nearly 0.4.0

Compare IEEE floating point types
Documentation 
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use crate::nearly_eq::{NearlyEqEps, NearlyEqUlps};
use crate::tolerance::{
    EpsTolerance, EpsToleranceType, Tolerance, UlpsTolerance, UlpsToleranceType,
};

/// A trait for nearly ordering comparison based on an absolute epsilon value.
pub trait NearlyOrdEps<Rhs = Self, LhsTol = Self, RhsTol = Rhs>:
    NearlyEqEps<Rhs, LhsTol, RhsTol>
where
    Rhs: ?Sized,
    LhsTol: ?Sized + EpsTolerance<RhsTol>,
    RhsTol: ?Sized,
{
    /// Returns whether `self` is strict less than `other` but not nearly equal to `other`
    /// based on an absolute epsilon value `eps`.
    ///
    /// See [nearly_ne_eps](NearlyEqEps::nearly_ne_eps()).
    fn nearly_lt_eps(&self, other: &Rhs, eps: &EpsToleranceType<LhsTol, RhsTol>) -> bool;

    /// Returns whether `self` is strict less than `other` or nearly equal to `other`
    /// based on an absolute epsilon value `eps`.
    ///
    /// See [nearly_eq_eps](NearlyEqEps::nearly_eq_eps()).
    fn nearly_le_eps(&self, other: &Rhs, eps: &EpsToleranceType<LhsTol, RhsTol>) -> bool {
        self.nearly_lt_eps(other, eps) || self.nearly_eq_eps(other, eps)
    }

    /// Returns whether `self` is strict greater than `other` but not nearly equal to `other`
    /// based on an absolute epsilon value `eps`.
    ///
    /// See [nearly_ne_eps](NearlyEqEps::nearly_ne_eps()).
    fn nearly_gt_eps(&self, other: &Rhs, eps: &EpsToleranceType<LhsTol, RhsTol>) -> bool;

    /// Returns whether `self` is strict greater than `other` or nearly equal to `other`
    /// based on an absolute epsilon value `eps`.
    ///
    /// See [nearly_eq_eps](NearlyEqEps::nearly_eq_eps()).
    fn nearly_ge_eps(&self, other: &Rhs, eps: &EpsToleranceType<LhsTol, RhsTol>) -> bool {
        self.nearly_gt_eps(other, eps) || self.nearly_eq_eps(other, eps)
    }
}

/// A trait for nearly ordering comparison based on an ulps value.
pub trait NearlyOrdUlps<Rhs = Self, LhsTol = Self, RhsTol = Rhs>:
    NearlyEqUlps<Rhs, LhsTol, RhsTol>
where
    Rhs: ?Sized,
    LhsTol: ?Sized + UlpsTolerance<RhsTol>,
    RhsTol: ?Sized,
{
    /// Returns whether `self` is strict less than `other` but not nearly equal to `other`
    /// based on an ulps value `ulps`.
    ///
    /// See [nearly_ne_ulps](NearlyEqUlps::nearly_ne_ulps()).
    fn nearly_lt_ulps(&self, other: &Rhs, ulps: &UlpsToleranceType<LhsTol, RhsTol>) -> bool;

    /// Returns whether `self` is strict less than `other` or nearly equal to `other`
    /// based on an ulps value `ulps`.
    ///
    /// See [nearly_eq_ulps](NearlyEqUlps::nearly_eq_ulps()).
    #[inline]
    fn nearly_le_ulps(&self, other: &Rhs, ulps: &UlpsToleranceType<LhsTol, RhsTol>) -> bool {
        self.nearly_lt_ulps(other, ulps) || self.nearly_eq_ulps(other, ulps)
    }

    /// Returns whether `self` is strict greater than `other` but not nearly equal to `other`
    /// based on an ulps value `ulps`.
    ///
    /// See [nearly_ne_ulps](NearlyEqUlps::nearly_ne_ulps()).
    fn nearly_gt_ulps(&self, other: &Rhs, ulps: &UlpsToleranceType<LhsTol, RhsTol>) -> bool;

    /// Returns whether `self` is strict greater than `other` or nearly equal to `other`
    /// based on an ulps value `ulps`.
    ///
    /// See [nearly_eq_ulps](NearlyEqUlps::nearly_eq_ulps()).
    #[inline]
    fn nearly_ge_ulps(&self, other: &Rhs, ulps: &UlpsToleranceType<LhsTol, RhsTol>) -> bool {
        self.nearly_gt_ulps(other, ulps) || self.nearly_eq_ulps(other, ulps)
    }
}

