/rust/registry/src/index.crates.io-6f17d22bba15001f/num-traits-0.2.19/src/ops/euclid.rs

Source (jump to first uncovered line)
use core::ops::{Div, Rem};

pub trait Euclid: Sized + Div<Self, Output = Self> + Rem<Self, Output = Self> {
    /// Calculates Euclidean division, the matching method for `rem_euclid`.
    ///
    /// This computes the integer `n` such that
    /// `self = n * v + self.rem_euclid(v)`.
    /// In other words, the result is `self / v` rounded to the integer `n`
    /// such that `self >= n * v`.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::Euclid;
    ///
    /// let a: i32 = 7;
    /// let b: i32 = 4;
    /// assert_eq!(Euclid::div_euclid(&a, &b), 1); // 7 > 4 * 1
    /// assert_eq!(Euclid::div_euclid(&-a, &b), -2); // -7 >= 4 * -2
    /// assert_eq!(Euclid::div_euclid(&a, &-b), -1); // 7 >= -4 * -1
    /// assert_eq!(Euclid::div_euclid(&-a, &-b), 2); // -7 >= -4 * 2
    /// ```
    fn div_euclid(&self, v: &Self) -> Self;

    /// Calculates the least nonnegative remainder of `self (mod v)`.
    ///
    /// In particular, the return value `r` satisfies `0.0 <= r < v.abs()` in
    /// most cases. However, due to a floating point round-off error it can
    /// result in `r == v.abs()`, violating the mathematical definition, if
    /// `self` is much smaller than `v.abs()` in magnitude and `self < 0.0`.
    /// This result is not an element of the function's codomain, but it is the
    /// closest floating point number in the real numbers and thus fulfills the
    /// property `self == self.div_euclid(v) * v + self.rem_euclid(v)`
    /// approximatively.
    ///
    /// # Examples
    ///
    /// ```
    /// use num_traits::Euclid;
    ///
    /// let a: i32 = 7;
    /// let b: i32 = 4;
    /// assert_eq!(Euclid::rem_euclid(&a, &b), 3);
    /// assert_eq!(Euclid::rem_euclid(&-a, &b), 1);
    /// assert_eq!(Euclid::rem_euclid(&a, &-b), 3);
    /// assert_eq!(Euclid::rem_euclid(&-a, &-b), 1);
    /// ```
    fn rem_euclid(&self, v: &Self) -> Self;

    /// Returns both the quotient and remainder from Euclidean division.
    ///
    /// By default, it internally calls both `Euclid::div_euclid` and `Euclid::rem_euclid`,
    /// but it can be overridden in order to implement some optimization.
    ///
    /// # Examples
    ///
    /// ```
    /// # use num_traits::Euclid;
    /// let x = 5u8;
    /// let y = 3u8;
    ///
    /// let div = Euclid::div_euclid(&x, &y);
    /// let rem = Euclid::rem_euclid(&x, &y);
    ///
    /// assert_eq!((div, rem), Euclid::div_rem_euclid(&x, &y));
    /// ```
    fn div_rem_euclid(&self, v: &Self) -> (Self, Self) {
        (self.div_euclid(v), self.rem_euclid(v))
    }
}

macro_rules! euclid_forward_impl {
    ($($t:ty)*) => {$(
        impl Euclid for $t {
            #[inline]
            fn div_euclid(&self, v: &$t) -> Self {
                <$t>::div_euclid(*self, *v)
            }

            #[inline]
            fn rem_euclid(&self, v: &$t) -> Self {
                <$t>::rem_euclid(*self, *v)
            }
        }
    )*}
}

euclid_forward_impl!(isize i8 i16 i32 i64 i128);
euclid_forward_impl!(usize u8 u16 u32 u64 u128);

#[cfg(feature = "std")]
euclid_forward_impl!(f32 f64);

