Implement impl-nalgebra feature.

Cargo.toml

@@ -21,14 +21,15 @@ maintenance = { status = "actively-developed" }
 
 [features]
 default = ["std"]
-serialization = ["serde", "serde_derive"]
-std = ["num-traits/std"]
 impl-cgmath = ["cgmath"]
-impl-nalgebra = ["nalgebra"]
+impl-nalgebra = ["alga", "nalgebra", "num-traits"]
+serialization = ["serde", "serde_derive"]
+std = []
 
 [dependencies]
+alga = { version = "0.9", optional = true }
 cgmath = { version = "0.17", optional = true }
 nalgebra = { version = ">=0.14, <0.19", optional = true }
-num-traits = { version = "0.2", default-features = false }
+num-traits = { version = "0.2", optional = true }
 serde =  { version = "1", optional = true }
 serde_derive = { version = "1", optional = true }

src/interpolate.rs

@@ -1,7 +1,11 @@
-#[cfg(feature = "std")] use std::ops::{Div, Mul};
+#[cfg(feature = "std")] use std::f32;
-#[cfg(not(feature = "std"))] use core::ops::{Div, Mul};
+#[cfg(not(feature = "std"))] use core::f32;
-
+#[cfg(not(feature = "std"))] use core::intrinsics::cosf32;
-use num_traits::Float;
+#[cfg(feature = "std")] use std::f64;
+#[cfg(not(feature = "std"))] use core::f64;
+#[cfg(not(feature = "std"))] use core::intrinsics::cosf64;
+#[cfg(feature = "std")] use std::ops::{Add, Mul, Sub};
+#[cfg(not(feature = "std"))] use core::ops::{Add, Mul, Sub};
 
 /// Keys that can be interpolated in between. Implementing this trait is required to perform
 /// sampling on splines.
@@ -20,15 +24,147 @@ pub trait Interpolate<T>: Sized + Copy {
   }
 }
 
+/// A trait for anything that supports additions, subtraction, multiplication and division.
+pub trait Additive:
+  Copy +
+  PartialEq +
+  PartialOrd +
+  Add<Self, Output = Self> +
+  Sub<Self, Output = Self> {
+}
+
+impl<T> Additive for T
+where T: Copy +
+         PartialEq +
+         PartialOrd +
+         Add<Self, Output = Self> +
+         Sub<Self, Output = Self> {
+}
+
+/// Linear combination.
+pub trait Linear<T> {
+  /// Apply an outer multiplication law.
+  fn outer_mul(self, t: T) -> Self;
+
+  /// Apply an outer division law.
+  fn outer_div(self, t: T) -> Self;
+}
+
+macro_rules! impl_linear_simple {
+  ($t:ty) => {
+    impl Linear<$t> for $t {
+      fn outer_mul(self, t: $t) -> Self {
+        self * t
+      }
+
+      /// Apply an outer division law.
+      fn outer_div(self, t: $t) -> Self {
+        self / t
+      }
+    }
+  }
+}
+
+impl_linear_simple!(f32);
+impl_linear_simple!(f64);
+
+macro_rules! impl_linear_cast {
+  ($t:ty, $q:ty) => {
+    impl Linear<$t> for $q {
+      fn outer_mul(self, t: $t) -> Self {
+        self * t as $q
+      }
+
+      /// Apply an outer division law.
+      fn outer_div(self, t: $t) -> Self {
+        self / t as $q
+      }
+    }
+  }
+}
+
+impl_linear_cast!(f32, f64);
+impl_linear_cast!(f64, f32);
+
+/// Types with a neutral element for multiplication.
+pub trait One {
+  /// Return the neutral element for the multiplicative monoid.
+  fn one() -> Self;
+}
+
+macro_rules! impl_one_float {
+  ($t:ty) => {
+    impl One for $t {
+      #[inline(always)]
+      fn one() -> Self {
+        1.
+      }
+    }
+  }
+}
+
+impl_one_float!(f32);
+impl_one_float!(f64);
+
+/// Types with a sane definition of π and cosine.
+pub trait Trigo {
+  /// π.
+  fn pi() -> Self;
+
+  /// Cosine of the argument.
+  fn cos(self) -> Self;
+}
+
+impl Trigo for f32 {
+  #[inline(always)]
+  fn pi() -> Self {
+    f32::consts::PI
+  }
+
+  #[inline(always)]
+  fn cos(self) -> Self {
+    #[cfg(feature = "std")]
+    {
+      self.cos()
+    }
+
+    #[cfg(not(feature = "std"))]
+    {
+      unsafe { cosf32(self) }
+    }
+  }
+}
+
+impl Trigo for f64 {
+  #[inline(always)]
+  fn pi() -> Self {
+    f64::consts::PI
+  }
+
+  #[inline(always)]
+  fn cos(self) -> Self {
+    #[cfg(feature = "std")]
+    {
+      self.cos()
+    }
+
+    #[cfg(not(feature = "std"))]
+    {
+      unsafe { cosf64(self) }
+    }
+  }
+}
+
 // Default implementation of Interpolate::cubic_hermite.
 //
 // `V` is the value being interpolated. `T` is the sampling value (also sometimes called time).
 pub(crate) fn cubic_hermite_def<V, T>(x: (V, T), a: (V, T), b: (V, T), y: (V, T), t: T) -> V
-where V: Float + Mul<T, Output = V> + Div<T, Output = V>,
+where V: Additive + Linear<T>,
-      T: Float {
+      T: Additive + Mul<T, Output = T> + One {
   // some stupid generic constants, because Rust doesn’t have polymorphic literals…
-  let two_t = T::one() + T::one(); // lolololol
+  let one_t = T::one();
-  let three_t = two_t + T::one(); // megalol
+  let two_t = one_t + one_t; // lolololol
+  let three_t = two_t + one_t; // megalol
 
