Start adding some gtx functions.

nalgebra-glm/README

@@ -4,3 +4,6 @@
 * equal overload with epsilon -> equal_epsilon
 * ortho(l, r, b, t) -> infinite_ortho
 * tweaked_infinite_perspective(fovy, aspect, near, ep) -> tweaked_infinite_perspective_ep
+* Function overload: the vec version is suffixed by _vec
+* Function overload: the methods taking an epsilon as suffixed by _eps
+* L1Norm and L2Norm between two vectors have been renamed: l1_distance, l2_distance

nalgebra-glm/src/common.rs

@@ -1,209 +1,202 @@
-use na::{Scalar, DefaultAllocator};
+use std::mem;
+use num::FromPrimitive;
+use na::{self, Scalar, Real, DefaultAllocator};
 
-use aliases::Vec;
-use traits::{Dimension, Alloc};
+use aliases::{Vec, Mat};
+use traits::{Number, Dimension, Alloc};
 
 
-pub fn abs<T>(x: T) -> T {
-    unimplemented!()
-
+pub fn abs<N: Number, R: Dimension, C: Dimension>(x: &Mat<N, R, C>) -> Mat<N, R, C>
+    where DefaultAllocator: Alloc<N, R, C> {
+     x.abs()
 }
 
-pub fn abs2<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<N, D>
+pub fn ceil<N: Real, D: Dimension>(x: &Vec<N, D>) -> Vec<N, D>
     where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
+    x.map(|x| x.ceil())
 }
 
-pub fn ceil<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<N, D>
+pub fn clamp<N: Number>(x: N, minVal: N, maxVal: N) -> N {
+    na::clamp(x, minVal, maxVal)
+}
+
+pub fn clamp2<N: Number, D: Dimension>(x: &Vec<N, D>,minVal: N, maxVal: N) -> Vec<N, D>
     where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
+    x.map(|x| na::clamp(x, minVal, maxVal))
 }
 
-pub fn clamp<T>(x: T, minVal: T, maxVal: T) -> T {
-    unimplemented!()
-
-}
-
-pub fn clamp2<N: Scalar, D: Dimension>(x: &Vec<N, D>,minVal: N, maxVal: N) -> Vec<N, D>
+pub fn clamp3<N: Number, D: Dimension>(x: &Vec<N, D>, minVal: &Vec<N, D>, maxVal: &Vec<N, D>) -> Vec<N, D>
     where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
+    na::clamp(x.clone(), minVal.clone(), maxVal.clone())
 }
 
-pub fn clamp3<N: Scalar, D: Dimension>(x: &Vec<N, D>, minVal: &Vec<N, D>, maxVal: &Vec<N, D>) -> Vec<N, D>
-    where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
+pub fn float_bits_to_int(v: f32) -> i32 {
+    unsafe { mem::transmute(v) }
 }
 
-pub fn floatBitsToInt(v: f32) -> i32 {
-    unimplemented!()
-
-}
-
-pub fn floatBitsToInt2<D: Dimension>(v: Vec<f32, D>) -> Vec<i32, D>
+pub fn float_bits_to_int_vec<D: Dimension>(v: Vec<f32, D>) -> Vec<i32, D>
     where DefaultAllocator: Alloc<f32, D> {
-    unimplemented!()
-
+    v.map(|v| float_bits_to_int(v))
 }
 
-pub fn floatBitsToUint(v: f32) -> u32 {
-        unimplemented!()
-
+pub fn float_bits_to_uint(v: f32) -> u32 {
+    unsafe { mem::transmute(v) }
 }
 
-pub fn floatBitsToUint2<D: Dimension>(v: &Vec<f32, D>) -> Vec<u32, D>
+pub fn float_bits_to_uint_vec<D: Dimension>(v: &Vec<f32, D>) -> Vec<u32, D>
     where DefaultAllocator: Alloc<f32, D> {
-        unimplemented!()
-
+    v.map(|v| float_bits_to_uint(v))
 }
-pub fn floor<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<N, D>
+
+pub fn floor<N: Real, D: Dimension>(x: &Vec<N, D>) -> Vec<N, D>
     where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
-}
-pub fn fma<T>(a: T, b: T, c: T) -> T {
-    unimplemented!()
-
+    x.map(|x| x.floor())
 }
 
-pub fn fract<T>(x: T) -> T {
-    unimplemented!()
-
+// FIXME: should be implemented for Vec/Mat?
+pub fn fma<N: Number>(a: N, b: N, c: N) -> N {
+    // FIXME: use an actual FMA
+    a * b + c
 }
 
-pub fn fract2<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<N, D>
+pub fn fract<N: Real>(x: N) -> N {
+    x.fract()
+}
+
+pub fn fract2<N: Real, D: Dimension>(x: &Vec<N, D>) -> Vec<N, D>
     where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
+    x.map(|x| x.fract())
+}
+
+//// FIXME: should be implemented for Vec/Mat?
+///// Returns the (significant, exponent) of this float number.
+//pub fn frexp<N: Real>(x: N, exp: N) -> (N, N) {
+//    // FIXME: is there a better approach?
+//    let e = x.log2().ceil();
+//    (x * (-e).exp2(), e)
+//}
+
+pub fn int_bits_to_float(v: i32) -> f32 {
+    unsafe { mem::transmute(v) }
 
 }
 
-pub fn frexp<T, I>(x: T, exp: I) -> T {
-    unimplemented!()
-
-}
-
-pub fn intBitsToFloat<N: Scalar, D: Dimension>(v: i32) -> f32 {
-    unimplemented!()
-
-}
-
-pub fn intBitsToFloat2<D: Dimension>(v: &Vec<u32, D>) -> Vec<f32, D>
+pub fn int_bits_to_float_vec<D: Dimension>(v: &Vec<i32, D>) -> Vec<f32, D>
     where DefaultAllocator: Alloc<f32, D> {
-        unimplemented!()
-
+    v.map(|v| int_bits_to_float(v))
 }
 
