_biggest_squared_minus_1 = four_z_squared_minus_1;
		biggest_index = 3;
	}

	biggest_val := math.sqrt(four_biggest_squared_minus_1 + 1) * 0.5;
	mult := 0.25 / biggest_val;

	q = 1;
	switch biggest_index {
	case 0:
		q.w = biggest_val;
		q.x = (m[1][2] - m[2][1]) * mult;
		q.y = (m[2][0] - m[0][2]) * mult;
		q.z = (m[0][1] - m[1][0]) * mult;
	case 1:
		q.w = (m[1][2] - m[2][1]) * mult;
		q.x = biggest_val;
		q.y = (m[0][1] + m[1][0]) * mult;
		q.z = (m[2][0] + m[0][2]) * mult;
	case 2:
		q.w = (m[2][0] - m[0][2]) * mult;
		q.x = (m[0][1] + m[1][0]) * mult;
		q.y = biggest_val;
		q.z = (m[1][2] + m[2][1]) * mult;
	case 3:
		q.w = (m[0][1] - m[1][0]) * mult;
		q.x = (m[2][0] + m[0][2]) * mult;
		q.y = (m[1][2] + m[2][1]) * mult;
		q.z = biggest_val;
	}
	return;
}
quaternion_from_matrix3 :: proc{
	quaternion_from_matrix3_f16,
	quaternion_from_matrix3_f32,
	quaternion_from_matrix3_f64,
};


quaternion_between_two_vector3_f16 :: proc(from, to: Vector3f16) -> (q: Quaternionf16) {
	x := normalize(from);
	y := normalize(to);

	cos_theta := dot(x, y);
	if abs(cos_theta + 1) < 2*F32_EPSILON {
		v := vector3_orthogonal(x);
		q.x = v.x;
		q.y = v.y;
		q.z = v.z;
		q.w = 0;
		return;
	}
	v := cross(x, y);
	w := cos_theta + 1;
	q.w = w;
	q.x = v.x;
	q.y = v.y;
	q.z = v.z;
	return normalize(q);
}
quaternion_between_two_vector3_f32 :: proc(from, to: Vector3f32) -> (q: Quaternionf32) {
	x := normalize(from);
	y := normalize(to);

	cos_theta := dot(x, y);
	if abs(cos_theta + 1) < 2*F32_EPSILON {
		v := vector3_orthogonal(x);
		q.x = v.x;
		q.y = v.y;
		q.z = v.z;
		q.w = 0;
		return;
	}
	v := cross(x, y);
	w := cos_theta + 1;
	q.w = w;
	q.x = v.x;
	q.y = v.y;
	q.z = v.z;
	return normalize(q);
}
quaternion_between_two_vector3_f64 :: proc(from, to: Vector3f64) -> (q: Quaternionf64) {
	x := normalize(from);
	y := normalize(to);

	cos_theta := dot(x, y);
	if abs(cos_theta + 1) < 2*F64_EPSILON {
		v := vector3_orthogonal(x);
		q.x = v.x;
		q.y = v.y;
		q.z = v.z;
		q.w = 0;
		return;
	}
	v := cross(x, y);
	w := cos_theta + 1;
	q.w = w;
	q.x = v.x;
	q.y = v.y;
	q.z = v.z;
	return normalize(q);
}
quaternion_between_two_vector3 :: proc{
	quaternion_between_two_vector3_f16,
	quaternion_between_two_vector3_f32,
	quaternion_between_two_vector3_f64,
};


matrix2_inverse_transpose_f16 :: proc(m: Matrix2f16) -> (c: Matrix2f16) {
	d := m[0][0]*m[1][1] - m[1][0]*m[0][1];
	id := 1.0/d;
	c[0][0] = +m[1][1] * id;
	c[0][1] = -m[0][1] * id;
	c[1][0] = -m[1][0] * id;
	c[1][1] = +m[0][0] * id;
	return c;
}
matrix2_inverse_transpose_f32 :: proc(m: Matrix2f32) -> (c: Matrix2f32) {
	d := m[0][0]*m[1][1] - m[1][0]*m[0][1];
	id := 1.0/d;
	c[0][0] = +m[1][1] * id;
	c[0][1] = -m[0][1] * id;
	c[1][0] = -m[1][0] * id;
	c[1][1] = +m[0][0] * id;
	return c;
}
matrix2_inverse_transpose_f64 :: proc(m: Matrix2f64) -> (c: Matrix2f64) {
	d := m[0][0]*m[1][1] - m[1][0]*m[0][1];
	id := 1.0/d;
	c[0][0] = +m[1][1] * id;
	c[0][1] = -m[0][1] * id;
	c[1][0] = -m[1][0] * id;
	c[1][1] = +m[0][0] * id;
	return c;
}
matrix2_inverse_transpose :: proc{
	matrix2_inverse_transpose_f16,
	matrix2_inverse_transpose_f32,
	matrix2_inverse_transpose_f64,
};


matrix2_determinant_f16 :: proc(m: Matrix2f16) -> f16 {
	return m[0][0]*m[1][1] - m[1][0]*m[0][1];
}
matrix2_determinant_f32 :: proc(m: Matrix2f32) -> f32 {
	return m[0][0]*m[1][1] - m[1][0]*m[0][1];
}
matrix2_determinant_f64 :: proc(m: Matrix2f64) -> f64 {
	return m[0][0]*m[1][1] - m[1][0]*m[0][1];
}
matrix2_determinant :: proc{
	matrix2_determinant_f16,
	matrix2_determinant_f32,
	matrix2_determinant_f64,
};


matrix2_inverse_f16 :: proc(m: Matrix2f16) -> (c: Matrix2f16) {
	d := m[0][0]*m[1][1] - m[1][0]*m[0][1];
	id := 1.0/d;
	c[0][0] = +m[1][1] * id;
	c[1][0] = -m[0][1] * id;
	c[0][1] = -m[1][0] * id;
	c[1][1] = +m[0][0] * id;
	return c;
}
matrix2_inverse_f32 :: proc(m: Matrix2f32) -> (c: Matrix2f32) {
	d := m[0][0]*m[1][1] - m[1][0]*m[0][1];
	id := 1.0/d;
	c[0][0] = +m[1][1] * id;
	c[1][0] = -m[0][1] * id;
	c[0][1] = -m[1][0] * id;
	c[1][1] = +m[0][0] * id;
	return c;
}
matrix2_inverse_f64 :: proc(m: Matrix2f64) -> (c: Matrix2f64) {
	d := m[0][0]*m[1][1] - m[1][0]*m[0][1];
	id := 1.0/d;
	c[0][0] = +m[1][1] * id;
	c[1][0] = -m[0][1] * id;
	c[0][1] = -m[1][0] * id;
	c[1][1] = +m[0][0] * id;
	return c;
}
matrix2_inverse :: proc{
	matrix2_inverse_f16,
	matrix2_inverse_f32,
	matrix2_inverse_f64,
};


matrix2_adjoint_f16 :: proc(m: Matrix2f16) -> (c: Matrix2f16) {
	c[0][0] = +m[1][1];
	c[0][1] = -m[1][0];
	c[1][0] = -m[0][1];
	c[1][1] = +m[0][0];
	return c;
}
matrix2_adjoint_f32 :: proc(m: Matrix2f32) -> (c: Matrix2f32) {
	c[0][0] = +m[1][1];
	c[0][1] = -m[1][0];
	c[1][0] = -m[0][1];
	c[1][1] = +m[0][0];
	return c;
}
matrix2_adjoint_f64 :: proc(m: Matrix2f64) -> (c: Matrix2f64) {
	c[0][0] = +m[1][1];
	c[0][1] = -m[1][0];
	c[1][0] = -m[0][1];
	c[1][1] = +m[0][0];
	return c;
}
matrix2_adjoint :: proc{
	matrix2_adjoint_f16,
	matrix2_adjoint_f32,
	matrix2_adjoint_f64,
};


matrix3_from_quaternion_f16 :: proc(q: Quaternionf16) -> (m: Matrix3f16) {
	qxx := q.x * q.x;
	qyy := q.y * q.y;
	qzz := q.z * q.z;
	qxz := q.x * q.z;
	qxy := q.x * q.y;
	qyz := q.y * q.z;
	qwx := q.w * q.x;
	qwy := q.w * q.y;
	qwz := q.w * q.z;

	m[0][0] = 1 - 2 * (qyy + qzz);
	m[0][1] = 2 * (qxy + qwz);
	m[0][2] = 2 * (qxz - qwy);

	m[1][0] = 2 * (qxy - qwz);
	m[1][1] = 1 - 2 * (qxx + qzz);
	m[1][2] = 2 * (qyz + qwx);