   // sampler stuff
   let t2 = t * t;
@@ -37,10 +173,10 @@ where V: Float + Mul<T, Output = V> + Div<T, Output = V>,
   let three_t2 = t2 * three_t;
 
   // tangents
-  let m0 = (b.0 - x.0) / (b.1 - x.1);
+  let m0 = (b.0 - x.0).outer_div(b.1 - x.1);
-  let m1 = (y.0 - a.0) / (y.1 - a.1);
+  let m1 = (y.0 - a.0).outer_div(y.1 - a.1);
 
-  a.0 * (two_t3 - three_t2 + T::one()) + m0 * (t3 - t2 * two_t + t) + b.0 * (three_t2 - two_t3) + m1 * (t3 - t2)
+  a.0.outer_mul(two_t3 - three_t2 + one_t) + m0.outer_mul(t3 - t2 * two_t + t) + b.0.outer_mul(three_t2 - two_t3) + m1.outer_mul(t3 - t2)
 }
 
 macro_rules! impl_interpolate_simple {
@@ -76,4 +212,3 @@ macro_rules! impl_interpolate_via {
 
 impl_interpolate_via!(f32, f64);
 impl_interpolate_via!(f64, f32);
-

src/lib.rs

@@ -97,6 +97,8 @@
 #![cfg_attr(not(feature = "std"), feature(alloc))]
 #![cfg_attr(not(feature = "std"), feature(core_intrinsics))]
 
+#[cfg(not(feature = "std"))] extern crate alloc;
+
 #[cfg(feature = "impl-cgmath")] mod cgmath;
 pub mod interpolate;
 pub mod interpolation;

src/nalgebra.rs

@@ -1,36 +1,63 @@
-use crate::Interpolate;
+use alga::general::{ClosedAdd, ClosedDiv, ClosedMul, ClosedSub};
+use nalgebra::{DefaultAllocator, DimName, Point, Scalar, Vector, Vector1, Vector2, Vector3, Vector4, Vector5, Vector6};
+use nalgebra::allocator::Allocator;
+use num_traits as nt;
+use std::ops::Mul;
 
- use nalgebra as na;
+use crate::interpolate::{Interpolate, Linear, Additive, One, cubic_hermite_def};
 
-use num_traits::Float;
+macro_rules! impl_interpolate_vector {
-
-macro_rules! impl_interpolate_na_vector {
   ($($t:tt)*) => {
-    impl<T, V> Interpolate<T> for $($t)*<V> where T: Float, V: na::Scalar + Interpolate<T> {
+    // implement Linear
+    impl<T> Linear<T> for $($t)*<T> where T: Scalar + ClosedMul + ClosedDiv {
+      fn outer_mul(self, t: T) -> Self {
+        self * t
+      }
+
+      fn outer_div(self, t: T) -> Self {
+        self / t
+      }
+    }
+
+    impl<T, V> Interpolate<T> for $($t)*<V>
+    where Self: Linear<T>,
+          T: Additive + One + Mul<T, Output = T>,
+          V: nt::One +
+             nt::Zero +
+             Additive +
+             Scalar +
+             ClosedAdd +
+             ClosedMul +
+             ClosedSub +
+             Interpolate<T> {
       fn lerp(a: Self, b: Self, t: T) -> Self {
-        na::Vector::zip_map(&a, &b, |c1, c2| Interpolate::lerp(c1, c2, t))
+        Vector::zip_map(&a, &b, |c1, c2| Interpolate::lerp(c1, c2, t))
+      }
+
+      fn cubic_hermite(x: (Self, T), a: (Self, T), b: (Self, T), y: (Self, T), t: T) -> Self {
+        cubic_hermite_def(x, a, b, y, t)
       }
     }
   }
 }
 
