Merge pull request #713 from rustsim/soa_simd

Switch to Simba and make the base and geometry modules mostly SIMD AoSoA friendly.

.circleci/Xargo.toml

@@ -0,0 +1,2 @@
+[target.x86_64-unknown-linux-gnu.dependencies]
+alloc = {}

.circleci/config.yml

@@ -0,0 +1,108 @@
+version: 2.1
+
+executors:
+  rust-nightly-executor:
+    docker:
+        - image: rustlang/rust:nightly
+  rust-executor:
+    docker:
+        - image: rust:latest
+
+
+jobs:
+  check-fmt:
+    executor: rust-executor
+    steps:
+      - checkout
+      - run:
+          name: install rustfmt
+          command: rustup component add rustfmt
+      - run:
+          name: check formatting
+          command: cargo fmt -- --check
+  build-native:
+    executor: rust-executor
+    steps:
+      - checkout
+      - run: apt-get update
+      - run: apt-get install -y cmake gfortran libblas-dev liblapack-dev
+      - run:
+          name: build --no-default-feature
+          command: cargo build --no-default-features;
+      - run:
+          name: build (default features)
+          command: cargo build;
+      - run:
+          name: build --all-features
+          command: cargo build --all-features
+      - run:
+          name: build nalgebra-glm
+          command: cargo build -p nalgebra-glm --all-features
+      - run:
+          name: build nalgebra-lapack
+          command: cd nalgebra-lapack; cargo build
+  test-native:
+    executor: rust-executor
+    steps:
+      - checkout
+      - run:
+          name: test
+          command: cargo test --all-features
+      - run:
+          name: test nalgebra-glm
+          command: cargo test -p nalgebra-glm --all-features
+  build-wasm:
+    executor: rust-executor
+    steps:
+      - checkout
+      - run:
+          name: install cargo-web
+          command: cargo install -f cargo-web;
+      - run:
+          name: build --all-features
+          command: cargo web build --verbose --target wasm32-unknown-unknown;
+      - run:
+          name: build nalgebra-glm
+          command: cargo build -p nalgebra-glm --all-features
+  build-no-std:
+    executor: rust-nightly-executor
+    steps:
+      - checkout
+      - run:
+          name: install xargo
+          command: cp .circleci/Xargo.toml .; rustup component add rust-src; cargo install -f xargo;
+      - run:
+          name: build
+          command: xargo build --verbose --no-default-features --target=x86_64-unknown-linux-gnu;
+      - run:
+          name: build --features alloc
+          command: xargo build --verbose --no-default-features --features alloc --target=x86_64-unknown-linux-gnu;
+  build-nightly:
+    executor: rust-nightly-executor
+    steps:
+      - checkout
+      - run:
+          name: build --all-features
+          command: cargo build --all-features
+
+
+workflows:
+  version: 2
+  build:
+    jobs:
+      - check-fmt
+      - build-native:
+          requires:
+            - check-fmt
+      - build-wasm:
+          requires:
+            - check-fmt
+      - build-no-std:
+          requires:
+            - check-fmt
+      - build-nightly:
+          requires:
+            - check-fmt
+      - test-native:
+          requires:
+            - build-native

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          = { version = "0.1", default-features = false }
+alga           = { version = "0.9", default-features = false, optional = true }
 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"
@@ -73,3 +71,6 @@ path = "benches/lib.rs"
 
 [profile.bench]
 lto = true
+
+#[patch.crates-io]
+#simba = { path = "../simba" }

benches/core/matrix.rs

@@ -50,11 +50,13 @@ fn mat_div_scalar(b: &mut criterion::Criterion) {
     let a = DMatrix::from_row_slice(1000, 1000, &vec![2.0; 1000000]);
     let n = 42.0;
 
-    b.bench_function("mat_div_scalar", move |bh| bh.iter(|| {
+    b.bench_function("mat_div_scalar", move |bh| {
+        bh.iter(|| {
             let mut aa = a.clone();
             let mut b = aa.slice_mut((0, 0), (1000, 1000));
             b /= n
-    }));
+        })
+    });
 }
 
 fn mat100_add_mat100(bench: &mut criterion::Criterion) {
@@ -138,9 +140,11 @@ fn copy_from(bench: &mut criterion::Criterion) {
     let a = DMatrix::<f64>::new_random(1000, 1000);
     let mut b = DMatrix::<f64>::new_random(1000, 1000);
 
-    bench.bench_function("copy_from", move |bh| bh.iter(|| {
+    bench.bench_function("copy_from", move |bh| {
+        bh.iter(|| {
             b.copy_from(&a);
-    }));
+        })
+    });
 }
 
 fn axpy(bench: &mut criterion::Criterion) {
@@ -148,9 +152,11 @@ fn axpy(bench: &mut criterion::Criterion) {
     let mut y = DVector::<f64>::from_element(100000, 3.0);
     let a = 42.0;
 
-    bench.bench_function("axpy", move |bh| bh.iter(|| {
+    bench.bench_function("axpy", move |bh| {
+        bh.iter(|| {
             y.axpy(a, &x, 1.0);
-    }));
+        })
+    });
 }
 
 fn tr_mul_to(bench: &mut criterion::Criterion) {
@@ -166,60 +172,57 @@ fn mat_mul_mat(bench: &mut criterion::Criterion) {
     let b = DMatrix::<f64>::new_random(100, 100);
     let mut ab = DMatrix::<f64>::from_element(100, 100, 0.0);
 
-    bench.bench_function("mat_mul_mat", move |bh| bh.iter(|| {
+    bench.bench_function("mat_mul_mat", move |bh| {
+        bh.iter(|| {
             test::black_box(a.mul_to(&b, &mut ab));
-    }));
+        })
+    });
 }
 
 fn mat100_from_fn(bench: &mut criterion::Criterion) {
-    bench.bench_function("mat100_from_fn", move |bh| bh.iter(|| DMatrix::from_fn(100, 100, |a, b| a + b)));
+    bench.bench_function("mat100_from_fn", move |bh| {
+        bh.iter(|| DMatrix::from_fn(100, 100, |a, b| a + b))
+    });
 }
 
 fn mat500_from_fn(bench: &mut criterion::Criterion) {
-    bench.bench_function("mat500_from_fn", move |bh| bh.iter(|| DMatrix::from_fn(500, 500, |a, b| a + b)));
+    bench.bench_function("mat500_from_fn", move |bh| {
+        bh.iter(|| DMatrix::from_fn(500, 500, |a, b| a + b))
+    });
 }
 
-criterion_group!(matrix,
+criterion_group!(
+    matrix,
     mat2_mul_m,
     mat3_mul_m,
     mat4_mul_m,
-
     mat2_tr_mul_m,
     mat3_tr_mul_m,
     mat4_tr_mul_m,
-
     mat2_add_m,
     mat3_add_m,
     mat4_add_m,
-
     mat2_sub_m,
     mat3_sub_m,
     mat4_sub_m,
-
     mat2_mul_v,
     mat3_mul_v,
     mat4_mul_v,
-
     mat2_tr_mul_v,
     mat3_tr_mul_v,
     mat4_tr_mul_v,
-
     mat2_mul_s,
     mat3_mul_s,
     mat4_mul_s,
-
     mat2_div_s,
     mat3_div_s,
     mat4_div_s,
-
     mat2_inv,
     mat3_inv,
     mat4_inv,
-
     mat2_transpose,
     mat3_transpose,
     mat4_transpose,
-
     mat_div_scalar,
     mat100_add_mat100,
     mat4_mul_mat4,

benches/core/vector.rs

@@ -55,7 +55,9 @@ fn vec10000_axpy_f64(bh: &mut criterion::Criterion) {
     let b = DVector::new_random(10000);
     let n = rng.gen::<f64>();
 
-    bh.bench_function("vec10000_axpy_f64", move |bh| bh.iter(|| a.axpy(n, &b, 1.0)));
+    bh.bench_function("vec10000_axpy_f64", move |bh| {
+        bh.iter(|| a.axpy(n, &b, 1.0))
+    });
 }
 
 fn vec10000_axpy_beta_f64(bh: &mut criterion::Criterion) {
@@ -66,7 +68,9 @@ fn vec10000_axpy_beta_f64(bh: &mut criterion::Criterion) {
     let n = rng.gen::<f64>();
     let beta = rng.gen::<f64>();
 
-    bh.bench_function("vec10000_axpy_beta_f64", move |bh| bh.iter(|| a.axpy(n, &b, beta)));
+    bh.bench_function("vec10000_axpy_beta_f64", move |bh| {
+        bh.iter(|| a.axpy(n, &b, beta))
+    });
 }
 
 fn vec10000_axpy_f64_slice(bh: &mut criterion::Criterion) {
@@ -76,12 +80,14 @@ fn vec10000_axpy_f64_slice(bh: &mut criterion::Criterion) {
     let b = DVector::new_random(10000);
     let n = rng.gen::<f64>();
 
-    bh.bench_function("vec10000_axpy_f64_slice", move |bh| bh.iter(|| {
+    bh.bench_function("vec10000_axpy_f64_slice", move |bh| {
+        bh.iter(|| {
             let mut a = a.fixed_rows_mut::<U10000>(0);
             let b = b.fixed_rows::<U10000>(0);
 
             a.axpy(n, &b, 1.0)
-    }));
+        })
+    });
 }
 
 fn vec10000_axpy_f64_static(bh: &mut criterion::Criterion) {
@@ -92,7 +98,9 @@ fn vec10000_axpy_f64_static(bh: &mut criterion::Criterion) {
     let n = rng.gen::<f64>();
 
     // NOTE: for some reasons, it is much faster if the arument are boxed (Box::new(VectorN...)).
-    bh.bench_function("vec10000_axpy_f64_static", move |bh| bh.iter(|| a.axpy(n, &b, 1.0)));
+    bh.bench_function("vec10000_axpy_f64_static", move |bh| {
+        bh.iter(|| a.axpy(n, &b, 1.0))
+    });
 }
 
 fn vec10000_axpy_f32(bh: &mut criterion::Criterion) {
@@ -102,7 +110,9 @@ fn vec10000_axpy_f32(bh: &mut criterion::Criterion) {
     let b = DVector::new_random(10000);
     let n = rng.gen::<f32>();
 
-    bh.bench_function("vec10000_axpy_f32", move |bh| bh.iter(|| a.axpy(n, &b, 1.0)));
+    bh.bench_function("vec10000_axpy_f32", move |bh| {
+        bh.iter(|| a.axpy(n, &b, 1.0))
+    });
 }
 
 fn vec10000_axpy_beta_f32(bh: &mut criterion::Criterion) {
@@ -113,51 +123,43 @@ fn vec10000_axpy_beta_f32(bh: &mut criterion::Criterion) {
     let n = rng.gen::<f32>();
     let beta = rng.gen::<f32>();
 
-    bh.bench_function("vec10000_axpy_beta_f32", move |bh| bh.iter(|| a.axpy(n, &b, beta)));
+    bh.bench_function("vec10000_axpy_beta_f32", move |bh| {
+        bh.iter(|| a.axpy(n, &b, beta))
+    });
 }
 
-criterion_group!(vector,
+criterion_group!(
+    vector,
     vec2_add_v_f32,
     vec3_add_v_f32,
     vec4_add_v_f32,
-
     vec2_add_v_f64,
     vec3_add_v_f64,
     vec4_add_v_f64,
-
     vec2_sub_v,
     vec3_sub_v,
     vec4_sub_v,
-
     vec2_mul_s,
     vec3_mul_s,
     vec4_mul_s,
-
     vec2_div_s,
     vec3_div_s,
     vec4_div_s,
-
     vec2_dot_f32,
     vec3_dot_f32,
     vec4_dot_f32,
-
     vec2_dot_f64,
     vec3_dot_f64,
     vec4_dot_f64,
-
     vec3_cross,
-
     vec2_norm,
     vec3_norm,
     vec4_norm,
-
     vec2_normalize,
     vec3_normalize,
     vec4_normalize,
-
     vec10000_dot_f64,
     vec10000_dot_f32,
-
     vec10000_axpy_f64,
     vec10000_axpy_beta_f64,
     vec10000_axpy_f64_slice,

benches/geometry/quaternion.rs

@@ -26,7 +26,8 @@ bench_unop!(unit_quaternion_inv, UnitQuaternion<f32>, inverse);
 // bench_unop_self!(quaternion_conjugate, Quaternion<f32>, conjugate);
 // bench_unop!(quaternion_normalize, Quaternion<f32>, normalize);
 
-criterion_group!(quaternion,
+criterion_group!(
+    quaternion,
     quaternion_add_q,
     quaternion_sub_q,
     quaternion_mul_q,

benches/linalg/bidiagonal.rs

@@ -6,63 +6,82 @@ mod macros;
 // Without unpack.
 fn bidiagonalize_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
-    bh.bench_function("bidiagonalize_100x100", move |bh| bh.iter(|| test::black_box(Bidiagonal::new(m.clone()))));
+    bh.bench_function("bidiagonalize_100x100", move |bh| {
+        bh.iter(|| test::black_box(Bidiagonal::new(m.clone())))
+    });
 }
 
 fn bidiagonalize_100x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 500);
-    bh.bench_function("bidiagonalize_100x500", move |bh| bh.iter(|| test::black_box(Bidiagonal::new(m.clone()))));
+    bh.bench_function("bidiagonalize_100x500", move |bh| {
+        bh.iter(|| test::black_box(Bidiagonal::new(m.clone())))
+    });
 }
 
 fn bidiagonalize_4x4(bh: &mut criterion::Criterion) {
     let m = Matrix4::<f64>::new_random();
-    bh.bench_function("bidiagonalize_4x4", move |bh| bh.iter(|| test::black_box(Bidiagonal::new(m.clone()))));
+    bh.bench_function("bidiagonalize_4x4", move |bh| {
+        bh.iter(|| test::black_box(Bidiagonal::new(m.clone())))
+    });
 }
 
 fn bidiagonalize_500x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 100);
-    bh.bench_function("bidiagonalize_500x100", move |bh| bh.iter(|| test::black_box(Bidiagonal::new(m.clone()))));
+    bh.bench_function("bidiagonalize_500x100", move |bh| {
+        bh.iter(|| test::black_box(Bidiagonal::new(m.clone())))
+    });
 }
 
 fn bidiagonalize_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
-    bh.bench_function("bidiagonalize_500x500", move |bh| bh.iter(|| test::black_box(Bidiagonal::new(m.clone()))));
+    bh.bench_function("bidiagonalize_500x500", move |bh| {
+        bh.iter(|| test::black_box(Bidiagonal::new(m.clone())))
+    });
 }
 
 // With unpack.
 fn bidiagonalize_unpack_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
-    bh.bench_function("bidiagonalize_unpack_100x100", move |bh| bh.iter(|| {
+    bh.bench_function("bidiagonalize_unpack_100x100", move |bh| {
+        bh.iter(|| {
             let bidiag = Bidiagonal::new(m.clone());
             let _ = bidiag.unpack();
-    }));
+        })
+    });
 }
 
 fn bidiagonalize_unpack_100x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 500);
-    bh.bench_function("bidiagonalize_unpack_100x500", move |bh| bh.iter(|| {
+    bh.bench_function("bidiagonalize_unpack_100x500", move |bh| {
+        bh.iter(|| {
             let bidiag = Bidiagonal::new(m.clone());
             let _ = bidiag.unpack();
-    }));
+        })
+    });
 }
 
 fn bidiagonalize_unpack_500x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 100);
-    bh.bench_function("bidiagonalize_unpack_500x100", move |bh| bh.iter(|| {
+    bh.bench_function("bidiagonalize_unpack_500x100", move |bh| {
+        bh.iter(|| {
             let bidiag = Bidiagonal::new(m.clone());
             let _ = bidiag.unpack();
-    }));
+        })
+    });
 }
 
 fn bidiagonalize_unpack_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
-    bh.bench_function("bidiagonalize_unpack_500x500", move |bh| bh.iter(|| {
+    bh.bench_function("bidiagonalize_unpack_500x500", move |bh| {
+        bh.iter(|| {
             let bidiag = Bidiagonal::new(m.clone());
             let _ = bidiag.unpack();
-    }));
+        })
+    });
 }
 
-criterion_group!(bidiagonal,
+criterion_group!(
+    bidiagonal,
     bidiagonalize_100x100,
     bidiagonalize_100x500,
     bidiagonalize_4x4,

benches/linalg/cholesky.rs

@@ -4,14 +4,18 @@ fn cholesky_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
     let m = &m * m.transpose();
 
-    bh.bench_function("cholesky_100x100", move |bh| bh.iter(|| test::black_box(Cholesky::new(m.clone()))));
+    bh.bench_function("cholesky_100x100", move |bh| {
+        bh.iter(|| test::black_box(Cholesky::new(m.clone())))
+    });
 }
 
 fn cholesky_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
     let m = &m * m.transpose();
 
-    bh.bench_function("cholesky_500x500", move |bh| bh.iter(|| test::black_box(Cholesky::new(m.clone()))));
+    bh.bench_function("cholesky_500x500", move |bh| {
+        bh.iter(|| test::black_box(Cholesky::new(m.clone())))
+    });
 }
 
 // With unpack.
@@ -19,19 +23,23 @@ fn cholesky_decompose_unpack_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
     let m = &m * m.transpose();
 
-    bh.bench_function("cholesky_decompose_unpack_100x100", move |bh| bh.iter(|| {
+    bh.bench_function("cholesky_decompose_unpack_100x100", move |bh| {
+        bh.iter(|| {
             let chol = Cholesky::new(m.clone()).unwrap();
             let _ = chol.unpack();
-    }));
+        })
+    });
 }
 fn cholesky_decompose_unpack_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
     let m = &m * m.transpose();
 
-    bh.bench_function("cholesky_decompose_unpack_500x500", move |bh| bh.iter(|| {
+    bh.bench_function("cholesky_decompose_unpack_500x500", move |bh| {
+        bh.iter(|| {
             let chol = Cholesky::new(m.clone()).unwrap();
             let _ = chol.unpack();
-    }));
+        })
+    });
 }
 
 fn cholesky_solve_10x10(bh: &mut criterion::Criterion) {
@@ -40,9 +48,11 @@ fn cholesky_solve_10x10(bh: &mut criterion::Criterion) {
     let v = DVector::<f64>::new_random(10);
     let chol = Cholesky::new(m.clone()).unwrap();
 
-    bh.bench_function("cholesky_solve_10x10", move |bh| bh.iter(|| {
+    bh.bench_function("cholesky_solve_10x10", move |bh| {
+        bh.iter(|| {
             let _ = chol.solve(&v);
-    }));
+        })
+    });
 }
 
 fn cholesky_solve_100x100(bh: &mut criterion::Criterion) {
@@ -51,9 +61,11 @@ fn cholesky_solve_100x100(bh: &mut criterion::Criterion) {
     let v = DVector::<f64>::new_random(100);
     let chol = Cholesky::new(m.clone()).unwrap();
 
-    bh.bench_function("cholesky_solve_100x100", move |bh| bh.iter(|| {
+    bh.bench_function("cholesky_solve_100x100", move |bh| {
+        bh.iter(|| {
             let _ = chol.solve(&v);
-    }));
+        })
+    });
 }
 
 fn cholesky_solve_500x500(bh: &mut criterion::Criterion) {
@@ -62,20 +74,23 @@ fn cholesky_solve_500x500(bh: &mut criterion::Criterion) {
     let v = DVector::<f64>::new_random(500);
     let chol = Cholesky::new(m.clone()).unwrap();
 
-    bh.bench_function("cholesky_solve_500x500", move |bh| bh.iter(|| {
+    bh.bench_function("cholesky_solve_500x500", move |bh| {
+        bh.iter(|| {
             let _ = chol.solve(&v);
-    }));
+        })
+    });
 }
 
-
 fn cholesky_inverse_10x10(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(10, 10);
     let m = &m * m.transpose();
     let chol = Cholesky::new(m.clone()).unwrap();
 
-    bh.bench_function("cholesky_inverse_10x10", move |bh| bh.iter(|| {
+    bh.bench_function("cholesky_inverse_10x10", move |bh| {
+        bh.iter(|| {
             let _ = chol.inverse();
-    }));
+        })
+    });
 }
 
 fn cholesky_inverse_100x100(bh: &mut criterion::Criterion) {
@@ -83,9 +98,11 @@ fn cholesky_inverse_100x100(bh: &mut criterion::Criterion) {
     let m = &m * m.transpose();
     let chol = Cholesky::new(m.clone()).unwrap();
 
-    bh.bench_function("cholesky_inverse_100x100", move |bh| bh.iter(|| {
+    bh.bench_function("cholesky_inverse_100x100", move |bh| {
+        bh.iter(|| {
             let _ = chol.inverse();
-    }));
+        })
+    });
 }
 
 fn cholesky_inverse_500x500(bh: &mut criterion::Criterion) {
@@ -93,12 +110,15 @@ fn cholesky_inverse_500x500(bh: &mut criterion::Criterion) {
     let m = &m * m.transpose();
     let chol = Cholesky::new(m.clone()).unwrap();
 
-    bh.bench_function("cholesky_inverse_500x500", move |bh| bh.iter(|| {
+    bh.bench_function("cholesky_inverse_500x500", move |bh| {
+        bh.iter(|| {
             let _ = chol.inverse();
-    }));
+        })
+    });
 }
 
-criterion_group!(cholesky,
+criterion_group!(
+    cholesky,
     cholesky_100x100,
     cholesky_500x500,
     cholesky_decompose_unpack_100x100,

benches/linalg/full_piv_lu.rs

@@ -3,93 +3,117 @@ use na::{DMatrix, DVector, FullPivLU};
 // Without unpack.
 fn full_piv_lu_decompose_10x10(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(10, 10);
-    bh.bench_function("full_piv_lu_decompose_10x10", move |bh| bh.iter(|| test::black_box(FullPivLU::new(m.clone()))));
+    bh.bench_function("full_piv_lu_decompose_10x10", move |bh| {
+        bh.iter(|| test::black_box(FullPivLU::new(m.clone())))
+    });
 }
 
 fn full_piv_lu_decompose_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
-    bh.bench_function("full_piv_lu_decompose_100x100", move |bh| bh.iter(|| test::black_box(FullPivLU::new(m.clone()))));
+    bh.bench_function("full_piv_lu_decompose_100x100", move |bh| {
+        bh.iter(|| test::black_box(FullPivLU::new(m.clone())))
+    });
 }
 
 fn full_piv_lu_decompose_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
-    bh.bench_function("full_piv_lu_decompose_500x500", move |bh| bh.iter(|| test::black_box(FullPivLU::new(m.clone()))));
+    bh.bench_function("full_piv_lu_decompose_500x500", move |bh| {
+        bh.iter(|| test::black_box(FullPivLU::new(m.clone())))
+    });
 }
 
 fn full_piv_lu_solve_10x10(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(10, 10);
     let lu = FullPivLU::new(m.clone());
 
-    bh.bench_function("full_piv_lu_solve_10x10", move |bh| bh.iter(|| {
+    bh.bench_function("full_piv_lu_solve_10x10", move |bh| {
+        bh.iter(|| {
             let mut b = DVector::<f64>::from_element(10, 1.0);
             lu.solve(&mut b);
-    }));
+        })
+    });
 }
 
 fn full_piv_lu_solve_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
     let lu = FullPivLU::new(m.clone());
 
-    bh.bench_function("full_piv_lu_solve_100x100", move |bh| bh.iter(|| {
+    bh.bench_function("full_piv_lu_solve_100x100", move |bh| {
+        bh.iter(|| {
             let mut b = DVector::<f64>::from_element(100, 1.0);
             lu.solve(&mut b);
-    }));
+        })
+    });
 }
 
 fn full_piv_lu_solve_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
     let lu = FullPivLU::new(m.clone());
 
-    bh.bench_function("full_piv_lu_solve_500x500", move |bh| bh.iter(|| {
+    bh.bench_function("full_piv_lu_solve_500x500", move |bh| {
+        bh.iter(|| {
             let mut b = DVector::<f64>::from_element(500, 1.0);
             lu.solve(&mut b);
-    }));
+        })
+    });
 }
 
 fn full_piv_lu_inverse_10x10(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(10, 10);
     let lu = FullPivLU::new(m.clone());
 
-    bh.bench_function("full_piv_lu_inverse_10x10", move |bh| bh.iter(|| test::black_box(lu.try_inverse())));
+    bh.bench_function("full_piv_lu_inverse_10x10", move |bh| {
+        bh.iter(|| test::black_box(lu.try_inverse()))
+    });
 }
 
 fn full_piv_lu_inverse_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
     let lu = FullPivLU::new(m.clone());
 
-    bh.bench_function("full_piv_lu_inverse_100x100", move |bh| bh.iter(|| test::black_box(lu.try_inverse())));
+    bh.bench_function("full_piv_lu_inverse_100x100", move |bh| {
+        bh.iter(|| test::black_box(lu.try_inverse()))
+    });
 }
 
 fn full_piv_lu_inverse_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
     let lu = FullPivLU::new(m.clone());
 
-    bh.bench_function("full_piv_lu_inverse_500x500", move |bh| bh.iter(|| test::black_box(lu.try_inverse())));
+    bh.bench_function("full_piv_lu_inverse_500x500", move |bh| {
+        bh.iter(|| test::black_box(lu.try_inverse()))
+    });
 }
 
 fn full_piv_lu_determinant_10x10(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(10, 10);
     let lu = FullPivLU::new(m.clone());
 
-    bh.bench_function("full_piv_lu_determinant_10x10", move |bh| bh.iter(|| test::black_box(lu.determinant())));
+    bh.bench_function("full_piv_lu_determinant_10x10", move |bh| {
+        bh.iter(|| test::black_box(lu.determinant()))
+    });
 }
 
-
 fn full_piv_lu_determinant_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
     let lu = FullPivLU::new(m.clone());
 
-    bh.bench_function("full_piv_lu_determinant_100x100", move |bh| bh.iter(|| test::black_box(lu.determinant())));
+    bh.bench_function("full_piv_lu_determinant_100x100", move |bh| {
+        bh.iter(|| test::black_box(lu.determinant()))
+    });
 }
 
 fn full_piv_lu_determinant_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
     let lu = FullPivLU::new(m.clone());
 
-    bh.bench_function("full_piv_lu_determinant_500x500", move |bh| bh.iter(|| test::black_box(lu.determinant())));
+    bh.bench_function("full_piv_lu_determinant_500x500", move |bh| {
+        bh.iter(|| test::black_box(lu.determinant()))
+    });
 }
 
-criterion_group!(full_piv_lu,
+criterion_group!(
+    full_piv_lu,
     full_piv_lu_decompose_10x10,
     full_piv_lu_decompose_100x100,
     //    full_piv_lu_decompose_500x500,

benches/linalg/hessenberg.rs

@@ -6,50 +6,65 @@ mod macros;
 // Without unpack.
 fn hessenberg_decompose_4x4(bh: &mut criterion::Criterion) {
     let m = Matrix4::<f64>::new_random();
-    bh.bench_function("hessenberg_decompose_4x4", move |bh| bh.iter(|| test::black_box(Hessenberg::new(m.clone()))));
+    bh.bench_function("hessenberg_decompose_4x4", move |bh| {
+        bh.iter(|| test::black_box(Hessenberg::new(m.clone())))
+    });
 }
 
 fn hessenberg_decompose_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
-    bh.bench_function("hessenberg_decompose_100x100", move |bh| bh.iter(|| test::black_box(Hessenberg::new(m.clone()))));
+    bh.bench_function("hessenberg_decompose_100x100", move |bh| {
+        bh.iter(|| test::black_box(Hessenberg::new(m.clone())))
+    });
 }
 
 fn hessenberg_decompose_200x200(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(200, 200);
-    bh.bench_function("hessenberg_decompose_200x200", move |bh| bh.iter(|| test::black_box(Hessenberg::new(m.clone()))));
+    bh.bench_function("hessenberg_decompose_200x200", move |bh| {
+        bh.iter(|| test::black_box(Hessenberg::new(m.clone())))
+    });
 }
 
 fn hessenberg_decompose_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
-    bh.bench_function("hessenberg_decompose_500x500", move |bh| bh.iter(|| test::black_box(Hessenberg::new(m.clone()))));
+    bh.bench_function("hessenberg_decompose_500x500", move |bh| {
+        bh.iter(|| test::black_box(Hessenberg::new(m.clone())))
+    });
 }
 
 // With unpack.
 fn hessenberg_decompose_unpack_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
-    bh.bench_function("hessenberg_decompose_unpack_100x100", move |bh| bh.iter(|| {
+    bh.bench_function("hessenberg_decompose_unpack_100x100", move |bh| {
+        bh.iter(|| {
             let hess = Hessenberg::new(m.clone());
             let _ = hess.unpack();
-    }));
+        })
+    });
 }
 
 fn hessenberg_decompose_unpack_200x200(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(200, 200);
-    bh.bench_function("hessenberg_decompose_unpack_200x200", move |bh| bh.iter(|| {
+    bh.bench_function("hessenberg_decompose_unpack_200x200", move |bh| {
+        bh.iter(|| {
             let hess = Hessenberg::new(m.clone());
             let _ = hess.unpack();
-    }));
+        })
+    });
 }
 
 fn hessenberg_decompose_unpack_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
-    bh.bench_function("hessenberg_decompose_unpack_500x500", move |bh| bh.iter(|| {
+    bh.bench_function("hessenberg_decompose_unpack_500x500", move |bh| {
+        bh.iter(|| {
             let hess = Hessenberg::new(m.clone());
             let _ = hess.unpack();
-    }));
+        })
+    });
 }
 
-criterion_group!(hessenberg,
+criterion_group!(
+    hessenberg,
     hessenberg_decompose_4x4,
     hessenberg_decompose_100x100,
     hessenberg_decompose_200x200,

benches/linalg/lu.rs

@@ -3,82 +3,104 @@ use na::{DMatrix, DVector, LU};
 // Without unpack.
 fn lu_decompose_10x10(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(10, 10);
-    bh.bench_function("lu_decompose_10x10", move |bh| bh.iter(|| test::black_box(LU::new(m.clone()))));
+    bh.bench_function("lu_decompose_10x10", move |bh| {
+        bh.iter(|| test::black_box(LU::new(m.clone())))
+    });
 }
 
 fn lu_decompose_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
-    bh.bench_function("lu_decompose_100x100", move |bh| bh.iter(|| test::black_box(LU::new(m.clone()))));
+    bh.bench_function("lu_decompose_100x100", move |bh| {
+        bh.iter(|| test::black_box(LU::new(m.clone())))
+    });
 }
 
 fn lu_decompose_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
-    bh.bench_function("lu_decompose_500x500", move |bh| bh.iter(|| test::black_box(LU::new(m.clone()))));
+    bh.bench_function("lu_decompose_500x500", move |bh| {
+        bh.iter(|| test::black_box(LU::new(m.clone())))
+    });
 }
 
 fn lu_solve_10x10(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(10, 10);
     let lu = LU::new(m.clone());
 
-    bh.bench_function("lu_solve_10x10", move |bh| bh.iter(|| {
+    bh.bench_function("lu_solve_10x10", move |bh| {
+        bh.iter(|| {
             let mut b = DVector::<f64>::from_element(10, 1.0);
             lu.solve(&mut b);
-    }));
+        })
+    });
 }
 
 fn lu_solve_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
     let lu = LU::new(m.clone());
 
-    bh.bench_function("lu_solve_100x100", move |bh| bh.iter(|| {
+    bh.bench_function("lu_solve_100x100", move |bh| {
+        bh.iter(|| {
             let mut b = DVector::<f64>::from_element(100, 1.0);
             lu.solve(&mut b);
-    }));
+        })
+    });
 }
 
 fn lu_solve_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
     let lu = LU::new(m.clone());
 
-    bh.bench_function("", move |bh| bh.iter(|| {
+    bh.bench_function("", move |bh| {
+        bh.iter(|| {
             let mut b = DVector::<f64>::from_element(500, 1.0);
             lu.solve(&mut b);
-    }));
+        })
+    });
 }
 
 fn lu_inverse_10x10(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(10, 10);
     let lu = LU::new(m.clone());
 
-    bh.bench_function("lu_inverse_10x10", move |bh| bh.iter(|| test::black_box(lu.try_inverse())));
+    bh.bench_function("lu_inverse_10x10", move |bh| {
+        bh.iter(|| test::black_box(lu.try_inverse()))
+    });
 }
 
 fn lu_inverse_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
     let lu = LU::new(m.clone());
 
-    bh.bench_function("lu_inverse_100x100", move |bh| bh.iter(|| test::black_box(lu.try_inverse())));
+    bh.bench_function("lu_inverse_100x100", move |bh| {
+        bh.iter(|| test::black_box(lu.try_inverse()))
+    });
 }
 
 fn lu_inverse_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
     let lu = LU::new(m.clone());
 
-    bh.bench_function("lu_inverse_500x500", move |bh| bh.iter(|| test::black_box(lu.try_inverse())));
+    bh.bench_function("lu_inverse_500x500", move |bh| {
+        bh.iter(|| test::black_box(lu.try_inverse()))
+    });
 }
 
 fn lu_determinant_10x10(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(10, 10);
     let lu = LU::new(m.clone());
 
-    bh.bench_function("lu_determinant_10x10", move |bh| bh.iter(|| test::black_box(lu.determinant())));
+    bh.bench_function("lu_determinant_10x10", move |bh| {
+        bh.iter(|| test::black_box(lu.determinant()))
+    });
 }
 
 fn lu_determinant_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
     let lu = LU::new(m.clone());
 
-    bh.bench_function("lu_determinant_100x100", move |bh| bh.iter(|| test::black_box(lu.determinant())));
+    bh.bench_function("lu_determinant_100x100", move |bh| {
+        bh.iter(|| test::black_box(lu.determinant()))
+    });
 }
 
 fn lu_determinant_500x500(bh: &mut criterion::Criterion) {
@@ -88,7 +110,8 @@ fn lu_determinant_500x500(bh: &mut criterion::Criterion) {
     bh.bench_function("", move |bh| bh.iter(|| test::black_box(lu.determinant())));
 }
 
-criterion_group!(lu,
+criterion_group!(
+    lu,
     lu_decompose_10x10,
     lu_decompose_100x100,
     //    lu_decompose_500x500,

benches/linalg/qr.rs

@@ -6,115 +6,145 @@ mod macros;
 // Without unpack.
 fn qr_decompose_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
-    bh.bench_function("qr_decompose_100x100", move |bh| bh.iter(|| test::black_box(QR::new(m.clone()))));
+    bh.bench_function("qr_decompose_100x100", move |bh| {
+        bh.iter(|| test::black_box(QR::new(m.clone())))
+    });
 }
 
 fn qr_decompose_100x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 500);
-    bh.bench_function("qr_decompose_100x500", move |bh| bh.iter(|| test::black_box(QR::new(m.clone()))));
+    bh.bench_function("qr_decompose_100x500", move |bh| {
+        bh.iter(|| test::black_box(QR::new(m.clone())))
+    });
 }
 
 fn qr_decompose_4x4(bh: &mut criterion::Criterion) {
     let m = Matrix4::<f64>::new_random();
-    bh.bench_function("qr_decompose_4x4", move |bh| bh.iter(|| test::black_box(QR::new(m.clone()))));
+    bh.bench_function("qr_decompose_4x4", move |bh| {
+        bh.iter(|| test::black_box(QR::new(m.clone())))
+    });
 }
 
 fn qr_decompose_500x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 100);
-    bh.bench_function("qr_decompose_500x100", move |bh| bh.iter(|| test::black_box(QR::new(m.clone()))));
+    bh.bench_function("qr_decompose_500x100", move |bh| {
+        bh.iter(|| test::black_box(QR::new(m.clone())))
+    });
 }
 
 fn qr_decompose_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
-    bh.bench_function("qr_decompose_500x500", move |bh| bh.iter(|| test::black_box(QR::new(m.clone()))));
+    bh.bench_function("qr_decompose_500x500", move |bh| {
+        bh.iter(|| test::black_box(QR::new(m.clone())))
+    });
 }
 
 // With unpack.
 fn qr_decompose_unpack_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
-    bh.bench_function("qr_decompose_unpack_100x100", move |bh| bh.iter(|| {
+    bh.bench_function("qr_decompose_unpack_100x100", move |bh| {
+        bh.iter(|| {
             let qr = QR::new(m.clone());
             let _ = qr.unpack();
-    }));
+        })
+    });
 }
 
 fn qr_decompose_unpack_100x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 500);
-    bh.bench_function("qr_decompose_unpack_100x500", move |bh| bh.iter(|| {
+    bh.bench_function("qr_decompose_unpack_100x500", move |bh| {
+        bh.iter(|| {
             let qr = QR::new(m.clone());
             let _ = qr.unpack();
-    }));
+        })
+    });
 }
 
 fn qr_decompose_unpack_500x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 100);
-    bh.bench_function("qr_decompose_unpack_500x100", move |bh| bh.iter(|| {
+    bh.bench_function("qr_decompose_unpack_500x100", move |bh| {
+        bh.iter(|| {
             let qr = QR::new(m.clone());
             let _ = qr.unpack();
-    }));
+        })
+    });
 }
 
 fn qr_decompose_unpack_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
-    bh.bench_function("qr_decompose_unpack_500x500", move |bh| bh.iter(|| {
+    bh.bench_function("qr_decompose_unpack_500x500", move |bh| {
+        bh.iter(|| {
             let qr = QR::new(m.clone());
             let _ = qr.unpack();
-    }));
+        })
+    });
 }
 
 fn qr_solve_10x10(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(10, 10);
     let qr = QR::new(m.clone());
 
-    bh.bench_function("qr_solve_10x10", move |bh| bh.iter(|| {
+    bh.bench_function("qr_solve_10x10", move |bh| {
+        bh.iter(|| {
             let mut b = DVector::<f64>::from_element(10, 1.0);
             qr.solve(&mut b);
-    }));
+        })
+    });
 }
 
 fn qr_solve_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
     let qr = QR::new(m.clone());
 
-    bh.bench_function("qr_solve_100x100", move |bh| bh.iter(|| {
+    bh.bench_function("qr_solve_100x100", move |bh| {
+        bh.iter(|| {
             let mut b = DVector::<f64>::from_element(100, 1.0);
             qr.solve(&mut b);
-    }));
+        })
+    });
 }
 
 fn qr_solve_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
     let qr = QR::new(m.clone());
 
-    bh.bench_function("qr_solve_500x500", move |bh| bh.iter(|| {
+    bh.bench_function("qr_solve_500x500", move |bh| {
+        bh.iter(|| {
             let mut b = DVector::<f64>::from_element(500, 1.0);
             qr.solve(&mut b);
-    }));
+        })
+    });
 }
 
 fn qr_inverse_10x10(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(10, 10);
     let qr = QR::new(m.clone());
 
-    bh.bench_function("qr_inverse_10x10", move |bh| bh.iter(|| test::black_box(qr.try_inverse())));
+    bh.bench_function("qr_inverse_10x10", move |bh| {
+        bh.iter(|| test::black_box(qr.try_inverse()))
+    });
 }
 
 fn qr_inverse_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
     let qr = QR::new(m.clone());
 
-    bh.bench_function("qr_inverse_100x100", move |bh| bh.iter(|| test::black_box(qr.try_inverse())));
+    bh.bench_function("qr_inverse_100x100", move |bh| {
+        bh.iter(|| test::black_box(qr.try_inverse()))
+    });
 }
 
 fn qr_inverse_500x500(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(500, 500);
     let qr = QR::new(m.clone());
 
-    bh.bench_function("qr_inverse_500x500", move |bh| bh.iter(|| test::black_box(qr.try_inverse())));
+    bh.bench_function("qr_inverse_500x500", move |bh| {
+        bh.iter(|| test::black_box(qr.try_inverse()))
+    });
 }
 
-
+criterion_group!(
-criterion_group!(qr,
+    qr,
     qr_decompose_100x100,
     qr_decompose_100x500,
     qr_decompose_4x4,

benches/linalg/schur.rs

@@ -2,45 +2,62 @@ use na::{Matrix4, Schur};
 
 fn schur_decompose_4x4(bh: &mut criterion::Criterion) {
     let m = Matrix4::<f64>::new_random();
-    bh.bench_function("schur_decompose_4x4", move |bh| bh.iter(|| test::black_box(Schur::new(m.clone()))));
+    bh.bench_function("schur_decompose_4x4", move |bh| {
+        bh.iter(|| test::black_box(Schur::new(m.clone())))
+    });
 }
 
 fn schur_decompose_10x10(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(10, 10);
-    bh.bench_function("schur_decompose_10x10", move |bh| bh.iter(|| test::black_box(Schur::new(m.clone()))));
+    bh.bench_function("schur_decompose_10x10", move |bh| {
+        bh.iter(|| test::black_box(Schur::new(m.clone())))
+    });
 }
 
 fn schur_decompose_100x100(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(100, 100);
-    bh.bench_function("schur_decompose_100x100", move |bh| bh.iter(|| test::black_box(Schur::new(m.clone()))));
+    bh.bench_function("schur_decompose_100x100", move |bh| {
+        bh.iter(|| test::black_box(Schur::new(m.clone())))
+    });
 }
 
 fn schur_decompose_200x200(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(200, 200);
-    bh.bench_function("schur_decompose_200x200", move |bh| bh.iter(|| test::black_box(Schur::new(m.clone()))));
+    bh.bench_function("schur_decompose_200x200", move |bh| {
+        bh.iter(|| test::black_box(Schur::new(m.clone())))
+    });
 }
 
 fn eigenvalues_4x4(bh: &mut criterion::Criterion) {
     let m = Matrix4::<f64>::new_random();
-    bh.bench_function("eigenvalues_4x4", move |bh| bh.iter(|| test::black_box(m.complex_eigenvalues())));
+    bh.bench_function("eigenvalues_4x4", move |bh| {
+        bh.iter(|| test::black_box(m.complex_eigenvalues()))
+    });
 }
 
 fn eigenvalues_10x10(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(10, 10);
-    bh.bench_function("eigenvalues_10x10", move |bh| bh.iter(|| test::black_box(m.complex_eigenvalues())));
+    bh.bench_function("eigenvalues_10x10", move |bh| {
+        bh.iter(|| test::black_box(m.complex_eigenvalues()))
+    });
 }
 
 fn eigenvalues_100x100(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(100, 100);
-    bh.bench_function("eigenvalues_100x100", move |bh| bh.iter(|| test::black_box(m.complex_eigenvalues())));
+    bh.bench_function("eigenvalues_100x100", move |bh| {
+        bh.iter(|| test::black_box(m.complex_eigenvalues()))
+    });
 }
 
 fn eigenvalues_200x200(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(200, 200);
-    bh.bench_function("eigenvalues_200x200", move |bh| bh.iter(|| test::black_box(m.complex_eigenvalues())));
+    bh.bench_function("eigenvalues_200x200", move |bh| {
+        bh.iter(|| test::black_box(m.complex_eigenvalues()))
+    });
 }
 
-criterion_group!(schur,
+criterion_group!(
+    schur,
     schur_decompose_4x4,
     schur_decompose_10x10,
     schur_decompose_100x100,

benches/linalg/solve.rs

@@ -4,76 +4,92 @@ fn solve_l_triangular_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
     let v = DVector::<f64>::new_random(100);
 
