Rename Real to RealField.

examples/dimensional_genericity.rs

@@ -4,7 +4,7 @@ extern crate nalgebra as na;
 use alga::linear::FiniteDimInnerSpace;
 use na::allocator::Allocator;
 use na::dimension::Dim;
-use na::{DefaultAllocator, Real, Unit, Vector2, Vector3, VectorN};
+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
@@ -14,12 +14,12 @@ where V: FiniteDimInnerSpace + Copy {
 }
 
 /// Reflects a vector wrt. the hyperplane with normal `plane_normal`.
-fn reflect_wrt_hyperplane_with_dimensional_genericity<N: Real, D: Dim>(
+fn reflect_wrt_hyperplane_with_dimensional_genericity<N: RealField, D: Dim>(
     plane_normal: &Unit<VectorN<N, D>>,
     vector: &VectorN<N, D>,
 ) -> VectorN<N, D>
 where
-    N: Real,
+    N: RealField,
     D: Dim,
     DefaultAllocator: Allocator<N, D>,
 {
@@ -29,7 +29,7 @@ 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: Real {
+where N: RealField {
     let n = plane_normal.as_ref(); // Get the underlying Vector2
     vector - n * (n.dot(vector) * na::convert(2.0))
 }
@@ -37,7 +37,7 @@ where N: Real {
 /// 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: Real {
+where N: RealField {
     let n = plane_normal.as_ref(); // Get the underlying Vector3
     vector - n * (n.dot(vector) * na::convert(2.0))
 }

examples/scalar_genericity.rs

@@ -1,7 +1,7 @@
 extern crate alga;
 extern crate nalgebra as na;
 
-use alga::general::{Real, RingCommutative};
+use alga::general::{RealField, RingCommutative};
 use na::{Scalar, Vector3};
 
 fn print_vector<N: Scalar>(m: &Vector3<N>) {
@@ -14,11 +14,11 @@ fn print_squared_norm<N: Scalar + RingCommutative>(v: &Vector3<N>) {
     println!("{:?}", sqnorm);
 }
 
-fn print_norm<N: Real>(v: &Vector3<N>) {
+fn print_norm<N: RealField>(v: &Vector3<N>) {
     // NOTE: alternatively, nalgebra already defines `v.norm()`.
     let norm = v.dot(v).sqrt();
 
-    // The Real bound implies that N is Display so we can
+    // The RealField bound implies that N is Display so we can
     // use "{}" instead of "{:?}" for the format string.
     println!("{}", norm)
 }

nalgebra-glm/src/common.rs

@@ -1,4 +1,4 @@
-use na::{self, DefaultAllocator, Real};
+use na::{self, DefaultAllocator, RealField};
 use num::FromPrimitive;
 use std::mem;
 
@@ -43,7 +43,7 @@ where DefaultAllocator: Alloc<N, R, C> {
 /// * [`fract`](fn.fract.html)
 /// * [`round`](fn.round.html)
 /// * [`trunc`](fn.trunc.html)
-pub fn ceil<N: Real, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
+pub fn ceil<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     x.map(|x| x.ceil())
 }
@@ -222,7 +222,7 @@ where DefaultAllocator: Alloc<f32, D> {
 /// * [`fract`](fn.fract.html)
 /// * [`round`](fn.round.html)
 /// * [`trunc`](fn.trunc.html)
-pub fn floor<N: Real, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
+pub fn floor<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     x.map(|x| x.floor())
 }
@@ -249,14 +249,14 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`floor`](fn.floor.html)
 /// * [`round`](fn.round.html)
 /// * [`trunc`](fn.trunc.html)
-pub fn fract<N: Real, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
+pub fn fract<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     x.map(|x| x.fract())
 }
 
 //// FIXME: should be implemented for TVec/TMat?
 ///// Returns the (significant, exponent) of this float number.
-//pub fn frexp<N: Real>(x: N, exp: N) -> (N, N) {
+//pub fn frexp<N: RealField>(x: N, exp: N) -> (N, N) {
 //    // FIXME: is there a better approach?
 //    let e = x.log2().ceil();
 //    (x * (-e).exp2(), e)
@@ -310,7 +310,7 @@ where DefaultAllocator: Alloc<f32, D> {
 //}
 
 ///// Returns the (significant, exponent) of this float number.
-//pub fn ldexp<N: Real>(x: N, exp: N) -> N {
+//pub fn ldexp<N: RealField>(x: N, exp: N) -> N {
 //    // FIXME: is there a better approach?
 //    x * (exp).exp2()
 //}
@@ -499,7 +499,7 @@ pub fn modf<N: Number>(x: N, i: N) -> N {
 /// * [`floor`](fn.floor.html)
 /// * [`fract`](fn.fract.html)
 /// * [`trunc`](fn.trunc.html)
-pub fn round<N: Real, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
+pub fn round<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     x.map(|x| x.round())
 }
@@ -576,7 +576,7 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`floor`](fn.floor.html)
 /// * [`fract`](fn.fract.html)
 /// * [`round`](fn.round.html)
-pub fn trunc<N: Real, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
+pub fn trunc<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     x.map(|x| x.trunc())
 }

nalgebra-glm/src/constructors.rs

@@ -1,6 +1,6 @@
 #![cfg_attr(rustfmt, rustfmt_skip)]
 
-use na::{Scalar, Real, U2, U3, U4};
+use na::{Scalar, RealField, U2, U3, U4};
 use crate::aliases::{TMat, Qua, TVec1, TVec2, TVec3, TVec4, TMat2, TMat2x3, TMat2x4, TMat3, TMat3x2, TMat3x4,
               TMat4, TMat4x2, TMat4x3};
 
@@ -168,6 +168,6 @@ pub fn mat4<N: Scalar>(m11: N, m12: N, m13: N, m14: N,
 }
 
 /// Creates a new quaternion.
-pub fn quat<N: Real>(x: N, y: N, z: N, w: N) -> Qua<N> {
+pub fn quat<N: RealField>(x: N, y: N, z: N, w: N) -> Qua<N> {
     Qua::new(w, x, y, z)
 }

nalgebra-glm/src/exponential.rs

@@ -1,5 +1,5 @@
 use crate::aliases::TVec;
-use na::{DefaultAllocator, Real};
+use na::{DefaultAllocator, RealField};
 use crate::traits::{Alloc, Dimension};
 
 /// Component-wise exponential.
@@ -7,7 +7,7 @@ use crate::traits::{Alloc, Dimension};
 /// # See also:
 ///
 /// * [`exp2`](fn.exp2.html)
-pub fn exp<N: Real, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
+pub fn exp<N: RealField, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     v.map(|x| x.exp())
 }
@@ -17,7 +17,7 @@ where DefaultAllocator: Alloc<N, D> {
 /// # See also:
 ///
 /// * [`exp`](fn.exp.html)
-pub fn exp2<N: Real, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
+pub fn exp2<N: RealField, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     v.map(|x| x.exp2())
 }
@@ -27,7 +27,7 @@ where DefaultAllocator: Alloc<N, D> {
 /// # See also:
 ///
 /// * [`sqrt`](fn.sqrt.html)
-pub fn inversesqrt<N: Real, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
+pub fn inversesqrt<N: RealField, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     v.map(|x| N::one() / x.sqrt())
 }
@@ -37,7 +37,7 @@ where DefaultAllocator: Alloc<N, D> {
 /// # See also:
 ///
 /// * [`log2`](fn.log2.html)
-pub fn log<N: Real, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
+pub fn log<N: RealField, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     v.map(|x| x.ln())
 }
@@ -47,13 +47,13 @@ where DefaultAllocator: Alloc<N, D> {
 /// # See also:
 ///
 /// * [`log`](fn.log.html)
-pub fn log2<N: Real, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
+pub fn log2<N: RealField, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     v.map(|x| x.log2())
 }
 
 /// Component-wise power.
-pub fn pow<N: Real, D: Dimension>(base: &TVec<N, D>, exponent: &TVec<N, D>) -> TVec<N, D>
+pub fn pow<N: RealField, D: Dimension>(base: &TVec<N, D>, exponent: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     base.zip_map(exponent, |b, e| b.powf(e))
 }
@@ -66,7 +66,7 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`exp2`](fn.exp2.html)
 /// * [`inversesqrt`](fn.inversesqrt.html)
 /// * [`pow`](fn.pow.html)
-pub fn sqrt<N: Real, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
+pub fn sqrt<N: RealField, D: Dimension>(v: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     v.map(|x| x.sqrt())
 }

nalgebra-glm/src/ext/matrix_clip_space.rs

@@ -1,55 +1,55 @@
 use crate::aliases::TMat4;
-use na::{Real};
+use na::{RealField};
 
-//pub fn frustum<N: Real>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
+//pub fn frustum<N: RealField>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
 //    unimplemented!()
 //}
 
-//pub fn frustum_lh<N: Real>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
+//pub fn frustum_lh<N: RealField>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
 //    unimplemented!()
 //}
 //
-//pub fn frustum_lr_no<N: Real>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
+//pub fn frustum_lr_no<N: RealField>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
 //    unimplemented!()
 //}
 //
-//pub fn frustum_lh_zo<N: Real>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
+//pub fn frustum_lh_zo<N: RealField>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
 //    unimplemented!()
 //}
 //
-//pub fn frustum_no<N: Real>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
+//pub fn frustum_no<N: RealField>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
 //    unimplemented!()
 //}
 //
-//pub fn frustum_rh<N: Real>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
+//pub fn frustum_rh<N: RealField>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
 //    unimplemented!()
 //}
 //
-//pub fn frustum_rh_no<N: Real>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
+//pub fn frustum_rh_no<N: RealField>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
 //    unimplemented!()
 //}
 //
-//pub fn frustum_rh_zo<N: Real>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
+//pub fn frustum_rh_zo<N: RealField>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
 //    unimplemented!()
 //}
 //
-//pub fn frustum_zo<N: Real>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
+//pub fn frustum_zo<N: RealField>(left: N, right: N, bottom: N, top: N, near: N, far: N) -> TMat4<N> {
 //    unimplemented!()
 //}
 
-//pub fn infinite_perspective<N: Real>(fovy: N, aspect: N, near: N) -> TMat4<N> {
+//pub fn infinite_perspective<N: RealField>(fovy: N, aspect: N, near: N) -> TMat4<N> {
 //    unimplemented!()
 //}
 //
-//pub fn infinite_perspective_lh<N: Real>(fovy: N, aspect: N, near: N) -> TMat4<N> {
+//pub fn infinite_perspective_lh<N: RealField>(fovy: N, aspect: N, near: N) -> TMat4<N> {
 //    unimplemented!()
 //}
 //
-//pub fn infinite_perspective_rh<N: Real>(fovy: N, aspect: N, near: N) -> TMat4<N> {
+//pub fn infinite_perspective_rh<N: RealField>(fovy: N, aspect: N, near: N) -> TMat4<N> {
 //    unimplemented!()
 //}
 //
-//pub fn infinite_ortho<N: Real>(left: N, right: N, bottom: N, top: N) -> TMat4<N> {
+//pub fn infinite_ortho<N: RealField>(left: N, right: N, bottom: N, top: N) -> TMat4<N> {
 //    unimplemented!()
 //}
 
@@ -64,7 +64,7 @@ use na::{Real};
 /// * `znear` - Distance from the viewer to the near clipping plane
 /// * `zfar` - Distance from the viewer to the far clipping plane
 ///
-pub fn ortho<N: Real>(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> TMat4<N> {
+pub fn ortho<N: RealField>(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> TMat4<N> {
     ortho_rh_no(left, right, bottom, top, znear, zfar)
 }
 
@@ -79,7 +79,7 @@ pub fn ortho<N: Real>(left: N, right: N, bottom: N, top: N, znear: N, zfar: 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<N: Real>(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> TMat4<N> {
+pub fn ortho_lh<N: RealField>(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> TMat4<N> {
     ortho_lh_no(left, right, bottom, top, znear, zfar)
 }
 
@@ -94,7 +94,7 @@ pub fn ortho_lh<N: Real>(left: N, right: N, bottom: N, top: N, znear: N, zfar: 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_no<N: Real>(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();
 
@@ -119,7 +119,7 @@ pub fn ortho_lh_no<N: Real>(left: N, right: N, bottom: N, top: N, znear: N, zfar
 /// * `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: Real>(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();
@@ -145,7 +145,7 @@ pub fn ortho_lh_zo<N: Real>(left: N, right: N, bottom: N, top: N, znear: N, zfar
 /// * `znear` - Distance from the viewer to the near clipping plane
 /// * `zfar` - Distance from the viewer to the far clipping plane
 ///
-pub fn ortho_no<N: Real>(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> TMat4<N> {
+pub fn ortho_no<N: RealField>(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> TMat4<N> {
     ortho_rh_no(left, right, bottom, top, znear, zfar)
 }
 
@@ -160,7 +160,7 @@ pub fn ortho_no<N: Real>(left: N, right: N, bottom: N, top: N, znear: N, zfar: 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<N: Real>(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> TMat4<N> {
+pub fn ortho_rh<N: RealField>(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> TMat4<N> {
     ortho_rh_no(left, right, bottom, top, znear, zfar)
 }
 
@@ -175,7 +175,7 @@ pub fn ortho_rh<N: Real>(left: N, right: N, bottom: N, top: N, znear: N, zfar: 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_no<N: Real>(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();
 
@@ -200,7 +200,7 @@ pub fn ortho_rh_no<N: Real>(left: N, right: N, bottom: N, top: N, znear: N, zfar
 /// * `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: Real>(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();
@@ -226,7 +226,7 @@ pub fn ortho_rh_zo<N: Real>(left: N, right: N, bottom: N, top: N, znear: N, zfar
 /// * `znear` - Distance from the viewer to the near clipping plane
 /// * `zfar` - Distance from the viewer to the far clipping plane
 ///
-pub fn ortho_zo<N: Real>(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> TMat4<N> {
+pub fn ortho_zo<N: RealField>(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> TMat4<N> {
     ortho_rh_zo(left, right, bottom, top, znear, zfar)
 }
 
@@ -240,7 +240,7 @@ pub fn ortho_zo<N: Real>(left: N, right: N, bottom: N, top: N, znear: N, zfar: 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<N: Real>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_fov<N: RealField>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
     perspective_fov_rh_no(fov, width, height, near, far)
 }
 
@@ -254,7 +254,7 @@ pub fn perspective_fov<N: Real>(fov: N, width: N, height: N, near: N, far: 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<N: Real>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_fov_lh<N: RealField>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
     perspective_fov_lh_no(fov, width, height, near, far)
 }
 
@@ -268,7 +268,7 @@ pub fn perspective_fov_lh<N: Real>(fov: N, width: N, height: N, near: N, far: 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_no<N: Real>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_fov_lh_no<N: RealField>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
     assert!(
         width > N::zero(),
         "The width must be greater than zero"
@@ -307,7 +307,7 @@ pub fn perspective_fov_lh_no<N: Real>(fov: N, width: N, height: N, near: N, far:
 /// * `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: Real>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_fov_lh_zo<N: RealField>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
     assert!(
         width > N::zero(),
         "The width must be greater than zero"
@@ -346,7 +346,7 @@ pub fn perspective_fov_lh_zo<N: Real>(fov: N, width: N, height: N, near: N, far:
 /// * `near` - Distance from the viewer to the near clipping plane
 /// * `far` - Distance from the viewer to the far clipping plane
 ///
-pub fn perspective_fov_no<N: Real>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_fov_no<N: RealField>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
     perspective_fov_rh_no(fov, width, height, near, far)
 }
 
@@ -360,7 +360,7 @@ pub fn perspective_fov_no<N: Real>(fov: N, width: N, height: N, near: N, far: 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<N: Real>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_fov_rh<N: RealField>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
     perspective_fov_rh_no(fov, width, height, near, far)
 }
 
@@ -374,7 +374,7 @@ pub fn perspective_fov_rh<N: Real>(fov: N, width: N, height: N, near: N, far: 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_no<N: Real>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_fov_rh_no<N: RealField>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
     assert!(
         width > N::zero(),
         "The width must be greater than zero"
@@ -413,7 +413,7 @@ pub fn perspective_fov_rh_no<N: Real>(fov: N, width: N, height: N, near: N, far:
 /// * `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: Real>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_fov_rh_zo<N: RealField>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
     assert!(
         width > N::zero(),
         "The width must be greater than zero"
@@ -452,7 +452,7 @@ pub fn perspective_fov_rh_zo<N: Real>(fov: N, width: N, height: N, near: N, far:
 /// * `near` - Distance from the viewer to the near clipping plane
 /// * `far` - Distance from the viewer to the far clipping plane
 ///
-pub fn perspective_fov_zo<N: Real>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_fov_zo<N: RealField>(fov: N, width: N, height: N, near: N, far: N) -> TMat4<N> {
     perspective_fov_rh_zo(fov, width, height, near, far)
 }
 
@@ -467,7 +467,7 @@ pub fn perspective_fov_zo<N: Real>(fov: N, width: N, height: N, near: N, far: N)
 ///
 /// # Important note
 /// The `aspect` and `fovy` argument are interchanged compared to the original GLM API.
-pub fn perspective<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective<N: RealField>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
     // TODO: Breaking change - revert back to proper glm conventions?
     //
     //       Prior to changes to support configuring the behaviour of this function it was simply
@@ -496,7 +496,7 @@ pub fn perspective<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
 ///
 /// # Important note
 /// The `aspect` and `fovy` argument are interchanged compared to the original GLM API.
-pub fn perspective_lh<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_lh<N: RealField>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
     perspective_lh_no(aspect, fovy, near, far)
 }
 
@@ -511,7 +511,7 @@ pub fn perspective_lh<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N>
 ///
 /// # Important note
 /// The `aspect` and `fovy` argument are interchanged compared to the original GLM API.
-pub fn perspective_lh_no<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_lh_no<N: RealField>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
     assert!(
         !relative_eq!(far - near, N::zero()),
         "The near-plane and far-plane must not be superimposed."
@@ -547,7 +547,7 @@ pub fn perspective_lh_no<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<
 ///
 /// # Important note
 /// The `aspect` and `fovy` argument are interchanged compared to the original GLM API.
-pub fn perspective_lh_zo<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_lh_zo<N: RealField>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
     assert!(
         !relative_eq!(far - near, N::zero()),
         "The near-plane and far-plane must not be superimposed."
@@ -583,7 +583,7 @@ pub fn perspective_lh_zo<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<
 ///
 /// # Important note
 /// The `aspect` and `fovy` argument are interchanged compared to the original GLM API.
-pub fn perspective_no<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_no<N: RealField>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
     perspective_rh_no(aspect, fovy, near, far)
 }
 
@@ -598,7 +598,7 @@ pub fn perspective_no<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N>
 ///
 /// # Important note
 /// The `aspect` and `fovy` argument are interchanged compared to the original GLM API.
-pub fn perspective_rh<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_rh<N: RealField>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
     perspective_rh_no(aspect, fovy, near, far)
 }
 
@@ -613,7 +613,7 @@ pub fn perspective_rh<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N>
 ///
 /// # Important note
 /// The `aspect` and `fovy` argument are interchanged compared to the original GLM API.
-pub fn perspective_rh_no<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_rh_no<N: RealField>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
     assert!(
         !relative_eq!(far - near, N::zero()),
         "The near-plane and far-plane must not be superimposed."
@@ -650,7 +650,7 @@ pub fn perspective_rh_no<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<
 ///
 /// # Important note
 /// The `aspect` and `fovy` argument are interchanged compared to the original GLM API.
-pub fn perspective_rh_zo<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_rh_zo<N: RealField>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
     assert!(
         !relative_eq!(far - near, N::zero()),
         "The near-plane and far-plane must not be superimposed."
@@ -687,14 +687,14 @@ pub fn perspective_rh_zo<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<
 ///
 /// # Important note
 /// The `aspect` and `fovy` argument are interchanged compared to the original GLM API.
-pub fn perspective_zo<N: Real>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
+pub fn perspective_zo<N: RealField>(aspect: N, fovy: N, near: N, far: N) -> TMat4<N> {
     perspective_rh_zo(aspect, fovy, near, far)
 }
 
-//pub fn tweaked_infinite_perspective<N: Real>(fovy: N, aspect: N, near: N) -> TMat4<N> {
+//pub fn tweaked_infinite_perspective<N: RealField>(fovy: N, aspect: N, near: N) -> TMat4<N> {
 //    unimplemented!()
 //}
 //
-//pub fn tweaked_infinite_perspective_ep<N: Real>(fovy: N, aspect: N, near: N, ep: N) -> TMat4<N> {
+//pub fn tweaked_infinite_perspective_ep<N: RealField>(fovy: N, aspect: N, near: N, ep: N) -> TMat4<N> {
 //    unimplemented!()
 //}

nalgebra-glm/src/ext/matrix_projection.rs

@@ -1,4 +1,4 @@
-use na::{self, Real, U3};
+use na::{self, RealField, U3};
 
 use crate::aliases::{TMat4, TVec2, TVec3, TVec4};
 
@@ -9,7 +9,7 @@ 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: Real>(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,
@@ -41,7 +41,7 @@ pub fn pick_matrix<N: Real>(center: &TVec2<N>, delta: &TVec2<N>, viewport: &TVec
 /// * [`unproject`](fn.unproject.html)
 /// * [`unproject_no`](fn.unproject_no.html)
 /// * [`unproject_zo`](fn.unproject_zo.html)
-pub fn project<N: Real>(
+pub fn project<N: RealField>(
     obj: &TVec3<N>,
     model: &TMat4<N>,
     proj: &TMat4<N>,
@@ -69,7 +69,7 @@ pub fn project<N: Real>(
 /// * [`unproject`](fn.unproject.html)
 /// * [`unproject_no`](fn.unproject_no.html)
 /// * [`unproject_zo`](fn.unproject_zo.html)
-pub fn project_no<N: Real>(
+pub fn project_no<N: RealField>(
     obj: &TVec3<N>,
     model: &TMat4<N>,
     proj: &TMat4<N>,
@@ -98,7 +98,7 @@ pub fn project_no<N: Real>(
 /// * [`unproject`](fn.unproject.html)
 /// * [`unproject_no`](fn.unproject_no.html)
 /// * [`unproject_zo`](fn.unproject_zo.html)
-pub fn project_zo<N: Real>(
+pub fn project_zo<N: RealField>(
     obj: &TVec3<N>,
     model: &TMat4<N>,
     proj: &TMat4<N>,
@@ -132,7 +132,7 @@ pub fn project_zo<N: Real>(
 /// * [`project_zo`](fn.project_zo.html)
 /// * [`unproject_no`](fn.unproject_no.html)
 /// * [`unproject_zo`](fn.unproject_zo.html)
-pub fn unproject<N: Real>(
+pub fn unproject<N: RealField>(
     win: &TVec3<N>,
     model: &TMat4<N>,
     proj: &TMat4<N>,
@@ -160,7 +160,7 @@ pub fn unproject<N: Real>(
 /// * [`project_zo`](fn.project_zo.html)
 /// * [`unproject`](fn.unproject.html)
 /// * [`unproject_zo`](fn.unproject_zo.html)
-pub fn unproject_no<N: Real>(
+pub fn unproject_no<N: RealField>(
     win: &TVec3<N>,
     model: &TMat4<N>,
     proj: &TMat4<N>,
@@ -198,7 +198,7 @@ pub fn unproject_no<N: Real>(
 /// * [`project_zo`](fn.project_zo.html)
 /// * [`unproject`](fn.unproject.html)
 /// * [`unproject_no`](fn.unproject_no.html)
-pub fn unproject_zo<N: Real>(
+pub fn unproject_zo<N: RealField>(
     win: &TVec3<N>,
     model: &TMat4<N>,
     proj: &TMat4<N>,

nalgebra-glm/src/ext/matrix_transform.rs

@@ -1,4 +1,4 @@
-use na::{DefaultAllocator, Point3, Real, Rotation3, Unit};
+use na::{DefaultAllocator, Point3, RealField, Rotation3, Unit};
 
 use crate::aliases::{TMat, TMat4, TVec, TVec3};
 use crate::traits::{Alloc, Dimension, Number};
@@ -21,7 +21,7 @@ where DefaultAllocator: Alloc<N, D, D> {
 ///
 /// * [`look_at_lh`](fn.look_at_lh.html)
 /// * [`look_at_rh`](fn.look_at_rh.html)
-pub fn look_at<N: Real>(eye: &TVec3<N>, center: &TVec3<N>, up: &TVec3<N>) -> TMat4<N> {
+pub fn look_at<N: RealField>(eye: &TVec3<N>, center: &TVec3<N>, up: &TVec3<N>) -> TMat4<N> {
     look_at_rh(eye, center, up)
 }
 
@@ -37,7 +37,7 @@ pub fn look_at<N: Real>(eye: &TVec3<N>, center: &TVec3<N>, up: &TVec3<N>) -> TMa
 ///
 /// * [`look_at`](fn.look_at.html)
 /// * [`look_at_rh`](fn.look_at_rh.html)
-pub fn look_at_lh<N: Real>(eye: &TVec3<N>, center: &TVec3<N>, up: &TVec3<N>) -> TMat4<N> {
+pub fn look_at_lh<N: RealField>(eye: &TVec3<N>, center: &TVec3<N>, up: &TVec3<N>) -> TMat4<N> {
     TMat::look_at_lh(&Point3::from(*eye), &Point3::from(*center), up)
 }
 
@@ -53,7 +53,7 @@ pub fn look_at_lh<N: Real>(eye: &TVec3<N>, center: &TVec3<N>, up: &TVec3<N>) ->
 ///
 /// * [`look_at`](fn.look_at.html)
 /// * [`look_at_lh`](fn.look_at_lh.html)
-pub fn look_at_rh<N: Real>(eye: &TVec3<N>, center: &TVec3<N>, up: &TVec3<N>) -> TMat4<N> {
+pub fn look_at_rh<N: RealField>(eye: &TVec3<N>, center: &TVec3<N>, up: &TVec3<N>) -> TMat4<N> {
     TMat::look_at_rh(&Point3::from(*eye), &Point3::from(*center), up)
 }
 
@@ -72,7 +72,7 @@ pub fn look_at_rh<N: Real>(eye: &TVec3<N>, center: &TVec3<N>, up: &TVec3<N>) ->
 /// * [`rotate_z`](fn.rotate_z.html)
 /// * [`scale`](fn.scale.html)
 /// * [`translate`](fn.translate.html)
-pub fn rotate<N: Real>(m: &TMat4<N>, angle: N, axis: &TVec3<N>) -> TMat4<N> {
+pub fn rotate<N: RealField>(m: &TMat4<N>, angle: N, axis: &TVec3<N>) -> TMat4<N> {
     m * Rotation3::from_axis_angle(&Unit::new_normalize(*axis), angle).to_homogeneous()
 }
 
@@ -90,7 +90,7 @@ pub fn rotate<N: Real>(m: &TMat4<N>, angle: N, axis: &TVec3<N>) -> TMat4<N> {
 /// * [`rotate_z`](fn.rotate_z.html)
 /// * [`scale`](fn.scale.html)
 /// * [`translate`](fn.translate.html)
-pub fn rotate_x<N: Real>(m: &TMat4<N>, angle: N) -> TMat4<N> {
+pub fn rotate_x<N: RealField>(m: &TMat4<N>, angle: N) -> TMat4<N> {
     rotate(m, angle, &TVec::x())
 }
 
@@ -108,7 +108,7 @@ pub fn rotate_x<N: Real>(m: &TMat4<N>, angle: N) -> TMat4<N> {
 /// * [`rotate_z`](fn.rotate_z.html)
 /// * [`scale`](fn.scale.html)
 /// * [`translate`](fn.translate.html)
-pub fn rotate_y<N: Real>(m: &TMat4<N>, angle: N) -> TMat4<N> {
+pub fn rotate_y<N: RealField>(m: &TMat4<N>, angle: N) -> TMat4<N> {
     rotate(m, angle, &TVec::y())
 }
 
@@ -126,7 +126,7 @@ pub fn rotate_y<N: Real>(m: &TMat4<N>, angle: N) -> TMat4<N> {
 /// * [`rotate_y`](fn.rotate_y.html)
 /// * [`scale`](fn.scale.html)
 /// * [`translate`](fn.translate.html)
-pub fn rotate_z<N: Real>(m: &TMat4<N>, angle: N) -> TMat4<N> {
+pub fn rotate_z<N: RealField>(m: &TMat4<N>, angle: N) -> TMat4<N> {
     rotate(m, angle, &TVec::z())
 }
 

nalgebra-glm/src/ext/quaternion_common.rs

@@ -1,36 +1,36 @@
-use na::{self, Real, Unit};
+use na::{self, RealField, Unit};
 
 use crate::aliases::Qua;
 
 /// The conjugate of `q`.
-pub fn quat_conjugate<N: Real>(q: &Qua<N>) -> Qua<N> {
+pub fn quat_conjugate<N: RealField>(q: &Qua<N>) -> Qua<N> {
     q.conjugate()
 }
 
 /// The inverse of `q`.
-pub fn quat_inverse<N: Real>(q: &Qua<N>) -> Qua<N> {
+pub fn quat_inverse<N: RealField>(q: &Qua<N>) -> Qua<N> {
     q.try_inverse().unwrap_or_else(na::zero)
 }
 
-//pub fn quat_isinf<N: Real>(x: &Qua<N>) -> TVec<bool, U4> {
+//pub fn quat_isinf<N: RealField>(x: &Qua<N>) -> TVec<bool, U4> {
 //    x.coords.map(|e| e.is_inf())
 //}
 
-//pub fn quat_isnan<N: Real>(x: &Qua<N>) -> TVec<bool, U4> {
+//pub fn quat_isnan<N: RealField>(x: &Qua<N>) -> TVec<bool, U4> {
 //    x.coords.map(|e| e.is_nan())
 //}
 
 /// Interpolate linearly between `x` and `y`.
-pub fn quat_lerp<N: Real>(x: &Qua<N>, y: &Qua<N>, a: N) -> Qua<N> {
+pub fn quat_lerp<N: RealField>(x: &Qua<N>, y: &Qua<N>, a: N) -> Qua<N> {
     x.lerp(y, a)
 }
 
-//pub fn quat_mix<N: Real>(x: &Qua<N>, y: &Qua<N>, a: N) -> Qua<N> {
+//pub fn quat_mix<N: RealField>(x: &Qua<N>, y: &Qua<N>, a: N) -> Qua<N> {
 //    x * (N::one() - a) + y * a
 //}
 
 /// Interpolate spherically between `x` and `y`.
-pub fn quat_slerp<N: Real>(x: &Qua<N>, y: &Qua<N>, a: N) -> Qua<N> {
+pub fn quat_slerp<N: RealField>(x: &Qua<N>, y: &Qua<N>, a: N) -> Qua<N> {
     Unit::new_normalize(*x)
         .slerp(&Unit::new_normalize(*y), a)
         .into_inner()

nalgebra-glm/src/ext/quaternion_geometric.rs

@@ -1,28 +1,28 @@
-use na::Real;
+use na::RealField;
 
 use crate::aliases::Qua;
 
 /// Multiplies two quaternions.
-pub fn quat_cross<N: Real>(q1: &Qua<N>, q2: &Qua<N>) -> Qua<N> {
+pub fn quat_cross<N: RealField>(q1: &Qua<N>, q2: &Qua<N>) -> Qua<N> {
     q1 * q2
 }
 
 /// The scalar product of two quaternions.
-pub fn quat_dot<N: Real>(x: &Qua<N>, y: &Qua<N>) -> N {
+pub fn quat_dot<N: RealField>(x: &Qua<N>, y: &Qua<N>) -> N {
     x.dot(y)
 }
 
 /// The magnitude of the quaternion `q`.
-pub fn quat_length<N: Real>(q: &Qua<N>) -> N {
+pub fn quat_length<N: RealField>(q: &Qua<N>) -> N {
     q.norm()
 }
 
 /// The magnitude of the quaternion `q`.
-pub fn quat_magnitude<N: Real>(q: &Qua<N>) -> N {
+pub fn quat_magnitude<N: RealField>(q: &Qua<N>) -> N {
     q.norm()
 }
 
 /// Normalizes the quaternion `q`.
-pub fn quat_normalize<N: Real>(q: &Qua<N>) -> Qua<N> {
+pub fn quat_normalize<N: RealField>(q: &Qua<N>) -> Qua<N> {
     q.normalize()
 }

nalgebra-glm/src/ext/quaternion_relational.rs

@@ -1,23 +1,23 @@
-use na::{Real, U4};
+use na::{RealField, U4};
 
 use crate::aliases::{Qua, TVec};
 
 /// Component-wise equality comparison between two quaternions.
-pub fn quat_equal<N: Real>(x: &Qua<N>, y: &Qua<N>) -> TVec<bool, U4> {
+pub fn quat_equal<N: RealField>(x: &Qua<N>, y: &Qua<N>) -> TVec<bool, U4> {
     crate::equal(&x.coords, &y.coords)
 }
 
 /// Component-wise approximate equality comparison between two quaternions.
-pub fn quat_equal_eps<N: Real>(x: &Qua<N>, y: &Qua<N>, epsilon: N) -> TVec<bool, U4> {
+pub fn quat_equal_eps<N: RealField>(x: &Qua<N>, y: &Qua<N>, epsilon: N) -> TVec<bool, U4> {
     crate::equal_eps(&x.coords, &y.coords, epsilon)
 }
 
 /// Component-wise non-equality comparison between two quaternions.
-pub fn quat_not_equal<N: Real>(x: &Qua<N>, y: &Qua<N>) -> TVec<bool, U4> {
+pub fn quat_not_equal<N: RealField>(x: &Qua<N>, y: &Qua<N>) -> TVec<bool, U4> {
     crate::not_equal(&x.coords, &y.coords)
 }
 
 /// Component-wise approximate non-equality comparison between two quaternions.
-pub fn quat_not_equal_eps<N: Real>(x: &Qua<N>, y: &Qua<N>, epsilon: N) -> TVec<bool, U4> {
+pub fn quat_not_equal_eps<N: RealField>(x: &Qua<N>, y: &Qua<N>, epsilon: N) -> TVec<bool, U4> {
     crate::not_equal_eps(&x.coords, &y.coords, epsilon)
 }

nalgebra-glm/src/ext/quaternion_transform.rs

@@ -1,27 +1,27 @@
-use na::{Real, Unit, UnitQuaternion};
+use na::{RealField, Unit, UnitQuaternion};
 
 use crate::aliases::{Qua, TVec3};
 
 /// Computes the quaternion exponential.
-pub fn quat_exp<N: Real>(q: &Qua<N>) -> Qua<N> {
+pub fn quat_exp<N: RealField>(q: &Qua<N>) -> Qua<N> {
     q.exp()
 }
 
 /// Computes the quaternion logarithm.
-pub fn quat_log<N: Real>(q: &Qua<N>) -> Qua<N> {
+pub fn quat_log<N: RealField>(q: &Qua<N>) -> Qua<N> {
     q.ln()
 }
 
 /// Raises the quaternion `q` to the power `y`.
-pub fn quat_pow<N: Real>(q: &Qua<N>, y: N) -> Qua<N> {
+pub fn quat_pow<N: RealField>(q: &Qua<N>, y: N) -> Qua<N> {
     q.powf(y)
 }
 
 /// Builds a quaternion from an axis and an angle, and right-multiply it to the quaternion `q`.
-pub fn quat_rotate<N: Real>(q: &Qua<N>, angle: N, axis: &TVec3<N>) -> Qua<N> {
+pub fn quat_rotate<N: RealField>(q: &Qua<N>, angle: N, axis: &TVec3<N>) -> Qua<N> {
     q * UnitQuaternion::from_axis_angle(&Unit::new_normalize(*axis), angle).into_inner()
 }
 
-//pub fn quat_sqrt<N: Real>(q: &Qua<N>) -> Qua<N> {
+//pub fn quat_sqrt<N: RealField>(q: &Qua<N>) -> Qua<N> {
 //    unimplemented!()
 //}

nalgebra-glm/src/ext/quaternion_trigonometric.rs

@@ -1,19 +1,19 @@
-use na::{Real, Unit, UnitQuaternion};
+use na::{RealField, Unit, UnitQuaternion};
 
 use crate::aliases::{Qua, TVec3};
 