#[cfg(not(feature = "std"))]
impl Euclid for f32 {
    #[inline]
    fn div_euclid(&self, v: &f32) -> f32 {
        let q = <f32 as crate::float::FloatCore>::trunc(self / v);
        if self % v < 0.0 {
            return if *v > 0.0 { q - 1.0 } else { q + 1.0 };
        }
        q
    }

    #[inline]
    fn rem_euclid(&self, v: &f32) -> f32 {
        let r = self % v;
        if r < 0.0 {
            r + <f32 as crate::float::FloatCore>::abs(*v)
        } else {
            r
        }
    }
}

#[cfg(not(feature = "std"))]
impl Euclid for f64 {
    #[inline]
    fn div_euclid(&self, v: &f64) -> f64 {
        let q = <f64 as crate::float::FloatCore>::trunc(self / v);
        if self % v < 0.0 {
            return if *v > 0.0 { q - 1.0 } else { q + 1.0 };
        }
        q
    }

    #[inline]
    fn rem_euclid(&self, v: &f64) -> f64 {
        let r = self % v;
        if r < 0.0 {
            r + <f64 as crate::float::FloatCore>::abs(*v)
        } else {
            r
        }
    }
}

pub trait CheckedEuclid: Euclid {
    /// Performs euclid division that returns `None` instead of panicking on division by zero
    /// and instead of wrapping around on underflow and overflow.
    fn checked_div_euclid(&self, v: &Self) -> Option<Self>;

    /// Finds the euclid remainder of dividing two numbers, checking for underflow, overflow and
    /// division by zero. If any of that happens, `None` is returned.
    fn checked_rem_euclid(&self, v: &Self) -> Option<Self>;

    /// Returns both the quotient and remainder from checked Euclidean division.
    ///
    /// By default, it internally calls both `CheckedEuclid::checked_div_euclid` and `CheckedEuclid::checked_rem_euclid`,
    /// but it can be overridden in order to implement some optimization.
    /// # Examples
    ///
    /// ```
    /// # use num_traits::CheckedEuclid;
    /// let x = 5u8;
    /// let y = 3u8;
    ///
    /// let div = CheckedEuclid::checked_div_euclid(&x, &y);
    /// let rem = CheckedEuclid::checked_rem_euclid(&x, &y);
    ///
    /// assert_eq!(Some((div.unwrap(), rem.unwrap())), CheckedEuclid::checked_div_rem_euclid(&x, &y));
    /// ```
    fn checked_div_rem_euclid(&self, v: &Self) -> Option<(Self, Self)> {
        Some((self.checked_div_euclid(v)?, self.checked_rem_euclid(v)?))
    }
}

macro_rules! checked_euclid_forward_impl {
    ($($t:ty)*) => {$(
        impl CheckedEuclid for $t {
            #[inline]
            fn checked_div_euclid(&self, v: &$t) -> Option<Self> {
                <$t>::checked_div_euclid(*self, *v)
            }

            #[inline]
            fn checked_rem_euclid(&self, v: &$t) -> Option<Self> {
                <$t>::checked_rem_euclid(*self, *v)
            }
        }
    )*}
}

checked_euclid_forward_impl!(isize i8 i16 i32 i64 i128);
checked_euclid_forward_impl!(usize u8 u16 u32 u64 u128);

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn euclid_unsigned() {
        macro_rules! test_euclid {
            ($($t:ident)+) => {
                $(
                    {
                        let x: $t = 10;
                        let y: $t = 3;
                        let div = Euclid::div_euclid(&x, &y);
                        let rem = Euclid::rem_euclid(&x, &y);
                        assert_eq!(div, 3);
                        assert_eq!(rem, 1);
                        assert_eq!((div, rem), Euclid::div_rem_euclid(&x, &y));
                    }
                )+
            };
        }