-    bh.bench_function("solve_l_triangular_100x100", move |bh| bh.iter(|| {
+    bh.bench_function("solve_l_triangular_100x100", move |bh| {
+        bh.iter(|| {
             let _ = m.solve_lower_triangular(&v);
-    }));
+        })
+    });
 }
 
 fn solve_l_triangular_1000x1000(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(1000, 1000);
     let v = DVector::<f64>::new_random(1000);
 
-    bh.bench_function("solve_l_triangular_1000x1000", move |bh| bh.iter(|| {
+    bh.bench_function("solve_l_triangular_1000x1000", move |bh| {
+        bh.iter(|| {
             let _ = m.solve_lower_triangular(&v);
-    }));
+        })
+    });
 }
 
 fn tr_solve_l_triangular_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
     let v = DVector::<f64>::new_random(100);
 
-    bh.bench_function("tr_solve_l_triangular_100x100", move |bh| bh.iter(|| {
+    bh.bench_function("tr_solve_l_triangular_100x100", move |bh| {
+        bh.iter(|| {
             let _ = m.tr_solve_lower_triangular(&v);
-    }));
+        })
+    });
 }
 
 fn tr_solve_l_triangular_1000x1000(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(1000, 1000);
     let v = DVector::<f64>::new_random(1000);
 
-    bh.bench_function("tr_solve_l_triangular_1000x1000", move |bh| bh.iter(|| {
+    bh.bench_function("tr_solve_l_triangular_1000x1000", move |bh| {
+        bh.iter(|| {
             let _ = m.tr_solve_lower_triangular(&v);
-    }));
+        })
+    });
 }
 
 fn solve_u_triangular_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
     let v = DVector::<f64>::new_random(100);
 
-    bh.bench_function("solve_u_triangular_100x100", move |bh| bh.iter(|| {
+    bh.bench_function("solve_u_triangular_100x100", move |bh| {
+        bh.iter(|| {
             let _ = m.solve_upper_triangular(&v);
-    }));
+        })
+    });
 }
 
 fn solve_u_triangular_1000x1000(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(1000, 1000);
     let v = DVector::<f64>::new_random(1000);
 
-    bh.bench_function("solve_u_triangular_1000x1000", move |bh| bh.iter(|| {
+    bh.bench_function("solve_u_triangular_1000x1000", move |bh| {
+        bh.iter(|| {
             let _ = m.solve_upper_triangular(&v);
-    }));
+        })
+    });
 }
 
 fn tr_solve_u_triangular_100x100(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(100, 100);
     let v = DVector::<f64>::new_random(100);
 
-    bh.bench_function("tr_solve_u_triangular_100x100", move |bh| bh.iter(|| {
+    bh.bench_function("tr_solve_u_triangular_100x100", move |bh| {
+        bh.iter(|| {
             let _ = m.tr_solve_upper_triangular(&v);
-    }));
+        })
+    });
 }
 
 fn tr_solve_u_triangular_1000x1000(bh: &mut criterion::Criterion) {
     let m = DMatrix::<f64>::new_random(1000, 1000);
     let v = DVector::<f64>::new_random(1000);
 
-    bh.bench_function("tr_solve_u_triangular_1000x1000", move |bh| bh.iter(|| {
+    bh.bench_function("tr_solve_u_triangular_1000x1000", move |bh| {
+        bh.iter(|| {
             let _ = m.tr_solve_upper_triangular(&v);
-    }));
+        })
+    });
 }
 
-
+criterion_group!(
-criterion_group!(solve,
+    solve,
     solve_l_triangular_100x100,
     solve_l_triangular_1000x1000,
     tr_solve_l_triangular_100x100,

benches/linalg/svd.rs

@@ -2,86 +2,118 @@ use na::{Matrix4, SVD};
 
 fn svd_decompose_4x4(bh: &mut criterion::Criterion) {
     let m = Matrix4::<f64>::new_random();
-    bh.bench_function("svd_decompose_4x4", move |bh| bh.iter(|| test::black_box(SVD::new(m.clone(), true, true))));
+    bh.bench_function("svd_decompose_4x4", move |bh| {
+        bh.iter(|| test::black_box(SVD::new(m.clone(), true, true)))
+    });
 }
 
 fn svd_decompose_10x10(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(10, 10);
-    bh.bench_function("svd_decompose_10x10", move |bh| bh.iter(|| test::black_box(SVD::new(m.clone(), true, true))));
+    bh.bench_function("svd_decompose_10x10", move |bh| {
+        bh.iter(|| test::black_box(SVD::new(m.clone(), true, true)))
+    });
 }
 
 fn svd_decompose_100x100(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(100, 100);
-    bh.bench_function("svd_decompose_100x100", move |bh| bh.iter(|| test::black_box(SVD::new(m.clone(), true, true))));
+    bh.bench_function("svd_decompose_100x100", move |bh| {
+        bh.iter(|| test::black_box(SVD::new(m.clone(), true, true)))
+    });
 }
 
 fn svd_decompose_200x200(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(200, 200);
-    bh.bench_function("svd_decompose_200x200", move |bh| bh.iter(|| test::black_box(SVD::new(m.clone(), true, true))));
+    bh.bench_function("svd_decompose_200x200", move |bh| {
+        bh.iter(|| test::black_box(SVD::new(m.clone(), true, true)))
+    });
 }
 
 fn rank_4x4(bh: &mut criterion::Criterion) {
     let m = Matrix4::<f64>::new_random();
-    bh.bench_function("rank_4x4", move |bh| bh.iter(|| test::black_box(m.rank(1.0e-10))));
+    bh.bench_function("rank_4x4", move |bh| {
+        bh.iter(|| test::black_box(m.rank(1.0e-10)))
+    });
 }
 
 fn rank_10x10(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(10, 10);
-    bh.bench_function("rank_10x10", move |bh| bh.iter(|| test::black_box(m.rank(1.0e-10))));
+    bh.bench_function("rank_10x10", move |bh| {
+        bh.iter(|| test::black_box(m.rank(1.0e-10)))
+    });
 }
 
 fn rank_100x100(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(100, 100);
-    bh.bench_function("rank_100x100", move |bh| bh.iter(|| test::black_box(m.rank(1.0e-10))));
+    bh.bench_function("rank_100x100", move |bh| {
+        bh.iter(|| test::black_box(m.rank(1.0e-10)))
+    });
 }
 
 fn rank_200x200(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(200, 200);
-    bh.bench_function("rank_200x200", move |bh| bh.iter(|| test::black_box(m.rank(1.0e-10))));
+    bh.bench_function("rank_200x200", move |bh| {
+        bh.iter(|| test::black_box(m.rank(1.0e-10)))
+    });
 }
 
 fn singular_values_4x4(bh: &mut criterion::Criterion) {
     let m = Matrix4::<f64>::new_random();
-    bh.bench_function("singular_values_4x4", move |bh| bh.iter(|| test::black_box(m.singular_values())));
+    bh.bench_function("singular_values_4x4", move |bh| {
+        bh.iter(|| test::black_box(m.singular_values()))
+    });
 }
 
 fn singular_values_10x10(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(10, 10);
-    bh.bench_function("singular_values_10x10", move |bh| bh.iter(|| test::black_box(m.singular_values())));
+    bh.bench_function("singular_values_10x10", move |bh| {
+        bh.iter(|| test::black_box(m.singular_values()))
+    });
 }
 
 fn singular_values_100x100(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(100, 100);
-    bh.bench_function("singular_values_100x100", move |bh| bh.iter(|| test::black_box(m.singular_values())));
+    bh.bench_function("singular_values_100x100", move |bh| {
+        bh.iter(|| test::black_box(m.singular_values()))
+    });
 }
 
 fn singular_values_200x200(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(200, 200);
-    bh.bench_function("singular_values_200x200", move |bh| bh.iter(|| test::black_box(m.singular_values())));
+    bh.bench_function("singular_values_200x200", move |bh| {
+        bh.iter(|| test::black_box(m.singular_values()))
+    });
 }
 
 fn pseudo_inverse_4x4(bh: &mut criterion::Criterion) {
     let m = Matrix4::<f64>::new_random();
-    bh.bench_function("pseudo_inverse_4x4", move |bh| bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10))));
+    bh.bench_function("pseudo_inverse_4x4", move |bh| {
+        bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10)))
+    });
 }
 
 fn pseudo_inverse_10x10(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(10, 10);
-    bh.bench_function("pseudo_inverse_10x10", move |bh| bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10))));
+    bh.bench_function("pseudo_inverse_10x10", move |bh| {
+        bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10)))
+    });
 }
 
 fn pseudo_inverse_100x100(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(100, 100);
-    bh.bench_function("pseudo_inverse_100x100", move |bh| bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10))));
+    bh.bench_function("pseudo_inverse_100x100", move |bh| {
+        bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10)))
+    });
 }
 
 fn pseudo_inverse_200x200(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(200, 200);
-    bh.bench_function("pseudo_inverse_200x200", move |bh| bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10))));
+    bh.bench_function("pseudo_inverse_200x200", move |bh| {
+        bh.iter(|| test::black_box(m.clone().pseudo_inverse(1.0e-10)))
+    });
 }
 
-
+criterion_group!(
-criterion_group!(svd,
+    svd,
     svd_decompose_4x4,
     svd_decompose_10x10,
     svd_decompose_100x100,

benches/linalg/symmetric_eigen.rs

@@ -2,25 +2,34 @@ use na::{Matrix4, SymmetricEigen};
 
 fn symmetric_eigen_decompose_4x4(bh: &mut criterion::Criterion) {
     let m = Matrix4::<f64>::new_random();
-    bh.bench_function("symmetric_eigen_decompose_4x4", move |bh| bh.iter(|| test::black_box(SymmetricEigen::new(m.clone()))));
+    bh.bench_function("symmetric_eigen_decompose_4x4", move |bh| {
+        bh.iter(|| test::black_box(SymmetricEigen::new(m.clone())))
+    });
 }
 
 fn symmetric_eigen_decompose_10x10(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(10, 10);
-    bh.bench_function("symmetric_eigen_decompose_10x10", move |bh| bh.iter(|| test::black_box(SymmetricEigen::new(m.clone()))));
+    bh.bench_function("symmetric_eigen_decompose_10x10", move |bh| {
+        bh.iter(|| test::black_box(SymmetricEigen::new(m.clone())))
+    });
 }
 
 fn symmetric_eigen_decompose_100x100(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(100, 100);
-    bh.bench_function("symmetric_eigen_decompose_100x100", move |bh| bh.iter(|| test::black_box(SymmetricEigen::new(m.clone()))));
+    bh.bench_function("symmetric_eigen_decompose_100x100", move |bh| {
+        bh.iter(|| test::black_box(SymmetricEigen::new(m.clone())))
+    });
 }
 
 fn symmetric_eigen_decompose_200x200(bh: &mut criterion::Criterion) {
     let m = crate::reproductible_dmatrix(200, 200);
-    bh.bench_function("symmetric_eigen_decompose_200x200", move |bh| bh.iter(|| test::black_box(SymmetricEigen::new(m.clone()))));
+    bh.bench_function("symmetric_eigen_decompose_200x200", move |bh| {
+        bh.iter(|| test::black_box(SymmetricEigen::new(m.clone())))
+    });
 }
 
-criterion_group!(symmetric_eigen,
+criterion_group!(
+    symmetric_eigen,
     symmetric_eigen_decompose_4x4,
     symmetric_eigen_decompose_10x10,
     symmetric_eigen_decompose_100x100,

examples/dimensional_genericity.rs

@@ -1,18 +1,9 @@
-extern crate alga;
 extern crate nalgebra as na;
 
-use alga::linear::FiniteDimInnerSpace;
 use na::allocator::Allocator;
 use na::dimension::Dim;
 use na::{DefaultAllocator, RealField, Unit, Vector2, Vector3, VectorN};
 
-/// Reflects a vector wrt. the hyperplane with normal `plane_normal`.
-fn reflect_wrt_hyperplane_with_algebraic_genericity<V>(plane_normal: &Unit<V>, vector: &V) -> V
-where V: FiniteDimInnerSpace + Copy {
-    let n = plane_normal.as_ref(); // Get the underlying vector of type `V`.
-    *vector - *n * (n.dot(vector) * na::convert(2.0))
-}
-
 /// Reflects a vector wrt. the hyperplane with normal `plane_normal`.
 fn reflect_wrt_hyperplane_with_dimensional_genericity<N: RealField, D: Dim>(
     plane_normal: &Unit<VectorN<N, D>>,
@@ -29,7 +20,9 @@ where
 
 /// Reflects a 2D vector wrt. the 2D line with normal `plane_normal`.
 fn reflect_wrt_hyperplane2<N>(plane_normal: &Unit<Vector2<N>>, vector: &Vector2<N>) -> Vector2<N>
-where N: RealField {
+where
+    N: RealField,
+{
     let n = plane_normal.as_ref(); // Get the underlying Vector2
     vector - n * (n.dot(vector) * na::convert(2.0))
 }
@@ -37,7 +30,9 @@ where N: RealField {
 /// Reflects a 3D vector wrt. the 3D plane with normal `plane_normal`.
 /// /!\ This is an exact replicate of `reflect_wrt_hyperplane2, but for 3D.
 fn reflect_wrt_hyperplane3<N>(plane_normal: &Unit<Vector3<N>>, vector: &Vector3<N>) -> Vector3<N>
-where N: RealField {
+where
+    N: RealField,
+{
     let n = plane_normal.as_ref(); // Get the underlying Vector3
     vector - n * (n.dot(vector) * na::convert(2.0))
 }
@@ -50,15 +45,6 @@ fn main() {
     let v3 = Vector3::new(1.0, 2.0, 3.0); // 3D vector to be reflected.
 
     // We can call the same function for 2D and 3D.
-    assert_eq!(
-        reflect_wrt_hyperplane_with_algebraic_genericity(&plane2, &v2).y,
-        -2.0
-    );
-    assert_eq!(
-        reflect_wrt_hyperplane_with_algebraic_genericity(&plane3, &v3).y,
-        -2.0
-    );
-
     assert_eq!(
         reflect_wrt_hyperplane_with_dimensional_genericity(&plane2, &v2).y,
         -2.0

examples/identity.rs

@@ -1,39 +0,0 @@
-extern crate alga;
-extern crate nalgebra as na;
-
-use alga::linear::Transformation;
-use na::{Id, Isometry3, Point3, Vector3};
-
-/*
- * Applies `n` times the transformation `t` to the vector `v` and sum each
- * intermediate value.
- */
-fn complicated_algorithm<T>(v: &Vector3<f32>, t: &T, n: usize) -> Vector3<f32>
-where T: Transformation<Point3<f32>> {
-    let mut result = *v;
-
-    // Do lots of operations involving t.
-    for _ in 0..n {
-        result = v + t.transform_vector(&result);
-    }
-
-    result
-}
-
-/*
- * The two following calls are equivalent in term of result.
- */
-fn main() {
-    let v = Vector3::new(1.0, 2.0, 3.0);
-
-    // The specialization generated by the compiler will do vector additions only.
-    let result1 = complicated_algorithm(&v, &Id::new(), 100000);
-
-    // The specialization generated by the compiler will also include matrix multiplications.
-    let iso = Isometry3::identity();
-    let result2 = complicated_algorithm(&v, &iso, 100000);
-
-    // They both return the same result.
-    assert!(result1 == Vector3::new(100001.0, 200002.0, 300003.0));
-    assert!(result2 == Vector3::new(100001.0, 200002.0, 300003.0));
-}

examples/scalar_genericity.rs

@@ -1,19 +1,12 @@
-extern crate alga;
 extern crate nalgebra as na;
 
-use alga::general::{RealField, RingCommutative};
 use na::{Scalar, Vector3};
+use simba::scalar::RealField;
 
 fn print_vector<N: Scalar>(m: &Vector3<N>) {
     println!("{:?}", m)
 }
 
-fn print_squared_norm<N: Scalar + RingCommutative>(v: &Vector3<N>) {
-    // NOTE: alternatively, nalgebra already defines `v.squared_norm()`.
-    let sqnorm = v.dot(v);
-    println!("{:?}", sqnorm);
-}
-
 fn print_norm<N: RealField>(v: &Vector3<N>) {
     // NOTE: alternatively, nalgebra already defines `v.norm()`.
     let norm = v.dot(v).sqrt();
@@ -28,6 +21,5 @@ fn main() {
     let v2 = Vector3::new(1.0, 2.0, 3.0);
 
     print_vector(&v1);
-    print_squared_norm(&v1);
     print_norm(&v2);
 }

examples/transform_conversion.rs

@@ -18,6 +18,6 @@ fn main() {
     assert!(iso_fail.is_none());
 
     // Similarity -> Isometry conversion can be forced at your own risks.
-    let iso_forced: Isometry2<f32> = unsafe { na::convert_unchecked(sim_with_scaling) };
+    let iso_forced: Isometry2<f32> = na::convert_unchecked(sim_with_scaling);
     assert_eq!(iso_success.unwrap(), iso_forced);
 }

examples/transform_matrix4.rs

@@ -1,4 +1,3 @@
-extern crate alga;
 #[macro_use]
 extern crate approx;
 extern crate nalgebra as na;

examples/transform_vector_point3.rs

@@ -1,4 +1,3 @@
-extern crate alga;
 extern crate nalgebra as na;
 
 use na::{Matrix4, Point3, Vector3, Vector4};

nalgebra-glm/Cargo.toml

@@ -15,7 +15,7 @@ edition = "2018"
 
 [features]
 default         = [ "std" ]
-std             = [ "nalgebra/std", "alga/std" ]
+std             = [ "nalgebra/std", "simba/std" ]
 stdweb          = [ "nalgebra/stdweb" ]
 arbitrary       = [ "nalgebra/arbitrary" ]
 serde-serialize = [ "nalgebra/serde-serialize" ]
@@ -24,5 +24,5 @@ abomonation-serialize = [ "nalgebra/abomonation-serialize" ]
 [dependencies]
 num-traits = { version = "0.2", default-features = false }
 approx = { version = "0.3", default-features = false }
-alga = { version = "0.9", default-features = false }
+simba = { version = "0.1", default-features = false }
 nalgebra = { path =  "..", version = "0.20", default-features = false }

nalgebra-glm/src/common.rs

@@ -1,6 +1,6 @@
+use core::mem;
 use na::{self, DefaultAllocator, RealField};
 use num::FromPrimitive;
-use core::mem;
 
 use crate::aliases::{TMat, TVec};
 use crate::traits::{Alloc, Dimension, Number};
@@ -22,7 +22,9 @@ use crate::traits::{Alloc, Dimension, Number};
 ///
 /// * [`sign`](fn.sign.html)
 pub fn abs<N: Number, R: Dimension, C: Dimension>(x: &TMat<N, R, C>) -> TMat<N, R, C>
-where DefaultAllocator: Alloc<N, R, C> {
+where
+    DefaultAllocator: Alloc<N, R, C>,
+{
     x.abs()
 }
 
@@ -44,7 +46,9 @@ where DefaultAllocator: Alloc<N, R, C> {
 /// * [`round`](fn.round.html)
 /// * [`trunc`](fn.trunc.html)
 pub fn ceil<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.map(|x| x.ceil())
 }
 
@@ -94,7 +98,9 @@ pub fn clamp_scalar<N: Number>(x: N, min_val: N, max_val: N) -> N {
 /// * [`clamp_scalar`](fn.clamp_scalar.html)
 /// * [`clamp_vec`](fn.clamp_vec.html)
 pub fn clamp<N: Number, D: Dimension>(x: &TVec<N, D>, min_val: N, max_val: N) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.map(|x| na::clamp(x, min_val, max_val))
 }
 
@@ -167,7 +173,9 @@ pub fn float_bits_to_int(v: f32) -> i32 {
 /// * [`uint_bits_to_float`](fn.uint_bits_to_float.html)
 /// * [`uint_bits_to_float_scalar`](fn.uint_bits_to_float_scalar.html)
 pub fn float_bits_to_int_vec<D: Dimension>(v: &TVec<f32, D>) -> TVec<i32, D>
-where DefaultAllocator: Alloc<f32, D> {
+where
+    DefaultAllocator: Alloc<f32, D>,
+{
     v.map(float_bits_to_int)
 }
 
@@ -202,7 +210,9 @@ pub fn float_bits_to_uint(v: f32) -> u32 {
 /// * [`uint_bits_to_float`](fn.uint_bits_to_float.html)
 /// * [`uint_bits_to_float_scalar`](fn.uint_bits_to_float_scalar.html)
 pub fn float_bits_to_uint_vec<D: Dimension>(v: &TVec<f32, D>) -> TVec<u32, D>
-where DefaultAllocator: Alloc<f32, D> {
+where
+    DefaultAllocator: Alloc<f32, D>,
+{
     v.map(float_bits_to_uint)
 }
 
@@ -223,7 +233,9 @@ where DefaultAllocator: Alloc<f32, D> {
 /// * [`round`](fn.round.html)
 /// * [`trunc`](fn.trunc.html)
 pub fn floor<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.map(|x| x.floor())
 }
 
@@ -250,7 +262,9 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`round`](fn.round.html)
 /// * [`trunc`](fn.trunc.html)
 pub fn fract<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.map(|x| x.fract())
 }
 
@@ -293,7 +307,9 @@ pub fn int_bits_to_float(v: i32) -> f32 {
 /// * [`uint_bits_to_float`](fn.uint_bits_to_float.html)
 /// * [`uint_bits_to_float_scalar`](fn.uint_bits_to_float_scalar.html)
 pub fn int_bits_to_float_vec<D: Dimension>(v: &TVec<i32, D>) -> TVec<f32, D>
-where DefaultAllocator: Alloc<f32, D> {
+where
+    DefaultAllocator: Alloc<f32, D>,
+{
     v.map(int_bits_to_float)
 }
 
@@ -352,7 +368,9 @@ pub fn mix_scalar<N: Number>(x: N, y: N, a: N) -> N {
 /// * [`mix_scalar`](fn.mix_scalar.html)
 /// * [`mix_vec`](fn.mix_vec.html)
 pub fn mix<N: Number, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>, a: N) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x * (N::one() - a) + y * a
 }
 
@@ -425,7 +443,9 @@ pub fn lerp_scalar<N: Number>(x: N, y: N, a: N) -> N {
 /// * [`lerp_scalar`](fn.lerp_scalar.html)
 /// * [`lerp_vec`](fn.lerp_vec.html)
 pub fn lerp<N: Number, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>, a: N) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     mix(x, y, a)
 }
 
@@ -468,7 +488,9 @@ where
 ///
 /// * [`modf`](fn.modf.html)
 pub fn modf_vec<N: Number, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.zip_map(y, |x, y| x % y)
 }
 
@@ -500,7 +522,9 @@ pub fn modf<N: Number>(x: N, i: N) -> N {
 /// * [`fract`](fn.fract.html)
 /// * [`trunc`](fn.trunc.html)
 pub fn round<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.map(|x| x.round())
 }
 
@@ -524,7 +548,9 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`abs`](fn.abs.html)
 ///
 pub fn sign<N: Number, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.map(|x| if x.is_zero() { N::zero() } else { x.signum() })
 }
 
@@ -550,13 +576,17 @@ pub fn step_scalar<N: Number>(edge: N, x: N) -> N {
 
 /// Returns 0.0 if `x[i] < edge`, otherwise it returns 1.0.
 pub fn step<N: Number, D: Dimension>(edge: N, x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.map(|x| step_scalar(edge, x))
 }
 
 /// Returns 0.0 if `x[i] < edge[i]`, otherwise it returns 1.0.
 pub fn step_vec<N: Number, D: Dimension>(edge: &TVec<N, D>, x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     edge.zip_map(x, step_scalar)
 }
 
@@ -577,7 +607,9 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`fract`](fn.fract.html)
 /// * [`round`](fn.round.html)
 pub fn trunc<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.map(|x| x.trunc())
 }
 
@@ -612,6 +644,8 @@ pub fn uint_bits_to_float_scalar(v: u32) -> f32 {
 /// * [`int_bits_to_float_vec`](fn.int_bits_to_float_vec.html)
 /// * [`uint_bits_to_float_scalar`](fn.uint_bits_to_float_scalar.html)
 pub fn uint_bits_to_float<D: Dimension>(v: &TVec<u32, D>) -> TVec<f32, D>
-where DefaultAllocator: Alloc<f32, D> {
+where
+    DefaultAllocator: Alloc<f32, D>,
+{
     v.map(uint_bits_to_float_scalar)
 }

nalgebra-glm/src/exponential.rs

@@ -1,6 +1,6 @@
 use crate::aliases::TVec;
-use na::{DefaultAllocator, RealField};
 use crate::traits::{Alloc, Dimension};
+use na::{DefaultAllocator, RealField};
 
 /// Component-wise exponential.
 ///
@@ -8,7 +8,9 @@ use crate::traits::{Alloc, Dimension};
 ///
 /// * [`exp2`](fn.exp2.html)
 pub fn exp<N: RealField, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     v.map(|x| x.exp())
 }
 
@@ -18,7 +20,9 @@ where DefaultAllocator: Alloc<N, D> {
 ///
 /// * [`exp`](fn.exp.html)
 pub fn exp2<N: RealField, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     v.map(|x| x.exp2())
 }
 
@@ -28,7 +32,9 @@ where DefaultAllocator: Alloc<N, D> {
 ///
 /// * [`sqrt`](fn.sqrt.html)
 pub fn inversesqrt<N: RealField, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     v.map(|x| N::one() / x.sqrt())
 }
 
@@ -38,7 +44,9 @@ where DefaultAllocator: Alloc<N, D> {
 ///
 /// * [`log2`](fn.log2.html)
 pub fn log<N: RealField, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     v.map(|x| x.ln())
 }
 
@@ -48,13 +56,17 @@ where DefaultAllocator: Alloc<N, D> {
 ///
 /// * [`log`](fn.log.html)
 pub fn log2<N: RealField, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     v.map(|x| x.log2())
 }
 
 /// Component-wise power.
 pub fn pow<N: RealField, D: Dimension>(base: &TVec<N, D>, exponent: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     base.zip_map(exponent, |b, e| b.powf(e))
 }
 
@@ -67,6 +79,8 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`inversesqrt`](fn.inversesqrt.html)
 /// * [`pow`](fn.pow.html)
 pub fn sqrt<N: RealField, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     v.map(|x| x.sqrt())
 }

nalgebra-glm/src/ext/matrix_clip_space.rs

@@ -1,5 +1,5 @@
 use crate::aliases::TMat4;
-use na::{RealField};
+use na::RealField;
 
 //pub fn frustum<N: RealField>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
 //    unimplemented!()
@@ -90,7 +90,14 @@ pub fn ortho_lh<N: RealField>(left: N, right: N, bottom: N, top: N, znear: N, zf
 /// * `znear` - Distance from the viewer to the near clipping plane
 /// * `zfar` - Distance from the viewer to the far clipping plane
 ///
-pub fn ortho_lh_no<N: RealField>(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> TMat4<N> {
+pub fn ortho_lh_no<N: RealField>(
+    left: N,
+    right: N,
+    bottom: N,
+    top: N,
+    znear: N,
+    zfar: N,
+) -> TMat4<N> {
     let two: N = crate::convert(2.0);
     let mut mat: TMat4<N> = TMat4::<N>::identity();
 
@@ -115,7 +122,14 @@ pub fn ortho_lh_no<N: RealField>(left: N, right: N, bottom: N, top: N, znear: N,
 /// * `znear` - Distance from the viewer to the near clipping plane
 /// * `zfar` - Distance from the viewer to the far clipping plane
 ///
-pub fn ortho_lh_zo<N: RealField>(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> TMat4<N> {
+pub fn ortho_lh_zo<N: RealField>(
+    left: N,
+    right: N,
+    bottom: N,
+    top: N,
+    znear: N,
+    zfar: N,
+) -> TMat4<N> {
     let one: N = N::one();
     let two: N = crate::convert(2.0);
     let mut mat: TMat4<N> = TMat4::<N>::identity();
@@ -171,7 +185,14 @@ pub fn ortho_rh<N: RealField>(left: N, right: N, bottom: N, top: N, znear: N, zf
 /// * `znear` - Distance from the viewer to the near clipping plane
 /// * `zfar` - Distance from the viewer to the far clipping plane
 ///
-pub fn ortho_rh_no<N: RealField>(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> TMat4<N> {
+pub fn ortho_rh_no<N: RealField>(
+    left: N,
+    right: N,
+    bottom: N,
+    top: N,
+    znear: N,
+    zfar: N,
+) -> TMat4<N> {
     let two: N = crate::convert(2.0);
     let mut mat: TMat4<N> = TMat4::<N>::identity();
 
@@ -196,7 +217,14 @@ pub fn ortho_rh_no<N: RealField>(left: N, right: N, bottom: N, top: N, znear: N,
 /// * `znear` - Distance from the viewer to the near clipping plane
 /// * `zfar` - Distance from the viewer to the far clipping plane
 ///
-pub fn ortho_rh_zo<N: RealField>(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> TMat4<N> {
+pub fn ortho_rh_zo<N: RealField>(
+    left: N,
+    right: N,
+    bottom: N,
+    top: N,
+    znear: N,
+    zfar: N,
+) -> TMat4<N> {
     let one: N = N::one();
     let two: N = crate::convert(2.0);
     let mut mat: TMat4<N> = TMat4::<N>::identity();
@@ -264,19 +292,16 @@ pub fn perspective_fov_lh<N: RealField>(fov: N, width: N, height: N, near: N, fa
 /// * `near` - Distance from the viewer to the near clipping plane
 /// * `far` - Distance from the viewer to the far clipping plane
 ///
-pub fn perspective_fov_lh_no<N: RealField>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_fov_lh_no<N: RealField>(
-    assert!(
+    fov: N,
-        width > N::zero(),
+    width: N,
-        "The width must be greater than zero"
+    height: N,
-    );
+    near: N,
-    assert!(
+    far: N,
-        height > N::zero(),
+) -> TMat4<N> {
-        "The height must be greater than zero."
+    assert!(width > N::zero(), "The width must be greater than zero");
-    );
+    assert!(height > N::zero(), "The height must be greater than zero.");
-    assert!(
+    assert!(fov > N::zero(), "The fov must be greater than zero");
-        fov > N::zero(),
-        "The fov must be greater than zero"
-    );
 
     let mut mat = TMat4::zeros();
 
@@ -303,19 +328,16 @@ pub fn perspective_fov_lh_no<N: RealField>(fov: N, width: N, height: N, near: N,
 /// * `near` - Distance from the viewer to the near clipping plane
 /// * `far` - Distance from the viewer to the far clipping plane
 ///
-pub fn perspective_fov_lh_zo<N: RealField>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_fov_lh_zo<N: RealField>(
-    assert!(
+    fov: N,
-        width > N::zero(),
+    width: N,
-        "The width must be greater than zero"
+    height: N,
-    );
+    near: N,
-    assert!(
+    far: N,
-        height > N::zero(),
+) -> TMat4<N> {
-        "The height must be greater than zero."
+    assert!(width > N::zero(), "The width must be greater than zero");
-    );
+    assert!(height > N::zero(), "The height must be greater than zero.");
-    assert!(
+    assert!(fov > N::zero(), "The fov must be greater than zero");
-        fov > N::zero(),
-        "The fov must be greater than zero"
-    );
 
     let mut mat = TMat4::zeros();
 
@@ -370,19 +392,16 @@ pub fn perspective_fov_rh<N: RealField>(fov: N, width: N, height: N, near: N, fa
 /// * `near` - Distance from the viewer to the near clipping plane
 /// * `far` - Distance from the viewer to the far clipping plane
 ///
-pub fn perspective_fov_rh_no<N: RealField>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_fov_rh_no<N: RealField>(
-    assert!(
+    fov: N,
-        width > N::zero(),
+    width: N,
-        "The width must be greater than zero"
+    height: N,
-    );
+    near: N,
-    assert!(
+    far: N,
-        height > N::zero(),
+) -> TMat4<N> {
-        "The height must be greater than zero."
+    assert!(width > N::zero(), "The width must be greater than zero");
-    );
+    assert!(height > N::zero(), "The height must be greater than zero.");
-    assert!(
+    assert!(fov > N::zero(), "The fov must be greater than zero");
-        fov > N::zero(),
-        "The fov must be greater than zero"
-    );
 
     let mut mat = TMat4::zeros();
 
@@ -409,19 +428,16 @@ pub fn perspective_fov_rh_no<N: RealField>(fov: N, width: N, height: N, near: N,
 /// * `near` - Distance from the viewer to the near clipping plane
 /// * `far` - Distance from the viewer to the far clipping plane
 ///
-pub fn perspective_fov_rh_zo<N: RealField>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_fov_rh_zo<N: RealField>(
-    assert!(
+    fov: N,
-        width > N::zero(),
+    width: N,
-        "The width must be greater than zero"
+    height: N,
-    );
+    near: N,
-    assert!(
+    far: N,
-        height > N::zero(),
+) -> TMat4<N> {
-        "The height must be greater than zero."
+    assert!(width > N::zero(), "The width must be greater than zero");
-    );
+    assert!(height > N::zero(), "The height must be greater than zero.");
-    assert!(
+    assert!(fov > N::zero(), "The fov must be greater than zero");
-        fov > N::zero(),
-        "The fov must be greater than zero"
-    );
 
     let mut mat = TMat4::zeros();
 

nalgebra-glm/src/ext/matrix_projection.rs

@@ -9,7 +9,11 @@ use crate::aliases::{TMat4, TVec2, TVec3, TVec4};
 /// * `center` - Specify the center of a picking region in window coordinates.
 /// * `delta` - Specify the width and height, respectively, of the picking region in window coordinates.
 /// * `viewport` - Rendering viewport.
-pub fn pick_matrix<N: RealField>(center: &TVec2<N>, delta: &TVec2<N>, viewport: &TVec4<N>) -> TMat4<N> {
+pub fn pick_matrix<N: RealField>(
+    center: &TVec2<N>,
+    delta: &TVec2<N>,
+    viewport: &TVec4<N>,
+) -> TMat4<N> {
     let shift = TVec3::new(
         (viewport.z - (center.x - viewport.x) * na::convert(2.0)) / delta.x,
         (viewport.w - (center.y - viewport.y) * na::convert(2.0)) / delta.y,
@@ -46,8 +50,7 @@ pub fn project<N: RealField>(
     model: &TMat4<N>,
     proj: &TMat4<N>,
     viewport: TVec4<N>,
-) -> TVec3<N>
+) -> TVec3<N> {
-{
     project_no(obj, model, proj, viewport)
 }
 
@@ -74,8 +77,7 @@ pub fn project_no<N: RealField>(
     model: &TMat4<N>,
     proj: &TMat4<N>,
     viewport: TVec4<N>,
-) -> TVec3<N>
+) -> TVec3<N> {
-{
     let proj = project_zo(obj, model, proj, viewport);
     TVec3::new(proj.x, proj.y, proj.z * na::convert(0.5) + na::convert(0.5))
 }
@@ -103,8 +105,7 @@ pub fn project_zo<N: RealField>(
     model: &TMat4<N>,
     proj: &TMat4<N>,
     viewport: TVec4<N>,
-) -> TVec3<N>
+) -> TVec3<N> {
-{
     let normalized = proj * model * TVec4::new(obj.x, obj.y, obj.z, N::one());
     let scale = N::one() / normalized.w;
 
@@ -137,8 +138,7 @@ pub fn unproject<N: RealField>(
     model: &TMat4<N>,
     proj: &TMat4<N>,
     viewport: TVec4<N>,
-) -> TVec3<N>
+) -> TVec3<N> {
-{
     unproject_no(win, model, proj, viewport)
 }
 
@@ -165,8 +165,7 @@ pub fn unproject_no<N: RealField>(
     model: &TMat4<N>,
     proj: &TMat4<N>,
     viewport: TVec4<N>,
-) -> TVec3<N>
+) -> TVec3<N> {
-{
     let _2: N = na::convert(2.0);
     let transform = (proj * model).try_inverse().unwrap_or_else(TMat4::zeros);
     let pt = TVec4::new(
@@ -203,8 +202,7 @@ pub fn unproject_zo<N: RealField>(
     model: &TMat4<N>,
     proj: &TMat4<N>,
     viewport: TVec4<N>,
-) -> TVec3<N>
+) -> TVec3<N> {
-{
     let _2: N = na::convert(2.0);
     let transform = (proj * model).try_inverse().unwrap_or_else(TMat4::zeros);
     let pt = TVec4::new(

nalgebra-glm/src/ext/matrix_transform.rs

@@ -5,7 +5,9 @@ use crate::traits::{Alloc, Dimension, Number};
 
 /// The identity matrix.
 pub fn identity<N: Number, D: Dimension>() -> TMat<N, D, D>
-where DefaultAllocator: Alloc<N, D, D> {
+where
+    DefaultAllocator: Alloc<N, D, D>,
+{
     TMat::<N, D, D>::identity()
 }
 

nalgebra-glm/src/ext/mod.rs

@@ -1,19 +1,13 @@
 //! (Reexported) Additional features not specified by GLSL specification
 
 pub use self::matrix_clip_space::{
-    ortho, ortho_lh, ortho_lh_no, ortho_lh_zo, ortho_no, ortho_rh, ortho_rh_no, ortho_rh_zo,
+    infinite_perspective_rh_no, infinite_perspective_rh_zo, ortho, ortho_lh, ortho_lh_no,
-    ortho_zo,
+    ortho_lh_zo, ortho_no, ortho_rh, ortho_rh_no, ortho_rh_zo, ortho_zo, perspective,
-
-    perspective, perspective_lh, perspective_lh_no, perspective_lh_zo, perspective_no,
-    perspective_rh, perspective_rh_no, perspective_rh_zo, perspective_zo,
-
     perspective_fov, perspective_fov_lh, perspective_fov_lh_no, perspective_fov_lh_zo,
     perspective_fov_no, perspective_fov_rh, perspective_fov_rh_no, perspective_fov_rh_zo,
-    perspective_fov_zo,
+    perspective_fov_zo, perspective_lh, perspective_lh_no, perspective_lh_zo, perspective_no,
-
+    perspective_rh, perspective_rh_no, perspective_rh_zo, perspective_zo,
-    infinite_perspective_rh_no, infinite_perspective_rh_zo,
+    reversed_infinite_perspective_rh_zo, reversed_perspective_rh_zo,
-
-    reversed_perspective_rh_zo, reversed_infinite_perspective_rh_zo,
 };
 pub use self::matrix_projection::{
     pick_matrix, project, project_no, project_zo, unproject, unproject_no, unproject_zo,
@@ -35,7 +29,9 @@ pub use self::quaternion_relational::{
 };
 pub use self::quaternion_transform::{quat_exp, quat_log, quat_pow, quat_rotate};
 pub use self::quaternion_trigonometric::{quat_angle, quat_angle_axis, quat_axis};
-pub use self::scalar_common::{max3_scalar, max4_scalar, min3_scalar, min4_scalar};
+pub use self::scalar_common::{
+    max2_scalar, max3_scalar, max4_scalar, min2_scalar, min3_scalar, min4_scalar,
+};
 pub use self::scalar_constants::{epsilon, pi};
 pub use self::vector_common::{max, max2, max3, max4, min, min2, min3, min4};
 pub use self::vector_relational::{equal_eps, equal_eps_vec, not_equal_eps, not_equal_eps_vec};

nalgebra-glm/src/ext/scalar_common.rs

@@ -1,7 +1,51 @@
-use na;
-
 use crate::traits::Number;
 
+/// Returns the maximum among two values.
+///
+/// # Examples:
+///
+/// ```
+/// # use nalgebra_glm as glm;
+/// assert_eq!(2.0, glm::max2_scalar(1.0, 2.0));
+/// assert_eq!(1, glm::max2_scalar(0, 1));
+/// ```
+///
+/// # See also:
+///
+/// * [`max4_scalar`](fn.max4_scalar.html)
+/// * [`min3_scalar`](fn.min3_scalar.html)
+/// * [`min4_scalar`](fn.min4_scalar.html)
+pub fn max2_scalar<N: Number>(a: N, b: N) -> N {
+    if a >= b {
+        a
+    } else {
+        b
+    }
+}
+
+/// Returns the maximum among two values.
+///
+/// # Examples:
+///
+/// ```
+/// # use nalgebra_glm as glm;
+/// assert_eq!(1.0, glm::min2_scalar(1.0, 2.0));
+/// assert_eq!(0, glm::min2_scalar(0, 1));
+/// ```
+///
+/// # See also:
+///
+/// * [`max4_scalar`](fn.max4_scalar.html)
+/// * [`min3_scalar`](fn.min3_scalar.html)
+/// * [`min4_scalar`](fn.min4_scalar.html)
+pub fn min2_scalar<N: Number>(a: N, b: N) -> N {
+    if a <= b {
+        a
+    } else {
+        b
+    }
+}
+
 /// Returns the maximum among three values.
 ///
 /// # Examples:
@@ -18,7 +62,7 @@ use crate::traits::Number;
 /// * [`min3_scalar`](fn.min3_scalar.html)
 /// * [`min4_scalar`](fn.min4_scalar.html)
 pub fn max3_scalar<N: Number>(a: N, b: N, c: N) -> N {
-    na::sup(&na::sup(&a, &b), &c)
+    max2_scalar(max2_scalar(a, b), c)
 }
 
 /// Returns the maximum among four values.
@@ -37,7 +81,7 @@ pub fn max3_scalar<N: Number>(a: N, b: N, c: N) -> N {
 /// * [`min3_scalar`](fn.min3_scalar.html)
 /// * [`min4_scalar`](fn.min4_scalar.html)
 pub fn max4_scalar<N: Number>(a: N, b: N, c: N, d: N) -> N {
-    na::sup(&na::sup(&a, &b), &na::sup(&c, &d))
+    max2_scalar(max2_scalar(a, b), max2_scalar(c, d))
 }
 
 /// Returns the minimum among three values.
@@ -56,7 +100,7 @@ pub fn max4_scalar<N: Number>(a: N, b: N, c: N, d: N) -> N {
 /// * [`max4_scalar`](fn.max4_scalar.html)
 /// * [`min4_scalar`](fn.min4_scalar.html)
 pub fn min3_scalar<N: Number>(a: N, b: N, c: N) -> N {
-    na::inf(&na::inf(&a, &b), &c)
+    min2_scalar(min2_scalar(a, b), c)
 }
 
 /// Returns the minimum among four values.
@@ -75,5 +119,5 @@ pub fn min3_scalar<N: Number>(a: N, b: N, c: N) -> N {
 /// * [`max4_scalar`](fn.max4_scalar.html)
 /// * [`min3_scalar`](fn.min3_scalar.html)
 pub fn min4_scalar<N: Number>(a: N, b: N, c: N, d: N) -> N {
-    na::inf(&na::inf(&a, &b), &na::inf(&c, &d))
+    min2_scalar(min2_scalar(a, b), min2_scalar(c, d))
 }

nalgebra-glm/src/ext/vector_common.rs

@@ -17,8 +17,10 @@ use crate::traits::{Alloc, Dimension, Number};
 /// * [`min3`](fn.min3.html)
 /// * [`min4`](fn.min4.html)
 pub fn max<N: Number, D: Dimension>(a: &TVec<N, D>, b: N) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
-    a.map(|a| na::sup(&a, &b))
+    DefaultAllocator: Alloc<N, D>,
+{
+    a.map(|a| crate::max2_scalar(a, b))
 }
 
