crates/glam/src/f32/sse2/mat2.rs - platform/external/rust/android-crates-io - Git at Google

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

 use crate::{f32::math, swizzles::*, DMat2, Mat3, Mat3A, Vec2};
 use core::fmt;
 use core::iter::{Product, Sum};
 use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};

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

 #[repr(C)]
 union UnionCast {
     a: [f32; 4],
     v: Mat2,
 }

 /// Creates a 2x2 matrix from two column vectors.
 #[inline(always)]
 #[must_use]
 pub const fn mat2(x_axis: Vec2, y_axis: Vec2) -> Mat2 {
     Mat2::from_cols(x_axis, y_axis)
 }

 /// A 2x2 column major matrix.
 ///
 /// SIMD vector types are used for storage on supported platforms.
 ///
 /// This type is 16 byte aligned.
 #[derive(Clone, Copy)]
 #[repr(transparent)]
 pub struct Mat2(pub(crate) __m128);

 impl Mat2 {
     /// A 2x2 matrix with all elements set to `0.0`.
     pub const ZERO: Self = Self::from_cols(Vec2::ZERO, Vec2::ZERO);

     /// A 2x2 identity matrix, where all diagonal elements are `1`, and all off-diagonal elements are `0`.
     pub const IDENTITY: Self = Self::from_cols(Vec2::X, Vec2::Y);

     /// All NAN:s.
     pub const NAN: Self = Self::from_cols(Vec2::NAN, Vec2::NAN);

     #[allow(clippy::too_many_arguments)]
     #[inline(always)]
     #[must_use]
     const fn new(m00: f32, m01: f32, m10: f32, m11: f32) -> Self {
         unsafe {
             UnionCast {
                 a: [m00, m01, m10, m11],
             }
             .v
         }
     }

     /// Creates a 2x2 matrix from two column vectors.
     #[inline(always)]
     #[must_use]
     pub const fn from_cols(x_axis: Vec2, y_axis: Vec2) -> Self {
         unsafe {
             UnionCast {
                 a: [x_axis.x, x_axis.y, y_axis.x, y_axis.y],
             }
             .v
         }
     }

     /// Creates a 2x2 matrix from a `[f32; 4]` array stored in column major order.
     /// If your data is stored in row major you will need to `transpose` the returned
     /// matrix.
     #[inline]
     #[must_use]
     pub const fn from_cols_array(m: &[f32; 4]) -> Self {
         Self::new(m[0], m[1], m[2], m[3])
     }

     /// Creates a `[f32; 4]` array storing data in column major order.
     /// If you require data in row major order `transpose` the matrix first.
     #[inline]
     #[must_use]
     pub const fn to_cols_array(&self) -> [f32; 4] {
         unsafe { *(self as *const Self as *const [f32; 4]) }
     }

     /// Creates a 2x2 matrix from a `[[f32; 2]; 2]` 2D array stored in column major order.
     /// If your data is in row major order you will need to `transpose` the returned
     /// matrix.
     #[inline]
     #[must_use]
     pub const fn from_cols_array_2d(m: &[[f32; 2]; 2]) -> Self {
         Self::from_cols(Vec2::from_array(m[0]), Vec2::from_array(m[1]))
     }

     /// Creates a `[[f32; 2]; 2]` 2D array storing data in column major order.
     /// If you require data in row major order `transpose` the matrix first.
     #[inline]
     #[must_use]
     pub const fn to_cols_array_2d(&self) -> [[f32; 2]; 2] {
         unsafe { *(self as *const Self as *const [[f32; 2]; 2]) }
     }

     /// Creates a 2x2 matrix with its diagonal set to `diagonal` and all other entries set to 0.
     #[doc(alias = "scale")]
     #[inline]
     #[must_use]
     pub const fn from_diagonal(diagonal: Vec2) -> Self {
         Self::new(diagonal.x, 0.0, 0.0, diagonal.y)
     }

     /// Creates a 2x2 matrix containing the combining non-uniform `scale` and rotation of
     /// `angle` (in radians).
     #[inline]
     #[must_use]
     pub fn from_scale_angle(scale: Vec2, angle: f32) -> Self {
         let (sin, cos) = math::sin_cos(angle);
         Self::new(cos * scale.x, sin * scale.x, -sin * scale.y, cos * scale.y)
     }

     /// Creates a 2x2 matrix containing a rotation of `angle` (in radians).
     #[inline]
     #[must_use]
     pub fn from_angle(angle: f32) -> Self {
         let (sin, cos) = math::sin_cos(angle);
         Self::new(cos, sin, -sin, cos)
     }

     /// Creates a 2x2 matrix from a 3x3 matrix, discarding the 2nd row and column.
     #[inline]
     #[must_use]
     pub fn from_mat3(m: Mat3) -> Self {
         Self::from_cols(m.x_axis.xy(), m.y_axis.xy())
     }

