src/lib: add features for non-std support

The column may not be normalized if the `factor` is on a scale of 1e-40.
Possibly, f32 just runs out of precision.

There is likely a better solution to the problem.

Cargo.toml

@@ -1,15 +1,15 @@
 [package]
-name    = "nalgebra"
-version = "0.32.3"
-authors = [ "Sébastien Crozet <developer@crozet.re>" ]
+name = "nalgebra"
+version = "0.32.6"
+authors = ["Sébastien Crozet <developer@crozet.re>"]
 
 description = "General-purpose linear algebra library with transformations and statically-sized or dynamically-sized matrices."
 documentation = "https://www.nalgebra.org/docs"
 homepage = "https://nalgebra.org"
 repository = "https://github.com/dimforge/nalgebra"
 readme = "README.md"
-categories = [ "science", "mathematics", "wasm", "no-std" ]
-keywords = [ "linear", "algebra", "matrix", "vector", "math" ]
+categories = ["science", "mathematics", "wasm", "no-std"]
+keywords = ["linear", "algebra", "matrix", "vector", "math"]
 license = "BSD-3-Clause"
 edition = "2018"
 exclude = ["/ci/*", "/.travis.yml", "/Makefile"]
@@ -22,104 +22,108 @@ name = "nalgebra"
 path = "src/lib.rs"
 
 [features]
-default = [ "std", "macros" ]
-std     = [ "matrixmultiply", "simba/std" ]
-sparse  = [ ]
-debug   = [ "approx/num-complex", "rand" ]
-alloc   = [ ]
-io      = [ "pest", "pest_derive" ]
-compare = [ "matrixcompare-core" ]
-libm    = [ "simba/libm" ]
-libm-force = [ "simba/libm_force" ]
-macros = [ "nalgebra-macros" ]
-cuda   = [ "cust_core", "simba/cuda" ]
+default = ["std", "macros"]
+std = ["matrixmultiply", "simba/std"]
+sparse = []
+debug = ["approx/num-complex", "rand"]
+alloc = []
+io = ["pest", "pest_derive"]
+compare = ["matrixcompare-core"]
+libm = ["simba/libm"]
+libm-force = ["simba/libm_force"]
+macros = ["nalgebra-macros"]
+cuda = ["cust_core", "simba/cuda"]
 
 
 # Conversion
-convert-mint = [ "mint" ]
-convert-bytemuck = [ "bytemuck" ]
-convert-glam014 = [ "glam014" ]
-convert-glam015 = [ "glam015" ]
-convert-glam016 = [ "glam016" ]
-convert-glam017 = [ "glam017" ]
-convert-glam018 = [ "glam018" ]
-convert-glam019 = [ "glam019" ]
-convert-glam020 = [ "glam020" ]
-convert-glam021 = [ "glam021" ]
-convert-glam022 = [ "glam022" ]
-convert-glam023 = [ "glam023" ]
-convert-glam024 = [ "glam024" ]
+convert-mint = ["mint"]
+convert-bytemuck = ["bytemuck"]
+convert-glam014 = ["glam014"]
+convert-glam015 = ["glam015"]
+convert-glam016 = ["glam016"]
+convert-glam017 = ["glam017"]
+convert-glam018 = ["glam018"]
+convert-glam019 = ["glam019"]
+convert-glam020 = ["glam020"]
+convert-glam021 = ["glam021"]
+convert-glam022 = ["glam022"]
+convert-glam023 = ["glam023"]
+convert-glam024 = ["glam024"]
+convert-glam025 = ["glam025"]
+convert-glam027 = ["glam027"]
 
 # Serialization
 ## To use serde in a #[no-std] environment, enable the
 ## `serde-serialize-no-std` feature instead of `serde-serialize`.
 ## Serialization of dynamically-sized matrices/vectors require
 ## `serde-serialize`.
-serde-serialize-no-std = [ "serde", "num-complex/serde" ]
-serde-serialize        = [ "serde-serialize-no-std", "serde/std" ]
-rkyv-serialize-no-std  = [ "rkyv/size_32" ]
-rkyv-serialize         = [ "rkyv-serialize-no-std", "rkyv/std", "rkyv/validation" ]
+serde-serialize-no-std = ["serde", "num-complex/serde"]
+serde-serialize = ["serde-serialize-no-std", "serde/std"]
+rkyv-serialize-no-std = ["rkyv/size_32"]
+rkyv-serialize = ["rkyv-serialize-no-std", "rkyv/std", "rkyv/validation"]
 
 # Randomness
 ## To use rand in a #[no-std] environment, enable the
 ## `rand-no-std` feature instead of `rand`.
-rand-no-std = [ "rand-package" ]
-rand        = [ "rand-no-std", "rand-package/std", "rand-package/std_rng", "rand_distr" ]
+rand-no-std = ["rand-package"]
+rand = ["rand-no-std", "rand-package/std", "rand-package/std_rng", "rand_distr"]
 
