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authorgingerBill <bill@gingerbill.org>2021-04-01 11:12:40 +0100
committergingerBill <bill@gingerbill.org>2021-04-01 11:12:40 +0100
commit0fc04a939e56f269aeaff2e97ba248411cebcd10 (patch)
tree5897d0aa6afc87bad2fd697e4bc5aad5f73d3fd4 /core/math
parent3e1b4c17ac9a5fc17d57b4e886844092c0bec5be (diff)
Add `f16` support to core:math/linalg
Diffstat (limited to 'core/math')
-rw-r--r--core/math/linalg/general.odin21
-rw-r--r--core/math/linalg/specific.odin831
-rw-r--r--core/math/linalg/specific_euler_angles.odin200
-rw-r--r--core/math/linalg/specific_euler_angles_f16.odin1356
4 files changed, 2284 insertions, 124 deletions
diff --git a/core/math/linalg/general.odin b/core/math/linalg/general.odin
index 84001184f..10e557aec 100644
--- a/core/math/linalg/general.odin
+++ b/core/math/linalg/general.odin
@@ -47,6 +47,9 @@ vector_dot :: proc(a, b: $T/[$N]$E) -> (c: E) where IS_NUMERIC(E) {
}
return;
}
+quaternion64_dot :: proc(a, b: $T/quaternion64) -> (c: f16) {
+ return a.w*a.w + a.x*b.x + a.y*b.y + a.z*b.z;
+}
quaternion128_dot :: proc(a, b: $T/quaternion128) -> (c: f32) {
return a.w*a.w + a.x*b.x + a.y*b.y + a.z*b.z;
}
@@ -54,7 +57,7 @@ quaternion256_dot :: proc(a, b: $T/quaternion256) -> (c: f64) {
return a.w*a.w + a.x*b.x + a.y*b.y + a.z*b.z;
}
-dot :: proc{scalar_dot, vector_dot, quaternion128_dot, quaternion256_dot};
+dot :: proc{scalar_dot, vector_dot, quaternion64_dot, quaternion128_dot, quaternion256_dot};
inner_product :: dot;
outer_product :: proc(a: $A/[$M]$E, b: $B/[$N]E) -> (out: [M][N]E) where IS_NUMERIC(E) {
@@ -230,6 +233,16 @@ matrix_mul_vector :: proc(a: $A/[$I][$J]$E, b: $B/[I]E) -> (c: B)
quaternion_mul_quaternion :: proc(q1, q2: $Q) -> Q where IS_QUATERNION(Q) {
return q1 * q2;
}
+
+quaternion64_mul_vector3 :: proc(q: $Q/quaternion64, v: $V/[3]$F/f16) -> V {
+ Raw_Quaternion :: struct {xyz: [3]f16, r: f16};
+
+ q := transmute(Raw_Quaternion)q;
+ v := transmute([3]f16)v;
+
+ t := cross(2*q.xyz, v);
+ return V(v + q.r*t + cross(q.xyz, t));
+}
quaternion128_mul_vector3 :: proc(q: $Q/quaternion128, v: $V/[3]$F/f32) -> V {
Raw_Quaternion :: struct {xyz: [3]f32, r: f32};
@@ -239,7 +252,6 @@ quaternion128_mul_vector3 :: proc(q: $Q/quaternion128, v: $V/[3]$F/f32) -> V {
t := cross(2*q.xyz, v);
return V(v + q.r*t + cross(q.xyz, t));
}
-
quaternion256_mul_vector3 :: proc(q: $Q/quaternion256, v: $V/[3]$F/f64) -> V {
Raw_Quaternion :: struct {xyz: [3]f64, r: f64};
@@ -249,12 +261,13 @@ quaternion256_mul_vector3 :: proc(q: $Q/quaternion256, v: $V/[3]$F/f64) -> V {
t := cross(2*q.xyz, v);
return V(v + q.r*t + cross(q.xyz, t));
}
-quaternion_mul_vector3 :: proc{quaternion128_mul_vector3, quaternion256_mul_vector3};
+quaternion_mul_vector3 :: proc{quaternion64_mul_vector3, quaternion128_mul_vector3, quaternion256_mul_vector3};
mul :: proc{
matrix_mul,
matrix_mul_differ,
matrix_mul_vector,
+ quaternion64_mul_vector3,
quaternion128_mul_vector3,
quaternion256_mul_vector3,
quaternion_mul_quaternion,
@@ -347,7 +360,9 @@ to_u32 :: #force_inline proc(v: $A/[$N]$T) -> [N]u32 { return array_cast(v, u3
to_u64 :: #force_inline proc(v: $A/[$N]$T) -> [N]u64 { return array_cast(v, u64); }
to_uint :: #force_inline proc(v: $A/[$N]$T) -> [N]uint { return array_cast(v, uint); }
+to_complex32 :: #force_inline proc(v: $A/[$N]$T) -> [N]complex32 { return array_cast(v, complex32); }
to_complex64 :: #force_inline proc(v: $A/[$N]$T) -> [N]complex64 { return array_cast(v, complex64); }
to_complex128 :: #force_inline proc(v: $A/[$N]$T) -> [N]complex128 { return array_cast(v, complex128); }
+to_quaternion64 :: #force_inline proc(v: $A/[$N]$T) -> [N]quaternion64 { return array_cast(v, quaternion64); }
to_quaternion128 :: #force_inline proc(v: $A/[$N]$T) -> [N]quaternion128 { return array_cast(v, quaternion128); }
to_quaternion256 :: #force_inline proc(v: $A/[$N]$T) -> [N]quaternion256 { return array_cast(v, quaternion256); }
diff --git a/core/math/linalg/specific.odin b/core/math/linalg/specific.odin
index f7b255961..3aa3b67f7 100644
--- a/core/math/linalg/specific.odin
+++ b/core/math/linalg/specific.odin
@@ -2,9 +2,39 @@ 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;
@@ -63,9 +93,15 @@ 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}};
@@ -76,9 +112,14 @@ 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};
@@ -118,7 +159,13 @@ 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);
@@ -134,11 +181,33 @@ vector4_srgb_to_linear_f64 :: proc(col: Vector4f64) -> Vector4f64 {
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;
@@ -182,12 +251,39 @@ vector4_linear_to_srgb_f64 :: proc(col: Vector4f64) -> Vector4f64 {
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;
@@ -243,11 +339,41 @@ vector4_hsl_to_rgb_f64 :: proc(h, s, l: f64, a: f64 = 1) -> Vector4f64 {
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;
@@ -277,7 +403,6 @@ vector4_rgb_to_hsl_f32 :: proc(col: Vector4f32) -> Vector4f32 {
return {h, s, l, a};
}
-
vector4_rgb_to_hsl_f64 :: proc(col: Vector4f64) -> Vector4f64 {
r := col.x;
g := col.y;
@@ -308,12 +433,22 @@ vector4_rgb_to_hsl_f64 :: proc(col: Vector4f64) -> Vector4f64 {
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);
@@ -333,11 +468,18 @@ quaternion_angle_axis_f64 :: proc(angle_radians: f64, axis: Vector3f64) -> (q: Q
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;
@@ -353,11 +495,19 @@ angle_from_quaternion_f64 :: proc(q: Quaternionf64) -> f64 {
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 {
@@ -375,11 +525,17 @@ axis_from_quaternion_f64 :: proc(q: Quaternionf64) -> Vector3f64 {
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);
@@ -391,11 +547,55 @@ angle_axis_from_quaternion_f64 :: proc(q: Quaternionf64) -> (angle: f64, axis: V
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));
@@ -483,11 +683,14 @@ quaternion_from_forward_and_up_f64 :: proc(forward, up: Vector3f64) -> Quaternio
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));
}
@@ -495,13 +698,20 @@ quaternion_look_at_f64 :: proc(eye, centre: Vector3f64, up: Vector3f64) -> Quate
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_f32 :: proc(a, b: Quaternionf32, t: f32) -> (c: Quaternionf32) {
+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;
@@ -516,12 +726,39 @@ quaternion_nlerp_f64 :: proc(a, b: Quaternionf64, t: f64) -> (c: Quaternionf64)
return normalize(c);
}
quaternion_nlerp :: proc{
+ quaternion_nlerp_f16,
quaternion_nlerp_f32,
quaternion_nlerp_f64,
};
-quaternion_slerp_f32 :: proc(x, y: Quaternionf32, t: f32) -> (q: Quaternionf32) {
+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 {
@@ -576,11 +813,16 @@ quaternion_slerp_f64 :: proc(x, y: Quaternionf64, t: f64) -> (q: Quaternionf64)
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);
@@ -590,11 +832,19 @@ quaternion_squad_f64 :: proc(q1, q2, s1, s2: Quaternionf64, h: f64) -> Quaternio
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];
@@ -610,11 +860,61 @@ quaternion_from_matrix4_f64 :: proc(m: Matrix4f64) -> (q: Quaternionf64) {
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];
@@ -714,11 +1014,33 @@ quaternion_from_matrix3_f64 :: proc(m: Matrix3f64) -> (q: Quaternionf64) {
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);
@@ -762,11 +1084,21 @@ quaternion_between_two_vector3_f64 :: proc(from, to: Vector3f64) -> (q: Quaterni
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;
@@ -786,11 +1118,15 @@ matrix2_inverse_transpose_f64 :: proc(m: Matrix2f64) -> (c: Matrix2f64) {
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];
}
@@ -798,11 +1134,21 @@ 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;
@@ -822,11 +1168,19 @@ matrix2_inverse_f64 :: proc(m: Matrix2f64) -> (c: Matrix2f64) {
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];
@@ -842,11 +1196,36 @@ matrix2_adjoint_f64 :: proc(m: Matrix2f64) -> (c: Matrix2f64) {
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;
@@ -896,11 +1275,15 @@ matrix3_from_quaternion_f64 :: proc(q: Quaternionf64) -> (m: Matrix3f64) {
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));
}
@@ -908,11 +1291,18 @@ 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]);
@@ -926,11 +1316,24 @@ matrix3_determinant_f64 :: proc(m: Matrix3f64) -> f64 {
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]);
@@ -956,11 +1359,24 @@ matrix3_adjoint_f64 :: proc(m: Matrix3f64) -> (adjoint: Matrix3f64) {
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);
@@ -984,11 +1400,18 @@ matrix3_inverse_transpose_f64 :: proc(m: Matrix3f64) -> (inverse_transpose: Matr
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];
@@ -1002,11 +1425,33 @@ matrix3_scale_f64 :: proc(s: Vector3f64) -> (m: Matrix3f64) {
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);
@@ -1050,11 +1495,22 @@ matrix3_rotate_f64 :: proc(angle_radians: f64, v: Vector3f64) -> (rot: Matrix3f6
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));
@@ -1076,11 +1532,39 @@ matrix3_look_at_f64 :: proc(eye, centre, up: Vector3f64) -> Matrix3f64 {
};
}
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;
@@ -1136,11 +1620,18 @@ matrix4_from_quaternion_f64 :: proc(q: Quaternionf64) -> (m: Matrix4f64) {
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);
@@ -1154,12 +1645,16 @@ matrix4_from_trs_f64 :: proc(t: Vector3f64, r: Quaternionf64, s: Vector3f64) ->
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));
}
@@ -1167,11 +1662,23 @@ 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 {