 /// Component-wise maximum between two vectors.
@@ -35,8 +37,10 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`min3`](fn.min3.html)
 /// * [`min4`](fn.min4.html)
 pub fn max2<N: Number, D: Dimension>(a: &TVec<N, D>, b: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
-    na::sup(a, b)
+    DefaultAllocator: Alloc<N, D>,
+{
+    a.zip_map(b, |a, b| crate::max2_scalar(a, b))
 }
 
 /// Component-wise maximum between three vectors.
@@ -53,7 +57,9 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`min3`](fn.min3.html)
 /// * [`min4`](fn.min4.html)
 pub fn max3<N: Number, D: Dimension>(a: &TVec<N, D>, b: &TVec<N, D>, c: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     max2(&max2(a, b), c)
 }
 
@@ -96,8 +102,10 @@ where
 /// * [`min3`](fn.min3.html)
 /// * [`min4`](fn.min4.html)
 pub fn min<N: Number, D: Dimension>(x: &TVec<N, D>, y: N) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
-    x.map(|x| na::inf(&x, &y))
+    DefaultAllocator: Alloc<N, D>,
+{
+    x.map(|x| crate::min2_scalar(x, y))
 }
 
 /// Component-wise minimum between two vectors.
@@ -114,8 +122,10 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`min3`](fn.min3.html)
 /// * [`min4`](fn.min4.html)
 pub fn min2<N: Number, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
-    na::inf(x, y)
+    DefaultAllocator: Alloc<N, D>,
+{
+    x.zip_map(y, |a, b| crate::min2_scalar(a, b))
 }
 
 /// Component-wise minimum between three vectors.
@@ -132,7 +142,9 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`min2`](fn.min2.html)
 /// * [`min4`](fn.min4.html)
 pub fn min3<N: Number, D: Dimension>(a: &TVec<N, D>, b: &TVec<N, D>, c: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     min2(&min2(a, b), c)
 }
 

nalgebra-glm/src/geometric.rs

@@ -14,13 +14,17 @@ pub fn cross<N: Number>(x: &TVec3<N>, y: &TVec3<N>) -> TVec3<N> {
 ///
 /// * [`distance2`](fn.distance2.html)
 pub fn distance<N: RealField, D: Dimension>(p0: &TVec<N, D>, p1: &TVec<N, D>) -> N
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     (p1 - p0).norm()
 }
 
 /// The dot product of two vectors.
 pub fn dot<N: Number, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.dot(y)
 }
 
@@ -50,7 +54,9 @@ where
 /// * [`magnitude`](fn.magnitude.html)
 /// * [`magnitude2`](fn.magnitude2.html)
 pub fn length<N: RealField, D: Dimension>(x: &TVec<N, D>) -> N
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.norm()
 }
 
@@ -64,26 +70,34 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`magnitude2`](fn.magnitude2.html)
 /// * [`nalgebra::norm`](../nalgebra/fn.norm.html)
 pub fn magnitude<N: RealField, D: Dimension>(x: &TVec<N, D>) -> N
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.norm()
 }
 
 /// Normalizes a vector.
 pub fn normalize<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.normalize()
 }
 
 /// For the incident vector `i` and surface orientation `n`, returns the reflection direction : `result = i - 2.0 * dot(n, i) * n`.
 pub fn reflect_vec<N: Number, D: Dimension>(i: &TVec<N, D>, n: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     let _2 = N::one() + N::one();
     i - n * (n.dot(i) * _2)
 }
 
 /// For the incident vector `i` and surface normal `n`, and the ratio of indices of refraction `eta`, return the refraction vector.
 pub fn refract_vec<N: RealField, D: Dimension>(i: &TVec<N, D>, n: &TVec<N, D>, eta: N) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     let ni = n.dot(i);
     let k = N::one() - eta * eta * (N::one() - ni * ni);
 

nalgebra-glm/src/gtc/matrix_access.rs

@@ -10,10 +10,7 @@ use crate::traits::{Alloc, Dimension};
 /// * [`row`](fn.row.html)
 /// * [`set_column`](fn.set_column.html)
 /// * [`set_row`](fn.set_row.html)
-pub fn column<N: Scalar, R: Dimension, C: Dimension>(
+pub fn column<N: Scalar, R: Dimension, C: Dimension>(m: &TMat<N, R, C>, index: usize) -> TVec<N, R>
-    m: &TMat<N, R, C>,
-    index: usize,
-) -> TVec<N, R>
 where
     DefaultAllocator: Alloc<N, R, C>,
 {
@@ -48,7 +45,9 @@ where
 /// * [`set_column`](fn.set_column.html)
 /// * [`set_row`](fn.set_row.html)
 pub fn row<N: Scalar, R: Dimension, C: Dimension>(m: &TMat<N, R, C>, index: usize) -> TVec<N, C>
-where DefaultAllocator: Alloc<N, R, C> {
+where
+    DefaultAllocator: Alloc<N, R, C>,
+{
     m.row(index).into_owned().transpose()
 }
 

nalgebra-glm/src/gtc/matrix_inverse.rs

@@ -5,14 +5,18 @@ use crate::traits::{Alloc, Dimension};
 
 /// Fast matrix inverse for affine matrix.
 pub fn affine_inverse<N: RealField, D: Dimension>(m: TMat<N, D, D>) -> TMat<N, D, D>
-where DefaultAllocator: Alloc<N, D, D> {
+where
+    DefaultAllocator: Alloc<N, D, D>,
+{
     // FIXME: this should be optimized.
     m.try_inverse().unwrap_or_else(TMat::<_, D, D>::zeros)
 }
 
 /// Compute the transpose of the inverse of a matrix.
 pub fn inverse_transpose<N: RealField, D: Dimension>(m: TMat<N, D, D>) -> TMat<N, D, D>
-where DefaultAllocator: Alloc<N, D, D> {
+where
+    DefaultAllocator: Alloc<N, D, D>,
+{
     m.try_inverse()
         .unwrap_or_else(TMat::<_, D, D>::zeros)
         .transpose()

nalgebra-glm/src/gtc/type_ptr.rs

@@ -76,7 +76,12 @@ pub fn mat2_to_mat3<N: Number>(m: &TMat2<N>) -> TMat3<N> {
 
 /// Converts a 3x3 matrix to a 2x2 matrix.
 pub fn mat3_to_mat2<N: Scalar>(m: &TMat3<N>) -> TMat2<N> {
-    TMat2::new(m.m11.inlined_clone(), m.m12.inlined_clone(), m.m21.inlined_clone(), m.m22.inlined_clone())
+    TMat2::new(
+        m.m11.inlined_clone(),
+        m.m12.inlined_clone(),
+        m.m21.inlined_clone(),
+        m.m22.inlined_clone(),
+    )
 }
 
 /// Converts a 3x3 matrix to a 4x4 matrix.
@@ -92,9 +97,15 @@ pub fn mat3_to_mat4<N: Number>(m: &TMat3<N>) -> TMat4<N> {
 /// Converts a 4x4 matrix to a 3x3 matrix.
 pub fn mat4_to_mat3<N: Scalar>(m: &TMat4<N>) -> TMat3<N> {
     TMat3::new(
-        m.m11.inlined_clone(), m.m12.inlined_clone(), m.m13.inlined_clone(),
+        m.m11.inlined_clone(),
-        m.m21.inlined_clone(), m.m22.inlined_clone(), m.m23.inlined_clone(),
+        m.m12.inlined_clone(),
-        m.m31.inlined_clone(), m.m32.inlined_clone(), m.m33.inlined_clone(),
+        m.m13.inlined_clone(),
+        m.m21.inlined_clone(),
+        m.m22.inlined_clone(),
+        m.m23.inlined_clone(),
+        m.m31.inlined_clone(),
+        m.m32.inlined_clone(),
+        m.m33.inlined_clone(),
     )
 }
 
@@ -110,7 +121,12 @@ pub fn mat2_to_mat4<N: Number>(m: &TMat2<N>) -> TMat4<N> {
 
 /// Converts a 4x4 matrix to a 2x2 matrix.
 pub fn mat4_to_mat2<N: Scalar>(m: &TMat4<N>) -> TMat2<N> {
-    TMat2::new(m.m11.inlined_clone(), m.m12.inlined_clone(), m.m21.inlined_clone(), m.m22.inlined_clone())
+    TMat2::new(
+        m.m11.inlined_clone(),
+        m.m12.inlined_clone(),
+        m.m21.inlined_clone(),
+        m.m22.inlined_clone(),
+    )
 }
 
 /// Creates a quaternion from a slice arranged as `[x, y, z, w]`.
@@ -297,7 +313,11 @@ pub fn vec3_to_vec3<N: Scalar>(v: &TVec3<N>) -> TVec3<N> {
 /// * [`vec3_to_vec2`](fn.vec3_to_vec2.html)
 /// * [`vec3_to_vec4`](fn.vec3_to_vec4.html)
 pub fn vec4_to_vec3<N: Scalar>(v: &TVec4<N>) -> TVec3<N> {
-    TVec3::new(v.x.inlined_clone(), v.y.inlined_clone(), v.z.inlined_clone())
+    TVec3::new(
+        v.x.inlined_clone(),
+        v.y.inlined_clone(),
+        v.z.inlined_clone(),
+    )
 }
 
 /// Creates a 3D vector from another vector.
@@ -386,12 +406,16 @@ pub fn make_vec4<N: Scalar>(ptr: &[N]) -> TVec4<N> {
 
 /// Converts a matrix or vector to a slice arranged in column-major order.
 pub fn value_ptr<N: Scalar, R: Dimension, C: Dimension>(x: &TMat<N, R, C>) -> &[N]
-where DefaultAllocator: Alloc<N, R, C> {
+where
+    DefaultAllocator: Alloc<N, R, C>,
+{
     x.as_slice()
 }
 
 /// Converts a matrix or vector to a mutable slice arranged in column-major order.
 pub fn value_ptr_mut<N: Scalar, R: Dimension, C: Dimension>(x: &mut TMat<N, R, C>) -> &mut [N]
-where DefaultAllocator: Alloc<N, R, C> {
+where
+    DefaultAllocator: Alloc<N, R, C>,
+{
     x.as_mut_slice()
 }

nalgebra-glm/src/gtx/component_wise.rs

@@ -22,7 +22,9 @@ use crate::traits::{Alloc, Dimension, Number};
 /// * [`comp_min`](fn.comp_min.html)
 /// * [`comp_mul`](fn.comp_mul.html)
 pub fn comp_add<N: Number, R: Dimension, C: Dimension>(m: &TMat<N, R, C>) -> N
-where DefaultAllocator: Alloc<N, R, C> {
+where
+    DefaultAllocator: Alloc<N, R, C>,
+{
     m.iter().fold(N::zero(), |x, y| x + *y)
 }
 
@@ -49,8 +51,11 @@ where DefaultAllocator: Alloc<N, R, C> {
 /// * [`max3`](fn.max3.html)
 /// * [`max4`](fn.max4.html)
 pub fn comp_max<N: Number, R: Dimension, C: Dimension>(m: &TMat<N, R, C>) -> N
-where DefaultAllocator: Alloc<N, R, C> {
+where
-    m.iter().fold(N::min_value(), |x, y| na::sup(&x, y))
+    DefaultAllocator: Alloc<N, R, C>,
+{
+    m.iter()
+        .fold(N::min_value(), |x, y| crate::max2_scalar(x, *y))
 }
 
 /// The minimum of every component of the given matrix or vector.
@@ -76,8 +81,11 @@ where DefaultAllocator: Alloc<N, R, C> {
 /// * [`min3`](fn.min3.html)
 /// * [`min4`](fn.min4.html)
 pub fn comp_min<N: Number, R: Dimension, C: Dimension>(m: &TMat<N, R, C>) -> N
-where DefaultAllocator: Alloc<N, R, C> {
+where
-    m.iter().fold(N::max_value(), |x, y| na::inf(&x, y))
+    DefaultAllocator: Alloc<N, R, C>,
+{
+    m.iter()
+        .fold(N::max_value(), |x, y| crate::min2_scalar(x, *y))
 }
 
 /// The product of every component of the given matrix or vector.
@@ -99,7 +107,9 @@ where DefaultAllocator: Alloc<N, R, C> {
 /// * [`comp_max`](fn.comp_max.html)
 /// * [`comp_min`](fn.comp_min.html)
 pub fn comp_mul<N: Number, R: Dimension, C: Dimension>(m: &TMat<N, R, C>) -> N
-where DefaultAllocator: Alloc<N, R, C> {
+where
+    DefaultAllocator: Alloc<N, R, C>,
+{
     m.iter().fold(N::one(), |x, y| x * *y)
 }
 

nalgebra-glm/src/gtx/norm.rs

@@ -9,7 +9,9 @@ use crate::traits::{Alloc, Dimension};
 ///
 /// * [`distance`](fn.distance.html)
 pub fn distance2<N: RealField, D: Dimension>(p0: &TVec<N, D>, p1: &TVec<N, D>) -> N
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     (p1 - p0).norm_squared()
 }
 
@@ -21,7 +23,9 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`l2_distance`](fn.l2_distance.html)
 /// * [`l2_norm`](fn.l2_norm.html)
 pub fn l1_distance<N: RealField, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     l1_norm(&(y - x))
 }
 
@@ -36,7 +40,9 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`l2_distance`](fn.l2_distance.html)
 /// * [`l2_norm`](fn.l2_norm.html)
 pub fn l1_norm<N: RealField, D: Dimension>(v: &TVec<N, D>) -> N
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     crate::comp_add(&v.abs())
 }
 
@@ -55,7 +61,9 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`magnitude`](fn.magnitude.html)
 /// * [`magnitude2`](fn.magnitude2.html)
 pub fn l2_distance<N: RealField, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     l2_norm(&(y - x))
 }
 
@@ -76,7 +84,9 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`magnitude`](fn.magnitude.html)
 /// * [`magnitude2`](fn.magnitude2.html)
 pub fn l2_norm<N: RealField, D: Dimension>(x: &TVec<N, D>) -> N
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.norm()
 }
 
@@ -92,7 +102,9 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`magnitude`](fn.magnitude.html)
 /// * [`magnitude2`](fn.magnitude2.html)
 pub fn length2<N: RealField, D: Dimension>(x: &TVec<N, D>) -> N
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.norm_squared()
 }
 
@@ -108,7 +120,9 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`magnitude`](fn.magnitude.html)
 /// * [`nalgebra::norm_squared`](../nalgebra/fn.norm_squared.html)
 pub fn magnitude2<N: RealField, D: Dimension>(x: &TVec<N, D>) -> N
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.norm_squared()
 }
 

nalgebra-glm/src/gtx/normalize_dot.rs

@@ -11,7 +11,9 @@ use crate::traits::{Alloc, Dimension};
 ///
 /// * [`normalize_dot`](fn.normalize_dot.html`)
 pub fn fast_normalize_dot<N: RealField, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     // XXX: improve those.
     x.normalize().dot(&y.normalize())
 }
@@ -22,7 +24,9 @@ where DefaultAllocator: Alloc<N, D> {
 ///
 /// * [`fast_normalize_dot`](fn.fast_normalize_dot.html`)
 pub fn normalize_dot<N: RealField, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     // XXX: improve those.
     x.normalize().dot(&y.normalize())
 }

nalgebra-glm/src/gtx/vector_angle.rs

@@ -5,7 +5,9 @@ use crate::traits::{Alloc, Dimension};
 
 /// The angle between two vectors.
 pub fn angle<N: RealField, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.angle(y)
 }
 

nalgebra-glm/src/gtx/vector_query.rs

@@ -22,11 +22,7 @@ pub fn are_collinear2d<N: Number>(v0: &TVec2<N>, v1: &TVec2<N>, epsilon: N) -> b
 }
 
 /// Returns `true` if two vectors are orthogonal (up to an epsilon).
-pub fn are_orthogonal<N: Number, D: Dimension>(
+pub fn are_orthogonal<N: Number, D: Dimension>(v0: &TVec<N, D>, v1: &TVec<N, D>, epsilon: N) -> bool
-    v0: &TVec<N, D>,
-    v1: &TVec<N, D>,
-    epsilon: N,
-) -> bool
 where
     DefaultAllocator: Alloc<N, D>,
 {
@@ -40,18 +36,24 @@ where
 
 /// Returns `true` if all the components of `v` are zero (up to an epsilon).
 pub fn is_comp_null<N: Number, D: Dimension>(v: &TVec<N, D>, epsilon: N) -> TVec<bool, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     v.map(|x| abs_diff_eq!(x, N::zero(), epsilon = epsilon))
 }
 
 /// Returns `true` if `v` has a magnitude of 1 (up to an epsilon).
 pub fn is_normalized<N: RealField, D: Dimension>(v: &TVec<N, D>, epsilon: N) -> bool
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     abs_diff_eq!(v.norm_squared(), N::one(), epsilon = epsilon * epsilon)
 }
 
 /// Returns `true` if `v` is zero (up to an epsilon).
 pub fn is_null<N: Number, D: Dimension>(v: &TVec<N, D>, epsilon: N) -> bool
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     abs_diff_eq!(*v, TVec::<N, D>::zeros(), epsilon = epsilon)
 }

nalgebra-glm/src/lib.rs

@@ -116,10 +116,10 @@
 extern crate num_traits as num;
 #[macro_use]
 extern crate approx;
-extern crate alga;
 extern crate nalgebra as na;
 
 pub use crate::aliases::*;
+pub use crate::traits::{Alloc, Dimension, Number};
 pub use common::{
     abs, ceil, clamp, clamp_scalar, clamp_vec, float_bits_to_int, float_bits_to_int_vec,
     float_bits_to_uint, float_bits_to_uint_vec, floor, fract, int_bits_to_float,
@@ -133,7 +133,6 @@ pub use geometric::{
     cross, distance, dot, faceforward, length, magnitude, normalize, reflect_vec, refract_vec,
 };
 pub use matrix::{determinant, inverse, matrix_comp_mult, outer_product, transpose};
-pub use crate::traits::{Alloc, Dimension, Number};
 pub use trigonometric::{
     acos, acosh, asin, asinh, atan, atan2, atanh, cos, cosh, degrees, radians, sin, sinh, tan, tanh,
 };
@@ -143,20 +142,20 @@ pub use vector_relational::{
 
 pub use ext::{
     epsilon, equal_columns, equal_columns_eps, equal_columns_eps_vec, equal_eps, equal_eps_vec,
-    identity, look_at, look_at_lh, look_at_rh, max, max2, max3, max3_scalar, max4, max4_scalar,
+    identity, infinite_perspective_rh_no, infinite_perspective_rh_zo, look_at, look_at_lh,
-    min, min2, min3, min3_scalar, min4, min4_scalar, not_equal_columns, not_equal_columns_eps,
+    look_at_rh, max, max2, max2_scalar, max3, max3_scalar, max4, max4_scalar, min, min2,
-    not_equal_columns_eps_vec, not_equal_eps, not_equal_eps_vec, ortho, perspective, perspective_fov,
+    min2_scalar, min3, min3_scalar, min4, min4_scalar, not_equal_columns, not_equal_columns_eps,
-    perspective_fov_lh,perspective_fov_lh_no, perspective_fov_lh_zo, perspective_fov_no,
+    not_equal_columns_eps_vec, not_equal_eps, not_equal_eps_vec, ortho, ortho_lh, ortho_lh_no,
-    perspective_fov_rh, perspective_fov_rh_no, perspective_fov_rh_zo, perspective_fov_zo,
+    ortho_lh_zo, ortho_no, ortho_rh, ortho_rh_no, ortho_rh_zo, ortho_zo, perspective,
-    perspective_lh, perspective_lh_no, perspective_lh_zo, perspective_no, perspective_rh,
+    perspective_fov, perspective_fov_lh, perspective_fov_lh_no, perspective_fov_lh_zo,
-    perspective_rh_no, perspective_rh_zo, perspective_zo, ortho_lh, ortho_lh_no, ortho_lh_zo,
+    perspective_fov_no, perspective_fov_rh, perspective_fov_rh_no, perspective_fov_rh_zo,
-    ortho_no, ortho_rh, ortho_rh_no, ortho_rh_zo, ortho_zo, pi, pick_matrix, project, project_no,
+    perspective_fov_zo, perspective_lh, perspective_lh_no, perspective_lh_zo, perspective_no,
-    project_zo, quat_angle, quat_angle_axis, quat_axis, quat_conjugate, quat_cross, quat_dot,
+    perspective_rh, perspective_rh_no, perspective_rh_zo, perspective_zo, pi, pick_matrix, project,
-    quat_equal, quat_equal_eps, quat_exp, quat_inverse, quat_length, quat_lerp, quat_log,
+    project_no, project_zo, quat_angle, quat_angle_axis, quat_axis, quat_conjugate, quat_cross,
+    quat_dot, quat_equal, quat_equal_eps, quat_exp, quat_inverse, quat_length, quat_lerp, quat_log,
     quat_magnitude, quat_normalize, quat_not_equal, quat_not_equal_eps, quat_pow, quat_rotate,
-    quat_slerp, rotate, rotate_x, rotate_y, rotate_z, scale, translate, unproject, unproject_no,
+    quat_slerp, reversed_infinite_perspective_rh_zo, reversed_perspective_rh_zo, rotate, rotate_x,
-    unproject_zo, infinite_perspective_rh_no, infinite_perspective_rh_zo,
+    rotate_y, rotate_z, scale, translate, unproject, unproject_no, unproject_zo,
-    reversed_perspective_rh_zo, reversed_infinite_perspective_rh_zo,
 };
 pub use gtc::{
     affine_inverse, column, e, euler, four_over_pi, golden_ratio, half_pi, inverse_transpose,

nalgebra-glm/src/matrix.rs

@@ -5,13 +5,17 @@ use crate::traits::{Alloc, Dimension, Number};
 
 /// The determinant of the matrix `m`.
 pub fn determinant<N: RealField, D: Dimension>(m: &TMat<N, D, D>) -> N
-where DefaultAllocator: Alloc<N, D, D> {
+where
+    DefaultAllocator: Alloc<N, D, D>,
+{
     m.determinant()
 }
 
 /// The inverse of the matrix `m`.
 pub fn inverse<N: RealField, D: Dimension>(m: &TMat<N, D, D>) -> TMat<N, D, D>
-where DefaultAllocator: Alloc<N, D, D> {
+where
+    DefaultAllocator: Alloc<N, D, D>,
+{
     m.clone()
         .try_inverse()
         .unwrap_or_else(TMat::<N, D, D>::zeros)
@@ -41,6 +45,8 @@ where
 
 /// The transpose of the matrix `m`.
 pub fn transpose<N: Scalar, R: Dimension, C: Dimension>(x: &TMat<N, R, C>) -> TMat<N, C, R>
-where DefaultAllocator: Alloc<N, R, C> {
+where
+    DefaultAllocator: Alloc<N, R, C>,
+{
     x.transpose()
 }

nalgebra-glm/src/traits.rs

@@ -1,9 +1,10 @@
 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::{ClosedAdd, ClosedMul, ClosedSub};
+use std::cmp::PartialOrd;
 
 /// A type-level number representing a vector, matrix row, or matrix column, dimension.
 pub trait Dimension: DimName + DimMin<Self, Output = Self> {}
@@ -11,13 +12,33 @@ impl<D: DimName + DimMin<D, Output = Self>> Dimension for D {}
 
 /// A number that can either be an integer or a float.
 pub trait Number:
-    Scalar + Copy + Ring + Lattice + AbsDiffEq<Epsilon = Self> + Signed + FromPrimitive + Bounded
+    Scalar
+    + Copy
+    + PartialOrd
+    + ClosedAdd
+    + ClosedSub
+    + ClosedMul
+    + AbsDiffEq<Epsilon = Self>
+    + Signed
+    + FromPrimitive
+    + Bounded
 {
 }
 
-impl<T: Scalar + Copy + Ring + Lattice + AbsDiffEq<Epsilon = Self> + Signed + FromPrimitive + Bounded>
+impl<
-    Number for T
+        T: Scalar
-{}
+            + Copy
+            + PartialOrd
+            + ClosedAdd
+            + ClosedSub
+            + ClosedMul
+            + AbsDiffEq<Epsilon = Self>
+            + Signed
+            + FromPrimitive
+            + Bounded,
+    > Number for T
+{
+}
 
 #[doc(hidden)]
 pub trait Alloc<N: Scalar, R: Dimension, C: Dimension = U1>:
@@ -50,7 +71,8 @@ pub trait Alloc<N: Scalar, R: Dimension, C: Dimension = U1>:
 {
 }
 
-impl<N: Scalar, R: Dimension, C: Dimension, T> Alloc<N, R, C> for T where T: Allocator<N, R>
+impl<N: Scalar, R: Dimension, C: Dimension, T> Alloc<N, R, C> for T where
+    T: Allocator<N, R>
         + Allocator<N, C>
         + Allocator<N, U1, R>
         + Allocator<N, U1, C>
@@ -76,4 +98,5 @@ 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-glm/src/trigonometric.rs

@@ -5,90 +5,120 @@ use crate::traits::{Alloc, Dimension};
 
 /// Component-wise arc-cosinus.
 pub fn acos<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.map(|e| e.acos())
 }
 
 /// Component-wise hyperbolic arc-cosinus.
 pub fn acosh<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.map(|e| e.acosh())
 }
 
 /// Component-wise arc-sinus.
 pub fn asin<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.map(|e| e.asin())
 }
 
 /// Component-wise hyperbolic arc-sinus.
 pub fn asinh<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.map(|e| e.asinh())
 }
 
 /// Component-wise arc-tangent of `y / x`.
 pub fn atan2<N: RealField, D: Dimension>(y: &TVec<N, D>, x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     y.zip_map(x, |y, x| y.atan2(x))
 }
 
 /// Component-wise arc-tangent.
 pub fn atan<N: RealField, D: Dimension>(y_over_x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     y_over_x.map(|e| e.atan())
 }
 
 /// Component-wise hyperbolic arc-tangent.
 pub fn atanh<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.map(|e| e.atanh())
 }
 
 /// Component-wise cosinus.
 pub fn cos<N: RealField, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     angle.map(|e| e.cos())
 }
 
 /// Component-wise hyperbolic cosinus.
 pub fn cosh<N: RealField, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     angle.map(|e| e.cosh())
 }
 
 /// Component-wise conversion from radians to degrees.
 pub fn degrees<N: RealField, D: Dimension>(radians: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     radians.map(|e| e * na::convert(180.0) / N::pi())
 }
 
 /// Component-wise conversion fro degrees to radians.
 pub fn radians<N: RealField, D: Dimension>(degrees: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     degrees.map(|e| e * N::pi() / na::convert(180.0))
 }
 
 /// Component-wise sinus.
 pub fn sin<N: RealField, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     angle.map(|e| e.sin())
 }
 
 /// Component-wise hyperbolic sinus.
 pub fn sinh<N: RealField, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     angle.map(|e| e.sinh())
 }
 
 /// Component-wise tangent.
 pub fn tan<N: RealField, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     angle.map(|e| e.tan())
 }
 
 /// Component-wise hyperbolic tangent.
 pub fn tanh<N: RealField, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     angle.map(|e| e.tanh())
 }

nalgebra-glm/src/vector_relational.rs

@@ -21,7 +21,9 @@ use crate::traits::{Alloc, Dimension, Number};
 /// * [`any`](fn.any.html)
 /// * [`not`](fn.not.html)
 pub fn all<D: Dimension>(v: &TVec<bool, D>) -> bool
-where DefaultAllocator: Alloc<bool, D> {
+where
+    DefaultAllocator: Alloc<bool, D>,
+{
     v.iter().all(|x| *x)
 }
 
@@ -46,7 +48,9 @@ where DefaultAllocator: Alloc<bool, D> {
 /// * [`all`](fn.all.html)
 /// * [`not`](fn.not.html)
 pub fn any<D: Dimension>(v: &TVec<bool, D>) -> bool
-where DefaultAllocator: Alloc<bool, D> {
+where
+    DefaultAllocator: Alloc<bool, D>,
+{
     v.iter().any(|x| *x)
 }
 
@@ -70,7 +74,9 @@ where DefaultAllocator: Alloc<bool, D> {
 /// * [`not`](fn.not.html)
 /// * [`not_equal`](fn.not_equal.html)
 pub fn equal<N: Number, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> TVec<bool, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.zip_map(y, |x, y| x == y)
 }
 
@@ -94,7 +100,9 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`not`](fn.not.html)
 /// * [`not_equal`](fn.not_equal.html)
 pub fn greater_than<N: Number, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> TVec<bool, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.zip_map(y, |x, y| x > y)
 }
 
@@ -117,10 +125,7 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`less_than_equal`](fn.less_than_equal.html)
 /// * [`not`](fn.not.html)
 /// * [`not_equal`](fn.not_equal.html)
-pub fn greater_than_equal<N: Number, D: Dimension>(
+pub fn greater_than_equal<N: Number, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> TVec<bool, D>
-    x: &TVec<N, D>,
-    y: &TVec<N, D>,
-) -> TVec<bool, D>
 where
     DefaultAllocator: Alloc<N, D>,
 {
@@ -147,7 +152,9 @@ where
 /// * [`not`](fn.not.html)
 /// * [`not_equal`](fn.not_equal.html)
 pub fn less_than<N: Number, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> TVec<bool, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.zip_map(y, |x, y| x < y)
 }
 
@@ -171,7 +178,9 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`not`](fn.not.html)
 /// * [`not_equal`](fn.not_equal.html)
 pub fn less_than_equal<N: Number, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> TVec<bool, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.zip_map(y, |x, y| x <= y)
 }
 
@@ -196,7 +205,9 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`less_than_equal`](fn.less_than_equal.html)
 /// * [`not_equal`](fn.not_equal.html)
 pub fn not<D: Dimension>(v: &TVec<bool, D>) -> TVec<bool, D>
-where DefaultAllocator: Alloc<bool, D> {
+where
+    DefaultAllocator: Alloc<bool, D>,
+{
     v.map(|x| !x)
 }
 
@@ -220,6 +231,8 @@ where DefaultAllocator: Alloc<bool, D> {
 /// * [`less_than_equal`](fn.less_than_equal.html)
 /// * [`not`](fn.not.html)
 pub fn not_equal<N: Number, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> TVec<bool, D>
-where DefaultAllocator: Alloc<N, D> {
+where
+    DefaultAllocator: Alloc<N, D>,
+{
     x.zip_map(y, |x, y| x != y)
 }

nalgebra-glm/tests/lib.rs

@@ -1,35 +1,35 @@
 extern crate nalgebra as na;
 extern crate nalgebra_glm as glm;
 
-use na::Perspective3;
-use na::Orthographic3;
 use glm::Mat4;
 use glm::Vec4;
+use na::Orthographic3;
+use na::Perspective3;
 
 #[test]
-pub fn orthographic_glm_nalgebra_same()
+pub fn orthographic_glm_nalgebra_same() {
-{
+    let na_mat: Mat4 =
-    let na_mat : Mat4 = Orthographic3::new(-100.0f32,100.0f32, -50.0f32, 50.0f32, 0.1f32, 100.0f32).into_inner();
+        Orthographic3::new(-100.0f32, 100.0f32, -50.0f32, 50.0f32, 0.1f32, 100.0f32).into_inner();
     let gl_mat: Mat4 = glm::ortho(-100.0f32, 100.0f32, -50.0f32, 50.0f32, 0.1f32, 100.0f32);
 
     assert_eq!(na_mat, gl_mat);
 }
 
 #[test]
-pub fn perspective_glm_nalgebra_same()
+pub fn perspective_glm_nalgebra_same() {
-{
+    let na_mat: Mat4 =
-    let na_mat : Mat4 = Perspective3::new(16.0f32/9.0f32, 3.14f32/2.0f32, 0.1f32, 100.0f32).into_inner();
+        Perspective3::new(16.0f32 / 9.0f32, 3.14f32 / 2.0f32, 0.1f32, 100.0f32).into_inner();
     let gl_mat: Mat4 = glm::perspective(16.0f32 / 9.0f32, 3.14f32 / 2.0f32, 0.1f32, 100.0f32);
 
     assert_eq!(na_mat, gl_mat);
 }
 
 #[test]
-pub fn orthographic_glm_nalgebra_project_same()
+pub fn orthographic_glm_nalgebra_project_same() {
-{
     let point = Vec4::new(1.0, 0.0, -20.0, 1.0);
 
-    let na_mat : Mat4 = Orthographic3::new(-100.0f32,100.0f32, -50.0f32, 50.0f32, 0.1f32, 100.0f32).into_inner();
+    let na_mat: Mat4 =
+        Orthographic3::new(-100.0f32, 100.0f32, -50.0f32, 50.0f32, 0.1f32, 100.0f32).into_inner();
     let gl_mat: Mat4 = glm::ortho(-100.0f32, 100.0f32, -50.0f32, 50.0f32, 0.1f32, 100.0f32);
 
     let na_pt = na_mat * point;
@@ -40,11 +40,11 @@ pub fn orthographic_glm_nalgebra_project_same()
 }
 
 #[test]
-pub fn perspective_glm_nalgebra_project_same()
+pub fn perspective_glm_nalgebra_project_same() {
-{
     let point = Vec4::new(1.0, 0.0, -20.0, 1.0);
 
-    let na_mat : Mat4 = Perspective3::new(16.0f32/9.0f32, 3.14f32/2.0f32, 0.1f32, 100.0f32).into_inner();
+    let na_mat: Mat4 =
+        Perspective3::new(16.0f32 / 9.0f32, 3.14f32 / 2.0f32, 0.1f32, 100.0f32).into_inner();
     let gl_mat: Mat4 = glm::perspective(16.0f32 / 9.0f32, 3.14f32 / 2.0f32, 0.1f32, 100.0f32);
 
     let na_pt = na_mat * point;

nalgebra-lapack/Cargo.toml

@@ -26,7 +26,7 @@ intel-mkl  = ["lapack-src/intel-mkl"]
 nalgebra      = { version = "0.20", path = ".." }
 num-traits    = "0.2"
 num-complex   = { version = "0.2", default-features = false }
-alga          = { version = "0.9", default-features = false }
+simba         = "0.1"
 serde         = { version = "1.0", optional = true }
 serde_derive  = { version = "1.0", optional = true }
 lapack        = { version = "0.16", default-features = false }

nalgebra-lapack/src/cholesky.rs

@@ -15,21 +15,18 @@ use lapack;
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(serialize = "DefaultAllocator: Allocator<N, D>,
-        serialize = "DefaultAllocator: Allocator<N, D>,
+         MatrixN<N, D>: Serialize"))
-         MatrixN<N, D>: Serialize"
-    ))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(deserialize = "DefaultAllocator: Allocator<N, D>,
-        deserialize = "DefaultAllocator: Allocator<N, D>,
+         MatrixN<N, D>: Deserialize<'de>"))
-         MatrixN<N, D>: Deserialize<'de>"
-    ))
 )]
 #[derive(Clone, Debug)]
 pub struct Cholesky<N: Scalar, D: Dim>
-where DefaultAllocator: Allocator<N, D, D>
+where
+    DefaultAllocator: Allocator<N, D, D>,
 {
     l: MatrixN<N, D>,
 }
@@ -38,10 +35,12 @@ impl<N: Scalar + Copy, D: Dim> Copy for Cholesky<N, D>
 where
     DefaultAllocator: Allocator<N, D, D>,
     MatrixN<N, D>: Copy,
-{}
+{
+}
 
 impl<N: CholeskyScalar + Zero, D: Dim> Cholesky<N, D>
-where DefaultAllocator: Allocator<N, D, D>
+where
+    DefaultAllocator: Allocator<N, D, D>,
 {
     /// Computes the cholesky decomposition of the given symmetric-definite-positive square
     /// matrix.
@@ -117,7 +116,9 @@ where DefaultAllocator: Allocator<N, D, D>
     /// Solves in-place the symmetric-definite-positive linear system `self * x = b`, where `x` is
     /// the unknown to be determined.
     pub fn solve_mut<R2: Dim, C2: Dim>(&self, b: &mut MatrixMN<N, R2, C2>) -> bool
-    where DefaultAllocator: Allocator<N, R2, C2> {
+    where
+        DefaultAllocator: Allocator<N, R2, C2>,
+    {
         let dim = self.l.nrows();
 
         assert!(

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;
 
@@ -18,23 +18,24 @@ 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>
-where DefaultAllocator: Allocator<N, D> + Allocator<N, D, D>
+where
+    DefaultAllocator: Allocator<N, D> + Allocator<N, D, D>,
 {
     /// The eigenvalues of the decomposed matrix.
     pub eigenvalues: VectorN<N, D>,
@@ -49,10 +50,12 @@ 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>
+where
+    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
 {
     /// Computes the eigenvalues and eigenvectors of the square matrix `m`.
     ///
@@ -61,8 +64,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
         mut m: MatrixN<N, D>,
         left_eigenvectors: bool,
         eigenvectors: bool,
-    ) -> Option<Eigen<N, D>>
+    ) -> Option<Eigen<N, D>> {
-    {
         assert!(
             m.is_square(),
             "Unable to compute the eigenvalue decomposition of a non-square matrix."
@@ -228,7 +230,9 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
     ///
     /// Panics if the eigenvalue computation does not converge.
     pub fn complex_eigenvalues(mut m: MatrixN<N, D>) -> VectorN<Complex<N>, D>
-    where DefaultAllocator: Allocator<Complex<N>, D> {
+    where
+        DefaultAllocator: Allocator<Complex<N>, D>,
+    {
         assert!(
             m.is_square(),
             "Unable to compute the eigenvalue decomposition of a non-square matrix."

nalgebra-lapack/src/hessenberg.rs

@@ -1,11 +1,11 @@
 use num::Zero;
 use num_complex::Complex;
 
+use crate::ComplexHelper;
 use na::allocator::Allocator;
 use na::dimension::{DimDiff, DimSub, U1};
 use na::storage::Storage;
 use na::{DefaultAllocator, Matrix, MatrixN, Scalar, VectorN};
-use crate::ComplexHelper;
 
 use lapack;
 
@@ -13,25 +13,22 @@ 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, 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: Scalar, D: DimSub<U1>>
-where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>
+where
+    DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>,
 {
     h: MatrixN<N, D>,
     tau: VectorN<N, DimDiff<D, U1>>,
@@ -42,10 +39,12 @@ where
     DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>,
     MatrixN<N, D>: Copy,
     VectorN<N, DimDiff<D, U1>>: Copy,
-{}
+{
+}
 
 impl<N: HessenbergScalar + Zero, D: DimSub<U1>> Hessenberg<N, D>
-where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>
+where
+    DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>,
 {
     /// Computes the hessenberg decomposition of the matrix `m`.
     pub fn new(mut m: MatrixN<N, D>) -> Self {
@@ -97,7 +96,8 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>
 }
 
 impl<N: HessenbergReal + Zero, D: DimSub<U1>> Hessenberg<N, D>
-where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>
+where
+    DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>,
 {
     /// Computes the matrices `(Q, H)` of this decomposition.
     #[inline]

nalgebra-lapack/src/lib.rs

@@ -73,11 +73,7 @@
     html_root_url = "https://nalgebra.org/rustdoc"
 )]
 
-extern crate alga;
-extern crate lapack;
-extern crate lapack_src;
 extern crate nalgebra as na;
-extern crate num_complex;
 extern crate num_traits as num;
 
 mod lapack_check;

nalgebra-lapack/src/lu.rs

@@ -1,11 +1,11 @@
 use num::{One, Zero};
 use num_complex::Complex;
 
+use crate::ComplexHelper;
 use na::allocator::Allocator;
 use na::dimension::{Dim, DimMin, DimMinimum, U1};
 use na::storage::Storage;
 use na::{DefaultAllocator, Matrix, MatrixMN, MatrixN, Scalar, VectorN};
-use crate::ComplexHelper;
 
 use lapack;
 
@@ -20,25 +20,22 @@ use lapack;
 #[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<i32, 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<i32, 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: Scalar, R: DimMin<C>, C: Dim>
-where DefaultAllocator: Allocator<i32, DimMinimum<R, C>> + Allocator<N, R, C>
+where
+    DefaultAllocator: Allocator<i32, DimMinimum<R, C>> + Allocator<N, R, C>,
 {
     lu: MatrixMN<N, R, C>,
     p: VectorN<i32, DimMinimum<R, C>>,
@@ -49,7 +46,8 @@ where
     DefaultAllocator: Allocator<N, R, C> + Allocator<i32, DimMinimum<R, C>>,
     MatrixMN<N, R, C>: Copy,
     VectorN<i32, DimMinimum<R, C>>: Copy,
-{}
+{
+}
 
 impl<N: LUScalar, R: Dim, C: Dim> LU<N, R, C>
 where
@@ -133,7 +131,9 @@ where
     /// Applies the permutation matrix to a given matrix or vector in-place.
     #[inline]
     pub fn permute<C2: Dim>(&self, rhs: &mut MatrixMN<N, R, C2>)
-    where DefaultAllocator: Allocator<N, R, C2> {
+    where
+        DefaultAllocator: Allocator<N, R, C2>,
+    {
         let (nrows, ncols) = rhs.shape();
 
         N::xlaswp(
@@ -148,7 +148,9 @@ where
     }
 
     fn generic_solve_mut<R2: Dim, C2: Dim>(&self, trans: u8, b: &mut MatrixMN<N, R2, C2>) -> bool
-    where DefaultAllocator: Allocator<N, R2, C2> + Allocator<i32, R2> {
+    where
+        DefaultAllocator: Allocator<N, R2, C2> + Allocator<i32, R2>,
+    {
         let dim = self.lu.nrows();
 
         assert!(
@@ -236,7 +238,9 @@ where
     ///
     /// Returns `false` if no solution was found (the decomposed matrix is singular).
     pub fn solve_mut<R2: Dim, C2: Dim>(&self, b: &mut MatrixMN<N, R2, C2>) -> bool
-    where DefaultAllocator: Allocator<N, R2, C2> + Allocator<i32, R2> {
+    where
+        DefaultAllocator: Allocator<N, R2, C2> + Allocator<i32, R2>,
+    {
         self.generic_solve_mut(b'N', b)
     }
 
@@ -245,7 +249,9 @@ where
     ///
     /// Returns `false` if no solution was found (the decomposed matrix is singular).
     pub fn solve_transpose_mut<R2: Dim, C2: Dim>(&self, b: &mut MatrixMN<N, R2, C2>) -> bool
-    where DefaultAllocator: Allocator<N, R2, C2> + Allocator<i32, R2> {
+    where
+        DefaultAllocator: Allocator<N, R2, C2> + Allocator<i32, R2>,
+    {
         self.generic_solve_mut(b'T', b)
     }
 