 # Tests
-arbitrary        = [ "quickcheck" ]
-proptest-support = [ "proptest" ]
-slow-tests       = []
-rkyv-safe-deser  = [ "rkyv-serialize", "rkyv/validation" ]
+arbitrary = ["quickcheck"]
+proptest-support = ["proptest"]
+slow-tests = []
+rkyv-safe-deser = ["rkyv-serialize", "rkyv/validation"]
 
 [dependencies]
 nalgebra-macros = { version = "0.2.1", path = "nalgebra-macros", optional = true }
-typenum        = "1.12"
-rand-package   = { package = "rand", version = "0.8", optional = true, default-features = false }
-num-traits     = { version = "0.2", default-features = false }
-num-complex    = { version = "0.4", default-features = false }
-num-rational   = { version = "0.4", default-features = false }
-approx         = { version = "0.5", default-features = false }
-simba          = { version = "0.8", default-features = false }
-alga           = { version = "0.9", default-features = false, optional = true }
-rand_distr     = { version = "0.4", default-features = false, optional = true }
+typenum = "1.12"
+rand-package = { package = "rand", version = "0.8", optional = true, default-features = false }
+num-traits = { version = "0.2", default-features = false }
+num-complex = { version = "0.4", default-features = false }
+num-rational = { version = "0.4", default-features = false }
+approx = { version = "0.5", default-features = false }
+simba = { version = "0.8", default-features = false }
+alga = { version = "0.9", default-features = false, optional = true }
+rand_distr = { version = "0.4", default-features = false, optional = true }
 matrixmultiply = { version = "0.3", optional = true }
-serde          = { version = "1.0", default-features = false, features = [ "derive" ], optional = true }
-rkyv           = { version = "0.7.41", default-features = false, optional = true }
-mint           = { version = "0.5", optional = true }
-quickcheck     = { version = "1", optional = true }
-pest           = { version = "2", optional = true }
-pest_derive    = { version = "2", optional = true }
-bytemuck       = { version = "1.5", optional = true }
+serde = { version = "1.0", default-features = false, features = ["derive"], optional = true }
+rkyv = { version = "0.7.41", default-features = false, optional = true }
+mint = { version = "0.5", optional = true }
+quickcheck = { version = "1", optional = true }
+pest = { version = "2", optional = true }
+pest_derive = { version = "2", optional = true }
+bytemuck = { version = "1.5", optional = true }
 matrixcompare-core = { version = "0.1", optional = true }
-proptest       = { version = "1", optional = true, default-features = false, features = ["std"] }
-glam014        = { package = "glam", version = "0.14", optional = true }
-glam015        = { package = "glam", version = "0.15", optional = true }
-glam016        = { package = "glam", version = "0.16", optional = true }
-glam017        = { package = "glam", version = "0.17", optional = true }
-glam018        = { package = "glam", version = "0.18", optional = true }
-glam019        = { package = "glam", version = "0.19", optional = true }
-glam020        = { package = "glam", version = "0.20", optional = true }
-glam021        = { package = "glam", version = "0.21", optional = true }
-glam022        = { package = "glam", version = "0.22", optional = true }
-glam023        = { package = "glam", version = "0.23", optional = true }
-glam024        = { package = "glam", version = "0.24", optional = true }
-cust_core      = { version = "0.1", optional = true }
-rayon          = { version = "1.6", optional = true }
+proptest = { version = "1", optional = true, default-features = false, features = ["std"] }
+glam014 = { package = "glam", version = "0.14", optional = true }
+glam015 = { package = "glam", version = "0.15", optional = true }
+glam016 = { package = "glam", version = "0.16", optional = true }
+glam017 = { package = "glam", version = "0.17", optional = true }
+glam018 = { package = "glam", version = "0.18", optional = true }
+glam019 = { package = "glam", version = "0.19", optional = true }
+glam020 = { package = "glam", version = "0.20", optional = true }
+glam021 = { package = "glam", version = "0.21", optional = true }
+glam022 = { package = "glam", version = "0.22", optional = true }
+glam023 = { package = "glam", version = "0.23", optional = true }
+glam024 = { package = "glam", version = "0.24", optional = true }
+glam025 = { package = "glam", version = "0.25", optional = true }
+glam027 = { package = "glam", version = "0.27", optional = true }
+cust_core = { version = "0.1", optional = true }
+rayon = { version = "1.6", optional = true }
 
 [dev-dependencies]
 serde_json = "1.0"
 rand_xorshift = "0.3"
 rand_isaac = "0.3"
 criterion = { version = "0.4", features = ["html_reports"] }
-nalgebra = { path = ".", features = ["debug", "compare", "rand", "macros"]}
+nalgebra = { path = ".", features = ["debug", "compare", "rand", "macros"] }
 