	m[2][0] = 2 * (qxz + qwy);
	m[2][1] = 2 * (qyz - qwx);
	m[2][2] = 1 - 2 * (qxx + qyy);
	return m;
}
matrix3_from_quaternion_f32 :: proc(q: Quaternionf32) -> (m: Matrix3f32) {
	qxx := q.x * q.x;
	qyy := q.y * q.y;
	qzz := q.z * q.z;
	qxz := q.x * q.z;
	qxy := q.x * q.y;
	qyz := q.y * q.z;
	qwx := q.w * q.x;
	qwy := q.w * q.y;
	qwz := q.w * q.z;

	m[0][0] = 1 - 2 * (qyy + qzz);
	m[0][1] = 2 * (qxy + qwz);
	m[0][2] = 2 * (qxz - qwy);

	m[1][0] = 2 * (qxy - qwz);
	m[1][1] = 1 - 2 * (qxx + qzz);
	m[1][2] = 2 * (qyz + qwx);

	m[2][0] = 2 * (qxz + qwy);
	m[2][1] = 2 * (qyz - qwx);
	m[2][2] = 1 - 2 * (qxx + qyy);
	return m;
}
matrix3_from_quaternion_f64 :: proc(q: Quaternionf64) -> (m: Matrix3f64) {
	qxx := q.x * q.x;
	qyy := q.y * q.y;
	qzz := q.z * q.z;
	qxz := q.x * q.z;
	qxy := q.x * q.y;
	qyz := q.y * q.z;
	qwx := q.w * q.x;
	qwy := q.w * q.y;
	qwz := q.w * q.z;

	m[0][0] = 1 - 2 * (qyy + qzz);
	m[0][1] = 2 * (qxy + qwz);
	m[0][2] = 2 * (qxz - qwy);

	m[1][0] = 2 * (qxy - qwz);
	m[1][1] = 1 - 2 * (qxx + qzz);
	m[1][2] = 2 * (qyz + qwx);

	m[2][0] = 2 * (qxz + qwy);
	m[2][1] = 2 * (qyz - qwx);
	m[2][2] = 1 - 2 * (qxx + qyy);
	return m;
}
matrix3_from_quaternion :: proc{
	matrix3_from_quaternion_f16,
	matrix3_from_quaternion_f32,
	matrix3_from_quaternion_f64,
};


matrix3_inverse_f16 :: proc(m: Matrix3f16) -> Matrix3f16 {
	return transpose(matrix3_inverse_transpose(m));
}
matrix3_inverse_f32 :: proc(m: Matrix3f32) -> Matrix3f32 {
	return transpose(matrix3_inverse_transpose(m));
}
matrix3_inverse_f64 :: proc(m: Matrix3f64) -> Matrix3f64 {
	return transpose(matrix3_inverse_transpose(m));
}
matrix3_inverse :: proc{
	matrix3_inverse_f16,
	matrix3_inverse_f32,
	matrix3_inverse_f64,
};


matrix3_determinant_f16 :: proc(m: Matrix3f16) -> f16 {
	a := +m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2]);
	b := -m[1][0] * (m[0][1] * m[2][2] - m[2][1] * m[0][2]);
	c := +m[2][0] * (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
	return a + b + c;
}
matrix3_determinant_f32 :: proc(m: Matrix3f32) -> f32 {
	a := +m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2]);
	b := -m[1][0] * (m[0][1] * m[2][2] - m[2][1] * m[0][2]);
	c := +m[2][0] * (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
	return a + b + c;
}
matrix3_determinant_f64 :: proc(m: Matrix3f64) -> f64 {
	a := +m[0][0] * (m[1][1] * m[2][2] - m[2][1] * m[1][2]);
	b := -m[1][0] * (m[0][1] * m[2][2] - m[2][1] * m[0][2]);
	c := +m[2][0] * (m[0][1] * m[1][2] - m[1][1] * m[0][2]);
	return a + b + c;
}
matrix3_determinant :: proc{
	matrix3_determinant_f16,
	matrix3_determinant_f32,
	matrix3_determinant_f64,
};


matrix3_adjoint_f16 :: proc(m: Matrix3f16) -> (adjoint: Matrix3f16) {
	adjoint[0][0] = +(m[1][1] * m[2][2] - m[1][2] * m[2][1]);
	adjoint[1][0] = -(m[0][1] * m[2][2] - m[0][2] * m[2][1]);
	adjoint[2][0] = +(m[0][1] * m[1][2] - m[0][2] * m[1][1]);
	adjoint[0][1] = -(m[1][0] * m[2][2] - m[1][2] * m[2][0]);
	adjoint[1][1] = +(m[0][0] * m[2][2] - m[0][2] * m[2][0]);
	adjoint[2][1] = -(m[0][0] * m[1][2] - m[0][2] * m[1][0]);
	adjoint[0][2] = +(m[1][0] * m[2][1] - m[1][1] * m[2][0]);
	adjoint[1][2] = -(m[0][0] * m[2][1] - m[0][1] * m[2][0]);
	adjoint[2][2] = +(m[0][0] * m[1][1] - m[0][1] * m[1][0]);
	return adjoint;
}
matrix3_adjoint_f32 :: proc(m: Matrix3f32) -> (adjoint: Matrix3f32) {
	adjoint[0][0] = +(m[1][1] * m[2][2] - m[1][2] * m[2][1]);
	adjoint[1][0] = -(m[0][1] * m[2][2] - m[0][2] * m[2][1]);
	adjoint[2][0] = +(m[0][1] * m[1][2] - m[0][2] * m[1][1]);
	adjoint[0][1] = -(m[1][0] * m[2][2] - m[1][2] * m[2][0]);
	adjoint[1][1] = +(m[0][0] * m[2][2] - m[0][2] * m[2][0]);
	adjoint[2][1] = -(m[0][0] * m[1][2] - m[0][2] * m[1][0]);
	adjoint[0][2] = +(m[1][0] * m[2][1] - m[1][1] * m[2][0]);
	adjoint[1][2] = -(m[0][0] * m[2][1] - m[0][1] * m[2][0]);
	adjoint[2][2] = +(m[0][0] * m[1][1] - m[0][1] * m[1][0]);
	return adjoint;
}
matrix3_adjoint_f64 :: proc(m: Matrix3f64) -> (adjoint: Matrix3f64) {
	adjoint[0][0] = +(m[1][1] * m[2][2] - m[1][2] * m[2][1]);
	adjoint[1][0] = -(m[0][1] * m[2][2] - m[0][2] * m[2][1]);
	adjoint[2][0] = +(m[0][1] * m[1][2] - m[0][2] * m[1][1]);
	adjoint[0][1] = -(m[1][0] * m[2][2] - m[1][2] * m[2][0]);
	adjoint[1][1] = +(m[0][0] * m[2][2] - m[0][2] * m[2][0]);
	adjoint[2][1] = -(m[0][0] * m[1][2] - m[0][2] * m[1][0]);
	adjoint[0][2] = +(m[1][0] * m[2][1] - m[1][1] * m[2][0]);
	adjoint[1][2] = -(m[0][0] * m[2][1] - m[0][1] * m[2][0]);
	adjoint[2][2] = +(m[0][0] * m[1][1] - m[0][1] * m[1][0]);
	return adjoint;
}
matrix3_adjoint :: proc{
	matrix3_adjoint_f16,
	matrix3_adjoint_f32,
	matrix3_adjoint_f64,
};



matrix3_inverse_transpose_f16 :: proc(m: Matrix3f16) -> (inverse_transpose: Matrix3f16) {
	adjoint := matrix3_adjoint(m);
	determinant := matrix3_determinant(m);
	inv_determinant := 1.0 / determinant;
	for i in 0..<3 {
		for j in 0..<3 {
			inverse_transpose[i][j] = adjoint[i][j] * inv_determinant;
		}
	}
	return;
}
matrix3_inverse_transpose_f32 :: proc(m: Matrix3f32) -> (inverse_transpose: Matrix3f32) {
	adjoint := matrix3_adjoint(m);
	determinant := matrix3_determinant(m);
	inv_determinant := 1.0 / determinant;
	for i in 0..<3 {
		for j in 0..<3 {
			inverse_transpose[i][j] = adjoint[i][j] * inv_determinant;
		}
	}
	return;
}
matrix3_inverse_transpose_f64 :: proc(m: Matrix3f64) -> (inverse_transpose: Matrix3f64) {
	adjoint := matrix3_adjoint(m);
	determinant := matrix3_determinant(m);
	inv_determinant := 1.0 / determinant;
	for i in 0..<3 {
		for j in 0..<3 {
			inverse_transpose[i][j] = adjoint[i][j] * inv_determinant;
		}
	}
	return;
}
matrix3_inverse_transpose :: proc{
	matrix3_inverse_transpose_f16,
	matrix3_inverse_transpose_f32,
	matrix3_inverse_transpose_f64,
};