     /// Creates a 2x2 matrix from the minor of the given 3x3 matrix, discarding the `i`th column
     /// and `j`th row.
     ///
     /// # Panics
     ///
     /// Panics if `i` or `j` is greater than 2.
     #[inline]
     #[must_use]
     pub fn from_mat3_minor(m: Mat3, i: usize, j: usize) -> Self {
         match (i, j) {
             (0, 0) => Self::from_cols(m.y_axis.yz(), m.z_axis.yz()),
             (0, 1) => Self::from_cols(m.y_axis.xz(), m.z_axis.xz()),
             (0, 2) => Self::from_cols(m.y_axis.xy(), m.z_axis.xy()),
             (1, 0) => Self::from_cols(m.x_axis.yz(), m.z_axis.yz()),
             (1, 1) => Self::from_cols(m.x_axis.xz(), m.z_axis.xz()),
             (1, 2) => Self::from_cols(m.x_axis.xy(), m.z_axis.xy()),
             (2, 0) => Self::from_cols(m.x_axis.yz(), m.y_axis.yz()),
             (2, 1) => Self::from_cols(m.x_axis.xz(), m.y_axis.xz()),
             (2, 2) => Self::from_cols(m.x_axis.xy(), m.y_axis.xy()),
             _ => panic!("index out of bounds"),
         }
     }

     /// Creates a 2x2 matrix from a 3x3 matrix, discarding the 2nd row and column.
     #[inline]
     #[must_use]
     pub fn from_mat3a(m: Mat3A) -> Self {
         Self::from_cols(m.x_axis.xy(), m.y_axis.xy())
     }

     /// Creates a 2x2 matrix from the minor of the given 3x3 matrix, discarding the `i`th column
     /// and `j`th row.
     ///
     /// # Panics
     ///
     /// Panics if `i` or `j` is greater than 2.
     #[inline]
     #[must_use]
     pub fn from_mat3a_minor(m: Mat3A, i: usize, j: usize) -> Self {
         match (i, j) {
             (0, 0) => Self::from_cols(m.y_axis.yz(), m.z_axis.yz()),
             (0, 1) => Self::from_cols(m.y_axis.xz(), m.z_axis.xz()),
             (0, 2) => Self::from_cols(m.y_axis.xy(), m.z_axis.xy()),
             (1, 0) => Self::from_cols(m.x_axis.yz(), m.z_axis.yz()),
             (1, 1) => Self::from_cols(m.x_axis.xz(), m.z_axis.xz()),
             (1, 2) => Self::from_cols(m.x_axis.xy(), m.z_axis.xy()),
             (2, 0) => Self::from_cols(m.x_axis.yz(), m.y_axis.yz()),
             (2, 1) => Self::from_cols(m.x_axis.xz(), m.y_axis.xz()),
             (2, 2) => Self::from_cols(m.x_axis.xy(), m.y_axis.xy()),
             _ => panic!("index out of bounds"),
         }
     }

     /// Creates a 2x2 matrix from the first 4 values in `slice`.
     ///
     /// # Panics
     ///
     /// Panics if `slice` is less than 4 elements long.
     #[inline]
     #[must_use]
     pub const fn from_cols_slice(slice: &[f32]) -> Self {
         Self::new(slice[0], slice[1], slice[2], slice[3])
     }

     /// Writes the columns of `self` to the first 4 elements in `slice`.
     ///
     /// # Panics
     ///
     /// Panics if `slice` is less than 4 elements long.
     #[inline]
     pub fn write_cols_to_slice(self, slice: &mut [f32]) {
         slice[0] = self.x_axis.x;
         slice[1] = self.x_axis.y;
         slice[2] = self.y_axis.x;
         slice[3] = self.y_axis.y;
     }

     /// Returns the matrix column for the given `index`.
     ///
     /// # Panics
     ///
     /// Panics if `index` is greater than 1.
     #[inline]
     #[must_use]
     pub fn col(&self, index: usize) -> Vec2 {
         match index {
             0 => self.x_axis,
             1 => self.y_axis,
             _ => panic!("index out of bounds"),
         }
     }

     /// Returns a mutable reference to the matrix column for the given `index`.
     ///
     /// # Panics
     ///
     /// Panics if `index` is greater than 1.
     #[inline]
     pub fn col_mut(&mut self, index: usize) -> &mut Vec2 {
         match index {
             0 => &mut self.x_axis,
             1 => &mut self.y_axis,
             _ => panic!("index out of bounds"),
         }
     }

     /// Returns the matrix row for the given `index`.
     ///
     /// # Panics
     ///
     /// Panics if `index` is greater than 1.
     #[inline]
     #[must_use]
     pub fn row(&self, index: usize) -> Vec2 {
         match index {
             0 => Vec2::new(self.x_axis.x, self.y_axis.x),
             1 => Vec2::new(self.x_axis.y, self.y_axis.y),
             _ => panic!("index out of bounds"),
         }
     }

     /// Returns `true` if, and only if, all elements are finite.
     /// If any element is either `NaN`, positive or negative infinity, this will return `false`.
     #[inline]
     #[must_use]
     pub fn is_finite(&self) -> bool {
         self.x_axis.is_finite() && self.y_axis.is_finite()
     }

     /// Returns `true` if any elements are `NaN`.
     #[inline]
     #[must_use]
     pub fn is_nan(&self) -> bool {
         self.x_axis.is_nan() || self.y_axis.is_nan()
     }

     /// Returns the transpose of `self`.
     #[inline]
     #[must_use]
     pub fn transpose(&self) -> Self {
         Self(unsafe { _mm_shuffle_ps(self.0, self.0, 0b11_01_10_00) })
     }