-pub fn isinf<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<bool, D>
+//pub fn isinf<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<bool, D>
+//    where DefaultAllocator: Alloc<N, D> {
+//        unimplemented!()
+//
+//}
+//
+//pub fn isnan<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<bool, D>
+//    where DefaultAllocator: Alloc<N, D> {
+//        unimplemented!()
+//
+//}
+
+///// Returns the (significant, exponent) of this float number.
+//pub fn ldexp<N: Real>(x: N, exp: N) -> N {
+//    // FIXME: is there a better approach?
+//    x * (exp).exp2()
+//}
+
+pub fn max<N: Number>(x: N, y: N) -> N {
+    na::sup(&x, &y)
+}
+
+pub fn max2<N: Number, D: Dimension>(x: &Vec<N, D>, y: N) -> Vec<N, D>
     where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
+    x.map(|x| na::sup(&x, &y))
 }
 
-pub fn isnan<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<bool, D>
+pub fn max3<N: Number, D: Dimension>(x: &Vec<N, D>, y: &Vec<N, D>) -> Vec<N, D>
     where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
+    na::sup(x, y)
 }
 
-pub fn ldexp<T, I>(x: T, exp: I) -> T {
-    unimplemented!()
-
+pub fn min<N: Number>(x: N, y: N) -> N {
+    na::inf(&x, &y)
 }
 
-pub fn max<T>(x: T, y: T) -> T {
-    unimplemented!()
-
-}
-
-pub fn max2<N: Scalar, D: Dimension>(x: &Vec<N, D>,y: N) -> Vec<N, D>
+pub fn min2<N: Number, D: Dimension>(x: &Vec<N, D>,y: N) -> Vec<N, D>
     where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
+    x.map(|x| na::inf(&x, &y))
 }
-pub fn max3<N: Scalar, D: Dimension>(x: &Vec<N, D>, y: &Vec<N, D>) -> Vec<N, D>
+
+pub fn min3<N: Number, D: Dimension>(x: &Vec<N, D>, y: &Vec<N, D>) -> Vec<N, D>
     where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
-}
-pub fn min<T>(x: T, y: T) -> T {
-    unimplemented!()
-
+    na::inf(x, y)
 }
 
-pub fn min2<N: Scalar, D: Dimension>(x: &Vec<N, D>,y: N) -> Vec<N, D>
+pub fn mix<N: Number>(x: N, y: N, a: N) -> N {
+    x * (N::one() - a) + y * a
+}
+
+pub fn mod_<N: Number, D: Dimension>(x: &Vec<N, D>, y: &Vec<N, D>) -> Vec<N, D>
     where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
+    x.zip_map(y, |x, y| x % y)
 }
-pub fn min3<N: Scalar, D: Dimension>(x: &Vec<N, D>, y: &Vec<N, D>) -> Vec<N, D>
+
+pub fn modf<N: Number>(x: N, i: N) -> N {
+    x % i
+}
+
+pub fn round<N: Real, D: Dimension>(x: &Vec<N, D>) -> Vec<N, D>
     where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
-}
-pub fn mix<T>(x: T, y: T, a: T) -> T {
-    unimplemented!()
+    x.map(|x| x.round())
 
 }
 
-pub fn mod_<N: Scalar, D: Dimension>(x: &Vec<N, D>, y: &Vec<N, D>) -> Vec<N, D>
+//pub fn roundEven<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<N, D>
+//    where DefaultAllocator: Alloc<N, D> {
+//        unimplemented!()
+//}
+
+pub fn sign<N: Number, D: Dimension>(x: &Vec<N, D>) -> Vec<N, D>
     where DefaultAllocator: Alloc<N, D> {
-    unimplemented!()
-
-}
-pub fn modf<T>(x: T, i: &T) -> T {
-    unimplemented!()
-
+    x.map(|x| x.signum())
 }
 
-pub fn round<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<N, D>
+pub fn smoothstep<N: Number>(edge0: N, edge1: N, x: N) -> N {
+    let _3: N = FromPrimitive::from_f64(3.0).unwrap();
+    let _2: N = FromPrimitive::from_f64(2.0).unwrap();
+    let t = na::clamp((x - edge0) / (edge1 - edge0), N::zero(), N::one());
+    t * t * (_3 - t * _2)
+}
+
+pub fn step<N: Number>(edge: N, x: N) -> N {
+    if edge > x {
+        N::zero()
+    } else {
+        N::one()
+    }
+}
+
+pub fn step2<N: Number, D: Dimension>(edge: N, x: &Vec<N, D>) -> Vec<N, D>
     where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
+    x.map(|x| step(edge, x))
 }
-pub fn roundEven<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<N, D>
+
+pub fn step3<N: Number, D: Dimension>(edge: &Vec<N, D>, x: &Vec<N, D>) -> Vec<N, D>
     where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
+    edge.zip_map(x, |edge, x| step(edge, x))
 }
-pub fn sign<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<N, D>
+
+pub fn trunc<N: Real, D: Dimension>(x: &Vec<N, D>) -> Vec<N, D>
     where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
+    x.map(|x| x.trunc())
+}
+
+pub fn uint_bits_to_float(v: u32) -> f32 {
+    unsafe { mem::transmute(v) }
 
