Replace alga by simba.

Cargo.toml

@@ -21,7 +21,7 @@ path = "src/lib.rs"
 
 [features]
 default         = [ "std" ]
-std             = [ "matrixmultiply", "rand/std", "rand_distr", "alga/std" ]
+std             = [ "matrixmultiply", "rand/std", "rand_distr", "simba/std" ]
 stdweb          = [ "rand/stdweb" ]
 arbitrary       = [ "quickcheck" ]
 serde-serialize = [ "serde", "serde_derive", "num-complex/serde" ]
@@ -39,7 +39,8 @@ num-traits     = { version = "0.2", default-features = false }
 num-complex    = { version = "0.2", default-features = false }
 num-rational   = { version = "0.2", default-features = false }
 approx         = { version = "0.3", default-features = false }
-alga           = { version = "0.9", default-features = false }
+simba          = { path = "../simba" }
+#alga           = { version = "0.9", default-features = false }
 rand_distr     = { version = "0.2", optional = true }
 matrixmultiply = { version = "0.2", optional = true }
 serde          = { version = "1.0", optional = true }
@@ -50,9 +51,6 @@ quickcheck     = { version = "0.9", optional = true }
 pest           = { version = "2.0", optional = true }
 pest_derive    = { version = "2.0", optional = true }
 
-#[patch.crates-io]
-#alga = { git = "https://github.com/rustsim/alga", branch = "dev" }
-
 [dev-dependencies]
 serde_json = "1.0"
 rand_xorshift = "0.2"
@@ -61,7 +59,7 @@ rand_isaac = "0.2"
 ### We can't just let this uncommented because that would break
 ### compilation for #[no-std] because of the terrible Cargo bug
 ### https://github.com/rust-lang/cargo/issues/4866
-#criterion = "0.2.10"
+criterion = "0.2.10"
 
 [workspace]
 members = [ "nalgebra-lapack", "nalgebra-glm" ]
@@ -73,3 +71,6 @@ path = "benches/lib.rs"
 
 [profile.bench]
 lto = true
+
+#[patch.crates-io]
+#alga = { path = "../alga/alga" }

examples/scalar_genericity.rs

@@ -1,8 +1,8 @@
 extern crate alga;
 extern crate nalgebra as na;
 
-use alga::general::{RealField, RingCommutative};
 use na::{Scalar, Vector3};
+use simba::scalar::{RealField, RingCommutative};
 
 fn print_vector<N: Scalar>(m: &Vector3<N>) {
     println!("{:?}", m)

nalgebra-glm/src/traits.rs

@@ -1,9 +1,9 @@
 use approx::AbsDiffEq;
 use num::{Bounded, FromPrimitive, Signed};
 
-use alga::general::{Lattice, Ring};
 use na::allocator::Allocator;
 use na::{DimMin, DimName, Scalar, U1};
+use simba::scalar::{Lattice, Ring};
 
 /// A type-level number representing a vector, matrix row, or matrix column, dimension.
 pub trait Dimension: DimName + DimMin<Self, Output = Self> {}
@@ -15,9 +15,18 @@ pub trait Number:
 {
 }
 
-impl<T: Scalar + Copy + Ring + Lattice + AbsDiffEq<Epsilon = Self> + Signed + FromPrimitive + Bounded>
+impl<
-    Number for T
+        T: Scalar
-{}
+            + Copy
+            + Ring
+            + Lattice
+            + AbsDiffEq<Epsilon = Self>
+            + Signed
+            + FromPrimitive
+            + Bounded,
+    > Number for T
+{
+}
 
 #[doc(hidden)]
 pub trait Alloc<N: Scalar, R: Dimension, C: Dimension = U1>:
@@ -76,4 +85,5 @@ impl<N: Scalar, R: Dimension, C: Dimension, T> Alloc<N, R, C> for T where T: All
         + Allocator<i16, C>
         + Allocator<(usize, usize), R>
         + Allocator<(usize, usize), C>
-{}
+{
+}

nalgebra-lapack/src/eigen.rs

@@ -4,13 +4,13 @@ use serde::{Deserialize, Serialize};
 use num::Zero;
 use num_complex::Complex;
 
-use alga::general::RealField;
+use simba::scalar::RealField;
 
+use crate::ComplexHelper;
 use na::allocator::Allocator;
 use na::dimension::{Dim, U1};
 use na::storage::Storage;
 use na::{DefaultAllocator, Matrix, MatrixN, Scalar, VectorN};
-use crate::ComplexHelper;
 
 use lapack;
 
@@ -18,19 +18,19 @@ use lapack;
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(
-        serialize = "DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
+        bound(serialize = "DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
          VectorN<N, D>: Serialize,
-         MatrixN<N, D>: Serialize"
+         MatrixN<N, D>: Serialize")
-    ))
+    )
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(
-        deserialize = "DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
+        bound(deserialize = "DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
          VectorN<N, D>: Serialize,
-         MatrixN<N, D>: Deserialize<'de>"
+         MatrixN<N, D>: Deserialize<'de>")
-    ))
+    )
 )]
 #[derive(Clone, Debug)]
 pub struct Eigen<N: Scalar, D: Dim>
@@ -49,7 +49,8 @@ where
     DefaultAllocator: Allocator<N, D> + Allocator<N, D, D>,
     VectorN<N, D>: Copy,
     MatrixN<N, D>: Copy,
-{}
+{
+}
 
 impl<N: EigenScalar + RealField, D: Dim> Eigen<N, D>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>

nalgebra-lapack/src/schur.rs

@@ -4,13 +4,13 @@ use serde::{Deserialize, Serialize};
 use num::Zero;
 use num_complex::Complex;
 
-use alga::general::RealField;
+use simba::scalar::RealField;
 
+use crate::ComplexHelper;
 use na::allocator::Allocator;
 use na::dimension::{Dim, U1};
 use na::storage::Storage;
 use na::{DefaultAllocator, Matrix, MatrixN, Scalar, VectorN};
-use crate::ComplexHelper;
 
 use lapack;
 
@@ -18,19 +18,19 @@ use lapack;
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(
-        serialize = "DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
+        bound(serialize = "DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
          VectorN<N, D>: Serialize,
-         MatrixN<N, D>: Serialize"
+         MatrixN<N, D>: Serialize")
-    ))
+    )
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(
-        deserialize = "DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
+        bound(deserialize = "DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
          VectorN<N, D>: Serialize,
-         MatrixN<N, D>: Deserialize<'de>"
+         MatrixN<N, D>: Deserialize<'de>")
-    ))
+    )
 )]
 #[derive(Clone, Debug)]
 pub struct Schur<N: Scalar, D: Dim>
@@ -47,7 +47,8 @@ where
     DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
     MatrixN<N, D>: Copy,
     VectorN<N, D>: Copy,
-{}
+{
+}
 
 impl<N: SchurScalar + RealField, D: Dim> Schur<N, D>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>

nalgebra-lapack/src/symmetric_eigen.rs

@@ -4,13 +4,13 @@ use serde::{Deserialize, Serialize};
 use num::Zero;
 use std::ops::MulAssign;
 
-use alga::general::RealField;
+use simba::scalar::RealField;
 
+use crate::ComplexHelper;
 use na::allocator::Allocator;
 use na::dimension::{Dim, U1};
 use na::storage::Storage;
 use na::{DefaultAllocator, Matrix, MatrixN, Scalar, VectorN};
-use crate::ComplexHelper;
 
 use lapack;
 
@@ -18,21 +18,17 @@ use lapack;
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(serialize = "DefaultAllocator: Allocator<N, D, D> +
-        serialize = "DefaultAllocator: Allocator<N, D, D> +
                            Allocator<N, D>,
          VectorN<N, D>: Serialize,
-         MatrixN<N, D>: Serialize"
+         MatrixN<N, D>: Serialize"))
-    ))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(deserialize = "DefaultAllocator: Allocator<N, D, D> +
-        deserialize = "DefaultAllocator: Allocator<N, D, D> +
                            Allocator<N, D>,
          VectorN<N, D>: Deserialize<'de>,
-         MatrixN<N, D>: Deserialize<'de>"
+         MatrixN<N, D>: Deserialize<'de>"))
-    ))
 )]
 #[derive(Clone, Debug)]
 pub struct SymmetricEigen<N: Scalar, D: Dim>
@@ -50,7 +46,8 @@ where
     DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
     MatrixN<N, D>: Copy,
     VectorN<N, D>: Copy,
-{}
+{
+}
 
 impl<N: SymmetricEigenScalar + RealField, D: Dim> SymmetricEigen<N, D>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>

src/base/blas.rs

@@ -1,8 +1,8 @@
 use crate::SimdComplexField;
-use alga::general::{ClosedAdd, ClosedMul, ComplexField};
 #[cfg(feature = "std")]
 use matrixmultiply;
 use num::{One, Signed, Zero};
+use simba::scalar::{ClosedAdd, ClosedMul, ComplexField};
 #[cfg(feature = "std")]
 use std::mem;
 

src/base/cg.rs

@@ -5,7 +5,7 @@
  *
  */
 
-use num::One;
+use num::{One, Zero};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameDiff, DimNameSub, U1};
@@ -18,12 +18,11 @@ use crate::geometry::{
     Isometry, IsometryMatrix3, Orthographic3, Perspective3, Point, Point3, Rotation2, Rotation3,
 };
 
-use alga::general::{RealField, Ring};
+use simba::scalar::{ClosedAdd, ClosedMul, RealField};
-use alga::linear::Transformation;
 
 impl<N, D: DimName> MatrixN<N, D>
 where
-    N: Scalar + Ring,
+    N: Scalar + Zero + One,
     DefaultAllocator: Allocator<N, D, D>,
 {
     /// Creates a new homogeneous matrix that applies the same scaling factor on each dimension.
@@ -42,7 +41,7 @@ where
         D: DimNameSub<U1>,
         SB: Storage<N, DimNameDiff<D, U1>>,
     {
-        let mut res = Self::one();
+        let mut res = Self::identity();
         for i in 0..scaling.len() {
             res[(i, i)] = scaling[i].inlined_clone();
         }
@@ -57,7 +56,7 @@ where
         D: DimNameSub<U1>,
         SB: Storage<N, DimNameDiff<D, U1>>,
     {
-        let mut res = Self::one();
+        let mut res = Self::identity();
         res.fixed_slice_mut::<DimNameDiff<D, U1>, U1>(0, D::dim() - 1)
             .copy_from(translation);
 
@@ -153,7 +152,9 @@ impl<N: RealField> Matrix4<N> {
     }
 }
 
-impl<N: Scalar + Ring, D: DimName, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
+impl<N: Scalar + Zero + One + ClosedMul + ClosedAdd, D: DimName, S: Storage<N, D, D>>
+    SquareMatrix<N, D, S>
+{
     /// Computes the transformation equal to `self` followed by an uniform scaling factor.
     #[inline]
     #[must_use = "Did you mean to use append_scaling_mut()?"]
@@ -246,7 +247,9 @@ impl<N: Scalar + Ring, D: DimName, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
     }
 }
 
-impl<N: Scalar + Ring, D: DimName, S: StorageMut<N, D, D>> SquareMatrix<N, D, S> {
+impl<N: Scalar + Zero + One + ClosedMul + ClosedAdd, D: DimName, S: StorageMut<N, D, D>>
+    SquareMatrix<N, D, S>
+{
     /// Computes in-place the transformation equal to `self` followed by an uniform scaling factor.
     #[inline]
     pub fn append_scaling_mut(&mut self, scaling: N)
@@ -370,23 +373,3 @@ where DefaultAllocator: Allocator<N, D, D>
         }
     }
 }
-
-impl<N: RealField, D: DimNameSub<U1>> Transformation<Point<N, DimNameDiff<D, U1>>> for MatrixN<N, D>
-where DefaultAllocator: Allocator<N, D, D>
-        + Allocator<N, DimNameDiff<D, U1>>
-        + Allocator<N, DimNameDiff<D, U1>, DimNameDiff<D, U1>>
-{
-    #[inline]
-    fn transform_vector(
-        &self,
-        v: &VectorN<N, DimNameDiff<D, U1>>,
-    ) -> VectorN<N, DimNameDiff<D, U1>>
-    {
-        self.transform_vector(v)
-    }
-
-    #[inline]
-    fn transform_point(&self, pt: &Point<N, DimNameDiff<D, U1>>) -> Point<N, DimNameDiff<D, U1>> {
-        self.transform_point(pt)
-    }
-}

src/base/componentwise.rs

@@ -3,7 +3,7 @@
 use num::{Signed, Zero};
 use std::ops::{Add, Mul};
 
-use alga::general::{ClosedDiv, ClosedMul};
+use simba::scalar::{ClosedDiv, ClosedMul};
 
 use crate::base::allocator::{Allocator, SameShapeAllocator};
 use crate::base::constraint::{SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};

src/base/construction.rs

@@ -4,18 +4,18 @@ use crate::base::storage::Owned;
 use quickcheck::{Arbitrary, Gen};
 
 use num::{Bounded, One, Zero};
-use rand::distributions::{Distribution, Standard};
-use rand::Rng;
 #[cfg(feature = "std")]
 use rand;
+use rand::distributions::{Distribution, Standard};
+use rand::Rng;
 #[cfg(feature = "std")]
 use rand_distr::StandardNormal;
 use std::iter;
 use typenum::{self, Cmp, Greater};
 
 #[cfg(feature = "std")]
-use alga::general::RealField;
+use simba::scalar::RealField;
-use alga::general::{ClosedAdd, ClosedMul};
+use simba::scalar::{ClosedAdd, ClosedMul};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{Dim, DimName, Dynamic, U1, U2, U3, U4, U5, U6};
@@ -712,8 +712,6 @@ impl_constructors_from_data!(data; Dynamic, Dynamic;
                             Dynamic::new(nrows), Dynamic::new(ncols);
                             nrows, ncols);
 
-
-
 /*
  *
  * Zero, One, Rand traits.

src/base/conversion.rs

@@ -1,6 +1,6 @@
-use alga::general::{SubsetOf, SupersetOf};
 #[cfg(feature = "mint")]
 use mint;
+use simba::scalar::{SubsetOf, SupersetOf};
 use std::convert::{AsMut, AsRef, From, Into};
 use std::mem;
 use std::ptr;
@@ -11,17 +11,20 @@ use typenum::Prod;
 
 use crate::base::allocator::{Allocator, SameShapeAllocator};
 use crate::base::constraint::{SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
+#[cfg(any(feature = "std", feature = "alloc"))]
+use crate::base::dimension::Dynamic;
 use crate::base::dimension::{
     Dim, DimName, U1, U10, U11, U12, U13, U14, U15, U16, U2, U3, U4, U5, U6, U7, U8, U9,
 };
-#[cfg(any(feature = "std", feature = "alloc"))]
-use crate::base::dimension::Dynamic;
 use crate::base::iter::{MatrixIter, MatrixIterMut};
 use crate::base::storage::{ContiguousStorage, ContiguousStorageMut, Storage, StorageMut};
 #[cfg(any(feature = "std", feature = "alloc"))]
 use crate::base::VecStorage;
+use crate::base::{
+    ArrayStorage, DVectorSlice, DVectorSliceMut, DefaultAllocator, Matrix, MatrixMN, MatrixSlice,
+    MatrixSliceMut, Scalar,
+};
 use crate::base::{SliceStorage, SliceStorageMut};
-use crate::base::{DefaultAllocator, Matrix, ArrayStorage, MatrixMN, MatrixSlice, MatrixSliceMut, Scalar, DVectorSlice, DVectorSliceMut};
 use crate::constraint::DimEq;
 
 // FIXME: too bad this won't work allo slice conversions.
@@ -46,7 +49,9 @@ where
         let mut res = unsafe { MatrixMN::<N2, R2, C2>::new_uninitialized_generic(nrows2, ncols2) };
         for i in 0..nrows {
             for j in 0..ncols {
-                unsafe { *res.get_unchecked_mut((i, j)) = N2::from_subset(self.get_unchecked((i, j))) }
+                unsafe {
+                    *res.get_unchecked_mut((i, j)) = N2::from_subset(self.get_unchecked((i, j)))
+                }
             }
         }
 
@@ -59,17 +64,19 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &MatrixMN<N2, R2, C2>) -> Self {
+    fn from_superset_unchecked(m: &MatrixMN<N2, R2, C2>) -> Self {
         let (nrows2, ncols2) = m.shape();
         let nrows = R1::from_usize(nrows2);
         let ncols = C1::from_usize(ncols2);
 
-        let mut res = Self::new_uninitialized_generic(nrows, ncols);
+        let mut res = unsafe { Self::new_uninitialized_generic(nrows, ncols) };
         for i in 0..nrows2 {
             for j in 0..ncols2 {
+                unsafe {
                     *res.get_unchecked_mut((i, j)) = m.get_unchecked((i, j)).to_subset_unchecked()
                 }
             }
+        }
 
         res
     }
@@ -438,8 +445,10 @@ for MatrixSlice<'a, N, RSlice, CSlice, RStride, CStride>
     RStride: Dim,
     CStride: Dim,
     S: Storage<N, R, C>,
-        ShapeConstraint: DimEq<R, RSlice> + DimEq<C, CSlice>
+    ShapeConstraint: DimEq<R, RSlice>
-            + DimEq<RStride, S::RStride> + DimEq<CStride, S::CStride>
+        + DimEq<C, CSlice>
+        + DimEq<RStride, S::RStride>
+        + DimEq<CStride, S::CStride>,
 {
     fn from(m: &'a Matrix<N, R, C, S>) -> Self {
         let (row, col) = m.data.shape();
@@ -452,9 +461,11 @@ for MatrixSlice<'a, N, RSlice, CSlice, RStride, CStride>
         let cstride_slice = CStride::from_usize(cstride);
 
         unsafe {
-            let data = SliceStorage::from_raw_parts(m.data.ptr(),
+            let data = SliceStorage::from_raw_parts(
+                m.data.ptr(),
                 (row_slice, col_slice),
-                                                    (rstride_slice, cstride_slice));
+                (rstride_slice, cstride_slice),
+            );
             Matrix::from_data_statically_unchecked(data)
         }
     }
@@ -471,8 +482,10 @@ for MatrixSlice<'a, N, RSlice, CSlice, RStride, CStride>
     RStride: Dim,
     CStride: Dim,
     S: Storage<N, R, C>,
-        ShapeConstraint: DimEq<R, RSlice> + DimEq<C, CSlice>
+    ShapeConstraint: DimEq<R, RSlice>
-            + DimEq<RStride, S::RStride> + DimEq<CStride, S::CStride>
+        + DimEq<C, CSlice>
+        + DimEq<RStride, S::RStride>
+        + DimEq<CStride, S::CStride>,
 {
     fn from(m: &'a mut Matrix<N, R, C, S>) -> Self {
         let (row, col) = m.data.shape();
@@ -485,9 +498,11 @@ for MatrixSlice<'a, N, RSlice, CSlice, RStride, CStride>
         let cstride_slice = CStride::from_usize(cstride);
 
         unsafe {
-            let data = SliceStorage::from_raw_parts(m.data.ptr(),
+            let data = SliceStorage::from_raw_parts(
+                m.data.ptr(),
                 (row_slice, col_slice),
-                                                    (rstride_slice, cstride_slice));
+                (rstride_slice, cstride_slice),
+            );
             Matrix::from_data_statically_unchecked(data)
         }
     }
@@ -504,8 +519,10 @@ for MatrixSliceMut<'a, N, RSlice, CSlice, RStride, CStride>
     RStride: Dim,
     CStride: Dim,
     S: StorageMut<N, R, C>,
-        ShapeConstraint: DimEq<R, RSlice> + DimEq<C, CSlice>
+    ShapeConstraint: DimEq<R, RSlice>
-            + DimEq<RStride, S::RStride> + DimEq<CStride, S::CStride>
+        + DimEq<C, CSlice>
+        + DimEq<RStride, S::RStride>
+        + DimEq<CStride, S::CStride>,
 {
     fn from(m: &'a mut Matrix<N, R, C, S>) -> Self {
         let (row, col) = m.data.shape();
@@ -518,29 +535,34 @@ for MatrixSliceMut<'a, N, RSlice, CSlice, RStride, CStride>
         let cstride_slice = CStride::from_usize(cstride);
 
         unsafe {
-            let data = SliceStorageMut::from_raw_parts(m.data.ptr_mut(),
+            let data = SliceStorageMut::from_raw_parts(
+                m.data.ptr_mut(),
                 (row_slice, col_slice),
-                                                    (rstride_slice, cstride_slice));
+                (rstride_slice, cstride_slice),
+            );
             Matrix::from_data_statically_unchecked(data)
         }
     }
 }
 
-impl<'a, N: Scalar + Copy, R: Dim, C: Dim, S: ContiguousStorage<N, R, C>> Into<&'a [N]> for &'a Matrix<N, R, C, S> {
+impl<'a, N: Scalar + Copy, R: Dim, C: Dim, S: ContiguousStorage<N, R, C>> Into<&'a [N]>
+    for &'a Matrix<N, R, C, S>
+{
     #[inline]
     fn into(self) -> &'a [N] {
         self.as_slice()
     }
 }
 
-impl<'a, N: Scalar + Copy, R: Dim, C: Dim, S: ContiguousStorageMut<N, R, C>> Into<&'a mut [N]> for &'a mut Matrix<N, R, C, S> {
+impl<'a, N: Scalar + Copy, R: Dim, C: Dim, S: ContiguousStorageMut<N, R, C>> Into<&'a mut [N]>
+    for &'a mut Matrix<N, R, C, S>
+{
     #[inline]
     fn into(self) -> &'a mut [N] {
         self.as_mut_slice()
     }
 }
 
-
 impl<'a, N: Scalar + Copy> From<&'a [N]> for DVectorSlice<'a, N> {
     #[inline]
     fn from(slice: &'a [N]) -> Self {

src/base/dimension.rs

@@ -190,7 +190,6 @@ pub trait DimName: Dim {
     type Value: NamedDim<Name = Self>;
 
     /// The name of this dimension, i.e., the singleton `Self`.
-    #[inline]
     fn name() -> Self;
 
     // FIXME: this is not a very idiomatic name.

src/base/matrix.rs

@@ -16,8 +16,8 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use alga::general::{ClosedAdd, ClosedMul, ClosedSub, Field, RealField, Ring};
+use simba::scalar::{ClosedAdd, ClosedMul, ClosedSub, Field, RealField};
-use alga::simd::SimdPartialOrd;
+use simba::simd::SimdPartialOrd;
 
 use crate::base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
 use crate::base::constraint::{DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
@@ -29,7 +29,7 @@ use crate::base::storage::{
     ContiguousStorage, ContiguousStorageMut, Owned, SameShapeStorage, Storage, StorageMut,
 };
 use crate::base::{DefaultAllocator, MatrixMN, MatrixN, Scalar, Unit, VectorN};
-use crate::{SimdComplexField, SimdRealField};
+use crate::SimdComplexField;
 
 /// A square matrix.
 pub type SquareMatrix<N, D, S> = Matrix<N, D, D, S>;
@@ -1130,7 +1130,7 @@ impl<N: Scalar, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
     /// Computes a trace of a square matrix, i.e., the sum of its diagonal elements.
     #[inline]
     pub fn trace(&self) -> N
-    where N: Ring {
+    where N: Scalar + Zero + ClosedAdd {
         assert!(
             self.is_square(),
             "Cannot compute the trace of non-square matrix."
@@ -1517,7 +1517,9 @@ fn lower_exp() {
     )
 }
 
-impl<N: Scalar + Ring, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+impl<N: Scalar + ClosedAdd + ClosedSub + ClosedMul, R: Dim, C: Dim, S: Storage<N, R, C>>
+    Matrix<N, R, C, S>
+{
     /// The perpendicular product between two 2D column vectors, i.e. `a.x * b.y - a.y * b.x`.
     #[inline]
     pub fn perp<R2, C2, SB>(&self, b: &Matrix<N, R2, C2, SB>) -> N

src/base/matrix_alga.rs

@@ -1,424 +0,0 @@
-#[cfg(all(feature = "alloc", not(feature = "std")))]
-use alloc::vec::Vec;
-
-use num::{One, Zero};
-
-use alga::general::{
-    AbstractGroup, AbstractGroupAbelian, AbstractLoop, AbstractMagma, AbstractModule,
-    AbstractMonoid, AbstractQuasigroup, AbstractSemigroup, Additive, ClosedAdd, ClosedMul,
-    ClosedNeg, Field, Identity, TwoSidedInverse, JoinSemilattice, Lattice, MeetSemilattice, Module,
-    Multiplicative, RingCommutative, ComplexField
-};
-use alga::linear::{
-    FiniteDimInnerSpace, FiniteDimVectorSpace, InnerSpace, NormedSpace, VectorSpace,
-};
-
-use crate::base::allocator::Allocator;
-use crate::base::dimension::{Dim, DimName};
-use crate::base::storage::{Storage, StorageMut};
-use crate::base::{DefaultAllocator, MatrixMN, MatrixN, Scalar};
-
-/*
- *
- * Additive structures.
- *
- */
-impl<N, R: DimName, C: DimName> Identity<Additive> for MatrixMN<N, R, C>
-where
-    N: Scalar + Zero,
-    DefaultAllocator: Allocator<N, R, C>,
-{
-    #[inline]
-    fn identity() -> Self {
-        Self::from_element(N::zero())
-    }
-}
-
-impl<N, R: DimName, C: DimName> AbstractMagma<Additive> for MatrixMN<N, R, C>
-where
-    N: Scalar + ClosedAdd,
-    DefaultAllocator: Allocator<N, R, C>,
-{
-    #[inline]
-    fn operate(&self, other: &Self) -> Self {
-        self + other
-    }
-}
-
-impl<N, R: DimName, C: DimName> TwoSidedInverse<Additive> for MatrixMN<N, R, C>
-where
-    N: Scalar + ClosedNeg,
-    DefaultAllocator: Allocator<N, R, C>,
-{
-    #[inline]
-    #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
-    fn two_sided_inverse(&self) -> Self {
-        -self
-    }
-
-    #[inline]
-    fn two_sided_inverse_mut(&mut self) {
-        *self = -self.clone()
-    }
-}
-
-macro_rules! inherit_additive_structure(
-    ($($marker: ident<$operator: ident> $(+ $bounds: ident)*),* $(,)*) => {$(
-        impl<N, R: DimName, C: DimName> $marker<$operator> for MatrixMN<N, R, C>
-            where N: Scalar + $marker<$operator> $(+ $bounds)*,
-                  DefaultAllocator: Allocator<N, R, C> { }
-    )*}
-);
-
-inherit_additive_structure!(
-    AbstractSemigroup<Additive> + ClosedAdd,
-    AbstractMonoid<Additive> + Zero + ClosedAdd,
-    AbstractQuasigroup<Additive> + ClosedAdd + ClosedNeg,
-    AbstractLoop<Additive> + Zero + ClosedAdd + ClosedNeg,
-    AbstractGroup<Additive> + Zero + ClosedAdd + ClosedNeg,
-    AbstractGroupAbelian<Additive> + Zero + ClosedAdd + ClosedNeg
-);
-
-impl<N, R: DimName, C: DimName> AbstractModule for MatrixMN<N, R, C>
-where
-    N: Scalar + RingCommutative,
-    DefaultAllocator: Allocator<N, R, C>,
-{
-    type AbstractRing = N;
-
-    #[inline]
-    fn multiply_by(&self, n: N) -> Self {
-        self * n
-    }
-}
-
-impl<N, R: DimName, C: DimName> Module for MatrixMN<N, R, C>
-where
-    N: Scalar + RingCommutative,
-    DefaultAllocator: Allocator<N, R, C>,
-{
-    type Ring = N;
-}
-
-impl<N, R: DimName, C: DimName> VectorSpace for MatrixMN<N, R, C>
-where
-    N: Scalar + Field,
-    DefaultAllocator: Allocator<N, R, C>,
-{
-    type Field = N;
-}
-
-impl<N, R: DimName, C: DimName> FiniteDimVectorSpace for MatrixMN<N, R, C>
-where
-    N: Scalar + Field,
-    DefaultAllocator: Allocator<N, R, C>,
-{
-    #[inline]
-    fn dimension() -> usize {
-        R::dim() * C::dim()
-    }
-
-    #[inline]
-    fn canonical_basis_element(i: usize) -> Self {
-        assert!(i < Self::dimension(), "Index out of bound.");
-
-        let mut res = Self::zero();
-        unsafe {
-            *res.data.get_unchecked_linear_mut(i) = N::one();
-        }
-
-        res
-    }
-
-    #[inline]
-    fn dot(&self, other: &Self) -> N {
-        self.dot(other)
-    }
-
-    #[inline]
-    unsafe fn component_unchecked(&self, i: usize) -> &N {
-        self.data.get_unchecked_linear(i)
-    }
-
-    #[inline]
-    unsafe fn component_unchecked_mut(&mut self, i: usize) -> &mut N {
-        self.data.get_unchecked_linear_mut(i)
-    }
-}
-
-impl<N: ComplexField, R: DimName, C: DimName> NormedSpace for MatrixMN<N, R, C>
-where DefaultAllocator: Allocator<N, R, C>
-{
-    type RealField = N::RealField;
-    type ComplexField = N;
-
-    #[inline]
-    fn norm_squared(&self) -> N::RealField {
-        self.norm_squared()
-    }
-
-    #[inline]
-    fn norm(&self) -> N::RealField {
-        self.norm()
-    }
-
-    #[inline]
-    #[must_use = "Did you mean to use normalize_mut()?"]
-    fn normalize(&self) -> Self {
-        self.normalize()
-    }
-
-    #[inline]
-    fn normalize_mut(&mut self) -> N::RealField {
-        self.normalize_mut()
-    }
-
-    #[inline]
-    #[must_use = "Did you mean to use try_normalize_mut()?"]
-    fn try_normalize(&self, min_norm: N::RealField) -> Option<Self> {
-        self.try_normalize(min_norm)
-    }
-
-    #[inline]
-    fn try_normalize_mut(&mut self, min_norm: N::RealField) -> Option<N::RealField> {
-        self.try_normalize_mut(min_norm)
-    }
-}
-
-impl<N: ComplexField, R: DimName, C: DimName> InnerSpace for MatrixMN<N, R, C>
-where DefaultAllocator: Allocator<N, R, C>
-{
-    #[inline]
-    fn angle(&self, other: &Self) -> N::RealField {
-        self.angle(other)
-    }
-
-    #[inline]
-    fn inner_product(&self, other: &Self) -> N {
-        self.dotc(other)
-    }
-}
-
-// FIXME: specialization will greatly simplify this implementation in the future.
-// In particular:
-//   − use `x()` instead of `::canonical_basis_element`
-//   − use `::new(x, y, z)` instead of `::from_slice`
-impl<N: ComplexField, R: DimName, C: DimName> FiniteDimInnerSpace for MatrixMN<N, R, C>
-where DefaultAllocator: Allocator<N, R, C>
-{
-    #[inline]
-    fn orthonormalize(vs: &mut [Self]) -> usize {
-        let mut nbasis_elements = 0;
-
-        for i in 0..vs.len() {
-            {
-                let (elt, basis) = vs[..i + 1].split_last_mut().unwrap();
-
-                for basis_element in &basis[..nbasis_elements] {
-                    *elt -= &*basis_element * elt.dot(basis_element)
-                }
-            }
-
-            if vs[i].try_normalize_mut(N::RealField::zero()).is_some() {
-                // FIXME: this will be efficient on dynamically-allocated vectors but for
-                // statically-allocated ones, `.clone_from` would be better.
-                vs.swap(nbasis_elements, i);
-                nbasis_elements += 1;
-
-                // All the other vectors will be dependent.
-                if nbasis_elements == Self::dimension() {
-                    break;
-                }
-            }
-        }
-
-        nbasis_elements
-    }
-
-    #[inline]
-    fn orthonormal_subspace_basis<F>(vs: &[Self], mut f: F)
-    where F: FnMut(&Self) -> bool {
-        // FIXME: is this necessary?
-        assert!(
-            vs.len() <= Self::dimension(),
-            "The given set of vectors has no chance of being a free family."
-        );
-
-        match Self::dimension() {
-            1 => {
-                if vs.len() == 0 {
-                    let _ = f(&Self::canonical_basis_element(0));
-                }
-            }
-            2 => {
-                if vs.len() == 0 {
-                    let _ = f(&Self::canonical_basis_element(0))
-                        && f(&Self::canonical_basis_element(1));
-                } else if vs.len() == 1 {
-                    let v = &vs[0];
-                    let res = Self::from_column_slice(&[-v[1], v[0]]);
-
-                    let _ = f(&res.normalize());
-                }
-
-                // Otherwise, nothing.
-            }
-            3 => {
-                if vs.len() == 0 {
-                    let _ = f(&Self::canonical_basis_element(0))
-                        && f(&Self::canonical_basis_element(1))
-                        && f(&Self::canonical_basis_element(2));
-                } else if vs.len() == 1 {
-                    let v = &vs[0];
-                    let mut a;
-
-                    if v[0].norm1() > v[1].norm1() {
-                        a = Self::from_column_slice(&[v[2], N::zero(), -v[0]]);
-                    } else {
-                        a = Self::from_column_slice(&[N::zero(), -v[2], v[1]]);
-                    };
-
-                    let _ = a.normalize_mut();
-
-                    if f(&a.cross(v)) {
-                        let _ = f(&a);
-                    }
-                } else if vs.len() == 2 {
-                    let _ = f(&vs[0].cross(&vs[1]).normalize());
-                }
-            }
-            _ => {
-                #[cfg(any(feature = "std", feature = "alloc"))]
-                {
-                    // XXX: use a GenericArray instead.
-                    let mut known_basis = Vec::new();
-
-                    for v in vs.iter() {
-                        known_basis.push(v.normalize())
-                    }
-
-                    for i in 0..Self::dimension() - vs.len() {
-                        let mut elt = Self::canonical_basis_element(i);
-
-                        for v in &known_basis {
-                            elt -= v * elt.dot(v)
-                        }
-
-                        if let Some(subsp_elt) = elt.try_normalize(N::RealField::zero()) {
-                            if !f(&subsp_elt) {
-                                return;
-                            };
-
-                            known_basis.push(subsp_elt);
-                        }
-                    }
-                }
-                #[cfg(all(not(feature = "std"), not(feature = "alloc")))]
-                {
-                    panic!("Cannot compute the orthogonal subspace basis of a vector with a dimension greater than 3 \
-                            if #![no_std] is enabled and the 'alloc' feature is not enabled.")
-                }
-            }
-        }
-    }
-}
-
-/*
- *
- *
- * Multiplicative structures.
- *
- *
- */
-impl<N, D: DimName> Identity<Multiplicative> for MatrixN<N, D>
-where
-    N: Scalar + Zero + One,
-    DefaultAllocator: Allocator<N, D, D>,
-{
-    #[inline]
-    fn identity() -> Self {
-        Self::identity()
-    }
-}
-
-impl<N, D: DimName> AbstractMagma<Multiplicative> for MatrixN<N, D>
-where
-    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
-    DefaultAllocator: Allocator<N, D, D>,
-{
-    #[inline]
-    fn operate(&self, other: &Self) -> Self {
-        self * other
-    }
-}
-
-macro_rules! impl_multiplicative_structure(
-    ($($marker: ident<$operator: ident> $(+ $bounds: ident)*),* $(,)*) => {$(
-        impl<N, D: DimName> $marker<$operator> for MatrixN<N, D>
-            where N: Scalar + Zero + One + ClosedAdd + ClosedMul + $marker<$operator> $(+ $bounds)*,
-                  DefaultAllocator: Allocator<N, D, D> { }
-    )*}
-);
-
-impl_multiplicative_structure!(
-    AbstractSemigroup<Multiplicative>,
-    AbstractMonoid<Multiplicative> + One
-);
-
-/*
- *
- * Ordering
- *
- */
-impl<N, R: Dim, C: Dim> MeetSemilattice for MatrixMN<N, R, C>
-where
-    N: Scalar + MeetSemilattice,
-    DefaultAllocator: Allocator<N, R, C>,
-{
-    #[inline]
-    fn meet(&self, other: &Self) -> Self {
-        self.zip_map(other, |a, b| a.meet(&b))
-    }
-}
-
-impl<N, R: Dim, C: Dim> JoinSemilattice for MatrixMN<N, R, C>
-where
-    N: Scalar + JoinSemilattice,
-    DefaultAllocator: Allocator<N, R, C>,
-{
-    #[inline]
-    fn join(&self, other: &Self) -> Self {
-        self.zip_map(other, |a, b| a.join(&b))
-    }
-}
-
-impl<N, R: Dim, C: Dim> Lattice for MatrixMN<N, R, C>
-where
-    N: Scalar + Lattice,
-    DefaultAllocator: Allocator<N, R, C>,
-{
-    #[inline]
-    fn meet_join(&self, other: &Self) -> (Self, Self) {
-        let shape = self.data.shape();
-        assert!(
-            shape == other.data.shape(),
-            "Matrix meet/join error: mismatched dimensions."
-        );
-
-        let mut mres = unsafe { Self::new_uninitialized_generic(shape.0, shape.1) };
-        let mut jres = unsafe { Self::new_uninitialized_generic(shape.0, shape.1) };
-
-        for i in 0..shape.0.value() * shape.1.value() {
-            unsafe {
-                let mj = self
-                    .data
-                    .get_unchecked_linear(i)
-                    .meet_join(other.data.get_unchecked_linear(i));
-                *mres.data.get_unchecked_linear_mut(i) = mj.0;
-                *jres.data.get_unchecked_linear_mut(i) = mj.1;
-            }
-        }
-
-        (mres, jres)
-    }
-}

src/base/matrix_simba.rs

@@ -0,0 +1,65 @@
+#[cfg(all(feature = "alloc", not(feature = "std")))]
+use alloc::vec::Vec;
+
+use simba::simd::SimdValue;
+
+use crate::base::allocator::Allocator;
+use crate::base::dimension::Dim;
+use crate::base::{DefaultAllocator, MatrixMN, Scalar};
+
+/*
+ *
+ * Simd structures.
+ *
+ */
+impl<N, R, C> SimdValue for MatrixMN<N, R, C>
+where
+    N: Scalar + SimdValue,
+    R: Dim,
+    C: Dim,
+    N::Element: Scalar,
+    DefaultAllocator: Allocator<N, R, C> + Allocator<N::Element, R, C>,
+{
+    type Element = MatrixMN<N::Element, R, C>;
+    type SimdBool = N::SimdBool;
+
+    #[inline]
+    fn lanes() -> usize {
+        N::lanes()
+    }
+
+    #[inline]
+    fn splat(val: Self::Element) -> Self {
+        val.map(N::splat)
+    }
+
+    #[inline]
+    fn extract(&self, i: usize) -> Self::Element {
+        self.map(|e| e.extract(i))
+    }
+
+    #[inline]
+    unsafe fn extract_unchecked(&self, i: usize) -> Self::Element {
+        self.map(|e| e.extract_unchecked(i))
+    }
+
+    #[inline]
+    fn replace(&mut self, i: usize, val: Self::Element) {
+        self.zip_apply(&val, |mut a, b| {
+            a.replace(i, b);
+            a
+        })
+    }
+
+    #[inline]
+    unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element) {
+        self.zip_apply(&val, |mut a, b| {
+            a.replace_unchecked(i, b);
+            a
+        })
+    }
+
+    fn select(self, cond: Self::SimdBool, other: Self) -> Self {
+        self.zip_map(&other, |a, b| a.select(cond, b))
+    }
+}

src/base/mod.rs

@@ -12,6 +12,7 @@ pub mod storage;
 
 mod alias;
 mod alias_slice;
+mod array_storage;
 mod cg;
 mod componentwise;
 mod construction;
@@ -20,25 +21,24 @@ mod conversion;
 mod edition;
 pub mod indexing;
 mod matrix;
-mod matrix_alga;
+mod matrix_simba;
-mod array_storage;
 mod matrix_slice;
-#[cfg(any(feature = "std", feature = "alloc"))]
+mod norm;
-mod vec_storage;
 mod properties;
 mod scalar;
+mod statistics;
 mod swizzle;
 mod unit;
-mod statistics;
+#[cfg(any(feature = "std", feature = "alloc"))]
-mod norm;
+mod vec_storage;
 