@@ -253,10 +259,7 @@ where
     /// be determined.
     ///
     /// Returns `false` if no solution was found (the decomposed matrix is singular).
-    pub fn solve_adjoint_mut<R2: Dim, C2: Dim>(
+    pub fn solve_adjoint_mut<R2: Dim, C2: Dim>(&self, b: &mut MatrixMN<N, R2, C2>) -> bool
-        &self,
-        b: &mut MatrixMN<N, R2, C2>,
-    ) -> bool
     where
         DefaultAllocator: Allocator<N, R2, C2> + Allocator<i32, R2>,
     {

nalgebra-lapack/src/qr.rs

@@ -4,11 +4,11 @@ use serde::{Deserialize, Serialize};
 use num::Zero;
 use num_complex::Complex;
 
+use crate::ComplexHelper;
 use na::allocator::Allocator;
 use na::dimension::{Dim, DimMin, DimMinimum, U1};
 use na::storage::Storage;
 use na::{DefaultAllocator, Matrix, MatrixMN, Scalar, VectorN};
-use crate::ComplexHelper;
 
 use lapack;
 
@@ -16,25 +16,22 @@ use lapack;
 #[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: Scalar, R: DimMin<C>, C: Dim>
-where DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>>
+where
+    DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>>,
 {
     qr: MatrixMN<N, R, C>,
     tau: VectorN<N, DimMinimum<R, C>>,
@@ -45,13 +42,15 @@ where
     DefaultAllocator: Allocator<N, R, C> + Allocator<N, DimMinimum<R, C>>,
     MatrixMN<N, R, C>: Copy,
     VectorN<N, DimMinimum<R, C>>: Copy,
-{}
+{
+}
 
 impl<N: QRScalar + Zero, R: DimMin<C>, C: Dim> QR<N, R, C>
-where DefaultAllocator: Allocator<N, R, C>
+where
+    DefaultAllocator: Allocator<N, R, C>
         + Allocator<N, R, DimMinimum<R, C>>
         + Allocator<N, DimMinimum<R, C>, C>
-        + Allocator<N, DimMinimum<R, C>>
+        + Allocator<N, DimMinimum<R, C>>,
 {
     /// Computes the QR decomposition of the matrix `m`.
     pub fn new(mut m: MatrixMN<N, R, C>) -> Self {
@@ -98,10 +97,11 @@ where DefaultAllocator: Allocator<N, R, C>
 }
 
 impl<N: QRReal + Zero, R: DimMin<C>, C: Dim> QR<N, R, C>
-where DefaultAllocator: Allocator<N, R, C>
+where
+    DefaultAllocator: Allocator<N, R, C>
         + Allocator<N, R, DimMinimum<R, C>>
         + Allocator<N, DimMinimum<R, C>, C>
-        + Allocator<N, DimMinimum<R, C>>
+        + Allocator<N, DimMinimum<R, C>>,
 {
     /// Retrieves the matrices `(Q, R)` of this decompositions.
     pub fn unpack(

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;
 
@@ -18,23 +18,24 @@ 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>
-where DefaultAllocator: Allocator<N, D> + Allocator<N, D, D>
+where
+    DefaultAllocator: Allocator<N, D> + Allocator<N, D, D>,
 {
     re: VectorN<N, D>,
     im: VectorN<N, D>,
@@ -47,10 +48,12 @@ 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>
+where
+    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
 {
     /// Computes the eigenvalues and real Schur form of the matrix `m`.
     ///
@@ -145,7 +148,9 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
 
     /// Computes the complex eigenvalues of the decomposed matrix.
     pub fn complex_eigenvalues(&self) -> VectorN<Complex<N>, D>
-    where DefaultAllocator: Allocator<Complex<N>, D> {
+    where
+        DefaultAllocator: Allocator<Complex<N>, D>,
+    {
         let mut out = unsafe { VectorN::new_uninitialized_generic(self.t.data.shape().0, U1) };
 
         for i in 0..out.len() {

nalgebra-lapack/src/svd.rs

@@ -15,29 +15,26 @@ use lapack;
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(serialize = "DefaultAllocator: Allocator<N, DimMinimum<R, C>> +
-        serialize = "DefaultAllocator: Allocator<N, DimMinimum<R, C>> +
                            Allocator<N, R, R> +
                            Allocator<N, C, C>,
          MatrixN<N, R>: Serialize,
          MatrixN<N, C>: Serialize,
-         VectorN<N, DimMinimum<R, C>>: Serialize"
+         VectorN<N, DimMinimum<R, C>>: Serialize"))
-    ))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
-    serde(bound(
+    serde(bound(serialize = "DefaultAllocator: Allocator<N, DimMinimum<R, C>> +
-        serialize = "DefaultAllocator: Allocator<N, DimMinimum<R, C>> +
                            Allocator<N, R, R> +
                            Allocator<N, C, C>,
          MatrixN<N, R>: Deserialize<'de>,
          MatrixN<N, C>: Deserialize<'de>,
-         VectorN<N, DimMinimum<R, C>>: Deserialize<'de>"
+         VectorN<N, DimMinimum<R, C>>: Deserialize<'de>"))
-    ))
 )]
 #[derive(Clone, Debug)]
 pub struct SVD<N: Scalar, R: DimMin<C>, C: Dim>
-where DefaultAllocator: Allocator<N, R, R> + Allocator<N, DimMinimum<R, C>> + Allocator<N, C, C>
+where
+    DefaultAllocator: Allocator<N, R, R> + Allocator<N, DimMinimum<R, C>> + Allocator<N, C, C>,
 {
     /// The left-singular vectors `U` of this SVD.
     pub u: MatrixN<N, R>, // FIXME: should be MatrixMN<N, R, DimMinimum<R, C>>
@@ -53,25 +50,28 @@ where
     MatrixMN<N, R, R>: Copy,
     MatrixMN<N, C, C>: Copy,
     VectorN<N, DimMinimum<R, C>>: Copy,
-{}
+{
+}
 
 /// Trait implemented by floats (`f32`, `f64`) and complex floats (`Complex<f32>`, `Complex<f64>`)
 /// supported by the Singular Value Decompotition.
 pub trait SVDScalar<R: DimMin<C>, C: Dim>: Scalar
-where DefaultAllocator: Allocator<Self, R, R>
+where
+    DefaultAllocator: Allocator<Self, R, R>
         + Allocator<Self, R, C>
         + Allocator<Self, DimMinimum<R, C>>
-        + Allocator<Self, C, C>
+        + Allocator<Self, C, C>,
 {
     /// Computes the SVD decomposition of `m`.
     fn compute(m: MatrixMN<Self, R, C>) -> Option<SVD<Self, R, C>>;
 }
 
 impl<N: SVDScalar<R, C>, R: DimMin<C>, C: Dim> SVD<N, R, C>
-where DefaultAllocator: Allocator<N, R, R>
+where
+    DefaultAllocator: Allocator<N, R, R>
         + Allocator<N, R, C>
         + Allocator<N, DimMinimum<R, C>>
-        + Allocator<N, C, C>
+        + Allocator<N, C, C>,
 {
     /// Computes the Singular Value Decomposition of `matrix`.
     pub fn new(m: MatrixMN<N, R, C>) -> Option<Self> {

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;
 
@@ -18,25 +18,22 @@ 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>
-where DefaultAllocator: Allocator<N, D> + Allocator<N, D, D>
+where
+    DefaultAllocator: Allocator<N, D> + Allocator<N, D, D>,
 {
     /// The eigenvectors of the decomposed matrix.
     pub eigenvectors: MatrixN<N, D>,
@@ -50,10 +47,12 @@ 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>
+where
+    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
 {
     /// Computes the eigenvalues and eigenvectors of the symmetric matrix `m`.
     ///
@@ -82,8 +81,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
     fn do_decompose(
         mut m: MatrixN<N, D>,
         eigenvectors: bool,
-    ) -> Option<(VectorN<N, D>, Option<MatrixN<N, D>>)>
+    ) -> Option<(VectorN<N, D>, Option<MatrixN<N, D>>)> {
-    {
         assert!(
             m.is_square(),
             "Unable to compute the eigenvalue decomposition of a non-square matrix."

src/base/alias.rs

@@ -1,9 +1,9 @@
 #[cfg(any(feature = "alloc", feature = "std"))]
 use crate::base::dimension::Dynamic;
 use crate::base::dimension::{U1, U2, U3, U4, U5, U6};
+use crate::base::storage::Owned;
 #[cfg(any(feature = "std", feature = "alloc"))]
 use crate::base::vec_storage::VecStorage;
-use crate::base::storage::Owned;
 use crate::base::Matrix;
 
 /*

src/base/alias_slice.rs

@@ -179,20 +179,27 @@ pub type VectorSliceN<'a, N, D, RStride = U1, CStride = D> =
     Matrix<N, D, U1, SliceStorage<'a, N, D, U1, RStride, CStride>>;
 
 /// A column vector slice dynamic numbers of rows and columns.
-pub type DVectorSlice<'a, N, RStride = U1, CStride = Dynamic> = VectorSliceN<'a, N, Dynamic, RStride, CStride>;
+pub type DVectorSlice<'a, N, RStride = U1, CStride = Dynamic> =
+    VectorSliceN<'a, N, Dynamic, RStride, CStride>;
 
 /// A 1D column vector slice.
-pub type VectorSlice1<'a, N, RStride = U1, CStride = U1> = VectorSliceN<'a, N, U1, RStride, CStride>;
+pub type VectorSlice1<'a, N, RStride = U1, CStride = U1> =
+    VectorSliceN<'a, N, U1, RStride, CStride>;
 /// A 2D column vector slice.
-pub type VectorSlice2<'a, N, RStride = U1, CStride = U2> = VectorSliceN<'a, N, U2, RStride, CStride>;
+pub type VectorSlice2<'a, N, RStride = U1, CStride = U2> =
+    VectorSliceN<'a, N, U2, RStride, CStride>;
 /// A 3D column vector slice.
-pub type VectorSlice3<'a, N, RStride = U1, CStride = U3> = VectorSliceN<'a, N, U3, RStride, CStride>;
+pub type VectorSlice3<'a, N, RStride = U1, CStride = U3> =
+    VectorSliceN<'a, N, U3, RStride, CStride>;
 /// A 4D column vector slice.
-pub type VectorSlice4<'a, N, RStride = U1, CStride = U4> = VectorSliceN<'a, N, U4, RStride, CStride>;
+pub type VectorSlice4<'a, N, RStride = U1, CStride = U4> =
+    VectorSliceN<'a, N, U4, RStride, CStride>;
 /// A 5D column vector slice.
-pub type VectorSlice5<'a, N, RStride = U1, CStride = U5> = VectorSliceN<'a, N, U5, RStride, CStride>;
+pub type VectorSlice5<'a, N, RStride = U1, CStride = U5> =
+    VectorSliceN<'a, N, U5, RStride, CStride>;
 /// A 6D column vector slice.
-pub type VectorSlice6<'a, N, RStride = U1, CStride = U6> = VectorSliceN<'a, N, U6, RStride, CStride>;
+pub type VectorSlice6<'a, N, RStride = U1, CStride = U6> =
+    VectorSliceN<'a, N, U6, RStride, CStride>;
 
 /*
  *
@@ -371,17 +378,24 @@ pub type VectorSliceMutN<'a, N, D, RStride = U1, CStride = D> =
     Matrix<N, D, U1, SliceStorageMut<'a, N, D, U1, RStride, CStride>>;
 
 /// A mutable column vector slice dynamic numbers of rows and columns.
-pub type DVectorSliceMut<'a, N, RStride = U1, CStride = Dynamic> = VectorSliceMutN<'a, N, Dynamic, RStride, CStride>;
+pub type DVectorSliceMut<'a, N, RStride = U1, CStride = Dynamic> =
+    VectorSliceMutN<'a, N, Dynamic, RStride, CStride>;
 
 /// A 1D mutable column vector slice.
-pub type VectorSliceMut1<'a, N, RStride = U1, CStride = U1> = VectorSliceMutN<'a, N, U1, RStride, CStride>;
+pub type VectorSliceMut1<'a, N, RStride = U1, CStride = U1> =
+    VectorSliceMutN<'a, N, U1, RStride, CStride>;
 /// A 2D mutable column vector slice.
-pub type VectorSliceMut2<'a, N, RStride = U1, CStride = U2> = VectorSliceMutN<'a, N, U2, RStride, CStride>;
+pub type VectorSliceMut2<'a, N, RStride = U1, CStride = U2> =
+    VectorSliceMutN<'a, N, U2, RStride, CStride>;
 /// A 3D mutable column vector slice.
-pub type VectorSliceMut3<'a, N, RStride = U1, CStride = U3> = VectorSliceMutN<'a, N, U3, RStride, CStride>;
+pub type VectorSliceMut3<'a, N, RStride = U1, CStride = U3> =
+    VectorSliceMutN<'a, N, U3, RStride, CStride>;
 /// A 4D mutable column vector slice.
-pub type VectorSliceMut4<'a, N, RStride = U1, CStride = U4> = VectorSliceMutN<'a, N, U4, RStride, CStride>;
+pub type VectorSliceMut4<'a, N, RStride = U1, CStride = U4> =
+    VectorSliceMutN<'a, N, U4, RStride, CStride>;
 /// A 5D mutable column vector slice.
-pub type VectorSliceMut5<'a, N, RStride = U1, CStride = U5> = VectorSliceMutN<'a, N, U5, RStride, CStride>;
+pub type VectorSliceMut5<'a, N, RStride = U1, CStride = U5> =
+    VectorSliceMutN<'a, N, U5, RStride, CStride>;
 /// A 6D mutable column vector slice.
-pub type VectorSliceMut6<'a, N, RStride = U1, CStride = U6> = VectorSliceMutN<'a, N, U6, RStride, CStride>;
+pub type VectorSliceMut6<'a, N, RStride = U1, CStride = U6> =
+    VectorSliceMutN<'a, N, U6, RStride, CStride>;

src/base/allocator.rs

@@ -79,7 +79,8 @@ where
     N: Scalar,
     DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, SameShapeR<R1, R2>, SameShapeC<C1, C2>>,
     ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,
-{}
+{
+}
 
 // XXX: Bad name.
 /// Restricts the given number of rows to be equal.
@@ -100,4 +101,5 @@ where
     N: Scalar,
     DefaultAllocator: Allocator<N, R1, U1> + Allocator<N, SameShapeR<R1, R2>>,
     ShapeConstraint: SameNumberOfRows<R1, R2>,
-{}
+{
+}

src/base/array_storage.rs

@@ -111,7 +111,8 @@ where
     R::Value: Mul<C::Value>,
     Prod<R::Value, C::Value>: ArrayLength<N>,
     GenericArray<N, Prod<R::Value, C::Value>>: Copy,
-{}
+{
+}
 
 impl<N, R, C> Clone for ArrayStorage<N, R, C>
 where
@@ -136,7 +137,8 @@ where
     C: DimName,
     R::Value: Mul<C::Value>,
     Prod<R::Value, C::Value>: ArrayLength<N>,
-{}
+{
+}
 
 impl<N, R, C> PartialEq for ArrayStorage<N, R, C>
 where
@@ -186,13 +188,17 @@ where
 
     #[inline]
     fn into_owned(self) -> Owned<N, R, C>
-    where DefaultAllocator: Allocator<N, R, C> {
+    where
+        DefaultAllocator: Allocator<N, R, C>,
+    {
         self
     }
 
     #[inline]
     fn clone_owned(&self) -> Owned<N, R, C>
-    where DefaultAllocator: Allocator<N, R, C> {
+    where
+        DefaultAllocator: Allocator<N, R, C>,
+    {
         let it = self.iter().cloned();
 
         DefaultAllocator::allocate_from_iterator(self.shape().0, self.shape().1, it)
@@ -232,7 +238,8 @@ where
     R::Value: Mul<C::Value>,
     Prod<R::Value, C::Value>: ArrayLength<N>,
     DefaultAllocator: Allocator<N, R, C, Buffer = Self>,
-{}
+{
+}
 
 unsafe impl<N, R, C> ContiguousStorageMut<N, R, C> for ArrayStorage<N, R, C>
 where
@@ -242,7 +249,8 @@ where
     R::Value: Mul<C::Value>,
     Prod<R::Value, C::Value>: ArrayLength<N>,
     DefaultAllocator: Allocator<N, R, C, Buffer = Self>,
-{}
+{
+}
 
 /*
  *
@@ -260,7 +268,9 @@ where
     Prod<R::Value, C::Value>: ArrayLength<N>,
 {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
-    where S: Serializer {
+    where
+        S: Serializer,
+    {
         let mut serializer = serializer.serialize_seq(Some(R::dim() * C::dim()))?;
 
         for e in self.iter() {
@@ -281,7 +291,9 @@ where
     Prod<R::Value, C::Value>: ArrayLength<N>,
 {
     fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
-    where D: Deserializer<'a> {
+    where
+        D: Deserializer<'a>,
+    {
         deserializer.deserialize_seq(ArrayStorageVisitor::new())
     }
 }
@@ -326,12 +338,15 @@ where
 
     #[inline]
     fn visit_seq<V>(self, mut visitor: V) -> Result<ArrayStorage<N, R, C>, V::Error>
-    where V: SeqAccess<'a> {
+    where
+        V: SeqAccess<'a>,
+    {
         let mut out: Self::Value = unsafe { mem::uninitialized() };
         let mut curr = 0;
 
         while let Some(value) = visitor.next_element()? {
-            *out.get_mut(curr).ok_or_else(|| V::Error::invalid_length(curr, &self))? = value;
+            *out.get_mut(curr)
+                .ok_or_else(|| V::Error::invalid_length(curr, &self))? = value;
             curr += 1;
         }
 

src/base/blas.rs

@@ -1,7 +1,8 @@
-use alga::general::{ClosedAdd, ClosedMul, ComplexField};
+use crate::SimdComplexField;
 #[cfg(feature = "std")]
 use matrixmultiply;
 use num::{One, Signed, Zero};
+use simba::scalar::{ClosedAdd, ClosedMul, ComplexField};
 #[cfg(feature = "std")]
 use std::mem;
 
@@ -11,8 +12,9 @@ use crate::base::constraint::{
 };
 use crate::base::dimension::{Dim, Dynamic, U1, U2, U3, U4};
 use crate::base::storage::{Storage, StorageMut};
-use crate::base::{DefaultAllocator, Matrix, Scalar, SquareMatrix, Vector, DVectorSlice, VectorSliceN};
+use crate::base::{
-
+    DVectorSlice, DefaultAllocator, Matrix, Scalar, SquareMatrix, Vector, VectorSliceN,
+};
 
 // FIXME: find a way to avoid code duplication just for complex number support.
 impl<N: ComplexField, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
@@ -102,7 +104,9 @@ impl<N: Scalar + PartialOrd, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
     /// ```
     #[inline]
     pub fn iamax(&self) -> usize
-        where N: Signed {
+    where
+        N: Signed,
+    {
         assert!(!self.is_empty(), "The input vector must not be empty.");
 
         let mut the_max = unsafe { self.vget_unchecked(0).abs() };
@@ -173,7 +177,9 @@ impl<N: Scalar + PartialOrd, D: Dim, S: Storage<N, D>> Vector<N, D, S> {
     /// ```
     #[inline]
     pub fn iamin(&self) -> usize
-        where N: Signed {
+    where
+        N: Signed,
+    {
         assert!(!self.is_empty(), "The input vector must not be empty.");
 
         let mut the_min = unsafe { self.vget_unchecked(0).abs() };
@@ -229,7 +235,6 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     }
 }
 
-
 impl<N: Scalar + PartialOrd + Signed, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Computes the index of the matrix component with the largest absolute value.
     ///
@@ -264,10 +269,15 @@ impl<N: Scalar + PartialOrd + Signed, R: Dim, C: Dim, S: Storage<N, R, C>> Matri
 }
 
 impl<N, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
-where N: Scalar + Zero + ClosedAdd + ClosedMul
+where
+    N: Scalar + Zero + ClosedAdd + ClosedMul,
 {
     #[inline(always)]
-    fn dotx<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>, conjugate: impl Fn(N) -> N) -> N
+    fn dotx<R2: Dim, C2: Dim, SB>(
+        &self,
+        rhs: &Matrix<N, R2, C2, SB>,
+        conjugate: impl Fn(N) -> N,
+    ) -> N
     where
         SB: Storage<N, R2, C2>,
         ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,
@@ -281,27 +291,36 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
         // because the `for` loop below won't be very efficient on those.
         if (R::is::<U2>() || R2::is::<U2>()) && (C::is::<U1>() || C2::is::<U1>()) {
             unsafe {
-                let a = conjugate(self.get_unchecked((0, 0)).inlined_clone()) * rhs.get_unchecked((0, 0)).inlined_clone();
+                let a = conjugate(self.get_unchecked((0, 0)).inlined_clone())
-                let b = conjugate(self.get_unchecked((1, 0)).inlined_clone()) * rhs.get_unchecked((1, 0)).inlined_clone();
+                    * rhs.get_unchecked((0, 0)).inlined_clone();
+                let b = conjugate(self.get_unchecked((1, 0)).inlined_clone())
+                    * rhs.get_unchecked((1, 0)).inlined_clone();
 
                 return a + b;
             }
         }
         if (R::is::<U3>() || R2::is::<U3>()) && (C::is::<U1>() || C2::is::<U1>()) {
             unsafe {
-                let a = conjugate(self.get_unchecked((0, 0)).inlined_clone()) * rhs.get_unchecked((0, 0)).inlined_clone();
+                let a = conjugate(self.get_unchecked((0, 0)).inlined_clone())
-                let b = conjugate(self.get_unchecked((1, 0)).inlined_clone()) * rhs.get_unchecked((1, 0)).inlined_clone();
+                    * rhs.get_unchecked((0, 0)).inlined_clone();
-                let c = conjugate(self.get_unchecked((2, 0)).inlined_clone()) * rhs.get_unchecked((2, 0)).inlined_clone();
+                let b = conjugate(self.get_unchecked((1, 0)).inlined_clone())
+                    * rhs.get_unchecked((1, 0)).inlined_clone();
+                let c = conjugate(self.get_unchecked((2, 0)).inlined_clone())
+                    * rhs.get_unchecked((2, 0)).inlined_clone();
 
                 return a + b + c;
             }
         }
         if (R::is::<U4>() || R2::is::<U4>()) && (C::is::<U1>() || C2::is::<U1>()) {
             unsafe {
-                let mut a = conjugate(self.get_unchecked((0, 0)).inlined_clone()) * rhs.get_unchecked((0, 0)).inlined_clone();
+                let mut a = conjugate(self.get_unchecked((0, 0)).inlined_clone())
-                let mut b = conjugate(self.get_unchecked((1, 0)).inlined_clone()) * rhs.get_unchecked((1, 0)).inlined_clone();
+                    * rhs.get_unchecked((0, 0)).inlined_clone();
-                let c = conjugate(self.get_unchecked((2, 0)).inlined_clone()) * rhs.get_unchecked((2, 0)).inlined_clone();
+                let mut b = conjugate(self.get_unchecked((1, 0)).inlined_clone())
-                let d = conjugate(self.get_unchecked((3, 0)).inlined_clone()) * rhs.get_unchecked((3, 0)).inlined_clone();
+                    * rhs.get_unchecked((1, 0)).inlined_clone();
+                let c = conjugate(self.get_unchecked((2, 0)).inlined_clone())
+                    * rhs.get_unchecked((2, 0)).inlined_clone();
+                let d = conjugate(self.get_unchecked((3, 0)).inlined_clone())
+                    * rhs.get_unchecked((3, 0)).inlined_clone();
 
                 a += c;
                 b += d;
@@ -341,14 +360,38 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
             acc7 = N::zero();
 
             while self.nrows() - i >= 8 {
-                acc0 += unsafe { conjugate(self.get_unchecked((i + 0, j)).inlined_clone()) * rhs.get_unchecked((i + 0, j)).inlined_clone() };
+                acc0 += unsafe {
-                acc1 += unsafe { conjugate(self.get_unchecked((i + 1, j)).inlined_clone()) * rhs.get_unchecked((i + 1, j)).inlined_clone() };
+                    conjugate(self.get_unchecked((i + 0, j)).inlined_clone())
-                acc2 += unsafe { conjugate(self.get_unchecked((i + 2, j)).inlined_clone()) * rhs.get_unchecked((i + 2, j)).inlined_clone() };
+                        * rhs.get_unchecked((i + 0, j)).inlined_clone()
-                acc3 += unsafe { conjugate(self.get_unchecked((i + 3, j)).inlined_clone()) * rhs.get_unchecked((i + 3, j)).inlined_clone() };
+                };
-                acc4 += unsafe { conjugate(self.get_unchecked((i + 4, j)).inlined_clone()) * rhs.get_unchecked((i + 4, j)).inlined_clone() };
+                acc1 += unsafe {
-                acc5 += unsafe { conjugate(self.get_unchecked((i + 5, j)).inlined_clone()) * rhs.get_unchecked((i + 5, j)).inlined_clone() };
+                    conjugate(self.get_unchecked((i + 1, j)).inlined_clone())
-                acc6 += unsafe { conjugate(self.get_unchecked((i + 6, j)).inlined_clone()) * rhs.get_unchecked((i + 6, j)).inlined_clone() };
+                        * rhs.get_unchecked((i + 1, j)).inlined_clone()
-                acc7 += unsafe { conjugate(self.get_unchecked((i + 7, j)).inlined_clone()) * rhs.get_unchecked((i + 7, j)).inlined_clone() };
+                };
+                acc2 += unsafe {
+                    conjugate(self.get_unchecked((i + 2, j)).inlined_clone())
+                        * rhs.get_unchecked((i + 2, j)).inlined_clone()
+                };
+                acc3 += unsafe {
+                    conjugate(self.get_unchecked((i + 3, j)).inlined_clone())
+                        * rhs.get_unchecked((i + 3, j)).inlined_clone()
+                };
+                acc4 += unsafe {
+                    conjugate(self.get_unchecked((i + 4, j)).inlined_clone())
+                        * rhs.get_unchecked((i + 4, j)).inlined_clone()
+                };
+                acc5 += unsafe {
+                    conjugate(self.get_unchecked((i + 5, j)).inlined_clone())
+                        * rhs.get_unchecked((i + 5, j)).inlined_clone()
+                };
+                acc6 += unsafe {
+                    conjugate(self.get_unchecked((i + 6, j)).inlined_clone())
+                        * rhs.get_unchecked((i + 6, j)).inlined_clone()
+                };
+                acc7 += unsafe {
+                    conjugate(self.get_unchecked((i + 7, j)).inlined_clone())
+                        * rhs.get_unchecked((i + 7, j)).inlined_clone()
+                };
                 i += 8;
             }
 
@@ -358,14 +401,16 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
             res += acc3 + acc7;
 
             for k in i..self.nrows() {
-                res += unsafe { conjugate(self.get_unchecked((k, j)).inlined_clone()) * rhs.get_unchecked((k, j)).inlined_clone() }
+                res += unsafe {
+                    conjugate(self.get_unchecked((k, j)).inlined_clone())
+                        * rhs.get_unchecked((k, j)).inlined_clone()
+                }
             }
         }
 
         res
     }
 
-
     /// The dot product between two vectors or matrices (seen as vectors).
     ///
     /// This is equal to `self.transpose() * rhs`. For the sesquilinear complex dot product, use
@@ -420,11 +465,11 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
     #[inline]
     pub fn dotc<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> N
     where
-            N: ComplexField,
+        N: SimdComplexField,
         SB: Storage<N, R2, C2>,
         ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,
     {
-        self.dotx(rhs, ComplexField::conjugate)
+        self.dotx(rhs, N::simd_conjugate)
     }
 
     /// The dot product between the transpose of `self` and `rhs`.
@@ -460,7 +505,10 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
 
         for j in 0..self.nrows() {
             for i in 0..self.ncols() {
-                res += unsafe { self.get_unchecked((j, i)).inlined_clone() * rhs.get_unchecked((i, j)).inlined_clone() }
+                res += unsafe {
+                    self.get_unchecked((j, i)).inlined_clone()
+                        * rhs.get_unchecked((i, j)).inlined_clone()
+                }
             }
         }
 
@@ -468,21 +516,38 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
     }
 }
 
-fn array_axcpy<N>(y: &mut [N], a: N, x: &[N], c: N, beta: N, stride1: usize, stride2: usize, len: usize)
+fn array_axcpy<N>(
-where N: Scalar + Zero + ClosedAdd + ClosedMul {
+    y: &mut [N],
+    a: N,
+    x: &[N],
+    c: N,
+    beta: N,
+    stride1: usize,
+    stride2: usize,
+    len: usize,
+) where
+    N: Scalar + Zero + ClosedAdd + ClosedMul,
+{
     for i in 0..len {
         unsafe {
             let y = y.get_unchecked_mut(i * stride1);
-            *y = a.inlined_clone() * x.get_unchecked(i * stride2).inlined_clone() * c.inlined_clone() + beta.inlined_clone() * y.inlined_clone();
+            *y = a.inlined_clone()
+                * x.get_unchecked(i * stride2).inlined_clone()
+                * c.inlined_clone()
+                + beta.inlined_clone() * y.inlined_clone();
         }
     }
 }
 
 fn array_axc<N>(y: &mut [N], a: N, x: &[N], c: N, stride1: usize, stride2: usize, len: usize)
-where N: Scalar + Zero + ClosedAdd + ClosedMul {
+where
+    N: Scalar + Zero + ClosedAdd + ClosedMul,
+{
     for i in 0..len {
         unsafe {
-            *y.get_unchecked_mut(i * stride1) = a.inlined_clone() * x.get_unchecked(i * stride2).inlined_clone() * c.inlined_clone();
+            *y.get_unchecked_mut(i * stride1) = a.inlined_clone()
+                * x.get_unchecked(i * stride2).inlined_clone()
+                * c.inlined_clone();
         }
     }
 }
@@ -613,7 +678,6 @@ where
         }
     }
 
-
     #[inline(always)]
     fn xxgemv<D2: Dim, D3: Dim, SB, SC>(
         &mut self,
@@ -621,7 +685,10 @@ where
         a: &SquareMatrix<N, D2, SB>,
         x: &Vector<N, D3, SC>,
         beta: N,
-        dot: impl Fn(&DVectorSlice<N, SB::RStride, SB::CStride>, &DVectorSlice<N, SC::RStride, SC::CStride>) -> N,
+        dot: impl Fn(
+            &DVectorSlice<N, SB::RStride, SB::CStride>,
+            &DVectorSlice<N, SC::RStride, SC::CStride>,
+        ) -> N,
     ) where
         N: One,
         SB: Storage<N, D2, D2>,
@@ -660,8 +727,11 @@ where
                 val = x.vget_unchecked(j).inlined_clone();
                 *self.vget_unchecked_mut(j) += alpha.inlined_clone() * dot;
             }
-            self.rows_range_mut(j + 1..)
+            self.rows_range_mut(j + 1..).axpy(
-                .axpy(alpha.inlined_clone() * val, &col2.rows_range(j + 1..), N::one());
+                alpha.inlined_clone() * val,
+                &col2.rows_range(j + 1..),
+                N::one(),
+            );
         }
     }
 
@@ -765,7 +835,7 @@ where
         x: &Vector<N, D3, SC>,
         beta: N,
     ) where
-        N: ComplexField,
+        N: SimdComplexField,
         SB: Storage<N, D2, D2>,
         SC: Storage<N, D3>,
         ShapeConstraint: DimEq<D, D2> + AreMultipliable<D2, D2, D3, U1>,
@@ -773,7 +843,6 @@ where
         self.xxgemv(alpha, a, x, beta, |a, b| a.dotc(b))
     }
 
-
     #[inline(always)]
     fn gemv_xx<R2: Dim, C2: Dim, D3: Dim, SB, SC>(
         &mut self,
@@ -809,12 +878,12 @@ where
         } else {
             for j in 0..ncols2 {
                 let val = unsafe { self.vget_unchecked_mut(j) };
-                *val = alpha.inlined_clone() * dot(&a.column(j), x) + beta.inlined_clone() * val.inlined_clone();
+                *val = alpha.inlined_clone() * dot(&a.column(j), x)
+                    + beta.inlined_clone() * val.inlined_clone();
             }
         }
     }
 
-
     /// Computes `self = alpha * a.transpose() * x + beta * self`, where `a` is a matrix, `x` a vector, and
     /// `alpha, beta` two scalars.
     ///
@@ -876,7 +945,7 @@ where
         x: &Vector<N, D3, SC>,
         beta: N,
     ) where
-        N: ComplexField,
+        N: SimdComplexField,
         SB: Storage<N, R2, C2>,
         SC: Storage<N, D3>,
         ShapeConstraint: DimEq<D, C2> + AreMultipliable<C2, R2, D3, U1>,
@@ -886,7 +955,8 @@ where
 }
 
 impl<N, R1: Dim, C1: Dim, S: StorageMut<N, R1, C1>> Matrix<N, R1, C1, S>
-where N: Scalar + Zero + ClosedAdd + ClosedMul
+where
+    N: Scalar + Zero + ClosedAdd + ClosedMul,
 {
     #[inline(always)]
     fn gerx<D2: Dim, D3: Dim, SB, SC>(
@@ -914,7 +984,8 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
         for j in 0..ncols1 {
             // FIXME: avoid bound checks.
             let val = unsafe { conjugate(y.vget_unchecked(j).inlined_clone()) };
-            self.column_mut(j).axpy(alpha.inlined_clone() * val, x, beta.inlined_clone());
+            self.column_mut(j)
+                .axpy(alpha.inlined_clone() * val, x, beta.inlined_clone());
         }
     }
 
@@ -975,12 +1046,12 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
         y: &Vector<N, D3, SC>,
         beta: N,
     ) where
-        N: ComplexField,
+        N: SimdComplexField,
         SB: Storage<N, D2>,
         SC: Storage<N, D3>,
         ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,
     {
-        self.gerx(alpha, x, y, beta, ComplexField::conjugate)
+        self.gerx(alpha, x, y, beta, SimdComplexField::simd_conjugate)
     }
 
     /// Computes `self = alpha * a * b + beta * self`, where `a, b, self` are matrices.
@@ -1032,7 +1103,8 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
                 || R2::is::<Dynamic>()
                 || C2::is::<Dynamic>()
                 || R3::is::<Dynamic>()
-                || C3::is::<Dynamic>() {
+                || C3::is::<Dynamic>()
+            {
                 // matrixmultiply can be used only if the std feature is available.
                 let nrows1 = self.nrows();
                 let (nrows2, ncols2) = a.shape();
@@ -1125,10 +1197,14 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
             }
         }
 
-
         for j1 in 0..ncols1 {
             // FIXME: avoid bound checks.
-            self.column_mut(j1).gemv(alpha.inlined_clone(), a, &b.column(j1), beta.inlined_clone());
+            self.column_mut(j1).gemv(
+                alpha.inlined_clone(),
+                a,
+                &b.column(j1),
+                beta.inlined_clone(),
+            );
         }
     }
 
@@ -1185,11 +1261,15 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
 
         for j1 in 0..ncols1 {
             // FIXME: avoid bound checks.
-            self.column_mut(j1).gemv_tr(alpha.inlined_clone(), a, &b.column(j1), beta.inlined_clone());
+            self.column_mut(j1).gemv_tr(
+                alpha.inlined_clone(),
+                a,
+                &b.column(j1),
+                beta.inlined_clone(),
+            );
         }
     }
 
-
     /// Computes `self = alpha * a.adjoint() * b + beta * self`, where `a, b, self` are matrices.
     /// `alpha` and `beta` are scalar.
     ///
@@ -1220,7 +1300,7 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
         b: &Matrix<N, R3, C3, SC>,
         beta: N,
     ) where
-        N: ComplexField,
+        N: SimdComplexField,
         SB: Storage<N, R2, C2>,
         SC: Storage<N, R3, C3>,
         ShapeConstraint: SameNumberOfRows<R1, C2>
@@ -1249,7 +1329,8 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
 }
 
 impl<N, R1: Dim, C1: Dim, S: StorageMut<N, R1, C1>> Matrix<N, R1, C1, S>
-where N: Scalar + Zero + ClosedAdd + ClosedMul
+where
+    N: Scalar + Zero + ClosedAdd + ClosedMul,
 {
     #[inline(always)]
     fn xxgerx<D2: Dim, D3: Dim, SB, SC>(
@@ -1386,17 +1467,18 @@ where N: Scalar + Zero + ClosedAdd + ClosedMul
         y: &Vector<N, D3, SC>,
         beta: N,
     ) where
-        N: ComplexField,
+        N: SimdComplexField,
         SB: Storage<N, D2>,
         SC: Storage<N, D3>,
         ShapeConstraint: DimEq<R1, D2> + DimEq<C1, D3>,
     {
-        self.xxgerx(alpha, x, y, beta, ComplexField::conjugate)
+        self.xxgerx(alpha, x, y, beta, SimdComplexField::simd_conjugate)
     }
 }
 
 impl<N, D1: Dim, S: StorageMut<N, D1, D1>> SquareMatrix<N, D1, S>
-where N: Scalar + Zero + One + ClosedAdd + ClosedMul
+where
+    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
 {
     /// Computes the quadratic form `self = alpha * lhs * mid * lhs.transpose() + beta * self`.
     ///
@@ -1534,11 +1616,13 @@ where N: Scalar + Zero + One + ClosedAdd + ClosedMul
             DimEq<D3, R4> + DimEq<D1, C4> + DimEq<D2, D3> + AreMultipliable<C4, R4, D2, U1>,
     {
         work.gemv(N::one(), mid, &rhs.column(0), N::zero());
-        self.column_mut(0).gemv_tr(alpha.inlined_clone(), &rhs, work, beta.inlined_clone());
+        self.column_mut(0)
+            .gemv_tr(alpha.inlined_clone(), &rhs, work, beta.inlined_clone());
 
         for j in 1..rhs.ncols() {
             work.gemv(N::one(), mid, &rhs.column(j), N::zero());
-            self.column_mut(j).gemv_tr(alpha.inlined_clone(), &rhs, work, beta.inlined_clone());
+            self.column_mut(j)
+                .gemv_tr(alpha.inlined_clone(), &rhs, work, beta.inlined_clone());
         }
     }
 

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()?"]
@@ -246,11 +247,15 @@ 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)
-    where D: DimNameSub<U1> {
+    where
+        D: DimNameSub<U1>,
+    {
         let mut to_scale = self.fixed_rows_mut::<DimNameDiff<D, U1>>(0);
         to_scale *= scaling;
     }
@@ -258,7 +263,9 @@ impl<N: Scalar + Ring, D: DimName, S: StorageMut<N, D, D>> SquareMatrix<N, D, S>
     /// Computes in-place the transformation equal to an uniform scaling factor followed by `self`.
     #[inline]
     pub fn prepend_scaling_mut(&mut self, scaling: N)
-    where D: DimNameSub<U1> {
+    where
+        D: DimNameSub<U1>,
+    {
         let mut to_scale = self.fixed_columns_mut::<DimNameDiff<D, U1>>(0);
         to_scale *= scaling;
     }
@@ -328,17 +335,17 @@ impl<N: Scalar + Ring, D: DimName, S: StorageMut<N, D, D>> SquareMatrix<N, D, S>
 }
 
 impl<N: RealField, D: DimNameSub<U1>, S: Storage<N, D, D>> SquareMatrix<N, D, S>
-where DefaultAllocator: Allocator<N, D, D>
+where
+    DefaultAllocator: Allocator<N, D, D>
         + Allocator<N, DimNameDiff<D, U1>>
-        + Allocator<N, DimNameDiff<D, U1>, DimNameDiff<D, U1>>
+        + Allocator<N, DimNameDiff<D, U1>, DimNameDiff<D, U1>>,
 {
     /// Transforms the given vector, assuming the matrix `self` uses homogeneous coordinates.
     #[inline]
     pub fn transform_vector(
         &self,
         v: &VectorN<N, DimNameDiff<D, U1>>,
-    ) -> VectorN<N, DimNameDiff<D, U1>>
+    ) -> VectorN<N, DimNameDiff<D, U1>> {
-    {
         let transform = self.fixed_slice::<DimNameDiff<D, U1>, DimNameDiff<D, U1>>(0, 0);
         let normalizer = self.fixed_slice::<U1, DimNameDiff<D, U1>>(D::dim() - 1, 0);
         let n = normalizer.tr_dot(&v);
@@ -355,8 +362,7 @@ where DefaultAllocator: Allocator<N, D, D>
     pub fn transform_point(
         &self,
         pt: &Point<N, DimNameDiff<D, U1>>,
-    ) -> Point<N, DimNameDiff<D, U1>>
+    ) -> Point<N, DimNameDiff<D, U1>> {
-    {
         let transform = self.fixed_slice::<DimNameDiff<D, U1>, DimNameDiff<D, U1>>(0, 0);
         let translation = self.fixed_slice::<DimNameDiff<D, U1>, U1>(0, D::dim() - 1);
         let normalizer = self.fixed_slice::<U1, DimNameDiff<D, U1>>(D::dim() - 1, 0);
@@ -370,23 +376,3 @@ 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 +3,8 @@
 use num::{Signed, Zero};
 use std::ops::{Add, Mul};
 
-use alga::general::{ClosedDiv, ClosedMul};
+use simba::scalar::{ClosedDiv, ClosedMul};
+use simba::simd::SimdPartialOrd;
 
 use crate::base::allocator::{Allocator, SameShapeAllocator};
 use crate::base::constraint::{SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
@@ -235,3 +236,31 @@ component_binop_impl!(
     ";
     // FIXME: add other operators like bitshift, etc. ?
 );
+
+/*
+ * inf/sup
+ */
+impl<N, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
+where
+    N: Scalar + SimdPartialOrd,
+    DefaultAllocator: Allocator<N, R, C>,
+{
+    /// Computes the infimum (aka. componentwise min) of two matrices/vectors.
+    #[inline]
+    pub fn inf(&self, other: &Self) -> MatrixMN<N, R, C> {
+        self.zip_map(other, |a, b| a.simd_min(b))
+    }
+
+    /// Computes the supremum (aka. componentwise max) of two matrices/vectors.
+    #[inline]
+    pub fn sup(&self, other: &Self) -> MatrixMN<N, R, C> {
+        self.zip_map(other, |a, b| a.simd_max(b))
+    }
+
+    /// Computes the (infimum, supremum) of two matrices/vectors.
+    #[inline]
+    pub fn inf_sup(&self, other: &Self) -> (MatrixMN<N, R, C>, MatrixMN<N, R, C>) {
+        // FIXME: can this be optimized?
+        (self.inf(other), self.sup(other))
+    }
+}

src/base/constraint.rs

@@ -8,8 +8,10 @@ pub struct ShapeConstraint;
 /// Constraints `C1` and `R2` to be equivalent.
 pub trait AreMultipliable<R1: Dim, C1: Dim, R2: Dim, C2: Dim>: DimEq<C1, R2> {}
 
-impl<R1: Dim, C1: Dim, R2: Dim, C2: Dim> AreMultipliable<R1, C1, R2, C2> for ShapeConstraint where ShapeConstraint: DimEq<C1, R2>
+impl<R1: Dim, C1: Dim, R2: Dim, C2: Dim> AreMultipliable<R1, C1, R2, C2> for ShapeConstraint where
-{}
+    ShapeConstraint: DimEq<C1, R2>
+{
+}
 