matrix3_scale_f16 :: proc(s: Vector3f16) -> (m: Matrix3f16) {
	m[0][0] = s[0];
	m[1][1] = s[1];
	m[2][2] = s[2];
	return m;
}
matrix3_scale_f32 :: proc(s: Vector3f32) -> (m: Matrix3f32) {
	m[0][0] = s[0];
	m[1][1] = s[1];
	m[2][2] = s[2];
	return m;
}
matrix3_scale_f64 :: proc(s: Vector3f64) -> (m: Matrix3f64) {
	m[0][0] = s[0];
	m[1][1] = s[1];
	m[2][2] = s[2];
	return m;
}
matrix3_scale :: proc{
	matrix3_scale_f16,
	matrix3_scale_f32,
	matrix3_scale_f64,
};


matrix3_rotate_f16 :: proc(angle_radians: f16, v: Vector3f16) -> (rot: Matrix3f16) {
	c := math.cos(angle_radians);
	s := math.sin(angle_radians);

	a := normalize(v);
	t := a * (1-c);

	rot[0][0] = c + t[0]*a[0];
	rot[0][1] = 0 + t[0]*a[1] + s*a[2];
	rot[0][2] = 0 + t[0]*a[2] - s*a[1];

	rot[1][0] = 0 + t[1]*a[0] - s*a[2];
	rot[1][1] = c + t[1]*a[1];
	rot[1][2] = 0 + t[1]*a[2] + s*a[0];

	rot[2][0] = 0 + t[2]*a[0] + s*a[1];
	rot[2][1] = 0 + t[2]*a[1] - s*a[0];
	rot[2][2] = c + t[2]*a[2];

	return rot;
}
matrix3_rotate_f32 :: proc(angle_radians: f32, v: Vector3f32) -> (rot: Matrix3f32) {
	c := math.cos(angle_radians);
	s := math.sin(angle_radians);

	a := normalize(v);
	t := a * (1-c);

	rot[0][0] = c + t[0]*a[0];
	rot[0][1] = 0 + t[0]*a[1] + s*a[2];
	rot[0][2] = 0 + t[0]*a[2] - s*a[1];

	rot[1][0] = 0 + t[1]*a[0] - s*a[2];
	rot[1][1] = c + t[1]*a[1];
	rot[1][2] = 0 + t[1]*a[2] + s*a[0];

	rot[2][0] = 0 + t[2]*a[0] + s*a[1];
	rot[2][1] = 0 + t[2]*a[1] - s*a[0];
	rot[2][2] = c + t[2]*a[2];

	return rot;
}
matrix3_rotate_f64 :: proc(angle_radians: f64, v: Vector3f64) -> (rot: Matrix3f64) {
	c := math.cos(angle_radians);
	s := math.sin(angle_radians);

	a := normalize(v);
	t := a * (1-c);

	rot[0][0] = c + t[0]*a[0];
	rot[0][1] = 0 + t[0]*a[1] + s*a[2];
	rot[0][2] = 0 + t[0]*a[2] - s*a[1];

	rot[1][0] = 0 + t[1]*a[0] - s*a[2];
	rot[1][1] = c + t[1]*a[1];
	rot[1][2] = 0 + t[1]*a[2] + s*a[0];

	rot[2][0] = 0 + t[2]*a[0] + s*a[1];
	rot[2][1] = 0 + t[2]*a[1] - s*a[0];
	rot[2][2] = c + t[2]*a[2];

	return rot;
}
matrix3_rotate :: proc{
	matrix3_rotate_f16,
	matrix3_rotate_f32,
	matrix3_rotate_f64,
};


matrix3_look_at_f16 :: proc(eye, centre, up: Vector3f16) -> Matrix3f16 {
	f := normalize(centre - eye);
	s := normalize(cross(f, up));
	u := cross(s, f);
	return Matrix3f16{
		{+s.x, +u.x, -f.x},
		{+s.y, +u.y, -f.y},
		{+s.z, +u.z, -f.z},
	};
}
matrix3_look_at_f32 :: proc(eye, centre, up: Vector3f32) -> Matrix3f32 {
	f := normalize(centre - eye);
	s := normalize(cross(f, up));
	u := cross(s, f);
	return Matrix3f32{
		{+s.x, +u.x, -f.x},
		{+s.y, +u.y, -f.y},
		{+s.z, +u.z, -f.z},
	};
}
matrix3_look_at_f64 :: proc(eye, centre, up: Vector3f64) -> Matrix3f64 {
	f := normalize(centre - eye);
	s := normalize(cross(f, up));
	u := cross(s, f);
	return Matrix3f64{
		{+s.x, +u.x, -f.x},
		{+s.y, +u.y, -f.y},
		{+s.z, +u.z, -f.z},
	};
}
matrix3_look_at :: proc{
	matrix3_look_at_f16,
	matrix3_look_at_f32,
	matrix3_look_at_f64,
};


matrix4_from_quaternion_f16 :: proc(q: Quaternionf16) -> (m: Matrix4f16) {
	qxx := q.x * q.x;
	qyy := q.y * q.y;
	qzz := q.z * q.z;
	qxz := q.x * q.z;
	qxy := q.x * q.y;
	qyz := q.y * q.z;
	qwx := q.w * q.x;
	qwy := q.w * q.y;
	qwz := q.w * q.z;

	m[0][0] = 1 - 2 * (qyy + qzz);
	m[0][1] = 2 * (qxy + qwz);
	m[0][2] = 2 * (qxz - qwy);

	m[1][0] = 2 * (qxy - qwz);
	m[1][1] = 1 - 2 * (qxx + qzz);
	m[1][2] = 2 * (qyz + qwx);

	m[2][0] = 2 * (qxz + qwy);
	m[2][1] = 2 * (qyz - qwx);
	m[2][2] = 1 - 2 * (qxx + qyy);

	m[3][3] = 1;

	return m;
}
matrix4_from_quaternion_f32 :: proc(q: Quaternionf32) -> (m: Matrix4f32) {
	qxx := q.x * q.x;
	qyy := q.y * q.y;
	qzz := q.z * q.z;
	qxz := q.x * q.z;
	qxy := q.x * q.y;
	qyz := q.y * q.z;
	qwx := q.w * q.x;
	qwy := q.w * q.y;
	qwz := q.w * q.z;

	m[0][0] = 1 - 2 * (qyy + qzz);
	m[0][1] = 2 * (qxy + qwz);
	m[0][2] = 2 * (qxz - qwy);

	m[1][0] = 2 * (qxy - qwz);
	m[1][1] = 1 - 2 * (qxx + qzz);
	m[1][2] = 2 * (qyz + qwx);

	m[2][0] = 2 * (qxz + qwy);
	m[2][1] = 2 * (qyz - qwx);
	m[2][2] = 1 - 2 * (qxx + qyy);

	m[3][3] = 1;

	return m;
}
matrix4_from_quaternion_f64 :: proc(q: Quaternionf64) -> (m: Matrix4f64) {
	qxx := q.x * q.x;
	qyy := q.y * q.y;
	qzz := q.z * q.z;
	qxz := q.x * q.z;
	qxy := q.x * q.y;
	qyz := q.y * q.z;
	qwx := q.w * q.x;
	qwy := q.w * q.y;
	qwz := q.w * q.z;

	m[0][0] = 1 - 2 * (qyy + qzz);
	m[0][1] = 2 * (qxy + qwz);
	m[0][2] = 2 * (qxz - qwy);

	m[1][0] = 2 * (qxy - qwz);
	m[1][1] = 1 - 2 * (qxx + qzz);
	m[1][2] = 2 * (qyz + qwx);

	m[2][0] = 2 * (qxz + qwy);
	m[2][1] = 2 * (qyz - qwx);
	m[2][2] = 1 - 2 * (qxx + qyy);

	m[3][3] = 1;

	return m;
}
matrix4_from_quaternion :: proc{
	matrix4_from_quaternion_f16,
	matrix4_from_quaternion_f32,
	matrix4_from_quaternion_f64,
};