 }
 
-pub fn smoothstep<T>(edge0: T, edge1: T, x: T) -> T {
-    unimplemented!()
-
-}
-
-pub fn step<T>(edge: T, x: T) -> T {
-    unimplemented!()
-
-}
-
-pub fn step2<N: Scalar, D: Dimension>(edge: N, x: &Vec<N, D>) -> Vec<N, D>
-    where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
-}
-pub fn step3<N: Scalar, D: Dimension>(edge: &Vec<N, D>, x: &Vec<N, D>) -> Vec<N, D>
-    where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
-}
-pub fn trunc<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<N, D>
-    where DefaultAllocator: Alloc<N, D> {
-        unimplemented!()
-
-}
-pub fn uintBitsToFloat(v: u32) -> f32 {
-    unimplemented!()
-
-}
-pub fn uintBitsToFloat2<D: Dimension>(v: &Vec<u32, D>) -> Vec<f32, D>
+pub fn uint_bits_to_float_vec<D: Dimension>(v: &Vec<u32, D>) -> Vec<f32, D>
     where DefaultAllocator: Alloc<f32, D> {
-    unimplemented!()
+    v.map(|v| uint_bits_to_float(v))
 }

nalgebra-glm/src/ext_matrix_projection.rs

@@ -1,32 +1,67 @@
-use na::{Real, U2, U3, U4};
+use na::{self, Real, U2, U3, U4, Vector3, Vector4, Matrix4};
 
 use aliases::{Mat, Vec};
 
 
-pub fn pickMatrix<N: Real>(center: &Vec<N, U2>, delta: &Vec<N, U2>, viewport: &Vec<N, U4>) -> Mat<N, U4, U4> {
-    unimplemented!()
+pub fn pick_matrix<N: Real>(center: &Vec<N, U2>, delta: &Vec<N, U2>, viewport: &Vec<N, U4>) -> Mat<N, U4, U4> {
+    let shift = Vector3::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,
+        N::zero()
+    );
+
+    let result = Matrix4::new_translation(&shift);
+    result.prepend_nonuniform_scaling(&Vector3::new(viewport.z / delta.x, viewport.w / delta.y, N::one()))
 }
 
 pub fn project<N: Real>(obj: &Vec<N, U3>, model: &Mat<N, U4, U4>, proj: &Mat<N, U4, U4>, viewport: Vec<N, U4>) -> Vec<N, U3> {
-    unimplemented!()
+    project_no(obj, model, proj, viewport)
 }
 
-pub fn projectNO<N: Real>(obj: &Vec<N, U3>, model: &Mat<N, U4, U4>, proj: &Mat<N, U4, U4>, viewport: Vec<N, U4>) -> Vec<N, U3> {
-    unimplemented!()
+pub fn project_no<N: Real>(obj: &Vec<N, U3>, model: &Mat<N, U4, U4>, proj: &Mat<N, U4, U4>, viewport: Vec<N, U4>) -> Vec<N, U3> {
+    let proj = project_zo(obj, model, proj, viewport);
+    Vector3::new(proj.x, proj.y, proj.z * na::convert(0.5) + na::convert(0.5))
 }
 
-pub fn projectZO<N: Real>(obj: &Vec<N, U3>, model: &Mat<N, U4, U4>, proj: &Mat<N, U4, U4>, viewport: Vec<N, U4>) -> Vec<N, U3> {
-    unimplemented!()
+pub fn project_zo<N: Real>(obj: &Vec<N, U3>, model: &Mat<N, U4, U4>, proj: &Mat<N, U4, U4>, viewport: Vec<N, U4>) -> Vec<N, U3> {
+    let mut normalized = proj * model * Vector4::new(obj.x, obj.y, obj.z, N::one());
+    let scale = N::one() / normalized.w;
+
+    Vector3::new(
+        viewport.x + (viewport.z * (normalized.x * scale + N::one()) * na::convert(0.5)),
+        viewport.y + (viewport.w * (normalized.y * scale + N::one()) * na::convert(0.5)),
+        normalized.z * scale,
+    )
 }
 
-pub fn unProject<N: Real>(win: &Vec<N, U3>, model: &Mat<N, U4, U4>, proj: &Mat<N, U4, U4>, viewport: Vec<N, U4>) -> Vec<N, U3> {
-    unimplemented!()
+pub fn unproject<N: Real>(win: &Vec<N, U3>, model: &Mat<N, U4, U4>, proj: &Mat<N, U4, U4>, viewport: Vec<N, U4>) -> Vec<N, U3> {
+    unproject_no(win, model, proj, viewport)
 }
 
-pub fn unProjectNO<N: Real>(win: &Vec<N, U3>, model: &Mat<N, U4, U4>, proj: &Mat<N, U4, U4>, viewport: Vec<N, U4>) -> Vec<N, U3> {
-    unimplemented!()
+pub fn unproject_no<N: Real>(win: &Vec<N, U3>, model: &Mat<N, U4, U4>, proj: &Mat<N, U4, U4>, viewport: Vec<N, U4>) -> Vec<N, U3> {
+    let _2: N = na::convert(2.0);
+    let transform = (proj * model).try_inverse().unwrap_or(Matrix4::zeros());
+    let pt = Vector4::new(
+        _2 * (win.x - viewport.x) / viewport.z - N::one(),
+        _2 * (win.y - viewport.y) / viewport.w - N::one(),
+        _2 * win.z - N::one(),
+        N::one(),
+    );
+
+    let result = transform * pt;
+    result.fixed_rows::<U3>(0) / result.w
 }
 
-pub fn unProjectZO<N: Real>(win: &Vec<N, U3>, model: &Mat<N, U4, U4>, proj: &Mat<N, U4, U4>, viewport: Vec<N, U4>) -> Vec<N, U3> {
-    unimplemented!()
+pub fn unproject_zo<N: Real>(win: &Vec<N, U3>, model: &Mat<N, U4, U4>, proj: &Mat<N, U4, U4>, viewport: Vec<N, U4>) -> Vec<N, U3> {
+    let _2: N = na::convert(2.0);
+    let transform = (proj * model).try_inverse().unwrap_or(Matrix4::zeros());
+    let pt = Vector4::new(
+        _2 * (win.x - viewport.x) / viewport.z - N::one(),
+        _2 * (win.y - viewport.y) / viewport.w - N::one(),
+        win.z,
+        N::one(),
+    );
+
+    let result = transform * pt;
+    result.fixed_rows::<U3>(0) / result.w
 }

nalgebra-glm/src/ext_matrix_transform.rs

@@ -26,9 +26,9 @@ pub fn rotate<N: Real>(m: &Mat<N, U4, U4>, angle: N, axis: &Vec<N, U3>) -> Mat<N
 }
 
 pub fn scale<N: Number>(m: &Mat<N, U4, U4>, v: &Vec<N, U3>) -> Mat<N, U4, U4> {
-    m.append_nonuniform_scaling(v)
+    m.prepend_nonuniform_scaling(v)
 }
 
 pub fn translate<N: Number>(m: &Mat<N, U4, U4>, v: &Vec<N, U3>) -> Mat<N, U4, U4> {
-    m.append_translation(v)
+    m.prepend_translation(v)
 }

nalgebra-glm/src/ext_scalar_common.rs

@@ -1,41 +1,19 @@
-use na::Scalar;
+use na;
 