        test_euclid!(usize u8 u16 u32 u64);
    }

    #[test]
    fn euclid_signed() {
        macro_rules! test_euclid {
            ($($t:ident)+) => {
                $(
                    {
                        let x: $t = 10;
                        let y: $t = -3;
                        assert_eq!(Euclid::div_euclid(&x, &y), -3);
                        assert_eq!(Euclid::div_euclid(&-x, &y), 4);
                        assert_eq!(Euclid::rem_euclid(&x, &y), 1);
                        assert_eq!(Euclid::rem_euclid(&-x, &y), 2);
                        assert_eq!((Euclid::div_euclid(&x, &y), Euclid::rem_euclid(&x, &y)), Euclid::div_rem_euclid(&x, &y));
                        let x: $t = $t::min_value() + 1;
                        let y: $t = -1;
                        assert_eq!(Euclid::div_euclid(&x, &y), $t::max_value());
                    }
                )+
            };
        }

        test_euclid!(isize i8 i16 i32 i64 i128);
    }

    #[test]
    fn euclid_float() {
        macro_rules! test_euclid {
            ($($t:ident)+) => {
                $(
                    {
                        let x: $t = 12.1;
                        let y: $t = 3.2;
                        assert!(Euclid::div_euclid(&x, &y) * y + Euclid::rem_euclid(&x, &y) - x
                        <= 46.4 * <$t as crate::float::FloatCore>::epsilon());
                        assert!(Euclid::div_euclid(&x, &-y) * -y + Euclid::rem_euclid(&x, &-y) - x
                        <= 46.4 * <$t as crate::float::FloatCore>::epsilon());
                        assert!(Euclid::div_euclid(&-x, &y) * y + Euclid::rem_euclid(&-x, &y) + x
                        <= 46.4 * <$t as crate::float::FloatCore>::epsilon());
                        assert!(Euclid::div_euclid(&-x, &-y) * -y + Euclid::rem_euclid(&-x, &-y) + x
                        <= 46.4 * <$t as crate::float::FloatCore>::epsilon());
                        assert_eq!((Euclid::div_euclid(&x, &y), Euclid::rem_euclid(&x, &y)), Euclid::div_rem_euclid(&x, &y));
                    }
                )+
            };
        }

        test_euclid!(f32 f64);
    }

    #[test]
    fn euclid_checked() {
        macro_rules! test_euclid_checked {
            ($($t:ident)+) => {
                $(
                    {
                        assert_eq!(CheckedEuclid::checked_div_euclid(&$t::min_value(), &-1), None);
                        assert_eq!(CheckedEuclid::checked_rem_euclid(&$t::min_value(), &-1), None);
                        assert_eq!(CheckedEuclid::checked_div_euclid(&1, &0), None);
                        assert_eq!(CheckedEuclid::checked_rem_euclid(&1, &0), None);
                    }
                )+
            };
        }