matrix4_from_trs_f16 :: proc(t: Vector3f16, r: Quaternionf16, s: Vector3f16) -> Matrix4f16 {
	translation := matrix4_translate(t);
	rotation := matrix4_from_quaternion(r);
	scale := matrix4_scale(s);
	return mul(translation, mul(rotation, scale));
}
matrix4_from_trs_f32 :: proc(t: Vector3f32, r: Quaternionf32, s: Vector3f32) -> Matrix4f32 {
	translation := matrix4_translate(t);
	rotation := matrix4_from_quaternion(r);
	scale := matrix4_scale(s);
	return mul(translation, mul(rotation, scale));
}
matrix4_from_trs_f64 :: proc(t: Vector3f64, r: Quaternionf64, s: Vector3f64) -> Matrix4f64 {
	translation := matrix4_translate(t);
	rotation := matrix4_from_quaternion(r);
	scale := matrix4_scale(s);
	return mul(translation, mul(rotation, scale));
}
matrix4_from_trs :: proc{
	matrix4_from_trs_f16,
	matrix4_from_trs_f32,
	matrix4_from_trs_f64,
};



matrix4_inverse_f16 :: proc(m: Matrix4f16) -> Matrix4f16 {
	return transpose(matrix4_inverse_transpose(m));
}
matrix4_inverse_f32 :: proc(m: Matrix4f32) -> Matrix4f32 {
	return transpose(matrix4_inverse_transpose(m));
}
matrix4_inverse_f64 :: proc(m: Matrix4f64) -> Matrix4f64 {
	return transpose(matrix4_inverse_transpose(m));
}
matrix4_inverse :: proc{
	matrix4_inverse_f16,
	matrix4_inverse_f32,
	matrix4_inverse_f64,
};


matrix4_minor_f16 :: proc(m: Matrix4f16, c, r: int) -> f16 {
	cut_down: Matrix3f16;
	for i in 0..<3 {
		col := i if i < c else i+1;
		for j in 0..<3 {
			row := j if j < r else j+1;
			cut_down[i][j] = m[col][row];
		}
	}
	return matrix3_determinant(cut_down);
}
matrix4_minor_f32 :: proc(m: Matrix4f32, c, r: int) -> f32 {
	cut_down: Matrix3f32;
	for i in 0..<3 {
		col := i if i < c else i+1;
		for j in 0..<3 {
			row := j if j < r else j+1;
			cut_down[i][j] = m[col][row];
		}
	}
	return matrix3_determinant(cut_down);
}
matrix4_minor_f64 :: proc(m: Matrix4f64, c, r: int) -> f64 {
	cut_down: Matrix3f64;
	for i in 0..<3 {
		col := i if i < c else i+1;
		for j in 0..<3 {
			row := j if j < r else j+1;
			cut_down[i][j] = m[col][row];
		}
	}
	return matrix3_determinant(cut_down);
}
matrix4_minor :: proc{
	matrix4_minor_f16,
	matrix4_minor_f32,
	matrix4_minor_f64,
};


matrix4_cofactor_f16 :: proc(m: Matrix4f16, c, r: int) -> f16 {
	sign, minor: f16;
	sign = 1 if (c + r) % 2 == 0 else -1;
	minor = matrix4_minor(m, c, r);
	return sign * minor;
}
matrix4_cofactor_f32 :: proc(m: Matrix4f32, c, r: int) -> f32 {
	sign, minor: f32;
	sign = 1 if (c + r) % 2 == 0 else -1;
	minor = matrix4_minor(m, c, r);
	return sign * minor;
}
matrix4_cofactor_f64 :: proc(m: Matrix4f64, c, r: int) -> f64 {
	sign, minor: f64;
	sign = 1 if (c + r) % 2 == 0 else -1;
	minor = matrix4_minor(m, c, r);
	return sign * minor;
}
matrix4_cofactor :: proc{
	matrix4_cofactor_f16,
	matrix4_cofactor_f32,
	matrix4_cofactor_f64,
};


matrix4_adjoint_f16 :: proc(m: Matrix4f16) -> (adjoint: Matrix4f16) {
	for i in 0..<4 {
		for j in 0..<4 {
			adjoint[i][j] = matrix4_cofactor(m, i, j);
		}
	}
	return;
}
matrix4_adjoint_f32 :: proc(m: Matrix4f32) -> (adjoint: Matrix4f32) {
	for i in 0..<4 {
		for j in 0..<4 {
			adjoint[i][j] = matrix4_cofactor(m, i, j);
		}
	}
	return;
}
matrix4_adjoint_f64 :: proc(m: Matrix4f64) -> (adjoint: Matrix4f64) {
	for i in 0..<4 {
		for j in 0..<4 {
			adjoint[i][j] = matrix4_cofactor(m, i, j);
		}
	}
	return;
}
matrix4_adjoint :: proc{
	matrix4_adjoint_f16,
	matrix4_adjoint_f32,
	matrix4_adjoint_f64,
};


matrix4_determinant_f16 :: proc(m: Matrix4f16) -> (determinant: f16) {
	adjoint := matrix4_adjoint(m);
	for i in 0..<4 {
		determinant += m[i][0] * adjoint[i][0];
	}
	return;
}
matrix4_determinant_f32 :: proc(m: Matrix4f32) -> (determinant: f32) {
	adjoint := matrix4_adjoint(m);
	for i in 0..<4 {
		determinant += m[i][0] * adjoint[i][0];
	}
	return;
}
matrix4_determinant_f64 :: proc(m: Matrix4f64) -> (determinant: f64) {
	adjoint := matrix4_adjoint(m);
	for i in 0..<4 {
		determinant += m[i][0] * adjoint[i][0];
	}
	return;
}
matrix4_determinant :: proc{
	matrix4_determinant_f16,
	matrix4_determinant_f32,
	matrix4_determinant_f64,
};


matrix4_inverse_transpose_f16 :: proc(m: Matrix4f16) -> (inverse_transpose: Matrix4f16) {
	adjoint := matrix4_adjoint(m);
	determinant: f16 = 0;
	for i in 0..<4 {
		determinant += m[i][0] * adjoint[i][0];
	}
	inv_determinant := 1.0 / determinant;
	for i in 0..<4 {
		for j in 0..<4 {
			inverse_transpose[i][j] = adjoint[i][j] * inv_determinant;
		}
	}
	return;
}
matrix4_inverse_transpose_f32 :: proc(m: Matrix4f32) -> (inverse_transpose: Matrix4f32) {
	adjoint := matrix4_adjoint(m);
	determinant: f32 = 0;
	for i in 0..<4 {
		determinant += m[i][0] * adjoint[i][0];
	}
	inv_determinant := 1.0 / determinant;
	for i in 0..<4 {
		for j in 0..<4 {
			inverse_transpose[i][j] = adjoint[i][j] * inv_determinant;
		}
	}
	return;
}
matrix4_inverse_transpose_f64 :: proc(m: Matrix4f64) -> (inverse_transpose: Matrix4f64) {
	adjoint := matrix4_adjoint(m);
	determinant: f64 = 0;
	for i in 0..<4 {
		determinant += m[i][0] * adjoint[i][0];
	}
	inv_determinant := 1.0 / determinant;
	for i in 0..<4 {
		for j in 0..<4 {
			inverse_transpose[i][j] = adjoint[i][j] * inv_determinant;
		}
	}
	return;
}
matrix4_inverse_transpose :: proc{
	matrix4_inverse_transpose_f16,
	matrix4_inverse_transpose_f32,
	matrix4_inverse_transpose_f64,
};


matrix4_translate_f16 :: proc(v: Vector3f16) -> Matrix4f16 {
	m := MATRIX4F16_IDENTITY;
	m[3][0] = v[0];
	m[3][1] = v[1];
	m[3][2] = v[2];
	return m;
}
matrix4_translate_f32 :: proc(v: Vector3f32) -> Matrix4f32 {
	m := MATRIX4F32_IDENTITY;
	m[3][0] = v[0];
	m[3][1] = v[1];
	m[3][2] = v[2];
	return m;
}
matrix4_translate_f64 :: proc(v: Vector3f64) -> Matrix4f64 {
	m := MATRIX4F64_IDENTITY;
	m[3][0] = v[0];
	m[3][1] = v[1];
	m[3][2] = v[2];
	return m;
}
matrix4_translate :: proc{
	matrix4_translate_f16,
	matrix4_translate_f32,
	matrix4_translate_f64,
};


matrix4_rotate_f16 :: proc(angle_radians: f16, v: Vector3f16) -> Matrix4f16 {
	c := math.cos(angle_radians);
	s := math.sin(angle_radians);

	a := normalize(v);
	t := a * (1-c);

	rot := MATRIX4F16_IDENTITY;

	rot[0][0] = c + t[0]*a[0];
	rot[0][1] = 0 + t[0]*a[1] + s*a[2];
	rot[0][2] = 0 + t[0]*a[2] - s*a[1];
	rot[0][3] = 0;