@@ -1195,11 +1702,18 @@ matrix4_minor_f64 :: proc(m: Matrix4f64, c, r: int) -> f64 {
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;
@@ -1213,11 +1727,20 @@ matrix4_cofactor_f64 :: proc(m: Matrix4f64, c, r: int) -> f64 {
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 {
@@ -1235,11 +1758,19 @@ matrix4_adjoint_f64 :: proc(m: Matrix4f64) -> (adjoint: Matrix4f64) {
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 {
@@ -1255,11 +1786,26 @@ matrix4_determinant_f64 :: proc(m: Matrix4f64) -> (determinant: f64) {
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;
@@ -1289,11 +1835,19 @@ matrix4_inverse_transpose_f64 :: proc(m: Matrix4f64) -> (inverse_transpose: Matr
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];
@@ -1309,11 +1863,38 @@ matrix4_translate_f64 :: proc(v: Vector3f64) -> Matrix4f64 {
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);
@@ -1367,11 +1948,19 @@ matrix4_rotate_f64 :: proc(angle_radians: f64, v: Vector3f64) -> Matrix4f64 {
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];
@@ -1387,11 +1976,26 @@ matrix4_scale_f64 :: proc(v: Vector3f64) -> (m: Matrix4f64) {
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));
@@ -1421,12 +2025,26 @@ matrix4_look_at_f64 :: proc(eye, centre, up: Vector3f64, flip_z_axis := true) ->
};
}
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);
@@ -1456,11 +2074,28 @@ matrix4_perspective_f64 :: proc(fovy, aspect, near, far: f64, flip_z_axis := tru
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);
@@ -1492,11 +2127,27 @@ matrix_ortho3d_f64 :: proc(left, right, bottom, top, near, far: f64, flip_z_axis
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);
@@ -1526,12 +2177,18 @@ matrix4_infinite_perspective_f64 :: proc(fovy, aspect, near: f64, flip_z_axis :=
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;
@@ -1543,11 +2200,18 @@ matrix2_from_scalar_f64 :: proc(f: f64) -> (m: Matrix2f64) {
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;
@@ -1561,11 +2225,19 @@ matrix3_from_scalar_f64 :: proc(f: f64) -> (m: Matrix3f64) {
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;
@@ -1581,11 +2253,17 @@ matrix4_from_scalar_f64 :: proc(f: f64) -> (m: Matrix4f64) {
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];
@@ -1597,11 +2275,17 @@ matrix2_from_matrix3_f64 :: proc(m: Matrix3f64) -> (r: Matrix2f64) {
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];
@@ -1613,11 +2297,18 @@ matrix2_from_matrix4_f64 :: proc(m: Matrix4f64) -> (r: Matrix2f64) {
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;
@@ -1631,11 +2322,18 @@ matrix3_from_matrix2_f64 :: proc(m: Matrix2f64) -> (r: Matrix3f64) {
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];
@@ -1649,11 +2347,19 @@ matrix3_from_matrix4_f64 :: proc(m: Matrix4f64) -> (r: Matrix3f64) {
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;
@@ -1669,11 +2375,19 @@ matrix4_from_matrix2_f64 :: proc(m: Matrix2f64) -> (r: Matrix4f64) {
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;
@@ -1689,11 +2403,16 @@ matrix4_from_matrix3_f64 :: proc(m: Matrix3f64) -> (r: Matrix4f64) {
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;
@@ -1703,23 +2422,29 @@ quaternion_from_scalar_f64 :: proc(f: f64) -> (q: Quaternionf64) {
return;
}
quaternion_from_scalar :: proc{
+ quaternion_from_scalar_f16,
quaternion_from_scalar_f32,
quaternion_from_scalar_f64,
};
-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_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_matrix2f64 :: proc{matrix2_from_scalar_f64, matrix2_from_matrix3_f64, matrix2_from_matrix4_f64};
+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_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_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};
@@ -1727,28 +2452,40 @@ to_quaternionf64 :: proc{quaternion_from_scalar_f64, quaternion_from_matrix3_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]);
@@ -1768,11 +2505,26 @@ matrix2_orthonormalize_f64 :: proc(m: Matrix2f64) -> (r: Matrix2f64) {
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]);
@@ -1802,11 +2554,15 @@ matrix3_orthonormalize_f64 :: proc(m: Matrix3f64) -> (r: Matrix3f64) {
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));
}
@@ -1814,22 +2570,29 @@ 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_f32,
- matrix2_orthonormalize_f64,
- matrix3_orthonormalize_f32,
-
- matrix3_orthonormalize_f64,
- vector3_orthonormalize_f32,
- vector3_orthonormalize_f64,
+ 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;
@@ -1851,11 +2614,23 @@ matrix4_orientation_f64 :: proc(normal, up: Vector3f64) -> Matrix4f64 {
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);
@@ -1879,11 +2654,24 @@ euclidean_from_polar_f64 :: proc(polar: Vector2f64) -> Vector3f64 {
};
}
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;
@@ -1909,6 +2697,7 @@ polar_from_euclidean_f64 :: proc(euclidean: Vector3f64) -> Vector3f64 {
};
}
polar_from_euclidean :: proc{
+ polar_from_euclidean_f16,
polar_from_euclidean_f32,
polar_from_euclidean_f64,
};
diff --git a/core/math/linalg/specific_euler_angles.odin b/core/math/linalg/specific_euler_angles.odin
index 53b33cfe0..000edda12 100644
--- a/core/math/linalg/specific_euler_angles.odin
+++ b/core/math/linalg/specific_euler_angles.odin
@@ -19,109 +19,109 @@ Euler_Angle_Order :: enum {
}
-quaternion_from_euler_angles :: proc{quaternion_from_euler_angles_f32, quaternion_from_euler_angles_f64};
-quaternion_from_euler_angle_x :: proc{quaternion_from_euler_angle_x_f32, quaternion_from_euler_angle_x_f64};
-quaternion_from_euler_angle_y :: proc{quaternion_from_euler_angle_y_f32, quaternion_from_euler_angle_y_f64};
-quaternion_from_euler_angle_z :: proc{quaternion_from_euler_angle_z_f32, quaternion_from_euler_angle_z_f64};
-quaternion_from_pitch_yaw_roll :: proc{quaternion_from_pitch_yaw_roll_f32, quaternion_from_pitch_yaw_roll_f64};
+quaternion_from_euler_angles :: proc{quaternion_from_euler_angles_f16, quaternion_from_euler_angles_f32, quaternion_from_euler_angles_f64};
+quaternion_from_euler_angle_x :: proc{quaternion_from_euler_angle_x_f16, quaternion_from_euler_angle_x_f32, quaternion_from_euler_angle_x_f64};
+quaternion_from_euler_angle_y :: proc{quaternion_from_euler_angle_y_f16, quaternion_from_euler_angle_y_f32, quaternion_from_euler_angle_y_f64};
+quaternion_from_euler_angle_z :: proc{quaternion_from_euler_angle_z_f16, quaternion_from_euler_angle_z_f32, quaternion_from_euler_angle_z_f64};
+quaternion_from_pitch_yaw_roll :: proc{quaternion_from_pitch_yaw_roll_f16, quaternion_from_pitch_yaw_roll_f32, quaternion_from_pitch_yaw_roll_f64};
-euler_angles_from_quaternion :: proc{euler_angles_from_quaternion_f32, euler_angles_from_quaternion_f64};
-euler_angles_xyz_from_quaternion :: proc{euler_angles_xyz_from_quaternion_f32, euler_angles_xyz_from_quaternion_f64};
-euler_angles_yxz_from_quaternion :: proc{euler_angles_yxz_from_quaternion_f32, euler_angles_yxz_from_quaternion_f64};
-euler_angles_xzx_from_quaternion :: proc{euler_angles_xzx_from_quaternion_f32, euler_angles_xzx_from_quaternion_f64};
-euler_angles_xyx_from_quaternion :: proc{euler_angles_xyx_from_quaternion_f32, euler_angles_xyx_from_quaternion_f64};
-euler_angles_yxy_from_quaternion :: proc{euler_angles_yxy_from_quaternion_f32, euler_angles_yxy_from_quaternion_f64};
-euler_angles_yzy_from_quaternion :: proc{euler_angles_yzy_from_quaternion_f32, euler_angles_yzy_from_quaternion_f64};
-euler_angles_zyz_from_quaternion :: proc{euler_angles_zyz_from_quaternion_f32, euler_angles_zyz_from_quaternion_f64};
-euler_angles_zxz_from_quaternion :: proc{euler_angles_zxz_from_quaternion_f32, euler_angles_zxz_from_quaternion_f64};
-euler_angles_xzy_from_quaternion :: proc{euler_angles_xzy_from_quaternion_f32, euler_angles_xzy_from_quaternion_f64};
-euler_angles_yzx_from_quaternion :: proc{euler_angles_yzx_from_quaternion_f32, euler_angles_yzx_from_quaternion_f64};
-euler_angles_zyx_from_quaternion :: proc{euler_angles_zyx_from_quaternion_f32, euler_angles_zyx_from_quaternion_f64};
-euler_angles_zxy_from_quaternion :: proc{euler_angles_zxy_from_quaternion_f32, euler_angles_zxy_from_quaternion_f64};
+euler_angles_from_quaternion :: proc{euler_angles_from_quaternion_f16, euler_angles_from_quaternion_f32, euler_angles_from_quaternion_f64};
+euler_angles_xyz_from_quaternion :: proc{euler_angles_xyz_from_quaternion_f16, euler_angles_xyz_from_quaternion_f32, euler_angles_xyz_from_quaternion_f64};
+euler_angles_yxz_from_quaternion :: proc{euler_angles_yxz_from_quaternion_f16, euler_angles_yxz_from_quaternion_f32, euler_angles_yxz_from_quaternion_f64};
+euler_angles_xzx_from_quaternion :: proc{euler_angles_xzx_from_quaternion_f16, euler_angles_xzx_from_quaternion_f32, euler_angles_xzx_from_quaternion_f64};
+euler_angles_xyx_from_quaternion :: proc{euler_angles_xyx_from_quaternion_f16, euler_angles_xyx_from_quaternion_f32, euler_angles_xyx_from_quaternion_f64};
+euler_angles_yxy_from_quaternion :: proc{euler_angles_yxy_from_quaternion_f16, euler_angles_yxy_from_quaternion_f32, euler_angles_yxy_from_quaternion_f64};
+euler_angles_yzy_from_quaternion :: proc{euler_angles_yzy_from_quaternion_f16, euler_angles_yzy_from_quaternion_f32, euler_angles_yzy_from_quaternion_f64};
+euler_angles_zyz_from_quaternion :: proc{euler_angles_zyz_from_quaternion_f16, euler_angles_zyz_from_quaternion_f32, euler_angles_zyz_from_quaternion_f64};
+euler_angles_zxz_from_quaternion :: proc{euler_angles_zxz_from_quaternion_f16, euler_angles_zxz_from_quaternion_f32, euler_angles_zxz_from_quaternion_f64};
