glam_det 2.0.0

// Copyright (C) 2020-2025 glam-det authors. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

// Generated from quat.rs.tera template. Edit the template, not the generated file.

use crate::f32::simd_alias::{Mat4, Quat, UnitVec3A, UnitVec4, Vec3A, Vec4};
use crate::{
    euler::EulerRot::{self, *},
    sse2, FloatEx, Mat3, UnitDQuat, UnitVec2, UnitVec3, Vec3,
};

use crate::nums::*;

#[cfg(target_arch = "x86")]
use core::arch::x86::*;
#[cfg(target_arch = "x86_64")]
use core::arch::x86_64::*;

use auto_ops_det::{impl_op_ex, impl_op_ex_commutative};
#[cfg(not(target_arch = "spirv"))]
use core::fmt;
use core::iter::Product;
use core::ops::{self, Deref, Neg};

union UnionCast {
    a: [f32; 4],
    v: UnitQuat,
}

union VecUnionCast {
    v: Quat,
    uv: UnitQuat,
}

impl Quat {
    #[inline]
    pub fn as_unit_quat_unchecked(self) -> UnitQuat {
        unsafe { VecUnionCast { v: self }.uv }
    }
}

impl UnitQuat {
    #[inline]
    pub fn as_quat(self) -> Quat {
        unsafe { VecUnionCast { uv: self }.v }
    }
}

/// A quaternion representing an orientation.
///
/// This quaternion is intended to be of unit length but may denormalize due to
/// floating point "error creep" which can occur when successive quaternion
/// operations are applied.
///
/// This type is 16 byte aligned.
#[derive(Clone, Copy)]
#[repr(transparent)]
pub struct UnitQuat(pub(crate) __m128);

impl UnitQuat {
    /// The identity unit quaternion. Corresponds to no rotation.
    pub const IDENTITY: Self = Self::from_xyzw_unchecked(0.0_f32, 0.0_f32, 0.0_f32, 1.0_f32);

    /// Creates a new rotation quaternion.
    #[inline]
    pub const fn from_xyzw_unchecked(x: f32, y: f32, z: f32, w: f32) -> Self {
        unsafe { UnionCast { a: [x, y, z, w] }.v }
    }

    /// Creates a rotation quaternion from an array.
    #[inline]
    pub const fn from_array_unchecked(a: [f32; 4]) -> Self {
        Self::from_xyzw_unchecked(a[0], a[1], a[2], a[3])
    }

    /// Creates a new rotation quaternion from a 4D unit vector.
    #[inline]
    pub fn from_unit_vec4(v: UnitVec4) -> Self {
        let q: Self = Self(v.0);
        glam_assert!(q.is_normalized(), "{:?} is not normalized.", q);
        q
    }

    /// Creates a rotation quaternion from a slice.
    ///
    /// # Panics
    ///
    /// Panics if `slice` length is less than 4.
    #[inline]
    pub fn from_slice_unchecked(slice: &[f32]) -> Self {
        assert!(slice.len() >= 4);
        Self(unsafe { _mm_loadu_ps(slice.as_ptr()) })
    }

    /// Writes the quaternion to an unaligned slice.
    ///
    /// # Panics
    ///
    /// Panics if `slice` length is less than 4.
    #[inline]
    pub fn write_to_slice(self, slice: &mut [f32]) {
        assert!(slice.len() >= 4);
        unsafe { _mm_storeu_ps(slice.as_mut_ptr(), self.0) }
    }

    /// Create a unit quaternion for a unit-length `axis` and `angle` (in radians).
    #[inline]
    pub fn from_axis_angle(axis: UnitVec3, angle: f32) -> Self {
        #[cfg_attr(
            not(any(
                all(debug_assertions, feature = "debug-glam-assert"),
                feature = "glam-assert"
            )),
            allow(clippy::let_and_return)
        )]
        let q = Quat::from_axis_angle(axis, angle).as_unit_quat_unchecked();
        glam_assert!(q.is_normalized(), "{:?} is not normalized.", q);
        q
    }