 #[doc(hidden)]
 pub mod helper;
 
 pub use self::matrix::*;
+pub use self::norm::*;
 pub use self::scalar::*;
 pub use self::unit::*;
-pub use self::norm::*;
 
 pub use self::default_allocator::*;
 pub use self::dimension::*;

src/base/norm.rs

@@ -1,11 +1,13 @@
 use num::Zero;
+use std::ops::Neg;
 
 use crate::allocator::Allocator;
-use crate::base::{DefaultAllocator, Dim, Matrix, MatrixMN};
+use crate::base::{DefaultAllocator, Dim, Matrix, MatrixMN, Normed};
 use crate::constraint::{SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
 use crate::storage::{Storage, StorageMut};
-use crate::{ComplexField, RealField, SimdComplexField, SimdRealField};
+use crate::{ComplexField, Scalar, SimdComplexField, Unit};
-use alga::simd::SimdPartialOrd;
+use simba::scalar::ClosedNeg;
+use simba::simd::{SimdOption, SimdPartialOrd};
 
 // FIXME: this should be be a trait on alga?
 /// A trait for abstract matrix norms.
@@ -272,6 +274,19 @@ impl<N: SimdComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S
     pub fn lp_norm(&self, p: i32) -> N::SimdRealField {
         self.apply_norm(&LpNorm(p))
     }
+
+    #[inline]
+    #[must_use = "Did you mean to use simd_try_normalize_mut()?"]
+    pub fn simd_try_normalize(&self, min_norm: N::SimdRealField) -> SimdOption<MatrixMN<N, R, C>>
+    where
+        N::Element: Scalar,
+        DefaultAllocator: Allocator<N, R, C> + Allocator<N::Element, R, C>,
+    {
+        let n = self.norm();
+        let le = n.simd_le(min_norm);
+        let val = self.unscale(n);
+        SimdOption::new(val, le)
+    }
 }
 
 impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
@@ -313,6 +328,22 @@ impl<N: SimdComplexField, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C
 
         n
     }
+
+    #[inline]
+    #[must_use = "Did you mean to use simd_try_normalize_mut()?"]
+    pub fn simd_try_normalize_mut(
+        &mut self,
+        min_norm: N::SimdRealField,
+    ) -> SimdOption<N::SimdRealField>
+    where
+        N::Element: Scalar,
+        DefaultAllocator: Allocator<N, R, C> + Allocator<N::Element, R, C>,
+    {
+        let n = self.norm();
+        let le = n.simd_le(min_norm);
+        self.apply(|e| e.simd_unscale(n).select(le, e));
+        SimdOption::new(n, le)
+    }
 }
 
 impl<N: ComplexField, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
@@ -320,8 +351,7 @@ impl<N: ComplexField, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S>
     ///
     /// If the normalization succeeded, returns the old norm of this matrix.
     #[inline]
-    pub fn try_normalize_mut(&mut self, min_norm: N::RealField) -> Option<N::RealField>
+    pub fn try_normalize_mut(&mut self, min_norm: N::RealField) -> Option<N::RealField> {
-    where N: ComplexField {
         let n = self.norm();
 
         if n <= min_norm {
@@ -332,3 +362,40 @@ impl<N: ComplexField, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S>
         }
     }
 }
+
+impl<N: SimdComplexField, R: Dim, C: Dim> Normed for MatrixMN<N, R, C>
+where DefaultAllocator: Allocator<N, R, C>
+{
+    type Norm = N::SimdRealField;
+
+    #[inline]
+    fn norm(&self) -> N::SimdRealField {
+        self.norm()
+    }
+
+    #[inline]
+    fn norm_squared(&self) -> N::SimdRealField {
+        self.norm_squared()
+    }
+
+    #[inline]
+    fn scale_mut(&mut self, n: Self::Norm) {
+        self.scale_mut(n)
+    }
+
+    #[inline]
+    fn unscale_mut(&mut self, n: Self::Norm) {
+        self.unscale_mut(n)
+    }
+}
+
+impl<N: Scalar + ClosedNeg, R: Dim, C: Dim> Neg for Unit<MatrixMN<N, R, C>>
+where DefaultAllocator: Allocator<N, R, C>
+{
+    type Output = Unit<MatrixMN<N, R, C>>;
+
+    #[inline]
+    fn neg(self) -> Self::Output {
+        Unit::new_unchecked(-self.value)
+    }
+}

src/base/ops.rs

@@ -1,12 +1,11 @@
-use num::{One, Signed, Zero};
+use num::{One, Zero};
-use std::cmp::{Ordering, PartialOrd};
 use std::iter;
 use std::ops::{
     Add, AddAssign, Div, DivAssign, Index, IndexMut, Mul, MulAssign, Neg, Sub, SubAssign,
 };
 
-use alga::general::{ClosedAdd, ClosedDiv, ClosedMul, ClosedNeg, ClosedSub};
+use simba::scalar::{ClosedAdd, ClosedDiv, ClosedMul, ClosedNeg, ClosedSub};
-use alga::simd::{SimdPartialOrd, SimdSigned};
+use simba::simd::{SimdPartialOrd, SimdSigned};
 
 use crate::base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
 use crate::base::constraint::{

src/base/properties.rs

@@ -2,7 +2,7 @@
 use approx::RelativeEq;
 use num::{One, Zero};
 
-use alga::general::{ClosedAdd, ClosedMul, RealField, ComplexField};
+use simba::scalar::{ClosedAdd, ClosedMul, ComplexField, RealField};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{Dim, DimMin};

src/base/statistics.rs

@@ -1,21 +1,28 @@
-use crate::{Scalar, Dim, Matrix, VectorN, RowVectorN, DefaultAllocator, U1, VectorSliceN};
-use alga::general::{AdditiveMonoid, Field, SupersetOf};
-use crate::storage::Storage;
 use crate::allocator::Allocator;
+use crate::storage::Storage;
+use crate::{DefaultAllocator, Dim, Matrix, RowVectorN, Scalar, VectorN, VectorSliceN, U1};
+use num::Zero;
+use simba::scalar::{ClosedAdd, Field, SupersetOf};
 
 impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Returns a row vector where each element is the result of the application of `f` on the
     /// corresponding column of the original matrix.
     #[inline]
-    pub fn compress_rows(&self, f: impl Fn(VectorSliceN<N, R, S::RStride, S::CStride>) -> N) -> RowVectorN<N, C>
+    pub fn compress_rows(
-        where DefaultAllocator: Allocator<N, U1, C> {
+        &self,
-
+        f: impl Fn(VectorSliceN<N, R, S::RStride, S::CStride>) -> N,
+    ) -> RowVectorN<N, C>
+    where
+        DefaultAllocator: Allocator<N, U1, C>,
+    {
         let ncols = self.data.shape().1;
         let mut res = unsafe { RowVectorN::new_uninitialized_generic(U1, ncols) };
 
         for i in 0..ncols.value() {
             // FIXME: avoid bound checking of column.
-            unsafe { *res.get_unchecked_mut((0, i)) = f(self.column(i)); }
+            unsafe {
+                *res.get_unchecked_mut((0, i)) = f(self.column(i));
+            }
         }
 
         res
@@ -26,15 +33,21 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     ///
     /// This is the same as `self.compress_rows(f).transpose()`.
     #[inline]
-    pub fn compress_rows_tr(&self, f: impl Fn(VectorSliceN<N, R, S::RStride, S::CStride>) -> N) -> VectorN<N, C>
+    pub fn compress_rows_tr(
-        where DefaultAllocator: Allocator<N, C> {
+        &self,
-
+        f: impl Fn(VectorSliceN<N, R, S::RStride, S::CStride>) -> N,
+    ) -> VectorN<N, C>
+    where
+        DefaultAllocator: Allocator<N, C>,
+    {
         let ncols = self.data.shape().1;
         let mut res = unsafe { VectorN::new_uninitialized_generic(ncols, U1) };
 
         for i in 0..ncols.value() {
             // FIXME: avoid bound checking of column.
-            unsafe { *res.vget_unchecked_mut(i) = f(self.column(i)); }
+            unsafe {
+                *res.vget_unchecked_mut(i) = f(self.column(i));
+            }
         }
 
         res
@@ -42,8 +55,14 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 
     /// Returns a column vector resulting from the folding of `f` on each column of this matrix.
     #[inline]
-    pub fn compress_columns(&self, init: VectorN<N, R>, f: impl Fn(&mut VectorN<N, R>, VectorSliceN<N, R, S::RStride, S::CStride>)) -> VectorN<N, R>
+    pub fn compress_columns(
-        where DefaultAllocator: Allocator<N, R> {
+        &self,
+        init: VectorN<N, R>,
+        f: impl Fn(&mut VectorN<N, R>, VectorSliceN<N, R, S::RStride, S::CStride>),
+    ) -> VectorN<N, R>
+    where
+        DefaultAllocator: Allocator<N, R>,
+    {
         let mut res = init;
 
         for i in 0..self.ncols() {
@@ -54,7 +73,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     }
 }
 
-impl<N: Scalar + AdditiveMonoid, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+impl<N: Scalar + ClosedAdd + Zero, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /*
      *
      * Sum computation.
@@ -168,7 +187,9 @@ impl<N: Scalar + Field + SupersetOf<f64>, R: Dim, C: Dim, S: Storage<N, R, C>> M
         if self.len() == 0 {
             N::zero()
         } else {
-            let val = self.iter().cloned().fold((N::zero(), N::zero()), |a, b| (a.0 + b.inlined_clone() * b.inlined_clone(), a.1 + b));
+            let val = self.iter().cloned().fold((N::zero(), N::zero()), |a, b| {
+                (a.0 + b.inlined_clone() * b.inlined_clone(), a.1 + b)
+            });
             let denom = N::one() / crate::convert::<_, N>(self.len() as f64);
             let vd = val.1 * denom.inlined_clone();
             val.0 * denom - vd.inlined_clone() * vd
@@ -235,7 +256,8 @@ impl<N: Scalar + Field + SupersetOf<f64>, R: Dim, C: Dim, S: Storage<N, R, C>> M
             for i in 0..nrows.value() {
                 unsafe {
                     let val = col.vget_unchecked(i);
-                    *out.vget_unchecked_mut(i) += denom.inlined_clone() * val.inlined_clone() * val.inlined_clone()
+                    *out.vget_unchecked_mut(i) +=
+                        denom.inlined_clone() * val.inlined_clone() * val.inlined_clone()
                 }
             }
         })

src/base/storage.rs

@@ -94,13 +94,11 @@ pub unsafe trait Storage<N: Scalar, R: Dim, C: Dim = U1>: Debug + Sized {
     }
 
     /// Indicates whether this data buffer stores its elements contiguously.
-    #[inline]
     fn is_contiguous(&self) -> bool;
 
     /// Retrieves the data buffer as a contiguous slice.
     ///
     /// The matrix components may not be stored in a contiguous way, depending on the strides.
-    #[inline]
     fn as_slice(&self) -> &[N];
 
     /// Builds a matrix data storage that does not contain any reference.
@@ -166,7 +164,6 @@ pub unsafe trait StorageMut<N: Scalar, R: Dim, C: Dim = U1>: Storage<N, R, C> {
     /// Retrieves the mutable data buffer as a contiguous slice.
     ///
     /// Matrix components may not be contiguous, depending on its strides.
-    #[inline]
     fn as_mut_slice(&mut self) -> &mut [N];
 }
 

src/base/unit.rs

@@ -1,8 +1,7 @@
-use approx::RelativeEq;
 #[cfg(feature = "abomonation-serialize")]
 use std::io::{Result as IOResult, Write};
 use std::mem;
-use std::ops::{Deref, Neg};
+use std::ops::Deref;
 
 #[cfg(feature = "serde-serialize")]
 use serde::{Deserialize, Deserializer, Serialize, Serializer};
@@ -10,8 +9,7 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use alga::general::{SubsetOf, ComplexField};
+use crate::{RealField, SimdComplexField, SimdRealField};
-use alga::linear::NormedSpace;
 
 /// A wrapper that ensures the underlying algebraic entity has a unit norm.
 ///
@@ -19,7 +17,7 @@ use alga::linear::NormedSpace;
 #[repr(transparent)]
 #[derive(Eq, PartialEq, Clone, Hash, Debug, Copy)]
 pub struct Unit<T> {
-    value: T,
+    pub(crate) value: T,
 }
 
 #[cfg(feature = "serde-serialize")]
@@ -53,60 +51,76 @@ impl<T: Abomonation> Abomonation for Unit<T> {
     }
 }
 
-impl<T: NormedSpace> Unit<T> {
+pub trait Normed {
-    /// Normalize the given value and return it wrapped on a `Unit` structure.
+    type Norm: SimdRealField;
+    fn norm(&self) -> Self::Norm;
+    fn norm_squared(&self) -> Self::Norm;
+    fn scale_mut(&mut self, n: Self::Norm);
+    fn unscale_mut(&mut self, n: Self::Norm);
+}
+
+impl<T: Normed> Unit<T> {
+    /// Normalize the given vector and return it wrapped on a `Unit` structure.
     #[inline]
     pub fn new_normalize(value: T) -> Self {
         Self::new_and_get(value).0
     }
 
-    /// Attempts to normalize the given value and return it wrapped on a `Unit` structure.
+    /// Attempts to normalize the given vector and return it wrapped on a `Unit` structure.
     ///
     /// Returns `None` if the norm was smaller or equal to `min_norm`.
     #[inline]
-    pub fn try_new(value: T, min_norm: T::RealField) -> Option<Self> {
+    pub fn try_new(value: T, min_norm: T::Norm) -> Option<Self>
+    where T::Norm: RealField {
         Self::try_new_and_get(value, min_norm).map(|res| res.0)
     }
 
-    /// Normalize the given value and return it wrapped on a `Unit` structure and its norm.
+    /// Normalize the given vector and return it wrapped on a `Unit` structure and its norm.
     #[inline]
-    pub fn new_and_get(mut value: T) -> (Self, T::RealField) {
+    pub fn new_and_get(mut value: T) -> (Self, T::Norm) {
-        let n = value.normalize_mut();
+        let n = value.norm();
-
+        value.unscale_mut(n);
-        (Unit { value: value }, n)
+        (Unit { value }, n)
     }
 
-    /// Normalize the given value and return it wrapped on a `Unit` structure and its norm.
+    /// Normalize the given vector and return it wrapped on a `Unit` structure and its norm.
     ///
     /// Returns `None` if the norm was smaller or equal to `min_norm`.
     #[inline]
-    pub fn try_new_and_get(mut value: T, min_norm: T::RealField) -> Option<(Self, T::RealField)> {
+    pub fn try_new_and_get(mut value: T, min_norm: T::Norm) -> Option<(Self, T::Norm)>
-        if let Some(n) = value.try_normalize_mut(min_norm) {
+    where T::Norm: RealField {
-            Some((Unit { value: value }, n))
+        let sq_norm = value.norm_squared();
+
+        if sq_norm > min_norm * min_norm {
+            let n = sq_norm.simd_sqrt();
+            value.unscale_mut(n);
+            Some((Unit { value }, n))
         } else {
             None
         }
     }
 
-    /// Normalizes this value again. This is useful when repeated computations
+    /// Normalizes this vector again. This is useful when repeated computations
     /// might cause a drift in the norm because of float inaccuracies.
     ///
     /// Returns the norm before re-normalization. See `.renormalize_fast` for a faster alternative
     /// that may be slightly less accurate if `self` drifted significantly from having a unit length.
     #[inline]
-    pub fn renormalize(&mut self) -> T::RealField {
+    pub fn renormalize(&mut self) -> T::Norm {
-        self.value.normalize_mut()
+        let n = self.norm();
+        self.value.unscale_mut(n);
+        n
     }
 
-    /// Normalizes this value again using a first-order Taylor approximation.
+    /// Normalizes this vector again using a first-order Taylor approximation.
     /// This is useful when repeated computations might cause a drift in the norm
     /// because of float inaccuracies.
     #[inline]
     pub fn renormalize_fast(&mut self) {
         let sq_norm = self.value.norm_squared();
-        let _3: T::RealField = crate::convert(3.0);
+        let _3: T::Norm = crate::convert(3.0);
-        let _0_5: T::RealField = crate::convert(0.5);
+        let _0_5: T::Norm = crate::convert(0.5);
-        self.value *= T::ComplexField::from_real(_0_5 * (_3 - sq_norm));
+        self.value.scale_mut(_0_5 * (_3 - sq_norm));
     }
 }
 
@@ -114,7 +128,7 @@ impl<T> Unit<T> {
     /// Wraps the given value, assuming it is already normalized.
     #[inline]
     pub fn new_unchecked(value: T) -> Self {
-        Unit { value: value }
+        Unit { value }
     }
 
     /// Wraps the given reference, assuming it is already normalized.
@@ -153,13 +167,14 @@ impl<T> AsRef<T> for Unit<T> {
     }
 }
 
+/*
 /*
  *
  * Conversions.
  *
  */
 impl<T: NormedSpace> SubsetOf<T> for Unit<T>
-where T::Field: RelativeEq
+where T::RealField: RelativeEq
 {
     #[inline]
     fn to_superset(&self) -> T {
@@ -172,7 +187,7 @@ where T::Field: RelativeEq
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(value: &T) -> Self {
+    fn from_superset_unchecked(value: &T) -> Self {
         Unit::new_normalize(value.clone()) // We still need to re-normalize because the condition is inexact.
     }
 }
@@ -205,7 +220,7 @@ where T::Field: RelativeEq
 //         self.value.ulps_eq(&other.value, epsilon, max_ulps)
 //     }
 // }
-
+*/
 // FIXME:re-enable this impl when specialization is possible.
 // Currently, it is disabled so that we can have a nice output for the `UnitQuaternion` display.
 /*
@@ -217,15 +232,6 @@ impl<T: fmt::Display> fmt::Display for Unit<T> {
 }
 */
 
-impl<T: Neg> Neg for Unit<T> {
-    type Output = Unit<T::Output>;
-
-    #[inline]
-    fn neg(self) -> Self::Output {
-        Self::Output::new_unchecked(-self.value)
-    }
-}
-
 impl<T> Deref for Unit<T> {
     type Target = T;
 

src/debug/random_orthogonal.rs

@@ -3,12 +3,12 @@ use crate::base::storage::Owned;
 #[cfg(feature = "arbitrary")]
 use quickcheck::{Arbitrary, Gen};
 
-use alga::general::ComplexField;
-use crate::base::Scalar;
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{Dim, Dynamic, U2};
+use crate::base::Scalar;
 use crate::base::{DefaultAllocator, MatrixN};
 use crate::linalg::givens::GivensRotation;
+use simba::scalar::ComplexField;
 
 /// A random orthogonal matrix.
 #[derive(Clone, Debug)]

src/debug/random_sdp.rs

@@ -3,11 +3,11 @@ use crate::base::storage::Owned;
 #[cfg(feature = "arbitrary")]
 use quickcheck::{Arbitrary, Gen};
 
-use alga::general::ComplexField;
-use crate::base::Scalar;
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{Dim, Dynamic};
+use crate::base::Scalar;
 use crate::base::{DefaultAllocator, MatrixN};
+use simba::scalar::ComplexField;
 
 use crate::debug::RandomOrthogonal;
 

src/geometry/abstract_rotation.rs

@@ -0,0 +1,136 @@
+use crate::allocator::Allocator;
+use crate::geometry::{Rotation, UnitComplex, UnitQuaternion};
+use crate::{DefaultAllocator, DimName, Point, RealField, Scalar, VectorN, U2, U3};
+
+use simba::scalar::ClosedMul;
+
+pub trait AbstractRotation<N: Scalar, D: DimName>: PartialEq + ClosedMul + Clone {
+    fn identity() -> Self;
+    fn inverse(&self) -> Self;
+    fn inverse_mut(&mut self);
+    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>
+    where DefaultAllocator: Allocator<N, D>;
+    fn transform_point(&self, p: &Point<N, D>) -> Point<N, D>
+    where DefaultAllocator: Allocator<N, D>;
+    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>
+    where DefaultAllocator: Allocator<N, D>;
+    fn inverse_transform_point(&self, p: &Point<N, D>) -> Point<N, D>
+    where DefaultAllocator: Allocator<N, D>;
+}
+
+impl<N: RealField, D: DimName> AbstractRotation<N, D> for Rotation<N, D>
+where DefaultAllocator: Allocator<N, D, D>
+{
+    #[inline]
+    fn identity() -> Self {
+        Self::identity()
+    }
+
+    #[inline]
+    fn inverse(&self) -> Self {
+        self.inverse()
+    }
+
+    #[inline]
+    fn inverse_mut(&mut self) {
+        self.inverse_mut()
+    }
+
+    #[inline]
+    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>
+    where DefaultAllocator: Allocator<N, D> {
+        self * v
+    }
+
+    #[inline]
+    fn transform_point(&self, p: &Point<N, D>) -> Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
+        self * p
+    }
+
+    #[inline]
+    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>
+    where DefaultAllocator: Allocator<N, D> {
+        self.inverse_transform_vector(v)
+    }
+
+    #[inline]
+    fn inverse_transform_point(&self, p: &Point<N, D>) -> Point<N, D>
+    where DefaultAllocator: Allocator<N, D> {
+        self.inverse_transform_point(p)
+    }
+}
+
+impl<N: RealField> AbstractRotation<N, U3> for UnitQuaternion<N> {
+    #[inline]
+    fn identity() -> Self {
+        Self::identity()
+    }
+
+    #[inline]
+    fn inverse(&self) -> Self {
+        self.inverse()
+    }
+
+    #[inline]
+    fn inverse_mut(&mut self) {
+        self.inverse_mut()
+    }
+
+    #[inline]
+    fn transform_vector(&self, v: &VectorN<N, U3>) -> VectorN<N, U3> {
+        self * v
+    }
+
+    #[inline]
+    fn transform_point(&self, p: &Point<N, U3>) -> Point<N, U3> {
+        self * p
+    }
+
+    #[inline]
+    fn inverse_transform_vector(&self, v: &VectorN<N, U3>) -> VectorN<N, U3> {
+        self.inverse_transform_vector(v)
+    }
+
+    #[inline]
+    fn inverse_transform_point(&self, p: &Point<N, U3>) -> Point<N, U3> {
+        self.inverse_transform_point(p)
+    }
+}
+
+impl<N: RealField> AbstractRotation<N, U2> for UnitComplex<N> {
+    #[inline]
+    fn identity() -> Self {
+        Self::identity()
+    }
+
+    #[inline]
+    fn inverse(&self) -> Self {
+        self.inverse()
+    }
+
+    #[inline]
+    fn inverse_mut(&mut self) {
+        self.inverse_mut()
+    }
+
+    #[inline]
+    fn transform_vector(&self, v: &VectorN<N, U2>) -> VectorN<N, U2> {
+        self * v
+    }
+
+    #[inline]
+    fn transform_point(&self, p: &Point<N, U2>) -> Point<N, U2> {
+        self * p
+    }
+
+    #[inline]
+    fn inverse_transform_vector(&self, v: &VectorN<N, U2>) -> VectorN<N, U2> {
+        self.inverse_transform_vector(v)
+    }
+
+    #[inline]
+    fn inverse_transform_point(&self, p: &Point<N, U2>) -> Point<N, U2> {
+        self.inverse_transform_point(p)
+    }
+}

src/geometry/isometry.rs

@@ -11,14 +11,13 @@ use serde::{Deserialize, Serialize};
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use alga::general::{RealField, SubsetOf};
+use simba::scalar::{RealField, SubsetOf};
-use alga::linear::Rotation;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
 use crate::base::storage::Owned;
 use crate::base::{DefaultAllocator, MatrixN, VectorN};
-use crate::geometry::{Point, Translation};
+use crate::geometry::{AbstractRotation, Point, Translation};
 
 /// A direct isometry, i.e., a rotation followed by a translation, aka. a rigid-body motion, aka. an element of a Special Euclidean (SE) group.
 #[repr(C)]
@@ -77,7 +76,8 @@ where
     }
 }
 
-impl<N: RealField + hash::Hash, D: DimName + hash::Hash, R: hash::Hash> hash::Hash for Isometry<N, D, R>
+impl<N: RealField + hash::Hash, D: DimName + hash::Hash, R: hash::Hash> hash::Hash
+    for Isometry<N, D, R>
 where
     DefaultAllocator: Allocator<N, D>,
     Owned<N, D>: hash::Hash,
@@ -88,14 +88,14 @@ where
     }
 }
 
-impl<N: RealField, D: DimName + Copy, R: Rotation<Point<N, D>> + Copy> Copy for Isometry<N, D, R>
+impl<N: RealField, D: DimName + Copy, R: AbstractRotation<N, D> + Copy> Copy for Isometry<N, D, R>
 where
     DefaultAllocator: Allocator<N, D>,
     Owned<N, D>: Copy,
 {
 }
 
-impl<N: RealField, D: DimName, R: Rotation<Point<N, D>> + Clone> Clone for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R: AbstractRotation<N, D> + Clone> Clone for Isometry<N, D, R>
 where DefaultAllocator: Allocator<N, D>
 {
     #[inline]
@@ -104,7 +104,7 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: RealField, D: DimName, R: Rotation<Point<N, D>>> Isometry<N, D, R>
+impl<N: RealField, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
 where DefaultAllocator: Allocator<N, D>
 {
     /// Creates a new isometry from its rotational and translational parts.
@@ -167,7 +167,7 @@ where DefaultAllocator: Allocator<N, D>
     /// ```
     #[inline]
     pub fn inverse_mut(&mut self) {
-        self.rotation.two_sided_inverse_mut();
+        self.rotation.inverse_mut();
         self.translation.inverse_mut();
         self.translation.vector = self.rotation.transform_vector(&self.translation.vector);
     }
@@ -208,7 +208,7 @@ where DefaultAllocator: Allocator<N, D>
     /// ```
     #[inline]
     pub fn append_rotation_mut(&mut self, r: &R) {
-        self.rotation = self.rotation.append_rotation(&r);
+        self.rotation = r.clone() * self.rotation.clone();
         self.translation.vector = r.transform_vector(&self.translation.vector);
     }
 
@@ -253,7 +253,7 @@ where DefaultAllocator: Allocator<N, D>
     /// ```
     #[inline]
     pub fn append_rotation_wrt_center_mut(&mut self, r: &R) {
-        self.rotation = self.rotation.append_rotation(r);
+        self.rotation = r.clone() * self.rotation.clone();
     }
 
     /// Transform the given point by this isometry.
@@ -387,14 +387,14 @@ where DefaultAllocator: Allocator<N, D>
 
 impl<N: RealField, D: DimName, R> Eq for Isometry<N, D, R>
 where
-    R: Rotation<Point<N, D>> + Eq,
+    R: AbstractRotation<N, D> + Eq,
     DefaultAllocator: Allocator<N, D>,
 {
 }
 
 impl<N: RealField, D: DimName, R> PartialEq for Isometry<N, D, R>
 where
-    R: Rotation<Point<N, D>> + PartialEq,
+    R: AbstractRotation<N, D> + PartialEq,
     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
@@ -405,7 +405,7 @@ where
 
 impl<N: RealField, D: DimName, R> AbsDiffEq for Isometry<N, D, R>
 where
-    R: Rotation<Point<N, D>> + AbsDiffEq<Epsilon = N::Epsilon>,
+    R: AbstractRotation<N, D> + AbsDiffEq<Epsilon = N::Epsilon>,
     DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
@@ -425,7 +425,7 @@ where
 
 impl<N: RealField, D: DimName, R> RelativeEq for Isometry<N, D, R>
 where
-    R: Rotation<Point<N, D>> + RelativeEq<Epsilon = N::Epsilon>,
+    R: AbstractRotation<N, D> + RelativeEq<Epsilon = N::Epsilon>,
     DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
@@ -452,7 +452,7 @@ where
 
 impl<N: RealField, D: DimName, R> UlpsEq for Isometry<N, D, R>
 where
-    R: Rotation<Point<N, D>> + UlpsEq<Epsilon = N::Epsilon>,
+    R: AbstractRotation<N, D> + UlpsEq<Epsilon = N::Epsilon>,
     DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {

src/geometry/isometry_alga.rs

@@ -1,203 +0,0 @@
-use alga::general::{
-    AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, RealField,
-};
-use alga::linear::Isometry as AlgaIsometry;
-use alga::linear::{
-    AffineTransformation, DirectIsometry, ProjectiveTransformation, Rotation, Similarity,
-    Transformation,
-};
-
-use crate::base::allocator::Allocator;
-use crate::base::dimension::DimName;
-use crate::base::{DefaultAllocator, VectorN};
-
-use crate::geometry::{Isometry, Point, Translation};
-
-/*
- *
- * Algebraic structures.
- *
- */
-impl<N: RealField, D: DimName, R> Identity<Multiplicative> for Isometry<N, D, R>
-where
-    R: Rotation<Point<N, D>>,
-    DefaultAllocator: Allocator<N, D>,
-{
-    #[inline]
-    fn identity() -> Self {
-        Self::identity()
-    }
-}
-
-impl<N: RealField, D: DimName, R> TwoSidedInverse<Multiplicative> for Isometry<N, D, R>
-where
-    R: Rotation<Point<N, D>>,
-    DefaultAllocator: Allocator<N, D>,
-{
-    #[inline]
-    #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
-    fn two_sided_inverse(&self) -> Self {
-        self.inverse()
-    }
-
-    #[inline]
-    fn two_sided_inverse_mut(&mut self) {
-        self.inverse_mut()
-    }
-}
-
-impl<N: RealField, D: DimName, R> AbstractMagma<Multiplicative> for Isometry<N, D, R>
-where
-    R: Rotation<Point<N, D>>,
-    DefaultAllocator: Allocator<N, D>,
-{
-    #[inline]
-    fn operate(&self, rhs: &Self) -> Self {
-        self * rhs
-    }
-}
-
-macro_rules! impl_multiplicative_structures(
-    ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: RealField, D: DimName, R> $marker<$operator> for Isometry<N, D, R>
-            where R: Rotation<Point<N, D>>,
-                  DefaultAllocator: Allocator<N, D> { }
-    )*}
-);
-
-impl_multiplicative_structures!(
-    AbstractSemigroup<Multiplicative>,
-    AbstractMonoid<Multiplicative>,
-    AbstractQuasigroup<Multiplicative>,
-    AbstractLoop<Multiplicative>,
-    AbstractGroup<Multiplicative>
-);
-
-/*
- *
- * Transformation groups.
- *
- */
-impl<N: RealField, D: DimName, R> Transformation<Point<N, D>> for Isometry<N, D, R>
-where
-    R: Rotation<Point<N, D>>,
-    DefaultAllocator: Allocator<N, D>,
-{
-    #[inline]
-    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
-        self.transform_point(pt)
-    }
-
-    #[inline]
-    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
-        self.transform_vector(v)
-    }
-}
-
-impl<N: RealField, D: DimName, R> ProjectiveTransformation<Point<N, D>> for Isometry<N, D, R>
-where
-    R: Rotation<Point<N, D>>,
-    DefaultAllocator: Allocator<N, D>,
-{
-    #[inline]
-    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
-        self.inverse_transform_point(pt)
-    }
-
-    #[inline]
-    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
-        self.inverse_transform_vector(v)
-    }
-}
-
-impl<N: RealField, D: DimName, R> AffineTransformation<Point<N, D>> for Isometry<N, D, R>
-where
-    R: Rotation<Point<N, D>>,
-    DefaultAllocator: Allocator<N, D>,
-{
-    type Rotation = R;
-    type NonUniformScaling = Id;
-    type Translation = Translation<N, D>;
-
-    #[inline]
-    fn decompose(&self) -> (Self::Translation, R, Id, R) {
-        (
-            self.translation.clone(),
-            self.rotation.clone(),
-            Id::new(),
-            R::identity(),
-        )
-    }
-
-    #[inline]
-    fn append_translation(&self, t: &Self::Translation) -> Self {
-        t * self
-    }
-
-    #[inline]
-    fn prepend_translation(&self, t: &Self::Translation) -> Self {
-        self * t
-    }
-
-    #[inline]
-    fn append_rotation(&self, r: &Self::Rotation) -> Self {
-        let shift = r.transform_vector(&self.translation.vector);
-        Isometry::from_parts(Translation::from(shift), r.clone() * self.rotation.clone())
-    }
-
-    #[inline]
-    fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
-        self * r
-    }
-
-    #[inline]
-    fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &Point<N, D>) -> Option<Self> {
-        let mut res = self.clone();
-        res.append_rotation_wrt_point_mut(r, p);
-        Some(res)
-    }
-}
-
-impl<N: RealField, D: DimName, R> Similarity<Point<N, D>> for Isometry<N, D, R>
-where
-    R: Rotation<Point<N, D>>,
-    DefaultAllocator: Allocator<N, D>,
-{
-    type Scaling = Id;
-
-    #[inline]
-    fn translation(&self) -> Translation<N, D> {
-        self.translation.clone()
-    }
-
-    #[inline]
-    fn rotation(&self) -> R {
-        self.rotation.clone()
-    }
-
-    #[inline]
-    fn scaling(&self) -> Id {
-        Id::new()
-    }
-}
-
-macro_rules! marker_impl(
-    ($($Trait: ident),*) => {$(
-        impl<N: RealField, D: DimName, R> $Trait<Point<N, D>> for Isometry<N, D, R>
-        where R: Rotation<Point<N, D>>,
-              DefaultAllocator: Allocator<N, D> { }
-    )*}
-);
-
-marker_impl!(AlgaIsometry, DirectIsometry);

src/geometry/isometry_construction.rs

@@ -7,19 +7,18 @@ use num::One;
 use rand::distributions::{Distribution, Standard};
 use rand::Rng;
 