     /// Returns the determinant of `self`.
     #[inline]
     #[must_use]
     pub fn determinant(&self) -> f32 {
         unsafe {
             let abcd = self.0;
             let dcba = _mm_shuffle_ps(abcd, abcd, 0b00_01_10_11);
             let prod = _mm_mul_ps(abcd, dcba);
             let det = _mm_sub_ps(prod, _mm_shuffle_ps(prod, prod, 0b01_01_01_01));
             _mm_cvtss_f32(det)
         }
     }

     /// Returns the inverse of `self`.
     ///
     /// If the matrix is not invertible the returned matrix will be invalid.
     ///
     /// # Panics
     ///
     /// Will panic if the determinant of `self` is zero when `glam_assert` is enabled.
     #[inline]
     #[must_use]
     pub fn inverse(&self) -> Self {
         unsafe {
             const SIGN: __m128 = crate::sse2::m128_from_f32x4([1.0, -1.0, -1.0, 1.0]);
             let abcd = self.0;
             let dcba = _mm_shuffle_ps(abcd, abcd, 0b00_01_10_11);
             let prod = _mm_mul_ps(abcd, dcba);
             let sub = _mm_sub_ps(prod, _mm_shuffle_ps(prod, prod, 0b01_01_01_01));
             let det = _mm_shuffle_ps(sub, sub, 0b00_00_00_00);
             let tmp = _mm_div_ps(SIGN, det);
             glam_assert!(Mat2(tmp).is_finite());
             let dbca = _mm_shuffle_ps(abcd, abcd, 0b00_10_01_11);
             Self(_mm_mul_ps(dbca, tmp))
         }
     }

     /// Transforms a 2D vector.
     #[inline]
     #[must_use]
     pub fn mul_vec2(&self, rhs: Vec2) -> Vec2 {
         unsafe {
             use crate::Align16;
             use core::mem::MaybeUninit;
             let abcd = self.0;
             let xxyy = _mm_set_ps(rhs.y, rhs.y, rhs.x, rhs.x);
             let axbxcydy = _mm_mul_ps(abcd, xxyy);
             let cydyaxbx = _mm_shuffle_ps(axbxcydy, axbxcydy, 0b01_00_11_10);
             let result = _mm_add_ps(axbxcydy, cydyaxbx);
             let mut out: MaybeUninit<Align16<Vec2>> = MaybeUninit::uninit();
             _mm_store_ps(out.as_mut_ptr().cast(), result);
             out.assume_init().0
         }
     }

     /// Multiplies two 2x2 matrices.
     #[inline]
     #[must_use]
     pub fn mul_mat2(&self, rhs: &Self) -> Self {
         unsafe {
             let abcd = self.0;
             let rhs = rhs.0;
             let xxyy0 = _mm_shuffle_ps(rhs, rhs, 0b01_01_00_00);
             let xxyy1 = _mm_shuffle_ps(rhs, rhs, 0b11_11_10_10);
             let axbxcydy0 = _mm_mul_ps(abcd, xxyy0);
             let axbxcydy1 = _mm_mul_ps(abcd, xxyy1);
             let cydyaxbx0 = _mm_shuffle_ps(axbxcydy0, axbxcydy0, 0b01_00_11_10);
             let cydyaxbx1 = _mm_shuffle_ps(axbxcydy1, axbxcydy1, 0b01_00_11_10);
             let result0 = _mm_add_ps(axbxcydy0, cydyaxbx0);
             let result1 = _mm_add_ps(axbxcydy1, cydyaxbx1);
             Self(_mm_shuffle_ps(result0, result1, 0b01_00_01_00))
         }
     }

     /// Adds two 2x2 matrices.
     #[inline]
     #[must_use]
     pub fn add_mat2(&self, rhs: &Self) -> Self {
         Self(unsafe { _mm_add_ps(self.0, rhs.0) })
     }

     /// Subtracts two 2x2 matrices.
     #[inline]
     #[must_use]
     pub fn sub_mat2(&self, rhs: &Self) -> Self {
         Self(unsafe { _mm_sub_ps(self.0, rhs.0) })
     }

     /// Multiplies a 2x2 matrix by a scalar.
     #[inline]
     #[must_use]
     pub fn mul_scalar(&self, rhs: f32) -> Self {
         Self(unsafe { _mm_mul_ps(self.0, _mm_set_ps1(rhs)) })
     }

     /// Divides a 2x2 matrix by a scalar.
     #[inline]
     #[must_use]
     pub fn div_scalar(&self, rhs: f32) -> Self {
         Self(unsafe { _mm_div_ps(self.0, _mm_set_ps1(rhs)) })
     }

     /// 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 matrices 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]
     #[must_use]
     pub fn abs_diff_eq(&self, rhs: Self, max_abs_diff: f32) -> bool {
         self.x_axis.abs_diff_eq(rhs.x_axis, max_abs_diff)
             && self.y_axis.abs_diff_eq(rhs.y_axis, max_abs_diff)
     }

     /// Takes the absolute value of each element in `self`
     #[inline]
     #[must_use]
     pub fn abs(&self) -> Self {
         Self::from_cols(self.x_axis.abs(), self.y_axis.abs())
     }