 /// The rotation angle of this quaternion assumed to be normalized.
-pub fn quat_angle<N: Real>(x: &Qua<N>) -> N {
+pub fn quat_angle<N: RealField>(x: &Qua<N>) -> N {
     UnitQuaternion::from_quaternion(*x).angle()
 }
 
 /// Creates a quaternion from an axis and an angle.
-pub fn quat_angle_axis<N: Real>(angle: N, axis: &TVec3<N>) -> Qua<N> {
+pub fn quat_angle_axis<N: RealField>(angle: N, axis: &TVec3<N>) -> Qua<N> {
     UnitQuaternion::from_axis_angle(&Unit::new_normalize(*axis), angle).into_inner()
 }
 
 /// The rotation axis of a quaternion assumed to be normalized.
-pub fn quat_axis<N: Real>(x: &Qua<N>) -> TVec3<N> {
+pub fn quat_axis<N: RealField>(x: &Qua<N>) -> TVec3<N> {
     if let Some(a) = UnitQuaternion::from_quaternion(*x).axis() {
         a.into_inner()
     } else {

nalgebra-glm/src/ext/scalar_constants.rs

@@ -1,5 +1,5 @@
 use approx::AbsDiffEq;
-use na::Real;
+use na::RealField;
 
 /// Default epsilon value used for approximate comparison.
 pub fn epsilon<N: AbsDiffEq<Epsilon = N>>() -> N {
@@ -22,6 +22,6 @@ pub fn epsilon<N: AbsDiffEq<Epsilon = N>>() -> N {
 /// * [`two_over_pi`](fn.two_over_pi.html)
 /// * [`two_over_root_pi`](fn.two_over_root_pi.html)
 /// * [`two_pi`](fn.two_pi.html)
-pub fn pi<N: Real>() -> N {
+pub fn pi<N: RealField>() -> N {
     N::pi()
 }

nalgebra-glm/src/geometric.rs

@@ -1,4 +1,4 @@
-use na::{DefaultAllocator, Real};
+use na::{DefaultAllocator, RealField};
 
 use crate::aliases::{TVec, TVec3};
 use crate::traits::{Alloc, Dimension, Number};
@@ -13,7 +13,7 @@ pub fn cross<N: Number, D: Dimension>(x: &TVec3<N>, y: &TVec3<N>) -> TVec3<N> {
 /// # See also:
 ///
 /// * [`distance2`](fn.distance2.html)
-pub fn distance<N: Real, D: Dimension>(p0: &TVec<N, D>, p1: &TVec<N, D>) -> N
+pub fn distance<N: RealField, D: Dimension>(p0: &TVec<N, D>, p1: &TVec<N, D>) -> N
 where DefaultAllocator: Alloc<N, D> {
     (p1 - p0).norm()
 }
@@ -49,7 +49,7 @@ where
 /// * [`length2`](fn.length2.html)
 /// * [`magnitude`](fn.magnitude.html)
 /// * [`magnitude2`](fn.magnitude2.html)
-pub fn length<N: Real, D: Dimension>(x: &TVec<N, D>) -> N
+pub fn length<N: RealField, D: Dimension>(x: &TVec<N, D>) -> N
 where DefaultAllocator: Alloc<N, D> {
     x.norm()
 }
@@ -63,13 +63,13 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`length`](fn.length.html)
 /// * [`magnitude2`](fn.magnitude2.html)
 /// * [`nalgebra::norm`](../nalgebra/fn.norm.html)
-pub fn magnitude<N: Real, D: Dimension>(x: &TVec<N, D>) -> N
+pub fn magnitude<N: RealField, D: Dimension>(x: &TVec<N, D>) -> N
 where DefaultAllocator: Alloc<N, D> {
     x.norm()
 }
 
 /// Normalizes a vector.
-pub fn normalize<N: Real, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
+pub fn normalize<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     x.normalize()
 }
@@ -82,7 +82,7 @@ where DefaultAllocator: Alloc<N, D> {
 }
 
 /// 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: Real, D: Dimension>(i: &TVec<N, D>, n: &TVec<N, D>, eta: N) -> TVec<N, D>
+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> {
     let ni = n.dot(i);
     let k = N::one() - eta * eta * (N::one() - ni * ni);

nalgebra-glm/src/gtc/constants.rs

@@ -1,14 +1,14 @@
-use na::{self, Real};
+use na::{self, RealField};
 
 /// The Euler constant.
 ///
 /// This is a shorthand alias for [`euler`](fn.euler.html).
-pub fn e<N: Real>() -> N {
+pub fn e<N: RealField>() -> N {
     N::e()
 }
 
 /// The Euler constant.
-pub fn euler<N: Real>() -> N {
+pub fn euler<N: RealField>() -> N {
     N::e()
 }
 
@@ -28,12 +28,12 @@ pub fn euler<N: Real>() -> N {
 /// * [`two_over_pi`](fn.two_over_pi.html)
 /// * [`two_over_root_pi`](fn.two_over_root_pi.html)
 /// * [`two_pi`](fn.two_pi.html)
-pub fn four_over_pi<N: Real>() -> N {
+pub fn four_over_pi<N: RealField>() -> N {
     na::convert::<_, N>(4.0) / N::pi()
 }
 
 /// Returns the golden ratio.
-pub fn golden_ratio<N: Real>() -> N {
+pub fn golden_ratio<N: RealField>() -> N {
     (N::one() + root_five()) / na::convert(2.0)
 }
 
@@ -53,7 +53,7 @@ pub fn golden_ratio<N: Real>() -> N {
 /// * [`two_over_pi`](fn.two_over_pi.html)
 /// * [`two_over_root_pi`](fn.two_over_root_pi.html)
 /// * [`two_pi`](fn.two_pi.html)
-pub fn half_pi<N: Real>() -> N {
+pub fn half_pi<N: RealField>() -> N {
     N::frac_pi_2()
 }
 
@@ -63,7 +63,7 @@ pub fn half_pi<N: Real>() -> N {
 ///
 /// * [`ln_ten`](fn.ln_ten.html)
 /// * [`ln_two`](fn.ln_two.html)
-pub fn ln_ln_two<N: Real>() -> N {
+pub fn ln_ln_two<N: RealField>() -> N {
     N::ln_2().ln()
 }
 
@@ -73,7 +73,7 @@ pub fn ln_ln_two<N: Real>() -> N {
 ///
 /// * [`ln_ln_two`](fn.ln_ln_two.html)
 /// * [`ln_two`](fn.ln_two.html)
-pub fn ln_ten<N: Real>() -> N {
+pub fn ln_ten<N: RealField>() -> N {
     N::ln_10()
 }
 
@@ -83,7 +83,7 @@ pub fn ln_ten<N: Real>() -> N {
 ///
 /// * [`ln_ln_two`](fn.ln_ln_two.html)
 /// * [`ln_ten`](fn.ln_ten.html)
-pub fn ln_two<N: Real>() -> N {
+pub fn ln_two<N: RealField>() -> N {
     N::ln_2()
 }
 
@@ -106,12 +106,12 @@ pub use na::one;
 /// * [`two_over_pi`](fn.two_over_pi.html)
 /// * [`two_over_root_pi`](fn.two_over_root_pi.html)
 /// * [`two_pi`](fn.two_pi.html)
-pub fn one_over_pi<N: Real>() -> N {
+pub fn one_over_pi<N: RealField>() -> N {
     N::frac_1_pi()
 }
 
 /// Returns `1 / sqrt(2)`.
-pub fn one_over_root_two<N: Real>() -> N {
+pub fn one_over_root_two<N: RealField>() -> N {
     N::one() / root_two()
 }
 
@@ -131,7 +131,7 @@ pub fn one_over_root_two<N: Real>() -> N {
 /// * [`two_over_pi`](fn.two_over_pi.html)
 /// * [`two_over_root_pi`](fn.two_over_root_pi.html)
 /// * [`two_pi`](fn.two_pi.html)
-pub fn one_over_two_pi<N: Real>() -> N {
+pub fn one_over_two_pi<N: RealField>() -> N {
     N::frac_1_pi() * na::convert(0.5)
 }
 
@@ -151,7 +151,7 @@ pub fn one_over_two_pi<N: Real>() -> N {
 /// * [`two_over_pi`](fn.two_over_pi.html)
 /// * [`two_over_root_pi`](fn.two_over_root_pi.html)
 /// * [`two_pi`](fn.two_pi.html)
-pub fn quarter_pi<N: Real>() -> N {
+pub fn quarter_pi<N: RealField>() -> N {
     N::frac_pi_4()
 }
 
@@ -161,7 +161,7 @@ pub fn quarter_pi<N: Real>() -> N {
 ///
 /// * [`root_three`](fn.root_three.html)
 /// * [`root_two`](fn.root_two.html)
-pub fn root_five<N: Real>() -> N {
+pub fn root_five<N: RealField>() -> N {
     na::convert::<_, N>(5.0).sqrt()
 }
 
@@ -181,12 +181,12 @@ pub fn root_five<N: Real>() -> N {
 /// * [`two_over_pi`](fn.two_over_pi.html)
 /// * [`two_over_root_pi`](fn.two_over_root_pi.html)
 /// * [`two_pi`](fn.two_pi.html)
-pub fn root_half_pi<N: Real>() -> N {
+pub fn root_half_pi<N: RealField>() -> N {
     (N::pi() / na::convert(2.0)).sqrt()
 }
 
 /// Returns `sqrt(ln(4))`.
-pub fn root_ln_four<N: Real>() -> N {
+pub fn root_ln_four<N: RealField>() -> N {
     na::convert::<_, N>(4.0).ln().sqrt()
 }
 
@@ -206,7 +206,7 @@ pub fn root_ln_four<N: Real>() -> N {
 /// * [`two_over_pi`](fn.two_over_pi.html)
 /// * [`two_over_root_pi`](fn.two_over_root_pi.html)
 /// * [`two_pi`](fn.two_pi.html)
-pub fn root_pi<N: Real>() -> N {
+pub fn root_pi<N: RealField>() -> N {
     N::pi().sqrt()
 }
 
@@ -216,7 +216,7 @@ pub fn root_pi<N: Real>() -> N {
 ///
 /// * [`root_five`](fn.root_five.html)
 /// * [`root_two`](fn.root_two.html)
-pub fn root_three<N: Real>() -> N {
+pub fn root_three<N: RealField>() -> N {
     na::convert::<_, N>(3.0).sqrt()
 }
 
@@ -226,8 +226,8 @@ pub fn root_three<N: Real>() -> N {
 ///
 /// * [`root_five`](fn.root_five.html)
 /// * [`root_three`](fn.root_three.html)
-pub fn root_two<N: Real>() -> N {
+pub fn root_two<N: RealField>() -> N {
-    // FIXME: there should be a crate::sqrt_2() on the Real trait.
+    // FIXME: there should be a crate::sqrt_2() on the RealField trait.
     na::convert::<_, N>(2.0).sqrt()
 }
 
@@ -247,7 +247,7 @@ pub fn root_two<N: Real>() -> N {
 /// * [`two_over_pi`](fn.two_over_pi.html)
 /// * [`two_over_root_pi`](fn.two_over_root_pi.html)
 /// * [`two_pi`](fn.two_pi.html)
-pub fn root_two_pi<N: Real>() -> N {
+pub fn root_two_pi<N: RealField>() -> N {
     N::two_pi().sqrt()
 }
 
@@ -256,7 +256,7 @@ pub fn root_two_pi<N: Real>() -> N {
 /// # See also:
 ///
 /// * [`two_thirds`](fn.two_thirds.html)
-pub fn third<N: Real>() -> N {
+pub fn third<N: RealField>() -> N {
     na::convert(1.0 / 3.0)
 }
 
@@ -276,7 +276,7 @@ pub fn third<N: Real>() -> N {
 /// * [`two_over_pi`](fn.two_over_pi.html)
 /// * [`two_over_root_pi`](fn.two_over_root_pi.html)
 /// * [`two_pi`](fn.two_pi.html)
-pub fn three_over_two_pi<N: Real>() -> N {
+pub fn three_over_two_pi<N: RealField>() -> N {
     na::convert::<_, N>(3.0) / N::two_pi()
 }
 
@@ -295,7 +295,7 @@ pub fn three_over_two_pi<N: Real>() -> N {
 /// * [`three_over_two_pi`](fn.three_over_two_pi.html)
 /// * [`two_over_root_pi`](fn.two_over_root_pi.html)
 /// * [`two_pi`](fn.two_pi.html)
-pub fn two_over_pi<N: Real>() -> N {
+pub fn two_over_pi<N: RealField>() -> N {
     N::frac_2_pi()
 }
 
@@ -315,7 +315,7 @@ pub fn two_over_pi<N: Real>() -> N {
 /// * [`three_over_two_pi`](fn.three_over_two_pi.html)
 /// * [`two_over_pi`](fn.two_over_pi.html)
 /// * [`two_pi`](fn.two_pi.html)
-pub fn two_over_root_pi<N: Real>() -> N {
+pub fn two_over_root_pi<N: RealField>() -> N {
     N::frac_2_sqrt_pi()
 }
 
@@ -335,7 +335,7 @@ pub fn two_over_root_pi<N: Real>() -> N {
 /// * [`three_over_two_pi`](fn.three_over_two_pi.html)
 /// * [`two_over_pi`](fn.two_over_pi.html)
 /// * [`two_over_root_pi`](fn.two_over_root_pi.html)
-pub fn two_pi<N: Real>() -> N {
+pub fn two_pi<N: RealField>() -> N {
     N::two_pi()
 }
 
@@ -344,7 +344,7 @@ pub fn two_pi<N: Real>() -> N {
 /// # See also:
 ///
 /// * [`third`](fn.third.html)
-pub fn two_thirds<N: Real>() -> N {
+pub fn two_thirds<N: RealField>() -> N {
     na::convert(2.0 / 3.0)
 }
 

nalgebra-glm/src/gtc/matrix_inverse.rs

@@ -1,17 +1,17 @@
-use na::{DefaultAllocator, Real};
+use na::{DefaultAllocator, RealField};
 
 use crate::aliases::TMat;
 use crate::traits::{Alloc, Dimension};
 
 /// Fast matrix inverse for affine matrix.
-pub fn affine_inverse<N: Real, D: Dimension>(m: TMat<N, D, D>) -> TMat<N, D, D>
+pub fn affine_inverse<N: RealField, D: Dimension>(m: TMat<N, D, D>) -> TMat<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: Real, D: Dimension>(m: TMat<N, D, D>) -> TMat<N, D, D>
+pub fn inverse_transpose<N: RealField, D: Dimension>(m: TMat<N, D, D>) -> TMat<N, D, D>
 where DefaultAllocator: Alloc<N, D, D> {
     m.try_inverse()
         .unwrap_or_else(TMat::<_, D, D>::zeros)

nalgebra-glm/src/gtc/packing.rs

@@ -1,4 +1,4 @@
-use na::{Scalar, Real, DefaultAllocator, U3, U4};
+use na::{Scalar, RealField, DefaultAllocator, U3, U4};
 
 use crate::traits::{Alloc, Dimension};
 use crate::aliases::*;
@@ -53,7 +53,7 @@ pub fn packRGBM<N: Scalar>(rgb: &TVec3<N>) -> TVec4<N> {
     unimplemented!()
 }
 
-pub fn packSnorm<I: Scalar, N: Real, D: Dimension>(v: TVec<N, D>) -> TVec<I, D>
+pub fn packSnorm<I: Scalar, N: RealField, D: Dimension>(v: TVec<N, D>) -> TVec<I, D>
     where DefaultAllocator: Alloc<N, D> + Alloc<I, D> {
     unimplemented!()
 }
@@ -102,7 +102,7 @@ pub fn packUint4x8(v: &U8Vec4) -> i32 {
     unimplemented!()
 }
 
-pub fn packUnorm<UI: Scalar, N: Real, D: Dimension>(v: &TVec<N, D>) -> TVec<UI, D>
+pub fn packUnorm<UI: Scalar, N: RealField, D: Dimension>(v: &TVec<N, D>) -> TVec<UI, D>
     where DefaultAllocator: Alloc<N, D> + Alloc<UI, D> {
     unimplemented!()
 }
@@ -196,7 +196,7 @@ pub fn unpackRGBM<N: Scalar>(rgbm: &TVec4<N>) -> TVec3<N> {
     unimplemented!()
 }
 
-pub fn unpackSnorm<I: Scalar, N: Real, D: Dimension>(v: &TVec<I, D>) -> TVec<N, D>
+pub fn unpackSnorm<I: Scalar, N: RealField, D: Dimension>(v: &TVec<I, D>) -> TVec<N, D>
     where DefaultAllocator: Alloc<N, D> + Alloc<I, D> {
     unimplemented!()
 }
@@ -245,7 +245,7 @@ pub fn unpackUint4x8(p: i32) -> U8Vec4 {
     unimplemented!()
 }
 
-pub fn unpackUnorm<UI: Scalar, N: Real, D: Dimension>(v: &TVec<UI, D>) -> TVec<N, D>
+pub fn unpackUnorm<UI: Scalar, N: RealField, D: Dimension>(v: &TVec<UI, D>) -> TVec<N, D>
     where DefaultAllocator: Alloc<N, D> + Alloc<UI, D> {
     unimplemented!()
 }

nalgebra-glm/src/gtc/quaternion.rs

@@ -1,36 +1,36 @@
-use na::{Real, UnitQuaternion, U4};
+use na::{RealField, UnitQuaternion, U4};
 
 use crate::aliases::{Qua, TMat4, TVec, TVec3};
 
 /// Euler angles of the quaternion `q` as (pitch, yaw, roll).
-pub fn quat_euler_angles<N: Real>(x: &Qua<N>) -> TVec3<N> {
+pub fn quat_euler_angles<N: RealField>(x: &Qua<N>) -> TVec3<N> {
     let q = UnitQuaternion::new_unchecked(*x);
     let a = q.euler_angles();
     TVec3::new(a.2, a.1, a.0)
 }
 
 /// Component-wise `>` comparison between two quaternions.
-pub fn quat_greater_than<N: Real>(x: &Qua<N>, y: &Qua<N>) -> TVec<bool, U4> {
+pub fn quat_greater_than<N: RealField>(x: &Qua<N>, y: &Qua<N>) -> TVec<bool, U4> {
     crate::greater_than(&x.coords, &y.coords)
 }
 
 /// Component-wise `>=` comparison between two quaternions.
-pub fn quat_greater_than_equal<N: Real>(x: &Qua<N>, y: &Qua<N>) -> TVec<bool, U4> {
+pub fn quat_greater_than_equal<N: RealField>(x: &Qua<N>, y: &Qua<N>) -> TVec<bool, U4> {
     crate::greater_than_equal(&x.coords, &y.coords)
 }
 
 /// Component-wise `<` comparison between two quaternions.
-pub fn quat_less_than<N: Real>(x: &Qua<N>, y: &Qua<N>) -> TVec<bool, U4> {
+pub fn quat_less_than<N: RealField>(x: &Qua<N>, y: &Qua<N>) -> TVec<bool, U4> {
     crate::less_than(&x.coords, &y.coords)
 }
 
 /// Component-wise `<=` comparison between two quaternions.
-pub fn quat_less_than_equal<N: Real>(x: &Qua<N>, y: &Qua<N>) -> TVec<bool, U4> {
+pub fn quat_less_than_equal<N: RealField>(x: &Qua<N>, y: &Qua<N>) -> TVec<bool, U4> {
     crate::less_than_equal(&x.coords, &y.coords)
 }
 
 /// Convert a quaternion to a rotation matrix in homogeneous coordinates.
-pub fn quat_cast<N: Real>(x: &Qua<N>) -> TMat4<N> {
+pub fn quat_cast<N: RealField>(x: &Qua<N>) -> TMat4<N> {
     crate::quat_to_mat4(x)
 }
 
@@ -41,34 +41,34 @@ pub fn quat_cast<N: Real>(x: &Qua<N>) -> TMat4<N> {
 /// * `direction` - Direction vector point at where to look
 /// * `up` - Object up vector
 ///
-pub fn quat_look_at<N: Real>(direction: &TVec3<N>, up: &TVec3<N>) -> Qua<N> {
+pub fn quat_look_at<N: RealField>(direction: &TVec3<N>, up: &TVec3<N>) -> Qua<N> {
     quat_look_at_rh(direction, up)
 }
 
 /// Computes a left-handed look-at quaternion (equivalent to a left-handed look-at matrix).
-pub fn quat_look_at_lh<N: Real>(direction: &TVec3<N>, up: &TVec3<N>) -> Qua<N> {
+pub fn quat_look_at_lh<N: RealField>(direction: &TVec3<N>, up: &TVec3<N>) -> Qua<N> {
     UnitQuaternion::look_at_lh(direction, up).into_inner()
 }
 
 /// Computes a right-handed look-at quaternion (equivalent to a right-handed look-at matrix).
-pub fn quat_look_at_rh<N: Real>(direction: &TVec3<N>, up: &TVec3<N>) -> Qua<N> {
+pub fn quat_look_at_rh<N: RealField>(direction: &TVec3<N>, up: &TVec3<N>) -> Qua<N> {
     UnitQuaternion::look_at_rh(direction, up).into_inner()
 }
 
 /// The "roll" Euler angle of the quaternion `x` assumed to be normalized.
-pub fn quat_roll<N: Real>(x: &Qua<N>) -> N {
+pub fn quat_roll<N: RealField>(x: &Qua<N>) -> N {
     // FIXME: optimize this.
     quat_euler_angles(x).z
 }
 
 /// The "yaw" Euler angle of the quaternion `x` assumed to be normalized.
-pub fn quat_yaw<N: Real>(x: &Qua<N>) -> N {
+pub fn quat_yaw<N: RealField>(x: &Qua<N>) -> N {
     // FIXME: optimize this.
     quat_euler_angles(x).y
 }
 
 /// The "pitch" Euler angle of the quaternion `x` assumed to be normalized.
-pub fn quat_pitch<N: Real>(x: &Qua<N>) -> N {
+pub fn quat_pitch<N: RealField>(x: &Qua<N>) -> N {
     // FIXME: optimize this.
     quat_euler_angles(x).x
 }

nalgebra-glm/src/gtc/round.rs

@@ -1,4 +1,4 @@
-use na::{Scalar, Real, U3, DefaultAllocator};
+use na::{Scalar, RealField, U3, DefaultAllocator};
 
 use crate::traits::{Number, Alloc, Dimension};
 use crate::aliases::TVec;

nalgebra-glm/src/gtc/type_ptr.rs

@@ -1,4 +1,4 @@
-use na::{DefaultAllocator, Quaternion, Real, Scalar};
+use na::{DefaultAllocator, Quaternion, RealField, Scalar};
 
 use crate::aliases::{
     Qua, TMat, TMat2, TMat2x3, TMat2x4, TMat3, TMat3x2, TMat3x4, TMat4, TMat4x2, TMat4x3, TVec1,
@@ -112,7 +112,7 @@ pub fn mat4_to_mat2<N: Scalar>(m: &TMat4<N>) -> TMat2<N> {
 }
 
 /// Creates a quaternion from a slice arranged as `[x, y, z, w]`.
-pub fn make_quat<N: Real>(ptr: &[N]) -> Qua<N> {
+pub fn make_quat<N: RealField>(ptr: &[N]) -> Qua<N> {
     Quaternion::from(TVec4::from_column_slice(ptr))
 }
 

nalgebra-glm/src/gtx/euler_angles.rs

@@ -1,163 +1,163 @@
-use na::{Real, U3, U4};
+use na::{RealField, U3, U4};
 
 use crate::aliases::{TVec, TMat};
 
-pub fn derivedEulerAngleX<N: Real>(angleX: N, angularVelocityX: N) -> TMat4<N> {
+pub fn derivedEulerAngleX<N: RealField>(angleX: N, angularVelocityX: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn derivedEulerAngleY<N: Real>(angleY: N, angularVelocityY: N) -> TMat4<N> {
+pub fn derivedEulerAngleY<N: RealField>(angleY: N, angularVelocityY: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn derivedEulerAngleZ<N: Real>(angleZ: N, angularVelocityZ: N) -> TMat4<N> {
+pub fn derivedEulerAngleZ<N: RealField>(angleZ: N, angularVelocityZ: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleX<N: Real>(angleX: N) -> TMat4<N> {
+pub fn eulerAngleX<N: RealField>(angleX: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleXY<N: Real>(angleX: N, angleY: N) -> TMat4<N> {
+pub fn eulerAngleXY<N: RealField>(angleX: N, angleY: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleXYX<N: Real>(t1: N, t2: N, t3: N) -> TMat4<N> {
+pub fn eulerAngleXYX<N: RealField>(t1: N, t2: N, t3: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleXYZ<N: Real>(t1: N, t2: N, t3: N) -> TMat4<N> {
+pub fn eulerAngleXYZ<N: RealField>(t1: N, t2: N, t3: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleXZ<N: Real>(angleX: N, angleZ: N) -> TMat4<N> {
+pub fn eulerAngleXZ<N: RealField>(angleX: N, angleZ: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleXZX<N: Real>(t1: N, t2: N, t3: N) -> TMat4<N> {
+pub fn eulerAngleXZX<N: RealField>(t1: N, t2: N, t3: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleXZY<N: Real>(t1: N, t2: N, t3: N) -> TMat4<N> {
+pub fn eulerAngleXZY<N: RealField>(t1: N, t2: N, t3: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleY<N: Real>(angleY: N) -> TMat4<N> {
+pub fn eulerAngleY<N: RealField>(angleY: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleYX<N: Real>(angleY: N, angleX: N) -> TMat4<N> {
+pub fn eulerAngleYX<N: RealField>(angleY: N, angleX: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleYXY<N: Real>(t1: N, t2: N, t3: N) -> TMat4<N> {
+pub fn eulerAngleYXY<N: RealField>(t1: N, t2: N, t3: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleYXZ<N: Real>(yaw: N, pitch: N, roll: N) -> TMat4<N> {
+pub fn eulerAngleYXZ<N: RealField>(yaw: N, pitch: N, roll: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleYZ<N: Real>(angleY: N, angleZ: N) -> TMat4<N> {
+pub fn eulerAngleYZ<N: RealField>(angleY: N, angleZ: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleYZX<N: Real>(t1: N, t2: N, t3: N) -> TMat4<N> {
+pub fn eulerAngleYZX<N: RealField>(t1: N, t2: N, t3: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleYZY<N: Real>(t1: N, t2: N, t3: N) -> TMat4<N> {
+pub fn eulerAngleYZY<N: RealField>(t1: N, t2: N, t3: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleZ<N: Real>(angleZ: N) -> TMat4<N> {
+pub fn eulerAngleZ<N: RealField>(angleZ: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleZX<N: Real>(angle: N, angleX: N) -> TMat4<N> {
+pub fn eulerAngleZX<N: RealField>(angle: N, angleX: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleZXY<N: Real>(t1: N, t2: N, t3: N) -> TMat4<N> {
+pub fn eulerAngleZXY<N: RealField>(t1: N, t2: N, t3: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleZXZ<N: Real>(t1: N, t2: N, t3: N) -> TMat4<N> {
+pub fn eulerAngleZXZ<N: RealField>(t1: N, t2: N, t3: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleZY<N: Real>(angleZ: N, angleY: N) -> TMat4<N> {
+pub fn eulerAngleZY<N: RealField>(angleZ: N, angleY: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleZYX<N: Real>(t1: N, t2: N, t3: N) -> TMat4<N> {
+pub fn eulerAngleZYX<N: RealField>(t1: N, t2: N, t3: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn eulerAngleZYZ<N: Real>(t1: N, t2: N, t3: N) -> TMat4<N> {
+pub fn eulerAngleZYZ<N: RealField>(t1: N, t2: N, t3: N) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn extractEulerAngleXYX<N: Real>(M: &TMat4<N>) -> (N, N, N) {
+pub fn extractEulerAngleXYX<N: RealField>(M: &TMat4<N>) -> (N, N, N) {
     unimplemented!()
 }
 
-pub fn extractEulerAngleXYZ<N: Real>(M: &TMat4<N>) -> (N, N, N) {
+pub fn extractEulerAngleXYZ<N: RealField>(M: &TMat4<N>) -> (N, N, N) {
     unimplemented!()
 }
 
-pub fn extractEulerAngleXZX<N: Real>(M: &TMat4<N>) -> (N, N, N) {
+pub fn extractEulerAngleXZX<N: RealField>(M: &TMat4<N>) -> (N, N, N) {
     unimplemented!()
 }
 
-pub fn extractEulerAngleXZY<N: Real>(M: &TMat4<N>) -> (N, N, N) {
+pub fn extractEulerAngleXZY<N: RealField>(M: &TMat4<N>) -> (N, N, N) {
     unimplemented!()
 }
 
-pub fn extractEulerAngleYXY<N: Real>(M: &TMat4<N>) -> (N, N, N) {
+pub fn extractEulerAngleYXY<N: RealField>(M: &TMat4<N>) -> (N, N, N) {
     unimplemented!()
 }
 
-pub fn extractEulerAngleYXZ<N: Real>(M: &TMat4<N>) -> (N, N, N) {
+pub fn extractEulerAngleYXZ<N: RealField>(M: &TMat4<N>) -> (N, N, N) {
     unimplemented!()
 }
 
-pub fn extractEulerAngleYZX<N: Real>(M: &TMat4<N>) -> (N, N, N) {
+pub fn extractEulerAngleYZX<N: RealField>(M: &TMat4<N>) -> (N, N, N) {
     unimplemented!()
 }
 
-pub fn extractEulerAngleYZY<N: Real>(M: &TMat4<N>) -> (N, N, N) {
+pub fn extractEulerAngleYZY<N: RealField>(M: &TMat4<N>) -> (N, N, N) {
     unimplemented!()
 }
 
-pub fn extractEulerAngleZXY<N: Real>(M: &TMat4<N>) -> (N, N, N) {
+pub fn extractEulerAngleZXY<N: RealField>(M: &TMat4<N>) -> (N, N, N) {
     unimplemented!()
 }
 
-pub fn extractEulerAngleZXZ<N: Real>(M: &TMat4<N>) -> (N, N, N) {
+pub fn extractEulerAngleZXZ<N: RealField>(M: &TMat4<N>) -> (N, N, N) {
     unimplemented!()
 }
 
-pub fn extractEulerAngleZYX<N: Real>(M: &TMat4<N>) -> (N, N, N) {
+pub fn extractEulerAngleZYX<N: RealField>(M: &TMat4<N>) -> (N, N, N) {
     unimplemented!()
 }
 
-pub fn extractEulerAngleZYZ<N: Real>(M: &TMat4<N>) -> (N, N, N) {
+pub fn extractEulerAngleZYZ<N: RealField>(M: &TMat4<N>) -> (N, N, N) {
     unimplemented!()
 }
 
-pub fn orientate2<N: Real>(angle: N) -> TMat3x3<N> {
+pub fn orientate2<N: RealField>(angle: N) -> TMat3x3<N> {
     unimplemented!()
 }
 
-pub fn orientate3<N: Real>(angles: TVec3<N>) -> TMat3x3<N> {
+pub fn orientate3<N: RealField>(angles: TVec3<N>) -> TMat3x3<N> {
     unimplemented!()
 }
 
-pub fn orientate4<N: Real>(angles: TVec3<N>) -> TMat4<N> {
+pub fn orientate4<N: RealField>(angles: TVec3<N>) -> TMat4<N> {
     unimplemented!()
 }
 
-pub fn yawPitchRoll<N: Real>(yaw: N, pitch: N, roll: N) -> TMat4<N> {
+pub fn yawPitchRoll<N: RealField>(yaw: N, pitch: N, roll: N) -> TMat4<N> {
     unimplemented!()
 }

nalgebra-glm/src/gtx/matrix_cross_product.rs

@@ -1,4 +1,4 @@
-use na::Real;
+use na::RealField;
 
 use crate::aliases::{TMat3, TMat4, TVec3};
 
@@ -7,7 +7,7 @@ use crate::aliases::{TMat3, TMat4, TVec3};
 /// # See also:
 ///
 /// * [`matrix_cross`](fn.matrix_cross.html)
-pub fn matrix_cross3<N: Real>(x: &TVec3<N>) -> TMat3<N> {
+pub fn matrix_cross3<N: RealField>(x: &TVec3<N>) -> TMat3<N> {
     x.cross_matrix()
 }
 
@@ -16,6 +16,6 @@ pub fn matrix_cross3<N: Real>(x: &TVec3<N>) -> TMat3<N> {
 /// # See also:
 ///
 /// * [`matrix_cross3`](fn.matrix_cross3.html)
-pub fn matrix_cross<N: Real>(x: &TVec3<N>) -> TMat4<N> {
+pub fn matrix_cross<N: RealField>(x: &TVec3<N>) -> TMat4<N> {
     crate::mat3_to_mat4(&x.cross_matrix())
 }

nalgebra-glm/src/gtx/norm.rs

@@ -1,4 +1,4 @@
-use na::{DefaultAllocator, Real};
+use na::{DefaultAllocator, RealField};
 
 use crate::aliases::TVec;
 use crate::traits::{Alloc, Dimension};
@@ -8,7 +8,7 @@ use crate::traits::{Alloc, Dimension};
 /// # See also:
 ///
 /// * [`distance`](fn.distance.html)
-pub fn distance2<N: Real, D: Dimension>(p0: &TVec<N, D>, p1: &TVec<N, D>) -> N
+pub fn distance2<N: RealField, D: Dimension>(p0: &TVec<N, D>, p1: &TVec<N, D>) -> N
 where DefaultAllocator: Alloc<N, D> {
     (p1 - p0).norm_squared()
 }
@@ -20,7 +20,7 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`l1_norm`](fn.l1_norm.html)
 /// * [`l2_distance`](fn.l2_distance.html)
 /// * [`l2_norm`](fn.l2_norm.html)
-pub fn l1_distance<N: Real, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
+pub fn l1_distance<N: RealField, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
 where DefaultAllocator: Alloc<N, D> {
     l1_norm(&(y - x))
 }
@@ -35,7 +35,7 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`l1_distance`](fn.l1_distance.html)
 /// * [`l2_distance`](fn.l2_distance.html)
 /// * [`l2_norm`](fn.l2_norm.html)
-pub fn l1_norm<N: Real, D: Dimension>(v: &TVec<N, D>) -> N
+pub fn l1_norm<N: RealField, D: Dimension>(v: &TVec<N, D>) -> N
 where DefaultAllocator: Alloc<N, D> {
     crate::comp_add(&v.abs())
 }
@@ -54,7 +54,7 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`length2`](fn.length2.html)
 /// * [`magnitude`](fn.magnitude.html)
 /// * [`magnitude2`](fn.magnitude2.html)
-pub fn l2_distance<N: Real, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
+pub fn l2_distance<N: RealField, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
 where DefaultAllocator: Alloc<N, D> {
     l2_norm(&(y - x))
 }
@@ -75,7 +75,7 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`length2`](fn.length2.html)
 /// * [`magnitude`](fn.magnitude.html)
 /// * [`magnitude2`](fn.magnitude2.html)
-pub fn l2_norm<N: Real, D: Dimension>(x: &TVec<N, D>) -> N
+pub fn l2_norm<N: RealField, D: Dimension>(x: &TVec<N, D>) -> N
 where DefaultAllocator: Alloc<N, D> {
     x.norm()
 }
@@ -91,7 +91,7 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`length`](fn.length.html)
 /// * [`magnitude`](fn.magnitude.html)
 /// * [`magnitude2`](fn.magnitude2.html)
-pub fn length2<N: Real, D: Dimension>(x: &TVec<N, D>) -> N
+pub fn length2<N: RealField, D: Dimension>(x: &TVec<N, D>) -> N
 where DefaultAllocator: Alloc<N, D> {
     x.norm_squared()
 }
@@ -107,17 +107,17 @@ where DefaultAllocator: Alloc<N, D> {
 /// * [`length2`](fn.length2.html)
 /// * [`magnitude`](fn.magnitude.html)
 /// * [`nalgebra::norm_squared`](../nalgebra/fn.norm_squared.html)
-pub fn magnitude2<N: Real, D: Dimension>(x: &TVec<N, D>) -> N
+pub fn magnitude2<N: RealField, D: Dimension>(x: &TVec<N, D>) -> N
 where DefaultAllocator: Alloc<N, D> {
     x.norm_squared()
 }
 