-use alga::general::RealField;
+use simba::scalar::RealField;
-use alga::linear::Rotation as AlgaRotation;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, U2, U3};
 use crate::base::{DefaultAllocator, Vector2, Vector3};
 
 use crate::geometry::{
-    Isometry, Point, Point3, Rotation, Rotation2, Rotation3, Translation, UnitComplex,
+    AbstractRotation, Isometry, Point, Point3, Rotation, Rotation2, Rotation3, Translation,
-    UnitQuaternion, Translation2, Translation3
+    Translation2, Translation3, UnitComplex, UnitQuaternion,
 };
 
-impl<N: RealField, D: DimName, R: AlgaRotation<Point<N, D>>> Isometry<N, D, R>
+impl<N: RealField, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
 where DefaultAllocator: Allocator<N, D>
 {
     /// Creates a new identity isometry.
@@ -65,7 +64,7 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: RealField, D: DimName, R: AlgaRotation<Point<N, D>>> One for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R: AbstractRotation<N, D>> One for Isometry<N, D, R>
 where DefaultAllocator: Allocator<N, D>
 {
     /// Creates a new identity isometry.
@@ -77,7 +76,7 @@ where DefaultAllocator: Allocator<N, D>
 
 impl<N: RealField, D: DimName, R> Distribution<Isometry<N, D, R>> for Standard
 where
-    R: AlgaRotation<Point<N, D>>,
+    R: AbstractRotation<N, D>,
     Standard: Distribution<N> + Distribution<R>,
     DefaultAllocator: Allocator<N, D>,
 {
@@ -91,7 +90,7 @@ where
 impl<N, D: DimName, R> Arbitrary for Isometry<N, D, R>
 where
     N: RealField + Arbitrary + Send,
-    R: AlgaRotation<Point<N, D>> + Arbitrary + Send,
+    R: AbstractRotation<N, D> + Arbitrary + Send,
     Owned<N, D>: Send,
     DefaultAllocator: Allocator<N, D>,
 {

src/geometry/isometry_conversion.rs

@@ -1,11 +1,12 @@
-use alga::general::{RealField, SubsetOf, SupersetOf};
+use simba::scalar::{RealField, SubsetOf, SupersetOf};
-use alga::linear::Rotation;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimMin, DimName, DimNameAdd, DimNameSum, U1};
 use crate::base::{DefaultAllocator, MatrixN};
 
-use crate::geometry::{Isometry, Point, Similarity, SuperTCategoryOf, TAffine, Transform, Translation};
+use crate::geometry::{
+    AbstractRotation, Isometry, Similarity, SuperTCategoryOf, TAffine, Transform, Translation,
+};
 
 /*
  * This file provides the following conversions:
@@ -21,8 +22,8 @@ impl<N1, N2, D: DimName, R1, R2> SubsetOf<Isometry<N2, D, R2>> for Isometry<N1,
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R1: Rotation<Point<N1, D>> + SubsetOf<R2>,
+    R1: AbstractRotation<N1, D> + SubsetOf<R2>,
-    R2: Rotation<Point<N2, D>>,
+    R2: AbstractRotation<N2, D>,
     DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
@@ -37,7 +38,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(iso: &Isometry<N2, D, R2>) -> Self {
+    fn from_superset_unchecked(iso: &Isometry<N2, D, R2>) -> Self {
         Isometry::from_parts(
             iso.translation.to_subset_unchecked(),
             iso.rotation.to_subset_unchecked(),
@@ -49,8 +50,8 @@ impl<N1, N2, D: DimName, R1, R2> SubsetOf<Similarity<N2, D, R2>> for Isometry<N1
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R1: Rotation<Point<N1, D>> + SubsetOf<R2>,
+    R1: AbstractRotation<N1, D> + SubsetOf<R2>,
-    R2: Rotation<Point<N2, D>>,
+    R2: AbstractRotation<N2, D>,
     DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
@@ -64,7 +65,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(sim: &Similarity<N2, D, R2>) -> Self {
+    fn from_superset_unchecked(sim: &Similarity<N2, D, R2>) -> Self {
         crate::convert_ref_unchecked(&sim.isometry)
     }
 }
@@ -74,7 +75,7 @@ where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     C: SuperTCategoryOf<TAffine>,
-    R: Rotation<Point<N1, D>>
+    R: AbstractRotation<N1, D>
         + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>>
         + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
     D: DimNameAdd<U1> + DimMin<D, Output = D>, // needed by .is_special_orthogonal()
@@ -98,7 +99,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
+    fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
@@ -107,7 +108,7 @@ impl<N1, N2, D, R> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Isometry<N1, D,
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R: Rotation<Point<N1, D>>
+    R: AbstractRotation<N1, D>
         + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>>
         + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
     D: DimNameAdd<U1> + DimMin<D, Output = D>, // needed by .is_special_orthogonal()
@@ -139,7 +140,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
+    fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
         let t = m.fixed_slice::<D, U1>(0, D::dim()).into_owned();
         let t = Translation {
             vector: crate::convert_unchecked(t),

src/geometry/isometry_ops.rs

@@ -1,13 +1,14 @@
+use num::{One, Zero};
 use std::ops::{Div, DivAssign, Mul, MulAssign};
 
-use alga::general::RealField;
+use simba::scalar::{ClosedAdd, ClosedMul, RealField};
-use alga::linear::Rotation as AlgaRotation;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, U1, U3, U4};
 use crate::base::{DefaultAllocator, Unit, VectorN};
+use crate::Scalar;
 
-use crate::geometry::{Isometry, Point, Rotation, Translation, UnitQuaternion};
+use crate::geometry::{AbstractRotation, Isometry, Point, Rotation, Translation, UnitQuaternion};
 
 // FIXME: there are several cloning of rotations that we could probably get rid of (but we didn't
 // yet because that would require to add a bound like `where for<'a, 'b> &'a R: Mul<&'b R, Output = R>`
@@ -65,7 +66,7 @@ macro_rules! isometry_binop_impl(
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      $action: expr; $($lives: tt),*) => {
         impl<$($lives ,)* N: RealField, D: DimName, R> $Op<$Rhs> for $Lhs
-            where R: AlgaRotation<Point<N, D>>,
+            where R: AbstractRotation<N, D>,
                   DefaultAllocator: Allocator<N, D> {
             type Output = $Output;
 
@@ -112,7 +113,7 @@ macro_rules! isometry_binop_assign_impl_all(
      [val] => $action_val: expr;
      [ref] => $action_ref: expr;) => {
         impl<N: RealField, D: DimName, R> $OpAssign<$Rhs> for $Lhs
-            where R: AlgaRotation<Point<N, D>>,
+            where R: AbstractRotation<N, D>,
                   DefaultAllocator: Allocator<N, D> {
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: $Rhs) {
@@ -121,7 +122,7 @@ macro_rules! isometry_binop_assign_impl_all(
         }
 
         impl<'b, N: RealField, D: DimName, R> $OpAssign<&'b $Rhs> for $Lhs
-            where R: AlgaRotation<Point<N, D>>,
+            where R: AbstractRotation<N, D>,
                   DefaultAllocator: Allocator<N, D> {
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: &'b $Rhs) {
@@ -189,39 +190,38 @@ isometry_binop_assign_impl_all!(
 
 // Isometry ×= R
 // Isometry ÷= R
-isometry_binop_assign_impl_all!(
+md_assign_impl_all!(
-    MulAssign, mul_assign;
+    MulAssign, mul_assign where N: RealField;
-    self: Isometry<N, D, R>, rhs: R;
+    (D, U1), (D, D) for D: DimName;
+    self: Isometry<N, D, Rotation<N, D>>, rhs: Rotation<N, D>;
     [val] => self.rotation *= rhs;
     [ref] => self.rotation *= rhs.clone();
 );
 
-isometry_binop_assign_impl_all!(
+md_assign_impl_all!(
-    DivAssign, div_assign;
+    DivAssign, div_assign where N: RealField;
-    self: Isometry<N, D, R>, rhs: R;
+    (D, U1), (D, D) for D: DimName;
+    self: Isometry<N, D, Rotation<N, D>>, rhs: Rotation<N, D>;
     // FIXME: don't invert explicitly?
-    [val] => *self *= rhs.two_sided_inverse();
+    [val] => *self *= rhs.inverse();
-    [ref] => *self *= rhs.two_sided_inverse();
+    [ref] => *self *= rhs.inverse();
 );
 
-// Isometry × R
+md_assign_impl_all!(
-// Isometry ÷ R
+    MulAssign, mul_assign where N: RealField;
-isometry_binop_impl_all!(
+    (U3, U3), (U3, U3) for;
-    Mul, mul;
+    self: Isometry<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>;
-    self: Isometry<N, D, R>, rhs: R, Output = Isometry<N, D, R>;
+    [val] => self.rotation *= rhs;
-    [val val] => Isometry::from_parts(self.translation, self.rotation * rhs);
+    [ref] => self.rotation *= rhs.clone();
-    [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() * rhs); // FIXME: do not clone.
-    [val ref] => Isometry::from_parts(self.translation, self.rotation * rhs.clone());
-    [ref ref] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() * rhs.clone());
 );
 
-isometry_binop_impl_all!(
+md_assign_impl_all!(
-    Div, div;
+    DivAssign, div_assign where N: RealField;
-    self: Isometry<N, D, R>, rhs: R, Output = Isometry<N, D, R>;
+    (U3, U3), (U3, U3) for;
-    [val val] => Isometry::from_parts(self.translation, self.rotation / rhs);
+    self: Isometry<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>;
-    [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() / rhs);
+    // FIXME: don't invert explicitly?
-    [val ref] => Isometry::from_parts(self.translation, self.rotation / rhs.clone());
+    [val] => *self *= rhs.inverse();
-    [ref ref] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() / rhs.clone());
+    [ref] => *self *= rhs.inverse();
 );
 
 // Isometry × Point
@@ -357,6 +357,18 @@ isometry_from_composition_impl_all!(
     [ref ref] => Isometry::from_parts(Translation::from( self * &right.vector), self.clone());
 );
 
+// Isometry × Rotation
+isometry_from_composition_impl_all!(
+    Mul, mul;
+    (D, D), (D, U1) for D: DimName;
+    self: Isometry<N, D, Rotation<N, D>>, rhs: Rotation<N, D>,
+    Output = Isometry<N, D, Rotation<N, D>>;
+    [val val] => Isometry::from_parts(self.translation, self.rotation * rhs);
+    [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() * rhs); // FIXME: do not clone.
+    [val ref] => Isometry::from_parts(self.translation, self.rotation * rhs.clone());
+    [ref ref] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() * rhs.clone());
+);
+
 // Rotation × Isometry
 isometry_from_composition_impl_all!(
     Mul, mul;
@@ -372,6 +384,18 @@ isometry_from_composition_impl_all!(
     };
 );
 
+// Isometry ÷ Rotation
+isometry_from_composition_impl_all!(
+    Div, div;
+    (D, D), (D, U1) for D: DimName;
+    self: Isometry<N, D, Rotation<N, D>>, rhs: Rotation<N, D>,
+    Output = Isometry<N, D, Rotation<N, D>>;
+    [val val] => Isometry::from_parts(self.translation, self.rotation / rhs);
+    [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() / rhs); // FIXME: do not clone.
+    [val ref] => Isometry::from_parts(self.translation, self.rotation / rhs.clone());
+    [ref ref] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() / rhs.clone());
+);
+
 // Rotation ÷ Isometry
 isometry_from_composition_impl_all!(
     Div, div;
@@ -385,6 +409,18 @@ isometry_from_composition_impl_all!(
     [ref ref] => self * right.inverse();
 );
 
+// Isometry × UnitQuaternion
+isometry_from_composition_impl_all!(
+    Mul, mul;
+    (U4, U1), (U3, U1);
+    self: Isometry<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>,
+    Output = Isometry<N, U3, UnitQuaternion<N>>;
+    [val val] => Isometry::from_parts(self.translation, self.rotation * rhs);
+    [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() * rhs); // FIXME: do not clone.
+    [val ref] => Isometry::from_parts(self.translation, self.rotation * rhs.clone());
+    [ref ref] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() * rhs.clone());
+);
+
 // UnitQuaternion × Isometry
 isometry_from_composition_impl_all!(
     Mul, mul;
@@ -400,6 +436,18 @@ isometry_from_composition_impl_all!(
     };
 );
 
+// Isometry ÷ UnitQuaternion
+isometry_from_composition_impl_all!(
+    Div, div;
+    (U4, U1), (U3, U1);
+    self: Isometry<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>,
+    Output = Isometry<N, U3, UnitQuaternion<N>>;
+    [val val] => Isometry::from_parts(self.translation, self.rotation / rhs);
+    [ref val] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() / rhs); // FIXME: do not clone.
+    [val ref] => Isometry::from_parts(self.translation, self.rotation / rhs.clone());
+    [ref ref] => Isometry::from_parts(self.translation.clone(), self.rotation.clone() / rhs.clone());
+);
+
 // UnitQuaternion ÷ Isometry
 isometry_from_composition_impl_all!(
     Div, div;

src/geometry/isometry_simba.rs

@@ -0,0 +1,62 @@
+use simba::simd::SimdValue;
+
+use crate::base::allocator::Allocator;
+use crate::base::dimension::DimName;
+use crate::base::{DefaultAllocator, Scalar};
+use crate::RealField;
+
+use crate::geometry::{AbstractRotation, Isometry, Translation};
+
+impl<N: RealField, D: DimName, R> SimdValue for Isometry<N, D, R>
+where
+    N::Element: Scalar,
+    R: SimdValue<SimdBool = N::SimdBool> + AbstractRotation<N, D>,
+    R::Element: AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    type Element = Isometry<N::Element, D, R::Element>;
+    type SimdBool = N::SimdBool;
+
+    #[inline]
+    fn lanes() -> usize {
+        N::lanes()
+    }
+
+    #[inline]
+    fn splat(val: Self::Element) -> Self {
+        Isometry::from_parts(Translation::splat(val.translation), R::splat(val.rotation))
+    }
+
+    #[inline]
+    fn extract(&self, i: usize) -> Self::Element {
+        Isometry::from_parts(self.translation.extract(i), self.rotation.extract(i))
+    }
+
+    #[inline]
+    unsafe fn extract_unchecked(&self, i: usize) -> Self::Element {
+        Isometry::from_parts(
+            self.translation.extract_unchecked(i),
+            self.rotation.extract_unchecked(i),
+        )
+    }
+
+    #[inline]
+    fn replace(&mut self, i: usize, val: Self::Element) {
+        self.translation.replace(i, val.translation);
+        self.rotation.replace(i, val.rotation);
+    }
+
+    #[inline]
+    unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element) {
+        self.translation.replace_unchecked(i, val.translation);
+        self.rotation.replace_unchecked(i, val.rotation);
+    }
+
+    #[inline]
+    fn select(self, cond: Self::SimdBool, other: Self) -> Self {
+        Isometry::from_parts(
+            self.translation.select(cond, other.translation),
+            self.rotation.select(cond, other.rotation),
+        )
+    }
+}

src/geometry/mod.rs

@@ -3,34 +3,36 @@
 
 mod op_macros;
 
+mod abstract_rotation;
+
 mod point;
-mod point_alga;
 mod point_alias;
 mod point_construction;
 mod point_conversion;
 mod point_coordinates;
 mod point_ops;
+mod point_simba;
 
 mod rotation;
-mod rotation_alga; // FIXME: implement Rotation methods.
 mod rotation_alias;
 mod rotation_construction;
 mod rotation_conversion;
 mod rotation_ops;
+mod rotation_simba; // FIXME: implement Rotation methods.
 mod rotation_specialization;
 
 mod quaternion;
-mod quaternion_alga;
 mod quaternion_construction;
 mod quaternion_conversion;
 mod quaternion_coordinates;
 mod quaternion_ops;
+mod quaternion_simba;
 
 mod unit_complex;
-mod unit_complex_alga;
 mod unit_complex_construction;
 mod unit_complex_conversion;
 mod unit_complex_ops;
+mod unit_complex_simba;
 
 mod translation;
 mod translation_alga;
@@ -41,33 +43,35 @@ mod translation_coordinates;
 mod translation_ops;
 
 mod isometry;
-mod isometry_alga;
 mod isometry_alias;
 mod isometry_construction;
 mod isometry_conversion;
 mod isometry_ops;
+mod isometry_simba;
 
 mod similarity;
-mod similarity_alga;
 mod similarity_alias;
 mod similarity_construction;
 mod similarity_conversion;
 mod similarity_ops;
+mod similarity_simba;
 
 mod swizzle;
 
 mod transform;
-mod transform_alga;
 mod transform_alias;
 mod transform_construction;
 mod transform_conversion;
 mod transform_ops;
+mod transform_simba;
 
 mod reflection;
 
 mod orthographic;
 mod perspective;
 
+pub use self::abstract_rotation::AbstractRotation;
+
 pub use self::point::*;
 pub use self::point_alias::*;
 

src/geometry/op_macros.rs

@@ -1,6 +1,5 @@
 #![macro_use]
 
-
 // FIXME: merge with `md_impl`.
 /// Macro for the implementation of multiplication and division.
 macro_rules! md_impl(
@@ -88,7 +87,7 @@ macro_rules! md_assign_impl(
      // Operator, operator method, and scalar bounds.
      $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)*;
      // Storage dimensions, and dimension bounds.
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),+
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),*
      // [Optional] Extra allocator bounds.
      $(where $ConstraintType: ty: $ConstraintBound: ident $(<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*>)* )*;
      // Argument identifiers and types.
@@ -116,7 +115,7 @@ macro_rules! md_assign_impl_all(
      // Operator, operator method, and scalar bounds.
      $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)*;
      // Storage dimensions, and dimension bounds.
-     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),+
+     ($R1: ty, $C1: ty),($R2: ty, $C2: ty) for $($Dims: ident: $DimsBound: ident $(<$($BoundParam: ty),*>)*),*
      // [Optional] Extra allocator bounds.
      $(where $ConstraintType: ty: $ConstraintBound: ident$(<$($ConstraintBoundParams: ty $( = $EqBound: ty )*),*>)* )*;
      // Argument identifiers and types.
@@ -126,14 +125,14 @@ macro_rules! md_assign_impl_all(
      [ref] => $action_ref: expr;) => {
         md_assign_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
+            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),*
             $(where $ConstraintType: $ConstraintBound $(<$($ConstraintBoundParams $( = $EqBound )*),*>)*)*;
             $lhs: $Lhs, $rhs: $Rhs;
             $action_val; );
 
         md_assign_impl!(
             $Op, $op $(where N: $($ScalarBounds),*)*;
-            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),+
+            ($R1, $C1),($R2, $C2) for $($Dims: $DimsBound $(<$($BoundParam),*>)*),*
             $(where $ConstraintType: $ConstraintBound $(<$($ConstraintBoundParams $( = $EqBound )*),*>)*)*;
             $lhs: $Lhs, $rhs: &'b $Rhs;
             $action_ref; 'b);

src/geometry/orthographic.rs

@@ -7,7 +7,7 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 use std::fmt;
 use std::mem;
 
-use alga::general::RealField;
+use simba::scalar::RealField;
 
 use crate::base::dimension::U3;
 use crate::base::helper;

src/geometry/perspective.rs

@@ -8,7 +8,7 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 use std::fmt;
 use std::mem;
 
-use alga::general::RealField;
+use simba::scalar::RealField;
 
 use crate::base::dimension::U3;
 use crate::base::helper;
@@ -170,7 +170,8 @@ impl<N: RealField> Perspective3<N> {
     pub fn znear(&self) -> N {
         let ratio = (-self.matrix[(2, 2)] + N::one()) / (-self.matrix[(2, 2)] - N::one());
 
-        self.matrix[(2, 3)] / (ratio * crate::convert(2.0)) - self.matrix[(2, 3)] / crate::convert(2.0)
+        self.matrix[(2, 3)] / (ratio * crate::convert(2.0))
+            - self.matrix[(2, 3)] / crate::convert(2.0)
     }
 
     /// Gets the far plane offset of the view frustum.

src/geometry/point_alga.rs

@@ -1,83 +0,0 @@
-use alga::general::{Field, JoinSemilattice, Lattice, MeetSemilattice, RealField};
-use alga::linear::{AffineSpace, EuclideanSpace};
-
-use crate::base::allocator::Allocator;
-use crate::base::dimension::DimName;
-use crate::base::{DefaultAllocator, Scalar, VectorN};
-
-use crate::geometry::Point;
-
-impl<N: Scalar + Field, D: DimName> AffineSpace for Point<N, D>
-where
-    N: Scalar + Field,
-    DefaultAllocator: Allocator<N, D>,
-{
-    type Translation = VectorN<N, D>;
-}
-
-impl<N: RealField, D: DimName> EuclideanSpace for Point<N, D>
-where DefaultAllocator: Allocator<N, D>
-{
-    type Coordinates = VectorN<N, D>;
-    type RealField = N;
-
-    #[inline]
-    fn origin() -> Self {
-        Self::origin()
-    }
-
-    #[inline]
-    fn coordinates(&self) -> Self::Coordinates {
-        self.coords.clone()
-    }
-
-    #[inline]
-    fn from_coordinates(coords: Self::Coordinates) -> Self {
-        Self::from(coords)
-    }
-
-    #[inline]
-    fn scale_by(&self, n: N) -> Self {
-        self * n
-    }
-}
-
-/*
- *
- * Ordering
- *
- */
-impl<N, D: DimName> MeetSemilattice for Point<N, D>
-where
-    N: Scalar + MeetSemilattice,
-    DefaultAllocator: Allocator<N, D>,
-{
-    #[inline]
-    fn meet(&self, other: &Self) -> Self {
-        Self::from(self.coords.meet(&other.coords))
-    }
-}
-
-impl<N, D: DimName> JoinSemilattice for Point<N, D>
-where
-    N: Scalar + JoinSemilattice,
-    DefaultAllocator: Allocator<N, D>,
-{
-    #[inline]
-    fn join(&self, other: &Self) -> Self {
-        Self::from(self.coords.join(&other.coords))
-    }
-}
-
-impl<N, D: DimName> Lattice for Point<N, D>
-where
-    N: Scalar + Lattice,
-    DefaultAllocator: Allocator<N, D>,
-{
-    #[inline]
-    fn meet_join(&self, other: &Self) -> (Self, Self) {
-        let (meet, join) = self.coords.meet_join(&other.coords);
-
-        (Self::from(meet), Self::from(join))
-    }
-}

src/geometry/point_construction.rs

@@ -5,10 +5,10 @@ use num::{Bounded, One, Zero};
 use rand::distributions::{Distribution, Standard};
 use rand::Rng;
 
-use alga::general::ClosedDiv;
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1, U2, U3, U4, U5, U6};
 use crate::base::{DefaultAllocator, Scalar, VectorN};
+use simba::scalar::ClosedDiv;
 
 use crate::geometry::Point;
 

src/geometry/point_conversion.rs

@@ -1,5 +1,5 @@
-use alga::general::{ClosedDiv, SubsetOf, SupersetOf};
 use num::{One, Zero};
+use simba::scalar::{ClosedDiv, SubsetOf, SupersetOf};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
@@ -44,7 +44,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &Point<N2, D>) -> Self {
+    fn from_superset_unchecked(m: &Point<N2, D>) -> Self {
         Self::from(Matrix::from_superset_unchecked(&m.coords))
     }
 }
@@ -71,10 +71,10 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(v: &VectorN<N2, DimNameSum<D, U1>>) -> Self {
+    fn from_superset_unchecked(v: &VectorN<N2, DimNameSum<D, U1>>) -> Self {
         let coords = v.fixed_slice::<D, U1>(0, 0) / v[D::dim()].inlined_clone();
         Self {
-            coords: crate::convert_unchecked(coords)
+            coords: crate::convert_unchecked(coords),
         }
     }
 }
@@ -142,13 +142,10 @@ where
 }
 
 impl<N: Scalar, D: DimName> From<VectorN<N, D>> for Point<N, D>
-    where
+where DefaultAllocator: Allocator<N, D>
-        DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn from(coords: VectorN<N, D>) -> Self {
-        Point {
+        Point { coords }
-            coords
-        }
     }
 }

src/geometry/point_ops.rs

@@ -3,10 +3,12 @@ use std::ops::{
     Add, AddAssign, Div, DivAssign, Index, IndexMut, Mul, MulAssign, Neg, Sub, SubAssign,
 };
 
-use alga::general::{ClosedAdd, ClosedDiv, ClosedMul, ClosedNeg, ClosedSub};
+use simba::scalar::{ClosedAdd, ClosedDiv, ClosedMul, ClosedNeg, ClosedSub};
 
 use crate::base::allocator::{Allocator, SameShapeAllocator};
-use crate::base::constraint::{AreMultipliable, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
+use crate::base::constraint::{
+    AreMultipliable, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint,
+};
 use crate::base::dimension::{Dim, DimName, U1};
 use crate::base::storage::Storage;
 use crate::base::{DefaultAllocator, Matrix, Scalar, Vector, VectorSum};

src/geometry/point_simba.rs

@@ -0,0 +1,51 @@
+use simba::simd::SimdValue;
+
+use crate::base::allocator::Allocator;
+use crate::base::dimension::DimName;
+use crate::base::{DefaultAllocator, Scalar, VectorN};
+
+use crate::geometry::Point;
+
+impl<N: Scalar + SimdValue, D: DimName> SimdValue for Point<N, D>
+where
+    N::Element: Scalar,
+    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+{
+    type Element = Point<N::Element, D>;
+    type SimdBool = N::SimdBool;
+
+    #[inline]
+    fn lanes() -> usize {
+        N::lanes()
+    }
+
+    #[inline]
+    fn splat(val: Self::Element) -> Self {
+        VectorN::splat(val.coords).into()
+    }
+
+    #[inline]
+    fn extract(&self, i: usize) -> Self::Element {
+        self.coords.extract(i).into()
+    }
+
+    #[inline]
+    unsafe fn extract_unchecked(&self, i: usize) -> Self::Element {
+        self.coords.extract_unchecked(i).into()
+    }
+
+    #[inline]
+    fn replace(&mut self, i: usize, val: Self::Element) {
+        self.coords.replace(i, val.coords)
+    }
+
+    #[inline]
+    unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element) {
+        self.coords.replace_unchecked(i, val.coords)
+    }
+
+    #[inline]
+    fn select(self, cond: Self::SimdBool, other: Self) -> Self {
+        self.coords.select(cond, other.coords).into()
+    }
+}

src/geometry/quaternion.rs

@@ -13,11 +13,12 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use alga::general::RealField;
+use simba::scalar::RealField;
+use simba::simd::SimdRealField;
 
 use crate::base::dimension::{U1, U3, U4};
 use crate::base::storage::{CStride, RStride};
-use crate::base::{Matrix3, Matrix4, MatrixSlice, MatrixSliceMut, Unit, Vector3, Vector4};
+use crate::base::{Matrix3, Matrix4, MatrixSlice, MatrixSliceMut, Normed, Unit, Vector3, Vector4};
 
 use crate::geometry::{Point3, Rotation};
 
@@ -25,13 +26,13 @@ use crate::geometry::{Point3, Rotation};
 /// that may be used as a rotation.
 #[repr(C)]
 #[derive(Debug)]
-pub struct Quaternion<N: RealField> {
+pub struct Quaternion<N: SimdRealField> {
     /// This quaternion as a 4D vector of coordinates in the `[ x, y, z, w ]` storage order.
     pub coords: Vector4<N>,
 }
 
 #[cfg(feature = "abomonation-serialize")]
-impl<N: RealField> Abomonation for Quaternion<N>
+impl<N: SimdRealField> Abomonation for Quaternion<N>
 where Vector4<N>: Abomonation
 {
     unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
@@ -47,9 +48,9 @@ where Vector4<N>: Abomonation
     }
 }
 
-impl<N: RealField + Eq> Eq for Quaternion<N> {}
+impl<N: SimdRealField + Eq> Eq for Quaternion<N> {}
 
-impl<N: RealField> PartialEq for Quaternion<N> {
+impl<N: SimdRealField> PartialEq for Quaternion<N> {
     fn eq(&self, rhs: &Self) -> bool {
         self.coords == rhs.coords ||
         // Account for the double-covering of S², i.e. q = -q
@@ -57,15 +58,15 @@ impl<N: RealField> PartialEq for Quaternion<N> {
     }
 }
 
-impl<N: RealField + hash::Hash> hash::Hash for Quaternion<N> {
+impl<N: SimdRealField + hash::Hash> hash::Hash for Quaternion<N> {
     fn hash<H: hash::Hasher>(&self, state: &mut H) {
         self.coords.hash(state)
     }
 }
 
-impl<N: RealField> Copy for Quaternion<N> {}
+impl<N: SimdRealField> Copy for Quaternion<N> {}
 
-impl<N: RealField> Clone for Quaternion<N> {
+impl<N: SimdRealField> Clone for Quaternion<N> {
     #[inline]
     fn clone(&self) -> Self {
         Self::from(self.coords.clone())
@@ -73,7 +74,7 @@ impl<N: RealField> Clone for Quaternion<N> {
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<N: RealField> Serialize for Quaternion<N>
+impl<N: SimdRealField> Serialize for Quaternion<N>
 where Owned<N, U4>: Serialize
 {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
@@ -83,7 +84,7 @@ where Owned<N, U4>: Serialize
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<'a, N: RealField> Deserialize<'a> for Quaternion<N>
+impl<'a, N: SimdRealField> Deserialize<'a> for Quaternion<N>
 where Owned<N, U4>: Deserialize<'a>
 {
     fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
@@ -94,7 +95,7 @@ where Owned<N, U4>: Deserialize<'a>
     }
 }
 
-impl<N: RealField> Quaternion<N> {
+impl<N: SimdRealField> Quaternion<N> {
     /// Moves this unit quaternion into one that owns its data.
     #[inline]
     #[deprecated(note = "This method is a no-op and will be removed in a future release.")]
@@ -146,36 +147,6 @@ impl<N: RealField> Quaternion<N> {
         Self::from_parts(self.w, -self.imag())
     }
 
-    /// Inverts this quaternion if it is not zero.
-    ///
-    /// # Example
-    /// ```
-    /// # #[macro_use] extern crate approx;
-    /// # use nalgebra::Quaternion;
-    /// let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
-    /// let inv_q = q.try_inverse();
-    ///
-    /// assert!(inv_q.is_some());
-    /// assert_relative_eq!(inv_q.unwrap() * q, Quaternion::identity());
-    ///
-    /// //Non-invertible case
-    /// let q = Quaternion::new(0.0, 0.0, 0.0, 0.0);
-    /// let inv_q = q.try_inverse();
-    ///
-    /// assert!(inv_q.is_none());
-    /// ```
-    #[inline]
-    #[must_use = "Did you mean to use try_inverse_mut()?"]
-    pub fn try_inverse(&self) -> Option<Self> {
-        let mut res = Self::from(self.coords.clone_owned());
-
-        if res.try_inverse_mut() {
-            Some(res)
-        } else {
-            None
-        }
-    }
-
     /// Linear interpolation between two quaternion.
     ///
     /// Computes `self * (1 - t) + other * t`.
@@ -309,6 +280,38 @@ impl<N: RealField> Quaternion<N> {
     pub fn dot(&self, rhs: &Self) -> N {
         self.coords.dot(&rhs.coords)
     }
+}
+
+impl<N: RealField> Quaternion<N> {
+    /// Inverts this quaternion if it is not zero.
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # use nalgebra::Quaternion;
+    /// let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
+    /// let inv_q = q.try_inverse();
+    ///
+    /// assert!(inv_q.is_some());
+    /// assert_relative_eq!(inv_q.unwrap() * q, Quaternion::identity());
+    ///
+    /// //Non-invertible case
+    /// let q = Quaternion::new(0.0, 0.0, 0.0, 0.0);
+    /// let inv_q = q.try_inverse();
+    ///
+    /// assert!(inv_q.is_none());
+    /// ```
+    #[inline]
+    #[must_use = "Did you mean to use try_inverse_mut()?"]
+    pub fn try_inverse(&self) -> Option<Self> {
+        let mut res = self.clone();
+
+        if res.try_inverse_mut() {
+            Some(res)
+        } else {
+            None
+        }
+    }
 