     #[inline]
     pub fn as_dmat2(&self) -> DMat2 {
         DMat2::from_cols(self.x_axis.as_dvec2(), self.y_axis.as_dvec2())
     }
 }

 impl Default for Mat2 {
     #[inline]
     fn default() -> Self {
         Self::IDENTITY
     }
 }

 impl Add<Mat2> for Mat2 {
     type Output = Self;
     #[inline]
     fn add(self, rhs: Self) -> Self::Output {
         self.add_mat2(&rhs)
     }
 }

 impl AddAssign<Mat2> for Mat2 {
     #[inline]
     fn add_assign(&mut self, rhs: Self) {
         *self = self.add_mat2(&rhs);
     }
 }

 impl Sub<Mat2> for Mat2 {
     type Output = Self;
     #[inline]
     fn sub(self, rhs: Self) -> Self::Output {
         self.sub_mat2(&rhs)
     }
 }

 impl SubAssign<Mat2> for Mat2 {
     #[inline]
     fn sub_assign(&mut self, rhs: Self) {
         *self = self.sub_mat2(&rhs);
     }
 }

 impl Neg for Mat2 {
     type Output = Self;
     #[inline]
     fn neg(self) -> Self::Output {
         Self(unsafe { _mm_xor_ps(self.0, _mm_set1_ps(-0.0)) })
     }
 }

 impl Mul<Mat2> for Mat2 {
     type Output = Self;
     #[inline]
     fn mul(self, rhs: Self) -> Self::Output {
         self.mul_mat2(&rhs)
     }
 }

 impl MulAssign<Mat2> for Mat2 {
     #[inline]
     fn mul_assign(&mut self, rhs: Self) {
         *self = self.mul_mat2(&rhs);
     }
 }

 impl Mul<Vec2> for Mat2 {
     type Output = Vec2;
     #[inline]
     fn mul(self, rhs: Vec2) -> Self::Output {
         self.mul_vec2(rhs)
     }
 }

 impl Mul<Mat2> for f32 {
     type Output = Mat2;
     #[inline]
     fn mul(self, rhs: Mat2) -> Self::Output {
         rhs.mul_scalar(self)
     }
 }

 impl Mul<f32> for Mat2 {
     type Output = Self;
     #[inline]
     fn mul(self, rhs: f32) -> Self::Output {
         self.mul_scalar(rhs)
     }
 }

 impl MulAssign<f32> for Mat2 {
     #[inline]
     fn mul_assign(&mut self, rhs: f32) {
         *self = self.mul_scalar(rhs);
     }
 }

 impl Div<Mat2> for f32 {
     type Output = Mat2;
     #[inline]
     fn div(self, rhs: Mat2) -> Self::Output {
         rhs.div_scalar(self)
     }
 }

 impl Div<f32> for Mat2 {
     type Output = Self;
     #[inline]
     fn div(self, rhs: f32) -> Self::Output {
         self.div_scalar(rhs)
     }
 }

 impl DivAssign<f32> for Mat2 {
     #[inline]
     fn div_assign(&mut self, rhs: f32) {
         *self = self.div_scalar(rhs);
     }
 }

 impl Sum<Self> for Mat2 {
     fn sum<I>(iter: I) -> Self
     where
         I: Iterator<Item = Self>,
     {
         iter.fold(Self::ZERO, Self::add)
     }
 }

 impl<'a> Sum<&'a Self> for Mat2 {
     fn sum<I>(iter: I) -> Self
     where
         I: Iterator<Item = &'a Self>,
     {
         iter.fold(Self::ZERO, |a, &b| Self::add(a, b))
     }
 }

 impl Product for Mat2 {
     fn product<I>(iter: I) -> Self
     where
         I: Iterator<Item = Self>,
     {
         iter.fold(Self::IDENTITY, Self::mul)
     }
 }

 impl<'a> Product<&'a Self> for Mat2 {
     fn product<I>(iter: I) -> Self
     where
         I: Iterator<Item = &'a Self>,
     {
         iter.fold(Self::IDENTITY, |a, &b| Self::mul(a, b))
     }
 }

 impl PartialEq for Mat2 {
     #[inline]
     fn eq(&self, rhs: &Self) -> bool {
         self.x_axis.eq(&rhs.x_axis) && self.y_axis.eq(&rhs.y_axis)
     }
 }

 #[cfg(not(target_arch = "spirv"))]
 impl AsRef<[f32; 4]> for Mat2 {
     #[inline]
     fn as_ref(&self) -> &[f32; 4] {
         unsafe { &*(self as *const Self as *const [f32; 4]) }
     }
 }

 #[cfg(not(target_arch = "spirv"))]
 impl AsMut<[f32; 4]> for Mat2 {
     #[inline]
     fn as_mut(&mut self) -> &mut [f32; 4] {
         unsafe { &mut *(self as *mut Self as *mut [f32; 4]) }
     }
 }

 impl core::ops::Deref for Mat2 {
     type Target = crate::deref::Cols2<Vec2>;
     #[inline]
     fn deref(&self) -> &Self::Target {
         unsafe { &*(self as *const Self as *const Self::Target) }
     }
 }

 impl core::ops::DerefMut for Mat2 {
     #[inline]
     fn deref_mut(&mut self) -> &mut Self::Target {
         unsafe { &mut *(self as *mut Self as *mut Self::Target) }
     }
 }

 impl fmt::Debug for Mat2 {
     fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
         fmt.debug_struct(stringify!(Mat2))
             .field("x_axis", &self.x_axis)
             .field("y_axis", &self.y_axis)
             .finish()
     }
 }

 impl fmt::Display for Mat2 {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
         if let Some(p) = f.precision() {
             write!(f, "[{:.*}, {:.*}]", p, self.x_axis, p, self.y_axis)
         } else {
             write!(f, "[{}, {}]", self.x_axis, self.y_axis)
         }
     }
 }
	// Generated from mat.rs.tera template. Edit the template, not the generated file.