+euler_angles_xzy_from_quaternion :: proc{euler_angles_xzy_from_quaternion_f16, euler_angles_xzy_from_quaternion_f32, euler_angles_xzy_from_quaternion_f64};
+euler_angles_yzx_from_quaternion :: proc{euler_angles_yzx_from_quaternion_f16, euler_angles_yzx_from_quaternion_f32, euler_angles_yzx_from_quaternion_f64};
+euler_angles_zyx_from_quaternion :: proc{euler_angles_zyx_from_quaternion_f16, euler_angles_zyx_from_quaternion_f32, euler_angles_zyx_from_quaternion_f64};
+euler_angles_zxy_from_quaternion :: proc{euler_angles_zxy_from_quaternion_f16, euler_angles_zxy_from_quaternion_f32, euler_angles_zxy_from_quaternion_f64};
-roll_from_quaternion :: proc{roll_from_quaternion_f32, roll_from_quaternion_f64};
-pitch_from_quaternion :: proc{pitch_from_quaternion_f32, pitch_from_quaternion_f64};
-yaw_from_quaternion :: proc{yaw_from_quaternion_f32, yaw_from_quaternion_f64};
-pitch_yaw_roll_from_quaternion :: proc{pitch_yaw_roll_from_quaternion_f32, pitch_yaw_roll_from_quaternion_f64};
+roll_from_quaternion :: proc{roll_from_quaternion_f16, roll_from_quaternion_f32, roll_from_quaternion_f64};
+pitch_from_quaternion :: proc{pitch_from_quaternion_f16, pitch_from_quaternion_f32, pitch_from_quaternion_f64};
+yaw_from_quaternion :: proc{yaw_from_quaternion_f16, yaw_from_quaternion_f32, yaw_from_quaternion_f64};
+pitch_yaw_roll_from_quaternion :: proc{pitch_yaw_roll_from_quaternion_f16, pitch_yaw_roll_from_quaternion_f32, pitch_yaw_roll_from_quaternion_f64};
-matrix3_from_euler_angles :: proc{matrix3_from_euler_angles_f32, matrix3_from_euler_angles_f64};
-matrix3_from_euler_angle_x :: proc{matrix3_from_euler_angle_x_f32, matrix3_from_euler_angle_x_f64};
-matrix3_from_euler_angle_y :: proc{matrix3_from_euler_angle_y_f32, matrix3_from_euler_angle_y_f64};
-matrix3_from_euler_angle_z :: proc{matrix3_from_euler_angle_z_f32, matrix3_from_euler_angle_z_f64};
-matrix3_from_derived_euler_angle_x :: proc{matrix3_from_derived_euler_angle_x_f32, matrix3_from_derived_euler_angle_x_f64};
-matrix3_from_derived_euler_angle_y :: proc{matrix3_from_derived_euler_angle_y_f32, matrix3_from_derived_euler_angle_y_f64};
-matrix3_from_derived_euler_angle_z :: proc{matrix3_from_derived_euler_angle_z_f32, matrix3_from_derived_euler_angle_z_f64};
-matrix3_from_euler_angles_xy :: proc{matrix3_from_euler_angles_xy_f32, matrix3_from_euler_angles_xy_f64};
-matrix3_from_euler_angles_yx :: proc{matrix3_from_euler_angles_yx_f32, matrix3_from_euler_angles_yx_f64};
-matrix3_from_euler_angles_xz :: proc{matrix3_from_euler_angles_xz_f32, matrix3_from_euler_angles_xz_f64};
-matrix3_from_euler_angles_zx :: proc{matrix3_from_euler_angles_zx_f32, matrix3_from_euler_angles_zx_f64};
-matrix3_from_euler_angles_yz :: proc{matrix3_from_euler_angles_yz_f32, matrix3_from_euler_angles_yz_f64};
-matrix3_from_euler_angles_zy :: proc{matrix3_from_euler_angles_zy_f32, matrix3_from_euler_angles_zy_f64};
-matrix3_from_euler_angles_xyz :: proc{matrix3_from_euler_angles_xyz_f32, matrix3_from_euler_angles_xyz_f64};
-matrix3_from_euler_angles_yxz :: proc{matrix3_from_euler_angles_yxz_f32, matrix3_from_euler_angles_yxz_f64};
-matrix3_from_euler_angles_xzx :: proc{matrix3_from_euler_angles_xzx_f32, matrix3_from_euler_angles_xzx_f64};
-matrix3_from_euler_angles_xyx :: proc{matrix3_from_euler_angles_xyx_f32, matrix3_from_euler_angles_xyx_f64};
-matrix3_from_euler_angles_yxy :: proc{matrix3_from_euler_angles_yxy_f32, matrix3_from_euler_angles_yxy_f64};
-matrix3_from_euler_angles_yzy :: proc{matrix3_from_euler_angles_yzy_f32, matrix3_from_euler_angles_yzy_f64};
-matrix3_from_euler_angles_zyz :: proc{matrix3_from_euler_angles_zyz_f32, matrix3_from_euler_angles_zyz_f64};
-matrix3_from_euler_angles_zxz :: proc{matrix3_from_euler_angles_zxz_f32, matrix3_from_euler_angles_zxz_f64};
-matrix3_from_euler_angles_xzy :: proc{matrix3_from_euler_angles_xzy_f32, matrix3_from_euler_angles_xzy_f64};
-matrix3_from_euler_angles_yzx :: proc{matrix3_from_euler_angles_yzx_f32, matrix3_from_euler_angles_yzx_f64};
-matrix3_from_euler_angles_zyx :: proc{matrix3_from_euler_angles_zyx_f32, matrix3_from_euler_angles_zyx_f64};
-matrix3_from_euler_angles_zxy :: proc{matrix3_from_euler_angles_zxy_f32, matrix3_from_euler_angles_zxy_f64};
-matrix3_from_yaw_pitch_roll :: proc{matrix3_from_yaw_pitch_roll_f32, matrix3_from_yaw_pitch_roll_f64};
+matrix3_from_euler_angles :: proc{matrix3_from_euler_angles_f16, matrix3_from_euler_angles_f32, matrix3_from_euler_angles_f64};
+matrix3_from_euler_angle_x :: proc{matrix3_from_euler_angle_x_f16, matrix3_from_euler_angle_x_f32, matrix3_from_euler_angle_x_f64};
+matrix3_from_euler_angle_y :: proc{matrix3_from_euler_angle_y_f16, matrix3_from_euler_angle_y_f32, matrix3_from_euler_angle_y_f64};
+matrix3_from_euler_angle_z :: proc{matrix3_from_euler_angle_z_f16, matrix3_from_euler_angle_z_f32, matrix3_from_euler_angle_z_f64};
+matrix3_from_derived_euler_angle_x :: proc{matrix3_from_derived_euler_angle_x_f16, matrix3_from_derived_euler_angle_x_f32, matrix3_from_derived_euler_angle_x_f64};
+matrix3_from_derived_euler_angle_y :: proc{matrix3_from_derived_euler_angle_y_f16, matrix3_from_derived_euler_angle_y_f32, matrix3_from_derived_euler_angle_y_f64};
+matrix3_from_derived_euler_angle_z :: proc{matrix3_from_derived_euler_angle_z_f16, matrix3_from_derived_euler_angle_z_f32, matrix3_from_derived_euler_angle_z_f64};
+matrix3_from_euler_angles_xy :: proc{matrix3_from_euler_angles_xy_f16, matrix3_from_euler_angles_xy_f32, matrix3_from_euler_angles_xy_f64};
+matrix3_from_euler_angles_yx :: proc{matrix3_from_euler_angles_yx_f16, matrix3_from_euler_angles_yx_f32, matrix3_from_euler_angles_yx_f64};
+matrix3_from_euler_angles_xz :: proc{matrix3_from_euler_angles_xz_f16, matrix3_from_euler_angles_xz_f32, matrix3_from_euler_angles_xz_f64};
+matrix3_from_euler_angles_zx :: proc{matrix3_from_euler_angles_zx_f16, matrix3_from_euler_angles_zx_f32, matrix3_from_euler_angles_zx_f64};
+matrix3_from_euler_angles_yz :: proc{matrix3_from_euler_angles_yz_f16, matrix3_from_euler_angles_yz_f32, matrix3_from_euler_angles_yz_f64};
+matrix3_from_euler_angles_zy :: proc{matrix3_from_euler_angles_zy_f16, matrix3_from_euler_angles_zy_f32, matrix3_from_euler_angles_zy_f64};
+matrix3_from_euler_angles_xyz :: proc{matrix3_from_euler_angles_xyz_f16, matrix3_from_euler_angles_xyz_f32, matrix3_from_euler_angles_xyz_f64};
+matrix3_from_euler_angles_yxz :: proc{matrix3_from_euler_angles_yxz_f16, matrix3_from_euler_angles_yxz_f32, matrix3_from_euler_angles_yxz_f64};
+matrix3_from_euler_angles_xzx :: proc{matrix3_from_euler_angles_xzx_f16, matrix3_from_euler_angles_xzx_f32, matrix3_from_euler_angles_xzx_f64};
+matrix3_from_euler_angles_xyx :: proc{matrix3_from_euler_angles_xyx_f16, matrix3_from_euler_angles_xyx_f32, matrix3_from_euler_angles_xyx_f64};
+matrix3_from_euler_angles_yxy :: proc{matrix3_from_euler_angles_yxy_f16, matrix3_from_euler_angles_yxy_f32, matrix3_from_euler_angles_yxy_f64};
+matrix3_from_euler_angles_yzy :: proc{matrix3_from_euler_angles_yzy_f16, matrix3_from_euler_angles_yzy_f32, matrix3_from_euler_angles_yzy_f64};
+matrix3_from_euler_angles_zyz :: proc{matrix3_from_euler_angles_zyz_f16, matrix3_from_euler_angles_zyz_f32, matrix3_from_euler_angles_zyz_f64};
+matrix3_from_euler_angles_zxz :: proc{matrix3_from_euler_angles_zxz_f16, matrix3_from_euler_angles_zxz_f32, matrix3_from_euler_angles_zxz_f64};
+matrix3_from_euler_angles_xzy :: proc{matrix3_from_euler_angles_xzy_f16, matrix3_from_euler_angles_xzy_f32, matrix3_from_euler_angles_xzy_f64};
+matrix3_from_euler_angles_yzx :: proc{matrix3_from_euler_angles_yzx_f16, matrix3_from_euler_angles_yzx_f32, matrix3_from_euler_angles_yzx_f64};
+matrix3_from_euler_angles_zyx :: proc{matrix3_from_euler_angles_zyx_f16, matrix3_from_euler_angles_zyx_f32, matrix3_from_euler_angles_zyx_f64};
+matrix3_from_euler_angles_zxy :: proc{matrix3_from_euler_angles_zxy_f16, matrix3_from_euler_angles_zxy_f32, matrix3_from_euler_angles_zxy_f64};
+matrix3_from_yaw_pitch_roll :: proc{matrix3_from_yaw_pitch_roll_f16, matrix3_from_yaw_pitch_roll_f32, matrix3_from_yaw_pitch_roll_f64};
-euler_angles_from_matrix3 :: proc{euler_angles_from_matrix3_f32, euler_angles_from_matrix3_f64};
-euler_angles_xyz_from_matrix3 :: proc{euler_angles_xyz_from_matrix3_f32, euler_angles_xyz_from_matrix3_f64};
-euler_angles_yxz_from_matrix3 :: proc{euler_angles_yxz_from_matrix3_f32, euler_angles_yxz_from_matrix3_f64};
-euler_angles_xzx_from_matrix3 :: proc{euler_angles_xzx_from_matrix3_f32, euler_angles_xzx_from_matrix3_f64};
-euler_angles_xyx_from_matrix3 :: proc{euler_angles_xyx_from_matrix3_f32, euler_angles_xyx_from_matrix3_f64};
-euler_angles_yxy_from_matrix3 :: proc{euler_angles_yxy_from_matrix3_f32, euler_angles_yxy_from_matrix3_f64};
-euler_angles_yzy_from_matrix3 :: proc{euler_angles_yzy_from_matrix3_f32, euler_angles_yzy_from_matrix3_f64};
-euler_angles_zyz_from_matrix3 :: proc{euler_angles_zyz_from_matrix3_f32, euler_angles_zyz_from_matrix3_f64};
-euler_angles_zxz_from_matrix3 :: proc{euler_angles_zxz_from_matrix3_f32, euler_angles_zxz_from_matrix3_f64};
-euler_angles_xzy_from_matrix3 :: proc{euler_angles_xzy_from_matrix3_f32, euler_angles_xzy_from_matrix3_f64};
-euler_angles_yzx_from_matrix3 :: proc{euler_angles_yzx_from_matrix3_f32, euler_angles_yzx_from_matrix3_f64};
-euler_angles_zyx_from_matrix3 :: proc{euler_angles_zyx_from_matrix3_f32, euler_angles_zyx_from_matrix3_f64};