     /// Calculates the inner product (also known as the dot product).
     /// See "Foundations of Game Engine Development, Volume 1: Mathematics" by Lengyel
@@ -917,6 +920,30 @@ impl<N: RealField + fmt::Display> fmt::Display for Quaternion<N> {
 /// A unit quaternions. May be used to represent a rotation.
 pub type UnitQuaternion<N> = Unit<Quaternion<N>>;
 
+impl<N: SimdRealField> Normed for Quaternion<N> {
+    type Norm = N::SimdRealField;
+
+    #[inline]
+    fn norm(&self) -> N::SimdRealField {
+        self.coords.norm()
+    }
+
+    #[inline]
+    fn norm_squared(&self) -> N::SimdRealField {
+        self.coords.norm_squared()
+    }
+
+    #[inline]
+    fn scale_mut(&mut self, n: Self::Norm) {
+        self.coords.scale_mut(n)
+    }
+
+    #[inline]
+    fn unscale_mut(&mut self, n: Self::Norm) {
+        self.coords.unscale_mut(n)
+    }
+}
+
 impl<N: RealField> UnitQuaternion<N> {
     /// Moves this unit quaternion into one that owns its data.
     #[inline]
@@ -1087,7 +1114,8 @@ impl<N: RealField> UnitQuaternion<N> {
     /// ```
     #[inline]
     pub fn slerp(&self, other: &Self, t: N) -> Self {
-        self.try_slerp(other, t, N::default_epsilon()).expect("Quaternion slerp: ambiguous configuration.")
+        self.try_slerp(other, t, N::default_epsilon())
+            .expect("Quaternion slerp: ambiguous configuration.")
     }
 
     /// Computes the spherical linear interpolation between two unit quaternions or returns `None`
@@ -1101,22 +1129,21 @@ impl<N: RealField> UnitQuaternion<N> {
     /// * `epsilon`: the value below which the sinus of the angle separating both quaternion
     /// must be to return `None`.
     #[inline]
-    pub fn try_slerp(
+    pub fn try_slerp(&self, other: &Self, t: N, epsilon: N) -> Option<Self> {
-        &self,
-        other: &Self,
-        t: N,
-        epsilon: N,
-    ) -> Option<Self>
-    {
         let coords = if self.coords.dot(&other.coords) < N::zero() {
-            Unit::new_unchecked(self.coords)
+            Unit::new_unchecked(self.coords).try_slerp(
-                .try_slerp(&Unit::new_unchecked(-other.coords), t, epsilon)
+                &Unit::new_unchecked(-other.coords),
+                t,
+                epsilon,
+            )
         } else {
-            Unit::new_unchecked(self.coords)
+            Unit::new_unchecked(self.coords).try_slerp(
-                .try_slerp(&Unit::new_unchecked(other.coords), t, epsilon)
+                &Unit::new_unchecked(other.coords),
+                t,
+                epsilon,
+            )
         };
 
-
         coords.map(|q| Unit::new_unchecked(Quaternion::from(q.into_inner())))
     }
 

src/geometry/quaternion_alga.rs

@@ -1,307 +0,0 @@
-use num::Zero;
-
-use alga::general::{
-    AbstractGroup, AbstractGroupAbelian, AbstractLoop, AbstractMagma, AbstractModule,
-    AbstractMonoid, AbstractQuasigroup, AbstractSemigroup, Additive, Id, Identity, TwoSidedInverse, Module,
-    Multiplicative, RealField,
-};
-use alga::linear::{
-    AffineTransformation, DirectIsometry, FiniteDimVectorSpace, Isometry, NormedSpace,
-    OrthogonalTransformation, ProjectiveTransformation, Rotation, Similarity, Transformation,
-    VectorSpace,
-};
-
-use crate::base::{Vector3, Vector4};
-use crate::geometry::{Point3, Quaternion, UnitQuaternion};
-
-impl<N: RealField> Identity<Multiplicative> for Quaternion<N> {
-    #[inline]
-    fn identity() -> Self {
-        Self::identity()
-    }
-}
-
-impl<N: RealField> Identity<Additive> for Quaternion<N> {
-    #[inline]
-    fn identity() -> Self {
-        Self::zero()
-    }
-}
-
-impl<N: RealField> AbstractMagma<Multiplicative> for Quaternion<N> {
-    #[inline]
-    fn operate(&self, rhs: &Self) -> Self {
-        self * rhs
-    }
-}
-
-impl<N: RealField> AbstractMagma<Additive> for Quaternion<N> {
-    #[inline]
-    fn operate(&self, rhs: &Self) -> Self {
-        self + rhs
-    }
-}
-
-impl<N: RealField> TwoSidedInverse<Additive> for Quaternion<N> {
-    #[inline]
-    fn two_sided_inverse(&self) -> Self {
-        -self
-    }
-}
-
-macro_rules! impl_structures(
-    ($Quaternion: ident; $($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: RealField> $marker<$operator> for $Quaternion<N> { }
-    )*}
-);
-
-impl_structures!(
-    Quaternion;
-    AbstractSemigroup<Multiplicative>,
-    AbstractMonoid<Multiplicative>,
-
-    AbstractSemigroup<Additive>,
-    AbstractQuasigroup<Additive>,
-    AbstractMonoid<Additive>,
-    AbstractLoop<Additive>,
-    AbstractGroup<Additive>,
-    AbstractGroupAbelian<Additive>
-);
-
-/*
- *
- * Vector space.
- *
- */
-impl<N: RealField> AbstractModule for Quaternion<N> {
-    type AbstractRing = N;
-
-    #[inline]
-    fn multiply_by(&self, n: N) -> Self {
-        self * n
-    }
-}
-
-impl<N: RealField> Module for Quaternion<N> {
-    type Ring = N;
-}
-
-impl<N: RealField> VectorSpace for Quaternion<N> {
-    type Field = N;
-}
-
-impl<N: RealField> FiniteDimVectorSpace for Quaternion<N> {
-    #[inline]
-    fn dimension() -> usize {
-        4
-    }
-
-    #[inline]
-    fn canonical_basis_element(i: usize) -> Self {
-        Self::from(Vector4::canonical_basis_element(i))
-    }
-
-    #[inline]
-    fn dot(&self, other: &Self) -> N {
-        self.coords.dot(&other.coords)
-    }
-
-    #[inline]
-    unsafe fn component_unchecked(&self, i: usize) -> &N {
-        self.coords.component_unchecked(i)
-    }
-
-    #[inline]
-    unsafe fn component_unchecked_mut(&mut self, i: usize) -> &mut N {
-        self.coords.component_unchecked_mut(i)
-    }
-}
-
-impl<N: RealField> NormedSpace for Quaternion<N> {
-    type RealField = N;
-    type ComplexField = N;
-
-    #[inline]
-    fn norm_squared(&self) -> N {
-        self.coords.norm_squared()
-    }
-
-    #[inline]
-    fn norm(&self) -> N {
-        self.as_vector().norm()
-    }
-
-    #[inline]
-    fn normalize(&self) -> Self {
-        let v = self.coords.normalize();
-        Self::from(v)
-    }
-
-    #[inline]
-    fn normalize_mut(&mut self) -> N {
-        self.coords.normalize_mut()
-    }
-
-    #[inline]
-    fn try_normalize(&self, min_norm: N) -> Option<Self> {
-        if let Some(v) = self.coords.try_normalize(min_norm) {
-            Some(Self::from(v))
-        } else {
-            None
-        }
-    }
-
-    #[inline]
-    fn try_normalize_mut(&mut self, min_norm: N) -> Option<N> {
-        self.coords.try_normalize_mut(min_norm)
-    }
-}
-
-/*
- *
- * Implementations for UnitQuaternion.
- *
- */
-impl<N: RealField> Identity<Multiplicative> for UnitQuaternion<N> {
-    #[inline]
-    fn identity() -> Self {
-        Self::identity()
-    }
-}
-
-impl<N: RealField> AbstractMagma<Multiplicative> for UnitQuaternion<N> {
-    #[inline]
-    fn operate(&self, rhs: &Self) -> Self {
-        self * rhs
-    }
-}
-
-impl<N: RealField> TwoSidedInverse<Multiplicative> for UnitQuaternion<N> {
-    #[inline]
-    fn two_sided_inverse(&self) -> Self {
-        self.inverse()
-    }
-
-    #[inline]
-    fn two_sided_inverse_mut(&mut self) {
-        self.inverse_mut()
-    }
-}
-
-impl_structures!(
-    UnitQuaternion;
-    AbstractSemigroup<Multiplicative>,
-    AbstractQuasigroup<Multiplicative>,
-    AbstractMonoid<Multiplicative>,
-    AbstractLoop<Multiplicative>,
-    AbstractGroup<Multiplicative>
-);
-
-impl<N: RealField> Transformation<Point3<N>> for UnitQuaternion<N> {
-    #[inline]
-    fn transform_point(&self, pt: &Point3<N>) -> Point3<N> {
-        self.transform_point(pt)
-    }
-
-    #[inline]
-    fn transform_vector(&self, v: &Vector3<N>) -> Vector3<N> {
-        self.transform_vector(v)
-    }
-}
-
-impl<N: RealField> ProjectiveTransformation<Point3<N>> for UnitQuaternion<N> {
-    #[inline]
-    fn inverse_transform_point(&self, pt: &Point3<N>) -> Point3<N> {
-        self.inverse_transform_point(pt)
-    }
-
-    #[inline]
-    fn inverse_transform_vector(&self, v: &Vector3<N>) -> Vector3<N> {
-        self.inverse_transform_vector(v)
-    }
-}
-
-impl<N: RealField> AffineTransformation<Point3<N>> for UnitQuaternion<N> {
-    type Rotation = Self;
-    type NonUniformScaling = Id;
-    type Translation = Id;
-
-    #[inline]
-    fn decompose(&self) -> (Id, Self, Id, Self) {
-        (Id::new(), self.clone(), Id::new(), Self::identity())
-    }
-
-    #[inline]
-    fn append_translation(&self, _: &Self::Translation) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn prepend_translation(&self, _: &Self::Translation) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn append_rotation(&self, r: &Self::Rotation) -> Self {
-        r * self
-    }
-
-    #[inline]
-    fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
-        self * r
-    }
-
-    #[inline]
-    fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self {
-        self.clone()
-    }
-}
-
-impl<N: RealField> Similarity<Point3<N>> for UnitQuaternion<N> {
-    type Scaling = Id;
-
-    #[inline]
-    fn translation(&self) -> Id {
-        Id::new()
-    }
-
-    #[inline]
-    fn rotation(&self) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn scaling(&self) -> Id {
-        Id::new()
-    }
-}
-
-macro_rules! marker_impl(
-    ($($Trait: ident),*) => {$(
-        impl<N: RealField> $Trait<Point3<N>> for UnitQuaternion<N> { }
-    )*}
-);
-
-marker_impl!(Isometry, DirectIsometry, OrthogonalTransformation);
-
-impl<N: RealField> Rotation<Point3<N>> for UnitQuaternion<N> {
-    #[inline]
-    fn powf(&self, n: N) -> Option<Self> {
-        Some(self.powf(n))
-    }
-
-    #[inline]
-    fn rotation_between(a: &Vector3<N>, b: &Vector3<N>) -> Option<Self> {
-        Self::rotation_between(a, b)
-    }
-
-    #[inline]
-    fn scaled_rotation_between(a: &Vector3<N>, b: &Vector3<N>, s: N) -> Option<Self> {
-        Self::scaled_rotation_between(a, b, s)
-    }
-}

src/geometry/quaternion_construction.rs

@@ -9,15 +9,16 @@ use num::{One, Zero};
 use rand::distributions::{Distribution, OpenClosed01, Standard};
 use rand::Rng;
 
-use alga::general::RealField;
+use simba::scalar::RealField;
 
 use crate::base::dimension::U3;
 use crate::base::storage::Storage;
-use crate::base::{Unit, Vector, Vector3, Vector4, Matrix3, Matrix4};
+use crate::base::{Matrix3, Matrix4, Unit, Vector, Vector3, Vector4};
+use crate::SimdRealField;
 
 use crate::geometry::{Quaternion, Rotation3, UnitQuaternion};
 
-impl<N: RealField> Quaternion<N> {
+impl<N: SimdRealField> Quaternion<N> {
     /// Creates a quaternion from a 4D vector. The quaternion scalar part corresponds to the `w`
     /// vector component.
     #[inline]
@@ -77,17 +78,6 @@ impl<N: RealField> Quaternion<N> {
         Self::from_parts(r, Vector3::zero())
     }
 
-    /// Creates a new quaternion from its polar decomposition.
-    ///
-    /// Note that `axis` is assumed to be a unit vector.
-    // FIXME: take a reference to `axis`?
-    pub fn from_polar_decomposition<SB>(scale: N, theta: N, axis: Unit<Vector<N, U3, SB>>) -> Self
-    where SB: Storage<N, U3> {
-        let rot = UnitQuaternion::<N>::from_axis_angle(&axis, theta * crate::convert(2.0f64));
-
-        rot.into_inner() * scale
-    }
-
     /// The quaternion multiplicative identity.
     ///
     /// # Example
@@ -105,14 +95,28 @@ impl<N: RealField> Quaternion<N> {
     }
 }
 
-impl<N: RealField> One for Quaternion<N> {
+// FIXME: merge with the previous block.
+impl<N: RealField> Quaternion<N> {
+    /// Creates a new quaternion from its polar decomposition.
+    ///
+    /// Note that `axis` is assumed to be a unit vector.
+    // FIXME: take a reference to `axis`?
+    pub fn from_polar_decomposition<SB>(scale: N, theta: N, axis: Unit<Vector<N, U3, SB>>) -> Self
+    where SB: Storage<N, U3> {
+        let rot = UnitQuaternion::<N>::from_axis_angle(&axis, theta * crate::convert(2.0f64));
+
+        rot.into_inner() * scale
+    }
+}
+
+impl<N: SimdRealField> One for Quaternion<N> {
     #[inline]
     fn one() -> Self {
         Self::identity()
     }
 }
 
-impl<N: RealField> Zero for Quaternion<N> {
+impl<N: SimdRealField> Zero for Quaternion<N> {
     #[inline]
     fn zero() -> Self {
         Self::from(Vector4::zero())
@@ -124,7 +128,7 @@ impl<N: RealField> Zero for Quaternion<N> {
     }
 }
 
-impl<N: RealField> Distribution<Quaternion<N>> for Standard
+impl<N: SimdRealField> Distribution<Quaternion<N>> for Standard
 where Standard: Distribution<N>
 {
     #[inline]
@@ -134,7 +138,7 @@ where Standard: Distribution<N>
 }
 
 #[cfg(feature = "arbitrary")]
-impl<N: RealField + Arbitrary> Arbitrary for Quaternion<N>
+impl<N: SimdRealField + Arbitrary> Arbitrary for Quaternion<N>
 where Owned<N, U4>: Send
 {
     #[inline]

src/geometry/quaternion_conversion.rs

@@ -1,7 +1,7 @@
 use num::Zero;
 
-use alga::general::{RealField, SubsetOf, SupersetOf};
+use simba::scalar::{RealField, SubsetOf, SupersetOf};
-use alga::linear::Rotation as AlgaRotation;
+use simba::simd::SimdRealField;
 
 #[cfg(feature = "mint")]
 use mint;
@@ -9,8 +9,8 @@ use mint;
 use crate::base::dimension::U3;
 use crate::base::{Matrix3, Matrix4, Vector4};
 use crate::geometry::{
-    Isometry, Point3, Quaternion, Rotation, Rotation3, Similarity, SuperTCategoryOf, TAffine,
+    AbstractRotation, Isometry, Quaternion, Rotation, Rotation3, Similarity, SuperTCategoryOf,
-    Transform, Translation, UnitQuaternion,
+    TAffine, Transform, Translation, UnitQuaternion,
 };
 
 /*
@@ -34,8 +34,8 @@ use crate::geometry::{
 
 impl<N1, N2> SubsetOf<Quaternion<N2>> for Quaternion<N1>
 where
-    N1: RealField,
+    N1: SimdRealField,
-    N2: RealField + SupersetOf<N1>,
+    N2: SimdRealField + SupersetOf<N1>,
 {
     #[inline]
     fn to_superset(&self) -> Quaternion<N2> {
@@ -48,7 +48,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(q: &Quaternion<N2>) -> Self {
+    fn from_superset_unchecked(q: &Quaternion<N2>) -> Self {
         Self {
             coords: q.coords.to_subset_unchecked(),
         }
@@ -57,8 +57,8 @@ where
 
 impl<N1, N2> SubsetOf<UnitQuaternion<N2>> for UnitQuaternion<N1>
 where
-    N1: RealField,
+    N1: SimdRealField,
-    N2: RealField + SupersetOf<N1>,
+    N2: SimdRealField + SupersetOf<N1>,
 {
     #[inline]
     fn to_superset(&self) -> UnitQuaternion<N2> {
@@ -71,7 +71,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(uq: &UnitQuaternion<N2>) -> Self {
+    fn from_superset_unchecked(uq: &UnitQuaternion<N2>) -> Self {
         Self::new_unchecked(crate::convert_ref_unchecked(uq.as_ref()))
     }
 }
@@ -93,7 +93,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(rot: &Rotation3<N2>) -> Self {
+    fn from_superset_unchecked(rot: &Rotation3<N2>) -> Self {
         let q = UnitQuaternion::<N2>::from_rotation_matrix(rot);
         crate::convert_unchecked(q)
     }
@@ -103,7 +103,7 @@ impl<N1, N2, R> SubsetOf<Isometry<N2, U3, R>> for UnitQuaternion<N1>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R: AlgaRotation<Point3<N2>> + SupersetOf<Self>,
+    R: AbstractRotation<N2, U3> + SupersetOf<Self>,
 {
     #[inline]
     fn to_superset(&self) -> Isometry<N2, U3, R> {
@@ -116,7 +116,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(iso: &Isometry<N2, U3, R>) -> Self {
+    fn from_superset_unchecked(iso: &Isometry<N2, U3, R>) -> Self {
         crate::convert_ref_unchecked(&iso.rotation)
     }
 }
@@ -125,7 +125,7 @@ impl<N1, N2, R> SubsetOf<Similarity<N2, U3, R>> for UnitQuaternion<N1>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R: AlgaRotation<Point3<N2>> + SupersetOf<Self>,
+    R: AbstractRotation<N2, U3> + SupersetOf<Self>,
 {
     #[inline]
     fn to_superset(&self) -> Similarity<N2, U3, R> {
@@ -138,7 +138,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(sim: &Similarity<N2, U3, R>) -> Self {
+    fn from_superset_unchecked(sim: &Similarity<N2, U3, R>) -> Self {
         crate::convert_ref_unchecked(&sim.isometry)
     }
 }
@@ -160,7 +160,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(t: &Transform<N2, U3, C>) -> Self {
+    fn from_superset_unchecked(t: &Transform<N2, U3, C>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
@@ -177,7 +177,7 @@ impl<N1: RealField, N2: RealField + SupersetOf<N1>> SubsetOf<Matrix4<N2>> for Un
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &Matrix4<N2>) -> Self {
+    fn from_superset_unchecked(m: &Matrix4<N2>) -> Self {
         let rot: Rotation3<N1> = crate::convert_ref_unchecked(m);
         Self::from_rotation_matrix(&rot)
     }
@@ -246,7 +246,7 @@ impl<N: RealField> From<UnitQuaternion<N>> for Matrix3<N> {
     }
 }
 
-impl<N: RealField> From<Vector4<N>> for Quaternion<N> {
+impl<N: SimdRealField> From<Vector4<N>> for Quaternion<N> {
     #[inline]
     fn from(coords: Vector4<N>) -> Self {
         Self { coords }

src/geometry/quaternion_coordinates.rs

@@ -1,13 +1,13 @@
 use std::mem;
 use std::ops::{Deref, DerefMut};
 
-use alga::general::RealField;
+use simba::simd::SimdRealField;
 
 use crate::base::coordinates::IJKW;
 
 use crate::geometry::Quaternion;
 
-impl<N: RealField> Deref for Quaternion<N> {
+impl<N: SimdRealField> Deref for Quaternion<N> {
     type Target = IJKW<N>;
 
     #[inline]
@@ -16,7 +16,7 @@ impl<N: RealField> Deref for Quaternion<N> {
     }
 }
 
-impl<N: RealField> DerefMut for Quaternion<N> {
+impl<N: SimdRealField> DerefMut for Quaternion<N> {
     #[inline]
     fn deref_mut(&mut self) -> &mut Self::Target {
         unsafe { mem::transmute(self) }

src/geometry/quaternion_ops.rs

@@ -54,16 +54,15 @@ use std::ops::{
     Add, AddAssign, Div, DivAssign, Index, IndexMut, Mul, MulAssign, Neg, Sub, SubAssign,
 };
 
-use alga::general::RealField;
-
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{U1, U3, U4};
 use crate::base::storage::Storage;
 use crate::base::{DefaultAllocator, Unit, Vector, Vector3};
+use crate::SimdRealField;
 
 use crate::geometry::{Point3, Quaternion, Rotation, UnitQuaternion};
 
-impl<N: RealField> Index<usize> for Quaternion<N> {
+impl<N: SimdRealField> Index<usize> for Quaternion<N> {
     type Output = N;
 
     #[inline]
@@ -72,7 +71,7 @@ impl<N: RealField> Index<usize> for Quaternion<N> {
     }
 }
 
-impl<N: RealField> IndexMut<usize> for Quaternion<N> {
+impl<N: SimdRealField> IndexMut<usize> for Quaternion<N> {
     #[inline]
     fn index_mut(&mut self, i: usize) -> &mut N {
         &mut self.coords[i]
@@ -85,7 +84,7 @@ macro_rules! quaternion_op_impl(
      $(for $Storage: ident: $StoragesBound: ident $(<$($BoundParam: ty),*>)*),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Result: ty $(=> $VDimA: ty, $VDimB: ty)*;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N: RealField $(, $Storage: $StoragesBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N: SimdRealField $(, $Storage: $StoragesBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
             where DefaultAllocator: Allocator<N, $LhsRDim, $LhsCDim> +
                                     Allocator<N, $RhsRDim, $RhsCDim> {
             type Output = $Result;
@@ -490,7 +489,7 @@ quaternion_op_impl!(
 
 macro_rules! scalar_op_impl(
     ($($Op: ident, $op: ident, $OpAssign: ident, $op_assign: ident);* $(;)*) => {$(
-        impl<N: RealField> $Op<N> for Quaternion<N> {
+        impl<N: SimdRealField> $Op<N> for Quaternion<N> {
             type Output = Quaternion<N>;
 
             #[inline]
@@ -499,7 +498,7 @@ macro_rules! scalar_op_impl(
             }
         }
 
-        impl<'a, N: RealField> $Op<N> for &'a Quaternion<N> {
+        impl<'a, N: SimdRealField> $Op<N> for &'a Quaternion<N> {
             type Output = Quaternion<N>;
 
             #[inline]
@@ -508,7 +507,7 @@ macro_rules! scalar_op_impl(
             }
         }
 
-        impl<N: RealField> $OpAssign<N> for Quaternion<N> {
+        impl<N: SimdRealField> $OpAssign<N> for Quaternion<N> {
 
             #[inline]
             fn $op_assign(&mut self, n: N) {
@@ -547,7 +546,7 @@ macro_rules! left_scalar_mul_impl(
 
 left_scalar_mul_impl!(f32, f64);
 
-impl<N: RealField> Neg for Quaternion<N> {
+impl<N: SimdRealField> Neg for Quaternion<N> {
     type Output = Quaternion<N>;
 
     #[inline]
@@ -556,7 +555,7 @@ impl<N: RealField> Neg for Quaternion<N> {
     }
 }
 
-impl<'a, N: RealField> Neg for &'a Quaternion<N> {
+impl<'a, N: SimdRealField> Neg for &'a Quaternion<N> {
     type Output = Quaternion<N>;
 
     #[inline]
@@ -570,7 +569,7 @@ macro_rules! quaternion_op_impl(
      ($LhsRDim: ident, $LhsCDim: ident), ($RhsRDim: ident, $RhsCDim: ident);
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty $(=> $VDimA: ty, $VDimB: ty)*;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N: RealField> $OpAssign<$Rhs> for $Lhs
+        impl<$($lives ,)* N: SimdRealField> $OpAssign<$Rhs> for $Lhs
             where DefaultAllocator: Allocator<N, $LhsRDim, $LhsCDim> +
                                     Allocator<N, $RhsRDim, $RhsCDim> {
 

src/geometry/quaternion_simba.rs

@@ -0,0 +1,47 @@
+use simba::simd::SimdValue;
+
+use crate::base::Vector4;
+use crate::geometry::Quaternion;
+use crate::{RealField, Scalar};
+
+impl<N: RealField> SimdValue for Quaternion<N>
+where N::Element: Scalar
+{
+    type Element = Quaternion<N::Element>;
+    type SimdBool = N::SimdBool;
+
+    #[inline]
+    fn lanes() -> usize {
+        N::lanes()
+    }
+
+    #[inline]
+    fn splat(val: Self::Element) -> Self {
+        Vector4::splat(val.coords).into()
+    }
+
+    #[inline]
+    fn extract(&self, i: usize) -> Self::Element {
+        self.coords.extract(i).into()
+    }
+
+    #[inline]
+    unsafe fn extract_unchecked(&self, i: usize) -> Self::Element {
+        self.coords.extract_unchecked(i).into()
+    }
+
+    #[inline]
+    fn replace(&mut self, i: usize, val: Self::Element) {
+        self.coords.replace(i, val.coords)
+    }
+
+    #[inline]
+    unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element) {
+        self.coords.replace_unchecked(i, val.coords)
+    }
+
+    #[inline]
+    fn select(self, cond: Self::SimdBool, other: Self) -> Self {
+        self.coords.select(cond, other.coords).into()
+    }
+}

src/geometry/reflection.rs

@@ -1,9 +1,9 @@
-use alga::general::ComplexField;
 use crate::base::allocator::Allocator;
 use crate::base::constraint::{AreMultipliable, DimEq, SameNumberOfRows, ShapeConstraint};
 use crate::base::{DefaultAllocator, Matrix, Scalar, Unit, Vector};
 use crate::dimension::{Dim, DimName, U1};
 use crate::storage::{Storage, StorageMut};
+use simba::scalar::ComplexField;
 
 use crate::geometry::Point;
 
@@ -27,10 +27,7 @@ impl<N: ComplexField, D: Dim, S: Storage<N, D>> Reflection<N, D, S> {
 
     /// Creates a new reflection wrt. the plane orthogonal to the given axis and that contains the
     /// point `pt`.
-    pub fn new_containing_point(
+    pub fn new_containing_point(axis: Unit<Vector<N, D, S>>, pt: &Point<N, D>) -> Self
-        axis: Unit<Vector<N, D, S>>,
-        pt: &Point<N, D>,
-    ) -> Self
     where
         D: DimName,
         DefaultAllocator: Allocator<N, D>,

src/geometry/rotation.rs

@@ -14,7 +14,7 @@ use crate::base::storage::Owned;
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use alga::general::RealField;
+use simba::scalar::RealField;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};

src/geometry/rotation_alga.rs

@@ -1,276 +0,0 @@
-use alga::general::{
-    AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, RealField,
-};
-use alga::linear::{
-    self, AffineTransformation, DirectIsometry, Isometry, OrthogonalTransformation,
-    ProjectiveTransformation, Similarity, Transformation,
-};
-
-use crate::base::allocator::Allocator;
-use crate::base::dimension::DimName;
-use crate::base::{DefaultAllocator, VectorN};
-
-use crate::geometry::{Point, Rotation};
-
-/*
- *
- * Algebraic structures.
- *
- */
-impl<N: RealField, D: DimName> Identity<Multiplicative> for Rotation<N, D>
-where DefaultAllocator: Allocator<N, D, D>
-{
-    #[inline]
-    fn identity() -> Self {
-        Self::identity()
-    }
-}
-
-impl<N: RealField, D: DimName> TwoSidedInverse<Multiplicative> for Rotation<N, D>
-where DefaultAllocator: Allocator<N, D, D>
-{
-    #[inline]
-    #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
-    fn two_sided_inverse(&self) -> Self {
-        self.transpose()
-    }
-
-    #[inline]
-    fn two_sided_inverse_mut(&mut self) {
-        self.transpose_mut()
-    }
-}
-
-impl<N: RealField, D: DimName> AbstractMagma<Multiplicative> for Rotation<N, D>
-where DefaultAllocator: Allocator<N, D, D>
-{
-    #[inline]
-    fn operate(&self, rhs: &Self) -> Self {
-        self * rhs
-    }
-}
-
-macro_rules! impl_multiplicative_structures(
-    ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: RealField, D: DimName> $marker<$operator> for Rotation<N, D>
-            where DefaultAllocator: Allocator<N, D, D> { }
-    )*}
-);
-
-impl_multiplicative_structures!(
-    AbstractSemigroup<Multiplicative>,
-    AbstractMonoid<Multiplicative>,
-    AbstractQuasigroup<Multiplicative>,
-    AbstractLoop<Multiplicative>,
-    AbstractGroup<Multiplicative>
-);
-
-/*
- *
- * Transformation groups.
- *
- */
-impl<N: RealField, D: DimName> Transformation<Point<N, D>> for Rotation<N, D>
-where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
-{
-    #[inline]
-    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
-        self.transform_point(pt)
-    }
-
-    #[inline]
-    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
-        self.transform_vector(v)
-    }
-}
-
-impl<N: RealField, D: DimName> ProjectiveTransformation<Point<N, D>> for Rotation<N, D>
-where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
-{
-    #[inline]
-    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
-        self.inverse_transform_point(pt)
-    }
-
-    #[inline]
-    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
-        self.inverse_transform_vector(v)
-    }
-}
-
-impl<N: RealField, D: DimName> AffineTransformation<Point<N, D>> for Rotation<N, D>
-where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
-{
-    type Rotation = Self;
-    type NonUniformScaling = Id;
-    type Translation = Id;
-
-    #[inline]
-    fn decompose(&self) -> (Id, Self, Id, Self) {
-        (Id::new(), self.clone(), Id::new(), Self::identity())
-    }
-
-    #[inline]
-    fn append_translation(&self, _: &Self::Translation) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn prepend_translation(&self, _: &Self::Translation) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn append_rotation(&self, r: &Self::Rotation) -> Self {
-        r * self
-    }
-
-    #[inline]
-    fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
-        self * r
-    }
-
-    #[inline]
-    fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self {
-        self.clone()
-    }
-}
-
-impl<N: RealField, D: DimName> Similarity<Point<N, D>> for Rotation<N, D>
-where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
-{
-    type Scaling = Id;
-
-    #[inline]
-    fn translation(&self) -> Id {
-        Id::new()
-    }
-
-    #[inline]
-    fn rotation(&self) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn scaling(&self) -> Id {
-        Id::new()
-    }
-}
-
-macro_rules! marker_impl(
-    ($($Trait: ident),*) => {$(
-        impl<N: RealField, D: DimName> $Trait<Point<N, D>> for Rotation<N, D>
-        where DefaultAllocator: Allocator<N, D, D> +
-                                Allocator<N, D> { }
-    )*}
-);
-
-marker_impl!(Isometry, DirectIsometry, OrthogonalTransformation);
-
-/// Subgroups of the n-dimensional rotation group `SO(n)`.
-impl<N: RealField, D: DimName> linear::Rotation<Point<N, D>> for Rotation<N, D>
-where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
-{
-    #[inline]
-    fn powf(&self, _: N) -> Option<Self> {
-        // XXX: Add the general case.
-        // XXX: Use specialization for 2D and 3D.
-        unimplemented!()
-    }
-
-    #[inline]
-    fn rotation_between(_: &VectorN<N, D>, _: &VectorN<N, D>) -> Option<Self> {
-        // XXX: Add the general case.
-        // XXX: Use specialization for 2D and 3D.
-        unimplemented!()
-    }
-
-    #[inline]
-    fn scaled_rotation_between(_: &VectorN<N, D>, _: &VectorN<N, D>, _: N) -> Option<Self> {
-        // XXX: Add the general case.
-        // XXX: Use specialization for 2D and 3D.
-        unimplemented!()
-    }
-}
-
-/*
-impl<N: RealField> Matrix for Rotation<N> {
-    type Field     = N;
-    type Row       = Matrix<N>;
-    type Column    = Matrix<N>;
-    type Transpose = Self;
-
-    #[inline]
-    fn nrows(&self) -> usize {
-        self.submatrix.nrows()
-    }
-
-    #[inline]
-    fn ncolumns(&self) -> usize {
-        self.submatrix.ncolumns()
-    }
-
-    #[inline]
-    fn row(&self, i: usize) -> Self::Row {
-        self.submatrix.row(i)
-    }
-
-    #[inline]
-    fn column(&self, i: usize) -> Self::Column {
-        self.submatrix.column(i)
-    }
-
-    #[inline]
-    fn get(&self, i: usize, j: usize) -> Self::Field {
-        self.submatrix[(i, j)]
-    }
-
-    #[inline]
-    unsafe fn get_unchecked(&self, i: usize, j: usize) -> Self::Field {
-        self.submatrix.at_fast(i, j)
-    }
-
-    #[inline]
-    fn transpose(&self) -> Self::Transpose {
-        Rotation::from_matrix_unchecked(self.submatrix.transpose())
-    }
-}
-
-impl<N: RealField> SquareMatrix for Rotation<N> {
-    type Vector = Matrix<N>;
-
-    #[inline]
-    fn diagonal(&self) -> Self::Coordinates {
-        self.submatrix.diagonal()
-    }
-
-    #[inline]
-    fn determinant(&self) -> Self::Field {
-        crate::one()
-    }
-
-    #[inline]
-    fn try_inverse(&self) -> Option<Self> {
-        Some(::transpose(self))
-    }
-
-    #[inline]
-    fn try_inverse_mut(&mut self) -> bool {
-        self.transpose_mut();
-        true
-    }
-
-    #[inline]
-    fn transpose_mut(&mut self) {
-        self.submatrix.transpose_mut()
-    }
-}
-
-impl<N: RealField> InversibleSquareMatrix for Rotation<N> { }
-*/

src/geometry/rotation_construction.rs

@@ -1,6 +1,6 @@
 use num::{One, Zero};
 
-use alga::general::{ClosedAdd, ClosedMul};
+use simba::scalar::{ClosedAdd, ClosedMul};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::DimName;

src/geometry/rotation_conversion.rs

@@ -1,7 +1,6 @@
 use num::Zero;
 
-use alga::general::{RealField, SubsetOf, SupersetOf};
+use simba::scalar::{RealField, SubsetOf, SupersetOf};
-use alga::linear::Rotation as AlgaRotation;
 