	use crate::{f32::math, swizzles::*, DMat2, Mat3, Mat3A, Vec2};
	use core::fmt;
	use core::iter::{Product, Sum};
	use core::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};

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

	#[repr(C)]
	union UnionCast {
	a: [f32; 4],
	v: Mat2,
	}

	/// Creates a 2x2 matrix from two column vectors.
	#[inline(always)]
	#[must_use]
	pub const fn mat2(x_axis: Vec2, y_axis: Vec2) -> Mat2 {
	Mat2::from_cols(x_axis, y_axis)
	}

	/// A 2x2 column major matrix.
	///
	/// SIMD vector types are used for storage on supported platforms.
	///
	/// This type is 16 byte aligned.
	#[derive(Clone, Copy)]
	#[repr(transparent)]
	pub struct Mat2(pub(crate) __m128);

	impl Mat2 {
	/// A 2x2 matrix with all elements set to `0.0`.
	pub const ZERO: Self = Self::from_cols(Vec2::ZERO, Vec2::ZERO);

	/// A 2x2 identity matrix, where all diagonal elements are `1`, and all off-diagonal elements are `0`.
	pub const IDENTITY: Self = Self::from_cols(Vec2::X, Vec2::Y);

	/// All NAN:s.
	pub const NAN: Self = Self::from_cols(Vec2::NAN, Vec2::NAN);

	#[allow(clippy::too_many_arguments)]
	#[inline(always)]
	#[must_use]
	const fn new(m00: f32, m01: f32, m10: f32, m11: f32) -> Self {
	unsafe {
	UnionCast {
	a: [m00, m01, m10, m11],
	}
	.v
	}
	}

	/// Creates a 2x2 matrix from two column vectors.
	#[inline(always)]
	#[must_use]
	pub const fn from_cols(x_axis: Vec2, y_axis: Vec2) -> Self {
	unsafe {
	UnionCast {
	a: [x_axis.x, x_axis.y, y_axis.x, y_axis.y],
	}
	.v
	}
	}

	/// Creates a 2x2 matrix from a `[f32; 4]` array stored in column major order.
	/// If your data is stored in row major you will need to `transpose` the returned
	/// matrix.
	#[inline]
	#[must_use]
	pub const fn from_cols_array(m: &[f32; 4]) -> Self {
	Self::new(m[0], m[1], m[2], m[3])
	}

	/// Creates a `[f32; 4]` array storing data in column major order.
	/// If you require data in row major order `transpose` the matrix first.
	#[inline]
	#[must_use]
	pub const fn to_cols_array(&self) -> [f32; 4] {
	unsafe { (self as const Self as *const [f32; 4]) }
	}

	/// Creates a 2x2 matrix from a `[[f32; 2]; 2]` 2D array stored in column major order.
	/// If your data is in row major order you will need to `transpose` the returned
	/// matrix.
	#[inline]
	#[must_use]
	pub const fn from_cols_array_2d(m: &[[f32; 2]; 2]) -> Self {
	Self::from_cols(Vec2::from_array(m[0]), Vec2::from_array(m[1]))
	}

	/// Creates a `[[f32; 2]; 2]` 2D array storing data in column major order.
	/// If you require data in row major order `transpose` the matrix first.
	#[inline]
	#[must_use]
	pub const fn to_cols_array_2d(&self) -> [[f32; 2]; 2] {
	unsafe { (self as const Self as *const [[f32; 2]; 2]) }
	}

	/// Creates a 2x2 matrix with its diagonal set to `diagonal` and all other entries set to 0.
	#[doc(alias = "scale")]
	#[inline]
	#[must_use]
	pub const fn from_diagonal(diagonal: Vec2) -> Self {
	Self::new(diagonal.x, 0.0, 0.0, diagonal.y)
	}

	/// Creates a 2x2 matrix containing the combining non-uniform `scale` and rotation of
	/// `angle` (in radians).
	#[inline]
	#[must_use]
	pub fn from_scale_angle(scale: Vec2, angle: f32) -> Self {
	let (sin, cos) = math::sin_cos(angle);
	Self::new(cos * scale.x, sin * scale.x, -sin * scale.y, cos * scale.y)
	}

	/// Creates a 2x2 matrix containing a rotation of `angle` (in radians).
	#[inline]
	#[must_use]
	pub fn from_angle(angle: f32) -> Self {
	let (sin, cos) = math::sin_cos(angle);
	Self::new(cos, sin, -sin, cos)
	}

	/// Creates a 2x2 matrix from a 3x3 matrix, discarding the 2nd row and column.
	#[inline]
	#[must_use]
	pub fn from_mat3(m: Mat3) -> Self {
	Self::from_cols(m.x_axis.xy(), m.y_axis.xy())
	}