 /// Constraints `D1` and `D2` to be equivalent.
 pub trait DimEq<D1: Dim, D2: Dim> {

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};
@@ -28,7 +28,8 @@ use crate::base::{DefaultAllocator, Matrix, MatrixMN, MatrixN, Scalar, Unit, Vec
  *
  */
 impl<N: Scalar, R: Dim, C: Dim> MatrixMN<N, R, C>
-where DefaultAllocator: Allocator<N, R, C>
+where
+    DefaultAllocator: Allocator<N, R, C>,
 {
     /// Creates a new uninitialized matrix. If the matrix has a compile-time dimension, this panics
     /// if `nrows != R::to_usize()` or `ncols != C::to_usize()`.
@@ -56,14 +57,18 @@ where DefaultAllocator: Allocator<N, R, C>
     /// Creates a matrix with all its elements set to 0.
     #[inline]
     pub fn zeros_generic(nrows: R, ncols: C) -> Self
-    where N: Zero {
+    where
+        N: Zero,
+    {
         Self::from_element_generic(nrows, ncols, N::zero())
     }
 
     /// Creates a matrix with all its elements filled by an iterator.
     #[inline]
     pub fn from_iterator_generic<I>(nrows: R, ncols: C, iter: I) -> Self
-    where I: IntoIterator<Item = N> {
+    where
+        I: IntoIterator<Item = N>,
+    {
         Self::from_data(DefaultAllocator::allocate_from_iterator(nrows, ncols, iter))
     }
 
@@ -102,7 +107,9 @@ where DefaultAllocator: Allocator<N, R, C>
     /// coordinates.
     #[inline]
     pub fn from_fn_generic<F>(nrows: R, ncols: C, mut f: F) -> Self
-    where F: FnMut(usize, usize) -> N {
+    where
+        F: FnMut(usize, usize) -> N,
+    {
         let mut res = unsafe { Self::new_uninitialized_generic(nrows, ncols) };
 
         for j in 0..ncols.value() {
@@ -120,7 +127,9 @@ where DefaultAllocator: Allocator<N, R, C>
     /// to the identity matrix. All other entries are set to zero.
     #[inline]
     pub fn identity_generic(nrows: R, ncols: C) -> Self
-    where N: Zero + One {
+    where
+        N: Zero + One,
+    {
         Self::from_diagonal_element_generic(nrows, ncols, N::one())
     }
 
@@ -130,7 +139,9 @@ where DefaultAllocator: Allocator<N, R, C>
     /// to the identity matrix. All other entries are set to zero.
     #[inline]
     pub fn from_diagonal_element_generic(nrows: R, ncols: C, elt: N) -> Self
-    where N: Zero + One {
+    where
+        N: Zero + One,
+    {
         let mut res = Self::zeros_generic(nrows, ncols);
 
         for i in 0..crate::min(nrows.value(), ncols.value()) {
@@ -146,7 +157,9 @@ where DefaultAllocator: Allocator<N, R, C>
     /// Panics if `elts.len()` is larger than the minimum among `nrows` and `ncols`.
     #[inline]
     pub fn from_partial_diagonal_generic(nrows: R, ncols: C, elts: &[N]) -> Self
-    where N: Zero {
+    where
+        N: Zero,
+    {
         let mut res = Self::zeros_generic(nrows, ncols);
         assert!(
             elts.len() <= crate::min(nrows.value(), ncols.value()),
@@ -178,7 +191,9 @@ where DefaultAllocator: Allocator<N, R, C>
     /// ```
     #[inline]
     pub fn from_rows<SB>(rows: &[Matrix<N, U1, C, SB>]) -> Self
-    where SB: Storage<N, U1, C> {
+    where
+        SB: Storage<N, U1, C>,
+    {
         assert!(rows.len() > 0, "At least one row must be given.");
         let nrows = R::try_to_usize().unwrap_or(rows.len());
         let ncols = rows[0].len();
@@ -218,7 +233,9 @@ where DefaultAllocator: Allocator<N, R, C>
     /// ```
     #[inline]
     pub fn from_columns<SB>(columns: &[Vector<N, R, SB>]) -> Self
-    where SB: Storage<N, R> {
+    where
+        SB: Storage<N, R>,
+    {
         assert!(columns.len() > 0, "At least one column must be given.");
         let ncols = C::try_to_usize().unwrap_or(columns.len());
         let nrows = columns[0].len();
@@ -244,7 +261,9 @@ where DefaultAllocator: Allocator<N, R, C>
     #[inline]
     #[cfg(feature = "std")]
     pub fn new_random_generic(nrows: R, ncols: C) -> Self
-    where Standard: Distribution<N> {
+    where
+        Standard: Distribution<N>,
+    {
         Self::from_fn_generic(nrows, ncols, |_, _| rand::random())
     }
 
@@ -255,8 +274,7 @@ where DefaultAllocator: Allocator<N, R, C>
         ncols: C,
         distribution: &Distr,
         rng: &mut G,
-    ) -> Self
+    ) -> Self {
-    {
         Self::from_fn_generic(nrows, ncols, |_, _| distribution.sample(rng))
     }
 
@@ -309,7 +327,9 @@ where
     /// ```
     #[inline]
     pub fn from_diagonal<SB: Storage<N, D>>(diag: &Vector<N, D, SB>) -> Self
-    where N: Zero {
+    where
+        N: Zero,
+    {
         let (dim, _) = diag.data.shape();
         let mut res = Self::zeros_generic(dim, dim);
 
@@ -712,8 +732,6 @@ impl_constructors_from_data!(data; Dynamic, Dynamic;
                             Dynamic::new(nrows), Dynamic::new(ncols);
                             nrows, ncols);
 
-
-
 /*
  *
  * Zero, One, Rand traits.
@@ -996,7 +1014,9 @@ where
     /// The column vector with a 1 as its first component, and zero elsewhere.
     #[inline]
     pub fn x() -> Self
-    where R::Value: Cmp<typenum::U0, Output = Greater> {
+    where
+        R::Value: Cmp<typenum::U0, Output = Greater>,
+    {
         let mut res = Self::zeros();
         unsafe {
             *res.vget_unchecked_mut(0) = N::one();
@@ -1008,7 +1028,9 @@ where
     /// The column vector with a 1 as its second component, and zero elsewhere.
     #[inline]
     pub fn y() -> Self
-    where R::Value: Cmp<typenum::U1, Output = Greater> {
+    where
+        R::Value: Cmp<typenum::U1, Output = Greater>,
+    {
         let mut res = Self::zeros();
         unsafe {
             *res.vget_unchecked_mut(1) = N::one();
@@ -1020,7 +1042,9 @@ where
     /// The column vector with a 1 as its third component, and zero elsewhere.
     #[inline]
     pub fn z() -> Self
-    where R::Value: Cmp<typenum::U2, Output = Greater> {
+    where
+        R::Value: Cmp<typenum::U2, Output = Greater>,
+    {
         let mut res = Self::zeros();
         unsafe {
             *res.vget_unchecked_mut(2) = N::one();
@@ -1032,7 +1056,9 @@ where
     /// The column vector with a 1 as its fourth component, and zero elsewhere.
     #[inline]
     pub fn w() -> Self
-    where R::Value: Cmp<typenum::U3, Output = Greater> {
+    where
+        R::Value: Cmp<typenum::U3, Output = Greater>,
+    {
         let mut res = Self::zeros();
         unsafe {
             *res.vget_unchecked_mut(3) = N::one();
@@ -1044,7 +1070,9 @@ where
     /// The column vector with a 1 as its fifth component, and zero elsewhere.
     #[inline]
     pub fn a() -> Self
-    where R::Value: Cmp<typenum::U4, Output = Greater> {
+    where
+        R::Value: Cmp<typenum::U4, Output = Greater>,
+    {
         let mut res = Self::zeros();
         unsafe {
             *res.vget_unchecked_mut(4) = N::one();
@@ -1056,7 +1084,9 @@ where
     /// The column vector with a 1 as its sixth component, and zero elsewhere.
     #[inline]
     pub fn b() -> Self
-    where R::Value: Cmp<typenum::U5, Output = Greater> {
+    where
+        R::Value: Cmp<typenum::U5, Output = Greater>,
+    {
         let mut res = Self::zeros();
         unsafe {
             *res.vget_unchecked_mut(5) = N::one();
@@ -1068,42 +1098,54 @@ where
     /// The unit column vector with a 1 as its first component, and zero elsewhere.
     #[inline]
     pub fn x_axis() -> Unit<Self>
-    where R::Value: Cmp<typenum::U0, Output = Greater> {
+    where
+        R::Value: Cmp<typenum::U0, Output = Greater>,
+    {
         Unit::new_unchecked(Self::x())
     }
 
     /// The unit column vector with a 1 as its second component, and zero elsewhere.
     #[inline]
     pub fn y_axis() -> Unit<Self>
-    where R::Value: Cmp<typenum::U1, Output = Greater> {
+    where
+        R::Value: Cmp<typenum::U1, Output = Greater>,
+    {
         Unit::new_unchecked(Self::y())
     }
 
     /// The unit column vector with a 1 as its third component, and zero elsewhere.
     #[inline]
     pub fn z_axis() -> Unit<Self>
-    where R::Value: Cmp<typenum::U2, Output = Greater> {
+    where
+        R::Value: Cmp<typenum::U2, Output = Greater>,
+    {
         Unit::new_unchecked(Self::z())
     }
 
     /// The unit column vector with a 1 as its fourth component, and zero elsewhere.
     #[inline]
     pub fn w_axis() -> Unit<Self>
-    where R::Value: Cmp<typenum::U3, Output = Greater> {
+    where
+        R::Value: Cmp<typenum::U3, Output = Greater>,
+    {
         Unit::new_unchecked(Self::w())
     }
 
     /// The unit column vector with a 1 as its fifth component, and zero elsewhere.
     #[inline]
     pub fn a_axis() -> Unit<Self>
-    where R::Value: Cmp<typenum::U4, Output = Greater> {
+    where
+        R::Value: Cmp<typenum::U4, Output = Greater>,
+    {
         Unit::new_unchecked(Self::a())
     }
 
     /// The unit column vector with a 1 as its sixth component, and zero elsewhere.
     #[inline]
     pub fn b_axis() -> Unit<Self>
-    where R::Value: Cmp<typenum::U5, Output = Greater> {
+    where
+        R::Value: Cmp<typenum::U5, Output = Greater>,
+    {
         Unit::new_unchecked(Self::b())
     }
 }

src/base/construction_slice.rs

@@ -23,8 +23,7 @@ impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim>
         ncols: C,
         rstride: RStride,
         cstride: CStride,
-    ) -> Self
+    ) -> Self {
-    {
         let data = SliceStorage::from_raw_parts(
             data.as_ptr().offset(start as isize),
             (nrows, ncols),
@@ -44,8 +43,7 @@ impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim>
         ncols: C,
         rstride: RStride,
         cstride: CStride,
-    ) -> Self
+    ) -> Self {
-    {
         // NOTE: The assertion implements the following formula, but without subtractions to avoid
         // underflow panics:
         //      len >= (ncols - 1) * cstride + (nrows - 1) * rstride + 1
@@ -76,8 +74,7 @@ impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim>
         ncols: C,
         rstride: RStride,
         cstride: CStride,
-    ) -> Self
+    ) -> Self {
-    {
         let data = SliceStorageMut::from_raw_parts(
             data.as_mut_ptr().offset(start as isize),
             (nrows, ncols),
@@ -97,8 +94,7 @@ impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim>
         ncols: C,
         rstride: RStride,
         cstride: CStride,
-    ) -> Self
+    ) -> Self {
-    {
         // NOTE: The assertion implements the following formula, but without subtractions to avoid
         // underflow panics:
         //      len >= (ncols - 1) * cstride + (nrows - 1) * rstride + 1
@@ -108,24 +104,27 @@ impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim>
             "Matrix slice: input data buffer to small."
         );
 
-        assert!({
+        assert!(
+            {
                 let nrows = nrows.value();
                 let ncols = ncols.value();
                 let rstride = rstride.value();
                 let cstride = cstride.value();
 
-            nrows * ncols <= 1 ||
+                nrows * ncols <= 1
-                match (rstride, cstride) {
+                    || match (rstride, cstride) {
                         (0, 0) => false,      // otherwise: matrix[(0, 0)] == index[(nrows - 1, ncols - 1)],
                         (0, _) => nrows <= 1, // otherwise: matrix[(0, 0)] == index[(nrows - 1, 0)],
                         (_, 0) => ncols <= 1, // otherwise: matrix[(0, 0)] == index[(0, ncols - 1)],
-                    (_, _) => {           // otherwise: matrix[(0, numer)] == index[(denom, 0)]
+                        (_, _) => {
+                            // otherwise: matrix[(0, numer)] == index[(denom, 0)]
                             let ratio = Ratio::new(rstride, cstride);
                             nrows <= *ratio.denom() || ncols <= *ratio.numer()
                         }
                     }
             },
-            "Matrix slice: dimensions and strides result in aliased indices.");
+            "Matrix slice: dimensions and strides result in aliased indices."
+        );
 
         unsafe {
             Self::from_slice_with_strides_generic_unchecked(data, 0, nrows, ncols, rstride, cstride)
@@ -144,8 +143,7 @@ impl<'a, N: Scalar, R: Dim, C: Dim> MatrixSliceMN<'a, N, R, C> {
         start: usize,
         nrows: R,
         ncols: C,
-    ) -> Self
+    ) -> Self {
-    {
         Self::from_slice_with_strides_generic_unchecked(data, start, nrows, ncols, U1, nrows)
     }
 
@@ -170,8 +168,7 @@ impl<'a, N: Scalar, R: Dim, C: Dim> MatrixSliceMutMN<'a, N, R, C> {
         start: usize,
         nrows: R,
         ncols: C,
-    ) -> Self
+    ) -> Self {
-    {
         Self::from_slice_with_strides_generic_unchecked(data, start, nrows, ncols, U1, nrows)
     }
 

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;
@@ -9,19 +9,24 @@ use generic_array::ArrayLength;
 use std::ops::Mul;
 use typenum::Prod;
 
+use simba::simd::{PrimitiveSimdValue, SimdValue};
+
 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 +51,9 @@ 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 +66,19 @@ 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
     }
@@ -436,8 +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();
@@ -450,9 +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)
         }
     }
@@ -469,8 +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();
@@ -483,9 +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)
         }
     }
@@ -502,8 +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();
@@ -516,29 +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 {
@@ -552,3 +576,108 @@ impl<'a, N: Scalar + Copy> From<&'a mut [N]> for DVectorSliceMut<'a, N> {
         Self::from_slice(slice, slice.len())
     }
 }
+
+impl<N: Scalar + PrimitiveSimdValue, R: Dim, C: Dim> From<[MatrixMN<N::Element, R, C>; 2]>
+    for MatrixMN<N, R, C>
+where
+    N: From<[<N as SimdValue>::Element; 2]>,
+    N::Element: Scalar + SimdValue,
+    DefaultAllocator: Allocator<N, R, C> + Allocator<N::Element, R, C>,
+{
+    #[inline]
+    fn from(arr: [MatrixMN<N::Element, R, C>; 2]) -> Self {
+        let (nrows, ncols) = arr[0].data.shape();
+
+        Self::from_fn_generic(nrows, ncols, |i, j| {
+            [
+                arr[0][(i, j)].inlined_clone(),
+                arr[1][(i, j)].inlined_clone(),
+            ]
+            .into()
+        })
+    }
+}
+
+impl<N: Scalar + PrimitiveSimdValue, R: Dim, C: Dim> From<[MatrixMN<N::Element, R, C>; 4]>
+    for MatrixMN<N, R, C>
+where
+    N: From<[<N as SimdValue>::Element; 4]>,
+    N::Element: Scalar + SimdValue,
+    DefaultAllocator: Allocator<N, R, C> + Allocator<N::Element, R, C>,
+{
+    #[inline]
+    fn from(arr: [MatrixMN<N::Element, R, C>; 4]) -> Self {
+        let (nrows, ncols) = arr[0].data.shape();
+
+        Self::from_fn_generic(nrows, ncols, |i, j| {
+            [
+                arr[0][(i, j)].inlined_clone(),
+                arr[1][(i, j)].inlined_clone(),
+                arr[2][(i, j)].inlined_clone(),
+                arr[3][(i, j)].inlined_clone(),
+            ]
+            .into()
+        })
+    }
+}
+
+impl<N: Scalar + PrimitiveSimdValue, R: Dim, C: Dim> From<[MatrixMN<N::Element, R, C>; 8]>
+    for MatrixMN<N, R, C>
+where
+    N: From<[<N as SimdValue>::Element; 8]>,
+    N::Element: Scalar + SimdValue,
+    DefaultAllocator: Allocator<N, R, C> + Allocator<N::Element, R, C>,
+{
+    #[inline]
+    fn from(arr: [MatrixMN<N::Element, R, C>; 8]) -> Self {
+        let (nrows, ncols) = arr[0].data.shape();
+
+        Self::from_fn_generic(nrows, ncols, |i, j| {
+            [
+                arr[0][(i, j)].inlined_clone(),
+                arr[1][(i, j)].inlined_clone(),
+                arr[2][(i, j)].inlined_clone(),
+                arr[3][(i, j)].inlined_clone(),
+                arr[4][(i, j)].inlined_clone(),
+                arr[5][(i, j)].inlined_clone(),
+                arr[6][(i, j)].inlined_clone(),
+                arr[7][(i, j)].inlined_clone(),
+            ]
+            .into()
+        })
+    }
+}
+
+impl<N: Scalar + PrimitiveSimdValue, R: Dim, C: Dim> From<[MatrixMN<N::Element, R, C>; 16]>
+    for MatrixMN<N, R, C>
+where
+    N: From<[<N as SimdValue>::Element; 16]>,
+    N::Element: Scalar + SimdValue,
+    DefaultAllocator: Allocator<N, R, C> + Allocator<N::Element, R, C>,
+{
+    fn from(arr: [MatrixMN<N::Element, R, C>; 16]) -> Self {
+        let (nrows, ncols) = arr[0].data.shape();
+
+        Self::from_fn_generic(nrows, ncols, |i, j| {
+            [
+                arr[0][(i, j)].inlined_clone(),
+                arr[1][(i, j)].inlined_clone(),
+                arr[2][(i, j)].inlined_clone(),
+                arr[3][(i, j)].inlined_clone(),
+                arr[4][(i, j)].inlined_clone(),
+                arr[5][(i, j)].inlined_clone(),
+                arr[6][(i, j)].inlined_clone(),
+                arr[7][(i, j)].inlined_clone(),
+                arr[8][(i, j)].inlined_clone(),
+                arr[9][(i, j)].inlined_clone(),
+                arr[10][(i, j)].inlined_clone(),
+                arr[11][(i, j)].inlined_clone(),
+                arr[12][(i, j)].inlined_clone(),
+                arr[13][(i, j)].inlined_clone(),
+                arr[14][(i, j)].inlined_clone(),
+                arr[15][(i, j)].inlined_clone(),
+            ]
+            .into()
+        })
+    }
+}

src/base/default_allocator.rs

@@ -15,13 +15,13 @@ use generic_array::ArrayLength;
 use typenum::Prod;
 
 use crate::base::allocator::{Allocator, Reallocator};
+use crate::base::array_storage::ArrayStorage;
 #[cfg(any(feature = "alloc", feature = "std"))]
 use crate::base::dimension::Dynamic;
 use crate::base::dimension::{Dim, DimName};
-use crate::base::array_storage::ArrayStorage;
+use crate::base::storage::{Storage, StorageMut};
 #[cfg(any(feature = "std", feature = "alloc"))]
 use crate::base::vec_storage::VecStorage;
-use crate::base::storage::{Storage, StorageMut};
 use crate::base::Scalar;
 
 /*
@@ -55,8 +55,7 @@ where
         nrows: R,
         ncols: C,
         iter: I,
-    ) -> Self::Buffer
+    ) -> Self::Buffer {
-    {
         let mut res = unsafe { Self::allocate_uninitialized(nrows, ncols) };
         let mut count = 0;
 
@@ -95,8 +94,7 @@ impl<N: Scalar, C: Dim> Allocator<N, Dynamic, C> for DefaultAllocator {
         nrows: Dynamic,
         ncols: C,
         iter: I,
-    ) -> Self::Buffer
+    ) -> Self::Buffer {
-    {
         let it = iter.into_iter();
         let res: Vec<N> = it.collect();
         assert!(res.len() == nrows.value() * ncols.value(),
@@ -126,8 +124,7 @@ impl<N: Scalar, R: DimName> Allocator<N, R, Dynamic> for DefaultAllocator {
         nrows: R,
         ncols: Dynamic,
         iter: I,
-    ) -> Self::Buffer
+    ) -> Self::Buffer {
-    {
         let it = iter.into_iter();
         let res: Vec<N> = it.collect();
         assert!(res.len() == nrows.value() * ncols.value(),
@@ -158,8 +155,7 @@ where
         rto: RTo,
         cto: CTo,
         buf: <Self as Allocator<N, RFrom, CFrom>>::Buffer,
-    ) -> ArrayStorage<N, RTo, CTo>
+    ) -> ArrayStorage<N, RTo, CTo> {
-    {
         let mut res = <Self as Allocator<N, RTo, CTo>>::allocate_uninitialized(rto, cto);
 
         let (rfrom, cfrom) = buf.shape();
@@ -187,8 +183,7 @@ where
         rto: Dynamic,
         cto: CTo,
         buf: ArrayStorage<N, RFrom, CFrom>,
-    ) -> VecStorage<N, Dynamic, CTo>
+    ) -> VecStorage<N, Dynamic, CTo> {
-    {
         let mut res = <Self as Allocator<N, Dynamic, CTo>>::allocate_uninitialized(rto, cto);
 
         let (rfrom, cfrom) = buf.shape();
@@ -216,8 +211,7 @@ where
         rto: RTo,
         cto: Dynamic,
         buf: ArrayStorage<N, RFrom, CFrom>,
-    ) -> VecStorage<N, RTo, Dynamic>
+    ) -> VecStorage<N, RTo, Dynamic> {
-    {
         let mut res = <Self as Allocator<N, RTo, Dynamic>>::allocate_uninitialized(rto, cto);
 
         let (rfrom, cfrom) = buf.shape();
@@ -240,8 +234,7 @@ impl<N: Scalar, CFrom: Dim, CTo: Dim> Reallocator<N, Dynamic, CFrom, Dynamic, CT
         rto: Dynamic,
         cto: CTo,
         buf: VecStorage<N, Dynamic, CFrom>,
-    ) -> VecStorage<N, Dynamic, CTo>
+    ) -> VecStorage<N, Dynamic, CTo> {
-    {
         let new_buf = buf.resize(rto.value() * cto.value());
         VecStorage::new(rto, cto, new_buf)
     }
@@ -256,8 +249,7 @@ impl<N: Scalar, CFrom: Dim, RTo: DimName> Reallocator<N, Dynamic, CFrom, RTo, Dy
         rto: RTo,
         cto: Dynamic,
         buf: VecStorage<N, Dynamic, CFrom>,
-    ) -> VecStorage<N, RTo, Dynamic>
+    ) -> VecStorage<N, RTo, Dynamic> {
-    {
         let new_buf = buf.resize(rto.value() * cto.value());
         VecStorage::new(rto, cto, new_buf)
     }
@@ -272,8 +264,7 @@ impl<N: Scalar, RFrom: DimName, CTo: Dim> Reallocator<N, RFrom, Dynamic, Dynamic
         rto: Dynamic,
         cto: CTo,
         buf: VecStorage<N, RFrom, Dynamic>,
-    ) -> VecStorage<N, Dynamic, CTo>
+    ) -> VecStorage<N, Dynamic, CTo> {
-    {
         let new_buf = buf.resize(rto.value() * cto.value());
         VecStorage::new(rto, cto, new_buf)
     }
@@ -288,8 +279,7 @@ impl<N: Scalar, RFrom: DimName, RTo: DimName> Reallocator<N, RFrom, Dynamic, RTo
         rto: RTo,
         cto: Dynamic,
         buf: VecStorage<N, RFrom, Dynamic>,
-    ) -> VecStorage<N, RTo, Dynamic>
+    ) -> VecStorage<N, RTo, Dynamic> {
-    {
         let new_buf = buf.resize(rto.value() * cto.value());
         VecStorage::new(rto, cto, new_buf)
     }

src/base/dimension.rs

@@ -30,7 +30,9 @@ impl Dynamic {
 #[cfg(feature = "serde-serialize")]
 impl Serialize for Dynamic {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
-    where S: Serializer {
+    where
+        S: Serializer,
+    {
         self.value.serialize(serializer)
     }
 }
@@ -38,7 +40,9 @@ impl Serialize for Dynamic {
 #[cfg(feature = "serde-serialize")]
 impl<'de> Deserialize<'de> for Dynamic {
     fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
-    where D: Deserializer<'de> {
+    where
+        D: Deserializer<'de>,
+    {
         usize::deserialize(deserializer).map(|x| Dynamic { value: x })
     }
 }

src/base/edition.rs

@@ -22,7 +22,9 @@ impl<N: Scalar + Zero, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Extracts the upper triangular part of this matrix (including the diagonal).
     #[inline]
     pub fn upper_triangle(&self) -> MatrixMN<N, R, C>
-    where DefaultAllocator: Allocator<N, R, C> {
+    where
+        DefaultAllocator: Allocator<N, R, C>,
+    {
         let mut res = self.clone_owned();
         res.fill_lower_triangle(N::zero(), 1);
 
@@ -32,7 +34,9 @@ impl<N: Scalar + Zero, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Extracts the lower triangular part of this matrix (including the diagonal).
     #[inline]
     pub fn lower_triangle(&self) -> MatrixMN<N, R, C>
-    where DefaultAllocator: Allocator<N, R, C> {
+    where
+        DefaultAllocator: Allocator<N, R, C>,
+    {
         let mut res = self.clone_owned();
         res.fill_upper_triangle(N::zero(), 1);
 
@@ -64,7 +68,10 @@ impl<N: Scalar + Zero, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
             let src = self.column(j);
 
             for (destination, source) in irows.clone().enumerate() {
-                unsafe { *res.vget_unchecked_mut(destination) = src.vget_unchecked(*source).inlined_clone() }
+                unsafe {
+                    *res.vget_unchecked_mut(destination) =
+                        src.vget_unchecked(*source).inlined_clone()
+                }
             }
         }
 
@@ -104,7 +111,9 @@ impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
     /// Fills `self` with the identity matrix.
     #[inline]
     pub fn fill_with_identity(&mut self)
-    where N: Zero + One {
+    where
+        N: Zero + One,
+    {
         self.fill(N::zero());
         self.fill_diagonal(N::one());
     }
@@ -693,7 +702,9 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// rows and/or columns than `self`, then the extra rows or columns are filled with `val`.
     #[cfg(any(feature = "std", feature = "alloc"))]
     pub fn resize(self, new_nrows: usize, new_ncols: usize, val: N) -> DMatrix<N>
-    where DefaultAllocator: Reallocator<N, R, C, Dynamic, Dynamic> {
+    where
+        DefaultAllocator: Reallocator<N, R, C, Dynamic, Dynamic>,
+    {
         self.resize_generic(Dynamic::new(new_nrows), Dynamic::new(new_ncols), val)
     }
 
@@ -703,7 +714,9 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// rows than `self`, then the extra rows are filled with `val`.
     #[cfg(any(feature = "std", feature = "alloc"))]
     pub fn resize_vertically(self, new_nrows: usize, val: N) -> MatrixMN<N, Dynamic, C>
-    where DefaultAllocator: Reallocator<N, R, C, Dynamic, C> {
+    where
+        DefaultAllocator: Reallocator<N, R, C, Dynamic, C>,
+    {
         let ncols = self.data.shape().1;
         self.resize_generic(Dynamic::new(new_nrows), ncols, val)
     }
@@ -714,7 +727,9 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// columns than `self`, then the extra columns are filled with `val`.
     #[cfg(any(feature = "std", feature = "alloc"))]
     pub fn resize_horizontally(self, new_ncols: usize, val: N) -> MatrixMN<N, R, Dynamic>
-    where DefaultAllocator: Reallocator<N, R, C, R, Dynamic> {
+    where
+        DefaultAllocator: Reallocator<N, R, C, R, Dynamic>,
+    {
         let nrows = self.data.shape().0;
         self.resize_generic(nrows, Dynamic::new(new_ncols), val)
     }
@@ -724,7 +739,9 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// The values are copied such that `self[(i, j)] == result[(i, j)]`. If the result has more
     /// rows and/or columns than `self`, then the extra rows or columns are filled with `val`.
     pub fn fixed_resize<R2: DimName, C2: DimName>(self, val: N) -> MatrixMN<N, R2, C2>
-    where DefaultAllocator: Reallocator<N, R, C, R2, C2> {
+    where
+        DefaultAllocator: Reallocator<N, R, C, R2, C2>,
+    {
         self.resize_generic(R2::name(), C2::name(), val)
     }
 
@@ -805,7 +822,9 @@ impl<N: Scalar> DMatrix<N> {
     ///
     /// Defined only for owned fully-dynamic matrices, i.e., `DMatrix`.
     pub fn resize_mut(&mut self, new_nrows: usize, new_ncols: usize, val: N)
-    where DefaultAllocator: Reallocator<N, Dynamic, Dynamic, Dynamic, Dynamic> {
+    where
+        DefaultAllocator: Reallocator<N, Dynamic, Dynamic, Dynamic, Dynamic>,
+    {
         let placeholder = unsafe { Self::new_uninitialized(0, 0) };
         let old = mem::replace(self, placeholder);
         let new = old.resize(new_nrows, new_ncols, val);
@@ -815,7 +834,8 @@ impl<N: Scalar> DMatrix<N> {
 
 #[cfg(any(feature = "std", feature = "alloc"))]
 impl<N: Scalar, C: Dim> MatrixMN<N, Dynamic, C>
-where DefaultAllocator: Allocator<N, Dynamic, C>
+where
+    DefaultAllocator: Allocator<N, Dynamic, C>,
 {
     /// Changes the number of rows of this matrix in-place.
     ///
@@ -825,7 +845,9 @@ where DefaultAllocator: Allocator<N, Dynamic, C>
     /// Defined only for owned matrices with a dynamic number of rows (for example, `DVector`).
     #[cfg(any(feature = "std", feature = "alloc"))]
     pub fn resize_vertically_mut(&mut self, new_nrows: usize, val: N)
-    where DefaultAllocator: Reallocator<N, Dynamic, C, Dynamic, C> {
+    where
+        DefaultAllocator: Reallocator<N, Dynamic, C, Dynamic, C>,
+    {
         let placeholder =
             unsafe { Self::new_uninitialized_generic(Dynamic::new(0), self.data.shape().1) };
         let old = mem::replace(self, placeholder);
@@ -836,7 +858,8 @@ where DefaultAllocator: Allocator<N, Dynamic, C>
 
 #[cfg(any(feature = "std", feature = "alloc"))]
 impl<N: Scalar, R: Dim> MatrixMN<N, R, Dynamic>
-where DefaultAllocator: Allocator<N, R, Dynamic>
+where
+    DefaultAllocator: Allocator<N, R, Dynamic>,
 {
     /// Changes the number of column of this matrix in-place.
     ///
@@ -846,7 +869,9 @@ where DefaultAllocator: Allocator<N, R, Dynamic>
     /// Defined only for owned matrices with a dynamic number of columns (for example, `DVector`).
     #[cfg(any(feature = "std", feature = "alloc"))]
     pub fn resize_horizontally_mut(&mut self, new_ncols: usize, val: N)
-    where DefaultAllocator: Reallocator<N, R, Dynamic, R, Dynamic> {
+    where
+        DefaultAllocator: Reallocator<N, R, Dynamic, R, Dynamic>,
+    {
         let placeholder =
             unsafe { Self::new_uninitialized_generic(self.data.shape().0, Dynamic::new(0)) };
         let old = mem::replace(self, placeholder);
@@ -861,8 +886,7 @@ unsafe fn compress_rows<N: Scalar>(
     ncols: usize,
     i: usize,
     nremove: usize,
-)
+) {
-{
     let new_nrows = nrows - nremove;
 
     if new_nrows == 0 || ncols == 0 {
@@ -901,8 +925,7 @@ unsafe fn extend_rows<N: Scalar>(
     ncols: usize,
     i: usize,
     ninsert: usize,
-)
+) {
-{
     let new_nrows = nrows + ninsert;
 
     if new_nrows == 0 || ncols == 0 {

src/base/helper.rs

@@ -18,7 +18,9 @@ pub fn reject<G: Gen, F: FnMut(&T) -> bool, T: Arbitrary>(g: &mut G, f: F) -> T
 #[doc(hidden)]
 #[inline]
 pub fn reject_rand<G: Rng + ?Sized, F: FnMut(&T) -> bool, T>(g: &mut G, f: F) -> T
-where Standard: Distribution<T> {
+where
+    Standard: Distribution<T>,
+{
     use std::iter;
     iter::repeat(()).map(|_| g.gen()).find(f).unwrap()
 }

src/base/indexing.rs

@@ -1,13 +1,14 @@
 //! Indexing
 
-use crate::base::{Dim, DimName, DimDiff, DimSub, Dynamic, Matrix, MatrixSlice, MatrixSliceMut, Scalar, U1};
 use crate::base::storage::{Storage, StorageMut};
+use crate::base::{
+    Dim, DimDiff, DimName, DimSub, Dynamic, Matrix, MatrixSlice, MatrixSliceMut, Scalar, U1,
+};
 
 use std::ops;
 
 // N.B.: Not a public trait!
-trait DimRange<D: Dim>
+trait DimRange<D: Dim> {
-{
     /// The number of elements indexed by this range.
     type Length: Dim;
 
@@ -68,15 +69,27 @@ impl<D: Dim> DimRange<D> for ops::Range<usize> {
 
 #[test]
 fn dimrange_range_usize() {
-    use std::usize::MAX;
     use crate::base::dimension::U0;
+    use std::usize::MAX;
     assert_eq!(DimRange::contained_by(&(0..0), U0), false);
     assert_eq!(DimRange::contained_by(&(0..1), U0), false);
     assert_eq!(DimRange::contained_by(&(0..1), U1), true);
-    assert_eq!(DimRange::contained_by(&((MAX - 1)..MAX), Dynamic::new(MAX)), true);
+    assert_eq!(
-    assert_eq!(DimRange::length(&((MAX - 1)..MAX), Dynamic::new(MAX)), Dynamic::new(1));
+        DimRange::contained_by(&((MAX - 1)..MAX), Dynamic::new(MAX)),
-    assert_eq!(DimRange::length(&(MAX..(MAX - 1)), Dynamic::new(MAX)), Dynamic::new(0));
+        true
-    assert_eq!(DimRange::length(&(MAX..MAX), Dynamic::new(MAX)), Dynamic::new(0));
+    );
+    assert_eq!(
+        DimRange::length(&((MAX - 1)..MAX), Dynamic::new(MAX)),
+        Dynamic::new(1)
+    );
+    assert_eq!(
+        DimRange::length(&(MAX..(MAX - 1)), Dynamic::new(MAX)),
+        Dynamic::new(0)
+    );
+    assert_eq!(
+        DimRange::length(&(MAX..MAX), Dynamic::new(MAX)),
+        Dynamic::new(0)
+    );
 }
 
 impl<D: Dim> DimRange<D> for ops::RangeFrom<usize> {
@@ -100,18 +113,28 @@ impl<D: Dim> DimRange<D> for ops::RangeFrom<usize> {
 
 #[test]
 fn dimrange_rangefrom_usize() {
-    use std::usize::MAX;
     use crate::base::dimension::U0;
+    use std::usize::MAX;
     assert_eq!(DimRange::contained_by(&(0..), U0), false);
     assert_eq!(DimRange::contained_by(&(0..), U0), false);
     assert_eq!(DimRange::contained_by(&(0..), U1), true);
-    assert_eq!(DimRange::contained_by(&((MAX - 1)..), Dynamic::new(MAX)), true);
+    assert_eq!(
-    assert_eq!(DimRange::length(&((MAX - 1)..), Dynamic::new(MAX)), Dynamic::new(1));
+        DimRange::contained_by(&((MAX - 1)..), Dynamic::new(MAX)),
-    assert_eq!(DimRange::length(&(MAX..), Dynamic::new(MAX)), Dynamic::new(0));
+        true
+    );
+    assert_eq!(
+        DimRange::length(&((MAX - 1)..), Dynamic::new(MAX)),
+        Dynamic::new(1)
+    );
+    assert_eq!(
+        DimRange::length(&(MAX..), Dynamic::new(MAX)),
+        Dynamic::new(0)
+    );
 }
 
 impl<D: Dim, T: Dim> DimRange<D> for ops::RangeFrom<T>
-where D: DimSub<T>
+where
+    D: DimSub<T>,
 {
     type Length = DimDiff<D, T>;
 
@@ -133,7 +156,7 @@ where D: DimSub<T>
 
 #[test]
 fn dimrange_rangefrom_dimname() {
-    use crate::base::dimension::{U5, U4};
+    use crate::base::dimension::{U4, U5};
     assert_eq!(DimRange::length(&(U1..), U5), U4);
 }
 
@@ -173,8 +196,7 @@ impl<D: Dim> DimRange<D> for ops::RangeInclusive<usize> {
 
     #[inline(always)]
     fn length(&self, _: D) -> Self::Length {
-        Dynamic::new(
+        Dynamic::new(if self.end() < self.start() {
-            if self.end() < self.start() {
             0
         } else {
             self.end().wrapping_sub(self.start().wrapping_sub(1))
@@ -189,21 +211,38 @@ impl<D: Dim> DimRange<D> for ops::RangeInclusive<usize> {
 
 #[test]
 fn dimrange_rangeinclusive_usize() {
-    use std::usize::MAX;
     use crate::base::dimension::U0;
+    use std::usize::MAX;
     assert_eq!(DimRange::contained_by(&(0..=0), U0), false);
     assert_eq!(DimRange::contained_by(&(0..=0), U1), true);
-    assert_eq!(DimRange::contained_by(&(MAX..=MAX), Dynamic::new(MAX)), false);
+    assert_eq!(
-    assert_eq!(DimRange::contained_by(&((MAX-1)..=MAX), Dynamic::new(MAX)), false);
+        DimRange::contained_by(&(MAX..=MAX), Dynamic::new(MAX)),
-    assert_eq!(DimRange::contained_by(&((MAX-1)..=(MAX-1)), Dynamic::new(MAX)), true);
+        false
+    );
+    assert_eq!(
+        DimRange::contained_by(&((MAX - 1)..=MAX), Dynamic::new(MAX)),
+        false
+    );
+    assert_eq!(
+        DimRange::contained_by(&((MAX - 1)..=(MAX - 1)), Dynamic::new(MAX)),
+        true
+    );
     assert_eq!(DimRange::length(&(0..=0), U1), Dynamic::new(1));
-    assert_eq!(DimRange::length(&((MAX - 1)..=MAX), Dynamic::new(MAX)), Dynamic::new(2));
+    assert_eq!(
-    assert_eq!(DimRange::length(&(MAX..=(MAX - 1)), Dynamic::new(MAX)), Dynamic::new(0));
+        DimRange::length(&((MAX - 1)..=MAX), Dynamic::new(MAX)),
-    assert_eq!(DimRange::length(&(MAX..=MAX), Dynamic::new(MAX)), Dynamic::new(1));
+        Dynamic::new(2)
+    );
+    assert_eq!(
+        DimRange::length(&(MAX..=(MAX - 1)), Dynamic::new(MAX)),
+        Dynamic::new(0)
+    );
+    assert_eq!(
+        DimRange::length(&(MAX..=MAX), Dynamic::new(MAX)),
+        Dynamic::new(1)
+    );
 }
 
-impl<D: Dim> DimRange<D> for ops::RangeTo<usize>
+impl<D: Dim> DimRange<D> for ops::RangeTo<usize> {
-{
     type Length = Dynamic;
 
     #[inline(always)]
@@ -224,18 +263,26 @@ impl<D: Dim> DimRange<D> for ops::RangeTo<usize>
 
 #[test]
 fn dimrange_rangeto_usize() {
-    use std::usize::MAX;
     use crate::base::dimension::U0;
+    use std::usize::MAX;
     assert_eq!(DimRange::contained_by(&(..0), U0), true);
     assert_eq!(DimRange::contained_by(&(..1), U0), false);
     assert_eq!(DimRange::contained_by(&(..0), U1), true);
-    assert_eq!(DimRange::contained_by(&(..(MAX - 1)), Dynamic::new(MAX)), true);
+    assert_eq!(
-    assert_eq!(DimRange::length(&(..(MAX - 1)), Dynamic::new(MAX)), Dynamic::new(MAX - 1));
+        DimRange::contained_by(&(..(MAX - 1)), Dynamic::new(MAX)),
-    assert_eq!(DimRange::length(&(..MAX), Dynamic::new(MAX)), Dynamic::new(MAX));
+        true
+    );
+    assert_eq!(
+        DimRange::length(&(..(MAX - 1)), Dynamic::new(MAX)),
+        Dynamic::new(MAX - 1)
+    );
+    assert_eq!(
+        DimRange::length(&(..MAX), Dynamic::new(MAX)),
+        Dynamic::new(MAX)
+    );
 }
 
-impl<D: Dim> DimRange<D> for ops::RangeToInclusive<usize>
+impl<D: Dim> DimRange<D> for ops::RangeToInclusive<usize> {
-{
     type Length = Dynamic;
 
     #[inline(always)]
@@ -256,19 +303,27 @@ impl<D: Dim> DimRange<D> for ops::RangeToInclusive<usize>
 
 #[test]
 fn dimrange_rangetoinclusive_usize() {
-    use std::usize::MAX;
     use crate::base::dimension::U0;
+    use std::usize::MAX;
     assert_eq!(DimRange::contained_by(&(..=0), U0), false);
     assert_eq!(DimRange::contained_by(&(..=1), U0), false);
     assert_eq!(DimRange::contained_by(&(..=0), U1), true);
-    assert_eq!(DimRange::contained_by(&(..=(MAX)), Dynamic::new(MAX)), false);
+    assert_eq!(
-    assert_eq!(DimRange::contained_by(&(..=(MAX - 1)), Dynamic::new(MAX)), true);
+        DimRange::contained_by(&(..=(MAX)), Dynamic::new(MAX)),
-    assert_eq!(DimRange::length(&(..=(MAX - 1)), Dynamic::new(MAX)), Dynamic::new(MAX));
+        false
+    );
+    assert_eq!(
+        DimRange::contained_by(&(..=(MAX - 1)), Dynamic::new(MAX)),
+        true
+    );
+    assert_eq!(
+        DimRange::length(&(..=(MAX - 1)), Dynamic::new(MAX)),
+        Dynamic::new(MAX)
+    );
 }
 
 /// A helper trait used for indexing operations.
 pub trait MatrixIndex<'a, N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>>: Sized {
-
     /// The output type returned by methods.
     type Output: 'a;
 
@@ -303,7 +358,9 @@ pub trait MatrixIndex<'a, N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>>: Sized
 }
 