	rot[1][0] = 0 + t[1]*a[0] - s*a[2];
	rot[1][1] = c + t[1]*a[1];
	rot[1][2] = 0 + t[1]*a[2] + s*a[0];
	rot[1][3] = 0;

	rot[2][0] = 0 + t[2]*a[0] + s*a[1];
	rot[2][1] = 0 + t[2]*a[1] - s*a[0];
	rot[2][2] = c + t[2]*a[2];
	rot[2][3] = 0;

	return rot;
}
matrix4_rotate_f32 :: proc(angle_radians: f32, v: Vector3f32) -> Matrix4f32 {
	c := math.cos(angle_radians);
	s := math.sin(angle_radians);

	a := normalize(v);
	t := a * (1-c);

	rot := MATRIX4F32_IDENTITY;

	rot[0][0] = c + t[0]*a[0];
	rot[0][1] = 0 + t[0]*a[1] + s*a[2];
	rot[0][2] = 0 + t[0]*a[2] - s*a[1];
	rot[0][3] = 0;

	rot[1][0] = 0 + t[1]*a[0] - s*a[2];
	rot[1][1] = c + t[1]*a[1];
	rot[1][2] = 0 + t[1]*a[2] + s*a[0];
	rot[1][3] = 0;

	rot[2][0] = 0 + t[2]*a[0] + s*a[1];
	rot[2][1] = 0 + t[2]*a[1] - s*a[0];
	rot[2][2] = c + t[2]*a[2];
	rot[2][3] = 0;

	return rot;
}
matrix4_rotate_f64 :: proc(angle_radians: f64, v: Vector3f64) -> Matrix4f64 {
	c := math.cos(angle_radians);
	s := math.sin(angle_radians);

	a := normalize(v);
	t := a * (1-c);

	rot := MATRIX4F64_IDENTITY;

	rot[0][0] = c + t[0]*a[0];
	rot[0][1] = 0 + t[0]*a[1] + s*a[2];
	rot[0][2] = 0 + t[0]*a[2] - s*a[1];
	rot[0][3] = 0;

	rot[1][0] = 0 + t[1]*a[0] - s*a[2];
	rot[1][1] = c + t[1]*a[1];
	rot[1][2] = 0 + t[1]*a[2] + s*a[0];
	rot[1][3] = 0;

	rot[2][0] = 0 + t[2]*a[0] + s*a[1];
	rot[2][1] = 0 + t[2]*a[1] - s*a[0];
	rot[2][2] = c + t[2]*a[2];
	rot[2][3] = 0;

	return rot;
}
matrix4_rotate :: proc{
	matrix4_rotate_f16,
	matrix4_rotate_f32,
	matrix4_rotate_f64,
};


matrix4_scale_f16 :: proc(v: Vector3f16) -> (m: Matrix4f16) {
	m[0][0] = v[0];
	m[1][1] = v[1];
	m[2][2] = v[2];
	m[3][3] = 1;
	return;
}
matrix4_scale_f32 :: proc(v: Vector3f32) -> (m: Matrix4f32) {
	m[0][0] = v[0];
	m[1][1] = v[1];
	m[2][2] = v[2];
	m[3][3] = 1;
	return;
}
matrix4_scale_f64 :: proc(v: Vector3f64) -> (m: Matrix4f64) {
	m[0][0] = v[0];
	m[1][1] = v[1];
	m[2][2] = v[2];
	m[3][3] = 1;
	return;
}
matrix4_scale :: proc{
	matrix4_scale_f16,
	matrix4_scale_f32,
	matrix4_scale_f64,
};


matrix4_look_at_f16 :: proc(eye, centre, up: Vector3f16, flip_z_axis := true) -> (m: Matrix4f16) {
	f := normalize(centre - eye);
	s := normalize(cross(f, up));
	u := cross(s, f);

	fe := dot(f, eye);

	return {
		{+s.x, +u.x, -f.x, 0},
		{+s.y, +u.y, -f.y, 0},
		{+s.z, +u.z, -f.z, 0},
		{-dot(s, eye), -dot(u, eye), +fe if flip_z_axis else -fe, 1},
	};
}
matrix4_look_at_f32 :: proc(eye, centre, up: Vector3f32, flip_z_axis := true) -> (m: Matrix4f32) {
	f := normalize(centre - eye);
	s := normalize(cross(f, up));
	u := cross(s, f);

	fe := dot(f, eye);

	return {
		{+s.x, +u.x, -f.x, 0},
		{+s.y, +u.y, -f.y, 0},
		{+s.z, +u.z, -f.z, 0},
		{-dot(s, eye), -dot(u, eye), +fe if flip_z_axis else -fe, 1},
	};
}
matrix4_look_at_f64 :: proc(eye, centre, up: Vector3f64, flip_z_axis := true) -> (m: Matrix4f64) {
	f := normalize(centre - eye);
	s := normalize(cross(f, up));
	u := cross(s, f);

	fe := dot(f, eye);

	return {
		{+s.x, +u.x, -f.x, 0},
		{+s.y, +u.y, -f.y, 0},
		{+s.z, +u.z, -f.z, 0},
		{-dot(s, eye), -dot(u, eye), +fe if flip_z_axis else -fe, 1},
	};
}
matrix4_look_at :: proc{
	matrix4_look_at_f16,
	matrix4_look_at_f32,
	matrix4_look_at_f64,
};


matrix4_perspective_f16 :: proc(fovy, aspect, near, far: f16, flip_z_axis := true) -> (m: Matrix4f16) {
	tan_half_fovy := math.tan(0.5 * fovy);
	m[0][0] = 1 / (aspect*tan_half_fovy);
	m[1][1] = 1 / (tan_half_fovy);
	m[2][2] = +(far + near) / (far - near);
	m[2][3] = +1;
	m[3][2] = -2*far*near / (far - near);

	if flip_z_axis {
		m[2] = -m[2];
	}

	return;
}
matrix4_perspective_f32 :: proc(fovy, aspect, near, far: f32, flip_z_axis := true) -> (m: Matrix4f32) {
	tan_half_fovy := math.tan(0.5 * fovy);
	m[0][0] = 1 / (aspect*tan_half_fovy);
	m[1][1] = 1 / (tan_half_fovy);
	m[2][2] = +(far + near) / (far - near);
	m[2][3] = +1;
	m[3][2] = -2*far*near / (far - near);

	if flip_z_axis {
		m[2] = -m[2];
	}

	return;
}
matrix4_perspective_f64 :: proc(fovy, aspect, near, far: f64, flip_z_axis := true) -> (m: Matrix4f64) {
	tan_half_fovy := math.tan(0.5 * fovy);
	m[0][0] = 1 / (aspect*tan_half_fovy);
	m[1][1] = 1 / (tan_half_fovy);
	m[2][2] = +(far + near) / (far - near);
	m[2][3] = +1;
	m[3][2] = -2*far*near / (far - near);

	if flip_z_axis {
		m[2] = -m[2];
	}

	return;
}
matrix4_perspective :: proc{
	matrix4_perspective_f16,
	matrix4_perspective_f32,
	matrix4_perspective_f64,
};



matrix_ortho3d_f16 :: proc(left, right, bottom, top, near, far: f16, flip_z_axis := true) -> (m: Matrix4f16) {
	m[0][0] = +2 / (right - left);
	m[1][1] = +2 / (top - bottom);
	m[2][2] = +2 / (far - near);
	m[3][0] = -(right + left)   / (right - left);
	m[3][1] = -(top   + bottom) / (top - bottom);
	m[3][2] = -(far + near) / (far- near);
	m[3][3] = 1;

	if flip_z_axis {
		m[2] = -m[2];
	}

	return;
}
matrix_ortho3d_f32 :: proc(left, right, bottom, top, near, far: f32, flip_z_axis := true) -> (m: Matrix4f32) {
	m[0][0] = +2 / (right - left);
	m[1][1] = +2 / (top - bottom);
	m[2][2] = +2 / (far - near);
	m[3][0] = -(right + left)   / (right - left);
	m[3][1] = -(top   + bottom) / (top - bottom);
	m[3][2] = -(far + near) / (far- near);
	m[3][3] = 1;

	if flip_z_axis {
		m[2] = -m[2];
	}

	return;
}
matrix_ortho3d_f64 :: proc(left, right, bottom, top, near, far: f64, flip_z_axis := true) -> (m: Matrix4f64) {
	m[0][0] = +2 / (right - left);
	m[1][1] = +2 / (top - bottom);
	m[2][2] = +2 / (far - near);
	m[3][0] = -(right + left)   / (right - left);
	m[3][1] = -(top   + bottom) / (top - bottom);
	m[3][2] = -(far + near) / (far- near);
	m[3][3] = 1;

