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extern crate num;
/// The default epsilon value used for floating point comparisons.
pub static EPSILON: f64 = 1.0E-8;
pub trait Float: num::Float{
/// Tells if the two floating-point values `self` and `y` are considered equal
/// within the specified `absolute == relative` tolerence value.
///
/// The method of comparison used is described at:
///
/// http://realtimecollisiondetection.net/blog/?p=89
///
/// Also consider using the `equal` method.
///
/// # Examples
///
/// ```
/// use fiz_math::Float;
///
/// assert!(0.9.almost_equal(1.0, 0.1000001));
/// assert!(0.9.almost_equal(1.0, 0.1));
/// ```
fn almost_equal<T: Float>(self, y: Self, abs_tol: T) -> bool;
/// equal is short-hand for `self.almost_equal(y, fiz_math::EPSILON)`.
///
/// # Examples
///
/// ```
/// use fiz_math::Float;
///
/// assert!(1.00000001.equal(1.0));
/// assert!(1.0.equal(1.0));
/// assert!(!0.9.equal(1.0));
/// ```
fn equal(self, y: Self) -> bool;
/// lerp performs a linear interpolation between `self` and `b`. The `t`
/// parameter is a number in the range 0.0 - 1.0.
///
/// The interpolation method is precise, as such it is guaranteed that
/// `a.lerp(b, 1.0) == a`.
///
/// # Examples
///
/// ```
/// use fiz_math::Float;
///
/// assert_eq!(0.0.lerp(10.0, 0.0), 0.0);
/// assert_eq!(0.0.lerp(10.0, 0.5), 5.0);
/// assert_eq!(0.0.lerp(10.0, 1.0), 10.0);
/// ```
fn lerp(self, b: Self, t: Self) -> Self;
}
impl<T: num::Float> Float for T {
fn almost_equal<N: num::Float>(self, y: T, abs_tol: N) -> bool {
let r = T::from(1.0).unwrap().max(self.abs().max(y.abs()));
self == y || ((self - y).abs() <= T::from(abs_tol).unwrap() * r)
}
fn equal(self, y: T) -> bool {
self.almost_equal(y, T::from(EPSILON).unwrap())
}
fn lerp(self, b: Self, t: Self) -> Self {
(T::one() - t) * self + t * b
}
}