    /// Create a unit quaternion that rotates `v.length()` radians around `v.normalize()`.
    ///
    /// `from_scaled_axis(Vec3::ZERO)` results in the identity quaternion.
    #[inline]
    pub fn from_scaled_axis(v: Vec3) -> Self {
        #[cfg_attr(
            not(any(
                all(debug_assertions, feature = "debug-glam-assert"),
                feature = "glam-assert"
            )),
            allow(clippy::let_and_return)
        )]
        let q = Quat::from_scaled_axis(v).as_unit_quat_unchecked();
        glam_assert!(q.is_normalized(), "{:?} is not normalized.", q);
        q
    }

    /// Creates a unit quaternion from the `angle` (in radians) around the x axis.
    #[inline]
    pub fn from_rotation_x(angle: f32) -> Self {
        glam_assert!(angle.is_finite(), "angle {:?} is not finite.", angle);
        let (s, c) = (angle * 0.5_f32).sin_cosf();
        Self::from_xyzw_unchecked(s, 0.0_f32, 0.0_f32, c)
    }

    /// Creates a unit quaternion from the `angle` (in radians) around the y axis.
    #[inline]
    pub fn from_rotation_y(angle: f32) -> Self {
        glam_assert!(angle.is_finite(), "angle {:?} is not finite.", angle);
        let (s, c) = (angle * 0.5_f32).sin_cosf();
        Self::from_xyzw_unchecked(0.0_f32, s, 0.0_f32, c)
    }

    /// Creates a unit quaternion from the `angle` (in radians) around the z axis.
    #[inline]
    pub fn from_rotation_z(angle: f32) -> Self {
        glam_assert!(angle.is_finite(), "angle {:?} is not finite.", angle);
        let (s, c) = (angle * 0.5_f32).sin_cosf();
        Self::from_xyzw_unchecked(0.0_f32, 0.0_f32, s, c)
    }

    #[inline]
    /// Creates a unit quaternion from the given Euler rotation sequence and the angles (in radians).
    pub fn from_euler(euler: EulerRot, a: f32, b: f32, c: f32) -> Self {
        let (sa, ca) = (a * 0.5_f32).sin_cosf();
        let (sb, cb) = (b * 0.5_f32).sin_cosf();
        let (sc, cc) = (c * 0.5_f32).sin_cosf();
        match euler {
            ZYX => Self::from_xyzw_unchecked(
                ca * cb * sc - cc * sa * sb,
                ca * cc * sb + cb * sa * sc,
                cb * cc * sa - ca * sb * sc,
                ca * cb * cc + sa * sb * sc,
            ),
            ZXY => Self::from_xyzw_unchecked(
                ca * cc * sb - cb * sa * sc,
                cc * sa * sb + ca * cb * sc,
                cb * cc * sa + ca * sb * sc,
                ca * cb * cc - sa * sb * sc,
            ),
            YXZ => Self::from_xyzw_unchecked(
                ca * cc * sb + cb * sa * sc,
                cb * cc * sa - ca * sb * sc,
                ca * cb * sc - cc * sa * sb,
                ca * cb * cc + sa * sb * sc,
            ),
            YZX => Self::from_xyzw_unchecked(
                cc * sa * sb + ca * cb * sc,
                cb * cc * sa + ca * sb * sc,
                ca * cc * sb - cb * sa * sc,
                ca * cb * cc - sa * sb * sc,
            ),
            XYZ => Self::from_xyzw_unchecked(
                cb * cc * sa + ca * sb * sc,
                ca * cc * sb - cb * sa * sc,
                cc * sa * sb + ca * cb * sc,
                ca * cb * cc - sa * sb * sc,
            ),
            XZY => Self::from_xyzw_unchecked(
                cb * cc * sa - ca * sb * sc,
                ca * cb * sc - cc * sa * sb,
                ca * cc * sb + cb * sa * sc,
                ca * cb * cc + sa * sb * sc,
            ),
            ZYZ => Self::from_xyzw_unchecked(
                ca * sb * sc - cc * sa * sb,
                ca * cc * sb + sa * sb * sc,
                cb * cc * sa + ca * cb * sc,
                ca * cb * cc - cb * sa * sc,
            ),
            ZXZ => Self::from_xyzw_unchecked(
                ca * cc * sb + sa * sb * sc,
                cc * sa * sb - ca * sb * sc,
                cb * cc * sa + ca * cb * sc,
                ca * cb * cc - cb * sa * sc,
            ),
            YXY => Self::from_xyzw_unchecked(
                ca * cc * sb + sa * sb * sc,
                cb * cc * sa + ca * cb * sc,
                ca * sb * sc - cc * sa * sb,
                ca * cb * cc - cb * sa * sc,
            ),
            YZY => Self::from_xyzw_unchecked(
                cc * sa * sb - ca * sb * sc,
                cb * cc * sa + ca * cb * sc,
                ca * cc * sb + sa * sb * sc,
                ca * cb * cc - cb * sa * sc,
            ),
            XYX => Self::from_xyzw_unchecked(
                cb * cc * sa + ca * cb * sc,
                ca * cc * sb + sa * sb * sc,
                cc * sa * sb - ca * sb * sc,
                ca * cb * cc - cb * sa * sc,
            ),
            XZX => Self::from_xyzw_unchecked(
                cb * cc * sa + ca * cb * sc,
                ca * sb * sc - cc * sa * sb,
                ca * cc * sb + sa * sb * sc,
                ca * cb * cc - cb * sa * sc,
            ),
        }
        .renormalize()
    }

