1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153

#[cfg(feature = "num-complex")]
use num_complex::Complex;
#[cfg(not(feature = "std"))]
use num_traits::float::FloatCore;
use std::{cell, mem};

use AbsDiffEq;

/// Equality comparisons between two numbers using both the absolute difference and ULPs
/// (Units in Last Place) based comparisons.
pub trait UlpsEq<Rhs = Self>: AbsDiffEq<Rhs>
where
    Rhs: ?Sized,
{
    /// The default ULPs to tolerate when testing values that are far-apart.
    ///
    /// This is used when no `max_ulps` value is supplied to the [`ulps_eq`] macro.
    fn default_max_ulps() -> u32;

    /// A test for equality that uses units in the last place (ULP) if the values are far apart.
    fn ulps_eq(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool;

    /// The inverse of [`UlpsEq::ulps_eq`].
    fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
        !Self::ulps_eq(self, other, epsilon, max_ulps)
    }
}

///////////////////////////////////////////////////////////////////////////////////////////////////
// Base implementations
///////////////////////////////////////////////////////////////////////////////////////////////////

// Implementation based on: [Comparing Floating Point Numbers, 2012 Edition]
// (https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/)
macro_rules! impl_ulps_eq {
    ($T:ident, $U:ident) => {
        impl UlpsEq for $T {
            #[inline]
            fn default_max_ulps() -> u32 {
                4
            }

            #[inline]
            fn ulps_eq(&self, other: &$T, epsilon: $T, max_ulps: u32) -> bool {
                // For when the numbers are really close together
                if $T::abs_diff_eq(self, other, epsilon) {
                    return true;
                }

                // Trivial negative sign check
                if self.signum() != other.signum() {
                    return false;
                }

                // ULPS difference comparison
                let int_self: $U = unsafe { mem::transmute(*self) };
                let int_other: $U = unsafe { mem::transmute(*other) };

                $U::abs(int_self - int_other) <= max_ulps as $U
            }
        }
    };
}

impl_ulps_eq!(f32, i32);
impl_ulps_eq!(f64, i64);

///////////////////////////////////////////////////////////////////////////////////////////////////
// Derived implementations
///////////////////////////////////////////////////////////////////////////////////////////////////

impl<'a, T: UlpsEq + ?Sized> UlpsEq for &'a T {
    #[inline]
    fn default_max_ulps() -> u32 {
        T::default_max_ulps()
    }

    #[inline]
    fn ulps_eq(&self, other: &&'a T, epsilon: T::Epsilon, max_ulps: u32) -> bool {
        T::ulps_eq(*self, *other, epsilon, max_ulps)
    }
}

impl<'a, T: UlpsEq + ?Sized> UlpsEq for &'a mut T {
    #[inline]
    fn default_max_ulps() -> u32 {
        T::default_max_ulps()
    }

    #[inline]
    fn ulps_eq(&self, other: &&'a mut T, epsilon: T::Epsilon, max_ulps: u32) -> bool {
        T::ulps_eq(*self, *other, epsilon, max_ulps)
    }
}

impl<T: UlpsEq + Copy> UlpsEq for cell::Cell<T> {
    #[inline]
    fn default_max_ulps() -> u32 {
        T::default_max_ulps()
    }

    #[inline]
    fn ulps_eq(&self, other: &cell::Cell<T>, epsilon: T::Epsilon, max_ulps: u32) -> bool {
        T::ulps_eq(&self.get(), &other.get(), epsilon, max_ulps)
    }
}

impl<T: UlpsEq + ?Sized> UlpsEq for cell::RefCell<T> {
    #[inline]
    fn default_max_ulps() -> u32 {
        T::default_max_ulps()
    }

    #[inline]
    fn ulps_eq(&self, other: &cell::RefCell<T>, epsilon: T::Epsilon, max_ulps: u32) -> bool {
        T::ulps_eq(&self.borrow(), &other.borrow(), epsilon, max_ulps)
    }
}

impl<A, B> UlpsEq<[B]> for [A]
where
    A: UlpsEq<B>,
    A::Epsilon: Clone,
{
    #[inline]
    fn default_max_ulps() -> u32 {
        A::default_max_ulps()
    }

    #[inline]
    fn ulps_eq(&self, other: &[B], epsilon: A::Epsilon, max_ulps: u32) -> bool {
        self.len() == other.len()
            && Iterator::zip(self.iter(), other)
                .all(|(x, y)| A::ulps_eq(x, y, epsilon.clone(), max_ulps.clone()))
    }
}

#[cfg(feature = "num-complex")]
impl<T: UlpsEq> UlpsEq for Complex<T>
where
    T::Epsilon: Clone,
{
    #[inline]
    fn default_max_ulps() -> u32 {
        T::default_max_ulps()
    }

    #[inline]
    fn ulps_eq(&self, other: &Complex<T>, epsilon: T::Epsilon, max_ulps: u32) -> bool {
        T::ulps_eq(&self.re, &other.re, epsilon.clone(), max_ulps)
            && T::ulps_eq(&self.im, &other.im, epsilon.clone(), max_ulps)
    }
}