-euler_angles_zxy_from_matrix3 :: proc{euler_angles_zxy_from_matrix3_f32, euler_angles_zxy_from_matrix3_f64};
+euler_angles_from_matrix3 :: proc{euler_angles_from_matrix3_f16, euler_angles_from_matrix3_f32, euler_angles_from_matrix3_f64};
+euler_angles_xyz_from_matrix3 :: proc{euler_angles_xyz_from_matrix3_f16, euler_angles_xyz_from_matrix3_f32, euler_angles_xyz_from_matrix3_f64};
+euler_angles_yxz_from_matrix3 :: proc{euler_angles_yxz_from_matrix3_f16, euler_angles_yxz_from_matrix3_f32, euler_angles_yxz_from_matrix3_f64};
+euler_angles_xzx_from_matrix3 :: proc{euler_angles_xzx_from_matrix3_f16, euler_angles_xzx_from_matrix3_f32, euler_angles_xzx_from_matrix3_f64};
+euler_angles_xyx_from_matrix3 :: proc{euler_angles_xyx_from_matrix3_f16, euler_angles_xyx_from_matrix3_f32, euler_angles_xyx_from_matrix3_f64};
+euler_angles_yxy_from_matrix3 :: proc{euler_angles_yxy_from_matrix3_f16, euler_angles_yxy_from_matrix3_f32, euler_angles_yxy_from_matrix3_f64};
+euler_angles_yzy_from_matrix3 :: proc{euler_angles_yzy_from_matrix3_f16, euler_angles_yzy_from_matrix3_f32, euler_angles_yzy_from_matrix3_f64};
+euler_angles_zyz_from_matrix3 :: proc{euler_angles_zyz_from_matrix3_f16, euler_angles_zyz_from_matrix3_f32, euler_angles_zyz_from_matrix3_f64};
+euler_angles_zxz_from_matrix3 :: proc{euler_angles_zxz_from_matrix3_f16, euler_angles_zxz_from_matrix3_f32, euler_angles_zxz_from_matrix3_f64};
+euler_angles_xzy_from_matrix3 :: proc{euler_angles_xzy_from_matrix3_f16, euler_angles_xzy_from_matrix3_f32, euler_angles_xzy_from_matrix3_f64};
+euler_angles_yzx_from_matrix3 :: proc{euler_angles_yzx_from_matrix3_f16, euler_angles_yzx_from_matrix3_f32, euler_angles_yzx_from_matrix3_f64};
+euler_angles_zyx_from_matrix3 :: proc{euler_angles_zyx_from_matrix3_f16, euler_angles_zyx_from_matrix3_f32, euler_angles_zyx_from_matrix3_f64};
+euler_angles_zxy_from_matrix3 :: proc{euler_angles_zxy_from_matrix3_f16, euler_angles_zxy_from_matrix3_f32, euler_angles_zxy_from_matrix3_f64};
-matrix4_from_euler_angles :: proc{matrix4_from_euler_angles_f32, matrix4_from_euler_angles_f64};
-matrix4_from_euler_angle_x :: proc{matrix4_from_euler_angle_x_f32, matrix4_from_euler_angle_x_f64};
-matrix4_from_euler_angle_y :: proc{matrix4_from_euler_angle_y_f32, matrix4_from_euler_angle_y_f64};
-matrix4_from_euler_angle_z :: proc{matrix4_from_euler_angle_z_f32, matrix4_from_euler_angle_z_f64};
-matrix4_from_derived_euler_angle_x :: proc{matrix4_from_derived_euler_angle_x_f32, matrix4_from_derived_euler_angle_x_f64};
-matrix4_from_derived_euler_angle_y :: proc{matrix4_from_derived_euler_angle_y_f32, matrix4_from_derived_euler_angle_y_f64};
-matrix4_from_derived_euler_angle_z :: proc{matrix4_from_derived_euler_angle_z_f32, matrix4_from_derived_euler_angle_z_f64};
-matrix4_from_euler_angles_xy :: proc{matrix4_from_euler_angles_xy_f32, matrix4_from_euler_angles_xy_f64};
-matrix4_from_euler_angles_yx :: proc{matrix4_from_euler_angles_yx_f32, matrix4_from_euler_angles_yx_f64};
-matrix4_from_euler_angles_xz :: proc{matrix4_from_euler_angles_xz_f32, matrix4_from_euler_angles_xz_f64};
-matrix4_from_euler_angles_zx :: proc{matrix4_from_euler_angles_zx_f32, matrix4_from_euler_angles_zx_f64};
-matrix4_from_euler_angles_yz :: proc{matrix4_from_euler_angles_yz_f32, matrix4_from_euler_angles_yz_f64};
-matrix4_from_euler_angles_zy :: proc{matrix4_from_euler_angles_zy_f32, matrix4_from_euler_angles_zy_f64};
-matrix4_from_euler_angles_xyz :: proc{matrix4_from_euler_angles_xyz_f32, matrix4_from_euler_angles_xyz_f64};
-matrix4_from_euler_angles_yxz :: proc{matrix4_from_euler_angles_yxz_f32, matrix4_from_euler_angles_yxz_f64};
-matrix4_from_euler_angles_xzx :: proc{matrix4_from_euler_angles_xzx_f32, matrix4_from_euler_angles_xzx_f64};
-matrix4_from_euler_angles_xyx :: proc{matrix4_from_euler_angles_xyx_f32, matrix4_from_euler_angles_xyx_f64};
-matrix4_from_euler_angles_yxy :: proc{matrix4_from_euler_angles_yxy_f32, matrix4_from_euler_angles_yxy_f64};
-matrix4_from_euler_angles_yzy :: proc{matrix4_from_euler_angles_yzy_f32, matrix4_from_euler_angles_yzy_f64};
-matrix4_from_euler_angles_zyz :: proc{matrix4_from_euler_angles_zyz_f32, matrix4_from_euler_angles_zyz_f64};
-matrix4_from_euler_angles_zxz :: proc{matrix4_from_euler_angles_zxz_f32, matrix4_from_euler_angles_zxz_f64};
-matrix4_from_euler_angles_xzy :: proc{matrix4_from_euler_angles_xzy_f32, matrix4_from_euler_angles_xzy_f64};
-matrix4_from_euler_angles_yzx :: proc{matrix4_from_euler_angles_yzx_f32, matrix4_from_euler_angles_yzx_f64};
-matrix4_from_euler_angles_zyx :: proc{matrix4_from_euler_angles_zyx_f32, matrix4_from_euler_angles_zyx_f64};
-matrix4_from_euler_angles_zxy :: proc{matrix4_from_euler_angles_zxy_f32, matrix4_from_euler_angles_zxy_f64};
-matrix4_from_yaw_pitch_roll :: proc{matrix4_from_yaw_pitch_roll_f32, matrix4_from_yaw_pitch_roll_f64};
+matrix4_from_euler_angles :: proc{matrix4_from_euler_angles_f16, matrix4_from_euler_angles_f32, matrix4_from_euler_angles_f64};
+matrix4_from_euler_angle_x :: proc{matrix4_from_euler_angle_x_f16, matrix4_from_euler_angle_x_f32, matrix4_from_euler_angle_x_f64};
+matrix4_from_euler_angle_y :: proc{matrix4_from_euler_angle_y_f16, matrix4_from_euler_angle_y_f32, matrix4_from_euler_angle_y_f64};
+matrix4_from_euler_angle_z :: proc{matrix4_from_euler_angle_z_f16, matrix4_from_euler_angle_z_f32, matrix4_from_euler_angle_z_f64};
+matrix4_from_derived_euler_angle_x :: proc{matrix4_from_derived_euler_angle_x_f16, matrix4_from_derived_euler_angle_x_f32, matrix4_from_derived_euler_angle_x_f64};
+matrix4_from_derived_euler_angle_y :: proc{matrix4_from_derived_euler_angle_y_f16, matrix4_from_derived_euler_angle_y_f32, matrix4_from_derived_euler_angle_y_f64};
+matrix4_from_derived_euler_angle_z :: proc{matrix4_from_derived_euler_angle_z_f16, matrix4_from_derived_euler_angle_z_f32, matrix4_from_derived_euler_angle_z_f64};
+matrix4_from_euler_angles_xy :: proc{matrix4_from_euler_angles_xy_f16, matrix4_from_euler_angles_xy_f32, matrix4_from_euler_angles_xy_f64};
+matrix4_from_euler_angles_yx :: proc{matrix4_from_euler_angles_yx_f16, matrix4_from_euler_angles_yx_f32, matrix4_from_euler_angles_yx_f64};
+matrix4_from_euler_angles_xz :: proc{matrix4_from_euler_angles_xz_f16, matrix4_from_euler_angles_xz_f32, matrix4_from_euler_angles_xz_f64};
+matrix4_from_euler_angles_zx :: proc{matrix4_from_euler_angles_zx_f16, matrix4_from_euler_angles_zx_f32, matrix4_from_euler_angles_zx_f64};
+matrix4_from_euler_angles_yz :: proc{matrix4_from_euler_angles_yz_f16, matrix4_from_euler_angles_yz_f32, matrix4_from_euler_angles_yz_f64};
+matrix4_from_euler_angles_zy :: proc{matrix4_from_euler_angles_zy_f16, matrix4_from_euler_angles_zy_f32, matrix4_from_euler_angles_zy_f64};
+matrix4_from_euler_angles_xyz :: proc{matrix4_from_euler_angles_xyz_f16, matrix4_from_euler_angles_xyz_f32, matrix4_from_euler_angles_xyz_f64};
+matrix4_from_euler_angles_yxz :: proc{matrix4_from_euler_angles_yxz_f16, matrix4_from_euler_angles_yxz_f32, matrix4_from_euler_angles_yxz_f64};
+matrix4_from_euler_angles_xzx :: proc{matrix4_from_euler_angles_xzx_f16, matrix4_from_euler_angles_xzx_f32, matrix4_from_euler_angles_xzx_f64};
+matrix4_from_euler_angles_xyx :: proc{matrix4_from_euler_angles_xyx_f16, matrix4_from_euler_angles_xyx_f32, matrix4_from_euler_angles_xyx_f64};
+matrix4_from_euler_angles_yxy :: proc{matrix4_from_euler_angles_yxy_f16, matrix4_from_euler_angles_yxy_f32, matrix4_from_euler_angles_yxy_f64};
+matrix4_from_euler_angles_yzy :: proc{matrix4_from_euler_angles_yzy_f16, matrix4_from_euler_angles_yzy_f32, matrix4_from_euler_angles_yzy_f64};
+matrix4_from_euler_angles_zyz :: proc{matrix4_from_euler_angles_zyz_f16, matrix4_from_euler_angles_zyz_f32, matrix4_from_euler_angles_zyz_f64};
+matrix4_from_euler_angles_zxz :: proc{matrix4_from_euler_angles_zxz_f16, matrix4_from_euler_angles_zxz_f32, matrix4_from_euler_angles_zxz_f64};
+matrix4_from_euler_angles_xzy :: proc{matrix4_from_euler_angles_xzy_f16, matrix4_from_euler_angles_xzy_f32, matrix4_from_euler_angles_xzy_f64};
+matrix4_from_euler_angles_yzx :: proc{matrix4_from_euler_angles_yzx_f16, matrix4_from_euler_angles_yzx_f32, matrix4_from_euler_angles_yzx_f64};
+matrix4_from_euler_angles_zyx :: proc{matrix4_from_euler_angles_zyx_f16, matrix4_from_euler_angles_zyx_f32, matrix4_from_euler_angles_zyx_f64};
+matrix4_from_euler_angles_zxy :: proc{matrix4_from_euler_angles_zxy_f16, matrix4_from_euler_angles_zxy_f32, matrix4_from_euler_angles_zxy_f64};
+matrix4_from_yaw_pitch_roll :: proc{matrix4_from_yaw_pitch_roll_f16, matrix4_from_yaw_pitch_roll_f32, matrix4_from_yaw_pitch_roll_f64};
-euler_angles_from_matrix4 :: proc{euler_angles_from_matrix4_f32, euler_angles_from_matrix4_f64};
-euler_angles_xyz_from_matrix4 :: proc{euler_angles_xyz_from_matrix4_f32, euler_angles_xyz_from_matrix4_f64};
-euler_angles_yxz_from_matrix4 :: proc{euler_angles_yxz_from_matrix4_f32, euler_angles_yxz_from_matrix4_f64};
-euler_angles_xzx_from_matrix4 :: proc{euler_angles_xzx_from_matrix4_f32, euler_angles_xzx_from_matrix4_f64};
-euler_angles_xyx_from_matrix4 :: proc{euler_angles_xyx_from_matrix4_f32, euler_angles_xyx_from_matrix4_f64};
-euler_angles_yxy_from_matrix4 :: proc{euler_angles_yxy_from_matrix4_f32, euler_angles_yxy_from_matrix4_f64};
-euler_angles_yzy_from_matrix4 :: proc{euler_angles_yzy_from_matrix4_f32, euler_angles_yzy_from_matrix4_f64};
-euler_angles_zyz_from_matrix4 :: proc{euler_angles_zyz_from_matrix4_f32, euler_angles_zyz_from_matrix4_f64};