    #[inline]
    /// Creates a unit quaternion from the given the angles (in radians).
    /// Default euler rotation sequence is `Z -> Y -> X` as roll (z-axis) -> yaw (y-axis) -> pitch (x-axis).
    /// First apply the z-axis rotation.
    pub fn from_euler_default(a: f32, b: f32, c: f32) -> Self {
        Self::from_euler(EulerRot::default(), a, b, c)
    }

    /// From the columns of a 3x3 rotation matrix.
    #[inline]
    pub(crate) fn from_rotation_axes(x_axis: Vec3, y_axis: Vec3, z_axis: Vec3) -> Self {
        #[cfg_attr(
            not(any(
                all(debug_assertions, feature = "debug-glam-assert"),
                feature = "glam-assert"
            )),
            allow(clippy::let_and_return)
        )]
        let q = Quat::from_rotation_axes(x_axis, y_axis, z_axis).as_unit_quat_unchecked();
        glam_assert!(q.is_normalized(), "{:?} is not normalized.", q);
        q
    }

    /// Creates a unit quaternion from a 3x3 rotation matrix.
    #[inline]
    pub fn from_mat3(mat: &Mat3) -> Self {
        Self::from_rotation_axes(mat.x_axis, mat.y_axis, mat.z_axis)
    }

    /// Creates a unit quaternion from a 3x3 rotation matrix inside a homogeneous 4x4 matrix.
    #[inline]
    pub fn from_mat4(mat: &Mat4) -> Self {
        Self::from_rotation_axes(
            mat.x_axis.truncate(),
            mat.y_axis.truncate(),
            mat.z_axis.truncate(),
        )
    }

    /// Creates a quaternion from a 3x3 rotation matrix inside a 3D affine transform.
    #[inline]
    pub fn from_affine3(a: &crate::Affine3A) -> Self {
        #[allow(clippy::useless_conversion)]
        Self::from_rotation_axes(
            a.matrix3.x_axis.into(),
            a.matrix3.y_axis.into(),
            a.matrix3.z_axis.into(),
        )
    }

    /// Gets the minimal rotation for transforming `from` to `to`.  The rotation is in the
    /// plane spanned by the two vectors.  Will rotate at most 180 degrees.
    #[inline]
    pub fn from_rotation_arc(from: UnitVec3, to: UnitVec3) -> Self {
        #[cfg_attr(
            not(any(
                all(debug_assertions, feature = "debug-glam-assert"),
                feature = "glam-assert"
            )),
            allow(clippy::let_and_return)
        )]
        let q = Quat::from_rotation_arc(from, to).as_unit_quat_unchecked();
        glam_assert!(q.is_normalized(), "{:?} is not normalized.", q);
        q
    }

    /// Gets the minimal rotation for transforming `from` to either `to` or `-to`.  This means
    /// that the resulting quaternion will rotate `from` so that it is colinear with `to`.
    ///
    /// The rotation is in the plane spanned by the two vectors.  Will rotate at most 90
    /// degrees.
    #[inline]
    pub fn from_rotation_arc_colinear(from: UnitVec3, to: UnitVec3) -> Self {
        #[cfg_attr(
            not(any(
                all(debug_assertions, feature = "debug-glam-assert"),
                feature = "glam-assert"
            )),
            allow(clippy::let_and_return)
        )]
        let q = Quat::from_rotation_arc_colinear(from, to).as_unit_quat_unchecked();
        glam_assert!(q.is_normalized(), "{:?} is not normalized.", q);
        q
    }