/// A trait for nearly ordering comparison based on a tolerance including an absolute epsilon value
/// and an ulps value.
///
/// See [Tolerance].
/// This trait combines the traits [NearlyOrdEps] and [NearlyOrdUlps].
pub trait NearlyOrdTol<Rhs = Self, LhsTol = Self, RhsTol = Rhs>:
    NearlyOrdEps<Rhs, LhsTol, RhsTol> + NearlyOrdUlps<Rhs, LhsTol, RhsTol>
where
    Rhs: ?Sized,
    LhsTol: ?Sized + EpsTolerance<RhsTol> + UlpsTolerance<RhsTol>,
    RhsTol: ?Sized,
{
    /// Returns whether `self` is strict less than `other` but not nearly equal to `other`
    /// based on a tolerance `tol`.
    ///
    /// Returns true if `self` is strict less than `other` but not nearly equal to `other`
    /// based on an absolute epsilon value `tol.eps` and not nearly equal to `other` based
    /// on an ulps value `tol.ulps`.
    ///
    /// See [nearly_ne_eps](NearlyEqEps::nearly_ne_eps()) and
    /// [nearly_ne_ulps](NearlyEqUlps::nearly_ne_ulps()).
    #[inline]
    fn nearly_lt_tol(&self, other: &Rhs, tol: &Tolerance<LhsTol, RhsTol>) -> bool {
        self.nearly_lt_eps(other, &tol.eps) || self.nearly_lt_ulps(other, &tol.ulps)
    }

    /// Returns whether `self` is strict less than `other` or nearly equal to `other`
    /// based on a tolerance `tol`.
    ///
    /// Returns true if `self` is strict less than `other` or nearly equal to `other`
    /// based on an absolute epsilon value `tol.eps` or nearly equal to `other` based
    /// on an ulps value `tol.ulps`.
    ///
    /// See [nearly_eq_eps](NearlyEqEps::nearly_eq_eps()) and
    /// [nearly_eq_ulps](NearlyEqUlps::nearly_eq_ulps()).
    #[inline]
    fn nearly_le_tol(&self, other: &Rhs, tol: &Tolerance<LhsTol, RhsTol>) -> bool {
        self.nearly_le_eps(other, &tol.eps) || self.nearly_le_ulps(other, &tol.ulps)
    }

    /// Returns whether `self` is strict greater than `other` but not nearly equal to `other`
    /// based on a tolerance `tol`.
    ///
    /// Returns true if `self` is strict greater than `other` but not nearly equal to `other`
    /// based on an absolute epsilon value `tol.eps` and not nearly equal to `other` based
    /// on an ulps value `tol.ulps`.
    ///
    /// See [nearly_ne_eps](NearlyEqEps::nearly_ne_eps()) and
    /// [nearly_ne_ulps](NearlyEqUlps::nearly_ne_ulps()).
    #[inline]
    fn nearly_gt_tol(&self, other: &Rhs, tol: &Tolerance<LhsTol, RhsTol>) -> bool {
        self.nearly_gt_eps(other, &tol.eps) || self.nearly_gt_ulps(other, &tol.ulps)
    }

    /// Returns whether `self` is strict greater than `other` or nearly equal to `other`
    /// based on a tolerance `tol`.
    ///
    /// Returns true if `self` is strict greater than `other` or nearly equal to `other`
    /// based on an absolute epsilon value `tol.eps` or nearly equal to `other` based
    /// on an ulps value `tol.ulps`.
    ///
    /// See [nearly_eq_eps](NearlyEqEps::nearly_eq_eps()) and
    /// [nearly_eq_ulps](NearlyEqUlps::nearly_eq_ulps()).
    #[inline]
    fn nearly_ge_tol(&self, other: &Rhs, tol: &Tolerance<LhsTol, RhsTol>) -> bool {
        self.nearly_ge_eps(other, &tol.eps) || self.nearly_ge_ulps(other, &tol.ulps)
    }
}

/// A trait for nearly ordering comparison based on a default tolerance.
///
/// This trait is a convenience trait to use nearly ordering comparison with a default tolerance.
/// This is the same as using the [NearlyOrdTol] trait with [Tolerance::default()].
pub trait NearlyOrd<Rhs = Self, LhsTol = Self, RhsTol = Rhs>:
    NearlyOrdTol<Rhs, LhsTol, RhsTol>
where
    Rhs: ?Sized,
    LhsTol: ?Sized + EpsTolerance<RhsTol> + UlpsTolerance<RhsTol>,
    RhsTol: ?Sized,
{
    /// Returns whether `self` is strict less than `other` but not nearly equal to `other`
    /// based on the default tolerance for comparisons of `self` with `other`.
    #[inline]
    fn nearly_lt(&self, other: &Rhs) -> bool {
        self.nearly_lt_tol(other, &Tolerance::<LhsTol, RhsTol>::default())
    }

    /// Returns whether `self` is strict less than `other` or nearly equal to `other`
    /// based on the default tolerance for comparisons of `self` with `other`.
    #[inline]
    fn nearly_le(&self, other: &Rhs) -> bool {
        self.nearly_le_tol(other, &Tolerance::<LhsTol, RhsTol>::default())
    }

    /// Returns whether `self` is strict greater than `other` but not nearly equal to `other`
    /// based on the default tolerance for comparisons of `self` with `other`.
    #[inline]
    fn nearly_gt(&self, other: &Rhs) -> bool {
        self.nearly_gt_tol(other, &Tolerance::<LhsTol, RhsTol>::default())
    }

    /// Returns whether `self` is strict greater than `other` or nearly equal to `other`
    /// based on the default tolerance for comparisons of `self` with `other`.
    #[inline]
    fn nearly_ge(&self, other: &Rhs) -> bool {
        self.nearly_ge_tol(other, &Tolerance::<LhsTol, RhsTol>::default())
    }
}