-euler_angles_zxz_from_matrix4 :: proc{euler_angles_zxz_from_matrix4_f32, euler_angles_zxz_from_matrix4_f64};
-euler_angles_xzy_from_matrix4 :: proc{euler_angles_xzy_from_matrix4_f32, euler_angles_xzy_from_matrix4_f64};
-euler_angles_yzx_from_matrix4 :: proc{euler_angles_yzx_from_matrix4_f32, euler_angles_yzx_from_matrix4_f64};
-euler_angles_zyx_from_matrix4 :: proc{euler_angles_zyx_from_matrix4_f32, euler_angles_zyx_from_matrix4_f64};
-euler_angles_zxy_from_matrix4 :: proc{euler_angles_zxy_from_matrix4_f32, euler_angles_zxy_from_matrix4_f64};
+euler_angles_from_matrix4 :: proc{euler_angles_from_matrix4_f16, euler_angles_from_matrix4_f32, euler_angles_from_matrix4_f64};
+euler_angles_xyz_from_matrix4 :: proc{euler_angles_xyz_from_matrix4_f16, euler_angles_xyz_from_matrix4_f32, euler_angles_xyz_from_matrix4_f64};
+euler_angles_yxz_from_matrix4 :: proc{euler_angles_yxz_from_matrix4_f16, euler_angles_yxz_from_matrix4_f32, euler_angles_yxz_from_matrix4_f64};
+euler_angles_xzx_from_matrix4 :: proc{euler_angles_xzx_from_matrix4_f16, euler_angles_xzx_from_matrix4_f32, euler_angles_xzx_from_matrix4_f64};
+euler_angles_xyx_from_matrix4 :: proc{euler_angles_xyx_from_matrix4_f16, euler_angles_xyx_from_matrix4_f32, euler_angles_xyx_from_matrix4_f64};
+euler_angles_yxy_from_matrix4 :: proc{euler_angles_yxy_from_matrix4_f16, euler_angles_yxy_from_matrix4_f32, euler_angles_yxy_from_matrix4_f64};
+euler_angles_yzy_from_matrix4 :: proc{euler_angles_yzy_from_matrix4_f16, euler_angles_yzy_from_matrix4_f32, euler_angles_yzy_from_matrix4_f64};
+euler_angles_zyz_from_matrix4 :: proc{euler_angles_zyz_from_matrix4_f16, euler_angles_zyz_from_matrix4_f32, euler_angles_zyz_from_matrix4_f64};
+euler_angles_zxz_from_matrix4 :: proc{euler_angles_zxz_from_matrix4_f16, euler_angles_zxz_from_matrix4_f32, euler_angles_zxz_from_matrix4_f64};
+euler_angles_xzy_from_matrix4 :: proc{euler_angles_xzy_from_matrix4_f16, euler_angles_xzy_from_matrix4_f32, euler_angles_xzy_from_matrix4_f64};
+euler_angles_yzx_from_matrix4 :: proc{euler_angles_yzx_from_matrix4_f16, euler_angles_yzx_from_matrix4_f32, euler_angles_yzx_from_matrix4_f64};
+euler_angles_zyx_from_matrix4 :: proc{euler_angles_zyx_from_matrix4_f16, euler_angles_zyx_from_matrix4_f32, euler_angles_zyx_from_matrix4_f64};
+euler_angles_zxy_from_matrix4 :: proc{euler_angles_zxy_from_matrix4_f16, euler_angles_zxy_from_matrix4_f32, euler_angles_zxy_from_matrix4_f64};
diff --git a/core/math/linalg/specific_euler_angles_f16.odin b/core/math/linalg/specific_euler_angles_f16.odin
new file mode 100644
index 000000000..bcfac6039
--- /dev/null
+++ b/core/math/linalg/specific_euler_angles_f16.odin
@@ -0,0 +1,1356 @@
+package linalg
+
+import "core:math"
+
+euler_angles_from_matrix3_f16 :: proc(m: Matrix3f16, order: Euler_Angle_Order) -> (t1, t2, t3: f16) {
+ switch order {
+ case .XYZ: t1, t2, t3 = euler_angles_xyz_from_matrix3(m);
+ case .XZY: t1, t2, t3 = euler_angles_xzy_from_matrix3(m);
+ case .YXZ: t1, t2, t3 = euler_angles_yxz_from_matrix3(m);
+ case .YZX: t1, t2, t3 = euler_angles_yzx_from_matrix3(m);
+ case .ZXY: t1, t2, t3 = euler_angles_zxy_from_matrix3(m);
+ case .ZYX: t1, t2, t3 = euler_angles_zyx_from_matrix3(m);
+ case .XYX: t1, t2, t3 = euler_angles_xyx_from_matrix3(m);
+ case .XZX: t1, t2, t3 = euler_angles_xzx_from_matrix3(m);
+ case .YXY: t1, t2, t3 = euler_angles_yxy_from_matrix3(m);
+ case .YZY: t1, t2, t3 = euler_angles_yzy_from_matrix3(m);
+ case .ZXZ: t1, t2, t3 = euler_angles_zxz_from_matrix3(m);
+ case .ZYZ: t1, t2, t3 = euler_angles_zyz_from_matrix3(m);
+ }
+ return;
+}
+euler_angles_from_matrix4_f16 :: proc(m: Matrix4f16, order: Euler_Angle_Order) -> (t1, t2, t3: f16) {
+ switch order {
+ case .XYZ: t1, t2, t3 = euler_angles_xyz_from_matrix4(m);
+ case .XZY: t1, t2, t3 = euler_angles_xzy_from_matrix4(m);
+ case .YXZ: t1, t2, t3 = euler_angles_yxz_from_matrix4(m);
+ case .YZX: t1, t2, t3 = euler_angles_yzx_from_matrix4(m);
+ case .ZXY: t1, t2, t3 = euler_angles_zxy_from_matrix4(m);
+ case .ZYX: t1, t2, t3 = euler_angles_zyx_from_matrix4(m);
+ case .XYX: t1, t2, t3 = euler_angles_xyx_from_matrix4(m);
+ case .XZX: t1, t2, t3 = euler_angles_xzx_from_matrix4(m);
+ case .YXY: t1, t2, t3 = euler_angles_yxy_from_matrix4(m);
+ case .YZY: t1, t2, t3 = euler_angles_yzy_from_matrix4(m);
+ case .ZXZ: t1, t2, t3 = euler_angles_zxz_from_matrix4(m);
+ case .ZYZ: t1, t2, t3 = euler_angles_zyz_from_matrix4(m);
+ }
+ return;
+}
+euler_angles_from_quaternion_f16 :: proc(m: Quaternionf16, order: Euler_Angle_Order) -> (t1, t2, t3: f16) {
+ switch order {
+ case .XYZ: t1, t2, t3 = euler_angles_xyz_from_quaternion(m);
+ case .XZY: t1, t2, t3 = euler_angles_xzy_from_quaternion(m);
+ case .YXZ: t1, t2, t3 = euler_angles_yxz_from_quaternion(m);
+ case .YZX: t1, t2, t3 = euler_angles_yzx_from_quaternion(m);
+ case .ZXY: t1, t2, t3 = euler_angles_zxy_from_quaternion(m);
+ case .ZYX: t1, t2, t3 = euler_angles_zyx_from_quaternion(m);
+ case .XYX: t1, t2, t3 = euler_angles_xyx_from_quaternion(m);
+ case .XZX: t1, t2, t3 = euler_angles_xzx_from_quaternion(m);
+ case .YXY: t1, t2, t3 = euler_angles_yxy_from_quaternion(m);
+ case .YZY: t1, t2, t3 = euler_angles_yzy_from_quaternion(m);
+ case .ZXZ: t1, t2, t3 = euler_angles_zxz_from_quaternion(m);
+ case .ZYZ: t1, t2, t3 = euler_angles_zyz_from_quaternion(m);
+ }
+ return;
+}
+
+matrix3_from_euler_angles_f16 :: proc(t1, t2, t3: f16, order: Euler_Angle_Order) -> (m: Matrix3f16) {
+ switch order {
+ case .XYZ: return matrix3_from_euler_angles_xyz(t1, t2, t3); // m1, m2, m3 = X(t1), Y(t2), Z(t3);
+ case .XZY: return matrix3_from_euler_angles_xzy(t1, t2, t3); // m1, m2, m3 = X(t1), Z(t2), Y(t3);
+ case .YXZ: return matrix3_from_euler_angles_yxz(t1, t2, t3); // m1, m2, m3 = Y(t1), X(t2), Z(t3);
+ case .YZX: return matrix3_from_euler_angles_yzx(t1, t2, t3); // m1, m2, m3 = Y(t1), Z(t2), X(t3);
+ case .ZXY: return matrix3_from_euler_angles_zxy(t1, t2, t3); // m1, m2, m3 = Z(t1), X(t2), Y(t3);
+ case .ZYX: return matrix3_from_euler_angles_zyx(t1, t2, t3); // m1, m2, m3 = Z(t1), Y(t2), X(t3);
+ case .XYX: return matrix3_from_euler_angles_xyx(t1, t2, t3); // m1, m2, m3 = X(t1), Y(t2), X(t3);
+ case .XZX: return matrix3_from_euler_angles_xzx(t1, t2, t3); // m1, m2, m3 = X(t1), Z(t2), X(t3);
+ case .YXY: return matrix3_from_euler_angles_yxy(t1, t2, t3); // m1, m2, m3 = Y(t1), X(t2), Y(t3);
+ case .YZY: return matrix3_from_euler_angles_yzy(t1, t2, t3); // m1, m2, m3 = Y(t1), Z(t2), Y(t3);
+ case .ZXZ: return matrix3_from_euler_angles_zxz(t1, t2, t3); // m1, m2, m3 = Z(t1), X(t2), Z(t3);
+ case .ZYZ: return matrix3_from_euler_angles_zyz(t1, t2, t3); // m1, m2, m3 = Z(t1), Y(t2), Z(t3);
+ }
+ return;
+}
+matrix4_from_euler_angles_f16 :: proc(t1, t2, t3: f16, order: Euler_Angle_Order) -> (m: Matrix4f16) {
+ switch order {
+ case .XYZ: return matrix4_from_euler_angles_xyz(t1, t2, t3); // m1, m2, m3 = X(t1), Y(t2), Z(t3);
+ case .XZY: return matrix4_from_euler_angles_xzy(t1, t2, t3); // m1, m2, m3 = X(t1), Z(t2), Y(t3);
+ case .YXZ: return matrix4_from_euler_angles_yxz(t1, t2, t3); // m1, m2, m3 = Y(t1), X(t2), Z(t3);
+ case .YZX: return matrix4_from_euler_angles_yzx(t1, t2, t3); // m1, m2, m3 = Y(t1), Z(t2), X(t3);
+ case .ZXY: return matrix4_from_euler_angles_zxy(t1, t2, t3); // m1, m2, m3 = Z(t1), X(t2), Y(t3);
+ case .ZYX: return matrix4_from_euler_angles_zyx(t1, t2, t3); // m1, m2, m3 = Z(t1), Y(t2), X(t3);
+ case .XYX: return matrix4_from_euler_angles_xyx(t1, t2, t3); // m1, m2, m3 = X(t1), Y(t2), X(t3);
+ case .XZX: return matrix4_from_euler_angles_xzx(t1, t2, t3); // m1, m2, m3 = X(t1), Z(t2), X(t3);
+ case .YXY: return matrix4_from_euler_angles_yxy(t1, t2, t3); // m1, m2, m3 = Y(t1), X(t2), Y(t3);
+ case .YZY: return matrix4_from_euler_angles_yzy(t1, t2, t3); // m1, m2, m3 = Y(t1), Z(t2), Y(t3);
+ case .ZXZ: return matrix4_from_euler_angles_zxz(t1, t2, t3); // m1, m2, m3 = Z(t1), X(t2), Z(t3);
+ case .ZYZ: return matrix4_from_euler_angles_zyz(t1, t2, t3); // m1, m2, m3 = Z(t1), Y(t2), Z(t3);
+ }
+ return;
+}
+
+quaternion_from_euler_angles_f16 :: proc(t1, t2, t3: f16, order: Euler_Angle_Order) -> Quaternionf16 {
+ X :: quaternion_from_euler_angle_x;
+ Y :: quaternion_from_euler_angle_y;
+ Z :: quaternion_from_euler_angle_z;
+
+ q1, q2, q3: Quaternionf16;
+
+ switch order {
+ case .XYZ: q1, q2, q3 = X(t1), Y(t2), Z(t3);
+ case .XZY: q1, q2, q3 = X(t1), Z(t2), Y(t3);
+ case .YXZ: q1, q2, q3 = Y(t1), X(t2), Z(t3);
+ case .YZX: q1, q2, q3 = Y(t1), Z(t2), X(t3);
+ case .ZXY: q1, q2, q3 = Z(t1), X(t2), Y(t3);
+ case .ZYX: q1, q2, q3 = Z(t1), Y(t2), X(t3);
+ case .XYX: q1, q2, q3 = X(t1), Y(t2), X(t3);
+ case .XZX: q1, q2, q3 = X(t1), Z(t2), X(t3);
+ case .YXY: q1, q2, q3 = Y(t1), X(t2), Y(t3);
+ case .YZY: q1, q2, q3 = Y(t1), Z(t2), Y(t3);
+ case .ZXZ: q1, q2, q3 = Z(t1), X(t2), Z(t3);
+ case .ZYZ: q1, q2, q3 = Z(t1), Y(t2), Z(t3);
+ }
+
+ return q1 * (q2 * q3);
+}
+
+
+// Quaternionf16s
+
+quaternion_from_euler_angle_x_f16 :: proc(angle_x: f16) -> (q: Quaternionf16) {
+ return quaternion_angle_axis_f16(angle_x, {1, 0, 0});
+}
+quaternion_from_euler_angle_y_f16 :: proc(angle_y: f16) -> (q: Quaternionf16) {
+ return quaternion_angle_axis_f16(angle_y, {0, 1, 0});
+}
+quaternion_from_euler_angle_z_f16 :: proc(angle_z: f16) -> (q: Quaternionf16) {
+ return quaternion_angle_axis_f16(angle_z, {0, 0, 1});
+}
+
+quaternion_from_pitch_yaw_roll_f16 :: proc(pitch, yaw, roll: f16) -> Quaternionf16 {
+ a, b, c := pitch, yaw, roll;
+