-//pub fn lxNorm<N: Real, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>, unsigned int Depth) -> N
+//pub fn lxNorm<N: RealField, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>, unsigned int Depth) -> N
 //    where DefaultAllocator: Alloc<N, D> {
 //    unimplemented!()
 //}
 //
-//pub fn lxNorm<N: Real, D: Dimension>(x: &TVec<N, D>, unsigned int Depth) -> N
+//pub fn lxNorm<N: RealField, D: Dimension>(x: &TVec<N, D>, unsigned int Depth) -> N
 //    where DefaultAllocator: Alloc<N, D> {
 //    unimplemented!()
 //}

nalgebra-glm/src/gtx/normal.rs

@@ -1,10 +1,10 @@
-use na::Real;
+use na::RealField;
 
 use crate::aliases::TVec3;
 
 /// The normal vector of the given triangle.
 ///
 /// The normal is computed as the normalized vector `cross(p2 - p1, p3 - p1)`.
-pub fn triangle_normal<N: Real>(p1: &TVec3<N>, p2: &TVec3<N>, p3: &TVec3<N>) -> TVec3<N> {
+pub fn triangle_normal<N: RealField>(p1: &TVec3<N>, p2: &TVec3<N>, p3: &TVec3<N>) -> TVec3<N> {
     (p2 - p1).cross(&(p3 - p1)).normalize()
 }

nalgebra-glm/src/gtx/normalize_dot.rs

@@ -1,4 +1,4 @@
-use na::{DefaultAllocator, Real};
+use na::{DefaultAllocator, RealField};
 
 use crate::aliases::TVec;
 use crate::traits::{Alloc, Dimension};
@@ -10,7 +10,7 @@ use crate::traits::{Alloc, Dimension};
 /// # See also:
 ///
 /// * [`normalize_dot`](fn.normalize_dot.html`)
-pub fn fast_normalize_dot<N: Real, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
+pub fn fast_normalize_dot<N: RealField, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
 where DefaultAllocator: Alloc<N, D> {
     // XXX: improve those.
     x.normalize().dot(&y.normalize())
@@ -21,7 +21,7 @@ where DefaultAllocator: Alloc<N, D> {
 /// # See also:
 ///
 /// * [`fast_normalize_dot`](fn.fast_normalize_dot.html`)
-pub fn normalize_dot<N: Real, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
+pub fn normalize_dot<N: RealField, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
 where DefaultAllocator: Alloc<N, D> {
     // XXX: improve those.
     x.normalize().dot(&y.normalize())

nalgebra-glm/src/gtx/quaternion.rs

@@ -1,97 +1,97 @@
-use na::{Real, Rotation3, Unit, UnitQuaternion, U3};
+use na::{RealField, Rotation3, Unit, UnitQuaternion, U3};
 
 use crate::aliases::{Qua, TMat3, TMat4, TVec3, TVec4};
 
 /// Rotate the vector `v` by the quaternion `q` assumed to be normalized.
-pub fn quat_cross_vec<N: Real>(q: &Qua<N>, v: &TVec3<N>) -> TVec3<N> {
+pub fn quat_cross_vec<N: RealField>(q: &Qua<N>, v: &TVec3<N>) -> TVec3<N> {
     UnitQuaternion::new_unchecked(*q) * v
 }
 
 /// Rotate the vector `v` by the inverse of the quaternion `q` assumed to be normalized.
-pub fn quat_inv_cross_vec<N: Real>(v: &TVec3<N>, q: &Qua<N>) -> TVec3<N> {
+pub fn quat_inv_cross_vec<N: RealField>(v: &TVec3<N>, q: &Qua<N>) -> TVec3<N> {
     UnitQuaternion::new_unchecked(*q).inverse() * v
 }
 
 /// The quaternion `w` component.
-pub fn quat_extract_real_component<N: Real>(q: &Qua<N>) -> N {
+pub fn quat_extract_real_component<N: RealField>(q: &Qua<N>) -> N {
     q.w
 }
 
 /// Normalized linear interpolation between two quaternions.
-pub fn quat_fast_mix<N: Real>(x: &Qua<N>, y: &Qua<N>, a: N) -> Qua<N> {
+pub fn quat_fast_mix<N: RealField>(x: &Qua<N>, y: &Qua<N>, a: N) -> Qua<N> {
     Unit::new_unchecked(*x)
         .nlerp(&Unit::new_unchecked(*y), a)
         .into_inner()
 }
 
-//pub fn quat_intermediate<N: Real>(prev: &Qua<N>, curr: &Qua<N>, next: &Qua<N>) -> Qua<N> {
+//pub fn quat_intermediate<N: RealField>(prev: &Qua<N>, curr: &Qua<N>, next: &Qua<N>) -> Qua<N> {
 //    unimplemented!()
 //}
 
 /// The squared magnitude of a quaternion `q`.
-pub fn quat_length2<N: Real>(q: &Qua<N>) -> N {
+pub fn quat_length2<N: RealField>(q: &Qua<N>) -> N {
     q.norm_squared()
 }
 
 /// The squared magnitude of a quaternion `q`.
-pub fn quat_magnitude2<N: Real>(q: &Qua<N>) -> N {
+pub fn quat_magnitude2<N: RealField>(q: &Qua<N>) -> N {
     q.norm_squared()
 }
 
 /// The quaternion representing the identity rotation.
-pub fn quat_identity<N: Real>() -> Qua<N> {
+pub fn quat_identity<N: RealField>() -> Qua<N> {
     UnitQuaternion::identity().into_inner()
 }
 
 /// Rotates a vector by a quaternion assumed to be normalized.
-pub fn quat_rotate_vec3<N: Real>(q: &Qua<N>, v: &TVec3<N>) -> TVec3<N> {
+pub fn quat_rotate_vec3<N: RealField>(q: &Qua<N>, v: &TVec3<N>) -> TVec3<N> {
     UnitQuaternion::new_unchecked(*q) * v
 }
 
 /// Rotates a vector in homogeneous coordinates by a quaternion assumed to be normalized.
-pub fn quat_rotate_vec<N: Real>(q: &Qua<N>, v: &TVec4<N>) -> TVec4<N> {
+pub fn quat_rotate_vec<N: RealField>(q: &Qua<N>, v: &TVec4<N>) -> TVec4<N> {
     let rotated = Unit::new_unchecked(*q) * v.fixed_rows::<U3>(0);
     TVec4::new(rotated.x, rotated.y, rotated.z, v.w)
 }
 
 /// The rotation required to align `orig` to `dest`.
-pub fn quat_rotation<N: Real>(orig: &TVec3<N>, dest: &TVec3<N>) -> Qua<N> {
+pub fn quat_rotation<N: RealField>(orig: &TVec3<N>, dest: &TVec3<N>) -> Qua<N> {
     UnitQuaternion::rotation_between(orig, dest)
         .unwrap_or_else(UnitQuaternion::identity)
         .into_inner()
 }
 
 /// The spherical linear interpolation between two quaternions.
-pub fn quat_short_mix<N: Real>(x: &Qua<N>, y: &Qua<N>, a: N) -> Qua<N> {
+pub fn quat_short_mix<N: RealField>(x: &Qua<N>, y: &Qua<N>, a: N) -> Qua<N> {
     Unit::new_normalize(*x)
         .slerp(&Unit::new_normalize(*y), a)
         .into_inner()
 }
 
-//pub fn quat_squad<N: Real>(q1: &Qua<N>, q2: &Qua<N>, s1: &Qua<N>, s2: &Qua<N>, h: N) -> Qua<N> {
+//pub fn quat_squad<N: RealField>(q1: &Qua<N>, q2: &Qua<N>, s1: &Qua<N>, s2: &Qua<N>, h: N) -> Qua<N> {
 //    unimplemented!()
 //}
 
 /// Converts a quaternion to a rotation matrix.
-pub fn quat_to_mat3<N: Real>(x: &Qua<N>) -> TMat3<N> {
+pub fn quat_to_mat3<N: RealField>(x: &Qua<N>) -> TMat3<N> {
     UnitQuaternion::new_unchecked(*x)
         .to_rotation_matrix()
         .into_inner()
 }
 
 /// Converts a quaternion to a rotation matrix in homogenous coordinates.
-pub fn quat_to_mat4<N: Real>(x: &Qua<N>) -> TMat4<N> {
+pub fn quat_to_mat4<N: RealField>(x: &Qua<N>) -> TMat4<N> {
     UnitQuaternion::new_unchecked(*x).to_homogeneous()
 }
 
 /// Converts a rotation matrix to a quaternion.
-pub fn mat3_to_quat<N: Real>(x: &TMat3<N>) -> Qua<N> {
+pub fn mat3_to_quat<N: RealField>(x: &TMat3<N>) -> Qua<N> {
     let r = Rotation3::from_matrix_unchecked(*x);
     UnitQuaternion::from_rotation_matrix(&r).into_inner()
 }
 
 /// Converts a rotation matrix in homogeneous coordinates to a quaternion.
-pub fn to_quat<N: Real>(x: &TMat4<N>) -> Qua<N> {
+pub fn to_quat<N: RealField>(x: &TMat4<N>) -> Qua<N> {
     let rot = x.fixed_slice::<U3, U3>(0, 0).into_owned();
     mat3_to_quat(&rot)
 }

nalgebra-glm/src/gtx/rotate_normalized_axis.rs

@@ -1,4 +1,4 @@
-use na::{Real, Rotation3, Unit, UnitQuaternion};
+use na::{RealField, Rotation3, Unit, UnitQuaternion};
 
 use crate::aliases::{Qua, TMat4, TVec3};
 
@@ -9,7 +9,7 @@ use crate::aliases::{Qua, TMat4, TVec3};
 /// * `m` - Input matrix multiplied by this rotation matrix.
 /// * `angle` - Rotation angle expressed in radians.
 /// * `axis` - Rotation axis, must be normalized.
-pub fn rotate_normalized_axis<N: Real>(m: &TMat4<N>, angle: N, axis: &TVec3<N>) -> TMat4<N> {
+pub fn rotate_normalized_axis<N: RealField>(m: &TMat4<N>, angle: N, axis: &TVec3<N>) -> TMat4<N> {
     m * Rotation3::from_axis_angle(&Unit::new_unchecked(*axis), angle).to_homogeneous()
 }
 
@@ -20,6 +20,6 @@ pub fn rotate_normalized_axis<N: Real>(m: &TMat4<N>, angle: N, axis: &TVec3<N>)
 /// * `q` - Source orientation.
 /// * `angle` - Angle expressed in radians.
 /// * `axis` - Normalized axis of the rotation, must be normalized.
-pub fn quat_rotate_normalized_axis<N: Real>(q: &Qua<N>, angle: N, axis: &TVec3<N>) -> Qua<N> {
+pub fn quat_rotate_normalized_axis<N: RealField>(q: &Qua<N>, angle: N, axis: &TVec3<N>) -> Qua<N> {
     q * UnitQuaternion::from_axis_angle(&Unit::new_unchecked(*axis), angle).into_inner()
 }

nalgebra-glm/src/gtx/rotate_vector.rs

@@ -1,9 +1,9 @@
-use na::{Real, Rotation3, Unit, UnitComplex};
+use na::{RealField, Rotation3, Unit, UnitComplex};
 
 use crate::aliases::{TMat4, TVec2, TVec3, TVec4};
 
 /// Build the rotation matrix needed to align `normal` and `up`.
-pub fn orientation<N: Real>(normal: &TVec3<N>, up: &TVec3<N>) -> TMat4<N> {
+pub fn orientation<N: RealField>(normal: &TVec3<N>, up: &TVec3<N>) -> TMat4<N> {
     if let Some(r) = Rotation3::rotation_between(normal, up) {
         r.to_homogeneous()
     } else {
@@ -12,52 +12,52 @@ pub fn orientation<N: Real>(normal: &TVec3<N>, up: &TVec3<N>) -> TMat4<N> {
 }
 
 /// Rotate a two dimensional vector.
-pub fn rotate_vec2<N: Real>(v: &TVec2<N>, angle: N) -> TVec2<N> {
+pub fn rotate_vec2<N: RealField>(v: &TVec2<N>, angle: N) -> TVec2<N> {
     UnitComplex::new(angle) * v
 }
 
 /// Rotate a three dimensional vector around an axis.
-pub fn rotate_vec3<N: Real>(v: &TVec3<N>, angle: N, normal: &TVec3<N>) -> TVec3<N> {
+pub fn rotate_vec3<N: RealField>(v: &TVec3<N>, angle: N, normal: &TVec3<N>) -> TVec3<N> {
     Rotation3::from_axis_angle(&Unit::new_normalize(*normal), angle) * v
 }
 
 /// Rotate a thee dimensional vector in homogeneous coordinates around an axis.
-pub fn rotate_vec4<N: Real>(v: &TVec4<N>, angle: N, normal: &TVec3<N>) -> TVec4<N> {
+pub fn rotate_vec4<N: RealField>(v: &TVec4<N>, angle: N, normal: &TVec3<N>) -> TVec4<N> {
     Rotation3::from_axis_angle(&Unit::new_normalize(*normal), angle).to_homogeneous() * v
 }
 
 /// Rotate a three dimensional vector around the `X` axis.
-pub fn rotate_x_vec3<N: Real>(v: &TVec3<N>, angle: N) -> TVec3<N> {
+pub fn rotate_x_vec3<N: RealField>(v: &TVec3<N>, angle: N) -> TVec3<N> {
     Rotation3::from_axis_angle(&TVec3::x_axis(), angle) * v
 }
 
 /// Rotate a three dimensional vector in homogeneous coordinates around the `X` axis.
-pub fn rotate_x_vec4<N: Real>(v: &TVec4<N>, angle: N) -> TVec4<N> {
+pub fn rotate_x_vec4<N: RealField>(v: &TVec4<N>, angle: N) -> TVec4<N> {
     Rotation3::from_axis_angle(&TVec3::x_axis(), angle).to_homogeneous() * v
 }
 
 /// Rotate a three dimensional vector around the `Y` axis.
-pub fn rotate_y_vec3<N: Real>(v: &TVec3<N>, angle: N) -> TVec3<N> {
+pub fn rotate_y_vec3<N: RealField>(v: &TVec3<N>, angle: N) -> TVec3<N> {
     Rotation3::from_axis_angle(&TVec3::y_axis(), angle) * v
 }
 
 /// Rotate a three dimensional vector in homogeneous coordinates around the `Y` axis.
-pub fn rotate_y_vec4<N: Real>(v: &TVec4<N>, angle: N) -> TVec4<N> {
+pub fn rotate_y_vec4<N: RealField>(v: &TVec4<N>, angle: N) -> TVec4<N> {
     Rotation3::from_axis_angle(&TVec3::y_axis(), angle).to_homogeneous() * v
 }
 
 /// Rotate a three dimensional vector around the `Z` axis.
-pub fn rotate_z_vec3<N: Real>(v: &TVec3<N>, angle: N) -> TVec3<N> {
+pub fn rotate_z_vec3<N: RealField>(v: &TVec3<N>, angle: N) -> TVec3<N> {
     Rotation3::from_axis_angle(&TVec3::z_axis(), angle) * v
 }
 
 /// Rotate a three dimensional vector in homogeneous coordinates around the `Z` axis.
-pub fn rotate_z_vec4<N: Real>(v: &TVec4<N>, angle: N) -> TVec4<N> {
+pub fn rotate_z_vec4<N: RealField>(v: &TVec4<N>, angle: N) -> TVec4<N> {
     Rotation3::from_axis_angle(&TVec3::z_axis(), angle).to_homogeneous() * v
 }
 
 /// Computes a spherical linear interpolation between the vectors `x` and `y` assumed to be normalized.
-pub fn slerp<N: Real>(x: &TVec3<N>, y: &TVec3<N>, a: N) -> TVec3<N> {
+pub fn slerp<N: RealField>(x: &TVec3<N>, y: &TVec3<N>, a: N) -> TVec3<N> {
     Unit::new_unchecked(*x)
         .slerp(&Unit::new_unchecked(*y), a)
         .into_inner()

nalgebra-glm/src/gtx/transform.rs

@@ -1,4 +1,4 @@
-use na::{Real, Rotation2, Rotation3, Unit};
+use na::{RealField, Rotation2, Rotation3, Unit};
 
 use crate::aliases::{TMat3, TMat4, TVec2, TVec3};
 use crate::traits::Number;
@@ -12,7 +12,7 @@ use crate::traits::Number;
 /// * [`rotation2d`](fn.rotation2d.html)
 /// * [`scaling2d`](fn.scaling2d.html)
 /// * [`translation2d`](fn.translation2d.html)
-pub fn rotation<N: Real>(angle: N, v: &TVec3<N>) -> TMat4<N> {
+pub fn rotation<N: RealField>(angle: N, v: &TVec3<N>) -> TMat4<N> {
     Rotation3::from_axis_angle(&Unit::new_normalize(*v), angle).to_homogeneous()
 }
 
@@ -51,7 +51,7 @@ pub fn translation<N: Number>(v: &TVec3<N>) -> TMat4<N> {
 /// * [`translation`](fn.translation.html)
 /// * [`scaling2d`](fn.scaling2d.html)
 /// * [`translation2d`](fn.translation2d.html)
-pub fn rotation2d<N: Real>(angle: N) -> TMat3<N> {
+pub fn rotation2d<N: RealField>(angle: N) -> TMat3<N> {
     Rotation2::new(angle).to_homogeneous()
 }
 

nalgebra-glm/src/gtx/transform2d.rs

@@ -1,4 +1,4 @@
-use na::{Real, UnitComplex};
+use na::{RealField, UnitComplex};
 
 use crate::aliases::{TMat3, TVec2};
 use crate::traits::Number;
@@ -12,7 +12,7 @@ use crate::traits::Number;
 /// * [`scaling2d`](fn.scaling2d.html)
 /// * [`translate2d`](fn.translate2d.html)
 /// * [`translation2d`](fn.translation2d.html)
-pub fn rotate2d<N: Real>(m: &TMat3<N>, angle: N) -> TMat3<N> {
+pub fn rotate2d<N: RealField>(m: &TMat3<N>, angle: N) -> TMat3<N> {
     m * UnitComplex::new(angle).to_homogeneous()
 }
 

nalgebra-glm/src/gtx/vector_angle.rs

@@ -1,18 +1,18 @@
-use na::{DefaultAllocator, Real};
+use na::{DefaultAllocator, RealField};
 
 use crate::aliases::TVec;
 use crate::traits::{Alloc, Dimension};
 
 /// The angle between two vectors.
-pub fn angle<N: Real, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
+pub fn angle<N: RealField, D: Dimension>(x: &TVec<N, D>, y: &TVec<N, D>) -> N
 where DefaultAllocator: Alloc<N, D> {
     x.angle(y)
 }
 
-//pub fn oriented_angle<N: Real>(x: &TVec2<N>, y: &TVec2<N>) -> N {
+//pub fn oriented_angle<N: RealField>(x: &TVec2<N>, y: &TVec2<N>) -> N {
 //    unimplemented!()
 //}
 //
-//pub fn oriented_angle_ref<N: Real>(x: &TVec3<N>, y: &TVec3<N>, refv: &TVec3<N>) -> N {
+//pub fn oriented_angle_ref<N: RealField>(x: &TVec3<N>, y: &TVec3<N>, refv: &TVec3<N>) -> N {
 //    unimplemented!()
 //}

nalgebra-glm/src/gtx/vector_query.rs

@@ -1,4 +1,4 @@
-use na::{DefaultAllocator, Real};
+use na::{DefaultAllocator, RealField};
 
 use crate::aliases::{TVec, TVec2, TVec3};
 use crate::traits::{Alloc, Dimension, Number};
@@ -45,7 +45,7 @@ where DefaultAllocator: Alloc<N, D> {
 }
 
 /// Returns `true` if `v` has a magnitude of 1 (up to an epsilon).
-pub fn is_normalized<N: Real, D: Dimension>(v: &TVec<N, D>, epsilon: N) -> bool
+pub fn is_normalized<N: RealField, D: Dimension>(v: &TVec<N, D>, epsilon: N) -> bool
 where DefaultAllocator: Alloc<N, D> {
     abs_diff_eq!(v.norm_squared(), N::one(), epsilon = epsilon * epsilon)
 }

nalgebra-glm/src/integer.rs

@@ -1,4 +1,4 @@
-use na::{Scalar, Real, U3, DefaultAllocator};
+use na::{Scalar, RealField, U3, DefaultAllocator};
 
 use crate::traits::{Number, Alloc, Dimension};
 use crate::aliases::TVec;

nalgebra-glm/src/lib.rs

@@ -191,7 +191,7 @@ pub use gtx::{
 pub use na::{
     convert, convert_ref, convert_ref_unchecked, convert_unchecked, try_convert, try_convert_ref,
 };
-pub use na::{DefaultAllocator, Real, Scalar, U1, U2, U3, U4};
+pub use na::{DefaultAllocator, RealField, Scalar, U1, U2, U3, U4};
 
 mod aliases;
 mod common;

nalgebra-glm/src/matrix.rs

@@ -1,16 +1,16 @@
-use na::{DefaultAllocator, Real, Scalar};
+use na::{DefaultAllocator, RealField, Scalar};
 
 use crate::aliases::{TMat, TVec};
 use crate::traits::{Alloc, Dimension, Number};
 
 /// The determinant of the matrix `m`.
-pub fn determinant<N: Real, D: Dimension>(m: &TMat<N, D, D>) -> N
+pub fn determinant<N: RealField, D: Dimension>(m: &TMat<N, D, D>) -> N
 where DefaultAllocator: Alloc<N, D, D> {
     m.determinant()
 }
 
 /// The inverse of the matrix `m`.
-pub fn inverse<N: Real, D: Dimension>(m: &TMat<N, D, D>) -> TMat<N, D, D>
+pub fn inverse<N: RealField, D: Dimension>(m: &TMat<N, D, D>) -> TMat<N, D, D>
 where DefaultAllocator: Alloc<N, D, D> {
     m.clone()
         .try_inverse()

nalgebra-glm/src/trigonometric.rs

@@ -1,94 +1,94 @@
-use na::{self, DefaultAllocator, Real};
+use na::{self, DefaultAllocator, RealField};
 
 use crate::aliases::TVec;
 use crate::traits::{Alloc, Dimension};
 
 /// Component-wise arc-cosinus.
-pub fn acos<N: Real, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
+pub fn acos<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     x.map(|e| e.acos())
 }
 
 /// Component-wise hyperbolic arc-cosinus.
-pub fn acosh<N: Real, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
+pub fn acosh<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     x.map(|e| e.acosh())
 }
 
 /// Component-wise arc-sinus.
-pub fn asin<N: Real, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
+pub fn asin<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     x.map(|e| e.asin())
 }
 
 /// Component-wise hyperbolic arc-sinus.
-pub fn asinh<N: Real, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
+pub fn asinh<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     x.map(|e| e.asinh())
 }
 
 /// Component-wise arc-tangent of `y / x`.
-pub fn atan2<N: Real, D: Dimension>(y: &TVec<N, D>, x: &TVec<N, D>) -> TVec<N, D>
+pub fn atan2<N: RealField, D: Dimension>(y: &TVec<N, D>, x: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     y.zip_map(x, |y, x| y.atan2(x))
 }
 
 /// Component-wise arc-tangent.
-pub fn atan<N: Real, D: Dimension>(y_over_x: &TVec<N, D>) -> TVec<N, D>
+pub fn atan<N: RealField, D: Dimension>(y_over_x: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     y_over_x.map(|e| e.atan())
 }
 
 /// Component-wise hyperbolic arc-tangent.
-pub fn atanh<N: Real, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
+pub fn atanh<N: RealField, D: Dimension>(x: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     x.map(|e| e.atanh())
 }
 
 /// Component-wise cosinus.
-pub fn cos<N: Real, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
+pub fn cos<N: RealField, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     angle.map(|e| e.cos())
 }
 
 /// Component-wise hyperbolic cosinus.
-pub fn cosh<N: Real, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
+pub fn cosh<N: RealField, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     angle.map(|e| e.cosh())
 }
 
 /// Component-wise conversion from radians to degrees.
-pub fn degrees<N: Real, D: Dimension>(radians: &TVec<N, D>) -> TVec<N, D>
+pub fn degrees<N: RealField, D: Dimension>(radians: &TVec<N, D>) -> TVec<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: Real, D: Dimension>(degrees: &TVec<N, D>) -> TVec<N, D>
+pub fn radians<N: RealField, D: Dimension>(degrees: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     degrees.map(|e| e * N::pi() / na::convert(180.0))
 }
 
 /// Component-wise sinus.
-pub fn sin<N: Real, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
+pub fn sin<N: RealField, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     angle.map(|e| e.sin())
 }
 
 /// Component-wise hyperbolic sinus.
-pub fn sinh<N: Real, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
+pub fn sinh<N: RealField, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     angle.map(|e| e.sinh())
 }
 
 /// Component-wise tangent.
-pub fn tan<N: Real, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
+pub fn tan<N: RealField, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     angle.map(|e| e.tan())
 }
 
 /// Component-wise hyperbolic tangent.
-pub fn tanh<N: Real, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
+pub fn tanh<N: RealField, D: Dimension>(angle: &TVec<N, D>) -> TVec<N, D>
 where DefaultAllocator: Alloc<N, D> {
     angle.map(|e| e.tanh())
 }

nalgebra-lapack/src/eigen.rs

@@ -4,7 +4,7 @@ use serde::{Deserialize, Serialize};
 use num::Zero;
 use num_complex::Complex;
 
-use alga::general::Real;
+use alga::general::RealField;
 
 use na::allocator::Allocator;
 use na::dimension::{Dim, U1};
@@ -51,7 +51,7 @@ where
     MatrixN<N, D>: Copy,
 {}
 
-impl<N: EigenScalar + Real, D: Dim> Eigen<N, D>
+impl<N: EigenScalar + RealField, D: Dim> Eigen<N, D>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
 {
     /// Computes the eigenvalues and eigenvectors of the square matrix `m`.

nalgebra-lapack/src/schur.rs

@@ -4,7 +4,7 @@ use serde::{Deserialize, Serialize};
 use num::Zero;
 use num_complex::Complex;
 
-use alga::general::Real;
+use alga::general::RealField;
 
 use na::allocator::Allocator;
 use na::dimension::{Dim, U1};
@@ -49,7 +49,7 @@ where
     VectorN<N, D>: Copy,
 {}
 
-impl<N: SchurScalar + Real, D: Dim> Schur<N, D>
+impl<N: SchurScalar + RealField, D: Dim> Schur<N, D>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
 {
     /// Computes the eigenvalues and real Schur form of the matrix `m`.
@@ -161,7 +161,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
  * Lapack functions dispatch.
  *
  */
-/// Trait implemented by scalars for which Lapack implements the Real Schur decomposition.
+/// Trait implemented by scalars for which Lapack implements the RealField Schur decomposition.
 pub trait SchurScalar: Scalar {
     #[allow(missing_docs)]
     fn xgees(

nalgebra-lapack/src/symmetric_eigen.rs

@@ -4,7 +4,7 @@ use serde::{Deserialize, Serialize};
 use num::Zero;
 use std::ops::MulAssign;
 
-use alga::general::Real;
+use alga::general::RealField;
 
 use na::allocator::Allocator;
 use na::dimension::{Dim, U1};
@@ -52,7 +52,7 @@ where
     VectorN<N, D>: Copy,
 {}
 
-impl<N: SymmetricEigenScalar + Real, D: Dim> SymmetricEigen<N, D>
+impl<N: SymmetricEigenScalar + RealField, D: Dim> SymmetricEigen<N, D>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
 {
     /// Computes the eigenvalues and eigenvectors of the symmetric matrix `m`.

src/base/cg.rs

@@ -18,7 +18,7 @@ use crate::geometry::{
     Isometry, IsometryMatrix3, Orthographic3, Perspective3, Point, Point3, Rotation2, Rotation3,
 };
 
-use alga::general::{Real, Ring};
+use alga::general::{RealField, Ring};
 use alga::linear::Transformation;
 
 impl<N, D: DimName> MatrixN<N, D>
@@ -65,7 +65,7 @@ where
     }
 }
 
-impl<N: Real> Matrix3<N> {
+impl<N: RealField> Matrix3<N> {
     /// Builds a 2 dimensional homogeneous rotation matrix from an angle in radian.
     #[inline]
     pub fn new_rotation(angle: N) -> Self {
@@ -73,7 +73,7 @@ impl<N: Real> Matrix3<N> {
     }
 }
 
-impl<N: Real> Matrix4<N> {
+impl<N: RealField> Matrix4<N> {
     /// Builds a 3D homogeneous rotation matrix from an axis and an angle (multiplied together).
     ///
     /// Returns the identity matrix if the given argument is zero.
@@ -320,7 +320,7 @@ impl<N: Scalar + Ring, D: DimName, S: StorageMut<N, D, D>> SquareMatrix<N, D, S>
     }
 }
 
-impl<N: Real, D: DimNameSub<U1>, S: Storage<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>
         + Allocator<N, DimNameDiff<D, U1>>
         + Allocator<N, DimNameDiff<D, U1>, DimNameDiff<D, U1>>
@@ -364,7 +364,7 @@ where DefaultAllocator: Allocator<N, D, D>
     }
 }
 
-impl<N: Real, D: DimNameSub<U1>> Transformation<Point<N, DimNameDiff<D, U1>>> for MatrixN<N, 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>>

src/base/construction.rs

@@ -12,7 +12,7 @@ use std::iter;
 use typenum::{self, Cmp, Greater};
 
 #[cfg(feature = "std")]
-use alga::general::Real;
+use alga::general::RealField;
 use alga::general::{ClosedAdd, ClosedMul};
 
 use crate::base::allocator::Allocator;
@@ -795,7 +795,7 @@ where
 }
 
 #[cfg(feature = "std")]
-impl<N: Real, D: DimName> Distribution<Unit<VectorN<N, D>>> for Standard
+impl<N: RealField, D: DimName> Distribution<Unit<VectorN<N, D>>> for Standard
 where
     DefaultAllocator: Allocator<N, D>,
     StandardNormal: Distribution<N>,

src/base/matrix.rs

@@ -16,7 +16,7 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use alga::general::{ClosedAdd, ClosedMul, ClosedSub, Real, Ring, ComplexField, Field};
+use alga::general::{ClosedAdd, ClosedMul, ClosedSub, RealField, Ring, ComplexField, Field};
 
 use crate::base::allocator::{Allocator, SameShapeAllocator, SameShapeC, SameShapeR};
 use crate::base::constraint::{DimEq, SameNumberOfColumns, SameNumberOfRows, ShapeConstraint};
@@ -983,14 +983,14 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 
     /// Divides each component of the complex matrix `self` by the given real.
     #[inline]
-    pub fn unscale(&self, real: N::Real) -> MatrixMN<N, R, C>
+    pub fn unscale(&self, real: N::RealField) -> MatrixMN<N, R, C>
         where DefaultAllocator: Allocator<N, R, C> {
         self.map(|e| e.unscale(real))
     }
 
     /// Multiplies each component of the complex matrix `self` by the given real.
     #[inline]
-    pub fn scale(&self, real: N::Real) -> MatrixMN<N, R, C>
+    pub fn scale(&self, real: N::RealField) -> MatrixMN<N, R, C>
         where DefaultAllocator: Allocator<N, R, C> {
         self.map(|e| e.scale(real))
     }
@@ -1005,13 +1005,13 @@ impl<N: ComplexField, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S>
 
     /// Divides each component of the complex matrix `self` by the given real.
     #[inline]
-    pub fn unscale_mut(&mut self, real: N::Real) {
+    pub fn unscale_mut(&mut self, real: N::RealField) {
         self.apply(|e| e.unscale(real))
     }
 
     /// Multiplies each component of the complex matrix `self` by the given real.
     #[inline]
-    pub fn scale_mut(&mut self, real: N::Real) {
+    pub fn scale_mut(&mut self, real: N::RealField) {
         self.apply(|e| e.scale(real))
     }
 }
@@ -1544,7 +1544,7 @@ where DefaultAllocator: Allocator<N, U3>
 impl<N: ComplexField, 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::Real
+    pub fn angle<R2: Dim, C2: Dim, SB>(&self, other: &Matrix<N, R2, C2, SB>) -> N::RealField
     where
         SB: Storage<N, R2, C2>,
         ShapeConstraint: DimEq<R, R2> + DimEq<C, C2>,
@@ -1554,14 +1554,14 @@ 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::Real::zero()
+            N::RealField::zero()
         } else {
             let cang = prod.real() / (n1 * n2);
 
-            if cang > N::Real::one() {
+            if cang > N::RealField::one() {
-                N::Real::zero()
+                N::RealField::zero()
-            } else if cang < -N::Real::one() {
+            } else if cang < -N::RealField::one() {
-                N::Real::pi()
+                N::RealField::pi()
             } else {
                 cang.acos()
             }
@@ -1597,13 +1597,13 @@ impl<N: ComplexField, D: Dim, S: Storage<N, D>> Unit<Vector<N, D, S>> {
     pub fn slerp<S2: Storage<N, D>>(
         &self,
         rhs: &Unit<Vector<N, D, S2>>,
-        t: N::Real,
+        t: N::RealField,
     ) -> Unit<VectorN<N, D>>
     where
         DefaultAllocator: Allocator<N, D>,
     {
         // FIXME: the result is wrong when self and rhs are collinear with opposite direction.
-        self.try_slerp(rhs, t, N::Real::default_epsilon())
+        self.try_slerp(rhs, t, N::RealField::default_epsilon())
             .unwrap_or(Unit::new_unchecked(self.clone_owned()))
     }
 
@@ -1614,8 +1614,8 @@ impl<N: ComplexField, D: Dim, S: Storage<N, D>> Unit<Vector<N, D, S>> {
     pub fn try_slerp<S2: Storage<N, D>>(
         &self,
         rhs: &Unit<Vector<N, D, S2>>,
-        t: N::Real,
+        t: N::RealField,
-        epsilon: N::Real,
+        epsilon: N::RealField,
     ) -> Option<Unit<VectorN<N, D>>>
     where
         DefaultAllocator: Allocator<N, D>,
@@ -1623,18 +1623,18 @@ impl<N: ComplexField, D: Dim, S: Storage<N, D>> Unit<Vector<N, D, S>> {
         let (c_hang, c_hang_sign) = self.dotc(rhs).to_exp();
 
         // self == other
-        if c_hang >= N::Real::one() {
+        if c_hang >= N::RealField::one() {
             return Some(Unit::new_unchecked(self.clone_owned()));
         }
 
         let hang = c_hang.acos();
-        let s_hang = (N::Real::one() - c_hang * c_hang).sqrt();
+        let s_hang = (N::RealField::one() - c_hang * c_hang).sqrt();
 
         // FIXME: what if s_hang is 0.0 ? The result is not well-defined.
-        if relative_eq!(s_hang, N::Real::zero(), epsilon = epsilon) {
+        if relative_eq!(s_hang, N::RealField::zero(), epsilon = epsilon) {
             None
         } else {
-            let ta = ((N::Real::one() - t) * hang).sin() / s_hang;
+            let ta = ((N::RealField::one() - t) * hang).sin() / s_hang;
             let tb = (t * hang).sin() / s_hang;
             let mut res = self.scale(ta);
             res.axpy(c_hang_sign.scale(tb), &**rhs, N::one());

src/base/matrix_alga.rs

@@ -148,16 +148,16 @@ where
 impl<N: ComplexField, R: DimName, C: DimName> NormedSpace for MatrixMN<N, R, C>
 where DefaultAllocator: Allocator<N, R, C>
 {
-    type Real = N::Real;
+    type RealField = N::RealField;
     type ComplexField = N;
 
     #[inline]
-    fn norm_squared(&self) -> N::Real {
+    fn norm_squared(&self) -> N::RealField {
         self.norm_squared()
     }
 
     #[inline]
-    fn norm(&self) -> N::Real {
+    fn norm(&self) -> N::RealField {
         self.norm()
     }
 
@@ -167,17 +167,17 @@ where DefaultAllocator: Allocator<N, R, C>
     }
 
     #[inline]
-    fn normalize_mut(&mut self) -> N::Real {
+    fn normalize_mut(&mut self) -> N::RealField {
         self.normalize_mut()
     }
 