        test_euclid_checked!(isize i8 i16 i32 i64 i128);
    }
}

Coverage Report

Created: 2025-07-18 06:52

Line	Count	Source (jump to first uncovered line)
1		use core::ops::{Div, Rem};
2
3		pub trait Euclid: Sized + Div<Self, Output = Self> + Rem<Self, Output = Self> {
4		/// Calculates Euclidean division, the matching method for `rem_euclid`.
5		///
6		/// This computes the integer `n` such that
7		/// `self = n * v + self.rem_euclid(v)`.
8		/// In other words, the result is `self / v` rounded to the integer `n`
9		/// such that `self >= n * v`.
10		///
11		/// # Examples
12		///
13		/// ```
14		/// use num_traits::Euclid;
15		///
16		/// let a: i32 = 7;
17		/// let b: i32 = 4;
18		/// assert_eq!(Euclid::div_euclid(&a, &b), 1); // 7 > 4 * 1
19		/// assert_eq!(Euclid::div_euclid(&-a, &b), -2); // -7 >= 4 * -2
20		/// assert_eq!(Euclid::div_euclid(&a, &-b), -1); // 7 >= -4 * -1
21		/// assert_eq!(Euclid::div_euclid(&-a, &-b), 2); // -7 >= -4 * 2
22		/// ```
23		fn div_euclid(&self, v: &Self) -> Self;
24
25		/// Calculates the least nonnegative remainder of `self (mod v)`.
26		///
27		/// In particular, the return value `r` satisfies `0.0 <= r < v.abs()` in
28		/// most cases. However, due to a floating point round-off error it can
29		/// result in `r == v.abs()`, violating the mathematical definition, if
30		/// `self` is much smaller than `v.abs()` in magnitude and `self < 0.0`.
31		/// This result is not an element of the function's codomain, but it is the
32		/// closest floating point number in the real numbers and thus fulfills the
33		/// property `self == self.div_euclid(v) * v + self.rem_euclid(v)`
34		/// approximatively.
35		///
36		/// # Examples
37		///
38		/// ```
39		/// use num_traits::Euclid;
40		///
41		/// let a: i32 = 7;
42		/// let b: i32 = 4;
43		/// assert_eq!(Euclid::rem_euclid(&a, &b), 3);
44		/// assert_eq!(Euclid::rem_euclid(&-a, &b), 1);
45		/// assert_eq!(Euclid::rem_euclid(&a, &-b), 3);
46		/// assert_eq!(Euclid::rem_euclid(&-a, &-b), 1);
47		/// ```
48		fn rem_euclid(&self, v: &Self) -> Self;
49
50		/// Returns both the quotient and remainder from Euclidean division.
51		///
52		/// By default, it internally calls both `Euclid::div_euclid` and `Euclid::rem_euclid`,
53		/// but it can be overridden in order to implement some optimization.
54		///
55		/// # Examples
56		///
57		/// ```
58		/// # use num_traits::Euclid;
59		/// let x = 5u8;
60		/// let y = 3u8;
61		///
62		/// let div = Euclid::div_euclid(&x, &y);
63		/// let rem = Euclid::rem_euclid(&x, &y);
64		///
65		/// assert_eq!((div, rem), Euclid::div_rem_euclid(&x, &y));
66		/// ```
67	0	fn div_rem_euclid(&self, v: &Self) -> (Self, Self) {
68	0	(self.div_euclid(v), self.rem_euclid(v))
69	0	}
70		}
71
72		macro_rules! euclid_forward_impl {
73		($($t:ty)*) => {$(
74		impl Euclid for $t {
75		#[inline]
76	0	fn div_euclid(&self, v: &$t) -> Self {
77	0	<$t>::div_euclid(self, v)