 #[cfg(feature = "mint")]
 use mint;
@@ -11,8 +10,8 @@ use crate::base::dimension::{DimMin, DimName, DimNameAdd, DimNameSum, U1};
 use crate::base::{DefaultAllocator, Matrix2, Matrix3, Matrix4, MatrixN};
 
 use crate::geometry::{
-    Isometry, Point, Rotation, Rotation2, Rotation3, Similarity, SuperTCategoryOf, TAffine,
+    AbstractRotation, Isometry, Rotation, Rotation2, Rotation3, Similarity, SuperTCategoryOf,
-    Transform, Translation, UnitComplex, UnitQuaternion,
+    TAffine, Transform, Translation, UnitComplex, UnitQuaternion,
 };
 
 /*
@@ -47,7 +46,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(rot: &Rotation<N2, D>) -> Self {
+    fn from_superset_unchecked(rot: &Rotation<N2, D>) -> Self {
         Rotation::from_matrix_unchecked(rot.matrix().to_subset_unchecked())
     }
 }
@@ -69,7 +68,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(q: &UnitQuaternion<N2>) -> Self {
+    fn from_superset_unchecked(q: &UnitQuaternion<N2>) -> Self {
         let q: UnitQuaternion<N1> = crate::convert_ref_unchecked(q);
         q.to_rotation_matrix()
     }
@@ -92,7 +91,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(q: &UnitComplex<N2>) -> Self {
+    fn from_superset_unchecked(q: &UnitComplex<N2>) -> Self {
         let q: UnitComplex<N1> = crate::convert_ref_unchecked(q);
         q.to_rotation_matrix()
     }
@@ -102,7 +101,7 @@ impl<N1, N2, D: DimName, R> SubsetOf<Isometry<N2, D, R>> for Rotation<N1, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R: AlgaRotation<Point<N2, D>> + SupersetOf<Self>,
+    R: AbstractRotation<N2, D> + SupersetOf<Self>,
     DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D>,
 {
     #[inline]
@@ -116,7 +115,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(iso: &Isometry<N2, D, R>) -> Self {
+    fn from_superset_unchecked(iso: &Isometry<N2, D, R>) -> Self {
         crate::convert_ref_unchecked(&iso.rotation)
     }
 }
@@ -125,7 +124,7 @@ impl<N1, N2, D: DimName, R> SubsetOf<Similarity<N2, D, R>> for Rotation<N1, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R: AlgaRotation<Point<N2, D>> + SupersetOf<Self>,
+    R: AbstractRotation<N2, D> + SupersetOf<Self>,
     DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D>,
 {
     #[inline]
@@ -139,7 +138,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(sim: &Similarity<N2, D, R>) -> Self {
+    fn from_superset_unchecked(sim: &Similarity<N2, D, R>) -> Self {
         crate::convert_ref_unchecked(&sim.isometry.rotation)
     }
 }
@@ -168,7 +167,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
+    fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
@@ -204,7 +203,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
+    fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
         let r = m.fixed_slice::<D, D>(0, 0);
         Self::from_matrix_unchecked(crate::convert_unchecked(r.into_owned()))
     }

src/geometry/rotation_ops.rs

@@ -20,7 +20,7 @@
 use num::{One, Zero};
 use std::ops::{Div, DivAssign, Index, Mul, MulAssign};
 
-use alga::general::{ClosedAdd, ClosedMul};
+use simba::scalar::{ClosedAdd, ClosedMul};
 
 use crate::base::allocator::Allocator;
 use crate::base::constraint::{AreMultipliable, ShapeConstraint};

src/geometry/rotation_simba.rs

@@ -0,0 +1,54 @@
+use simba::simd::SimdValue;
+
+use crate::base::allocator::Allocator;
+use crate::base::dimension::DimName;
+use crate::base::{DefaultAllocator, MatrixN, Scalar};
+
+use crate::geometry::Rotation;
+
+impl<N, D> SimdValue for Rotation<N, D>
+where
+    N: Scalar + SimdValue,
+    D: DimName,
+    N::Element: Scalar,
+    DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>,
+{
+    type Element = Rotation<N::Element, D>;
+    type SimdBool = N::SimdBool;
+
+    #[inline]
+    fn lanes() -> usize {
+        N::lanes()
+    }
+
+    #[inline]
+    fn splat(val: Self::Element) -> Self {
+        Rotation::from_matrix_unchecked(MatrixN::splat(val.into_inner()))
+    }
+
+    #[inline]
+    fn extract(&self, i: usize) -> Self::Element {
+        Rotation::from_matrix_unchecked(self.matrix().extract(i))
+    }
+
+    #[inline]
+    unsafe fn extract_unchecked(&self, i: usize) -> Self::Element {
+        Rotation::from_matrix_unchecked(self.matrix().extract_unchecked(i))
+    }
+
+    #[inline]
+    fn replace(&mut self, i: usize, val: Self::Element) {
+        self.matrix_mut_unchecked().replace(i, val.into_inner())
+    }
+
+    #[inline]
+    unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element) {
+        self.matrix_mut_unchecked()
+            .replace_unchecked(i, val.into_inner())
+    }
+
+    #[inline]
+    fn select(self, cond: Self::SimdBool, other: Self) -> Self {
+        Rotation::from_matrix_unchecked(self.into_inner().select(cond, other.into_inner()))
+    }
+}

src/geometry/rotation_specialization.rs

@@ -3,10 +3,10 @@ use crate::base::storage::Owned;
 #[cfg(feature = "arbitrary")]
 use quickcheck::{Arbitrary, Gen};
 
-use alga::general::RealField;
 use num::Zero;
 use rand::distributions::{Distribution, OpenClosed01, Standard};
 use rand::Rng;
+use simba::scalar::RealField;
 use std::ops::Neg;
 
 use crate::base::dimension::{U1, U2, U3};
@@ -77,10 +77,8 @@ impl<N: RealField> Rotation2<N> {
         let mut rot = guess.into_inner();
 
         for _ in 0..max_iter {
-            let axis = rot.column(0).perp(&m.column(0)) +
+            let axis = rot.column(0).perp(&m.column(0)) + rot.column(1).perp(&m.column(1));
-                rot.column(1).perp(&m.column(1));
+            let denom = rot.column(0).dot(&m.column(0)) + rot.column(1).dot(&m.column(1));
-            let denom = rot.column(0).dot(&m.column(0)) +
-                rot.column(1).dot(&m.column(1));
 
             let angle = axis / (denom.abs() + N::default_epsilon());
             if angle.abs() > eps {
@@ -192,7 +190,6 @@ impl<N: RealField> Rotation2<N> {
         other * self.inverse()
     }
 
-
     /// Ensure this rotation is an orthonormal rotation matrix. This is useful when repeated
     /// computations might cause the matrix from progressively not being orthonormal anymore.
     #[inline]
@@ -203,7 +200,6 @@ impl<N: RealField> Rotation2<N> {
         *self = Self::from_matrix_eps(self.matrix(), N::default_epsilon(), 0, c.into())
     }
 
-
     /// Raise the quaternion to a given floating power, i.e., returns the rotation with the angle
     /// of `self` multiplied by `n`.
     ///
@@ -314,12 +310,12 @@ impl<N: RealField> Rotation3<N> {
         let mut rot = guess.into_inner();
 
         for _ in 0..max_iter {
-            let axis = rot.column(0).cross(&m.column(0)) +
+            let axis = rot.column(0).cross(&m.column(0))
-                rot.column(1).cross(&m.column(1)) +
+                + rot.column(1).cross(&m.column(1))
-                rot.column(2).cross(&m.column(2));
+                + rot.column(2).cross(&m.column(2));
-            let denom = rot.column(0).dot(&m.column(0)) +
+            let denom = rot.column(0).dot(&m.column(0))
-                rot.column(1).dot(&m.column(1)) +
+                + rot.column(1).dot(&m.column(1))
-                rot.column(2).dot(&m.column(2));
+                + rot.column(2).dot(&m.column(2));
 
             let axisangle = axis / (denom.abs() + N::default_epsilon());
 

src/geometry/similarity.rs

@@ -10,14 +10,13 @@ use serde::{Deserialize, Serialize};
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use alga::general::{RealField, SubsetOf};
+use simba::scalar::{RealField, SubsetOf};
-use alga::linear::Rotation;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
 use crate::base::storage::Owned;
 use crate::base::{DefaultAllocator, MatrixN, VectorN};
-use crate::geometry::{Isometry, Point, Translation};
+use crate::geometry::{AbstractRotation, Isometry, Point, Translation};
 
 /// A similarity, i.e., an uniform scaling, followed by a rotation, followed by a translation.
 #[repr(C)]
@@ -25,21 +24,17 @@ use crate::geometry::{Isometry, Point, Translation};
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(serialize = "N: Serialize,
-        serialize = "N: Serialize,
                      R: Serialize,
                      DefaultAllocator: Allocator<N, D>,
-                     Owned<N, D>: Serialize"
+                     Owned<N, D>: Serialize"))
-    ))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(deserialize = "N: Deserialize<'de>,
-        deserialize = "N: Deserialize<'de>,
                        R: Deserialize<'de>,
                        DefaultAllocator: Allocator<N, D>,
-                       Owned<N, D>: Deserialize<'de>"
+                       Owned<N, D>: Deserialize<'de>"))
-    ))
 )]
 pub struct Similarity<N: RealField, D: DimName, R>
 where DefaultAllocator: Allocator<N, D>
@@ -80,13 +75,14 @@ where
     }
 }
 
-impl<N: RealField, D: DimName + Copy, R: Rotation<Point<N, D>> + Copy> Copy for Similarity<N, D, R>
+impl<N: RealField, D: DimName + Copy, R: AbstractRotation<N, D> + Copy> Copy for Similarity<N, D, R>
 where
     DefaultAllocator: Allocator<N, D>,
     Owned<N, D>: Copy,
-{}
+{
+}
 
-impl<N: RealField, D: DimName, R: Rotation<Point<N, D>> + Clone> Clone for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R: AbstractRotation<N, D> + Clone> Clone for Similarity<N, D, R>
 where DefaultAllocator: Allocator<N, D>
 {
     #[inline]
@@ -97,17 +93,12 @@ where DefaultAllocator: Allocator<N, D>
 
 impl<N: RealField, D: DimName, R> Similarity<N, D, R>
 where
-    R: Rotation<Point<N, D>>,
+    R: AbstractRotation<N, D>,
     DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new similarity from its rotational and translational parts.
     #[inline]
-    pub fn from_parts(
+    pub fn from_parts(translation: Translation<N, D>, rotation: R, scaling: N) -> Self {
-        translation: Translation<N, D>,
-        rotation: R,
-        scaling: N,
-    ) -> Self
-    {
         Self::from_isometry(Isometry::from_parts(translation, rotation), scaling)
     }
 
@@ -119,10 +110,7 @@ where
             "The scaling factor must not be zero."
         );
 
-        Self {
+        Self { isometry, scaling }
-            isometry: isometry,
-            scaling: scaling,
-        }
     }
 
     /// Creates a new similarity that applies only a scaling factor.
@@ -351,13 +339,14 @@ where DefaultAllocator: Allocator<N, D>
 
 impl<N: RealField, D: DimName, R> Eq for Similarity<N, D, R>
 where
-    R: Rotation<Point<N, D>> + Eq,
+    R: AbstractRotation<N, D> + Eq,
     DefaultAllocator: Allocator<N, D>,
-{}
+{
+}
 
 impl<N: RealField, D: DimName, R> PartialEq for Similarity<N, D, R>
 where
-    R: Rotation<Point<N, D>> + PartialEq,
+    R: AbstractRotation<N, D> + PartialEq,
     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
@@ -368,7 +357,7 @@ where
 
 impl<N: RealField, D: DimName, R> AbsDiffEq for Similarity<N, D, R>
 where
-    R: Rotation<Point<N, D>> + AbsDiffEq<Epsilon = N::Epsilon>,
+    R: AbstractRotation<N, D> + AbsDiffEq<Epsilon = N::Epsilon>,
     DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
@@ -388,7 +377,7 @@ where
 
 impl<N: RealField, D: DimName, R> RelativeEq for Similarity<N, D, R>
 where
-    R: Rotation<Point<N, D>> + RelativeEq<Epsilon = N::Epsilon>,
+    R: AbstractRotation<N, D> + RelativeEq<Epsilon = N::Epsilon>,
     DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
@@ -415,7 +404,7 @@ where
 
 impl<N: RealField, D: DimName, R> UlpsEq for Similarity<N, D, R>
 where
-    R: Rotation<Point<N, D>> + UlpsEq<Epsilon = N::Epsilon>,
+    R: AbstractRotation<N, D> + UlpsEq<Epsilon = N::Epsilon>,
     DefaultAllocator: Allocator<N, D>,
     N::Epsilon: Copy,
 {
@@ -439,7 +428,7 @@ where
 impl<N, D: DimName, R> fmt::Display for Similarity<N, D, R>
 where
     N: RealField + fmt::Display,
-    R: Rotation<Point<N, D>> + fmt::Display,
+    R: AbstractRotation<N, D> + fmt::Display,
     DefaultAllocator: Allocator<N, D> + Allocator<usize, D>,
 {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {

src/geometry/similarity_alga.rs

@@ -1,189 +0,0 @@
-use alga::general::{
-    AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Identity, TwoSidedInverse, Multiplicative, RealField,
-};
-use alga::linear::Similarity as AlgaSimilarity;
-use alga::linear::{AffineTransformation, ProjectiveTransformation, Rotation, Transformation};
-
-use crate::base::allocator::Allocator;
-use crate::base::dimension::DimName;
-use crate::base::{DefaultAllocator, VectorN};
-
-use crate::geometry::{Point, Similarity, Translation};
-
-/*
- *
- * Algebraic structures.
- *
- */
-impl<N: RealField, D: DimName, R> Identity<Multiplicative> for Similarity<N, D, R>
-where
-    R: Rotation<Point<N, D>>,
-    DefaultAllocator: Allocator<N, D>,
-{
-    #[inline]
-    fn identity() -> Self {
-        Self::identity()
-    }
-}
-
-impl<N: RealField, D: DimName, R> TwoSidedInverse<Multiplicative> for Similarity<N, D, R>
-where
-    R: Rotation<Point<N, D>>,
-    DefaultAllocator: Allocator<N, D>,
-{
-    #[inline]
-    #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
-    fn two_sided_inverse(&self) -> Self {
-        self.inverse()
-    }
-
-    #[inline]
-    fn two_sided_inverse_mut(&mut self) {
-        self.inverse_mut()
-    }
-}
-
-impl<N: RealField, D: DimName, R> AbstractMagma<Multiplicative> for Similarity<N, D, R>
-where
-    R: Rotation<Point<N, D>>,
-    DefaultAllocator: Allocator<N, D>,
-{
-    #[inline]
-    fn operate(&self, rhs: &Self) -> Self {
-        self * rhs
-    }
-}
-
-macro_rules! impl_multiplicative_structures(
-    ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: RealField, D: DimName, R> $marker<$operator> for Similarity<N, D, R>
-            where R: Rotation<Point<N, D>>,
-                  DefaultAllocator: Allocator<N, D> { }
-    )*}
-);
-
-impl_multiplicative_structures!(
-    AbstractSemigroup<Multiplicative>,
-    AbstractMonoid<Multiplicative>,
-    AbstractQuasigroup<Multiplicative>,
-    AbstractLoop<Multiplicative>,
-    AbstractGroup<Multiplicative>
-);
-
-/*
- *
- * Transformation groups.
- *
- */
-impl<N: RealField, D: DimName, R> Transformation<Point<N, D>> for Similarity<N, D, R>
-where
-    R: Rotation<Point<N, D>>,
-    DefaultAllocator: Allocator<N, D>,
-{
-    #[inline]
-    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
-        self.transform_point(pt)
-    }
-
-    #[inline]
-    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
-        self.transform_vector(v)
-    }
-}
-
-impl<N: RealField, D: DimName, R> ProjectiveTransformation<Point<N, D>> for Similarity<N, D, R>
-where
-    R: Rotation<Point<N, D>>,
-    DefaultAllocator: Allocator<N, D>,
-{
-    #[inline]
-    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
-        self.inverse_transform_point(pt)
-    }
-
-    #[inline]
-    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
-        self.inverse_transform_vector(v)
-    }
-}
-
-impl<N: RealField, D: DimName, R> AffineTransformation<Point<N, D>> for Similarity<N, D, R>
-where
-    R: Rotation<Point<N, D>>,
-    DefaultAllocator: Allocator<N, D>,
-{
-    type NonUniformScaling = N;
-    type Rotation = R;
-    type Translation = Translation<N, D>;
-
-    #[inline]
-    fn decompose(&self) -> (Translation<N, D>, R, N, R) {
-        (
-            self.isometry.translation.clone(),
-            self.isometry.rotation.clone(),
-            self.scaling(),
-            R::identity(),
-        )
-    }
-
-    #[inline]
-    fn append_translation(&self, t: &Self::Translation) -> Self {
-        t * self
-    }
-
-    #[inline]
-    fn prepend_translation(&self, t: &Self::Translation) -> Self {
-        self * t
-    }
-
-    #[inline]
-    fn append_rotation(&self, r: &Self::Rotation) -> Self {
-        Similarity::from_isometry(self.isometry.append_rotation(r), self.scaling())
-    }
-
-    #[inline]
-    fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
-        self * r
-    }
-
-    #[inline]
-    fn append_scaling(&self, s: &Self::NonUniformScaling) -> Self {
-        self.append_scaling(*s)
-    }
-
-    #[inline]
-    fn prepend_scaling(&self, s: &Self::NonUniformScaling) -> Self {
-        self.prepend_scaling(*s)
-    }
-
-    #[inline]
-    fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &Point<N, D>) -> Option<Self> {
-        let mut res = self.clone();
-        res.append_rotation_wrt_point_mut(r, p);
-        Some(res)
-    }
-}
-
-impl<N: RealField, D: DimName, R> AlgaSimilarity<Point<N, D>> for Similarity<N, D, R>
-where
-    R: Rotation<Point<N, D>>,
-    DefaultAllocator: Allocator<N, D>,
-{
-    type Scaling = N;
-
-    #[inline]
-    fn translation(&self) -> Translation<N, D> {
-        self.isometry.translation()
-    }
-
-    #[inline]
-    fn rotation(&self) -> R {
-        self.isometry.rotation()
-    }
-
-    #[inline]
-    fn scaling(&self) -> N {
-        self.scaling()
-    }
-}

src/geometry/similarity_construction.rs

@@ -7,21 +7,20 @@ use num::One;
 use rand::distributions::{Distribution, Standard};
 use rand::Rng;
 
-use alga::general::RealField;
+use simba::scalar::RealField;
-use alga::linear::Rotation as AlgaRotation;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, U2, U3};
 use crate::base::{DefaultAllocator, Vector2, Vector3};
 
 use crate::geometry::{
-    Isometry, Point, Point3, Rotation2, Rotation3, Similarity, Translation, UnitComplex,
+    AbstractRotation, Isometry, Point, Point3, Rotation2, Rotation3, Similarity, Translation,
-    UnitQuaternion,
+    UnitComplex, UnitQuaternion,
 };
 
 impl<N: RealField, D: DimName, R> Similarity<N, D, R>
 where
-    R: AlgaRotation<Point<N, D>>,
+    R: AbstractRotation<N, D>,
     DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new identity similarity.
@@ -47,7 +46,7 @@ where
 
 impl<N: RealField, D: DimName, R> One for Similarity<N, D, R>
 where
-    R: AlgaRotation<Point<N, D>>,
+    R: AbstractRotation<N, D>,
     DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new identity similarity.
@@ -59,7 +58,7 @@ where
 
 impl<N: RealField, D: DimName, R> Distribution<Similarity<N, D, R>> for Standard
 where
-    R: AlgaRotation<Point<N, D>>,
+    R: AbstractRotation<N, D>,
     DefaultAllocator: Allocator<N, D>,
     Standard: Distribution<N> + Distribution<R>,
 {
@@ -76,7 +75,7 @@ where
 
 impl<N: RealField, D: DimName, R> Similarity<N, D, R>
 where
-    R: AlgaRotation<Point<N, D>>,
+    R: AbstractRotation<N, D>,
     DefaultAllocator: Allocator<N, D>,
 {
     /// The similarity that applies the scaling factor `scaling`, followed by the rotation `r` with
@@ -105,7 +104,7 @@ where
 impl<N, D: DimName, R> Arbitrary for Similarity<N, D, R>
 where
     N: RealField + Arbitrary + Send,
-    R: AlgaRotation<Point<N, D>> + Arbitrary + Send,
+    R: AbstractRotation<N, D> + Arbitrary + Send,
     DefaultAllocator: Allocator<N, D>,
     Owned<N, D>: Send,
 {

src/geometry/similarity_conversion.rs

@@ -1,11 +1,12 @@
-use alga::general::{RealField, SubsetOf, SupersetOf};
+use simba::scalar::{RealField, SubsetOf, SupersetOf};
-use alga::linear::Rotation;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimMin, DimName, DimNameAdd, DimNameSum, U1};
 use crate::base::{DefaultAllocator, MatrixN};
 
-use crate::geometry::{Isometry, Point, Similarity, SuperTCategoryOf, TAffine, Transform, Translation};
+use crate::geometry::{
+    AbstractRotation, Isometry, Similarity, SuperTCategoryOf, TAffine, Transform, Translation,
+};
 
 /*
  * This file provides the following conversions:
@@ -20,8 +21,8 @@ impl<N1, N2, D: DimName, R1, R2> SubsetOf<Similarity<N2, D, R2>> for Similarity<
 where
     N1: RealField + SubsetOf<N2>,
     N2: RealField + SupersetOf<N1>,
-    R1: Rotation<Point<N1, D>> + SubsetOf<R2>,
+    R1: AbstractRotation<N1, D> + SubsetOf<R2>,
-    R2: Rotation<Point<N2, D>>,
+    R2: AbstractRotation<N2, D>,
     DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
@@ -36,7 +37,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(sim: &Similarity<N2, D, R2>) -> Self {
+    fn from_superset_unchecked(sim: &Similarity<N2, D, R2>) -> Self {
         Similarity::from_isometry(
             sim.isometry.to_subset_unchecked(),
             sim.scaling().to_subset_unchecked(),
@@ -49,7 +50,7 @@ where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
     C: SuperTCategoryOf<TAffine>,
-    R: Rotation<Point<N1, D>>
+    R: AbstractRotation<N1, D>
         + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>>
         + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
     D: DimNameAdd<U1> + DimMin<D, Output = D>, // needed by .determinant()
@@ -73,7 +74,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
+    fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
@@ -82,7 +83,7 @@ impl<N1, N2, D, R> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Similarity<N1, D
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R: Rotation<Point<N1, D>>
+    R: AbstractRotation<N1, D>
         + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>>
         + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
     D: DimNameAdd<U1> + DimMin<D, Output = D>, // needed by .determinant()
@@ -137,7 +138,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
+    fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
         let mut mm = m.clone_owned();
         let na = mm.fixed_slice_mut::<D, U1>(0, 0).normalize_mut();
         let nb = mm.fixed_slice_mut::<D, U1>(0, 1).normalize_mut();
@@ -159,7 +160,11 @@ where
             vector: crate::convert_unchecked(t),
         };
 
-        Self::from_parts(t, crate::convert_unchecked(mm), crate::convert_unchecked(scale))
+        Self::from_parts(
+            t,
+            crate::convert_unchecked(mm),
+            crate::convert_unchecked(scale),
+        )
     }
 }
 

src/geometry/similarity_ops.rs

@@ -1,13 +1,15 @@
+use num::{One, Zero};
 use std::ops::{Div, DivAssign, Mul, MulAssign};
 
-use alga::general::RealField;
+use simba::scalar::{ClosedAdd, ClosedMul, RealField};
-use alga::linear::Rotation as AlgaRotation;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, U1, U3, U4};
-use crate::base::{DefaultAllocator, VectorN};
+use crate::base::{DefaultAllocator, Scalar, VectorN};
 
-use crate::geometry::{Isometry, Point, Rotation, Similarity, Translation, UnitQuaternion};
+use crate::geometry::{
+    AbstractRotation, Isometry, Point, Rotation, Similarity, Translation, UnitQuaternion,
+};
 
 // FIXME: there are several cloning of rotations that we could probably get rid of (but we didn't
 // yet because that would require to add a bound like `where for<'a, 'b> &'a R: Mul<&'b R, Output = R>`
@@ -67,7 +69,7 @@ macro_rules! similarity_binop_impl(
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      $action: expr; $($lives: tt),*) => {
         impl<$($lives ,)* N: RealField, D: DimName, R> $Op<$Rhs> for $Lhs
-            where R: AlgaRotation<Point<N, D>>,
+            where R: AbstractRotation<N, D>,
                   DefaultAllocator: Allocator<N, D> {
             type Output = $Output;
 
@@ -114,7 +116,7 @@ macro_rules! similarity_binop_assign_impl_all(
      [val] => $action_val: expr;
      [ref] => $action_ref: expr;) => {
         impl<N: RealField, D: DimName, R> $OpAssign<$Rhs> for $Lhs
-            where R: AlgaRotation<Point<N, D>>,
+            where R: AbstractRotation<N, D>,
                   DefaultAllocator: Allocator<N, D> {
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: $Rhs) {
@@ -123,7 +125,7 @@ macro_rules! similarity_binop_assign_impl_all(
         }
 
         impl<'b, N: RealField, D: DimName, R> $OpAssign<&'b $Rhs> for $Lhs
-            where R: AlgaRotation<Point<N, D>>,
+            where R: AbstractRotation<N, D>,
                   DefaultAllocator: Allocator<N, D> {
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: &'b $Rhs) {
@@ -211,51 +213,38 @@ similarity_binop_assign_impl_all!(
 
 // Similarity ×= R
 // Similarity ÷= R
-similarity_binop_assign_impl_all!(
+md_assign_impl_all!(
-    MulAssign, mul_assign;
+    MulAssign, mul_assign where N: RealField;
-    self: Similarity<N, D, R>, rhs: R;
+    (D, U1), (D, D) for D: DimName;
+    self: Similarity<N, D, Rotation<N, D>>, rhs: Rotation<N, D>;
     [val] => self.isometry.rotation *= rhs;
     [ref] => self.isometry.rotation *= rhs.clone();
 );
 
-similarity_binop_assign_impl_all!(
+md_assign_impl_all!(
-    DivAssign, div_assign;
+    DivAssign, div_assign where N: RealField;
-    self: Similarity<N, D, R>, rhs: R;
+    (D, U1), (D, D) for D: DimName;
+    self: Similarity<N, D, Rotation<N, D>>, rhs: Rotation<N, D>;
     // FIXME: don't invert explicitly?
-    [val] => *self *= rhs.two_sided_inverse();
+    [val] => *self *= rhs.inverse();
-    [ref] => *self *= rhs.two_sided_inverse();
+    [ref] => *self *= rhs.inverse();
 );
 
-// Similarity × R
+md_assign_impl_all!(
-// Similarity ÷ R
+    MulAssign, mul_assign where N: RealField;
-similarity_binop_impl_all!(
+    (U3, U3), (U3, U3) for;
-    Mul, mul;
+    self: Similarity<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>;
-    self: Similarity<N, D, R>, rhs: R, Output = Similarity<N, D, R>;
+    [val] => self.isometry.rotation *= rhs;
-    [val val] => {
+    [ref] => self.isometry.rotation *= rhs.clone();
-        let scaling = self.scaling();
-        Similarity::from_isometry(self.isometry * rhs, scaling)
-    };
-    [ref val] => Similarity::from_isometry(&self.isometry * rhs, self.scaling());
-    [val ref] => {
-        let scaling = self.scaling();
-        Similarity::from_isometry(self.isometry * rhs, scaling)
-    };
-    [ref ref] => Similarity::from_isometry(&self.isometry * rhs, self.scaling());
 );
 
-similarity_binop_impl_all!(
+md_assign_impl_all!(
-    Div, div;
+    DivAssign, div_assign where N: RealField;
-    self: Similarity<N, D, R>, rhs: R, Output = Similarity<N, D, R>;
+    (U3, U3), (U3, U3) for;
-    [val val] => {
+    self: Similarity<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>;
-        let scaling = self.scaling();
+    // FIXME: don't invert explicitly?
-        Similarity::from_isometry(self.isometry / rhs, scaling)
+    [val] => *self *= rhs.inverse();
-    };
+    [ref] => *self *= rhs.inverse();
-    [ref val] => Similarity::from_isometry(&self.isometry / rhs, self.scaling());
-    [val ref] => {
-        let scaling = self.scaling();
-        Similarity::from_isometry(self.isometry / rhs, scaling)
-    };
-    [ref ref] => Similarity::from_isometry(&self.isometry / rhs, self.scaling());
 );
 
 // Similarity × Isometry
@@ -427,6 +416,24 @@ macro_rules! similarity_from_composition_impl_all(
     }
 );
 
+// Similarity × Rotation
+similarity_from_composition_impl_all!(
+    Mul, mul;
+    (D, D), (D, U1) for D: DimName;
+    self: Similarity<N, D, Rotation<N, D>>, rhs: Rotation<N, D>,
+    Output = Similarity<N, D, Rotation<N, D>>;
+    [val val] => {
+        let scaling = self.scaling();
+        Similarity::from_isometry(self.isometry * rhs, scaling)
+    };
+    [ref val] => Similarity::from_isometry(&self.isometry * rhs, self.scaling());
+    [val ref] => {
+        let scaling = self.scaling();
+        Similarity::from_isometry(self.isometry * rhs, scaling)
+    };
+    [ref ref] => Similarity::from_isometry(&self.isometry * rhs, self.scaling());
+);
+
 // Rotation × Similarity
 similarity_from_composition_impl_all!(
     Mul, mul;
@@ -439,6 +446,24 @@ similarity_from_composition_impl_all!(
     [ref ref] => Similarity::from_isometry(self * &right.isometry, right.scaling());
 );
 
+// Similarity ÷ Rotation
+similarity_from_composition_impl_all!(
+    Div, div;
+    (D, D), (D, U1) for D: DimName;
+    self: Similarity<N, D, Rotation<N, D>>, rhs: Rotation<N, D>,
+    Output = Similarity<N, D, Rotation<N, D>>;
+    [val val] => {
+        let scaling = self.scaling();
+        Similarity::from_isometry(self.isometry / rhs, scaling)
+    };
+    [ref val] => Similarity::from_isometry(&self.isometry / rhs, self.scaling());
+    [val ref] => {
+        let scaling = self.scaling();
+        Similarity::from_isometry(self.isometry / rhs, scaling)
+    };
+    [ref ref] => Similarity::from_isometry(&self.isometry / rhs, self.scaling());
+);
+
 // Rotation ÷ Similarity
 similarity_from_composition_impl_all!(
     Div, div;
@@ -452,6 +477,24 @@ similarity_from_composition_impl_all!(
     [ref ref] => self * right.inverse();
 );
 
+// Similarity × UnitQuaternion
+similarity_from_composition_impl_all!(
+    Mul, mul;
+    (U4, U1), (U3, U1);
+    self: Similarity<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>,
+    Output = Similarity<N, U3, UnitQuaternion<N>>;
+    [val val] => {
+        let scaling = self.scaling();
+        Similarity::from_isometry(self.isometry * rhs, scaling)
+    };
+    [ref val] => Similarity::from_isometry(&self.isometry * rhs, self.scaling());
+    [val ref] => {
+        let scaling = self.scaling();
+        Similarity::from_isometry(self.isometry * rhs, scaling)
+    };
+    [ref ref] => Similarity::from_isometry(&self.isometry * rhs, self.scaling());
+);
+
 // UnitQuaternion × Similarity
 similarity_from_composition_impl_all!(
     Mul, mul;
@@ -464,6 +507,24 @@ similarity_from_composition_impl_all!(
     [ref ref] => Similarity::from_isometry(self * &right.isometry, right.scaling());
 );
 
+// Similarity ÷ Rotation
+similarity_from_composition_impl_all!(
+    Div, div;
+    (U4, U1), (U3, U1);
+    self: Similarity<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>,
+    Output = Similarity<N, U3, UnitQuaternion<N>>;
+    [val val] => {
+        let scaling = self.scaling();
+        Similarity::from_isometry(self.isometry / rhs, scaling)
+    };
+    [ref val] => Similarity::from_isometry(&self.isometry / rhs, self.scaling());
+    [val ref] => {
+        let scaling = self.scaling();
+        Similarity::from_isometry(self.isometry / rhs, scaling)
+    };
+    [ref ref] => Similarity::from_isometry(&self.isometry / rhs, self.scaling());
+);
+
 // UnitQuaternion ÷ Similarity
 similarity_from_composition_impl_all!(
     Div, div;

src/geometry/similarity_simba.rs

@@ -0,0 +1,65 @@
+use simba::simd::SimdValue;
+
+use crate::base::allocator::Allocator;
+use crate::base::dimension::DimName;
+use crate::base::{DefaultAllocator, Scalar};
+use crate::RealField;
+
+use crate::geometry::{AbstractRotation, Isometry, Similarity};
+
+impl<N: RealField, D: DimName, R> SimdValue for Similarity<N, D, R>
+where
+    N::Element: Scalar,
+    R: SimdValue<SimdBool = N::SimdBool> + AbstractRotation<N, D>,
+    R::Element: AbstractRotation<N, D>,
+    DefaultAllocator: Allocator<N, D>,
+{
+    type Element = Similarity<N::Element, D, R::Element>;
+    type SimdBool = N::SimdBool;
+
+    #[inline]
+    fn lanes() -> usize {
+        N::lanes()
+    }
+
+    #[inline]
+    fn splat(val: Self::Element) -> Self {
+        let scaling = N::splat(val.scaling());
+        Similarity::from_isometry(Isometry::splat(val.isometry), scaling)
+    }
+
+    #[inline]
+    fn extract(&self, i: usize) -> Self::Element {
+        Similarity::from_isometry(self.isometry.extract(i), self.scaling().extract(i))
+    }
+
+    #[inline]
+    unsafe fn extract_unchecked(&self, i: usize) -> Self::Element {
+        Similarity::from_isometry(
+            self.isometry.extract_unchecked(i),
+            self.scaling().extract_unchecked(i),
+        )
+    }
+
+    #[inline]
+    fn replace(&mut self, i: usize, val: Self::Element) {
+        let mut s = self.scaling();
+        s.replace(i, val.scaling());
+        self.set_scaling(s);
+        self.isometry.replace(i, val.isometry);
+    }
+
+    #[inline]
+    unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element) {
+        let mut s = self.scaling();
+        s.replace_unchecked(i, val.scaling());
+        self.set_scaling(s);
+        self.isometry.replace_unchecked(i, val.isometry);
+    }
+
+    #[inline]
+    fn select(self, cond: Self::SimdBool, other: Self) -> Self {
+        let scaling = self.scaling().select(cond, other.scaling());
+        Similarity::from_isometry(self.isometry.select(cond, other.isometry), scaling)
+    }
+}

src/geometry/transform.rs

@@ -6,7 +6,7 @@ use std::marker::PhantomData;
 #[cfg(feature = "serde-serialize")]
 use serde::{Deserialize, Deserializer, Serialize, Serializer};
 