-pub fn fmax<N: Scalar>(a: N, b: N) -> N {
-    unimplemented!()
+use traits::Number;
+
+pub fn max3<N: Number>(a: N, b: N, c: N) -> N {
+    na::sup(&na::sup(&a, &b), &c)
 }
 
-pub fn fmax3<N: Scalar>(a: N, b: N, C: N) -> N {
-    unimplemented!()
+pub fn max4<N: Number>(a: N, b: N, c: N, d: N) -> N {
+    na::sup(&na::sup(&a, &b), &na::sup(&c, &d))
 }
 
-pub fn fmax4<N: Scalar>(a: N, b: N, C: N, D: N) -> N {
-    unimplemented!()
+pub fn min3<N: Number>(a: N, b: N, c: N) -> N {
+    na::inf(&na::inf(&a, &b), &c)
 }
 
-pub fn fmin<N: Scalar>(a: N, b: N) -> N {
-    unimplemented!()
-}
-
-pub fn fmin3<N: Scalar>(a: N, b: N, c: N) -> N {
-    unimplemented!()
-}
-
-pub fn fmin4<N: Scalar>(a: N, b: N, c: N, d: N) -> N {
-    unimplemented!()
-}
-
-pub fn max3<N: Scalar>(a: N, b: N, c: N) -> N {
-    unimplemented!()
-}
-
-pub fn max4<N: Scalar>(a: N, b: N, c: N, d: N) -> N {
-    unimplemented!()
-}
-
-pub fn min3<N: Scalar>(a: N, b: N, c: N) -> N {
-    unimplemented!()
-}
-
-pub fn min4<N: Scalar>(a: N, b: N, c: N, d: N) -> N {
-    unimplemented!()
+pub fn min4<N: Number>(a: N, b: N, c: N, d: N) -> N {
+    na::inf(&na::inf(&a, &b), &na::inf(&c, &d))
 }

nalgebra-glm/src/gtc_integer.rs

@@ -1,18 +1,18 @@
-use na::{Scalar, DefaultAllocator};
+//use na::{Scalar, DefaultAllocator};
+//
+//use traits::{Alloc, Dimension};
+//use aliases::Vec;
 
-use traits::{Alloc, Dimension};
-use aliases::Vec;
-
-pub fn iround<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<i64, D>
-    where DefaultAllocator: Alloc<N, D> {
-    unimplemented!()
-}
-
-pub fn log2<I>(x: I) -> I {
-    unimplemented!()
-}
-
-pub fn uround<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<u64, D>
-    where DefaultAllocator: Alloc<N, D> {
-    unimplemented!()
-}
+//pub fn iround<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<i32, D>
+//    where DefaultAllocator: Alloc<N, D> {
+//    x.map(|x| x.round())
+//}
+//
+//pub fn log2<I>(x: I) -> I {
+//    unimplemented!()
+//}
+//
+//pub fn uround<N: Scalar, D: Dimension>(x: &Vec<N, D>) -> Vec<u32, D>
+//    where DefaultAllocator: Alloc<N, D> {
+//    unimplemented!()
+//}

nalgebra-glm/src/gtx_component_wise.rs

@@ -0,0 +1,28 @@
+use na::{self, Scalar, Real, DefaultAllocator};
+
+use traits::{Number, Alloc, Dimension};
+use aliases::Mat;
+
+
+pub fn comp_add<N: Number, R: Dimension, C: Dimension>(m: &Mat<N, R, C>) -> N
+    where DefaultAllocator: Alloc<N, R, C> {
+    m.iter().fold(N::zero(), |x, y| x + *y)
+}
+
+pub fn comp_max<N: Number, R: Dimension, C: Dimension>(m: &Mat<N, R, C>) -> N
+    where DefaultAllocator: Alloc<N, R, C> {
+    m.iter().fold(N::min_value(), |x, y| na::sup(&x, y))
+}
+
+pub fn comp_min<N: Number, R: Dimension, C: Dimension>(m: &Mat<N, R, C>) -> N
+    where DefaultAllocator: Alloc<N, R, C> {
+    m.iter().fold(N::max_value(), |x, y| na::inf(&x, y))
+}
+
+pub fn comp_mul<N: Number, R: Dimension, C: Dimension>(m: &Mat<N, R, C>) -> N
+    where DefaultAllocator: Alloc<N, R, C> {
+    m.iter().fold(N::one(), |x, y| x * *y)
+}
+
+//pub fn vec< L, floatType, Q > compNormalize (vec< L, T, Q > const &v)
+//pub fn vec< L, T, Q > compScale (vec< L, floatType, Q > const &v)