78	0	} Unexecuted instantiation: <isize as num_traits::ops::euclid::Euclid>::div_euclid Unexecuted instantiation: <i8 as num_traits::ops::euclid::Euclid>::div_euclid Unexecuted instantiation: <i16 as num_traits::ops::euclid::Euclid>::div_euclid Unexecuted instantiation: <i32 as num_traits::ops::euclid::Euclid>::div_euclid Unexecuted instantiation: <i64 as num_traits::ops::euclid::Euclid>::div_euclid Unexecuted instantiation: <i128 as num_traits::ops::euclid::Euclid>::div_euclid Unexecuted instantiation: <usize as num_traits::ops::euclid::Euclid>::div_euclid Unexecuted instantiation: <u8 as num_traits::ops::euclid::Euclid>::div_euclid Unexecuted instantiation: <u16 as num_traits::ops::euclid::Euclid>::div_euclid Unexecuted instantiation: <u32 as num_traits::ops::euclid::Euclid>::div_euclid Unexecuted instantiation: <u64 as num_traits::ops::euclid::Euclid>::div_euclid Unexecuted instantiation: <u128 as num_traits::ops::euclid::Euclid>::div_euclid
79
80		#[inline]
81	0	fn rem_euclid(&self, v: &$t) -> Self {
82	0	<$t>::rem_euclid(self, v)
83	0	} Unexecuted instantiation: <isize as num_traits::ops::euclid::Euclid>::rem_euclid Unexecuted instantiation: <i8 as num_traits::ops::euclid::Euclid>::rem_euclid Unexecuted instantiation: <i16 as num_traits::ops::euclid::Euclid>::rem_euclid Unexecuted instantiation: <i32 as num_traits::ops::euclid::Euclid>::rem_euclid Unexecuted instantiation: <i64 as num_traits::ops::euclid::Euclid>::rem_euclid Unexecuted instantiation: <i128 as num_traits::ops::euclid::Euclid>::rem_euclid Unexecuted instantiation: <usize as num_traits::ops::euclid::Euclid>::rem_euclid Unexecuted instantiation: <u8 as num_traits::ops::euclid::Euclid>::rem_euclid Unexecuted instantiation: <u16 as num_traits::ops::euclid::Euclid>::rem_euclid Unexecuted instantiation: <u32 as num_traits::ops::euclid::Euclid>::rem_euclid Unexecuted instantiation: <u64 as num_traits::ops::euclid::Euclid>::rem_euclid Unexecuted instantiation: <u128 as num_traits::ops::euclid::Euclid>::rem_euclid
84		}
85		)*}
86		}
87
88		euclid_forward_impl!(isize i8 i16 i32 i64 i128);
89		euclid_forward_impl!(usize u8 u16 u32 u64 u128);
90
91		#[cfg(feature = "std")]
92		euclid_forward_impl!(f32 f64);
93
94		#[cfg(not(feature = "std"))]
95		impl Euclid for f32 {
96		#[inline]
97	0	fn div_euclid(&self, v: &f32) -> f32 {
98	0	let q = <f32 as crate::float::FloatCore>::trunc(self / v);
99	0	if self % v < 0.0 {
100	0	return if *v > 0.0 { q - 1.0 } else { q + 1.0 };
101	0	}
102	0	q
103	0	}
104
105		#[inline]
106	0	fn rem_euclid(&self, v: &f32) -> f32 {
107	0	let r = self % v;
108	0	if r < 0.0 {
109	0	r + <f32 as crate::float::FloatCore>::abs(*v)
110		} else {
111	0	r
112		}
113	0	}
114		}
115
116		#[cfg(not(feature = "std"))]
117		impl Euclid for f64 {
118		#[inline]
119	0	fn div_euclid(&self, v: &f64) -> f64 {
120	0	let q = <f64 as crate::float::FloatCore>::trunc(self / v);
121	0	if self % v < 0.0 {
122	0	return if *v > 0.0 { q - 1.0 } else { q + 1.0 };
123	0	}
124	0	q
125	0	}
126
127		#[inline]
128	0	fn rem_euclid(&self, v: &f64) -> f64 {
129	0	let r = self % v;
130	0	if r < 0.0 {
131	0	r + <f64 as crate::float::FloatCore>::abs(*v)
132		} else {
133	0	r
134		}
135	0	}
136		}
137
138		pub trait CheckedEuclid: Euclid {
139		/// Performs euclid division that returns `None` instead of panicking on division by zero
140		/// and instead of wrapping around on underflow and overflow.
141		fn checked_div_euclid(&self, v: &Self) -> Option<Self>;
142
