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Diffstat (limited to 'src/ops/euclid.rs')
| -rw-r--r-- | src/ops/euclid.rs | 347 |
1 files changed, 347 insertions, 0 deletions
diff --git a/src/ops/euclid.rs b/src/ops/euclid.rs new file mode 100644 index 0000000..99b5127 --- /dev/null +++ b/src/ops/euclid.rs @@ -0,0 +1,347 @@ +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; +} + +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: &$t) -> Self { + self % v + } + } + )*} +} + +euclid_int_impl!(isize i8 i16 i32 i64); +euclid_uint_impl!(usize u8 u16 u32 u64); +#[cfg(has_i128)] +euclid_int_impl!(i128); +#[cfg(has_i128)] +euclid_uint_impl!(u128); + +#[cfg(all(has_div_euclid, feature = "std"))] +euclid_forward_impl!(f32 f64); + +#[cfg(not(all(has_div_euclid, feature = "std")))] +impl Euclid for f32 { + #[inline] + fn div_euclid(&self, v: &f32) -> f32 { + let q = <f32 as ::float::FloatCore>::trunc(self / v); + if self % v < 0.0 { + return if *v > 0.0 { q - 1.0 } else { q + 1.0 }; + } + q + } + + #[inline] + fn rem_euclid(&self, v: &f32) -> f32 { + let r = self % v; + if r < 0.0 { + r + <f32 as ::float::FloatCore>::abs(*v) + } else { + r + } + } +} + +#[cfg(not(all(has_div_euclid, feature = "std")))] +impl Euclid for f64 { + #[inline] + fn div_euclid(&self, v: &f64) -> f64 { + let q = <f64 as ::float::FloatCore>::trunc(self / v); + if self % v < 0.0 { + return if *v > 0.0 { q - 1.0 } else { q + 1.0 }; + } + q + } + + #[inline] + fn rem_euclid(&self, v: &f64) -> f64 { + let r = self % v; + if r < 0.0 { + r + <f64 as ::float::FloatCore>::abs(*v) + } else { + r + } + } +} + +pub trait CheckedEuclid: Euclid { + /// Performs euclid division that returns `None` instead of panicking on division by zero + /// and instead of wrapping around on underflow and overflow. + fn checked_div_euclid(&self, v: &Self) -> Option<Self>; + + /// Finds the euclid remainder of dividing two numbers, checking for underflow, overflow and + /// division by zero. If any of that happens, `None` is returned. + fn checked_rem_euclid(&self, v: &Self) -> Option<Self>; +} + +macro_rules! checked_euclid_forward_impl { + ($($t:ty)*) => {$( + #[cfg(has_div_euclid)] + impl CheckedEuclid for $t { + #[inline] + fn checked_div_euclid(&self, v: &$t) -> Option<Self> { + <$t>::checked_div_euclid(*self, *v) + } + + #[inline] + fn checked_rem_euclid(&self, v: &$t) -> Option<Self> { + <$t>::checked_rem_euclid(*self, *v) + } + } + )*} +} + +macro_rules! checked_euclid_int_impl { + ($($t:ty)*) => {$( + 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<$t> { + if *v == 0 { + None + } else { + Some(Euclid::rem_euclid(self, v)) + } + } + } + )*} +} + +checked_euclid_int_impl!(isize i8 i16 i32 i64); +checked_euclid_uint_impl!(usize u8 u16 u32 u64); +#[cfg(has_i128)] +checked_euclid_int_impl!(i128); +#[cfg(has_i128)] +checked_euclid_uint_impl!(u128); + +#[cfg(test)] +mod tests { + use super::*; + + #[test] + fn euclid_unsigned() { + macro_rules! test_euclid { + ($($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), $t::max_value()); + } + )+ + }; + } + + test_euclid!(isize i8 i16 i32 i64); + } + + #[test] + fn euclid_float() { + macro_rules! test_euclid { + ($($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 ::float::FloatCore>::epsilon()); + assert!(Euclid::div_euclid(&x, &-y) * -y + Euclid::rem_euclid(&x, &-y) - x + <= 46.4 * <$t as ::float::FloatCore>::epsilon()); + assert!(Euclid::div_euclid(&-x, &y) * y + Euclid::rem_euclid(&-x, &y) + x + <= 46.4 * <$t as ::float::FloatCore>::epsilon()); + assert!(Euclid::div_euclid(&-x, &-y) * -y + Euclid::rem_euclid(&-x, &-y) + x + <= 46.4 * <$t as ::float::FloatCore>::epsilon()); + } + )+ + }; + } + + test_euclid!(f32 f64); + } + + #[test] + fn euclid_checked() { + macro_rules! test_euclid_checked { + ($($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); + } +} |