    /// Gets the minimal rotation for transforming `from` to `to`.  The resulting rotation is
    /// around the z axis. Will rotate at most 180 degrees.
    #[inline]
    pub fn from_rotation_arc_2d(from: UnitVec2, to: UnitVec2) -> Self {
        #[cfg_attr(
            not(any(
                all(debug_assertions, feature = "debug-glam-assert"),
                feature = "glam-assert"
            )),
            allow(clippy::let_and_return)
        )]
        let q = Quat::from_rotation_arc_2d(from, to).as_unit_quat_unchecked();
        glam_assert!(q.is_normalized(), "{:?} is not normalized.", q);
        q
    }

    /// Returns the rotation axis and angle (in radians) of `self`.
    #[inline]
    pub fn to_axis_angle(self) -> (UnitVec3, f32) {
        const EPSILON: f64 = 1.0e-8;
        const EPSILON_SQUARED: f64 = EPSILON * EPSILON;

        let w = self.w;
        let v3 = self.xyz();
        let sin_theta_abs = v3.length();

        let angle_valid = sin_theta_abs > EPSILON_SQUARED as f32;

        let axis0 = v3 * sin_theta_abs.recip();
        let axis1 = Vec3::X;

        let a = if angle_valid { axis0 } else { axis1 };
        let angle = if angle_valid {
            (sin_theta_abs * w.signumf()).atan2f(w.absf()) * 2.0_f32
        } else {
            0.0_f32
        };

        (a.as_unit_vec3_unchecked(), angle)
    }

    /// Returns the rotation axis scaled by the rotation in radians.
    #[inline]
    pub fn to_scaled_axis(self) -> Vec3 {
        let (axis, angle) = self.to_axis_angle();
        axis * angle
    }

    /// Returns the rotation angles for the given euler rotation sequence.
    #[inline]
    pub fn to_euler(self, euler: EulerRot) -> (f32, f32, f32) {
        const PI: f32 = core::f32::consts::PI;
        #[allow(non_snake_case)]
        let TWO_PI: f32 = PI + PI;
        #[allow(clippy::excessive_precision)]
        const SQRT_2: f32 = 1.41421356237309504880168872420969808;

        let not_proper = euler.not_proper();
        let (i, j, k) = euler.map_sequence();
        let levi_civita_sig = euler.levi_civita_sig();
        let q = [self.w, self.x, self.y, self.z];

        let (a, b, c, d) = if not_proper {
            (
                (q[0] - q[j]) / SQRT_2,
                (q[k] * levi_civita_sig + q[i]) / SQRT_2,
                (q[0] + q[j]) / SQRT_2,
                (q[k] * levi_civita_sig - q[i]) / SQRT_2,
            )
        } else {
            (q[0], q[i], q[j], q[k] * levi_civita_sig)
        };

        let cos_theta_2 = 2.0_f32 * (a * a + b * b) - 1.0_f32;
        let theta_positive = b.atan2f(a);
        let theta_negative = -d.atan2f(c);

        let mut theta_1: f32;
        let mut theta_2: f32;
        let mut theta_3: f32;

        if cos_theta_2 + f32::EPSILON >= 1.0 {
            theta_1 = 0.0;
            theta_2 = 0.0;
            theta_3 = 2.0 * theta_positive;
        } else if cos_theta_2 - f32::EPSILON <= -1.0 {
            theta_1 = 0.0;
            theta_2 = PI;
            theta_3 = -2.0 * theta_negative;
        } else {
            theta_1 = theta_positive + theta_negative;
            theta_2 = cos_theta_2.acosf();
            theta_3 = theta_positive - theta_negative;
        };

        if not_proper {
            theta_3 *= levi_civita_sig;
            theta_2 -= PI / 2.0_f32;
        }

        theta_1 %= TWO_PI;
        theta_3 %= TWO_PI;

        if theta_1.absf() >= PI {
            theta_1 -= theta_1.signumf() * TWO_PI;
        }
        if theta_3.absf() >= PI {
            theta_3 -= theta_3.signumf() * TWO_PI;
        }