143		/// Finds the euclid remainder of dividing two numbers, checking for underflow, overflow and
144		/// division by zero. If any of that happens, `None` is returned.
145		fn checked_rem_euclid(&self, v: &Self) -> Option<Self>;
146
147		/// Returns both the quotient and remainder from checked Euclidean division.
148		///
149		/// By default, it internally calls both `CheckedEuclid::checked_div_euclid` and `CheckedEuclid::checked_rem_euclid`,
150		/// but it can be overridden in order to implement some optimization.
151		/// # Examples
152		///
153		/// ```
154		/// # use num_traits::CheckedEuclid;
155		/// let x = 5u8;
156		/// let y = 3u8;
157		///
158		/// let div = CheckedEuclid::checked_div_euclid(&x, &y);
159		/// let rem = CheckedEuclid::checked_rem_euclid(&x, &y);
160		///
161		/// assert_eq!(Some((div.unwrap(), rem.unwrap())), CheckedEuclid::checked_div_rem_euclid(&x, &y));
162		/// ```
163	0	fn checked_div_rem_euclid(&self, v: &Self) -> Option<(Self, Self)> {
164	0	Some((self.checked_div_euclid(v)?, self.checked_rem_euclid(v)?))
165	0	}
166		}
167
168		macro_rules! checked_euclid_forward_impl {
169		($($t:ty)*) => {$(
170		impl CheckedEuclid for $t {
171		#[inline]
172	0	fn checked_div_euclid(&self, v: &$t) -> Option<Self> {
173	0	<$t>::checked_div_euclid(self, v)
174	0	} Unexecuted instantiation: <isize as num_traits::ops::euclid::CheckedEuclid>::checked_div_euclid Unexecuted instantiation: <i8 as num_traits::ops::euclid::CheckedEuclid>::checked_div_euclid Unexecuted instantiation: <i16 as num_traits::ops::euclid::CheckedEuclid>::checked_div_euclid Unexecuted instantiation: <i32 as num_traits::ops::euclid::CheckedEuclid>::checked_div_euclid Unexecuted instantiation: <i64 as num_traits::ops::euclid::CheckedEuclid>::checked_div_euclid Unexecuted instantiation: <i128 as num_traits::ops::euclid::CheckedEuclid>::checked_div_euclid Unexecuted instantiation: <usize as num_traits::ops::euclid::CheckedEuclid>::checked_div_euclid Unexecuted instantiation: <u8 as num_traits::ops::euclid::CheckedEuclid>::checked_div_euclid Unexecuted instantiation: <u16 as num_traits::ops::euclid::CheckedEuclid>::checked_div_euclid Unexecuted instantiation: <u32 as num_traits::ops::euclid::CheckedEuclid>::checked_div_euclid Unexecuted instantiation: <u64 as num_traits::ops::euclid::CheckedEuclid>::checked_div_euclid Unexecuted instantiation: <u128 as num_traits::ops::euclid::CheckedEuclid>::checked_div_euclid
175
176		#[inline]
177	0	fn checked_rem_euclid(&self, v: &$t) -> Option<Self> {
178	0	<$t>::checked_rem_euclid(self, v)
179	0	} Unexecuted instantiation: <isize as num_traits::ops::euclid::CheckedEuclid>::checked_rem_euclid Unexecuted instantiation: <i8 as num_traits::ops::euclid::CheckedEuclid>::checked_rem_euclid Unexecuted instantiation: <i16 as num_traits::ops::euclid::CheckedEuclid>::checked_rem_euclid Unexecuted instantiation: <i32 as num_traits::ops::euclid::CheckedEuclid>::checked_rem_euclid Unexecuted instantiation: <i64 as num_traits::ops::euclid::CheckedEuclid>::checked_rem_euclid Unexecuted instantiation: <i128 as num_traits::ops::euclid::CheckedEuclid>::checked_rem_euclid Unexecuted instantiation: <usize as num_traits::ops::euclid::CheckedEuclid>::checked_rem_euclid Unexecuted instantiation: <u8 as num_traits::ops::euclid::CheckedEuclid>::checked_rem_euclid Unexecuted instantiation: <u16 as num_traits::ops::euclid::CheckedEuclid>::checked_rem_euclid Unexecuted instantiation: <u32 as num_traits::ops::euclid::CheckedEuclid>::checked_rem_euclid Unexecuted instantiation: <u64 as num_traits::ops::euclid::CheckedEuclid>::checked_rem_euclid Unexecuted instantiation: <u128 as num_traits::ops::euclid::CheckedEuclid>::checked_rem_euclid
