diff --git a/CHANGELOG.md b/CHANGELOG.md
index b38659c..16bee14 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,9 @@
+# Unreleased
+
+- Add `padding` field to `Pose3` for better compatibility with `bytemuck` and `spirv`.
+- Fix various internal implementation details that are incompatible with `spirv`/`naga`.
+- Update to `glam 0.32`.
+
 # v0.1.3
 
 - Add `From`/`Into` conversions between f32 and f64 type variants.
diff --git a/Cargo.toml b/Cargo.toml
index 2eedb52..0205b14 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -6,7 +6,7 @@ authors = ["Sébastien Crozet <developer@crozet.re>"]
 description = "Extensions for glam: Pose2, Pose3, Rot2, and matrix utilities."
 documentation = "https://docs.rs/glamx"
 homepage = "https://dimforge.com"
-repository = "https://github.com/dimforge/parry"
+repository = "https://github.com/dimforge/glamx"
 readme = "README.md"
 keywords = ["math", "geometry", "rotation", "pose", "glam"]
 categories = ["mathematics", "game-development", "no-std"]
@@ -61,15 +61,15 @@ rand = ["glam/rand"]
 encase = ["glam/encase"]
 
 [dependencies]
-glam = { version = "0.30", default-features = false }
+glam = { version = "0.32", default-features = false }
 simba = { version = "0.9", default-features = false }
 num-traits = { version = "0.2", default-features = false, features = ["libm"] }
 approx = { version = "0.5", default-features = false, optional = true }
 serde = { version = "1.0", optional = true, features = ["derive"] }
 bytemuck = { version = "1", features = ["derive"], optional = true }
-nalgebra = { version = "0.34", default-features = false, features = ["convert-glam030"], optional = true }
+nalgebra = { version = "0.34", default-features = false, features = ["convert-glam032"], optional = true }
 rkyv = { version = "0.8", optional = true, default-features = false }
 
 [dev-dependencies]
 approx = "0.5"
-glam = { version = "0.30", features = ["approx"] }
+glam = { version = "0.32", features = ["approx"] }
diff --git a/src/eigen3.rs b/src/eigen3.rs
index 8dfb535..0467ed0 100644
--- a/src/eigen3.rs
+++ b/src/eigen3.rs
@@ -6,6 +6,8 @@
 //!
 //! Adapted from <https://github.com/Jondolf/barry/tree/main/src/math/eigen>
 
+#![allow(clippy::manual_swap)] // Needed for spirv compatibility.
+
 use glam::Vec3Swizzles;
 use num_traits::float::FloatConst;
 
@@ -63,7 +65,12 @@ macro_rules! impl_symmetric_eigen3 {
                 if p1 == 0.0 {
                     // The matrix is diagonal.
                     let mut eigenvalues = [mat.x_axis.x, mat.y_axis.y, mat.z_axis.z];
-                    eigenvalues.sort_by(|a, b| a.partial_cmp(b).unwrap_or(core::cmp::Ordering::Equal));
+                    // Simple 3-element sorting network (no alloc needed).
+                    // NOTE: manual swaps instead of .swap() to avoid ptr::swap which
+                    // generates memcpy unsupported in SPIR-V.
+                    if eigenvalues[0] > eigenvalues[1] { let t = eigenvalues[0]; eigenvalues[0] = eigenvalues[1]; eigenvalues[1] = t; }
+                    if eigenvalues[1] > eigenvalues[2] { let t = eigenvalues[1]; eigenvalues[1] = eigenvalues[2]; eigenvalues[2] = t; }
+                    if eigenvalues[0] > eigenvalues[1] { let t = eigenvalues[0]; eigenvalues[0] = eigenvalues[1]; eigenvalues[1] = t; }
                     <$Vec3>::from_array(eigenvalues)
                 } else {
                     let q = (mat.x_axis.x + mat.y_axis.y + mat.z_axis.z) / 3.0;
@@ -71,9 +78,17 @@ macro_rules! impl_symmetric_eigen3 {
                         + (mat.y_axis.y - q).powi(2)
                         + (mat.z_axis.z - q).powi(2)
                         + 2.0 * p1;
+
                     let p = (p2 / 6.0).sqrt();
-                    let mat_b = 1.0 / p * (mat - q * <$Mat3>::IDENTITY);
-                    let r = mat_b.determinant() / 2.0;
+
+                    // NOTE: `p` shouldn’t be zero, but in some platforms (nvidia gpus apparently),
+                    //       denormals can be flushed resulting in a zero.
+                    let r = if p != 0.0 {
+                        let mat_b = 1.0 / p * (mat - q * <$Mat3>::IDENTITY);
+                        mat_b.determinant() / 2.0
+                    } else {
+                        1.0 // Will result in phy == 0.0
+                    };
 