        (theta_3, theta_2, theta_1)
    }

    #[inline]
    /// Returns the rotation angles for the given euler rotation sequence.
    /// Default euler rotation sequence is `Z -> Y -> X` as roll (z-axis) -> yaw (y-axis) -> pitch (x-axis).
    /// First apply the z-axis rotation.
    pub fn to_euler_default(self) -> (f32, f32, f32) {
        self.to_euler(EulerRot::default())
    }

    /// `[x, y, z, w]`
    #[inline]
    pub fn to_array(&self) -> [f32; 4] {
        [self.x, self.y, self.z, self.w]
    }

    /// Returns the vector part of the quaternion.
    #[inline]
    pub fn xyz(self) -> Vec3 {
        Vec3::new(self.x, self.y, self.z)
    }

    /// Returns the quaternion conjugate of `self`. For a unit quaternion the
    /// conjugate is also the inverse.
    #[must_use]
    #[inline]
    pub fn conjugate(self) -> Self {
        const SIGN: __m128 = sse2::m128_from_f32x4([-0.0, -0.0, -0.0, 0.0]);
        Self(unsafe { _mm_xor_ps(self.0, SIGN) })
    }

    /// Returns the inverse of a unit quaternion.
    #[must_use]
    #[inline]
    pub fn inverse(self) -> Self {
        self.conjugate()
    }

    /// Computes the dot product of `self` and `rhs`.
    /// The dot product is equal to the cosine of the angle between two unit quaternion.
    #[inline]
    pub fn dot(self, rhs: Self) -> f32 {
        Vec4::from(self).dot(Vec4::from(rhs))
    }

    /// Returns whether `self` of length `1.0` or not.
    ///
    /// Uses a precision threshold of `1e-6`.
    #[inline]
    pub fn is_normalized(self) -> bool {
        Vec4::from(self).is_normalized()
    }

    /// Returns `self` normalized to length 1.0.
    /// Unit quaternion may denormalize due to loating point "error creep" which
    /// can occur when successive quaternion operations are applied.
    ///
    /// For valid results, `self` must _not_ be of length zero or infinite.
    ///
    /// Panics
    ///
    /// Will panic if `self` is zero or infinite length when `glam_assert` is enabled.
    #[must_use]
    #[inline]
    pub fn renormalize(self) -> Self {
        Self::from_unit_vec4(Vec4::from(self).normalize_to_unit())
    }

    #[inline]
    pub fn is_near_identity(self) -> bool {
        // Based on https://github.com/nfrechette/rtm `rtm::quat_near_identity`

        let threshold_angle = 0.002_847_144_6;

        // Because of floating point precision, we cannot represent very small rotations.
        // The closest f32 to 1.0 that is not 1.0 itself yields:
        // 0.99999994.acosf() * 2.0  = 0.000690533954 rad
        //
        // An error threshold of 1.e-6 is used by default.
        // (1.0 - 1.e-6).acosf() * 2.0 = 0.00284714461 rad
        // (1.0 - 1.e-7).acosf() * 2.0 = 0.00097656250 rad
        //
        // We don't really care about the angle value itself, only if it's close to 0.
        // This will happen whenever quat.w is close to 1.0.
        // If the quat.w is close to -1.0, the angle will be near 2*PI which is close to
        // a negative 0 rotation. By forcing quat.w to be positive, we'll end up with
        // the shortest path.
        let positive_w_angle = self.w.absf().acos_approx() * 2.0_f32;

        positive_w_angle < threshold_angle
    }

    /// Returns the angle (in radians) for the minimal rotation
    /// for transforming this quaternion into another.
    #[inline]
    pub fn angle_between(self, rhs: Self) -> f32 {
        self.dot(rhs).absf().acos_approx() * 2.0_f32
    }

    /// Returns true if the absolute difference of all elements between `self` and `rhs`
    /// is less than or equal to `max_abs_diff`.
    ///
    /// This can be used to compare if two quaternions contain similar elements. It works
    /// best when comparing with a known value. The `max_abs_diff` that should be used used
    /// depends on the values being compared against.
    ///
    /// For more see
    /// [comparing floating point numbers](https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/).
    #[inline]
    pub fn abs_diff_eq(self, rhs: Self, max_abs_diff: f32) -> bool {
        Vec4::from(self).abs_diff_eq(Vec4::from(rhs), max_abs_diff)
    }