180		}
181		)*}
182		}
183
184		checked_euclid_forward_impl!(isize i8 i16 i32 i64 i128);
185		checked_euclid_forward_impl!(usize u8 u16 u32 u64 u128);
186
187		#[cfg(test)]
188		mod tests {
189		use super::*;
190
191		#[test]
192		fn euclid_unsigned() {
193		macro_rules! test_euclid {
194		($($t:ident)+) => {
195		$(
196		{
197		let x: $t = 10;
198		let y: $t = 3;
199		let div = Euclid::div_euclid(&x, &y);
200		let rem = Euclid::rem_euclid(&x, &y);
201		assert_eq!(div, 3);
202		assert_eq!(rem, 1);
203		assert_eq!((div, rem), Euclid::div_rem_euclid(&x, &y));
204		}
205		)+
206		};
207		}
208
209		test_euclid!(usize u8 u16 u32 u64);
210		}
211
212		#[test]
213		fn euclid_signed() {
214		macro_rules! test_euclid {
215		($($t:ident)+) => {
216		$(
217		{
218		let x: $t = 10;
219		let y: $t = -3;
220		assert_eq!(Euclid::div_euclid(&x, &y), -3);
221		assert_eq!(Euclid::div_euclid(&-x, &y), 4);
222		assert_eq!(Euclid::rem_euclid(&x, &y), 1);
223		assert_eq!(Euclid::rem_euclid(&-x, &y), 2);
224		assert_eq!((Euclid::div_euclid(&x, &y), Euclid::rem_euclid(&x, &y)), Euclid::div_rem_euclid(&x, &y));
225		let x: $t = $t::min_value() + 1;
226		let y: $t = -1;
227		assert_eq!(Euclid::div_euclid(&x, &y), $t::max_value());
228		}
229		)+
230		};
231		}
232
233		test_euclid!(isize i8 i16 i32 i64 i128);
234		}
235
236		#[test]
237		fn euclid_float() {
238		macro_rules! test_euclid {
239		($($t:ident)+) => {
240		$(
241		{
242		let x: $t = 12.1;
243		let y: $t = 3.2;
244		assert!(Euclid::div_euclid(&x, &y) * y + Euclid::rem_euclid(&x, &y) - x
245		<= 46.4 * <$t as crate::float::FloatCore>::epsilon());
246		assert!(Euclid::div_euclid(&x, &-y) * -y + Euclid::rem_euclid(&x, &-y) - x
247		<= 46.4 * <$t as crate::float::FloatCore>::epsilon());
248		assert!(Euclid::div_euclid(&-x, &y) * y + Euclid::rem_euclid(&-x, &y) + x
249		<= 46.4 * <$t as crate::float::FloatCore>::epsilon());
250		assert!(Euclid::div_euclid(&-x, &-y) * -y + Euclid::rem_euclid(&-x, &-y) + x
251		<= 46.4 * <$t as crate::float::FloatCore>::epsilon());
252		assert_eq!((Euclid::div_euclid(&x, &y), Euclid::rem_euclid(&x, &y)), Euclid::div_rem_euclid(&x, &y));
253		}
254		)+
255		};
256		}
257
258		test_euclid!(f32 f64);
259		}
260
261		#[test]
262		fn euclid_checked() {
263		macro_rules! test_euclid_checked {
264		($($t:ident)+) => {
265		$(
266		{
267		assert_eq!(CheckedEuclid::checked_div_euclid(&$t::min_value(), &-1), None);
268		assert_eq!(CheckedEuclid::checked_rem_euclid(&$t::min_value(), &-1), None);
269		assert_eq!(CheckedEuclid::checked_div_euclid(&1, &0), None);
270		assert_eq!(CheckedEuclid::checked_rem_euclid(&1, &0), None);
271		}
272		)+
273		};
274		}
275
276		test_euclid_checked!(isize i8 i16 i32 i64 i128);
277		}
278		}