+ ca, sa := math.cos(a*0.5), math.sin(a*0.5);
+ cb, sb := math.cos(b*0.5), math.sin(b*0.5);
+ cc, sc := math.cos(c*0.5), math.sin(c*0.5);
+
+ q: Quaternionf16;
+ q.x = sa*cb*cc - ca*sb*sc;
+ q.y = ca*sb*cc + sa*cb*sc;
+ q.z = ca*cb*sc - sa*sb*cc;
+ q.w = ca*cb*cc + sa*sb*sc;
+ return q;
+}
+
+roll_from_quaternion_f16 :: proc(q: Quaternionf16) -> f16 {
+ return math.atan2(2 * q.x*q.y + q.w*q.z, q.w*q.w + q.x*q.x - q.y*q.y - q.z*q.z);
+}
+
+pitch_from_quaternion_f16 :: proc(q: Quaternionf16) -> f16 {
+ y := 2 * (q.y*q.z + q.w*q.w);
+ x := q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z;
+
+ if abs(x) <= F16_EPSILON && abs(y) <= F16_EPSILON {
+ return 2 * math.atan2(q.x, q.w);
+ }
+
+ return math.atan2(y, x);
+}
+
+yaw_from_quaternion_f16 :: proc(q: Quaternionf16) -> f16 {
+ return math.asin(clamp(-2 * (q.x*q.z - q.w*q.y), -1, 1));
+}
+
+
+pitch_yaw_roll_from_quaternion_f16 :: proc(q: Quaternionf16) -> (pitch, yaw, roll: f16) {
+ pitch = pitch_from_quaternion(q);
+ yaw = yaw_from_quaternion(q);
+ roll = roll_from_quaternion(q);
+ return;
+}
+
+euler_angles_xyz_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) {
+ return euler_angles_xyz_from_matrix4(matrix4_from_quaternion(q));
+}
+euler_angles_yxz_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) {
+ return euler_angles_yxz_from_matrix4(matrix4_from_quaternion(q));
+}
+euler_angles_xzx_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) {
+ return euler_angles_xzx_from_matrix4(matrix4_from_quaternion(q));
+}
+euler_angles_xyx_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) {
+ return euler_angles_xyx_from_matrix4(matrix4_from_quaternion(q));
+}
+euler_angles_yxy_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) {
+ return euler_angles_yxy_from_matrix4(matrix4_from_quaternion(q));
+}
+euler_angles_yzy_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) {
+ return euler_angles_yzy_from_matrix4(matrix4_from_quaternion(q));
+}
+euler_angles_zyz_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) {
+ return euler_angles_zyz_from_matrix4(matrix4_from_quaternion(q));
+}
+euler_angles_zxz_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) {
+ return euler_angles_zxz_from_matrix4(matrix4_from_quaternion(q));
+}
+euler_angles_xzy_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) {
+ return euler_angles_xzy_from_matrix4(matrix4_from_quaternion(q));
+}
+euler_angles_yzx_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) {
+ return euler_angles_yzx_from_matrix4(matrix4_from_quaternion(q));
+}
+euler_angles_zyx_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) {
+ return euler_angles_zyx_from_matrix4(matrix4_from_quaternion(q));
+}
+euler_angles_zxy_from_quaternion_f16 :: proc(q: Quaternionf16) -> (t1, t2, t3: f16) {
+ return euler_angles_zxy_from_matrix4(matrix4_from_quaternion(q));
+}
+
+
+// Matrix3
+
+
+matrix3_from_euler_angle_x_f16 :: proc(angle_x: f16) -> (m: Matrix3f16) {
+ cos_x, sin_x := math.cos(angle_x), math.sin(angle_x);
+ m[0][0] = 1;
+ m[1][1] = +cos_x;
+ m[2][1] = +sin_x;
+ m[1][2] = -sin_x;
+ m[2][2] = +cos_x;
+ return;
+}
+matrix3_from_euler_angle_y_f16 :: proc(angle_y: f16) -> (m: Matrix3f16) {
+ cos_y, sin_y := math.cos(angle_y), math.sin(angle_y);
+ m[0][0] = +cos_y;
+ m[2][0] = -sin_y;
+ m[1][1] = 1;
+ m[0][2] = +sin_y;
+ m[2][2] = +cos_y;
+ return;
+}
+matrix3_from_euler_angle_z_f16 :: proc(angle_z: f16) -> (m: Matrix3f16) {
+ cos_z, sin_z := math.cos(angle_z), math.sin(angle_z);
+ m[0][0] = +cos_z;
+ m[1][0] = +sin_z;
+ m[1][1] = +cos_z;
+ m[0][1] = -sin_z;
+ m[2][2] = 1;
+ return;
+}
+
+
+matrix3_from_derived_euler_angle_x_f16 :: proc(angle_x: f16, angular_velocity_x: f16) -> (m: Matrix3f16) {
+ cos_x := math.cos(angle_x) * angular_velocity_x;
+ sin_x := math.sin(angle_x) * angular_velocity_x;
+ m[0][0] = 1;
+ m[1][1] = +cos_x;
+ m[2][1] = +sin_x;
+ m[1][2] = -sin_x;
+ m[2][2] = +cos_x;
+ return;
+}
+matrix3_from_derived_euler_angle_y_f16 :: proc(angle_y: f16, angular_velocity_y: f16) -> (m: Matrix3f16) {
+ cos_y := math.cos(angle_y) * angular_velocity_y;
+ sin_y := math.sin(angle_y) * angular_velocity_y;
+ m[0][0] = +cos_y;
+ m[2][0] = -sin_y;
+ m[1][1] = 1;
+ m[0][2] = +sin_y;
+ m[2][2] = +cos_y;
+ return;
+}
+matrix3_from_derived_euler_angle_z_f16 :: proc(angle_z: f16, angular_velocity_z: f16) -> (m: Matrix3f16) {
+ cos_z := math.cos(angle_z) * angular_velocity_z;
+ sin_z := math.sin(angle_z) * angular_velocity_z;
+ m[0][0] = +cos_z;
+ m[1][0] = +sin_z;
+ m[1][1] = +cos_z;
+ m[0][1] = -sin_z;
+ m[2][2] = 1;
+ return;
+}
+
+
+matrix3_from_euler_angles_xy_f16 :: proc(angle_x, angle_y: f16) -> (m: Matrix3f16) {
+ cos_x, sin_x := math.cos(angle_x), math.sin(angle_x);
+ cos_y, sin_y := math.cos(angle_y), math.sin(angle_y);
+ m[0][0] = cos_y;
+ m[1][0] = -sin_x * - sin_y;
+ m[2][0] = -cos_x * - sin_y;
+ m[1][1] = cos_x;
+ m[2][1] = sin_x;
+ m[0][2] = sin_y;
+ m[1][2] = -sin_x * cos_y;
+ m[2][2] = cos_x * cos_y;
+ return;
+}
+
+
+matrix3_from_euler_angles_yx_f16 :: proc(angle_y, angle_x: f16) -> (m: Matrix3f16) {
+ cos_x, sin_x := math.cos(angle_x), math.sin(angle_x);
+ cos_y, sin_y := math.cos(angle_y), math.sin(angle_y);
+ m[0][0] = cos_y;
+ m[2][0] = -sin_y;
+ m[0][1] = sin_y*sin_x;
+ m[1][1] = cos_x;
+ m[2][1] = cos_y*sin_x;
+ m[0][2] = sin_y*cos_x;
+ m[1][2] = -sin_x;
+ m[2][2] = cos_y*cos_x;
+ return;
+}
+
+matrix3_from_euler_angles_xz_f16 :: proc(angle_x, angle_z: f16) -> (m: Matrix3f16) {
+ return mul(matrix3_from_euler_angle_x(angle_x), matrix3_from_euler_angle_z(angle_z));
+}
+matrix3_from_euler_angles_zx_f16 :: proc(angle_z, angle_x: f16) -> (m: Matrix3f16) {
+ return mul(matrix3_from_euler_angle_z(angle_z), matrix3_from_euler_angle_x(angle_x));
+}
+matrix3_from_euler_angles_yz_f16 :: proc(angle_y, angle_z: f16) -> (m: Matrix3f16) {
+ return mul(matrix3_from_euler_angle_y(angle_y), matrix3_from_euler_angle_z(angle_z));
+}
+matrix3_from_euler_angles_zy_f16 :: proc(angle_z, angle_y: f16) -> (m: Matrix3f16) {
+ return mul(matrix3_from_euler_angle_z(angle_z), matrix3_from_euler_angle_y(angle_y));
+}
+
+
+matrix3_from_euler_angles_xyz_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) {
+ c1 := math.cos(-t1);
+ c2 := math.cos(-t2);
+ c3 := math.cos(-t3);
+ s1 := math.sin(-t1);
+ s2 := math.sin(-t2);
+ s3 := math.sin(-t3);
+
+ m[0][0] = c2 * c3;
+ m[0][1] =-c1 * s3 + s1 * s2 * c3;
+ m[0][2] = s1 * s3 + c1 * s2 * c3;
+ m[1][0] = c2 * s3;
+ m[1][1] = c1 * c3 + s1 * s2 * s3;
+ m[1][2] =-s1 * c3 + c1 * s2 * s3;
+ m[2][0] =-s2;
+ m[2][1] = s1 * c2;
+ m[2][2] = c1 * c2;
+ return;
+}
+
+matrix3_from_euler_angles_yxz_f16 :: proc(yaw, pitch, roll: f16) -> (m: Matrix3f16) {
+ ch := math.cos(yaw);
+ sh := math.sin(yaw);
+ cp := math.cos(pitch);
+ sp := math.sin(pitch);
+ cb := math.cos(roll);
+ sb := math.sin(roll);
+
+ m[0][0] = ch * cb + sh * sp * sb;
+ m[0][1] = sb * cp;
+ m[0][2] = -sh * cb + ch * sp * sb;
+ m[1][0] = -ch * sb + sh * sp * cb;
+ m[1][1] = cb * cp;
+ m[1][2] = sb * sh + ch * sp * cb;
+ m[2][0] = sh * cp;
+ m[2][1] = -sp;
+ m[2][2] = ch * cp;
+ return;
+}
+
+matrix3_from_euler_angles_xzx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c2;
+ m[0][1] = c1 * s2;
+ m[0][2] = s1 * s2;
+ m[1][0] =-c3 * s2;
+ m[1][1] = c1 * c2 * c3 - s1 * s3;
+ m[1][2] = c1 * s3 + c2 * c3 * s1;
+ m[2][0] = s2 * s3;
+ m[2][1] =-c3 * s1 - c1 * c2 * s3;
+ m[2][2] = c1 * c3 - c2 * s1 * s3;
+ return;
+}
+
+matrix3_from_euler_angles_xyx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c2;
+ m[0][1] = s1 * s2;
+ m[0][2] =-c1 * s2;
+ m[1][0] = s2 * s3;
+ m[1][1] = c1 * c3 - c2 * s1 * s3;
+ m[1][2] = c3 * s1 + c1 * c2 * s3;
+ m[2][0] = c3 * s2;
+ m[2][1] =-c1 * s3 - c2 * c3 * s1;
+ m[2][2] = c1 * c2 * c3 - s1 * s3;
+ return;
+}
+
+matrix3_from_euler_angles_yxy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c1 * c3 - c2 * s1 * s3;
+ m[0][1] = s2* s3;
+ m[0][2] =-c3 * s1 - c1 * c2 * s3;
+ m[1][0] = s1 * s2;
+ m[1][1] = c2;
+ m[1][2] = c1 * s2;
+ m[2][0] = c1 * s3 + c2 * c3 * s1;
+ m[2][1] =-c3 * s2;
+ m[2][2] = c1 * c2 * c3 - s1 * s3;
+ return;
+}
+
+matrix3_from_euler_angles_yzy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c1 * c2 * c3 - s1 * s3;
+ m[0][1] = c3 * s2;
+ m[0][2] =-c1 * s3 - c2 * c3 * s1;
+ m[1][0] =-c1 * s2;
+ m[1][1] = c2;
+ m[1][2] = s1 * s2;
+ m[2][0] = c3 * s1 + c1 * c2 * s3;
+ m[2][1] = s2 * s3;
+ m[2][2] = c1 * c3 - c2 * s1 * s3;
+ return;
+}
+
+matrix3_from_euler_angles_zyz_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c1 * c2 * c3 - s1 * s3;
+ m[0][1] = c1 * s3 + c2 * c3 * s1;
+ m[0][2] =-c3 * s2;
+ m[1][0] =-c3 * s1 - c1 * c2 * s3;
+ m[1][1] = c1 * c3 - c2 * s1 * s3;
+ m[1][2] = s2 * s3;
+ m[2][0] = c1 * s2;
+ m[2][1] = s1 * s2;
+ m[2][2] = c2;
+ return;
+}
+
+matrix3_from_euler_angles_zxz_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c1 * c3 - c2 * s1 * s3;
+ m[0][1] = c3 * s1 + c1 * c2 * s3;
+ m[0][2] = s2 *s3;
+ m[1][0] =-c1 * s3 - c2 * c3 * s1;
+ m[1][1] = c1 * c2 * c3 - s1 * s3;
+ m[1][2] = c3 * s2;
+ m[2][0] = s1 * s2;
+ m[2][1] =-c1 * s2;
+ m[2][2] = c2;
+ return;
+}
+
+
+matrix3_from_euler_angles_xzy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c2 * c3;
+ m[0][1] = s1 * s3 + c1 * c3 * s2;
+ m[0][2] = c3 * s1 * s2 - c1 * s3;
+ m[1][0] =-s2;
+ m[1][1] = c1 * c2;
+ m[1][2] = c2 * s1;
+ m[2][0] = c2 * s3;
+ m[2][1] = c1 * s2 * s3 - c3 * s1;
+ m[2][2] = c1 * c3 + s1 * s2 *s3;
+ return;
+}
+
+matrix3_from_euler_angles_yzx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c1 * c2;
+ m[0][1] = s2;