-impl_interpolate_na_vector!(na::Vector1);
+impl_interpolate_vector!(Vector1);
-impl_interpolate_na_vector!(na::Vector2);
+impl_interpolate_vector!(Vector2);
-impl_interpolate_na_vector!(na::Vector3);
+impl_interpolate_vector!(Vector3);
-impl_interpolate_na_vector!(na::Vector4);
+impl_interpolate_vector!(Vector4);
-impl_interpolate_na_vector!(na::Vector5);
+impl_interpolate_vector!(Vector5);
-impl_interpolate_na_vector!(na::Vector6);
+impl_interpolate_vector!(Vector6);
 
-impl<T, N, D> Interpolate<T> for na::Point<N, D>
+impl<T, D> Linear<T> for Point<T, D>
-where D: na::DimName,
+where D: DimName,
-      na::DefaultAllocator: na::allocator::Allocator<N, D>,
+      DefaultAllocator: Allocator<T, D>,
-      <na::DefaultAllocator as na::allocator::Allocator<N, D>>::Buffer: Copy,
+      <DefaultAllocator as Allocator<T, D>>::Buffer: Copy,
-      N: na::Scalar + Interpolate<T>,
+      T: Scalar + ClosedDiv + ClosedMul {
-      T: Float {
+  fn outer_mul(self, t: T) -> Self {
-  fn lerp(a: Self, b: Self, t: T) -> Self {
+    self * t
-    // The 'coords' of a point is just a vector, so we can interpolate component-wise
+  }
-    // over these vectors.
+
-    let coords = na::Vector::zip_map(&a.coords, &b.coords, |c1, c2| Interpolate::lerp(c1, c2, t));
+  fn outer_div(self, t: T) -> Self {
-    na::Point::from(coords)
+    self / t
   }
 }

src/spline.rs

@@ -1,14 +1,14 @@
 #[cfg(feature = "serialization")] use serde_derive::{Deserialize, Serialize};
-#[cfg(feature = "std")] use std::cmp::Ordering;
-#[cfg(not(feature = "std"))] use core::cmp::Ordering;
 #[cfg(not(feature = "std"))] use alloc::vec::Vec;
+#[cfg(feature = "std")] use std::cmp::Ordering;
+#[cfg(feature = "std")] use std::ops::{Div, Mul};
+#[cfg(not(feature = "std"))] use core::ops::{Div, Mul};
+#[cfg(not(feature = "std"))] use core::cmp::Ordering;
 
-use crate::interpolate::Interpolate;
+use crate::interpolate::{Interpolate, Additive, One, Trigo};
 use crate::interpolation::Interpolation;
 use crate::key::Key;
 
-use num_traits::{Float, FloatConst};
-
 /// Spline curve used to provide interpolation between control points (keys).
 #[derive(Debug, Clone)]
 #[cfg_attr(feature = "serialization", derive(Deserialize, Serialize))]
@@ -53,7 +53,7 @@ impl<T, V> Spline<T, V> {
   /// sampling impossible. For instance, `Interpolate::CatmullRom` requires *four* keys. If you’re
   /// near the beginning of the spline or its end, ensure you have enough keys around to make the
   /// sampling.
-  pub fn sample(&self, t: T) -> Option<V> where T: Float + FloatConst, V: Interpolate<T> {
+  pub fn sample(&self, t: T) -> Option<V> where T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T>, V: Interpolate<T> {
     let keys = &self.0;
     let i = search_lower_cp(keys, t)?;
     let cp0 = &keys[i];
@@ -76,7 +76,7 @@ impl<T, V> Spline<T, V> {
         let two_t = T::one() + T::one();
         let cp1 = &keys[i+1];
         let nt = normalize_time(t, cp0, cp1);
-        let cos_nt = (T::one() - (nt * T::PI()).cos()) / two_t;
+        let cos_nt = (T::one() - (nt * T::pi()).cos()) / two_t;
 
         Some(Interpolate::lerp(cp0.value, cp1.value, cos_nt))
       }
@@ -108,7 +108,7 @@ impl<T, V> Spline<T, V> {
   /// # Error
   ///
   /// This function returns `None` if you have no key.
-  pub fn clamped_sample(&self, t: T) -> Option<V> where T: Float + FloatConst, V: Interpolate<T> {
+  pub fn clamped_sample(&self, t: T) -> Option<V> where T: Additive + One + Trigo + Mul<T, Output = T> + Div<T, Output = T>, V: Interpolate<T> {
     if self.0.is_empty() {
       return None;
     }
@@ -136,7 +136,7 @@ pub(crate) fn normalize_time<T, V>(
   t: T,
   cp: &Key<T, V>,
   cp1: &Key<T, V>
-) -> T where T: Float {
+) -> T where T: Additive + Div<T, Output = T> {
   assert!(cp1.t != cp.t, "overlapping keys");
   (t - cp.t) / (cp1.t - cp.t)
 }