nalgebra-glm/src/gtx_euler_angles.rs

@@ -0,0 +1,41 @@
+pub fn mat< 4, 4, T, defaultp > 	derivedEulerAngleX (T const &angleX, T const &angularVelocityX)
+pub fn mat< 4, 4, T, defaultp > 	derivedEulerAngleY (T const &angleY, T const &angularVelocityY)
+pub fn mat< 4, 4, T, defaultp > 	derivedEulerAngleZ (T const &angleZ, T const &angularVelocityZ)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleX (T const &angleX)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleXY (T const &angleX, T const &angleY)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleXYX (T const &t1, T const &t2, T const &t3)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleXYZ (T const &t1, T const &t2, T const &t3)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleXZ (T const &angleX, T const &angleZ)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleXZX (T const &t1, T const &t2, T const &t3)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleXZY (T const &t1, T const &t2, T const &t3)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleY (T const &angleY)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleYX (T const &angleY, T const &angleX)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleYXY (T const &t1, T const &t2, T const &t3)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleYXZ (T const &yaw, T const &pitch, T const &roll)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleYZ (T const &angleY, T const &angleZ)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleYZX (T const &t1, T const &t2, T const &t3)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleYZY (T const &t1, T const &t2, T const &t3)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleZ (T const &angleZ)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleZX (T const &angle, T const &angleX)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleZXY (T const &t1, T const &t2, T const &t3)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleZXZ (T const &t1, T const &t2, T const &t3)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleZY (T const &angleZ, T const &angleY)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleZYX (T const &t1, T const &t2, T const &t3)
+pub fn mat< 4, 4, T, defaultp > 	eulerAngleZYZ (T const &t1, T const &t2, T const &t3)
+pub fn void 	extractEulerAngleXYX (mat< 4, 4, T, defaultp > const &M, T &t1, T &t2, T &t3)
+pub fn void 	extractEulerAngleXYZ (mat< 4, 4, T, defaultp > const &M, T &t1, T &t2, T &t3)
+pub fn void 	extractEulerAngleXZX (mat< 4, 4, T, defaultp > const &M, T &t1, T &t2, T &t3)
+pub fn void 	extractEulerAngleXZY (mat< 4, 4, T, defaultp > const &M, T &t1, T &t2, T &t3)
+pub fn void 	extractEulerAngleYXY (mat< 4, 4, T, defaultp > const &M, T &t1, T &t2, T &t3)
+pub fn void 	extractEulerAngleYXZ (mat< 4, 4, T, defaultp > const &M, T &t1, T &t2, T &t3)
+pub fn void 	extractEulerAngleYZX (mat< 4, 4, T, defaultp > const &M, T &t1, T &t2, T &t3)
+pub fn void 	extractEulerAngleYZY (mat< 4, 4, T, defaultp > const &M, T &t1, T &t2, T &t3)
+pub fn void 	extractEulerAngleZXY (mat< 4, 4, T, defaultp > const &M, T &t1, T &t2, T &t3)
+pub fn void 	extractEulerAngleZXZ (mat< 4, 4, T, defaultp > const &M, T &t1, T &t2, T &t3)
+pub fn void 	extractEulerAngleZYX (mat< 4, 4, T, defaultp > const &M, T &t1, T &t2, T &t3)
+pub fn void 	extractEulerAngleZYZ (mat< 4, 4, T, defaultp > const &M, T &t1, T &t2, T &t3)
+pub fn mat< 2, 2, T, defaultp > 	orientate2 (T const &angle)
+pub fn mat< 3, 3, T, defaultp > 	orientate3 (T const &angle)
+pub fn mat< 3, 3, T, Q > 	orientate3 (vec< 3, T, Q > const &angles)
+pub fn mat< 4, 4, T, Q > 	orientate4 (vec< 3, T, Q > const &angles)
+pub fn mat< 4, 4, T, defaultp > 	yawPitchRoll (T const &yaw, T const &pitch, T const &roll)

nalgebra-glm/src/gtx_exterior_product.rs

@@ -0,0 +1,8 @@
+use na::U2;
+
+use traits::Number;
+use aliases::Vec;
+
+pub fn cross<N: Number>(v: &Vec<N, U2>, u: &Vec<N, U2>) -> N {
+    v.perp(u)
+}

nalgebra-glm/src/gtx_handed_coordinate_space.rs

@@ -0,0 +1,12 @@
+use na::U3;
+
+use traits::Number;
+use aliases::Vec;
+
+pub fn left_handed<N: Number>(a: &Vec<N, U3>, b: &Vec<N, U3>, c: &Vec<N, U3>) -> bool {
+    a.cross(b).dot(c) < N::zero()
+}
+
+pub fn right_handed<N: Number>(a: &Vec<N, U3>, b: &Vec<N, U3>, c: &Vec<N, U3>) -> bool {
+    a.cross(b).dot(c) > N::zero()
+}

nalgebra-glm/src/gtx_matrix_cross_product.rs

@@ -0,0 +1,19 @@
+use na::{self, Real, U3, U4, Matrix4};
+
+use aliases::{Vec, Mat};
+
+pub fn matrix_cross3<N: Real>(x: &Vec<N, U3>) -> Mat<N, U3, U3> {
+    x.cross_matrix()
+}
+
+pub fn matrix_cross4<N: Real>(x: &Vec<N, U3>) -> Mat<N, U4, U4> {
+    let m = x.cross_matrix();
+
+    // FIXME: use a dedicated constructor from Matrix3 to Matrix4.
+    Matrix4::new(
+        m.m11, m.m12, m.m13, N::zero(),
+        m.m21, m.m22, m.m23, N::zero(),
+        m.m31, m.m32, m.m33, N::zero(),
+        N::zero(), N::zero(), N::zero(), N::one(),
+    )
+}