 /// A helper trait used for indexing operations.
-pub trait MatrixIndexMut<'a, N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>>: MatrixIndex<'a, N, R, C, S> {
+pub trait MatrixIndexMut<'a, N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>>:
+    MatrixIndex<'a, N, R, C, S>
+{
     /// The output type returned by methods.
     type OutputMut: 'a;
 
@@ -432,14 +489,13 @@ pub trait MatrixIndexMut<'a, N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>>:
 ///                         4, 7,
 ///                         5, 8)));
 /// ```
-impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
+impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
-{
     /// Produces a view of the data at the given index, or
     /// `None` if the index is out of bounds.
     #[inline]
     pub fn get<'a, I>(&'a self, index: I) -> Option<I::Output>
     where
-        I: MatrixIndex<'a, N, R, C, S>
+        I: MatrixIndex<'a, N, R, C, S>,
     {
         index.get(self)
     }
@@ -450,7 +506,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
     pub fn get_mut<'a, I>(&'a mut self, index: I) -> Option<I::OutputMut>
     where
         S: StorageMut<N, R, C>,
-        I: MatrixIndexMut<'a, N, R, C, S>
+        I: MatrixIndexMut<'a, N, R, C, S>,
     {
         index.get_mut(self)
     }
@@ -460,7 +516,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
     #[inline]
     pub fn index<'a, I>(&'a self, index: I) -> I::Output
     where
-        I: MatrixIndex<'a, N, R, C, S>
+        I: MatrixIndex<'a, N, R, C, S>,
     {
         index.index(self)
     }
@@ -471,7 +527,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
     pub fn index_mut<'a, I>(&'a mut self, index: I) -> I::OutputMut
     where
         S: StorageMut<N, R, C>,
-        I: MatrixIndexMut<'a, N, R, C, S>
+        I: MatrixIndexMut<'a, N, R, C, S>,
     {
         index.index_mut(self)
     }
@@ -481,7 +537,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
     #[inline]
     pub unsafe fn get_unchecked<'a, I>(&'a self, index: I) -> I::Output
     where
-        I: MatrixIndex<'a, N, R, C, S>
+        I: MatrixIndex<'a, N, R, C, S>,
     {
         index.get_unchecked(self)
     }
@@ -492,7 +548,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S>
     pub unsafe fn get_unchecked_mut<'a, I>(&'a mut self, index: I) -> I::OutputMut
     where
         S: StorageMut<N, R, C>,
-        I: MatrixIndexMut<'a, N, R, C, S>
+        I: MatrixIndexMut<'a, N, R, C, S>,
     {
         index.get_unchecked_mut(self)
     }
@@ -505,7 +561,7 @@ where
     N: Scalar,
     R: Dim,
     C: Dim,
-    S: Storage<N, R, C>
+    S: Storage<N, R, C>,
 {
     type Output = &'a N;
 
@@ -527,14 +583,15 @@ where
     N: Scalar,
     R: Dim,
     C: Dim,
-    S: StorageMut<N, R, C>
+    S: StorageMut<N, R, C>,
 {
     type OutputMut = &'a mut N;
 
     #[doc(hidden)]
     #[inline(always)]
     unsafe fn get_unchecked_mut(self, matrix: &'a mut Matrix<N, R, C, S>) -> Self::OutputMut
-    where S: StorageMut<N, R, C>,
+    where
+        S: StorageMut<N, R, C>,
     {
         matrix.data.get_unchecked_linear_mut(self)
     }
@@ -547,7 +604,7 @@ where
     N: Scalar,
     R: Dim,
     C: Dim,
-    S: Storage<N, R, C>
+    S: Storage<N, R, C>,
 {
     type Output = &'a N;
 
@@ -572,14 +629,15 @@ where
     N: Scalar,
     R: Dim,
     C: Dim,
-    S: StorageMut<N, R, C>
+    S: StorageMut<N, R, C>,
 {
     type OutputMut = &'a mut N;
 
     #[doc(hidden)]
     #[inline(always)]
     unsafe fn get_unchecked_mut(self, matrix: &'a mut Matrix<N, R, C, S>) -> Self::OutputMut
-    where S: StorageMut<N, R, C>,
+    where
+        S: StorageMut<N, R, C>,
     {
         let (row, col) = self;
         matrix.data.get_unchecked_mut(row, col)

src/base/iter.rs

@@ -5,7 +5,7 @@ use std::mem;
 
 use crate::base::dimension::{Dim, U1};
 use crate::base::storage::{Storage, StorageMut};
-use crate::base::{Scalar, Matrix, MatrixSlice, MatrixSliceMut};
+use crate::base::{Matrix, MatrixSlice, MatrixSliceMut, Scalar};
 
 macro_rules! iterator {
     (struct $Name:ident for $Storage:ident.$ptr: ident -> $Ptr:ty, $Ref:ty, $SRef: ty) => {
@@ -125,7 +125,6 @@ macro_rules! iterator {
 iterator!(struct MatrixIter for Storage.ptr -> *const N, &'a N, &'a S);
 iterator!(struct MatrixIterMut for StorageMut.ptr_mut -> *mut N, &'a mut N, &'a mut S);
 
-
 /*
  *
  * Row iterators.
@@ -135,17 +134,14 @@ iterator!(struct MatrixIterMut for StorageMut.ptr_mut -> *mut N, &'a mut N, &'a
 /// An iterator through the rows of a matrix.
 pub struct RowIter<'a, N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> {
     mat: &'a Matrix<N, R, C, S>,
-    curr: usize
+    curr: usize,
 }
 
 impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> RowIter<'a, N, R, C, S> {
     pub(crate) fn new(mat: &'a Matrix<N, R, C, S>) -> Self {
-        RowIter {
+        RowIter { mat, curr: 0 }
-            mat, curr: 0
     }
 }
-}
-
 
 impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> Iterator for RowIter<'a, N, R, C, S> {
     type Item = MatrixSlice<'a, N, U1, C, S::RStride, S::CStride>;
@@ -163,7 +159,10 @@ impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> Iterator for RowIt
 
     #[inline]
     fn size_hint(&self) -> (usize, Option<usize>) {
-        (self.mat.nrows() - self.curr, Some(self.mat.nrows() - self.curr))
+        (
+            self.mat.nrows() - self.curr,
+            Some(self.mat.nrows() - self.curr),
+        )
     }
 
     #[inline]
@@ -172,19 +171,20 @@ impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> Iterator for RowIt
     }
 }
 
-impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> ExactSizeIterator for RowIter<'a, N, R, C, S> {
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> ExactSizeIterator
+    for RowIter<'a, N, R, C, S>
+{
     #[inline]
     fn len(&self) -> usize {
         self.mat.nrows() - self.curr
     }
 }
 
-
 /// An iterator through the mutable rows of a matrix.
 pub struct RowIterMut<'a, N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> {
     mat: *mut Matrix<N, R, C, S>,
     curr: usize,
-    phantom: PhantomData<&'a mut Matrix<N, R, C, S>>
+    phantom: PhantomData<&'a mut Matrix<N, R, C, S>>,
 }
 
 impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> RowIterMut<'a, N, R, C, S> {
@@ -192,19 +192,18 @@ impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> RowIterMut<'a,
         RowIterMut {
             mat,
             curr: 0,
-            phantom: PhantomData
+            phantom: PhantomData,
         }
     }
 
     fn nrows(&self) -> usize {
-        unsafe {
+        unsafe { (*self.mat).nrows() }
-            (*self.mat).nrows()
-        }
     }
 }
 
-
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> Iterator
-impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> Iterator for RowIterMut<'a, N, R, C, S> {
+    for RowIterMut<'a, N, R, C, S>
+{
     type Item = MatrixSliceMut<'a, N, U1, C, S::RStride, S::CStride>;
 
     #[inline]
@@ -229,14 +228,15 @@ impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> Iterator for Ro
     }
 }
 
-impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> ExactSizeIterator for RowIterMut<'a, N, R, C, S> {
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> ExactSizeIterator
+    for RowIterMut<'a, N, R, C, S>
+{
     #[inline]
     fn len(&self) -> usize {
         self.nrows() - self.curr
     }
 }
 
-
 /*
  *
  * Column iterators.
@@ -246,19 +246,18 @@ impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> ExactSizeIterat
 /// An iterator through the columns of a matrix.
 pub struct ColumnIter<'a, N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> {
     mat: &'a Matrix<N, R, C, S>,
-    curr: usize
+    curr: usize,
 }
 
 impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> ColumnIter<'a, N, R, C, S> {
     pub(crate) fn new(mat: &'a Matrix<N, R, C, S>) -> Self {
-        ColumnIter {
+        ColumnIter { mat, curr: 0 }
-            mat, curr: 0
-        }
     }
 }
 
-
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> Iterator
-impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> Iterator for ColumnIter<'a, N, R, C, S> {
+    for ColumnIter<'a, N, R, C, S>
+{
     type Item = MatrixSlice<'a, N, R, U1, S::RStride, S::CStride>;
 
     #[inline]
@@ -274,7 +273,10 @@ impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> Iterator for Colum
 
     #[inline]
     fn size_hint(&self) -> (usize, Option<usize>) {
-        (self.mat.ncols() - self.curr, Some(self.mat.ncols() - self.curr))
+        (
+            self.mat.ncols() - self.curr,
+            Some(self.mat.ncols() - self.curr),
+        )
     }
 
     #[inline]
@@ -283,19 +285,20 @@ impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> Iterator for Colum
     }
 }
 
-impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> ExactSizeIterator for ColumnIter<'a, N, R, C, S> {
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> ExactSizeIterator
+    for ColumnIter<'a, N, R, C, S>
+{
     #[inline]
     fn len(&self) -> usize {
         self.mat.ncols() - self.curr
     }
 }
 
-
 /// An iterator through the mutable columns of a matrix.
 pub struct ColumnIterMut<'a, N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> {
     mat: *mut Matrix<N, R, C, S>,
     curr: usize,
-    phantom: PhantomData<&'a mut Matrix<N, R, C, S>>
+    phantom: PhantomData<&'a mut Matrix<N, R, C, S>>,
 }
 
 impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> ColumnIterMut<'a, N, R, C, S> {
@@ -303,19 +306,18 @@ impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> ColumnIterMut<'
         ColumnIterMut {
             mat,
             curr: 0,
-            phantom: PhantomData
+            phantom: PhantomData,
         }
     }
 
     fn ncols(&self) -> usize {
-        unsafe {
+        unsafe { (*self.mat).ncols() }
-            (*self.mat).ncols()
-        }
     }
 }
 
-
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> Iterator
-impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> Iterator for ColumnIterMut<'a, N, R, C, S> {
+    for ColumnIterMut<'a, N, R, C, S>
+{
     type Item = MatrixSliceMut<'a, N, R, U1, S::RStride, S::CStride>;
 
     #[inline]
@@ -340,10 +342,11 @@ impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> Iterator for Co
     }
 }
 
-impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> ExactSizeIterator for ColumnIterMut<'a, N, R, C, S> {
+impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> ExactSizeIterator
+    for ColumnIterMut<'a, N, R, C, S>
+{
     #[inline]
     fn len(&self) -> usize {
         self.ncols() - self.curr
     }
 }
-

src/base/matrix.rs

@@ -16,16 +16,20 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use alga::general::{ClosedAdd, ClosedMul, ClosedSub, RealField, Ring, ComplexField, Field};
+use simba::scalar::{ClosedAdd, ClosedMul, ClosedSub, Field, RealField};
+use simba::simd::SimdPartialOrd;
 
 use crate::base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
 use crate::base::constraint::{DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
 use crate::base::dimension::{Dim, DimAdd, DimSum, IsNotStaticOne, U1, U2, U3};
-use crate::base::iter::{MatrixIter, MatrixIterMut, RowIter, RowIterMut, ColumnIter, ColumnIterMut};
+use crate::base::iter::{
+    ColumnIter, ColumnIterMut, MatrixIter, MatrixIterMut, RowIter, RowIterMut,
+};
 use crate::base::storage::{
     ContiguousStorage, ContiguousStorageMut, Owned, SameShapeStorage, Storage, StorageMut,
 };
 use crate::base::{DefaultAllocator, MatrixMN, MatrixN, Scalar, Unit, VectorN};
+use crate::SimdComplexField;
 
 /// A square matrix.
 pub type SquareMatrix<N, D, S> = Matrix<N, D, D, S>;
@@ -99,7 +103,9 @@ where
     S: Serialize,
 {
     fn serialize<T>(&self, serializer: T) -> Result<T::Ok, T::Error>
-    where T: Serializer {
+    where
+        T: Serializer,
+    {
         self.data.serialize(serializer)
     }
 }
@@ -113,7 +119,9 @@ where
     S: Deserialize<'de>,
 {
     fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
-    where D: Deserializer<'de> {
+    where
+        D: Deserializer<'de>,
+    {
         S::deserialize(deserializer).map(|x| Matrix {
             data: x,
             _phantoms: PhantomData,
@@ -363,7 +371,9 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Moves this matrix into one that owns its data.
     #[inline]
     pub fn into_owned(self) -> MatrixMN<N, R, C>
-    where DefaultAllocator: Allocator<N, R, C> {
+    where
+        DefaultAllocator: Allocator<N, R, C>,
+    {
         Matrix::from_data(self.data.into_owned())
     }
 
@@ -397,7 +407,9 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Clones this matrix to one that owns its data.
     #[inline]
     pub fn clone_owned(&self) -> MatrixMN<N, R, C>
-    where DefaultAllocator: Allocator<N, R, C> {
+    where
+        DefaultAllocator: Allocator<N, R, C>,
+    {
         Matrix::from_data(self.data.clone_owned())
     }
 
@@ -433,7 +445,9 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Returns a matrix containing the result of `f` applied to each of its entries.
     #[inline]
     pub fn map<N2: Scalar, F: FnMut(N) -> N2>(&self, mut f: F) -> MatrixMN<N2, R, C>
-    where DefaultAllocator: Allocator<N2, R, C> {
+    where
+        DefaultAllocator: Allocator<N2, R, C>,
+    {
         let (nrows, ncols) = self.data.shape();
 
         let mut res = unsafe { MatrixMN::new_uninitialized_generic(nrows, ncols) };
@@ -450,6 +464,24 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
         res
     }
 
+    /// Similar to `self.iter().fold(init, f)` except that `init` is replaced by a closure.
+    ///
+    /// The initialization closure is given the first component of this matrix:
+    /// - If the matrix has no component (0 rows or 0 columns) then `init_f` is called with `None`
+    /// and its return value is the value returned by this method.
+    /// - If the matrix has has least one component, then `init_f` is called with the first component
+    /// to compute the initial value. Folding then continues on all the remaining components of the matrix.
+    #[inline]
+    pub fn fold_with<N2>(
+        &self,
+        init_f: impl FnOnce(Option<&N>) -> N2,
+        f: impl FnMut(N2, &N) -> N2,
+    ) -> N2 {
+        let mut it = self.iter();
+        let init = init_f(it.next());
+        it.fold(init, f)
+    }
+
     /// Returns a matrix containing the result of `f` applied to each of its entries. Unlike `map`,
     /// `f` also gets passed the row and column index, i.e. `f(row, col, value)`.
     #[inline]
@@ -572,13 +604,18 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 
     /// Folds a function `f` on each pairs of entries from `self` and `rhs`.
     #[inline]
-    pub fn zip_fold<N2, R2, C2, S2, Acc>(&self, rhs: &Matrix<N2, R2, C2, S2>, init: Acc, mut f: impl FnMut(Acc, N, N2) -> Acc) -> Acc
+    pub fn zip_fold<N2, R2, C2, S2, Acc>(
+        &self,
+        rhs: &Matrix<N2, R2, C2, S2>,
+        init: Acc,
+        mut f: impl FnMut(Acc, N, N2) -> Acc,
+    ) -> Acc
     where
         N2: Scalar,
         R2: Dim,
         C2: Dim,
         S2: Storage<N2, R2, C2>,
-            ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>
+        ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
     {
         let (nrows, ncols) = self.data.shape();
 
@@ -631,7 +668,9 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     #[inline]
     #[must_use = "Did you mean to use transpose_mut()?"]
     pub fn transpose(&self) -> MatrixMN<N, C, R>
-    where DefaultAllocator: Allocator<N, C, R> {
+    where
+        DefaultAllocator: Allocator<N, C, R>,
+    {
         let (nrows, ncols) = self.data.shape();
 
         unsafe {
@@ -737,7 +776,8 @@ impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
         for j in 0..ncols {
             for i in 0..nrows {
                 unsafe {
-                    *self.get_unchecked_mut((i, j)) = slice.get_unchecked(i + j * nrows).inlined_clone();
+                    *self.get_unchecked_mut((i, j)) =
+                        slice.get_unchecked(i + j * nrows).inlined_clone();
                 }
             }
         }
@@ -816,12 +856,17 @@ impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
     /// Replaces each component of `self` by the result of a closure `f` applied on its components
     /// joined with the components from `rhs`.
     #[inline]
-    pub fn zip_apply<N2, R2, C2, S2>(&mut self, rhs: &Matrix<N2, R2, C2, S2>, mut f: impl FnMut(N, N2) -> N)
+    pub fn zip_apply<N2, R2, C2, S2>(
-        where N2: Scalar,
+        &mut self,
+        rhs: &Matrix<N2, R2, C2, S2>,
+        mut f: impl FnMut(N, N2) -> N,
+    ) where
+        N2: Scalar,
         R2: Dim,
         C2: Dim,
         S2: Storage<N2, R2, C2>,
-              ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
+        ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
+    {
         let (nrows, ncols) = self.shape();
 
         assert!(
@@ -840,12 +885,16 @@ impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
         }
     }
 
-
     /// Replaces each component of `self` by the result of a closure `f` applied on its components
     /// joined with the components from `b` and `c`.
     #[inline]
-    pub fn zip_zip_apply<N2, R2, C2, S2, N3, R3, C3, S3>(&mut self, b: &Matrix<N2, R2, C2, S2>, c: &Matrix<N3, R3, C3, S3>, mut f: impl FnMut(N, N2, N3) -> N)
+    pub fn zip_zip_apply<N2, R2, C2, S2, N3, R3, C3, S3>(
-        where N2: Scalar,
+        &mut self,
+        b: &Matrix<N2, R2, C2, S2>,
+        c: &Matrix<N3, R3, C3, S3>,
+        mut f: impl FnMut(N, N2, N3) -> N,
+    ) where
+        N2: Scalar,
         R2: Dim,
         C2: Dim,
         S2: Storage<N2, R2, C2>,
@@ -854,7 +903,8 @@ impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
         C3: Dim,
         S3: Storage<N3, R3, C3>,
         ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
-              ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
+        ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
+    {
         let (nrows, ncols) = self.shape();
 
         assert!(
@@ -933,7 +983,7 @@ impl<N: Scalar, D: Dim, S: StorageMut<N, D, D>> Matrix<N, D, D, S> {
     }
 }
 
-impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+impl<N: SimdComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// Takes the adjoint (aka. conjugate-transpose) of `self` and store the result into `out`.
     #[inline]
     pub fn adjoint_to<R2, C2, SB>(&self, out: &mut Matrix<N, R2, C2, SB>)
@@ -953,7 +1003,7 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
         for i in 0..nrows {
             for j in 0..ncols {
                 unsafe {
-                    *out.get_unchecked_mut((j, i)) = self.get_unchecked((i, j)).conjugate();
+                    *out.get_unchecked_mut((j, i)) = self.get_unchecked((i, j)).simd_conjugate();
                 }
             }
         }
@@ -963,7 +1013,9 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     #[inline]
     #[must_use = "Did you mean to use adjoint_mut()?"]
     pub fn adjoint(&self) -> MatrixMN<N, C, R>
-    where DefaultAllocator: Allocator<N, C, R> {
+    where
+        DefaultAllocator: Allocator<N, C, R>,
+    {
         let (nrows, ncols) = self.data.shape();
 
         unsafe {
@@ -991,7 +1043,9 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     #[deprecated(note = "Renamed `self.adjoint()`.")]
     #[inline]
     pub fn conjugate_transpose(&self) -> MatrixMN<N, C, R>
-        where DefaultAllocator: Allocator<N, C, R> {
+    where
+        DefaultAllocator: Allocator<N, C, R>,
+    {
         self.adjoint()
     }
 
@@ -999,48 +1053,54 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     #[inline]
     #[must_use = "Did you mean to use conjugate_mut()?"]
     pub fn conjugate(&self) -> MatrixMN<N, R, C>
-        where DefaultAllocator: Allocator<N, R, C> {
+    where
-        self.map(|e| e.conjugate())
+        DefaultAllocator: Allocator<N, R, C>,
+    {
+        self.map(|e| e.simd_conjugate())
     }
 
     /// Divides each component of the complex matrix `self` by the given real.
     #[inline]
     #[must_use = "Did you mean to use unscale_mut()?"]
-    pub fn unscale(&self, real: N::RealField) -> MatrixMN<N, R, C>
+    pub fn unscale(&self, real: N::SimdRealField) -> MatrixMN<N, R, C>
-        where DefaultAllocator: Allocator<N, R, C> {
+    where
-        self.map(|e| e.unscale(real))
+        DefaultAllocator: Allocator<N, R, C>,
+    {
+        self.map(|e| e.simd_unscale(real))
     }
 
     /// Multiplies each component of the complex matrix `self` by the given real.
     #[inline]
     #[must_use = "Did you mean to use scale_mut()?"]
-    pub fn scale(&self, real: N::RealField) -> MatrixMN<N, R, C>
+    pub fn scale(&self, real: N::SimdRealField) -> MatrixMN<N, R, C>
-        where DefaultAllocator: Allocator<N, R, C> {
+    where
-        self.map(|e| e.scale(real))
+        DefaultAllocator: Allocator<N, R, C>,
+    {
+        self.map(|e| e.simd_scale(real))
     }
 }
 
-impl<N: ComplexField, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
+impl<N: SimdComplexField, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
     /// The conjugate of the complex matrix `self` computed in-place.
     #[inline]
     pub fn conjugate_mut(&mut self) {
-        self.apply(|e| e.conjugate())
+        self.apply(|e| e.simd_conjugate())
     }
 
     /// Divides each component of the complex matrix `self` by the given real.
     #[inline]
-    pub fn unscale_mut(&mut self, real: N::RealField) {
+    pub fn unscale_mut(&mut self, real: N::SimdRealField) {
-        self.apply(|e| e.unscale(real))
+        self.apply(|e| e.simd_unscale(real))
     }
 
     /// Multiplies each component of the complex matrix `self` by the given real.
     #[inline]
-    pub fn scale_mut(&mut self, real: N::RealField) {
+    pub fn scale_mut(&mut self, real: N::SimdRealField) {
-        self.apply(|e| e.scale(real))
+        self.apply(|e| e.simd_scale(real))
     }
 }
 
-impl<N: ComplexField, D: Dim, S: StorageMut<N, D, D>> Matrix<N, D, D, S> {
+impl<N: SimdComplexField, D: Dim, S: StorageMut<N, D, D>> Matrix<N, D, D, S> {
     /// Sets `self` to its adjoint.
     #[deprecated(note = "Renamed to `self.adjoint_mut()`.")]
     pub fn conjugate_transform_mut(&mut self) {
@@ -1061,8 +1121,8 @@ impl<N: ComplexField, D: Dim, S: StorageMut<N, D, D>> Matrix<N, D, D, S> {
                 unsafe {
                     let ref_ij = self.get_unchecked_mut((i, j)) as *mut N;
                     let ref_ji = self.get_unchecked_mut((j, i)) as *mut N;
-                    let conj_ij = (*ref_ij).conjugate();
+                    let conj_ij = (*ref_ij).simd_conjugate();
-                    let conj_ji = (*ref_ji).conjugate();
+                    let conj_ji = (*ref_ji).simd_conjugate();
                     *ref_ij = conj_ji;
                     *ref_ji = conj_ij;
                 }
@@ -1070,7 +1130,7 @@ impl<N: ComplexField, D: Dim, S: StorageMut<N, D, D>> Matrix<N, D, D, S> {
 
             {
                 let diag = unsafe { self.get_unchecked_mut((i, i)) };
-                *diag = diag.conjugate();
+                *diag = diag.simd_conjugate();
             }
         }
     }
@@ -1080,7 +1140,9 @@ impl<N: Scalar, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
     /// The diagonal of this matrix.
     #[inline]
     pub fn diagonal(&self) -> VectorN<N, D>
-        where DefaultAllocator: Allocator<N, D> {
+    where
+        DefaultAllocator: Allocator<N, D>,
+    {
         self.map_diagonal(|e| e)
     }
 
@@ -1089,7 +1151,9 @@ impl<N: Scalar, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
     /// This is a more efficient version of `self.diagonal().map(f)` since this
     /// allocates only once.
     pub fn map_diagonal<N2: Scalar>(&self, mut f: impl FnMut(N) -> N2) -> VectorN<N2, D>
-        where DefaultAllocator: Allocator<N2, D> {
+    where
+        DefaultAllocator: Allocator<N2, D>,
+    {
         assert!(
             self.is_square(),
             "Unable to get the diagonal of a non-square matrix."
@@ -1110,7 +1174,9 @@ 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."
@@ -1127,12 +1193,17 @@ impl<N: Scalar, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
     }
 }
 
-impl<N: ComplexField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
+impl<N: SimdComplexField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
     /// The symmetric part of `self`, i.e., `0.5 * (self + self.transpose())`.
     #[inline]
     pub fn symmetric_part(&self) -> MatrixMN<N, D, D>
-        where DefaultAllocator: Allocator<N, D, D> {
+    where
-        assert!(self.is_square(), "Cannot compute the symmetric part of a non-square matrix.");
+        DefaultAllocator: Allocator<N, D, D>,
+    {
+        assert!(
+            self.is_square(),
+            "Cannot compute the symmetric part of a non-square matrix."
+        );
         let mut tr = self.transpose();
         tr += self;
         tr *= crate::convert::<_, N>(0.5);
@@ -1142,8 +1213,13 @@ impl<N: ComplexField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
     /// The hermitian part of `self`, i.e., `0.5 * (self + self.adjoint())`.
     #[inline]
     pub fn hermitian_part(&self) -> MatrixMN<N, D, D>
-        where DefaultAllocator: Allocator<N, D, D> {
+    where
-        assert!(self.is_square(), "Cannot compute the hermitian part of a non-square matrix.");
+        DefaultAllocator: Allocator<N, D, D>,
+    {
+        assert!(
+            self.is_square(),
+            "Cannot compute the hermitian part of a non-square matrix."
+        );
 
         let mut tr = self.adjoint();
         tr += self;
@@ -1152,20 +1228,26 @@ impl<N: ComplexField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S> {
     }
 }
 
-impl<N: Scalar + Zero + One, D: DimAdd<U1> + IsNotStaticOne, S: Storage<N, D, D>> Matrix<N, D, D, S> {
+impl<N: Scalar + Zero + One, D: DimAdd<U1> + IsNotStaticOne, S: Storage<N, D, D>>
-
+    Matrix<N, D, D, S>
+{
     /// Yields the homogeneous matrix for this matrix, i.e., appending an additional dimension and
     /// and setting the diagonal element to `1`.
     #[inline]
     pub fn to_homogeneous(&self) -> MatrixN<N, DimSum<D, U1>>
-    where DefaultAllocator: Allocator<N, DimSum<D, U1>, DimSum<D, U1>> {
+    where
-        assert!(self.is_square(), "Only square matrices can currently be transformed to homogeneous coordinates.");
+        DefaultAllocator: Allocator<N, DimSum<D, U1>, DimSum<D, U1>>,
+    {
+        assert!(
+            self.is_square(),
+            "Only square matrices can currently be transformed to homogeneous coordinates."
+        );
         let dim = DimSum::<D, U1>::from_usize(self.nrows() + 1);
         let mut res = MatrixN::identity_generic(dim, dim);
-        res.generic_slice_mut::<D, D>((0, 0), self.data.shape()).copy_from(&self);
+        res.generic_slice_mut::<D, D>((0, 0), self.data.shape())
+            .copy_from(&self);
         res
     }
-
 }
 
 impl<N: Scalar + Zero, D: DimAdd<U1>, S: Storage<N, D>> Vector<N, D, S> {
@@ -1173,7 +1255,9 @@ impl<N: Scalar + Zero, D: DimAdd<U1>, S: Storage<N, D>> Vector<N, D, S> {
     /// coordinates.
     #[inline]
     pub fn to_homogeneous(&self) -> VectorN<N, DimSum<D, U1>>
-    where DefaultAllocator: Allocator<N, DimSum<D, U1>> {
+    where
+        DefaultAllocator: Allocator<N, DimSum<D, U1>>,
+    {
         self.push(N::zero())
     }
 
@@ -1198,7 +1282,9 @@ impl<N: Scalar + Zero, D: DimAdd<U1>, S: Storage<N, D>> Vector<N, D, S> {
     /// Constructs a new vector of higher dimension by appending `element` to the end of `self`.
     #[inline]
     pub fn push(&self, element: N) -> VectorN<N, DimSum<D, U1>>
-    where DefaultAllocator: Allocator<N, DimSum<D, U1>> {
+    where
+        DefaultAllocator: Allocator<N, DimSum<D, U1>>,
+    {
         let len = self.len();
         let hnrows = DimSum::<D, U1>::from_usize(len + 1);
         let mut res = unsafe { VectorN::<N, _>::new_uninitialized_generic(hnrows, U1) };
@@ -1248,8 +1334,7 @@ where
         other: &Self,
         epsilon: Self::Epsilon,
         max_relative: Self::Epsilon,
-    ) -> bool
+    ) -> bool {
-    {
         self.relative_eq(other, epsilon, max_relative)
     }
 }
@@ -1366,7 +1451,8 @@ impl<N, R: Dim, C: Dim, S> Eq for Matrix<N, R, C, S>
 where
     N: Scalar + Eq,
     S: Storage<N, R, C>,
-{}
+{
+}
 
 impl<N, R, R2, C, C2, S, S2> PartialEq<Matrix<N, R2, C2, S2>> for Matrix<N, R, C, S>
 where
@@ -1376,7 +1462,7 @@ where
     R: Dim,
     R2: Dim,
     S: Storage<N, R, C>,
-    S2: Storage<N, R2, C2>
+    S2: Storage<N, R2, C2>,
 {
     #[inline]
     fn eq(&self, right: &Matrix<N, R2, C2, S2>) -> bool {
@@ -1396,7 +1482,9 @@ macro_rules! impl_fmt {
                 #[cfg(feature = "std")]
                 fn val_width<N: Scalar + $trait>(val: &N, f: &mut fmt::Formatter) -> usize {
                     match f.precision() {
-                        Some(precision) => format!($fmt_str_with_precision, val, precision).chars().count(),
+                        Some(precision) => format!($fmt_str_with_precision, val, precision)
+                            .chars()
+                            .count(),
                         None => format!($fmt_str_without_precision, val).chars().count(),
                     }
                 }
@@ -1440,7 +1528,9 @@ macro_rules! impl_fmt {
                         let pad = max_length_with_space - number_length;
                         write!(f, " {:>thepad$}", "", thepad = pad)?;
                         match f.precision() {
-                            Some(precision) => write!(f, $fmt_str_with_precision, (*self)[(i, j)], precision)?,
+                            Some(precision) => {
+                                write!(f, $fmt_str_with_precision, (*self)[(i, j)], precision)?
+                            }
                             None => write!(f, $fmt_str_without_precision, (*self)[(i, j)])?,
                         }
                     }
@@ -1470,16 +1560,21 @@ impl_fmt!(fmt::Pointer, "{:p}", "{:.1$p}");
 #[test]
 fn lower_exp() {
     let test = crate::Matrix2::new(1e6, 2e5, 2e-5, 1.);
-    assert_eq!(format!("{:e}", test), r"
+    assert_eq!(
+        format!("{:e}", test),
+        r"
   ┌           ┐
   │  1e6  2e5 │
   │ 2e-5  1e0 │
   └           ┘
 
-")
+"
+    )
 }
 
-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
@@ -1496,7 +1591,8 @@ impl<N: Scalar + Ring, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 
         unsafe {
             self.get_unchecked((0, 0)).inlined_clone() * b.get_unchecked((1, 0)).inlined_clone()
-                - self.get_unchecked((1, 0)).inlined_clone() * b.get_unchecked((0, 0)).inlined_clone()
+                - self.get_unchecked((1, 0)).inlined_clone()
+                    * b.get_unchecked((0, 0)).inlined_clone()
         }
     }
 
@@ -1539,9 +1635,12 @@ impl<N: Scalar + Ring, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
                 let by = b.get_unchecked((1, 0));
                 let bz = b.get_unchecked((2, 0));
 
-                *res.get_unchecked_mut((0, 0)) = ay.inlined_clone() * bz.inlined_clone() - az.inlined_clone() * by.inlined_clone();
+                *res.get_unchecked_mut((0, 0)) = ay.inlined_clone() * bz.inlined_clone()
-                *res.get_unchecked_mut((1, 0)) = az.inlined_clone() * bx.inlined_clone() - ax.inlined_clone() * bz.inlined_clone();
+                    - az.inlined_clone() * by.inlined_clone();
-                *res.get_unchecked_mut((2, 0)) = ax.inlined_clone() * by.inlined_clone() - ay.inlined_clone() * bx.inlined_clone();
+                *res.get_unchecked_mut((1, 0)) = az.inlined_clone() * bx.inlined_clone()
+                    - ax.inlined_clone() * bz.inlined_clone();
+                *res.get_unchecked_mut((2, 0)) = ax.inlined_clone() * by.inlined_clone()
+                    - ay.inlined_clone() * bx.inlined_clone();
 
                 res
             }
@@ -1560,9 +1659,12 @@ impl<N: Scalar + Ring, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
                 let by = b.get_unchecked((0, 1));
                 let bz = b.get_unchecked((0, 2));
 
-                *res.get_unchecked_mut((0, 0)) = ay.inlined_clone() * bz.inlined_clone() - az.inlined_clone() * by.inlined_clone();
+                *res.get_unchecked_mut((0, 0)) = ay.inlined_clone() * bz.inlined_clone()
-                *res.get_unchecked_mut((0, 1)) = az.inlined_clone() * bx.inlined_clone() - ax.inlined_clone() * bz.inlined_clone();
+                    - az.inlined_clone() * by.inlined_clone();
-                *res.get_unchecked_mut((0, 2)) = ax.inlined_clone() * by.inlined_clone() - ay.inlined_clone() * bx.inlined_clone();
+                *res.get_unchecked_mut((0, 1)) = az.inlined_clone() * bx.inlined_clone()
+                    - ax.inlined_clone() * bz.inlined_clone();
+                *res.get_unchecked_mut((0, 2)) = ax.inlined_clone() * by.inlined_clone()
+                    - ay.inlined_clone() * bx.inlined_clone();
 
                 res
             }
@@ -1571,7 +1673,8 @@ impl<N: Scalar + Ring, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 }
 
 impl<N: Scalar + Field, S: Storage<N, U3>> Vector<N, U3, S>
-where DefaultAllocator: Allocator<N, U3>
+where
+    DefaultAllocator: Allocator<N, U3>,
 {
     /// Computes the matrix `M` such that for all vector `v` we have `M * v == self.cross(&v)`.
     #[inline]
@@ -1590,10 +1693,10 @@ where DefaultAllocator: Allocator<N, U3>
     }
 }
 
-impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
+impl<N: SimdComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// The smallest angle between two vectors.
     #[inline]
-    pub fn angle<R2: Dim, C2: Dim, SB>(&self, other: &Matrix<N, R2, C2, SB>) -> N::RealField
+    pub fn angle<R2: Dim, C2: Dim, SB>(&self, other: &Matrix<N, R2, C2, SB>) -> N::SimdRealField
     where
         SB: Storage<N, R2, C2>,
         ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,
@@ -1603,17 +1706,11 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
         let n2 = other.norm();
 
         if n1.is_zero() || n2.is_zero() {
-            N::RealField::zero()
+            N::SimdRealField::zero()
         } else {
-            let cang = prod.real() / (n1 * n2);
+            let cang = prod.simd_real() / (n1 * n2);
-
+            cang.simd_clamp(-N::SimdRealField::one(), N::SimdRealField::one())
-            if cang > N::RealField::one() {
+                .simd_acos()
-                N::RealField::zero()
-            } else if cang < -N::RealField::one() {
-                N::RealField::pi()
-            } else {
-                cang.acos()
-            }
         }
     }
 }
@@ -1634,7 +1731,9 @@ impl<N: Scalar + Zero + One + ClosedAdd + ClosedSub + ClosedMul, D: Dim, S: Stor
     /// assert_eq!(x.lerp(&y, 0.1), Vector3::new(1.9, 3.8, 5.7));
     /// ```
     pub fn lerp<S2: Storage<N, D>>(&self, rhs: &Vector<N, D, S2>, t: N) -> VectorN<N, D>
-    where DefaultAllocator: Allocator<N, D> {
+    where
+        DefaultAllocator: Allocator<N, D>,
+    {
         let mut res = self.clone_owned();
         res.axpy(t.inlined_clone(), rhs, N::one() - t);
         res
@@ -1742,8 +1841,7 @@ where
         other: &Self,
         epsilon: Self::Epsilon,
         max_relative: Self::Epsilon,
-    ) -> bool
+    ) -> bool {
-    {
         self.as_ref()
             .relative_eq(other.as_ref(), epsilon, max_relative)
     }

src/base/matrix_alga.rs

@@ -6,8 +6,8 @@ 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,
+    ClosedNeg, ComplexField, Field, Identity, JoinSemilattice, Lattice, MeetSemilattice, Module,
-    Multiplicative, RingCommutative, ComplexField
+    Multiplicative, RingCommutative, TwoSidedInverse,
 };
 use alga::linear::{
     FiniteDimInnerSpace, FiniteDimVectorSpace, InnerSpace, NormedSpace, VectorSpace,
@@ -146,19 +146,25 @@ where
     }
 }
 
-impl<N: ComplexField, R: DimName, C: DimName> NormedSpace for MatrixMN<N, R, C>
+impl<
-where DefaultAllocator: Allocator<N, R, C>
+        N: ComplexField + simba::scalar::ComplexField<RealField = <N as ComplexField>::RealField>,
+        R: DimName,
+        C: DimName,
+    > NormedSpace for MatrixMN<N, R, C>
+where
+    <N as ComplexField>::RealField: simba::scalar::RealField,
+    DefaultAllocator: Allocator<N, R, C>,
 {
-    type RealField = N::RealField;
+    type RealField = <N as ComplexField>::RealField;
     type ComplexField = N;
 
     #[inline]
-    fn norm_squared(&self) -> N::RealField {
+    fn norm_squared(&self) -> <N as ComplexField>::RealField {
         self.norm_squared()
     }
 
     #[inline]
-    fn norm(&self) -> N::RealField {
+    fn norm(&self) -> <N as ComplexField>::RealField {
         self.norm()
     }
 
@@ -169,27 +175,36 @@ where DefaultAllocator: Allocator<N, R, C>
     }
 
     #[inline]
-    fn normalize_mut(&mut self) -> N::RealField {
+    fn normalize_mut(&mut self) -> <N as ComplexField>::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> {
+    fn try_normalize(&self, min_norm: <N as ComplexField>::RealField) -> Option<Self> {
         self.try_normalize(min_norm)
     }
 
     #[inline]
-    fn try_normalize_mut(&mut self, min_norm: N::RealField) -> Option<N::RealField> {
+    fn try_normalize_mut(
+        &mut self,
+        min_norm: <N as ComplexField>::RealField,
+    ) -> Option<<N as ComplexField>::RealField> {
         self.try_normalize_mut(min_norm)
     }
 }
 
-impl<N: ComplexField, R: DimName, C: DimName> InnerSpace for MatrixMN<N, R, C>
+impl<
-where DefaultAllocator: Allocator<N, R, C>
+        N: ComplexField + simba::scalar::ComplexField<RealField = <N as ComplexField>::RealField>,
+        R: DimName,
+        C: DimName,
+    > InnerSpace for MatrixMN<N, R, C>
+where
+    <N as ComplexField>::RealField: simba::scalar::RealField,
+    DefaultAllocator: Allocator<N, R, C>,
 {
     #[inline]
-    fn angle(&self, other: &Self) -> N::RealField {
+    fn angle(&self, other: &Self) -> <N as ComplexField>::RealField {
         self.angle(other)
     }
 
@@ -203,8 +218,14 @@ where DefaultAllocator: Allocator<N, R, C>
 // 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>
+impl<
-where DefaultAllocator: Allocator<N, R, C>
+        N: ComplexField + simba::scalar::ComplexField<RealField = <N as ComplexField>::RealField>,
+        R: DimName,
+        C: DimName,
+    > FiniteDimInnerSpace for MatrixMN<N, R, C>
+where
+    <N as ComplexField>::RealField: simba::scalar::RealField,
+    DefaultAllocator: Allocator<N, R, C>,
 {
     #[inline]
     fn orthonormalize(vs: &mut [Self]) -> usize {
@@ -219,7 +240,10 @@ where DefaultAllocator: Allocator<N, R, C>
                 }
             }
 
-            if vs[i].try_normalize_mut(N::RealField::zero()).is_some() {
+            if vs[i]
+                .try_normalize_mut(<N as ComplexField>::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);
@@ -237,7 +261,9 @@ where DefaultAllocator: Allocator<N, R, C>
 
     #[inline]
     fn orthonormal_subspace_basis<F>(vs: &[Self], mut f: F)
-    where F: FnMut(&Self) -> bool {
+    where
+        F: FnMut(&Self) -> bool,
+    {
         // FIXME: is this necessary?
         assert!(
             vs.len() <= Self::dimension(),
@@ -272,7 +298,7 @@ where DefaultAllocator: Allocator<N, R, C>
                     let v = &vs[0];
                     let mut a;
 
-                    if v[0].norm1() > v[1].norm1() {
+                    if ComplexField::norm1(v[0]) > ComplexField::norm1(v[1]) {
                         a = Self::from_column_slice(&[v[2], N::zero(), -v[0]]);
                     } else {
                         a = Self::from_column_slice(&[N::zero(), -v[2], v[1]]);
@@ -304,7 +330,9 @@ where DefaultAllocator: Allocator<N, R, C>
                             elt -= v * elt.dot(v)
                         }
 
-                        if let Some(subsp_elt) = elt.try_normalize(N::RealField::zero()) {
+                        if let Some(subsp_elt) =
+                            elt.try_normalize(<N as ComplexField>::RealField::zero())
+                        {
                             if !f(&subsp_elt) {
                                 return;
                             };

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/matrix_slice.rs

@@ -4,9 +4,9 @@ use std::slice;
 
 use crate::base::allocator::Allocator;
 use crate::base::default_allocator::DefaultAllocator;
-use crate::base::dimension::{Dim, DimName, Dynamic, U1, IsNotStaticOne};
+use crate::base::dimension::{Dim, DimName, Dynamic, IsNotStaticOne, U1};
 use crate::base::iter::MatrixIter;
-use crate::base::storage::{Owned, Storage, StorageMut, ContiguousStorage, ContiguousStorageMut};
+use crate::base::storage::{ContiguousStorage, ContiguousStorageMut, Owned, Storage, StorageMut};
 use crate::base::{Matrix, Scalar};
 
 macro_rules! slice_storage_impl(
@@ -198,13 +198,31 @@ unsafe impl<'a, N: Scalar, R: Dim, C: Dim, RStride: Dim, CStride: Dim> StorageMu
     }
 }
 