	if flip_z_axis {
		m[2] = -m[2];
	}

	return;
}
matrix_ortho3d :: proc{
	matrix_ortho3d_f16,
	matrix_ortho3d_f32,
	matrix_ortho3d_f64,
};



matrix4_infinite_perspective_f16 :: proc(fovy, aspect, near: f16, flip_z_axis := true) -> (m: Matrix4f16) {
	tan_half_fovy := math.tan(0.5 * fovy);
	m[0][0] = 1 / (aspect*tan_half_fovy);
	m[1][1] = 1 / (tan_half_fovy);
	m[2][2] = +1;
	m[2][3] = +1;
	m[3][2] = -2*near;

	if flip_z_axis {
		m[2] = -m[2];
	}

	return;
}
matrix4_infinite_perspective_f32 :: proc(fovy, aspect, near: f32, flip_z_axis := true) -> (m: Matrix4f32) {
	tan_half_fovy := math.tan(0.5 * fovy);
	m[0][0] = 1 / (aspect*tan_half_fovy);
	m[1][1] = 1 / (tan_half_fovy);
	m[2][2] = +1;
	m[2][3] = +1;
	m[3][2] = -2*near;

	if flip_z_axis {
		m[2] = -m[2];
	}

	return;
}
matrix4_infinite_perspective_f64 :: proc(fovy, aspect, near: f64, flip_z_axis := true) -> (m: Matrix4f64) {
	tan_half_fovy := math.tan(0.5 * fovy);
	m[0][0] = 1 / (aspect*tan_half_fovy);
	m[1][1] = 1 / (tan_half_fovy);
	m[2][2] = +1;
	m[2][3] = +1;
	m[3][2] = -2*near;

	if flip_z_axis {
		m[2] = -m[2];
	}

	return;
}
matrix4_infinite_perspective :: proc{
	matrix4_infinite_perspective_f16,
	matrix4_infinite_perspective_f32,
	matrix4_infinite_perspective_f64,
};



matrix2_from_scalar_f16 :: proc(f: f16) -> (m: Matrix2f16) {
	m[0][0], m[0][1] = f, 0;
	m[1][0], m[1][1] = 0, f;
	return;
}
matrix2_from_scalar_f32 :: proc(f: f32) -> (m: Matrix2f32) {
	m[0][0], m[0][1] = f, 0;
	m[1][0], m[1][1] = 0, f;
	return;
}
matrix2_from_scalar_f64 :: proc(f: f64) -> (m: Matrix2f64) {
	m[0][0], m[0][1] = f, 0;
	m[1][0], m[1][1] = 0, f;
	return;
}
matrix2_from_scalar :: proc{
	matrix2_from_scalar_f16,
	matrix2_from_scalar_f32,
	matrix2_from_scalar_f64,
};


matrix3_from_scalar_f16 :: proc(f: f16) -> (m: Matrix3f16) {
	m[0][0], m[0][1], m[0][2] = f, 0, 0;
	m[1][0], m[1][1], m[1][2] = 0, f, 0;
	m[2][0], m[2][1], m[2][2] = 0, 0, f;
	return;
}
matrix3_from_scalar_f32 :: proc(f: f32) -> (m: Matrix3f32) {
	m[0][0], m[0][1], m[0][2] = f, 0, 0;
	m[1][0], m[1][1], m[1][2] = 0, f, 0;
	m[2][0], m[2][1], m[2][2] = 0, 0, f;
	return;
}
matrix3_from_scalar_f64 :: proc(f: f64) -> (m: Matrix3f64) {
	m[0][0], m[0][1], m[0][2] = f, 0, 0;
	m[1][0], m[1][1], m[1][2] = 0, f, 0;
	m[2][0], m[2][1], m[2][2] = 0, 0, f;
	return;
}
matrix3_from_scalar :: proc{
	matrix3_from_scalar_f16,
	matrix3_from_scalar_f32,
	matrix3_from_scalar_f64,
};


matrix4_from_scalar_f16 :: proc(f: f16) -> (m: Matrix4f16) {
	m[0][0], m[0][1], m[0][2], m[0][3] = f, 0, 0, 0;
	m[1][0], m[1][1], m[1][2], m[1][3] = 0, f, 0, 0;
	m[2][0], m[2][1], m[2][2], m[2][3] = 0, 0, f, 0;
	m[3][0], m[3][1], m[3][2], m[3][3] = 0, 0, 0, f;
	return;
}
matrix4_from_scalar_f32 :: proc(f: f32) -> (m: Matrix4f32) {
	m[0][0], m[0][1], m[0][2], m[0][3] = f, 0, 0, 0;
	m[1][0], m[1][1], m[1][2], m[1][3] = 0, f, 0, 0;
	m[2][0], m[2][1], m[2][2], m[2][3] = 0, 0, f, 0;
	m[3][0], m[3][1], m[3][2], m[3][3] = 0, 0, 0, f;
	return;
}
matrix4_from_scalar_f64 :: proc(f: f64) -> (m: Matrix4f64) {
	m[0][0], m[0][1], m[0][2], m[0][3] = f, 0, 0, 0;
	m[1][0], m[1][1], m[1][2], m[1][3] = 0, f, 0, 0;
	m[2][0], m[2][1], m[2][2], m[2][3] = 0, 0, f, 0;
	m[3][0], m[3][1], m[3][2], m[3][3] = 0, 0, 0, f;
	return;
}
matrix4_from_scalar :: proc{
	matrix4_from_scalar_f16,
	matrix4_from_scalar_f32,
	matrix4_from_scalar_f64,
};


matrix2_from_matrix3_f16 :: proc(m: Matrix3f16) -> (r: Matrix2f16) {
	r[0][0], r[0][1] = m[0][0], m[0][1];
	r[1][0], r[1][1] = m[1][0], m[1][1];
	return;
}
matrix2_from_matrix3_f32 :: proc(m: Matrix3f32) -> (r: Matrix2f32) {
	r[0][0], r[0][1] = m[0][0], m[0][1];
	r[1][0], r[1][1] = m[1][0], m[1][1];
	return;
}
matrix2_from_matrix3_f64 :: proc(m: Matrix3f64) -> (r: Matrix2f64) {
	r[0][0], r[0][1] = m[0][0], m[0][1];
	r[1][0], r[1][1] = m[1][0], m[1][1];
	return;
}
matrix2_from_matrix3 :: proc{
	matrix2_from_matrix3_f16,
	matrix2_from_matrix3_f32,
	matrix2_from_matrix3_f64,
};


matrix2_from_matrix4_f16 :: proc(m: Matrix4f16) -> (r: Matrix2f16) {
	r[0][0], r[0][1] = m[0][0], m[0][1];
	r[1][0], r[1][1] = m[1][0], m[1][1];
	return;
}
matrix2_from_matrix4_f32 :: proc(m: Matrix4f32) -> (r: Matrix2f32) {
	r[0][0], r[0][1] = m[0][0], m[0][1];
	r[1][0], r[1][1] = m[1][0], m[1][1];
	return;
}
matrix2_from_matrix4_f64 :: proc(m: Matrix4f64) -> (r: Matrix2f64) {
	r[0][0], r[0][1] = m[0][0], m[0][1];
	r[1][0], r[1][1] = m[1][0], m[1][1];
	return;
}
matrix2_from_matrix4 :: proc{
	matrix2_from_matrix4_f16,
	matrix2_from_matrix4_f32,
	matrix2_from_matrix4_f64,
};


matrix3_from_matrix2_f16 :: proc(m: Matrix2f16) -> (r: Matrix3f16) {
	r[0][0], r[0][1], r[0][2] = m[0][0], m[0][1], 0;
	r[1][0], r[1][1], r[1][2] = m[1][0], m[1][1], 0;
	r[2][0], r[2][1], r[2][2] =       0,       0, 1;
	return;
}
matrix3_from_matrix2_f32 :: proc(m: Matrix2f32) -> (r: Matrix3f32) {
	r[0][0], r[0][1], r[0][2] = m[0][0], m[0][1], 0;
	r[1][0], r[1][1], r[1][2] = m[1][0], m[1][1], 0;
	r[2][0], r[2][1], r[2][2] =       0,       0, 1;
	return;
}
matrix3_from_matrix2_f64 :: proc(m: Matrix2f64) -> (r: Matrix3f64) {
	r[0][0], r[0][1], r[0][2] = m[0][0], m[0][1], 0;
	r[1][0], r[1][1], r[1][2] = m[1][0], m[1][1], 0;
	r[2][0], r[2][1], r[2][2] =       0,       0, 1;
	return;
}
matrix3_from_matrix2 :: proc{
	matrix3_from_matrix2_f16,
	matrix3_from_matrix2_f32,
	matrix3_from_matrix2_f64,
};