nalgebra-glm/src/gtx_matrix_operation.rs

@@ -0,0 +1,42 @@
+use na::{Matrix2, Matrix2x3, Matrix2x4, Matrix3, Matrix3x2, Matrix3x4, Matrix4, Matrix4x2, Matrix4x3,
+         U2, U3, U4};
+
+use traits::Number;
+use aliases::{Vec, Mat};
+
+
+pub fn diagonal2x2<N: Number>(v: &Vec<N, U2>) -> Mat<N, U2, U2> {
+    Matrix2::from_diagonal(v)
+}
+
+pub fn diagonal2x3<N: Number>(v: &Vec<N, U2>) -> Mat<N, U2, U3> {
+    Matrix2x3::from_partial_diagonal(v.as_slice())
+}
+
+pub fn diagonal2x4<N: Number>(v: &Vec<N, U2>) -> Mat<N, U2, U4> {
+    Matrix2x4::from_partial_diagonal(v.as_slice())
+}
+
+pub fn diagonal3x2<N: Number>(v: &Vec<N, U3>) -> Mat<N, U3, U2> {
+    Matrix3x2::from_partial_diagonal(v.as_slice())
+}
+
+pub fn diagonal3x3<N: Number>(v: &Vec<N, U3>) -> Mat<N, U3, U3> {
+    Matrix3::from_diagonal(v)
+}
+
+pub fn diagonal3x4<N: Number>(v: &Vec<N, U3>) -> Mat<N, U3, U4> {
+    Matrix3x4::from_partial_diagonal(v.as_slice())
+}
+
+pub fn diagonal4x2<N: Number>(v: &Vec<N, U4>) -> Mat<N, U4, U2> {
+    Matrix4x2::from_partial_diagonal(v.as_slice())
+}
+
+pub fn diagonal4x3<N: Number>(v: &Vec<N, U4>) -> Mat<N, U4, U3> {
+    Matrix4x3::from_partial_diagonal(v.as_slice())
+}
+
+pub fn diagonal4x4<N: Number>(v: &Vec<N, U4>) -> Mat<N, U4, U4> {
+    Matrix4::from_diagonal(v)
+}

nalgebra-glm/src/gtx_norm.rs

@@ -0,0 +1,44 @@
+use na::{Real, DefaultAllocator};
+
+use traits::{Alloc, Dimension};
+use aliases::Vec;
+
+pub fn distance2<N: Real, D: Dimension>(p0: &Vec<N, D>, p1: &Vec<N, D>) -> N
+    where DefaultAllocator: Alloc<N, D> {
+    (p1 - p0).norm_squared()
+}
+
+pub fn l1_distance<N: Real, D: Dimension>(x: &Vec<N, D>, y: &Vec<N, D>) -> N
+    where DefaultAllocator: Alloc<N, D> {
+    l1_norm(&(x - y))
+}
+
+pub fn l1_norm<N: Real, D: Dimension>(v: &Vec<N, D>) -> N
+    where DefaultAllocator: Alloc<N, D> {
+    ::comp_add(&v.abs())
+}
+
+pub fn l2_distance<N: Real, D: Dimension>(x: &Vec<N, D>, y: &Vec<N, D>) -> N
+    where DefaultAllocator: Alloc<N, D> {
+    l2_norm(&(y - x))
+}
+
+pub fn l2_norm<N: Real, D: Dimension>(x: &Vec<N, D>) -> N
+    where DefaultAllocator: Alloc<N, D> {
+    x.norm()
+}
+
+pub fn length2<N: Real, D: Dimension>(x: &Vec<N, D>) -> N
+    where DefaultAllocator: Alloc<N, D> {
+    x.norm_squared()
+}
+
+//pub fn lxNorm<N: Real, D: Dimension>(x: &Vec<N, D>, y: &Vec<N, D>, unsigned int Depth) -> N
+//    where DefaultAllocator: Alloc<N, D> {
+//    unimplemented!()
+//}
+//
+//pub fn lxNorm<N: Real, D: Dimension>(x: &Vec<N, D>, unsigned int Depth) -> N
+//    where DefaultAllocator: Alloc<N, D> {
+//    unimplemented!()
+//}

nalgebra-glm/src/gtx_normal.rs

@@ -0,0 +1,7 @@
+use na::{Real, U3};
+
+use aliases::Vec;
+
+pub fn triangleNormal<N: Real>(p1: &Vec<N, U3>, p2: &Vec<N, U3>, p3: &Vec<N, U3>) -> Vec<N, U3> {
+    (p2 - p1).cross(&(p3 - p1)).normalize()
+}

nalgebra-glm/src/gtx_normalize_dot.rs

@@ -0,0 +1,17 @@
+use na::{Real, DefaultAllocator};
+
+use traits::{Dimension, Alloc};
+use aliases::Vec;
+
+
+pub fn fastNormalizeDot<N: Real, D: Dimension>(x: &Vec<N, D>, y: &Vec<N, D>) -> N
+    where DefaultAllocator: Alloc<N, D> {
+    // XXX: improve those.
+    x.normalize().dot(&y.normalize())
+}
+
+pub fn normalizeDot<N: Real, D: Dimension>(x: &Vec<N, D>, y: &Vec<N, D>) -> N
+    where DefaultAllocator: Alloc<N, D> {
+    // XXX: improve those.
+    x.normalize().dot(&y.normalize())
+}

nalgebra-glm/src/gtx_quaternion.rs

@@ -0,0 +1,16 @@
+pub fn vec< 3, T, Q > 	cross (qua< T, Q > const &q, vec< 3, T, Q > const &v)
+pub fn vec< 3, T, Q > 	cross (vec< 3, T, Q > const &v, qua< T, Q > const &q)
+pub fn T 	extractRealComponent (qua< T, Q > const &q)
+pub fn qua< T, Q > 	fastMix (qua< T, Q > const &x, qua< T, Q > const &y, T const &a)
+pub fn qua< T, Q > 	intermediate (qua< T, Q > const &prev, qua< T, Q > const &curr, qua< T, Q > const &next)
+pub fn T 	length2 (qua< T, Q > const &q)
+pub fn qua< T, Q > 	quat_identity ()
+pub fn vec< 3, T, Q > 	rotate (qua< T, Q > const &q, vec< 3, T, Q > const &v)
+pub fn vec< 4, T, Q > 	rotate (qua< T, Q > const &q, vec< 4, T, Q > const &v)
+pub fn qua< T, Q > 	rotation (vec< 3, T, Q > const &orig, vec< 3, T, Q > const &dest)
+pub fn qua< T, Q > 	shortMix (qua< T, Q > const &x, qua< T, Q > const &y, T const &a)
+pub fn qua< T, Q > 	squad (qua< T, Q > const &q1, qua< T, Q > const &q2, qua< T, Q > const &s1, qua< T, Q > const &s2, T const &h)
+pub fn mat< 3, 3, T, Q > 	toMat3 (qua< T, Q > const &x)
+pub fn mat< 4, 4, T, Q > 	toMat4 (qua< T, Q > const &x)
+pub fn qua< T, Q > 	toQuat (mat< 3, 3, T, Q > const &x)
+pub fn qua< T, Q > 	toQuat (mat< 4, 4, T, Q > const &x)