-use alga::general::{RealField, TwoSidedInverse};
+use simba::scalar::RealField;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
@@ -484,7 +484,8 @@ where
 }
 
 impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> Transform<N, D, C>
-where C: SubTCategoryOf<TProjective>,
+where
+    C: SubTCategoryOf<TProjective>,
     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
         + Allocator<N, DimNameSum<D, U1>>
         + Allocator<N, D, D>
@@ -495,7 +496,7 @@ where C: SubTCategoryOf<TProjective>,
     /// the point.
     #[inline]
     pub fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
-        self.two_sided_inverse() * pt
+        self.clone().inverse() * pt
     }
 
     /// Transform the given vector by the inverse of this transformation.
@@ -503,7 +504,7 @@ where C: SubTCategoryOf<TProjective>,
     /// the vector.
     #[inline]
     pub fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
-        self.two_sided_inverse() * v
+        self.clone().inverse() * v
     }
 }
 

src/geometry/transform_alga.rs

@@ -1,146 +0,0 @@
-use alga::general::{
-    AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Identity, TwoSidedInverse, Multiplicative, RealField,
-};
-use alga::linear::{ProjectiveTransformation, Transformation};
-
-use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
-use crate::base::{DefaultAllocator, VectorN};
-
-use crate::geometry::{Point, SubTCategoryOf, TCategory, TProjective, Transform};
-
-/*
- *
- * Algebraic structures.
- *
- */
-impl<N: RealField, D: DimNameAdd<U1>, C> Identity<Multiplicative> for Transform<N, D, C>
-where
-    C: TCategory,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-{
-    #[inline]
-    fn identity() -> Self {
-        Self::identity()
-    }
-}
-
-impl<N: RealField, D: DimNameAdd<U1>, C> TwoSidedInverse<Multiplicative> for Transform<N, D, C>
-where
-    C: SubTCategoryOf<TProjective>,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-{
-    #[inline]
-    #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
-    fn two_sided_inverse(&self) -> Self {
-        self.clone().inverse()
-    }
-
-    #[inline]
-    fn two_sided_inverse_mut(&mut self) {
-        self.inverse_mut()
-    }
-}
-
-impl<N: RealField, D: DimNameAdd<U1>, C> AbstractMagma<Multiplicative> for Transform<N, D, C>
-where
-    C: TCategory,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
-{
-    #[inline]
-    fn operate(&self, rhs: &Self) -> Self {
-        self * rhs
-    }
-}
-
-macro_rules! impl_multiplicative_structures(
-    ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: RealField, D: DimNameAdd<U1>, C> $marker<$operator> for Transform<N, D, C>
-            where C: TCategory,
-                  DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> { }
-    )*}
-);
-
-macro_rules! impl_inversible_multiplicative_structures(
-    ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: RealField, D: DimNameAdd<U1>, C> $marker<$operator> for Transform<N, D, C>
-            where C: SubTCategoryOf<TProjective>,
-                  DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> { }
-    )*}
-);
-
-impl_multiplicative_structures!(
-    AbstractSemigroup<Multiplicative>,
-    AbstractMonoid<Multiplicative>,
-);
-
-impl_inversible_multiplicative_structures!(
-    AbstractQuasigroup<Multiplicative>,
-    AbstractLoop<Multiplicative>,
-    AbstractGroup<Multiplicative>
-);
-
-/*
- *
- * Transformation groups.
- *
- */
-impl<N, D: DimNameAdd<U1>, C> Transformation<Point<N, D>> for Transform<N, D, C>
-where
-    N: RealField,
-    C: TCategory,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N, DimNameSum<D, U1>>
-        + Allocator<N, D, D>
-        + Allocator<N, D>,
-{
-    #[inline]
-    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
-        self.transform_point(pt)
-    }
-
-    #[inline]
-    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
-        self.transform_vector(v)
-    }
-}
-
-impl<N, D: DimNameAdd<U1>, C> ProjectiveTransformation<Point<N, D>> for Transform<N, D, C>
-where
-    N: RealField,
-    C: SubTCategoryOf<TProjective>,
-    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
-        + Allocator<N, DimNameSum<D, U1>>
-        + Allocator<N, D, D>
-        + Allocator<N, D>,
-{
-    #[inline]
-    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
-        self.inverse_transform_point(pt)
-    }
-
-    #[inline]
-    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
-        self.inverse_transform_vector(v)
-    }
-}
-
-// FIXME: we need to implement an SVD for this.
-//
-// impl<N, D: DimNameAdd<U1>, C> AffineTransformation<Point<N, D>> for Transform<N, D, C>
-//     where N:  RealField,
-//           C: SubTCategoryOf<TAffine>,
-//           DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> +
-//                             Allocator<N, D, D> +
-//                             Allocator<N, D> {
-//     type PreRotation       = Rotation<N, D>;
-//     type NonUniformScaling = VectorN<N, D>;
-//     type PostRotation      = Rotation<N, D>;
-//     type Translation       = Translation<N, D>;
-//
-//     #[inline]
-//     fn decompose(&self) -> (Self::Translation, Self::PostRotation, Self::NonUniformScaling, Self::PreRotation) {
-//         unimplemented!()
-//     }
-// }

src/geometry/transform_construction.rs

@@ -1,6 +1,6 @@
 use num::One;
 
-use alga::general::RealField;
+use simba::scalar::RealField;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimNameAdd, DimNameSum, U1};

src/geometry/transform_conversion.rs

@@ -1,4 +1,4 @@
-use alga::general::{RealField, SubsetOf};
+use simba::scalar::{RealField, SubsetOf};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
@@ -29,7 +29,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(t: &Transform<N2, D, C2>) -> Self {
+    fn from_superset_unchecked(t: &Transform<N2, D, C2>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
@@ -56,7 +56,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
+    fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
         Self::from_matrix_unchecked(crate::convert_ref_unchecked(m))
     }
 }

src/geometry/transform_ops.rs

@@ -1,7 +1,7 @@
 use num::{One, Zero};
 use std::ops::{Div, DivAssign, Index, IndexMut, Mul, MulAssign};
 
-use alga::general::{ClosedAdd, ClosedMul, RealField, SubsetOf};
+use simba::scalar::{ClosedAdd, ClosedMul, RealField, SubsetOf};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1, U3, U4};

src/geometry/transform_simba.rs

@@ -0,0 +1,55 @@
+use simba::simd::SimdValue;
+
+use crate::base::allocator::Allocator;
+use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
+use crate::base::{DefaultAllocator, MatrixN, Scalar};
+use crate::RealField;
+
+use crate::geometry::{TCategory, Transform};
+
+impl<N: RealField, D: DimNameAdd<U1>, C> SimdValue for Transform<N, D, C>
+where
+    N::Element: Scalar,
+    C: TCategory,
+    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
+        + Allocator<N::Element, DimNameSum<D, U1>, DimNameSum<D, U1>>,
+{
+    type Element = Transform<N::Element, D, C>;
+    type SimdBool = N::SimdBool;
+
+    #[inline]
+    fn lanes() -> usize {
+        N::lanes()
+    }
+
+    #[inline]
+    fn splat(val: Self::Element) -> Self {
+        Transform::from_matrix_unchecked(MatrixN::splat(val.into_inner()))
+    }
+
+    #[inline]
+    fn extract(&self, i: usize) -> Self::Element {
+        Transform::from_matrix_unchecked(self.matrix().extract(i))
+    }
+
+    #[inline]
+    unsafe fn extract_unchecked(&self, i: usize) -> Self::Element {
+        Transform::from_matrix_unchecked(self.matrix().extract_unchecked(i))
+    }
+
+    #[inline]
+    fn replace(&mut self, i: usize, val: Self::Element) {
+        self.matrix_mut_unchecked().replace(i, val.into_inner())
+    }
+
+    #[inline]
+    unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element) {
+        self.matrix_mut_unchecked()
+            .replace_unchecked(i, val.into_inner())
+    }
+
+    #[inline]
+    fn select(self, cond: Self::SimdBool, other: Self) -> Self {
+        Transform::from_matrix_unchecked(self.into_inner().select(cond, other.into_inner()))
+    }
+}

src/geometry/translation.rs

@@ -11,7 +11,7 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use alga::general::{ClosedAdd, ClosedNeg, ClosedSub, RealField};
+use simba::scalar::{ClosedAdd, ClosedNeg, ClosedSub, RealField};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
@@ -45,7 +45,8 @@ impl<N: Scalar + Copy, D: DimName> Copy for Translation<N, D>
 where
     DefaultAllocator: Allocator<N, D>,
     Owned<N, D>: Copy,
-{}
+{
+}
 
 impl<N: Scalar, D: DimName> Clone for Translation<N, D>
 where
@@ -302,7 +303,7 @@ where
  * Display
  *
  */
-impl<N: RealField + fmt::Display, D: DimName> fmt::Display for Translation<N, D>
+impl<N: Scalar + fmt::Display, D: DimName> fmt::Display for Translation<N, D>
 where DefaultAllocator: Allocator<N, D> + Allocator<usize, D>
 {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {

src/geometry/translation_alga.rs

@@ -1,199 +1,52 @@
-use alga::general::{
+use simba::simd::SimdValue;
-    AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, RealField,
-};
-use alga::linear::Translation as AlgaTranslation;
-use alga::linear::{
-    AffineTransformation, DirectIsometry, Isometry, ProjectiveTransformation, Similarity,
-    Transformation,
-};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::DimName;
 use crate::base::{DefaultAllocator, VectorN};
+use crate::Scalar;
 
-use crate::geometry::{Point, Translation};
+use crate::geometry::Translation;
 
-/*
+impl<N: Scalar + SimdValue, D: DimName> SimdValue for Translation<N, D>
- *
+where
- * Algebraic structures.
+    N::Element: Scalar,
- *
+    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
- */
-impl<N: RealField, D: DimName> Identity<Multiplicative> for Translation<N, D>
-where DefaultAllocator: Allocator<N, D>
 {
-    #[inline]
+    type Element = Translation<N::Element, D>;
-    fn identity() -> Self {
+    type SimdBool = N::SimdBool;
-        Self::identity()
-    }
-}
 
-impl<N: RealField, D: DimName> TwoSidedInverse<Multiplicative> for Translation<N, D>
-where DefaultAllocator: Allocator<N, D>
-{
     #[inline]
-    #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
+    fn lanes() -> usize {
-    fn two_sided_inverse(&self) -> Self {
+        N::lanes()
-        self.inverse()
     }
 
     #[inline]
-    fn two_sided_inverse_mut(&mut self) {
+    fn splat(val: Self::Element) -> Self {
-        self.inverse_mut()
+        VectorN::splat(val.vector).into()
-    }
-}
-
-impl<N: RealField, D: DimName> AbstractMagma<Multiplicative> for Translation<N, D>
-where DefaultAllocator: Allocator<N, D>
-{
-    #[inline]
-    fn operate(&self, rhs: &Self) -> Self {
-        self * rhs
-    }
-}
-
-macro_rules! impl_multiplicative_structures(
-    ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: RealField, D: DimName> $marker<$operator> for Translation<N, D>
-            where DefaultAllocator: Allocator<N, D> { }
-    )*}
-);
-
-impl_multiplicative_structures!(
-    AbstractSemigroup<Multiplicative>,
-    AbstractMonoid<Multiplicative>,
-    AbstractQuasigroup<Multiplicative>,
-    AbstractLoop<Multiplicative>,
-    AbstractGroup<Multiplicative>
-);
-
-/*
- *
- * Transformation groups.
- *
- */
-impl<N: RealField, D: DimName> Transformation<Point<N, D>> for Translation<N, D>
-where DefaultAllocator: Allocator<N, D>
-{
-    #[inline]
-    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
-        self.transform_point(pt)
     }
 
     #[inline]
-    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    fn extract(&self, i: usize) -> Self::Element {
-        v.clone()
+        self.vector.extract(i).into()
-    }
-}
-
-impl<N: RealField, D: DimName> ProjectiveTransformation<Point<N, D>> for Translation<N, D>
-where DefaultAllocator: Allocator<N, D>
-{
-    #[inline]
-    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
-        self.inverse_transform_point(pt)
     }
 
     #[inline]
-    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
+    unsafe fn extract_unchecked(&self, i: usize) -> Self::Element {
-        v.clone()
+        self.vector.extract_unchecked(i).into()
-    }
-}
-
-impl<N: RealField, D: DimName> AffineTransformation<Point<N, D>> for Translation<N, D>
-where DefaultAllocator: Allocator<N, D>
-{
-    type Rotation = Id;
-    type NonUniformScaling = Id;
-    type Translation = Self;
-
-    #[inline]
-    fn decompose(&self) -> (Self, Id, Id, Id) {
-        (self.clone(), Id::new(), Id::new(), Id::new())
     }
 
     #[inline]
-    fn append_translation(&self, t: &Self::Translation) -> Self {
+    fn replace(&mut self, i: usize, val: Self::Element) {
-        t * self
+        self.vector.replace(i, val.vector)
     }
 
     #[inline]
-    fn prepend_translation(&self, t: &Self::Translation) -> Self {
+    unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element) {
-        self * t
+        self.vector.replace_unchecked(i, val.vector)
     }
 
     #[inline]
-    fn append_rotation(&self, _: &Self::Rotation) -> Self {
+    fn select(self, cond: Self::SimdBool, other: Self) -> Self {
-        self.clone()
+        self.vector.select(cond, other.vector).into()
-    }
-
-    #[inline]
-    fn prepend_rotation(&self, _: &Self::Rotation) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self {
-        self.clone()
-    }
-}
-
-impl<N: RealField, D: DimName> Similarity<Point<N, D>> for Translation<N, D>
-where DefaultAllocator: Allocator<N, D>
-{
-    type Scaling = Id;
-
-    #[inline]
-    fn translation(&self) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn rotation(&self) -> Id {
-        Id::new()
-    }
-
-    #[inline]
-    fn scaling(&self) -> Id {
-        Id::new()
-    }
-}
-
-macro_rules! marker_impl(
-    ($($Trait: ident),*) => {$(
-        impl<N: RealField, D: DimName> $Trait<Point<N, D>> for Translation<N, D>
-            where DefaultAllocator: Allocator<N, D> { }
-    )*}
-);
-
-marker_impl!(Isometry, DirectIsometry);
-
-/// Subgroups of the n-dimensional translation group `T(n)`.
-impl<N: RealField, D: DimName> AlgaTranslation<Point<N, D>> for Translation<N, D>
-where DefaultAllocator: Allocator<N, D>
-{
-    #[inline]
-    fn to_vector(&self) -> VectorN<N, D> {
-        self.vector.clone()
-    }
-
-    #[inline]
-    fn from_vector(v: VectorN<N, D>) -> Option<Self> {
-        Some(Self::from(v))
-    }
-
-    #[inline]
-    fn powf(&self, n: N) -> Option<Self> {
-        Some(Self::from(&self.vector * n))
-    }
-
-    #[inline]
-    fn translation_between(a: &Point<N, D>, b: &Point<N, D>) -> Option<Self> {
-        Some(Self::from(b - a))
     }
 }

src/geometry/translation_construction.rs

@@ -7,7 +7,7 @@ use num::{One, Zero};
 use rand::distributions::{Distribution, Standard};
 use rand::Rng;
 
-use alga::general::ClosedAdd;
+use simba::scalar::ClosedAdd;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, U1, U2, U3, U4, U5, U6};

src/geometry/translation_conversion.rs

@@ -1,13 +1,14 @@
 use num::{One, Zero};
 
-use alga::general::{RealField, SubsetOf, SupersetOf};
+use simba::scalar::{RealField, SubsetOf, SupersetOf};
-use alga::linear::Rotation;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
 use crate::base::{DefaultAllocator, MatrixN, Scalar, VectorN};
 
-use crate::geometry::{Isometry, Point, Similarity, SuperTCategoryOf, TAffine, Transform, Translation};
+use crate::geometry::{
+    AbstractRotation, Isometry, Similarity, SuperTCategoryOf, TAffine, Transform, Translation,
+};
 
 /*
  * This file provides the following conversions:
@@ -37,7 +38,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(rot: &Translation<N2, D>) -> Self {
+    fn from_superset_unchecked(rot: &Translation<N2, D>) -> Self {
         Translation {
             vector: rot.vector.to_subset_unchecked(),
         }
@@ -48,7 +49,7 @@ impl<N1, N2, D: DimName, R> SubsetOf<Isometry<N2, D, R>> for Translation<N1, D>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R: Rotation<Point<N2, D>>,
+    R: AbstractRotation<N2, D>,
     DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
@@ -62,7 +63,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(iso: &Isometry<N2, D, R>) -> Self {
+    fn from_superset_unchecked(iso: &Isometry<N2, D, R>) -> Self {
         Self::from_superset_unchecked(&iso.translation)
     }
 }
@@ -71,7 +72,7 @@ impl<N1, N2, D: DimName, R> SubsetOf<Similarity<N2, D, R>> for Translation<N1, D
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R: Rotation<Point<N2, D>>,
+    R: AbstractRotation<N2, D>,
     DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
     #[inline]
@@ -85,7 +86,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(sim: &Similarity<N2, D, R>) -> Self {
+    fn from_superset_unchecked(sim: &Similarity<N2, D, R>) -> Self {
         Self::from_superset_unchecked(&sim.isometry.translation)
     }
 }
@@ -112,7 +113,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
+    fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
@@ -145,7 +146,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
+    fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
         let t = m.fixed_slice::<D, U1>(0, D::dim());
         Self {
             vector: crate::convert_unchecked(t.into_owned()),

src/geometry/translation_ops.rs

@@ -1,6 +1,6 @@
 use std::ops::{Div, DivAssign, Mul, MulAssign};
 
-use alga::general::{ClosedAdd, ClosedSub};
+use simba::scalar::{ClosedAdd, ClosedSub};
 
 use crate::base::allocator::{Allocator, SameShapeAllocator};
 use crate::base::constraint::{SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};

src/geometry/unit_complex.rs

@@ -2,13 +2,44 @@ use approx::{AbsDiffEq, RelativeEq, UlpsEq};
 use num_complex::Complex;
 use std::fmt;
 
-use alga::general::RealField;
+use crate::base::{Matrix2, Matrix3, Normed, Unit, Vector1, Vector2};
-use crate::base::{Matrix2, Matrix3, Unit, Vector1, Vector2};
+use crate::geometry::{Point2, Rotation2};
-use crate::geometry::{Rotation2, Point2};
+use simba::scalar::RealField;
+use simba::simd::SimdRealField;
 
 /// A complex number with a norm equal to 1.
 pub type UnitComplex<N> = Unit<Complex<N>>;
 
+impl<N: SimdRealField> Normed for Complex<N> {
+    type Norm = N::SimdRealField;
+
+    #[inline]
+    fn norm(&self) -> N::SimdRealField {
+        // We don't use `.norm_sqr()` because it requires
+        // some very strong Num trait requirements.
+        (self.re * self.re + self.im * self.im).simd_sqrt()
+    }
+
+    #[inline]
+    fn norm_squared(&self) -> N::SimdRealField {
+        // We don't use `.norm_sqr()` because it requires
+        // some very strong Num trait requirements.
+        self.re * self.re + self.im * self.im
+    }
+
+    #[inline]
+    fn scale_mut(&mut self, n: Self::Norm) {
+        self.re *= n;
+        self.im *= n;
+    }
+
+    #[inline]
+    fn unscale_mut(&mut self, n: Self::Norm) {
+        self.re /= n;
+        self.im /= n;
+    }
+}
+
 impl<N: RealField> UnitComplex<N> {
     /// The rotation angle in `]-pi; pi]` of this unit complex number.
     ///

src/geometry/unit_complex_alga.rs

@@ -1,180 +0,0 @@
-use alga::general::{
-    AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, RealField,
-};
-use alga::linear::{
-    AffineTransformation, DirectIsometry, Isometry, OrthogonalTransformation,
-    ProjectiveTransformation, Rotation, Similarity, Transformation,
-};
-
-use crate::base::allocator::Allocator;
-use crate::base::dimension::U2;
-use crate::base::{DefaultAllocator, Vector2};
-use crate::geometry::{Point2, UnitComplex};
-
-/*
- *
- * Implementations for UnitComplex.
- *
- */
-impl<N: RealField> Identity<Multiplicative> for UnitComplex<N> {
-    #[inline]
-    fn identity() -> Self {
-        Self::identity()
-    }
-}
-
-impl<N: RealField> AbstractMagma<Multiplicative> for UnitComplex<N> {
-    #[inline]
-    fn operate(&self, rhs: &Self) -> Self {
-        self * rhs
-    }
-}
-
-impl<N: RealField> TwoSidedInverse<Multiplicative> for UnitComplex<N> {
-    #[inline]
-    #[must_use = "Did you mean to use two_sided_inverse_mut()?"]
-    fn two_sided_inverse(&self) -> Self {
-        self.inverse()
-    }
-
-    #[inline]
-    fn two_sided_inverse_mut(&mut self) {
-        self.inverse_mut()
-    }
-}
-
-macro_rules! impl_structures(
-    ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: RealField> $marker<$operator> for UnitComplex<N> {
-        }
-    )*}
-);
-
-impl_structures!(
-    AbstractSemigroup<Multiplicative>,
-    AbstractQuasigroup<Multiplicative>,
-    AbstractMonoid<Multiplicative>,
-    AbstractLoop<Multiplicative>,
-    AbstractGroup<Multiplicative>
-);
-
-impl<N: RealField> Transformation<Point2<N>> for UnitComplex<N>
-where DefaultAllocator: Allocator<N, U2>
-{
-    #[inline]
-    fn transform_point(&self, pt: &Point2<N>) -> Point2<N> {
-        self.transform_point(pt)
-    }
-
-    #[inline]
-    fn transform_vector(&self, v: &Vector2<N>) -> Vector2<N> {
-        self.transform_vector(v)
-    }
-}
-
-impl<N: RealField> ProjectiveTransformation<Point2<N>> for UnitComplex<N>
-where DefaultAllocator: Allocator<N, U2>
-{
-    #[inline]
-    fn inverse_transform_point(&self, pt: &Point2<N>) -> Point2<N> {
-        self.inverse_transform_point(pt)
-    }
-
-    #[inline]
-    fn inverse_transform_vector(&self, v: &Vector2<N>) -> Vector2<N> {
-        self.inverse_transform_vector(v)
-    }
-}
-
-impl<N: RealField> AffineTransformation<Point2<N>> for UnitComplex<N>
-where DefaultAllocator: Allocator<N, U2>
-{
-    type Rotation = Self;
-    type NonUniformScaling = Id;
-    type Translation = Id;
-
-    #[inline]
-    fn decompose(&self) -> (Id, Self, Id, Self) {
-        (Id::new(), self.clone(), Id::new(), Self::identity())
-    }
-
-    #[inline]
-    fn append_translation(&self, _: &Self::Translation) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn prepend_translation(&self, _: &Self::Translation) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn append_rotation(&self, r: &Self::Rotation) -> Self {
-        r * self
-    }
-
-    #[inline]
-    fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
-        self * r
-    }
-
-    #[inline]
-    fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self {
-        self.clone()
-    }
-}
-
-impl<N: RealField> Similarity<Point2<N>> for UnitComplex<N>
-where DefaultAllocator: Allocator<N, U2>
-{
-    type Scaling = Id;
-
-    #[inline]
-    fn translation(&self) -> Id {
-        Id::new()
-    }
-
-    #[inline]
-    fn rotation(&self) -> Self {
-        self.clone()
-    }
-
-    #[inline]
-    fn scaling(&self) -> Id {
-        Id::new()
-    }
-}
-
-macro_rules! marker_impl(
-    ($($Trait: ident),*) => {$(
-        impl<N: RealField> $Trait<Point2<N>> for UnitComplex<N>
-        where DefaultAllocator: Allocator<N, U2> { }
-    )*}
-);
-
-marker_impl!(Isometry, DirectIsometry, OrthogonalTransformation);
-
-impl<N: RealField> Rotation<Point2<N>> for UnitComplex<N>
-where DefaultAllocator: Allocator<N, U2>
-{
-    #[inline]
-    fn powf(&self, n: N) -> Option<Self> {
-        Some(self.powf(n))
-    }
-
-    #[inline]
-    fn rotation_between(a: &Vector2<N>, b: &Vector2<N>) -> Option<Self> {
-        Some(Self::rotation_between(a, b))
-    }
-
-    #[inline]
-    fn scaled_rotation_between(a: &Vector2<N>, b: &Vector2<N>, s: N) -> Option<Self> {
-        Some(Self::scaled_rotation_between(a, b, s))
-    }
-}

src/geometry/unit_complex_construction.rs

@@ -6,11 +6,11 @@ use num_complex::Complex;
 use rand::distributions::{Distribution, OpenClosed01, Standard};
 use rand::Rng;
 
-use alga::general::RealField;
 use crate::base::dimension::{U1, U2};
 use crate::base::storage::Storage;
-use crate::base::{Unit, Vector, Matrix2};
+use crate::base::{Matrix2, Unit, Vector};
 use crate::geometry::{Rotation2, UnitComplex};
+use simba::scalar::RealField;
 
 impl<N: RealField> UnitComplex<N> {
     /// The unit complex number multiplicative identity.

src/geometry/unit_complex_conversion.rs

@@ -1,14 +1,13 @@
 use num::Zero;
 use num_complex::Complex;
 
-use alga::general::{RealField, SubsetOf, SupersetOf};
+use simba::scalar::{RealField, SubsetOf, SupersetOf};
-use alga::linear::Rotation as AlgaRotation;
 
 use crate::base::dimension::U2;
 use crate::base::{Matrix2, Matrix3};
 use crate::geometry::{
-    Isometry, Point2, Rotation2, Similarity, SuperTCategoryOf, TAffine, Transform, Translation,
+    AbstractRotation, Isometry, Rotation2, Similarity, SuperTCategoryOf, TAffine, Transform,
-    UnitComplex
+    Translation, UnitComplex,
 };
 
 /*
@@ -42,7 +41,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(uq: &UnitComplex<N2>) -> Self {
+    fn from_superset_unchecked(uq: &UnitComplex<N2>) -> Self {
         Self::new_unchecked(crate::convert_ref_unchecked(uq.as_ref()))
     }
 }
@@ -64,7 +63,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(rot: &Rotation2<N2>) -> Self {
+    fn from_superset_unchecked(rot: &Rotation2<N2>) -> Self {
         let q = UnitComplex::<N2>::from_rotation_matrix(rot);
         crate::convert_unchecked(q)
     }
@@ -74,7 +73,7 @@ impl<N1, N2, R> SubsetOf<Isometry<N2, U2, R>> for UnitComplex<N1>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R: AlgaRotation<Point2<N2>> + SupersetOf<Self>,
+    R: AbstractRotation<N2, U2> + SupersetOf<Self>,
 {
     #[inline]
     fn to_superset(&self) -> Isometry<N2, U2, R> {
@@ -87,7 +86,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(iso: &Isometry<N2, U2, R>) -> Self {
+    fn from_superset_unchecked(iso: &Isometry<N2, U2, R>) -> Self {
         crate::convert_ref_unchecked(&iso.rotation)
     }
 }
@@ -96,7 +95,7 @@ impl<N1, N2, R> SubsetOf<Similarity<N2, U2, R>> for UnitComplex<N1>
 where
     N1: RealField,
     N2: RealField + SupersetOf<N1>,
-    R: AlgaRotation<Point2<N2>> + SupersetOf<Self>,
+    R: AbstractRotation<N2, U2> + SupersetOf<Self>,
 {
     #[inline]
     fn to_superset(&self) -> Similarity<N2, U2, R> {
@@ -109,7 +108,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(sim: &Similarity<N2, U2, R>) -> Self {
+    fn from_superset_unchecked(sim: &Similarity<N2, U2, R>) -> Self {
         crate::convert_ref_unchecked(&sim.isometry)
     }
 }
@@ -131,7 +130,7 @@ where
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(t: &Transform<N2, U2, C>) -> Self {
+    fn from_superset_unchecked(t: &Transform<N2, U2, C>) -> Self {
         Self::from_superset_unchecked(t.matrix())
     }
 }
@@ -148,13 +147,12 @@ impl<N1: RealField, N2: RealField + SupersetOf<N1>> SubsetOf<Matrix3<N2>> for Un
     }
 
     #[inline]
-    unsafe fn from_superset_unchecked(m: &Matrix3<N2>) -> Self {
+    fn from_superset_unchecked(m: &Matrix3<N2>) -> Self {
         let rot: Rotation2<N1> = crate::convert_ref_unchecked(m);
         Self::from_rotation_matrix(&rot)
     }
 }
 
-
 impl<N: RealField> From<UnitComplex<N>> for Rotation2<N> {
     #[inline]
     fn from(q: UnitComplex<N>) -> Self {

src/geometry/unit_complex_ops.rs

@@ -1,11 +1,11 @@
 use std::ops::{Div, DivAssign, Mul, MulAssign};
 
-use alga::general::RealField;
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{U1, U2};
 use crate::base::storage::Storage;
 use crate::base::{DefaultAllocator, Unit, Vector, Vector2};
 use crate::geometry::{Isometry, Point2, Rotation, Similarity, Translation, UnitComplex};
+use simba::scalar::RealField;
 
 /*
  * This file provides:

src/geometry/unit_complex_simba.rs

@@ -0,0 +1,50 @@
+use num_complex::Complex;
+use simba::simd::SimdValue;
+use std::ops::Deref;
+
+use crate::base::{Scalar, Unit};
+use crate::geometry::UnitComplex;
+use crate::RealField;
+
+impl<N: RealField> SimdValue for UnitComplex<N>
+where N::Element: Scalar
+{
+    type Element = UnitComplex<N::Element>;
+    type SimdBool = N::SimdBool;
+
+    #[inline]
+    fn lanes() -> usize {
+        N::lanes()
+    }
+
+    #[inline]
+    fn splat(val: Self::Element) -> Self {
+        Unit::new_unchecked(Complex::splat(val.into_inner()))
+    }
+
+    #[inline]
+    fn extract(&self, i: usize) -> Self::Element {
+        Unit::new_unchecked(self.deref().extract(i))
+    }
+
+    #[inline]
+    unsafe fn extract_unchecked(&self, i: usize) -> Self::Element {
+        Unit::new_unchecked(self.deref().extract_unchecked(i))
+    }
+
+    #[inline]
+    fn replace(&mut self, i: usize, val: Self::Element) {
+        self.as_mut_unchecked().replace(i, val.into_inner())
+    }
+
+    #[inline]
+    unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element) {
+        self.as_mut_unchecked()
+            .replace_unchecked(i, val.into_inner())
+    }
+
+    #[inline]
+    fn select(self, cond: Self::SimdBool, other: Self) -> Self {
+        Unit::new_unchecked(self.into_inner().select(cond, other.into_inner()))
+    }
+}

src/lib.rs

@@ -68,8 +68,6 @@ an optimized set of tools for computer graphics and physics. Those features incl
 * 3D projections for computer graphics: `Perspective3`, `Orthographic3`.
 * Matrix factorizations: `Cholesky`, `QR`, `LU`, `FullPivLU`, `SVD`, `Schur`, `Hessenberg`, `SymmetricEigen`.
 * Insertion and removal of rows of columns of a matrix.
-* Implements traits from the [alga](https://crates.io/crates/alga) crate for
-  generic programming.
 */
 
 // #![feature(plugin)]
@@ -81,7 +79,7 @@ an optimized set of tools for computer graphics and physics. Those features incl
 #![deny(non_upper_case_globals)]
 #![deny(unused_qualifications)]
 #![deny(unused_results)]
-#![deny(missing_docs)]
+#![allow(missing_docs)] // XXX: deny that
 #![doc(
     html_favicon_url = "https://nalgebra.org/img/favicon.ico",
     html_root_url = "https://nalgebra.org/rustdoc"
@@ -106,18 +104,11 @@ extern crate mint;
 
 #[macro_use]
 extern crate approx;
-extern crate generic_array;
 #[cfg(feature = "std")]
 extern crate matrixmultiply;
-extern crate num_complex;
-extern crate num_rational;
 extern crate num_traits as num;
-extern crate rand;
 #[cfg(feature = "std")]
 extern crate rand_distr;
-extern crate typenum;
-
-extern crate alga;
 
 #[cfg(all(feature = "alloc", not(feature = "std")))]
 extern crate alloc;
@@ -152,35 +143,17 @@ pub use crate::sparse::*;
 )]
 pub use base as core;
 
+use simba::scalar::SupersetOf;
 use std::cmp::{self, Ordering, PartialOrd};
 
-use alga::general::{
+use num::{One, Signed, Zero};
-    Additive, AdditiveGroup, Identity, JoinSemilattice, Lattice, MeetSemilattice, Multiplicative,
-    SupersetOf, TwoSidedInverse,
-};
-use alga::linear::SquareMatrix as AlgaSquareMatrix;
-use alga::linear::{EuclideanSpace, FiniteDimVectorSpace, InnerSpace, NormedSpace};
-use num::Signed;
 
-#[allow(deprecated)]
+use base::allocator::Allocator;
-pub use alga::general::Real;
-pub use alga::general::{ComplexField, Id, RealField};
-pub use alga::simd::{SimdComplexField, SimdRealField};
 pub use num_complex::Complex;
-
+pub use simba::scalar::{
-/*
+    ClosedAdd, ClosedDiv, ClosedMul, ClosedSub, ComplexField, Field, RealField,
- *
+};
- * Multiplicative identity.
+pub use simba::simd::{SimdBool, SimdComplexField, SimdRealField};
- *
- */
-/// Gets the ubiquitous multiplicative identity element.
-///
-/// Same as `Id::new()`.
-#[deprecated(note = "use `Id::new()` instead.")]
-#[inline]
-pub fn id() -> Id {
-    Id::new()
-}
 
 /// Gets the multiplicative identity element.
 ///
@@ -189,8 +162,8 @@ pub fn id() -> Id {
 /// * [`origin`](../nalgebra/fn.origin.html)
 /// * [`zero`](fn.zero.html)
 #[inline]
-pub fn one<T: Identity<Multiplicative>>() -> T {
+pub fn one<T: One>() -> T {
-    T::identity()
+    T::one()
 }
 
 /// Gets the additive identity element.
@@ -200,36 +173,8 @@ pub fn one<T: Identity<Multiplicative>>() -> T {
 /// * [`one`](fn.one.html)
 /// * [`origin`](../nalgebra/fn.origin.html)
 #[inline]
-pub fn zero<T: Identity<Additive>>() -> T {
+pub fn zero<T: Zero>() -> T {
-    T::identity()
+    T::zero()
-}
-
-/// Gets the origin of the given point.
-///
-/// # See also:
-///
-/// * [`one`](fn.one.html)
-/// * [`zero`](fn.zero.html)
-///
-/// # Deprecated
-/// Use [Point::origin] instead.
-///
-/// Or, use [EuclideanSpace::origin](https://docs.rs/alga/0.7.2/alga/linear/trait.EuclideanSpace.html#tymethod.origin).
-#[deprecated(note = "use `Point::origin` instead")]
-#[inline]
-pub fn origin<P: EuclideanSpace>() -> P {
-    P::origin()
-}
-
-/*
- *
- * Dimension
- *
- */
-/// The dimension of the given algebraic entity seen as a vector space.
-#[inline]
-pub fn dimension<V: FiniteDimVectorSpace>() -> usize {
-    V::dimension()
 }
 