matrix3_from_matrix4_f16 :: proc(m: Matrix4f16) -> (r: Matrix3f16) {
	r[0][0], r[0][1], r[0][2] = m[0][0], m[0][1], m[0][2];
	r[1][0], r[1][1], r[1][2] = m[1][0], m[1][1], m[1][2];
	r[2][0], r[2][1], r[2][2] = m[2][0], m[2][1], m[2][2];
	return;
}
matrix3_from_matrix4_f32 :: proc(m: Matrix4f32) -> (r: Matrix3f32) {
	r[0][0], r[0][1], r[0][2] = m[0][0], m[0][1], m[0][2];
	r[1][0], r[1][1], r[1][2] = m[1][0], m[1][1], m[1][2];
	r[2][0], r[2][1], r[2][2] = m[2][0], m[2][1], m[2][2];
	return;
}
matrix3_from_matrix4_f64 :: proc(m: Matrix4f64) -> (r: Matrix3f64) {
	r[0][0], r[0][1], r[0][2] = m[0][0], m[0][1], m[0][2];
	r[1][0], r[1][1], r[1][2] = m[1][0], m[1][1], m[1][2];
	r[2][0], r[2][1], r[2][2] = m[2][0], m[2][1], m[2][2];
	return;
}
matrix3_from_matrix4 :: proc{
	matrix3_from_matrix4_f16,
	matrix3_from_matrix4_f32,
	matrix3_from_matrix4_f64,
};


matrix4_from_matrix2_f16 :: proc(m: Matrix2f16) -> (r: Matrix4f16) {
	r[0][0], r[0][1], r[0][2], r[0][3] = m[0][0], m[0][1], 0, 0;
	r[1][0], r[1][1], r[1][2], r[1][3] = m[1][0], m[1][1], 0, 0;
	r[2][0], r[2][1], r[2][2], r[2][3] =       0,       0, 1, 0;
	r[3][0], r[3][1], r[3][2], r[3][3] =       0,       0, 0, 1;
	return;
}
matrix4_from_matrix2_f32 :: proc(m: Matrix2f32) -> (r: Matrix4f32) {
	r[0][0], r[0][1], r[0][2], r[0][3] = m[0][0], m[0][1], 0, 0;
	r[1][0], r[1][1], r[1][2], r[1][3] = m[1][0], m[1][1], 0, 0;
	r[2][0], r[2][1], r[2][2], r[2][3] =       0,       0, 1, 0;
	r[3][0], r[3][1], r[3][2], r[3][3] =       0,       0, 0, 1;
	return;
}
matrix4_from_matrix2_f64 :: proc(m: Matrix2f64) -> (r: Matrix4f64) {
	r[0][0], r[0][1], r[0][2], r[0][3] = m[0][0], m[0][1], 0, 0;
	r[1][0], r[1][1], r[1][2], r[1][3] = m[1][0], m[1][1], 0, 0;
	r[2][0], r[2][1], r[2][2], r[2][3] =       0,       0, 1, 0;
	r[3][0], r[3][1], r[3][2], r[3][3] =       0,       0, 0, 1;
	return;
}
matrix4_from_matrix2 :: proc{
	matrix4_from_matrix2_f16,
	matrix4_from_matrix2_f32,
	matrix4_from_matrix2_f64,
};


matrix4_from_matrix3_f16 :: proc(m: Matrix3f16) -> (r: Matrix4f16) {
	r[0][0], r[0][1], r[0][2], r[0][3] = m[0][0], m[0][1], m[0][2], 0;
	r[1][0], r[1][1], r[1][2], r[1][3] = m[1][0], m[1][1], m[1][2], 0;
	r[2][0], r[2][1], r[2][2], r[2][3] = m[2][0], m[2][1], m[2][2], 0;
	r[3][0], r[3][1], r[3][2], r[3][3] =       0,       0,       0, 1;
	return;
}
matrix4_from_matrix3_f32 :: proc(m: Matrix3f32) -> (r: Matrix4f32) {
	r[0][0], r[0][1], r[0][2], r[0][3] = m[0][0], m[0][1], m[0][2], 0;
	r[1][0], r[1][1], r[1][2], r[1][3] = m[1][0], m[1][1], m[1][2], 0;
	r[2][0], r[2][1], r[2][2], r[2][3] = m[2][0], m[2][1], m[2][2], 0;
	r[3][0], r[3][1], r[3][2], r[3][3] =       0,       0,       0, 1;
	return;
}
matrix4_from_matrix3_f64 :: proc(m: Matrix3f64) -> (r: Matrix4f64) {
	r[0][0], r[0][1], r[0][2], r[0][3] = m[0][0], m[0][1], m[0][2], 0;
	r[1][0], r[1][1], r[1][2], r[1][3] = m[1][0], m[1][1], m[1][2], 0;
	r[2][0], r[2][1], r[2][2], r[2][3] = m[2][0], m[2][1], m[2][2], 0;
	r[3][0], r[3][1], r[3][2], r[3][3] =       0,       0,       0, 1;
	return;
}
matrix4_from_matrix3 :: proc{
	matrix4_from_matrix3_f16,
	matrix4_from_matrix3_f32,
	matrix4_from_matrix3_f64,
};


quaternion_from_scalar_f16 :: proc(f: f16) -> (q: Quaternionf16) {
	q.w = f;
	return;
}
quaternion_from_scalar_f32 :: proc(f: f32) -> (q: Quaternionf32) {
	q.w = f;
	return;
}
quaternion_from_scalar_f64 :: proc(f: f64) -> (q: Quaternionf64) {
	q.w = f;
	return;
}
quaternion_from_scalar :: proc{
	quaternion_from_scalar_f16,
	quaternion_from_scalar_f32,
	quaternion_from_scalar_f64,
};



to_matrix2f16    :: proc{matrix2_from_scalar_f16,    matrix2_from_matrix3_f16,    matrix2_from_matrix4_f16};
to_matrix3f16    :: proc{matrix3_from_scalar_f16,    matrix3_from_matrix2_f16,    matrix3_from_matrix4_f16, matrix3_from_quaternion_f16};
to_matrix4f16    :: proc{matrix4_from_scalar_f16,    matrix4_from_matrix2_f16,    matrix4_from_matrix3_f16, matrix4_from_quaternion_f16};
to_quaternionf16 :: proc{quaternion_from_scalar_f16, quaternion_from_matrix3_f16, quaternion_from_matrix4_f16};


to_matrix2f32    :: proc{matrix2_from_scalar_f32,    matrix2_from_matrix3_f32,    matrix2_from_matrix4_f32};
to_matrix3f32    :: proc{matrix3_from_scalar_f32,    matrix3_from_matrix2_f32,    matrix3_from_matrix4_f32, matrix3_from_quaternion_f32};
to_matrix4f32    :: proc{matrix4_from_scalar_f32,    matrix4_from_matrix2_f32,    matrix4_from_matrix3_f32, matrix4_from_quaternion_f32};
to_quaternionf32 :: proc{quaternion_from_scalar_f32, quaternion_from_matrix3_f32, quaternion_from_matrix4_f32};



to_matrix2f64    :: proc{matrix2_from_scalar_f64,    matrix2_from_matrix3_f64,    matrix2_from_matrix4_f64};
to_matrix3f64    :: proc{matrix3_from_scalar_f64,    matrix3_from_matrix2_f64,    matrix3_from_matrix4_f64, matrix3_from_quaternion_f64};
to_matrix4f64    :: proc{matrix4_from_scalar_f64,    matrix4_from_matrix2_f64,    matrix4_from_matrix3_f64, matrix4_from_quaternion_f64};
to_quaternionf64 :: proc{quaternion_from_scalar_f64, quaternion_from_matrix3_f64, quaternion_from_matrix4_f64};





to_matrix2f :: proc{
	matrix2_from_scalar_f16, matrix2_from_matrix3_f16, matrix2_from_matrix4_f16,
	matrix2_from_scalar_f32, matrix2_from_matrix3_f32, matrix2_from_matrix4_f32,
	matrix2_from_scalar_f64, matrix2_from_matrix3_f64, matrix2_from_matrix4_f64,
};