-unsafe impl<'a, N: Scalar, R: Dim, CStride: Dim> ContiguousStorage<N, R, U1> for SliceStorage<'a, N, R, U1, U1, CStride> { }
+unsafe impl<'a, N: Scalar, R: Dim, CStride: Dim> ContiguousStorage<N, R, U1>
-unsafe impl<'a, N: Scalar, R: Dim, CStride: Dim> ContiguousStorage<N, R, U1> for SliceStorageMut<'a, N, R, U1, U1, CStride> { }
+    for SliceStorage<'a, N, R, U1, U1, CStride>
-unsafe impl<'a, N: Scalar, R: Dim, CStride: Dim> ContiguousStorageMut<N, R, U1> for SliceStorageMut<'a, N, R, U1, U1, CStride> { }
+{
+}
+unsafe impl<'a, N: Scalar, R: Dim, CStride: Dim> ContiguousStorage<N, R, U1>
+    for SliceStorageMut<'a, N, R, U1, U1, CStride>
+{
+}
+unsafe impl<'a, N: Scalar, R: Dim, CStride: Dim> ContiguousStorageMut<N, R, U1>
+    for SliceStorageMut<'a, N, R, U1, U1, CStride>
+{
+}
 
-unsafe impl<'a, N: Scalar, R: DimName, C: Dim + IsNotStaticOne> ContiguousStorage<N, R, C> for SliceStorage<'a, N, R, C, U1, R> { }
+unsafe impl<'a, N: Scalar, R: DimName, C: Dim + IsNotStaticOne> ContiguousStorage<N, R, C>
-unsafe impl<'a, N: Scalar, R: DimName, C: Dim + IsNotStaticOne> ContiguousStorage<N, R, C> for SliceStorageMut<'a, N, R, C, U1, R> { }
+    for SliceStorage<'a, N, R, C, U1, R>
-unsafe impl<'a, N: Scalar, R: DimName, C: Dim + IsNotStaticOne> ContiguousStorageMut<N, R, C> for SliceStorageMut<'a, N, R, C, U1, R> { }
+{
+}
+unsafe impl<'a, N: Scalar, R: DimName, C: Dim + IsNotStaticOne> ContiguousStorage<N, R, C>
+    for SliceStorageMut<'a, N, R, C, U1, R>
+{
+}
+unsafe impl<'a, N: Scalar, R: DimName, C: Dim + IsNotStaticOne> ContiguousStorageMut<N, R, C>
+    for SliceStorageMut<'a, N, R, C, U1, R>
+{
+}
 
 impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     #[inline]
@@ -213,8 +231,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
         start: (usize, usize),
         shape: (usize, usize),
         steps: (usize, usize),
-    )
+    ) {
-    {
         let my_shape = self.shape();
         // NOTE: we don't do any subtraction to avoid underflow for zero-sized matrices.
         //
@@ -811,8 +828,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     pub fn rows_range<RowRange: SliceRange<R>>(
         &self,
         rows: RowRange,
-    ) -> MatrixSlice<N, RowRange::Size, C, S::RStride, S::CStride>
+    ) -> MatrixSlice<N, RowRange::Size, C, S::RStride, S::CStride> {
-    {
         self.slice_range(rows, ..)
     }
 
@@ -821,8 +837,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     pub fn columns_range<ColRange: SliceRange<C>>(
         &self,
         cols: ColRange,
-    ) -> MatrixSlice<N, R, ColRange::Size, S::RStride, S::CStride>
+    ) -> MatrixSlice<N, R, ColRange::Size, S::RStride, S::CStride> {
-    {
         self.slice_range(.., cols)
     }
 }
@@ -851,8 +866,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
     pub fn rows_range_mut<RowRange: SliceRange<R>>(
         &mut self,
         rows: RowRange,
-    ) -> MatrixSliceMut<N, RowRange::Size, C, S::RStride, S::CStride>
+    ) -> MatrixSliceMut<N, RowRange::Size, C, S::RStride, S::CStride> {
-    {
         self.slice_range_mut(rows, ..)
     }
 
@@ -861,13 +875,11 @@ impl<N: Scalar, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
     pub fn columns_range_mut<ColRange: SliceRange<C>>(
         &mut self,
         cols: ColRange,
-    ) -> MatrixSliceMut<N, R, ColRange::Size, S::RStride, S::CStride>
+    ) -> MatrixSliceMut<N, R, ColRange::Size, S::RStride, S::CStride> {
-    {
         self.slice_range_mut(.., cols)
     }
 }
 
-
 impl<'a, N, R, C, RStride, CStride> From<MatrixSliceMut<'a, N, R, C, RStride, CStride>>
     for MatrixSlice<'a, N, R, C, RStride, CStride>
 where

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 +21,26 @@ mod conversion;
 mod edition;
 pub mod indexing;
 mod matrix;
+#[cfg(feature = "alga")]
 mod matrix_alga;
-mod array_storage;
+mod matrix_simba;
 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

@@ -1,24 +1,41 @@
+#[cfg(all(feature = "alloc", not(feature = "std")))]
+use alloc::vec::Vec;
+
 use num::Zero;
+use std::ops::Neg;
 
 use crate::allocator::Allocator;
-use crate::{RealField, ComplexField};
+use crate::base::{DefaultAllocator, Dim, DimName, Matrix, MatrixMN, Normed, VectorN};
+use crate::constraint::{SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
 use crate::storage::{Storage, StorageMut};
-use crate::base::{DefaultAllocator, Matrix, Dim, MatrixMN};
+use crate::{ComplexField, Scalar, SimdComplexField, Unit};
-use crate::constraint::{SameNumberOfRows, SameNumberOfColumns, ShapeConstraint};
+use simba::scalar::ClosedNeg;
-
+use simba::simd::{SimdOption, SimdPartialOrd};
 
 // FIXME: this should be be a trait on alga?
 /// A trait for abstract matrix norms.
 ///
 /// This may be moved to the alga crate in the future.
-pub trait Norm<N: ComplexField> {
+pub trait Norm<N: SimdComplexField> {
     /// Apply this norm to the given matrix.
-    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::RealField
+    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::SimdRealField
-        where R: Dim, C: Dim, S: Storage<N, R, C>;
+    where
+        R: Dim,
+        C: Dim,
+        S: Storage<N, R, C>;
     /// Use the metric induced by this norm to compute the metric distance between the two given matrices.
-    fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N::RealField
+    fn metric_distance<R1, C1, S1, R2, C2, S2>(
-        where R1: Dim, C1: Dim, S1: Storage<N, R1, C1>,
+        &self,
-              R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
+        m1: &Matrix<N, R1, C1, S1>,
+        m2: &Matrix<N, R2, C2, S2>,
+    ) -> N::SimdRealField
+    where
+        R1: Dim,
+        C1: Dim,
+        S1: Storage<N, R1, C1>,
+        R2: Dim,
+        C2: Dim,
+        S2: Storage<N, R2, C2>,
         ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>;
 }
 
@@ -29,81 +46,123 @@ pub struct LpNorm(pub i32);
 /// L-infinite norm aka. Chebytchev norm aka. uniform norm aka. suppremum norm.
 pub struct UniformNorm;
 
-impl<N: ComplexField> Norm<N> for EuclideanNorm {
+impl<N: SimdComplexField> Norm<N> for EuclideanNorm {
     #[inline]
-    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::RealField
+    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::SimdRealField
-        where R: Dim, C: Dim, S: Storage<N, R, C> {
+    where
-        m.norm_squared().sqrt()
+        R: Dim,
+        C: Dim,
+        S: Storage<N, R, C>,
+    {
+        m.norm_squared().simd_sqrt()
     }
 
     #[inline]
-    fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N::RealField
+    fn metric_distance<R1, C1, S1, R2, C2, S2>(
-        where R1: Dim, C1: Dim, S1: Storage<N, R1, C1>,
+        &self,
-              R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
+        m1: &Matrix<N, R1, C1, S1>,
-              ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
+        m2: &Matrix<N, R2, C2, S2>,
-        m1.zip_fold(m2, N::RealField::zero(), |acc, a, b| {
+    ) -> N::SimdRealField
+    where
+        R1: Dim,
+        C1: Dim,
+        S1: Storage<N, R1, C1>,
+        R2: Dim,
+        C2: Dim,
+        S2: Storage<N, R2, C2>,
+        ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,
+    {
+        m1.zip_fold(m2, N::SimdRealField::zero(), |acc, a, b| {
             let diff = a - b;
-            acc + diff.modulus_squared()
+            acc + diff.simd_modulus_squared()
-        }).sqrt()
+        })
+        .simd_sqrt()
     }
 }
 
-impl<N: ComplexField> Norm<N> for LpNorm {
+impl<N: SimdComplexField> Norm<N> for LpNorm {
     #[inline]
-    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::RealField
+    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::SimdRealField
-        where R: Dim, C: Dim, S: Storage<N, R, C> {
+    where
-        m.fold(N::RealField::zero(), |a, b| {
+        R: Dim,
-            a + b.modulus().powi(self.0)
+        C: Dim,
-        }).powf(crate::convert(1.0 / (self.0 as f64)))
+        S: Storage<N, R, C>,
+    {
+        m.fold(N::SimdRealField::zero(), |a, b| {
+            a + b.simd_modulus().simd_powi(self.0)
+        })
+        .simd_powf(crate::convert(1.0 / (self.0 as f64)))
     }
 
     #[inline]
-    fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N::RealField
+    fn metric_distance<R1, C1, S1, R2, C2, S2>(
-        where R1: Dim, C1: Dim, S1: Storage<N, R1, C1>,
+        &self,
-              R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
+        m1: &Matrix<N, R1, C1, S1>,
-              ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
+        m2: &Matrix<N, R2, C2, S2>,
-        m1.zip_fold(m2, N::RealField::zero(), |acc, a, b| {
+    ) -> N::SimdRealField
+    where
+        R1: Dim,
+        C1: Dim,
+        S1: Storage<N, R1, C1>,
+        R2: Dim,
+        C2: Dim,
+        S2: Storage<N, R2, C2>,
+        ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,
+    {
+        m1.zip_fold(m2, N::SimdRealField::zero(), |acc, a, b| {
             let diff = a - b;
-            acc + diff.modulus().powi(self.0)
+            acc + diff.simd_modulus().simd_powi(self.0)
-        }).powf(crate::convert(1.0 / (self.0 as f64)))
+        })
+        .simd_powf(crate::convert(1.0 / (self.0 as f64)))
     }
 }
 
-impl<N: ComplexField> Norm<N> for UniformNorm {
+impl<N: SimdComplexField> Norm<N> for UniformNorm {
     #[inline]
-    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::RealField
+    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::SimdRealField
-        where R: Dim, C: Dim, S: Storage<N, R, C> {
+    where
+        R: Dim,
+        C: Dim,
+        S: Storage<N, R, C>,
+    {
         // NOTE: we don't use `m.amax()` here because for the complex
         // numbers this will return the max norm1 instead of the modulus.
-        m.fold(N::RealField::zero(), |acc, a| acc.max(a.modulus()))
+        m.fold(N::SimdRealField::zero(), |acc, a| {
+            acc.simd_max(a.simd_modulus())
+        })
     }
 
     #[inline]
-    fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N::RealField
+    fn metric_distance<R1, C1, S1, R2, C2, S2>(
-        where R1: Dim, C1: Dim, S1: Storage<N, R1, C1>,
+        &self,
-              R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
+        m1: &Matrix<N, R1, C1, S1>,
-              ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2> {
+        m2: &Matrix<N, R2, C2, S2>,
-        m1.zip_fold(m2, N::RealField::zero(), |acc, a, b| {
+    ) -> N::SimdRealField
-            let val = (a - b).modulus();
+    where
-            if val > acc {
+        R1: Dim,
-                val
+        C1: Dim,
-            } else {
+        S1: Storage<N, R1, C1>,
-                acc
+        R2: Dim,
-            }
+        C2: Dim,
+        S2: Storage<N, R2, C2>,
+        ShapeConstraint: SameNumberOfRows<R1, R2> + SameNumberOfColumns<C1, C2>,
+    {
+        m1.zip_fold(m2, N::SimdRealField::zero(), |acc, a, b| {
+            let val = (a - b).simd_modulus();
+            acc.simd_max(val)
         })
     }
 }
 
-
+impl<N: SimdComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
-impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// The squared L2 norm of this vector.
     #[inline]
-    pub fn norm_squared(&self) -> N::RealField {
+    pub fn norm_squared(&self) -> N::SimdRealField {
-        let mut res = N::RealField::zero();
+        let mut res = N::SimdRealField::zero();
 
         for i in 0..self.ncols() {
             let col = self.column(i);
-            res += col.dotc(&col).real()
+            res += col.dotc(&col).simd_real()
         }
 
         res
@@ -113,17 +172,21 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     ///
     /// Use `.apply_norm` to apply a custom norm.
     #[inline]
-    pub fn norm(&self) -> N::RealField {
+    pub fn norm(&self) -> N::SimdRealField {
-        self.norm_squared().sqrt()
+        self.norm_squared().simd_sqrt()
     }
 
     /// Compute the distance between `self` and `rhs` using the metric induced by the euclidean norm.
     ///
     /// Use `.apply_metric_distance` to apply a custom norm.
     #[inline]
-    pub fn metric_distance<R2, C2, S2>(&self, rhs: &Matrix<N, R2, C2, S2>) -> N::RealField
+    pub fn metric_distance<R2, C2, S2>(&self, rhs: &Matrix<N, R2, C2, S2>) -> N::SimdRealField
-        where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
+    where
-              ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
+        R2: Dim,
+        C2: Dim,
+        S2: Storage<N, R2, C2>,
+        ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
+    {
         self.apply_metric_distance(rhs, &EuclideanNorm)
     }
 
@@ -140,7 +203,7 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// assert_eq!(v.apply_norm(&EuclideanNorm), v.norm());
     /// ```
     #[inline]
-    pub fn apply_norm(&self, norm: &impl Norm<N>) -> N::RealField {
+    pub fn apply_norm(&self, norm: &impl Norm<N>) -> N::SimdRealField {
         norm.norm(self)
     }
 
@@ -159,9 +222,17 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// assert_eq!(v1.apply_metric_distance(&v2, &EuclideanNorm), (v1 - v2).norm());
     /// ```
     #[inline]
-    pub fn apply_metric_distance<R2, C2, S2>(&self, rhs: &Matrix<N, R2, C2, S2>, norm: &impl Norm<N>) -> N::RealField
+    pub fn apply_metric_distance<R2, C2, S2>(
-        where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
+        &self,
-              ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
+        rhs: &Matrix<N, R2, C2, S2>,
+        norm: &impl Norm<N>,
+    ) -> N::SimdRealField
+    where
+        R2: Dim,
+        C2: Dim,
+        S2: Storage<N, R2, C2>,
+        ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2>,
+    {
         norm.metric_distance(self, rhs)
     }
 
@@ -171,7 +242,7 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     ///
     /// This function is simply implemented as a call to `norm()`
     #[inline]
-    pub fn magnitude(&self) -> N::RealField {
+    pub fn magnitude(&self) -> N::SimdRealField {
         self.norm()
     }
 
@@ -181,18 +252,63 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     ///
     /// This function is simply implemented as a call to `norm_squared()`
     #[inline]
-    pub fn magnitude_squared(&self) -> N::RealField {
+    pub fn magnitude_squared(&self) -> N::SimdRealField {
         self.norm_squared()
     }
 
+    /// Sets the magnitude of this vector.
+    #[inline]
+    pub fn set_magnitude(&mut self, magnitude: N::SimdRealField)
+    where
+        S: StorageMut<N, R, C>,
+    {
+        let n = self.norm();
+        self.scale_mut(magnitude / n)
+    }
 
+    /// Returns a normalized version of this matrix.
+    #[inline]
+    #[must_use = "Did you mean to use normalize_mut()?"]
+    pub fn normalize(&self) -> MatrixMN<N, R, C>
+    where
+        DefaultAllocator: Allocator<N, R, C>,
+    {
+        self.unscale(self.norm())
+    }
+
+    /// The Lp norm of this matrix.
+    #[inline]
+    pub fn lp_norm(&self, p: i32) -> N::SimdRealField {
+        self.apply_norm(&LpNorm(p))
+    }
+
+    /// Attempts to normalize `self`.
+    ///
+    /// The components of this matrix can be SIMD types.
+    #[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> {
     /// Sets the magnitude of this vector unless it is smaller than `min_magnitude`.
     ///
     /// If `self.magnitude()` is smaller than `min_magnitude`, it will be left unchanged.
     /// Otherwise this is equivalent to: `*self = self.normalize() * magnitude.
     #[inline]
     pub fn try_set_magnitude(&mut self, magnitude: N::RealField, min_magnitude: N::RealField)
-        where S: StorageMut<N, R, C> {
+    where
+        S: StorageMut<N, R, C>,
+    {
         let n = self.norm();
 
         if n >= min_magnitude {
@@ -200,19 +316,15 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
         }
     }
 
-    /// Returns a normalized version of this matrix.
-    #[inline]
-    #[must_use = "Did you mean to use normalize_mut()?"]
-    pub fn normalize(&self) -> MatrixMN<N, R, C>
-        where DefaultAllocator: Allocator<N, R, C> {
-        self.unscale(self.norm())
-    }
-
     /// Returns a normalized version of this matrix unless its norm as smaller or equal to `eps`.
+    ///
+    /// The components of this matrix cannot be SIMD types (see `simd_try_normalize`) instead.
     #[inline]
     #[must_use = "Did you mean to use try_normalize_mut()?"]
     pub fn try_normalize(&self, min_norm: N::RealField) -> Option<MatrixMN<N, R, C>>
-        where DefaultAllocator: Allocator<N, R, C> {
+    where
+        DefaultAllocator: Allocator<N, R, C>,
+    {
         let n = self.norm();
 
         if n <= min_norm {
@@ -221,25 +333,41 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
             Some(self.unscale(n))
         }
     }
-
-    /// The Lp norm of this matrix.
-    #[inline]
-    pub fn lp_norm(&self, p: i32) -> N::RealField {
-        self.apply_norm(&LpNorm(p))
-    }
 }
 
-
+impl<N: SimdComplexField, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
-impl<N: ComplexField, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S> {
     /// Normalizes this matrix in-place and returns its norm.
+    ///
+    /// The components of the matrix cannot be SIMD types (see `simd_try_normalize_mut` instead).
     #[inline]
-    pub fn normalize_mut(&mut self) -> N::RealField {
+    pub fn normalize_mut(&mut self) -> N::SimdRealField {
         let n = self.norm();
         self.unscale_mut(n);
 
         n
     }
 
+    /// Normalizes this matrix in-place and return its norm.
+    ///
+    /// The components of the matrix can be SIMD types.
+    #[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> {
     /// Normalizes this matrix in-place or does nothing if its norm is smaller or equal to `eps`.
     ///
     /// If the normalization succeeded, returns the old norm of this matrix.
@@ -255,3 +383,189 @@ 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)
+    }
+}
+
+// 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, D: DimName> VectorN<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
+{
+    /// The i-the canonical basis element.
+    #[inline]
+    fn canonical_basis_element(i: usize) -> Self {
+        assert!(i < D::dim(), "Index out of bound.");
+
+        let mut res = Self::zero();
+        unsafe {
+            *res.data.get_unchecked_linear_mut(i) = N::one();
+        }
+
+        res
+    }
+
+    /// Orthonormalizes the given family of vectors. The largest free family of vectors is moved at
+    /// the beginning of the array and its size is returned. Vectors at an indices larger or equal to
+    /// this length can be modified to an arbitrary value.
+    #[inline]
+    pub 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 == D::dim() {
+                    break;
+                }
+            }
+        }
+
+        nbasis_elements
+    }
+
+    /// Applies the given closure to each element of the orthonormal basis of the subspace
+    /// orthogonal to free family of vectors `vs`. If `vs` is not a free family, the result is
+    /// unspecified.
+    // FIXME: return an iterator instead when `-> impl Iterator` will be supported by Rust.
+    #[inline]
+    pub fn orthonormal_subspace_basis<F>(vs: &[Self], mut f: F)
+    where
+        F: FnMut(&Self) -> bool,
+    {
+        // FIXME: is this necessary?
+        assert!(
+            vs.len() <= D::dim(),
+            "The given set of vectors has no chance of being a free family."
+        );
+
+        match D::dim() {
+            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..D::dim() - 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.")
+                }
+            }
+        }
+    }
+}

src/base/ops.rs

@@ -1,11 +1,11 @@
-use num::{One, Signed, Zero};
+use num::{One, Zero};
-use std::cmp::{PartialOrd, Ordering};
 use std::iter;
 use std::ops::{
     Add, AddAssign, Div, DivAssign, Index, IndexMut, Mul, MulAssign, Neg, Sub, SubAssign,
 };
 
-use alga::general::{ComplexField, ClosedAdd, ClosedDiv, ClosedMul, ClosedNeg, ClosedSub};
+use simba::scalar::{ClosedAdd, ClosedDiv, ClosedMul, ClosedNeg, ClosedSub};
+use simba::simd::{SimdPartialOrd, SimdSigned};
 
 use crate::base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
 use crate::base::constraint::{
@@ -14,6 +14,7 @@ use crate::base::constraint::{
 use crate::base::dimension::{Dim, DimMul, DimName, DimProd, Dynamic};
 use crate::base::storage::{ContiguousStorageMut, Storage, StorageMut};
 use crate::base::{DefaultAllocator, Matrix, MatrixMN, MatrixN, MatrixSum, Scalar, VectorSliceN};
+use crate::SimdComplexField;
 
 /*
  *
@@ -445,7 +446,9 @@ where
     /// # use nalgebra::DMatrix;
     /// iter::empty::<&DMatrix<f64>>().sum::<DMatrix<f64>>(); // panics!
     /// ```
-    fn sum<I: Iterator<Item = &'a MatrixMN<N, Dynamic, C>>>(mut iter: I) -> MatrixMN<N, Dynamic, C> {
+    fn sum<I: Iterator<Item = &'a MatrixMN<N, Dynamic, C>>>(
+        mut iter: I,
+    ) -> MatrixMN<N, Dynamic, C> {
         if let Some(first) = iter.next() {
             iter.fold(first.clone(), |acc, x| acc + x)
         } else {
@@ -693,7 +696,7 @@ where
     #[inline]
     pub fn ad_mul<R2: Dim, C2: Dim, SB>(&self, rhs: &Matrix<N, R2, C2, SB>) -> MatrixMN<N, C1, C2>
     where
-            N: ComplexField,
+        N: SimdComplexField,
         SB: Storage<N, R2, C2>,
         DefaultAllocator: Allocator<N, C1, C2>,
         ShapeConstraint: SameNumberOfRows<R1, R2>,
@@ -710,7 +713,10 @@ where
         &self,
         rhs: &Matrix<N, R2, C2, SB>,
         out: &mut Matrix<N, R3, C3, SC>,
-        dot: impl Fn(&VectorSliceN<N, R1, SA::RStride, SA::CStride>, &VectorSliceN<N, R2, SB::RStride, SB::CStride>) -> N,
+        dot: impl Fn(
+            &VectorSliceN<N, R1, SA::RStride, SA::CStride>,
+            &VectorSliceN<N, R2, SB::RStride, SB::CStride>,
+        ) -> N,
     ) where
         SB: Storage<N, R2, C2>,
         SC: StorageMut<N, R3, C3>,
@@ -760,7 +766,7 @@ where
         rhs: &Matrix<N, R2, C2, SB>,
         out: &mut Matrix<N, R3, C3, SC>,
     ) where
-        N: ComplexField,
+        N: SimdComplexField,
         SB: Storage<N, R2, C2>,
         SC: StorageMut<N, R3, C3>,
         ShapeConstraint: SameNumberOfRows<R1, R2> + DimEq<C1, R3> + DimEq<C2, C3>,
@@ -813,7 +819,8 @@ where
                             let coeff = self.get_unchecked((i1, j1)).inlined_clone();
 
                             for i2 in 0..nrows2.value() {
-                                *data_res = coeff.inlined_clone() * rhs.get_unchecked((i2, j2)).inlined_clone();
+                                *data_res = coeff.inlined_clone()
+                                    * rhs.get_unchecked((i2, j2)).inlined_clone();
                                 data_res = data_res.offset(1);
                             }
                         }
@@ -831,7 +838,9 @@ impl<N: Scalar + ClosedAdd, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C,
     #[inline]
     #[must_use = "Did you mean to use add_scalar_mut()?"]
     pub fn add_scalar(&self, rhs: N) -> MatrixMN<N, R, C>
-    where DefaultAllocator: Allocator<N, R, C> {
+    where
+        DefaultAllocator: Allocator<N, R, C>,
+    {
         let mut res = self.clone_owned();
         res.add_scalar_mut(rhs);
         res
@@ -840,7 +849,9 @@ impl<N: Scalar + ClosedAdd, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C,
     /// Adds a scalar to `self` in-place.
     #[inline]
     pub fn add_scalar_mut(&mut self, rhs: N)
-    where S: StorageMut<N, R, C> {
+    where
+        S: StorageMut<N, R, C>,
+    {
         for e in self.iter_mut() {
             *e += rhs.inlined_clone()
         }
@@ -868,23 +879,6 @@ where
 }
 
 impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
-    #[inline(always)]
-    fn xcmp<N2>(&self, abs: impl Fn(N) -> N2, ordering: Ordering) -> N2
-        where N2: Scalar + PartialOrd + Zero {
-        let mut iter = self.iter();
-        let mut max = iter.next().cloned().map_or(N2::zero(), &abs);
-
-        for e in iter {
-            let ae = abs(e.inlined_clone());
-
-            if ae.partial_cmp(&max) == Some(ordering) {
-                    max = ae;
-            }
-        }
-
-        max
-    }
-
     /// Returns the absolute value of the component with the largest absolute value.
     /// # Example
     /// ```
@@ -894,8 +888,13 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// ```
     #[inline]
     pub fn amax(&self) -> N
-        where N: PartialOrd + Signed {
+    where
-        self.xcmp(|e| e.abs(), Ordering::Greater)
+        N: Zero + SimdSigned + SimdPartialOrd,
+    {
+        self.fold_with(
+            |e| e.unwrap_or(&N::zero()).simd_abs(),
+            |a, b| a.simd_max(b.simd_abs()),
+        )
     }
 
     /// Returns the the 1-norm of the complex component with the largest 1-norm.
@@ -908,9 +907,14 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     ///     Complex::new(1.0, 3.0)).camax(), 5.0);
     /// ```
     #[inline]
-    pub fn camax(&self) -> N::RealField
+    pub fn camax(&self) -> N::SimdRealField
-        where N: ComplexField {
+    where
-        self.xcmp(|e| e.norm1(), Ordering::Greater)
+        N: SimdComplexField,
+    {
+        self.fold_with(
+            |e| e.unwrap_or(&N::zero()).simd_norm1(),
+            |a, b| a.simd_max(b.simd_norm1()),
+        )
     }
 
     /// Returns the component with the largest value.
@@ -923,8 +927,13 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// ```
     #[inline]
     pub fn max(&self) -> N
-        where N: PartialOrd + Zero {
+    where
-        self.xcmp(|e| e, Ordering::Greater)
+        N: SimdPartialOrd + Zero,
+    {
+        self.fold_with(
+            |e| e.map(|e| e.inlined_clone()).unwrap_or(N::zero()),
+            |a, b| a.simd_max(b.inlined_clone()),
+        )
     }
 
     /// Returns the absolute value of the component with the smallest absolute value.
@@ -936,8 +945,13 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// ```
     #[inline]
     pub fn amin(&self) -> N
-        where N: PartialOrd + Signed {
+    where
-        self.xcmp(|e| e.abs(), Ordering::Less)
+        N: Zero + SimdPartialOrd + SimdSigned,
+    {
+        self.fold_with(
+            |e| e.map(|e| e.simd_abs()).unwrap_or(N::zero()),
+            |a, b| a.simd_min(b.simd_abs()),
+        )
     }
 
     /// Returns the the 1-norm of the complex component with the smallest 1-norm.
@@ -950,9 +964,17 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     ///     Complex::new(1.0, 3.0)).camin(), 3.0);
     /// ```
     #[inline]
-    pub fn camin(&self) -> N::RealField
+    pub fn camin(&self) -> N::SimdRealField
-        where N: ComplexField {
+    where
-        self.xcmp(|e| e.norm1(), Ordering::Less)
+        N: SimdComplexField,
+    {
+        self.fold_with(
+            |e| {
+                e.map(|e| e.simd_norm1())
+                    .unwrap_or(N::SimdRealField::zero())
+            },
+            |a, b| a.simd_min(b.simd_norm1()),
+        )
     }
 
     /// Returns the component with the smallest value.
@@ -965,7 +987,12 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     /// ```
     #[inline]
     pub fn min(&self) -> N
-        where N: PartialOrd + Zero {
+    where
-        self.xcmp(|e| e, Ordering::Less)
+        N: SimdPartialOrd + Zero,
+    {
+        self.fold_with(
+            |e| e.map(|e| e.inlined_clone()).unwrap_or(N::zero()),
+            |a, b| a.simd_min(b.inlined_clone()),
+        )
     }
 }

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};
@@ -102,7 +102,8 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 }
 
 impl<N: RealField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S>
-where DefaultAllocator: Allocator<N, D, D>
+where
+    DefaultAllocator: Allocator<N, D, D>,
 {
     /// Checks that this matrix is orthogonal and has a determinant equal to 1.
     #[inline]

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.
@@ -95,7 +114,9 @@ impl<N: Scalar + AdditiveMonoid, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N,
     /// ```
     #[inline]
     pub fn row_sum(&self) -> RowVectorN<N, C>
-        where DefaultAllocator: Allocator<N, U1, C> {
+    where
+        DefaultAllocator: Allocator<N, U1, C>,
+    {
         self.compress_rows(|col| col.sum())
     }
 
@@ -116,7 +137,9 @@ impl<N: Scalar + AdditiveMonoid, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N,
     /// ```
     #[inline]
     pub fn row_sum_tr(&self) -> VectorN<N, C>
-        where DefaultAllocator: Allocator<N, C> {
+    where
+        DefaultAllocator: Allocator<N, C>,
+    {
         self.compress_rows_tr(|col| col.sum())
     }
 
@@ -137,7 +160,9 @@ impl<N: Scalar + AdditiveMonoid, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N,
     /// ```
     #[inline]
     pub fn column_sum(&self) -> VectorN<N, R>
-        where DefaultAllocator: Allocator<N, R> {
+    where
+        DefaultAllocator: Allocator<N, R>,
+    {
         let nrows = self.data.shape().0;
         self.compress_columns(VectorN::zeros_generic(nrows, U1), |out, col| {
             *out += col;
@@ -168,7 +193,9 @@ 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
@@ -189,7 +216,9 @@ impl<N: Scalar + Field + SupersetOf<f64>, R: Dim, C: Dim, S: Storage<N, R, C>> M
     /// ```
     #[inline]
     pub fn row_variance(&self) -> RowVectorN<N, C>
-        where DefaultAllocator: Allocator<N, U1, C> {
+    where
+        DefaultAllocator: Allocator<N, U1, C>,
+    {
         self.compress_rows(|col| col.variance())
     }
 
@@ -206,7 +235,9 @@ impl<N: Scalar + Field + SupersetOf<f64>, R: Dim, C: Dim, S: Storage<N, R, C>> M
     /// ```
     #[inline]
     pub fn row_variance_tr(&self) -> VectorN<N, C>
-        where DefaultAllocator: Allocator<N, C> {
+    where
+        DefaultAllocator: Allocator<N, C>,
+    {
         self.compress_rows_tr(|col| col.variance())
     }
 
@@ -224,7 +255,9 @@ impl<N: Scalar + Field + SupersetOf<f64>, R: Dim, C: Dim, S: Storage<N, R, C>> M
     /// ```
     #[inline]
     pub fn column_variance(&self) -> VectorN<N, R>
-        where DefaultAllocator: Allocator<N, R> {
+    where
+        DefaultAllocator: Allocator<N, R>,
+    {
         let (nrows, ncols) = self.data.shape();
 
         let mut mean = self.column_mean();
@@ -235,7 +268,8 @@ 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()
                 }
             }
         })
@@ -281,7 +315,9 @@ impl<N: Scalar + Field + SupersetOf<f64>, R: Dim, C: Dim, S: Storage<N, R, C>> M
     /// ```
     #[inline]
     pub fn row_mean(&self) -> RowVectorN<N, C>
-        where DefaultAllocator: Allocator<N, U1, C> {
+    where
+        DefaultAllocator: Allocator<N, U1, C>,
+    {
         self.compress_rows(|col| col.mean())
     }
 
@@ -298,7 +334,9 @@ impl<N: Scalar + Field + SupersetOf<f64>, R: Dim, C: Dim, S: Storage<N, R, C>> M
     /// ```
     #[inline]
     pub fn row_mean_tr(&self) -> VectorN<N, C>
-        where DefaultAllocator: Allocator<N, C> {
+    where
+        DefaultAllocator: Allocator<N, C>,
+    {
         self.compress_rows_tr(|col| col.mean())
     }
 
@@ -315,7 +353,9 @@ impl<N: Scalar + Field + SupersetOf<f64>, R: Dim, C: Dim, S: Storage<N, R, C>> M
     /// ```
     #[inline]
     pub fn column_mean(&self) -> VectorN<N, R>
-        where DefaultAllocator: Allocator<N, R> {
+    where
+        DefaultAllocator: Allocator<N, R>,
+    {
         let (nrows, ncols) = self.data.shape();
         let denom = N::one() / crate::convert::<_, N>(ncols.value() as f64);
         self.compress_columns(VectorN::zeros_generic(nrows, U1), |out, col| {

src/base/storage.rs

@@ -103,11 +103,13 @@ pub unsafe trait Storage<N: Scalar, R: Dim, C: Dim = U1>: Debug + Sized {
 
     /// Builds a matrix data storage that does not contain any reference.
     fn into_owned(self) -> Owned<N, R, C>
-    where DefaultAllocator: Allocator<N, R, C>;
+    where
+        DefaultAllocator: Allocator<N, R, C>;
 
     /// Clones this data storage to one that does not contain any reference.
     fn clone_owned(&self) -> Owned<N, R, C>
-    where DefaultAllocator: Allocator<N, R, C>;
+    where
+        DefaultAllocator: Allocator<N, R, C>;
 }
 
 /// Trait implemented by matrix data storage that can provide a mutable access to its elements.

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 +9,9 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use alga::general::{SubsetOf, ComplexField};
+use crate::allocator::Allocator;
-use alga::linear::NormedSpace;
+use crate::base::DefaultAllocator;
+use crate::{Dim, MatrixMN, RealField, Scalar, SimdComplexField, SimdRealField};
 
 /// A wrapper that ensures the underlying algebraic entity has a unit norm.
 ///
@@ -19,13 +19,15 @@ 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")]
 impl<T: Serialize> Serialize for Unit<T> {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
-    where S: Serializer {
+    where
+        S: Serializer,
+    {
         self.value.serialize(serializer)
     }
 }
@@ -33,7 +35,9 @@ impl<T: Serialize> Serialize for Unit<T> {
 #[cfg(feature = "serde-serialize")]
 impl<'de, T: Deserialize<'de>> Deserialize<'de> for Unit<T> {
     fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
-    where D: Deserializer<'de> {
+    where
+        D: Deserializer<'de>,
+    {
         T::deserialize(deserializer).map(|x| Unit { value: x })
     }
 }
@@ -53,60 +57,86 @@ impl<T: Abomonation> Abomonation for Unit<T> {
     }
 }
 
-impl<T: NormedSpace> Unit<T> {
+/// Trait implemented by entities scan be be normalized and put in an `Unit` struct.
-    /// Normalize the given value and return it wrapped on a `Unit` structure.
+pub trait Normed {
+    /// The type of the norm.
+    type Norm: SimdRealField;
+    /// Computes the norm.
+    fn norm(&self) -> Self::Norm;
+    /// Computes the squared norm.
+    fn norm_squared(&self) -> Self::Norm;
+    /// Multiply `self` by n.
+    fn scale_mut(&mut self, n: Self::Norm);
+    /// Divides `self` by n.
+    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
-            Some((Unit { value: value }, n))
+        T::Norm: RealField,
+    {
+        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 +144,7 @@ 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 +183,14 @@ 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 +203,7 @@ 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 +236,7 @@ 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 +248,6 @@ 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;
 
@@ -234,3 +256,92 @@ impl<T> Deref for Unit<T> {
         unsafe { mem::transmute(self) }
     }
 }
+
+// NOTE: we can't use a generic implementation for `Unit<T>` because
+// num_complex::Complex does not implement `From[Complex<...>...]` (and can't
+// because of the orphan rules).
+impl<N: Scalar + simba::simd::PrimitiveSimdValue, R: Dim, C: Dim>
+    From<[Unit<MatrixMN<N::Element, R, C>>; 2]> for Unit<MatrixMN<N, R, C>>
+where
+    N: From<[<N as simba::simd::SimdValue>::Element; 2]>,
+    N::Element: Scalar,
+    DefaultAllocator: Allocator<N, R, C> + Allocator<N::Element, R, C>,
+{
+    #[inline]
+    fn from(arr: [Unit<MatrixMN<N::Element, R, C>>; 2]) -> Self {
+        Self::new_unchecked(MatrixMN::from([
+            arr[0].clone().into_inner(),
+            arr[1].clone().into_inner(),
+        ]))
+    }
+}
+
+impl<N: Scalar + simba::simd::PrimitiveSimdValue, R: Dim, C: Dim>
+    From<[Unit<MatrixMN<N::Element, R, C>>; 4]> for Unit<MatrixMN<N, R, C>>
+where
+    N: From<[<N as simba::simd::SimdValue>::Element; 4]>,
+    N::Element: Scalar,
+    DefaultAllocator: Allocator<N, R, C> + Allocator<N::Element, R, C>,
+{
+    #[inline]
+    fn from(arr: [Unit<MatrixMN<N::Element, R, C>>; 4]) -> Self {
+        Self::new_unchecked(MatrixMN::from([
+            arr[0].clone().into_inner(),
+            arr[1].clone().into_inner(),
+            arr[2].clone().into_inner(),
+            arr[3].clone().into_inner(),
+        ]))
+    }
+}
+
+impl<N: Scalar + simba::simd::PrimitiveSimdValue, R: Dim, C: Dim>
+    From<[Unit<MatrixMN<N::Element, R, C>>; 8]> for Unit<MatrixMN<N, R, C>>
+where
+    N: From<[<N as simba::simd::SimdValue>::Element; 8]>,
+    N::Element: Scalar,
+    DefaultAllocator: Allocator<N, R, C> + Allocator<N::Element, R, C>,
+{
+    #[inline]
+    fn from(arr: [Unit<MatrixMN<N::Element, R, C>>; 8]) -> Self {
+        Self::new_unchecked(MatrixMN::from([
+            arr[0].clone().into_inner(),
+            arr[1].clone().into_inner(),
+            arr[2].clone().into_inner(),
+            arr[3].clone().into_inner(),
+            arr[4].clone().into_inner(),
+            arr[5].clone().into_inner(),
+            arr[6].clone().into_inner(),
+            arr[7].clone().into_inner(),
+        ]))
+    }
+}
+
+impl<N: Scalar + simba::simd::PrimitiveSimdValue, R: Dim, C: Dim>
+    From<[Unit<MatrixMN<N::Element, R, C>>; 16]> for Unit<MatrixMN<N, R, C>>
+where
+    N: From<[<N as simba::simd::SimdValue>::Element; 16]>,
+    N::Element: Scalar,
+    DefaultAllocator: Allocator<N, R, C> + Allocator<N::Element, R, C>,
+{
+    #[inline]
+    fn from(arr: [Unit<MatrixMN<N::Element, R, C>>; 16]) -> Self {
+        Self::new_unchecked(MatrixMN::from([
+            arr[0].clone().into_inner(),
+            arr[1].clone().into_inner(),
+            arr[2].clone().into_inner(),
+            arr[3].clone().into_inner(),
+            arr[4].clone().into_inner(),
+            arr[5].clone().into_inner(),
+            arr[6].clone().into_inner(),
+            arr[7].clone().into_inner(),
+            arr[8].clone().into_inner(),
+            arr[9].clone().into_inner(),
+            arr[10].clone().into_inner(),
+            arr[11].clone().into_inner(),
+            arr[12].clone().into_inner(),
+            arr[13].clone().into_inner(),
+            arr[14].clone().into_inner(),
+            arr[15].clone().into_inner(),
+        ]))
+    }
+}

src/base/vec_storage.rs

@@ -5,11 +5,11 @@ use std::io::{Result as IOResult, Write};
 use alloc::vec::Vec;
 
 use crate::base::allocator::Allocator;
+use crate::base::constraint::{SameNumberOfRows, ShapeConstraint};
 use crate::base::default_allocator::DefaultAllocator;
 use crate::base::dimension::{Dim, DimName, Dynamic, U1};
 use crate::base::storage::{ContiguousStorage, ContiguousStorageMut, Owned, Storage, StorageMut};
 use crate::base::{Scalar, Vector};
-use crate::base::constraint::{SameNumberOfRows, ShapeConstraint};
 
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
@@ -89,8 +89,7 @@ impl<N, R: Dim, C: Dim> VecStorage<N, R, C> {
     }
 }
 
-impl<N, R: Dim, C: Dim> Into<Vec<N>> for VecStorage<N, R, C>
+impl<N, R: Dim, C: Dim> Into<Vec<N>> for VecStorage<N, R, C> {
-{
     fn into(self) -> Vec<N> {
         self.data
     }
@@ -103,7 +102,8 @@ impl<N, R: Dim, C: Dim> Into<Vec<N>> for VecStorage<N, R, C>
  *
  */
 unsafe impl<N: Scalar, C: Dim> Storage<N, Dynamic, C> for VecStorage<N, Dynamic, C>
-where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self>
+where
+    DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self>,
 {
     type RStride = U1;
     type CStride = Dynamic;
@@ -130,13 +130,17 @@ where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self>
 
     #[inline]
     fn into_owned(self) -> Owned<N, Dynamic, C>
-    where DefaultAllocator: Allocator<N, Dynamic, C> {
+    where
+        DefaultAllocator: Allocator<N, Dynamic, C>,
+    {
         self
     }
 
     #[inline]
     fn clone_owned(&self) -> Owned<N, Dynamic, C>
-    where DefaultAllocator: Allocator<N, Dynamic, C> {
+    where
+        DefaultAllocator: Allocator<N, Dynamic, C>,
+    {
         self.clone()
     }
 
@@ -147,7 +151,8 @@ where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self>
 }
 
 unsafe impl<N: Scalar, R: DimName> Storage<N, R, Dynamic> for VecStorage<N, R, Dynamic>
-where DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self>
+where
+    DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self>,
 {
     type RStride = U1;
     type CStride = R;
@@ -174,13 +179,17 @@ where DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self>
 