+ m[0][2] =-c2 * s1;
+ m[1][0] = s1 * s3 - c1 * c3 * s2;
+ m[1][1] = c2 * c3;
+ m[1][2] = c1 * s3 + c3 * s1 * s2;
+ m[2][0] = c3 * s1 + c1 * s2 * s3;
+ m[2][1] =-c2 * s3;
+ m[2][2] = c1 * c3 - s1 * s2 * s3;
+ return;
+}
+
+matrix3_from_euler_angles_zyx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c1 * c2;
+ m[0][1] = c2 * s1;
+ m[0][2] =-s2;
+ m[1][0] = c1 * s2 * s3 - c3 * s1;
+ m[1][1] = c1 * c3 + s1 * s2 * s3;
+ m[1][2] = c2 * s3;
+ m[2][0] = s1 * s3 + c1 * c3 * s2;
+ m[2][1] = c3 * s1 * s2 - c1 * s3;
+ m[2][2] = c2 * c3;
+ return;
+}
+
+matrix3_from_euler_angles_zxy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix3f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c1 * c3 - s1 * s2 * s3;
+ m[0][1] = c3 * s1 + c1 * s2 * s3;
+ m[0][2] =-c2 * s3;
+ m[1][0] =-c2 * s1;
+ m[1][1] = c1 * c2;
+ m[1][2] = s2;
+ m[2][0] = c1 * s3 + c3 * s1 * s2;
+ m[2][1] = s1 * s3 - c1 * c3 * s2;
+ m[2][2] = c2 * c3;
+ return;
+}
+
+
+matrix3_from_yaw_pitch_roll_f16 :: proc(yaw, pitch, roll: f16) -> (m: Matrix3f16) {
+ ch := math.cos(yaw);
+ sh := math.sin(yaw);
+ cp := math.cos(pitch);
+ sp := math.sin(pitch);
+ cb := math.cos(roll);
+ sb := math.sin(roll);
+
+ m[0][0] = ch * cb + sh * sp * sb;
+ m[0][1] = sb * cp;
+ m[0][2] = -sh * cb + ch * sp * sb;
+ m[1][0] = -ch * sb + sh * sp * cb;
+ m[1][1] = cb * cp;
+ m[1][2] = sb * sh + ch * sp * cb;
+ m[2][0] = sh * cp;
+ m[2][1] = -sp;
+ m[2][2] = ch * cp;
+ return m;
+}
+
+euler_angles_xyz_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[2][1], m[2][2]);
+ C2 := math.sqrt(m[0][0]*m[0][0] + m[1][0]*m[1][0]);
+ T2 := math.atan2(-m[2][0], C2);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(S1*m[0][2] - C1*m[0][1], C1*m[1][1] - S1*m[1][2]);
+ t1 = -T1;
+ t2 = -T2;
+ t3 = -T3;
+ return;
+}
+
+euler_angles_yxz_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[2][0], m[2][2]);
+ C2 := math.sqrt(m[0][1]*m[0][1] + m[1][1]*m[1][1]);
+ T2 := math.atan2(-m[2][1], C2);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(S1*m[1][2] - C1*m[1][0], C1*m[0][0] - S1*m[0][2]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_xzx_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[0][2], m[0][1]);
+ S2 := math.sqrt(m[1][0]*m[1][0] + m[2][0]*m[2][0]);
+ T2 := math.atan2(S2, m[0][0]);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(C1*m[1][2] - S1*m[1][1], C1*m[2][2] - S1*m[2][1]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_xyx_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[0][1], -m[0][2]);
+ S2 := math.sqrt(m[1][0]*m[1][0] + m[2][0]*m[2][0]);
+ T2 := math.atan2(S2, m[0][0]);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(-C1*m[2][1] - S1*m[2][2], C1*m[1][1] + S1*m[1][2]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_yxy_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[1][0], m[1][2]);
+ S2 := math.sqrt(m[0][1]*m[0][1] + m[2][1]*m[2][1]);
+ T2 := math.atan2(S2, m[1][1]);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(C1*m[2][0] - S1*m[2][2], C1*m[0][0] - S1*m[0][2]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_yzy_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[1][2], -m[1][0]);
+ S2 := math.sqrt(m[0][1]*m[0][1] + m[2][1]*m[2][1]);
+ T2 := math.atan2(S2, m[1][1]);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(-S1*m[0][0] - C1*m[0][2], S1*m[2][0] + C1*m[2][2]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+euler_angles_zyz_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[2][1], m[2][0]);
+ S2 := math.sqrt(m[0][2]*m[0][2] + m[1][2]*m[1][2]);
+ T2 := math.atan2(S2, m[2][2]);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(C1*m[0][1] - S1*m[0][0], C1*m[1][1] - S1*m[1][0]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_zxz_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[2][0], -m[2][1]);
+ S2 := math.sqrt(m[0][2]*m[0][2] + m[1][2]*m[1][2]);
+ T2 := math.atan2(S2, m[2][2]);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(-C1*m[1][0] - S1*m[1][1], C1*m[0][0] + S1*m[0][1]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_xzy_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[1][2], m[1][1]);
+ C2 := math.sqrt(m[0][0]*m[0][0] + m[2][0]*m[2][0]);
+ T2 := math.atan2(-m[1][0], C2);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(S1*m[0][1] - C1*m[0][2], C1*m[2][2] - S1*m[2][1]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_yzx_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(-m[0][2], m[0][0]);
+ C2 := math.sqrt(m[1][1]*m[1][1] + m[2][1]*m[2][1]);
+ T2 := math.atan2(m[0][1], C2);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(S1*m[1][0] + C1*m[1][2], S1*m[2][0] + C1*m[2][2]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_zyx_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[0][1], m[0][0]);
+ C2 := math.sqrt(m[1][2]*m[1][2] + m[2][2]*m[2][2]);
+ T2 := math.atan2(-m[0][2], C2);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(S1*m[2][0] - C1*m[2][1], C1*m[1][1] - S1*m[1][0]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_zxy_from_matrix3_f16 :: proc(m: Matrix3f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(-m[1][0], m[1][1]);
+ C2 := math.sqrt(m[0][2]*m[0][2] + m[2][2]*m[2][2]);
+ T2 := math.atan2(m[1][2], C2);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(C1*m[2][0] + S1*m[2][1], C1*m[0][0] + S1*m[0][1]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+
+// Matrix4
+
+
+matrix4_from_euler_angle_x_f16 :: proc(angle_x: f16) -> (m: Matrix4f16) {
+ cos_x, sin_x := math.cos(angle_x), math.sin(angle_x);
+ m[0][0] = 1;
+ m[1][1] = +cos_x;
+ m[2][1] = +sin_x;
+ m[1][2] = -sin_x;
+ m[2][2] = +cos_x;
+ m[3][3] = 1;
+ return;
+}
+matrix4_from_euler_angle_y_f16 :: proc(angle_y: f16) -> (m: Matrix4f16) {
+ cos_y, sin_y := math.cos(angle_y), math.sin(angle_y);
+ m[0][0] = +cos_y;
+ m[2][0] = -sin_y;
+ m[1][1] = 1;
+ m[0][2] = +sin_y;
+ m[2][2] = +cos_y;
+ m[3][3] = 1;
+ return;
+}
+matrix4_from_euler_angle_z_f16 :: proc(angle_z: f16) -> (m: Matrix4f16) {
+ cos_z, sin_z := math.cos(angle_z), math.sin(angle_z);
+ m[0][0] = +cos_z;
+ m[1][0] = +sin_z;
+ m[1][1] = +cos_z;
+ m[0][1] = -sin_z;
+ m[2][2] = 1;
+ m[3][3] = 1;
+ return;
+}
+
+
+matrix4_from_derived_euler_angle_x_f16 :: proc(angle_x: f16, angular_velocity_x: f16) -> (m: Matrix4f16) {
+ cos_x := math.cos(angle_x) * angular_velocity_x;
+ sin_x := math.sin(angle_x) * angular_velocity_x;
+ m[0][0] = 1;
+ m[1][1] = +cos_x;
+ m[2][1] = +sin_x;
+ m[1][2] = -sin_x;
+ m[2][2] = +cos_x;
+ m[3][3] = 1;
+ return;
+}
+matrix4_from_derived_euler_angle_y_f16 :: proc(angle_y: f16, angular_velocity_y: f16) -> (m: Matrix4f16) {
+ cos_y := math.cos(angle_y) * angular_velocity_y;
+ sin_y := math.sin(angle_y) * angular_velocity_y;
+ m[0][0] = +cos_y;
+ m[2][0] = -sin_y;
+ m[1][1] = 1;
+ m[0][2] = +sin_y;
+ m[2][2] = +cos_y;
+ m[3][3] = 1;
+ return;
+}
+matrix4_from_derived_euler_angle_z_f16 :: proc(angle_z: f16, angular_velocity_z: f16) -> (m: Matrix4f16) {
+ cos_z := math.cos(angle_z) * angular_velocity_z;
+ sin_z := math.sin(angle_z) * angular_velocity_z;
+ m[0][0] = +cos_z;
+ m[1][0] = +sin_z;
+ m[1][1] = +cos_z;
+ m[0][1] = -sin_z;
+ m[2][2] = 1;
+ m[3][3] = 1;
+ return;
+}
+
+
+matrix4_from_euler_angles_xy_f16 :: proc(angle_x, angle_y: f16) -> (m: Matrix4f16) {
+ cos_x, sin_x := math.cos(angle_x), math.sin(angle_x);
+ cos_y, sin_y := math.cos(angle_y), math.sin(angle_y);
+ m[0][0] = cos_y;
+ m[1][0] = -sin_x * - sin_y;
+ m[2][0] = -cos_x * - sin_y;
+ m[1][1] = cos_x;
+ m[2][1] = sin_x;
+ m[0][2] = sin_y;
+ m[1][2] = -sin_x * cos_y;
+ m[2][2] = cos_x * cos_y;
+ m[3][3] = 1;
+ return;
+}
+
+
+matrix4_from_euler_angles_yx_f16 :: proc(angle_y, angle_x: f16) -> (m: Matrix4f16) {
+ cos_x, sin_x := math.cos(angle_x), math.sin(angle_x);
+ cos_y, sin_y := math.cos(angle_y), math.sin(angle_y);
+ m[0][0] = cos_y;
+ m[2][0] = -sin_y;
+ m[0][1] = sin_y*sin_x;
+ m[1][1] = cos_x;
+ m[2][1] = cos_y*sin_x;
+ m[0][2] = sin_y*cos_x;
+ m[1][2] = -sin_x;
+ m[2][2] = cos_y*cos_x;
+ m[3][3] = 1;
+ return;
+}
+
+matrix4_from_euler_angles_xz_f16 :: proc(angle_x, angle_z: f16) -> (m: Matrix4f16) {
+ return mul(matrix4_from_euler_angle_x(angle_x), matrix4_from_euler_angle_z(angle_z));
+}
+matrix4_from_euler_angles_zx_f16 :: proc(angle_z, angle_x: f16) -> (m: Matrix4f16) {
+ return mul(matrix4_from_euler_angle_z(angle_z), matrix4_from_euler_angle_x(angle_x));
+}
+matrix4_from_euler_angles_yz_f16 :: proc(angle_y, angle_z: f16) -> (m: Matrix4f16) {
+ return mul(matrix4_from_euler_angle_y(angle_y), matrix4_from_euler_angle_z(angle_z));
+}
+matrix4_from_euler_angles_zy_f16 :: proc(angle_z, angle_y: f16) -> (m: Matrix4f16) {
+ return mul(matrix4_from_euler_angle_z(angle_z), matrix4_from_euler_angle_y(angle_y));
+}
+
+
+matrix4_from_euler_angles_xyz_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) {
+ c1 := math.cos(-t1);
+ c2 := math.cos(-t2);
+ c3 := math.cos(-t3);
+ s1 := math.sin(-t1);
+ s2 := math.sin(-t2);
+ s3 := math.sin(-t3);
+
+ m[0][0] = c2 * c3;
+ m[0][1] =-c1 * s3 + s1 * s2 * c3;
+ m[0][2] = s1 * s3 + c1 * s2 * c3;
+ m[0][3] = 0;
+ m[1][0] = c2 * s3;
+ m[1][1] = c1 * c3 + s1 * s2 * s3;
+ m[1][2] =-s1 * c3 + c1 * s2 * s3;
+ m[1][3] = 0;
+ m[2][0] =-s2;
+ m[2][1] = s1 * c2;
+ m[2][2] = c1 * c2;
+ m[2][3] = 0;
+ m[3][0] = 0;
+ m[3][1] = 0;
+ m[3][2] = 0;
+ m[3][3] = 1;
+ return;
+}
+
+matrix4_from_euler_angles_yxz_f16 :: proc(yaw, pitch, roll: f16) -> (m: Matrix4f16) {
+ ch := math.cos(yaw);
+ sh := math.sin(yaw);
+ cp := math.cos(pitch);
+ sp := math.sin(pitch);