nalgebra-glm/src/gtx_rotate_normalized_axis.rs

@@ -0,0 +1,11 @@
+use na::{Real, Rotation3, UnitQuaternion, Unit, U3, U4};
+
+use aliases::{Vec, Mat, Qua};
+
+pub fn rotateNormalizedAxis<N: Real>(m: &Mat<N, U4, U4>, angle: N, axis: &Vec<N, U3>) -> Mat<N, U4, U4> {
+    m * Rotation3::from_axis_angle(&Unit::new_unchecked(*axis), angle).to_homogeneous()
+}
+
+pub fn rotateNormalizedAxis2<N: Real>(q: &Qua<N>, angle: N, axis: &Vec<N, U3>) -> Qua<N> {
+    q * UnitQuaternion::from_axis_angle(&Unit::new_unchecked(*axis), angle).unwrap()
+}

nalgebra-glm/src/gtx_rotate_vector.rs

@@ -0,0 +1,45 @@
+use na::{Real, U2, U3, U4};
+
+pub fn orientation<N: Real>(Normal: &Vec<N, U3>, Up: &Vec<N, U3>) -> Mat<N, U4, U4> {
+    unimplemented!()
+}
+
+pub fn rotate2<N: Real>(v: &Vec<N, U2>, angle: N) -> Vec<N, U2> {
+    unimplemented!()
+}
+
+pub fn rotate<N: Real>(v: &Vec<N, U3>, angle: N, normal: &Vec<N, U3>) -> Vec<N, U3> {
+    unimplemented!()
+}
+
+pub fn rotate4<N: Real>(v: &Vec<N, U4>, angle: N, normal: &Vec<N, U3>) -> Vec<N, U4> {
+    unimplemented!()
+}
+
+pub fn rotateX<N: Real>(v: &Vec<N, U3>, angle: N) -> Vec<N, U3> {
+    unimplemented!()
+}
+
+pub fn rotateX4<N: Real>(v: &Vec<N, U4>, angle: N) -> Vec<N, U4> {
+    unimplemented!()
+}
+
+pub fn rotateY<N: Real>(v: &Vec<N, U3>, angle: N) -> Vec<N, U3> {
+    unimplemented!()
+}
+
+pub fn rotateY4<N: Real>(v: &Vec<N, U4>, angle: N) -> Vec<N, U4> {
+    unimplemented!()
+}
+
+pub fn rotateZ<N: Real>(v: &Vec<N, U3>, angle: N) -> Vec<N, U3> {
+    unimplemented!()
+}
+
+pub fn rotateZ4<N: Real>(v: &Vec<N, U4>, angle: N) -> Vec<N, U4> {
+    unimplemented!()
+}
+
+pub fn slerp<N: Real>(x: &Vec<N, U3>, y: &Vec<N, U3>, a: N) -> Vec<N, U3> {
+    unimplemented!()
+}

nalgebra-glm/src/gtx_transform.rs

@@ -0,0 +1,17 @@
+use na::{Real, Unit, Rotation3, Matrix4, U3, U4};
+
+use traits::Number;
+use aliases::{Vec, Mat};
+
+
+pub fn rotate<N: Real>(angle: N, v: &Vec<N, U3>) -> Mat<N, U4, U4> {
+    Rotation3::from_axis_angle(&Unit::new_normalize(*v), angle).to_homogeneous()
+}
+
+pub fn scale<N: Number>(v: &Vec<N, U3>) -> Mat<N, U4, U4> {
+    Matrix4::new_nonuniform_scaling(v)
+}
+
+pub fn translate<N: Number>(v: &Vec<N, U3>) -> Mat<N, U4, U4> {
+    Matrix4::new_translation(v)
+}

nalgebra-glm/src/gtx_transform2.rs

@@ -0,0 +1,9 @@
+pub fn mat< 3, 3, T, Q > 	proj2D (mat< 3, 3, T, Q > const &m, vec< 3, T, Q > const &normal)
+pub fn mat< 4, 4, T, Q > 	proj3D (mat< 4, 4, T, Q > const &m, vec< 3, T, Q > const &normal)
+pub fn mat< 4, 4, T, Q > 	scaleBias (T scale, T bias)
+pub fn mat< 4, 4, T, Q > 	scaleBias (mat< 4, 4, T, Q > const &m, T scale, T bias)
+pub fn mat< 3, 3, T, Q > 	shearX2D (mat< 3, 3, T, Q > const &m, T y)
+pub fn mat< 4, 4, T, Q > 	shearX3D (mat< 4, 4, T, Q > const &m, T y, T z)
+pub fn mat< 3, 3, T, Q > 	shearY2D (mat< 3, 3, T, Q > const &m, T x)
+pub fn mat< 4, 4, T, Q > 	shearY3D (mat< 4, 4, T, Q > const &m, T x, T z)
+pub fn mat< 4, 4, T, Q > 	shearZ3D (mat< 4, 4, T, Q > const &m, T x, T y)

nalgebra-glm/src/gtx_transform2d.rs

@@ -0,0 +1,5 @@
+pub fn mat< 3, 3, T, Q > 	rotate (mat< 3, 3, T, Q > const &m, T angle)
+pub fn mat< 3, 3, T, Q > 	scale (mat< 3, 3, T, Q > const &m, vec< 2, T, Q > const &v)
+pub fn mat< 3, 3, T, Q > 	shearX (mat< 3, 3, T, Q > const &m, T y)
+pub fn mat< 3, 3, T, Q > 	shearY (mat< 3, 3, T, Q > const &m, T x)
+pub fn mat< 3, 3, T, Q > 	translate (mat< 3, 3, T, Q > const &m, vec< 2, T, Q > const &v)