                     // r should be in the [-1, 1] range for a symmetric matrix,
                     // but computation error can leave it slightly outside this range.
diff --git a/src/lib.rs b/src/lib.rs
index c2813c3..63090b7 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -36,8 +36,6 @@
 #[cfg(feature = "std")]
 extern crate std;
 
-extern crate alloc;
-
 // Re-export approx for convenience
 #[cfg(feature = "approx")]
 pub use approx;
diff --git a/src/pose2.rs b/src/pose2.rs
index 4f3d131..7fa86fa 100644
--- a/src/pose2.rs
+++ b/src/pose2.rs
@@ -10,6 +10,7 @@ macro_rules! impl_pose2 {
         #[derive(Copy, Clone, Debug, PartialEq)]
         #[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
         #[cfg_attr(feature = "rkyv", derive(rkyv::Archive, rkyv::Serialize, rkyv::Deserialize))]
+        #[repr(C)]
         $(#[$attr])*
         pub struct $Pose2 {
             /// The rotational part of the pose.
@@ -352,7 +353,8 @@ impl_pose2!(
     glam::Vec2,
     glam::Vec3,
     glam::Mat2,
-    glam::Mat3
+    glam::Mat3,
+    #[cfg_attr(feature = "bytemuck", derive(bytemuck::Pod, bytemuck::Zeroable))]
 );
 impl_pose2!(
     DPose2,
diff --git a/src/pose3.rs b/src/pose3.rs
index 49cb222..89ba212 100644
--- a/src/pose3.rs
+++ b/src/pose3.rs
@@ -5,17 +5,24 @@ use core::ops::{Mul, MulAssign};
 
 /// Macro to generate a 3D pose type for a specific scalar type.
 macro_rules! impl_pose3 {
-    ($Pose3:ident, $Rot3:ident, $Real:ty, $Vec3:ty, $Mat4: ty $(, #[$attr:meta])*) => {
+    ($Pose3:ident, $Rot3:ident, $Real:ty, $Vec3:ty, $Mat4: ty $(, $Padding: ty, $bytemuck: ident)?) => {
         #[doc = concat!("A 3D pose (rotation + translation), representing a rigid body transformation (", stringify!($Real), " precision).")]
         #[derive(Copy, Clone, Debug, PartialEq)]
         #[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
         #[cfg_attr(feature = "rkyv", derive(rkyv::Archive, rkyv::Serialize, rkyv::Deserialize))]
-        $(#[$attr])*
+        $(#[cfg_attr(feature = "bytemuck", derive($bytemuck::Pod, $bytemuck::Zeroable))])*
+        #[repr(C)]
         pub struct $Pose3 {
             /// The rotational part of the pose.
             pub rotation: $Rot3,
             /// The translational part of the pose.
             pub translation: $Vec3,
+            $(
+            /// Explicit padding for compatibility with bytemuck and targets like spirv.
+            ///
+            /// Can have any value as it is never read from or written to.
+            pub padding: $Padding,
+            )*
         }
 
         impl $Pose3 {
@@ -23,6 +30,7 @@ macro_rules! impl_pose3 {
             pub const IDENTITY: Self = Self {
                 rotation: $Rot3::IDENTITY,
                 translation: <$Vec3>::ZERO,
+                $(padding: 0 as $Padding,)*
             };
 
             /// Creates the identity pose.
@@ -37,6 +45,7 @@ macro_rules! impl_pose3 {
                 Self {
                     rotation: $Rot3::IDENTITY,
                     translation,
+                    $(padding: 0 as $Padding,)*
                 }
             }
 
@@ -52,6 +61,7 @@ macro_rules! impl_pose3 {
                 Self {
                     rotation,
                     translation: <$Vec3>::ZERO,
+                    $(padding: 0 as $Padding,)*
                 }
             }
 
@@ -61,6 +71,7 @@ macro_rules! impl_pose3 {
                 Self {
                     rotation,
                     translation,
+                    $(padding: 0 as $Padding,)*
                 }
             }
 