 /*
@@ -245,7 +190,7 @@ pub fn dimension<V: FiniteDimVectorSpace>() -> usize {
 /// The range must not be empty.
 #[inline]
 pub fn wrap<T>(mut val: T, min: T, max: T) -> T
-where T: Copy + PartialOrd + AdditiveGroup {
+where T: Copy + PartialOrd + ClosedAdd + ClosedSub {
     assert!(min < max, "Invalid wrapping bounds.");
     let width = max - min;
 
@@ -310,23 +255,23 @@ pub fn abs<T: Signed>(a: &T) -> T {
     a.abs()
 }
 
-/// Returns the infimum of `a` and `b`.
+///// Returns the infimum of `a` and `b`.
-#[inline]
+//#[inline]
-pub fn inf<T: MeetSemilattice>(a: &T, b: &T) -> T {
+//pub fn inf<T: MeetSemilattice>(a: &T, b: &T) -> T {
-    a.meet(b)
+//    a.meet(b)
-}
+//}
-
+//
-/// Returns the supremum of `a` and `b`.
+///// Returns the supremum of `a` and `b`.
-#[inline]
+//#[inline]
-pub fn sup<T: JoinSemilattice>(a: &T, b: &T) -> T {
+//pub fn sup<T: JoinSemilattice>(a: &T, b: &T) -> T {
-    a.join(b)
+//    a.join(b)
-}
+//}
-
+//
-/// Returns simultaneously the infimum and supremum of `a` and `b`.
+///// Returns simultaneously the infimum and supremum of `a` and `b`.
-#[inline]
+//#[inline]
-pub fn inf_sup<T: Lattice>(a: &T, b: &T) -> (T, T) {
+//pub fn inf_sup<T: Lattice>(a: &T, b: &T) -> (T, T) {
-    a.meet_join(b)
+//    a.meet_join(b)
-}
+//}
 
 /// Compare `a` and `b` using a partial ordering relation.
 #[inline]
@@ -414,175 +359,6 @@ pub fn partial_sort2<'a, T: PartialOrd>(a: &'a T, b: &'a T) -> Option<(&'a T, &'
     }
 }
 
-/*
- * Inverse
- */
-
-/// Tries to gets an inverted copy of a square matrix.
-///
-/// # See also:
-///
-/// * [`inverse`](fn.inverse.html)
-#[deprecated(note = "use the `.try_inverse()` method instead")]
-#[inline]
-pub fn try_inverse<M: AlgaSquareMatrix>(m: &M) -> Option<M> {
-    m.try_inverse()
-}
-
-/// Computes the multiplicative inverse of an (always invertible) algebraic entity.
-///
-/// # See also:
-///
-/// * [`try_inverse`](fn.try_inverse.html)
-#[deprecated(note = "use the `.inverse()` method instead")]
-#[inline]
-pub fn inverse<M: TwoSidedInverse<Multiplicative>>(m: &M) -> M {
-    m.two_sided_inverse()
-}
-
-/*
- * Inner vector space
- */
-
-/// Computes the dot product of two vectors.
-///
-/// ## Deprecated
-/// Use these methods instead:
-///   - [Matrix::dot]
-///   - [Quaternion::dot]
-///
-/// Or, use [FiniteDimVectorSpace::dot](https://docs.rs/alga/0.7.2/alga/linear/trait.FiniteDimVectorSpace.html#tymethod.dot).
-#[deprecated(note = "use `Matrix::dot` or `Quaternion::dot` instead")]
-#[inline]
-pub fn dot<V: FiniteDimVectorSpace>(a: &V, b: &V) -> V::Field {
-    a.dot(b)
-}
-
-/// Computes the smallest angle between two vectors.
-///
-/// ## Deprecated
-/// Use [Matrix::angle] instead.
-///
-/// Or, use [InnerSpace::angle](https://docs.rs/alga/0.7.2/alga/linear/trait.InnerSpace.html#method.angle).
-#[deprecated(note = "use `Matrix::angle` instead")]
-#[inline]
-pub fn angle<V: InnerSpace>(a: &V, b: &V) -> V::RealField {
-    a.angle(b)
-}
-
-/*
- * Normed space
- */
-
-/// Computes the L2 (Euclidean) norm of a vector.
-///
-/// # See also:
-///
-/// * [`magnitude`](fn.magnitude.html)
-/// * [`magnitude_squared`](fn.magnitude_squared.html)
-/// * [`norm_squared`](fn.norm_squared.html)
-///
-/// # Deprecated
-/// Use these methods instead:
-/// * [Matrix::norm]
-/// * [Quaternion::norm]
-///
-/// Or, use [NormedSpace::norm](https://docs.rs/alga/0.7.2/alga/linear/trait.NormedSpace.html#tymethod.norm).
-#[deprecated(note = "use `Matrix::norm` or `Quaternion::norm` instead")]
-#[inline]
-pub fn norm<V: NormedSpace>(v: &V) -> V::RealField {
-    v.norm()
-}
-
-/// Computes the squared L2 (Euclidean) norm of the vector `v`.
-///
-/// # See also:
-///
-/// * [`magnitude`](fn.magnitude.html)
-/// * [`magnitude_squared`](fn.magnitude_squared.html)
-/// * [`norm`](fn.norm.html)
-///
-/// # Deprecated
-/// Use these methods instead:
-/// * [Matrix::norm_squared]
-/// * [Quaternion::norm_squared]
-///
-/// Or, use [NormedSpace::norm_squared](https://docs.rs/alga/0.7.2/alga/linear/trait.NormedSpace.html#tymethod.norm_squared).
-#[deprecated(note = "use `Matrix::norm_squared` or `Quaternion::norm_squared` instead")]
-#[inline]
-pub fn norm_squared<V: NormedSpace>(v: &V) -> V::RealField {
-    v.norm_squared()
-}
-
-/// A synonym for [`norm`](fn.norm.html), aka length.
-///
-/// # See also:
-///
-/// * [`magnitude_squared`](fn.magnitude_squared.html)
-/// * [`norm`](fn.norm.html)
-/// * [`norm_squared`](fn.norm_squared.html)
-///
-/// # Deprecated
-/// Use these methods instead:
-/// * [Matrix::magnitude]
-/// * [Quaternion::magnitude]
-///
-/// Or, use [NormedSpace::norm](https://docs.rs/alga/0.7.2/alga/linear/trait.NormedSpace.html#tymethod.norm).
-#[deprecated(note = "use `Matrix::magnitude` or `Quaternion::magnitude` instead")]
-#[inline]
-pub fn magnitude<V: NormedSpace>(v: &V) -> V::RealField {
-    v.norm()
-}
-
-/// A synonym for [`norm_squared`](fn.norm_squared.html),
-///  aka length squared.
-///
-/// # See also:
-///
-/// * [`magnitude`](fn.magnitude.html)
-/// * [`norm`](fn.norm.html)
-/// * [`norm_squared`](fn.norm_squared.html)
-///
-/// # Deprecated
-/// Use these methods instead:
-/// * [Matrix::magnitude_squared]
-/// * [Quaternion::magnitude_squared]
-///
-/// Or, use [NormedSpace::norm_squared](https://docs.rs/alga/0.7.2/alga/linear/trait.NormedSpace.html#tymethod.norm_squared).
-#[deprecated(note = "use `Matrix::magnitude_squared` or `Quaternion::magnitude_squared` instead")]
-#[inline]
-pub fn magnitude_squared<V: NormedSpace>(v: &V) -> V::RealField {
-    v.norm_squared()
-}
-
-/// Computes the normalized version of the vector `v`.
-///
-/// # Deprecated
-/// Use these methods instead:
-/// * [Matrix::normalize]
-/// * [Quaternion::normalize]
-///
-/// Or, use [NormedSpace::normalize](https://docs.rs/alga/0.7.2/alga/linear/trait.NormedSpace.html#tymethod.normalize).
-#[deprecated(note = "use `Matrix::normalize` or `Quaternion::normalize` instead")]
-#[inline]
-pub fn normalize<V: NormedSpace>(v: &V) -> V {
-    v.normalize()
-}
-
-/// Computes the normalized version of the vector `v` or returns `None` if its norm is smaller than `min_norm`.
-///
-/// # Deprecated
-/// Use these methods instead:
-/// * [Matrix::try_normalize]
-/// * [Quaternion::try_normalize]
-///
-/// Or, use [NormedSpace::try_normalize](https://docs.rs/alga/0.7.2/alga/linear/trait.NormedSpace.html#tymethod.try_normalize).
-#[deprecated(note = "use `Matrix::try_normalize` or `Quaternion::try_normalize` instead")]
-#[inline]
-pub fn try_normalize<V: NormedSpace>(v: &V, min_norm: V::RealField) -> Option<V> {
-    v.try_normalize(min_norm)
-}
-
 /*
  *
  * Point operations.
@@ -595,8 +371,9 @@ pub fn try_normalize<V: NormedSpace>(v: &V, min_norm: V::RealField) -> Option<V>
 /// * [distance](fn.distance.html)
 /// * [distance_squared](fn.distance_squared.html)
 #[inline]
-pub fn center<P: EuclideanSpace>(p1: &P, p2: &P) -> P {
+pub fn center<N: SimdComplexField, D: DimName>(p1: &Point<N, D>, p2: &Point<N, D>) -> Point<N, D>
-    P::from_coordinates((p1.coordinates() + p2.coordinates()) * convert(0.5))
+where DefaultAllocator: Allocator<N, D> {
+    ((&p1.coords + &p2.coords) * convert::<_, N>(0.5)).into()
 }
 
 /// The distance between two points.
@@ -606,8 +383,14 @@ pub fn center<P: EuclideanSpace>(p1: &P, p2: &P) -> P {
 /// * [center](fn.center.html)
 /// * [distance_squared](fn.distance_squared.html)
 #[inline]
-pub fn distance<P: EuclideanSpace>(p1: &P, p2: &P) -> P::RealField {
+pub fn distance<N: SimdComplexField, D: DimName>(
-    (p2.coordinates() - p1.coordinates()).norm()
+    p1: &Point<N, D>,
+    p2: &Point<N, D>,
+) -> N::SimdRealField
+where
+    DefaultAllocator: Allocator<N, D>,
+{
+    (&p2.coords - &p1.coords).norm()
 }
 
 /// The squared distance between two points.
@@ -617,8 +400,14 @@ pub fn distance<P: EuclideanSpace>(p1: &P, p2: &P) -> P::RealField {
 /// * [center](fn.center.html)
 /// * [distance](fn.distance.html)
 #[inline]
-pub fn distance_squared<P: EuclideanSpace>(p1: &P, p2: &P) -> P::RealField {
+pub fn distance_squared<N: SimdComplexField, D: DimName>(
-    (p2.coordinates() - p1.coordinates()).norm_squared()
+    p1: &Point<N, D>,
+    p2: &Point<N, D>,
+) -> N::SimdRealField
+where
+    DefaultAllocator: Allocator<N, D>,
+{
+    (&p2.coords - &p1.coords).norm_squared()
 }
 
 /*
@@ -683,7 +472,7 @@ pub fn is_convertible<From: SupersetOf<To>, To>(t: &From) -> bool {
 /// * [try_convert](fn.try_convert.html)
 /// * [try_convert_ref](fn.try_convert_ref.html)
 #[inline]
-pub unsafe fn convert_unchecked<From: SupersetOf<To>, To>(t: From) -> To {
+pub fn convert_unchecked<From: SupersetOf<To>, To>(t: From) -> To {
     t.to_subset_unchecked()
 }
 
@@ -726,6 +515,6 @@ pub fn try_convert_ref<From: SupersetOf<To>, To>(t: &From) -> Option<To> {
 /// * [try_convert](fn.try_convert.html)
 /// * [try_convert_ref](fn.try_convert_ref.html)
 #[inline]
-pub unsafe fn convert_ref_unchecked<From: SupersetOf<To>, To>(t: &From) -> To {
+pub fn convert_ref_unchecked<From: SupersetOf<To>, To>(t: &From) -> To {
     t.to_subset_unchecked()
 }

src/linalg/balancing.rs

@@ -1,6 +1,6 @@
 //! Functions for balancing a matrix.
 
-use alga::general::RealField;
+use simba::scalar::RealField;
 use std::ops::{DivAssign, MulAssign};
 
 use crate::allocator::Allocator;

src/linalg/bidiagonal.rs

@@ -1,11 +1,11 @@
 #[cfg(feature = "serde-serialize")]
 use serde::{Deserialize, Serialize};
 
-use alga::general::ComplexField;
 use crate::allocator::Allocator;
 use crate::base::{DefaultAllocator, Matrix, MatrixMN, MatrixN, Unit, VectorN};
 use crate::dimension::{Dim, DimDiff, DimMin, DimMinimum, DimSub, U1};
 use crate::storage::Storage;
+use simba::scalar::ComplexField;
 
 use crate::geometry::Reflection;
 use crate::linalg::householder;
@@ -14,27 +14,23 @@ use crate::linalg::householder;
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(serialize = "DimMinimum<R, C>: DimSub<U1>,
-        serialize = "DimMinimum<R, C>: DimSub<U1>,
          DefaultAllocator: Allocator<N, R, C>             +
                            Allocator<N, DimMinimum<R, C>> +
                            Allocator<N, DimDiff<DimMinimum<R, C>, U1>>,
          MatrixMN<N, R, C>: Serialize,
          VectorN<N, DimMinimum<R, C>>: Serialize,
-         VectorN<N, DimDiff<DimMinimum<R, C>, U1>>: Serialize"
+         VectorN<N, DimDiff<DimMinimum<R, C>, U1>>: Serialize"))
-    ))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(deserialize = "DimMinimum<R, C>: DimSub<U1>,
-        deserialize = "DimMinimum<R, C>: DimSub<U1>,
          DefaultAllocator: Allocator<N, R, C>             +
                            Allocator<N, DimMinimum<R, C>> +
                            Allocator<N, DimDiff<DimMinimum<R, C>, U1>>,
          MatrixMN<N, R, C>: Deserialize<'de>,
          VectorN<N, DimMinimum<R, C>>: Deserialize<'de>,
-         VectorN<N, DimDiff<DimMinimum<R, C>, U1>>: Deserialize<'de>"
+         VectorN<N, DimDiff<DimMinimum<R, C>, U1>>: Deserialize<'de>"))
-    ))
 )]
 #[derive(Clone, Debug)]
 pub struct Bidiagonal<N: ComplexField, R: DimMin<C>, C: Dim>
@@ -63,7 +59,8 @@ where
     MatrixMN<N, R, C>: Copy,
     VectorN<N, DimMinimum<R, C>>: Copy,
     VectorN<N, DimDiff<DimMinimum<R, C>, U1>>: Copy,
-{}
+{
+}
 
 impl<N: ComplexField, R: DimMin<C>, C: Dim> Bidiagonal<N, R, C>
 where
@@ -174,11 +171,9 @@ where
         MatrixN<N, DimMinimum<R, C>>,
         MatrixMN<N, DimMinimum<R, C>, C>,
     )
-    where
+    where DefaultAllocator: Allocator<N, DimMinimum<R, C>, DimMinimum<R, C>>
-        DefaultAllocator: Allocator<N, DimMinimum<R, C>, DimMinimum<R, C>>
             + Allocator<N, R, DimMinimum<R, C>>
-            + Allocator<N, DimMinimum<R, C>, C>,
+            + Allocator<N, DimMinimum<R, C>, C> {
-    {
         // FIXME: optimize by calling a reallocator.
         (self.u(), self.d(), self.v_t())
     }
@@ -186,9 +181,7 @@ where
     /// Retrieves the upper trapezoidal submatrix `R` of this decomposition.
     #[inline]
     pub fn d(&self) -> MatrixN<N, DimMinimum<R, C>>
-    where
+    where DefaultAllocator: Allocator<N, DimMinimum<R, C>, DimMinimum<R, C>> {
-        DefaultAllocator: Allocator<N, DimMinimum<R, C>, DimMinimum<R, C>>,
-    {
         let (nrows, ncols) = self.uv.data.shape();
 
         let d = nrows.min(ncols);

src/linalg/cholesky.rs

@@ -2,12 +2,12 @@
 use serde::{Deserialize, Serialize};
 
 use num::One;
-use alga::general::ComplexField;
+use simba::scalar::ComplexField;
 
 use crate::allocator::Allocator;
 use crate::base::{DefaultAllocator, Matrix, MatrixMN, MatrixN, SquareMatrix, Vector};
 use crate::constraint::{SameNumberOfRows, ShapeConstraint};
-use crate::dimension::{Dim, DimAdd, DimSum, DimDiff, DimSub, Dynamic, U1};
+use crate::dimension::{Dim, DimAdd, DimDiff, DimSub, DimSum, Dynamic, U1};
 use crate::storage::{Storage, StorageMut};
 
 /// The Cholesky decomposition of a symmetric-definite-positive matrix.
@@ -24,8 +24,7 @@ use crate::storage::{Storage, StorageMut};
 )]
 #[derive(Clone, Debug)]
 pub struct Cholesky<N: ComplexField, D: Dim>
-where
+where DefaultAllocator: Allocator<N, D, D>
-    DefaultAllocator: Allocator<N, D, D>,
 {
     chol: MatrixN<N, D>,
 }
@@ -38,8 +37,7 @@ where
 }
 
 impl<N: ComplexField, D: DimSub<Dynamic>> Cholesky<N, D>
-where
+where DefaultAllocator: Allocator<N, D, D>
-    DefaultAllocator: Allocator<N, D, D>,
 {
     /// Attempts to compute the Cholesky decomposition of `matrix`.
     ///
@@ -176,22 +174,38 @@ where
         let mut col = col.into_owned();
         // for an explanation of the formulas, see https://en.wikipedia.org/wiki/Cholesky_decomposition#Updating_the_decomposition
         let n = col.nrows();
-        assert_eq!(n, self.chol.nrows() + 1, "The new column must have the size of the factored matrix plus one.");
+        assert_eq!(
+            n,
+            self.chol.nrows() + 1,
+            "The new column must have the size of the factored matrix plus one."
+        );
         assert!(j < n, "j needs to be within the bound of the new matrix.");
 
         // loads the data into a new matrix with an additional jth row/column
-        let mut chol = unsafe { Matrix::new_uninitialized_generic(self.chol.data.shape().0.add(U1), self.chol.data.shape().1.add(U1)) };
+        let mut chol = unsafe {
-        chol.slice_range_mut(..j, ..j).copy_from(&self.chol.slice_range(..j, ..j));
+            Matrix::new_uninitialized_generic(
-        chol.slice_range_mut(..j, j + 1..).copy_from(&self.chol.slice_range(..j, j..));
+                self.chol.data.shape().0.add(U1),
-        chol.slice_range_mut(j + 1.., ..j).copy_from(&self.chol.slice_range(j.., ..j));
+                self.chol.data.shape().1.add(U1),
-        chol.slice_range_mut(j + 1.., j + 1..).copy_from(&self.chol.slice_range(j.., j..));
+            )
+        };
+        chol.slice_range_mut(..j, ..j)
+            .copy_from(&self.chol.slice_range(..j, ..j));
+        chol.slice_range_mut(..j, j + 1..)
+            .copy_from(&self.chol.slice_range(..j, j..));
+        chol.slice_range_mut(j + 1.., ..j)
+            .copy_from(&self.chol.slice_range(j.., ..j));
+        chol.slice_range_mut(j + 1.., j + 1..)
+            .copy_from(&self.chol.slice_range(j.., j..));
 
         // update the jth row
         let top_left_corner = self.chol.slice_range(..j, ..j);
 
         let col_j = col[j];
         let (mut new_rowj_adjoint, mut new_colj) = col.rows_range_pair_mut(..j, j + 1..);
-        assert!(top_left_corner.solve_lower_triangular_mut(&mut new_rowj_adjoint), "Cholesky::insert_column : Unable to solve lower triangular system!");
+        assert!(
+            top_left_corner.solve_lower_triangular_mut(&mut new_rowj_adjoint),
+            "Cholesky::insert_column : Unable to solve lower triangular system!"
+        );
 
         new_rowj_adjoint.adjoint_to(&mut chol.slice_range_mut(j, ..j));
 
@@ -202,36 +216,51 @@ where
         // update the jth column
         let bottom_left_corner = self.chol.slice_range(j.., ..j);
         // new_colj = (col_jplus - bottom_left_corner * new_rowj.adjoint()) / center_element;
-        new_colj.gemm(-N::one() / center_element, &bottom_left_corner, &new_rowj_adjoint, N::one() / center_element);
+        new_colj.gemm(
+            -N::one() / center_element,
+            &bottom_left_corner,
+            &new_rowj_adjoint,
+            N::one() / center_element,
+        );
         chol.slice_range_mut(j + 1.., j).copy_from(&new_colj);
 
         // update the bottom right corner
         let mut bottom_right_corner = chol.slice_range_mut(j + 1.., j + 1..);
-        Self::xx_rank_one_update(&mut bottom_right_corner, &mut new_colj, -N::RealField::one());
+        Self::xx_rank_one_update(
+            &mut bottom_right_corner,
+            &mut new_colj,
+            -N::RealField::one(),
+        );
 
         Cholesky { chol }
     }
 
     /// Updates the decomposition such that we get the decomposition of the factored matrix with its `j`th column removed.
     /// Since the matrix is square, the `j`th row will also be removed.
-    pub fn remove_column(
+    pub fn remove_column(&self, j: usize) -> Cholesky<N, DimDiff<D, U1>>
-        &self,
-        j: usize,
-    ) -> Cholesky<N, DimDiff<D, U1>>
     where
         D: DimSub<U1>,
-            DefaultAllocator: Allocator<N, DimDiff<D, U1>, DimDiff<D, U1>> + Allocator<N, D>
+        DefaultAllocator: Allocator<N, DimDiff<D, U1>, DimDiff<D, U1>> + Allocator<N, D>,
     {
         let n = self.chol.nrows();
         assert!(n > 0, "The matrix needs at least one column.");
         assert!(j < n, "j needs to be within the bound of the matrix.");
 
         // loads the data into a new matrix except for the jth row/column
-        let mut chol = unsafe { Matrix::new_uninitialized_generic(self.chol.data.shape().0.sub(U1), self.chol.data.shape().1.sub(U1)) };
+        let mut chol = unsafe {
-        chol.slice_range_mut(..j, ..j).copy_from(&self.chol.slice_range(..j, ..j));
+            Matrix::new_uninitialized_generic(
-        chol.slice_range_mut(..j, j..).copy_from(&self.chol.slice_range(..j, j + 1..));
+                self.chol.data.shape().0.sub(U1),
-        chol.slice_range_mut(j.., ..j).copy_from(&self.chol.slice_range(j + 1.., ..j));
+                self.chol.data.shape().1.sub(U1),
-        chol.slice_range_mut(j.., j..).copy_from(&self.chol.slice_range(j + 1.., j + 1..));
+            )
+        };
+        chol.slice_range_mut(..j, ..j)
+            .copy_from(&self.chol.slice_range(..j, ..j));
+        chol.slice_range_mut(..j, j..)
+            .copy_from(&self.chol.slice_range(..j, j + 1..));
+        chol.slice_range_mut(j.., ..j)
+            .copy_from(&self.chol.slice_range(j + 1.., ..j));
+        chol.slice_range_mut(j.., j..)
+            .copy_from(&self.chol.slice_range(j + 1.., j + 1..));
 
         // updates the bottom right corner
         let mut bottom_right_corner = chol.slice_range_mut(j.., j..);
@@ -247,8 +276,11 @@ where
     ///
     /// This helper method is called by `rank_one_update` but also `insert_column` and `remove_column`
     /// where it is used on a square slice of the decomposition
-    fn xx_rank_one_update<Dm, Sm, Rx, Sx>(chol : &mut Matrix<N, Dm, Dm, Sm>, x: &mut Vector<N, Rx, Sx>, sigma: N::RealField)
+    fn xx_rank_one_update<Dm, Sm, Rx, Sx>(
-        where
+        chol: &mut Matrix<N, Dm, Dm, Sm>,
+        x: &mut Vector<N, Rx, Sx>,
+        sigma: N::RealField,
+    ) where
         //N: ComplexField,
         Dm: Dim,
         Rx: Dim,
@@ -293,8 +325,7 @@ where
 }
 
 impl<N: ComplexField, D: DimSub<Dynamic>, S: Storage<N, D, D>> SquareMatrix<N, D, S>
-where
+where DefaultAllocator: Allocator<N, D, D>
-    DefaultAllocator: Allocator<N, D, D>,
 {
     /// Attempts to compute the Cholesky decomposition of this matrix.
     ///

src/linalg/determinant.rs

@@ -1,4 +1,4 @@
-use alga::general::ComplexField;
+use simba::scalar::ComplexField;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::DimMin;

src/linalg/eigen.rs

@@ -1,8 +1,8 @@
 #[cfg(feature = "serde-serialize")]
-use serde::{Serialize, Deserialize};
+use serde::{Deserialize, Serialize};
 
-use alga::general::ComplexField;
 use num_complex::Complex;
+use simba::scalar::ComplexField;
 use std::cmp;
 use std::fmt::Display;
 use std::ops::MulAssign;
@@ -10,7 +10,9 @@ use std::ops::MulAssign;
 use crate::allocator::Allocator;
 use crate::base::dimension::{Dim, DimDiff, DimSub, Dynamic, U1, U2, U3};
 use crate::base::storage::Storage;
-use crate::base::{DefaultAllocator, Hessenberg, MatrixN, SquareMatrix, Unit, Vector2, Vector3, VectorN};
+use crate::base::{
+    DefaultAllocator, Hessenberg, MatrixN, SquareMatrix, Unit, Vector2, Vector3, VectorN,
+};
 use crate::constraint::{DimEq, ShapeConstraint};
 
 use crate::geometry::{Reflection, UnitComplex};
@@ -21,28 +23,19 @@ use crate::linalg::Schur;
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(
+    serde(bound(serialize = "DefaultAllocator: Allocator<N, D>,
-        bound(
-            serialize = "DefaultAllocator: Allocator<N, D>,
          VectorN<N, D>: Serialize,
-         MatrixN<N, D>: Serialize"
+         MatrixN<N, D>: Serialize"))
-        )
-    )
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(
+    serde(bound(deserialize = "DefaultAllocator: Allocator<N, D>,
-        bound(
-            deserialize = "DefaultAllocator: Allocator<N, D>,
          VectorN<N, D>: Serialize,
-         MatrixN<N, D>: Deserialize<'de>"
+         MatrixN<N, D>: Deserialize<'de>"))
-        )
-    )
 )]
 #[derive(Clone, Debug)]
 pub struct Eigen<N: ComplexField, D: Dim>
-where
+where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
-    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
 {
     pub eigenvectors: MatrixN<N, D>,
     pub eigenvalues: VectorN<N, D>,

src/linalg/full_piv_lu.rs

@@ -1,12 +1,12 @@
 #[cfg(feature = "serde-serialize")]
 use serde::{Deserialize, Serialize};
 
-use alga::general::ComplexField;
 use crate::allocator::Allocator;
 use crate::base::{DefaultAllocator, Matrix, MatrixMN, MatrixN};
 use crate::constraint::{SameNumberOfRows, ShapeConstraint};
 use crate::dimension::{Dim, DimMin, DimMinimum};
 use crate::storage::{Storage, StorageMut};
+use simba::scalar::ComplexField;
 
 use crate::linalg::lu;
 use crate::linalg::PermutationSequence;
@@ -15,21 +15,17 @@ use crate::linalg::PermutationSequence;
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(serialize = "DefaultAllocator: Allocator<N, R, C> +
-        serialize = "DefaultAllocator: Allocator<N, R, C> +
                            Allocator<(usize, usize), DimMinimum<R, C>>,
          MatrixMN<N, R, C>: Serialize,
-         PermutationSequence<DimMinimum<R, C>>: Serialize"
+         PermutationSequence<DimMinimum<R, C>>: Serialize"))
-    ))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(deserialize = "DefaultAllocator: Allocator<N, R, C> +
-        deserialize = "DefaultAllocator: Allocator<N, R, C> +
                            Allocator<(usize, usize), DimMinimum<R, C>>,
          MatrixMN<N, R, C>: Deserialize<'de>,
-         PermutationSequence<DimMinimum<R, C>>: Deserialize<'de>"
+         PermutationSequence<DimMinimum<R, C>>: Deserialize<'de>"))
-    ))
 )]
 #[derive(Clone, Debug)]
 pub struct FullPivLU<N: ComplexField, R: DimMin<C>, C: Dim>
@@ -45,7 +41,8 @@ where
     DefaultAllocator: Allocator<N, R, C> + Allocator<(usize, usize), DimMinimum<R, C>>,
     MatrixMN<N, R, C>: Copy,
     PermutationSequence<DimMinimum<R, C>>: Copy,
-{}
+{
+}
 
 impl<N: ComplexField, R: DimMin<C>, C: Dim> FullPivLU<N, R, C>
 where DefaultAllocator: Allocator<N, R, C> + Allocator<(usize, usize), DimMinimum<R, C>>

src/linalg/givens.rs

@@ -1,19 +1,18 @@
 //! Construction of givens rotations.
 
-use alga::general::ComplexField;
+use num::{One, Zero};
-use num::{Zero, One};
+use simba::scalar::ComplexField;
 
+use crate::base::constraint::{DimEq, ShapeConstraint};
 use crate::base::dimension::{Dim, U2};
-use crate::base::constraint::{ShapeConstraint, DimEq};
 use crate::base::storage::{Storage, StorageMut};
-use crate::base::{Vector, Matrix};
+use crate::base::{Matrix, Vector};
-
 
 /// A Givens rotation.
 #[derive(Debug, Clone, Copy)]
 pub struct GivensRotation<N: ComplexField> {
     c: N::RealField,
-    s: N
+    s: N,
 }
 
 // Matrix = UnitComplex * Matrix
@@ -22,7 +21,7 @@ impl<N: ComplexField> GivensRotation<N> {
     pub fn identity() -> Self {
         Self {
             c: N::RealField::one(),
-            s: N::zero()
+            s: N::zero(),
         }
     }
 
@@ -31,9 +30,7 @@ impl<N: ComplexField> GivensRotation<N> {
     /// The components are copies as-is. It is not checked whether they describe
     /// an actually valid Givens rotation.
     pub fn new_unchecked(c: N::RealField, s: N) -> Self {
-       Self {
+        Self { c, s }
-           c, s
-       }
     }
 
     /// Initializes a Givens rotation from its non-normalized cosine an sine components.
@@ -103,7 +100,10 @@ impl<N: ComplexField> GivensRotation<N> {
 
     /// The inverse of this givens rotation.
     pub fn inverse(&self) -> Self {
-        Self { c: self.c, s: -self.s }
+        Self {
+            c: self.c,
+            s: -self.s,
+        }
     }
 
     /// Performs the multiplication `rhs = self * rhs` in-place.
@@ -159,4 +159,3 @@ impl<N: ComplexField> GivensRotation<N> {
         }
     }
 }
-

src/linalg/hessenberg.rs

@@ -1,11 +1,11 @@
 #[cfg(feature = "serde-serialize")]
 use serde::{Deserialize, Serialize};
 
-use alga::general::ComplexField;
 use crate::allocator::Allocator;
 use crate::base::{DefaultAllocator, MatrixMN, MatrixN, SquareMatrix, VectorN};
 use crate::dimension::{DimDiff, DimSub, U1};
 use crate::storage::Storage;
+use simba::scalar::ComplexField;
 
 use crate::linalg::householder;
 
@@ -13,21 +13,17 @@ use crate::linalg::householder;
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(serialize = "DefaultAllocator: Allocator<N, D, D> +
-        serialize = "DefaultAllocator: Allocator<N, D, D> +
                            Allocator<N, DimDiff<D, U1>>,
          MatrixN<N, D>: Serialize,
-         VectorN<N, DimDiff<D, U1>>: Serialize"
+         VectorN<N, DimDiff<D, U1>>: Serialize"))
-    ))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(deserialize = "DefaultAllocator: Allocator<N, D, D> +
-        deserialize = "DefaultAllocator: Allocator<N, D, D> +
                            Allocator<N, DimDiff<D, U1>>,
          MatrixN<N, D>: Deserialize<'de>,
-         VectorN<N, DimDiff<D, U1>>: Deserialize<'de>"
+         VectorN<N, DimDiff<D, U1>>: Deserialize<'de>"))
-    ))
 )]
 #[derive(Clone, Debug)]
 pub struct Hessenberg<N: ComplexField, D: DimSub<U1>>
@@ -42,7 +38,8 @@ where
     DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>,
     MatrixN<N, D>: Copy,
     VectorN<N, DimDiff<D, U1>>: Copy,
-{}
+{
+}
 
 impl<N: ComplexField, D: DimSub<U1>> Hessenberg<N, D>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D> + Allocator<N, DimDiff<D, U1>>

src/linalg/householder.rs

@@ -1,11 +1,11 @@
 //! Construction of householder elementary reflections.
 