    /// Performs a linear interpolation between `self` and `rhs` based on
    /// the value `s`.
    ///
    /// When `s` is `0.0`, the result will be equal to `self`.  When `s`
    /// is `1.0`, the result will be equal to `rhs`.
    #[inline]
    #[doc(alias = "mix")]
    pub fn lerp(self, end: Self, s: f32) -> Self {
        const NEG_ZERO: __m128 = sse2::m128_from_f32x4([-0.0; 4]);
        let start = self.0;
        let end = end.0;
        unsafe {
            let dot = crate::sse2::dot4_into_m128(start, end);
            // Calculate the bias, if the dot product is positive or zero, there is no bias
            // but if it is negative, we want to flip the 'end' rotation XYZW components
            let bias = _mm_and_ps(dot, NEG_ZERO);
            let interpolated = _mm_add_ps(
                _mm_mul_ps(_mm_sub_ps(_mm_xor_ps(end, bias), start), _mm_set_ps1(s)),
                start,
            );
            Quat(interpolated).normalize_to_unit()
        }
    }

    /// Performs a spherical linear interpolation between `self` and `end`
    /// based on the value `s`.
    ///
    /// When `s` is `0.0`, the result will be equal to `self`.  When `s`
    /// is `1.0`, the result will be equal to `end`.
    #[inline]
    pub fn slerp(self, mut end: Self, s: f32) -> Self {
        // http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/

        const DOT_THRESHOLD: f32 = 0.9995;

        // Note that a rotation can be represented by two quaternions: `q` and
        // `-q`. The slerp path between `q` and `end` will be different from the
        // path between `-q` and `end`. One path will take the long way around and
        // one will take the short way. In order to correct for this, the `dot`
        // product between `self` and `end` should be positive. If the `dot`
        // product is negative, slerp between `self` and `-end`.
        let mut dot = self.dot(end);

        if dot < 0.0 {
            end = -end;
            dot = -dot;
        }

        if dot > DOT_THRESHOLD {
            self.lerp(end, s)
        } else {
            let theta = dot.acos_approx();
            let x = 1.0 - s;
            let y = s;
            let z = 1.0;

            unsafe {
                let tmp = _mm_mul_ps(_mm_set_ps1(theta), _mm_set_ps(0.0, z, y, x));
                let tmp = sse2::m128_sin(tmp);

                let scale1 = _mm_shuffle_ps(tmp, tmp, 0b00_00_00_00);
                let scale2 = _mm_shuffle_ps(tmp, tmp, 0b01_01_01_01);
                let theta_sin = _mm_shuffle_ps(tmp, tmp, 0b10_10_10_10);

                Self(_mm_div_ps(
                    _mm_add_ps(_mm_mul_ps(self.0, scale1), _mm_mul_ps(end.0, scale2)),
                    theta_sin,
                ))
            }
        }
    }

    /// Multiplies a unit quaternion and a 3D vector, returning the rotated vector.
    #[inline]
    pub fn mul_vec3(self, rhs: Vec3) -> Vec3 {
        self.mul_vec3a(rhs.into()).into()
    }

    /// Multiplies two unit quaternions. If they each represent a rotation, the result will
    /// represent the combined rotation.
    ///
    /// Note that due to floating point rounding the result may not be perfectly normalized.
    #[inline]
    pub fn mul_unit_quat(self, rhs: Self) -> Self {
        // Based on https://github.com/nfrechette/rtm `rtm::quat_mul`
        const CONTROL_WZYX: __m128 = sse2::m128_from_f32x4([1.0, -1.0, 1.0, -1.0]);
        const CONTROL_ZWXY: __m128 = sse2::m128_from_f32x4([1.0, 1.0, -1.0, -1.0]);
        const CONTROL_YXWZ: __m128 = sse2::m128_from_f32x4([-1.0, 1.0, 1.0, -1.0]);

        let lhs = self.0;
        let rhs = rhs.0;

