use core::ops::{Div, Rem}; pub trait Euclid: Sized + Div + Rem { /// 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; } macro_rules! euclid_forward_impl { ($($t:ty)*) => {$( #[cfg(has_div_euclid)] 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 { <$t>::rem_euclid(*self, *v) } } )*} } macro_rules! euclid_int_impl { ($($t:ty)*) => {$( euclid_forward_impl!($t); #[cfg(not(has_div_euclid))] impl Euclid for $t { #[inline] fn div_euclid(&self, v: &$t) -> Self { let q = self / v; if self % v < 0 { return if *v > 0 { q - 1 } else { q + 1 } } q } #[inline] fn rem_euclid(&self, v: &$t) -> Self { let r = self % v; if r < 0 { if *v < 0 { r - v } else { r + v } } else { r } } } )*} } macro_rules! euclid_uint_impl { ($($t:ty)*) => {$( euclid_forward_impl!($t); #[cfg(not(has_div_euclid))] impl Euclid for $t { #[inline] fn div_euclid(&self, v: &$t) -> Self { self / v } #[inline] fn rem_euclid(&self, v: &$t) -> Self { self % v } } )*} } euclid_int_impl!(isize i8 i16 i32 i64 i128); euclid_uint_impl!(usize u8 u16 u32 u64 u128); #[cfg(all(has_div_euclid, feature = "std"))] euclid_forward_impl!(f32 f64); #[cfg(not(all(has_div_euclid, feature = "std")))] impl Euclid for f32 { #[inline] fn div_euclid(&self, v: &f32) -> f32 { let q = ::trunc(self / v); if self % v < 0.0 { return if *v > 0.0 { q - 1.0 } else { q + 1.0 }; } q } #[inline] fn rem_euclid(&self, v: &f32) -> f32 { let r = self % v; if r < 0.0 { r + ::abs(*v) } else { r } } } #[cfg(not(all(has_div_euclid, feature = "std")))] impl Euclid for f64 { #[inline] fn div_euclid(&self, v: &f64) -> f64 { let q = ::trunc(self / v); if self % v < 0.0 { return if *v > 0.0 { q - 1.0 } else { q + 1.0 }; } q } #[inline] fn rem_euclid(&self, v: &f64) -> f64 { let r = self % v; if r < 0.0 { r + ::abs(*v) } else { r } } } pub trait CheckedEuclid: Euclid { /// Performs euclid division that returns `None` instead of panicking on division by zero /// and instead of wrapping around on underflow and overflow. fn checked_div_euclid(&self, v: &Self) -> Option; /// Finds the euclid remainder of dividing two numbers, checking for underflow, overflow and /// division by zero. If any of that happens, `None` is returned. fn checked_rem_euclid(&self, v: &Self) -> Option; } macro_rules! checked_euclid_forward_impl { ($($t:ty)*) => {$( #[cfg(has_div_euclid)] impl CheckedEuclid for $t { #[inline] fn checked_div_euclid(&self, v: &$t) -> Option { <$t>::checked_div_euclid(*self, *v) } #[inline] fn checked_rem_euclid(&self, v: &$t) -> Option { <$t>::checked_rem_euclid(*self, *v) } } )*} } macro_rules! checked_euclid_int_impl { ($($t:ty)*) => {$( checked_euclid_forward_impl!($t); #[cfg(not(has_div_euclid))] impl CheckedEuclid for $t { #[inline] fn checked_div_euclid(&self, v: &$t) -> Option<$t> { if *v == 0 || (*self == Self::min_value() && *v == -1) { None } else { Some(Euclid::div_euclid(self, v)) } } #[inline] fn checked_rem_euclid(&self, v: &$t) -> Option<$t> { if *v == 0 || (*self == Self::min_value() && *v == -1) { None } else { Some(Euclid::rem_euclid(self, v)) } } } )*} } macro_rules! checked_euclid_uint_impl { ($($t:ty)*) => {$( checked_euclid_forward_impl!($t); #[cfg(not(has_div_euclid))] impl CheckedEuclid for $t { #[inline] fn checked_div_euclid(&self, v: &$t) -> Option<$t> { if *v == 0 { None } else { Some(Euclid::div_euclid(self, v)) } } #[inline] fn checked_rem_euclid(&self, v: &$t) -> Option<$t> { if *v == 0 { None } else { Some(Euclid::rem_euclid(self, v)) } } } )*} } checked_euclid_int_impl!(isize i8 i16 i32 i64 i128); checked_euclid_uint_impl!(usize u8 u16 u32 u64 u128); #[cfg(test)] mod tests { use super::*; #[test] fn euclid_unsigned() { macro_rules! test_euclid { ($($t:ident)+) => { $( { let x: $t = 10; let y: $t = 3; assert_eq!(Euclid::div_euclid(&x, &y), 3); assert_eq!(Euclid::rem_euclid(&x, &y), 1); } )+ }; } test_euclid!(usize u8 u16 u32 u64); } #[test] fn euclid_signed() { macro_rules! test_euclid { ($($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); 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 * <$t as crate::float::FloatCore>::epsilon()); } )+ }; } test_euclid!(f32 f64); } #[test] fn euclid_checked() { macro_rules! test_euclid_checked { ($($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); } }