     #[inline]
-    fn try_normalize(&self, min_norm: N::Real) -> Option<Self> {
+    fn try_normalize(&self, min_norm: N::RealField) -> Option<Self> {
         self.try_normalize(min_norm)
     }
 
     #[inline]
-    fn try_normalize_mut(&mut self, min_norm: N::Real) -> Option<N::Real> {
+    fn try_normalize_mut(&mut self, min_norm: N::RealField) -> Option<N::RealField> {
         self.try_normalize_mut(min_norm)
     }
 }
@@ -186,7 +186,7 @@ impl<N: ComplexField, R: DimName, C: DimName> InnerSpace for MatrixMN<N, R, C>
 where DefaultAllocator: Allocator<N, R, C>
 {
     #[inline]
-    fn angle(&self, other: &Self) -> N::Real {
+    fn angle(&self, other: &Self) -> N::RealField {
         self.angle(other)
     }
 
@@ -216,7 +216,7 @@ where DefaultAllocator: Allocator<N, R, C>
                 }
             }
 
-            if vs[i].try_normalize_mut(N::Real::zero()).is_some() {
+            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);
@@ -301,7 +301,7 @@ where DefaultAllocator: Allocator<N, R, C>
                             elt -= v * elt.dot(v)
                         }
 
-                        if let Some(subsp_elt) = elt.try_normalize(N::Real::zero()) {
+                        if let Some(subsp_elt) = elt.try_normalize(N::RealField::zero()) {
                             if !f(&subsp_elt) {
                                 return;
                             };

src/base/norm.rs

@@ -1,7 +1,7 @@
 use num::Zero;
 
 use crate::allocator::Allocator;
-use crate::{Real, ComplexField};
+use crate::{RealField, ComplexField};
 use crate::storage::{Storage, StorageMut};
 use crate::base::{DefaultAllocator, Matrix, Dim, MatrixMN};
 use crate::constraint::{SameNumberOfRows, SameNumberOfColumns, ShapeConstraint};
@@ -13,10 +13,10 @@ use crate::constraint::{SameNumberOfRows, SameNumberOfColumns, ShapeConstraint};
 /// This may be moved to the alga crate in the future.
 pub trait Norm<N: ComplexField> {
     /// Apply this norm to the given matrix.
-    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::Real
+    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::RealField
         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::Real
+    fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N::RealField
         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>;
@@ -31,17 +31,17 @@ pub struct UniformNorm;
 
 impl<N: ComplexField> Norm<N> for EuclideanNorm {
     #[inline]
-    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::Real
+    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::RealField
         where R: Dim, C: Dim, S: Storage<N, R, C> {
         m.norm_squared().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::Real
+    fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N::RealField
         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::Real::zero(), |acc, a, b| {
+        m1.zip_fold(m2, N::RealField::zero(), |acc, a, b| {
             let diff = a - b;
             acc + diff.modulus_squared()
         }).sqrt()
@@ -50,19 +50,19 @@ impl<N: ComplexField> Norm<N> for EuclideanNorm {
 
 impl<N: ComplexField> Norm<N> for LpNorm {
     #[inline]
-    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::Real
+    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::RealField
         where R: Dim, C: Dim, S: Storage<N, R, C> {
-        m.fold(N::Real::zero(), |a, b| {
+        m.fold(N::RealField::zero(), |a, b| {
             a + b.modulus().powi(self.0)
         }).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::Real
+    fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N::RealField
         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::Real::zero(), |acc, a, b| {
+        m1.zip_fold(m2, N::RealField::zero(), |acc, a, b| {
             let diff = a - b;
             acc + diff.modulus().powi(self.0)
         }).powf(crate::convert(1.0 / (self.0 as f64)))
@@ -71,19 +71,19 @@ impl<N: ComplexField> Norm<N> for LpNorm {
 
 impl<N: ComplexField> Norm<N> for UniformNorm {
     #[inline]
-    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::Real
+    fn norm<R, C, S>(&self, m: &Matrix<N, R, C, S>) -> N::RealField
         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::Real::zero(), |acc, a| acc.max(a.modulus()))
+        m.fold(N::RealField::zero(), |acc, a| acc.max(a.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::Real
+    fn metric_distance<R1, C1, S1, R2, C2, S2>(&self, m1: &Matrix<N, R1, C1, S1>, m2: &Matrix<N, R2, C2, S2>) -> N::RealField
         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::Real::zero(), |acc, a, b| {
+        m1.zip_fold(m2, N::RealField::zero(), |acc, a, b| {
             let val = (a - b).modulus();
             if val > acc {
                 val
@@ -98,8 +98,8 @@ impl<N: ComplexField> Norm<N> for UniformNorm {
 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::Real {
+    pub fn norm_squared(&self) -> N::RealField {
-        let mut res = N::Real::zero();
+        let mut res = N::RealField::zero();
 
         for i in 0..self.ncols() {
             let col = self.column(i);
@@ -113,7 +113,7 @@ 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::Real {
+    pub fn norm(&self) -> N::RealField {
         self.norm_squared().sqrt()
     }
 
@@ -121,7 +121,7 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     ///
     /// 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::Real
+    pub fn metric_distance<R2, C2, S2>(&self, rhs: &Matrix<N, R2, C2, S2>) -> N::RealField
         where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
               ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
         self.apply_metric_distance(rhs, &EuclideanNorm)
@@ -140,7 +140,7 @@ 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::Real {
+    pub fn apply_norm(&self, norm: &impl Norm<N>) -> N::RealField {
         norm.norm(self)
     }
 
@@ -159,7 +159,7 @@ 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::Real
+    pub fn apply_metric_distance<R2, C2, S2>(&self, rhs: &Matrix<N, R2, C2, S2>, norm: &impl Norm<N>) -> N::RealField
         where R2: Dim, C2: Dim, S2: Storage<N, R2, C2>,
               ShapeConstraint: SameNumberOfRows<R, R2> + SameNumberOfColumns<C, C2> {
         norm.metric_distance(self, rhs)
@@ -171,7 +171,7 @@ 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::Real {
+    pub fn magnitude(&self) -> N::RealField {
         self.norm()
     }
 
@@ -181,7 +181,7 @@ 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_squared()`
     #[inline]
-    pub fn magnitude_squared(&self) -> N::Real {
+    pub fn magnitude_squared(&self) -> N::RealField {
         self.norm_squared()
     }
 
@@ -194,7 +194,7 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 
     /// Returns a normalized version of this matrix unless its norm as smaller or equal to `eps`.
     #[inline]
-    pub fn try_normalize(&self, min_norm: N::Real) -> Option<MatrixMN<N, R, C>>
+    pub fn try_normalize(&self, min_norm: N::RealField) -> Option<MatrixMN<N, R, C>>
         where DefaultAllocator: Allocator<N, R, C> {
         let n = self.norm();
 
@@ -207,7 +207,7 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 
     /// The Lp norm of this matrix.
     #[inline]
-    pub fn lp_norm(&self, p: i32) -> N::Real {
+    pub fn lp_norm(&self, p: i32) -> N::RealField {
         self.apply_norm(&LpNorm(p))
     }
 }
@@ -216,7 +216,7 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<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.
     #[inline]
-    pub fn normalize_mut(&mut self) -> N::Real {
+    pub fn normalize_mut(&mut self) -> N::RealField {
         let n = self.norm();
         self.unscale_mut(n);
 
@@ -227,7 +227,7 @@ impl<N: ComplexField, R: Dim, C: Dim, S: StorageMut<N, R, C>> Matrix<N, R, C, S>
     ///
     /// If the normalization succeeded, returns the old normal of this matrix.
     #[inline]
-    pub fn try_normalize_mut(&mut self, min_norm: N::Real) -> Option<N::Real> {
+    pub fn try_normalize_mut(&mut self, min_norm: N::RealField) -> Option<N::RealField> {
         let n = self.norm();
 
         if n <= min_norm {

src/base/ops.rs

@@ -832,7 +832,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 
     /// Returns the the 1-norm of the complex component with the largest 1-norm.
     #[inline]
-    pub fn camax(&self) -> N::Real
+    pub fn camax(&self) -> N::RealField
         where N: ComplexField {
         self.xcmp(|e| e.norm1(), |a, b| a > b)
     }
@@ -853,7 +853,7 @@ impl<N: Scalar, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
 
     /// Returns the the 1-norm of the complex component with the smallest 1-norm.
     #[inline]
-    pub fn camin(&self) -> N::Real
+    pub fn camin(&self) -> N::RealField
         where N: ComplexField {
         self.xcmp(|e| e.norm1(), |a, b| a < b)
     }

src/base/properties.rs

@@ -2,7 +2,7 @@
 use approx::RelativeEq;
 use num::{One, Zero};
 
-use alga::general::{ClosedAdd, ClosedMul, Real, ComplexField};
+use alga::general::{ClosedAdd, ClosedMul, RealField, ComplexField};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{Dim, DimMin};
@@ -101,7 +101,7 @@ impl<N: ComplexField, R: Dim, C: Dim, S: Storage<N, R, C>> Matrix<N, R, C, S> {
     }
 }
 
-impl<N: Real, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S>
+impl<N: RealField, D: Dim, S: Storage<N, D, D>> SquareMatrix<N, D, S>
 where DefaultAllocator: Allocator<N, D, D>
 {
     /// Checks that this matrix is orthogonal and has a determinant equal to 1.

src/base/unit.rs

@@ -64,13 +64,13 @@ impl<T: NormedSpace> Unit<T> {
     ///
     /// Returns `None` if the norm was smaller or equal to `min_norm`.
     #[inline]
-    pub fn try_new(value: T, min_norm: T::Real) -> Option<Self> {
+    pub fn try_new(value: T, min_norm: T::RealField) -> Option<Self> {
         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.
     #[inline]
-    pub fn new_and_get(mut value: T) -> (Self, T::Real) {
+    pub fn new_and_get(mut value: T) -> (Self, T::RealField) {
         let n = value.normalize_mut();
 
         (Unit { value: value }, n)
@@ -80,7 +80,7 @@ impl<T: NormedSpace> Unit<T> {
     ///
     /// 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::Real) -> Option<(Self, T::Real)> {
+    pub fn try_new_and_get(mut value: T, min_norm: T::RealField) -> Option<(Self, T::RealField)> {
         if let Some(n) = value.try_normalize_mut(min_norm) {
             Some((Unit { value: value }, n))
         } else {
@@ -94,7 +94,7 @@ impl<T: NormedSpace> Unit<T> {
     /// 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::Real {
+    pub fn renormalize(&mut self) -> T::RealField {
         self.value.normalize_mut()
     }
 
@@ -104,8 +104,8 @@ impl<T: NormedSpace> Unit<T> {
     #[inline]
     pub fn renormalize_fast(&mut self) {
         let sq_norm = self.value.norm_squared();
-        let _3: T::Real = crate::convert(3.0);
+        let _3: T::RealField = crate::convert(3.0);
-        let _0_5: T::Real = crate::convert(0.5);
+        let _0_5: T::RealField = crate::convert(0.5);
         self.value *= T::ComplexField::from_real(_0_5 * (_3 - sq_norm));
     }
 }

src/geometry/isometry.rs

@@ -11,7 +11,7 @@ use serde::{Deserialize, Serialize};
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use alga::general::{Real, SubsetOf};
+use alga::general::{RealField, SubsetOf};
 use alga::linear::Rotation;
 
 use crate::base::allocator::Allocator;
@@ -36,7 +36,7 @@ use crate::geometry::{Point, Translation};
                        DefaultAllocator: Allocator<N, D>,
                        Owned<N, D>: Deserialize<'de>"))
 )]
-pub struct Isometry<N: Real, D: DimName, R>
+pub struct Isometry<N: RealField, D: DimName, R>
 where DefaultAllocator: Allocator<N, D>
 {
     /// The pure rotational part of this isometry.
@@ -55,7 +55,7 @@ where DefaultAllocator: Allocator<N, D>
 #[cfg(feature = "abomonation-serialize")]
 impl<N, D, R> Abomonation for Isometry<N, D, R>
 where
-    N: Real,
+    N: RealField,
     D: DimName,
     R: Abomonation,
     Translation<N, D>: Abomonation,
@@ -77,7 +77,7 @@ where
     }
 }
 
-impl<N: Real + hash::Hash, D: DimName + hash::Hash, R: hash::Hash> hash::Hash for Isometry<N, D, R>
+impl<N: RealField + hash::Hash, D: DimName + hash::Hash, R: hash::Hash> hash::Hash for Isometry<N, D, R>
 where
     DefaultAllocator: Allocator<N, D>,
     Owned<N, D>: hash::Hash,
@@ -88,14 +88,14 @@ where
     }
 }
 
-impl<N: Real, D: DimName + Copy, R: Rotation<Point<N, D>> + Copy> Copy for Isometry<N, D, R>
+impl<N: RealField, D: DimName + Copy, R: Rotation<Point<N, D>> + Copy> Copy for Isometry<N, D, R>
 where
     DefaultAllocator: Allocator<N, D>,
     Owned<N, D>: Copy,
 {
 }
 
-impl<N: Real, D: DimName, R: Rotation<Point<N, D>> + Clone> Clone for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R: Rotation<Point<N, D>> + Clone> Clone for Isometry<N, D, R>
 where DefaultAllocator: Allocator<N, D>
 {
     #[inline]
@@ -104,7 +104,7 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: Real, D: DimName, R: Rotation<Point<N, D>>> Isometry<N, D, R>
+impl<N: RealField, D: DimName, R: Rotation<Point<N, D>>> Isometry<N, D, R>
 where DefaultAllocator: Allocator<N, D>
 {
     /// Creates a new isometry from its rotational and translational parts.
@@ -260,7 +260,7 @@ 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: Real, D: DimName, R> Isometry<N, D, R>
+impl<N: RealField, D: DimName, R> Isometry<N, D, R>
 where DefaultAllocator: Allocator<N, D>
 {
     /// Converts this isometry into its equivalent homogeneous transformation matrix.
@@ -293,14 +293,14 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: Real, D: DimName, R> Eq for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R> Eq for Isometry<N, D, R>
 where
     R: Rotation<Point<N, D>> + Eq,
     DefaultAllocator: Allocator<N, D>,
 {
 }
 
-impl<N: Real, D: DimName, R> PartialEq for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R> PartialEq for Isometry<N, D, R>
 where
     R: Rotation<Point<N, D>> + PartialEq,
     DefaultAllocator: Allocator<N, D>,
@@ -311,7 +311,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> AbsDiffEq for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R> AbsDiffEq for Isometry<N, D, R>
 where
     R: Rotation<Point<N, D>> + AbsDiffEq<Epsilon = N::Epsilon>,
     DefaultAllocator: Allocator<N, D>,
@@ -331,7 +331,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> RelativeEq for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R> RelativeEq for Isometry<N, D, R>
 where
     R: Rotation<Point<N, D>> + RelativeEq<Epsilon = N::Epsilon>,
     DefaultAllocator: Allocator<N, D>,
@@ -358,7 +358,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> UlpsEq for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R> UlpsEq for Isometry<N, D, R>
 where
     R: Rotation<Point<N, D>> + UlpsEq<Epsilon = N::Epsilon>,
     DefaultAllocator: Allocator<N, D>,
@@ -382,7 +382,7 @@ where
  * Display
  *
  */
-impl<N: Real + fmt::Display, D: DimName, R> fmt::Display for Isometry<N, D, R>
+impl<N: RealField + fmt::Display, D: DimName, R> fmt::Display for Isometry<N, D, R>
 where
     R: fmt::Display,
     DefaultAllocator: Allocator<N, D> + Allocator<usize, D>,

src/geometry/isometry_alga.rs

@@ -1,6 +1,6 @@
 use alga::general::{
     AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, Real,
+    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, RealField,
 };
 use alga::linear::Isometry as AlgaIsometry;
 use alga::linear::{
@@ -19,7 +19,7 @@ use crate::geometry::{Isometry, Point, Translation};
  * Algebraic structures.
  *
  */
-impl<N: Real, D: DimName, R> Identity<Multiplicative> for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R> Identity<Multiplicative> for Isometry<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -30,7 +30,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> TwoSidedInverse<Multiplicative> for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R> TwoSidedInverse<Multiplicative> for Isometry<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -46,7 +46,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> AbstractMagma<Multiplicative> for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R> AbstractMagma<Multiplicative> for Isometry<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -59,7 +59,7 @@ where
 
 macro_rules! impl_multiplicative_structures(
     ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: Real, D: DimName, R> $marker<$operator> for Isometry<N, D, R>
+        impl<N: RealField, D: DimName, R> $marker<$operator> for Isometry<N, D, R>
             where R: Rotation<Point<N, D>>,
                   DefaultAllocator: Allocator<N, D> { }
     )*}
@@ -78,7 +78,7 @@ impl_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N: Real, D: DimName, R> Transformation<Point<N, D>> for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R> Transformation<Point<N, D>> for Isometry<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -94,7 +94,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> ProjectiveTransformation<Point<N, D>> for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R> ProjectiveTransformation<Point<N, D>> for Isometry<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -111,7 +111,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> AffineTransformation<Point<N, D>> for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R> AffineTransformation<Point<N, D>> for Isometry<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -169,7 +169,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> Similarity<Point<N, D>> for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R> Similarity<Point<N, D>> for Isometry<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -194,7 +194,7 @@ where
 
 macro_rules! marker_impl(
     ($($Trait: ident),*) => {$(
-        impl<N: Real, D: DimName, R> $Trait<Point<N, D>> for Isometry<N, D, R>
+        impl<N: RealField, D: DimName, R> $Trait<Point<N, D>> for Isometry<N, D, R>
         where R: Rotation<Point<N, D>>,
               DefaultAllocator: Allocator<N, D> { }
     )*}

src/geometry/isometry_construction.rs

@@ -7,7 +7,7 @@ use num::One;
 use rand::distributions::{Distribution, Standard};
 use rand::Rng;
 
-use alga::general::Real;
+use alga::general::RealField;
 use alga::linear::Rotation as AlgaRotation;
 
 use crate::base::allocator::Allocator;
@@ -19,7 +19,7 @@ use crate::geometry::{
     UnitQuaternion, Translation2, Translation3
 };
 
-impl<N: Real, D: DimName, R: AlgaRotation<Point<N, D>>> Isometry<N, D, R>
+impl<N: RealField, D: DimName, R: AlgaRotation<Point<N, D>>> Isometry<N, D, R>
 where DefaultAllocator: Allocator<N, D>
 {
     /// Creates a new identity isometry.
@@ -65,7 +65,7 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: Real, D: DimName, R: AlgaRotation<Point<N, D>>> One for Isometry<N, D, R>
+impl<N: RealField, D: DimName, R: AlgaRotation<Point<N, D>>> One for Isometry<N, D, R>
 where DefaultAllocator: Allocator<N, D>
 {
     /// Creates a new identity isometry.
@@ -75,7 +75,7 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: Real, D: DimName, R> Distribution<Isometry<N, D, R>> for Standard
+impl<N: RealField, D: DimName, R> Distribution<Isometry<N, D, R>> for Standard
 where
     R: AlgaRotation<Point<N, D>>,
     Standard: Distribution<N> + Distribution<R>,
@@ -90,7 +90,7 @@ where
 #[cfg(feature = "arbitrary")]
 impl<N, D: DimName, R> Arbitrary for Isometry<N, D, R>
 where
-    N: Real + Arbitrary + Send,
+    N: RealField + Arbitrary + Send,
     R: AlgaRotation<Point<N, D>> + Arbitrary + Send,
     Owned<N, D>: Send,
     DefaultAllocator: Allocator<N, D>,
@@ -108,7 +108,7 @@ where
  */
 
 // 2D rotation.
-impl<N: Real> Isometry<N, U2, Rotation2<N>> {
+impl<N: RealField> Isometry<N, U2, Rotation2<N>> {
     /// Creates a new 2D isometry from a translation and a rotation angle.
     ///
     /// Its rotational part is represented as a 2x2 rotation matrix.
@@ -143,7 +143,7 @@ impl<N: Real> Isometry<N, U2, Rotation2<N>> {
     }
 }
 
-impl<N: Real> Isometry<N, U2, UnitComplex<N>> {
+impl<N: RealField> Isometry<N, U2, UnitComplex<N>> {
     /// Creates a new 2D isometry from a translation and a rotation angle.
     ///
     /// Its rotational part is represented as an unit complex number.
@@ -181,7 +181,7 @@ impl<N: Real> Isometry<N, U2, UnitComplex<N>> {
 // 3D rotation.
 macro_rules! isometry_construction_impl(
     ($RotId: ident < $($RotParams: ident),*>, $RRDim: ty, $RCDim: ty) => {
-        impl<N: Real> Isometry<N, U3, $RotId<$($RotParams),*>> {
+        impl<N: RealField> Isometry<N, U3, $RotId<$($RotParams),*>> {
             /// Creates a new isometry from a translation and a rotation axis-angle.
             ///
             /// # Example

src/geometry/isometry_conversion.rs

@@ -1,4 +1,4 @@
-use alga::general::{Real, SubsetOf, SupersetOf};
+use alga::general::{RealField, SubsetOf, SupersetOf};
 use alga::linear::Rotation;
 
 use crate::base::allocator::Allocator;
@@ -19,8 +19,8 @@ use crate::geometry::{Isometry, Point, Similarity, SuperTCategoryOf, TAffine, Tr
 
 impl<N1, N2, D: DimName, R1, R2> SubsetOf<Isometry<N2, D, R2>> for Isometry<N1, D, R1>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     R1: Rotation<Point<N1, D>> + SubsetOf<R2>,
     R2: Rotation<Point<N2, D>>,
     DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
@@ -47,8 +47,8 @@ where
 
 impl<N1, N2, D: DimName, R1, R2> SubsetOf<Similarity<N2, D, R2>> for Isometry<N1, D, R1>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     R1: Rotation<Point<N1, D>> + SubsetOf<R2>,
     R2: Rotation<Point<N2, D>>,
     DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
@@ -71,8 +71,8 @@ where
 
 impl<N1, N2, D, R, C> SubsetOf<Transform<N2, D, C>> for Isometry<N1, D, R>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     C: SuperTCategoryOf<TAffine>,
     R: Rotation<Point<N1, D>>
         + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>>
@@ -105,8 +105,8 @@ where
 
 impl<N1, N2, D, R> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Isometry<N1, D, R>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     R: Rotation<Point<N1, D>>
         + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>>
         + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
@@ -149,7 +149,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> From<Isometry<N, D, R>> for MatrixN<N, DimNameSum<D, U1>>
+impl<N: RealField, 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>>>,

src/geometry/isometry_ops.rs

@@ -1,6 +1,6 @@
 use std::ops::{Div, DivAssign, Mul, MulAssign};
 
-use alga::general::Real;
+use alga::general::RealField;
 use alga::linear::Rotation as AlgaRotation;
 
 use crate::base::allocator::Allocator;
@@ -64,7 +64,7 @@ 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: Real, D: DimName, R> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N: RealField, D: DimName, R> $Op<$Rhs> for $Lhs
             where R: AlgaRotation<Point<N, D>>,
                   DefaultAllocator: Allocator<N, D> {
             type Output = $Output;
@@ -111,7 +111,7 @@ 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: Real, D: DimName, R> $OpAssign<$Rhs> for $Lhs
+        impl<N: RealField, D: DimName, R> $OpAssign<$Rhs> for $Lhs
             where R: AlgaRotation<Point<N, D>>,
                   DefaultAllocator: Allocator<N, D> {
             #[inline]
@@ -120,7 +120,7 @@ macro_rules! isometry_binop_assign_impl_all(
             }
         }
 
-        impl<'b, N: Real, D: DimName, R> $OpAssign<&'b $Rhs> for $Lhs
+        impl<'b, N: RealField, D: DimName, R> $OpAssign<&'b $Rhs> for $Lhs
             where R: AlgaRotation<Point<N, D>>,
                   DefaultAllocator: Allocator<N, D> {
             #[inline]
@@ -286,7 +286,7 @@ macro_rules! isometry_from_composition_impl(
      ($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: Real $(, $Dims: $DimsBound)*> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N: RealField $(, $Dims: $DimsBound)*> $Op<$Rhs> for $Lhs
             where DefaultAllocator: Allocator<N, $R1, $C1> +
                                     Allocator<N, $R2, $C2> {
             type Output = $Output;

src/geometry/orthographic.rs

@@ -7,7 +7,7 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 use std::fmt;
 use std::mem;
 
-use alga::general::Real;
+use alga::general::RealField;
 
 use crate::base::dimension::U3;
 use crate::base::helper;
@@ -17,26 +17,26 @@ use crate::base::{Matrix4, Vector, Vector3};
 use crate::geometry::{Point3, Projective3};
 
 /// A 3D orthographic projection stored as an homogeneous 4x4 matrix.
-pub struct Orthographic3<N: Real> {
+pub struct Orthographic3<N: RealField> {
     matrix: Matrix4<N>,
 }
 
-impl<N: Real> Copy for Orthographic3<N> {}
+impl<N: RealField> Copy for Orthographic3<N> {}
 
-impl<N: Real> Clone for Orthographic3<N> {
+impl<N: RealField> Clone for Orthographic3<N> {
     #[inline]
     fn clone(&self) -> Self {
         Self::from_matrix_unchecked(self.matrix.clone())
     }
 }
 
-impl<N: Real> fmt::Debug for Orthographic3<N> {
+impl<N: RealField> fmt::Debug for Orthographic3<N> {
     fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
         self.matrix.fmt(f)
     }
 }
 
-impl<N: Real> PartialEq for Orthographic3<N> {
+impl<N: RealField> PartialEq for Orthographic3<N> {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
         self.matrix == right.matrix
@@ -44,7 +44,7 @@ impl<N: Real> PartialEq for Orthographic3<N> {
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<N: Real + Serialize> Serialize for Orthographic3<N> {
+impl<N: RealField + Serialize> Serialize for Orthographic3<N> {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
     where S: Serializer {
         self.matrix.serialize(serializer)
@@ -52,7 +52,7 @@ impl<N: Real + Serialize> Serialize for Orthographic3<N> {
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<'a, N: Real + Deserialize<'a>> Deserialize<'a> for Orthographic3<N> {
+impl<'a, N: RealField + Deserialize<'a>> Deserialize<'a> for Orthographic3<N> {
     fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
     where Des: Deserializer<'a> {
         let matrix = Matrix4::<N>::deserialize(deserializer)?;
@@ -61,7 +61,7 @@ impl<'a, N: Real + Deserialize<'a>> Deserialize<'a> for Orthographic3<N> {
     }
 }
 
-impl<N: Real> Orthographic3<N> {
+impl<N: RealField> Orthographic3<N> {
     /// Creates a new orthographic projection matrix.
     ///
     /// This follows the OpenGL convention, so this will flip the `z` axis.
@@ -678,7 +678,7 @@ impl<N: Real> Orthographic3<N> {
     }
 }
 
-impl<N: Real> Distribution<Orthographic3<N>> for Standard
+impl<N: RealField> Distribution<Orthographic3<N>> for Standard
 where Standard: Distribution<N>
 {
     fn sample<R: Rng + ?Sized>(&self, r: &mut R) -> Orthographic3<N> {
@@ -694,7 +694,7 @@ where Standard: Distribution<N>
 }
 
 #[cfg(feature = "arbitrary")]
-impl<N: Real + Arbitrary> Arbitrary for Orthographic3<N>
+impl<N: RealField + Arbitrary> Arbitrary for Orthographic3<N>
 where Matrix4<N>: Send
 {
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
@@ -709,7 +709,7 @@ where Matrix4<N>: Send
     }
 }
 
-impl<N: Real> From<Orthographic3<N>> for Matrix4<N> {
+impl<N: RealField> From<Orthographic3<N>> for Matrix4<N> {
     #[inline]
     fn from(orth: Orthographic3<N>) -> Self {
         orth.into_inner()

src/geometry/perspective.rs

@@ -8,7 +8,7 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 use std::fmt;
 use std::mem;
 
-use alga::general::Real;
+use alga::general::RealField;
 
 use crate::base::dimension::U3;
 use crate::base::helper;
@@ -22,22 +22,22 @@ pub struct Perspective3<N: Scalar> {
     matrix: Matrix4<N>,
 }
 
-impl<N: Real> Copy for Perspective3<N> {}
+impl<N: RealField> Copy for Perspective3<N> {}
 
-impl<N: Real> Clone for Perspective3<N> {
+impl<N: RealField> Clone for Perspective3<N> {
     #[inline]
     fn clone(&self) -> Self {
         Self::from_matrix_unchecked(self.matrix.clone())
     }
 }
 
-impl<N: Real> fmt::Debug for Perspective3<N> {
+impl<N: RealField> fmt::Debug for Perspective3<N> {
     fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
         self.matrix.fmt(f)
     }
 }
 
-impl<N: Real> PartialEq for Perspective3<N> {
+impl<N: RealField> PartialEq for Perspective3<N> {
     #[inline]
     fn eq(&self, right: &Self) -> bool {
         self.matrix == right.matrix
@@ -45,7 +45,7 @@ impl<N: Real> PartialEq for Perspective3<N> {
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<N: Real + Serialize> Serialize for Perspective3<N> {
+impl<N: RealField + Serialize> Serialize for Perspective3<N> {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
     where S: Serializer {
         self.matrix.serialize(serializer)
@@ -53,7 +53,7 @@ impl<N: Real + Serialize> Serialize for Perspective3<N> {
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<'a, N: Real + Deserialize<'a>> Deserialize<'a> for Perspective3<N> {
+impl<'a, N: RealField + Deserialize<'a>> Deserialize<'a> for Perspective3<N> {
     fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
     where Des: Deserializer<'a> {
         let matrix = Matrix4::<N>::deserialize(deserializer)?;
@@ -62,7 +62,7 @@ impl<'a, N: Real + Deserialize<'a>> Deserialize<'a> for Perspective3<N> {
     }
 }
 
-impl<N: Real> Perspective3<N> {
+impl<N: RealField> Perspective3<N> {
     /// Creates a new perspective matrix from the aspect ratio, y field of view, and near/far planes.
     pub fn new(aspect: N, fovy: N, znear: N, zfar: N) -> Self {
         assert!(
@@ -261,7 +261,7 @@ impl<N: Real> Perspective3<N> {
     }
 }
 
-impl<N: Real> Distribution<Perspective3<N>> for Standard
+impl<N: RealField> Distribution<Perspective3<N>> for Standard
 where Standard: Distribution<N>
 {
     fn sample<'a, R: Rng + ?Sized>(&self, r: &'a mut R) -> Perspective3<N> {
@@ -274,7 +274,7 @@ where Standard: Distribution<N>
 }
 
 #[cfg(feature = "arbitrary")]
-impl<N: Real + Arbitrary> Arbitrary for Perspective3<N> {
+impl<N: RealField + Arbitrary> Arbitrary for Perspective3<N> {
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
         let znear = Arbitrary::arbitrary(g);
         let zfar = helper::reject(g, |&x: &N| !(x - znear).is_zero());
@@ -284,7 +284,7 @@ impl<N: Real + Arbitrary> Arbitrary for Perspective3<N> {
     }
 }
 
-impl<N: Real> From<Perspective3<N>> for Matrix4<N> {
+impl<N: RealField> From<Perspective3<N>> for Matrix4<N> {
     #[inline]
     fn from(orth: Perspective3<N>) -> Self {
         orth.into_inner()

src/geometry/point_alga.rs

@@ -1,4 +1,4 @@
-use alga::general::{Field, JoinSemilattice, Lattice, MeetSemilattice, Real};
+use alga::general::{Field, JoinSemilattice, Lattice, MeetSemilattice, RealField};
 use alga::linear::{AffineSpace, EuclideanSpace};
 
 use crate::base::allocator::Allocator;
@@ -15,11 +15,11 @@ where
     type Translation = VectorN<N, D>;
 }
 
-impl<N: Real, D: DimName> EuclideanSpace for Point<N, D>
+impl<N: RealField, D: DimName> EuclideanSpace for Point<N, D>
 where DefaultAllocator: Allocator<N, D>
 {
     type Coordinates = VectorN<N, D>;
-    type Real = N;
+    type RealField = N;
 
     #[inline]
     fn origin() -> Self {

src/geometry/quaternion.rs

@@ -13,7 +13,7 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use alga::general::Real;
+use alga::general::RealField;
 
 use crate::base::dimension::{U1, U3, U4};
 use crate::base::storage::{CStride, RStride};
@@ -25,13 +25,13 @@ use crate::geometry::Rotation;
 /// that may be used as a rotation.
 #[repr(C)]
 #[derive(Debug)]
-pub struct Quaternion<N: Real> {
+pub struct Quaternion<N: RealField> {
     /// This quaternion as a 4D vector of coordinates in the `[ x, y, z, w ]` storage order.
     pub coords: Vector4<N>,
 }
 
 #[cfg(feature = "abomonation-serialize")]
-impl<N: Real> Abomonation for Quaternion<N>
+impl<N: RealField> Abomonation for Quaternion<N>
 where Vector4<N>: Abomonation
 {
     unsafe fn entomb<W: Write>(&self, writer: &mut W) -> IOResult<()> {
@@ -47,9 +47,9 @@ where Vector4<N>: Abomonation
     }
 }
 
-impl<N: Real + Eq> Eq for Quaternion<N> {}
+impl<N: RealField + Eq> Eq for Quaternion<N> {}
 
-impl<N: Real> PartialEq for Quaternion<N> {
+impl<N: RealField> PartialEq for Quaternion<N> {
     fn eq(&self, rhs: &Self) -> bool {
         self.coords == rhs.coords ||
         // Account for the double-covering of S², i.e. q = -q
@@ -57,15 +57,15 @@ impl<N: Real> PartialEq for Quaternion<N> {
     }
 }
 
-impl<N: Real + hash::Hash> hash::Hash for Quaternion<N> {
+impl<N: RealField + hash::Hash> hash::Hash for Quaternion<N> {
     fn hash<H: hash::Hasher>(&self, state: &mut H) {
         self.coords.hash(state)
     }
 }
 
-impl<N: Real> Copy for Quaternion<N> {}
+impl<N: RealField> Copy for Quaternion<N> {}
 
-impl<N: Real> Clone for Quaternion<N> {
+impl<N: RealField> Clone for Quaternion<N> {
     #[inline]
     fn clone(&self) -> Self {
         Self::from(self.coords.clone())
@@ -73,7 +73,7 @@ impl<N: Real> Clone for Quaternion<N> {
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<N: Real> Serialize for Quaternion<N>
+impl<N: RealField> Serialize for Quaternion<N>
 where Owned<N, U4>: Serialize
 {
     fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
@@ -83,7 +83,7 @@ where Owned<N, U4>: Serialize
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<'a, N: Real> Deserialize<'a> for Quaternion<N>
+impl<'a, N: RealField> Deserialize<'a> for Quaternion<N>
 where Owned<N, U4>: Deserialize<'a>
 {
     fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
@@ -94,7 +94,7 @@ where Owned<N, U4>: Deserialize<'a>
     }
 }
 
-impl<N: Real> Quaternion<N> {
+impl<N: RealField> Quaternion<N> {
     /// Moves this unit quaternion into one that owns its data.
     #[inline]
     #[deprecated(note = "This method is a no-op and will be removed in a future release.")]
@@ -508,7 +508,7 @@ impl<N: Real> Quaternion<N> {
     }
 }
 
-impl<N: Real + AbsDiffEq<Epsilon = N>> AbsDiffEq for Quaternion<N> {
+impl<N: RealField + AbsDiffEq<Epsilon = N>> AbsDiffEq for Quaternion<N> {
     type Epsilon = N;
 
     #[inline]
@@ -524,7 +524,7 @@ impl<N: Real + AbsDiffEq<Epsilon = N>> AbsDiffEq for Quaternion<N> {
     }
 }
 
-impl<N: Real + RelativeEq<Epsilon = N>> RelativeEq for Quaternion<N> {
+impl<N: RealField + RelativeEq<Epsilon = N>> RelativeEq for Quaternion<N> {
     #[inline]
     fn default_max_relative() -> Self::Epsilon {
         N::default_max_relative()
@@ -544,7 +544,7 @@ impl<N: Real + RelativeEq<Epsilon = N>> RelativeEq for Quaternion<N> {
     }
 }
 