        unsafe {
            let r_xxxx = _mm_shuffle_ps(lhs, lhs, 0b00_00_00_00);
            let r_yyyy = _mm_shuffle_ps(lhs, lhs, 0b01_01_01_01);
            let r_zzzz = _mm_shuffle_ps(lhs, lhs, 0b10_10_10_10);
            let r_wwww = _mm_shuffle_ps(lhs, lhs, 0b11_11_11_11);

            let lxrw_lyrw_lzrw_lwrw = _mm_mul_ps(r_wwww, rhs);
            let l_wzyx = _mm_shuffle_ps(rhs, rhs, 0b00_01_10_11);

            let lwrx_lzrx_lyrx_lxrx = _mm_mul_ps(r_xxxx, l_wzyx);
            let l_zwxy = _mm_shuffle_ps(l_wzyx, l_wzyx, 0b10_11_00_01);

            let lwrx_nlzrx_lyrx_nlxrx = _mm_mul_ps(lwrx_lzrx_lyrx_lxrx, CONTROL_WZYX);

            let lzry_lwry_lxry_lyry = _mm_mul_ps(r_yyyy, l_zwxy);
            let l_yxwz = _mm_shuffle_ps(l_zwxy, l_zwxy, 0b00_01_10_11);

            let lzry_lwry_nlxry_nlyry = _mm_mul_ps(lzry_lwry_lxry_lyry, CONTROL_ZWXY);

            let lyrz_lxrz_lwrz_lzrz = _mm_mul_ps(r_zzzz, l_yxwz);
            let result0 = _mm_add_ps(lxrw_lyrw_lzrw_lwrw, lwrx_nlzrx_lyrx_nlxrx);

            let nlyrz_lxrz_lwrz_wlzrz = _mm_mul_ps(lyrz_lxrz_lwrz_lzrz, CONTROL_YXWZ);
            let result1 = _mm_add_ps(lzry_lwry_nlxry_nlyry, nlyrz_lxrz_lwrz_wlzrz);

            Self(_mm_add_ps(result0, result1))
        }
    }

    /// Multiplies a quaternion and a 3D vector, returning the rotated vector.
    #[inline]
    pub fn mul_vec3a(self, rhs: Vec3A) -> Vec3A {
        unsafe {
            const TWO: __m128 = sse2::m128_from_f32x4([2.0; 4]);
            let w = _mm_shuffle_ps(self.0, self.0, 0b11_11_11_11);
            let b = self.0;
            let b2 = sse2::dot3_into_m128(b, b);
            Vec3A(_mm_add_ps(
                _mm_add_ps(
                    _mm_mul_ps(rhs.0, _mm_sub_ps(_mm_mul_ps(w, w), b2)),
                    _mm_mul_ps(b, _mm_mul_ps(sse2::dot3_into_m128(rhs.0, b), TWO)),
                ),
                _mm_mul_ps(Vec3A(b).cross(rhs).into(), _mm_mul_ps(w, TWO)),
            ))
        }
    }

    #[inline]
    pub fn as_f64(self) -> UnitDQuat {
        UnitDQuat::from_xyzw_unchecked(self.x as f64, self.y as f64, self.z as f64, self.w as f64)
    }
}

#[cfg(not(target_arch = "spirv"))]
impl fmt::Debug for UnitQuat {
    fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
        fmt.debug_tuple(stringify!(UnitQuat))
            .field(&self.x)
            .field(&self.y)
            .field(&self.z)
            .field(&self.w)
            .finish()
    }
}

#[cfg(not(target_arch = "spirv"))]
impl fmt::Display for UnitQuat {
    fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
        write!(fmt, "[{}, {}, {}, {}]", self.x, self.y, self.z, self.w)
    }
}

impl_op_ex!(+ |a: &UnitQuat, b: &UnitQuat| -> Quat{
    Quat::from_vec4(Vec4::from(a) + Vec4::from(b))
});

impl_op_ex!(-|a: &UnitQuat, b: &UnitQuat| -> Quat {
    Quat::from_vec4(Vec4::from(a) - Vec4::from(b))
});

impl_op_ex_commutative!(*|a: &UnitQuat, b: &f32| -> Quat { Quat::from_vec4(Vec4::from(a) * b) });