     #[inline]
     fn into_owned(self) -> Owned<N, R, Dynamic>
-    where DefaultAllocator: Allocator<N, R, Dynamic> {
+    where
+        DefaultAllocator: Allocator<N, R, Dynamic>,
+    {
         self
     }
 
     #[inline]
     fn clone_owned(&self) -> Owned<N, R, Dynamic>
-    where DefaultAllocator: Allocator<N, R, Dynamic> {
+    where
+        DefaultAllocator: Allocator<N, R, Dynamic>,
+    {
         self.clone()
     }
 
@@ -196,7 +205,8 @@ where DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self>
  *
  */
 unsafe impl<N: Scalar, C: Dim> StorageMut<N, Dynamic, C> for VecStorage<N, Dynamic, C>
-where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self>
+where
+    DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self>,
 {
     #[inline]
     fn ptr_mut(&mut self) -> *mut N {
@@ -209,14 +219,19 @@ where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self>
     }
 }
 
-unsafe impl<N: Scalar, C: Dim> ContiguousStorage<N, Dynamic, C> for VecStorage<N, Dynamic, C> where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self>
+unsafe impl<N: Scalar, C: Dim> ContiguousStorage<N, Dynamic, C> for VecStorage<N, Dynamic, C> where
-{}
+    DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self>
+{
+}
 
-unsafe impl<N: Scalar, C: Dim> ContiguousStorageMut<N, Dynamic, C> for VecStorage<N, Dynamic, C> where DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self>
+unsafe impl<N: Scalar, C: Dim> ContiguousStorageMut<N, Dynamic, C> for VecStorage<N, Dynamic, C> where
-{}
+    DefaultAllocator: Allocator<N, Dynamic, C, Buffer = Self>
+{
+}
 
 unsafe impl<N: Scalar, R: DimName> StorageMut<N, R, Dynamic> for VecStorage<N, R, Dynamic>
-where DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self>
+where
+    DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self>,
 {
     #[inline]
     fn ptr_mut(&mut self) -> *mut N {
@@ -244,14 +259,17 @@ impl<N: Abomonation, R: Dim, C: Dim> Abomonation for VecStorage<N, R, C> {
     }
 }
 
-unsafe impl<N: Scalar, R: DimName> ContiguousStorage<N, R, Dynamic> for VecStorage<N, R, Dynamic> where DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self>
+unsafe impl<N: Scalar, R: DimName> ContiguousStorage<N, R, Dynamic> for VecStorage<N, R, Dynamic> where
-{}
+    DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self>
-
-unsafe impl<N: Scalar, R: DimName> ContiguousStorageMut<N, R, Dynamic> for VecStorage<N, R, Dynamic> where DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self>
-{}
-
-impl<N, R: Dim> Extend<N> for VecStorage<N, R, Dynamic>
 {
+}
+
+unsafe impl<N: Scalar, R: DimName> ContiguousStorageMut<N, R, Dynamic> for VecStorage<N, R, Dynamic> where
+    DefaultAllocator: Allocator<N, R, Dynamic, Buffer = Self>
+{
+}
+
+impl<N, R: Dim> Extend<N> for VecStorage<N, R, Dynamic> {
     /// Extends the number of columns of the `VecStorage` with elements
     /// from the given iterator.
     ///
@@ -259,8 +277,7 @@ impl<N, R: Dim> Extend<N> for VecStorage<N, R, Dynamic>
     /// This function panics if the number of elements yielded by the
     /// given iterator is not a multiple of the number of rows of the
     /// `VecStorage`.
-    fn extend<I: IntoIterator<Item=N>>(&mut self, iter: I)
+    fn extend<I: IntoIterator<Item = N>>(&mut self, iter: I) {
-    {
         self.data.extend(iter);
         self.ncols = Dynamic::new(self.data.len() / self.nrows.value());
         assert!(self.data.len() % self.nrows.value() == 0,
@@ -268,8 +285,7 @@ impl<N, R: Dim> Extend<N> for VecStorage<N, R, Dynamic>
     }
 }
 
-impl<'a, N: 'a + Copy, R: Dim> Extend<&'a N> for VecStorage<N, R, Dynamic>
+impl<'a, N: 'a + Copy, R: Dim> Extend<&'a N> for VecStorage<N, R, Dynamic> {
-{
     /// Extends the number of columns of the `VecStorage` with elements
     /// from the given iterator.
     ///
@@ -277,8 +293,7 @@ impl<'a, N: 'a + Copy, R: Dim> Extend<&'a N> for VecStorage<N, R, Dynamic>
     /// This function panics if the number of elements yielded by the
     /// given iterator is not a multiple of the number of rows of the
     /// `VecStorage`.
-    fn extend<I: IntoIterator<Item=&'a N>>(&mut self, iter: I)
+    fn extend<I: IntoIterator<Item = &'a N>>(&mut self, iter: I) {
-    {
         self.extend(iter.into_iter().copied())
     }
 }
@@ -298,8 +313,7 @@ where
     /// This function panics if the number of rows of each `Vector`
     /// yielded by the iterator is not equal to the number of rows
     /// of this `VecStorage`.
-    fn extend<I: IntoIterator<Item=Vector<N, RV, SV>>>(&mut self, iter: I)
+    fn extend<I: IntoIterator<Item = Vector<N, RV, SV>>>(&mut self, iter: I) {
-    {
         let nrows = self.nrows.value();
         let iter = iter.into_iter();
         let (lower, _upper) = iter.size_hint();
@@ -312,12 +326,10 @@ where
     }
 }
 
-impl<N> Extend<N> for VecStorage<N, Dynamic, U1>
+impl<N> Extend<N> for VecStorage<N, Dynamic, U1> {
-{
     /// Extends the number of rows of the `VecStorage` with elements
     /// from the given iterator.
-    fn extend<I: IntoIterator<Item=N>>(&mut self, iter: I)
+    fn extend<I: IntoIterator<Item = N>>(&mut self, iter: I) {
-    {
         self.data.extend(iter);
         self.nrows = Dynamic::new(self.data.len());
     }

src/debug/random_orthogonal.rs

@@ -3,23 +3,25 @@ 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)]
 pub struct RandomOrthogonal<N: Scalar, D: Dim = Dynamic>
-where DefaultAllocator: Allocator<N, D, D>
+where
+    DefaultAllocator: Allocator<N, D, D>,
 {
     m: MatrixN<N, D>,
 }
 
 impl<N: ComplexField, D: Dim> RandomOrthogonal<N, D>
-where DefaultAllocator: Allocator<N, D, D>
+where
+    DefaultAllocator: Allocator<N, D, D>,
 {
     /// Retrieve the generated matrix.
     pub fn unwrap(self) -> MatrixN<N, D> {

src/debug/random_sdp.rs

@@ -3,24 +3,26 @@ 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;
 
 /// A random, well-conditioned, symmetric definite-positive matrix.
 #[derive(Clone, Debug)]
 pub struct RandomSDP<N: Scalar, D: Dim = Dynamic>
-where DefaultAllocator: Allocator<N, D, D>
+where
+    DefaultAllocator: Allocator<N, D, D>,
 {
     m: MatrixN<N, D>,
 }
 
 impl<N: ComplexField, D: Dim> RandomSDP<N, D>
-where DefaultAllocator: Allocator<N, D, D>
+where
+    DefaultAllocator: Allocator<N, D, D>,
 {
     /// Retrieve the generated matrix.
     pub fn unwrap(self) -> MatrixN<N, D> {

src/geometry/abstract_rotation.rs

@@ -0,0 +1,164 @@
+use crate::allocator::Allocator;
+use crate::geometry::{Rotation, UnitComplex, UnitQuaternion};
+use crate::{DefaultAllocator, DimName, Point, Scalar, SimdRealField, VectorN, U2, U3};
+
+use simba::scalar::ClosedMul;
+
+/// Trait implemented by rotations that can be used inside of an `Isometry` or `Similarity`.
+pub trait AbstractRotation<N: Scalar, D: DimName>: PartialEq + ClosedMul + Clone {
+    /// The rotation identity.
+    fn identity() -> Self;
+    /// The rotation inverse.
+    fn inverse(&self) -> Self;
+    /// Change `self` to its inverse.
+    fn inverse_mut(&mut self);
+    /// Apply the rotation to the given vector.
+    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>
+    where
+        DefaultAllocator: Allocator<N, D>;
+    /// Apply the rotation to the given point.
+    fn transform_point(&self, p: &Point<N, D>) -> Point<N, D>
+    where
+        DefaultAllocator: Allocator<N, D>;
+    /// Apply the inverse rotation to the given vector.
+    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>
+    where
+        DefaultAllocator: Allocator<N, D>;
+    /// Apply the inverse rotation to the given point.
+    fn inverse_transform_point(&self, p: &Point<N, D>) -> Point<N, D>
+    where
+        DefaultAllocator: Allocator<N, D>;
+}
+
+impl<N: SimdRealField, D: DimName> AbstractRotation<N, D> for Rotation<N, D>
+where
+    N::Element: SimdRealField,
+    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: SimdRealField> AbstractRotation<N, U3> for UnitQuaternion<N>
+where
+    N::Element: SimdRealField,
+{
+    #[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: SimdRealField> AbstractRotation<N, U2> for UnitComplex<N>
+where
+    N::Element: SimdRealField,
+{
+    #[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

@@ -3,7 +3,6 @@ use std::fmt;
 use std::hash;
 #[cfg(feature = "abomonation-serialize")]
 use std::io::{Result as IOResult, Write};
-use std::marker::PhantomData;
 
 #[cfg(feature = "serde-serialize")]
 use serde::{Deserialize, Serialize};
@@ -11,14 +10,14 @@ 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 simba::simd::SimdRealField;
 
 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::base::{DefaultAllocator, MatrixN, Scalar, 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)]
@@ -36,26 +35,20 @@ use crate::geometry::{Point, Translation};
                        DefaultAllocator: Allocator<N, D>,
                        Owned<N, D>: Deserialize<'de>"))
 )]
-pub struct Isometry<N: RealField, D: DimName, R>
+pub struct Isometry<N: Scalar, D: DimName, R>
-where DefaultAllocator: Allocator<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
 {
     /// The pure rotational part of this isometry.
     pub rotation: R,
     /// The pure translational part of this isometry.
     pub translation: Translation<N, D>,
-
-    // One dummy private field just to prevent explicit construction.
-    #[cfg_attr(
-        feature = "serde-serialize",
-        serde(skip_serializing, skip_deserializing)
-    )]
-    _noconstruct: PhantomData<N>,
 }
 
 #[cfg(feature = "abomonation-serialize")]
 impl<N, D, R> Abomonation for Isometry<N, D, R>
 where
-    N: RealField,
+    N: SimdRealField,
     D: DimName,
     R: Abomonation,
     Translation<N, D>: Abomonation,
@@ -77,7 +70,8 @@ where
     }
 }
 
-impl<N: RealField + hash::Hash, D: DimName + hash::Hash, R: hash::Hash> hash::Hash for Isometry<N, D, R>
+impl<N: Scalar + 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,
@@ -88,15 +82,17 @@ where
     }
 }
 
-impl<N: RealField, D: DimName + Copy, R: Rotation<Point<N, D>> + Copy> Copy for Isometry<N, D, R>
+impl<N: Scalar + Copy, 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: Scalar, D: DimName, R: AbstractRotation<N, D> + Clone> Clone for Isometry<N, D, R>
-where DefaultAllocator: Allocator<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn clone(&self) -> Self {
@@ -104,8 +100,9 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: RealField, D: DimName, R: Rotation<Point<N, D>>> Isometry<N, D, R>
+impl<N: Scalar, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
-where DefaultAllocator: Allocator<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new isometry from its rotational and translational parts.
     ///
@@ -124,12 +121,17 @@ where DefaultAllocator: Allocator<N, D>
     #[inline]
     pub fn from_parts(translation: Translation<N, D>, rotation: R) -> Self {
         Self {
-            rotation: rotation,
+            rotation,
-            translation: translation,
+            translation,
-            _noconstruct: PhantomData,
+        }
     }
 }
 
+impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
+where
+    N::Element: SimdRealField,
+    DefaultAllocator: Allocator<N, D>,
+{
     /// Inverts `self`.
     ///
     /// # Example
@@ -167,7 +169,7 @@ 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 +210,7 @@ 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 +255,7 @@ 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.
@@ -352,8 +354,9 @@ where DefaultAllocator: Allocator<N, D>
 // and makes it hard to use it, e.g., for Transform × Isometry implementation.
 // This is OK since all constructors of the isometry enforce the Rotation bound already (and
 // explicit struct construction is prevented by the dummy ZST field).
-impl<N: RealField, D: DimName, R> Isometry<N, D, R>
+impl<N: SimdRealField, D: DimName, R> Isometry<N, D, R>
-where DefaultAllocator: Allocator<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
 {
     /// Converts this isometry into its equivalent homogeneous transformation matrix.
     ///
@@ -385,16 +388,16 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: RealField, D: DimName, R> Eq for Isometry<N, D, R>
+impl<N: SimdRealField, 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>
+impl<N: SimdRealField, 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 +408,7 @@ 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 +428,7 @@ 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,
 {
@@ -440,8 +443,7 @@ where
         other: &Self,
         epsilon: Self::Epsilon,
         max_relative: Self::Epsilon,
-    ) -> bool
+    ) -> bool {
-    {
         self.translation
             .relative_eq(&other.translation, epsilon, max_relative)
             && self
@@ -452,7 +454,7 @@ 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

@@ -1,6 +1,6 @@
 use alga::general::{
     AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, RealField,
+    AbstractSemigroup, Id, Identity, Multiplicative, RealField, TwoSidedInverse,
 };
 use alga::linear::Isometry as AlgaIsometry;
 use alga::linear::{
@@ -12,16 +12,17 @@ use crate::base::allocator::Allocator;
 use crate::base::dimension::DimName;
 use crate::base::{DefaultAllocator, VectorN};
 
-use crate::geometry::{Isometry, Point, Translation};
+use crate::geometry::{AbstractRotation, Isometry, Point, Translation};
 
 /*
  *
  * Algebraic structures.
  *
  */
-impl<N: RealField, D: DimName, R> Identity<Multiplicative> for Isometry<N, D, R>
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> Identity<Multiplicative>
+    for Isometry<N, D, R>
 where
-    R: Rotation<Point<N, D>>,
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
@@ -30,9 +31,10 @@ where
     }
 }
 
-impl<N: RealField, D: DimName, R> TwoSidedInverse<Multiplicative> for Isometry<N, D, R>
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> TwoSidedInverse<Multiplicative>
+    for Isometry<N, D, R>
 where
-    R: Rotation<Point<N, D>>,
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
@@ -47,9 +49,10 @@ where
     }
 }
 
-impl<N: RealField, D: DimName, R> AbstractMagma<Multiplicative> for Isometry<N, D, R>
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> AbstractMagma<Multiplicative>
+    for Isometry<N, D, R>
 where
-    R: Rotation<Point<N, D>>,
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
@@ -60,8 +63,8 @@ where
 
 macro_rules! impl_multiplicative_structures(
     ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: RealField, D: DimName, R> $marker<$operator> for Isometry<N, D, R>
+        impl<N: RealField + simba::scalar::RealField, D: DimName, R> $marker<$operator> for Isometry<N, D, R>
-            where R: Rotation<Point<N, D>>,
+            where R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
                   DefaultAllocator: Allocator<N, D> { }
     )*}
 );
@@ -79,9 +82,10 @@ impl_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N: RealField, D: DimName, R> Transformation<Point<N, D>> for Isometry<N, D, R>
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> Transformation<Point<N, D>>
+    for Isometry<N, D, R>
 where
-    R: Rotation<Point<N, D>>,
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
@@ -95,9 +99,10 @@ where
     }
 }
 
-impl<N: RealField, D: DimName, R> ProjectiveTransformation<Point<N, D>> for Isometry<N, D, R>
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> ProjectiveTransformation<Point<N, D>>
+    for Isometry<N, D, R>
 where
-    R: Rotation<Point<N, D>>,
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
     DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
@@ -111,9 +116,10 @@ where
     }
 }
 
-impl<N: RealField, D: DimName, R> AffineTransformation<Point<N, D>> for Isometry<N, D, R>
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> AffineTransformation<Point<N, D>>
+    for Isometry<N, D, R>
 where
-    R: Rotation<Point<N, D>>,
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
     DefaultAllocator: Allocator<N, D>,
 {
     type Rotation = R;
@@ -126,7 +132,7 @@ where
             self.translation.clone(),
             self.rotation.clone(),
             Id::new(),
-            R::identity(),
+            <R as AbstractRotation<N, D>>::identity(),
         )
     }
 
@@ -142,13 +148,13 @@ where
 
     #[inline]
     fn append_rotation(&self, r: &Self::Rotation) -> Self {
-        let shift = r.transform_vector(&self.translation.vector);
+        let shift = Transformation::transform_vector(r, &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
+        Isometry::from_parts(self.translation.clone(), self.rotation.prepend_rotation(r))
     }
 
     #[inline]
@@ -169,9 +175,10 @@ where
     }
 }
 
-impl<N: RealField, D: DimName, R> Similarity<Point<N, D>> for Isometry<N, D, R>
+impl<N: RealField + simba::scalar::RealField, D: DimName, R> Similarity<Point<N, D>>
+    for Isometry<N, D, R>
 where
-    R: Rotation<Point<N, D>>,
+    R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
     DefaultAllocator: Allocator<N, D>,
 {
     type Scaling = Id;
@@ -194,8 +201,8 @@ where
 
 macro_rules! marker_impl(
     ($($Trait: ident),*) => {$(
-        impl<N: RealField, D: DimName, R> $Trait<Point<N, D>> for Isometry<N, D, R>
+        impl<N: RealField + simba::scalar::RealField, D: DimName, R> $Trait<Point<N, D>> for Isometry<N, D, R>
-        where R: Rotation<Point<N, D>>,
+        where R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
               DefaultAllocator: Allocator<N, D> { }
     )*}
 );

src/geometry/isometry_construction.rs

@@ -7,20 +7,22 @@ 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 simba::simd::SimdRealField;
 
 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: SimdRealField, D: DimName, R: AbstractRotation<N, D>> Isometry<N, D, R>
-where DefaultAllocator: Allocator<N, D>
+where
+    N::Element: SimdRealField,
+    DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new identity isometry.
     ///
@@ -65,8 +67,10 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: RealField, D: DimName, R: AlgaRotation<Point<N, D>>> One for Isometry<N, D, R>
+impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> One for Isometry<N, D, R>
-where DefaultAllocator: Allocator<N, D>
+where
+    N::Element: SimdRealField,
+    DefaultAllocator: Allocator<N, D>,
 {
     /// Creates a new identity isometry.
     #[inline]
@@ -77,7 +81,7 @@ 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>,
 {
@@ -90,8 +94,9 @@ where
 #[cfg(feature = "arbitrary")]
 impl<N, D: DimName, R> Arbitrary for Isometry<N, D, R>
 where
-    N: RealField + Arbitrary + Send,
+    N: SimdRealField + Arbitrary + Send,
-    R: AlgaRotation<Point<N, D>> + Arbitrary + Send,
+    N::Element: SimdRealField,
+    R: AbstractRotation<N, D> + Arbitrary + Send,
     Owned<N, D>: Send,
     DefaultAllocator: Allocator<N, D>,
 {
@@ -108,7 +113,10 @@ where
  */
 
 // 2D rotation.
-impl<N: RealField> Isometry<N, U2, Rotation2<N>> {
+impl<N: SimdRealField> Isometry<N, U2, Rotation2<N>>
+where
+    N::Element: SimdRealField,
+{
     /// Creates a new 2D isometry from a translation and a rotation angle.
     ///
     /// Its rotational part is represented as a 2x2 rotation matrix.
@@ -143,7 +151,10 @@ impl<N: RealField> Isometry<N, U2, Rotation2<N>> {
     }
 }
 
-impl<N: RealField> Isometry<N, U2, UnitComplex<N>> {
+impl<N: SimdRealField> Isometry<N, U2, UnitComplex<N>>
+where
+    N::Element: SimdRealField,
+{
     /// Creates a new 2D isometry from a translation and a rotation angle.
     ///
     /// Its rotational part is represented as an unit complex number.
@@ -181,7 +192,8 @@ impl<N: RealField> Isometry<N, U2, UnitComplex<N>> {
 // 3D rotation.
 macro_rules! isometry_construction_impl(
     ($RotId: ident < $($RotParams: ident),*>, $RRDim: ty, $RCDim: ty) => {
-        impl<N: RealField> Isometry<N, U3, $RotId<$($RotParams),*>> {
+        impl<N: SimdRealField> Isometry<N, U3, $RotId<$($RotParams),*>>
+        where N::Element: SimdRealField {
             /// Creates a new isometry from a translation and a rotation axis-angle.
             ///
             /// # Example

src/geometry/isometry_conversion.rs

@@ -1,11 +1,13 @@
-use alga::general::{RealField, SubsetOf, SupersetOf};
+use simba::scalar::{RealField, SubsetOf, SupersetOf};
-use alga::linear::Rotation;
+use simba::simd::{PrimitiveSimdValue, SimdRealField, SimdValue};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimMin, DimName, DimNameAdd, DimNameSum, U1};
-use crate::base::{DefaultAllocator, MatrixN};
+use crate::base::{DefaultAllocator, MatrixN, Scalar};
 
-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 +23,8 @@ 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 +39,7 @@ 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 +51,8 @@ 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 +66,7 @@ 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 +76,7 @@ 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 +100,7 @@ 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 +109,7 @@ 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 +141,7 @@ 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),
@@ -149,7 +151,7 @@ where
     }
 }
 
-impl<N: RealField, D: DimName, R> From<Isometry<N, D, R>> for MatrixN<N, DimNameSum<D, U1>>
+impl<N: SimdRealField, D: DimName, R> From<Isometry<N, D, R>> for MatrixN<N, DimNameSum<D, U1>>
 where
     D: DimNameAdd<U1>,
     R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>,
@@ -160,3 +162,141 @@ where
         iso.to_homogeneous()
     }
 }
+
+impl<N: Scalar + PrimitiveSimdValue, D: DimName, R> From<[Isometry<N::Element, D, R::Element>; 2]>
+    for Isometry<N, D, R>
+where
+    N: From<[<N as SimdValue>::Element; 2]>,
+    R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 2]>,
+    R::Element: AbstractRotation<N::Element, D>,
+    N::Element: Scalar + Copy,
+    R::Element: Scalar + Copy,
+    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+{
+    #[inline]
+    fn from(arr: [Isometry<N::Element, D, R::Element>; 2]) -> Self {
+        let tra = Translation::from([arr[0].translation.clone(), arr[1].translation.clone()]);
+        let rot = R::from([arr[0].rotation.clone(), arr[0].rotation.clone()]);
+
+        Self::from_parts(tra, rot)
+    }
+}
+
+impl<N: Scalar + PrimitiveSimdValue, D: DimName, R> From<[Isometry<N::Element, D, R::Element>; 4]>
+    for Isometry<N, D, R>
+where
+    N: From<[<N as SimdValue>::Element; 4]>,
+    R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 4]>,
+    R::Element: AbstractRotation<N::Element, D>,
+    N::Element: Scalar + Copy,
+    R::Element: Scalar + Copy,
+    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+{
+    #[inline]
+    fn from(arr: [Isometry<N::Element, D, R::Element>; 4]) -> Self {
+        let tra = Translation::from([
+            arr[0].translation.clone(),
+            arr[1].translation.clone(),
+            arr[2].translation.clone(),
+            arr[3].translation.clone(),
+        ]);
+        let rot = R::from([
+            arr[0].rotation.clone(),
+            arr[1].rotation.clone(),
+            arr[2].rotation.clone(),
+            arr[3].rotation.clone(),
+        ]);
+
+        Self::from_parts(tra, rot)
+    }
+}
+
+impl<N: Scalar + PrimitiveSimdValue, D: DimName, R> From<[Isometry<N::Element, D, R::Element>; 8]>
+    for Isometry<N, D, R>
+where
+    N: From<[<N as SimdValue>::Element; 8]>,
+    R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 8]>,
+    R::Element: AbstractRotation<N::Element, D>,
+    N::Element: Scalar + Copy,
+    R::Element: Scalar + Copy,
+    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+{
+    #[inline]
+    fn from(arr: [Isometry<N::Element, D, R::Element>; 8]) -> Self {
+        let tra = Translation::from([
+            arr[0].translation.clone(),
+            arr[1].translation.clone(),
+            arr[2].translation.clone(),
+            arr[3].translation.clone(),
+            arr[4].translation.clone(),
+            arr[5].translation.clone(),
+            arr[6].translation.clone(),
+            arr[7].translation.clone(),
+        ]);
+        let rot = R::from([
+            arr[0].rotation.clone(),
+            arr[1].rotation.clone(),
+            arr[2].rotation.clone(),
+            arr[3].rotation.clone(),
+            arr[4].rotation.clone(),
+            arr[5].rotation.clone(),
+            arr[6].rotation.clone(),
+            arr[7].rotation.clone(),
+        ]);
+
+        Self::from_parts(tra, rot)
+    }
+}
+
+impl<N: Scalar + PrimitiveSimdValue, D: DimName, R> From<[Isometry<N::Element, D, R::Element>; 16]>
+    for Isometry<N, D, R>
+where
+    N: From<[<N as SimdValue>::Element; 16]>,
+    R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 16]>,
+    R::Element: AbstractRotation<N::Element, D>,
+    N::Element: Scalar + Copy,
+    R::Element: Scalar + Copy,
+    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
+{
+    #[inline]
+    fn from(arr: [Isometry<N::Element, D, R::Element>; 16]) -> Self {
+        let tra = Translation::from([
+            arr[0].translation.clone(),
+            arr[1].translation.clone(),
+            arr[2].translation.clone(),
+            arr[3].translation.clone(),
+            arr[4].translation.clone(),
+            arr[5].translation.clone(),
+            arr[6].translation.clone(),
+            arr[7].translation.clone(),
+            arr[8].translation.clone(),
+            arr[9].translation.clone(),
+            arr[10].translation.clone(),
+            arr[11].translation.clone(),
+            arr[12].translation.clone(),
+            arr[13].translation.clone(),
+            arr[14].translation.clone(),
+            arr[15].translation.clone(),
+        ]);
+        let rot = R::from([
+            arr[0].rotation.clone(),
+            arr[1].rotation.clone(),
+            arr[2].rotation.clone(),
+            arr[3].rotation.clone(),
+            arr[4].rotation.clone(),
+            arr[5].rotation.clone(),
+            arr[6].rotation.clone(),
+            arr[7].rotation.clone(),
+            arr[8].rotation.clone(),
+            arr[9].rotation.clone(),
+            arr[10].rotation.clone(),
+            arr[11].rotation.clone(),
+            arr[12].rotation.clone(),
+            arr[13].rotation.clone(),
+            arr[14].rotation.clone(),
+            arr[15].rotation.clone(),
+        ]);
+
+        Self::from_parts(tra, rot)
+    }
+}

src/geometry/isometry_ops.rs

@@ -1,13 +1,17 @@
+use num::{One, Zero};
 use std::ops::{Div, DivAssign, Mul, MulAssign};
 
-use alga::general::RealField;
+use simba::scalar::{ClosedAdd, ClosedMul};
-use alga::linear::Rotation as AlgaRotation;
+use simba::simd::SimdRealField;
 
 use crate::base::allocator::Allocator;
-use crate::base::dimension::{DimName, U1, U3, U4};
+use crate::base::dimension::{DimName, U1, U2, 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, UnitComplex, 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>`
@@ -64,8 +68,9 @@ macro_rules! isometry_binop_impl(
     ($Op: ident, $op: ident;
      $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 $Lhs
+        impl<$($lives ,)* N: SimdRealField, D: DimName, R> $Op<$Rhs> for $Lhs
-            where R: AlgaRotation<Point<N, D>>,
+            where N::Element: SimdRealField,
+                  R: AbstractRotation<N, D>,
                   DefaultAllocator: Allocator<N, D> {
             type Output = $Output;
 
@@ -111,8 +116,9 @@ macro_rules! isometry_binop_assign_impl_all(
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      [val] => $action_val: expr;
      [ref] => $action_ref: expr;) => {
-        impl<N: RealField, D: DimName, R> $OpAssign<$Rhs> for $Lhs
+        impl<N: SimdRealField, D: DimName, R> $OpAssign<$Rhs> for $Lhs
-            where R: AlgaRotation<Point<N, D>>,
+            where N::Element: SimdRealField,
+                  R: AbstractRotation<N, D>,
                   DefaultAllocator: Allocator<N, D> {
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: $Rhs) {
@@ -120,8 +126,9 @@ macro_rules! isometry_binop_assign_impl_all(
             }
         }
 
-        impl<'b, N: RealField, D: DimName, R> $OpAssign<&'b $Rhs> for $Lhs
+        impl<'b, N: SimdRealField, D: DimName, R> $OpAssign<&'b $Rhs> for $Lhs
-            where R: AlgaRotation<Point<N, D>>,
+            where N::Element: SimdRealField,
+                  R: AbstractRotation<N, D>,
                   DefaultAllocator: Allocator<N, D> {
             #[inline]
             fn $op_assign(&mut $lhs, $rhs: &'b $Rhs) {
@@ -189,39 +196,55 @@ 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: SimdRealField for N::Element: SimdRealField;
-    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: SimdRealField for N::Element: SimdRealField;
-    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: SimdRealField for N::Element: SimdRealField;
-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: SimdRealField for N::Element: SimdRealField;
-    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();
+);
+
+md_assign_impl_all!(
+    MulAssign, mul_assign where N: SimdRealField for N::Element: SimdRealField;
+    (U2, U2), (U2, U2) for;
+    self: Isometry<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>;
+    [val] => self.rotation *= rhs;
+    [ref] => self.rotation *= rhs.clone();
+);
+
+md_assign_impl_all!(
+    DivAssign, div_assign where N: SimdRealField for N::Element: SimdRealField;
+    (U2, U2), (U2, U2) for;
+    self: Isometry<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>;
+    // FIXME: don't invert explicitly?
+    [val] => *self *= rhs.inverse();
+    [ref] => *self *= rhs.inverse();
 );
 
 // Isometry × Point
@@ -286,8 +309,9 @@ macro_rules! isometry_from_composition_impl(
      ($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(for $Dims: ident: $DimsBound: ident),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N: RealField $(, $Dims: $DimsBound)*> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N: SimdRealField $(, $Dims: $DimsBound)*> $Op<$Rhs> for $Lhs
-            where DefaultAllocator: Allocator<N, $R1, $C1> +
+            where N::Element: SimdRealField,
+                  DefaultAllocator: Allocator<N, $R1, $C1> +
                                     Allocator<N, $R2, $C2> {
             type Output = $Output;
 
@@ -357,6 +381,18 @@ 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 +408,18 @@ 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 +433,18 @@ 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 +460,18 @@ 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;
@@ -434,3 +506,27 @@ isometry_from_composition_impl_all!(
     [val ref] => Isometry::from_parts(self, right.clone());
     [ref ref] => Isometry::from_parts(self.clone(), right.clone());
 );
+
+// Isometry × UnitComplex
+isometry_from_composition_impl_all!(
+    Mul, mul;
+    (U2, U1), (U2, U1);
+    self: Isometry<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>,
+    Output = Isometry<N, U2, UnitComplex<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());
+);
+
+// Isometry ÷ UnitComplex
+isometry_from_composition_impl_all!(
+    Div, div;
+    (U2, U1), (U2, U1);
+    self: Isometry<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>,
+    Output = Isometry<N, U2, UnitComplex<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());
+);

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;
+use crate::SimdRealField;
+
+use crate::geometry::{AbstractRotation, Isometry, Translation};
+
+impl<N: SimdRealField, D: DimName, R> SimdValue for Isometry<N, D, R>
+where
+    N::Element: SimdRealField,
+    R: SimdValue<SimdBool = N::SimdBool> + AbstractRotation<N, D>,
+    R::Element: AbstractRotation<N::Element, D>,
+    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, 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

@@ -3,71 +3,91 @@
 
 mod op_macros;
 
+mod abstract_rotation;
+
 mod point;
+#[cfg(feature = "alga")]
 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.
+#[cfg(feature = "alga")]
+mod rotation_alga;
 mod rotation_alias;
 mod rotation_construction;
 mod rotation_conversion;
 mod rotation_ops;
+mod rotation_simba; // FIXME: implement Rotation methods.
 mod rotation_specialization;
 
 mod quaternion;
+#[cfg(feature = "alga")]
 mod quaternion_alga;
 mod quaternion_construction;
 mod quaternion_conversion;
 mod quaternion_coordinates;
 mod quaternion_ops;
+mod quaternion_simba;
 
 mod unit_complex;
+#[cfg(feature = "alga")]
 mod unit_complex_alga;
 mod unit_complex_construction;
 mod unit_complex_conversion;
 mod unit_complex_ops;
+mod unit_complex_simba;
 
 mod translation;
+#[cfg(feature = "alga")]
 mod translation_alga;
 mod translation_alias;
 mod translation_construction;
 mod translation_conversion;
 mod translation_coordinates;
 mod translation_ops;
+mod translation_simba;
 
 mod isometry;
+#[cfg(feature = "alga")]
 mod isometry_alga;
 mod isometry_alias;
 mod isometry_construction;
 mod isometry_conversion;
 mod isometry_ops;
+mod isometry_simba;
 
 mod similarity;
+#[cfg(feature = "alga")]
 mod similarity_alga;
 mod similarity_alias;
 mod similarity_construction;
 mod similarity_conversion;
 mod similarity_ops;
+mod similarity_simba;
 
 mod swizzle;
 
 mod transform;
+#[cfg(feature = "alga")]
 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(
@@ -86,9 +85,9 @@ macro_rules! md_impl_all(
 macro_rules! md_assign_impl(
     (
      // Operator, operator method, and scalar bounds.
-     $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)*;
+     $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)* $(for N::Element: $ElementBounds: ident)*;
      // Storage dimensions, and dimension bounds.
-     ($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.
@@ -97,6 +96,7 @@ macro_rules! md_assign_impl(
      $action: expr; $($lives: tt),*) => {
         impl<$($lives ,)* N $(, $Dims: $DimsBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
             where N: Scalar + Zero + One + ClosedAdd + ClosedMul $($(+ $ScalarBounds)*)*,
+                  $(N::Element: $ElementBounds,)*
                   DefaultAllocator: Allocator<N, $R1, $C1> +
                                     Allocator<N, $R2, $C2>,
                   $( $ConstraintType: $ConstraintBound $(<$( $ConstraintBoundParams $( = $EqBound )*),*>)* ),*
@@ -114,9 +114,9 @@ macro_rules! md_assign_impl(
 macro_rules! md_assign_impl_all(
     (
      // Operator, operator method, and scalar bounds.
-     $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)*;
+     $Op: ident, $op: ident $(where N: $($ScalarBounds: ident),*)* $(for N::Element: $($ElementBounds: 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.
@@ -125,15 +125,15 @@ macro_rules! md_assign_impl_all(
      [val] => $action_val: expr;
      [ref] => $action_ref: expr;) => {
         md_assign_impl!(
-            $Op, $op $(where N: $($ScalarBounds),*)*;
+            $Op, $op $(where N: $($ScalarBounds),*)* $(for N::Element: $($ElementBounds),*)*;
-            ($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),*)*;
+            $Op, $op $(where N: $($ScalarBounds),*)* $(for N::Element: $($ElementBounds),*)*;
-            ($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;
@@ -46,7 +46,9 @@ impl<N: RealField> PartialEq for Orthographic3<N> {
 #[cfg(feature = "serde-serialize")]
 impl<N: RealField + Serialize> Serialize for Orthographic3<N> {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
-    where S: Serializer {
+    where
+        S: Serializer,
+    {
         self.matrix.serialize(serializer)
     }
 }
@@ -54,7 +56,9 @@ impl<N: RealField + Serialize> Serialize for Orthographic3<N> {
 #[cfg(feature = "serde-serialize")]
 impl<'a, N: RealField + Deserialize<'a>> Deserialize<'a> for Orthographic3<N> {
     fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
-    where Des: Deserializer<'a> {
+    where
+        Des: Deserializer<'a>,
+    {
         let matrix = Matrix4::<N>::deserialize(deserializer)?;
 
         Ok(Self::from_matrix_unchecked(matrix))
@@ -480,7 +484,9 @@ impl<N: RealField> Orthographic3<N> {
     /// ```
     #[inline]
     pub fn project_vector<SB>(&self, p: &Vector<N, U3, SB>) -> Vector3<N>
-    where SB: Storage<N, U3> {
+    where
+        SB: Storage<N, U3>,
+    {
         Vector3::new(
             self.matrix[(0, 0)] * p[0],
             self.matrix[(1, 1)] * p[1],
@@ -679,7 +685,8 @@ impl<N: RealField> Orthographic3<N> {
 }
 
 impl<N: RealField> Distribution<Orthographic3<N>> for Standard
-where Standard: Distribution<N>
+where
+    Standard: Distribution<N>,
 {
     fn sample<R: Rng + ?Sized>(&self, r: &mut R) -> Orthographic3<N> {
         let left = r.gen();
@@ -695,7 +702,8 @@ where Standard: Distribution<N>
 
 #[cfg(feature = "arbitrary")]
 impl<N: RealField + Arbitrary> Arbitrary for Orthographic3<N>
-where Matrix4<N>: Send
+where
+    Matrix4<N>: Send,
 {
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
         let left = Arbitrary::arbitrary(g);

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;
@@ -47,7 +47,9 @@ impl<N: RealField> PartialEq for Perspective3<N> {
 #[cfg(feature = "serde-serialize")]
 impl<N: RealField + Serialize> Serialize for Perspective3<N> {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
-    where S: Serializer {
+    where
+        S: Serializer,
+    {
         self.matrix.serialize(serializer)
     }
 }
@@ -55,7 +57,9 @@ impl<N: RealField + Serialize> Serialize for Perspective3<N> {
 #[cfg(feature = "serde-serialize")]
 impl<'a, N: RealField + Deserialize<'a>> Deserialize<'a> for Perspective3<N> {
     fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
-    where Des: Deserializer<'a> {
+    where
+        Des: Deserializer<'a>,
+    {
         let matrix = Matrix4::<N>::deserialize(deserializer)?;
 
         Ok(Self::from_matrix_unchecked(matrix))
@@ -170,7 +174,8 @@ 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.
@@ -211,7 +216,9 @@ impl<N: RealField> Perspective3<N> {
     /// Projects a vector. Faster than matrix multiplication.
     #[inline]
     pub fn project_vector<SB>(&self, p: &Vector<N, U3, SB>) -> Vector3<N>
-    where SB: Storage<N, U3> {
+    where
+        SB: Storage<N, U3>,
+    {
         let inverse_denom = -N::one() / p[2];
         Vector3::new(
             self.matrix[(0, 0)] * p[0] * inverse_denom,
@@ -262,7 +269,8 @@ impl<N: RealField> Perspective3<N> {
 }
 
 impl<N: RealField> Distribution<Perspective3<N>> for Standard
-where Standard: Distribution<N>
+where
+    Standard: Distribution<N>,
 {
     fn sample<'a, R: Rng + ?Sized>(&self, r: &'a mut R) -> Perspective3<N> {
         let znear = r.gen();

src/geometry/point.rs

@@ -12,6 +12,8 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
+use simba::simd::SimdPartialOrd;
+
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
 use crate::base::iter::{MatrixIter, MatrixIterMut};
@@ -21,7 +23,8 @@ use crate::base::{DefaultAllocator, Scalar, VectorN};
 #[repr(C)]
 #[derive(Debug, Clone)]
 pub struct Point<N: Scalar, D: DimName>
-where DefaultAllocator: Allocator<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
 {
     /// The coordinates of this point, i.e., the shift from the origin.
     pub coords: VectorN<N, D>,
@@ -51,7 +54,9 @@ where
     <DefaultAllocator as Allocator<N, D>>::Buffer: Serialize,
 {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
-    where S: Serializer {
+    where
+        S: Serializer,
+    {
         self.coords.serialize(serializer)
     }
 }
@@ -63,7 +68,9 @@ where
     <DefaultAllocator as Allocator<N, D>>::Buffer: Deserialize<'a>,
 {
     fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
-    where Des: Deserializer<'a> {
+    where
+        Des: Deserializer<'a>,
+    {
         let coords = VectorN::<N, D>::deserialize(deserializer)?;
 
         Ok(Self::from(coords))
@@ -92,7 +99,8 @@ where
 }
 
 impl<N: Scalar, D: DimName> Point<N, D>
-where DefaultAllocator: Allocator<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
 {
     /// Converts this point into a vector in homogeneous coordinates, i.e., appends a `1` at the
     /// end of it.
@@ -244,8 +252,7 @@ where
         other: &Self,
         epsilon: Self::Epsilon,
         max_relative: Self::Epsilon,
-    ) -> bool
+    ) -> bool {
-    {
         self.coords
             .relative_eq(&other.coords, epsilon, max_relative)
     }
@@ -270,7 +277,8 @@ where
 impl<N: Scalar + Eq, D: DimName> Eq for Point<N, D> where DefaultAllocator: Allocator<N, D> {}
 
 impl<N: Scalar, D: DimName> PartialEq for Point<N, D>
-where DefaultAllocator: Allocator<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
@@ -279,7 +287,8 @@ where DefaultAllocator: Allocator<N, D>
 }
 
 impl<N: Scalar + PartialOrd, D: DimName> PartialOrd for Point<N, D>
-where DefaultAllocator: Allocator<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
 {
     #[inline]
     fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
@@ -307,13 +316,41 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
+/*
+ * inf/sup
+ */
+impl<N: Scalar + SimdPartialOrd, D: DimName> Point<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
+{
+    /// Computes the infimum (aka. componentwise min) of two points.
+    #[inline]
+    pub fn inf(&self, other: &Self) -> Point<N, D> {
+        self.coords.inf(&other.coords).into()
+    }
+
+    /// Computes the supremum (aka. componentwise max) of two points.
+    #[inline]
+    pub fn sup(&self, other: &Self) -> Point<N, D> {
+        self.coords.sup(&other.coords).into()
+    }
+
+    /// Computes the (infimum, supremum) of two points.
+    #[inline]
+    pub fn inf_sup(&self, other: &Self) -> (Point<N, D>, Point<N, D>) {
+        let (inf, sup) = self.coords.inf_sup(&other.coords);
+        (inf.into(), sup.into())
+    }
+}
+
 /*
  *
  * Display
  *
  */
 impl<N: Scalar + fmt::Display, D: DimName> fmt::Display for Point<N, D>
-where DefaultAllocator: Allocator<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
 {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         write!(f, "{{")?;

src/geometry/point_alga.rs

@@ -15,8 +15,9 @@ where
     type Translation = VectorN<N, D>;
 }
 
-impl<N: RealField, D: DimName> EuclideanSpace for Point<N, D>
+impl<N: RealField + simba::scalar::RealField, D: DimName> EuclideanSpace for Point<N, D>
-where DefaultAllocator: Allocator<N, D>
+where
+    DefaultAllocator: Allocator<N, D>,
 {
     type Coordinates = VectorN<N, D>;
     type RealField = N;