-impl<N: Real + UlpsEq<Epsilon = N>> UlpsEq for Quaternion<N> {
+impl<N: RealField + UlpsEq<Epsilon = N>> UlpsEq for Quaternion<N> {
     #[inline]
     fn default_max_ulps() -> u32 {
         N::default_max_ulps()
@@ -558,7 +558,7 @@ impl<N: Real + UlpsEq<Epsilon = N>> UlpsEq for Quaternion<N> {
     }
 }
 
-impl<N: Real + fmt::Display> fmt::Display for Quaternion<N> {
+impl<N: RealField + fmt::Display> fmt::Display for Quaternion<N> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         write!(
             f,
@@ -571,7 +571,7 @@ impl<N: Real + fmt::Display> fmt::Display for Quaternion<N> {
 /// A unit quaternions. May be used to represent a rotation.
 pub type UnitQuaternion<N> = Unit<Quaternion<N>>;
 
-impl<N: Real> UnitQuaternion<N> {
+impl<N: RealField> UnitQuaternion<N> {
     /// Moves this unit quaternion into one that owns its data.
     #[inline]
     #[deprecated(
@@ -1007,7 +1007,7 @@ impl<N: Real> UnitQuaternion<N> {
     }
 }
 
-impl<N: Real + fmt::Display> fmt::Display for UnitQuaternion<N> {
+impl<N: RealField + fmt::Display> fmt::Display for UnitQuaternion<N> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         if let Some(axis) = self.axis() {
             let axis = axis.into_inner();
@@ -1029,7 +1029,7 @@ impl<N: Real + fmt::Display> fmt::Display for UnitQuaternion<N> {
     }
 }
 
-impl<N: Real + AbsDiffEq<Epsilon = N>> AbsDiffEq for UnitQuaternion<N> {
+impl<N: RealField + AbsDiffEq<Epsilon = N>> AbsDiffEq for UnitQuaternion<N> {
     type Epsilon = N;
 
     #[inline]
@@ -1043,7 +1043,7 @@ impl<N: Real + AbsDiffEq<Epsilon = N>> AbsDiffEq for UnitQuaternion<N> {
     }
 }
 
-impl<N: Real + RelativeEq<Epsilon = N>> RelativeEq for UnitQuaternion<N> {
+impl<N: RealField + RelativeEq<Epsilon = N>> RelativeEq for UnitQuaternion<N> {
     #[inline]
     fn default_max_relative() -> Self::Epsilon {
         N::default_max_relative()
@@ -1062,7 +1062,7 @@ impl<N: Real + RelativeEq<Epsilon = N>> RelativeEq for UnitQuaternion<N> {
     }
 }
 
-impl<N: Real + UlpsEq<Epsilon = N>> UlpsEq for UnitQuaternion<N> {
+impl<N: RealField + UlpsEq<Epsilon = N>> UlpsEq for UnitQuaternion<N> {
     #[inline]
     fn default_max_ulps() -> u32 {
         N::default_max_ulps()

src/geometry/quaternion_alga.rs

@@ -3,7 +3,7 @@ use num::Zero;
 use alga::general::{
     AbstractGroup, AbstractGroupAbelian, AbstractLoop, AbstractMagma, AbstractModule,
     AbstractMonoid, AbstractQuasigroup, AbstractSemigroup, Additive, Id, Identity, TwoSidedInverse, Module,
-    Multiplicative, Real,
+    Multiplicative, RealField,
 };
 use alga::linear::{
     AffineTransformation, DirectIsometry, FiniteDimVectorSpace, Isometry, NormedSpace,
@@ -14,35 +14,35 @@ use alga::linear::{
 use crate::base::{Vector3, Vector4};
 use crate::geometry::{Point3, Quaternion, UnitQuaternion};
 
-impl<N: Real> Identity<Multiplicative> for Quaternion<N> {
+impl<N: RealField> Identity<Multiplicative> for Quaternion<N> {
     #[inline]
     fn identity() -> Self {
         Self::identity()
     }
 }
 
-impl<N: Real> Identity<Additive> for Quaternion<N> {
+impl<N: RealField> Identity<Additive> for Quaternion<N> {
     #[inline]
     fn identity() -> Self {
         Self::zero()
     }
 }
 
-impl<N: Real> AbstractMagma<Multiplicative> for Quaternion<N> {
+impl<N: RealField> AbstractMagma<Multiplicative> for Quaternion<N> {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
         self * rhs
     }
 }
 
-impl<N: Real> AbstractMagma<Additive> for Quaternion<N> {
+impl<N: RealField> AbstractMagma<Additive> for Quaternion<N> {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
         self + rhs
     }
 }
 
-impl<N: Real> TwoSidedInverse<Additive> for Quaternion<N> {
+impl<N: RealField> TwoSidedInverse<Additive> for Quaternion<N> {
     #[inline]
     fn two_sided_inverse(&self) -> Self {
         -self
@@ -51,7 +51,7 @@ impl<N: Real> TwoSidedInverse<Additive> for Quaternion<N> {
 
 macro_rules! impl_structures(
     ($Quaternion: ident; $($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: Real> $marker<$operator> for $Quaternion<N> { }
+        impl<N: RealField> $marker<$operator> for $Quaternion<N> { }
     )*}
 );
 
@@ -73,7 +73,7 @@ impl_structures!(
  * Vector space.
  *
  */
-impl<N: Real> AbstractModule for Quaternion<N> {
+impl<N: RealField> AbstractModule for Quaternion<N> {
     type AbstractRing = N;
 
     #[inline]
@@ -82,15 +82,15 @@ impl<N: Real> AbstractModule for Quaternion<N> {
     }
 }
 
-impl<N: Real> Module for Quaternion<N> {
+impl<N: RealField> Module for Quaternion<N> {
     type Ring = N;
 }
 
-impl<N: Real> VectorSpace for Quaternion<N> {
+impl<N: RealField> VectorSpace for Quaternion<N> {
     type Field = N;
 }
 
-impl<N: Real> FiniteDimVectorSpace for Quaternion<N> {
+impl<N: RealField> FiniteDimVectorSpace for Quaternion<N> {
     #[inline]
     fn dimension() -> usize {
         4
@@ -117,8 +117,8 @@ impl<N: Real> FiniteDimVectorSpace for Quaternion<N> {
     }
 }
 
-impl<N: Real> NormedSpace for Quaternion<N> {
+impl<N: RealField> NormedSpace for Quaternion<N> {
-    type Real = N;
+    type RealField = N;
     type ComplexField = N;
 
     #[inline]
@@ -162,21 +162,21 @@ impl<N: Real> NormedSpace for Quaternion<N> {
  * Implementations for UnitQuaternion.
  *
  */
-impl<N: Real> Identity<Multiplicative> for UnitQuaternion<N> {
+impl<N: RealField> Identity<Multiplicative> for UnitQuaternion<N> {
     #[inline]
     fn identity() -> Self {
         Self::identity()
     }
 }
 
-impl<N: Real> AbstractMagma<Multiplicative> for UnitQuaternion<N> {
+impl<N: RealField> AbstractMagma<Multiplicative> for UnitQuaternion<N> {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
         self * rhs
     }
 }
 
-impl<N: Real> TwoSidedInverse<Multiplicative> for UnitQuaternion<N> {
+impl<N: RealField> TwoSidedInverse<Multiplicative> for UnitQuaternion<N> {
     #[inline]
     fn two_sided_inverse(&self) -> Self {
         self.inverse()
@@ -197,7 +197,7 @@ impl_structures!(
     AbstractGroup<Multiplicative>
 );
 
-impl<N: Real> Transformation<Point3<N>> for UnitQuaternion<N> {
+impl<N: RealField> Transformation<Point3<N>> for UnitQuaternion<N> {
     #[inline]
     fn transform_point(&self, pt: &Point3<N>) -> Point3<N> {
         self * pt
@@ -209,7 +209,7 @@ impl<N: Real> Transformation<Point3<N>> for UnitQuaternion<N> {
     }
 }
 
-impl<N: Real> ProjectiveTransformation<Point3<N>> for UnitQuaternion<N> {
+impl<N: RealField> ProjectiveTransformation<Point3<N>> for UnitQuaternion<N> {
     #[inline]
     fn inverse_transform_point(&self, pt: &Point3<N>) -> Point3<N> {
         // FIXME: would it be useful performancewise not to call inverse explicitly (i-e. implement
@@ -223,7 +223,7 @@ impl<N: Real> ProjectiveTransformation<Point3<N>> for UnitQuaternion<N> {
     }
 }
 
-impl<N: Real> AffineTransformation<Point3<N>> for UnitQuaternion<N> {
+impl<N: RealField> AffineTransformation<Point3<N>> for UnitQuaternion<N> {
     type Rotation = Self;
     type NonUniformScaling = Id;
     type Translation = Id;
@@ -264,7 +264,7 @@ impl<N: Real> AffineTransformation<Point3<N>> for UnitQuaternion<N> {
     }
 }
 
-impl<N: Real> Similarity<Point3<N>> for UnitQuaternion<N> {
+impl<N: RealField> Similarity<Point3<N>> for UnitQuaternion<N> {
     type Scaling = Id;
 
     #[inline]
@@ -285,13 +285,13 @@ impl<N: Real> Similarity<Point3<N>> for UnitQuaternion<N> {
 
 macro_rules! marker_impl(
     ($($Trait: ident),*) => {$(
-        impl<N: Real> $Trait<Point3<N>> for UnitQuaternion<N> { }
+        impl<N: RealField> $Trait<Point3<N>> for UnitQuaternion<N> { }
     )*}
 );
 
 marker_impl!(Isometry, DirectIsometry, OrthogonalTransformation);
 
-impl<N: Real> Rotation<Point3<N>> for UnitQuaternion<N> {
+impl<N: RealField> Rotation<Point3<N>> for UnitQuaternion<N> {
     #[inline]
     fn powf(&self, n: N) -> Option<Self> {
         Some(self.powf(n))

src/geometry/quaternion_construction.rs

@@ -9,7 +9,7 @@ use num::{One, Zero};
 use rand::distributions::{Distribution, OpenClosed01, Standard};
 use rand::Rng;
 
-use alga::general::Real;
+use alga::general::RealField;
 
 use crate::base::dimension::U3;
 use crate::base::storage::Storage;
@@ -19,7 +19,7 @@ use crate::base::{Unit, Vector, Vector4, Matrix3};
 
 use crate::geometry::{Quaternion, Rotation3, UnitQuaternion};
 
-impl<N: Real> Quaternion<N> {
+impl<N: RealField> Quaternion<N> {
     /// Creates a quaternion from a 4D vector. The quaternion scalar part corresponds to the `w`
     /// vector component.
     #[inline]
@@ -96,14 +96,14 @@ impl<N: Real> Quaternion<N> {
     }
 }
 
-impl<N: Real> One for Quaternion<N> {
+impl<N: RealField> One for Quaternion<N> {
     #[inline]
     fn one() -> Self {
         Self::identity()
     }
 }
 
-impl<N: Real> Zero for Quaternion<N> {
+impl<N: RealField> Zero for Quaternion<N> {
     #[inline]
     fn zero() -> Self {
         Self::new(N::zero(), N::zero(), N::zero(), N::zero())
@@ -115,7 +115,7 @@ impl<N: Real> Zero for Quaternion<N> {
     }
 }
 
-impl<N: Real> Distribution<Quaternion<N>> for Standard
+impl<N: RealField> Distribution<Quaternion<N>> for Standard
 where Standard: Distribution<N>
 {
     #[inline]
@@ -125,7 +125,7 @@ where Standard: Distribution<N>
 }
 
 #[cfg(feature = "arbitrary")]
-impl<N: Real + Arbitrary> Arbitrary for Quaternion<N>
+impl<N: RealField + Arbitrary> Arbitrary for Quaternion<N>
 where Owned<N, U4>: Send
 {
     #[inline]
@@ -139,7 +139,7 @@ where Owned<N, U4>: Send
     }
 }
 
-impl<N: Real> UnitQuaternion<N> {
+impl<N: RealField> UnitQuaternion<N> {
     /// The rotation identity.
     ///
     /// # Example
@@ -669,14 +669,14 @@ impl<N: Real> UnitQuaternion<N> {
     }
 }
 
-impl<N: Real> One for UnitQuaternion<N> {
+impl<N: RealField> One for UnitQuaternion<N> {
     #[inline]
     fn one() -> Self {
         Self::identity()
     }
 }
 
-impl<N: Real> Distribution<UnitQuaternion<N>> for Standard
+impl<N: RealField> Distribution<UnitQuaternion<N>> for Standard
 where OpenClosed01: Distribution<N>
 {
     /// Generate a uniformly distributed random rotation quaternion.
@@ -701,7 +701,7 @@ where OpenClosed01: Distribution<N>
 }
 
 #[cfg(feature = "arbitrary")]
-impl<N: Real + Arbitrary> Arbitrary for UnitQuaternion<N>
+impl<N: RealField + Arbitrary> Arbitrary for UnitQuaternion<N>
 where
     Owned<N, U4>: Send,
     Owned<N, U3>: Send,

src/geometry/quaternion_conversion.rs

@@ -1,6 +1,6 @@
 use num::Zero;
 
-use alga::general::{Real, SubsetOf, SupersetOf};
+use alga::general::{RealField, SubsetOf, SupersetOf};
 use alga::linear::Rotation as AlgaRotation;
 
 #[cfg(feature = "mint")]
@@ -34,8 +34,8 @@ use crate::geometry::{
 
 impl<N1, N2> SubsetOf<Quaternion<N2>> for Quaternion<N1>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
 {
     #[inline]
     fn to_superset(&self) -> Quaternion<N2> {
@@ -57,8 +57,8 @@ where
 
 impl<N1, N2> SubsetOf<UnitQuaternion<N2>> for UnitQuaternion<N1>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
 {
     #[inline]
     fn to_superset(&self) -> UnitQuaternion<N2> {
@@ -78,8 +78,8 @@ where
 
 impl<N1, N2> SubsetOf<Rotation<N2, U3>> for UnitQuaternion<N1>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
 {
     #[inline]
     fn to_superset(&self) -> Rotation3<N2> {
@@ -101,8 +101,8 @@ where
 
 impl<N1, N2, R> SubsetOf<Isometry<N2, U3, R>> for UnitQuaternion<N1>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     R: AlgaRotation<Point3<N2>> + SupersetOf<Self>,
 {
     #[inline]
@@ -123,8 +123,8 @@ where
 
 impl<N1, N2, R> SubsetOf<Similarity<N2, U3, R>> for UnitQuaternion<N1>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     R: AlgaRotation<Point3<N2>> + SupersetOf<Self>,
 {
     #[inline]
@@ -145,8 +145,8 @@ where
 
 impl<N1, N2, C> SubsetOf<Transform<N2, U3, C>> for UnitQuaternion<N1>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     C: SuperTCategoryOf<TAffine>,
 {
     #[inline]
@@ -165,7 +165,7 @@ where
     }
 }
 
-impl<N1: Real, N2: Real + SupersetOf<N1>> SubsetOf<Matrix4<N2>> for UnitQuaternion<N1> {
+impl<N1: RealField, N2: RealField + SupersetOf<N1>> SubsetOf<Matrix4<N2>> for UnitQuaternion<N1> {
     #[inline]
     fn to_superset(&self) -> Matrix4<N2> {
         self.to_homogeneous().to_superset()
@@ -184,14 +184,14 @@ impl<N1: Real, N2: Real + SupersetOf<N1>> SubsetOf<Matrix4<N2>> for UnitQuaterni
 }
 
 #[cfg(feature = "mint")]
-impl<N: Real> From<mint::Quaternion<N>> for Quaternion<N> {
+impl<N: RealField> From<mint::Quaternion<N>> for Quaternion<N> {
     fn from(q: mint::Quaternion<N>) -> Self {
         Self::new(q.s, q.v.x, q.v.y, q.v.z)
     }
 }
 
 #[cfg(feature = "mint")]
-impl<N: Real> Into<mint::Quaternion<N>> for Quaternion<N> {
+impl<N: RealField> Into<mint::Quaternion<N>> for Quaternion<N> {
     fn into(self) -> mint::Quaternion<N> {
         mint::Quaternion {
             v: mint::Vector3 {
@@ -205,7 +205,7 @@ impl<N: Real> Into<mint::Quaternion<N>> for Quaternion<N> {
 }
 
 #[cfg(feature = "mint")]
-impl<N: Real> Into<mint::Quaternion<N>> for UnitQuaternion<N> {
+impl<N: RealField> Into<mint::Quaternion<N>> for UnitQuaternion<N> {
     fn into(self) -> mint::Quaternion<N> {
         mint::Quaternion {
             v: mint::Vector3 {
@@ -218,35 +218,35 @@ impl<N: Real> Into<mint::Quaternion<N>> for UnitQuaternion<N> {
     }
 }
 
-impl<N: Real> From<UnitQuaternion<N>> for Matrix4<N> {
+impl<N: RealField> From<UnitQuaternion<N>> for Matrix4<N> {
     #[inline]
     fn from(q: UnitQuaternion<N>) -> Self {
         q.to_homogeneous()
     }
 }
 
-impl<N: Real> From<UnitQuaternion<N>> for Rotation3<N> {
+impl<N: RealField> From<UnitQuaternion<N>> for Rotation3<N> {
     #[inline]
     fn from(q: UnitQuaternion<N>) -> Self {
         q.to_rotation_matrix()
     }
 }
 
-impl<N: Real> From<Rotation3<N>> for UnitQuaternion<N> {
+impl<N: RealField> From<Rotation3<N>> for UnitQuaternion<N> {
     #[inline]
     fn from(q: Rotation3<N>) -> Self {
         Self::from_rotation_matrix(&q)
     }
 }
 
-impl<N: Real> From<UnitQuaternion<N>> for Matrix3<N> {
+impl<N: RealField> From<UnitQuaternion<N>> for Matrix3<N> {
     #[inline]
     fn from(q: UnitQuaternion<N>) -> Self {
         q.to_rotation_matrix().into_inner()
     }
 }
 
-impl<N: Real> From<Vector4<N>> for Quaternion<N> {
+impl<N: RealField> From<Vector4<N>> for Quaternion<N> {
     #[inline]
     fn from(coords: Vector4<N>) -> Self {
         Self { coords }

src/geometry/quaternion_coordinates.rs

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

src/geometry/quaternion_ops.rs

@@ -54,7 +54,7 @@ use std::ops::{
     Add, AddAssign, Div, DivAssign, Index, IndexMut, Mul, MulAssign, Neg, Sub, SubAssign,
 };
 
-use alga::general::Real;
+use alga::general::RealField;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{U1, U3, U4};
@@ -63,7 +63,7 @@ use crate::base::{DefaultAllocator, Unit, Vector, Vector3};
 
 use crate::geometry::{Point3, Quaternion, Rotation, UnitQuaternion};
 
-impl<N: Real> Index<usize> for Quaternion<N> {
+impl<N: RealField> Index<usize> for Quaternion<N> {
     type Output = N;
 
     #[inline]
@@ -72,7 +72,7 @@ impl<N: Real> Index<usize> for Quaternion<N> {
     }
 }
 
-impl<N: Real> IndexMut<usize> for Quaternion<N> {
+impl<N: RealField> IndexMut<usize> for Quaternion<N> {
     #[inline]
     fn index_mut(&mut self, i: usize) -> &mut N {
         &mut self.coords[i]
@@ -85,7 +85,7 @@ macro_rules! quaternion_op_impl(
      $(for $Storage: ident: $StoragesBound: ident $(<$($BoundParam: ty),*>)*),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Result: ty $(=> $VDimA: ty, $VDimB: ty)*;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N: Real $(, $Storage: $StoragesBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N: RealField $(, $Storage: $StoragesBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
             where DefaultAllocator: Allocator<N, $LhsRDim, $LhsCDim> +
                                     Allocator<N, $RhsRDim, $RhsCDim> {
             type Output = $Result;
@@ -490,7 +490,7 @@ quaternion_op_impl!(
 
 macro_rules! scalar_op_impl(
     ($($Op: ident, $op: ident, $OpAssign: ident, $op_assign: ident);* $(;)*) => {$(
-        impl<N: Real> $Op<N> for Quaternion<N> {
+        impl<N: RealField> $Op<N> for Quaternion<N> {
             type Output = Quaternion<N>;
 
             #[inline]
@@ -499,7 +499,7 @@ macro_rules! scalar_op_impl(
             }
         }
 
-        impl<'a, N: Real> $Op<N> for &'a Quaternion<N> {
+        impl<'a, N: RealField> $Op<N> for &'a Quaternion<N> {
             type Output = Quaternion<N>;
 
             #[inline]
@@ -508,7 +508,7 @@ macro_rules! scalar_op_impl(
             }
         }
 
-        impl<N: Real> $OpAssign<N> for Quaternion<N> {
+        impl<N: RealField> $OpAssign<N> for Quaternion<N> {
 
             #[inline]
             fn $op_assign(&mut self, n: N) {
@@ -547,7 +547,7 @@ macro_rules! left_scalar_mul_impl(
 
 left_scalar_mul_impl!(f32, f64);
 
-impl<N: Real> Neg for Quaternion<N> {
+impl<N: RealField> Neg for Quaternion<N> {
     type Output = Quaternion<N>;
 
     #[inline]
@@ -556,7 +556,7 @@ impl<N: Real> Neg for Quaternion<N> {
     }
 }
 
-impl<'a, N: Real> Neg for &'a Quaternion<N> {
+impl<'a, N: RealField> Neg for &'a Quaternion<N> {
     type Output = Quaternion<N>;
 
     #[inline]
@@ -570,7 +570,7 @@ macro_rules! quaternion_op_impl(
      ($LhsRDim: ident, $LhsCDim: ident), ($RhsRDim: ident, $RhsCDim: ident);
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty $(=> $VDimA: ty, $VDimB: ty)*;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N: Real> $OpAssign<$Rhs> for $Lhs
+        impl<$($lives ,)* N: RealField> $OpAssign<$Rhs> for $Lhs
             where DefaultAllocator: Allocator<N, $LhsRDim, $LhsCDim> +
                                     Allocator<N, $RhsRDim, $RhsCDim> {
 

src/geometry/rotation.rs

@@ -14,7 +14,7 @@ use crate::base::storage::Owned;
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use alga::general::Real;
+use alga::general::RealField;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
@@ -429,7 +429,7 @@ where
  */
 impl<N, D: DimName> fmt::Display for Rotation<N, D>
 where
-    N: Real + fmt::Display,
+    N: RealField + fmt::Display,
     DefaultAllocator: Allocator<N, D, D> + Allocator<usize, D, D>,
 {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {

src/geometry/rotation_alga.rs

@@ -1,6 +1,6 @@
 use alga::general::{
     AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, Real,
+    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, RealField,
 };
 use alga::linear::{
     self, AffineTransformation, DirectIsometry, Isometry, OrthogonalTransformation,
@@ -18,7 +18,7 @@ use crate::geometry::{Point, Rotation};
  * Algebraic structures.
  *
  */
-impl<N: Real, D: DimName> Identity<Multiplicative> for Rotation<N, D>
+impl<N: RealField, D: DimName> Identity<Multiplicative> for Rotation<N, D>
 where DefaultAllocator: Allocator<N, D, D>
 {
     #[inline]
@@ -27,7 +27,7 @@ where DefaultAllocator: Allocator<N, D, D>
     }
 }
 
-impl<N: Real, D: DimName> TwoSidedInverse<Multiplicative> for Rotation<N, D>
+impl<N: RealField, D: DimName> TwoSidedInverse<Multiplicative> for Rotation<N, D>
 where DefaultAllocator: Allocator<N, D, D>
 {
     #[inline]
@@ -41,7 +41,7 @@ where DefaultAllocator: Allocator<N, D, D>
     }
 }
 
-impl<N: Real, D: DimName> AbstractMagma<Multiplicative> for Rotation<N, D>
+impl<N: RealField, D: DimName> AbstractMagma<Multiplicative> for Rotation<N, D>
 where DefaultAllocator: Allocator<N, D, D>
 {
     #[inline]
@@ -52,7 +52,7 @@ where DefaultAllocator: Allocator<N, D, D>
 
 macro_rules! impl_multiplicative_structures(
     ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: Real, D: DimName> $marker<$operator> for Rotation<N, D>
+        impl<N: RealField, D: DimName> $marker<$operator> for Rotation<N, D>
             where DefaultAllocator: Allocator<N, D, D> { }
     )*}
 );
@@ -70,7 +70,7 @@ impl_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N: Real, D: DimName> Transformation<Point<N, D>> for Rotation<N, D>
+impl<N: RealField, D: DimName> Transformation<Point<N, D>> for Rotation<N, D>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
 {
     #[inline]
@@ -84,7 +84,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
     }
 }
 
-impl<N: Real, D: DimName> ProjectiveTransformation<Point<N, D>> for Rotation<N, D>
+impl<N: RealField, D: DimName> ProjectiveTransformation<Point<N, D>> for Rotation<N, D>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
 {
     #[inline]
@@ -98,7 +98,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
     }
 }
 
-impl<N: Real, D: DimName> AffineTransformation<Point<N, D>> for Rotation<N, D>
+impl<N: RealField, D: DimName> AffineTransformation<Point<N, D>> for Rotation<N, D>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
 {
     type Rotation = Self;
@@ -141,7 +141,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
     }
 }
 
-impl<N: Real, D: DimName> Similarity<Point<N, D>> for Rotation<N, D>
+impl<N: RealField, D: DimName> Similarity<Point<N, D>> for Rotation<N, D>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
 {
     type Scaling = Id;
@@ -164,7 +164,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
 
 macro_rules! marker_impl(
     ($($Trait: ident),*) => {$(
-        impl<N: Real, D: DimName> $Trait<Point<N, D>> for Rotation<N, D>
+        impl<N: RealField, D: DimName> $Trait<Point<N, D>> for Rotation<N, D>
         where DefaultAllocator: Allocator<N, D, D> +
                                 Allocator<N, D> { }
     )*}
@@ -173,7 +173,7 @@ macro_rules! marker_impl(
 marker_impl!(Isometry, DirectIsometry, OrthogonalTransformation);
 
 /// Subgroups of the n-dimensional rotation group `SO(n)`.
-impl<N: Real, D: DimName> linear::Rotation<Point<N, D>> for Rotation<N, D>
+impl<N: RealField, D: DimName> linear::Rotation<Point<N, D>> for Rotation<N, D>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
 {
     #[inline]
@@ -199,7 +199,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>
 }
 
 /*
-impl<N: Real> Matrix for Rotation<N> {
+impl<N: RealField> Matrix for Rotation<N> {
     type Field     = N;
     type Row       = Matrix<N>;
     type Column    = Matrix<N>;
@@ -241,7 +241,7 @@ impl<N: Real> Matrix for Rotation<N> {
     }
 }
 
-impl<N: Real> SquareMatrix for Rotation<N> {
+impl<N: RealField> SquareMatrix for Rotation<N> {
     type Vector = Matrix<N>;
 
     #[inline]
@@ -271,5 +271,5 @@ impl<N: Real> SquareMatrix for Rotation<N> {
     }
 }
 
-impl<N: Real> InversibleSquareMatrix for Rotation<N> { }
+impl<N: RealField> InversibleSquareMatrix for Rotation<N> { }
 */

src/geometry/rotation_conversion.rs

@@ -1,6 +1,6 @@
 use num::Zero;
 
-use alga::general::{Real, SubsetOf, SupersetOf};
+use alga::general::{RealField, SubsetOf, SupersetOf};
 use alga::linear::Rotation as AlgaRotation;
 
 #[cfg(feature = "mint")]
@@ -32,8 +32,8 @@ use crate::geometry::{
 
 impl<N1, N2, D: DimName> SubsetOf<Rotation<N2, D>> for Rotation<N1, D>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D, D>,
 {
     #[inline]
@@ -54,8 +54,8 @@ where
 
 impl<N1, N2> SubsetOf<UnitQuaternion<N2>> for Rotation3<N1>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
 {
     #[inline]
     fn to_superset(&self) -> UnitQuaternion<N2> {
@@ -77,8 +77,8 @@ where
 
 impl<N1, N2> SubsetOf<UnitComplex<N2>> for Rotation2<N1>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
 {
     #[inline]
     fn to_superset(&self) -> UnitComplex<N2> {
@@ -100,8 +100,8 @@ where
 
 impl<N1, N2, D: DimName, R> SubsetOf<Isometry<N2, D, R>> for Rotation<N1, D>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     R: AlgaRotation<Point<N2, D>> + SupersetOf<Self>,
     DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D>,
 {
@@ -123,8 +123,8 @@ where
 
 impl<N1, N2, D: DimName, R> SubsetOf<Similarity<N2, D, R>> for Rotation<N1, D>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     R: AlgaRotation<Point<N2, D>> + SupersetOf<Self>,
     DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D>,
 {
@@ -146,8 +146,8 @@ where
 
 impl<N1, N2, D, C> SubsetOf<Transform<N2, D, C>> for Rotation<N1, D>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     C: SuperTCategoryOf<TAffine>,
     D: DimNameAdd<U1> + DimMin<D, Output = D>, // needed by .is_special_orthogonal()
     DefaultAllocator: Allocator<N1, D, D>
@@ -175,8 +175,8 @@ where
 
 impl<N1, N2, D> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Rotation<N1, D>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     D: DimNameAdd<U1> + DimMin<D, Output = D>, // needed by .is_special_orthogonal()
     DefaultAllocator: Allocator<N1, D, D>
         + Allocator<N2, D, D>
@@ -211,34 +211,34 @@ where
 }
 
 #[cfg(feature = "mint")]
-impl<N: Real> From<mint::EulerAngles<N, mint::IntraXYZ>> for Rotation3<N> {
+impl<N: RealField> From<mint::EulerAngles<N, mint::IntraXYZ>> for Rotation3<N> {
     fn from(euler: mint::EulerAngles<N, mint::IntraXYZ>) -> Self {
         Self::from_euler_angles(euler.a, euler.b, euler.c)
     }
 }
 
-impl<N: Real> From<Rotation2<N>> for Matrix3<N> {
+impl<N: RealField> From<Rotation2<N>> for Matrix3<N> {
     #[inline]
     fn from(q: Rotation2<N>) ->Self {
         q.to_homogeneous()
     }
 }
 
-impl<N: Real> From<Rotation2<N>> for Matrix2<N> {
+impl<N: RealField> From<Rotation2<N>> for Matrix2<N> {
     #[inline]
     fn from(q: Rotation2<N>) -> Self {
         q.into_inner()
     }
 }
 
-impl<N: Real> From<Rotation3<N>> for Matrix4<N> {
+impl<N: RealField> From<Rotation3<N>> for Matrix4<N> {
     #[inline]
     fn from(q: Rotation3<N>) -> Self {
         q.to_homogeneous()
     }
 }
 
-impl<N: Real> From<Rotation3<N>> for Matrix3<N> {
+impl<N: RealField> From<Rotation3<N>> for Matrix3<N> {
     #[inline]
     fn from(q: Rotation3<N>) -> Self {
         q.into_inner()

src/geometry/rotation_specialization.rs

@@ -3,7 +3,7 @@ use crate::base::storage::Owned;
 #[cfg(feature = "arbitrary")]
 use quickcheck::{Arbitrary, Gen};
 
-use alga::general::Real;
+use alga::general::RealField;
 use num::Zero;
 use rand::distributions::{Distribution, OpenClosed01, Standard};
 use rand::Rng;
@@ -20,7 +20,7 @@ use crate::geometry::{Rotation2, Rotation3, UnitComplex, UnitQuaternion};
  * 2D Rotation matrix.
  *
  */
-impl<N: Real> Rotation2<N> {
+impl<N: RealField> Rotation2<N> {
     /// Builds a 2 dimensional rotation matrix from an angle in radian.
     ///
     /// # Example
@@ -232,7 +232,7 @@ impl<N: Real> Rotation2<N> {
     }
 }
 
-impl<N: Real> Distribution<Rotation2<N>> for Standard
+impl<N: RealField> Distribution<Rotation2<N>> for Standard
 where OpenClosed01: Distribution<N>
 {
     /// Generate a uniformly distributed random rotation.
@@ -243,7 +243,7 @@ where OpenClosed01: Distribution<N>
 }
 
 #[cfg(feature = "arbitrary")]
-impl<N: Real + Arbitrary> Arbitrary for Rotation2<N>
+impl<N: RealField + Arbitrary> Arbitrary for Rotation2<N>
 where Owned<N, U2, U2>: Send
 {
     #[inline]
@@ -257,7 +257,7 @@ where Owned<N, U2, U2>: Send
  * 3D Rotation matrix.
  *
  */
-impl<N: Real> Rotation3<N> {
+impl<N: RealField> Rotation3<N> {
     /// Builds a 3 dimensional rotation matrix from an axis and an angle.
     ///
     /// # Arguments
@@ -819,7 +819,7 @@ impl<N: Real> Rotation3<N> {
     }
 }
 
-impl<N: Real> Distribution<Rotation3<N>> for Standard
+impl<N: RealField> Distribution<Rotation3<N>> for Standard
 where OpenClosed01: Distribution<N>
 {
     /// Generate a uniformly distributed random rotation.
@@ -859,7 +859,7 @@ where OpenClosed01: Distribution<N>
 }
 
 #[cfg(feature = "arbitrary")]
-impl<N: Real + Arbitrary> Arbitrary for Rotation3<N>
+impl<N: RealField + Arbitrary> Arbitrary for Rotation3<N>
 where
     Owned<N, U3, U3>: Send,
     Owned<N, U3>: Send,

src/geometry/similarity.rs

@@ -10,7 +10,7 @@ use serde::{Deserialize, Serialize};
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use alga::general::{Real, SubsetOf};
+use alga::general::{RealField, SubsetOf};
 use alga::linear::Rotation;
 
 use crate::base::allocator::Allocator;
@@ -41,7 +41,7 @@ use crate::geometry::{Isometry, Point, Translation};
                        Owned<N, D>: Deserialize<'de>"
     ))
 )]
-pub struct Similarity<N: Real, D: DimName, R>
+pub struct Similarity<N: RealField, D: DimName, R>
 where DefaultAllocator: Allocator<N, D>
 {
     /// The part of this similarity that does not include the scaling factor.
@@ -50,7 +50,7 @@ where DefaultAllocator: Allocator<N, D>
 }
 
 #[cfg(feature = "abomonation-serialize")]
-impl<N: Real, D: DimName, R> Abomonation for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> Abomonation for Similarity<N, D, R>
 where
     Isometry<N, D, R>: Abomonation,
     DefaultAllocator: Allocator<N, D>,
@@ -68,7 +68,7 @@ where
     }
 }
 
-impl<N: Real + hash::Hash, D: DimName + hash::Hash, R: hash::Hash> hash::Hash
+impl<N: RealField + hash::Hash, D: DimName + hash::Hash, R: hash::Hash> hash::Hash
     for Similarity<N, D, R>
 where
     DefaultAllocator: Allocator<N, D>,
@@ -80,13 +80,13 @@ where
     }
 }
 
-impl<N: Real, D: DimName + Copy, R: Rotation<Point<N, D>> + Copy> Copy for Similarity<N, D, R>
+impl<N: RealField, D: DimName + Copy, R: Rotation<Point<N, D>> + Copy> Copy for Similarity<N, D, R>
 where
     DefaultAllocator: Allocator<N, D>,
     Owned<N, D>: Copy,
 {}
 
-impl<N: Real, D: DimName, R: Rotation<Point<N, D>> + Clone> Clone for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R: Rotation<Point<N, D>> + Clone> Clone for Similarity<N, D, R>
 where DefaultAllocator: Allocator<N, D>
 {
     #[inline]
@@ -95,7 +95,7 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: Real, D: DimName, R> Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> Similarity<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -244,7 +244,7 @@ where
 // and makes it harder 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 private scaling factor).
-impl<N: Real, D: DimName, R> Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> Similarity<N, D, R>
 where DefaultAllocator: Allocator<N, D>
 {
     /// Converts this similarity into its equivalent homogeneous transformation matrix.
@@ -265,13 +265,13 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: Real, D: DimName, R> Eq for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> Eq for Similarity<N, D, R>
 where
     R: Rotation<Point<N, D>> + Eq,
     DefaultAllocator: Allocator<N, D>,
 {}
 