to_matrix3 :: proc{
	matrix3_from_scalar_f16, matrix3_from_matrix2_f16, matrix3_from_matrix4_f16, matrix3_from_quaternion_f16,
	matrix3_from_scalar_f32, matrix3_from_matrix2_f32, matrix3_from_matrix4_f32, matrix3_from_quaternion_f32,
	matrix3_from_scalar_f64, matrix3_from_matrix2_f64, matrix3_from_matrix4_f64, matrix3_from_quaternion_f64,
};

to_matrix4 :: proc{
	matrix4_from_scalar_f16, matrix4_from_matrix2_f16, matrix4_from_matrix3_f16, matrix4_from_quaternion_f16,
	matrix4_from_scalar_f32, matrix4_from_matrix2_f32, matrix4_from_matrix3_f32, matrix4_from_quaternion_f32,
	matrix4_from_scalar_f64, matrix4_from_matrix2_f64, matrix4_from_matrix3_f64, matrix4_from_quaternion_f64,
};

to_quaternion :: proc{
	quaternion_from_scalar_f16, quaternion_from_matrix3_f16, quaternion_from_matrix4_f16,
	quaternion_from_scalar_f32, quaternion_from_matrix3_f32, quaternion_from_matrix4_f32,
	quaternion_from_scalar_f64, quaternion_from_matrix3_f64, quaternion_from_matrix4_f64,
};



matrix2_orthonormalize_f16 :: proc(m: Matrix2f16) -> (r: Matrix2f16) {
	r[0] = normalize(m[0]);

	d0 := dot(r[0], r[1]);
	r[1] -= r[0] * d0;
	r[1] = normalize(r[1]);

	return;
}
matrix2_orthonormalize_f32 :: proc(m: Matrix2f32) -> (r: Matrix2f32) {
	r[0] = normalize(m[0]);

	d0 := dot(r[0], r[1]);
	r[1] -= r[0] * d0;
	r[1] = normalize(r[1]);

	return;
}
matrix2_orthonormalize_f64 :: proc(m: Matrix2f64) -> (r: Matrix2f64) {
	r[0] = normalize(m[0]);

	d0 := dot(r[0], r[1]);
	r[1] -= r[0] * d0;
	r[1] = normalize(r[1]);

	return;
}
matrix2_orthonormalize :: proc{
	matrix2_orthonormalize_f16,
	matrix2_orthonormalize_f32,
	matrix2_orthonormalize_f64,
};


matrix3_orthonormalize_f16 :: proc(m: Matrix3f16) -> (r: Matrix3f16) {
	r[0] = normalize(m[0]);

	d0 := dot(r[0], r[1]);
	r[1] -= r[0] * d0;
	r[1] = normalize(r[1]);

	d1 := dot(r[1], r[2]);
	d0 = dot(r[0], r[2]);
	r[2] -= r[0]*d0 + r[1]*d1;
	r[2] = normalize(r[2]);

	return;
}
matrix3_orthonormalize_f32 :: proc(m: Matrix3f32) -> (r: Matrix3f32) {
	r[0] = normalize(m[0]);

	d0 := dot(r[0], r[1]);
	r[1] -= r[0] * d0;
	r[1] = normalize(r[1]);

	d1 := dot(r[1], r[2]);
	d0 = dot(r[0], r[2]);
	r[2] -= r[0]*d0 + r[1]*d1;
	r[2] = normalize(r[2]);

	return;
}
matrix3_orthonormalize_f64 :: proc(m: Matrix3f64) -> (r: Matrix3f64) {
	r[0] = normalize(m[0]);

	d0 := dot(r[0], r[1]);
	r[1] -= r[0] * d0;
	r[1] = normalize(r[1]);

	d1 := dot(r[1], r[2]);
	d0 = dot(r[0], r[2]);
	r[2] -= r[0]*d0 + r[1]*d1;
	r[2] = normalize(r[2]);

	return;
}
matrix3_orthonormalize :: proc{
	matrix3_orthonormalize_f16,
	matrix3_orthonormalize_f32,
	matrix3_orthonormalize_f64,
};


vector3_orthonormalize_f16 :: proc(x, y: Vector3f16) -> (z: Vector3f16) {
	return normalize(x - y * dot(y, x));
}
vector3_orthonormalize_f32 :: proc(x, y: Vector3f32) -> (z: Vector3f32) {
	return normalize(x - y * dot(y, x));
}
vector3_orthonormalize_f64 :: proc(x, y: Vector3f64) -> (z: Vector3f64) {
	return normalize(x - y * dot(y, x));
}
vector3_orthonormalize :: proc{
	vector3_orthonormalize_f16,
	vector3_orthonormalize_f32,
	vector3_orthonormalize_f64,
};


orthonormalize :: proc{
	matrix2_orthonormalize_f16, matrix3_orthonormalize_f16, vector3_orthonormalize_f16,
	matrix2_orthonormalize_f32, matrix3_orthonormalize_f32, vector3_orthonormalize_f32,
	matrix2_orthonormalize_f64, matrix3_orthonormalize_f64, vector3_orthonormalize_f64,
};


matrix4_orientation_f16 :: proc(normal, up: Vector3f16) -> Matrix4f16 {
	if all(equal(normal, up)) {
		return MATRIX4F16_IDENTITY;
	}

	rotation_axis := cross(up, normal);
	angle := math.acos(dot(normal, up));

	return matrix4_rotate(angle, rotation_axis);
}
matrix4_orientation_f32 :: proc(normal, up: Vector3f32) -> Matrix4f32 {
	if all(equal(normal, up)) {
		return MATRIX4F32_IDENTITY;
	}

	rotation_axis := cross(up, normal);
	angle := math.acos(dot(normal, up));

	return matrix4_rotate(angle, rotation_axis);
}
matrix4_orientation_f64 :: proc(normal, up: Vector3f64) -> Matrix4f64 {
	if all(equal(normal, up)) {
		return MATRIX4F64_IDENTITY;
	}

	rotation_axis := cross(up, normal);
	angle := math.acos(dot(normal, up));

	return matrix4_rotate(angle, rotation_axis);
}
matrix4_orientation :: proc{
	matrix4_orientation_f16,
	matrix4_orientation_f32,
	matrix4_orientation_f64,
};


euclidean_from_polar_f16 :: proc(polar: Vector2f16) -> Vector3f16 {
	latitude, longitude := polar.x, polar.y;
	cx, sx := math.cos(latitude), math.sin(latitude);
	cy, sy := math.cos(longitude), math.sin(longitude);

	return {
		cx*sy,
		sx,
		cx*cy,
	};
}
euclidean_from_polar_f32 :: proc(polar: Vector2f32) -> Vector3f32 {
	latitude, longitude := polar.x, polar.y;
	cx, sx := math.cos(latitude), math.sin(latitude);
	cy, sy := math.cos(longitude), math.sin(longitude);

	return {
		cx*sy,
		sx,
		cx*cy,
	};
}
euclidean_from_polar_f64 :: proc(polar: Vector2f64) -> Vector3f64 {
	latitude, longitude := polar.x, polar.y;
	cx, sx := math.cos(latitude), math.sin(latitude);
	cy, sy := math.cos(longitude), math.sin(longitude);

	return {
		cx*sy,
		sx,
		cx*cy,
	};
}
euclidean_from_polar :: proc{
	euclidean_from_polar_f16,
	euclidean_from_polar_f32,
	euclidean_from_polar_f64,
};


polar_from_euclidean_f16 :: proc(euclidean: Vector3f16) -> Vector3f16 {
	n := length(euclidean);
	tmp := euclidean / n;

	xz_dist := math.sqrt(tmp.x*tmp.x + tmp.z*tmp.z);

	return {
		math.asin(tmp.y),
		math.atan2(tmp.x, tmp.z),
		xz_dist,
	};
}
polar_from_euclidean_f32 :: proc(euclidean: Vector3f32) -> Vector3f32 {
	n := length(euclidean);
	tmp := euclidean / n;

	xz_dist := math.sqrt(tmp.x*tmp.x + tmp.z*tmp.z);

	return {
		math.asin(tmp.y),
		math.atan2(tmp.x, tmp.z),
		xz_dist,
	};
}
polar_from_euclidean_f64 :: proc(euclidean: Vector3f64) -> Vector3f64 {
	n := length(euclidean);
	tmp := euclidean / n;

	xz_dist := math.sqrt(tmp.x*tmp.x + tmp.z*tmp.z);

	return {
		math.asin(tmp.y),
		math.atan2(tmp.x, tmp.z),
		xz_dist,
	};
}
polar_from_euclidean :: proc{
	polar_from_euclidean_f16,
	polar_from_euclidean_f32,
	polar_from_euclidean_f64,
};