nalgebra-glm/src/gtx_vector_angle.rs

@@ -0,0 +1,3 @@
+pub fn T 	angle (vec< L, T, Q > const &x, vec< L, T, Q > const &y)
+pub fn T 	orientedAngle (vec< 2, T, Q > const &x, vec< 2, T, Q > const &y)
+pub fn T 	orientedAngle (vec< 3, T, Q > const &x, vec< 3, T, Q > const &y, vec< 3, T, Q > const &ref)

nalgebra-glm/src/gtx_vector_query.rs

@@ -0,0 +1,37 @@
+use na::{Real, DefaultAllocator, U2, U3};
+
+use traits::{Number, Dimension, Alloc};
+use aliases::Vec;
+
+pub fn are_collinear<N: Number>(v0: &Vec<N, U3>, v1: &Vec<N, U3>, epsilon: N) -> bool {
+    is_null(&v0.cross(v1), epsilon)
+}
+
+pub fn are_collinear2<N: Number>(v0: &Vec<N, U2>, v1: &Vec<N, U2>, epsilon: N) -> bool {
+    abs_diff_eq!(v0.perp(v1), N::zero(), epsilon = epsilon)
+}
+
+pub fn are_orthogonal<N: Number, D: Dimension>(v0: &Vec<N, D>, v1: &Vec<N, D>, epsilon: N) -> bool
+    where DefaultAllocator: Alloc<N, D> {
+    abs_diff_eq!(v0.dot(v1), N::zero(), epsilon = epsilon)
+}
+
+pub fn are_orthonormal<N: Number, D: Dimension>(v0: &Vec<N, D>, v1: &Vec<N, D>, epsilon: N) -> bool
+    where DefaultAllocator: Alloc<N, D> {
+    unimplemented!()
+}
+
+pub fn is_comp_null<N: Number, D: Dimension>(v: &Vec<N, D>, epsilon: N) -> Vec<bool, D>
+    where DefaultAllocator: Alloc<N, D> {
+    v.map(|x| abs_diff_eq!(x, N::zero(), epsilon = epsilon))
+}
+
+pub fn is_normalized<N: Real, D: Dimension>(v: &Vec<N, D>, epsilon: N) -> bool
+    where DefaultAllocator: Alloc<N, D> {
+    abs_diff_eq!(v.norm_squared(), N::one(), epsilon = epsilon * epsilon)
+}
+
+pub fn is_null<N: Number, D: Dimension>(v: &Vec<N, D>, epsilon: N) -> bool
+    where DefaultAllocator: Alloc<N, D> {
+    abs_diff_eq!(*v, Vec::<N, D>::zeros(), epsilon = epsilon)
+}

nalgebra-glm/src/lib.rs

@@ -15,6 +15,8 @@ pub use exponential::*;
 
 pub use ext_vector_relational::*;
 
+pub use gtx_component_wise::*;
+
 mod aliases;
 pub mod constructors;
 mod common;
@@ -39,15 +41,33 @@ pub mod ext_scalar_common;
 pub mod ext_scalar_constants;
 pub mod ext_vector_common;
 pub mod ext_vector_relational;
-pub mod gtc_bitfield;
+//pub mod gtc_bitfield;
 pub mod gtc_constants;
 pub mod gtc_epsilon;
-pub mod gtc_integer;
+//pub mod gtc_integer;
 pub mod gtc_matrix_access;
 pub mod gtc_matrix_inverse;
-pub mod gtc_packing;
+//pub mod gtc_packing;
 pub mod gtc_quaternion;
-pub mod gtc_reciprocal;
-pub mod gtc_round;
+//pub mod gtc_reciprocal;
+//pub mod gtc_round;
 pub mod gtc_type_ptr;
-pub mod gtc_ulp;
+//pub mod gtc_ulp;
+
+pub mod gtx_component_wise;
+//pub mod gtx_euler_angles;
+pub mod gtx_exterior_product;
+pub mod gtx_handed_coordinate_space;
+pub mod gtx_matrix_cross_product;
+pub mod gtx_matrix_operation;
+pub mod gtx_norm;
+pub mod gtx_normal;
+pub mod gtx_normalize_dot;
+//pub mod gtx_quaternion;
+pub mod gtx_rotate_normalized_axis;
+//pub mod gtx_rotate_vector;
+pub mod gtx_transform;
+//pub mod gtx_transform2;
+//pub mod gtx_transform2d;
+//pub mod gtx_vector_angle;
+pub mod gtx_vector_query;

nalgebra-glm/src/traits.rs

@@ -1,5 +1,5 @@
 use std::cmp::{PartialOrd, PartialEq};
-use num::Signed;
+use num::{Signed, FromPrimitive, Bounded};
 use approx::AbsDiffEq;
 
 use alga::general::{Ring, Lattice};
@@ -10,10 +10,10 @@ pub trait Dimension: DimName + DimMin<Self, Output = Self> {}
 impl<D: DimName + DimMin<D, Output = Self>> Dimension for D {}
 
 
-pub trait Number: Scalar + Ring + Lattice + AbsDiffEq<Epsilon = Self> + Signed {
+pub trait Number: Scalar + Ring + Lattice + AbsDiffEq<Epsilon = Self> + Signed + FromPrimitive + Bounded {
 }
 
-impl<T: Scalar + Ring + Lattice + AbsDiffEq<Epsilon = Self> + Signed> Number for T {
+impl<T: Scalar + Ring + Lattice + AbsDiffEq<Epsilon = Self> + Signed + FromPrimitive + Bounded> Number for T {
 }
 
 #[doc(hidden)]