	/// Creates a 2x2 matrix from the minor of the given 3x3 matrix, discarding the `i`th column
	/// and `j`th row.
	///
	/// # Panics
	///
	/// Panics if `i` or `j` is greater than 2.
	#[inline]
	#[must_use]
	pub fn from_mat3_minor(m: Mat3, i: usize, j: usize) -> Self {
	match (i, j) {
	(0, 0) => Self::from_cols(m.y_axis.yz(), m.z_axis.yz()),
	(0, 1) => Self::from_cols(m.y_axis.xz(), m.z_axis.xz()),
	(0, 2) => Self::from_cols(m.y_axis.xy(), m.z_axis.xy()),
	(1, 0) => Self::from_cols(m.x_axis.yz(), m.z_axis.yz()),
	(1, 1) => Self::from_cols(m.x_axis.xz(), m.z_axis.xz()),
	(1, 2) => Self::from_cols(m.x_axis.xy(), m.z_axis.xy()),
	(2, 0) => Self::from_cols(m.x_axis.yz(), m.y_axis.yz()),
	(2, 1) => Self::from_cols(m.x_axis.xz(), m.y_axis.xz()),
	(2, 2) => Self::from_cols(m.x_axis.xy(), m.y_axis.xy()),
	_ => panic!("index out of bounds"),
	}
	}

	/// Creates a 2x2 matrix from a 3x3 matrix, discarding the 2nd row and column.
	#[inline]
	#[must_use]
	pub fn from_mat3a(m: Mat3A) -> Self {
	Self::from_cols(m.x_axis.xy(), m.y_axis.xy())
	}

	/// Creates a 2x2 matrix from the minor of the given 3x3 matrix, discarding the `i`th column
	/// and `j`th row.
	///
	/// # Panics
	///
	/// Panics if `i` or `j` is greater than 2.
	#[inline]
	#[must_use]
	pub fn from_mat3a_minor(m: Mat3A, i: usize, j: usize) -> Self {
	match (i, j) {
	(0, 0) => Self::from_cols(m.y_axis.yz(), m.z_axis.yz()),
	(0, 1) => Self::from_cols(m.y_axis.xz(), m.z_axis.xz()),
	(0, 2) => Self::from_cols(m.y_axis.xy(), m.z_axis.xy()),
	(1, 0) => Self::from_cols(m.x_axis.yz(), m.z_axis.yz()),
	(1, 1) => Self::from_cols(m.x_axis.xz(), m.z_axis.xz()),
	(1, 2) => Self::from_cols(m.x_axis.xy(), m.z_axis.xy()),
	(2, 0) => Self::from_cols(m.x_axis.yz(), m.y_axis.yz()),
	(2, 1) => Self::from_cols(m.x_axis.xz(), m.y_axis.xz()),
	(2, 2) => Self::from_cols(m.x_axis.xy(), m.y_axis.xy()),
	_ => panic!("index out of bounds"),
	}
	}

	/// Creates a 2x2 matrix from the first 4 values in `slice`.
	///
	/// # Panics
	///
	/// Panics if `slice` is less than 4 elements long.
	#[inline]
	#[must_use]
	pub const fn from_cols_slice(slice: &[f32]) -> Self {
	Self::new(slice[0], slice[1], slice[2], slice[3])
	}

	/// Writes the columns of `self` to the first 4 elements in `slice`.
	///
	/// # Panics
	///
	/// Panics if `slice` is less than 4 elements long.
	#[inline]
	pub fn write_cols_to_slice(self, slice: &mut [f32]) {
	slice[0] = self.x_axis.x;
	slice[1] = self.x_axis.y;
	slice[2] = self.y_axis.x;
	slice[3] = self.y_axis.y;
	}

	/// Returns the matrix column for the given `index`.
	///
	/// # Panics
	///
	/// Panics if `index` is greater than 1.
	#[inline]
	#[must_use]
	pub fn col(&self, index: usize) -> Vec2 {
	match index {
	0 => self.x_axis,
	1 => self.y_axis,
	_ => panic!("index out of bounds"),
	}
	}

	/// Returns a mutable reference to the matrix column for the given `index`.
	///
	/// # Panics
	///
	/// Panics if `index` is greater than 1.
	#[inline]
	pub fn col_mut(&mut self, index: usize) -> &mut Vec2 {
	match index {
	0 => &mut self.x_axis,
	1 => &mut self.y_axis,
	_ => panic!("index out of bounds"),
	}
	}

	/// Returns the matrix row for the given `index`.
	///
	/// # Panics
	///
	/// Panics if `index` is greater than 1.
	#[inline]
	#[must_use]
	pub fn row(&self, index: usize) -> Vec2 {
	match index {
	0 => Vec2::new(self.x_axis.x, self.y_axis.x),
	1 => Vec2::new(self.x_axis.y, self.y_axis.y),
	_ => panic!("index out of bounds"),
	}
	}

	/// Returns `true` if, and only if, all elements are finite.
	/// If any element is either `NaN`, positive or negative infinity, this will return `false`.
	#[inline]
	#[must_use]
	pub fn is_finite(&self) -> bool {
	self.x_axis.is_finite() && self.y_axis.is_finite()
	}

	/// Returns `true` if any elements are `NaN`.
	#[inline]
	#[must_use]
	pub fn is_nan(&self) -> bool {
	self.x_axis.is_nan() \|\| self.y_axis.is_nan()
	}

	/// Returns the transpose of `self`.
	#[inline]
	#[must_use]
	pub fn transpose(&self) -> Self {
	Self(unsafe { _mm_shuffle_ps(self.0, self.0, 0b11_01_10_00) })
	}

	/// Returns the determinant of `self`.
	#[inline]
	#[must_use]
	pub fn determinant(&self) -> f32 {
	unsafe {
	let abcd = self.0;
	let dcba = _mm_shuffle_ps(abcd, abcd, 0b00_01_10_11);
	let prod = _mm_mul_ps(abcd, dcba);
	let det = _mm_sub_ps(prod, _mm_shuffle_ps(prod, prod, 0b01_01_01_01));
	_mm_cvtss_f32(det)
	}
	}