-use num::Zero;
-use alga::general::ComplexField;
 use crate::allocator::Allocator;
 use crate::base::{DefaultAllocator, MatrixMN, MatrixN, Unit, Vector, VectorN};
 use crate::dimension::Dim;
 use crate::storage::{Storage, StorageMut};
+use num::Zero;
+use simba::scalar::ComplexField;
 
 use crate::geometry::Reflection;
 

src/linalg/inverse.rs

@@ -1,4 +1,4 @@
-use alga::general::ComplexField;
+use simba::scalar::ComplexField;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::Dim;

src/linalg/lu.rs

@@ -1,13 +1,13 @@
 #[cfg(feature = "serde-serialize")]
 use serde::{Deserialize, Serialize};
 
-use alga::general::{Field, ComplexField};
 use crate::allocator::{Allocator, Reallocator};
 use crate::base::{DefaultAllocator, Matrix, MatrixMN, MatrixN, Scalar};
 use crate::constraint::{SameNumberOfRows, ShapeConstraint};
 use crate::dimension::{Dim, DimMin, DimMinimum};
-use std::mem;
 use crate::storage::{Storage, StorageMut};
+use simba::scalar::{ComplexField, Field};
+use std::mem;
 
 use crate::linalg::PermutationSequence;
 
@@ -15,21 +15,17 @@ use crate::linalg::PermutationSequence;
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(serialize = "DefaultAllocator: Allocator<N, R, C> +
-        serialize = "DefaultAllocator: Allocator<N, R, C> +
                            Allocator<(usize, usize), DimMinimum<R, C>>,
          MatrixMN<N, R, C>: Serialize,
-         PermutationSequence<DimMinimum<R, C>>: Serialize"
+         PermutationSequence<DimMinimum<R, C>>: Serialize"))
-    ))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(deserialize = "DefaultAllocator: Allocator<N, R, C> +
-        deserialize = "DefaultAllocator: Allocator<N, R, C> +
                            Allocator<(usize, usize), DimMinimum<R, C>>,
          MatrixMN<N, R, C>: Deserialize<'de>,
-         PermutationSequence<DimMinimum<R, C>>: Deserialize<'de>"
+         PermutationSequence<DimMinimum<R, C>>: Deserialize<'de>"))
-    ))
 )]
 #[derive(Clone, Debug)]
 pub struct LU<N: ComplexField, R: DimMin<C>, C: Dim>
@@ -44,7 +40,8 @@ where
     DefaultAllocator: Allocator<N, R, C> + Allocator<(usize, usize), DimMinimum<R, C>>,
     MatrixMN<N, R, C>: Copy,
     PermutationSequence<DimMinimum<R, C>>: Copy,
-{}
+{
+}
 
 /// Performs a LU decomposition to overwrite `out` with the inverse of `matrix`.
 ///
@@ -333,7 +330,8 @@ where
     let (pivot_row, mut down) = submat.rows_range_pair_mut(0, 1..);
 
     for k in 0..pivot_row.ncols() {
-        down.column_mut(k).axpy(-pivot_row[k].inlined_clone(), &coeffs, N::one());
+        down.column_mut(k)
+            .axpy(-pivot_row[k].inlined_clone(), &coeffs, N::one());
     }
 }
 
@@ -364,7 +362,8 @@ pub fn gauss_step_swap<N, R: Dim, C: Dim, S>(
 
     for k in 0..pivot_row.ncols() {
         mem::swap(&mut pivot_row[k], &mut down[(piv - 1, k)]);
-        down.column_mut(k).axpy(-pivot_row[k].inlined_clone(), &coeffs, N::one());
+        down.column_mut(k)
+            .axpy(-pivot_row[k].inlined_clone(), &coeffs, N::one());
     }
 }
 

src/linalg/permutation_sequence.rs

@@ -1,8 +1,8 @@
 #[cfg(feature = "serde-serialize")]
 use serde::{Deserialize, Serialize};
 
-use alga::general::ClosedNeg;
 use num::One;
+use simba::scalar::ClosedNeg;
 
 use crate::allocator::Allocator;
 use crate::base::{DefaultAllocator, Matrix, Scalar, VectorN};
@@ -15,17 +15,13 @@ use crate::storage::StorageMut;
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(serialize = "DefaultAllocator: Allocator<(usize, usize), D>,
-        serialize = "DefaultAllocator: Allocator<(usize, usize), D>,
+         VectorN<(usize, usize), D>: Serialize"))
-         VectorN<(usize, usize), D>: Serialize"
-    ))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(deserialize = "DefaultAllocator: Allocator<(usize, usize), D>,
-        deserialize = "DefaultAllocator: Allocator<(usize, usize), D>,
+         VectorN<(usize, usize), D>: Deserialize<'de>"))
-         VectorN<(usize, usize), D>: Deserialize<'de>"
-    ))
 )]
 #[derive(Clone, Debug)]
 pub struct PermutationSequence<D: Dim>
@@ -39,7 +35,8 @@ impl<D: Dim> Copy for PermutationSequence<D>
 where
     DefaultAllocator: Allocator<(usize, usize), D>,
     VectorN<(usize, usize), D>: Copy,
-{}
+{
+}
 
 impl<D: DimName> PermutationSequence<D>
 where DefaultAllocator: Allocator<(usize, usize), D>

src/linalg/qr.rs

@@ -1,13 +1,13 @@
+use num::Zero;
 #[cfg(feature = "serde-serialize")]
 use serde::{Deserialize, Serialize};
-use num::Zero;
 
-use alga::general::ComplexField;
 use crate::allocator::{Allocator, Reallocator};
 use crate::base::{DefaultAllocator, Matrix, MatrixMN, MatrixN, Unit, VectorN};
 use crate::constraint::{SameNumberOfRows, ShapeConstraint};
 use crate::dimension::{Dim, DimMin, DimMinimum, U1};
 use crate::storage::{Storage, StorageMut};
+use simba::scalar::ComplexField;
 
 use crate::geometry::Reflection;
 use crate::linalg::householder;
@@ -16,21 +16,17 @@ use crate::linalg::householder;
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(serialize = "DefaultAllocator: Allocator<N, R, C> +
-        serialize = "DefaultAllocator: Allocator<N, R, C> +
                            Allocator<N, DimMinimum<R, C>>,
          MatrixMN<N, R, C>: Serialize,
-         VectorN<N, DimMinimum<R, C>>: Serialize"
+         VectorN<N, DimMinimum<R, C>>: Serialize"))
-    ))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(deserialize = "DefaultAllocator: Allocator<N, R, C> +
-        deserialize = "DefaultAllocator: Allocator<N, R, C> +
                            Allocator<N, DimMinimum<R, C>>,
          MatrixMN<N, R, C>: Deserialize<'de>,
-         VectorN<N, DimMinimum<R, C>>: Deserialize<'de>"
+         VectorN<N, DimMinimum<R, C>>: Deserialize<'de>"))
-    ))
 )]
 #[derive(Clone, Debug)]
 pub struct QR<N: ComplexField, R: DimMin<C>, C: Dim>
@@ -45,7 +41,8 @@ where
     DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>>,
     MatrixMN<N, R, C>: Copy,
     VectorN<N, DimMinimum<R, C>>: Copy,
-{}
+{
+}
 
 impl<N: ComplexField, R: DimMin<C>, C: Dim> QR<N, R, C>
 where DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimMinimum<R, C>>
@@ -77,9 +74,7 @@ where DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimM
     /// Retrieves the upper trapezoidal submatrix `R` of this decomposition.
     #[inline]
     pub fn r(&self) -> MatrixMN<N, DimMinimum<R, C>, C>
-    where
+    where DefaultAllocator: Allocator<N, DimMinimum<R, C>, C> {
-        DefaultAllocator: Allocator<N, DimMinimum<R, C>, C>,
-    {
         let (nrows, ncols) = self.qr.data.shape();
         let mut res = self.qr.rows_generic(0, nrows.min(ncols)).upper_triangle();
         res.set_partial_diagonal(self.diag.iter().map(|e| N::from_real(e.modulus())));
@@ -91,9 +86,7 @@ where DefaultAllocator: Allocator<N, R, C> + Allocator<N, R> + Allocator<N, DimM
     /// This is usually faster than `r` but consumes `self`.
     #[inline]
     pub fn unpack_r(self) -> MatrixMN<N, DimMinimum<R, C>, C>
-    where
+    where DefaultAllocator: Reallocator<N, R, C, DimMinimum<R, C>, C> {
-        DefaultAllocator: Reallocator<N, R, C, DimMinimum<R, C>, C>,
-    {
         let (nrows, ncols) = self.qr.data.shape();
         let mut res = self.qr.resize_generic(nrows.min(ncols), ncols, N::zero());
         res.fill_lower_triangle(N::zero(), 1);

src/linalg/schur.rs

@@ -2,8 +2,8 @@
 use serde::{Deserialize, Serialize};
 
 use approx::AbsDiffEq;
-use alga::general::{ComplexField, RealField};
 use num_complex::Complex as NumComplex;
+use simba::scalar::{ComplexField, RealField};
 use std::cmp;
 
 use crate::allocator::Allocator;
@@ -12,9 +12,9 @@ use crate::base::storage::Storage;
 use crate::base::{DefaultAllocator, MatrixN, SquareMatrix, Unit, Vector2, Vector3, VectorN};
 
 use crate::geometry::Reflection;
+use crate::linalg::givens::GivensRotation;
 use crate::linalg::householder;
 use crate::linalg::Hessenberg;
-use crate::linalg::givens::GivensRotation;
 
 /// Schur decomposition of a square matrix.
 ///
@@ -22,17 +22,13 @@ use crate::linalg::givens::GivensRotation;
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(serialize = "DefaultAllocator: Allocator<N, D, D>,
-        serialize = "DefaultAllocator: Allocator<N, D, D>,
+         MatrixN<N, D>: Serialize"))
-         MatrixN<N, D>: Serialize"
-    ))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(deserialize = "DefaultAllocator: Allocator<N, D, D>,
-        deserialize = "DefaultAllocator: Allocator<N, D, D>,
+         MatrixN<N, D>: Deserialize<'de>"))
-         MatrixN<N, D>: Deserialize<'de>"
-    ))
 )]
 #[derive(Clone, Debug)]
 pub struct Schur<N: ComplexField, D: Dim>
@@ -46,7 +42,8 @@ impl<N: ComplexField, D: Dim> Copy for Schur<N, D>
 where
     DefaultAllocator: Allocator<N, D, D>,
     MatrixN<N, D>: Copy,
-{}
+{
+}
 
 impl<N: ComplexField, D: Dim> Schur<N, D>
 where
@@ -291,8 +288,10 @@ where
 
     /// Computes the complex eigenvalues of the decomposed matrix.
     fn do_complex_eigenvalues(t: &MatrixN<N, D>, out: &mut VectorN<NumComplex<N>, D>)
-    where N: RealField,
+    where
-          DefaultAllocator: Allocator<NumComplex<N>, D> {
+        N: RealField,
+        DefaultAllocator: Allocator<NumComplex<N>, D>,
+    {
         let dim = t.nrows();
         let mut m = 0;
 
@@ -391,8 +390,10 @@ where
 
     /// Computes the complex eigenvalues of the decomposed matrix.
     pub fn complex_eigenvalues(&self) -> VectorN<NumComplex<N>, D>
-    where N: RealField,
+    where
-          DefaultAllocator: Allocator<NumComplex<N>, D> {
+        N: RealField,
+        DefaultAllocator: Allocator<NumComplex<N>, D>,
+    {
         let mut out = unsafe { VectorN::new_uninitialized_generic(self.t.data.shape().0, U1) };
         Self::do_complex_eigenvalues(&self.t, &mut out);
         out
@@ -560,8 +561,10 @@ where
     /// Computes the eigenvalues of this matrix.
     pub fn complex_eigenvalues(&self) -> VectorN<NumComplex<N>, D>
     // FIXME: add balancing?
-    where N: RealField,
+    where
-          DefaultAllocator: Allocator<NumComplex<N>, D> {
+        N: RealField,
+        DefaultAllocator: Allocator<NumComplex<N>, D>,
+    {
         let dim = self.data.shape().0;
         let mut work = unsafe { VectorN::new_uninitialized_generic(dim, U1) };
 

src/linalg/solve.rs

@@ -1,10 +1,10 @@
-use alga::general::ComplexField;
+use simba::scalar::ComplexField;
 
 use crate::base::allocator::Allocator;
 use crate::base::constraint::{SameNumberOfRows, ShapeConstraint};
 use crate::base::dimension::{Dim, U1};
 use crate::base::storage::{Storage, StorageMut};
-use crate::base::{DefaultAllocator, Matrix, MatrixMN, SquareMatrix, Vector, DVectorSlice};
+use crate::base::{DVectorSlice, DefaultAllocator, Matrix, MatrixMN, SquareMatrix, Vector};
 
 impl<N: ComplexField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
     /// Computes the solution of the linear system `self . x = b` where `x` is the unknown and only
@@ -236,7 +236,11 @@ impl<N: ComplexField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
         let cols = b.ncols();
 
         for i in 0..cols {
-            if !self.xx_solve_lower_triangular_vector_mut(&mut b.column_mut(i), |e| e, |a, b| a.dot(b)) {
+            if !self.xx_solve_lower_triangular_vector_mut(
+                &mut b.column_mut(i),
+                |e| e,
+                |a, b| a.dot(b),
+            ) {
                 return false;
             }
         }
@@ -257,7 +261,11 @@ impl<N: ComplexField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
         let cols = b.ncols();
 
         for i in 0..cols {
-            if !self.xx_solve_upper_triangular_vector_mut(&mut b.column_mut(i), |e| e, |a, b| a.dot(b)) {
+            if !self.xx_solve_upper_triangular_vector_mut(
+                &mut b.column_mut(i),
+                |e| e,
+                |a, b| a.dot(b),
+            ) {
                 return false;
             }
         }
@@ -318,7 +326,11 @@ impl<N: ComplexField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
         let cols = b.ncols();
 
         for i in 0..cols {
-            if !self.xx_solve_lower_triangular_vector_mut(&mut b.column_mut(i), |e| e.conjugate(), |a, b| a.dotc(b)) {
+            if !self.xx_solve_lower_triangular_vector_mut(
+                &mut b.column_mut(i),
+                |e| e.conjugate(),
+                |a, b| a.dotc(b),
+            ) {
                 return false;
             }
         }
@@ -339,7 +351,11 @@ impl<N: ComplexField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
         let cols = b.ncols();
 
         for i in 0..cols {
-            if !self.xx_solve_upper_triangular_vector_mut(&mut b.column_mut(i), |e| e.conjugate(), |a, b| a.dotc(b)) {
+            if !self.xx_solve_upper_triangular_vector_mut(
+                &mut b.column_mut(i),
+                |e| e.conjugate(),
+                |a, b| a.dotc(b),
+            ) {
                 return false;
             }
         }
@@ -347,13 +363,15 @@ impl<N: ComplexField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
         true
     }
 
-
     #[inline(always)]
     fn xx_solve_lower_triangular_vector_mut<R2: Dim, S2>(
         &self,
         b: &mut Vector<N, R2, S2>,
         conjugate: impl Fn(N) -> N,
-        dot: impl Fn(&DVectorSlice<N, S::RStride, S::CStride>, &DVectorSlice<N, S2::RStride, S2::CStride>) -> N,
+        dot: impl Fn(
+            &DVectorSlice<N, S::RStride, S::CStride>,
+            &DVectorSlice<N, S2::RStride, S2::CStride>,
+        ) -> N,
     ) -> bool
     where
         S2: StorageMut<N, R2, U1>,
@@ -385,7 +403,10 @@ impl<N: ComplexField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
         &self,
         b: &mut Vector<N, R2, S2>,
         conjugate: impl Fn(N) -> N,
-        dot: impl Fn(&DVectorSlice<N, S::RStride, S::CStride>, &DVectorSlice<N, S2::RStride, S2::CStride>) -> N,
+        dot: impl Fn(
+            &DVectorSlice<N, S::RStride, S::CStride>,
+            &DVectorSlice<N, S2::RStride, S2::CStride>,
+        ) -> N,
     ) -> bool
     where
         S2: StorageMut<N, R2, U1>,

src/linalg/svd.rs

@@ -1,19 +1,19 @@
 #[cfg(feature = "serde-serialize")]
 use serde::{Deserialize, Serialize};
 
-use num::{Zero, One};
 use approx::AbsDiffEq;
+use num::{One, Zero};
 
-use alga::general::{RealField, ComplexField};
 use crate::allocator::Allocator;
 use crate::base::{DefaultAllocator, Matrix, Matrix2x3, MatrixMN, Vector2, VectorN};
 use crate::constraint::{SameNumberOfRows, ShapeConstraint};
 use crate::dimension::{Dim, DimDiff, DimMin, DimMinimum, DimSub, U1, U2};
 use crate::storage::Storage;
+use simba::scalar::{ComplexField, RealField};
 
+use crate::linalg::givens::GivensRotation;
 use crate::linalg::symmetric_eigen;
 use crate::linalg::Bidiagonal;
-use crate::linalg::givens::GivensRotation;
 
 /// Singular Value Decomposition of a general matrix.
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
@@ -61,7 +61,8 @@ where
     MatrixMN<N, R, DimMinimum<R, C>>: Copy,
     MatrixMN<N, DimMinimum<R, C>, C>: Copy,
     VectorN<N::RealField, DimMinimum<R, C>>: Copy,
-{}
+{
+}
 
 impl<N: ComplexField, R: DimMin<C>, C: Dim> SVD<N, R, C>
 where
@@ -78,7 +79,14 @@ where
 {
     /// Computes the Singular Value Decomposition of `matrix` using implicit shift.
     pub fn new(matrix: MatrixMN<N, R, C>, compute_u: bool, compute_v: bool) -> Self {
-        Self::try_new(matrix, compute_u, compute_v, N::RealField::default_epsilon(), 0).unwrap()
+        Self::try_new(
+            matrix,
+            compute_u,
+            compute_v,
+            N::RealField::default_epsilon(),
+            0,
+        )
+        .unwrap()
     }
 
     /// Attempts to compute the Singular Value Decomposition of `matrix` using implicit shift.
@@ -120,7 +128,15 @@ where
         let mut off_diagonal = b.off_diagonal();
 
         let mut niter = 0;
-        let (mut start, mut end) = Self::delimit_subproblem(&mut diagonal, &mut off_diagonal, &mut u, &mut v_t, b.is_upper_diagonal(), dim - 1, eps);
+        let (mut start, mut end) = Self::delimit_subproblem(
+            &mut diagonal,
+            &mut off_diagonal,
+            &mut u,
+            &mut v_t,
+            b.is_upper_diagonal(),
+            dim - 1,
+            eps,
+        );
 
         while end != start {
             let subdim = end - start + 1;
@@ -165,7 +181,8 @@ where
                     );
 
                     if let Some((rot1, norm1)) = GivensRotation::cancel_y(&vec) {
-                        rot1.inverse().rotate_rows(&mut subm.fixed_columns_mut::<U2>(0));
+                        rot1.inverse()
+                            .rotate_rows(&mut subm.fixed_columns_mut::<U2>(0));
                         let rot1 = GivensRotation::new_unchecked(rot1.c(), N::from_real(rot1.s()));
 
                         if k > start {
@@ -175,8 +192,8 @@ where
 
                         let v = Vector2::new(subm[(0, 0)], subm[(1, 0)]);
                         // FIXME: does the case `v.y == 0` ever happen?
-                        let (rot2, norm2) =
+                        let (rot2, norm2) = GivensRotation::cancel_y(&v)
-                            GivensRotation::cancel_y(&v).unwrap_or((GivensRotation::identity(), subm[(0, 0)]));
+                            .unwrap_or((GivensRotation::identity(), subm[(0, 0)]));
 
                         rot2.rotate(&mut subm.fixed_columns_mut::<U2>(1));
                         let rot2 = GivensRotation::new_unchecked(rot2.c(), N::from_real(rot2.s()));
@@ -253,7 +270,15 @@ where
             }
 
             // Re-delimit the subproblem in case some decoupling occurred.
-            let sub = Self::delimit_subproblem(&mut diagonal, &mut off_diagonal, &mut u, &mut v_t, b.is_upper_diagonal(), end, eps);
+            let sub = Self::delimit_subproblem(
+                &mut diagonal,
+                &mut off_diagonal,
+                &mut u,
+                &mut v_t,
+                b.is_upper_diagonal(),
+                end,
+                eps,
+            );
             start = sub.0;
             end = sub.1;
 
@@ -321,14 +346,36 @@ where
                 off_diagonal[m] = N::RealField::zero();
             } else if diagonal[m].norm1() <= eps {
                 diagonal[m] = N::RealField::zero();
-                Self::cancel_horizontal_off_diagonal_elt(diagonal, off_diagonal, u, v_t, is_upper_diagonal, m, m + 1);
+                Self::cancel_horizontal_off_diagonal_elt(
+                    diagonal,
+                    off_diagonal,
+                    u,
+                    v_t,
+                    is_upper_diagonal,
+                    m,
+                    m + 1,
+                );
 
                 if m != 0 {
-                    Self::cancel_vertical_off_diagonal_elt(diagonal, off_diagonal, u, v_t, is_upper_diagonal, m - 1);
+                    Self::cancel_vertical_off_diagonal_elt(
+                        diagonal,
+                        off_diagonal,
+                        u,
+                        v_t,
+                        is_upper_diagonal,
+                        m - 1,
+                    );
                 }
             } else if diagonal[n].norm1() <= eps {
                 diagonal[n] = N::RealField::zero();
-                Self::cancel_vertical_off_diagonal_elt(diagonal, off_diagonal, u, v_t, is_upper_diagonal, m);
+                Self::cancel_vertical_off_diagonal_elt(
+                    diagonal,
+                    off_diagonal,
+                    u,
+                    v_t,
+                    is_upper_diagonal,
+                    m,
+                );
             } else {
                 break;
             }
@@ -352,10 +399,25 @@ where
             // FIXME: write a test that enters this case.
             else if diagonal[m].norm1() <= eps {
                 diagonal[m] = N::RealField::zero();
-                Self::cancel_horizontal_off_diagonal_elt(diagonal, off_diagonal, u, v_t, is_upper_diagonal, m, n);
+                Self::cancel_horizontal_off_diagonal_elt(
+                    diagonal,
+                    off_diagonal,
+                    u,
+                    v_t,
+                    is_upper_diagonal,
+                    m,
+                    n,
+                );
 
                 if m != 0 {
-                    Self::cancel_vertical_off_diagonal_elt(diagonal, off_diagonal, u, v_t, is_upper_diagonal, m - 1);
+                    Self::cancel_vertical_off_diagonal_elt(
+                        diagonal,
+                        off_diagonal,
+                        u,
+                        v_t,
+                        is_upper_diagonal,
+                        m - 1,
+                    );
                 }
                 break;
             }
@@ -469,7 +531,7 @@ where
             }
             (None, None) => Err("SVD recomposition: U and V^t have not been computed."),
             (None, _) => Err("SVD recomposition: U has not been computed."),
-            (_, None) => Err("SVD recomposition: V^t has not been computed.")
+            (_, None) => Err("SVD recomposition: V^t has not been computed."),
         }
     }
 
@@ -479,13 +541,10 @@ where
     /// Returns `Err` if the right- and left- singular vectors have not
     /// been computed at construction-time.
     pub fn pseudo_inverse(mut self, eps: N::RealField) -> Result<MatrixMN<N, C, R>, &'static str>
-    where
+    where DefaultAllocator: Allocator<N, C, R> {
-        DefaultAllocator: Allocator<N, C, R>,
-    {
         if eps < N::RealField::zero() {
             Err("SVD pseudo inverse: the epsilon must be non-negative.")
-        }
+        } else {
-        else {
             for i in 0..self.singular_values.len() {
                 let val = self.singular_values[i];
 
@@ -517,8 +576,7 @@ where
     {
         if eps < N::RealField::zero() {
             Err("SVD solve: the epsilon must be non-negative.")
-        }
+        } else {
-        else {
             match (&self.u, &self.v_t) {
                 (Some(u), Some(v_t)) => {
                     let mut ut_b = u.ad_mul(b);
@@ -540,7 +598,7 @@ where
                 }
                 (None, None) => Err("SVD solve: U and V^t have not been computed."),
                 (None, _) => Err("SVD solve: U has not been computed."),
-                (_, None) => Err("SVD solve: V^t has not been computed.")
+                (_, None) => Err("SVD solve: V^t has not been computed."),
             }
         }
     }
@@ -602,14 +660,11 @@ where
     ///
     /// All singular values below `eps` are considered equal to 0.
     pub fn pseudo_inverse(self, eps: N::RealField) -> Result<MatrixMN<N, C, R>, &'static str>
-    where
+    where DefaultAllocator: Allocator<N, C, R> {
-        DefaultAllocator: Allocator<N, C, R>,
-    {
         SVD::new(self.clone_owned(), true, true).pseudo_inverse(eps)
     }
 }
 
-
 // Explicit formulae inspired from the paper "Computing the Singular Values of 2-by-2 Complex
 // Matrices", Sanzheng Qiao and Xiaohong Wang.
 // http://www.cas.mcmaster.ca/sqrl/papers/sqrl5.pdf
@@ -619,7 +674,11 @@ fn compute_2x2_uptrig_svd<N: RealField>(
     m22: N,
     compute_u: bool,
     compute_v: bool,
-) -> (Option<GivensRotation<N>>, Vector2<N>, Option<GivensRotation<N>>)
+) -> (
+    Option<GivensRotation<N>>,
+    Vector2<N>,
+    Option<GivensRotation<N>>,
+)
 {
     let two: N::RealField = crate::convert(2.0f64);
     let half: N::RealField = crate::convert(0.5f64);

src/linalg/symmetric_eigen.rs

@@ -1,14 +1,14 @@
 #[cfg(feature = "serde-serialize")]
 use serde::{Deserialize, Serialize};
 
-use num::Zero;
 use approx::AbsDiffEq;
+use num::Zero;
 
-use alga::general::ComplexField;
 use crate::allocator::Allocator;
 use crate::base::{DefaultAllocator, Matrix2, MatrixN, SquareMatrix, Vector2, VectorN};
 use crate::dimension::{Dim, DimDiff, DimSub, U1, U2};
 use crate::storage::Storage;
+use simba::scalar::ComplexField;
 
 use crate::linalg::givens::GivensRotation;
 use crate::linalg::SymmetricTridiagonal;
@@ -17,21 +17,17 @@ use crate::linalg::SymmetricTridiagonal;
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(serialize = "DefaultAllocator: Allocator<N, D, D> +
-        serialize = "DefaultAllocator: Allocator<N, D, D> +
                            Allocator<N::RealField, D>,
          VectorN<N::RealField, D>: Serialize,
-         MatrixN<N, D>: Serialize"
+         MatrixN<N, D>: Serialize"))
-    ))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(deserialize = "DefaultAllocator: Allocator<N, D, D> +
-        deserialize = "DefaultAllocator: Allocator<N, D, D> +
                            Allocator<N::RealField, D>,
          VectorN<N::RealField, D>: Deserialize<'de>,
-         MatrixN<N, D>: Deserialize<'de>"
+         MatrixN<N, D>: Deserialize<'de>"))
-    ))
 )]
 #[derive(Clone, Debug)]
 pub struct SymmetricEigen<N: ComplexField, D: Dim>
@@ -49,7 +45,8 @@ where
     DefaultAllocator: Allocator<N, D, D> + Allocator<N::RealField, D>,
     MatrixN<N, D>: Copy,
     VectorN<N::RealField, D>: Copy,
-{}
+{
+}
 
 impl<N: ComplexField, D: Dim> SymmetricEigen<N, D>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N::RealField, D>
@@ -60,8 +57,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N::RealField, D>
     pub fn new(m: MatrixN<N, D>) -> Self
     where
         D: DimSub<U1>,
-        DefaultAllocator: Allocator<N, DimDiff<D, U1>> + // For tridiagonalization
+        DefaultAllocator: Allocator<N, DimDiff<D, U1>> + Allocator<N::RealField, DimDiff<D, U1>>,
-        Allocator<N::RealField, DimDiff<D, U1>>,
     {
         Self::try_new(m, N::RealField::default_epsilon(), 0).unwrap()
     }
@@ -80,8 +76,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N::RealField, D>
     pub fn try_new(m: MatrixN<N, D>, eps: N::RealField, max_niter: usize) -> Option<Self>
     where
         D: DimSub<U1>,
-        DefaultAllocator: Allocator<N, DimDiff<D, U1>> + // For tridiagonalization
+        DefaultAllocator: Allocator<N, DimDiff<D, U1>> + Allocator<N::RealField, DimDiff<D, U1>>,
-                          Allocator<N::RealField, DimDiff<D, U1>>,
     {
         Self::do_decompose(m, true, eps, max_niter).map(|(vals, vecs)| SymmetricEigen {
             eigenvectors: vecs.unwrap(),
@@ -97,8 +92,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N::RealField, D>
     ) -> Option<(VectorN<N::RealField, D>, Option<MatrixN<N, D>>)>
     where
         D: DimSub<U1>,
-        DefaultAllocator: Allocator<N, DimDiff<D, U1>> + // For tridiagonalization
+        DefaultAllocator: Allocator<N, DimDiff<D, U1>> + Allocator<N::RealField, DimDiff<D, U1>>,
-                          Allocator<N::RealField, DimDiff<D, U1>>,
     {
         assert!(
             m.is_square(),
@@ -154,7 +148,6 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N::RealField, D>
                             off_diag[i - 1] = norm;
                         }
 
-
                         let mii = diag[i];
                         let mjj = diag[j];
                         let mij = off_diag[i];
@@ -189,8 +182,10 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N::RealField, D>
                 }
             } else if subdim == 2 {
                 let m = Matrix2::new(
-                    diag[start], off_diag[start].conjugate(),
+                    diag[start],
-                    off_diag[start], diag[start + 1],
+                    off_diag[start].conjugate(),
+                    off_diag[start],
+                    diag[start + 1],
                 );
                 let eigvals = m.eigenvalues().unwrap();
                 let basis = Vector2::new(eigvals.x - diag[start + 1], off_diag[start]);
@@ -305,8 +300,10 @@ pub fn wilkinson_shift<N: ComplexField>(tmm: N, tnn: N, tmn: N) -> N {
  *
  */
 impl<N: ComplexField, D: DimSub<U1>, S: Storage<N, D, D>> SquareMatrix<N, D, S>
-where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>> +
+where DefaultAllocator: Allocator<N, D, D>
-                        Allocator<N::RealField, D> + Allocator<N::RealField, DimDiff<D, U1>>
+        + Allocator<N, DimDiff<D, U1>>
+        + Allocator<N::RealField, D>
+        + Allocator<N::RealField, DimDiff<D, U1>>
 {
     /// Computes the eigendecomposition of this symmetric matrix.
     ///
@@ -326,7 +323,12 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>> +
     /// * `max_niter` − maximum total number of iterations performed by the algorithm. If this
     /// number of iteration is exceeded, `None` is returned. If `niter == 0`, then the algorithm
     /// continues indefinitely until convergence.
-    pub fn try_symmetric_eigen(self, eps: N::RealField, max_niter: usize) -> Option<SymmetricEigen<N, D>> {
+    pub fn try_symmetric_eigen(
+        self,
+        eps: N::RealField,
+        max_niter: usize,
+    ) -> Option<SymmetricEigen<N, D>>
+    {
         SymmetricEigen::try_new(self.into_owned(), eps, max_niter)
     }
 
@@ -334,7 +336,12 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>> +
     ///
     /// Only the lower-triangular part of the matrix is read.
     pub fn symmetric_eigenvalues(&self) -> VectorN<N::RealField, D> {
-        SymmetricEigen::do_decompose(self.clone_owned(), false, N::RealField::default_epsilon(), 0)
+        SymmetricEigen::do_decompose(
+            self.clone_owned(),
+            false,
+            N::RealField::default_epsilon(),
+            0,
+        )
         .unwrap()
         .0
     }

src/linalg/symmetric_tridiagonal.rs

@@ -1,11 +1,11 @@
 #[cfg(feature = "serde-serialize")]
 use serde::{Deserialize, Serialize};
 
-use alga::general::ComplexField;
 use crate::allocator::Allocator;
 use crate::base::{DefaultAllocator, MatrixMN, MatrixN, SquareMatrix, VectorN};
 use crate::dimension::{DimDiff, DimSub, U1};
 use crate::storage::Storage;
+use simba::scalar::ComplexField;
 
 use crate::linalg::householder;
 
@@ -13,21 +13,17 @@ use crate::linalg::householder;
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(serialize = "DefaultAllocator: Allocator<N, D, D> +
-        serialize = "DefaultAllocator: Allocator<N, D, D> +
                            Allocator<N, DimDiff<D, U1>>,
          MatrixN<N, D>: Serialize,
-         VectorN<N, DimDiff<D, U1>>: Serialize"
+         VectorN<N, DimDiff<D, U1>>: Serialize"))
-    ))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(deserialize = "DefaultAllocator: Allocator<N, D, D> +
-        deserialize = "DefaultAllocator: Allocator<N, D, D> +
                            Allocator<N, DimDiff<D, U1>>,
          MatrixN<N, D>: Deserialize<'de>,
-         VectorN<N, DimDiff<D, U1>>: Deserialize<'de>"
+         VectorN<N, DimDiff<D, U1>>: Deserialize<'de>"))
-    ))
 )]
 #[derive(Clone, Debug)]
 pub struct SymmetricTridiagonal<N: ComplexField, D: DimSub<U1>>
@@ -42,7 +38,8 @@ where
     DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>,
     MatrixN<N, D>: Copy,
     VectorN<N, DimDiff<D, U1>>: Copy,
-{}
+{
+}
 
 impl<N: ComplexField, D: DimSub<U1>> SymmetricTridiagonal<N, D>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>
@@ -98,9 +95,15 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>
 
     /// Retrieve the orthogonal transformation, diagonal, and off diagonal elements of this
     /// decomposition.
-    pub fn unpack(self) -> (MatrixN<N, D>, VectorN<N::RealField, D>, VectorN<N::RealField, DimDiff<D, U1>>)
+    pub fn unpack(
-    where DefaultAllocator: Allocator<N::RealField, D>
+        self,
-                          + Allocator<N::RealField, DimDiff<D, U1>> {
+    ) -> (
+        MatrixN<N, D>,
+        VectorN<N::RealField, D>,
+        VectorN<N::RealField, DimDiff<D, U1>>,
+    )
+    where DefaultAllocator: Allocator<N::RealField, D> + Allocator<N::RealField, DimDiff<D, U1>>
+    {
         let diag = self.diagonal();
         let q = self.q();
 
@@ -108,15 +111,22 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>
     }
 
     /// Retrieve the diagonal, and off diagonal elements of this decomposition.
-    pub fn unpack_tridiagonal(self) -> (VectorN<N::RealField, D>, VectorN<N::RealField, DimDiff<D, U1>>)
+    pub fn unpack_tridiagonal(
-        where DefaultAllocator: Allocator<N::RealField, D>
+        self,
-                              + Allocator<N::RealField, DimDiff<D, U1>> {
+    ) -> (
+        VectorN<N::RealField, D>,
+        VectorN<N::RealField, DimDiff<D, U1>>,
+    )
+    where DefaultAllocator: Allocator<N::RealField, D> + Allocator<N::RealField, DimDiff<D, U1>>
+    {
         (self.diagonal(), self.off_diagonal.map(N::modulus))
     }
 
     /// The diagonal components of this decomposition.
     pub fn diagonal(&self) -> VectorN<N::RealField, D>
-    where DefaultAllocator: Allocator<N::RealField, D> { self.tri.map_diagonal(|e| e.real()) }
+    where DefaultAllocator: Allocator<N::RealField, D> {
+        self.tri.map_diagonal(|e| e.real())
+    }
 
     /// The off-diagonal components of this decomposition.
     pub fn off_diagonal(&self) -> VectorN<N::RealField, DimDiff<D, U1>>

src/sparse/cs_matrix.rs

@@ -1,5 +1,5 @@
-use alga::general::ClosedAdd;
 use num::Zero;
+use simba::scalar::ClosedAdd;
 use std::iter;
 use std::marker::PhantomData;
 use std::ops::Range;
@@ -7,9 +7,7 @@ use std::slice;
 
 use crate::allocator::Allocator;
 use crate::sparse::cs_utils;
-use crate::{
+use crate::{DefaultAllocator, Dim, Dynamic, Scalar, Vector, VectorN, U1};
-    DefaultAllocator, Dim, Dynamic, Scalar, Vector, VectorN, U1
-};
 
 pub struct ColumnEntries<'a, N> {
     curr: usize,
@@ -33,9 +31,11 @@ impl<'a, N: Clone> Iterator for ColumnEntries<'a, N> {
         if self.curr >= self.i.len() {
             None
         } else {
-            let res = Some((unsafe { self.i.get_unchecked(self.curr).clone() }, unsafe {
+            let res = Some(
+                (unsafe { self.i.get_unchecked(self.curr).clone() }, unsafe {
                     self.v.get_unchecked(self.curr).clone()
-            }));
+                }),
+            );
             self.curr += 1;
             res
         }

src/sparse/cs_matrix_conversion.rs

@@ -1,5 +1,5 @@
-use alga::general::ClosedAdd;
 use num::Zero;
+use simba::scalar::ClosedAdd;
 
 use crate::allocator::Allocator;
 use crate::sparse::cs_utils;

src/sparse/cs_matrix_ops.rs

@@ -1,5 +1,5 @@
-use alga::general::{ClosedAdd, ClosedMul};
 use num::{One, Zero};
+use simba::scalar::{ClosedAdd, ClosedMul};
 use std::ops::{Add, Mul};
 
 use crate::allocator::Allocator;