 # For matrix comparison macro
 matrixcompare = "0.3.0"
 itertools = "0.10"
 
 [workspace]
-members = [ "nalgebra-lapack", "nalgebra-glm", "nalgebra-sparse", "nalgebra-macros" ]
+members = ["nalgebra-lapack", "nalgebra-glm", "nalgebra-sparse", "nalgebra-macros"]
 resolver = "2"
 
 [[example]]

src/lib.rs

@@ -94,6 +94,7 @@ an optimized set of tools for computer graphics and physics. Those features incl
     html_root_url = "https://docs.rs/nalgebra/0.25.0"
 )]
 #![cfg_attr(not(feature = "std"), no_std)]
+#![feature(const_fn, extended_key_value_attributes, array_methods)]
 
 /// Generates an appropriate deprecation note with a suggestion for replacement.
 ///

src/linalg/householder.rs

@@ -34,6 +34,17 @@ pub fn reflection_axis_mut<T: ComplexField, D: Dim, S: StorageMut<T, D>>(
 
     if !factor.is_zero() {
         column.unscale_mut(factor.sqrt());
+
+        // Normalize again, making sure the vector is unit-sized.
+        // If `factor` had a very small value, the first normalization
+        // (dividing by `factor.sqrt()`) might end up with a slightly
+        // non-unit vector (especially when using 32-bits float).
+        // Decompositions strongly rely on that unit-vector property,
+        // so we run a second normalization (that is much more numerically
+        // stable since the norm is close to 1) to ensure it has a unit
+        // size.
+        let _ = column.normalize_mut();
+
         (-signed_norm, true)
     } else {
         // TODO: not sure why we don't have a - sign here.

src/third_party/glam/mod.rs

@@ -20,3 +20,7 @@ mod v022;
 mod v023;
 #[cfg(feature = "glam024")]
 mod v024;
+#[cfg(feature = "glam025")]
+mod v025;
+#[cfg(feature = "glam027")]
+mod v027;

src/third_party/glam/v025/mod.rs

@@ -0,0 +1,18 @@
+#[path = "../common/glam_isometry.rs"]
+mod glam_isometry;
+#[path = "../common/glam_matrix.rs"]
+mod glam_matrix;
+#[path = "../common/glam_point.rs"]
+mod glam_point;
+#[path = "../common/glam_quaternion.rs"]
+mod glam_quaternion;
+#[path = "../common/glam_rotation.rs"]
+mod glam_rotation;
+#[path = "../common/glam_similarity.rs"]
+mod glam_similarity;
+#[path = "../common/glam_translation.rs"]
+mod glam_translation;
+#[path = "../common/glam_unit_complex.rs"]
+mod glam_unit_complex;
+
+pub(self) use glam025 as glam;

src/third_party/glam/v027/mod.rs

@@ -0,0 +1,18 @@
+#[path = "../common/glam_isometry.rs"]
+mod glam_isometry;
+#[path = "../common/glam_matrix.rs"]
+mod glam_matrix;
+#[path = "../common/glam_point.rs"]
+mod glam_point;
+#[path = "../common/glam_quaternion.rs"]
+mod glam_quaternion;
+#[path = "../common/glam_rotation.rs"]
+mod glam_rotation;
+#[path = "../common/glam_similarity.rs"]
+mod glam_similarity;
+#[path = "../common/glam_translation.rs"]
+mod glam_translation;
+#[path = "../common/glam_unit_complex.rs"]
+mod glam_unit_complex;
+
+pub(self) use glam027 as glam;

tests/linalg/eigen.rs

@@ -1,4 +1,4 @@
-use na::DMatrix;
+use na::{DMatrix, Matrix3};
 
 #[cfg(feature = "proptest-support")]
 mod proptest_tests {
@@ -116,6 +116,31 @@ fn symmetric_eigen_singular_24x24() {
     );
 }
 
+// Test for #1368
+#[test]
+fn very_small_deviation_from_identity() {
+    let m = Matrix3::<f32>::new(
+        1.0,
+        3.1575704e-23,
+        8.1146196e-23,
+        3.1575704e-23,
+        1.0,
+        1.7471054e-22,
+        8.1146196e-23,
+        1.7471054e-22,
+        1.0,
+    );
+
+    for v in m
+        .try_symmetric_eigen(f32::EPSILON, 0)
+        .unwrap()
+        .eigenvalues
+        .into_iter()
+    {
+        assert_relative_eq!(*v, 1.);
+    }
+}
+
 //  #[cfg(feature = "arbitrary")]
 //  quickcheck! {
 // TODO: full eigendecomposition is not implemented yet because of its complexity when some