+ cb := math.cos(roll);
+ sb := math.sin(roll);
+
+ m[0][0] = ch * cb + sh * sp * sb;
+ m[0][1] = sb * cp;
+ m[0][2] = -sh * cb + ch * sp * sb;
+ m[0][3] = 0;
+ m[1][0] = -ch * sb + sh * sp * cb;
+ m[1][1] = cb * cp;
+ m[1][2] = sb * sh + ch * sp * cb;
+ m[1][3] = 0;
+ m[2][0] = sh * cp;
+ m[2][1] = -sp;
+ m[2][2] = ch * cp;
+ m[2][3] = 0;
+ m[3][0] = 0;
+ m[3][1] = 0;
+ m[3][2] = 0;
+ m[3][3] = 1;
+ return;
+}
+
+matrix4_from_euler_angles_xzx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c2;
+ m[0][1] = c1 * s2;
+ m[0][2] = s1 * s2;
+ m[0][3] = 0;
+ m[1][0] =-c3 * s2;
+ m[1][1] = c1 * c2 * c3 - s1 * s3;
+ m[1][2] = c1 * s3 + c2 * c3 * s1;
+ m[1][3] = 0;
+ m[2][0] = s2 * s3;
+ m[2][1] =-c3 * s1 - c1 * c2 * s3;
+ m[2][2] = c1 * c3 - c2 * s1 * s3;
+ m[2][3] = 0;
+ m[3][0] = 0;
+ m[3][1] = 0;
+ m[3][2] = 0;
+ m[3][3] = 1;
+ return;
+}
+
+matrix4_from_euler_angles_xyx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c2;
+ m[0][1] = s1 * s2;
+ m[0][2] =-c1 * s2;
+ m[0][3] = 0;
+ m[1][0] = s2 * s3;
+ m[1][1] = c1 * c3 - c2 * s1 * s3;
+ m[1][2] = c3 * s1 + c1 * c2 * s3;
+ m[1][3] = 0;
+ m[2][0] = c3 * s2;
+ m[2][1] =-c1 * s3 - c2 * c3 * s1;
+ m[2][2] = c1 * c2 * c3 - s1 * s3;
+ m[2][3] = 0;
+ m[3][0] = 0;
+ m[3][1] = 0;
+ m[3][2] = 0;
+ m[3][3] = 1;
+ return;
+}
+
+matrix4_from_euler_angles_yxy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c1 * c3 - c2 * s1 * s3;
+ m[0][1] = s2* s3;
+ m[0][2] =-c3 * s1 - c1 * c2 * s3;
+ m[0][3] = 0;
+ m[1][0] = s1 * s2;
+ m[1][1] = c2;
+ m[1][2] = c1 * s2;
+ m[1][3] = 0;
+ m[2][0] = c1 * s3 + c2 * c3 * s1;
+ m[2][1] =-c3 * s2;
+ m[2][2] = c1 * c2 * c3 - s1 * s3;
+ m[2][3] = 0;
+ m[3][0] = 0;
+ m[3][1] = 0;
+ m[3][2] = 0;
+ m[3][3] = 1;
+ return;
+}
+
+matrix4_from_euler_angles_yzy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c1 * c2 * c3 - s1 * s3;
+ m[0][1] = c3 * s2;
+ m[0][2] =-c1 * s3 - c2 * c3 * s1;
+ m[0][3] = 0;
+ m[1][0] =-c1 * s2;
+ m[1][1] = c2;
+ m[1][2] = s1 * s2;
+ m[1][3] = 0;
+ m[2][0] = c3 * s1 + c1 * c2 * s3;
+ m[2][1] = s2 * s3;
+ m[2][2] = c1 * c3 - c2 * s1 * s3;
+ m[2][3] = 0;
+ m[3][0] = 0;
+ m[3][1] = 0;
+ m[3][2] = 0;
+ m[3][3] = 1;
+ return;
+}
+
+matrix4_from_euler_angles_zyz_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c1 * c2 * c3 - s1 * s3;
+ m[0][1] = c1 * s3 + c2 * c3 * s1;
+ m[0][2] =-c3 * s2;
+ m[0][3] = 0;
+ m[1][0] =-c3 * s1 - c1 * c2 * s3;
+ m[1][1] = c1 * c3 - c2 * s1 * s3;
+ m[1][2] = s2 * s3;
+ m[1][3] = 0;
+ m[2][0] = c1 * s2;
+ m[2][1] = s1 * s2;
+ m[2][2] = c2;
+ m[2][3] = 0;
+ m[3][0] = 0;
+ m[3][1] = 0;
+ m[3][2] = 0;
+ m[3][3] = 1;
+ return;
+}
+
+matrix4_from_euler_angles_zxz_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c1 * c3 - c2 * s1 * s3;
+ m[0][1] = c3 * s1 + c1 * c2 * s3;
+ m[0][2] = s2 *s3;
+ m[0][3] = 0;
+ m[1][0] =-c1 * s3 - c2 * c3 * s1;
+ m[1][1] = c1 * c2 * c3 - s1 * s3;
+ m[1][2] = c3 * s2;
+ m[1][3] = 0;
+ m[2][0] = s1 * s2;
+ m[2][1] =-c1 * s2;
+ m[2][2] = c2;
+ m[2][3] = 0;
+ m[3][0] = 0;
+ m[3][1] = 0;
+ m[3][2] = 0;
+ m[3][3] = 1;
+ return;
+}
+
+
+matrix4_from_euler_angles_xzy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c2 * c3;
+ m[0][1] = s1 * s3 + c1 * c3 * s2;
+ m[0][2] = c3 * s1 * s2 - c1 * s3;
+ m[0][3] = 0;
+ m[1][0] =-s2;
+ m[1][1] = c1 * c2;
+ m[1][2] = c2 * s1;
+ m[1][3] = 0;
+ m[2][0] = c2 * s3;
+ m[2][1] = c1 * s2 * s3 - c3 * s1;
+ m[2][2] = c1 * c3 + s1 * s2 *s3;
+ m[2][3] = 0;
+ m[3][0] = 0;
+ m[3][1] = 0;
+ m[3][2] = 0;
+ m[3][3] = 1;
+ return;
+}
+
+matrix4_from_euler_angles_yzx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c1 * c2;
+ m[0][1] = s2;
+ m[0][2] =-c2 * s1;
+ m[0][3] = 0;
+ m[1][0] = s1 * s3 - c1 * c3 * s2;
+ m[1][1] = c2 * c3;
+ m[1][2] = c1 * s3 + c3 * s1 * s2;
+ m[1][3] = 0;
+ m[2][0] = c3 * s1 + c1 * s2 * s3;
+ m[2][1] =-c2 * s3;
+ m[2][2] = c1 * c3 - s1 * s2 * s3;
+ m[2][3] = 0;
+ m[3][0] = 0;
+ m[3][1] = 0;
+ m[3][2] = 0;
+ m[3][3] = 1;
+ return;
+}
+
+matrix4_from_euler_angles_zyx_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c1 * c2;
+ m[0][1] = c2 * s1;
+ m[0][2] =-s2;
+ m[0][3] = 0;
+ m[1][0] = c1 * s2 * s3 - c3 * s1;
+ m[1][1] = c1 * c3 + s1 * s2 * s3;
+ m[1][2] = c2 * s3;
+ m[1][3] = 0;
+ m[2][0] = s1 * s3 + c1 * c3 * s2;
+ m[2][1] = c3 * s1 * s2 - c1 * s3;
+ m[2][2] = c2 * c3;
+ m[2][3] = 0;
+ m[3][0] = 0;
+ m[3][1] = 0;
+ m[3][2] = 0;
+ m[3][3] = 1;
+ return;
+}
+
+matrix4_from_euler_angles_zxy_f16 :: proc(t1, t2, t3: f16) -> (m: Matrix4f16) {
+ c1 := math.cos(t1);
+ s1 := math.sin(t1);
+ c2 := math.cos(t2);
+ s2 := math.sin(t2);
+ c3 := math.cos(t3);
+ s3 := math.sin(t3);
+
+ m[0][0] = c1 * c3 - s1 * s2 * s3;
+ m[0][1] = c3 * s1 + c1 * s2 * s3;
+ m[0][2] =-c2 * s3;
+ m[0][3] = 0;
+ m[1][0] =-c2 * s1;
+ m[1][1] = c1 * c2;
+ m[1][2] = s2;
+ m[1][3] = 0;
+ m[2][0] = c1 * s3 + c3 * s1 * s2;
+ m[2][1] = s1 * s3 - c1 * c3 * s2;
+ m[2][2] = c2 * c3;
+ m[2][3] = 0;
+ m[3][0] = 0;
+ m[3][1] = 0;
+ m[3][2] = 0;
+ m[3][3] = 1;
+ return;
+}
+
+
+matrix4_from_yaw_pitch_roll_f16 :: proc(yaw, pitch, roll: f16) -> (m: Matrix4f16) {
+ ch := math.cos(yaw);
+ sh := math.sin(yaw);
+ cp := math.cos(pitch);
+ sp := math.sin(pitch);
+ cb := math.cos(roll);
+ sb := math.sin(roll);
+
+ m[0][0] = ch * cb + sh * sp * sb;
+ m[0][1] = sb * cp;
+ m[0][2] = -sh * cb + ch * sp * sb;
+ m[0][3] = 0;
+ m[1][0] = -ch * sb + sh * sp * cb;
+ m[1][1] = cb * cp;
+ m[1][2] = sb * sh + ch * sp * cb;
+ m[1][3] = 0;
+ m[2][0] = sh * cp;
+ m[2][1] = -sp;
+ m[2][2] = ch * cp;
+ m[2][3] = 0;
+ m[3][0] = 0;
+ m[3][1] = 0;
+ m[3][2] = 0;
+ m[3][3] = 1;
+ return m;
+}
+
+euler_angles_xyz_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[2][1], m[2][2]);
+ C2 := math.sqrt(m[0][0]*m[0][0] + m[1][0]*m[1][0]);
+ T2 := math.atan2(-m[2][0], C2);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(S1*m[0][2] - C1*m[0][1], C1*m[1][1] - S1*m[1][2]);
+ t1 = -T1;
+ t2 = -T2;
+ t3 = -T3;
+ return;
+}
+
+euler_angles_yxz_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[2][0], m[2][2]);
+ C2 := math.sqrt(m[0][1]*m[0][1] + m[1][1]*m[1][1]);
+ T2 := math.atan2(-m[2][1], C2);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(S1*m[1][2] - C1*m[1][0], C1*m[0][0] - S1*m[0][2]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_xzx_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[0][2], m[0][1]);
+ S2 := math.sqrt(m[1][0]*m[1][0] + m[2][0]*m[2][0]);
+ T2 := math.atan2(S2, m[0][0]);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(C1*m[1][2] - S1*m[1][1], C1*m[2][2] - S1*m[2][1]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_xyx_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[0][1], -m[0][2]);
+ S2 := math.sqrt(m[1][0]*m[1][0] + m[2][0]*m[2][0]);
+ T2 := math.atan2(S2, m[0][0]);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(-C1*m[2][1] - S1*m[2][2], C1*m[1][1] + S1*m[1][2]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_yxy_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[1][0], m[1][2]);
+ S2 := math.sqrt(m[0][1]*m[0][1] + m[2][1]*m[2][1]);
+ T2 := math.atan2(S2, m[1][1]);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(C1*m[2][0] - S1*m[2][2], C1*m[0][0] - S1*m[0][2]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_yzy_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[1][2], -m[1][0]);
+ S2 := math.sqrt(m[0][1]*m[0][1] + m[2][1]*m[2][1]);
+ T2 := math.atan2(S2, m[1][1]);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(-S1*m[0][0] - C1*m[0][2], S1*m[2][0] + C1*m[2][2]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+euler_angles_zyz_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[2][1], m[2][0]);
+ S2 := math.sqrt(m[0][2]*m[0][2] + m[1][2]*m[1][2]);
+ T2 := math.atan2(S2, m[2][2]);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(C1*m[0][1] - S1*m[0][0], C1*m[1][1] - S1*m[1][0]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_zxz_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[2][0], -m[2][1]);
+ S2 := math.sqrt(m[0][2]*m[0][2] + m[1][2]*m[1][2]);
+ T2 := math.atan2(S2, m[2][2]);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(-C1*m[1][0] - S1*m[1][1], C1*m[0][0] + S1*m[0][1]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_xzy_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[1][2], m[1][1]);
+ C2 := math.sqrt(m[0][0]*m[0][0] + m[2][0]*m[2][0]);
+ T2 := math.atan2(-m[1][0], C2);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(S1*m[0][1] - C1*m[0][2], C1*m[2][2] - S1*m[2][1]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_yzx_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(-m[0][2], m[0][0]);
+ C2 := math.sqrt(m[1][1]*m[1][1] + m[2][1]*m[2][1]);
+ T2 := math.atan2(m[0][1], C2);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(S1*m[1][0] + C1*m[1][2], S1*m[2][0] + C1*m[2][2]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_zyx_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(m[0][1], m[0][0]);
+ C2 := math.sqrt(m[1][2]*m[1][2] + m[2][2]*m[2][2]);
+ T2 := math.atan2(-m[0][2], C2);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(S1*m[2][0] - C1*m[2][1], C1*m[1][1] - S1*m[1][0]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}
+
+euler_angles_zxy_from_matrix4_f16 :: proc(m: Matrix4f16) -> (t1, t2, t3: f16) {
+ T1 := math.atan2(-m[1][0], m[1][1]);
+ C2 := math.sqrt(m[0][2]*m[0][2] + m[2][2]*m[2][2]);
+ T2 := math.atan2(m[1][2], C2);
+ S1 := math.sin(T1);
+ C1 := math.cos(T1);
+ T3 := math.atan2(C1*m[2][0] + S1*m[2][1], C1*m[0][0] + S1*m[0][1]);
+ t1 = T1;
+ t2 = T2;
+ t3 = T3;
+ return;
+}