	/// Returns the inverse of `self`.
	///
	/// If the matrix is not invertible the returned matrix will be invalid.
	///
	/// # Panics
	///
	/// Will panic if the determinant of `self` is zero when `glam_assert` is enabled.
	#[inline]
	#[must_use]
	pub fn inverse(&self) -> Self {
	unsafe {
	const SIGN: __m128 = crate::sse2::m128_from_f32x4([1.0, -1.0, -1.0, 1.0]);
	let abcd = self.0;
	let dcba = _mm_shuffle_ps(abcd, abcd, 0b00_01_10_11);
	let prod = _mm_mul_ps(abcd, dcba);
	let sub = _mm_sub_ps(prod, _mm_shuffle_ps(prod, prod, 0b01_01_01_01));
	let det = _mm_shuffle_ps(sub, sub, 0b00_00_00_00);
	let tmp = _mm_div_ps(SIGN, det);
	glam_assert!(Mat2(tmp).is_finite());
	let dbca = _mm_shuffle_ps(abcd, abcd, 0b00_10_01_11);
	Self(_mm_mul_ps(dbca, tmp))
	}
	}

	/// Transforms a 2D vector.
	#[inline]
	#[must_use]
	pub fn mul_vec2(&self, rhs: Vec2) -> Vec2 {
	unsafe {
	use crate::Align16;
	use core::mem::MaybeUninit;
	let abcd = self.0;
	let xxyy = _mm_set_ps(rhs.y, rhs.y, rhs.x, rhs.x);
	let axbxcydy = _mm_mul_ps(abcd, xxyy);
	let cydyaxbx = _mm_shuffle_ps(axbxcydy, axbxcydy, 0b01_00_11_10);
	let result = _mm_add_ps(axbxcydy, cydyaxbx);
	let mut out: MaybeUninit<Align16<Vec2>> = MaybeUninit::uninit();
	_mm_store_ps(out.as_mut_ptr().cast(), result);
	out.assume_init().0
	}
	}

	/// Multiplies two 2x2 matrices.
	#[inline]
	#[must_use]
	pub fn mul_mat2(&self, rhs: &Self) -> Self {
	unsafe {
	let abcd = self.0;
	let rhs = rhs.0;
	let xxyy0 = _mm_shuffle_ps(rhs, rhs, 0b01_01_00_00);
	let xxyy1 = _mm_shuffle_ps(rhs, rhs, 0b11_11_10_10);
	let axbxcydy0 = _mm_mul_ps(abcd, xxyy0);
	let axbxcydy1 = _mm_mul_ps(abcd, xxyy1);
	let cydyaxbx0 = _mm_shuffle_ps(axbxcydy0, axbxcydy0, 0b01_00_11_10);
	let cydyaxbx1 = _mm_shuffle_ps(axbxcydy1, axbxcydy1, 0b01_00_11_10);
	let result0 = _mm_add_ps(axbxcydy0, cydyaxbx0);
	let result1 = _mm_add_ps(axbxcydy1, cydyaxbx1);
	Self(_mm_shuffle_ps(result0, result1, 0b01_00_01_00))
	}
	}

	/// Adds two 2x2 matrices.
	#[inline]
	#[must_use]
	pub fn add_mat2(&self, rhs: &Self) -> Self {
	Self(unsafe { _mm_add_ps(self.0, rhs.0) })
	}

	/// Subtracts two 2x2 matrices.
	#[inline]
	#[must_use]
	pub fn sub_mat2(&self, rhs: &Self) -> Self {
	Self(unsafe { _mm_sub_ps(self.0, rhs.0) })
	}

	/// Multiplies a 2x2 matrix by a scalar.
	#[inline]
	#[must_use]
	pub fn mul_scalar(&self, rhs: f32) -> Self {
	Self(unsafe { _mm_mul_ps(self.0, _mm_set_ps1(rhs)) })
	}

	/// Divides a 2x2 matrix by a scalar.
	#[inline]
	#[must_use]
	pub fn div_scalar(&self, rhs: f32) -> Self {
	Self(unsafe { _mm_div_ps(self.0, _mm_set_ps1(rhs)) })
	}

	/// 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 matrices 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]
	#[must_use]
	pub fn abs_diff_eq(&self, rhs: Self, max_abs_diff: f32) -> bool {
	self.x_axis.abs_diff_eq(rhs.x_axis, max_abs_diff)
	&& self.y_axis.abs_diff_eq(rhs.y_axis, max_abs_diff)
	}

	/// Takes the absolute value of each element in `self`
	#[inline]
	#[must_use]
	pub fn abs(&self) -> Self {
	Self::from_cols(self.x_axis.abs(), self.y_axis.abs())
	}