@@ -71,6 +82,7 @@ macro_rules! impl_pose3 {
                 Self {
                     rotation,
                     translation,
+                    $(padding: 0 as $Padding,)*
                 }
             }
 
@@ -80,6 +92,7 @@ macro_rules! impl_pose3 {
                 Self {
                     rotation: $Rot3::from_scaled_axis(axisangle.into()),
                     translation: <$Vec3>::ZERO,
+                    $(padding: 0 as $Padding,)*
                 }
             }
 
@@ -89,6 +102,7 @@ macro_rules! impl_pose3 {
                 Self {
                     rotation: self.rotation,
                     translation: self.translation + self.rotation * translation,
+                    $(padding: 0 as $Padding,)*
                 }
             }
 
@@ -98,6 +112,7 @@ macro_rules! impl_pose3 {
                 Self {
                     rotation: self.rotation,
                     translation: self.translation + translation,
+                    $(padding: 0 as $Padding,)*
                 }
             }
 
@@ -108,6 +123,7 @@ macro_rules! impl_pose3 {
                 Self {
                     rotation: inv_rot,
                     translation: inv_rot * (-self.translation),
+                    $(padding: 0 as $Padding,)*
                 }
             }
 
@@ -119,6 +135,7 @@ macro_rules! impl_pose3 {
                 $Pose3 {
                     translation: inv_rot1 * tr_12,
                     rotation: inv_rot1 * rhs.rotation,
+                    $(padding: 0 as $Padding,)*
                 }
             }
 
@@ -158,6 +175,7 @@ macro_rules! impl_pose3 {
                 Self {
                     rotation: self.rotation.slerp(other.rotation, t),
                     translation: self.translation.lerp(other.translation, t),
+                    $(padding: 0 as $Padding,)*
                 }
             }
 
@@ -189,6 +207,7 @@ macro_rules! impl_pose3 {
                 Self {
                     rotation,
                     translation: translation.into(),
+                    $(padding: 0 as $Padding,)*
                 }
             }
 
@@ -210,6 +229,7 @@ macro_rules! impl_pose3 {
                 $Pose3 {
                     rotation,
                     translation,
+                    $(padding: 0 as $Padding,)*
                 }
             }
 
@@ -228,6 +248,7 @@ macro_rules! impl_pose3 {
                 $Pose3 {
                     rotation: <$Rot3>::look_at_lh(eye.into(), target.into(), up.into()).inverse(),
                     translation: eye,
+                    $(padding: 0 as $Padding,)*
                 }
             }
         }
@@ -241,6 +262,7 @@ macro_rules! impl_pose3 {
                 Self {
                     rotation: self.rotation * rhs.rotation,
                     translation: self.translation + self.rotation * rhs.translation,
+                    $(padding: 0 as $Padding,)*
                 }
             }
         }
@@ -324,6 +346,7 @@ macro_rules! impl_pose3 {
                 $Pose3 {
                     translation: self * rhs.translation,
                     rotation: self * rhs.rotation,
+                    $(padding: 0 as $Padding,)*
                 }
             }
         }
@@ -336,6 +359,7 @@ macro_rules! impl_pose3 {
                 $Pose3 {
                     translation: self.translation,
                     rotation: self.rotation * rhs,
+                    $(padding: 0 as $Padding,)*
                 }
             }
         }
@@ -387,7 +411,7 @@ macro_rules! impl_pose3 {
     };
 }
 
-impl_pose3!(Pose3, Rot3, f32, glam::Vec3, glam::Mat4);
+impl_pose3!(Pose3, Rot3, f32, glam::Vec3, glam::Mat4, u32, bytemuck);
 impl_pose3!(Pose3A, Rot3, f32, glam::Vec3A, glam::Mat4);
 impl_pose3!(DPose3, DRot3, f64, glam::DVec3, glam::DMat4);
 
@@ -408,6 +432,7 @@ impl From<DPose3> for Pose3 {
         Self {
             rotation: p.rotation.as_quat(),
             translation: p.translation.as_vec3(),
+            padding: 0,
         }
     }
 }
@@ -449,6 +474,7 @@ impl From<Pose3A> for Pose3 {
         Self {
             rotation: p.rotation,
             translation: p.translation.into(),
+            padding: 0,
         }
     }
 }
@@ -481,6 +507,7 @@ mod nalgebra_conv {
                     iso.translation.y,
                     iso.translation.z,
                 ),
+                padding: 0,
             }
         }
     }