-impl<N: Real, D: DimName, R> PartialEq for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> PartialEq for Similarity<N, D, R>
 where
     R: Rotation<Point<N, D>> + PartialEq,
     DefaultAllocator: Allocator<N, D>,
@@ -282,7 +282,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> AbsDiffEq for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> AbsDiffEq for Similarity<N, D, R>
 where
     R: Rotation<Point<N, D>> + AbsDiffEq<Epsilon = N::Epsilon>,
     DefaultAllocator: Allocator<N, D>,
@@ -302,7 +302,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> RelativeEq for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> RelativeEq for Similarity<N, D, R>
 where
     R: Rotation<Point<N, D>> + RelativeEq<Epsilon = N::Epsilon>,
     DefaultAllocator: Allocator<N, D>,
@@ -329,7 +329,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> UlpsEq for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> UlpsEq for Similarity<N, D, R>
 where
     R: Rotation<Point<N, D>> + UlpsEq<Epsilon = N::Epsilon>,
     DefaultAllocator: Allocator<N, D>,
@@ -354,7 +354,7 @@ where
  */
 impl<N, D: DimName, R> fmt::Display for Similarity<N, D, R>
 where
-    N: Real + fmt::Display,
+    N: RealField + fmt::Display,
     R: Rotation<Point<N, D>> + fmt::Display,
     DefaultAllocator: Allocator<N, D> + Allocator<usize, D>,
 {

src/geometry/similarity_alga.rs

@@ -1,6 +1,6 @@
 use alga::general::{
     AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Identity, TwoSidedInverse, Multiplicative, Real,
+    AbstractSemigroup, Identity, TwoSidedInverse, Multiplicative, RealField,
 };
 use alga::linear::Similarity as AlgaSimilarity;
 use alga::linear::{AffineTransformation, ProjectiveTransformation, Rotation, Transformation};
@@ -16,7 +16,7 @@ use crate::geometry::{Point, Similarity, Translation};
  * Algebraic structures.
  *
  */
-impl<N: Real, D: DimName, R> Identity<Multiplicative> for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> Identity<Multiplicative> for Similarity<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -27,7 +27,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> TwoSidedInverse<Multiplicative> for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> TwoSidedInverse<Multiplicative> for Similarity<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -43,7 +43,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> AbstractMagma<Multiplicative> for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> AbstractMagma<Multiplicative> for Similarity<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -56,7 +56,7 @@ where
 
 macro_rules! impl_multiplicative_structures(
     ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: Real, D: DimName, R> $marker<$operator> for Similarity<N, D, R>
+        impl<N: RealField, D: DimName, R> $marker<$operator> for Similarity<N, D, R>
             where R: Rotation<Point<N, D>>,
                   DefaultAllocator: Allocator<N, D> { }
     )*}
@@ -75,7 +75,7 @@ impl_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N: Real, D: DimName, R> Transformation<Point<N, D>> for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> Transformation<Point<N, D>> for Similarity<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -91,7 +91,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> ProjectiveTransformation<Point<N, D>> for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> ProjectiveTransformation<Point<N, D>> for Similarity<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -107,7 +107,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> AffineTransformation<Point<N, D>> for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> AffineTransformation<Point<N, D>> for Similarity<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -164,7 +164,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> AlgaSimilarity<Point<N, D>> for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> AlgaSimilarity<Point<N, D>> for Similarity<N, D, R>
 where
     R: Rotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,

src/geometry/similarity_construction.rs

@@ -7,7 +7,7 @@ use num::One;
 use rand::distributions::{Distribution, Standard};
 use rand::Rng;
 
-use alga::general::Real;
+use alga::general::RealField;
 use alga::linear::Rotation as AlgaRotation;
 
 use crate::base::allocator::Allocator;
@@ -19,7 +19,7 @@ use crate::geometry::{
     UnitQuaternion,
 };
 
-impl<N: Real, D: DimName, R> Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> Similarity<N, D, R>
 where
     R: AlgaRotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -45,7 +45,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> One for Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> One for Similarity<N, D, R>
 where
     R: AlgaRotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -57,7 +57,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> Distribution<Similarity<N, D, R>> for Standard
+impl<N: RealField, D: DimName, R> Distribution<Similarity<N, D, R>> for Standard
 where
     R: AlgaRotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -74,7 +74,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> Similarity<N, D, R>
+impl<N: RealField, D: DimName, R> Similarity<N, D, R>
 where
     R: AlgaRotation<Point<N, D>>,
     DefaultAllocator: Allocator<N, D>,
@@ -104,7 +104,7 @@ where
 #[cfg(feature = "arbitrary")]
 impl<N, D: DimName, R> Arbitrary for Similarity<N, D, R>
 where
-    N: Real + Arbitrary + Send,
+    N: RealField + Arbitrary + Send,
     R: AlgaRotation<Point<N, D>> + Arbitrary + Send,
     DefaultAllocator: Allocator<N, D>,
     Owned<N, D>: Send,
@@ -127,7 +127,7 @@ where
  */
 
 // 2D rotation.
-impl<N: Real> Similarity<N, U2, Rotation2<N>> {
+impl<N: RealField> Similarity<N, U2, Rotation2<N>> {
     /// Creates a new similarity from a translation, a rotation, and an uniform scaling factor.
     ///
     /// # Example
@@ -150,7 +150,7 @@ impl<N: Real> Similarity<N, U2, Rotation2<N>> {
     }
 }
 
-impl<N: Real> Similarity<N, U2, UnitComplex<N>> {
+impl<N: RealField> Similarity<N, U2, UnitComplex<N>> {
     /// Creates a new similarity from a translation and a rotation angle.
     ///
     /// # Example
@@ -176,7 +176,7 @@ impl<N: Real> Similarity<N, U2, UnitComplex<N>> {
 // 3D rotation.
 macro_rules! similarity_construction_impl(
     ($Rot: ty) => {
-        impl<N: Real> Similarity<N, U3, $Rot> {
+        impl<N: RealField> Similarity<N, U3, $Rot> {
             /// Creates a new similarity from a translation, rotation axis-angle, and scaling
             /// factor.
             ///

src/geometry/similarity_conversion.rs

@@ -1,4 +1,4 @@
-use alga::general::{Real, SubsetOf, SupersetOf};
+use alga::general::{RealField, SubsetOf, SupersetOf};
 use alga::linear::Rotation;
 
 use crate::base::allocator::Allocator;
@@ -18,8 +18,8 @@ use crate::geometry::{Isometry, Point, Similarity, SuperTCategoryOf, TAffine, Tr
 
 impl<N1, N2, D: DimName, R1, R2> SubsetOf<Similarity<N2, D, R2>> for Similarity<N1, D, R1>
 where
-    N1: Real + SubsetOf<N2>,
+    N1: RealField + SubsetOf<N2>,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     R1: Rotation<Point<N1, D>> + SubsetOf<R2>,
     R2: Rotation<Point<N2, D>>,
     DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
@@ -46,8 +46,8 @@ where
 
 impl<N1, N2, D, R, C> SubsetOf<Transform<N2, D, C>> for Similarity<N1, D, R>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     C: SuperTCategoryOf<TAffine>,
     R: Rotation<Point<N1, D>>
         + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>>
@@ -80,8 +80,8 @@ where
 
 impl<N1, N2, D, R> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Similarity<N1, D, R>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     R: Rotation<Point<N1, D>>
         + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>>
         + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
@@ -163,7 +163,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, R> From<Similarity<N, D, R>> for MatrixN<N, DimNameSum<D, U1>>
+impl<N: RealField, D: DimName, R> From<Similarity<N, D, R>> for MatrixN<N, DimNameSum<D, U1>>
 where
     D: DimNameAdd<U1>,
     R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>,

src/geometry/similarity_ops.rs

@@ -1,6 +1,6 @@
 use std::ops::{Div, DivAssign, Mul, MulAssign};
 
-use alga::general::Real;
+use alga::general::RealField;
 use alga::linear::Rotation as AlgaRotation;
 
 use crate::base::allocator::Allocator;
@@ -66,7 +66,7 @@ macro_rules! similarity_binop_impl(
     ($Op: ident, $op: ident;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N: Real, D: DimName, R> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N: RealField, D: DimName, R> $Op<$Rhs> for $Lhs
             where R: AlgaRotation<Point<N, D>>,
                   DefaultAllocator: Allocator<N, D> {
             type Output = $Output;
@@ -113,7 +113,7 @@ macro_rules! similarity_binop_assign_impl_all(
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
      [val] => $action_val: expr;
      [ref] => $action_ref: expr;) => {
-        impl<N: Real, D: DimName, R> $OpAssign<$Rhs> for $Lhs
+        impl<N: RealField, D: DimName, R> $OpAssign<$Rhs> for $Lhs
             where R: AlgaRotation<Point<N, D>>,
                   DefaultAllocator: Allocator<N, D> {
             #[inline]
@@ -122,7 +122,7 @@ macro_rules! similarity_binop_assign_impl_all(
             }
         }
 
-        impl<'b, N: Real, D: DimName, R> $OpAssign<&'b $Rhs> for $Lhs
+        impl<'b, N: RealField, D: DimName, R> $OpAssign<&'b $Rhs> for $Lhs
             where R: AlgaRotation<Point<N, D>>,
                   DefaultAllocator: Allocator<N, D> {
             #[inline]
@@ -379,7 +379,7 @@ macro_rules! similarity_from_composition_impl(
      ($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: Real $(, $Dims: $DimsBound)*> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N: RealField $(, $Dims: $DimsBound)*> $Op<$Rhs> for $Lhs
             where DefaultAllocator: Allocator<N, $R1, $C1> +
                                     Allocator<N, $R2, $C2> {
             type Output = $Output;

src/geometry/transform.rs

@@ -6,7 +6,7 @@ use std::marker::PhantomData;
 #[cfg(feature = "serde-serialize")]
 use serde::{Deserialize, Deserializer, Serialize, Serializer};
 
-use alga::general::Real;
+use alga::general::RealField;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
@@ -26,7 +26,7 @@ pub trait TCategory: Any + Debug + Copy + PartialEq + Send {
 
     /// Checks that the given matrix is a valid homogeneous representation of an element of the
     /// category `Self`.
-    fn check_homogeneous_invariants<N: Real, D: DimName>(mat: &MatrixN<N, D>) -> bool
+    fn check_homogeneous_invariants<N: RealField, D: DimName>(mat: &MatrixN<N, D>) -> bool
     where
         N::Epsilon: Copy,
         DefaultAllocator: Allocator<N, D, D>;
@@ -69,7 +69,7 @@ pub enum TAffine {}
 
 impl TCategory for TGeneral {
     #[inline]
-    fn check_homogeneous_invariants<N: Real, D: DimName>(_: &MatrixN<N, D>) -> bool
+    fn check_homogeneous_invariants<N: RealField, D: DimName>(_: &MatrixN<N, D>) -> bool
     where
         N::Epsilon: Copy,
         DefaultAllocator: Allocator<N, D, D>,
@@ -80,7 +80,7 @@ impl TCategory for TGeneral {
 
 impl TCategory for TProjective {
     #[inline]
-    fn check_homogeneous_invariants<N: Real, D: DimName>(mat: &MatrixN<N, D>) -> bool
+    fn check_homogeneous_invariants<N: RealField, D: DimName>(mat: &MatrixN<N, D>) -> bool
     where
         N::Epsilon: Copy,
         DefaultAllocator: Allocator<N, D, D>,
@@ -96,7 +96,7 @@ impl TCategory for TAffine {
     }
 
     #[inline]
-    fn check_homogeneous_invariants<N: Real, D: DimName>(mat: &MatrixN<N, D>) -> bool
+    fn check_homogeneous_invariants<N: RealField, D: DimName>(mat: &MatrixN<N, D>) -> bool
     where
         N::Epsilon: Copy,
         DefaultAllocator: Allocator<N, D, D>,
@@ -155,7 +155,7 @@ super_tcategory_impl!(
 /// 3D transformation.
 #[repr(C)]
 #[derive(Debug)]
-pub struct Transform<N: Real, D: DimNameAdd<U1>, C: TCategory>
+pub struct Transform<N: RealField, D: DimNameAdd<U1>, C: TCategory>
 where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
 {
     matrix: MatrixN<N, DimNameSum<D, U1>>,
@@ -163,7 +163,7 @@ where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
 }
 
 // FIXME
-// impl<N: Real + hash::Hash, D: DimNameAdd<U1> + hash::Hash, C: TCategory> hash::Hash for Transform<N, D, C>
+// impl<N: RealField + hash::Hash, D: DimNameAdd<U1> + hash::Hash, C: TCategory> hash::Hash for Transform<N, D, C>
 //     where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
 //           Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: hash::Hash {
 //     fn hash<H: hash::Hasher>(&self, state: &mut H) {
@@ -171,14 +171,14 @@ where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
 //     }
 // }
 
-impl<N: Real, D: DimNameAdd<U1> + Copy, C: TCategory> Copy for Transform<N, D, C>
+impl<N: RealField, D: DimNameAdd<U1> + Copy, C: TCategory> Copy for Transform<N, D, C>
 where
     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
     Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: Copy,
 {
 }
 
-impl<N: Real, D: DimNameAdd<U1>, C: TCategory> Clone for Transform<N, D, C>
+impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> Clone for Transform<N, D, C>
 where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
 {
     #[inline]
@@ -188,7 +188,7 @@ where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<N: Real, D: DimNameAdd<U1>, C: TCategory> Serialize for Transform<N, D, C>
+impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> Serialize for Transform<N, D, C>
 where
     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
     Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: Serialize,
@@ -200,7 +200,7 @@ where
 }
 
 #[cfg(feature = "serde-serialize")]
-impl<'a, N: Real, D: DimNameAdd<U1>, C: TCategory> Deserialize<'a> for Transform<N, D, C>
+impl<'a, N: RealField, D: DimNameAdd<U1>, C: TCategory> Deserialize<'a> for Transform<N, D, C>
 where
     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
     Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: Deserialize<'a>,
@@ -213,10 +213,10 @@ where
     }
 }
 
-impl<N: Real + Eq, D: DimNameAdd<U1>, C: TCategory> Eq for Transform<N, D, C> where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
+impl<N: RealField + Eq, D: DimNameAdd<U1>, C: TCategory> Eq for Transform<N, D, C> where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
 {}
 
-impl<N: Real, D: DimNameAdd<U1>, C: TCategory> PartialEq for Transform<N, D, C>
+impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> PartialEq for Transform<N, D, C>
 where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
 {
     #[inline]
@@ -225,7 +225,7 @@ where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
     }
 }
 
-impl<N: Real, D: DimNameAdd<U1>, C: TCategory> Transform<N, D, C>
+impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> Transform<N, D, C>
 where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
 {
     /// Creates a new transformation from the given homogeneous matrix. The transformation category
@@ -452,7 +452,7 @@ where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
     }
 }
 
-impl<N: Real, D: DimNameAdd<U1>> Transform<N, D, TGeneral>
+impl<N: RealField, D: DimNameAdd<U1>> Transform<N, D, TGeneral>
 where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
 {
     /// A mutable reference to underlying matrix. Use `.matrix_mut_unchecked` instead if this
@@ -463,7 +463,7 @@ where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
     }
 }
 
-impl<N: Real, D: DimNameAdd<U1>, C: TCategory> AbsDiffEq for Transform<N, D, C>
+impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> AbsDiffEq for Transform<N, D, C>
 where
     N::Epsilon: Copy,
     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
@@ -481,7 +481,7 @@ where
     }
 }
 
-impl<N: Real, D: DimNameAdd<U1>, C: TCategory> RelativeEq for Transform<N, D, C>
+impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> RelativeEq for Transform<N, D, C>
 where
     N::Epsilon: Copy,
     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
@@ -504,7 +504,7 @@ where
     }
 }
 
-impl<N: Real, D: DimNameAdd<U1>, C: TCategory> UlpsEq for Transform<N, D, C>
+impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> UlpsEq for Transform<N, D, C>
 where
     N::Epsilon: Copy,
     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,

src/geometry/transform_alga.rs

@@ -1,6 +1,6 @@
 use alga::general::{
     AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Identity, TwoSidedInverse, Multiplicative, Real,
+    AbstractSemigroup, Identity, TwoSidedInverse, Multiplicative, RealField,
 };
 use alga::linear::{ProjectiveTransformation, Transformation};
 
@@ -15,7 +15,7 @@ use crate::geometry::{Point, SubTCategoryOf, TCategory, TProjective, Transform};
  * Algebraic structures.
  *
  */
-impl<N: Real, D: DimNameAdd<U1>, C> Identity<Multiplicative> for Transform<N, D, C>
+impl<N: RealField, D: DimNameAdd<U1>, C> Identity<Multiplicative> for Transform<N, D, C>
 where
     C: TCategory,
     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
@@ -26,7 +26,7 @@ where
     }
 }
 
-impl<N: Real, D: DimNameAdd<U1>, C> TwoSidedInverse<Multiplicative> for Transform<N, D, C>
+impl<N: RealField, D: DimNameAdd<U1>, C> TwoSidedInverse<Multiplicative> for Transform<N, D, C>
 where
     C: SubTCategoryOf<TProjective>,
     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
@@ -42,7 +42,7 @@ where
     }
 }
 
-impl<N: Real, D: DimNameAdd<U1>, C> AbstractMagma<Multiplicative> for Transform<N, D, C>
+impl<N: RealField, D: DimNameAdd<U1>, C> AbstractMagma<Multiplicative> for Transform<N, D, C>
 where
     C: TCategory,
     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
@@ -55,7 +55,7 @@ where
 
 macro_rules! impl_multiplicative_structures(
     ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: Real, D: DimNameAdd<U1>, C> $marker<$operator> for Transform<N, D, C>
+        impl<N: RealField, D: DimNameAdd<U1>, C> $marker<$operator> for Transform<N, D, C>
             where C: TCategory,
                   DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> { }
     )*}
@@ -63,7 +63,7 @@ macro_rules! impl_multiplicative_structures(
 
 macro_rules! impl_inversible_multiplicative_structures(
     ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: Real, D: DimNameAdd<U1>, C> $marker<$operator> for Transform<N, D, C>
+        impl<N: RealField, D: DimNameAdd<U1>, C> $marker<$operator> for Transform<N, D, C>
             where C: SubTCategoryOf<TProjective>,
                   DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> { }
     )*}
@@ -87,7 +87,7 @@ impl_inversible_multiplicative_structures!(
  */
 impl<N, D: DimNameAdd<U1>, C> Transformation<Point<N, D>> for Transform<N, D, C>
 where
-    N: Real,
+    N: RealField,
     C: TCategory,
     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
         + Allocator<N, DimNameSum<D, U1>>
@@ -107,7 +107,7 @@ where
 
 impl<N, D: DimNameAdd<U1>, C> ProjectiveTransformation<Point<N, D>> for Transform<N, D, C>
 where
-    N: Real,
+    N: RealField,
     C: SubTCategoryOf<TProjective>,
     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
         + Allocator<N, DimNameSum<D, U1>>
@@ -128,7 +128,7 @@ where
 // FIXME: we need to implement an SVD for this.
 //
 // impl<N, D: DimNameAdd<U1>, C> AffineTransformation<Point<N, D>> for Transform<N, D, C>
-//     where N:  Real,
+//     where N:  RealField,
 //           C: SubTCategoryOf<TAffine>,
 //           DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> +
 //                             Allocator<N, D, D> +

src/geometry/transform_construction.rs

@@ -1,6 +1,6 @@
 use num::One;
 
-use alga::general::Real;
+use alga::general::RealField;
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
@@ -8,7 +8,7 @@ use crate::base::{DefaultAllocator, MatrixN};
 
 use crate::geometry::{TCategory, Transform};
 
-impl<N: Real, D: DimNameAdd<U1>, C: TCategory> Transform<N, D, C>
+impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> Transform<N, D, C>
 where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
 {
     /// Creates a new identity transform.
@@ -45,7 +45,7 @@ where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
     }
 }
 
-impl<N: Real, D: DimNameAdd<U1>, C: TCategory> One for Transform<N, D, C>
+impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> One for Transform<N, D, C>
 where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
 {
     /// Creates a new identity transform.

src/geometry/transform_conversion.rs

@@ -1,4 +1,4 @@
-use alga::general::{Real, SubsetOf};
+use alga::general::{RealField, SubsetOf};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
@@ -8,8 +8,8 @@ use crate::geometry::{SuperTCategoryOf, TCategory, Transform};
 
 impl<N1, N2, D: DimName, C1, C2> SubsetOf<Transform<N2, D, C2>> for Transform<N1, D, C1>
 where
-    N1: Real + SubsetOf<N2>,
+    N1: RealField + SubsetOf<N2>,
-    N2: Real,
+    N2: RealField,
     C1: TCategory,
     C2: SuperTCategoryOf<C1>,
     D: DimNameAdd<U1>,
@@ -36,8 +36,8 @@ where
 
 impl<N1, N2, D: DimName, C> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Transform<N1, D, C>
 where
-    N1: Real + SubsetOf<N2>,
+    N1: RealField + SubsetOf<N2>,
-    N2: Real,
+    N2: RealField,
     C: TCategory,
     D: DimNameAdd<U1>,
     DefaultAllocator: Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>
@@ -61,7 +61,7 @@ where
     }
 }
 
-impl<N: Real, D: DimName, C> From<Transform<N, D, C>> for MatrixN<N, DimNameSum<D, U1>>
+impl<N: RealField, D: DimName, C> From<Transform<N, D, C>> for MatrixN<N, DimNameSum<D, U1>>
 where
     D: DimNameAdd<U1>,
     C: TCategory,

src/geometry/transform_ops.rs

@@ -1,7 +1,7 @@
 use num::{One, Zero};
 use std::ops::{Div, DivAssign, Index, IndexMut, Mul, MulAssign};
 
-use alga::general::{ClosedAdd, ClosedMul, Real, SubsetOf};
+use alga::general::{ClosedAdd, ClosedMul, RealField, SubsetOf};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1, U3, U4};
@@ -79,7 +79,7 @@ use crate::geometry::{
  * Indexing.
  *
  */
-impl<N: Real, D, C: TCategory> Index<(usize, usize)> for Transform<N, D, C>
+impl<N: RealField, D, C: TCategory> Index<(usize, usize)> for Transform<N, D, C>
 where
     D: DimName + DimNameAdd<U1>,
     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
@@ -93,7 +93,7 @@ where
 }
 
 // Only general transformations are mutably indexable.
-impl<N: Real, D> IndexMut<(usize, usize)> for Transform<N, D, TGeneral>
+impl<N: RealField, D> IndexMut<(usize, usize)> for Transform<N, D, TGeneral>
 where
     D: DimName + DimNameAdd<U1>,
     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
@@ -106,7 +106,7 @@ where
 
 // Transform × Vector
 md_impl_all!(
-    Mul, mul where N: Real;
+    Mul, mul where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory;
     self: Transform<N, D, C>, rhs: VectorN<N, D>, Output = VectorN<N, D>;
     [val val] => &self * &rhs;
@@ -130,7 +130,7 @@ md_impl_all!(
 
 // Transform × Point
 md_impl_all!(
-    Mul, mul where N: Real;
+    Mul, mul where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory
     where DefaultAllocator: Allocator<N, D, D>;
     self: Transform<N, D, C>, rhs: Point<N, D>, Output = Point<N, D>;
@@ -156,7 +156,7 @@ md_impl_all!(
 
 // Transform × Transform
 md_impl_all!(
-    Mul, mul where N: Real;
+    Mul, mul where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, CA: TCategoryMul<CB>, CB: TCategory;
     self: Transform<N, D, CA>, rhs: Transform<N, D, CB>, Output = Transform<N, D, CA::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.into_inner());
@@ -167,7 +167,7 @@ md_impl_all!(
 
 // Transform × Rotation
 md_impl_all!(
-    Mul, mul where N: Real;
+    Mul, mul where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Transform<N, D, C>, rhs: Rotation<N, D>, Output = Transform<N, D, C::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
@@ -178,7 +178,7 @@ md_impl_all!(
 
 // Rotation × Transform
 md_impl_all!(
-    Mul, mul where N: Real;
+    Mul, mul where N: RealField;
     (D, D), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Rotation<N, D>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
@@ -189,7 +189,7 @@ md_impl_all!(
 
 // Transform × UnitQuaternion
 md_impl_all!(
-    Mul, mul where N: Real;
+    Mul, mul where N: RealField;
     (U4, U4), (U4, U1) for C: TCategoryMul<TAffine>;
     self: Transform<N, U3, C>, rhs: UnitQuaternion<N>, Output = Transform<N, U3, C::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
@@ -200,7 +200,7 @@ md_impl_all!(
 
 // UnitQuaternion × Transform
 md_impl_all!(
-    Mul, mul where N: Real;
+    Mul, mul where N: RealField;
     (U4, U1), (U4, U4) for C: TCategoryMul<TAffine>;
     self: UnitQuaternion<N>, rhs: Transform<N, U3, C>, Output = Transform<N, U3, C::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.to_homogeneous() * rhs.into_inner());
@@ -211,7 +211,7 @@ md_impl_all!(
 
 // Transform × Isometry
 md_impl_all!(
-    Mul, mul where N: Real;
+    Mul, mul where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
     for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
     self: Transform<N, D, C>, rhs: Isometry<N, D, R>, Output = Transform<N, D, C::Representative>;
@@ -223,7 +223,7 @@ md_impl_all!(
 
 // Isometry × Transform
 md_impl_all!(
-    Mul, mul where N: Real;
+    Mul, mul where N: RealField;
     (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
     for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
     self: Isometry<N, D, R>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
@@ -235,7 +235,7 @@ md_impl_all!(
 
 // Transform × Similarity
 md_impl_all!(
-    Mul, mul where N: Real;
+    Mul, mul where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
     for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
     self: Transform<N, D, C>, rhs: Similarity<N, D, R>, Output = Transform<N, D, C::Representative>;
@@ -247,7 +247,7 @@ md_impl_all!(
 
 // Similarity × Transform
 md_impl_all!(
-    Mul, mul where N: Real;
+    Mul, mul where N: RealField;
     (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
     for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
     self: Similarity<N, D, R>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
@@ -267,7 +267,7 @@ md_impl_all!(
  */
 // Transform × Translation
 md_impl_all!(
-    Mul, mul where N: Real;
+    Mul, mul where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Transform<N, D, C>, rhs: Translation<N, D>, Output = Transform<N, D, C::Representative>;
     [val val] => Self::Output::from_matrix_unchecked(self.into_inner() * rhs.to_homogeneous());
@@ -278,7 +278,7 @@ md_impl_all!(
 
 // Translation × Transform
 md_impl_all!(
-    Mul, mul where N: Real;
+    Mul, mul where N: RealField;
     (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
     for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Translation<N, D>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
@@ -290,7 +290,7 @@ md_impl_all!(
 
 // Transform ÷ Transform
 md_impl_all!(
-    Div, div where N: Real;
+    Div, div where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, CA: TCategoryMul<CB>, CB: SubTCategoryOf<TProjective>;
     self: Transform<N, D, CA>, rhs: Transform<N, D, CB>, Output = Transform<N, D, CA::Representative>;
     [val val] => self * rhs.inverse();
@@ -301,7 +301,7 @@ md_impl_all!(
 
 // Transform ÷ Rotation
 md_impl_all!(
-    Div, div where N: Real;
+    Div, div where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Transform<N, D, C>, rhs: Rotation<N, D>, Output = Transform<N, D, C::Representative>;
     [val val] => self * rhs.inverse();
@@ -312,7 +312,7 @@ md_impl_all!(
 
 // Rotation ÷ Transform
 md_impl_all!(
-    Div, div where N: Real;
+    Div, div where N: RealField;
     (D, D), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Rotation<N, D>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
     [val val] => self.inverse() * rhs;
@@ -323,7 +323,7 @@ md_impl_all!(
 
 // Transform ÷ UnitQuaternion
 md_impl_all!(
-    Div, div where N: Real;
+    Div, div where N: RealField;
     (U4, U4), (U4, U1) for C: TCategoryMul<TAffine>;
     self: Transform<N, U3, C>, rhs: UnitQuaternion<N>, Output = Transform<N, U3, C::Representative>;
     [val val] => self * rhs.inverse();
@@ -334,7 +334,7 @@ md_impl_all!(
 
 // UnitQuaternion ÷ Transform
 md_impl_all!(
-    Div, div where N: Real;
+    Div, div where N: RealField;
     (U4, U1), (U4, U4) for C: TCategoryMul<TAffine>;
     self: UnitQuaternion<N>, rhs: Transform<N, U3, C>, Output = Transform<N, U3, C::Representative>;
     [val val] => self.inverse() * rhs;
@@ -345,7 +345,7 @@ md_impl_all!(
 
 //      // Transform ÷ Isometry
 //      md_impl_all!(
-//          Div, div where N: Real;
+//          Div, div where N: RealField;
 //          (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
 //          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
 //          where SB::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
@@ -358,7 +358,7 @@ md_impl_all!(
 
 //      // Isometry ÷ Transform
 //      md_impl_all!(
-//          Div, div where N: Real;
+//          Div, div where N: RealField;
 //          (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
 //          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
 //          where SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1> >;
@@ -371,7 +371,7 @@ md_impl_all!(
 
 //      // Transform ÷ Similarity
 //      md_impl_all!(
-//          Div, div where N: Real;
+//          Div, div where N: RealField;
 //          (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
 //          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
 //          where SB::Alloc: Allocator<N, D, D >
@@ -385,7 +385,7 @@ md_impl_all!(
 
 //      // Similarity ÷ Transform
 //      md_impl_all!(
-//          Div, div where N: Real;
+//          Div, div where N: RealField;
 //          (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
 //          for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >
 //          where SA::Alloc: Allocator<N, D, D >
@@ -399,7 +399,7 @@ md_impl_all!(
 
 // Transform ÷ Translation
 md_impl_all!(
-    Div, div where N: Real;
+    Div, div where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Transform<N, D, C>, rhs: Translation<N, D>, Output = Transform<N, D, C::Representative>;
     [val val] => self * rhs.inverse();
@@ -410,7 +410,7 @@ md_impl_all!(
 
 // Translation ÷ Transform
 md_impl_all!(
-    Div, div where N: Real;
+    Div, div where N: RealField;
     (D, U1), (DimNameSum<D, U1>, DimNameSum<D, U1>)
     for D: DimNameAdd<U1>, C: TCategoryMul<TAffine>;
     self: Translation<N, D>, rhs: Transform<N, D, C>, Output = Transform<N, D, C::Representative>;
@@ -422,7 +422,7 @@ md_impl_all!(
 
 // Transform ×= Transform
 md_assign_impl_all!(
-    MulAssign, mul_assign where N: Real;
+    MulAssign, mul_assign where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (DimNameSum<D, U1>, DimNameSum<D, U1>) for D: DimNameAdd<U1>, CA: TCategory, CB: SubTCategoryOf<CA>;
     self: Transform<N, D, CA>, rhs: Transform<N, D, CB>;
     [val] => *self.matrix_mut_unchecked() *= rhs.into_inner();
@@ -431,7 +431,7 @@ md_assign_impl_all!(
 
 // Transform ×= Similarity
 md_assign_impl_all!(
-    MulAssign, mul_assign where N: Real;
+    MulAssign, mul_assign where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
     for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
     self: Transform<N, D, C>, rhs: Similarity<N, D, R>;
@@ -441,7 +441,7 @@ md_assign_impl_all!(
 
 // Transform ×= Isometry
 md_assign_impl_all!(
-    MulAssign, mul_assign where N: Real;
+    MulAssign, mul_assign where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1)
     for D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>> >;
     self: Transform<N, D, C>, rhs: Isometry<N, D, R>;
@@ -459,7 +459,7 @@ md_assign_impl_all!(
  */
 // Transform ×= Translation
 md_assign_impl_all!(
-    MulAssign, mul_assign where N: Real;
+    MulAssign, mul_assign where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory;
     self: Transform<N, D, C>, rhs: Translation<N, D>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
@@ -468,7 +468,7 @@ md_assign_impl_all!(
 
 // Transform ×= Rotation
 md_assign_impl_all!(
-    MulAssign, mul_assign where N: Real;
+    MulAssign, mul_assign where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategory;
     self: Transform<N, D, C>, rhs: Rotation<N, D>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
@@ -477,7 +477,7 @@ md_assign_impl_all!(
 
 // Transform ×= UnitQuaternion
 md_assign_impl_all!(
-    MulAssign, mul_assign where N: Real;
+    MulAssign, mul_assign where N: RealField;
     (U4, U4), (U4, U1) for C: TCategory;
     self: Transform<N, U3, C>, rhs: UnitQuaternion<N>;
     [val] => *self.matrix_mut_unchecked() *= rhs.to_homogeneous();
@@ -486,7 +486,7 @@ md_assign_impl_all!(
 
 // Transform ÷= Transform
 md_assign_impl_all!(
-    DivAssign, div_assign where N: Real;
+    DivAssign, div_assign where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (DimNameSum<D, U1>, DimNameSum<D, U1>)
     for D: DimNameAdd<U1>, CA: SuperTCategoryOf<CB>, CB: SubTCategoryOf<TProjective>;
     self: Transform<N, D, CA>, rhs: Transform<N, D, CB>;
@@ -517,7 +517,7 @@ md_assign_impl_all!(
 
 // Transform ÷= Translation
 md_assign_impl_all!(
-    DivAssign, div_assign where N: Real;
+    DivAssign, div_assign where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, U1) for D: DimNameAdd<U1>, C: TCategory;
     self: Transform<N, D, C>, rhs: Translation<N, D>;
     [val] => *self *= rhs.inverse();
@@ -526,7 +526,7 @@ md_assign_impl_all!(
 
 // Transform ÷= Rotation
 md_assign_impl_all!(
-    DivAssign, div_assign where N: Real;
+    DivAssign, div_assign where N: RealField;
     (DimNameSum<D, U1>, DimNameSum<D, U1>), (D, D) for D: DimNameAdd<U1>, C: TCategory;
     self: Transform<N, D, C>, rhs: Rotation<N, D>;
     [val] => *self *= rhs.inverse();
@@ -535,7 +535,7 @@ md_assign_impl_all!(
 
 // Transform ÷= UnitQuaternion
 md_assign_impl_all!(
-    DivAssign, div_assign where N: Real;
+    DivAssign, div_assign where N: RealField;
     (U4, U4), (U4, U1) for C: TCategory;
     self: Transform<N, U3, C>, rhs: UnitQuaternion<N>;
     [val] => *self *= rhs.inverse();

src/geometry/translation.rs

@@ -11,7 +11,7 @@ use serde::{Deserialize, Deserializer, Serialize, Serializer};
 #[cfg(feature = "abomonation-serialize")]
 use abomonation::Abomonation;
 
-use alga::general::{ClosedNeg, Real};
+use alga::general::{ClosedNeg, RealField};
 