	#[inline]
	pub fn as_dmat2(&self) -> DMat2 {
	DMat2::from_cols(self.x_axis.as_dvec2(), self.y_axis.as_dvec2())
	}
	}

	impl Default for Mat2 {
	#[inline]
	fn default() -> Self {
	Self::IDENTITY
	}
	}

	impl Add<Mat2> for Mat2 {
	type Output = Self;
	#[inline]
	fn add(self, rhs: Self) -> Self::Output {
	self.add_mat2(&rhs)
	}
	}

	impl AddAssign<Mat2> for Mat2 {
	#[inline]
	fn add_assign(&mut self, rhs: Self) {
	*self = self.add_mat2(&rhs);
	}
	}

	impl Sub<Mat2> for Mat2 {
	type Output = Self;
	#[inline]
	fn sub(self, rhs: Self) -> Self::Output {
	self.sub_mat2(&rhs)
	}
	}

	impl SubAssign<Mat2> for Mat2 {
	#[inline]
	fn sub_assign(&mut self, rhs: Self) {
	*self = self.sub_mat2(&rhs);
	}
	}

	impl Neg for Mat2 {
	type Output = Self;
	#[inline]
	fn neg(self) -> Self::Output {
	Self(unsafe { _mm_xor_ps(self.0, _mm_set1_ps(-0.0)) })
	}
	}

	impl Mul<Mat2> for Mat2 {
	type Output = Self;
	#[inline]
	fn mul(self, rhs: Self) -> Self::Output {
	self.mul_mat2(&rhs)
	}
	}

	impl MulAssign<Mat2> for Mat2 {
	#[inline]
	fn mul_assign(&mut self, rhs: Self) {
	*self = self.mul_mat2(&rhs);
	}
	}

	impl Mul<Vec2> for Mat2 {
	type Output = Vec2;
	#[inline]
	fn mul(self, rhs: Vec2) -> Self::Output {
	self.mul_vec2(rhs)
	}
	}

	impl Mul<Mat2> for f32 {
	type Output = Mat2;
	#[inline]
	fn mul(self, rhs: Mat2) -> Self::Output {
	rhs.mul_scalar(self)
	}
	}

	impl Mul<f32> for Mat2 {
	type Output = Self;
	#[inline]
	fn mul(self, rhs: f32) -> Self::Output {
	self.mul_scalar(rhs)
	}
	}

	impl MulAssign<f32> for Mat2 {
	#[inline]
	fn mul_assign(&mut self, rhs: f32) {
	*self = self.mul_scalar(rhs);
	}
	}

	impl Div<Mat2> for f32 {
	type Output = Mat2;
	#[inline]
	fn div(self, rhs: Mat2) -> Self::Output {
	rhs.div_scalar(self)
	}
	}

	impl Div<f32> for Mat2 {
	type Output = Self;
	#[inline]
	fn div(self, rhs: f32) -> Self::Output {
	self.div_scalar(rhs)
	}
	}

	impl DivAssign<f32> for Mat2 {
	#[inline]
	fn div_assign(&mut self, rhs: f32) {
	*self = self.div_scalar(rhs);
	}
	}

	impl Sum<Self> for Mat2 {
	fn sum<I>(iter: I) -> Self
	where
	I: Iterator<Item = Self>,
	{
	iter.fold(Self::ZERO, Self::add)
	}
	}

	impl<'a> Sum<&'a Self> for Mat2 {
	fn sum<I>(iter: I) -> Self
	where
	I: Iterator<Item = &'a Self>,
	{
	iter.fold(Self::ZERO, \|a, &b\| Self::add(a, b))
	}
	}

	impl Product for Mat2 {
	fn product<I>(iter: I) -> Self
	where
	I: Iterator<Item = Self>,
	{
	iter.fold(Self::IDENTITY, Self::mul)
	}
	}

	impl<'a> Product<&'a Self> for Mat2 {
	fn product<I>(iter: I) -> Self
	where
	I: Iterator<Item = &'a Self>,
	{
	iter.fold(Self::IDENTITY, \|a, &b\| Self::mul(a, b))
	}
	}

	impl PartialEq for Mat2 {
	#[inline]
	fn eq(&self, rhs: &Self) -> bool {
	self.x_axis.eq(&rhs.x_axis) && self.y_axis.eq(&rhs.y_axis)
	}
	}

	#[cfg(not(target_arch = "spirv"))]
	impl AsRef<[f32; 4]> for Mat2 {
	#[inline]
	fn as_ref(&self) -> &[f32; 4] {
	unsafe { &(self as const Self as *const [f32; 4]) }
	}
	}

	#[cfg(not(target_arch = "spirv"))]
	impl AsMut<[f32; 4]> for Mat2 {
	#[inline]
	fn as_mut(&mut self) -> &mut [f32; 4] {
	unsafe { &mut (self as mut Self as *mut [f32; 4]) }
	}
	}

	impl core::ops::Deref for Mat2 {
	type Target = crate::deref::Cols2<Vec2>;
	#[inline]
	fn deref(&self) -> &Self::Target {
	unsafe { &(self as const Self as *const Self::Target) }
	}
	}

	impl core::ops::DerefMut for Mat2 {
	#[inline]
	fn deref_mut(&mut self) -> &mut Self::Target {
	unsafe { &mut (self as mut Self as *mut Self::Target) }
	}
	}

	impl fmt::Debug for Mat2 {
	fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
	fmt.debug_struct(stringify!(Mat2))
	.field("x_axis", &self.x_axis)
	.field("y_axis", &self.y_axis)
	.finish()
	}
	}

	impl fmt::Display for Mat2 {
	fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
	if let Some(p) = f.precision() {
	write!(f, "[{:.}, {:.}]", p, self.x_axis, p, self.y_axis)
	} else {
	write!(f, "[{}, {}]", self.x_axis, self.y_axis)
	}
	}
	}