impl_op_ex!(/ |a: &UnitQuat, b: &f32| -> Quat{
    Quat::from_vec4(Vec4::from(a) / b)
});

impl_op_ex!(*|a: &UnitQuat, b: &UnitQuat| -> UnitQuat { a.mul_unit_quat(*b) });

impl_op_ex!(*= |a: &mut UnitQuat, b: &UnitQuat| {
    *a = a.mul_unit_quat(*b)
});

impl_op_ex!(*|a: &UnitQuat, b: &Quat| -> Quat { a.as_quat().mul_quat(*b) });

impl_op_ex!(*|a: &Quat, b: &UnitQuat| -> Quat { a.mul_quat(b.as_quat()) });

impl_op_ex!(*= |a: &mut Quat, b: &UnitQuat| {
    *a = a.mul_quat(b.as_quat())
});

impl_op_ex!(*|a: &UnitQuat, b: &Vec3| -> Vec3 { a.mul_vec3(*b) });

impl_op_ex!(*|a: &UnitQuat, b: &UnitVec3| -> UnitVec3 {
    a.mul_vec3(b.as_vec3()).as_unit_vec3_unchecked()
});

impl_op_ex!(*|a: &UnitQuat, b: &Vec3A| -> Vec3A { a.mul_vec3a(*b) });

impl_op_ex!(*|a: &UnitQuat, b: &UnitVec3A| -> UnitVec3A {
    (a * b.as_vec3a()).as_unit_vec3a_unchecked()
});

impl Neg for UnitQuat {
    type Output = Self;
    #[inline]
    fn neg(self) -> Self {
        (self * -1.0_f32).as_unit_quat_unchecked()
    }
}

impl Default for UnitQuat {
    #[inline]
    fn default() -> Self {
        Self::IDENTITY
    }
}

impl PartialEq for UnitQuat {
    #[inline]
    fn eq(&self, rhs: &Self) -> bool {
        Vec4::from(*self).eq(&Vec4::from(*rhs))
    }
}

#[cfg(not(target_arch = "spirv"))]
impl AsRef<[f32; 4]> for UnitQuat {
    #[inline]
    fn as_ref(&self) -> &[f32; 4] {
        unsafe { &*(self as *const Self as *const [f32; 4]) }
    }
}

impl<'a> Product<&'a Self> for UnitQuat {
    fn product<I>(iter: I) -> Self
    where
        I: Iterator<Item = &'a Self>,
    {
        iter.fold(Self::IDENTITY, |a, &b| a * b)
    }
}

impl From<UnitQuat> for Vec4 {
    #[inline]
    fn from(q: UnitQuat) -> Self {
        Self(q.0)
    }
}

impl From<UnitQuat> for UnitVec4 {
    #[inline]
    fn from(q: UnitQuat) -> Self {
        Vec4::from(q).as_unit_vec4_unchecked()
    }
}

impl From<UnitQuat> for (f32, f32, f32, f32) {
    #[inline]
    fn from(q: UnitQuat) -> Self {
        Vec4::from(q).into()
    }
}

impl From<UnitQuat> for [f32; 4] {
    #[inline]
    fn from(q: UnitQuat) -> Self {
        Vec4::from(q).into()
    }
}

impl From<&UnitQuat> for Vec4 {
    #[inline]
    fn from(q: &UnitQuat) -> Self {
        Self(q.0)
    }
}

impl From<&UnitQuat> for UnitVec4 {
    #[inline]
    fn from(q: &UnitQuat) -> Self {
        Vec4::from(q).as_unit_vec4_unchecked()
    }
}

impl From<&UnitQuat> for (f32, f32, f32, f32) {
    #[inline]
    fn from(q: &UnitQuat) -> Self {
        Vec4::from(q).into()
    }
}

impl From<&UnitQuat> for [f32; 4] {
    #[inline]
    fn from(q: &UnitQuat) -> Self {
        Vec4::from(q).into()
    }
}

impl From<UnitQuat> for __m128 {
    #[inline]
    fn from(q: UnitQuat) -> Self {
        q.0
    }
}

impl Deref for UnitQuat {
    type Target = crate::deref::Vec4<f32>;
    #[inline]
    fn deref(&self) -> &Self::Target {
        unsafe { &*(self as *const Self).cast() }
    }
}