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{DimName, DimNameAdd, DimNameSum, U1};
@@ -263,7 +263,7 @@ where
  * Display
  *
  */
-impl<N: Real + fmt::Display, D: DimName> fmt::Display for Translation<N, D>
+impl<N: RealField + fmt::Display, D: DimName> fmt::Display for Translation<N, D>
 where DefaultAllocator: Allocator<N, D> + Allocator<usize, D>
 {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {

src/geometry/translation_alga.rs

@@ -1,6 +1,6 @@
 use alga::general::{
     AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, Real,
+    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, RealField,
 };
 use alga::linear::Translation as AlgaTranslation;
 use alga::linear::{
@@ -19,7 +19,7 @@ use crate::geometry::{Point, Translation};
  * Algebraic structures.
  *
  */
-impl<N: Real, D: DimName> Identity<Multiplicative> for Translation<N, D>
+impl<N: RealField, D: DimName> Identity<Multiplicative> for Translation<N, D>
 where DefaultAllocator: Allocator<N, D>
 {
     #[inline]
@@ -28,7 +28,7 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: Real, D: DimName> TwoSidedInverse<Multiplicative> for Translation<N, D>
+impl<N: RealField, D: DimName> TwoSidedInverse<Multiplicative> for Translation<N, D>
 where DefaultAllocator: Allocator<N, D>
 {
     #[inline]
@@ -42,7 +42,7 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: Real, D: DimName> AbstractMagma<Multiplicative> for Translation<N, D>
+impl<N: RealField, D: DimName> AbstractMagma<Multiplicative> for Translation<N, D>
 where DefaultAllocator: Allocator<N, D>
 {
     #[inline]
@@ -53,7 +53,7 @@ where DefaultAllocator: Allocator<N, D>
 
 macro_rules! impl_multiplicative_structures(
     ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: Real, D: DimName> $marker<$operator> for Translation<N, D>
+        impl<N: RealField, D: DimName> $marker<$operator> for Translation<N, D>
             where DefaultAllocator: Allocator<N, D> { }
     )*}
 );
@@ -71,7 +71,7 @@ impl_multiplicative_structures!(
  * Transformation groups.
  *
  */
-impl<N: Real, D: DimName> Transformation<Point<N, D>> for Translation<N, D>
+impl<N: RealField, D: DimName> Transformation<Point<N, D>> for Translation<N, D>
 where DefaultAllocator: Allocator<N, D>
 {
     #[inline]
@@ -85,7 +85,7 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: Real, D: DimName> ProjectiveTransformation<Point<N, D>> for Translation<N, D>
+impl<N: RealField, D: DimName> ProjectiveTransformation<Point<N, D>> for Translation<N, D>
 where DefaultAllocator: Allocator<N, D>
 {
     #[inline]
@@ -99,7 +99,7 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: Real, D: DimName> AffineTransformation<Point<N, D>> for Translation<N, D>
+impl<N: RealField, D: DimName> AffineTransformation<Point<N, D>> for Translation<N, D>
 where DefaultAllocator: Allocator<N, D>
 {
     type Rotation = Id;
@@ -142,7 +142,7 @@ where DefaultAllocator: Allocator<N, D>
     }
 }
 
-impl<N: Real, D: DimName> Similarity<Point<N, D>> for Translation<N, D>
+impl<N: RealField, D: DimName> Similarity<Point<N, D>> for Translation<N, D>
 where DefaultAllocator: Allocator<N, D>
 {
     type Scaling = Id;
@@ -165,7 +165,7 @@ where DefaultAllocator: Allocator<N, D>
 
 macro_rules! marker_impl(
     ($($Trait: ident),*) => {$(
-        impl<N: Real, D: DimName> $Trait<Point<N, D>> for Translation<N, D>
+        impl<N: RealField, D: DimName> $Trait<Point<N, D>> for Translation<N, D>
             where DefaultAllocator: Allocator<N, D> { }
     )*}
 );
@@ -173,7 +173,7 @@ macro_rules! marker_impl(
 marker_impl!(Isometry, DirectIsometry);
 
 /// Subgroups of the n-dimensional translation group `T(n)`.
-impl<N: Real, D: DimName> AlgaTranslation<Point<N, D>> for Translation<N, D>
+impl<N: RealField, D: DimName> AlgaTranslation<Point<N, D>> for Translation<N, D>
 where DefaultAllocator: Allocator<N, D>
 {
     #[inline]

src/geometry/translation_conversion.rs

@@ -1,6 +1,6 @@
 use num::{One, Zero};
 
-use alga::general::{Real, SubsetOf, SupersetOf};
+use alga::general::{RealField, SubsetOf, SupersetOf};
 use alga::linear::Rotation;
 
 use crate::base::allocator::Allocator;
@@ -46,8 +46,8 @@ where
 
 impl<N1, N2, D: DimName, R> SubsetOf<Isometry<N2, D, R>> for Translation<N1, D>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     R: Rotation<Point<N2, D>>,
     DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
@@ -69,8 +69,8 @@ where
 
 impl<N1, N2, D: DimName, R> SubsetOf<Similarity<N2, D, R>> for Translation<N1, D>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     R: Rotation<Point<N2, D>>,
     DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
 {
@@ -92,8 +92,8 @@ where
 
 impl<N1, N2, D, C> SubsetOf<Transform<N2, D, C>> for Translation<N1, D>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     C: SuperTCategoryOf<TAffine>,
     D: DimNameAdd<U1>,
     DefaultAllocator: Allocator<N1, D>
@@ -119,8 +119,8 @@ where
 
 impl<N1, N2, D> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Translation<N1, D>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     D: DimNameAdd<U1>,
     DefaultAllocator: Allocator<N1, D>
         + Allocator<N2, D>

src/geometry/unit_complex.rs

@@ -2,14 +2,14 @@ use approx::{AbsDiffEq, RelativeEq, UlpsEq};
 use num_complex::Complex;
 use std::fmt;
 
-use alga::general::Real;
+use alga::general::RealField;
 use crate::base::{Matrix2, Matrix3, Unit, Vector1};
 use crate::geometry::Rotation2;
 
 /// A complex number with a norm equal to 1.
 pub type UnitComplex<N> = Unit<Complex<N>>;
 
-impl<N: Real> UnitComplex<N> {
+impl<N: RealField> UnitComplex<N> {
     /// The rotation angle in `]-pi; pi]` of this unit complex number.
     ///
     /// # Example
@@ -253,13 +253,13 @@ impl<N: Real> UnitComplex<N> {
     }
 }
 
-impl<N: Real + fmt::Display> fmt::Display for UnitComplex<N> {
+impl<N: RealField + fmt::Display> fmt::Display for UnitComplex<N> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         write!(f, "UnitComplex angle: {}", self.angle())
     }
 }
 
-impl<N: Real> AbsDiffEq for UnitComplex<N> {
+impl<N: RealField> AbsDiffEq for UnitComplex<N> {
     type Epsilon = N;
 
     #[inline]
@@ -273,7 +273,7 @@ impl<N: Real> AbsDiffEq for UnitComplex<N> {
     }
 }
 
-impl<N: Real> RelativeEq for UnitComplex<N> {
+impl<N: RealField> RelativeEq for UnitComplex<N> {
     #[inline]
     fn default_max_relative() -> Self::Epsilon {
         N::default_max_relative()
@@ -292,7 +292,7 @@ impl<N: Real> RelativeEq for UnitComplex<N> {
     }
 }
 
-impl<N: Real> UlpsEq for UnitComplex<N> {
+impl<N: RealField> UlpsEq for UnitComplex<N> {
     #[inline]
     fn default_max_ulps() -> u32 {
         N::default_max_ulps()

src/geometry/unit_complex_alga.rs

@@ -1,6 +1,6 @@
 use alga::general::{
     AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
-    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, Real,
+    AbstractSemigroup, Id, Identity, TwoSidedInverse, Multiplicative, RealField,
 };
 use alga::linear::{
     AffineTransformation, DirectIsometry, Isometry, OrthogonalTransformation,
@@ -17,21 +17,21 @@ use crate::geometry::{Point2, UnitComplex};
  * Implementations for UnitComplex.
  *
  */
-impl<N: Real> Identity<Multiplicative> for UnitComplex<N> {
+impl<N: RealField> Identity<Multiplicative> for UnitComplex<N> {
     #[inline]
     fn identity() -> Self {
         Self::identity()
     }
 }
 
-impl<N: Real> AbstractMagma<Multiplicative> for UnitComplex<N> {
+impl<N: RealField> AbstractMagma<Multiplicative> for UnitComplex<N> {
     #[inline]
     fn operate(&self, rhs: &Self) -> Self {
         self * rhs
     }
 }
 
-impl<N: Real> TwoSidedInverse<Multiplicative> for UnitComplex<N> {
+impl<N: RealField> TwoSidedInverse<Multiplicative> for UnitComplex<N> {
     #[inline]
     fn two_sided_inverse(&self) -> Self {
         self.inverse()
@@ -45,7 +45,7 @@ impl<N: Real> TwoSidedInverse<Multiplicative> for UnitComplex<N> {
 
 macro_rules! impl_structures(
     ($($marker: ident<$operator: ident>),* $(,)*) => {$(
-        impl<N: Real> $marker<$operator> for UnitComplex<N> {
+        impl<N: RealField> $marker<$operator> for UnitComplex<N> {
         }
     )*}
 );
@@ -58,7 +58,7 @@ impl_structures!(
     AbstractGroup<Multiplicative>
 );
 
-impl<N: Real> Transformation<Point2<N>> for UnitComplex<N>
+impl<N: RealField> Transformation<Point2<N>> for UnitComplex<N>
 where DefaultAllocator: Allocator<N, U2>
 {
     #[inline]
@@ -72,7 +72,7 @@ where DefaultAllocator: Allocator<N, U2>
     }
 }
 
-impl<N: Real> ProjectiveTransformation<Point2<N>> for UnitComplex<N>
+impl<N: RealField> ProjectiveTransformation<Point2<N>> for UnitComplex<N>
 where DefaultAllocator: Allocator<N, U2>
 {
     #[inline]
@@ -88,7 +88,7 @@ where DefaultAllocator: Allocator<N, U2>
     }
 }
 
-impl<N: Real> AffineTransformation<Point2<N>> for UnitComplex<N>
+impl<N: RealField> AffineTransformation<Point2<N>> for UnitComplex<N>
 where DefaultAllocator: Allocator<N, U2>
 {
     type Rotation = Self;
@@ -131,7 +131,7 @@ where DefaultAllocator: Allocator<N, U2>
     }
 }
 
-impl<N: Real> Similarity<Point2<N>> for UnitComplex<N>
+impl<N: RealField> Similarity<Point2<N>> for UnitComplex<N>
 where DefaultAllocator: Allocator<N, U2>
 {
     type Scaling = Id;
@@ -154,14 +154,14 @@ where DefaultAllocator: Allocator<N, U2>
 
 macro_rules! marker_impl(
     ($($Trait: ident),*) => {$(
-        impl<N: Real> $Trait<Point2<N>> for UnitComplex<N>
+        impl<N: RealField> $Trait<Point2<N>> for UnitComplex<N>
         where DefaultAllocator: Allocator<N, U2> { }
     )*}
 );
 
 marker_impl!(Isometry, DirectIsometry, OrthogonalTransformation);
 
-impl<N: Real> Rotation<Point2<N>> for UnitComplex<N>
+impl<N: RealField> Rotation<Point2<N>> for UnitComplex<N>
 where DefaultAllocator: Allocator<N, U2>
 {
     #[inline]

src/geometry/unit_complex_construction.rs

@@ -6,13 +6,13 @@ use num_complex::Complex;
 use rand::distributions::{Distribution, OpenClosed01, Standard};
 use rand::Rng;
 
-use alga::general::Real;
+use alga::general::RealField;
 use crate::base::dimension::{U1, U2};
 use crate::base::storage::Storage;
 use crate::base::{Unit, Vector, Matrix2};
 use crate::geometry::{Rotation2, UnitComplex};
 
-impl<N: Real> UnitComplex<N> {
+impl<N: RealField> UnitComplex<N> {
     /// The unit complex number multiplicative identity.
     ///
     /// # Example
@@ -268,14 +268,14 @@ impl<N: Real> UnitComplex<N> {
     }
 }
 
-impl<N: Real> One for UnitComplex<N> {
+impl<N: RealField> One for UnitComplex<N> {
     #[inline]
     fn one() -> Self {
         Self::identity()
     }
 }
 
-impl<N: Real> Distribution<UnitComplex<N>> for Standard
+impl<N: RealField> Distribution<UnitComplex<N>> for Standard
 where OpenClosed01: Distribution<N>
 {
     /// Generate a uniformly distributed random `UnitComplex`.
@@ -286,7 +286,7 @@ where OpenClosed01: Distribution<N>
 }
 
 #[cfg(feature = "arbitrary")]
-impl<N: Real + Arbitrary> Arbitrary for UnitComplex<N> {
+impl<N: RealField + Arbitrary> Arbitrary for UnitComplex<N> {
     #[inline]
     fn arbitrary<G: Gen>(g: &mut G) -> Self {
         UnitComplex::from_angle(N::arbitrary(g))

src/geometry/unit_complex_conversion.rs

@@ -1,7 +1,7 @@
 use num::Zero;
 use num_complex::Complex;
 
-use alga::general::{Real, SubsetOf, SupersetOf};
+use alga::general::{RealField, SubsetOf, SupersetOf};
 use alga::linear::Rotation as AlgaRotation;
 
 use crate::base::dimension::U2;
@@ -28,8 +28,8 @@ use crate::geometry::{
 
 impl<N1, N2> SubsetOf<UnitComplex<N2>> for UnitComplex<N1>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
 {
     #[inline]
     fn to_superset(&self) -> UnitComplex<N2> {
@@ -49,8 +49,8 @@ where
 
 impl<N1, N2> SubsetOf<Rotation2<N2>> for UnitComplex<N1>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
 {
     #[inline]
     fn to_superset(&self) -> Rotation2<N2> {
@@ -72,8 +72,8 @@ where
 
 impl<N1, N2, R> SubsetOf<Isometry<N2, U2, R>> for UnitComplex<N1>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     R: AlgaRotation<Point2<N2>> + SupersetOf<Self>,
 {
     #[inline]
@@ -94,8 +94,8 @@ where
 
 impl<N1, N2, R> SubsetOf<Similarity<N2, U2, R>> for UnitComplex<N1>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     R: AlgaRotation<Point2<N2>> + SupersetOf<Self>,
 {
     #[inline]
@@ -116,8 +116,8 @@ where
 
 impl<N1, N2, C> SubsetOf<Transform<N2, U2, C>> for UnitComplex<N1>
 where
-    N1: Real,
+    N1: RealField,
-    N2: Real + SupersetOf<N1>,
+    N2: RealField + SupersetOf<N1>,
     C: SuperTCategoryOf<TAffine>,
 {
     #[inline]
@@ -136,7 +136,7 @@ where
     }
 }
 
-impl<N1: Real, N2: Real + SupersetOf<N1>> SubsetOf<Matrix3<N2>> for UnitComplex<N1> {
+impl<N1: RealField, N2: RealField + SupersetOf<N1>> SubsetOf<Matrix3<N2>> for UnitComplex<N1> {
     #[inline]
     fn to_superset(&self) -> Matrix3<N2> {
         self.to_homogeneous().to_superset()
@@ -155,28 +155,28 @@ impl<N1: Real, N2: Real + SupersetOf<N1>> SubsetOf<Matrix3<N2>> for UnitComplex<
 }
 
 
-impl<N: Real> From<UnitComplex<N>> for Rotation2<N> {
+impl<N: RealField> From<UnitComplex<N>> for Rotation2<N> {
     #[inline]
     fn from(q: UnitComplex<N>) -> Self {
         q.to_rotation_matrix()
     }
 }
 
-impl<N: Real> From<Rotation2<N>> for UnitComplex<N> {
+impl<N: RealField> From<Rotation2<N>> for UnitComplex<N> {
     #[inline]
     fn from(q: Rotation2<N>) -> Self {
         Self::from_rotation_matrix(&q)
     }
 }
 
-impl<N: Real> From<UnitComplex<N>> for Matrix3<N> {
+impl<N: RealField> From<UnitComplex<N>> for Matrix3<N> {
     #[inline]
     fn from(q: UnitComplex<N>) -> Matrix3<N> {
         q.to_homogeneous()
     }
 }
 
-impl<N: Real> From<UnitComplex<N>> for Matrix2<N> {
+impl<N: RealField> From<UnitComplex<N>> for Matrix2<N> {
     #[inline]
     fn from(q: UnitComplex<N>) -> Self {
         q.to_rotation_matrix().into_inner()

src/geometry/unit_complex_ops.rs

@@ -1,6 +1,6 @@
 use std::ops::{Div, DivAssign, Mul, MulAssign};
 
-use alga::general::Real;
+use alga::general::RealField;
 use crate::base::allocator::Allocator;
 use crate::base::dimension::{U1, U2};
 use crate::base::storage::Storage;
@@ -44,7 +44,7 @@ use crate::geometry::{Isometry, Point2, Rotation, Similarity, Translation, UnitC
  */
 
 // UnitComplex × UnitComplex
-impl<N: Real> Mul<Self> for UnitComplex<N> {
+impl<N: RealField> Mul<Self> for UnitComplex<N> {
     type Output = Self;
 
     #[inline]
@@ -53,7 +53,7 @@ impl<N: Real> Mul<Self> for UnitComplex<N> {
     }
 }
 
-impl<'a, N: Real> Mul<UnitComplex<N>> for &'a UnitComplex<N> {
+impl<'a, N: RealField> Mul<UnitComplex<N>> for &'a UnitComplex<N> {
     type Output = UnitComplex<N>;
 
     #[inline]
@@ -62,7 +62,7 @@ impl<'a, N: Real> Mul<UnitComplex<N>> for &'a UnitComplex<N> {
     }
 }
 
-impl<'b, N: Real> Mul<&'b UnitComplex<N>> for UnitComplex<N> {
+impl<'b, N: RealField> Mul<&'b UnitComplex<N>> for UnitComplex<N> {
     type Output = Self;
 
     #[inline]
@@ -71,7 +71,7 @@ impl<'b, N: Real> Mul<&'b UnitComplex<N>> for UnitComplex<N> {
     }
 }
 
-impl<'a, 'b, N: Real> Mul<&'b UnitComplex<N>> for &'a UnitComplex<N> {
+impl<'a, 'b, N: RealField> Mul<&'b UnitComplex<N>> for &'a UnitComplex<N> {
     type Output = UnitComplex<N>;
 
     #[inline]
@@ -81,7 +81,7 @@ impl<'a, 'b, N: Real> Mul<&'b UnitComplex<N>> for &'a UnitComplex<N> {
 }
 
 // UnitComplex ÷ UnitComplex
-impl<N: Real> Div<Self> for UnitComplex<N> {
+impl<N: RealField> Div<Self> for UnitComplex<N> {
     type Output = Self;
 
     #[inline]
@@ -90,7 +90,7 @@ impl<N: Real> Div<Self> for UnitComplex<N> {
     }
 }
 
-impl<'a, N: Real> Div<UnitComplex<N>> for &'a UnitComplex<N> {
+impl<'a, N: RealField> Div<UnitComplex<N>> for &'a UnitComplex<N> {
     type Output = UnitComplex<N>;
 
     #[inline]
@@ -99,7 +99,7 @@ impl<'a, N: Real> Div<UnitComplex<N>> for &'a UnitComplex<N> {
     }
 }
 
-impl<'b, N: Real> Div<&'b UnitComplex<N>> for UnitComplex<N> {
+impl<'b, N: RealField> Div<&'b UnitComplex<N>> for UnitComplex<N> {
     type Output = Self;
 
     #[inline]
@@ -108,7 +108,7 @@ impl<'b, N: Real> Div<&'b UnitComplex<N>> for UnitComplex<N> {
     }
 }
 
-impl<'a, 'b, N: Real> Div<&'b UnitComplex<N>> for &'a UnitComplex<N> {
+impl<'a, 'b, N: RealField> Div<&'b UnitComplex<N>> for &'a UnitComplex<N> {
     type Output = UnitComplex<N>;
 
     #[inline]
@@ -122,7 +122,7 @@ macro_rules! complex_op_impl(
      ($RDim: ident, $CDim: ident) $(for $Storage: ident: $StoragesBound: ident $(<$($BoundParam: ty),*>)*),*;
      $lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Result: ty;
      $action: expr; $($lives: tt),*) => {
-        impl<$($lives ,)* N: Real $(, $Storage: $StoragesBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
+        impl<$($lives ,)* N: RealField $(, $Storage: $StoragesBound $(<$($BoundParam),*>)*)*> $Op<$Rhs> for $Lhs
             where DefaultAllocator: Allocator<N, $RDim, $CDim> {
             type Output = $Result;
 
@@ -300,14 +300,14 @@ complex_op_impl_all!(
 );
 
 // UnitComplex ×= UnitComplex
-impl<N: Real> MulAssign<UnitComplex<N>> for UnitComplex<N> {
+impl<N: RealField> MulAssign<UnitComplex<N>> for UnitComplex<N> {
     #[inline]
     fn mul_assign(&mut self, rhs: UnitComplex<N>) {
         *self = &*self * rhs
     }
 }
 
-impl<'b, N: Real> MulAssign<&'b UnitComplex<N>> for UnitComplex<N> {
+impl<'b, N: RealField> MulAssign<&'b UnitComplex<N>> for UnitComplex<N> {
     #[inline]
     fn mul_assign(&mut self, rhs: &'b UnitComplex<N>) {
         *self = &*self * rhs
@@ -315,14 +315,14 @@ impl<'b, N: Real> MulAssign<&'b UnitComplex<N>> for UnitComplex<N> {
 }
 
 // UnitComplex /= UnitComplex
-impl<N: Real> DivAssign<UnitComplex<N>> for UnitComplex<N> {
+impl<N: RealField> DivAssign<UnitComplex<N>> for UnitComplex<N> {
     #[inline]
     fn div_assign(&mut self, rhs: UnitComplex<N>) {
         *self = &*self / rhs
     }
 }
 
-impl<'b, N: Real> DivAssign<&'b UnitComplex<N>> for UnitComplex<N> {
+impl<'b, N: RealField> DivAssign<&'b UnitComplex<N>> for UnitComplex<N> {
     #[inline]
     fn div_assign(&mut self, rhs: &'b UnitComplex<N>) {
         *self = &*self / rhs
@@ -330,7 +330,7 @@ impl<'b, N: Real> DivAssign<&'b UnitComplex<N>> for UnitComplex<N> {
 }
 
 // UnitComplex ×= Rotation
-impl<N: Real> MulAssign<Rotation<N, U2>> for UnitComplex<N>
+impl<N: RealField> MulAssign<Rotation<N, U2>> for UnitComplex<N>
 where DefaultAllocator: Allocator<N, U2, U2>
 {
     #[inline]
@@ -339,7 +339,7 @@ where DefaultAllocator: Allocator<N, U2, U2>
     }
 }
 
-impl<'b, N: Real> MulAssign<&'b Rotation<N, U2>> for UnitComplex<N>
+impl<'b, N: RealField> MulAssign<&'b Rotation<N, U2>> for UnitComplex<N>
 where DefaultAllocator: Allocator<N, U2, U2>
 {
     #[inline]
@@ -349,7 +349,7 @@ where DefaultAllocator: Allocator<N, U2, U2>
 }
 
 // UnitComplex ÷= Rotation
-impl<N: Real> DivAssign<Rotation<N, U2>> for UnitComplex<N>
+impl<N: RealField> DivAssign<Rotation<N, U2>> for UnitComplex<N>
 where DefaultAllocator: Allocator<N, U2, U2>
 {
     #[inline]
@@ -358,7 +358,7 @@ where DefaultAllocator: Allocator<N, U2, U2>
     }
 }
 
-impl<'b, N: Real> DivAssign<&'b Rotation<N, U2>> for UnitComplex<N>
+impl<'b, N: RealField> DivAssign<&'b Rotation<N, U2>> for UnitComplex<N>
 where DefaultAllocator: Allocator<N, U2, U2>
 {
     #[inline]
@@ -368,7 +368,7 @@ where DefaultAllocator: Allocator<N, U2, U2>
 }
 
 // Rotation ×= UnitComplex
-impl<N: Real> MulAssign<UnitComplex<N>> for Rotation<N, U2>
+impl<N: RealField> MulAssign<UnitComplex<N>> for Rotation<N, U2>
 where DefaultAllocator: Allocator<N, U2, U2>
 {
     #[inline]
@@ -377,7 +377,7 @@ where DefaultAllocator: Allocator<N, U2, U2>
     }
 }
 
-impl<'b, N: Real> MulAssign<&'b UnitComplex<N>> for Rotation<N, U2>
+impl<'b, N: RealField> MulAssign<&'b UnitComplex<N>> for Rotation<N, U2>
 where DefaultAllocator: Allocator<N, U2, U2>
 {
     #[inline]
@@ -387,7 +387,7 @@ where DefaultAllocator: Allocator<N, U2, U2>
 }
 
 // Rotation ÷= UnitComplex
-impl<N: Real> DivAssign<UnitComplex<N>> for Rotation<N, U2>
+impl<N: RealField> DivAssign<UnitComplex<N>> for Rotation<N, U2>
 where DefaultAllocator: Allocator<N, U2, U2>
 {
     #[inline]
@@ -396,7 +396,7 @@ where DefaultAllocator: Allocator<N, U2, U2>
     }
 }
 
-impl<'b, N: Real> DivAssign<&'b UnitComplex<N>> for Rotation<N, U2>
+impl<'b, N: RealField> DivAssign<&'b UnitComplex<N>> for Rotation<N, U2>
 where DefaultAllocator: Allocator<N, U2, U2>
 {
     #[inline]

src/io/matrix_market.rs

@@ -3,7 +3,7 @@ use std::path::Path;
 
 use pest::Parser;
 use crate::sparse::CsMatrix;
-use crate::Real;
+use crate::RealField;
 
 #[derive(Parser)]
 #[grammar = "io/matrix_market.pest"]
@@ -11,14 +11,14 @@ struct MatrixMarketParser;
 
 // FIXME: return an Error instead of an Option.
 /// Parses a Matrix Market file at the given path, and returns the corresponding sparse matrix.
-pub fn cs_matrix_from_matrix_market<N: Real, P: AsRef<Path>>(path: P) -> Option<CsMatrix<N>> {
+pub fn cs_matrix_from_matrix_market<N: RealField, P: AsRef<Path>>(path: P) -> Option<CsMatrix<N>> {
     let file = fs::read_to_string(path).ok()?;
     cs_matrix_from_matrix_market_str(&file)
 }
 
 // FIXME: return an Error instead of an Option.
 /// Parses a Matrix Market file described by the given string, and returns the corresponding sparse matrix.
-pub fn cs_matrix_from_matrix_market_str<N: Real>(data: &str) -> Option<CsMatrix<N>> {
+pub fn cs_matrix_from_matrix_market_str<N: RealField>(data: &str) -> Option<CsMatrix<N>> {
     let file = MatrixMarketParser::parse(Rule::Document, data)
         .unwrap()
         .next()?;

src/lib.rs

@@ -4,8 +4,8 @@
 **nalgebra** is a linear algebra library written for Rust targeting:
 
 * General-purpose linear algebra (still lacks a lot of features…)
-* Real time computer graphics.
+* RealField time computer graphics.
-* Real time computer physics.
+* RealField time computer physics.
 
 ## Using **nalgebra**
 You will need the last stable build of the [rust compiler](http://www.rust-lang.org)
@@ -160,7 +160,7 @@ use alga::linear::SquareMatrix as AlgaSquareMatrix;
 use alga::linear::{EuclideanSpace, FiniteDimVectorSpace, InnerSpace, NormedSpace};
 use num::Signed;
 
-pub use alga::general::{Id, Real, ComplexField};
+pub use alga::general::{Id, RealField, ComplexField};
 
 /*
  *
@@ -297,8 +297,8 @@ pub fn min<T: Ord>(a: T, b: T) -> T {
 
 /// The absolute value of `a`.
 ///
-/// Deprecated: Use [Matrix::abs] or [Real::abs] instead.
+/// Deprecated: Use [Matrix::abs] or [RealField::abs] instead.
-#[deprecated(note = "use `Matrix::abs` or `Real::abs` instead")]
+#[deprecated(note = "use `Matrix::abs` or `RealField::abs` instead")]
 #[inline]
 pub fn abs<T: Signed>(a: &T) -> T {
     a.abs()
@@ -460,7 +460,7 @@ pub fn dot<V: FiniteDimVectorSpace>(a: &V, b: &V) -> V::Field {
 /// Or, use [InnerSpace::angle](https://docs.rs/alga/0.7.2/alga/linear/trait.InnerSpace.html#method.angle).
 #[deprecated(note = "use `Matrix::angle` instead")]
 #[inline]
-pub fn angle<V: InnerSpace>(a: &V, b: &V) -> V::Real {
+pub fn angle<V: InnerSpace>(a: &V, b: &V) -> V::RealField {
     a.angle(b)
 }
 
@@ -484,7 +484,7 @@ pub fn angle<V: InnerSpace>(a: &V, b: &V) -> V::Real {
 /// Or, use [NormedSpace::norm](https://docs.rs/alga/0.7.2/alga/linear/trait.NormedSpace.html#tymethod.norm).
 #[deprecated(note = "use `Matrix::norm` or `Quaternion::norm` instead")]
 #[inline]
-pub fn norm<V: NormedSpace>(v: &V) -> V::Real {
+pub fn norm<V: NormedSpace>(v: &V) -> V::RealField {
     v.norm()
 }
 
@@ -504,7 +504,7 @@ pub fn norm<V: NormedSpace>(v: &V) -> V::Real {
 /// Or, use [NormedSpace::norm_squared](https://docs.rs/alga/0.7.2/alga/linear/trait.NormedSpace.html#tymethod.norm_squared).
 #[deprecated(note = "use `Matrix::norm_squared` or `Quaternion::norm_squared` instead")]
 #[inline]
-pub fn norm_squared<V: NormedSpace>(v: &V) -> V::Real {
+pub fn norm_squared<V: NormedSpace>(v: &V) -> V::RealField {
     v.norm_squared()
 }
 
@@ -524,7 +524,7 @@ pub fn norm_squared<V: NormedSpace>(v: &V) -> V::Real {
 /// Or, use [NormedSpace::norm](https://docs.rs/alga/0.7.2/alga/linear/trait.NormedSpace.html#tymethod.norm).
 #[deprecated(note = "use `Matrix::magnitude` or `Quaternion::magnitude` instead")]
 #[inline]
-pub fn magnitude<V: NormedSpace>(v: &V) -> V::Real {
+pub fn magnitude<V: NormedSpace>(v: &V) -> V::RealField {
     v.norm()
 }
 
@@ -545,7 +545,7 @@ pub fn magnitude<V: NormedSpace>(v: &V) -> V::Real {
 /// Or, use [NormedSpace::norm_squared](https://docs.rs/alga/0.7.2/alga/linear/trait.NormedSpace.html#tymethod.norm_squared).
 #[deprecated(note = "use `Matrix::magnitude_squared` or `Quaternion::magnitude_squared` instead")]
 #[inline]
-pub fn magnitude_squared<V: NormedSpace>(v: &V) -> V::Real {
+pub fn magnitude_squared<V: NormedSpace>(v: &V) -> V::RealField {
     v.norm_squared()
 }
 
@@ -573,7 +573,7 @@ pub fn normalize<V: NormedSpace>(v: &V) -> V {
 /// Or, use [NormedSpace::try_normalize](https://docs.rs/alga/0.7.2/alga/linear/trait.NormedSpace.html#tymethod.try_normalize).
 #[deprecated(note = "use `Matrix::try_normalize` or `Quaternion::try_normalize` instead")]
 #[inline]
-pub fn try_normalize<V: NormedSpace>(v: &V, min_norm: V::Real) -> Option<V> {
+pub fn try_normalize<V: NormedSpace>(v: &V, min_norm: V::RealField) -> Option<V> {
     v.try_normalize(min_norm)
 }
 
@@ -600,7 +600,7 @@ pub fn center<P: EuclideanSpace>(p1: &P, p2: &P) -> P {
 /// * [center](fn.center.html)
 /// * [distance_squared](fn.distance_squared.html)
 #[inline]
-pub fn distance<P: EuclideanSpace>(p1: &P, p2: &P) -> P::Real {
+pub fn distance<P: EuclideanSpace>(p1: &P, p2: &P) -> P::RealField {
     (p2.coordinates() - p1.coordinates()).norm()
 }
 
@@ -611,7 +611,7 @@ pub fn distance<P: EuclideanSpace>(p1: &P, p2: &P) -> P::Real {
 /// * [center](fn.center.html)
 /// * [distance](fn.distance.html)
 #[inline]
-pub fn distance_squared<P: EuclideanSpace>(p1: &P, p2: &P) -> P::Real {
+pub fn distance_squared<P: EuclideanSpace>(p1: &P, p2: &P) -> P::RealField {
     (p2.coordinates() - p1.coordinates()).norm_squared()
 }
 

src/linalg/balancing.rs

@@ -1,6 +1,6 @@
 //! Functions for balancing a matrix.
 
-use alga::general::Real;
+use alga::general::RealField;
 use std::ops::{DivAssign, MulAssign};
 
 use crate::allocator::Allocator;
@@ -12,7 +12,7 @@ use crate::base::{DefaultAllocator, MatrixN, VectorN};
 /// the corresponding diagonal transformation.
 ///
 /// See https://arxiv.org/pdf/1401.5766.pdf
-pub fn balance_parlett_reinsch<N: Real, D: Dim>(m: &mut MatrixN<N, D>) -> VectorN<N, D>
+pub fn balance_parlett_reinsch<N: RealField, D: Dim>(m: &mut MatrixN<N, D>) -> VectorN<N, D>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D> {
     assert!(m.is_square(), "Unable to balance a non-square matrix.");
 
@@ -64,7 +64,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D> {
 }
 
 /// Computes in-place `D * m * D.inverse()`, where `D` is the matrix with diagonal `d`.
-pub fn unbalance<N: Real, D: Dim>(m: &mut MatrixN<N, D>, d: &VectorN<N, D>)
+pub fn unbalance<N: RealField, D: Dim>(m: &mut MatrixN<N, D>, d: &VectorN<N, D>)
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, D> {
     assert!(m.is_square(), "Unable to unbalance a non-square matrix.");
     assert_eq!(m.nrows(), d.len(), "Unbalancing: mismatched dimensions.");

src/linalg/bidiagonal.rs

@@ -265,14 +265,14 @@ where
     }
 
     /// The diagonal part of this decomposed matrix.
-    pub fn diagonal(&self) -> VectorN<N::Real, DimMinimum<R, C>>
+    pub fn diagonal(&self) -> VectorN<N::RealField, DimMinimum<R, C>>
-        where DefaultAllocator: Allocator<N::Real, DimMinimum<R, C>> {
+        where DefaultAllocator: Allocator<N::RealField, DimMinimum<R, C>> {
         self.diagonal.map(|e| e.modulus())
     }
 
     /// The off-diagonal part of this decomposed matrix.
-    pub fn off_diagonal(&self) -> VectorN<N::Real, DimDiff<DimMinimum<R, C>, U1>>
+    pub fn off_diagonal(&self) -> VectorN<N::RealField, DimDiff<DimMinimum<R, C>, U1>>
-        where DefaultAllocator: Allocator<N::Real, DimDiff<DimMinimum<R, C>, U1>> {
+        where DefaultAllocator: Allocator<N::RealField, DimDiff<DimMinimum<R, C>, U1>> {
         self.off_diagonal.map(|e| e.modulus())
     }
 

src/linalg/givens.rs

@@ -12,7 +12,7 @@ use crate::base::{Vector, Matrix};
 /// A Givens rotation.
 #[derive(Debug, Clone, Copy)]
 pub struct GivensRotation<N: ComplexField> {
-    c: N::Real,
+    c: N::RealField,
     s: N
 }
 
@@ -21,7 +21,7 @@ impl<N: ComplexField> GivensRotation<N> {
     /// The Givents rotation that does nothing.
     pub fn identity() -> Self {
         Self {
-            c: N::Real::one(),
+            c: N::RealField::one(),
             s: N::zero()
         }
     }
@@ -30,7 +30,7 @@ impl<N: ComplexField> GivensRotation<N> {
     ///
     /// The components are copies as-is. It is not checked whether they describe
     /// an actually valid Givens rotation.
-    pub fn new_unchecked(c: N::Real, s: N) -> Self {
+    pub fn new_unchecked(c: N::RealField, s: N) -> Self {
        Self {
            c, s
        }
@@ -38,11 +38,11 @@ impl<N: ComplexField> GivensRotation<N> {
 
     /// Initializes a Givens rotation from its non-normalized cosine an sine components.
     pub fn new(c: N, s: N) -> (Self, N) {
-        Self::try_new(c, s, N::Real::zero()).unwrap()
+        Self::try_new(c, s, N::RealField::zero()).unwrap()
     }
 
     /// Initializes a Givens rotation form its non-normalized cosine an sine components.
-    pub fn try_new(c: N, s: N, eps: N::Real) -> Option<(Self, N)> {
+    pub fn try_new(c: N, s: N, eps: N::RealField) -> Option<(Self, N)> {
         let (mod0, sign0) = c.to_exp();
         let denom = (mod0 * mod0 + s.modulus_squared()).sqrt();
 
@@ -91,7 +91,7 @@ impl<N: ComplexField> GivensRotation<N> {
     }
 
     /// The cos part of this roration.
-    pub fn c(&self) -> N::Real {
+    pub fn c(&self) -> N::RealField {
         self.c
     }
 

src/linalg/schur.rs

@@ -2,7 +2,7 @@
 use serde::{Deserialize, Serialize};
 
 use approx::AbsDiffEq;
-use alga::general::{ComplexField, Real};
+use alga::general::{ComplexField, RealField};
 use num_complex::Complex as NumComplex;
 use std::cmp;
 
@@ -18,7 +18,7 @@ use crate::linalg::givens::GivensRotation;
 
 /// Schur decomposition of a square matrix.
 ///
-/// If this is a real matrix, this will be a Real Schur decomposition.
+/// If this is a real matrix, this will be a RealField Schur decomposition.
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
@@ -58,7 +58,7 @@ where
 {
     /// Computes the Schur decomposition of a square matrix.
     pub fn new(m: MatrixN<N, D>) -> Self {
-        Self::try_new(m, N::Real::default_epsilon(), 0).unwrap()
+        Self::try_new(m, N::RealField::default_epsilon(), 0).unwrap()
     }
 
     /// Attempts to compute the Schur decomposition of a square matrix.
@@ -72,7 +72,7 @@ where
     /// * `max_niter` − maximum total number of iterations performed by the algorithm. If this
     /// number of iteration is exceeded, `None` is returned. If `niter == 0`, then the algorithm
     /// continues indefinitely until convergence.
-    pub fn try_new(m: MatrixN<N, D>, eps: N::Real, max_niter: usize) -> Option<Self> {
+    pub fn try_new(m: MatrixN<N, D>, eps: N::RealField, max_niter: usize) -> Option<Self> {
         let mut work = unsafe { VectorN::new_uninitialized_generic(m.data.shape().0, U1) };
 
         Self::do_decompose(m, &mut work, eps, max_niter, true).map(|(q, t)| Schur {
@@ -84,7 +84,7 @@ where
     fn do_decompose(
         mut m: MatrixN<N, D>,
         work: &mut VectorN<N, D>,
-        eps: N::Real,
+        eps: N::RealField,
         max_niter: usize,
         compute_q: bool,
     ) -> Option<(Option<MatrixN<N, D>>, MatrixN<N, D>)>
@@ -291,7 +291,7 @@ where
 
     /// Computes the complex eigenvalues of the decomposed matrix.
     fn do_complex_eigenvalues(t: &MatrixN<N, D>, out: &mut VectorN<NumComplex<N>, D>)
-    where N: Real,
+    where N: RealField,
           DefaultAllocator: Allocator<NumComplex<N>, D> {
         let dim = t.nrows();
         let mut m = 0;
@@ -329,7 +329,7 @@ where
         }
     }
 
-    fn delimit_subproblem(t: &mut MatrixN<N, D>, eps: N::Real, end: usize) -> (usize, usize)
+    fn delimit_subproblem(t: &mut MatrixN<N, D>, eps: N::RealField, end: usize) -> (usize, usize)
     where
         D: DimSub<U1>,
         DefaultAllocator: Allocator<N, DimDiff<D, U1>>,
@@ -390,7 +390,7 @@ where
 
     /// Computes the complex eigenvalues of the decomposed matrix.
     pub fn complex_eigenvalues(&self) -> VectorN<NumComplex<N>, D>
-    where N: Real,
+    where N: RealField,
           DefaultAllocator: Allocator<NumComplex<N>, D> {
         let mut out = unsafe { VectorN::new_uninitialized_generic(self.t.data.shape().0, U1) };
         Self::do_complex_eigenvalues(&self.t, &mut out);
@@ -511,7 +511,7 @@ where
     /// * `max_niter` − maximum total number of iterations performed by the algorithm. If this
     /// number of iteration is exceeded, `None` is returned. If `niter == 0`, then the algorithm
     /// continues indefinitely until convergence.
-    pub fn try_schur(self, eps: N::Real, max_niter: usize) -> Option<Schur<N, D>> {
+    pub fn try_schur(self, eps: N::RealField, max_niter: usize) -> Option<Schur<N, D>> {
         Schur::try_new(self.into_owned(), eps, max_niter)
     }
 
@@ -543,7 +543,7 @@ where
         let schur = Schur::do_decompose(
             self.clone_owned(),
             &mut work,
-            N::Real::default_epsilon(),
+            N::RealField::default_epsilon(),
             0,
             false,
         )
@@ -558,7 +558,7 @@ where
     /// Computes the eigenvalues of this matrix.
     pub fn complex_eigenvalues(&self) -> VectorN<NumComplex<N>, D>
     // FIXME: add balancing?
-    where N: Real,
+    where N: RealField,
           DefaultAllocator: Allocator<NumComplex<N>, D> {
         let dim = self.data.shape().0;
         let mut work = unsafe { VectorN::new_uninitialized_generic(dim, U1) };

src/linalg/svd.rs

@@ -4,7 +4,7 @@ use serde::{Deserialize, Serialize};
 use num::{Zero, One};
 use approx::AbsDiffEq;
 
-use alga::general::{Real, ComplexField};
+use alga::general::{RealField, ComplexField};
 use crate::allocator::Allocator;
 use crate::base::{DefaultAllocator, Matrix, Matrix2x3, MatrixMN, Vector2, VectorN};
 use crate::constraint::{SameNumberOfRows, ShapeConstraint};
@@ -20,47 +20,47 @@ use crate::linalg::givens::GivensRotation;
 #[cfg_attr(
     feature = "serde-serialize",
     serde(bound(
-        serialize = "DefaultAllocator: Allocator<N::Real, DimMinimum<R, C>>    +
+        serialize = "DefaultAllocator: Allocator<N::RealField, DimMinimum<R, C>>    +
                            Allocator<N, DimMinimum<R, C>, C> +
                            Allocator<N, R, DimMinimum<R, C>>,
          MatrixMN<N, R, DimMinimum<R, C>>: Serialize,
          MatrixMN<N, DimMinimum<R, C>, C>: Serialize,
-         VectorN<N::Real, DimMinimum<R, C>>: Serialize"
+         VectorN<N::RealField, DimMinimum<R, C>>: Serialize"
     ))
 )]
 #[cfg_attr(
     feature = "serde-serialize",
     serde(bound(
-        deserialize = "DefaultAllocator: Allocator<N::Real, DimMinimum<R, C>>    +
+        deserialize = "DefaultAllocator: Allocator<N::RealField, DimMinimum<R, C>>    +
                            Allocator<N, DimMinimum<R, C>, C> +
                            Allocator<N, R, DimMinimum<R, C>>,
          MatrixMN<N, R, DimMinimum<R, C>>: Deserialize<'de>,
          MatrixMN<N, DimMinimum<R, C>, C>: Deserialize<'de>,
-         VectorN<N::Real, DimMinimum<R, C>>: Deserialize<'de>"
+         VectorN<N::RealField, DimMinimum<R, C>>: Deserialize<'de>"
     ))
 )]
 #[derive(Clone, Debug)]
 pub struct SVD<N: ComplexField, R: DimMin<C>, C: Dim>
 where DefaultAllocator: Allocator<N, DimMinimum<R, C>, C>
         + Allocator<N, R, DimMinimum<R, C>>
-        + Allocator<N::Real, DimMinimum<R, C>>
+        + Allocator<N::RealField, DimMinimum<R, C>>
 {
     /// The left-singular vectors `U` of this SVD.
     pub u: Option<MatrixMN<N, R, DimMinimum<R, C>>>,
     /// The right-singular vectors `V^t` of this SVD.
     pub v_t: Option<MatrixMN<N, DimMinimum<R, C>, C>>,
     /// The singular values of this SVD.
-    pub singular_values: VectorN<N::Real, DimMinimum<R, C>>,
+    pub singular_values: VectorN<N::RealField, DimMinimum<R, C>>,
 }
 
 impl<N: ComplexField, R: DimMin<C>, C: Dim> Copy for SVD<N, R, C>
 where
     DefaultAllocator: Allocator<N, DimMinimum<R, C>, C>
         + Allocator<N, R, DimMinimum<R, C>>
-        + Allocator<N::Real, DimMinimum<R, C>>,
+        + Allocator<N::RealField, DimMinimum<R, C>>,
     MatrixMN<N, R, DimMinimum<R, C>>: Copy,
     MatrixMN<N, DimMinimum<R, C>, C>: Copy,
-    VectorN<N::Real, DimMinimum<R, C>>: Copy,
+    VectorN<N::RealField, DimMinimum<R, C>>: Copy,
 {}
 
 impl<N: ComplexField, R: DimMin<C>, C: Dim> SVD<N, R, C>
@@ -73,12 +73,12 @@ where
         + Allocator<N, DimMinimum<R, C>, C>
         + Allocator<N, R, DimMinimum<R, C>>
         + Allocator<N, DimMinimum<R, C>>
-        + Allocator<N::Real, DimMinimum<R, C>>
+        + Allocator<N::RealField, DimMinimum<R, C>>
-        + Allocator<N::Real, DimDiff<DimMinimum<R, C>, U1>>,
+        + Allocator<N::RealField, DimDiff<DimMinimum<R, C>, U1>>,
 {
     /// Computes the Singular Value Decomposition of `matrix` using implicit shift.
     pub fn new(matrix: MatrixMN<N, R, C>, compute_u: bool, compute_v: bool) -> Self {
-        Self::try_new(matrix, compute_u, compute_v, N::Real::default_epsilon(), 0).unwrap()
+        Self::try_new(matrix, compute_u, compute_v, N::RealField::default_epsilon(), 0).unwrap()
     }
 
     /// Attempts to compute the Singular Value Decomposition of `matrix` using implicit shift.
@@ -95,7 +95,7 @@ where
         mut matrix: MatrixMN<N, R, C>,
         compute_u: bool,
         compute_v: bool,
-        eps: N::Real,
+        eps: N::RealField,
         max_niter: usize,
     ) -> Option<Self>
     {
@@ -150,7 +150,7 @@ where
 
                 for k in start..n {
                     let m12 = if k == n - 1 {
-                        N::Real::zero()
+                        N::RealField::zero()
                     } else {
                         off_diagonal[k + 1]
                     };
@@ -158,8 +158,8 @@ where
                     let mut subm = Matrix2x3::new(
                         diagonal[k],
                         off_diagonal[k],
-                        N::Real::zero(),
+                        N::RealField::zero(),
-                        N::Real::zero(),
+                        N::RealField::zero(),
                         diagonal[k + 1],
                         m12,
                     );
@@ -229,7 +229,7 @@ where
 
                 diagonal[start + 0] = s[0];
                 diagonal[start + 1] = s[1];
-                off_diagonal[start] = N::Real::zero();
+                off_diagonal[start] = N::RealField::zero();
 
                 if let Some(ref mut u) = u {
                     let rot = if b.is_upper_diagonal() {
@@ -269,7 +269,7 @@ where
         for i in 0..dim {
             let sval = diagonal[i];
 
-            if sval < N::Real::zero() {
+            if sval < N::RealField::zero() {
                 diagonal[i] = -sval;
 
                 if let Some(ref mut u) = u {
@@ -301,13 +301,13 @@ where
     */
 
     fn delimit_subproblem(
-        diagonal: &mut VectorN<N::Real, DimMinimum<R, C>>,
+        diagonal: &mut VectorN<N::RealField, DimMinimum<R, C>>,
-        off_diagonal: &mut VectorN<N::Real, DimDiff<DimMinimum<R, C>, U1>>,
+        off_diagonal: &mut VectorN<N::RealField, DimDiff<DimMinimum<R, C>, U1>>,
         u: &mut Option<MatrixMN<N, R, DimMinimum<R, C>>>,
         v_t: &mut Option<MatrixMN<N, DimMinimum<R, C>, C>>,
         is_upper_diagonal: bool,
         end: usize,
-        eps: N::Real,
+        eps: N::RealField,
     ) -> (usize, usize)
     {
         let mut n = end;
@@ -318,16 +318,16 @@ where
             if off_diagonal[m].is_zero()
                 || off_diagonal[m].norm1() <= eps * (diagonal[n].norm1() + diagonal[m].norm1())
             {
-                off_diagonal[m] = N::Real::zero();
+                off_diagonal[m] = N::RealField::zero();
             } else if diagonal[m].norm1() <= eps {
-                diagonal[m] = N::Real::zero();
+                diagonal[m] = N::RealField::zero();
                 Self::cancel_horizontal_off_diagonal_elt(diagonal, off_diagonal, u, v_t, is_upper_diagonal, m, m + 1);
 
                 if m != 0 {
                     Self::cancel_vertical_off_diagonal_elt(diagonal, off_diagonal, u, v_t, is_upper_diagonal, m - 1);
                 }
             } else if diagonal[n].norm1() <= eps {
-                diagonal[n] = N::Real::zero();
+                diagonal[n] = N::RealField::zero();
                 Self::cancel_vertical_off_diagonal_elt(diagonal, off_diagonal, u, v_t, is_upper_diagonal, m);
             } else {
                 break;
@@ -346,12 +346,12 @@ where
 
             if off_diagonal[m].norm1() <= eps * (diagonal[new_start].norm1() + diagonal[m].norm1())
             {
-                off_diagonal[m] = N::Real::zero();
+                off_diagonal[m] = N::RealField::zero();
                 break;
             }
             // FIXME: write a test that enters this case.
             else if diagonal[m].norm1() <= eps {
-                diagonal[m] = N::Real::zero();
+                diagonal[m] = N::RealField::zero();
                 Self::cancel_horizontal_off_diagonal_elt(diagonal, off_diagonal, u, v_t, is_upper_diagonal, m, n);
 
                 if m != 0 {
@@ -368,8 +368,8 @@ where
 
     // Cancels the i-th off-diagonal element using givens rotations.
     fn cancel_horizontal_off_diagonal_elt(
-        diagonal: &mut VectorN<N::Real, DimMinimum<R, C>>,
+        diagonal: &mut VectorN<N::RealField, DimMinimum<R, C>>,
-        off_diagonal: &mut VectorN<N::Real, DimDiff<DimMinimum<R, C>, U1>>,
+        off_diagonal: &mut VectorN<N::RealField, DimDiff<DimMinimum<R, C>, U1>>,
         u: &mut Option<MatrixMN<N, R, DimMinimum<R, C>>>,
         v_t: &mut Option<MatrixMN<N, DimMinimum<R, C>, C>>,
         is_upper_diagonal: bool,
@@ -378,7 +378,7 @@ where
     )
     {
         let mut v = Vector2::new(off_diagonal[i], diagonal[i + 1]);
-        off_diagonal[i] = N::Real::zero();
+        off_diagonal[i] = N::RealField::zero();
 
         for k in i..end {
             if let Some((rot, norm)) = GivensRotation::cancel_x(&v) {
@@ -407,8 +407,8 @@ where
 
     // Cancels the i-th off-diagonal element using givens rotations.
     fn cancel_vertical_off_diagonal_elt(
-        diagonal: &mut VectorN<N::Real, DimMinimum<R, C>>,
+        diagonal: &mut VectorN<N::RealField, DimMinimum<R, C>>,
-        off_diagonal: &mut VectorN<N::Real, DimDiff<DimMinimum<R, C>, U1>>,
+        off_diagonal: &mut VectorN<N::RealField, DimDiff<DimMinimum<R, C>, U1>>,
         u: &mut Option<MatrixMN<N, R, DimMinimum<R, C>>>,
         v_t: &mut Option<MatrixMN<N, DimMinimum<R, C>, C>>,
         is_upper_diagonal: bool,
@@ -416,7 +416,7 @@ where
     )
     {
         let mut v = Vector2::new(diagonal[i], off_diagonal[i]);
-        off_diagonal[i] = N::Real::zero();
+        off_diagonal[i] = N::RealField::zero();
 
         for k in (0..i + 1).rev() {
             if let Some((rot, norm)) = GivensRotation::cancel_y(&v) {
@@ -445,9 +445,9 @@ where
 
     /// Computes the rank of the decomposed matrix, i.e., the number of singular values greater
     /// than `eps`.
-    pub fn rank(&self, eps: N::Real) -> usize {
+    pub fn rank(&self, eps: N::RealField) -> usize {
         assert!(
-            eps >= N::Real::zero(),
+            eps >= N::RealField::zero(),
             "SVD rank: the epsilon must be non-negative."
         );
         self.singular_values.iter().filter(|e| **e > eps).count()
@@ -478,11 +478,11 @@ where
     /// Any singular value smaller than `eps` is assumed to be zero.
     /// Returns `Err` if the right- and left- singular vectors have not
     /// been computed at construction-time.
-    pub fn pseudo_inverse(mut self, eps: N::Real) -> Result<MatrixMN<N, C, R>, &'static str>
+    pub fn pseudo_inverse(mut self, eps: N::RealField) -> Result<MatrixMN<N, C, R>, &'static str>
     where
         DefaultAllocator: Allocator<N, C, R>,
     {
-        if eps < N::Real::zero() {
+        if eps < N::RealField::zero() {
             Err("SVD pseudo inverse: the epsilon must be non-negative.")
         }
         else {
@@ -490,9 +490,9 @@ where
                 let val = self.singular_values[i];
 
                 if val > eps {
-                    self.singular_values[i] = N::Real::one() / val;
+                    self.singular_values[i] = N::RealField::one() / val;
                 } else {
-                    self.singular_values[i] = N::Real::zero();
+                    self.singular_values[i] = N::RealField::zero();
                 }
             }
 
@@ -508,14 +508,14 @@ where
     pub fn solve<R2: Dim, C2: Dim, S2>(
         &self,
         b: &Matrix<N, R2, C2, S2>,
-        eps: N::Real,
+        eps: N::RealField,
     ) -> Result<MatrixMN<N, C, C2>, &'static str>
     where
         S2: Storage<N, R2, C2>,
         DefaultAllocator: Allocator<N, C, C2> + Allocator<N, DimMinimum<R, C>, C2>,
         ShapeConstraint: SameNumberOfRows<R, R2>,
     {
-        if eps < N::Real::zero() {
+        if eps < N::RealField::zero() {
             Err("SVD solve: the epsilon must be non-negative.")
         }
         else {
@@ -556,8 +556,8 @@ where
         + Allocator<N, DimMinimum<R, C>, C>
         + Allocator<N, R, DimMinimum<R, C>>
         + Allocator<N, DimMinimum<R, C>>
-        + Allocator<N::Real, DimMinimum<R, C>>
+        + Allocator<N::RealField, DimMinimum<R, C>>
-        + Allocator<N::Real, DimDiff<DimMinimum<R, C>, U1>>,
+        + Allocator<N::RealField, DimDiff<DimMinimum<R, C>, U1>>,
 {
     /// Computes the Singular Value Decomposition using implicit shift.
     pub fn svd(self, compute_u: bool, compute_v: bool) -> SVD<N, R, C> {
@@ -578,7 +578,7 @@ where
         self,
         compute_u: bool,
         compute_v: bool,
-        eps: N::Real,
+        eps: N::RealField,
         max_niter: usize,
     ) -> Option<SVD<N, R, C>>
     {
@@ -586,14 +586,14 @@ where
     }
 
     /// Computes the singular values of this matrix.
-    pub fn singular_values(&self) -> VectorN<N::Real, DimMinimum<R, C>> {
+    pub fn singular_values(&self) -> VectorN<N::RealField, DimMinimum<R, C>> {
         SVD::new(self.clone_owned(), false, false).singular_values
     }
 
     /// Computes the rank of this matrix.
     ///
     /// All singular values below `eps` are considered equal to 0.
-    pub fn rank(&self, eps: N::Real) -> usize {
+    pub fn rank(&self, eps: N::RealField) -> usize {
         let svd = SVD::new(self.clone_owned(), false, false);
         svd.rank(eps)
     }
@@ -601,7 +601,7 @@ where
     /// Computes the pseudo-inverse of this matrix.
     ///
     /// All singular values below `eps` are considered equal to 0.
-    pub fn pseudo_inverse(self, eps: N::Real) -> Result<MatrixMN<N, C, R>, &'static str>
+    pub fn pseudo_inverse(self, eps: N::RealField) -> Result<MatrixMN<N, C, R>, &'static str>
     where
         DefaultAllocator: Allocator<N, C, R>,
     {
@@ -613,7 +613,7 @@ where
 // Explicit formulae inspired from the paper "Computing the Singular Values of 2-by-2 Complex
 // Matrices", Sanzheng Qiao and Xiaohong Wang.
 // http://www.cas.mcmaster.ca/sqrl/papers/sqrl5.pdf
-fn compute_2x2_uptrig_svd<N: Real>(
+fn compute_2x2_uptrig_svd<N: RealField>(
     m11: N,
     m12: N,
     m22: N,
@@ -621,8 +621,8 @@ fn compute_2x2_uptrig_svd<N: Real>(
     compute_v: bool,
 ) -> (Option<GivensRotation<N>>, Vector2<N>, Option<GivensRotation<N>>)
 {
-    let two: N::Real = crate::convert(2.0f64);
+    let two: N::RealField = crate::convert(2.0f64);
-    let half: N::Real = crate::convert(0.5f64);
+    let half: N::RealField = crate::convert(0.5f64);
 
     let denom = (m11 + m22).hypot(m12) + (m11 - m22).hypot(m12);
 

src/linalg/symmetric_eigen.rs

@@ -19,8 +19,8 @@ use crate::linalg::SymmetricTridiagonal;
     feature = "serde-serialize",
     serde(bound(
         serialize = "DefaultAllocator: Allocator<N, D, D> +
-                           Allocator<N::Real, D>,
+                           Allocator<N::RealField, D>,
-         VectorN<N::Real, D>: Serialize,
+         VectorN<N::RealField, D>: Serialize,
          MatrixN<N, D>: Serialize"
     ))
 )]
@@ -28,31 +28,31 @@ use crate::linalg::SymmetricTridiagonal;
     feature = "serde-serialize",
     serde(bound(
         deserialize = "DefaultAllocator: Allocator<N, D, D> +
-                           Allocator<N::Real, D>,
+                           Allocator<N::RealField, D>,
-         VectorN<N::Real, D>: Deserialize<'de>,
+         VectorN<N::RealField, D>: Deserialize<'de>,
          MatrixN<N, D>: Deserialize<'de>"
     ))
 )]
 #[derive(Clone, Debug)]
 pub struct SymmetricEigen<N: ComplexField, D: Dim>
-where DefaultAllocator: Allocator<N, D, D> + Allocator<N::Real, D>
+where DefaultAllocator: Allocator<N, D, D> + Allocator<N::RealField, D>
 {
     /// The eigenvectors of the decomposed matrix.
     pub eigenvectors: MatrixN<N, D>,
 
     /// The unsorted eigenvalues of the decomposed matrix.
-    pub eigenvalues: VectorN<N::Real, D>,
+    pub eigenvalues: VectorN<N::RealField, D>,
 }
 
 impl<N: ComplexField, D: Dim> Copy for SymmetricEigen<N, D>
 where
-    DefaultAllocator: Allocator<N, D, D> + Allocator<N::Real, D>,
+    DefaultAllocator: Allocator<N, D, D> + Allocator<N::RealField, D>,
     MatrixN<N, D>: Copy,
-    VectorN<N::Real, D>: Copy,
+    VectorN<N::RealField, D>: Copy,
 {}
 
 impl<N: ComplexField, D: Dim> SymmetricEigen<N, D>
-where DefaultAllocator: Allocator<N, D, D> + Allocator<N::Real, D>
+where DefaultAllocator: Allocator<N, D, D> + Allocator<N::RealField, D>
 {
     /// Computes the eigendecomposition of the given symmetric matrix.
     ///
@@ -61,9 +61,9 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N::Real, D>
     where
         D: DimSub<U1>,
         DefaultAllocator: Allocator<N, DimDiff<D, U1>> + // For tridiagonalization
-        Allocator<N::Real, DimDiff<D, U1>>,
+        Allocator<N::RealField, DimDiff<D, U1>>,
     {
-        Self::try_new(m, N::Real::default_epsilon(), 0).unwrap()
+        Self::try_new(m, N::RealField::default_epsilon(), 0).unwrap()
     }
 
     /// Computes the eigendecomposition of the given symmetric matrix with user-specified
@@ -77,11 +77,11 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N::Real, D>
     /// * `max_niter` − maximum total number of iterations performed by the algorithm. If this
     /// number of iteration is exceeded, `None` is returned. If `niter == 0`, then the algorithm
     /// continues indefinitely until convergence.
-    pub fn try_new(m: MatrixN<N, D>, eps: N::Real, max_niter: usize) -> Option<Self>
+    pub fn try_new(m: MatrixN<N, D>, eps: N::RealField, max_niter: usize) -> Option<Self>
     where
         D: DimSub<U1>,
         DefaultAllocator: Allocator<N, DimDiff<D, U1>> + // For tridiagonalization
-                          Allocator<N::Real, DimDiff<D, U1>>,
+                          Allocator<N::RealField, DimDiff<D, U1>>,
     {
         Self::do_decompose(m, true, eps, max_niter).map(|(vals, vecs)| SymmetricEigen {
             eigenvectors: vecs.unwrap(),
@@ -92,13 +92,13 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N::Real, D>
     fn do_decompose(
         mut m: MatrixN<N, D>,
         eigenvectors: bool,
-        eps: N::Real,
+        eps: N::RealField,
         max_niter: usize,
-    ) -> Option<(VectorN<N::Real, D>, Option<MatrixN<N, D>>)>
+    ) -> Option<(VectorN<N::RealField, D>, Option<MatrixN<N, D>>)>
     where
         D: DimSub<U1>,
         DefaultAllocator: Allocator<N, DimDiff<D, U1>> + // For tridiagonalization
-                          Allocator<N::Real, DimDiff<D, U1>>,
+                          Allocator<N::RealField, DimDiff<D, U1>>,
     {
         assert!(
             m.is_square(),
@@ -226,14 +226,14 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N::Real, D>
     }
 
     fn delimit_subproblem(
-        diag: &VectorN<N::Real, D>,
+        diag: &VectorN<N::RealField, D>,
-        off_diag: &mut VectorN<N::Real, DimDiff<D, U1>>,
+        off_diag: &mut VectorN<N::RealField, DimDiff<D, U1>>,
         end: usize,
-        eps: N::Real,
+        eps: N::RealField,
     ) -> (usize, usize)
     where
         D: DimSub<U1>,
-        DefaultAllocator: Allocator<N::Real, DimDiff<D, U1>>,
+        DefaultAllocator: Allocator<N::RealField, DimDiff<D, U1>>,
     {
         let mut n = end;
 
@@ -258,7 +258,7 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N::Real, D>
             if off_diag[m].is_zero()
                 || off_diag[m].norm1() <= eps * (diag[new_start].norm1() + diag[m].norm1())
             {
-                off_diag[m] = N::Real::zero();
+                off_diag[m] = N::RealField::zero();
                 break;
             }
 
@@ -306,7 +306,7 @@ pub fn wilkinson_shift<N: ComplexField>(tmm: N, tnn: N, tmn: N) -> N {
  */
 impl<N: ComplexField, D: DimSub<U1>, S: Storage<N, D, D>> SquareMatrix<N, D, S>
 where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>> +
-                        Allocator<N::Real, D> + Allocator<N::Real, DimDiff<D, U1>>
+                        Allocator<N::RealField, D> + Allocator<N::RealField, DimDiff<D, U1>>
 {
     /// Computes the eigendecomposition of this symmetric matrix.
     ///
@@ -326,15 +326,15 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>> +
     /// * `max_niter` − maximum total number of iterations performed by the algorithm. If this
     /// number of iteration is exceeded, `None` is returned. If `niter == 0`, then the algorithm
     /// continues indefinitely until convergence.
-    pub fn try_symmetric_eigen(self, eps: N::Real, max_niter: usize) -> Option<SymmetricEigen<N, D>> {
+    pub fn try_symmetric_eigen(self, eps: N::RealField, max_niter: usize) -> Option<SymmetricEigen<N, D>> {
         SymmetricEigen::try_new(self.into_owned(), eps, max_niter)
     }
 
     /// Computes the eigenvalues of this symmetric matrix.
     ///
     /// Only the lower-triangular part of the matrix is read.
-    pub fn symmetric_eigenvalues(&self) -> VectorN<N::Real, D> {
+    pub fn symmetric_eigenvalues(&self) -> VectorN<N::RealField, D> {
-        SymmetricEigen::do_decompose(self.clone_owned(), false, N::Real::default_epsilon(), 0)
+        SymmetricEigen::do_decompose(self.clone_owned(), false, N::RealField::default_epsilon(), 0)
             .unwrap()
             .0
     }

src/linalg/symmetric_tridiagonal.rs

@@ -98,9 +98,9 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>
 
     /// Retrieve the orthogonal transformation, diagonal, and off diagonal elements of this
     /// decomposition.
-    pub fn unpack(self) -> (MatrixN<N, D>, VectorN<N::Real, D>, VectorN<N::Real, DimDiff<D, U1>>)
+    pub fn unpack(self) -> (MatrixN<N, D>, VectorN<N::RealField, D>, VectorN<N::RealField, DimDiff<D, U1>>)
-    where DefaultAllocator: Allocator<N::Real, D>
+    where DefaultAllocator: Allocator<N::RealField, D>
-                          + Allocator<N::Real, DimDiff<D, U1>> {
+                          + Allocator<N::RealField, DimDiff<D, U1>> {
         let diag = self.diagonal();
         let q = self.q();
 
@@ -108,19 +108,19 @@ where DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimDiff<D, U1>>
     }
 
     /// Retrieve the diagonal, and off diagonal elements of this decomposition.
-    pub fn unpack_tridiagonal(self) -> (VectorN<N::Real, D>, VectorN<N::Real, DimDiff<D, U1>>)
+    pub fn unpack_tridiagonal(self) -> (VectorN<N::RealField, D>, VectorN<N::RealField, DimDiff<D, U1>>)
-        where DefaultAllocator: Allocator<N::Real, D>
+        where DefaultAllocator: Allocator<N::RealField, D>
-                              + Allocator<N::Real, DimDiff<D, U1>> {
+                              + Allocator<N::RealField, DimDiff<D, U1>> {
         (self.diagonal(), self.off_diagonal.map(N::modulus))
     }
 
     /// The diagonal components of this decomposition.
-    pub fn diagonal(&self) -> VectorN<N::Real, D>
+    pub fn diagonal(&self) -> VectorN<N::RealField, D>
-    where DefaultAllocator: Allocator<N::Real, D> { self.tri.map_diagonal(|e| e.real()) }
+    where DefaultAllocator: Allocator<N::RealField, D> { self.tri.map_diagonal(|e| e.real()) }
 
     /// The off-diagonal components of this decomposition.
-    pub fn off_diagonal(&self) -> VectorN<N::Real, DimDiff<D, U1>>
+    pub fn off_diagonal(&self) -> VectorN<N::RealField, DimDiff<D, U1>>
-    where DefaultAllocator: Allocator<N::Real, DimDiff<D, U1>> {
+    where DefaultAllocator: Allocator<N::RealField, DimDiff<D, U1>> {
         self.off_diagonal.map(N::modulus)
     }
 

src/sparse/cs_matrix_cholesky.rs

@@ -3,10 +3,10 @@ use std::mem;
 
 use crate::allocator::Allocator;
 use crate::sparse::{CsMatrix, CsStorage, CsStorageIter, CsStorageIterMut, CsVecStorage};
-use crate::{DefaultAllocator, Dim, Real, VectorN, U1};
+use crate::{DefaultAllocator, Dim, RealField, VectorN, U1};
 
 /// The cholesky decomposition of a column compressed sparse matrix.
-pub struct CsCholesky<N: Real, D: Dim>
+pub struct CsCholesky<N: RealField, D: Dim>
 where DefaultAllocator: Allocator<usize, D> + Allocator<N, D>
 {
     // Non-zero pattern of the original matrix upper-triangular part.
@@ -25,7 +25,7 @@ where DefaultAllocator: Allocator<usize, D> + Allocator<N, D>
     work_c: VectorN<usize, D>,
 }
 
-impl<N: Real, D: Dim> CsCholesky<N, D>
+impl<N: RealField, D: Dim> CsCholesky<N, D>
 where DefaultAllocator: Allocator<usize, D> + Allocator<N, D>
 {
     /// Computes the cholesky decomposition of the sparse matrix `m`.

src/sparse/cs_matrix_solve.rs

@@ -2,9 +2,9 @@ use crate::allocator::Allocator;
 use crate::constraint::{SameNumberOfRows, ShapeConstraint};
 use crate::sparse::{CsMatrix, CsStorage, CsVector};
 use crate::storage::{Storage, StorageMut};
-use crate::{DefaultAllocator, Dim, Matrix, MatrixMN, Real, VectorN, U1};
+use crate::{DefaultAllocator, Dim, Matrix, MatrixMN, RealField, VectorN, U1};
 
-impl<N: Real, D: Dim, S: CsStorage<N, D, D>> CsMatrix<N, D, D, S> {
+impl<N: RealField, D: Dim, S: CsStorage<N, D, D>> CsMatrix<N, D, D, S> {
     /// Solve a lower-triangular system with a dense right-hand-side.
     pub fn solve_lower_triangular<R2: Dim, C2: Dim, S2>(
         &self,

tests/core/helper.rs

@@ -5,12 +5,12 @@ use quickcheck::{Arbitrary, Gen};
 use rand::distributions::{Standard, Distribution};
 use rand::Rng;
 use num_complex::Complex;
-use na::Real;
+use na::RealField;
 
 #[derive(Copy, Clone, Debug, PartialEq, Eq)]
 pub struct RandComplex<N>(pub Complex<N>);
 
-impl<N: Arbitrary + Real> Arbitrary for RandComplex<N> {
+impl<N: Arbitrary + RealField> Arbitrary for RandComplex<N> {
     #[inline]
     fn arbitrary<G: Gen>(rng: &mut G) -> Self {
         let im = Arbitrary::arbitrary(rng);
@@ -19,7 +19,7 @@ impl<N: Arbitrary + Real> Arbitrary for RandComplex<N> {
     }
 }
 
-impl<N: Real> Distribution<RandComplex<N>> for Standard
+impl<N: RealField> Distribution<RandComplex<N>> for Standard
     where
         Standard: Distribution<N>,
 {
@@ -43,7 +43,7 @@ impl<N: Arbitrary> Arbitrary for RandScalar<N> {
     }
 }
 
-impl<N: Real> Distribution<RandScalar<N>> for Standard
+impl<N: RealField> Distribution<RandScalar<N>> for Standard
     where
         Standard: Distribution<N>,
 {

tests/core/matrix.rs

@@ -4,7 +4,7 @@ use std::cmp::Ordering;
 use na::dimension::{U15, U8};
 use na::{
     self, DMatrix, DVector, Matrix2, Matrix2x3, Matrix2x4, Matrix3, Matrix3x2, Matrix3x4, Matrix4,
-    Matrix4x3, Matrix4x5, Matrix5, Matrix6, MatrixMN, Real, RowVector3, RowVector4, RowVector5,
+    Matrix4x3, Matrix4x5, Matrix5, Matrix6, MatrixMN, RealField, RowVector3, RowVector4, RowVector5,
     Vector1, Vector2, Vector3, Vector4, Vector5, Vector6,
 };
 
@@ -1022,7 +1022,7 @@ mod finite_dim_inner_space_tests {
      *
      */
     #[cfg(feature = "arbitrary")]
-    fn is_subspace_basis<T: FiniteDimInnerSpace<Real = f64, ComplexField = f64> + Display>(vs: &[T]) -> bool {
+    fn is_subspace_basis<T: FiniteDimInnerSpace<RealField = f64, ComplexField = f64> + Display>(vs: &[T]) -> bool {
         for i in 0..vs.len() {
             // Basis elements must be normalized.
             if !relative_eq!(vs[i].norm(), 1.0, epsilon = 1.0e-7) {

tests/geometry/rotation.rs

@@ -1,4 +1,4 @@
-use na::{Quaternion, Real, UnitQuaternion, Vector2, Vector3};
+use na::{Quaternion, RealField, UnitQuaternion, Vector2, Vector3};
 
 #[test]
 fn angle_2() {
@@ -32,7 +32,7 @@ fn quaternion_euler_angles_issue_494() {
 
 #[cfg(feature = "arbitrary")]
 mod quickcheck_tests {
-    use alga::general::Real;
+    use alga::general::RealField;
     use na::{self, Rotation2, Rotation3, Unit, Vector2, Vector3};
     use std::f64;